Properties

Label 170.2.c.a.69.2
Level $170$
Weight $2$
Character 170.69
Analytic conductor $1.357$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 170 = 2 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 170.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.35745683436\)
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 69.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 170.69
Dual form 170.2.c.a.69.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +2.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +2.00000 q^{9} +(-2.00000 + 1.00000i) q^{10} -6.00000 q^{11} -1.00000i q^{12} +3.00000i q^{13} +(-2.00000 + 1.00000i) q^{15} +1.00000 q^{16} -1.00000i q^{17} +2.00000i q^{18} +7.00000 q^{19} +(-1.00000 - 2.00000i) q^{20} -6.00000i q^{22} -8.00000i q^{23} +1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} -3.00000 q^{26} +5.00000i q^{27} +5.00000 q^{29} +(-1.00000 - 2.00000i) q^{30} +5.00000 q^{31} +1.00000i q^{32} -6.00000i q^{33} +1.00000 q^{34} -2.00000 q^{36} -8.00000i q^{37} +7.00000i q^{38} -3.00000 q^{39} +(2.00000 - 1.00000i) q^{40} -4.00000i q^{43} +6.00000 q^{44} +(2.00000 + 4.00000i) q^{45} +8.00000 q^{46} -3.00000i q^{47} +1.00000i q^{48} +7.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} +1.00000 q^{51} -3.00000i q^{52} +9.00000i q^{53} -5.00000 q^{54} +(-6.00000 - 12.0000i) q^{55} +7.00000i q^{57} +5.00000i q^{58} -5.00000 q^{59} +(2.00000 - 1.00000i) q^{60} -3.00000 q^{61} +5.00000i q^{62} -1.00000 q^{64} +(-6.00000 + 3.00000i) q^{65} +6.00000 q^{66} +2.00000i q^{67} +1.00000i q^{68} +8.00000 q^{69} -15.0000 q^{71} -2.00000i q^{72} -11.0000i q^{73} +8.00000 q^{74} +(-4.00000 - 3.00000i) q^{75} -7.00000 q^{76} -3.00000i q^{78} -8.00000 q^{79} +(1.00000 + 2.00000i) q^{80} +1.00000 q^{81} +4.00000i q^{83} +(2.00000 - 1.00000i) q^{85} +4.00000 q^{86} +5.00000i q^{87} +6.00000i q^{88} +1.00000 q^{89} +(-4.00000 + 2.00000i) q^{90} +8.00000i q^{92} +5.00000i q^{93} +3.00000 q^{94} +(7.00000 + 14.0000i) q^{95} -1.00000 q^{96} +9.00000i q^{97} +7.00000i q^{98} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{4} + 2q^{5} - 2q^{6} + 4q^{9} + O(q^{10}) \) \( 2q - 2q^{4} + 2q^{5} - 2q^{6} + 4q^{9} - 4q^{10} - 12q^{11} - 4q^{15} + 2q^{16} + 14q^{19} - 2q^{20} + 2q^{24} - 6q^{25} - 6q^{26} + 10q^{29} - 2q^{30} + 10q^{31} + 2q^{34} - 4q^{36} - 6q^{39} + 4q^{40} + 12q^{44} + 4q^{45} + 16q^{46} + 14q^{49} - 8q^{50} + 2q^{51} - 10q^{54} - 12q^{55} - 10q^{59} + 4q^{60} - 6q^{61} - 2q^{64} - 12q^{65} + 12q^{66} + 16q^{69} - 30q^{71} + 16q^{74} - 8q^{75} - 14q^{76} - 16q^{79} + 2q^{80} + 2q^{81} + 4q^{85} + 8q^{86} + 2q^{89} - 8q^{90} + 6q^{94} + 14q^{95} - 2q^{96} - 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).

\(n\) \(71\) \(137\)
\(\chi(n)\) \(1\) \(-1\)

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
\(3\) 1.00000i 0.577350i 0.957427 + 0.288675i \(0.0932147\pi\)
−0.957427 + 0.288675i \(0.906785\pi\)
\(4\) −1.00000 −0.500000
\(5\) 1.00000 + 2.00000i 0.447214 + 0.894427i
\(6\) −1.00000 −0.408248
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 2.00000 0.666667
\(10\) −2.00000 + 1.00000i −0.632456 + 0.316228i
\(11\) −6.00000 −1.80907 −0.904534 0.426401i \(-0.859781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 3.00000i 0.832050i 0.909353 + 0.416025i \(0.136577\pi\)
−0.909353 + 0.416025i \(0.863423\pi\)
\(14\) 0 0
\(15\) −2.00000 + 1.00000i −0.516398 + 0.258199i
\(16\) 1.00000 0.250000
\(17\) 1.00000i 0.242536i
\(18\) 2.00000i 0.471405i
\(19\) 7.00000 1.60591 0.802955 0.596040i \(-0.203260\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) −1.00000 2.00000i −0.223607 0.447214i
\(21\) 0 0
\(22\) 6.00000i 1.27920i
\(23\) 8.00000i 1.66812i −0.551677 0.834058i \(-0.686012\pi\)
0.551677 0.834058i \(-0.313988\pi\)
\(24\) 1.00000 0.204124
\(25\) −3.00000 + 4.00000i −0.600000 + 0.800000i
\(26\) −3.00000 −0.588348
\(27\) 5.00000i 0.962250i
\(28\) 0 0
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) −1.00000 2.00000i −0.182574 0.365148i
\(31\) 5.00000 0.898027 0.449013 0.893525i \(-0.351776\pi\)
0.449013 + 0.893525i \(0.351776\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 6.00000i 1.04447i
\(34\) 1.00000 0.171499
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) 8.00000i 1.31519i −0.753371 0.657596i \(-0.771573\pi\)
0.753371 0.657596i \(-0.228427\pi\)
\(38\) 7.00000i 1.13555i
\(39\) −3.00000 −0.480384
\(40\) 2.00000 1.00000i 0.316228 0.158114i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 6.00000 0.904534
\(45\) 2.00000 + 4.00000i 0.298142 + 0.596285i
\(46\) 8.00000 1.17954
\(47\) 3.00000i 0.437595i −0.975770 0.218797i \(-0.929787\pi\)
0.975770 0.218797i \(-0.0702134\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 7.00000 1.00000
\(50\) −4.00000 3.00000i −0.565685 0.424264i
\(51\) 1.00000 0.140028
\(52\) 3.00000i 0.416025i
\(53\) 9.00000i 1.23625i 0.786082 + 0.618123i \(0.212106\pi\)
−0.786082 + 0.618123i \(0.787894\pi\)
\(54\) −5.00000 −0.680414
\(55\) −6.00000 12.0000i −0.809040 1.61808i
\(56\) 0 0
\(57\) 7.00000i 0.927173i
\(58\) 5.00000i 0.656532i
\(59\) −5.00000 −0.650945 −0.325472 0.945552i \(-0.605523\pi\)
−0.325472 + 0.945552i \(0.605523\pi\)
\(60\) 2.00000 1.00000i 0.258199 0.129099i
\(61\) −3.00000 −0.384111 −0.192055 0.981384i \(-0.561515\pi\)
−0.192055 + 0.981384i \(0.561515\pi\)
\(62\) 5.00000i 0.635001i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −6.00000 + 3.00000i −0.744208 + 0.372104i
\(66\) 6.00000 0.738549
\(67\) 2.00000i 0.244339i 0.992509 + 0.122169i \(0.0389851\pi\)
−0.992509 + 0.122169i \(0.961015\pi\)
\(68\) 1.00000i 0.121268i
\(69\) 8.00000 0.963087
\(70\) 0 0
\(71\) −15.0000 −1.78017 −0.890086 0.455792i \(-0.849356\pi\)
−0.890086 + 0.455792i \(0.849356\pi\)
\(72\) 2.00000i 0.235702i
\(73\) 11.0000i 1.28745i −0.765256 0.643726i \(-0.777388\pi\)
0.765256 0.643726i \(-0.222612\pi\)
\(74\) 8.00000 0.929981
\(75\) −4.00000 3.00000i −0.461880 0.346410i
\(76\) −7.00000 −0.802955
\(77\) 0 0
\(78\) 3.00000i 0.339683i
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 1.00000 + 2.00000i 0.111803 + 0.223607i
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 4.00000i 0.439057i 0.975606 + 0.219529i \(0.0704519\pi\)
−0.975606 + 0.219529i \(0.929548\pi\)
\(84\) 0 0
\(85\) 2.00000 1.00000i 0.216930 0.108465i
\(86\) 4.00000 0.431331
\(87\) 5.00000i 0.536056i
\(88\) 6.00000i 0.639602i
\(89\) 1.00000 0.106000 0.0529999 0.998595i \(-0.483122\pi\)
0.0529999 + 0.998595i \(0.483122\pi\)
\(90\) −4.00000 + 2.00000i −0.421637 + 0.210819i
\(91\) 0 0
\(92\) 8.00000i 0.834058i
\(93\) 5.00000i 0.518476i
\(94\) 3.00000 0.309426
\(95\) 7.00000 + 14.0000i 0.718185 + 1.43637i
\(96\) −1.00000 −0.102062
\(97\) 9.00000i 0.913812i 0.889515 + 0.456906i \(0.151042\pi\)
−0.889515 + 0.456906i \(0.848958\pi\)
\(98\) 7.00000i 0.707107i
\(99\) −12.0000 −1.20605
\(100\) 3.00000 4.00000i 0.300000 0.400000i
\(101\) −12.0000 −1.19404 −0.597022 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(102\) 1.00000i 0.0990148i
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 3.00000 0.294174
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) 4.00000i 0.386695i 0.981130 + 0.193347i \(0.0619344\pi\)
−0.981130 + 0.193347i \(0.938066\pi\)
\(108\) 5.00000i 0.481125i
\(109\) −9.00000 −0.862044 −0.431022 0.902342i \(-0.641847\pi\)
−0.431022 + 0.902342i \(0.641847\pi\)
\(110\) 12.0000 6.00000i 1.14416 0.572078i
\(111\) 8.00000 0.759326
\(112\) 0 0
\(113\) 13.0000i 1.22294i −0.791269 0.611469i \(-0.790579\pi\)
0.791269 0.611469i \(-0.209421\pi\)
\(114\) −7.00000 −0.655610
\(115\) 16.0000 8.00000i 1.49201 0.746004i
\(116\) −5.00000 −0.464238
\(117\) 6.00000i 0.554700i
\(118\) 5.00000i 0.460287i
\(119\) 0 0
\(120\) 1.00000 + 2.00000i 0.0912871 + 0.182574i
\(121\) 25.0000 2.27273
\(122\) 3.00000i 0.271607i
\(123\) 0 0
\(124\) −5.00000 −0.449013
\(125\) −11.0000 2.00000i −0.983870 0.178885i
\(126\) 0 0
\(127\) 1.00000i 0.0887357i −0.999015 0.0443678i \(-0.985873\pi\)
0.999015 0.0443678i \(-0.0141274\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 4.00000 0.352180
\(130\) −3.00000 6.00000i −0.263117 0.526235i
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 6.00000i 0.522233i
\(133\) 0 0
\(134\) −2.00000 −0.172774
\(135\) −10.0000 + 5.00000i −0.860663 + 0.430331i
\(136\) −1.00000 −0.0857493
\(137\) 12.0000i 1.02523i −0.858619 0.512615i \(-0.828677\pi\)
0.858619 0.512615i \(-0.171323\pi\)
\(138\) 8.00000i 0.681005i
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 3.00000 0.252646
\(142\) 15.0000i 1.25877i
\(143\) 18.0000i 1.50524i
\(144\) 2.00000 0.166667
\(145\) 5.00000 + 10.0000i 0.415227 + 0.830455i
\(146\) 11.0000 0.910366
\(147\) 7.00000i 0.577350i
\(148\) 8.00000i 0.657596i
\(149\) 2.00000 0.163846 0.0819232 0.996639i \(-0.473894\pi\)
0.0819232 + 0.996639i \(0.473894\pi\)
\(150\) 3.00000 4.00000i 0.244949 0.326599i
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 7.00000i 0.567775i
\(153\) 2.00000i 0.161690i
\(154\) 0 0
\(155\) 5.00000 + 10.0000i 0.401610 + 0.803219i
\(156\) 3.00000 0.240192
\(157\) 14.0000i 1.11732i −0.829396 0.558661i \(-0.811315\pi\)
0.829396 0.558661i \(-0.188685\pi\)
\(158\) 8.00000i 0.636446i
\(159\) −9.00000 −0.713746
\(160\) −2.00000 + 1.00000i −0.158114 + 0.0790569i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 4.00000i 0.313304i −0.987654 0.156652i \(-0.949930\pi\)
0.987654 0.156652i \(-0.0500701\pi\)
\(164\) 0 0
\(165\) 12.0000 6.00000i 0.934199 0.467099i
\(166\) −4.00000 −0.310460
\(167\) 6.00000i 0.464294i 0.972681 + 0.232147i \(0.0745750\pi\)
−0.972681 + 0.232147i \(0.925425\pi\)
\(168\) 0 0
\(169\) 4.00000 0.307692
\(170\) 1.00000 + 2.00000i 0.0766965 + 0.153393i
\(171\) 14.0000 1.07061
\(172\) 4.00000i 0.304997i
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) −5.00000 −0.379049
\(175\) 0 0
\(176\) −6.00000 −0.452267
\(177\) 5.00000i 0.375823i
\(178\) 1.00000i 0.0749532i
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) −2.00000 4.00000i −0.149071 0.298142i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 3.00000i 0.221766i
\(184\) −8.00000 −0.589768
\(185\) 16.0000 8.00000i 1.17634 0.588172i
\(186\) −5.00000 −0.366618
\(187\) 6.00000i 0.438763i
\(188\) 3.00000i 0.218797i
\(189\) 0 0
\(190\) −14.0000 + 7.00000i −1.01567 + 0.507833i
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 26.0000i 1.87152i 0.352636 + 0.935760i \(0.385285\pi\)
−0.352636 + 0.935760i \(0.614715\pi\)
\(194\) −9.00000 −0.646162
\(195\) −3.00000 6.00000i −0.214834 0.429669i
\(196\) −7.00000 −0.500000
\(197\) 2.00000i 0.142494i −0.997459 0.0712470i \(-0.977302\pi\)
0.997459 0.0712470i \(-0.0226979\pi\)
\(198\) 12.0000i 0.852803i
\(199\) −7.00000 −0.496217 −0.248108 0.968732i \(-0.579809\pi\)
−0.248108 + 0.968732i \(0.579809\pi\)
\(200\) 4.00000 + 3.00000i 0.282843 + 0.212132i
\(201\) −2.00000 −0.141069
\(202\) 12.0000i 0.844317i
\(203\) 0 0
\(204\) −1.00000 −0.0700140
\(205\) 0 0
\(206\) 0 0
\(207\) 16.0000i 1.11208i
\(208\) 3.00000i 0.208013i
\(209\) −42.0000 −2.90520
\(210\) 0 0
\(211\) 16.0000 1.10149 0.550743 0.834675i \(-0.314345\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) 9.00000i 0.618123i
\(213\) 15.0000i 1.02778i
\(214\) −4.00000 −0.273434
\(215\) 8.00000 4.00000i 0.545595 0.272798i
\(216\) 5.00000 0.340207
\(217\) 0 0
\(218\) 9.00000i 0.609557i
\(219\) 11.0000 0.743311
\(220\) 6.00000 + 12.0000i 0.404520 + 0.809040i
\(221\) 3.00000 0.201802
\(222\) 8.00000i 0.536925i
\(223\) 15.0000i 1.00447i −0.864730 0.502237i \(-0.832510\pi\)
0.864730 0.502237i \(-0.167490\pi\)
\(224\) 0 0
\(225\) −6.00000 + 8.00000i −0.400000 + 0.533333i
\(226\) 13.0000 0.864747
\(227\) 9.00000i 0.597351i 0.954355 + 0.298675i \(0.0965448\pi\)
−0.954355 + 0.298675i \(0.903455\pi\)
\(228\) 7.00000i 0.463586i
\(229\) −18.0000 −1.18947 −0.594737 0.803921i \(-0.702744\pi\)
−0.594737 + 0.803921i \(0.702744\pi\)
\(230\) 8.00000 + 16.0000i 0.527504 + 1.05501i
\(231\) 0 0
\(232\) 5.00000i 0.328266i
\(233\) 27.0000i 1.76883i 0.466702 + 0.884414i \(0.345442\pi\)
−0.466702 + 0.884414i \(0.654558\pi\)
\(234\) −6.00000 −0.392232
\(235\) 6.00000 3.00000i 0.391397 0.195698i
\(236\) 5.00000 0.325472
\(237\) 8.00000i 0.519656i
\(238\) 0 0
\(239\) −10.0000 −0.646846 −0.323423 0.946254i \(-0.604834\pi\)
−0.323423 + 0.946254i \(0.604834\pi\)
\(240\) −2.00000 + 1.00000i −0.129099 + 0.0645497i
\(241\) −20.0000 −1.28831 −0.644157 0.764894i \(-0.722792\pi\)
−0.644157 + 0.764894i \(0.722792\pi\)
\(242\) 25.0000i 1.60706i
\(243\) 16.0000i 1.02640i
\(244\) 3.00000 0.192055
\(245\) 7.00000 + 14.0000i 0.447214 + 0.894427i
\(246\) 0 0
\(247\) 21.0000i 1.33620i
\(248\) 5.00000i 0.317500i
\(249\) −4.00000 −0.253490
\(250\) 2.00000 11.0000i 0.126491 0.695701i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 48.0000i 3.01773i
\(254\) 1.00000 0.0627456
\(255\) 1.00000 + 2.00000i 0.0626224 + 0.125245i
\(256\) 1.00000 0.0625000
\(257\) 28.0000i 1.74659i −0.487190 0.873296i \(-0.661978\pi\)
0.487190 0.873296i \(-0.338022\pi\)
\(258\) 4.00000i 0.249029i
\(259\) 0 0
\(260\) 6.00000 3.00000i 0.372104 0.186052i
\(261\) 10.0000 0.618984
\(262\) 6.00000i 0.370681i
\(263\) 27.0000i 1.66489i 0.554107 + 0.832446i \(0.313060\pi\)
−0.554107 + 0.832446i \(0.686940\pi\)
\(264\) −6.00000 −0.369274
\(265\) −18.0000 + 9.00000i −1.10573 + 0.552866i
\(266\) 0 0
\(267\) 1.00000i 0.0611990i
\(268\) 2.00000i 0.122169i
\(269\) 19.0000 1.15845 0.579225 0.815168i \(-0.303355\pi\)
0.579225 + 0.815168i \(0.303355\pi\)
\(270\) −5.00000 10.0000i −0.304290 0.608581i
\(271\) −6.00000 −0.364474 −0.182237 0.983255i \(-0.558334\pi\)
−0.182237 + 0.983255i \(0.558334\pi\)
\(272\) 1.00000i 0.0606339i
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 18.0000 24.0000i 1.08544 1.44725i
\(276\) −8.00000 −0.481543
\(277\) 2.00000i 0.120168i 0.998193 + 0.0600842i \(0.0191369\pi\)
−0.998193 + 0.0600842i \(0.980863\pi\)
\(278\) 0 0
\(279\) 10.0000 0.598684
\(280\) 0 0
\(281\) −33.0000 −1.96861 −0.984307 0.176462i \(-0.943535\pi\)
−0.984307 + 0.176462i \(0.943535\pi\)
\(282\) 3.00000i 0.178647i
\(283\) 11.0000i 0.653882i 0.945045 + 0.326941i \(0.106018\pi\)
−0.945045 + 0.326941i \(0.893982\pi\)
\(284\) 15.0000 0.890086
\(285\) −14.0000 + 7.00000i −0.829288 + 0.414644i
\(286\) 18.0000 1.06436
\(287\) 0 0
\(288\) 2.00000i 0.117851i
\(289\) −1.00000 −0.0588235
\(290\) −10.0000 + 5.00000i −0.587220 + 0.293610i
\(291\) −9.00000 −0.527589
\(292\) 11.0000i 0.643726i
\(293\) 19.0000i 1.10999i −0.831853 0.554996i \(-0.812720\pi\)
0.831853 0.554996i \(-0.187280\pi\)
\(294\) −7.00000 −0.408248
\(295\) −5.00000 10.0000i −0.291111 0.582223i
\(296\) −8.00000 −0.464991
\(297\) 30.0000i 1.74078i
\(298\) 2.00000i 0.115857i
\(299\) 24.0000 1.38796
\(300\) 4.00000 + 3.00000i 0.230940 + 0.173205i
\(301\) 0 0
\(302\) 8.00000i 0.460348i
\(303\) 12.0000i 0.689382i
\(304\) 7.00000 0.401478
\(305\) −3.00000 6.00000i −0.171780 0.343559i
\(306\) 2.00000 0.114332
\(307\) 24.0000i 1.36975i 0.728659 + 0.684876i \(0.240144\pi\)
−0.728659 + 0.684876i \(0.759856\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −10.0000 + 5.00000i −0.567962 + 0.283981i
\(311\) −4.00000 −0.226819 −0.113410 0.993548i \(-0.536177\pi\)
−0.113410 + 0.993548i \(0.536177\pi\)
\(312\) 3.00000i 0.169842i
\(313\) 22.0000i 1.24351i −0.783210 0.621757i \(-0.786419\pi\)
0.783210 0.621757i \(-0.213581\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 9.00000i 0.504695i
\(319\) −30.0000 −1.67968
\(320\) −1.00000 2.00000i −0.0559017 0.111803i
\(321\) −4.00000 −0.223258
\(322\) 0 0
\(323\) 7.00000i 0.389490i
\(324\) −1.00000 −0.0555556
\(325\) −12.0000 9.00000i −0.665640 0.499230i
\(326\) 4.00000 0.221540
\(327\) 9.00000i 0.497701i
\(328\) 0 0
\(329\) 0 0
\(330\) 6.00000 + 12.0000i 0.330289 + 0.660578i
\(331\) 7.00000 0.384755 0.192377 0.981321i \(-0.438380\pi\)
0.192377 + 0.981321i \(0.438380\pi\)
\(332\) 4.00000i 0.219529i
\(333\) 16.0000i 0.876795i
\(334\) −6.00000 −0.328305
\(335\) −4.00000 + 2.00000i −0.218543 + 0.109272i
\(336\) 0 0
\(337\) 13.0000i 0.708155i −0.935216 0.354078i \(-0.884795\pi\)
0.935216 0.354078i \(-0.115205\pi\)
\(338\) 4.00000i 0.217571i
\(339\) 13.0000 0.706063
\(340\) −2.00000 + 1.00000i −0.108465 + 0.0542326i
\(341\) −30.0000 −1.62459
\(342\) 14.0000i 0.757033i
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) 8.00000 + 16.0000i 0.430706 + 0.861411i
\(346\) 0 0
\(347\) 5.00000i 0.268414i −0.990953 0.134207i \(-0.957151\pi\)
0.990953 0.134207i \(-0.0428487\pi\)
\(348\) 5.00000i 0.268028i
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) −15.0000 −0.800641
\(352\) 6.00000i 0.319801i
\(353\) 8.00000i 0.425797i −0.977074 0.212899i \(-0.931710\pi\)
0.977074 0.212899i \(-0.0682904\pi\)
\(354\) 5.00000 0.265747
\(355\) −15.0000 30.0000i −0.796117 1.59223i
\(356\) −1.00000 −0.0529999
\(357\) 0 0
\(358\) 12.0000i 0.634220i
\(359\) 28.0000 1.47778 0.738892 0.673824i \(-0.235349\pi\)
0.738892 + 0.673824i \(0.235349\pi\)
\(360\) 4.00000 2.00000i 0.210819 0.105409i
\(361\) 30.0000 1.57895
\(362\) 2.00000i 0.105118i
\(363\) 25.0000i 1.31216i
\(364\) 0 0
\(365\) 22.0000 11.0000i 1.15153 0.575766i
\(366\) 3.00000 0.156813
\(367\) 10.0000i 0.521996i 0.965339 + 0.260998i \(0.0840516\pi\)
−0.965339 + 0.260998i \(0.915948\pi\)
\(368\) 8.00000i 0.417029i
\(369\) 0 0
\(370\) 8.00000 + 16.0000i 0.415900 + 0.831800i
\(371\) 0 0
\(372\) 5.00000i 0.259238i
\(373\) 14.0000i 0.724893i −0.932005 0.362446i \(-0.881942\pi\)
0.932005 0.362446i \(-0.118058\pi\)
\(374\) −6.00000 −0.310253
\(375\) 2.00000 11.0000i 0.103280 0.568038i
\(376\) −3.00000 −0.154713
\(377\) 15.0000i 0.772539i
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) −7.00000 14.0000i −0.359092 0.718185i
\(381\) 1.00000 0.0512316
\(382\) 0 0
\(383\) 27.0000i 1.37964i −0.723983 0.689818i \(-0.757691\pi\)
0.723983 0.689818i \(-0.242309\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −26.0000 −1.32337
\(387\) 8.00000i 0.406663i
\(388\) 9.00000i 0.456906i
\(389\) −30.0000 −1.52106 −0.760530 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) 6.00000 3.00000i 0.303822 0.151911i
\(391\) −8.00000 −0.404577
\(392\) 7.00000i 0.353553i
\(393\) 6.00000i 0.302660i
\(394\) 2.00000 0.100759
\(395\) −8.00000 16.0000i −0.402524 0.805047i
\(396\) 12.0000 0.603023
\(397\) 2.00000i 0.100377i 0.998740 + 0.0501886i \(0.0159822\pi\)
−0.998740 + 0.0501886i \(0.984018\pi\)
\(398\) 7.00000i 0.350878i
\(399\) 0 0
\(400\) −3.00000 + 4.00000i −0.150000 + 0.200000i
\(401\) −10.0000 −0.499376 −0.249688 0.968326i \(-0.580328\pi\)
−0.249688 + 0.968326i \(0.580328\pi\)
\(402\) 2.00000i 0.0997509i
\(403\) 15.0000i 0.747203i
\(404\) 12.0000 0.597022
\(405\) 1.00000 + 2.00000i 0.0496904 + 0.0993808i
\(406\) 0 0
\(407\) 48.0000i 2.37927i
\(408\) 1.00000i 0.0495074i
\(409\) 31.0000 1.53285 0.766426 0.642333i \(-0.222033\pi\)
0.766426 + 0.642333i \(0.222033\pi\)
\(410\) 0 0
\(411\) 12.0000 0.591916
\(412\) 0 0
\(413\) 0 0
\(414\) 16.0000 0.786357
\(415\) −8.00000 + 4.00000i −0.392705 + 0.196352i
\(416\) −3.00000 −0.147087
\(417\) 0 0
\(418\) 42.0000i 2.05429i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 20.0000 0.974740 0.487370 0.873195i \(-0.337956\pi\)
0.487370 + 0.873195i \(0.337956\pi\)
\(422\) 16.0000i 0.778868i
\(423\) 6.00000i 0.291730i
\(424\) 9.00000 0.437079
\(425\) 4.00000 + 3.00000i 0.194029 + 0.145521i
\(426\) 15.0000 0.726752
\(427\) 0 0
\(428\) 4.00000i 0.193347i
\(429\) 18.0000 0.869048
\(430\) 4.00000 + 8.00000i 0.192897 + 0.385794i
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 5.00000i 0.240563i
\(433\) 20.0000i 0.961139i 0.876957 + 0.480569i \(0.159570\pi\)
−0.876957 + 0.480569i \(0.840430\pi\)
\(434\) 0 0
\(435\) −10.0000 + 5.00000i −0.479463 + 0.239732i
\(436\) 9.00000 0.431022
\(437\) 56.0000i 2.67884i
\(438\) 11.0000i 0.525600i
\(439\) −16.0000 −0.763638 −0.381819 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) −12.0000 + 6.00000i −0.572078 + 0.286039i
\(441\) 14.0000 0.666667
\(442\) 3.00000i 0.142695i
\(443\) 10.0000i 0.475114i 0.971374 + 0.237557i \(0.0763467\pi\)
−0.971374 + 0.237557i \(0.923653\pi\)
\(444\) −8.00000 −0.379663
\(445\) 1.00000 + 2.00000i 0.0474045 + 0.0948091i
\(446\) 15.0000 0.710271
\(447\) 2.00000i 0.0945968i
\(448\) 0 0
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) −8.00000 6.00000i −0.377124 0.282843i
\(451\) 0 0
\(452\) 13.0000i 0.611469i
\(453\) 8.00000i 0.375873i
\(454\) −9.00000 −0.422391
\(455\) 0 0
\(456\) 7.00000 0.327805
\(457\) 12.0000i 0.561336i 0.959805 + 0.280668i \(0.0905560\pi\)
−0.959805 + 0.280668i \(0.909444\pi\)
\(458\) 18.0000i 0.841085i
\(459\) 5.00000 0.233380
\(460\) −16.0000 + 8.00000i −0.746004 + 0.373002i
\(461\) −20.0000 −0.931493 −0.465746 0.884918i \(-0.654214\pi\)
−0.465746 + 0.884918i \(0.654214\pi\)
\(462\) 0 0
\(463\) 31.0000i 1.44069i 0.693615 + 0.720346i \(0.256017\pi\)
−0.693615 + 0.720346i \(0.743983\pi\)
\(464\) 5.00000 0.232119
\(465\) −10.0000 + 5.00000i −0.463739 + 0.231869i
\(466\) −27.0000 −1.25075
\(467\) 14.0000i 0.647843i 0.946084 + 0.323921i \(0.105001\pi\)
−0.946084 + 0.323921i \(0.894999\pi\)
\(468\) 6.00000i 0.277350i
\(469\) 0 0
\(470\) 3.00000 + 6.00000i 0.138380 + 0.276759i
\(471\) 14.0000 0.645086
\(472\) 5.00000i 0.230144i
\(473\) 24.0000i 1.10352i
\(474\) 8.00000 0.367452
\(475\) −21.0000 + 28.0000i −0.963546 + 1.28473i
\(476\) 0 0
\(477\) 18.0000i 0.824163i
\(478\) 10.0000i 0.457389i
\(479\) 37.0000 1.69057 0.845287 0.534313i \(-0.179430\pi\)
0.845287 + 0.534313i \(0.179430\pi\)
\(480\) −1.00000 2.00000i −0.0456435 0.0912871i
\(481\) 24.0000 1.09431
\(482\) 20.0000i 0.910975i
\(483\) 0 0
\(484\) −25.0000 −1.13636
\(485\) −18.0000 + 9.00000i −0.817338 + 0.408669i
\(486\) −16.0000 −0.725775
\(487\) 2.00000i 0.0906287i 0.998973 + 0.0453143i \(0.0144289\pi\)
−0.998973 + 0.0453143i \(0.985571\pi\)
\(488\) 3.00000i 0.135804i
\(489\) 4.00000 0.180886
\(490\) −14.0000 + 7.00000i −0.632456 + 0.316228i
\(491\) −13.0000 −0.586682 −0.293341 0.956008i \(-0.594767\pi\)
−0.293341 + 0.956008i \(0.594767\pi\)
\(492\) 0 0
\(493\) 5.00000i 0.225189i
\(494\) −21.0000 −0.944835
\(495\) −12.0000 24.0000i −0.539360 1.07872i
\(496\) 5.00000 0.224507
\(497\) 0 0
\(498\) 4.00000i 0.179244i
\(499\) 28.0000 1.25345 0.626726 0.779240i \(-0.284395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(500\) 11.0000 + 2.00000i 0.491935 + 0.0894427i
\(501\) −6.00000 −0.268060
\(502\) 12.0000i 0.535586i
\(503\) 42.0000i 1.87269i −0.351085 0.936344i \(-0.614187\pi\)
0.351085 0.936344i \(-0.385813\pi\)
\(504\) 0 0
\(505\) −12.0000 24.0000i −0.533993 1.06799i
\(506\) −48.0000 −2.13386
\(507\) 4.00000i 0.177646i
\(508\) 1.00000i 0.0443678i
\(509\) 12.0000 0.531891 0.265945 0.963988i \(-0.414316\pi\)
0.265945 + 0.963988i \(0.414316\pi\)
\(510\) −2.00000 + 1.00000i −0.0885615 + 0.0442807i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 35.0000i 1.54529i
\(514\) 28.0000 1.23503
\(515\) 0 0
\(516\) −4.00000 −0.176090
\(517\) 18.0000i 0.791639i
\(518\) 0 0
\(519\) 0 0
\(520\) 3.00000 + 6.00000i 0.131559 + 0.263117i
\(521\) 28.0000 1.22670 0.613351 0.789810i \(-0.289821\pi\)
0.613351 + 0.789810i \(0.289821\pi\)
\(522\) 10.0000i 0.437688i
\(523\) 14.0000i 0.612177i 0.952003 + 0.306089i \(0.0990204\pi\)
−0.952003 + 0.306089i \(0.900980\pi\)
\(524\) −6.00000 −0.262111
\(525\) 0 0
\(526\) −27.0000 −1.17726
\(527\) 5.00000i 0.217803i
\(528\) 6.00000i 0.261116i
\(529\) −41.0000 −1.78261
\(530\) −9.00000 18.0000i −0.390935 0.781870i
\(531\) −10.0000 −0.433963
\(532\) 0 0
\(533\) 0 0
\(534\) −1.00000 −0.0432742
\(535\) −8.00000 + 4.00000i −0.345870 + 0.172935i
\(536\) 2.00000 0.0863868
\(537\) 12.0000i 0.517838i
\(538\) 19.0000i 0.819148i
\(539\) −42.0000 −1.80907
\(540\) 10.0000 5.00000i 0.430331 0.215166i
\(541\) −34.0000 −1.46177 −0.730887 0.682498i \(-0.760893\pi\)
−0.730887 + 0.682498i \(0.760893\pi\)
\(542\) 6.00000i 0.257722i
\(543\) 2.00000i 0.0858282i
\(544\) 1.00000 0.0428746
\(545\) −9.00000 18.0000i −0.385518 0.771035i
\(546\) 0 0
\(547\) 13.0000i 0.555840i −0.960604 0.277920i \(-0.910355\pi\)
0.960604 0.277920i \(-0.0896450\pi\)
\(548\) 12.0000i 0.512615i
\(549\) −6.00000 −0.256074
\(550\) 24.0000 + 18.0000i 1.02336 + 0.767523i
\(551\) 35.0000 1.49105
\(552\) 8.00000i 0.340503i
\(553\) 0 0
\(554\) −2.00000 −0.0849719
\(555\) 8.00000 + 16.0000i 0.339581 + 0.679162i
\(556\) 0 0
\(557\) 11.0000i 0.466085i −0.972467 0.233042i \(-0.925132\pi\)
0.972467 0.233042i \(-0.0748681\pi\)
\(558\) 10.0000i 0.423334i
\(559\) 12.0000 0.507546
\(560\) 0 0
\(561\) −6.00000 −0.253320
\(562\) 33.0000i 1.39202i
\(563\) 32.0000i 1.34864i 0.738440 + 0.674320i \(0.235563\pi\)
−0.738440 + 0.674320i \(0.764437\pi\)
\(564\) −3.00000 −0.126323
\(565\) 26.0000 13.0000i 1.09383 0.546914i
\(566\) −11.0000 −0.462364
\(567\) 0 0
\(568\) 15.0000i 0.629386i
\(569\) 21.0000 0.880366 0.440183 0.897908i \(-0.354914\pi\)
0.440183 + 0.897908i \(0.354914\pi\)
\(570\) −7.00000 14.0000i −0.293198 0.586395i
\(571\) −10.0000 −0.418487 −0.209243 0.977864i \(-0.567100\pi\)
−0.209243 + 0.977864i \(0.567100\pi\)
\(572\) 18.0000i 0.752618i
\(573\) 0 0
\(574\) 0 0
\(575\) 32.0000 + 24.0000i 1.33449 + 1.00087i
\(576\) −2.00000 −0.0833333
\(577\) 16.0000i 0.666089i −0.942911 0.333044i \(-0.891924\pi\)
0.942911 0.333044i \(-0.108076\pi\)
\(578\) 1.00000i 0.0415945i
\(579\) −26.0000 −1.08052
\(580\) −5.00000 10.0000i −0.207614 0.415227i
\(581\) 0 0
\(582\) 9.00000i 0.373062i
\(583\) 54.0000i 2.23645i
\(584\) −11.0000 −0.455183
\(585\) −12.0000 + 6.00000i −0.496139 + 0.248069i
\(586\) 19.0000 0.784883
\(587\) 36.0000i 1.48588i −0.669359 0.742940i \(-0.733431\pi\)
0.669359 0.742940i \(-0.266569\pi\)
\(588\) 7.00000i 0.288675i
\(589\) 35.0000 1.44215
\(590\) 10.0000 5.00000i 0.411693 0.205847i
\(591\) 2.00000 0.0822690
\(592\) 8.00000i 0.328798i
\(593\) 22.0000i 0.903432i 0.892162 + 0.451716i \(0.149188\pi\)
−0.892162 + 0.451716i \(0.850812\pi\)
\(594\) 30.0000 1.23091
\(595\) 0 0
\(596\) −2.00000 −0.0819232
\(597\) 7.00000i 0.286491i
\(598\) 24.0000i 0.981433i
\(599\) 32.0000 1.30748 0.653742 0.756717i \(-0.273198\pi\)
0.653742 + 0.756717i \(0.273198\pi\)
\(600\) −3.00000 + 4.00000i −0.122474 + 0.163299i
\(601\) −2.00000 −0.0815817 −0.0407909 0.999168i \(-0.512988\pi\)
−0.0407909 + 0.999168i \(0.512988\pi\)
\(602\) 0 0
\(603\) 4.00000i 0.162893i
\(604\) 8.00000 0.325515
\(605\) 25.0000 + 50.0000i 1.01639 + 2.03279i
\(606\) 12.0000 0.487467
\(607\) 12.0000i 0.487065i 0.969893 + 0.243532i \(0.0783062\pi\)
−0.969893 + 0.243532i \(0.921694\pi\)
\(608\) 7.00000i 0.283887i
\(609\) 0 0
\(610\) 6.00000 3.00000i 0.242933 0.121466i
\(611\) 9.00000 0.364101
\(612\) 2.00000i 0.0808452i
\(613\) 17.0000i 0.686624i −0.939222 0.343312i \(-0.888451\pi\)
0.939222 0.343312i \(-0.111549\pi\)
\(614\) −24.0000 −0.968561
\(615\) 0 0
\(616\) 0 0
\(617\) 29.0000i 1.16750i 0.811935 + 0.583748i \(0.198414\pi\)
−0.811935 + 0.583748i \(0.801586\pi\)
\(618\) 0 0
\(619\) −14.0000 −0.562708 −0.281354 0.959604i \(-0.590783\pi\)
−0.281354 + 0.959604i \(0.590783\pi\)
\(620\) −5.00000 10.0000i −0.200805 0.401610i
\(621\) 40.0000 1.60514
\(622\) 4.00000i 0.160385i
\(623\) 0 0
\(624\) −3.00000 −0.120096
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 22.0000 0.879297
\(627\) 42.0000i 1.67732i
\(628\) 14.0000i 0.558661i
\(629\) −8.00000 −0.318981
\(630\) 0 0
\(631\) −42.0000 −1.67199 −0.835997 0.548734i \(-0.815110\pi\)
−0.835997 + 0.548734i \(0.815110\pi\)
\(632\) 8.00000i 0.318223i
\(633\) 16.0000i 0.635943i
\(634\) 0 0
\(635\) 2.00000 1.00000i 0.0793676 0.0396838i
\(636\) 9.00000 0.356873
\(637\) 21.0000i 0.832050i
\(638\) 30.0000i 1.18771i
\(639\) −30.0000 −1.18678
\(640\) 2.00000 1.00000i 0.0790569 0.0395285i
\(641\) 18.0000 0.710957 0.355479 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) 4.00000i 0.157867i
\(643\) 44.0000i 1.73519i −0.497271 0.867595i \(-0.665665\pi\)
0.497271 0.867595i \(-0.334335\pi\)
\(644\) 0 0
\(645\) 4.00000 + 8.00000i 0.157500 + 0.315000i
\(646\) 7.00000 0.275411
\(647\) 17.0000i 0.668339i −0.942513 0.334169i \(-0.891544\pi\)
0.942513 0.334169i \(-0.108456\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 30.0000 1.17760
\(650\) 9.00000 12.0000i 0.353009 0.470679i
\(651\) 0 0
\(652\) 4.00000i 0.156652i
\(653\) 30.0000i 1.17399i 0.809590 + 0.586995i \(0.199689\pi\)
−0.809590 + 0.586995i \(0.800311\pi\)
\(654\) 9.00000 0.351928
\(655\) 6.00000 + 12.0000i 0.234439 + 0.468879i
\(656\) 0 0
\(657\) 22.0000i 0.858302i
\(658\) 0 0
\(659\) −19.0000 −0.740135 −0.370067 0.929005i \(-0.620665\pi\)
−0.370067 + 0.929005i \(0.620665\pi\)
\(660\) −12.0000 + 6.00000i −0.467099 + 0.233550i
\(661\) −16.0000 −0.622328 −0.311164 0.950356i \(-0.600719\pi\)
−0.311164 + 0.950356i \(0.600719\pi\)
\(662\) 7.00000i 0.272063i
\(663\) 3.00000i 0.116510i
\(664\) 4.00000 0.155230
\(665\) 0 0
\(666\) 16.0000 0.619987
\(667\) 40.0000i 1.54881i
\(668\) 6.00000i 0.232147i
\(669\) 15.0000 0.579934
\(670\) −2.00000 4.00000i −0.0772667 0.154533i
\(671\) 18.0000 0.694882
\(672\) 0 0
\(673\) 35.0000i 1.34915i −0.738206 0.674575i \(-0.764327\pi\)
0.738206 0.674575i \(-0.235673\pi\)
\(674\) 13.0000 0.500741
\(675\) −20.0000 15.0000i −0.769800 0.577350i
\(676\) −4.00000 −0.153846
\(677\) 24.0000i 0.922395i 0.887298 + 0.461197i \(0.152580\pi\)
−0.887298 + 0.461197i \(0.847420\pi\)
\(678\) 13.0000i 0.499262i
\(679\) 0 0
\(680\) −1.00000 2.00000i −0.0383482 0.0766965i
\(681\) −9.00000 −0.344881
\(682\) 30.0000i 1.14876i
\(683\) 45.0000i 1.72188i 0.508709 + 0.860939i \(0.330123\pi\)
−0.508709 + 0.860939i \(0.669877\pi\)
\(684\) −14.0000 −0.535303
\(685\) 24.0000 12.0000i 0.916993 0.458496i
\(686\) 0 0
\(687\) 18.0000i 0.686743i
\(688\) 4.00000i 0.152499i
\(689\) −27.0000 −1.02862
\(690\) −16.0000 + 8.00000i −0.609110 + 0.304555i
\(691\) −16.0000 −0.608669 −0.304334 0.952565i \(-0.598434\pi\)
−0.304334 + 0.952565i \(0.598434\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 5.00000 0.189797
\(695\) 0 0
\(696\) 5.00000 0.189525
\(697\) 0 0
\(698\) 2.00000i 0.0757011i
\(699\) −27.0000 −1.02123
\(700\) 0 0
\(701\) −12.0000 −0.453234 −0.226617 0.973984i \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) 15.0000i 0.566139i
\(703\) 56.0000i 2.11208i
\(704\) 6.00000 0.226134
\(705\) 3.00000 + 6.00000i 0.112987 + 0.225973i
\(706\) 8.00000 0.301084
\(707\) 0 0
\(708\) 5.00000i 0.187912i
\(709\) −23.0000 −0.863783 −0.431892 0.901926i \(-0.642154\pi\)
−0.431892 + 0.901926i \(0.642154\pi\)
\(710\) 30.0000 15.0000i 1.12588 0.562940i
\(711\) −16.0000 −0.600047
\(712\) 1.00000i 0.0374766i
\(713\) 40.0000i 1.49801i
\(714\) 0 0
\(715\) 36.0000 18.0000i 1.34632 0.673162i
\(716\) −12.0000 −0.448461
\(717\) 10.0000i 0.373457i
\(718\) 28.0000i 1.04495i
\(719\) 27.0000 1.00693 0.503465 0.864016i \(-0.332058\pi\)
0.503465 + 0.864016i \(0.332058\pi\)
\(720\) 2.00000 + 4.00000i 0.0745356 + 0.149071i
\(721\) 0 0
\(722\) 30.0000i 1.11648i
\(723\) 20.0000i 0.743808i
\(724\) −2.00000 −0.0743294
\(725\) −15.0000 + 20.0000i −0.557086 + 0.742781i
\(726\) −25.0000 −0.927837
\(727\) 29.0000i 1.07555i 0.843088 + 0.537775i \(0.180735\pi\)
−0.843088 + 0.537775i \(0.819265\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 11.0000 + 22.0000i 0.407128 + 0.814257i
\(731\) −4.00000 −0.147945
\(732\) 3.00000i 0.110883i
\(733\) 14.0000i 0.517102i −0.965998 0.258551i \(-0.916755\pi\)
0.965998 0.258551i \(-0.0832450\pi\)
\(734\) −10.0000 −0.369107
\(735\) −14.0000 + 7.00000i −0.516398 + 0.258199i
\(736\) 8.00000 0.294884
\(737\) 12.0000i 0.442026i
\(738\) 0 0
\(739\) 1.00000 0.0367856 0.0183928 0.999831i \(-0.494145\pi\)
0.0183928 + 0.999831i \(0.494145\pi\)
\(740\) −16.0000 + 8.00000i −0.588172 + 0.294086i
\(741\) −21.0000 −0.771454
\(742\) 0 0
\(743\) 24.0000i 0.880475i 0.897881 + 0.440237i \(0.145106\pi\)
−0.897881 + 0.440237i \(0.854894\pi\)
\(744\) 5.00000 0.183309
\(745\) 2.00000 + 4.00000i 0.0732743 + 0.146549i
\(746\) 14.0000 0.512576
\(747\) 8.00000i 0.292705i
\(748\) 6.00000i 0.219382i
\(749\) 0 0
\(750\) 11.0000 + 2.00000i 0.401663 + 0.0730297i
\(751\) 11.0000 0.401396 0.200698 0.979653i \(-0.435679\pi\)
0.200698 + 0.979653i \(0.435679\pi\)
\(752\) 3.00000i 0.109399i
\(753\) 12.0000i 0.437304i
\(754\) −15.0000 −0.546268
\(755\) −8.00000 16.0000i −0.291150 0.582300i
\(756\) 0 0
\(757\) 45.0000i 1.63555i 0.575536 + 0.817776i \(0.304793\pi\)
−0.575536 + 0.817776i \(0.695207\pi\)
\(758\) 20.0000i 0.726433i
\(759\) −48.0000 −1.74229
\(760\) 14.0000 7.00000i 0.507833 0.253917i
\(761\) 14.0000 0.507500 0.253750 0.967270i \(-0.418336\pi\)
0.253750 + 0.967270i \(0.418336\pi\)
\(762\) 1.00000i 0.0362262i
\(763\) 0 0
\(764\) 0 0
\(765\) 4.00000 2.00000i 0.144620 0.0723102i
\(766\) 27.0000 0.975550
\(767\) 15.0000i 0.541619i
\(768\) 1.00000i 0.0360844i
\(769\) −37.0000 −1.33425 −0.667127 0.744944i \(-0.732476\pi\)
−0.667127 + 0.744944i \(0.732476\pi\)
\(770\) 0 0
\(771\) 28.0000 1.00840
\(772\) 26.0000i 0.935760i
\(773\) 6.00000i 0.215805i −0.994161 0.107903i \(-0.965587\pi\)
0.994161 0.107903i \(-0.0344134\pi\)
\(774\) 8.00000 0.287554
\(775\) −15.0000 + 20.0000i −0.538816 + 0.718421i
\(776\) 9.00000 0.323081
\(777\) 0 0
\(778\) 30.0000i 1.07555i
\(779\) 0 0
\(780\) 3.00000 + 6.00000i 0.107417 + 0.214834i
\(781\) 90.0000 3.22045
\(782\) 8.00000i 0.286079i
\(783\) 25.0000i 0.893427i
\(784\) 7.00000 0.250000
\(785\) 28.0000 14.0000i 0.999363 0.499681i
\(786\) −6.00000 −0.214013
\(787\) 47.0000i 1.67537i 0.546154 + 0.837685i \(0.316091\pi\)
−0.546154 + 0.837685i \(0.683909\pi\)
\(788\) 2.00000i 0.0712470i
\(789\) −27.0000 −0.961225
\(790\) 16.0000 8.00000i 0.569254 0.284627i
\(791\) 0 0
\(792\) 12.0000i 0.426401i