Properties

Label 690.2.d.b.139.1
Level $690$
Weight $2$
Character 690.139
Analytic conductor $5.510$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 139.1
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 690.139
Dual form 690.2.d.b.139.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-0.707107 + 2.12132i) q^{5} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-0.707107 + 2.12132i) q^{5} +1.00000 q^{6} +2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(2.12132 + 0.707107i) q^{10} -4.24264 q^{11} -1.00000i q^{12} -0.828427i q^{13} +2.00000 q^{14} +(-2.12132 - 0.707107i) q^{15} +1.00000 q^{16} -6.82843i q^{17} +1.00000i q^{18} -6.24264 q^{19} +(0.707107 - 2.12132i) q^{20} -2.00000 q^{21} +4.24264i q^{22} -1.00000i q^{23} -1.00000 q^{24} +(-4.00000 - 3.00000i) q^{25} -0.828427 q^{26} -1.00000i q^{27} -2.00000i q^{28} -3.65685 q^{29} +(-0.707107 + 2.12132i) q^{30} +6.00000 q^{31} -1.00000i q^{32} -4.24264i q^{33} -6.82843 q^{34} +(-4.24264 - 1.41421i) q^{35} +1.00000 q^{36} -0.585786i q^{37} +6.24264i q^{38} +0.828427 q^{39} +(-2.12132 - 0.707107i) q^{40} -6.82843 q^{41} +2.00000i q^{42} +10.2426i q^{43} +4.24264 q^{44} +(0.707107 - 2.12132i) q^{45} -1.00000 q^{46} +0.828427i q^{47} +1.00000i q^{48} +3.00000 q^{49} +(-3.00000 + 4.00000i) q^{50} +6.82843 q^{51} +0.828427i q^{52} +10.5858i q^{53} -1.00000 q^{54} +(3.00000 - 9.00000i) q^{55} -2.00000 q^{56} -6.24264i q^{57} +3.65685i q^{58} -8.48528 q^{59} +(2.12132 + 0.707107i) q^{60} -0.585786 q^{61} -6.00000i q^{62} -2.00000i q^{63} -1.00000 q^{64} +(1.75736 + 0.585786i) q^{65} -4.24264 q^{66} +3.41421i q^{67} +6.82843i q^{68} +1.00000 q^{69} +(-1.41421 + 4.24264i) q^{70} -5.65685 q^{71} -1.00000i q^{72} +7.65685i q^{73} -0.585786 q^{74} +(3.00000 - 4.00000i) q^{75} +6.24264 q^{76} -8.48528i q^{77} -0.828427i q^{78} +3.65685 q^{79} +(-0.707107 + 2.12132i) q^{80} +1.00000 q^{81} +6.82843i q^{82} +1.41421i q^{83} +2.00000 q^{84} +(14.4853 + 4.82843i) q^{85} +10.2426 q^{86} -3.65685i q^{87} -4.24264i q^{88} -9.17157 q^{89} +(-2.12132 - 0.707107i) q^{90} +1.65685 q^{91} +1.00000i q^{92} +6.00000i q^{93} +0.828427 q^{94} +(4.41421 - 13.2426i) q^{95} +1.00000 q^{96} +6.00000i q^{97} -3.00000i q^{98} +4.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{4} + 4q^{6} - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{4} + 4q^{6} - 4q^{9} + 8q^{14} + 4q^{16} - 8q^{19} - 8q^{21} - 4q^{24} - 16q^{25} + 8q^{26} + 8q^{29} + 24q^{31} - 16q^{34} + 4q^{36} - 8q^{39} - 16q^{41} - 4q^{46} + 12q^{49} - 12q^{50} + 16q^{51} - 4q^{54} + 12q^{55} - 8q^{56} - 8q^{61} - 4q^{64} + 24q^{65} + 4q^{69} - 8q^{74} + 12q^{75} + 8q^{76} - 8q^{79} + 4q^{81} + 8q^{84} + 24q^{85} + 24q^{86} - 48q^{89} - 16q^{91} - 8q^{94} + 12q^{95} + 4q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(5\) −0.707107 + 2.12132i −0.316228 + 0.948683i
\(6\) 1.00000 0.408248
\(7\) 2.00000i 0.755929i 0.925820 + 0.377964i \(0.123376\pi\)
−0.925820 + 0.377964i \(0.876624\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 2.12132 + 0.707107i 0.670820 + 0.223607i
\(11\) −4.24264 −1.27920 −0.639602 0.768706i \(-0.720901\pi\)
−0.639602 + 0.768706i \(0.720901\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 0.828427i 0.229764i −0.993379 0.114882i \(-0.963351\pi\)
0.993379 0.114882i \(-0.0366490\pi\)
\(14\) 2.00000 0.534522
\(15\) −2.12132 0.707107i −0.547723 0.182574i
\(16\) 1.00000 0.250000
\(17\) 6.82843i 1.65614i −0.560627 0.828068i \(-0.689440\pi\)
0.560627 0.828068i \(-0.310560\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −6.24264 −1.43216 −0.716080 0.698018i \(-0.754065\pi\)
−0.716080 + 0.698018i \(0.754065\pi\)
\(20\) 0.707107 2.12132i 0.158114 0.474342i
\(21\) −2.00000 −0.436436
\(22\) 4.24264i 0.904534i
\(23\) 1.00000i 0.208514i
\(24\) −1.00000 −0.204124
\(25\) −4.00000 3.00000i −0.800000 0.600000i
\(26\) −0.828427 −0.162468
\(27\) 1.00000i 0.192450i
\(28\) 2.00000i 0.377964i
\(29\) −3.65685 −0.679061 −0.339530 0.940595i \(-0.610268\pi\)
−0.339530 + 0.940595i \(0.610268\pi\)
\(30\) −0.707107 + 2.12132i −0.129099 + 0.387298i
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 4.24264i 0.738549i
\(34\) −6.82843 −1.17107
\(35\) −4.24264 1.41421i −0.717137 0.239046i
\(36\) 1.00000 0.166667
\(37\) 0.585786i 0.0963027i −0.998840 0.0481513i \(-0.984667\pi\)
0.998840 0.0481513i \(-0.0153330\pi\)
\(38\) 6.24264i 1.01269i
\(39\) 0.828427 0.132655
\(40\) −2.12132 0.707107i −0.335410 0.111803i
\(41\) −6.82843 −1.06642 −0.533211 0.845983i \(-0.679015\pi\)
−0.533211 + 0.845983i \(0.679015\pi\)
\(42\) 2.00000i 0.308607i
\(43\) 10.2426i 1.56199i 0.624538 + 0.780994i \(0.285287\pi\)
−0.624538 + 0.780994i \(0.714713\pi\)
\(44\) 4.24264 0.639602
\(45\) 0.707107 2.12132i 0.105409 0.316228i
\(46\) −1.00000 −0.147442
\(47\) 0.828427i 0.120839i 0.998173 + 0.0604193i \(0.0192438\pi\)
−0.998173 + 0.0604193i \(0.980756\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 3.00000 0.428571
\(50\) −3.00000 + 4.00000i −0.424264 + 0.565685i
\(51\) 6.82843 0.956171
\(52\) 0.828427i 0.114882i
\(53\) 10.5858i 1.45407i 0.686601 + 0.727035i \(0.259102\pi\)
−0.686601 + 0.727035i \(0.740898\pi\)
\(54\) −1.00000 −0.136083
\(55\) 3.00000 9.00000i 0.404520 1.21356i
\(56\) −2.00000 −0.267261
\(57\) 6.24264i 0.826858i
\(58\) 3.65685i 0.480168i
\(59\) −8.48528 −1.10469 −0.552345 0.833616i \(-0.686267\pi\)
−0.552345 + 0.833616i \(0.686267\pi\)
\(60\) 2.12132 + 0.707107i 0.273861 + 0.0912871i
\(61\) −0.585786 −0.0750023 −0.0375011 0.999297i \(-0.511940\pi\)
−0.0375011 + 0.999297i \(0.511940\pi\)
\(62\) 6.00000i 0.762001i
\(63\) 2.00000i 0.251976i
\(64\) −1.00000 −0.125000
\(65\) 1.75736 + 0.585786i 0.217974 + 0.0726579i
\(66\) −4.24264 −0.522233
\(67\) 3.41421i 0.417113i 0.978010 + 0.208556i \(0.0668764\pi\)
−0.978010 + 0.208556i \(0.933124\pi\)
\(68\) 6.82843i 0.828068i
\(69\) 1.00000 0.120386
\(70\) −1.41421 + 4.24264i −0.169031 + 0.507093i
\(71\) −5.65685 −0.671345 −0.335673 0.941979i \(-0.608964\pi\)
−0.335673 + 0.941979i \(0.608964\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 7.65685i 0.896167i 0.893992 + 0.448084i \(0.147893\pi\)
−0.893992 + 0.448084i \(0.852107\pi\)
\(74\) −0.585786 −0.0680963
\(75\) 3.00000 4.00000i 0.346410 0.461880i
\(76\) 6.24264 0.716080
\(77\) 8.48528i 0.966988i
\(78\) 0.828427i 0.0938009i
\(79\) 3.65685 0.411428 0.205714 0.978612i \(-0.434048\pi\)
0.205714 + 0.978612i \(0.434048\pi\)
\(80\) −0.707107 + 2.12132i −0.0790569 + 0.237171i
\(81\) 1.00000 0.111111
\(82\) 6.82843i 0.754074i
\(83\) 1.41421i 0.155230i 0.996983 + 0.0776151i \(0.0247305\pi\)
−0.996983 + 0.0776151i \(0.975269\pi\)
\(84\) 2.00000 0.218218
\(85\) 14.4853 + 4.82843i 1.57115 + 0.523716i
\(86\) 10.2426 1.10449
\(87\) 3.65685i 0.392056i
\(88\) 4.24264i 0.452267i
\(89\) −9.17157 −0.972185 −0.486092 0.873907i \(-0.661578\pi\)
−0.486092 + 0.873907i \(0.661578\pi\)
\(90\) −2.12132 0.707107i −0.223607 0.0745356i
\(91\) 1.65685 0.173686
\(92\) 1.00000i 0.104257i
\(93\) 6.00000i 0.622171i
\(94\) 0.828427 0.0854457
\(95\) 4.41421 13.2426i 0.452889 1.35867i
\(96\) 1.00000 0.102062
\(97\) 6.00000i 0.609208i 0.952479 + 0.304604i \(0.0985241\pi\)
−0.952479 + 0.304604i \(0.901476\pi\)
\(98\) 3.00000i 0.303046i
\(99\) 4.24264 0.426401
\(100\) 4.00000 + 3.00000i 0.400000 + 0.300000i
\(101\) 13.3137 1.32476 0.662382 0.749166i \(-0.269546\pi\)
0.662382 + 0.749166i \(0.269546\pi\)
\(102\) 6.82843i 0.676115i
\(103\) 16.1421i 1.59053i 0.606261 + 0.795266i \(0.292669\pi\)
−0.606261 + 0.795266i \(0.707331\pi\)
\(104\) 0.828427 0.0812340
\(105\) 1.41421 4.24264i 0.138013 0.414039i
\(106\) 10.5858 1.02818
\(107\) 0.928932i 0.0898033i −0.998991 0.0449016i \(-0.985703\pi\)
0.998991 0.0449016i \(-0.0142974\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −12.5858 −1.20550 −0.602750 0.797930i \(-0.705928\pi\)
−0.602750 + 0.797930i \(0.705928\pi\)
\(110\) −9.00000 3.00000i −0.858116 0.286039i
\(111\) 0.585786 0.0556004
\(112\) 2.00000i 0.188982i
\(113\) 16.9706i 1.59646i −0.602355 0.798228i \(-0.705771\pi\)
0.602355 0.798228i \(-0.294229\pi\)
\(114\) −6.24264 −0.584677
\(115\) 2.12132 + 0.707107i 0.197814 + 0.0659380i
\(116\) 3.65685 0.339530
\(117\) 0.828427i 0.0765881i
\(118\) 8.48528i 0.781133i
\(119\) 13.6569 1.25192
\(120\) 0.707107 2.12132i 0.0645497 0.193649i
\(121\) 7.00000 0.636364
\(122\) 0.585786i 0.0530346i
\(123\) 6.82843i 0.615699i
\(124\) −6.00000 −0.538816
\(125\) 9.19239 6.36396i 0.822192 0.569210i
\(126\) −2.00000 −0.178174
\(127\) 2.00000i 0.177471i 0.996055 + 0.0887357i \(0.0282826\pi\)
−0.996055 + 0.0887357i \(0.971717\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −10.2426 −0.901814
\(130\) 0.585786 1.75736i 0.0513769 0.154131i
\(131\) −21.6569 −1.89217 −0.946084 0.323921i \(-0.894999\pi\)
−0.946084 + 0.323921i \(0.894999\pi\)
\(132\) 4.24264i 0.369274i
\(133\) 12.4853i 1.08261i
\(134\) 3.41421 0.294943
\(135\) 2.12132 + 0.707107i 0.182574 + 0.0608581i
\(136\) 6.82843 0.585533
\(137\) 8.48528i 0.724947i 0.931994 + 0.362473i \(0.118068\pi\)
−0.931994 + 0.362473i \(0.881932\pi\)
\(138\) 1.00000i 0.0851257i
\(139\) 16.9706 1.43942 0.719712 0.694273i \(-0.244274\pi\)
0.719712 + 0.694273i \(0.244274\pi\)
\(140\) 4.24264 + 1.41421i 0.358569 + 0.119523i
\(141\) −0.828427 −0.0697661
\(142\) 5.65685i 0.474713i
\(143\) 3.51472i 0.293916i
\(144\) −1.00000 −0.0833333
\(145\) 2.58579 7.75736i 0.214738 0.644214i
\(146\) 7.65685 0.633686
\(147\) 3.00000i 0.247436i
\(148\) 0.585786i 0.0481513i
\(149\) −12.7279 −1.04271 −0.521356 0.853339i \(-0.674574\pi\)
−0.521356 + 0.853339i \(0.674574\pi\)
\(150\) −4.00000 3.00000i −0.326599 0.244949i
\(151\) −4.34315 −0.353440 −0.176720 0.984261i \(-0.556549\pi\)
−0.176720 + 0.984261i \(0.556549\pi\)
\(152\) 6.24264i 0.506345i
\(153\) 6.82843i 0.552046i
\(154\) −8.48528 −0.683763
\(155\) −4.24264 + 12.7279i −0.340777 + 1.02233i
\(156\) −0.828427 −0.0663273
\(157\) 21.0711i 1.68165i −0.541304 0.840827i \(-0.682069\pi\)
0.541304 0.840827i \(-0.317931\pi\)
\(158\) 3.65685i 0.290924i
\(159\) −10.5858 −0.839507
\(160\) 2.12132 + 0.707107i 0.167705 + 0.0559017i
\(161\) 2.00000 0.157622
\(162\) 1.00000i 0.0785674i
\(163\) 6.82843i 0.534844i 0.963580 + 0.267422i \(0.0861717\pi\)
−0.963580 + 0.267422i \(0.913828\pi\)
\(164\) 6.82843 0.533211
\(165\) 9.00000 + 3.00000i 0.700649 + 0.233550i
\(166\) 1.41421 0.109764
\(167\) 3.17157i 0.245424i 0.992442 + 0.122712i \(0.0391591\pi\)
−0.992442 + 0.122712i \(0.960841\pi\)
\(168\) 2.00000i 0.154303i
\(169\) 12.3137 0.947208
\(170\) 4.82843 14.4853i 0.370323 1.11097i
\(171\) 6.24264 0.477387
\(172\) 10.2426i 0.780994i
\(173\) 8.82843i 0.671213i 0.942002 + 0.335606i \(0.108941\pi\)
−0.942002 + 0.335606i \(0.891059\pi\)
\(174\) −3.65685 −0.277225
\(175\) 6.00000 8.00000i 0.453557 0.604743i
\(176\) −4.24264 −0.319801
\(177\) 8.48528i 0.637793i
\(178\) 9.17157i 0.687438i
\(179\) 21.6569 1.61871 0.809355 0.587320i \(-0.199817\pi\)
0.809355 + 0.587320i \(0.199817\pi\)
\(180\) −0.707107 + 2.12132i −0.0527046 + 0.158114i
\(181\) −20.3848 −1.51519 −0.757594 0.652726i \(-0.773625\pi\)
−0.757594 + 0.652726i \(0.773625\pi\)
\(182\) 1.65685i 0.122814i
\(183\) 0.585786i 0.0433026i
\(184\) 1.00000 0.0737210
\(185\) 1.24264 + 0.414214i 0.0913608 + 0.0304536i
\(186\) 6.00000 0.439941
\(187\) 28.9706i 2.11854i
\(188\) 0.828427i 0.0604193i
\(189\) 2.00000 0.145479
\(190\) −13.2426 4.41421i −0.960722 0.320241i
\(191\) −10.8284 −0.783517 −0.391759 0.920068i \(-0.628133\pi\)
−0.391759 + 0.920068i \(0.628133\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 20.9706i 1.50949i −0.656016 0.754747i \(-0.727760\pi\)
0.656016 0.754747i \(-0.272240\pi\)
\(194\) 6.00000 0.430775
\(195\) −0.585786 + 1.75736i −0.0419490 + 0.125847i
\(196\) −3.00000 −0.214286
\(197\) 20.6274i 1.46964i −0.678261 0.734821i \(-0.737266\pi\)
0.678261 0.734821i \(-0.262734\pi\)
\(198\) 4.24264i 0.301511i
\(199\) 14.0000 0.992434 0.496217 0.868199i \(-0.334722\pi\)
0.496217 + 0.868199i \(0.334722\pi\)
\(200\) 3.00000 4.00000i 0.212132 0.282843i
\(201\) −3.41421 −0.240820
\(202\) 13.3137i 0.936749i
\(203\) 7.31371i 0.513322i
\(204\) −6.82843 −0.478086
\(205\) 4.82843 14.4853i 0.337232 1.01170i
\(206\) 16.1421 1.12468
\(207\) 1.00000i 0.0695048i
\(208\) 0.828427i 0.0574411i
\(209\) 26.4853 1.83203
\(210\) −4.24264 1.41421i −0.292770 0.0975900i
\(211\) −3.51472 −0.241963 −0.120982 0.992655i \(-0.538604\pi\)
−0.120982 + 0.992655i \(0.538604\pi\)
\(212\) 10.5858i 0.727035i
\(213\) 5.65685i 0.387601i
\(214\) −0.928932 −0.0635005
\(215\) −21.7279 7.24264i −1.48183 0.493944i
\(216\) 1.00000 0.0680414
\(217\) 12.0000i 0.814613i
\(218\) 12.5858i 0.852417i
\(219\) −7.65685 −0.517402
\(220\) −3.00000 + 9.00000i −0.202260 + 0.606780i
\(221\) −5.65685 −0.380521
\(222\) 0.585786i 0.0393154i
\(223\) 16.0000i 1.07144i 0.844396 + 0.535720i \(0.179960\pi\)
−0.844396 + 0.535720i \(0.820040\pi\)
\(224\) 2.00000 0.133631
\(225\) 4.00000 + 3.00000i 0.266667 + 0.200000i
\(226\) −16.9706 −1.12887
\(227\) 22.3848i 1.48573i 0.669441 + 0.742865i \(0.266534\pi\)
−0.669441 + 0.742865i \(0.733466\pi\)
\(228\) 6.24264i 0.413429i
\(229\) −10.2426 −0.676853 −0.338426 0.940993i \(-0.609895\pi\)
−0.338426 + 0.940993i \(0.609895\pi\)
\(230\) 0.707107 2.12132i 0.0466252 0.139876i
\(231\) 8.48528 0.558291
\(232\) 3.65685i 0.240084i
\(233\) 2.14214i 0.140336i 0.997535 + 0.0701680i \(0.0223535\pi\)
−0.997535 + 0.0701680i \(0.977646\pi\)
\(234\) 0.828427 0.0541560
\(235\) −1.75736 0.585786i −0.114637 0.0382125i
\(236\) 8.48528 0.552345
\(237\) 3.65685i 0.237538i
\(238\) 13.6569i 0.885242i
\(239\) 16.8284 1.08854 0.544270 0.838910i \(-0.316807\pi\)
0.544270 + 0.838910i \(0.316807\pi\)
\(240\) −2.12132 0.707107i −0.136931 0.0456435i
\(241\) 6.48528 0.417754 0.208877 0.977942i \(-0.433019\pi\)
0.208877 + 0.977942i \(0.433019\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 1.00000i 0.0641500i
\(244\) 0.585786 0.0375011
\(245\) −2.12132 + 6.36396i −0.135526 + 0.406579i
\(246\) −6.82843 −0.435365
\(247\) 5.17157i 0.329059i
\(248\) 6.00000i 0.381000i
\(249\) −1.41421 −0.0896221
\(250\) −6.36396 9.19239i −0.402492 0.581378i
\(251\) 0.727922 0.0459460 0.0229730 0.999736i \(-0.492687\pi\)
0.0229730 + 0.999736i \(0.492687\pi\)
\(252\) 2.00000i 0.125988i
\(253\) 4.24264i 0.266733i
\(254\) 2.00000 0.125491
\(255\) −4.82843 + 14.4853i −0.302368 + 0.907104i
\(256\) 1.00000 0.0625000
\(257\) 18.0000i 1.12281i −0.827541 0.561405i \(-0.810261\pi\)
0.827541 0.561405i \(-0.189739\pi\)
\(258\) 10.2426i 0.637679i
\(259\) 1.17157 0.0727980
\(260\) −1.75736 0.585786i −0.108987 0.0363289i
\(261\) 3.65685 0.226354
\(262\) 21.6569i 1.33796i
\(263\) 6.34315i 0.391135i −0.980690 0.195568i \(-0.937345\pi\)
0.980690 0.195568i \(-0.0626549\pi\)
\(264\) 4.24264 0.261116
\(265\) −22.4558 7.48528i −1.37945 0.459817i
\(266\) −12.4853 −0.765522
\(267\) 9.17157i 0.561291i
\(268\) 3.41421i 0.208556i
\(269\) 19.1716 1.16891 0.584456 0.811426i \(-0.301308\pi\)
0.584456 + 0.811426i \(0.301308\pi\)
\(270\) 0.707107 2.12132i 0.0430331 0.129099i
\(271\) 9.65685 0.586612 0.293306 0.956019i \(-0.405245\pi\)
0.293306 + 0.956019i \(0.405245\pi\)
\(272\) 6.82843i 0.414034i
\(273\) 1.65685i 0.100277i
\(274\) 8.48528 0.512615
\(275\) 16.9706 + 12.7279i 1.02336 + 0.767523i
\(276\) −1.00000 −0.0601929
\(277\) 13.5147i 0.812021i −0.913868 0.406010i \(-0.866920\pi\)
0.913868 0.406010i \(-0.133080\pi\)
\(278\) 16.9706i 1.01783i
\(279\) −6.00000 −0.359211
\(280\) 1.41421 4.24264i 0.0845154 0.253546i
\(281\) −1.85786 −0.110831 −0.0554154 0.998463i \(-0.517648\pi\)
−0.0554154 + 0.998463i \(0.517648\pi\)
\(282\) 0.828427i 0.0493321i
\(283\) 15.2132i 0.904331i 0.891934 + 0.452166i \(0.149348\pi\)
−0.891934 + 0.452166i \(0.850652\pi\)
\(284\) 5.65685 0.335673
\(285\) 13.2426 + 4.41421i 0.784426 + 0.261475i
\(286\) 3.51472 0.207830
\(287\) 13.6569i 0.806139i
\(288\) 1.00000i 0.0589256i
\(289\) −29.6274 −1.74279
\(290\) −7.75736 2.58579i −0.455528 0.151843i
\(291\) −6.00000 −0.351726
\(292\) 7.65685i 0.448084i
\(293\) 20.0416i 1.17084i 0.810729 + 0.585422i \(0.199071\pi\)
−0.810729 + 0.585422i \(0.800929\pi\)
\(294\) 3.00000 0.174964
\(295\) 6.00000 18.0000i 0.349334 1.04800i
\(296\) 0.585786 0.0340481
\(297\) 4.24264i 0.246183i
\(298\) 12.7279i 0.737309i
\(299\) −0.828427 −0.0479092
\(300\) −3.00000 + 4.00000i −0.173205 + 0.230940i
\(301\) −20.4853 −1.18075
\(302\) 4.34315i 0.249920i
\(303\) 13.3137i 0.764853i
\(304\) −6.24264 −0.358040
\(305\) 0.414214 1.24264i 0.0237178 0.0711534i
\(306\) 6.82843 0.390355
\(307\) 25.4558i 1.45284i −0.687250 0.726421i \(-0.741182\pi\)
0.687250 0.726421i \(-0.258818\pi\)
\(308\) 8.48528i 0.483494i
\(309\) −16.1421 −0.918294
\(310\) 12.7279 + 4.24264i 0.722897 + 0.240966i
\(311\) −21.7990 −1.23611 −0.618054 0.786136i \(-0.712079\pi\)
−0.618054 + 0.786136i \(0.712079\pi\)
\(312\) 0.828427i 0.0469005i
\(313\) 18.0000i 1.01742i 0.860938 + 0.508710i \(0.169877\pi\)
−0.860938 + 0.508710i \(0.830123\pi\)
\(314\) −21.0711 −1.18911
\(315\) 4.24264 + 1.41421i 0.239046 + 0.0796819i
\(316\) −3.65685 −0.205714
\(317\) 14.4853i 0.813574i 0.913523 + 0.406787i \(0.133351\pi\)
−0.913523 + 0.406787i \(0.866649\pi\)
\(318\) 10.5858i 0.593621i
\(319\) 15.5147 0.868657
\(320\) 0.707107 2.12132i 0.0395285 0.118585i
\(321\) 0.928932 0.0518479
\(322\) 2.00000i 0.111456i
\(323\) 42.6274i 2.37185i
\(324\) −1.00000 −0.0555556
\(325\) −2.48528 + 3.31371i −0.137859 + 0.183811i
\(326\) 6.82843 0.378192
\(327\) 12.5858i 0.695996i
\(328\) 6.82843i 0.377037i
\(329\) −1.65685 −0.0913453
\(330\) 3.00000 9.00000i 0.165145 0.495434i
\(331\) −20.4853 −1.12597 −0.562986 0.826466i \(-0.690348\pi\)
−0.562986 + 0.826466i \(0.690348\pi\)
\(332\) 1.41421i 0.0776151i
\(333\) 0.585786i 0.0321009i
\(334\) 3.17157 0.173541
\(335\) −7.24264 2.41421i −0.395708 0.131903i
\(336\) −2.00000 −0.109109
\(337\) 26.4853i 1.44275i 0.692547 + 0.721373i \(0.256488\pi\)
−0.692547 + 0.721373i \(0.743512\pi\)
\(338\) 12.3137i 0.669777i
\(339\) 16.9706 0.921714
\(340\) −14.4853 4.82843i −0.785575 0.261858i
\(341\) −25.4558 −1.37851
\(342\) 6.24264i 0.337563i
\(343\) 20.0000i 1.07990i
\(344\) −10.2426 −0.552246
\(345\) −0.707107 + 2.12132i −0.0380693 + 0.114208i
\(346\) 8.82843 0.474619
\(347\) 31.7990i 1.70706i 0.521044 + 0.853530i \(0.325543\pi\)
−0.521044 + 0.853530i \(0.674457\pi\)
\(348\) 3.65685i 0.196028i
\(349\) −2.68629 −0.143794 −0.0718969 0.997412i \(-0.522905\pi\)
−0.0718969 + 0.997412i \(0.522905\pi\)
\(350\) −8.00000 6.00000i −0.427618 0.320713i
\(351\) −0.828427 −0.0442182
\(352\) 4.24264i 0.226134i
\(353\) 2.14214i 0.114014i 0.998374 + 0.0570072i \(0.0181558\pi\)
−0.998374 + 0.0570072i \(0.981844\pi\)
\(354\) −8.48528 −0.450988
\(355\) 4.00000 12.0000i 0.212298 0.636894i
\(356\) 9.17157 0.486092
\(357\) 13.6569i 0.722797i
\(358\) 21.6569i 1.14460i
\(359\) −19.7990 −1.04495 −0.522475 0.852654i \(-0.674991\pi\)
−0.522475 + 0.852654i \(0.674991\pi\)
\(360\) 2.12132 + 0.707107i 0.111803 + 0.0372678i
\(361\) 19.9706 1.05108
\(362\) 20.3848i 1.07140i
\(363\) 7.00000i 0.367405i
\(364\) −1.65685 −0.0868428
\(365\) −16.2426 5.41421i −0.850179 0.283393i
\(366\) −0.585786 −0.0306195
\(367\) 1.02944i 0.0537362i −0.999639 0.0268681i \(-0.991447\pi\)
0.999639 0.0268681i \(-0.00855341\pi\)
\(368\) 1.00000i 0.0521286i
\(369\) 6.82843 0.355474
\(370\) 0.414214 1.24264i 0.0215339 0.0646018i
\(371\) −21.1716 −1.09917
\(372\) 6.00000i 0.311086i
\(373\) 23.2132i 1.20193i −0.799274 0.600967i \(-0.794782\pi\)
0.799274 0.600967i \(-0.205218\pi\)
\(374\) 28.9706 1.49803
\(375\) 6.36396 + 9.19239i 0.328634 + 0.474693i
\(376\) −0.828427 −0.0427229
\(377\) 3.02944i 0.156024i
\(378\) 2.00000i 0.102869i
\(379\) −23.2132 −1.19238 −0.596191 0.802843i \(-0.703320\pi\)
−0.596191 + 0.802843i \(0.703320\pi\)
\(380\) −4.41421 + 13.2426i −0.226444 + 0.679333i
\(381\) −2.00000 −0.102463
\(382\) 10.8284i 0.554031i
\(383\) 26.6274i 1.36060i 0.732935 + 0.680299i \(0.238150\pi\)
−0.732935 + 0.680299i \(0.761850\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 18.0000 + 6.00000i 0.917365 + 0.305788i
\(386\) −20.9706 −1.06737
\(387\) 10.2426i 0.520663i
\(388\) 6.00000i 0.304604i
\(389\) 30.3848 1.54057 0.770285 0.637700i \(-0.220114\pi\)
0.770285 + 0.637700i \(0.220114\pi\)
\(390\) 1.75736 + 0.585786i 0.0889873 + 0.0296624i
\(391\) −6.82843 −0.345328
\(392\) 3.00000i 0.151523i
\(393\) 21.6569i 1.09244i
\(394\) −20.6274 −1.03919
\(395\) −2.58579 + 7.75736i −0.130105 + 0.390315i
\(396\) −4.24264 −0.213201
\(397\) 19.6569i 0.986549i 0.869874 + 0.493275i \(0.164200\pi\)
−0.869874 + 0.493275i \(0.835800\pi\)
\(398\) 14.0000i 0.701757i
\(399\) 12.4853 0.625046
\(400\) −4.00000 3.00000i −0.200000 0.150000i
\(401\) 4.97056 0.248218 0.124109 0.992269i \(-0.460393\pi\)
0.124109 + 0.992269i \(0.460393\pi\)
\(402\) 3.41421i 0.170285i
\(403\) 4.97056i 0.247601i
\(404\) −13.3137 −0.662382
\(405\) −0.707107 + 2.12132i −0.0351364 + 0.105409i
\(406\) −7.31371 −0.362973
\(407\) 2.48528i 0.123191i
\(408\) 6.82843i 0.338058i
\(409\) −18.0000 −0.890043 −0.445021 0.895520i \(-0.646804\pi\)
−0.445021 + 0.895520i \(0.646804\pi\)
\(410\) −14.4853 4.82843i −0.715377 0.238459i
\(411\) −8.48528 −0.418548
\(412\) 16.1421i 0.795266i
\(413\) 16.9706i 0.835067i
\(414\) 1.00000 0.0491473
\(415\) −3.00000 1.00000i −0.147264 0.0490881i
\(416\) −0.828427 −0.0406170
\(417\) 16.9706i 0.831052i
\(418\) 26.4853i 1.29544i
\(419\) 39.0711 1.90875 0.954373 0.298616i \(-0.0965250\pi\)
0.954373 + 0.298616i \(0.0965250\pi\)
\(420\) −1.41421 + 4.24264i −0.0690066 + 0.207020i
\(421\) 1.75736 0.0856485 0.0428242 0.999083i \(-0.486364\pi\)
0.0428242 + 0.999083i \(0.486364\pi\)
\(422\) 3.51472i 0.171094i
\(423\) 0.828427i 0.0402795i
\(424\) −10.5858 −0.514091
\(425\) −20.4853 + 27.3137i −0.993682 + 1.32491i
\(426\) −5.65685 −0.274075
\(427\) 1.17157i 0.0566964i
\(428\) 0.928932i 0.0449016i
\(429\) −3.51472 −0.169692
\(430\) −7.24264 + 21.7279i −0.349271 + 1.04781i
\(431\) −8.48528 −0.408722 −0.204361 0.978896i \(-0.565512\pi\)
−0.204361 + 0.978896i \(0.565512\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 6.97056i 0.334984i −0.985873 0.167492i \(-0.946433\pi\)
0.985873 0.167492i \(-0.0535668\pi\)
\(434\) 12.0000 0.576018
\(435\) 7.75736 + 2.58579i 0.371937 + 0.123979i
\(436\) 12.5858 0.602750
\(437\) 6.24264i 0.298626i
\(438\) 7.65685i 0.365859i
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 9.00000 + 3.00000i 0.429058 + 0.143019i
\(441\) −3.00000 −0.142857
\(442\) 5.65685i 0.269069i
\(443\) 0.686292i 0.0326067i −0.999867 0.0163033i \(-0.994810\pi\)
0.999867 0.0163033i \(-0.00518975\pi\)
\(444\) −0.585786 −0.0278002
\(445\) 6.48528 19.4558i 0.307432 0.922295i
\(446\) 16.0000 0.757622
\(447\) 12.7279i 0.602010i
\(448\) 2.00000i 0.0944911i
\(449\) 17.1716 0.810377 0.405188 0.914233i \(-0.367206\pi\)
0.405188 + 0.914233i \(0.367206\pi\)
\(450\) 3.00000 4.00000i 0.141421 0.188562i
\(451\) 28.9706 1.36417
\(452\) 16.9706i 0.798228i
\(453\) 4.34315i 0.204059i
\(454\) 22.3848 1.05057
\(455\) −1.17157 + 3.51472i −0.0549242 + 0.164773i
\(456\) 6.24264 0.292338
\(457\) 34.9706i 1.63585i −0.575322 0.817927i \(-0.695123\pi\)
0.575322 0.817927i \(-0.304877\pi\)
\(458\) 10.2426i 0.478607i
\(459\) −6.82843 −0.318724
\(460\) −2.12132 0.707107i −0.0989071 0.0329690i
\(461\) −7.17157 −0.334013 −0.167007 0.985956i \(-0.553410\pi\)
−0.167007 + 0.985956i \(0.553410\pi\)
\(462\) 8.48528i 0.394771i
\(463\) 30.9706i 1.43932i −0.694325 0.719662i \(-0.744297\pi\)
0.694325 0.719662i \(-0.255703\pi\)
\(464\) −3.65685 −0.169765
\(465\) −12.7279 4.24264i −0.590243 0.196748i
\(466\) 2.14214 0.0992325
\(467\) 31.3553i 1.45095i 0.688247 + 0.725476i \(0.258380\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(468\) 0.828427i 0.0382941i
\(469\) −6.82843 −0.315307
\(470\) −0.585786 + 1.75736i −0.0270203 + 0.0810609i
\(471\) 21.0711 0.970904
\(472\) 8.48528i 0.390567i
\(473\) 43.4558i 1.99810i
\(474\) 3.65685 0.167965
\(475\) 24.9706 + 18.7279i 1.14573 + 0.859296i
\(476\) −13.6569 −0.625961
\(477\) 10.5858i 0.484690i
\(478\) 16.8284i 0.769714i
\(479\) −27.3137 −1.24800 −0.623998 0.781426i \(-0.714493\pi\)
−0.623998 + 0.781426i \(0.714493\pi\)
\(480\) −0.707107 + 2.12132i −0.0322749 + 0.0968246i
\(481\) −0.485281 −0.0221269
\(482\) 6.48528i 0.295396i
\(483\) 2.00000i 0.0910032i
\(484\) −7.00000 −0.318182
\(485\) −12.7279 4.24264i −0.577945 0.192648i
\(486\) 1.00000 0.0453609
\(487\) 39.9411i 1.80991i −0.425512 0.904953i \(-0.639906\pi\)
0.425512 0.904953i \(-0.360094\pi\)
\(488\) 0.585786i 0.0265173i
\(489\) −6.82843 −0.308792
\(490\) 6.36396 + 2.12132i 0.287494 + 0.0958315i
\(491\) −18.6274 −0.840644 −0.420322 0.907375i \(-0.638083\pi\)
−0.420322 + 0.907375i \(0.638083\pi\)
\(492\) 6.82843i 0.307849i
\(493\) 24.9706i 1.12462i
\(494\) 5.17157 0.232680
\(495\) −3.00000 + 9.00000i −0.134840 + 0.404520i
\(496\) 6.00000 0.269408
\(497\) 11.3137i 0.507489i
\(498\) 1.41421i 0.0633724i
\(499\) 37.4558 1.67675 0.838377 0.545091i \(-0.183505\pi\)
0.838377 + 0.545091i \(0.183505\pi\)
\(500\) −9.19239 + 6.36396i −0.411096 + 0.284605i
\(501\) −3.17157 −0.141695
\(502\) 0.727922i 0.0324888i
\(503\) 6.14214i 0.273864i −0.990580 0.136932i \(-0.956276\pi\)
0.990580 0.136932i \(-0.0437242\pi\)
\(504\) 2.00000 0.0890871
\(505\) −9.41421 + 28.2426i −0.418927 + 1.25678i
\(506\) 4.24264 0.188608
\(507\) 12.3137i 0.546871i
\(508\) 2.00000i 0.0887357i
\(509\) 10.9706 0.486262 0.243131 0.969994i \(-0.421826\pi\)
0.243131 + 0.969994i \(0.421826\pi\)
\(510\) 14.4853 + 4.82843i 0.641419 + 0.213806i
\(511\) −15.3137 −0.677439
\(512\) 1.00000i 0.0441942i
\(513\) 6.24264i 0.275619i
\(514\) −18.0000 −0.793946
\(515\) −34.2426 11.4142i −1.50891 0.502970i
\(516\) 10.2426 0.450907
\(517\) 3.51472i 0.154577i
\(518\) 1.17157i 0.0514760i
\(519\) −8.82843 −0.387525
\(520\) −0.585786 + 1.75736i −0.0256884 + 0.0770653i
\(521\) 40.2843 1.76489 0.882443 0.470419i \(-0.155897\pi\)
0.882443 + 0.470419i \(0.155897\pi\)
\(522\) 3.65685i 0.160056i
\(523\) 17.0711i 0.746466i −0.927738 0.373233i \(-0.878249\pi\)
0.927738 0.373233i \(-0.121751\pi\)
\(524\) 21.6569 0.946084
\(525\) 8.00000 + 6.00000i 0.349149 + 0.261861i
\(526\) −6.34315 −0.276574
\(527\) 40.9706i 1.78471i
\(528\) 4.24264i 0.184637i
\(529\) −1.00000 −0.0434783
\(530\) −7.48528 + 22.4558i −0.325140 + 0.975420i
\(531\) 8.48528 0.368230
\(532\) 12.4853i 0.541306i
\(533\) 5.65685i 0.245026i
\(534\) −9.17157 −0.396893
\(535\) 1.97056 + 0.656854i 0.0851949 + 0.0283983i
\(536\) −3.41421 −0.147472
\(537\) 21.6569i 0.934562i
\(538\) 19.1716i 0.826545i
\(539\) −12.7279 −0.548230
\(540\) −2.12132 0.707107i −0.0912871 0.0304290i
\(541\) −31.9411 −1.37326 −0.686628 0.727009i \(-0.740910\pi\)
−0.686628 + 0.727009i \(0.740910\pi\)
\(542\) 9.65685i 0.414797i
\(543\) 20.3848i 0.874794i
\(544\) −6.82843 −0.292766
\(545\) 8.89949 26.6985i 0.381212 1.14364i
\(546\) 1.65685 0.0709068
\(547\) 12.4853i 0.533832i −0.963720 0.266916i \(-0.913995\pi\)
0.963720 0.266916i \(-0.0860046\pi\)
\(548\) 8.48528i 0.362473i
\(549\) 0.585786 0.0250008
\(550\) 12.7279 16.9706i 0.542720 0.723627i
\(551\) 22.8284 0.972524
\(552\) 1.00000i 0.0425628i
\(553\) 7.31371i 0.311011i
\(554\) −13.5147 −0.574185
\(555\) −0.414214 + 1.24264i −0.0175824 + 0.0527472i
\(556\) −16.9706 −0.719712
\(557\) 38.8701i 1.64698i −0.567333 0.823489i \(-0.692025\pi\)
0.567333 0.823489i \(-0.307975\pi\)
\(558\) 6.00000i 0.254000i
\(559\) 8.48528 0.358889
\(560\) −4.24264 1.41421i −0.179284 0.0597614i
\(561\) −28.9706 −1.22314
\(562\) 1.85786i 0.0783693i
\(563\) 2.10051i 0.0885257i −0.999020 0.0442629i \(-0.985906\pi\)
0.999020 0.0442629i \(-0.0140939\pi\)
\(564\) 0.828427 0.0348831
\(565\) 36.0000 + 12.0000i 1.51453 + 0.504844i
\(566\) 15.2132 0.639459
\(567\) 2.00000i 0.0839921i
\(568\) 5.65685i 0.237356i
\(569\) −14.3431 −0.601296 −0.300648 0.953735i \(-0.597203\pi\)
−0.300648 + 0.953735i \(0.597203\pi\)
\(570\) 4.41421 13.2426i 0.184891 0.554673i
\(571\) −17.2721 −0.722814 −0.361407 0.932408i \(-0.617703\pi\)
−0.361407 + 0.932408i \(0.617703\pi\)
\(572\) 3.51472i 0.146958i
\(573\) 10.8284i 0.452364i
\(574\) −13.6569 −0.570026
\(575\) −3.00000 + 4.00000i −0.125109 + 0.166812i
\(576\) 1.00000 0.0416667
\(577\) 24.6274i 1.02525i −0.858612 0.512626i \(-0.828673\pi\)
0.858612 0.512626i \(-0.171327\pi\)
\(578\) 29.6274i 1.23234i
\(579\) 20.9706 0.871507
\(580\) −2.58579 + 7.75736i −0.107369 + 0.322107i
\(581\) −2.82843 −0.117343
\(582\) 6.00000i 0.248708i
\(583\) 44.9117i 1.86005i
\(584\) −7.65685 −0.316843
\(585\) −1.75736 0.585786i −0.0726579 0.0242193i
\(586\) 20.0416 0.827912
\(587\) 21.1716i 0.873844i −0.899499 0.436922i \(-0.856069\pi\)
0.899499 0.436922i \(-0.143931\pi\)
\(588\) 3.00000i 0.123718i
\(589\) −37.4558 −1.54334
\(590\) −18.0000 6.00000i −0.741048 0.247016i
\(591\) 20.6274 0.848499
\(592\) 0.585786i 0.0240757i
\(593\) 23.6569i 0.971471i −0.874106 0.485735i \(-0.838552\pi\)
0.874106 0.485735i \(-0.161448\pi\)
\(594\) 4.24264 0.174078
\(595\) −9.65685 + 28.9706i −0.395892 + 1.18768i
\(596\) 12.7279 0.521356
\(597\) 14.0000i 0.572982i
\(598\) 0.828427i 0.0338769i
\(599\) 11.8579 0.484499 0.242250 0.970214i \(-0.422115\pi\)
0.242250 + 0.970214i \(0.422115\pi\)
\(600\) 4.00000 + 3.00000i 0.163299 + 0.122474i
\(601\) 12.9706 0.529080 0.264540 0.964375i \(-0.414780\pi\)
0.264540 + 0.964375i \(0.414780\pi\)
\(602\) 20.4853i 0.834918i
\(603\) 3.41421i 0.139038i
\(604\) 4.34315 0.176720
\(605\) −4.94975 + 14.8492i −0.201236 + 0.603708i
\(606\) 13.3137 0.540832
\(607\) 16.9706i 0.688814i −0.938820 0.344407i \(-0.888080\pi\)
0.938820 0.344407i \(-0.111920\pi\)
\(608\) 6.24264i 0.253173i
\(609\) 7.31371 0.296366
\(610\) −1.24264 0.414214i −0.0503131 0.0167710i
\(611\) 0.686292 0.0277644
\(612\) 6.82843i 0.276023i
\(613\) 5.75736i 0.232538i −0.993218 0.116269i \(-0.962907\pi\)
0.993218 0.116269i \(-0.0370934\pi\)
\(614\) −25.4558 −1.02731
\(615\) 14.4853 + 4.82843i 0.584103 + 0.194701i
\(616\) 8.48528 0.341882
\(617\) 8.68629i 0.349697i 0.984595 + 0.174848i \(0.0559436\pi\)
−0.984595 + 0.174848i \(0.944056\pi\)
\(618\) 16.1421i 0.649332i
\(619\) −23.2132 −0.933017 −0.466509 0.884517i \(-0.654488\pi\)
−0.466509 + 0.884517i \(0.654488\pi\)
\(620\) 4.24264 12.7279i 0.170389 0.511166i
\(621\) −1.00000 −0.0401286
\(622\) 21.7990i 0.874060i
\(623\) 18.3431i 0.734903i
\(624\) 0.828427 0.0331636
\(625\) 7.00000 + 24.0000i 0.280000 + 0.960000i
\(626\) 18.0000 0.719425
\(627\) 26.4853i 1.05772i
\(628\) 21.0711i 0.840827i
\(629\) −4.00000 −0.159490
\(630\) 1.41421 4.24264i 0.0563436 0.169031i
\(631\) 40.8284 1.62535 0.812677 0.582714i \(-0.198009\pi\)
0.812677 + 0.582714i \(0.198009\pi\)
\(632\) 3.65685i 0.145462i
\(633\) 3.51472i 0.139698i
\(634\) 14.4853 0.575284
\(635\) −4.24264 1.41421i −0.168364 0.0561214i
\(636\) 10.5858 0.419754
\(637\) 2.48528i 0.0984704i
\(638\) 15.5147i 0.614234i
\(639\) 5.65685 0.223782
\(640\) −2.12132 0.707107i −0.0838525 0.0279508i
\(641\) 48.2843 1.90711 0.953557 0.301213i \(-0.0973914\pi\)
0.953557 + 0.301213i \(0.0973914\pi\)
\(642\) 0.928932i 0.0366620i
\(643\) 4.38478i 0.172919i 0.996255 + 0.0864593i \(0.0275553\pi\)
−0.996255 + 0.0864593i \(0.972445\pi\)
\(644\) −2.00000 −0.0788110
\(645\) 7.24264 21.7279i 0.285179 0.855536i
\(646\) 42.6274 1.67715
\(647\) 18.3431i 0.721143i 0.932731 + 0.360572i \(0.117418\pi\)
−0.932731 + 0.360572i \(0.882582\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 36.0000 1.41312
\(650\) 3.31371 + 2.48528i 0.129974 + 0.0974808i
\(651\) −12.0000 −0.470317
\(652\) 6.82843i 0.267422i
\(653\) 7.45584i 0.291770i −0.989302 0.145885i \(-0.953397\pi\)
0.989302 0.145885i \(-0.0466029\pi\)
\(654\) −12.5858 −0.492143
\(655\) 15.3137 45.9411i 0.598356 1.79507i
\(656\) −6.82843 −0.266605
\(657\) 7.65685i 0.298722i
\(658\) 1.65685i 0.0645909i
\(659\) 45.8995 1.78799 0.893995 0.448076i \(-0.147891\pi\)
0.893995 + 0.448076i \(0.147891\pi\)
\(660\) −9.00000 3.00000i −0.350325 0.116775i
\(661\) 34.7279 1.35076 0.675380 0.737470i \(-0.263980\pi\)
0.675380 + 0.737470i \(0.263980\pi\)
\(662\) 20.4853i 0.796183i
\(663\) 5.65685i 0.219694i
\(664\) −1.41421 −0.0548821
\(665\) 26.4853 + 8.82843i 1.02706 + 0.342352i
\(666\) 0.585786 0.0226988
\(667\) 3.65685i 0.141594i
\(668\) 3.17157i 0.122712i
\(669\) −16.0000 −0.618596
\(670\) −2.41421 + 7.24264i −0.0932692 + 0.279808i
\(671\) 2.48528 0.0959432
\(672\) 2.00000i 0.0771517i
\(673\) 27.9411i 1.07705i 0.842609 + 0.538526i \(0.181018\pi\)
−0.842609 + 0.538526i \(0.818982\pi\)
\(674\) 26.4853 1.02017
\(675\) −3.00000 + 4.00000i −0.115470 + 0.153960i
\(676\) −12.3137 −0.473604
\(677\) 40.5269i 1.55758i 0.627287 + 0.778788i \(0.284165\pi\)
−0.627287 + 0.778788i \(0.715835\pi\)
\(678\) 16.9706i 0.651751i
\(679\) −12.0000 −0.460518
\(680\) −4.82843 + 14.4853i −0.185162 + 0.555485i
\(681\) −22.3848 −0.857786
\(682\) 25.4558i 0.974755i
\(683\) 8.48528i 0.324680i −0.986735 0.162340i \(-0.948096\pi\)
0.986735 0.162340i \(-0.0519042\pi\)
\(684\) −6.24264 −0.238693
\(685\) −18.0000 6.00000i −0.687745 0.229248i
\(686\) 20.0000 0.763604
\(687\) 10.2426i 0.390781i
\(688\) 10.2426i 0.390497i
\(689\) 8.76955 0.334093
\(690\) 2.12132 + 0.707107i 0.0807573 + 0.0269191i
\(691\) −13.1716 −0.501070 −0.250535 0.968108i \(-0.580607\pi\)
−0.250535 + 0.968108i \(0.580607\pi\)
\(692\) 8.82843i 0.335606i
\(693\) 8.48528i 0.322329i
\(694\) 31.7990 1.20707
\(695\) −12.0000 + 36.0000i −0.455186 + 1.36556i
\(696\) 3.65685 0.138613
\(697\) 46.6274i 1.76614i
\(698\) 2.68629i 0.101678i
\(699\) −2.14214 −0.0810230
\(700\) −6.00000 + 8.00000i −0.226779 + 0.302372i
\(701\) −38.1838 −1.44218 −0.721090 0.692841i \(-0.756359\pi\)
−0.721090 + 0.692841i \(0.756359\pi\)
\(702\) 0.828427i 0.0312670i
\(703\) 3.65685i 0.137921i
\(704\) 4.24264 0.159901
\(705\) 0.585786 1.75736i 0.0220620 0.0661860i
\(706\) 2.14214 0.0806203
\(707\) 26.6274i 1.00143i
\(708\) 8.48528i 0.318896i
\(709\) −32.5858 −1.22378 −0.611892 0.790941i \(-0.709591\pi\)
−0.611892 + 0.790941i \(0.709591\pi\)
\(710\) −12.0000 4.00000i −0.450352 0.150117i
\(711\) −3.65685 −0.137143
\(712\) 9.17157i 0.343719i
\(713\) 6.00000i 0.224702i
\(714\) 13.6569 0.511095
\(715\) −7.45584 2.48528i −0.278833 0.0929443i
\(716\) −21.6569 −0.809355
\(717\) 16.8284i 0.628469i
\(718\) 19.7990i 0.738892i
\(719\) 0.142136 0.00530076 0.00265038 0.999996i \(-0.499156\pi\)
0.00265038 + 0.999996i \(0.499156\pi\)
\(720\) 0.707107 2.12132i 0.0263523 0.0790569i
\(721\) −32.2843 −1.20233
\(722\) 19.9706i 0.743227i
\(723\) 6.48528i 0.241190i
\(724\) 20.3848 0.757594
\(725\) 14.6274 + 10.9706i 0.543249 + 0.407436i
\(726\) 7.00000 0.259794
\(727\) 20.3431i 0.754486i 0.926114 + 0.377243i \(0.123128\pi\)
−0.926114 + 0.377243i \(0.876872\pi\)
\(728\) 1.65685i 0.0614071i
\(729\) −1.00000 −0.0370370
\(730\) −5.41421 + 16.2426i −0.200389 + 0.601167i
\(731\) 69.9411 2.58687
\(732\) 0.585786i 0.0216513i
\(733\) 11.4142i 0.421594i 0.977530 + 0.210797i \(0.0676058\pi\)
−0.977530 + 0.210797i \(0.932394\pi\)
\(734\) −1.02944 −0.0379972
\(735\) −6.36396 2.12132i −0.234738 0.0782461i
\(736\) −1.00000 −0.0368605
\(737\) 14.4853i 0.533572i
\(738\) 6.82843i 0.251358i
\(739\) 2.62742 0.0966511 0.0483255 0.998832i \(-0.484612\pi\)
0.0483255 + 0.998832i \(0.484612\pi\)
\(740\) −1.24264 0.414214i −0.0456804 0.0152268i
\(741\) −5.17157 −0.189982
\(742\) 21.1716i 0.777233i
\(743\) 13.6569i 0.501021i 0.968114 + 0.250511i \(0.0805985\pi\)
−0.968114 + 0.250511i \(0.919401\pi\)
\(744\) −6.00000 −0.219971
\(745\) 9.00000 27.0000i 0.329734 0.989203i
\(746\) −23.2132 −0.849896
\(747\) 1.41421i 0.0517434i
\(748\) 28.9706i 1.05927i
\(749\) 1.85786 0.0678849
\(750\) 9.19239 6.36396i 0.335659 0.232379i
\(751\) −43.1716 −1.57535 −0.787677 0.616089i \(-0.788716\pi\)
−0.787677 + 0.616089i \(0.788716\pi\)
\(752\) 0.828427i 0.0302096i
\(753\) 0.727922i 0.0265270i
\(754\) 3.02944 0.110326
\(755\) 3.07107 9.21320i 0.111768 0.335303i
\(756\) −2.00000 −0.0727393
\(757\) 33.7574i 1.22693i −0.789721 0.613466i \(-0.789775\pi\)
0.789721 0.613466i \(-0.210225\pi\)
\(758\) 23.2132i 0.843142i
\(759\) −4.24264 −0.153998
\(760\) 13.2426 + 4.41421i 0.480361 + 0.160120i
\(761\) −35.6569 −1.29256 −0.646280 0.763100i \(-0.723676\pi\)
−0.646280 + 0.763100i \(0.723676\pi\)
\(762\) 2.00000i 0.0724524i
\(763\) 25.1716i 0.911272i
\(764\) 10.8284 0.391759
\(765\) −14.4853 4.82843i −0.523716 0.174572i
\(766\) 26.6274 0.962088
\(767\) 7.02944i 0.253818i
\(768\) 1.00000i 0.0360844i
\(769\) −6.20101 −0.223614 −0.111807 0.993730i \(-0.535664\pi\)
−0.111807 + 0.993730i \(0.535664\pi\)
\(770\) 6.00000 18.0000i 0.216225 0.648675i
\(771\) 18.0000 0.648254
\(772\) 20.9706i 0.754747i
\(773\) 31.0711i 1.11755i −0.829320 0.558774i \(-0.811272\pi\)
0.829320 0.558774i \(-0.188728\pi\)
\(774\) −10.2426 −0.368164
\(775\) −24.0000 18.0000i −0.862105 0.646579i
\(776\) −6.00000 −0.215387
\(777\) 1.17157i 0.0420299i
\(778\) 30.3848i 1.08935i
\(779\) 42.6274 1.52729
\(780\) 0.585786 1.75736i 0.0209745 0.0629236i
\(781\) 24.0000 0.858788
\(782\) 6.82843i 0.244184i
\(783\) 3.65685i 0.130685i
\(784\) 3.00000 0.107143
\(785\) 44.6985 + 14.8995i 1.59536 + 0.531786i
\(786\) −21.6569 −0.772474
\(787\) 22.7279i 0.810163i 0.914281 + 0.405081i \(0.132757\pi\)
−0.914281 + 0.405081i \(0.867243\pi\)
\(788\) 20.6274i 0.734821i