Properties

Label 1110.2.u.b.401.1
Level $1110$
Weight $2$
Character 1110.401
Analytic conductor $8.863$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 401.1
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.b.191.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.41421 + 1.00000i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.70711 + 0.292893i) q^{6} +4.00000 q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.41421 + 1.00000i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.70711 + 0.292893i) q^{6} +4.00000 q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +1.00000 q^{10} -4.24264 q^{11} +(1.00000 - 1.41421i) q^{12} +(-1.00000 + 1.00000i) q^{13} +(-2.82843 + 2.82843i) q^{14} +(-0.292893 - 1.70711i) q^{15} -1.00000 q^{16} +(1.41421 + 1.41421i) q^{17} +(-2.70711 - 1.29289i) q^{18} +(-2.00000 + 2.00000i) q^{19} +(-0.707107 + 0.707107i) q^{20} +(5.65685 + 4.00000i) q^{21} +(3.00000 - 3.00000i) q^{22} +(4.24264 + 4.24264i) q^{23} +(0.292893 + 1.70711i) q^{24} +1.00000i q^{25} -1.41421i q^{26} +(-1.41421 + 5.00000i) q^{27} -4.00000i q^{28} +(1.41421 + 1.00000i) q^{30} +(5.00000 + 5.00000i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.00000 - 4.24264i) q^{33} -2.00000 q^{34} +(-2.82843 - 2.82843i) q^{35} +(2.82843 - 1.00000i) q^{36} +(6.00000 + 1.00000i) q^{37} -2.82843i q^{38} +(-2.41421 + 0.414214i) q^{39} -1.00000i q^{40} -5.65685 q^{41} +(-6.82843 + 1.17157i) q^{42} +(9.00000 - 9.00000i) q^{43} +4.24264i q^{44} +(1.29289 - 2.70711i) q^{45} -6.00000 q^{46} +1.41421i q^{47} +(-1.41421 - 1.00000i) q^{48} +9.00000 q^{49} +(-0.707107 - 0.707107i) q^{50} +(0.585786 + 3.41421i) q^{51} +(1.00000 + 1.00000i) q^{52} +2.82843i q^{53} +(-2.53553 - 4.53553i) q^{54} +(3.00000 + 3.00000i) q^{55} +(2.82843 + 2.82843i) q^{56} +(-4.82843 + 0.828427i) q^{57} +(2.82843 + 2.82843i) q^{59} +(-1.70711 + 0.292893i) q^{60} +(4.00000 + 4.00000i) q^{61} -7.07107 q^{62} +(4.00000 + 11.3137i) q^{63} +1.00000i q^{64} +1.41421 q^{65} +(7.24264 - 1.24264i) q^{66} -2.00000i q^{67} +(1.41421 - 1.41421i) q^{68} +(1.75736 + 10.2426i) q^{69} +4.00000 q^{70} -2.82843i q^{71} +(-1.29289 + 2.70711i) q^{72} +6.00000i q^{73} +(-4.94975 + 3.53553i) q^{74} +(-1.00000 + 1.41421i) q^{75} +(2.00000 + 2.00000i) q^{76} -16.9706 q^{77} +(1.41421 - 2.00000i) q^{78} +(-3.00000 + 3.00000i) q^{79} +(0.707107 + 0.707107i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(4.00000 - 4.00000i) q^{82} -2.82843i q^{83} +(4.00000 - 5.65685i) q^{84} -2.00000i q^{85} +12.7279i q^{86} +(-3.00000 - 3.00000i) q^{88} +(12.7279 - 12.7279i) q^{89} +(1.00000 + 2.82843i) q^{90} +(-4.00000 + 4.00000i) q^{91} +(4.24264 - 4.24264i) q^{92} +(2.07107 + 12.0711i) q^{93} +(-1.00000 - 1.00000i) q^{94} +2.82843 q^{95} +(1.70711 - 0.292893i) q^{96} +(-12.0000 + 12.0000i) q^{97} +(-6.36396 + 6.36396i) q^{98} +(-4.24264 - 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{6} + 16q^{7} + 4q^{9} + O(q^{10}) \) \( 4q - 4q^{6} + 16q^{7} + 4q^{9} + 4q^{10} + 4q^{12} - 4q^{13} - 4q^{15} - 4q^{16} - 8q^{18} - 8q^{19} + 12q^{22} + 4q^{24} + 20q^{31} - 24q^{33} - 8q^{34} + 24q^{37} - 4q^{39} - 16q^{42} + 36q^{43} + 8q^{45} - 24q^{46} + 36q^{49} + 8q^{51} + 4q^{52} + 4q^{54} + 12q^{55} - 8q^{57} - 4q^{60} + 16q^{61} + 16q^{63} + 12q^{66} + 24q^{69} + 16q^{70} - 8q^{72} - 4q^{75} + 8q^{76} - 12q^{79} - 28q^{81} + 16q^{82} + 16q^{84} - 12q^{88} + 4q^{90} - 16q^{91} - 20q^{93} - 4q^{94} + 4q^{96} - 48q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 1.41421 + 1.00000i 0.816497 + 0.577350i
\(4\) 1.00000i 0.500000i
\(5\) −0.707107 0.707107i −0.316228 0.316228i
\(6\) −1.70711 + 0.292893i −0.696923 + 0.119573i
\(7\) 4.00000 1.51186 0.755929 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.00000 + 2.82843i 0.333333 + 0.942809i
\(10\) 1.00000 0.316228
\(11\) −4.24264 −1.27920 −0.639602 0.768706i \(-0.720901\pi\)
−0.639602 + 0.768706i \(0.720901\pi\)
\(12\) 1.00000 1.41421i 0.288675 0.408248i
\(13\) −1.00000 + 1.00000i −0.277350 + 0.277350i −0.832050 0.554700i \(-0.812833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) −2.82843 + 2.82843i −0.755929 + 0.755929i
\(15\) −0.292893 1.70711i −0.0756247 0.440773i
\(16\) −1.00000 −0.250000
\(17\) 1.41421 + 1.41421i 0.342997 + 0.342997i 0.857493 0.514496i \(-0.172021\pi\)
−0.514496 + 0.857493i \(0.672021\pi\)
\(18\) −2.70711 1.29289i −0.638071 0.304738i
\(19\) −2.00000 + 2.00000i −0.458831 + 0.458831i −0.898272 0.439440i \(-0.855177\pi\)
0.439440 + 0.898272i \(0.355177\pi\)
\(20\) −0.707107 + 0.707107i −0.158114 + 0.158114i
\(21\) 5.65685 + 4.00000i 1.23443 + 0.872872i
\(22\) 3.00000 3.00000i 0.639602 0.639602i
\(23\) 4.24264 + 4.24264i 0.884652 + 0.884652i 0.994003 0.109351i \(-0.0348774\pi\)
−0.109351 + 0.994003i \(0.534877\pi\)
\(24\) 0.292893 + 1.70711i 0.0597866 + 0.348462i
\(25\) 1.00000i 0.200000i
\(26\) 1.41421i 0.277350i
\(27\) −1.41421 + 5.00000i −0.272166 + 0.962250i
\(28\) 4.00000i 0.755929i
\(29\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(30\) 1.41421 + 1.00000i 0.258199 + 0.182574i
\(31\) 5.00000 + 5.00000i 0.898027 + 0.898027i 0.995261 0.0972349i \(-0.0309998\pi\)
−0.0972349 + 0.995261i \(0.531000\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −6.00000 4.24264i −1.04447 0.738549i
\(34\) −2.00000 −0.342997
\(35\) −2.82843 2.82843i −0.478091 0.478091i
\(36\) 2.82843 1.00000i 0.471405 0.166667i
\(37\) 6.00000 + 1.00000i 0.986394 + 0.164399i
\(38\) 2.82843i 0.458831i
\(39\) −2.41421 + 0.414214i −0.386584 + 0.0663273i
\(40\) 1.00000i 0.158114i
\(41\) −5.65685 −0.883452 −0.441726 0.897150i \(-0.645634\pi\)
−0.441726 + 0.897150i \(0.645634\pi\)
\(42\) −6.82843 + 1.17157i −1.05365 + 0.180778i
\(43\) 9.00000 9.00000i 1.37249 1.37249i 0.515745 0.856742i \(-0.327515\pi\)
0.856742 0.515745i \(-0.172485\pi\)
\(44\) 4.24264i 0.639602i
\(45\) 1.29289 2.70711i 0.192733 0.403552i
\(46\) −6.00000 −0.884652
\(47\) 1.41421i 0.206284i 0.994667 + 0.103142i \(0.0328896\pi\)
−0.994667 + 0.103142i \(0.967110\pi\)
\(48\) −1.41421 1.00000i −0.204124 0.144338i
\(49\) 9.00000 1.28571
\(50\) −0.707107 0.707107i −0.100000 0.100000i
\(51\) 0.585786 + 3.41421i 0.0820265 + 0.478086i
\(52\) 1.00000 + 1.00000i 0.138675 + 0.138675i
\(53\) 2.82843i 0.388514i 0.980951 + 0.194257i \(0.0622296\pi\)
−0.980951 + 0.194257i \(0.937770\pi\)
\(54\) −2.53553 4.53553i −0.345042 0.617208i
\(55\) 3.00000 + 3.00000i 0.404520 + 0.404520i
\(56\) 2.82843 + 2.82843i 0.377964 + 0.377964i
\(57\) −4.82843 + 0.828427i −0.639541 + 0.109728i
\(58\) 0 0
\(59\) 2.82843 + 2.82843i 0.368230 + 0.368230i 0.866831 0.498601i \(-0.166153\pi\)
−0.498601 + 0.866831i \(0.666153\pi\)
\(60\) −1.70711 + 0.292893i −0.220387 + 0.0378124i
\(61\) 4.00000 + 4.00000i 0.512148 + 0.512148i 0.915184 0.403036i \(-0.132045\pi\)
−0.403036 + 0.915184i \(0.632045\pi\)
\(62\) −7.07107 −0.898027
\(63\) 4.00000 + 11.3137i 0.503953 + 1.42539i
\(64\) 1.00000i 0.125000i
\(65\) 1.41421 0.175412
\(66\) 7.24264 1.24264i 0.891507 0.152958i
\(67\) 2.00000i 0.244339i −0.992509 0.122169i \(-0.961015\pi\)
0.992509 0.122169i \(-0.0389851\pi\)
\(68\) 1.41421 1.41421i 0.171499 0.171499i
\(69\) 1.75736 + 10.2426i 0.211561 + 1.23307i
\(70\) 4.00000 0.478091
\(71\) 2.82843i 0.335673i −0.985815 0.167836i \(-0.946322\pi\)
0.985815 0.167836i \(-0.0536780\pi\)
\(72\) −1.29289 + 2.70711i −0.152369 + 0.319036i
\(73\) 6.00000i 0.702247i 0.936329 + 0.351123i \(0.114200\pi\)
−0.936329 + 0.351123i \(0.885800\pi\)
\(74\) −4.94975 + 3.53553i −0.575396 + 0.410997i
\(75\) −1.00000 + 1.41421i −0.115470 + 0.163299i
\(76\) 2.00000 + 2.00000i 0.229416 + 0.229416i
\(77\) −16.9706 −1.93398
\(78\) 1.41421 2.00000i 0.160128 0.226455i
\(79\) −3.00000 + 3.00000i −0.337526 + 0.337526i −0.855436 0.517909i \(-0.826710\pi\)
0.517909 + 0.855436i \(0.326710\pi\)
\(80\) 0.707107 + 0.707107i 0.0790569 + 0.0790569i
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 4.00000 4.00000i 0.441726 0.441726i
\(83\) 2.82843i 0.310460i −0.987878 0.155230i \(-0.950388\pi\)
0.987878 0.155230i \(-0.0496119\pi\)
\(84\) 4.00000 5.65685i 0.436436 0.617213i
\(85\) 2.00000i 0.216930i
\(86\) 12.7279i 1.37249i
\(87\) 0 0
\(88\) −3.00000 3.00000i −0.319801 0.319801i
\(89\) 12.7279 12.7279i 1.34916 1.34916i 0.462579 0.886578i \(-0.346924\pi\)
0.886578 0.462579i \(-0.153076\pi\)
\(90\) 1.00000 + 2.82843i 0.105409 + 0.298142i
\(91\) −4.00000 + 4.00000i −0.419314 + 0.419314i
\(92\) 4.24264 4.24264i 0.442326 0.442326i
\(93\) 2.07107 + 12.0711i 0.214760 + 1.25171i
\(94\) −1.00000 1.00000i −0.103142 0.103142i
\(95\) 2.82843 0.290191
\(96\) 1.70711 0.292893i 0.174231 0.0298933i
\(97\) −12.0000 + 12.0000i −1.21842 + 1.21842i −0.250229 + 0.968187i \(0.580506\pi\)
−0.968187 + 0.250229i \(0.919494\pi\)
\(98\) −6.36396 + 6.36396i −0.642857 + 0.642857i
\(99\) −4.24264 12.0000i −0.426401 1.20605i
\(100\) 1.00000 0.100000
\(101\) −15.5563 −1.54791 −0.773957 0.633238i \(-0.781726\pi\)
−0.773957 + 0.633238i \(0.781726\pi\)
\(102\) −2.82843 2.00000i −0.280056 0.198030i
\(103\) −10.0000 10.0000i −0.985329 0.985329i 0.0145647 0.999894i \(-0.495364\pi\)
−0.999894 + 0.0145647i \(0.995364\pi\)
\(104\) −1.41421 −0.138675
\(105\) −1.17157 6.82843i −0.114334 0.666386i
\(106\) −2.00000 2.00000i −0.194257 0.194257i
\(107\) 14.1421i 1.36717i −0.729870 0.683586i \(-0.760419\pi\)
0.729870 0.683586i \(-0.239581\pi\)
\(108\) 5.00000 + 1.41421i 0.481125 + 0.136083i
\(109\) 12.0000 12.0000i 1.14939 1.14939i 0.162719 0.986672i \(-0.447974\pi\)
0.986672 0.162719i \(-0.0520264\pi\)
\(110\) −4.24264 −0.404520
\(111\) 7.48528 + 7.41421i 0.710471 + 0.703726i
\(112\) −4.00000 −0.377964
\(113\) −4.24264 + 4.24264i −0.399114 + 0.399114i −0.877920 0.478806i \(-0.841070\pi\)
0.478806 + 0.877920i \(0.341070\pi\)
\(114\) 2.82843 4.00000i 0.264906 0.374634i
\(115\) 6.00000i 0.559503i
\(116\) 0 0
\(117\) −3.82843 1.82843i −0.353938 0.169038i
\(118\) −4.00000 −0.368230
\(119\) 5.65685 + 5.65685i 0.518563 + 0.518563i
\(120\) 1.00000 1.41421i 0.0912871 0.129099i
\(121\) 7.00000 0.636364
\(122\) −5.65685 −0.512148
\(123\) −8.00000 5.65685i −0.721336 0.510061i
\(124\) 5.00000 5.00000i 0.449013 0.449013i
\(125\) 0.707107 0.707107i 0.0632456 0.0632456i
\(126\) −10.8284 5.17157i −0.964673 0.460720i
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 21.7279 3.72792i 1.91304 0.328225i
\(130\) −1.00000 + 1.00000i −0.0877058 + 0.0877058i
\(131\) −8.48528 + 8.48528i −0.741362 + 0.741362i −0.972840 0.231478i \(-0.925644\pi\)
0.231478 + 0.972840i \(0.425644\pi\)
\(132\) −4.24264 + 6.00000i −0.369274 + 0.522233i
\(133\) −8.00000 + 8.00000i −0.693688 + 0.693688i
\(134\) 1.41421 + 1.41421i 0.122169 + 0.122169i
\(135\) 4.53553 2.53553i 0.390357 0.218224i
\(136\) 2.00000i 0.171499i
\(137\) 9.89949i 0.845771i 0.906183 + 0.422885i \(0.138983\pi\)
−0.906183 + 0.422885i \(0.861017\pi\)
\(138\) −8.48528 6.00000i −0.722315 0.510754i
\(139\) 16.0000i 1.35710i −0.734553 0.678551i \(-0.762608\pi\)
0.734553 0.678551i \(-0.237392\pi\)
\(140\) −2.82843 + 2.82843i −0.239046 + 0.239046i
\(141\) −1.41421 + 2.00000i −0.119098 + 0.168430i
\(142\) 2.00000 + 2.00000i 0.167836 + 0.167836i
\(143\) 4.24264 4.24264i 0.354787 0.354787i
\(144\) −1.00000 2.82843i −0.0833333 0.235702i
\(145\) 0 0
\(146\) −4.24264 4.24264i −0.351123 0.351123i
\(147\) 12.7279 + 9.00000i 1.04978 + 0.742307i
\(148\) 1.00000 6.00000i 0.0821995 0.493197i
\(149\) 9.89949i 0.810998i −0.914095 0.405499i \(-0.867098\pi\)
0.914095 0.405499i \(-0.132902\pi\)
\(150\) −0.292893 1.70711i −0.0239146 0.139385i
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) −2.82843 −0.229416
\(153\) −2.58579 + 5.41421i −0.209048 + 0.437713i
\(154\) 12.0000 12.0000i 0.966988 0.966988i
\(155\) 7.07107i 0.567962i
\(156\) 0.414214 + 2.41421i 0.0331636 + 0.193292i
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 4.24264i 0.337526i
\(159\) −2.82843 + 4.00000i −0.224309 + 0.317221i
\(160\) −1.00000 −0.0790569
\(161\) 16.9706 + 16.9706i 1.33747 + 1.33747i
\(162\) 0.949747 8.94975i 0.0746192 0.703159i
\(163\) −5.00000 5.00000i −0.391630 0.391630i 0.483638 0.875268i \(-0.339315\pi\)
−0.875268 + 0.483638i \(0.839315\pi\)
\(164\) 5.65685i 0.441726i
\(165\) 1.24264 + 7.24264i 0.0967394 + 0.563839i
\(166\) 2.00000 + 2.00000i 0.155230 + 0.155230i
\(167\) 12.7279 + 12.7279i 0.984916 + 0.984916i 0.999888 0.0149717i \(-0.00476583\pi\)
−0.0149717 + 0.999888i \(0.504766\pi\)
\(168\) 1.17157 + 6.82843i 0.0903888 + 0.526825i
\(169\) 11.0000i 0.846154i
\(170\) 1.41421 + 1.41421i 0.108465 + 0.108465i
\(171\) −7.65685 3.65685i −0.585534 0.279647i
\(172\) −9.00000 9.00000i −0.686244 0.686244i
\(173\) 2.82843 0.215041 0.107521 0.994203i \(-0.465709\pi\)
0.107521 + 0.994203i \(0.465709\pi\)
\(174\) 0 0
\(175\) 4.00000i 0.302372i
\(176\) 4.24264 0.319801
\(177\) 1.17157 + 6.82843i 0.0880608 + 0.513256i
\(178\) 18.0000i 1.34916i
\(179\) 12.7279 12.7279i 0.951330 0.951330i −0.0475398 0.998869i \(-0.515138\pi\)
0.998869 + 0.0475398i \(0.0151381\pi\)
\(180\) −2.70711 1.29289i −0.201776 0.0963666i
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) 5.65685i 0.419314i
\(183\) 1.65685 + 9.65685i 0.122478 + 0.713855i
\(184\) 6.00000i 0.442326i
\(185\) −3.53553 4.94975i −0.259938 0.363913i
\(186\) −10.0000 7.07107i −0.733236 0.518476i
\(187\) −6.00000 6.00000i −0.438763 0.438763i
\(188\) 1.41421 0.103142
\(189\) −5.65685 + 20.0000i −0.411476 + 1.45479i
\(190\) −2.00000 + 2.00000i −0.145095 + 0.145095i
\(191\) −2.82843 2.82843i −0.204658 0.204658i 0.597334 0.801992i \(-0.296227\pi\)
−0.801992 + 0.597334i \(0.796227\pi\)
\(192\) −1.00000 + 1.41421i −0.0721688 + 0.102062i
\(193\) 18.0000 18.0000i 1.29567 1.29567i 0.364442 0.931226i \(-0.381260\pi\)
0.931226 0.364442i \(-0.118740\pi\)
\(194\) 16.9706i 1.21842i
\(195\) 2.00000 + 1.41421i 0.143223 + 0.101274i
\(196\) 9.00000i 0.642857i
\(197\) 19.7990i 1.41062i −0.708899 0.705310i \(-0.750808\pi\)
0.708899 0.705310i \(-0.249192\pi\)
\(198\) 11.4853 + 5.48528i 0.816223 + 0.389822i
\(199\) −3.00000 3.00000i −0.212664 0.212664i 0.592734 0.805398i \(-0.298049\pi\)
−0.805398 + 0.592734i \(0.798049\pi\)
\(200\) −0.707107 + 0.707107i −0.0500000 + 0.0500000i
\(201\) 2.00000 2.82843i 0.141069 0.199502i
\(202\) 11.0000 11.0000i 0.773957 0.773957i
\(203\) 0 0
\(204\) 3.41421 0.585786i 0.239043 0.0410133i
\(205\) 4.00000 + 4.00000i 0.279372 + 0.279372i
\(206\) 14.1421 0.985329
\(207\) −7.75736 + 16.2426i −0.539174 + 1.12894i
\(208\) 1.00000 1.00000i 0.0693375 0.0693375i
\(209\) 8.48528 8.48528i 0.586939 0.586939i
\(210\) 5.65685 + 4.00000i 0.390360 + 0.276026i
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 2.82843 0.194257
\(213\) 2.82843 4.00000i 0.193801 0.274075i
\(214\) 10.0000 + 10.0000i 0.683586 + 0.683586i
\(215\) −12.7279 −0.868037
\(216\) −4.53553 + 2.53553i −0.308604 + 0.172521i
\(217\) 20.0000 + 20.0000i 1.35769 + 1.35769i
\(218\) 16.9706i 1.14939i
\(219\) −6.00000 + 8.48528i −0.405442 + 0.573382i
\(220\) 3.00000 3.00000i 0.202260 0.202260i
\(221\) −2.82843 −0.190261
\(222\) −10.5355 + 0.0502525i −0.707099 + 0.00337273i
\(223\) −12.0000 −0.803579 −0.401790 0.915732i \(-0.631612\pi\)
−0.401790 + 0.915732i \(0.631612\pi\)
\(224\) 2.82843 2.82843i 0.188982 0.188982i
\(225\) −2.82843 + 1.00000i −0.188562 + 0.0666667i
\(226\) 6.00000i 0.399114i
\(227\) 19.7990 + 19.7990i 1.31411 + 1.31411i 0.918361 + 0.395744i \(0.129513\pi\)
0.395744 + 0.918361i \(0.370487\pi\)
\(228\) 0.828427 + 4.82843i 0.0548639 + 0.319770i
\(229\) 26.0000 1.71813 0.859064 0.511868i \(-0.171046\pi\)
0.859064 + 0.511868i \(0.171046\pi\)
\(230\) 4.24264 + 4.24264i 0.279751 + 0.279751i
\(231\) −24.0000 16.9706i −1.57908 1.11658i
\(232\) 0 0
\(233\) 7.07107 0.463241 0.231621 0.972806i \(-0.425597\pi\)
0.231621 + 0.972806i \(0.425597\pi\)
\(234\) 4.00000 1.41421i 0.261488 0.0924500i
\(235\) 1.00000 1.00000i 0.0652328 0.0652328i
\(236\) 2.82843 2.82843i 0.184115 0.184115i
\(237\) −7.24264 + 1.24264i −0.470460 + 0.0807182i
\(238\) −8.00000 −0.518563
\(239\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(240\) 0.292893 + 1.70711i 0.0189062 + 0.110193i
\(241\) 3.00000 3.00000i 0.193247 0.193247i −0.603851 0.797098i \(-0.706368\pi\)
0.797098 + 0.603851i \(0.206368\pi\)
\(242\) −4.94975 + 4.94975i −0.318182 + 0.318182i
\(243\) −15.5563 + 1.00000i −0.997940 + 0.0641500i
\(244\) 4.00000 4.00000i 0.256074 0.256074i
\(245\) −6.36396 6.36396i −0.406579 0.406579i
\(246\) 9.65685 1.65685i 0.615699 0.105637i
\(247\) 4.00000i 0.254514i
\(248\) 7.07107i 0.449013i
\(249\) 2.82843 4.00000i 0.179244 0.253490i
\(250\) 1.00000i 0.0632456i
\(251\) 2.82843 2.82843i 0.178529 0.178529i −0.612185 0.790714i \(-0.709709\pi\)
0.790714 + 0.612185i \(0.209709\pi\)
\(252\) 11.3137 4.00000i 0.712697 0.251976i
\(253\) −18.0000 18.0000i −1.13165 1.13165i
\(254\) 8.48528 8.48528i 0.532414 0.532414i
\(255\) 2.00000 2.82843i 0.125245 0.177123i
\(256\) 1.00000 0.0625000
\(257\) −2.82843 2.82843i −0.176432 0.176432i 0.613366 0.789799i \(-0.289815\pi\)
−0.789799 + 0.613366i \(0.789815\pi\)
\(258\) −12.7279 + 18.0000i −0.792406 + 1.12063i
\(259\) 24.0000 + 4.00000i 1.49129 + 0.248548i
\(260\) 1.41421i 0.0877058i
\(261\) 0 0
\(262\) 12.0000i 0.741362i
\(263\) 26.8701 1.65688 0.828439 0.560079i \(-0.189229\pi\)
0.828439 + 0.560079i \(0.189229\pi\)
\(264\) −1.24264 7.24264i −0.0764792 0.445754i
\(265\) 2.00000 2.00000i 0.122859 0.122859i
\(266\) 11.3137i 0.693688i
\(267\) 30.7279 5.27208i 1.88052 0.322646i
\(268\) −2.00000 −0.122169
\(269\) 21.2132i 1.29339i −0.762748 0.646696i \(-0.776150\pi\)
0.762748 0.646696i \(-0.223850\pi\)
\(270\) −1.41421 + 5.00000i −0.0860663 + 0.304290i
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) −1.41421 1.41421i −0.0857493 0.0857493i
\(273\) −9.65685 + 1.65685i −0.584459 + 0.100277i
\(274\) −7.00000 7.00000i −0.422885 0.422885i
\(275\) 4.24264i 0.255841i
\(276\) 10.2426 1.75736i 0.616535 0.105781i
\(277\) −15.0000 15.0000i −0.901263 0.901263i 0.0942828 0.995545i \(-0.469944\pi\)
−0.995545 + 0.0942828i \(0.969944\pi\)
\(278\) 11.3137 + 11.3137i 0.678551 + 0.678551i
\(279\) −9.14214 + 19.1421i −0.547325 + 1.14601i
\(280\) 4.00000i 0.239046i
\(281\) 7.07107 + 7.07107i 0.421825 + 0.421825i 0.885832 0.464007i \(-0.153589\pi\)
−0.464007 + 0.885832i \(0.653589\pi\)
\(282\) −0.414214 2.41421i −0.0246661 0.143764i
\(283\) −15.0000 15.0000i −0.891657 0.891657i 0.103022 0.994679i \(-0.467149\pi\)
−0.994679 + 0.103022i \(0.967149\pi\)
\(284\) −2.82843 −0.167836
\(285\) 4.00000 + 2.82843i 0.236940 + 0.167542i
\(286\) 6.00000i 0.354787i
\(287\) −22.6274 −1.33565
\(288\) 2.70711 + 1.29289i 0.159518 + 0.0761845i
\(289\) 13.0000i 0.764706i
\(290\) 0 0
\(291\) −28.9706 + 4.97056i −1.69828 + 0.291380i
\(292\) 6.00000 0.351123
\(293\) 28.2843i 1.65238i −0.563388 0.826192i \(-0.690502\pi\)
0.563388 0.826192i \(-0.309498\pi\)
\(294\) −15.3640 + 2.63604i −0.896044 + 0.153737i
\(295\) 4.00000i 0.232889i
\(296\) 3.53553 + 4.94975i 0.205499 + 0.287698i
\(297\) 6.00000 21.2132i 0.348155 1.23091i
\(298\) 7.00000 + 7.00000i 0.405499 + 0.405499i
\(299\) −8.48528 −0.490716
\(300\) 1.41421 + 1.00000i 0.0816497 + 0.0577350i
\(301\) 36.0000 36.0000i 2.07501 2.07501i
\(302\) 0 0
\(303\) −22.0000 15.5563i −1.26387 0.893689i
\(304\) 2.00000 2.00000i 0.114708 0.114708i
\(305\) 5.65685i 0.323911i
\(306\) −2.00000 5.65685i −0.114332 0.323381i
\(307\) 4.00000i 0.228292i 0.993464 + 0.114146i \(0.0364132\pi\)
−0.993464 + 0.114146i \(0.963587\pi\)
\(308\) 16.9706i 0.966988i
\(309\) −4.14214 24.1421i −0.235638 1.37340i
\(310\) 5.00000 + 5.00000i 0.283981 + 0.283981i
\(311\) 8.48528 8.48528i 0.481156 0.481156i −0.424345 0.905501i \(-0.639495\pi\)
0.905501 + 0.424345i \(0.139495\pi\)
\(312\) −2.00000 1.41421i −0.113228 0.0800641i
\(313\) 6.00000 6.00000i 0.339140 0.339140i −0.516904 0.856044i \(-0.672915\pi\)
0.856044 + 0.516904i \(0.172915\pi\)
\(314\) 12.7279 12.7279i 0.718278 0.718278i
\(315\) 5.17157 10.8284i 0.291385 0.610113i
\(316\) 3.00000 + 3.00000i 0.168763 + 0.168763i
\(317\) −8.48528 −0.476581 −0.238290 0.971194i \(-0.576587\pi\)
−0.238290 + 0.971194i \(0.576587\pi\)
\(318\) −0.828427 4.82843i −0.0464559 0.270765i
\(319\) 0 0
\(320\) 0.707107 0.707107i 0.0395285 0.0395285i
\(321\) 14.1421 20.0000i 0.789337 1.11629i
\(322\) −24.0000 −1.33747
\(323\) −5.65685 −0.314756
\(324\) 5.65685 + 7.00000i 0.314270 + 0.388889i
\(325\) −1.00000 1.00000i −0.0554700 0.0554700i
\(326\) 7.07107 0.391630
\(327\) 28.9706 4.97056i 1.60208 0.274873i
\(328\) −4.00000 4.00000i −0.220863 0.220863i
\(329\) 5.65685i 0.311872i
\(330\) −6.00000 4.24264i −0.330289 0.233550i
\(331\) −4.00000 + 4.00000i −0.219860 + 0.219860i −0.808439 0.588579i \(-0.799687\pi\)
0.588579 + 0.808439i \(0.299687\pi\)
\(332\) −2.82843 −0.155230
\(333\) 3.17157 + 17.9706i 0.173801 + 0.984781i
\(334\) −18.0000 −0.984916
\(335\) −1.41421 + 1.41421i −0.0772667 + 0.0772667i
\(336\) −5.65685 4.00000i −0.308607 0.218218i
\(337\) 2.00000i 0.108947i 0.998515 + 0.0544735i \(0.0173480\pi\)
−0.998515 + 0.0544735i \(0.982652\pi\)
\(338\) −7.77817 7.77817i −0.423077 0.423077i
\(339\) −10.2426 + 1.75736i −0.556304 + 0.0954467i
\(340\) −2.00000 −0.108465
\(341\) −21.2132 21.2132i −1.14876 1.14876i
\(342\) 8.00000 2.82843i 0.432590 0.152944i
\(343\) 8.00000 0.431959
\(344\) 12.7279 0.686244
\(345\) 6.00000 8.48528i 0.323029 0.456832i
\(346\) −2.00000 + 2.00000i −0.107521 + 0.107521i
\(347\) −8.48528 + 8.48528i −0.455514 + 0.455514i −0.897180 0.441666i \(-0.854388\pi\)
0.441666 + 0.897180i \(0.354388\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) −2.82843 2.82843i −0.151186 0.151186i
\(351\) −3.58579 6.41421i −0.191395 0.342365i
\(352\) −3.00000 + 3.00000i −0.159901 + 0.159901i
\(353\) 24.0416 24.0416i 1.27961 1.27961i 0.338719 0.940887i \(-0.390006\pi\)
0.940887 0.338719i \(-0.109994\pi\)
\(354\) −5.65685 4.00000i −0.300658 0.212598i
\(355\) −2.00000 + 2.00000i −0.106149 + 0.106149i
\(356\) −12.7279 12.7279i −0.674579 0.674579i
\(357\) 2.34315 + 13.6569i 0.124012 + 0.722797i
\(358\) 18.0000i 0.951330i
\(359\) 11.3137i 0.597115i 0.954392 + 0.298557i \(0.0965054\pi\)
−0.954392 + 0.298557i \(0.903495\pi\)
\(360\) 2.82843 1.00000i 0.149071 0.0527046i
\(361\) 11.0000i 0.578947i
\(362\) −4.24264 + 4.24264i −0.222988 + 0.222988i
\(363\) 9.89949 + 7.00000i 0.519589 + 0.367405i
\(364\) 4.00000 + 4.00000i 0.209657 + 0.209657i
\(365\) 4.24264 4.24264i 0.222070 0.222070i
\(366\) −8.00000 5.65685i −0.418167 0.295689i
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) −4.24264 4.24264i −0.221163 0.221163i
\(369\) −5.65685 16.0000i −0.294484 0.832927i
\(370\) 6.00000 + 1.00000i 0.311925 + 0.0519875i
\(371\) 11.3137i 0.587378i
\(372\) 12.0711 2.07107i 0.625856 0.107380i
\(373\) 34.0000i 1.76045i 0.474554 + 0.880227i \(0.342610\pi\)
−0.474554 + 0.880227i \(0.657390\pi\)
\(374\) 8.48528 0.438763
\(375\) 1.70711 0.292893i 0.0881546 0.0151249i
\(376\) −1.00000 + 1.00000i −0.0515711 + 0.0515711i
\(377\) 0 0
\(378\) −10.1421 18.1421i −0.521655 0.933131i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 2.82843i 0.145095i
\(381\) −16.9706 12.0000i −0.869428 0.614779i
\(382\) 4.00000 0.204658
\(383\) −11.3137 11.3137i −0.578103 0.578103i 0.356277 0.934380i \(-0.384046\pi\)
−0.934380 + 0.356277i \(0.884046\pi\)
\(384\) −0.292893 1.70711i −0.0149466 0.0871154i
\(385\) 12.0000 + 12.0000i 0.611577 + 0.611577i
\(386\) 25.4558i 1.29567i
\(387\) 34.4558 + 16.4558i 1.75149 + 0.836498i
\(388\) 12.0000 + 12.0000i 0.609208 + 0.609208i
\(389\) 8.48528 + 8.48528i 0.430221 + 0.430221i 0.888703 0.458483i \(-0.151607\pi\)
−0.458483 + 0.888703i \(0.651607\pi\)
\(390\) −2.41421 + 0.414214i −0.122248 + 0.0209745i
\(391\) 12.0000i 0.606866i
\(392\) 6.36396 + 6.36396i 0.321429 + 0.321429i
\(393\) −20.4853 + 3.51472i −1.03335 + 0.177294i
\(394\) 14.0000 + 14.0000i 0.705310 + 0.705310i
\(395\) 4.24264 0.213470
\(396\) −12.0000 + 4.24264i −0.603023 + 0.213201i
\(397\) 18.0000i 0.903394i −0.892171 0.451697i \(-0.850819\pi\)
0.892171 0.451697i \(-0.149181\pi\)
\(398\) 4.24264 0.212664
\(399\) −19.3137 + 3.31371i −0.966895 + 0.165893i
\(400\) 1.00000i 0.0500000i
\(401\) 15.5563 15.5563i 0.776847 0.776847i −0.202446 0.979293i \(-0.564889\pi\)
0.979293 + 0.202446i \(0.0648892\pi\)
\(402\) 0.585786 + 3.41421i 0.0292164 + 0.170285i
\(403\) −10.0000 −0.498135
\(404\) 15.5563i 0.773957i
\(405\) 8.94975 + 0.949747i 0.444717 + 0.0471933i
\(406\) 0 0
\(407\) −25.4558 4.24264i −1.26180 0.210300i
\(408\) −2.00000 + 2.82843i −0.0990148 + 0.140028i
\(409\) 9.00000 + 9.00000i 0.445021 + 0.445021i 0.893695 0.448674i \(-0.148104\pi\)
−0.448674 + 0.893695i \(0.648104\pi\)
\(410\) −5.65685 −0.279372
\(411\) −9.89949 + 14.0000i −0.488306 + 0.690569i
\(412\) −10.0000 + 10.0000i −0.492665 + 0.492665i
\(413\) 11.3137 + 11.3137i 0.556711 + 0.556711i
\(414\) −6.00000 16.9706i −0.294884 0.834058i
\(415\) −2.00000 + 2.00000i −0.0981761 + 0.0981761i
\(416\) 1.41421i 0.0693375i
\(417\) 16.0000 22.6274i 0.783523 1.10807i
\(418\) 12.0000i 0.586939i
\(419\) 12.7279i 0.621800i 0.950443 + 0.310900i \(0.100630\pi\)
−0.950443 + 0.310900i \(0.899370\pi\)
\(420\) −6.82843 + 1.17157i −0.333193 + 0.0571669i
\(421\) −14.0000 14.0000i −0.682318 0.682318i 0.278204 0.960522i \(-0.410261\pi\)
−0.960522 + 0.278204i \(0.910261\pi\)
\(422\) 11.3137 11.3137i 0.550743 0.550743i
\(423\) −4.00000 + 1.41421i −0.194487 + 0.0687614i
\(424\) −2.00000 + 2.00000i −0.0971286 + 0.0971286i
\(425\) −1.41421 + 1.41421i −0.0685994 + 0.0685994i
\(426\) 0.828427 + 4.82843i 0.0401374 + 0.233938i
\(427\) 16.0000 + 16.0000i 0.774294 + 0.774294i
\(428\) −14.1421 −0.683586
\(429\) 10.2426 1.75736i 0.494519 0.0848461i
\(430\) 9.00000 9.00000i 0.434019 0.434019i
\(431\) −8.48528 + 8.48528i −0.408722 + 0.408722i −0.881293 0.472571i \(-0.843326\pi\)
0.472571 + 0.881293i \(0.343326\pi\)
\(432\) 1.41421 5.00000i 0.0680414 0.240563i
\(433\) −6.00000 −0.288342 −0.144171 0.989553i \(-0.546051\pi\)
−0.144171 + 0.989553i \(0.546051\pi\)
\(434\) −28.2843 −1.35769
\(435\) 0 0
\(436\) −12.0000 12.0000i −0.574696 0.574696i
\(437\) −16.9706 −0.811812
\(438\) −1.75736 10.2426i −0.0839699 0.489412i
\(439\) 5.00000 + 5.00000i 0.238637 + 0.238637i 0.816286 0.577649i \(-0.196030\pi\)
−0.577649 + 0.816286i \(0.696030\pi\)
\(440\) 4.24264i 0.202260i
\(441\) 9.00000 + 25.4558i 0.428571 + 1.21218i
\(442\) 2.00000 2.00000i 0.0951303 0.0951303i
\(443\) −2.82843 −0.134383 −0.0671913 0.997740i \(-0.521404\pi\)
−0.0671913 + 0.997740i \(0.521404\pi\)
\(444\) 7.41421 7.48528i 0.351863 0.355236i
\(445\) −18.0000 −0.853282
\(446\) 8.48528 8.48528i 0.401790 0.401790i
\(447\) 9.89949 14.0000i 0.468230 0.662177i
\(448\) 4.00000i 0.188982i
\(449\) 12.7279 + 12.7279i 0.600668 + 0.600668i 0.940490 0.339822i \(-0.110367\pi\)
−0.339822 + 0.940490i \(0.610367\pi\)
\(450\) 1.29289 2.70711i 0.0609476 0.127614i
\(451\) 24.0000 1.13012
\(452\) 4.24264 + 4.24264i 0.199557 + 0.199557i
\(453\) 0 0
\(454\) −28.0000 −1.31411
\(455\) 5.65685 0.265197
\(456\) −4.00000 2.82843i −0.187317 0.132453i
\(457\) −12.0000 + 12.0000i −0.561336 + 0.561336i −0.929687 0.368351i \(-0.879923\pi\)
0.368351 + 0.929687i \(0.379923\pi\)
\(458\) −18.3848 + 18.3848i −0.859064 + 0.859064i
\(459\) −9.07107 + 5.07107i −0.423401 + 0.236697i
\(460\) −6.00000 −0.279751
\(461\) 24.0416 + 24.0416i 1.11973 + 1.11973i 0.991781 + 0.127950i \(0.0408396\pi\)
0.127950 + 0.991781i \(0.459160\pi\)
\(462\) 28.9706 4.97056i 1.34783 0.231252i
\(463\) −22.0000 + 22.0000i −1.02243 + 1.02243i −0.0226840 + 0.999743i \(0.507221\pi\)
−0.999743 + 0.0226840i \(0.992779\pi\)
\(464\) 0 0
\(465\) 7.07107 10.0000i 0.327913 0.463739i
\(466\) −5.00000 + 5.00000i −0.231621 + 0.231621i
\(467\) −8.48528 8.48528i −0.392652 0.392652i 0.482980 0.875632i \(-0.339555\pi\)
−0.875632 + 0.482980i \(0.839555\pi\)
\(468\) −1.82843 + 3.82843i −0.0845191 + 0.176969i
\(469\) 8.00000i 0.369406i
\(470\) 1.41421i 0.0652328i
\(471\) −25.4558 18.0000i −1.17294 0.829396i
\(472\) 4.00000i 0.184115i
\(473\) −38.1838 + 38.1838i −1.75569 + 1.75569i
\(474\) 4.24264 6.00000i 0.194871 0.275589i
\(475\) −2.00000 2.00000i −0.0917663 0.0917663i
\(476\) 5.65685 5.65685i 0.259281 0.259281i
\(477\) −8.00000 + 2.82843i −0.366295 + 0.129505i
\(478\) 0 0
\(479\) −25.4558 25.4558i −1.16311 1.16311i −0.983792 0.179316i \(-0.942612\pi\)
−0.179316 0.983792i \(-0.557388\pi\)
\(480\) −1.41421 1.00000i −0.0645497 0.0456435i
\(481\) −7.00000 + 5.00000i −0.319173 + 0.227980i
\(482\) 4.24264i 0.193247i
\(483\) 7.02944 + 40.9706i 0.319850 + 1.86423i
\(484\) 7.00000i 0.318182i
\(485\) 16.9706 0.770594
\(486\) 10.2929 11.7071i 0.466895 0.531045i
\(487\) 22.0000 22.0000i 0.996915 0.996915i −0.00308010 0.999995i \(-0.500980\pi\)
0.999995 + 0.00308010i \(0.000980427\pi\)
\(488\) 5.65685i 0.256074i
\(489\) −2.07107 12.0711i −0.0936569 0.545873i
\(490\) 9.00000 0.406579
\(491\) 21.2132i 0.957338i 0.877995 + 0.478669i \(0.158881\pi\)
−0.877995 + 0.478669i \(0.841119\pi\)
\(492\) −5.65685 + 8.00000i −0.255031 + 0.360668i
\(493\) 0 0
\(494\) 2.82843 + 2.82843i 0.127257 + 0.127257i
\(495\) −5.48528 + 11.4853i −0.246545 + 0.516225i
\(496\) −5.00000 5.00000i −0.224507 0.224507i
\(497\) 11.3137i 0.507489i
\(498\) 0.828427 + 4.82843i 0.0371227 + 0.216367i
\(499\) −12.0000 12.0000i −0.537194 0.537194i 0.385510 0.922704i \(-0.374026\pi\)
−0.922704 + 0.385510i \(0.874026\pi\)
\(500\) −0.707107 0.707107i −0.0316228 0.0316228i
\(501\) 5.27208 + 30.7279i 0.235539 + 1.37282i
\(502\) 4.00000i 0.178529i
\(503\) 21.2132 + 21.2132i 0.945850 + 0.945850i 0.998607 0.0527574i \(-0.0168010\pi\)
−0.0527574 + 0.998607i \(0.516801\pi\)
\(504\) −5.17157 + 10.8284i −0.230360 + 0.482336i
\(505\) 11.0000 + 11.0000i 0.489494 + 0.489494i
\(506\) 25.4558 1.13165
\(507\) −11.0000 + 15.5563i −0.488527 + 0.690882i
\(508\) 12.0000i 0.532414i
\(509\) 24.0416 1.06563 0.532813 0.846233i \(-0.321135\pi\)
0.532813 + 0.846233i \(0.321135\pi\)
\(510\) 0.585786 + 3.41421i 0.0259391 + 0.151184i
\(511\) 24.0000i 1.06170i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −7.17157 12.8284i −0.316633 0.566389i
\(514\) 4.00000 0.176432
\(515\) 14.1421i 0.623177i
\(516\) −3.72792 21.7279i −0.164113 0.956518i
\(517\) 6.00000i 0.263880i
\(518\) −19.7990 + 14.1421i −0.869918 + 0.621370i
\(519\) 4.00000 + 2.82843i 0.175581 + 0.124154i
\(520\) 1.00000 + 1.00000i 0.0438529 + 0.0438529i
\(521\) −8.48528 −0.371747 −0.185873 0.982574i \(-0.559511\pi\)
−0.185873 + 0.982574i \(0.559511\pi\)
\(522\) 0 0
\(523\) −9.00000 + 9.00000i −0.393543 + 0.393543i −0.875948 0.482405i \(-0.839763\pi\)
0.482405 + 0.875948i \(0.339763\pi\)
\(524\) 8.48528 + 8.48528i 0.370681 + 0.370681i
\(525\) −4.00000 + 5.65685i −0.174574 + 0.246885i
\(526\) −19.0000 + 19.0000i −0.828439 + 0.828439i
\(527\) 14.1421i 0.616041i
\(528\) 6.00000 + 4.24264i 0.261116 + 0.184637i
\(529\) 13.0000i 0.565217i
\(530\) 2.82843i 0.122859i
\(531\) −5.17157 + 10.8284i −0.224427 + 0.469914i
\(532\) 8.00000 + 8.00000i 0.346844 + 0.346844i
\(533\) 5.65685 5.65685i 0.245026 0.245026i
\(534\) −18.0000 + 25.4558i −0.778936 + 1.10158i
\(535\) −10.0000 + 10.0000i −0.432338 + 0.432338i
\(536\) 1.41421 1.41421i 0.0610847 0.0610847i
\(537\) 30.7279 5.27208i 1.32601 0.227507i
\(538\) 15.0000 + 15.0000i 0.646696 + 0.646696i
\(539\) −38.1838 −1.64469
\(540\) −2.53553 4.53553i −0.109112 0.195178i
\(541\) 2.00000 2.00000i 0.0859867 0.0859867i −0.662805 0.748792i \(-0.730634\pi\)
0.748792 + 0.662805i \(0.230634\pi\)
\(542\) 5.65685 5.65685i 0.242983 0.242983i
\(543\) 8.48528 + 6.00000i 0.364138 + 0.257485i
\(544\) 2.00000 0.0857493
\(545\) −16.9706 −0.726939
\(546\) 5.65685 8.00000i 0.242091 0.342368i
\(547\) −21.0000 21.0000i −0.897895 0.897895i 0.0973546 0.995250i \(-0.468962\pi\)
−0.995250 + 0.0973546i \(0.968962\pi\)
\(548\) 9.89949 0.422885
\(549\) −7.31371 + 15.3137i −0.312141 + 0.653573i
\(550\) 3.00000 + 3.00000i 0.127920 + 0.127920i
\(551\) 0 0
\(552\) −6.00000 + 8.48528i −0.255377 + 0.361158i
\(553\) −12.0000 + 12.0000i −0.510292 + 0.510292i
\(554\) 21.2132 0.901263
\(555\) −0.0502525 10.5355i −0.00213310 0.447209i
\(556\) −16.0000 −0.678551
\(557\) 24.0416 24.0416i 1.01868 1.01868i 0.0188543 0.999822i \(-0.493998\pi\)
0.999822 0.0188543i \(-0.00600188\pi\)
\(558\) −7.07107 20.0000i −0.299342 0.846668i
\(559\) 18.0000i 0.761319i
\(560\) 2.82843 + 2.82843i 0.119523 + 0.119523i
\(561\) −2.48528 14.4853i −0.104929 0.611569i
\(562\) −10.0000 −0.421825
\(563\) −5.65685 5.65685i −0.238408 0.238408i 0.577783 0.816191i \(-0.303918\pi\)
−0.816191 + 0.577783i \(0.803918\pi\)
\(564\) 2.00000 + 1.41421i 0.0842152 + 0.0595491i
\(565\) 6.00000 0.252422
\(566\) 21.2132 0.891657
\(567\) −28.0000 + 22.6274i −1.17589 + 0.950262i
\(568\) 2.00000 2.00000i 0.0839181 0.0839181i
\(569\) −18.3848 + 18.3848i −0.770730 + 0.770730i −0.978234 0.207504i \(-0.933466\pi\)
0.207504 + 0.978234i \(0.433466\pi\)
\(570\) −4.82843 + 0.828427i −0.202241 + 0.0346990i
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) −4.24264 4.24264i −0.177394 0.177394i
\(573\) −1.17157 6.82843i −0.0489432 0.285262i
\(574\) 16.0000 16.0000i 0.667827 0.667827i
\(575\) −4.24264 + 4.24264i −0.176930 + 0.176930i
\(576\) −2.82843 + 1.00000i −0.117851 + 0.0416667i
\(577\) 20.0000 20.0000i 0.832611 0.832611i −0.155262 0.987873i \(-0.549622\pi\)
0.987873 + 0.155262i \(0.0496223\pi\)
\(578\) 9.19239 + 9.19239i 0.382353 + 0.382353i
\(579\) 43.4558 7.45584i 1.80596 0.309854i
\(580\) 0 0
\(581\) 11.3137i 0.469372i
\(582\) 16.9706 24.0000i 0.703452 0.994832i
\(583\) 12.0000i 0.496989i
\(584\) −4.24264 + 4.24264i −0.175562 + 0.175562i
\(585\) 1.41421 + 4.00000i 0.0584705 + 0.165380i
\(586\) 20.0000 + 20.0000i 0.826192 + 0.826192i
\(587\) −16.9706 + 16.9706i −0.700450 + 0.700450i −0.964507 0.264057i \(-0.914939\pi\)
0.264057 + 0.964507i \(0.414939\pi\)
\(588\) 9.00000 12.7279i 0.371154 0.524891i
\(589\) −20.0000 −0.824086
\(590\) 2.82843 + 2.82843i 0.116445 + 0.116445i
\(591\) 19.7990 28.0000i 0.814422 1.15177i
\(592\) −6.00000 1.00000i −0.246598 0.0410997i
\(593\) 15.5563i 0.638823i −0.947616 0.319411i \(-0.896515\pi\)
0.947616 0.319411i \(-0.103485\pi\)
\(594\) 10.7574 + 19.2426i 0.441380 + 0.789535i
\(595\) 8.00000i 0.327968i
\(596\) −9.89949 −0.405499
\(597\) −1.24264 7.24264i −0.0508579 0.296422i
\(598\) 6.00000 6.00000i 0.245358 0.245358i
\(599\) 16.9706i 0.693398i −0.937976 0.346699i \(-0.887302\pi\)
0.937976 0.346699i \(-0.112698\pi\)
\(600\) −1.70711 + 0.292893i −0.0696923 + 0.0119573i
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 50.9117i 2.07501i
\(603\) 5.65685 2.00000i 0.230365 0.0814463i
\(604\) 0 0
\(605\) −4.94975 4.94975i −0.201236 0.201236i
\(606\) 26.5563 4.55635i 1.07878 0.185089i
\(607\) −22.0000 22.0000i −0.892952 0.892952i 0.101848 0.994800i \(-0.467525\pi\)
−0.994800 + 0.101848i \(0.967525\pi\)
\(608\) 2.82843i 0.114708i
\(609\) 0 0
\(610\) 4.00000 + 4.00000i 0.161955 + 0.161955i
\(611\) −1.41421 1.41421i −0.0572130 0.0572130i
\(612\) 5.41421 + 2.58579i 0.218857 + 0.104524i
\(613\) 16.0000i 0.646234i −0.946359 0.323117i \(-0.895269\pi\)
0.946359 0.323117i \(-0.104731\pi\)
\(614\) −2.82843 2.82843i −0.114146 0.114146i
\(615\) 1.65685 + 9.65685i 0.0668108 + 0.389402i
\(616\) −12.0000 12.0000i −0.483494 0.483494i
\(617\) 21.2132 0.854011 0.427006 0.904249i \(-0.359568\pi\)
0.427006 + 0.904249i \(0.359568\pi\)
\(618\) 20.0000 + 14.1421i 0.804518 + 0.568880i
\(619\) 16.0000i 0.643094i 0.946894 + 0.321547i \(0.104203\pi\)
−0.946894 + 0.321547i \(0.895797\pi\)
\(620\) −7.07107 −0.283981
\(621\) −27.2132 + 15.2132i −1.09203 + 0.610485i
\(622\) 12.0000i 0.481156i
\(623\) 50.9117 50.9117i 2.03973 2.03973i
\(624\) 2.41421 0.414214i 0.0966459 0.0165818i
\(625\) −1.00000 −0.0400000
\(626\) 8.48528i 0.339140i
\(627\) 20.4853 3.51472i 0.818103 0.140364i
\(628\) 18.0000i 0.718278i
\(629\) 7.07107 + 9.89949i 0.281942 + 0.394719i
\(630\) 4.00000 + 11.3137i 0.159364 + 0.450749i
\(631\) 1.00000 + 1.00000i 0.0398094 + 0.0398094i 0.726731 0.686922i \(-0.241039\pi\)
−0.686922 + 0.726731i \(0.741039\pi\)
\(632\) −4.24264 −0.168763
\(633\) −22.6274 16.0000i −0.899359 0.635943i
\(634\) 6.00000 6.00000i 0.238290 0.238290i
\(635\) 8.48528 + 8.48528i 0.336728 + 0.336728i
\(636\) 4.00000 + 2.82843i 0.158610 + 0.112154i
\(637\) −9.00000 + 9.00000i −0.356593 + 0.356593i
\(638\) 0 0
\(639\) 8.00000 2.82843i 0.316475 0.111891i
\(640\) 1.00000i 0.0395285i
\(641\) 22.6274i 0.893729i −0.894602 0.446865i \(-0.852541\pi\)
0.894602 0.446865i \(-0.147459\pi\)
\(642\) 4.14214 + 24.1421i 0.163477 + 0.952814i
\(643\) 17.0000 + 17.0000i 0.670415 + 0.670415i 0.957812 0.287397i \(-0.0927899\pi\)
−0.287397 + 0.957812i \(0.592790\pi\)
\(644\) 16.9706 16.9706i 0.668734 0.668734i
\(645\) −18.0000 12.7279i −0.708749 0.501161i
\(646\) 4.00000 4.00000i 0.157378 0.157378i
\(647\) −22.6274 + 22.6274i −0.889576 + 0.889576i −0.994482 0.104907i \(-0.966546\pi\)
0.104907 + 0.994482i \(0.466546\pi\)
\(648\) −8.94975 0.949747i −0.351579 0.0373096i
\(649\) −12.0000 12.0000i −0.471041 0.471041i
\(650\) 1.41421 0.0554700
\(651\) 8.28427 + 48.2843i 0.324686 + 1.89241i
\(652\) −5.00000 + 5.00000i −0.195815 + 0.195815i
\(653\) 4.24264 4.24264i 0.166027 0.166027i −0.619203 0.785231i \(-0.712544\pi\)
0.785231 + 0.619203i \(0.212544\pi\)
\(654\) −16.9706 + 24.0000i −0.663602 + 0.938474i
\(655\) 12.0000 0.468879
\(656\) 5.65685 0.220863
\(657\) −16.9706 + 6.00000i −0.662085 + 0.234082i
\(658\) −4.00000 4.00000i −0.155936 0.155936i
\(659\) −9.89949 −0.385630 −0.192815 0.981235i \(-0.561762\pi\)
−0.192815 + 0.981235i \(0.561762\pi\)
\(660\) 7.24264 1.24264i 0.281919 0.0483697i
\(661\) 10.0000 + 10.0000i 0.388955 + 0.388955i 0.874315 0.485360i \(-0.161311\pi\)
−0.485360 + 0.874315i \(0.661311\pi\)
\(662\) 5.65685i 0.219860i
\(663\) −4.00000 2.82843i −0.155347 0.109847i
\(664\) 2.00000 2.00000i 0.0776151 0.0776151i
\(665\) 11.3137 0.438727
\(666\) −14.9497 10.4645i −0.579291 0.405490i
\(667\) 0 0
\(668\) 12.7279 12.7279i 0.492458 0.492458i
\(669\) −16.9706 12.0000i −0.656120 0.463947i
\(670\) 2.00000i 0.0772667i
\(671\) −16.9706 16.9706i −0.655141 0.655141i
\(672\) 6.82843 1.17157i 0.263412 0.0451944i
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) −1.41421 1.41421i −0.0544735 0.0544735i
\(675\) −5.00000 1.41421i −0.192450 0.0544331i
\(676\) 11.0000 0.423077
\(677\) −28.2843 −1.08705 −0.543526 0.839392i \(-0.682911\pi\)
−0.543526 + 0.839392i \(0.682911\pi\)
\(678\) 6.00000 8.48528i 0.230429 0.325875i
\(679\) −48.0000 + 48.0000i −1.84207 + 1.84207i
\(680\) 1.41421 1.41421i 0.0542326 0.0542326i
\(681\) 8.20101 + 47.7990i 0.314263 + 1.83166i
\(682\) 30.0000 1.14876
\(683\) −22.6274 22.6274i −0.865814 0.865814i 0.126192 0.992006i \(-0.459725\pi\)
−0.992006 + 0.126192i \(0.959725\pi\)
\(684\) −3.65685 + 7.65685i −0.139823 + 0.292767i
\(685\) 7.00000 7.00000i 0.267456 0.267456i
\(686\) −5.65685 + 5.65685i −0.215980 + 0.215980i
\(687\) 36.7696 + 26.0000i 1.40285 + 0.991962i
\(688\) −9.00000 + 9.00000i −0.343122 + 0.343122i
\(689\) −2.82843 2.82843i −0.107754 0.107754i
\(690\) 1.75736 + 10.2426i 0.0669015 + 0.389931i
\(691\) 28.0000i 1.06517i 0.846376 + 0.532585i \(0.178779\pi\)
−0.846376 + 0.532585i \(0.821221\pi\)
\(692\) 2.82843i 0.107521i
\(693\) −16.9706 48.0000i −0.644658 1.82337i
\(694\) 12.0000i 0.455514i
\(695\) −11.3137 + 11.3137i −0.429153 + 0.429153i
\(696\) 0 0
\(697\) −8.00000 8.00000i −0.303022 0.303022i
\(698\) 9.89949 9.89949i 0.374701 0.374701i
\(699\) 10.0000 + 7.07107i 0.378235 + 0.267452i
\(700\) 4.00000 0.151186
\(701\) 35.3553 + 35.3553i 1.33535 + 1.33535i 0.900503 + 0.434850i \(0.143198\pi\)
0.434850 + 0.900503i \(0.356802\pi\)
\(702\) 7.07107 + 2.00000i 0.266880 + 0.0754851i
\(703\) −14.0000 + 10.0000i −0.528020 + 0.377157i
\(704\) 4.24264i 0.159901i
\(705\) 2.41421 0.414214i 0.0909245 0.0156002i
\(706\) 34.0000i 1.27961i
\(707\) −62.2254 −2.34023
\(708\) 6.82843 1.17157i 0.256628 0.0440304i
\(709\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(710\) 2.82843i 0.106149i
\(711\) −11.4853 5.48528i −0.430732 0.205714i
\(712\) 18.0000 0.674579
\(713\) 42.4264i 1.58888i
\(714\) −11.3137 8.00000i −0.423405 0.299392i
\(715\) −6.00000 −0.224387
\(716\) −12.7279 12.7279i −0.475665 0.475665i
\(717\) 0 0
\(718\) −8.00000 8.00000i −0.298557 0.298557i
\(719\) 19.7990i 0.738378i 0.929354 + 0.369189i \(0.120364\pi\)
−0.929354 + 0.369189i \(0.879636\pi\)
\(720\) −1.29289 + 2.70711i −0.0481833 + 0.100888i
\(721\) −40.0000 40.0000i −1.48968 1.48968i
\(722\) −7.77817 7.77817i −0.289474 0.289474i
\(723\) 7.24264 1.24264i 0.269357 0.0462143i
\(724\) 6.00000i 0.222988i
\(725\) 0 0
\(726\) −11.9497 + 2.05025i −0.443497 + 0.0760920i
\(727\) 8.00000 + 8.00000i 0.296704 + 0.296704i 0.839721 0.543018i \(-0.182718\pi\)
−0.543018 + 0.839721i \(0.682718\pi\)
\(728\) −5.65685 −0.209657
\(729\) −23.0000 14.1421i −0.851852 0.523783i
\(730\) 6.00000i 0.222070i
\(731\) 25.4558 0.941518
\(732\) 9.65685 1.65685i 0.356928 0.0612391i
\(733\) 24.0000i 0.886460i −0.896408 0.443230i \(-0.853832\pi\)
0.896408 0.443230i \(-0.146168\pi\)
\(734\) −5.65685 + 5.65685i −0.208798 + 0.208798i
\(735\) −2.63604 15.3640i −0.0972318 0.566708i
\(736\) 6.00000 0.221163
\(737\) 8.48528i 0.312559i
\(738\) 15.3137 + 7.31371i 0.563705 + 0.269221i
\(739\) 40.0000i 1.47142i −0.677295 0.735712i \(-0.736848\pi\)
0.677295 0.735712i \(-0.263152\pi\)
\(740\) −4.94975 + 3.53553i −0.181956 + 0.129969i
\(741\) 4.00000 5.65685i 0.146944 0.207810i
\(742\) −8.00000 8.00000i −0.293689 0.293689i
\(743\) −49.4975 −1.81589 −0.907943 0.419093i \(-0.862348\pi\)
−0.907943 + 0.419093i \(0.862348\pi\)
\(744\) −7.07107 + 10.0000i −0.259238 + 0.366618i
\(745\) −7.00000 + 7.00000i −0.256460 + 0.256460i
\(746\) −24.0416 24.0416i −0.880227 0.880227i
\(747\) 8.00000 2.82843i 0.292705 0.103487i
\(748\) −6.00000 + 6.00000i −0.219382 + 0.219382i
\(749\) 56.5685i 2.06697i
\(750\) −1.00000 + 1.41421i −0.0365148 + 0.0516398i
\(751\) 2.00000i 0.0729810i 0.999334 + 0.0364905i \(0.0116179\pi\)
−0.999334 + 0.0364905i \(0.988382\pi\)
\(752\) 1.41421i 0.0515711i
\(753\) 6.82843 1.17157i 0.248842 0.0426945i
\(754\) 0 0
\(755\) 0 0
\(756\) 20.0000 + 5.65685i 0.727393 + 0.205738i
\(757\) −5.00000 + 5.00000i −0.181728 + 0.181728i −0.792108 0.610380i \(-0.791017\pi\)
0.610380 + 0.792108i \(0.291017\pi\)
\(758\) 0 0
\(759\) −7.45584 43.4558i −0.270630 1.57735i
\(760\) 2.00000 + 2.00000i 0.0725476 + 0.0725476i
\(761\) −22.6274 −0.820243 −0.410122 0.912031i \(-0.634514\pi\)
−0.410122 + 0.912031i \(0.634514\pi\)
\(762\) 20.4853 3.51472i 0.742103 0.127325i
\(763\) 48.0000 48.0000i 1.73772 1.73772i
\(764\) −2.82843 + 2.82843i −0.102329 + 0.102329i
\(765\) 5.65685 2.00000i 0.204524 0.0723102i
\(766\) 16.0000 0.578103
\(767\) −5.65685 −0.204257
\(768\) 1.41421 + 1.00000i 0.0510310 + 0.0360844i
\(769\) 19.0000 + 19.0000i 0.685158 + 0.685158i 0.961158 0.276000i \(-0.0890090\pi\)
−0.276000 + 0.961158i \(0.589009\pi\)
\(770\) −16.9706 −0.611577
\(771\) −1.17157 6.82843i −0.0421932 0.245920i
\(772\) −18.0000 18.0000i −0.647834 0.647834i
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) −36.0000 + 12.7279i −1.29399 + 0.457496i
\(775\) −5.00000 + 5.00000i −0.179605 + 0.179605i
\(776\) −16.9706 −0.609208
\(777\) 29.9411 + 29.6569i 1.07413 + 1.06393i