Properties

Label 690.2.d.b.139.4
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 139.4
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 690.139
Dual form 690.2.d.b.139.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(0.707107 + 2.12132i) q^{5} +1.00000 q^{6} -2.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(0.707107 + 2.12132i) q^{5} +1.00000 q^{6} -2.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-2.12132 + 0.707107i) q^{10} +4.24264 q^{11} +1.00000i q^{12} -4.82843i q^{13} +2.00000 q^{14} +(2.12132 - 0.707107i) q^{15} +1.00000 q^{16} +1.17157i q^{17} -1.00000i q^{18} +2.24264 q^{19} +(-0.707107 - 2.12132i) q^{20} -2.00000 q^{21} +4.24264i q^{22} +1.00000i q^{23} -1.00000 q^{24} +(-4.00000 + 3.00000i) q^{25} +4.82843 q^{26} +1.00000i q^{27} +2.00000i q^{28} +7.65685 q^{29} +(0.707107 + 2.12132i) q^{30} +6.00000 q^{31} +1.00000i q^{32} -4.24264i q^{33} -1.17157 q^{34} +(4.24264 - 1.41421i) q^{35} +1.00000 q^{36} +3.41421i q^{37} +2.24264i q^{38} -4.82843 q^{39} +(2.12132 - 0.707107i) q^{40} -1.17157 q^{41} -2.00000i q^{42} -1.75736i q^{43} -4.24264 q^{44} +(-0.707107 - 2.12132i) q^{45} -1.00000 q^{46} +4.82843i q^{47} -1.00000i q^{48} +3.00000 q^{49} +(-3.00000 - 4.00000i) q^{50} +1.17157 q^{51} +4.82843i q^{52} -13.4142i q^{53} -1.00000 q^{54} +(3.00000 + 9.00000i) q^{55} -2.00000 q^{56} -2.24264i q^{57} +7.65685i q^{58} +8.48528 q^{59} +(-2.12132 + 0.707107i) q^{60} -3.41421 q^{61} +6.00000i q^{62} +2.00000i q^{63} -1.00000 q^{64} +(10.2426 - 3.41421i) q^{65} +4.24264 q^{66} -0.585786i q^{67} -1.17157i q^{68} +1.00000 q^{69} +(1.41421 + 4.24264i) q^{70} +5.65685 q^{71} +1.00000i q^{72} +3.65685i q^{73} -3.41421 q^{74} +(3.00000 + 4.00000i) q^{75} -2.24264 q^{76} -8.48528i q^{77} -4.82843i q^{78} -7.65685 q^{79} +(0.707107 + 2.12132i) q^{80} +1.00000 q^{81} -1.17157i q^{82} +1.41421i q^{83} +2.00000 q^{84} +(-2.48528 + 0.828427i) q^{85} +1.75736 q^{86} -7.65685i q^{87} -4.24264i q^{88} -14.8284 q^{89} +(2.12132 - 0.707107i) q^{90} -9.65685 q^{91} -1.00000i q^{92} -6.00000i q^{93} -4.82843 q^{94} +(1.58579 + 4.75736i) q^{95} +1.00000 q^{96} -6.00000i q^{97} +3.00000i q^{98} -4.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{4} + 4q^{6} - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{4} + 4q^{6} - 4q^{9} + 8q^{14} + 4q^{16} - 8q^{19} - 8q^{21} - 4q^{24} - 16q^{25} + 8q^{26} + 8q^{29} + 24q^{31} - 16q^{34} + 4q^{36} - 8q^{39} - 16q^{41} - 4q^{46} + 12q^{49} - 12q^{50} + 16q^{51} - 4q^{54} + 12q^{55} - 8q^{56} - 8q^{61} - 4q^{64} + 24q^{65} + 4q^{69} - 8q^{74} + 12q^{75} + 8q^{76} - 8q^{79} + 4q^{81} + 8q^{84} + 24q^{85} + 24q^{86} - 48q^{89} - 16q^{91} - 8q^{94} + 12q^{95} + 4q^{96} + O(q^{100}) \)

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 \(-0.876624\pi\)
0.925820 0.377964i \(-0.123376\pi\)
\(8\) 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 \(-0.279099\pi\)
0.639602 + 0.768706i \(0.279099\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 4.82843i 1.33916i −0.742738 0.669582i \(-0.766473\pi\)
0.742738 0.669582i \(-0.233527\pi\)
\(14\) 2.00000 0.534522
\(15\) 2.12132 0.707107i 0.547723 0.182574i
\(16\) 1.00000 0.250000
\(17\) 1.17157i 0.284148i 0.989856 + 0.142074i \(0.0453771\pi\)
−0.989856 + 0.142074i \(0.954623\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 2.24264 0.514497 0.257249 0.966345i \(-0.417184\pi\)
0.257249 + 0.966345i \(0.417184\pi\)
\(20\) −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
\(26\) 4.82843 0.946932
\(27\) 1.00000i 0.192450i
\(28\) 2.00000i 0.377964i
\(29\) 7.65685 1.42184 0.710921 0.703272i \(-0.248278\pi\)
0.710921 + 0.703272i \(0.248278\pi\)
\(30\) 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
\(34\) −1.17157 −0.200923
\(35\) 4.24264 1.41421i 0.717137 0.239046i
\(36\) 1.00000 0.166667
\(37\) 3.41421i 0.561293i 0.959811 + 0.280647i \(0.0905489\pi\)
−0.959811 + 0.280647i \(0.909451\pi\)
\(38\) 2.24264i 0.363804i
\(39\) −4.82843 −0.773167
\(40\) 2.12132 0.707107i 0.335410 0.111803i
\(41\) −1.17157 −0.182969 −0.0914845 0.995807i \(-0.529161\pi\)
−0.0914845 + 0.995807i \(0.529161\pi\)
\(42\) 2.00000i 0.308607i
\(43\) 1.75736i 0.267995i −0.990982 0.133997i \(-0.957219\pi\)
0.990982 0.133997i \(-0.0427814\pi\)
\(44\) −4.24264 −0.639602
\(45\) −0.707107 2.12132i −0.105409 0.316228i
\(46\) −1.00000 −0.147442
\(47\) 4.82843i 0.704298i 0.935944 + 0.352149i \(0.114549\pi\)
−0.935944 + 0.352149i \(0.885451\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 3.00000 0.428571
\(50\) −3.00000 4.00000i −0.424264 0.565685i
\(51\) 1.17157 0.164053
\(52\) 4.82843i 0.669582i
\(53\) 13.4142i 1.84258i −0.388872 0.921292i \(-0.627135\pi\)
0.388872 0.921292i \(-0.372865\pi\)
\(54\) −1.00000 −0.136083
\(55\) 3.00000 + 9.00000i 0.404520 + 1.21356i
\(56\) −2.00000 −0.267261
\(57\) 2.24264i 0.297045i
\(58\) 7.65685i 1.00539i
\(59\) 8.48528 1.10469 0.552345 0.833616i \(-0.313733\pi\)
0.552345 + 0.833616i \(0.313733\pi\)
\(60\) −2.12132 + 0.707107i −0.273861 + 0.0912871i
\(61\) −3.41421 −0.437145 −0.218573 0.975821i \(-0.570140\pi\)
−0.218573 + 0.975821i \(0.570140\pi\)
\(62\) 6.00000i 0.762001i
\(63\) 2.00000i 0.251976i
\(64\) −1.00000 −0.125000
\(65\) 10.2426 3.41421i 1.27044 0.423481i
\(66\) 4.24264 0.522233
\(67\) 0.585786i 0.0715652i −0.999360 0.0357826i \(-0.988608\pi\)
0.999360 0.0357826i \(-0.0113924\pi\)
\(68\) 1.17157i 0.142074i
\(69\) 1.00000 0.120386
\(70\) 1.41421 + 4.24264i 0.169031 + 0.507093i
\(71\) 5.65685 0.671345 0.335673 0.941979i \(-0.391036\pi\)
0.335673 + 0.941979i \(0.391036\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 3.65685i 0.428002i 0.976833 + 0.214001i \(0.0686496\pi\)
−0.976833 + 0.214001i \(0.931350\pi\)
\(74\) −3.41421 −0.396894
\(75\) 3.00000 + 4.00000i 0.346410 + 0.461880i
\(76\) −2.24264 −0.257249
\(77\) 8.48528i 0.966988i
\(78\) 4.82843i 0.546712i
\(79\) −7.65685 −0.861463 −0.430732 0.902480i \(-0.641744\pi\)
−0.430732 + 0.902480i \(0.641744\pi\)
\(80\) 0.707107 + 2.12132i 0.0790569 + 0.237171i
\(81\) 1.00000 0.111111
\(82\) 1.17157i 0.129379i
\(83\) 1.41421i 0.155230i 0.996983 + 0.0776151i \(0.0247305\pi\)
−0.996983 + 0.0776151i \(0.975269\pi\)
\(84\) 2.00000 0.218218
\(85\) −2.48528 + 0.828427i −0.269567 + 0.0898555i
\(86\) 1.75736 0.189501
\(87\) 7.65685i 0.820901i
\(88\) 4.24264i 0.452267i
\(89\) −14.8284 −1.57181 −0.785905 0.618347i \(-0.787803\pi\)
−0.785905 + 0.618347i \(0.787803\pi\)
\(90\) 2.12132 0.707107i 0.223607 0.0745356i
\(91\) −9.65685 −1.01231
\(92\) 1.00000i 0.104257i
\(93\) 6.00000i 0.622171i
\(94\) −4.82843 −0.498014
\(95\) 1.58579 + 4.75736i 0.162698 + 0.488095i
\(96\) 1.00000 0.102062
\(97\) 6.00000i 0.609208i −0.952479 0.304604i \(-0.901476\pi\)
0.952479 0.304604i \(-0.0985241\pi\)
\(98\) 3.00000i 0.303046i
\(99\) −4.24264 −0.426401
\(100\) 4.00000 3.00000i 0.400000 0.300000i
\(101\) −9.31371 −0.926749 −0.463374 0.886163i \(-0.653361\pi\)
−0.463374 + 0.886163i \(0.653361\pi\)
\(102\) 1.17157i 0.116003i
\(103\) 12.1421i 1.19640i 0.801347 + 0.598200i \(0.204117\pi\)
−0.801347 + 0.598200i \(0.795883\pi\)
\(104\) −4.82843 −0.473466
\(105\) −1.41421 4.24264i −0.138013 0.414039i
\(106\) 13.4142 1.30290
\(107\) 15.0711i 1.45698i 0.685059 + 0.728488i \(0.259776\pi\)
−0.685059 + 0.728488i \(0.740224\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −15.4142 −1.47641 −0.738207 0.674574i \(-0.764327\pi\)
−0.738207 + 0.674574i \(0.764327\pi\)
\(110\) −9.00000 + 3.00000i −0.858116 + 0.286039i
\(111\) 3.41421 0.324063
\(112\) 2.00000i 0.188982i
\(113\) 16.9706i 1.59646i −0.602355 0.798228i \(-0.705771\pi\)
0.602355 0.798228i \(-0.294229\pi\)
\(114\) 2.24264 0.210043
\(115\) −2.12132 + 0.707107i −0.197814 + 0.0659380i
\(116\) −7.65685 −0.710921
\(117\) 4.82843i 0.446388i
\(118\) 8.48528i 0.781133i
\(119\) 2.34315 0.214796
\(120\) −0.707107 2.12132i −0.0645497 0.193649i
\(121\) 7.00000 0.636364
\(122\) 3.41421i 0.309108i
\(123\) 1.17157i 0.105637i
\(124\) −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 \(-0.971717\pi\)
0.996055 0.0887357i \(-0.0282826\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −1.75736 −0.154727
\(130\) 3.41421 + 10.2426i 0.299446 + 0.898339i
\(131\) −10.3431 −0.903685 −0.451842 0.892098i \(-0.649233\pi\)
−0.451842 + 0.892098i \(0.649233\pi\)
\(132\) 4.24264i 0.369274i
\(133\) 4.48528i 0.388923i
\(134\) 0.585786 0.0506042
\(135\) −2.12132 + 0.707107i −0.182574 + 0.0608581i
\(136\) 1.17157 0.100462
\(137\) 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 \(-0.755726\pi\)
−0.719712 + 0.694273i \(0.755726\pi\)
\(140\) −4.24264 + 1.41421i −0.358569 + 0.119523i
\(141\) 4.82843 0.406627
\(142\) 5.65685i 0.474713i
\(143\) 20.4853i 1.71307i
\(144\) −1.00000 −0.0833333
\(145\) 5.41421 + 16.2426i 0.449626 + 1.34888i
\(146\) −3.65685 −0.302643
\(147\) 3.00000i 0.247436i
\(148\) 3.41421i 0.280647i
\(149\) 12.7279 1.04271 0.521356 0.853339i \(-0.325426\pi\)
0.521356 + 0.853339i \(0.325426\pi\)
\(150\) −4.00000 + 3.00000i −0.326599 + 0.244949i
\(151\) −15.6569 −1.27414 −0.637068 0.770807i \(-0.719853\pi\)
−0.637068 + 0.770807i \(0.719853\pi\)
\(152\) 2.24264i 0.181902i
\(153\) 1.17157i 0.0947161i
\(154\) 8.48528 0.683763
\(155\) 4.24264 + 12.7279i 0.340777 + 1.02233i
\(156\) 4.82843 0.386584
\(157\) 6.92893i 0.552989i 0.961016 + 0.276494i \(0.0891728\pi\)
−0.961016 + 0.276494i \(0.910827\pi\)
\(158\) 7.65685i 0.609147i
\(159\) −13.4142 −1.06382
\(160\) −2.12132 + 0.707107i −0.167705 + 0.0559017i
\(161\) 2.00000 0.157622
\(162\) 1.00000i 0.0785674i
\(163\) 1.17157i 0.0917647i −0.998947 0.0458823i \(-0.985390\pi\)
0.998947 0.0458823i \(-0.0146099\pi\)
\(164\) 1.17157 0.0914845
\(165\) 9.00000 3.00000i 0.700649 0.233550i
\(166\) −1.41421 −0.109764
\(167\) 8.82843i 0.683164i −0.939852 0.341582i \(-0.889037\pi\)
0.939852 0.341582i \(-0.110963\pi\)
\(168\) 2.00000i 0.154303i
\(169\) −10.3137 −0.793362
\(170\) −0.828427 2.48528i −0.0635375 0.190612i
\(171\) −2.24264 −0.171499
\(172\) 1.75736i 0.133997i
\(173\) 3.17157i 0.241130i −0.992705 0.120565i \(-0.961529\pi\)
0.992705 0.120565i \(-0.0384707\pi\)
\(174\) 7.65685 0.580465
\(175\) 6.00000 + 8.00000i 0.453557 + 0.604743i
\(176\) 4.24264 0.319801
\(177\) 8.48528i 0.637793i
\(178\) 14.8284i 1.11144i
\(179\) 10.3431 0.773083 0.386542 0.922272i \(-0.373670\pi\)
0.386542 + 0.922272i \(0.373670\pi\)
\(180\) 0.707107 + 2.12132i 0.0527046 + 0.158114i
\(181\) 16.3848 1.21787 0.608935 0.793220i \(-0.291597\pi\)
0.608935 + 0.793220i \(0.291597\pi\)
\(182\) 9.65685i 0.715814i
\(183\) 3.41421i 0.252386i
\(184\) 1.00000 0.0737210
\(185\) −7.24264 + 2.41421i −0.532490 + 0.177497i
\(186\) 6.00000 0.439941
\(187\) 4.97056i 0.363484i
\(188\) 4.82843i 0.352149i
\(189\) 2.00000 0.145479
\(190\) −4.75736 + 1.58579i −0.345135 + 0.115045i
\(191\) −5.17157 −0.374202 −0.187101 0.982341i \(-0.559909\pi\)
−0.187101 + 0.982341i \(0.559909\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 12.9706i 0.933642i −0.884352 0.466821i \(-0.845399\pi\)
0.884352 0.466821i \(-0.154601\pi\)
\(194\) 6.00000 0.430775
\(195\) −3.41421 10.2426i −0.244497 0.733491i
\(196\) −3.00000 −0.214286
\(197\) 24.6274i 1.75463i −0.479914 0.877315i \(-0.659332\pi\)
0.479914 0.877315i \(-0.340668\pi\)
\(198\) 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
\(201\) −0.585786 −0.0413182
\(202\) 9.31371i 0.655310i
\(203\) 15.3137i 1.07481i
\(204\) −1.17157 −0.0820265
\(205\) −0.828427 2.48528i −0.0578599 0.173580i
\(206\) −12.1421 −0.845983
\(207\) 1.00000i 0.0695048i
\(208\) 4.82843i 0.334791i
\(209\) 9.51472 0.658147
\(210\) 4.24264 1.41421i 0.292770 0.0975900i
\(211\) −20.4853 −1.41026 −0.705132 0.709076i \(-0.749112\pi\)
−0.705132 + 0.709076i \(0.749112\pi\)
\(212\) 13.4142i 0.921292i
\(213\) 5.65685i 0.387601i
\(214\) −15.0711 −1.03024
\(215\) 3.72792 1.24264i 0.254242 0.0847474i
\(216\) 1.00000 0.0680414
\(217\) 12.0000i 0.814613i
\(218\) 15.4142i 1.04398i
\(219\) 3.65685 0.247107
\(220\) −3.00000 9.00000i −0.202260 0.606780i
\(221\) 5.65685 0.380521
\(222\) 3.41421i 0.229147i
\(223\) 16.0000i 1.07144i −0.844396 0.535720i \(-0.820040\pi\)
0.844396 0.535720i \(-0.179960\pi\)
\(224\) 2.00000 0.133631
\(225\) 4.00000 3.00000i 0.266667 0.200000i
\(226\) 16.9706 1.12887
\(227\) 14.3848i 0.954751i 0.878699 + 0.477376i \(0.158412\pi\)
−0.878699 + 0.477376i \(0.841588\pi\)
\(228\) 2.24264i 0.148523i
\(229\) −1.75736 −0.116130 −0.0580648 0.998313i \(-0.518493\pi\)
−0.0580648 + 0.998313i \(0.518493\pi\)
\(230\) −0.707107 2.12132i −0.0466252 0.139876i
\(231\) −8.48528 −0.558291
\(232\) 7.65685i 0.502697i
\(233\) 26.1421i 1.71263i 0.516455 + 0.856314i \(0.327251\pi\)
−0.516455 + 0.856314i \(0.672749\pi\)
\(234\) −4.82843 −0.315644
\(235\) −10.2426 + 3.41421i −0.668156 + 0.222719i
\(236\) −8.48528 −0.552345
\(237\) 7.65685i 0.497366i
\(238\) 2.34315i 0.151884i
\(239\) 11.1716 0.722629 0.361314 0.932444i \(-0.382328\pi\)
0.361314 + 0.932444i \(0.382328\pi\)
\(240\) 2.12132 0.707107i 0.136931 0.0456435i
\(241\) −10.4853 −0.675416 −0.337708 0.941251i \(-0.609652\pi\)
−0.337708 + 0.941251i \(0.609652\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 1.00000i 0.0641500i
\(244\) 3.41421 0.218573
\(245\) 2.12132 + 6.36396i 0.135526 + 0.406579i
\(246\) −1.17157 −0.0746968
\(247\) 10.8284i 0.688996i
\(248\) 6.00000i 0.381000i
\(249\) 1.41421 0.0896221
\(250\) 6.36396 9.19239i 0.402492 0.581378i
\(251\) −24.7279 −1.56081 −0.780406 0.625273i \(-0.784988\pi\)
−0.780406 + 0.625273i \(0.784988\pi\)
\(252\) 2.00000i 0.125988i
\(253\) 4.24264i 0.266733i
\(254\) 2.00000 0.125491
\(255\) 0.828427 + 2.48528i 0.0518781 + 0.155634i
\(256\) 1.00000 0.0625000
\(257\) 18.0000i 1.12281i 0.827541 + 0.561405i \(0.189739\pi\)
−0.827541 + 0.561405i \(0.810261\pi\)
\(258\) 1.75736i 0.109408i
\(259\) 6.82843 0.424298
\(260\) −10.2426 + 3.41421i −0.635222 + 0.211741i
\(261\) −7.65685 −0.473947
\(262\) 10.3431i 0.639002i
\(263\) 17.6569i 1.08877i 0.838836 + 0.544384i \(0.183237\pi\)
−0.838836 + 0.544384i \(0.816763\pi\)
\(264\) −4.24264 −0.261116
\(265\) 28.4558 9.48528i 1.74803 0.582676i
\(266\) 4.48528 0.275010
\(267\) 14.8284i 0.907485i
\(268\) 0.585786i 0.0357826i
\(269\) 24.8284 1.51382 0.756908 0.653521i \(-0.226709\pi\)
0.756908 + 0.653521i \(0.226709\pi\)
\(270\) −0.707107 2.12132i −0.0430331 0.129099i
\(271\) −1.65685 −0.100647 −0.0503234 0.998733i \(-0.516025\pi\)
−0.0503234 + 0.998733i \(0.516025\pi\)
\(272\) 1.17157i 0.0710370i
\(273\) 9.65685i 0.584459i
\(274\) −8.48528 −0.512615
\(275\) −16.9706 + 12.7279i −1.02336 + 0.767523i
\(276\) −1.00000 −0.0601929
\(277\) 30.4853i 1.83168i 0.401540 + 0.915842i \(0.368475\pi\)
−0.401540 + 0.915842i \(0.631525\pi\)
\(278\) 16.9706i 1.01783i
\(279\) −6.00000 −0.359211
\(280\) −1.41421 4.24264i −0.0845154 0.253546i
\(281\) −30.1421 −1.79813 −0.899065 0.437816i \(-0.855752\pi\)
−0.899065 + 0.437816i \(0.855752\pi\)
\(282\) 4.82843i 0.287529i
\(283\) 27.2132i 1.61766i 0.588045 + 0.808829i \(0.299898\pi\)
−0.588045 + 0.808829i \(0.700102\pi\)
\(284\) −5.65685 −0.335673
\(285\) 4.75736 1.58579i 0.281802 0.0939339i
\(286\) 20.4853 1.21132
\(287\) 2.34315i 0.138312i
\(288\) 1.00000i 0.0589256i
\(289\) 15.6274 0.919260
\(290\) −16.2426 + 5.41421i −0.953801 + 0.317934i
\(291\) −6.00000 −0.351726
\(292\) 3.65685i 0.214001i
\(293\) 28.0416i 1.63821i 0.573644 + 0.819105i \(0.305529\pi\)
−0.573644 + 0.819105i \(0.694471\pi\)
\(294\) 3.00000 0.174964
\(295\) 6.00000 + 18.0000i 0.349334 + 1.04800i
\(296\) 3.41421 0.198447
\(297\) 4.24264i 0.246183i
\(298\) 12.7279i 0.737309i
\(299\) 4.82843 0.279235
\(300\) −3.00000 4.00000i −0.173205 0.230940i
\(301\) −3.51472 −0.202585
\(302\) 15.6569i 0.900951i
\(303\) 9.31371i 0.535059i
\(304\) 2.24264 0.128624
\(305\) −2.41421 7.24264i −0.138237 0.414712i
\(306\) 1.17157 0.0669744
\(307\) 25.4558i 1.45284i −0.687250 0.726421i \(-0.741182\pi\)
0.687250 0.726421i \(-0.258818\pi\)
\(308\) 8.48528i 0.483494i
\(309\) 12.1421 0.690742
\(310\) −12.7279 + 4.24264i −0.722897 + 0.240966i
\(311\) 17.7990 1.00929 0.504644 0.863328i \(-0.331624\pi\)
0.504644 + 0.863328i \(0.331624\pi\)
\(312\) 4.82843i 0.273356i
\(313\) 18.0000i 1.01742i −0.860938 0.508710i \(-0.830123\pi\)
0.860938 0.508710i \(-0.169877\pi\)
\(314\) −6.92893 −0.391022
\(315\) −4.24264 + 1.41421i −0.239046 + 0.0796819i
\(316\) 7.65685 0.430732
\(317\) 2.48528i 0.139587i 0.997561 + 0.0697937i \(0.0222341\pi\)
−0.997561 + 0.0697937i \(0.977766\pi\)
\(318\) 13.4142i 0.752232i
\(319\) 32.4853 1.81883
\(320\) −0.707107 2.12132i −0.0395285 0.118585i
\(321\) 15.0711 0.841185
\(322\) 2.00000i 0.111456i
\(323\) 2.62742i 0.146193i
\(324\) −1.00000 −0.0555556
\(325\) 14.4853 + 19.3137i 0.803499 + 1.07133i
\(326\) 1.17157 0.0648874
\(327\) 15.4142i 0.852408i
\(328\) 1.17157i 0.0646893i
\(329\) 9.65685 0.532400
\(330\) 3.00000 + 9.00000i 0.165145 + 0.495434i
\(331\) −3.51472 −0.193186 −0.0965932 0.995324i \(-0.530795\pi\)
−0.0965932 + 0.995324i \(0.530795\pi\)
\(332\) 1.41421i 0.0776151i
\(333\) 3.41421i 0.187098i
\(334\) 8.82843 0.483070
\(335\) 1.24264 0.414214i 0.0678927 0.0226309i
\(336\) −2.00000 −0.109109
\(337\) 9.51472i 0.518300i −0.965837 0.259150i \(-0.916558\pi\)
0.965837 0.259150i \(-0.0834424\pi\)
\(338\) 10.3137i 0.560992i
\(339\) −16.9706 −0.921714
\(340\) 2.48528 0.828427i 0.134783 0.0449278i
\(341\) 25.4558 1.37851
\(342\) 2.24264i 0.121268i
\(343\) 20.0000i 1.07990i
\(344\) −1.75736 −0.0947505
\(345\) 0.707107 + 2.12132i 0.0380693 + 0.114208i
\(346\) 3.17157 0.170505
\(347\) 7.79899i 0.418672i 0.977844 + 0.209336i \(0.0671302\pi\)
−0.977844 + 0.209336i \(0.932870\pi\)
\(348\) 7.65685i 0.410450i
\(349\) −25.3137 −1.35501 −0.677506 0.735517i \(-0.736939\pi\)
−0.677506 + 0.735517i \(0.736939\pi\)
\(350\) −8.00000 + 6.00000i −0.427618 + 0.320713i
\(351\) 4.82843 0.257722
\(352\) 4.24264i 0.226134i
\(353\) 26.1421i 1.39141i 0.718330 + 0.695703i \(0.244907\pi\)
−0.718330 + 0.695703i \(0.755093\pi\)
\(354\) 8.48528 0.450988
\(355\) 4.00000 + 12.0000i 0.212298 + 0.636894i
\(356\) 14.8284 0.785905
\(357\) 2.34315i 0.124012i
\(358\) 10.3431i 0.546652i
\(359\) 19.7990 1.04495 0.522475 0.852654i \(-0.325009\pi\)
0.522475 + 0.852654i \(0.325009\pi\)
\(360\) −2.12132 + 0.707107i −0.111803 + 0.0372678i
\(361\) −13.9706 −0.735293
\(362\) 16.3848i 0.861165i
\(363\) 7.00000i 0.367405i
\(364\) 9.65685 0.506157
\(365\) −7.75736 + 2.58579i −0.406039 + 0.135346i
\(366\) −3.41421 −0.178464
\(367\) 34.9706i 1.82545i 0.408576 + 0.912724i \(0.366025\pi\)
−0.408576 + 0.912724i \(0.633975\pi\)
\(368\) 1.00000i 0.0521286i
\(369\) 1.17157 0.0609896
\(370\) −2.41421 7.24264i −0.125509 0.376527i
\(371\) −26.8284 −1.39286
\(372\) 6.00000i 0.311086i
\(373\) 19.2132i 0.994822i −0.867515 0.497411i \(-0.834284\pi\)
0.867515 0.497411i \(-0.165716\pi\)
\(374\) −4.97056 −0.257022
\(375\) −6.36396 + 9.19239i −0.328634 + 0.474693i
\(376\) 4.82843 0.249007
\(377\) 36.9706i 1.90408i
\(378\) 2.00000i 0.102869i
\(379\) 19.2132 0.986916 0.493458 0.869770i \(-0.335733\pi\)
0.493458 + 0.869770i \(0.335733\pi\)
\(380\) −1.58579 4.75736i −0.0813491 0.244047i
\(381\) −2.00000 −0.102463
\(382\) 5.17157i 0.264601i
\(383\) 18.6274i 0.951817i 0.879495 + 0.475908i \(0.157881\pi\)
−0.879495 + 0.475908i \(0.842119\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 18.0000 6.00000i 0.917365 0.305788i
\(386\) 12.9706 0.660184
\(387\) 1.75736i 0.0893316i
\(388\) 6.00000i 0.304604i
\(389\) −6.38478 −0.323721 −0.161861 0.986814i \(-0.551749\pi\)
−0.161861 + 0.986814i \(0.551749\pi\)
\(390\) 10.2426 3.41421i 0.518656 0.172885i
\(391\) −1.17157 −0.0592490
\(392\) 3.00000i 0.151523i
\(393\) 10.3431i 0.521743i
\(394\) 24.6274 1.24071
\(395\) −5.41421 16.2426i −0.272419 0.817256i
\(396\) 4.24264 0.213201
\(397\) 8.34315i 0.418730i −0.977838 0.209365i \(-0.932860\pi\)
0.977838 0.209365i \(-0.0671398\pi\)
\(398\) 14.0000i 0.701757i
\(399\) −4.48528 −0.224545
\(400\) −4.00000 + 3.00000i −0.200000 + 0.150000i
\(401\) −28.9706 −1.44672 −0.723360 0.690471i \(-0.757403\pi\)
−0.723360 + 0.690471i \(0.757403\pi\)
\(402\) 0.585786i 0.0292164i
\(403\) 28.9706i 1.44313i
\(404\) 9.31371 0.463374
\(405\) 0.707107 + 2.12132i 0.0351364 + 0.105409i
\(406\) 15.3137 0.760007
\(407\) 14.4853i 0.718009i
\(408\) 1.17157i 0.0580015i
\(409\) −18.0000 −0.890043 −0.445021 0.895520i \(-0.646804\pi\)
−0.445021 + 0.895520i \(0.646804\pi\)
\(410\) 2.48528 0.828427i 0.122739 0.0409131i
\(411\) 8.48528 0.418548
\(412\) 12.1421i 0.598200i
\(413\) 16.9706i 0.835067i
\(414\) 1.00000 0.0491473
\(415\) −3.00000 + 1.00000i −0.147264 + 0.0490881i
\(416\) 4.82843 0.236733
\(417\) 16.9706i 0.831052i
\(418\) 9.51472i 0.465380i
\(419\) 24.9289 1.21786 0.608929 0.793225i \(-0.291599\pi\)
0.608929 + 0.793225i \(0.291599\pi\)
\(420\) 1.41421 + 4.24264i 0.0690066 + 0.207020i
\(421\) 10.2426 0.499196 0.249598 0.968350i \(-0.419702\pi\)
0.249598 + 0.968350i \(0.419702\pi\)
\(422\) 20.4853i 0.997208i
\(423\) 4.82843i 0.234766i
\(424\) −13.4142 −0.651452
\(425\) −3.51472 4.68629i −0.170489 0.227319i
\(426\) 5.65685 0.274075
\(427\) 6.82843i 0.330451i
\(428\) 15.0711i 0.728488i
\(429\) −20.4853 −0.989039
\(430\) 1.24264 + 3.72792i 0.0599255 + 0.179776i
\(431\) 8.48528 0.408722 0.204361 0.978896i \(-0.434488\pi\)
0.204361 + 0.978896i \(0.434488\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 26.9706i 1.29612i −0.761588 0.648061i \(-0.775580\pi\)
0.761588 0.648061i \(-0.224420\pi\)
\(434\) 12.0000 0.576018
\(435\) 16.2426 5.41421i 0.778775 0.259592i
\(436\) 15.4142 0.738207
\(437\) 2.24264i 0.107280i
\(438\) 3.65685i 0.174731i
\(439\) 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
\(443\) 23.3137i 1.10767i 0.832627 + 0.553834i \(0.186836\pi\)
−0.832627 + 0.553834i \(0.813164\pi\)
\(444\) −3.41421 −0.162031
\(445\) −10.4853 31.4558i −0.497050 1.49115i
\(446\) 16.0000 0.757622
\(447\) 12.7279i 0.602010i
\(448\) 2.00000i 0.0944911i
\(449\) 22.8284 1.07734 0.538670 0.842517i \(-0.318927\pi\)
0.538670 + 0.842517i \(0.318927\pi\)
\(450\) 3.00000 + 4.00000i 0.141421 + 0.188562i
\(451\) −4.97056 −0.234055
\(452\) 16.9706i 0.798228i
\(453\) 15.6569i 0.735623i
\(454\) −14.3848 −0.675111
\(455\) −6.82843 20.4853i −0.320122 0.960365i
\(456\) −2.24264 −0.105021
\(457\) 1.02944i 0.0481550i 0.999710 + 0.0240775i \(0.00766485\pi\)
−0.999710 + 0.0240775i \(0.992335\pi\)
\(458\) 1.75736i 0.0821160i
\(459\) −1.17157 −0.0546843
\(460\) 2.12132 0.707107i 0.0989071 0.0329690i
\(461\) −12.8284 −0.597479 −0.298740 0.954335i \(-0.596566\pi\)
−0.298740 + 0.954335i \(0.596566\pi\)
\(462\) 8.48528i 0.394771i
\(463\) 2.97056i 0.138054i −0.997615 0.0690269i \(-0.978011\pi\)
0.997615 0.0690269i \(-0.0219894\pi\)
\(464\) 7.65685 0.355461
\(465\) 12.7279 4.24264i 0.590243 0.196748i
\(466\) −26.1421 −1.21101
\(467\) 39.3553i 1.82115i 0.413346 + 0.910574i \(0.364360\pi\)
−0.413346 + 0.910574i \(0.635640\pi\)
\(468\) 4.82843i 0.223194i
\(469\) −1.17157 −0.0540982
\(470\) −3.41421 10.2426i −0.157486 0.472458i
\(471\) 6.92893 0.319268
\(472\) 8.48528i 0.390567i
\(473\) 7.45584i 0.342820i
\(474\) −7.65685 −0.351691
\(475\) −8.97056 + 6.72792i −0.411598 + 0.308698i
\(476\) −2.34315 −0.107398
\(477\) 13.4142i 0.614195i
\(478\) 11.1716i 0.510976i
\(479\) −4.68629 −0.214122 −0.107061 0.994252i \(-0.534144\pi\)
−0.107061 + 0.994252i \(0.534144\pi\)
\(480\) 0.707107 + 2.12132i 0.0322749 + 0.0968246i
\(481\) 16.4853 0.751664
\(482\) 10.4853i 0.477591i
\(483\) 2.00000i 0.0910032i
\(484\) −7.00000 −0.318182
\(485\) 12.7279 4.24264i 0.577945 0.192648i
\(486\) 1.00000 0.0453609
\(487\) 27.9411i 1.26613i −0.774097 0.633067i \(-0.781796\pi\)
0.774097 0.633067i \(-0.218204\pi\)
\(488\) 3.41421i 0.154554i
\(489\) −1.17157 −0.0529804
\(490\) −6.36396 + 2.12132i −0.287494 + 0.0958315i
\(491\) 26.6274 1.20168 0.600839 0.799370i \(-0.294833\pi\)
0.600839 + 0.799370i \(0.294833\pi\)
\(492\) 1.17157i 0.0528186i
\(493\) 8.97056i 0.404014i
\(494\) 10.8284 0.487194
\(495\) −3.00000 9.00000i −0.134840 0.404520i
\(496\) 6.00000 0.269408
\(497\) 11.3137i 0.507489i
\(498\) 1.41421i 0.0633724i
\(499\) −13.4558 −0.602366 −0.301183 0.953566i \(-0.597382\pi\)
−0.301183 + 0.953566i \(0.597382\pi\)
\(500\) 9.19239 + 6.36396i 0.411096 + 0.284605i
\(501\) −8.82843 −0.394425
\(502\) 24.7279i 1.10366i
\(503\) 22.1421i 0.987269i −0.869669 0.493635i \(-0.835668\pi\)
0.869669 0.493635i \(-0.164332\pi\)
\(504\) 2.00000 0.0890871
\(505\) −6.58579 19.7574i −0.293064 0.879191i
\(506\) −4.24264 −0.188608
\(507\) 10.3137i 0.458048i
\(508\) 2.00000i 0.0887357i
\(509\) −22.9706 −1.01815 −0.509076 0.860721i \(-0.670013\pi\)
−0.509076 + 0.860721i \(0.670013\pi\)
\(510\) −2.48528 + 0.828427i −0.110050 + 0.0366834i
\(511\) 7.31371 0.323539
\(512\) 1.00000i 0.0441942i
\(513\) 2.24264i 0.0990150i
\(514\) −18.0000 −0.793946
\(515\) −25.7574 + 8.58579i −1.13500 + 0.378335i
\(516\) 1.75736 0.0773634
\(517\) 20.4853i 0.900942i
\(518\) 6.82843i 0.300024i
\(519\) −3.17157 −0.139217
\(520\) −3.41421 10.2426i −0.149723 0.449170i
\(521\) −16.2843 −0.713427 −0.356713 0.934214i \(-0.616103\pi\)
−0.356713 + 0.934214i \(0.616103\pi\)
\(522\) 7.65685i 0.335131i
\(523\) 2.92893i 0.128073i 0.997948 + 0.0640366i \(0.0203974\pi\)
−0.997948 + 0.0640366i \(0.979603\pi\)
\(524\) 10.3431 0.451842
\(525\) 8.00000 6.00000i 0.349149 0.261861i
\(526\) −17.6569 −0.769875
\(527\) 7.02944i 0.306207i
\(528\) 4.24264i 0.184637i
\(529\) −1.00000 −0.0434783
\(530\) 9.48528 + 28.4558i 0.412014 + 1.23604i
\(531\) −8.48528 −0.368230
\(532\) 4.48528i 0.194462i
\(533\) 5.65685i 0.245026i
\(534\) −14.8284 −0.641689
\(535\) −31.9706 + 10.6569i −1.38221 + 0.460736i
\(536\) −0.585786 −0.0253021
\(537\) 10.3431i 0.446340i
\(538\) 24.8284i 1.07043i
\(539\) 12.7279 0.548230
\(540\) 2.12132 0.707107i 0.0912871 0.0304290i
\(541\) 35.9411 1.54523 0.772615 0.634875i \(-0.218948\pi\)
0.772615 + 0.634875i \(0.218948\pi\)
\(542\) 1.65685i 0.0711680i
\(543\) 16.3848i 0.703138i
\(544\) −1.17157 −0.0502308
\(545\) −10.8995 32.6985i −0.466883 1.40065i
\(546\) −9.65685 −0.413275
\(547\) 4.48528i 0.191777i −0.995392 0.0958884i \(-0.969431\pi\)
0.995392 0.0958884i \(-0.0305692\pi\)
\(548\) 8.48528i 0.362473i
\(549\) 3.41421 0.145715
\(550\) −12.7279 16.9706i −0.542720 0.723627i
\(551\) 17.1716 0.731534
\(552\) 1.00000i 0.0425628i
\(553\) 15.3137i 0.651205i
\(554\) −30.4853 −1.29520
\(555\) 2.41421 + 7.24264i 0.102478 + 0.307433i
\(556\) 16.9706 0.719712
\(557\) 14.8701i 0.630065i −0.949081 0.315032i \(-0.897985\pi\)
0.949081 0.315032i \(-0.102015\pi\)
\(558\) 6.00000i 0.254000i
\(559\) −8.48528 −0.358889
\(560\) 4.24264 1.41421i 0.179284 0.0597614i
\(561\) 4.97056 0.209857
\(562\) 30.1421i 1.27147i
\(563\) 21.8995i 0.922954i 0.887152 + 0.461477i \(0.152680\pi\)
−0.887152 + 0.461477i \(0.847320\pi\)
\(564\) −4.82843 −0.203313
\(565\) 36.0000 12.0000i 1.51453 0.504844i
\(566\) −27.2132 −1.14386
\(567\) 2.00000i 0.0839921i
\(568\) 5.65685i 0.237356i
\(569\) −25.6569 −1.07559 −0.537796 0.843075i \(-0.680743\pi\)
−0.537796 + 0.843075i \(0.680743\pi\)
\(570\) 1.58579 + 4.75736i 0.0664213 + 0.199264i
\(571\) −42.7279 −1.78811 −0.894054 0.447959i \(-0.852151\pi\)
−0.894054 + 0.447959i \(0.852151\pi\)
\(572\) 20.4853i 0.856533i
\(573\) 5.17157i 0.216046i
\(574\) −2.34315 −0.0978010
\(575\) −3.00000 4.00000i −0.125109 0.166812i
\(576\) 1.00000 0.0416667
\(577\) 20.6274i 0.858731i −0.903131 0.429365i \(-0.858737\pi\)
0.903131 0.429365i \(-0.141263\pi\)
\(578\) 15.6274i 0.650015i
\(579\) −12.9706 −0.539038
\(580\) −5.41421 16.2426i −0.224813 0.674439i
\(581\) 2.82843 0.117343
\(582\) 6.00000i 0.248708i
\(583\) 56.9117i 2.35704i
\(584\) 3.65685 0.151322
\(585\) −10.2426 + 3.41421i −0.423481 + 0.141160i
\(586\) −28.0416 −1.15839
\(587\) 26.8284i 1.10733i 0.832740 + 0.553664i \(0.186771\pi\)
−0.832740 + 0.553664i \(0.813229\pi\)
\(588\) 3.00000i 0.123718i
\(589\) 13.4558 0.554438
\(590\) −18.0000 + 6.00000i −0.741048 + 0.247016i
\(591\) −24.6274 −1.01304
\(592\) 3.41421i 0.140323i
\(593\) 12.3431i 0.506872i 0.967352 + 0.253436i \(0.0815608\pi\)
−0.967352 + 0.253436i \(0.918439\pi\)
\(594\) −4.24264 −0.174078
\(595\) 1.65685 + 4.97056i 0.0679244 + 0.203773i
\(596\) −12.7279 −0.521356
\(597\) 14.0000i 0.572982i
\(598\) 4.82843i 0.197449i
\(599\) 40.1421 1.64016 0.820082 0.572247i \(-0.193928\pi\)
0.820082 + 0.572247i \(0.193928\pi\)
\(600\) 4.00000 3.00000i 0.163299 0.122474i
\(601\) −20.9706 −0.855407 −0.427704 0.903919i \(-0.640677\pi\)
−0.427704 + 0.903919i \(0.640677\pi\)
\(602\) 3.51472i 0.143249i
\(603\) 0.585786i 0.0238551i
\(604\) 15.6569 0.637068
\(605\) 4.94975 + 14.8492i 0.201236 + 0.603708i
\(606\) −9.31371 −0.378344
\(607\) 16.9706i 0.688814i −0.938820 0.344407i \(-0.888080\pi\)
0.938820 0.344407i \(-0.111920\pi\)
\(608\) 2.24264i 0.0909511i
\(609\) −15.3137 −0.620543
\(610\) 7.24264 2.41421i 0.293246 0.0977486i
\(611\) 23.3137 0.943172
\(612\) 1.17157i 0.0473580i
\(613\) 14.2426i 0.575255i 0.957742 + 0.287627i \(0.0928665\pi\)
−0.957742 + 0.287627i \(0.907134\pi\)
\(614\) 25.4558 1.02731
\(615\) −2.48528 + 0.828427i −0.100216 + 0.0334054i
\(616\) −8.48528 −0.341882
\(617\) 31.3137i 1.26064i −0.776334 0.630321i \(-0.782923\pi\)
0.776334 0.630321i \(-0.217077\pi\)
\(618\) 12.1421i 0.488428i
\(619\) 19.2132 0.772244 0.386122 0.922448i \(-0.373814\pi\)
0.386122 + 0.922448i \(0.373814\pi\)
\(620\) −4.24264 12.7279i −0.170389 0.511166i
\(621\) −1.00000 −0.0401286
\(622\) 17.7990i 0.713674i
\(623\) 29.6569i 1.18818i
\(624\) −4.82843 −0.193292
\(625\) 7.00000 24.0000i 0.280000 0.960000i
\(626\) 18.0000 0.719425
\(627\) 9.51472i 0.379981i
\(628\) 6.92893i 0.276494i
\(629\) −4.00000 −0.159490
\(630\) −1.41421 4.24264i −0.0563436 0.169031i
\(631\) 35.1716 1.40016 0.700079 0.714065i \(-0.253148\pi\)
0.700079 + 0.714065i \(0.253148\pi\)
\(632\) 7.65685i 0.304573i
\(633\) 20.4853i 0.814217i
\(634\) −2.48528 −0.0987031
\(635\) 4.24264 1.41421i 0.168364 0.0561214i
\(636\) 13.4142 0.531908
\(637\) 14.4853i 0.573928i
\(638\) 32.4853i 1.28610i
\(639\) −5.65685 −0.223782
\(640\) 2.12132 0.707107i 0.0838525 0.0279508i
\(641\) −8.28427 −0.327209 −0.163605 0.986526i \(-0.552312\pi\)
−0.163605 + 0.986526i \(0.552312\pi\)
\(642\) 15.0711i 0.594808i
\(643\) 32.3848i 1.27713i 0.769568 + 0.638565i \(0.220472\pi\)
−0.769568 + 0.638565i \(0.779528\pi\)
\(644\) −2.00000 −0.0788110
\(645\) −1.24264 3.72792i −0.0489289 0.146787i
\(646\) −2.62742 −0.103374
\(647\) 29.6569i 1.16593i −0.812497 0.582966i \(-0.801892\pi\)
0.812497 0.582966i \(-0.198108\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 36.0000 1.41312
\(650\) −19.3137 + 14.4853i −0.757546 + 0.568159i
\(651\) −12.0000 −0.470317
\(652\) 1.17157i 0.0458823i
\(653\) 43.4558i 1.70056i −0.526332 0.850279i \(-0.676433\pi\)
0.526332 0.850279i \(-0.323567\pi\)
\(654\) −15.4142 −0.602743
\(655\) −7.31371 21.9411i −0.285770 0.857311i
\(656\) −1.17157 −0.0457422
\(657\) 3.65685i 0.142667i
\(658\) 9.65685i 0.376463i
\(659\) 26.1005 1.01673 0.508366 0.861141i \(-0.330250\pi\)
0.508366 + 0.861141i \(0.330250\pi\)
\(660\) −9.00000 + 3.00000i −0.350325 + 0.116775i
\(661\) 9.27208 0.360642 0.180321 0.983608i \(-0.442286\pi\)
0.180321 + 0.983608i \(0.442286\pi\)
\(662\) 3.51472i 0.136603i
\(663\) 5.65685i 0.219694i
\(664\) 1.41421 0.0548821
\(665\) 9.51472 3.17157i 0.368965 0.122988i
\(666\) 3.41421 0.132298
\(667\) 7.65685i 0.296475i
\(668\) 8.82843i 0.341582i
\(669\) −16.0000 −0.618596
\(670\) 0.414214 + 1.24264i 0.0160025 + 0.0480074i
\(671\) −14.4853 −0.559198
\(672\) 2.00000i 0.0771517i
\(673\) 39.9411i 1.53962i 0.638275 + 0.769809i \(0.279648\pi\)
−0.638275 + 0.769809i \(0.720352\pi\)
\(674\) 9.51472 0.366493
\(675\) −3.00000 4.00000i −0.115470 0.153960i
\(676\) 10.3137 0.396681
\(677\) 24.5269i 0.942646i 0.881961 + 0.471323i \(0.156223\pi\)
−0.881961 + 0.471323i \(0.843777\pi\)
\(678\) 16.9706i 0.651751i
\(679\) −12.0000 −0.460518
\(680\) 0.828427 + 2.48528i 0.0317687 + 0.0953062i
\(681\) 14.3848 0.551226
\(682\) 25.4558i 0.974755i
\(683\) 8.48528i 0.324680i −0.986735 0.162340i \(-0.948096\pi\)
0.986735 0.162340i \(-0.0519042\pi\)
\(684\) 2.24264 0.0857495
\(685\) −18.0000 + 6.00000i −0.687745 + 0.229248i
\(686\) 20.0000 0.763604
\(687\) 1.75736i 0.0670474i
\(688\) 1.75736i 0.0669987i
\(689\) −64.7696 −2.46752
\(690\) −2.12132 + 0.707107i −0.0807573 + 0.0269191i
\(691\) −18.8284 −0.716267 −0.358134 0.933670i \(-0.616587\pi\)
−0.358134 + 0.933670i \(0.616587\pi\)
\(692\) 3.17157i 0.120565i
\(693\) 8.48528i 0.322329i
\(694\) −7.79899 −0.296046
\(695\) −12.0000 36.0000i −0.455186 1.36556i
\(696\) −7.65685 −0.290232
\(697\) 1.37258i 0.0519903i
\(698\) 25.3137i 0.958138i
\(699\) 26.1421 0.988786
\(700\) −6.00000 8.00000i −0.226779 0.302372i
\(701\) 38.1838 1.44218 0.721090 0.692841i \(-0.243641\pi\)
0.721090 + 0.692841i \(0.243641\pi\)
\(702\) 4.82843i 0.182237i
\(703\) 7.65685i 0.288784i
\(704\) −4.24264 −0.159901
\(705\) 3.41421 + 10.2426i 0.128587 + 0.385760i
\(706\) −26.1421 −0.983872
\(707\) 18.6274i 0.700556i
\(708\) 8.48528i 0.318896i
\(709\) −35.4142 −1.33001 −0.665004 0.746839i \(-0.731570\pi\)
−0.665004 + 0.746839i \(0.731570\pi\)
\(710\) −12.0000 + 4.00000i −0.450352 + 0.150117i
\(711\) 7.65685 0.287154
\(712\) 14.8284i 0.555719i
\(713\) 6.00000i 0.224702i
\(714\) 2.34315 0.0876900
\(715\) 43.4558 14.4853i 1.62516 0.541719i
\(716\) −10.3431 −0.386542
\(717\) 11.1716i 0.417210i
\(718\) 19.7990i 0.738892i
\(719\) −28.1421 −1.04952 −0.524762 0.851249i \(-0.675846\pi\)
−0.524762 + 0.851249i \(0.675846\pi\)
\(720\) −0.707107 2.12132i −0.0263523 0.0790569i
\(721\) 24.2843 0.904394
\(722\) 13.9706i 0.519931i
\(723\) 10.4853i 0.389952i
\(724\) −16.3848 −0.608935
\(725\) −30.6274 + 22.9706i −1.13747 + 0.853105i
\(726\) 7.00000 0.259794
\(727\) 31.6569i 1.17409i −0.809555 0.587044i \(-0.800292\pi\)
0.809555 0.587044i \(-0.199708\pi\)
\(728\) 9.65685i 0.357907i
\(729\) −1.00000 −0.0370370
\(730\) −2.58579 7.75736i −0.0957042 0.287113i
\(731\) 2.05887 0.0761502
\(732\) 3.41421i 0.126193i
\(733\) 8.58579i 0.317123i −0.987349 0.158562i \(-0.949314\pi\)
0.987349 0.158562i \(-0.0506857\pi\)
\(734\) −34.9706 −1.29079
\(735\) 6.36396 2.12132i 0.234738 0.0782461i
\(736\) −1.00000 −0.0368605
\(737\) 2.48528i 0.0915465i
\(738\) 1.17157i 0.0431262i
\(739\) −42.6274 −1.56807 −0.784037 0.620714i \(-0.786843\pi\)
−0.784037 + 0.620714i \(0.786843\pi\)
\(740\) 7.24264 2.41421i 0.266245 0.0887483i
\(741\) −10.8284 −0.397792
\(742\) 26.8284i 0.984903i
\(743\) 2.34315i 0.0859617i −0.999076 0.0429808i \(-0.986315\pi\)
0.999076 0.0429808i \(-0.0136854\pi\)
\(744\) −6.00000 −0.219971
\(745\) 9.00000 + 27.0000i 0.329734 + 0.989203i
\(746\) 19.2132 0.703445
\(747\) 1.41421i 0.0517434i
\(748\) 4.97056i 0.181742i
\(749\) 30.1421 1.10137
\(750\) −9.19239 6.36396i −0.335659 0.232379i
\(751\) −48.8284 −1.78177 −0.890887 0.454224i \(-0.849916\pi\)
−0.890887 + 0.454224i \(0.849916\pi\)
\(752\) 4.82843i 0.176075i
\(753\) 24.7279i 0.901136i
\(754\) 36.9706 1.34639
\(755\) −11.0711 33.2132i −0.402917 1.20875i
\(756\) −2.00000 −0.0727393
\(757\) 42.2426i 1.53533i 0.640848 + 0.767667i \(0.278583\pi\)
−0.640848 + 0.767667i \(0.721417\pi\)
\(758\) 19.2132i 0.697855i
\(759\) 4.24264 0.153998
\(760\) 4.75736 1.58579i 0.172568 0.0575225i
\(761\) −24.3431 −0.882438 −0.441219 0.897399i \(-0.645454\pi\)
−0.441219 + 0.897399i \(0.645454\pi\)
\(762\) 2.00000i 0.0724524i
\(763\) 30.8284i 1.11606i
\(764\) 5.17157 0.187101
\(765\) 2.48528 0.828427i 0.0898555 0.0299518i
\(766\) −18.6274 −0.673036
\(767\) 40.9706i 1.47936i
\(768\) 1.00000i 0.0360844i
\(769\) −45.7990 −1.65155 −0.825777 0.563997i \(-0.809263\pi\)
−0.825777 + 0.563997i \(0.809263\pi\)
\(770\) 6.00000 + 18.0000i 0.216225 + 0.648675i
\(771\) 18.0000 0.648254
\(772\) 12.9706i 0.466821i
\(773\) 16.9289i 0.608891i 0.952530 + 0.304446i \(0.0984712\pi\)
−0.952530 + 0.304446i \(0.901529\pi\)
\(774\) −1.75736 −0.0631670
\(775\) −24.0000 + 18.0000i −0.862105 + 0.646579i
\(776\) −6.00000 −0.215387
\(777\) 6.82843i 0.244968i
\(778\) 6.38478i 0.228905i
\(779\) −2.62742 −0.0941370
\(780\) 3.41421 + 10.2426i 0.122248 + 0.366745i
\(781\) 24.0000 0.858788
\(782\) 1.17157i 0.0418954i
\(783\) 7.65685i 0.273634i
\(784\) 3.00000 0.107143
\(785\) −14.6985 + 4.89949i −0.524611 + 0.174870i
\(786\) −10.3431 −0.368928
\(787\) 2.72792i 0.0972399i 0.998817 + 0.0486200i \(0.0154823\pi\)
−0.998817 + 0.0486200i \(0.984518\pi\)
\(788\) 24.6274i 0.877315i