Properties

Label 1110.2.d.g.889.4
Level $1110$
Weight $2$
Character 1110.889
Analytic conductor $8.863$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 889.4
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1110.889
Dual form 1110.2.d.g.889.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(0.707107 - 2.12132i) q^{5} +1.00000 q^{6} +2.41421i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(0.707107 - 2.12132i) q^{5} +1.00000 q^{6} +2.41421i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(2.12132 + 0.707107i) q^{10} -6.41421 q^{11} +1.00000i q^{12} +5.24264i q^{13} -2.41421 q^{14} +(-2.12132 - 0.707107i) q^{15} +1.00000 q^{16} -3.58579i q^{17} -1.00000i q^{18} +2.17157 q^{19} +(-0.707107 + 2.12132i) q^{20} +2.41421 q^{21} -6.41421i q^{22} +3.00000i q^{23} -1.00000 q^{24} +(-4.00000 - 3.00000i) q^{25} -5.24264 q^{26} +1.00000i q^{27} -2.41421i q^{28} -7.07107 q^{29} +(0.707107 - 2.12132i) q^{30} -3.65685 q^{31} +1.00000i q^{32} +6.41421i q^{33} +3.58579 q^{34} +(5.12132 + 1.70711i) q^{35} +1.00000 q^{36} +1.00000i q^{37} +2.17157i q^{38} +5.24264 q^{39} +(-2.12132 - 0.707107i) q^{40} -6.58579 q^{41} +2.41421i q^{42} +10.4853i q^{43} +6.41421 q^{44} +(-0.707107 + 2.12132i) q^{45} -3.00000 q^{46} +11.8995i q^{47} -1.00000i q^{48} +1.17157 q^{49} +(3.00000 - 4.00000i) q^{50} -3.58579 q^{51} -5.24264i q^{52} -3.82843i q^{53} -1.00000 q^{54} +(-4.53553 + 13.6066i) q^{55} +2.41421 q^{56} -2.17157i q^{57} -7.07107i q^{58} +13.0711 q^{59} +(2.12132 + 0.707107i) q^{60} -6.48528 q^{61} -3.65685i q^{62} -2.41421i q^{63} -1.00000 q^{64} +(11.1213 + 3.70711i) q^{65} -6.41421 q^{66} +0.828427i q^{67} +3.58579i q^{68} +3.00000 q^{69} +(-1.70711 + 5.12132i) q^{70} -9.41421 q^{71} +1.00000i q^{72} +2.17157i q^{73} -1.00000 q^{74} +(-3.00000 + 4.00000i) q^{75} -2.17157 q^{76} -15.4853i q^{77} +5.24264i q^{78} -12.2426 q^{79} +(0.707107 - 2.12132i) q^{80} +1.00000 q^{81} -6.58579i q^{82} +6.89949i q^{83} -2.41421 q^{84} +(-7.60660 - 2.53553i) q^{85} -10.4853 q^{86} +7.07107i q^{87} +6.41421i q^{88} -2.89949 q^{89} +(-2.12132 - 0.707107i) q^{90} -12.6569 q^{91} -3.00000i q^{92} +3.65685i q^{93} -11.8995 q^{94} +(1.53553 - 4.60660i) q^{95} +1.00000 q^{96} +6.72792i q^{97} +1.17157i q^{98} +6.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{4} + 4q^{6} - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{4} + 4q^{6} - 4q^{9} - 20q^{11} - 4q^{14} + 4q^{16} + 20q^{19} + 4q^{21} - 4q^{24} - 16q^{25} - 4q^{26} + 8q^{31} + 20q^{34} + 12q^{35} + 4q^{36} + 4q^{39} - 32q^{41} + 20q^{44} - 12q^{46} + 16q^{49} + 12q^{50} - 20q^{51} - 4q^{54} - 4q^{55} + 4q^{56} + 24q^{59} + 8q^{61} - 4q^{64} + 36q^{65} - 20q^{66} + 12q^{69} - 4q^{70} - 32q^{71} - 4q^{74} - 12q^{75} - 20q^{76} - 32q^{79} + 4q^{81} - 4q^{84} + 12q^{85} - 8q^{86} + 28q^{89} - 28q^{91} - 8q^{94} - 8q^{95} + 4q^{96} + 20q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 0.707107 2.12132i 0.316228 0.948683i
\(6\) 1.00000 0.408248
\(7\) 2.41421i 0.912487i 0.889855 + 0.456243i \(0.150805\pi\)
−0.889855 + 0.456243i \(0.849195\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 2.12132 + 0.707107i 0.670820 + 0.223607i
\(11\) −6.41421 −1.93396 −0.966979 0.254856i \(-0.917972\pi\)
−0.966979 + 0.254856i \(0.917972\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 5.24264i 1.45405i 0.686613 + 0.727023i \(0.259097\pi\)
−0.686613 + 0.727023i \(0.740903\pi\)
\(14\) −2.41421 −0.645226
\(15\) −2.12132 0.707107i −0.547723 0.182574i
\(16\) 1.00000 0.250000
\(17\) 3.58579i 0.869681i −0.900508 0.434840i \(-0.856805\pi\)
0.900508 0.434840i \(-0.143195\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 2.17157 0.498193 0.249096 0.968479i \(-0.419866\pi\)
0.249096 + 0.968479i \(0.419866\pi\)
\(20\) −0.707107 + 2.12132i −0.158114 + 0.474342i
\(21\) 2.41421 0.526825
\(22\) 6.41421i 1.36751i
\(23\) 3.00000i 0.625543i 0.949828 + 0.312772i \(0.101257\pi\)
−0.949828 + 0.312772i \(0.898743\pi\)
\(24\) −1.00000 −0.204124
\(25\) −4.00000 3.00000i −0.800000 0.600000i
\(26\) −5.24264 −1.02817
\(27\) 1.00000i 0.192450i
\(28\) 2.41421i 0.456243i
\(29\) −7.07107 −1.31306 −0.656532 0.754298i \(-0.727977\pi\)
−0.656532 + 0.754298i \(0.727977\pi\)
\(30\) 0.707107 2.12132i 0.129099 0.387298i
\(31\) −3.65685 −0.656790 −0.328395 0.944540i \(-0.606508\pi\)
−0.328395 + 0.944540i \(0.606508\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 6.41421i 1.11657i
\(34\) 3.58579 0.614957
\(35\) 5.12132 + 1.70711i 0.865661 + 0.288554i
\(36\) 1.00000 0.166667
\(37\) 1.00000i 0.164399i
\(38\) 2.17157i 0.352276i
\(39\) 5.24264 0.839494
\(40\) −2.12132 0.707107i −0.335410 0.111803i
\(41\) −6.58579 −1.02853 −0.514264 0.857632i \(-0.671935\pi\)
−0.514264 + 0.857632i \(0.671935\pi\)
\(42\) 2.41421i 0.372521i
\(43\) 10.4853i 1.59899i 0.600672 + 0.799495i \(0.294900\pi\)
−0.600672 + 0.799495i \(0.705100\pi\)
\(44\) 6.41421 0.966979
\(45\) −0.707107 + 2.12132i −0.105409 + 0.316228i
\(46\) −3.00000 −0.442326
\(47\) 11.8995i 1.73572i 0.496809 + 0.867860i \(0.334505\pi\)
−0.496809 + 0.867860i \(0.665495\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 1.17157 0.167368
\(50\) 3.00000 4.00000i 0.424264 0.565685i
\(51\) −3.58579 −0.502111
\(52\) 5.24264i 0.727023i
\(53\) 3.82843i 0.525875i −0.964813 0.262937i \(-0.915309\pi\)
0.964813 0.262937i \(-0.0846913\pi\)
\(54\) −1.00000 −0.136083
\(55\) −4.53553 + 13.6066i −0.611571 + 1.83471i
\(56\) 2.41421 0.322613
\(57\) 2.17157i 0.287632i
\(58\) 7.07107i 0.928477i
\(59\) 13.0711 1.70171 0.850854 0.525402i \(-0.176085\pi\)
0.850854 + 0.525402i \(0.176085\pi\)
\(60\) 2.12132 + 0.707107i 0.273861 + 0.0912871i
\(61\) −6.48528 −0.830355 −0.415178 0.909740i \(-0.636281\pi\)
−0.415178 + 0.909740i \(0.636281\pi\)
\(62\) 3.65685i 0.464421i
\(63\) 2.41421i 0.304162i
\(64\) −1.00000 −0.125000
\(65\) 11.1213 + 3.70711i 1.37943 + 0.459810i
\(66\) −6.41421 −0.789535
\(67\) 0.828427i 0.101208i 0.998719 + 0.0506042i \(0.0161147\pi\)
−0.998719 + 0.0506042i \(0.983885\pi\)
\(68\) 3.58579i 0.434840i
\(69\) 3.00000 0.361158
\(70\) −1.70711 + 5.12132i −0.204038 + 0.612115i
\(71\) −9.41421 −1.11726 −0.558631 0.829416i \(-0.688673\pi\)
−0.558631 + 0.829416i \(0.688673\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 2.17157i 0.254163i 0.991892 + 0.127082i \(0.0405610\pi\)
−0.991892 + 0.127082i \(0.959439\pi\)
\(74\) −1.00000 −0.116248
\(75\) −3.00000 + 4.00000i −0.346410 + 0.461880i
\(76\) −2.17157 −0.249096
\(77\) 15.4853i 1.76471i
\(78\) 5.24264i 0.593612i
\(79\) −12.2426 −1.37740 −0.688702 0.725044i \(-0.741819\pi\)
−0.688702 + 0.725044i \(0.741819\pi\)
\(80\) 0.707107 2.12132i 0.0790569 0.237171i
\(81\) 1.00000 0.111111
\(82\) 6.58579i 0.727278i
\(83\) 6.89949i 0.757318i 0.925536 + 0.378659i \(0.123615\pi\)
−0.925536 + 0.378659i \(0.876385\pi\)
\(84\) −2.41421 −0.263412
\(85\) −7.60660 2.53553i −0.825052 0.275017i
\(86\) −10.4853 −1.13066
\(87\) 7.07107i 0.758098i
\(88\) 6.41421i 0.683757i
\(89\) −2.89949 −0.307346 −0.153673 0.988122i \(-0.549110\pi\)
−0.153673 + 0.988122i \(0.549110\pi\)
\(90\) −2.12132 0.707107i −0.223607 0.0745356i
\(91\) −12.6569 −1.32680
\(92\) 3.00000i 0.312772i
\(93\) 3.65685i 0.379198i
\(94\) −11.8995 −1.22734
\(95\) 1.53553 4.60660i 0.157542 0.472627i
\(96\) 1.00000 0.102062
\(97\) 6.72792i 0.683117i 0.939861 + 0.341558i \(0.110955\pi\)
−0.939861 + 0.341558i \(0.889045\pi\)
\(98\) 1.17157i 0.118347i
\(99\) 6.41421 0.644653
\(100\) 4.00000 + 3.00000i 0.400000 + 0.300000i
\(101\) −5.31371 −0.528734 −0.264367 0.964422i \(-0.585163\pi\)
−0.264367 + 0.964422i \(0.585163\pi\)
\(102\) 3.58579i 0.355046i
\(103\) 15.0711i 1.48500i −0.669848 0.742498i \(-0.733641\pi\)
0.669848 0.742498i \(-0.266359\pi\)
\(104\) 5.24264 0.514083
\(105\) 1.70711 5.12132i 0.166597 0.499790i
\(106\) 3.82843 0.371850
\(107\) 16.0711i 1.55365i −0.629717 0.776824i \(-0.716829\pi\)
0.629717 0.776824i \(-0.283171\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −4.75736 −0.455672 −0.227836 0.973699i \(-0.573165\pi\)
−0.227836 + 0.973699i \(0.573165\pi\)
\(110\) −13.6066 4.53553i −1.29734 0.432446i
\(111\) 1.00000 0.0949158
\(112\) 2.41421i 0.228122i
\(113\) 2.82843i 0.266076i −0.991111 0.133038i \(-0.957527\pi\)
0.991111 0.133038i \(-0.0424732\pi\)
\(114\) 2.17157 0.203386
\(115\) 6.36396 + 2.12132i 0.593442 + 0.197814i
\(116\) 7.07107 0.656532
\(117\) 5.24264i 0.484682i
\(118\) 13.0711i 1.20329i
\(119\) 8.65685 0.793573
\(120\) −0.707107 + 2.12132i −0.0645497 + 0.193649i
\(121\) 30.1421 2.74019
\(122\) 6.48528i 0.587150i
\(123\) 6.58579i 0.593820i
\(124\) 3.65685 0.328395
\(125\) −9.19239 + 6.36396i −0.822192 + 0.569210i
\(126\) 2.41421 0.215075
\(127\) 9.58579i 0.850601i −0.905052 0.425300i \(-0.860168\pi\)
0.905052 0.425300i \(-0.139832\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 10.4853 0.923178
\(130\) −3.70711 + 11.1213i −0.325135 + 0.975404i
\(131\) 1.89949 0.165960 0.0829798 0.996551i \(-0.473556\pi\)
0.0829798 + 0.996551i \(0.473556\pi\)
\(132\) 6.41421i 0.558286i
\(133\) 5.24264i 0.454595i
\(134\) −0.828427 −0.0715652
\(135\) 2.12132 + 0.707107i 0.182574 + 0.0608581i
\(136\) −3.58579 −0.307479
\(137\) 17.5563i 1.49994i −0.661472 0.749970i \(-0.730068\pi\)
0.661472 0.749970i \(-0.269932\pi\)
\(138\) 3.00000i 0.255377i
\(139\) 2.48528 0.210799 0.105399 0.994430i \(-0.466388\pi\)
0.105399 + 0.994430i \(0.466388\pi\)
\(140\) −5.12132 1.70711i −0.432831 0.144277i
\(141\) 11.8995 1.00212
\(142\) 9.41421i 0.790023i
\(143\) 33.6274i 2.81207i
\(144\) −1.00000 −0.0833333
\(145\) −5.00000 + 15.0000i −0.415227 + 1.24568i
\(146\) −2.17157 −0.179721
\(147\) 1.17157i 0.0966297i
\(148\) 1.00000i 0.0821995i
\(149\) −3.51472 −0.287937 −0.143968 0.989582i \(-0.545986\pi\)
−0.143968 + 0.989582i \(0.545986\pi\)
\(150\) −4.00000 3.00000i −0.326599 0.244949i
\(151\) 2.41421 0.196466 0.0982330 0.995163i \(-0.468681\pi\)
0.0982330 + 0.995163i \(0.468681\pi\)
\(152\) 2.17157i 0.176138i
\(153\) 3.58579i 0.289894i
\(154\) 15.4853 1.24784
\(155\) −2.58579 + 7.75736i −0.207695 + 0.623086i
\(156\) −5.24264 −0.419747
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 12.2426i 0.973972i
\(159\) −3.82843 −0.303614
\(160\) 2.12132 + 0.707107i 0.167705 + 0.0559017i
\(161\) −7.24264 −0.570800
\(162\) 1.00000i 0.0785674i
\(163\) 15.1421i 1.18602i 0.805194 + 0.593012i \(0.202061\pi\)
−0.805194 + 0.593012i \(0.797939\pi\)
\(164\) 6.58579 0.514264
\(165\) 13.6066 + 4.53553i 1.05927 + 0.353091i
\(166\) −6.89949 −0.535505
\(167\) 18.6569i 1.44371i 0.692044 + 0.721855i \(0.256710\pi\)
−0.692044 + 0.721855i \(0.743290\pi\)
\(168\) 2.41421i 0.186261i
\(169\) −14.4853 −1.11425
\(170\) 2.53553 7.60660i 0.194467 0.583400i
\(171\) −2.17157 −0.166064
\(172\) 10.4853i 0.799495i
\(173\) 0.656854i 0.0499397i 0.999688 + 0.0249699i \(0.00794898\pi\)
−0.999688 + 0.0249699i \(0.992051\pi\)
\(174\) −7.07107 −0.536056
\(175\) 7.24264 9.65685i 0.547492 0.729990i
\(176\) −6.41421 −0.483490
\(177\) 13.0711i 0.982482i
\(178\) 2.89949i 0.217326i
\(179\) 18.8284 1.40730 0.703651 0.710545i \(-0.251552\pi\)
0.703651 + 0.710545i \(0.251552\pi\)
\(180\) 0.707107 2.12132i 0.0527046 0.158114i
\(181\) 20.5858 1.53013 0.765065 0.643953i \(-0.222707\pi\)
0.765065 + 0.643953i \(0.222707\pi\)
\(182\) 12.6569i 0.938188i
\(183\) 6.48528i 0.479406i
\(184\) 3.00000 0.221163
\(185\) 2.12132 + 0.707107i 0.155963 + 0.0519875i
\(186\) −3.65685 −0.268134
\(187\) 23.0000i 1.68193i
\(188\) 11.8995i 0.867860i
\(189\) −2.41421 −0.175608
\(190\) 4.60660 + 1.53553i 0.334198 + 0.111399i
\(191\) 8.65685 0.626388 0.313194 0.949689i \(-0.398601\pi\)
0.313194 + 0.949689i \(0.398601\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 9.31371i 0.670415i −0.942144 0.335208i \(-0.891194\pi\)
0.942144 0.335208i \(-0.108806\pi\)
\(194\) −6.72792 −0.483037
\(195\) 3.70711 11.1213i 0.265471 0.796414i
\(196\) −1.17157 −0.0836838
\(197\) 15.1421i 1.07883i −0.842039 0.539416i \(-0.818645\pi\)
0.842039 0.539416i \(-0.181355\pi\)
\(198\) 6.41421i 0.455838i
\(199\) −20.0000 −1.41776 −0.708881 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) −3.00000 + 4.00000i −0.212132 + 0.282843i
\(201\) 0.828427 0.0584327
\(202\) 5.31371i 0.373871i
\(203\) 17.0711i 1.19815i
\(204\) 3.58579 0.251055
\(205\) −4.65685 + 13.9706i −0.325249 + 0.975746i
\(206\) 15.0711 1.05005
\(207\) 3.00000i 0.208514i
\(208\) 5.24264i 0.363512i
\(209\) −13.9289 −0.963484
\(210\) 5.12132 + 1.70711i 0.353405 + 0.117802i
\(211\) 10.3848 0.714917 0.357459 0.933929i \(-0.383643\pi\)
0.357459 + 0.933929i \(0.383643\pi\)
\(212\) 3.82843i 0.262937i
\(213\) 9.41421i 0.645051i
\(214\) 16.0711 1.09860
\(215\) 22.2426 + 7.41421i 1.51694 + 0.505645i
\(216\) 1.00000 0.0680414
\(217\) 8.82843i 0.599313i
\(218\) 4.75736i 0.322209i
\(219\) 2.17157 0.146741
\(220\) 4.53553 13.6066i 0.305786 0.917357i
\(221\) 18.7990 1.26456
\(222\) 1.00000i 0.0671156i
\(223\) 9.65685i 0.646671i 0.946284 + 0.323335i \(0.104804\pi\)
−0.946284 + 0.323335i \(0.895196\pi\)
\(224\) −2.41421 −0.161306
\(225\) 4.00000 + 3.00000i 0.266667 + 0.200000i
\(226\) 2.82843 0.188144
\(227\) 12.0000i 0.796468i −0.917284 0.398234i \(-0.869623\pi\)
0.917284 0.398234i \(-0.130377\pi\)
\(228\) 2.17157i 0.143816i
\(229\) −18.7279 −1.23758 −0.618788 0.785558i \(-0.712376\pi\)
−0.618788 + 0.785558i \(0.712376\pi\)
\(230\) −2.12132 + 6.36396i −0.139876 + 0.419627i
\(231\) −15.4853 −1.01886
\(232\) 7.07107i 0.464238i
\(233\) 2.48528i 0.162816i −0.996681 0.0814081i \(-0.974058\pi\)
0.996681 0.0814081i \(-0.0259417\pi\)
\(234\) 5.24264 0.342722
\(235\) 25.2426 + 8.41421i 1.64665 + 0.548883i
\(236\) −13.0711 −0.850854
\(237\) 12.2426i 0.795245i
\(238\) 8.65685i 0.561141i
\(239\) −20.6274 −1.33428 −0.667138 0.744934i \(-0.732481\pi\)
−0.667138 + 0.744934i \(0.732481\pi\)
\(240\) −2.12132 0.707107i −0.136931 0.0456435i
\(241\) 2.58579 0.166565 0.0832826 0.996526i \(-0.473460\pi\)
0.0832826 + 0.996526i \(0.473460\pi\)
\(242\) 30.1421i 1.93761i
\(243\) 1.00000i 0.0641500i
\(244\) 6.48528 0.415178
\(245\) 0.828427 2.48528i 0.0529263 0.158779i
\(246\) −6.58579 −0.419894
\(247\) 11.3848i 0.724396i
\(248\) 3.65685i 0.232210i
\(249\) 6.89949 0.437238
\(250\) −6.36396 9.19239i −0.402492 0.581378i
\(251\) 4.82843 0.304768 0.152384 0.988321i \(-0.451305\pi\)
0.152384 + 0.988321i \(0.451305\pi\)
\(252\) 2.41421i 0.152081i
\(253\) 19.2426i 1.20977i
\(254\) 9.58579 0.601466
\(255\) −2.53553 + 7.60660i −0.158781 + 0.476344i
\(256\) 1.00000 0.0625000
\(257\) 9.58579i 0.597945i 0.954262 + 0.298972i \(0.0966439\pi\)
−0.954262 + 0.298972i \(0.903356\pi\)
\(258\) 10.4853i 0.652785i
\(259\) −2.41421 −0.150012
\(260\) −11.1213 3.70711i −0.689715 0.229905i
\(261\) 7.07107 0.437688
\(262\) 1.89949i 0.117351i
\(263\) 31.4142i 1.93708i 0.248851 + 0.968542i \(0.419947\pi\)
−0.248851 + 0.968542i \(0.580053\pi\)
\(264\) 6.41421 0.394768
\(265\) −8.12132 2.70711i −0.498889 0.166296i
\(266\) −5.24264 −0.321447
\(267\) 2.89949i 0.177446i
\(268\) 0.828427i 0.0506042i
\(269\) 25.6274 1.56253 0.781266 0.624199i \(-0.214574\pi\)
0.781266 + 0.624199i \(0.214574\pi\)
\(270\) −0.707107 + 2.12132i −0.0430331 + 0.129099i
\(271\) −6.82843 −0.414797 −0.207399 0.978256i \(-0.566500\pi\)
−0.207399 + 0.978256i \(0.566500\pi\)
\(272\) 3.58579i 0.217420i
\(273\) 12.6569i 0.766028i
\(274\) 17.5563 1.06062
\(275\) 25.6569 + 19.2426i 1.54717 + 1.16037i
\(276\) −3.00000 −0.180579
\(277\) 2.89949i 0.174214i 0.996199 + 0.0871069i \(0.0277622\pi\)
−0.996199 + 0.0871069i \(0.972238\pi\)
\(278\) 2.48528i 0.149057i
\(279\) 3.65685 0.218930
\(280\) 1.70711 5.12132i 0.102019 0.306057i
\(281\) −13.3848 −0.798469 −0.399234 0.916849i \(-0.630724\pi\)
−0.399234 + 0.916849i \(0.630724\pi\)
\(282\) 11.8995i 0.708605i
\(283\) 18.7990i 1.11748i −0.829342 0.558742i \(-0.811284\pi\)
0.829342 0.558742i \(-0.188716\pi\)
\(284\) 9.41421 0.558631
\(285\) −4.60660 1.53553i −0.272872 0.0909572i
\(286\) 33.6274 1.98843
\(287\) 15.8995i 0.938518i
\(288\) 1.00000i 0.0589256i
\(289\) 4.14214 0.243655
\(290\) −15.0000 5.00000i −0.880830 0.293610i
\(291\) 6.72792 0.394398
\(292\) 2.17157i 0.127082i
\(293\) 8.65685i 0.505739i −0.967500 0.252869i \(-0.918626\pi\)
0.967500 0.252869i \(-0.0813743\pi\)
\(294\) 1.17157 0.0683275
\(295\) 9.24264 27.7279i 0.538127 1.61438i
\(296\) 1.00000 0.0581238
\(297\) 6.41421i 0.372190i
\(298\) 3.51472i 0.203602i
\(299\) −15.7279 −0.909569
\(300\) 3.00000 4.00000i 0.173205 0.230940i
\(301\) −25.3137 −1.45906
\(302\) 2.41421i 0.138922i
\(303\) 5.31371i 0.305265i
\(304\) 2.17157 0.124548
\(305\) −4.58579 + 13.7574i −0.262581 + 0.787744i
\(306\) −3.58579 −0.204986
\(307\) 13.8995i 0.793286i 0.917973 + 0.396643i \(0.129825\pi\)
−0.917973 + 0.396643i \(0.870175\pi\)
\(308\) 15.4853i 0.882356i
\(309\) −15.0711 −0.857363
\(310\) −7.75736 2.58579i −0.440588 0.146863i
\(311\) −12.8284 −0.727433 −0.363717 0.931510i \(-0.618492\pi\)
−0.363717 + 0.931510i \(0.618492\pi\)
\(312\) 5.24264i 0.296806i
\(313\) 2.72792i 0.154191i −0.997024 0.0770956i \(-0.975435\pi\)
0.997024 0.0770956i \(-0.0245647\pi\)
\(314\) 0 0
\(315\) −5.12132 1.70711i −0.288554 0.0961846i
\(316\) 12.2426 0.688702
\(317\) 21.1716i 1.18911i −0.804053 0.594557i \(-0.797327\pi\)
0.804053 0.594557i \(-0.202673\pi\)
\(318\) 3.82843i 0.214688i
\(319\) 45.3553 2.53941
\(320\) −0.707107 + 2.12132i −0.0395285 + 0.118585i
\(321\) −16.0711 −0.897000
\(322\) 7.24264i 0.403617i
\(323\) 7.78680i 0.433269i
\(324\) −1.00000 −0.0555556
\(325\) 15.7279 20.9706i 0.872428 1.16324i
\(326\) −15.1421 −0.838645
\(327\) 4.75736i 0.263083i
\(328\) 6.58579i 0.363639i
\(329\) −28.7279 −1.58382
\(330\) −4.53553 + 13.6066i −0.249673 + 0.749019i
\(331\) 23.4558 1.28925 0.644625 0.764499i \(-0.277014\pi\)
0.644625 + 0.764499i \(0.277014\pi\)
\(332\) 6.89949i 0.378659i
\(333\) 1.00000i 0.0547997i
\(334\) −18.6569 −1.02086
\(335\) 1.75736 + 0.585786i 0.0960148 + 0.0320049i
\(336\) 2.41421 0.131706
\(337\) 27.9706i 1.52365i −0.647781 0.761827i \(-0.724303\pi\)
0.647781 0.761827i \(-0.275697\pi\)
\(338\) 14.4853i 0.787895i
\(339\) −2.82843 −0.153619
\(340\) 7.60660 + 2.53553i 0.412526 + 0.137509i
\(341\) 23.4558 1.27021
\(342\) 2.17157i 0.117425i
\(343\) 19.7279i 1.06521i
\(344\) 10.4853 0.565328
\(345\) 2.12132 6.36396i 0.114208 0.342624i
\(346\) −0.656854 −0.0353127
\(347\) 23.5563i 1.26457i 0.774735 + 0.632286i \(0.217883\pi\)
−0.774735 + 0.632286i \(0.782117\pi\)
\(348\) 7.07107i 0.379049i
\(349\) −28.0416 −1.50103 −0.750517 0.660851i \(-0.770195\pi\)
−0.750517 + 0.660851i \(0.770195\pi\)
\(350\) 9.65685 + 7.24264i 0.516181 + 0.387135i
\(351\) −5.24264 −0.279831
\(352\) 6.41421i 0.341879i
\(353\) 16.1421i 0.859159i 0.903029 + 0.429580i \(0.141338\pi\)
−0.903029 + 0.429580i \(0.858662\pi\)
\(354\) 13.0711 0.694719
\(355\) −6.65685 + 19.9706i −0.353309 + 1.05993i
\(356\) 2.89949 0.153673
\(357\) 8.65685i 0.458169i
\(358\) 18.8284i 0.995113i
\(359\) −29.0711 −1.53431 −0.767156 0.641460i \(-0.778329\pi\)
−0.767156 + 0.641460i \(0.778329\pi\)
\(360\) 2.12132 + 0.707107i 0.111803 + 0.0372678i
\(361\) −14.2843 −0.751804
\(362\) 20.5858i 1.08196i
\(363\) 30.1421i 1.58205i
\(364\) 12.6569 0.663399
\(365\) 4.60660 + 1.53553i 0.241121 + 0.0803735i
\(366\) −6.48528 −0.338991
\(367\) 15.2426i 0.795659i −0.917459 0.397830i \(-0.869763\pi\)
0.917459 0.397830i \(-0.130237\pi\)
\(368\) 3.00000i 0.156386i
\(369\) 6.58579 0.342842
\(370\) −0.707107 + 2.12132i −0.0367607 + 0.110282i
\(371\) 9.24264 0.479854
\(372\) 3.65685i 0.189599i
\(373\) 1.75736i 0.0909926i 0.998965 + 0.0454963i \(0.0144869\pi\)
−0.998965 + 0.0454963i \(0.985513\pi\)
\(374\) −23.0000 −1.18930
\(375\) 6.36396 + 9.19239i 0.328634 + 0.474693i
\(376\) 11.8995 0.613670
\(377\) 37.0711i 1.90926i
\(378\) 2.41421i 0.124174i
\(379\) 28.7279 1.47565 0.737827 0.674990i \(-0.235852\pi\)
0.737827 + 0.674990i \(0.235852\pi\)
\(380\) −1.53553 + 4.60660i −0.0787712 + 0.236314i
\(381\) −9.58579 −0.491095
\(382\) 8.65685i 0.442923i
\(383\) 14.6569i 0.748930i −0.927241 0.374465i \(-0.877826\pi\)
0.927241 0.374465i \(-0.122174\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −32.8492 10.9497i −1.67415 0.558051i
\(386\) 9.31371 0.474055
\(387\) 10.4853i 0.532997i
\(388\) 6.72792i 0.341558i
\(389\) 22.9706 1.16465 0.582327 0.812955i \(-0.302142\pi\)
0.582327 + 0.812955i \(0.302142\pi\)
\(390\) 11.1213 + 3.70711i 0.563150 + 0.187717i
\(391\) 10.7574 0.544023
\(392\) 1.17157i 0.0591734i
\(393\) 1.89949i 0.0958168i
\(394\) 15.1421 0.762850
\(395\) −8.65685 + 25.9706i −0.435574 + 1.30672i
\(396\) −6.41421 −0.322326
\(397\) 8.48528i 0.425864i 0.977067 + 0.212932i \(0.0683013\pi\)
−0.977067 + 0.212932i \(0.931699\pi\)
\(398\) 20.0000i 1.00251i
\(399\) 5.24264 0.262460
\(400\) −4.00000 3.00000i −0.200000 0.150000i
\(401\) −15.0416 −0.751143 −0.375572 0.926793i \(-0.622554\pi\)
−0.375572 + 0.926793i \(0.622554\pi\)
\(402\) 0.828427i 0.0413182i
\(403\) 19.1716i 0.955004i
\(404\) 5.31371 0.264367
\(405\) 0.707107 2.12132i 0.0351364 0.105409i
\(406\) 17.0711 0.847223
\(407\) 6.41421i 0.317941i
\(408\) 3.58579i 0.177523i
\(409\) −32.3848 −1.60132 −0.800662 0.599116i \(-0.795519\pi\)
−0.800662 + 0.599116i \(0.795519\pi\)
\(410\) −13.9706 4.65685i −0.689957 0.229986i
\(411\) −17.5563 −0.865991
\(412\) 15.0711i 0.742498i
\(413\) 31.5563i 1.55279i
\(414\) 3.00000 0.147442
\(415\) 14.6360 + 4.87868i 0.718455 + 0.239485i
\(416\) −5.24264 −0.257042
\(417\) 2.48528i 0.121705i
\(418\) 13.9289i 0.681286i
\(419\) 27.7279 1.35460 0.677299 0.735708i \(-0.263150\pi\)
0.677299 + 0.735708i \(0.263150\pi\)
\(420\) −1.70711 + 5.12132i −0.0832983 + 0.249895i
\(421\) −13.4558 −0.655798 −0.327899 0.944713i \(-0.606341\pi\)
−0.327899 + 0.944713i \(0.606341\pi\)
\(422\) 10.3848i 0.505523i
\(423\) 11.8995i 0.578573i
\(424\) −3.82843 −0.185925
\(425\) −10.7574 + 14.3431i −0.521809 + 0.695745i
\(426\) −9.41421 −0.456120
\(427\) 15.6569i 0.757688i
\(428\) 16.0711i 0.776824i
\(429\) −33.6274 −1.62355
\(430\) −7.41421 + 22.2426i −0.357545 + 1.07264i
\(431\) 29.8284 1.43678 0.718392 0.695638i \(-0.244878\pi\)
0.718392 + 0.695638i \(0.244878\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 23.4853i 1.12863i 0.825559 + 0.564315i \(0.190860\pi\)
−0.825559 + 0.564315i \(0.809140\pi\)
\(434\) 8.82843 0.423778
\(435\) 15.0000 + 5.00000i 0.719195 + 0.239732i
\(436\) 4.75736 0.227836
\(437\) 6.51472i 0.311641i
\(438\) 2.17157i 0.103762i
\(439\) −24.7279 −1.18020 −0.590100 0.807330i \(-0.700912\pi\)
−0.590100 + 0.807330i \(0.700912\pi\)
\(440\) 13.6066 + 4.53553i 0.648669 + 0.216223i
\(441\) −1.17157 −0.0557892
\(442\) 18.7990i 0.894177i
\(443\) 23.6569i 1.12397i 0.827147 + 0.561986i \(0.189962\pi\)
−0.827147 + 0.561986i \(0.810038\pi\)
\(444\) −1.00000 −0.0474579
\(445\) −2.05025 + 6.15076i −0.0971913 + 0.291574i
\(446\) −9.65685 −0.457265
\(447\) 3.51472i 0.166240i
\(448\) 2.41421i 0.114061i
\(449\) 13.7990 0.651215 0.325607 0.945505i \(-0.394431\pi\)
0.325607 + 0.945505i \(0.394431\pi\)
\(450\) −3.00000 + 4.00000i −0.141421 + 0.188562i
\(451\) 42.2426 1.98913
\(452\) 2.82843i 0.133038i
\(453\) 2.41421i 0.113430i
\(454\) 12.0000 0.563188
\(455\) −8.94975 + 26.8492i −0.419571 + 1.25871i
\(456\) −2.17157 −0.101693
\(457\) 0.970563i 0.0454010i −0.999742 0.0227005i \(-0.992774\pi\)
0.999742 0.0227005i \(-0.00722642\pi\)
\(458\) 18.7279i 0.875098i
\(459\) 3.58579 0.167370
\(460\) −6.36396 2.12132i −0.296721 0.0989071i
\(461\) 20.8284 0.970077 0.485038 0.874493i \(-0.338806\pi\)
0.485038 + 0.874493i \(0.338806\pi\)
\(462\) 15.4853i 0.720440i
\(463\) 29.8995i 1.38955i 0.719228 + 0.694774i \(0.244495\pi\)
−0.719228 + 0.694774i \(0.755505\pi\)
\(464\) −7.07107 −0.328266
\(465\) 7.75736 + 2.58579i 0.359739 + 0.119913i
\(466\) 2.48528 0.115128
\(467\) 40.2426i 1.86221i −0.364755 0.931104i \(-0.618847\pi\)
0.364755 0.931104i \(-0.381153\pi\)
\(468\) 5.24264i 0.242341i
\(469\) −2.00000 −0.0923514
\(470\) −8.41421 + 25.2426i −0.388119 + 1.16436i
\(471\) 0 0
\(472\) 13.0711i 0.601645i
\(473\) 67.2548i 3.09238i
\(474\) −12.2426 −0.562323
\(475\) −8.68629 6.51472i −0.398554 0.298916i
\(476\) −8.65685 −0.396786
\(477\) 3.82843i 0.175292i
\(478\) 20.6274i 0.943476i
\(479\) −6.17157 −0.281986 −0.140993 0.990011i \(-0.545030\pi\)
−0.140993 + 0.990011i \(0.545030\pi\)
\(480\) 0.707107 2.12132i 0.0322749 0.0968246i
\(481\) −5.24264 −0.239044
\(482\) 2.58579i 0.117779i
\(483\) 7.24264i 0.329552i
\(484\) −30.1421 −1.37010
\(485\) 14.2721 + 4.75736i 0.648062 + 0.216021i
\(486\) 1.00000 0.0453609
\(487\) 30.0000i 1.35943i −0.733476 0.679715i \(-0.762104\pi\)
0.733476 0.679715i \(-0.237896\pi\)
\(488\) 6.48528i 0.293575i
\(489\) 15.1421 0.684751
\(490\) 2.48528 + 0.828427i 0.112274 + 0.0374245i
\(491\) −16.4142 −0.740763 −0.370382 0.928880i \(-0.620773\pi\)
−0.370382 + 0.928880i \(0.620773\pi\)
\(492\) 6.58579i 0.296910i
\(493\) 25.3553i 1.14195i
\(494\) −11.3848 −0.512225
\(495\) 4.53553 13.6066i 0.203857 0.611571i
\(496\) −3.65685 −0.164198
\(497\) 22.7279i 1.01949i
\(498\) 6.89949i 0.309174i
\(499\) −7.48528 −0.335087 −0.167544 0.985865i \(-0.553583\pi\)
−0.167544 + 0.985865i \(0.553583\pi\)
\(500\) 9.19239 6.36396i 0.411096 0.284605i
\(501\) 18.6569 0.833527
\(502\) 4.82843i 0.215503i
\(503\) 23.6569i 1.05481i 0.849615 + 0.527403i \(0.176834\pi\)
−0.849615 + 0.527403i \(0.823166\pi\)
\(504\) −2.41421 −0.107538
\(505\) −3.75736 + 11.2721i −0.167200 + 0.501601i
\(506\) 19.2426 0.855440
\(507\) 14.4853i 0.643314i
\(508\) 9.58579i 0.425300i
\(509\) 30.3137 1.34363 0.671816 0.740718i \(-0.265515\pi\)
0.671816 + 0.740718i \(0.265515\pi\)
\(510\) −7.60660 2.53553i −0.336826 0.112275i
\(511\) −5.24264 −0.231921
\(512\) 1.00000i 0.0441942i
\(513\) 2.17157i 0.0958773i
\(514\) −9.58579 −0.422811
\(515\) −31.9706 10.6569i −1.40879 0.469597i
\(516\) −10.4853 −0.461589
\(517\) 76.3259i 3.35681i
\(518\) 2.41421i 0.106074i
\(519\) 0.656854 0.0288327
\(520\) 3.70711 11.1213i 0.162567 0.487702i
\(521\) −16.0416 −0.702797 −0.351398 0.936226i \(-0.614294\pi\)
−0.351398 + 0.936226i \(0.614294\pi\)
\(522\) 7.07107i 0.309492i
\(523\) 34.0000i 1.48672i 0.668894 + 0.743358i \(0.266768\pi\)
−0.668894 + 0.743358i \(0.733232\pi\)
\(524\) −1.89949 −0.0829798
\(525\) −9.65685 7.24264i −0.421460 0.316095i
\(526\) −31.4142 −1.36972
\(527\) 13.1127i 0.571198i
\(528\) 6.41421i 0.279143i
\(529\) 14.0000 0.608696
\(530\) 2.70711 8.12132i 0.117589 0.352768i
\(531\) −13.0711 −0.567236
\(532\) 5.24264i 0.227297i
\(533\) 34.5269i 1.49553i
\(534\) −2.89949 −0.125473
\(535\) −34.0919 11.3640i −1.47392 0.491307i
\(536\) 0.828427 0.0357826
\(537\) 18.8284i 0.812507i
\(538\) 25.6274i 1.10488i
\(539\) −7.51472 −0.323682
\(540\) −2.12132 0.707107i −0.0912871 0.0304290i
\(541\) 36.2132 1.55693 0.778464 0.627690i \(-0.215999\pi\)
0.778464 + 0.627690i \(0.215999\pi\)
\(542\) 6.82843i 0.293306i
\(543\) 20.5858i 0.883421i
\(544\) 3.58579 0.153739
\(545\) −3.36396 + 10.0919i −0.144096 + 0.432289i
\(546\) −12.6569 −0.541663
\(547\) 0.372583i 0.0159305i 0.999968 + 0.00796525i \(0.00253544\pi\)
−0.999968 + 0.00796525i \(0.997465\pi\)
\(548\) 17.5563i 0.749970i
\(549\) 6.48528 0.276785
\(550\) −19.2426 + 25.6569i −0.820509 + 1.09401i
\(551\) −15.3553 −0.654159
\(552\) 3.00000i 0.127688i
\(553\) 29.5563i 1.25686i
\(554\) −2.89949 −0.123188
\(555\) 0.707107 2.12132i 0.0300150 0.0900450i
\(556\) −2.48528 −0.105399
\(557\) 37.5563i 1.59131i 0.605748 + 0.795657i \(0.292874\pi\)
−0.605748 + 0.795657i \(0.707126\pi\)
\(558\) 3.65685i 0.154807i
\(559\) −54.9706 −2.32501
\(560\) 5.12132 + 1.70711i 0.216415 + 0.0721384i
\(561\) 23.0000 0.971061
\(562\) 13.3848i 0.564603i
\(563\) 16.5858i 0.699008i 0.936935 + 0.349504i \(0.113650\pi\)
−0.936935 + 0.349504i \(0.886350\pi\)
\(564\) −11.8995 −0.501059
\(565\) −6.00000 2.00000i −0.252422 0.0841406i
\(566\) 18.7990 0.790180
\(567\) 2.41421i 0.101387i
\(568\) 9.41421i 0.395012i
\(569\) −37.0416 −1.55287 −0.776433 0.630200i \(-0.782973\pi\)
−0.776433 + 0.630200i \(0.782973\pi\)
\(570\) 1.53553 4.60660i 0.0643164 0.192949i
\(571\) −28.0416 −1.17351 −0.586753 0.809766i \(-0.699594\pi\)
−0.586753 + 0.809766i \(0.699594\pi\)
\(572\) 33.6274i 1.40603i
\(573\) 8.65685i 0.361645i
\(574\) 15.8995 0.663632
\(575\) 9.00000 12.0000i 0.375326 0.500435i
\(576\) 1.00000 0.0416667
\(577\) 9.51472i 0.396103i −0.980192 0.198051i \(-0.936539\pi\)
0.980192 0.198051i \(-0.0634613\pi\)
\(578\) 4.14214i 0.172290i
\(579\) −9.31371 −0.387065
\(580\) 5.00000 15.0000i 0.207614 0.622841i
\(581\) −16.6569 −0.691043
\(582\) 6.72792i 0.278881i
\(583\) 24.5563i 1.01702i
\(584\) 2.17157 0.0898603
\(585\) −11.1213 3.70711i −0.459810 0.153270i
\(586\) 8.65685 0.357611
\(587\) 2.82843i 0.116742i 0.998295 + 0.0583708i \(0.0185906\pi\)
−0.998295 + 0.0583708i \(0.981409\pi\)
\(588\) 1.17157i 0.0483149i
\(589\) −7.94113 −0.327208
\(590\) 27.7279 + 9.24264i 1.14154 + 0.380513i
\(591\) −15.1421 −0.622864
\(592\) 1.00000i 0.0410997i
\(593\) 4.97056i 0.204117i 0.994778 + 0.102058i \(0.0325428\pi\)
−0.994778 + 0.102058i \(0.967457\pi\)
\(594\) 6.41421 0.263178
\(595\) 6.12132 18.3640i 0.250950 0.752849i
\(596\) 3.51472 0.143968
\(597\) 20.0000i 0.818546i
\(598\) 15.7279i 0.643163i
\(599\) −32.8701 −1.34303 −0.671517 0.740989i \(-0.734357\pi\)
−0.671517 + 0.740989i \(0.734357\pi\)
\(600\) 4.00000 + 3.00000i 0.163299 + 0.122474i
\(601\) 9.97056 0.406708 0.203354 0.979105i \(-0.434816\pi\)
0.203354 + 0.979105i \(0.434816\pi\)
\(602\) 25.3137i 1.03171i
\(603\) 0.828427i 0.0337362i
\(604\) −2.41421 −0.0982330
\(605\) 21.3137 63.9411i 0.866525 2.59958i
\(606\) −5.31371 −0.215855
\(607\) 11.8579i 0.481296i 0.970612 + 0.240648i \(0.0773599\pi\)
−0.970612 + 0.240648i \(0.922640\pi\)
\(608\) 2.17157i 0.0880689i
\(609\) −17.0711 −0.691755
\(610\) −13.7574 4.58579i −0.557019 0.185673i
\(611\) −62.3848 −2.52382
\(612\) 3.58579i 0.144947i
\(613\) 1.31371i 0.0530602i 0.999648 + 0.0265301i \(0.00844578\pi\)
−0.999648 + 0.0265301i \(0.991554\pi\)
\(614\) −13.8995 −0.560938
\(615\) 13.9706 + 4.65685i 0.563347 + 0.187782i
\(616\) −15.4853 −0.623920
\(617\) 35.6985i 1.43717i 0.695441 + 0.718583i \(0.255209\pi\)
−0.695441 + 0.718583i \(0.744791\pi\)
\(618\) 15.0711i 0.606247i
\(619\) 7.21320 0.289923 0.144962 0.989437i \(-0.453694\pi\)
0.144962 + 0.989437i \(0.453694\pi\)
\(620\) 2.58579 7.75736i 0.103848 0.311543i
\(621\) −3.00000 −0.120386
\(622\) 12.8284i 0.514373i
\(623\) 7.00000i 0.280449i
\(624\) 5.24264 0.209874
\(625\) 7.00000 + 24.0000i 0.280000 + 0.960000i
\(626\) 2.72792 0.109030
\(627\) 13.9289i 0.556268i
\(628\) 0 0
\(629\) 3.58579 0.142975
\(630\) 1.70711 5.12132i 0.0680128 0.204038i
\(631\) 7.51472 0.299156 0.149578 0.988750i \(-0.452208\pi\)
0.149578 + 0.988750i \(0.452208\pi\)
\(632\) 12.2426i 0.486986i
\(633\) 10.3848i 0.412758i
\(634\) 21.1716 0.840831
\(635\) −20.3345 6.77817i −0.806951 0.268984i
\(636\) 3.82843 0.151807
\(637\) 6.14214i 0.243360i
\(638\) 45.3553i 1.79564i
\(639\) 9.41421 0.372421
\(640\) −2.12132 0.707107i −0.0838525 0.0279508i
\(641\) −26.8284 −1.05966 −0.529830 0.848104i \(-0.677744\pi\)
−0.529830 + 0.848104i \(0.677744\pi\)
\(642\) 16.0711i 0.634274i
\(643\) 18.4558i 0.727827i −0.931433 0.363914i \(-0.881440\pi\)
0.931433 0.363914i \(-0.118560\pi\)
\(644\) 7.24264 0.285400
\(645\) 7.41421 22.2426i 0.291934 0.875803i
\(646\) 7.78680 0.306367
\(647\) 21.0000i 0.825595i 0.910823 + 0.412798i \(0.135448\pi\)
−0.910823 + 0.412798i \(0.864552\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −83.8406 −3.29103
\(650\) 20.9706 + 15.7279i 0.822533 + 0.616900i
\(651\) −8.82843 −0.346013
\(652\) 15.1421i 0.593012i
\(653\) 20.4853i 0.801651i 0.916154 + 0.400826i \(0.131277\pi\)
−0.916154 + 0.400826i \(0.868723\pi\)
\(654\) −4.75736 −0.186027
\(655\) 1.34315 4.02944i 0.0524810 0.157443i
\(656\) −6.58579 −0.257132
\(657\) 2.17157i 0.0847211i
\(658\) 28.7279i 1.11993i
\(659\) −51.1127 −1.99107 −0.995534 0.0944035i \(-0.969906\pi\)
−0.995534 + 0.0944035i \(0.969906\pi\)
\(660\) −13.6066 4.53553i −0.529636 0.176545i
\(661\) 25.2426 0.981825 0.490912 0.871209i \(-0.336663\pi\)
0.490912 + 0.871209i \(0.336663\pi\)
\(662\) 23.4558i 0.911637i
\(663\) 18.7990i 0.730092i
\(664\) 6.89949 0.267752
\(665\) 11.1213 + 3.70711i 0.431266 + 0.143755i
\(666\) 1.00000 0.0387492
\(667\) 21.2132i 0.821379i
\(668\) 18.6569i 0.721855i
\(669\) 9.65685 0.373356
\(670\) −0.585786 + 1.75736i −0.0226309 + 0.0678927i
\(671\) 41.5980 1.60587
\(672\) 2.41421i 0.0931303i
\(673\) 0.0294373i 0.00113472i 1.00000 0.000567361i \(0.000180597\pi\)
−1.00000 0.000567361i \(0.999819\pi\)
\(674\) 27.9706 1.07739
\(675\) 3.00000 4.00000i 0.115470 0.153960i
\(676\) 14.4853 0.557126
\(677\) 1.20101i 0.0461586i −0.999734 0.0230793i \(-0.992653\pi\)
0.999734 0.0230793i \(-0.00734702\pi\)
\(678\) 2.82843i 0.108625i
\(679\) −16.2426 −0.623335
\(680\) −2.53553 + 7.60660i −0.0972333 + 0.291700i
\(681\) −12.0000 −0.459841
\(682\) 23.4558i 0.898171i
\(683\) 16.9289i 0.647768i −0.946097 0.323884i \(-0.895011\pi\)
0.946097 0.323884i \(-0.104989\pi\)
\(684\) 2.17157 0.0830322
\(685\) −37.2426 12.4142i −1.42297 0.474323i
\(686\) −19.7279 −0.753216
\(687\) 18.7279i 0.714515i
\(688\) 10.4853i 0.399748i
\(689\) 20.0711 0.764647
\(690\) 6.36396 + 2.12132i 0.242272 + 0.0807573i
\(691\) 30.5858 1.16354 0.581769 0.813354i \(-0.302361\pi\)
0.581769 + 0.813354i \(0.302361\pi\)
\(692\) 0.656854i 0.0249699i
\(693\) 15.4853i 0.588237i
\(694\) −23.5563 −0.894187
\(695\) 1.75736 5.27208i 0.0666604 0.199981i
\(696\) 7.07107 0.268028
\(697\) 23.6152i 0.894490i
\(698\) 28.0416i 1.06139i
\(699\) −2.48528 −0.0940020
\(700\) −7.24264 + 9.65685i −0.273746 + 0.364995i
\(701\) 14.6274 0.552470 0.276235 0.961090i \(-0.410913\pi\)
0.276235 + 0.961090i \(0.410913\pi\)
\(702\) 5.24264i 0.197871i
\(703\) 2.17157i 0.0819024i
\(704\) 6.41421 0.241745
\(705\) 8.41421 25.2426i 0.316898 0.950693i
\(706\) −16.1421 −0.607517
\(707\) 12.8284i 0.482463i
\(708\) 13.0711i 0.491241i
\(709\) −44.0711 −1.65512 −0.827562 0.561375i \(-0.810273\pi\)
−0.827562 + 0.561375i \(0.810273\pi\)
\(710\) −19.9706 6.65685i −0.749482 0.249827i
\(711\) 12.2426 0.459135
\(712\) 2.89949i 0.108663i
\(713\) 10.9706i 0.410851i
\(714\) 8.65685 0.323975
\(715\) −71.3345 23.7782i −2.66776 0.889253i
\(716\) −18.8284 −0.703651
\(717\) 20.6274i 0.770345i
\(718\) 29.0711i 1.08492i
\(719\) −1.41421 −0.0527413 −0.0263706 0.999652i \(-0.508395\pi\)
−0.0263706 + 0.999652i \(0.508395\pi\)
\(720\) −0.707107 + 2.12132i −0.0263523 + 0.0790569i
\(721\) 36.3848 1.35504
\(722\) 14.2843i 0.531606i
\(723\) 2.58579i 0.0961664i
\(724\) −20.5858 −0.765065
\(725\) 28.2843 + 21.2132i 1.05045 + 0.787839i
\(726\) 30.1421 1.11868
\(727\) 20.3848i 0.756030i −0.925800 0.378015i \(-0.876607\pi\)
0.925800 0.378015i \(-0.123393\pi\)
\(728\) 12.6569i 0.469094i
\(729\) −1.00000 −0.0370370
\(730\) −1.53553 + 4.60660i −0.0568327 + 0.170498i
\(731\) 37.5980 1.39061
\(732\) 6.48528i 0.239703i
\(733\) 10.9706i 0.405207i −0.979261 0.202603i \(-0.935060\pi\)
0.979261 0.202603i \(-0.0649403\pi\)
\(734\) 15.2426 0.562616
\(735\) −2.48528 0.828427i −0.0916710 0.0305570i
\(736\) −3.00000 −0.110581
\(737\) 5.31371i 0.195733i
\(738\) 6.58579i 0.242426i
\(739\) 10.0000 0.367856 0.183928 0.982940i \(-0.441119\pi\)
0.183928 + 0.982940i \(0.441119\pi\)
\(740\) −2.12132 0.707107i −0.0779813 0.0259938i
\(741\) 11.3848 0.418230
\(742\) 9.24264i 0.339308i
\(743\) 51.3553i 1.88404i 0.335550 + 0.942022i \(0.391078\pi\)
−0.335550 + 0.942022i \(0.608922\pi\)
\(744\) 3.65685 0.134067
\(745\) −2.48528 + 7.45584i −0.0910537 + 0.273161i
\(746\) −1.75736 −0.0643415
\(747\) 6.89949i 0.252439i
\(748\) 23.0000i 0.840963i
\(749\) 38.7990 1.41768
\(750\) −9.19239 + 6.36396i −0.335659 + 0.232379i
\(751\) −35.1127 −1.28128 −0.640640 0.767841i \(-0.721331\pi\)
−0.640640 + 0.767841i \(0.721331\pi\)
\(752\) 11.8995i 0.433930i
\(753\) 4.82843i 0.175958i
\(754\) 37.0711 1.35005
\(755\) 1.70711 5.12132i 0.0621280 0.186384i
\(756\) 2.41421 0.0878041
\(757\) 16.2132i 0.589279i 0.955608 + 0.294639i \(0.0951995\pi\)
−0.955608 + 0.294639i \(0.904800\pi\)
\(758\) 28.7279i 1.04345i
\(759\) −19.2426 −0.698464
\(760\) −4.60660 1.53553i −0.167099 0.0556997i
\(761\) 25.3137 0.917621 0.458811 0.888534i \(-0.348276\pi\)
0.458811 + 0.888534i \(0.348276\pi\)
\(762\) 9.58579i 0.347256i
\(763\) 11.4853i 0.415795i
\(764\) −8.65685 −0.313194
\(765\) 7.60660 + 2.53553i 0.275017 + 0.0916724i
\(766\) 14.6569 0.529574
\(767\) 68.5269i 2.47436i
\(768\) 1.00000i 0.0360844i
\(769\) 19.5563 0.705220 0.352610 0.935770i \(-0.385294\pi\)
0.352610 + 0.935770i \(0.385294\pi\)
\(770\) 10.9497 32.8492i 0.394602 1.18380i
\(771\) 9.58579 0.345224
\(772\) 9.31371i 0.335208i
\(773\) 14.6569i 0.527170i 0.964636 + 0.263585i \(0.0849050\pi\)
−0.964636 + 0.263585i \(0.915095\pi\)
\(774\) 10.4853 0.376886
\(775\) 14.6274 + 10.9706i 0.525432 + 0.394074i
\(776\) 6.72792 0.241518
\(777\) 2.41421i 0.0866094i
\(778\) 22.9706i 0.823535i
\(779\) −14.3015 −0.512405
\(780\) −3.70711 + 11.1213i −0.132736 + 0.398207i
\(781\) 60.3848 2.16074
\(782\) 10.7574i 0.384682i
\(783\) 7.07107i 0.252699i
\(784\) 1.17157 0.0418419
\(785\) 0 0
\(786\) 1.89949 0.0677527
\(787\) 38.4853i 1.37185i 0.727671 + 0.685926i \(0.240603\pi\)
−0.727671 + 0.685926i \(0.759397\pi\)