Properties

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

Related objects

Downloads

Learn more

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.c.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} +1.41421 q^{11} +(-1.00000 + 1.41421i) q^{12} +(-3.00000 + 3.00000i) 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} +(4.00000 - 4.00000i) q^{19} +(0.707107 - 0.707107i) q^{20} +(5.65685 + 4.00000i) q^{21} +(-1.00000 + 1.00000i) q^{22} +(1.41421 + 1.41421i) q^{23} +(-0.292893 - 1.70711i) q^{24} +1.00000i q^{25} -4.24264i q^{26} +(1.41421 - 5.00000i) q^{27} +4.00000i q^{28} +(2.82843 - 2.82843i) q^{29} +(1.41421 + 1.00000i) q^{30} +(-3.00000 - 3.00000i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.00000 - 1.41421i) q^{33} -2.00000 q^{34} +(-2.82843 - 2.82843i) q^{35} +(2.82843 - 1.00000i) q^{36} +(-6.00000 - 1.00000i) q^{37} +5.65685i q^{38} +(7.24264 - 1.24264i) q^{39} +1.00000i q^{40} -5.65685 q^{41} +(-6.82843 + 1.17157i) q^{42} +(3.00000 - 3.00000i) q^{43} -1.41421i q^{44} +(-1.29289 + 2.70711i) q^{45} -2.00000 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} +(3.00000 + 3.00000i) q^{52} +2.82843i q^{53} +(2.53553 + 4.53553i) q^{54} +(1.00000 + 1.00000i) q^{55} +(-2.82843 - 2.82843i) q^{56} +(-9.65685 + 1.65685i) q^{57} +4.00000i q^{58} +(-8.48528 - 8.48528i) q^{59} +(-1.70711 + 0.292893i) q^{60} +(-6.00000 - 6.00000i) q^{61} +4.24264 q^{62} +(-4.00000 - 11.3137i) q^{63} +1.00000i q^{64} -4.24264 q^{65} +(2.41421 - 0.414214i) q^{66} -6.00000i q^{67} +(1.41421 - 1.41421i) q^{68} +(-0.585786 - 3.41421i) q^{69} +4.00000 q^{70} +2.82843i q^{71} +(-1.29289 + 2.70711i) q^{72} -10.0000i q^{73} +(4.94975 - 3.53553i) q^{74} +(1.00000 - 1.41421i) q^{75} +(-4.00000 - 4.00000i) q^{76} -5.65685 q^{77} +(-4.24264 + 6.00000i) q^{78} +(5.00000 - 5.00000i) 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} +4.24264i q^{86} +(-6.82843 + 1.17157i) q^{87} +(1.00000 + 1.00000i) q^{88} +(-1.41421 + 1.41421i) q^{89} +(-1.00000 - 2.82843i) q^{90} +(12.0000 - 12.0000i) q^{91} +(1.41421 - 1.41421i) q^{92} +(1.24264 + 7.24264i) q^{93} +(1.00000 + 1.00000i) q^{94} +5.65685 q^{95} +(-1.70711 + 0.292893i) q^{96} +(6.00000 - 6.00000i) q^{97} +(-6.36396 + 6.36396i) q^{98} +(1.41421 + 4.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{6} - 16q^{7} + 4q^{9} + O(q^{10}) \) \( 4q + 4q^{6} - 16q^{7} + 4q^{9} - 4q^{10} - 4q^{12} - 12q^{13} - 4q^{15} - 4q^{16} - 8q^{18} + 16q^{19} - 4q^{22} - 4q^{24} - 12q^{31} - 8q^{33} - 8q^{34} - 24q^{37} + 12q^{39} - 16q^{42} + 12q^{43} - 8q^{45} - 8q^{46} + 36q^{49} - 8q^{51} + 12q^{52} - 4q^{54} + 4q^{55} - 16q^{57} - 4q^{60} - 24q^{61} - 16q^{63} + 4q^{66} - 8q^{69} + 16q^{70} - 8q^{72} + 4q^{75} - 16q^{76} + 20q^{79} - 28q^{81} + 16q^{82} + 16q^{84} - 16q^{87} + 4q^{88} - 4q^{90} + 48q^{91} - 12q^{93} + 4q^{94} - 4q^{96} + 24q^{97} + O(q^{100}) \)

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 \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.00000 + 2.82843i 0.333333 + 0.942809i
\(10\) −1.00000 −0.316228
\(11\) 1.41421 0.426401 0.213201 0.977008i \(-0.431611\pi\)
0.213201 + 0.977008i \(0.431611\pi\)
\(12\) −1.00000 + 1.41421i −0.288675 + 0.408248i
\(13\) −3.00000 + 3.00000i −0.832050 + 0.832050i −0.987797 0.155747i \(-0.950222\pi\)
0.155747 + 0.987797i \(0.450222\pi\)
\(14\) 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
\(19\) 4.00000 4.00000i 0.917663 0.917663i −0.0791961 0.996859i \(-0.525235\pi\)
0.996859 + 0.0791961i \(0.0252353\pi\)
\(20\) 0.707107 0.707107i 0.158114 0.158114i
\(21\) 5.65685 + 4.00000i 1.23443 + 0.872872i
\(22\) −1.00000 + 1.00000i −0.213201 + 0.213201i
\(23\) 1.41421 + 1.41421i 0.294884 + 0.294884i 0.839006 0.544122i \(-0.183137\pi\)
−0.544122 + 0.839006i \(0.683137\pi\)
\(24\) −0.292893 1.70711i −0.0597866 0.348462i
\(25\) 1.00000i 0.200000i
\(26\) 4.24264i 0.832050i
\(27\) 1.41421 5.00000i 0.272166 0.962250i
\(28\) 4.00000i 0.755929i
\(29\) 2.82843 2.82843i 0.525226 0.525226i −0.393919 0.919145i \(-0.628881\pi\)
0.919145 + 0.393919i \(0.128881\pi\)
\(30\) 1.41421 + 1.00000i 0.258199 + 0.182574i
\(31\) −3.00000 3.00000i −0.538816 0.538816i 0.384365 0.923181i \(-0.374420\pi\)
−0.923181 + 0.384365i \(0.874420\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −2.00000 1.41421i −0.348155 0.246183i
\(34\) −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
\(38\) 5.65685i 0.917663i
\(39\) 7.24264 1.24264i 1.15975 0.198982i
\(40\) 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
\(43\) 3.00000 3.00000i 0.457496 0.457496i −0.440337 0.897833i \(-0.645141\pi\)
0.897833 + 0.440337i \(0.145141\pi\)
\(44\) 1.41421i 0.213201i
\(45\) −1.29289 + 2.70711i −0.192733 + 0.403552i
\(46\) −2.00000 −0.294884
\(47\) 1.41421i 0.206284i −0.994667 0.103142i \(-0.967110\pi\)
0.994667 0.103142i \(-0.0328896\pi\)
\(48\) 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
\(52\) 3.00000 + 3.00000i 0.416025 + 0.416025i
\(53\) 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
\(55\) 1.00000 + 1.00000i 0.134840 + 0.134840i
\(56\) −2.82843 2.82843i −0.377964 0.377964i
\(57\) −9.65685 + 1.65685i −1.27908 + 0.219456i
\(58\) 4.00000i 0.525226i
\(59\) −8.48528 8.48528i −1.10469 1.10469i −0.993837 0.110853i \(-0.964642\pi\)
−0.110853 0.993837i \(-0.535358\pi\)
\(60\) −1.70711 + 0.292893i −0.220387 + 0.0378124i
\(61\) −6.00000 6.00000i −0.768221 0.768221i 0.209572 0.977793i \(-0.432793\pi\)
−0.977793 + 0.209572i \(0.932793\pi\)
\(62\) 4.24264 0.538816
\(63\) −4.00000 11.3137i −0.503953 1.42539i
\(64\) 1.00000i 0.125000i
\(65\) −4.24264 −0.526235
\(66\) 2.41421 0.414214i 0.297169 0.0509862i
\(67\) 6.00000i 0.733017i −0.930415 0.366508i \(-0.880553\pi\)
0.930415 0.366508i \(-0.119447\pi\)
\(68\) 1.41421 1.41421i 0.171499 0.171499i
\(69\) −0.585786 3.41421i −0.0705204 0.411023i
\(70\) 4.00000 0.478091
\(71\) 2.82843i 0.335673i 0.985815 + 0.167836i \(0.0536780\pi\)
−0.985815 + 0.167836i \(0.946322\pi\)
\(72\) −1.29289 + 2.70711i −0.152369 + 0.319036i
\(73\) 10.0000i 1.17041i −0.810885 0.585206i \(-0.801014\pi\)
0.810885 0.585206i \(-0.198986\pi\)
\(74\) 4.94975 3.53553i 0.575396 0.410997i
\(75\) 1.00000 1.41421i 0.115470 0.163299i
\(76\) −4.00000 4.00000i −0.458831 0.458831i
\(77\) −5.65685 −0.644658
\(78\) −4.24264 + 6.00000i −0.480384 + 0.679366i
\(79\) 5.00000 5.00000i 0.562544 0.562544i −0.367485 0.930029i \(-0.619781\pi\)
0.930029 + 0.367485i \(0.119781\pi\)
\(80\) −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
\(86\) 4.24264i 0.457496i
\(87\) −6.82843 + 1.17157i −0.732084 + 0.125606i
\(88\) 1.00000 + 1.00000i 0.106600 + 0.106600i
\(89\) −1.41421 + 1.41421i −0.149906 + 0.149906i −0.778076 0.628170i \(-0.783804\pi\)
0.628170 + 0.778076i \(0.283804\pi\)
\(90\) −1.00000 2.82843i −0.105409 0.298142i
\(91\) 12.0000 12.0000i 1.25794 1.25794i
\(92\) 1.41421 1.41421i 0.147442 0.147442i
\(93\) 1.24264 + 7.24264i 0.128856 + 0.751027i
\(94\) 1.00000 + 1.00000i 0.103142 + 0.103142i
\(95\) 5.65685 0.580381
\(96\) −1.70711 + 0.292893i −0.174231 + 0.0298933i
\(97\) 6.00000 6.00000i 0.609208 0.609208i −0.333531 0.942739i \(-0.608240\pi\)
0.942739 + 0.333531i \(0.108240\pi\)
\(98\) −6.36396 + 6.36396i −0.642857 + 0.642857i
\(99\) 1.41421 + 4.00000i 0.142134 + 0.402015i
\(100\) 1.00000 0.100000
\(101\) 1.41421 0.140720 0.0703598 0.997522i \(-0.477585\pi\)
0.0703598 + 0.997522i \(0.477585\pi\)
\(102\) 2.82843 + 2.00000i 0.280056 + 0.198030i
\(103\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(104\) −4.24264 −0.416025
\(105\) 1.17157 + 6.82843i 0.114334 + 0.666386i
\(106\) −2.00000 2.00000i −0.194257 0.194257i
\(107\) 8.48528i 0.820303i −0.912017 0.410152i \(-0.865476\pi\)
0.912017 0.410152i \(-0.134524\pi\)
\(108\) −5.00000 1.41421i −0.481125 0.136083i
\(109\) 14.0000 14.0000i 1.34096 1.34096i 0.445848 0.895109i \(-0.352902\pi\)
0.895109 0.445848i \(-0.147098\pi\)
\(110\) −1.41421 −0.134840
\(111\) 7.48528 + 7.41421i 0.710471 + 0.703726i
\(112\) 4.00000 0.377964
\(113\) 1.41421 1.41421i 0.133038 0.133038i −0.637452 0.770490i \(-0.720012\pi\)
0.770490 + 0.637452i \(0.220012\pi\)
\(114\) 5.65685 8.00000i 0.529813 0.749269i
\(115\) 2.00000i 0.186501i
\(116\) −2.82843 2.82843i −0.262613 0.262613i
\(117\) −11.4853 5.48528i −1.06181 0.507114i
\(118\) 12.0000 1.10469
\(119\) −5.65685 5.65685i −0.518563 0.518563i
\(120\) 1.00000 1.41421i 0.0912871 0.129099i
\(121\) −9.00000 −0.818182
\(122\) 8.48528 0.768221
\(123\) 8.00000 + 5.65685i 0.721336 + 0.510061i
\(124\) −3.00000 + 3.00000i −0.269408 + 0.269408i
\(125\) −0.707107 + 0.707107i −0.0632456 + 0.0632456i
\(126\) 10.8284 + 5.17157i 0.964673 + 0.460720i
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −7.24264 + 1.24264i −0.637679 + 0.109408i
\(130\) 3.00000 3.00000i 0.263117 0.263117i
\(131\) −2.82843 + 2.82843i −0.247121 + 0.247121i −0.819788 0.572667i \(-0.805909\pi\)
0.572667 + 0.819788i \(0.305909\pi\)
\(132\) −1.41421 + 2.00000i −0.123091 + 0.174078i
\(133\) −16.0000 + 16.0000i −1.38738 + 1.38738i
\(134\) 4.24264 + 4.24264i 0.366508 + 0.366508i
\(135\) 4.53553 2.53553i 0.390357 0.218224i
\(136\) 2.00000i 0.171499i
\(137\) 21.2132i 1.81237i −0.422885 0.906183i \(-0.638983\pi\)
0.422885 0.906183i \(-0.361017\pi\)
\(138\) 2.82843 + 2.00000i 0.240772 + 0.170251i
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) −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
\(145\) 4.00000 0.332182
\(146\) 7.07107 + 7.07107i 0.585206 + 0.585206i
\(147\) −12.7279 9.00000i −1.04978 0.742307i
\(148\) −1.00000 + 6.00000i −0.0821995 + 0.493197i
\(149\) 18.3848i 1.50614i 0.657941 + 0.753070i \(0.271428\pi\)
−0.657941 + 0.753070i \(0.728572\pi\)
\(150\) 0.292893 + 1.70711i 0.0239146 + 0.139385i
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 5.65685 0.458831
\(153\) −2.58579 + 5.41421i −0.209048 + 0.437713i
\(154\) 4.00000 4.00000i 0.322329 0.322329i
\(155\) 4.24264i 0.340777i
\(156\) −1.24264 7.24264i −0.0994909 0.579875i
\(157\) −14.0000 −1.11732 −0.558661 0.829396i \(-0.688685\pi\)
−0.558661 + 0.829396i \(0.688685\pi\)
\(158\) 7.07107i 0.562544i
\(159\) 2.82843 4.00000i 0.224309 0.317221i
\(160\) 1.00000 0.0790569
\(161\) −5.65685 5.65685i −0.445823 0.445823i
\(162\) 0.949747 8.94975i 0.0746192 0.703159i
\(163\) −15.0000 15.0000i −1.17489 1.17489i −0.981029 0.193862i \(-0.937899\pi\)
−0.193862 0.981029i \(-0.562101\pi\)
\(164\) 5.65685i 0.441726i
\(165\) −0.414214 2.41421i −0.0322465 0.187946i
\(166\) 2.00000 + 2.00000i 0.155230 + 0.155230i
\(167\) −1.41421 1.41421i −0.109435 0.109435i 0.650269 0.759704i \(-0.274656\pi\)
−0.759704 + 0.650269i \(0.774656\pi\)
\(168\) 1.17157 + 6.82843i 0.0903888 + 0.526825i
\(169\) 5.00000i 0.384615i
\(170\) −1.41421 1.41421i −0.108465 0.108465i
\(171\) 15.3137 + 7.31371i 1.17107 + 0.559293i
\(172\) −3.00000 3.00000i −0.228748 0.228748i
\(173\) 19.7990 1.50529 0.752645 0.658427i \(-0.228778\pi\)
0.752645 + 0.658427i \(0.228778\pi\)
\(174\) 4.00000 5.65685i 0.303239 0.428845i
\(175\) 4.00000i 0.302372i
\(176\) −1.41421 −0.106600
\(177\) 3.51472 + 20.4853i 0.264182 + 1.53977i
\(178\) 2.00000i 0.149906i
\(179\) 7.07107 7.07107i 0.528516 0.528516i −0.391613 0.920130i \(-0.628083\pi\)
0.920130 + 0.391613i \(0.128083\pi\)
\(180\) 2.70711 + 1.29289i 0.201776 + 0.0963666i
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 16.9706i 1.25794i
\(183\) 2.48528 + 14.4853i 0.183717 + 1.07078i
\(184\) 2.00000i 0.147442i
\(185\) −3.53553 4.94975i −0.259938 0.363913i
\(186\) −6.00000 4.24264i −0.439941 0.311086i
\(187\) 2.00000 + 2.00000i 0.146254 + 0.146254i
\(188\) −1.41421 −0.103142
\(189\) −5.65685 + 20.0000i −0.411476 + 1.45479i
\(190\) −4.00000 + 4.00000i −0.290191 + 0.290191i
\(191\) 16.9706 + 16.9706i 1.22795 + 1.22795i 0.964739 + 0.263208i \(0.0847804\pi\)
0.263208 + 0.964739i \(0.415220\pi\)
\(192\) 1.00000 1.41421i 0.0721688 0.102062i
\(193\) −12.0000 + 12.0000i −0.863779 + 0.863779i −0.991775 0.127996i \(-0.959146\pi\)
0.127996 + 0.991775i \(0.459146\pi\)
\(194\) 8.48528i 0.609208i
\(195\) 6.00000 + 4.24264i 0.429669 + 0.303822i
\(196\) 9.00000i 0.642857i
\(197\) 2.82843i 0.201517i 0.994911 + 0.100759i \(0.0321270\pi\)
−0.994911 + 0.100759i \(0.967873\pi\)
\(198\) −3.82843 1.82843i −0.272074 0.129941i
\(199\) 1.00000 + 1.00000i 0.0708881 + 0.0708881i 0.741662 0.670774i \(-0.234038\pi\)
−0.670774 + 0.741662i \(0.734038\pi\)
\(200\) −0.707107 + 0.707107i −0.0500000 + 0.0500000i
\(201\) −6.00000 + 8.48528i −0.423207 + 0.598506i
\(202\) −1.00000 + 1.00000i −0.0703598 + 0.0703598i
\(203\) −11.3137 + 11.3137i −0.794067 + 0.794067i
\(204\) −3.41421 + 0.585786i −0.239043 + 0.0410133i
\(205\) −4.00000 4.00000i −0.279372 0.279372i
\(206\) 0 0
\(207\) −2.58579 + 5.41421i −0.179725 + 0.376314i
\(208\) 3.00000 3.00000i 0.208013 0.208013i
\(209\) 5.65685 5.65685i 0.391293 0.391293i
\(210\) −5.65685 4.00000i −0.390360 0.276026i
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) 2.82843 0.194257
\(213\) 2.82843 4.00000i 0.193801 0.274075i
\(214\) 6.00000 + 6.00000i 0.410152 + 0.410152i
\(215\) 4.24264 0.289346
\(216\) 4.53553 2.53553i 0.308604 0.172521i
\(217\) 12.0000 + 12.0000i 0.814613 + 0.814613i
\(218\) 19.7990i 1.34096i
\(219\) −10.0000 + 14.1421i −0.675737 + 0.955637i
\(220\) 1.00000 1.00000i 0.0674200 0.0674200i
\(221\) −8.48528 −0.570782
\(222\) −10.5355 + 0.0502525i −0.707099 + 0.00337273i
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) −2.82843 + 2.82843i −0.188982 + 0.188982i
\(225\) −2.82843 + 1.00000i −0.188562 + 0.0666667i
\(226\) 2.00000i 0.133038i
\(227\) −16.9706 16.9706i −1.12638 1.12638i −0.990762 0.135614i \(-0.956699\pi\)
−0.135614 0.990762i \(-0.543301\pi\)
\(228\) 1.65685 + 9.65685i 0.109728 + 0.639541i
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) −1.41421 1.41421i −0.0932505 0.0932505i
\(231\) 8.00000 + 5.65685i 0.526361 + 0.372194i
\(232\) 4.00000 0.262613
\(233\) −12.7279 −0.833834 −0.416917 0.908945i \(-0.636889\pi\)
−0.416917 + 0.908945i \(0.636889\pi\)
\(234\) 12.0000 4.24264i 0.784465 0.277350i
\(235\) 1.00000 1.00000i 0.0652328 0.0652328i
\(236\) −8.48528 + 8.48528i −0.552345 + 0.552345i
\(237\) −12.0711 + 2.07107i −0.784100 + 0.134530i
\(238\) 8.00000 0.518563
\(239\) −14.1421 14.1421i −0.914779 0.914779i 0.0818647 0.996643i \(-0.473912\pi\)
−0.996643 + 0.0818647i \(0.973912\pi\)
\(240\) 0.292893 + 1.70711i 0.0189062 + 0.110193i
\(241\) −13.0000 + 13.0000i −0.837404 + 0.837404i −0.988517 0.151113i \(-0.951714\pi\)
0.151113 + 0.988517i \(0.451714\pi\)
\(242\) 6.36396 6.36396i 0.409091 0.409091i
\(243\) 15.5563 1.00000i 0.997940 0.0641500i
\(244\) −6.00000 + 6.00000i −0.384111 + 0.384111i
\(245\) 6.36396 + 6.36396i 0.406579 + 0.406579i
\(246\) −9.65685 + 1.65685i −0.615699 + 0.105637i
\(247\) 24.0000i 1.52708i
\(248\) 4.24264i 0.269408i
\(249\) −2.82843 + 4.00000i −0.179244 + 0.253490i
\(250\) 1.00000i 0.0632456i
\(251\) −8.48528 + 8.48528i −0.535586 + 0.535586i −0.922229 0.386643i \(-0.873635\pi\)
0.386643 + 0.922229i \(0.373635\pi\)
\(252\) −11.3137 + 4.00000i −0.712697 + 0.251976i
\(253\) 2.00000 + 2.00000i 0.125739 + 0.125739i
\(254\) −11.3137 + 11.3137i −0.709885 + 0.709885i
\(255\) 2.00000 2.82843i 0.125245 0.177123i
\(256\) 1.00000 0.0625000
\(257\) 16.9706 + 16.9706i 1.05859 + 1.05859i 0.998173 + 0.0604217i \(0.0192445\pi\)
0.0604217 + 0.998173i \(0.480755\pi\)
\(258\) 4.24264 6.00000i 0.264135 0.373544i
\(259\) 24.0000 + 4.00000i 1.49129 + 0.248548i
\(260\) 4.24264i 0.263117i
\(261\) 10.8284 + 5.17157i 0.670263 + 0.320112i
\(262\) 4.00000i 0.247121i
\(263\) −26.8701 −1.65688 −0.828439 0.560079i \(-0.810771\pi\)
−0.828439 + 0.560079i \(0.810771\pi\)
\(264\) −0.414214 2.41421i −0.0254931 0.148585i
\(265\) −2.00000 + 2.00000i −0.122859 + 0.122859i
\(266\) 22.6274i 1.38738i
\(267\) 3.41421 0.585786i 0.208946 0.0358495i
\(268\) −6.00000 −0.366508
\(269\) 7.07107i 0.431131i 0.976489 + 0.215565i \(0.0691594\pi\)
−0.976489 + 0.215565i \(0.930841\pi\)
\(270\) −1.41421 + 5.00000i −0.0860663 + 0.304290i
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) −1.41421 1.41421i −0.0857493 0.0857493i
\(273\) −28.9706 + 4.97056i −1.75338 + 0.300832i
\(274\) 15.0000 + 15.0000i 0.906183 + 0.906183i
\(275\) 1.41421i 0.0852803i
\(276\) −3.41421 + 0.585786i −0.205512 + 0.0352602i
\(277\) 15.0000 + 15.0000i 0.901263 + 0.901263i 0.995545 0.0942828i \(-0.0300558\pi\)
−0.0942828 + 0.995545i \(0.530056\pi\)
\(278\) 0 0
\(279\) 5.48528 11.4853i 0.328395 0.687606i
\(280\) 4.00000i 0.239046i
\(281\) −4.24264 4.24264i −0.253095 0.253095i 0.569143 0.822238i \(-0.307275\pi\)
−0.822238 + 0.569143i \(0.807275\pi\)
\(282\) −0.414214 2.41421i −0.0246661 0.143764i
\(283\) −21.0000 21.0000i −1.24832 1.24832i −0.956461 0.291859i \(-0.905726\pi\)
−0.291859 0.956461i \(-0.594274\pi\)
\(284\) 2.82843 0.167836
\(285\) −8.00000 5.65685i −0.473879 0.335083i
\(286\) 6.00000i 0.354787i
\(287\) 22.6274 1.33565
\(288\) 2.70711 + 1.29289i 0.159518 + 0.0761845i
\(289\) 13.0000i 0.764706i
\(290\) −2.82843 + 2.82843i −0.166091 + 0.166091i
\(291\) −14.4853 + 2.48528i −0.849142 + 0.145690i
\(292\) −10.0000 −0.585206
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 15.3640 2.63604i 0.896044 0.153737i
\(295\) 12.0000i 0.698667i
\(296\) −3.53553 4.94975i −0.205499 0.287698i
\(297\) 2.00000 7.07107i 0.116052 0.410305i
\(298\) −13.0000 13.0000i −0.753070 0.753070i
\(299\) −8.48528 −0.490716
\(300\) −1.41421 1.00000i −0.0816497 0.0577350i
\(301\) −12.0000 + 12.0000i −0.691669 + 0.691669i
\(302\) 0 0
\(303\) −2.00000 1.41421i −0.114897 0.0812444i
\(304\) −4.00000 + 4.00000i −0.229416 + 0.229416i
\(305\) 8.48528i 0.485866i
\(306\) −2.00000 5.65685i −0.114332 0.323381i
\(307\) 28.0000i 1.59804i 0.601302 + 0.799022i \(0.294649\pi\)
−0.601302 + 0.799022i \(0.705351\pi\)
\(308\) 5.65685i 0.322329i
\(309\) 0 0
\(310\) 3.00000 + 3.00000i 0.170389 + 0.170389i
\(311\) −14.1421 + 14.1421i −0.801927 + 0.801927i −0.983397 0.181470i \(-0.941915\pi\)
0.181470 + 0.983397i \(0.441915\pi\)
\(312\) 6.00000 + 4.24264i 0.339683 + 0.240192i
\(313\) 24.0000 24.0000i 1.35656 1.35656i 0.478440 0.878120i \(-0.341202\pi\)
0.878120 0.478440i \(-0.158798\pi\)
\(314\) 9.89949 9.89949i 0.558661 0.558661i
\(315\) 5.17157 10.8284i 0.291385 0.610113i
\(316\) −5.00000 5.00000i −0.281272 0.281272i
\(317\) 25.4558 1.42974 0.714871 0.699256i \(-0.246485\pi\)
0.714871 + 0.699256i \(0.246485\pi\)
\(318\) 0.828427 + 4.82843i 0.0464559 + 0.270765i
\(319\) 4.00000 4.00000i 0.223957 0.223957i
\(320\) −0.707107 + 0.707107i −0.0395285 + 0.0395285i
\(321\) −8.48528 + 12.0000i −0.473602 + 0.669775i
\(322\) 8.00000 0.445823
\(323\) 11.3137 0.629512
\(324\) 5.65685 + 7.00000i 0.314270 + 0.388889i
\(325\) −3.00000 3.00000i −0.166410 0.166410i
\(326\) 21.2132 1.17489
\(327\) −33.7990 + 5.79899i −1.86909 + 0.320685i
\(328\) −4.00000 4.00000i −0.220863 0.220863i
\(329\) 5.65685i 0.311872i
\(330\) 2.00000 + 1.41421i 0.110096 + 0.0778499i
\(331\) −2.00000 + 2.00000i −0.109930 + 0.109930i −0.759932 0.650002i \(-0.774768\pi\)
0.650002 + 0.759932i \(0.274768\pi\)
\(332\) −2.82843 −0.155230
\(333\) −3.17157 17.9706i −0.173801 0.984781i
\(334\) 2.00000 0.109435
\(335\) 4.24264 4.24264i 0.231800 0.231800i
\(336\) −5.65685 4.00000i −0.308607 0.218218i
\(337\) 26.0000i 1.41631i −0.706057 0.708155i \(-0.749528\pi\)
0.706057 0.708155i \(-0.250472\pi\)
\(338\) 3.53553 + 3.53553i 0.192308 + 0.192308i
\(339\) −3.41421 + 0.585786i −0.185435 + 0.0318156i
\(340\) 2.00000 0.108465
\(341\) −4.24264 4.24264i −0.229752 0.229752i
\(342\) −16.0000 + 5.65685i −0.865181 + 0.305888i
\(343\) −8.00000 −0.431959
\(344\) 4.24264 0.228748
\(345\) 2.00000 2.82843i 0.107676 0.152277i
\(346\) −14.0000 + 14.0000i −0.752645 + 0.752645i
\(347\) −22.6274 + 22.6274i −1.21470 + 1.21470i −0.245241 + 0.969462i \(0.578867\pi\)
−0.969462 + 0.245241i \(0.921133\pi\)
\(348\) 1.17157 + 6.82843i 0.0628029 + 0.366042i
\(349\) 6.00000 0.321173 0.160586 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(350\) 2.82843 + 2.82843i 0.151186 + 0.151186i
\(351\) 10.7574 + 19.2426i 0.574185 + 1.02710i
\(352\) 1.00000 1.00000i 0.0533002 0.0533002i
\(353\) 18.3848 18.3848i 0.978523 0.978523i −0.0212513 0.999774i \(-0.506765\pi\)
0.999774 + 0.0212513i \(0.00676499\pi\)
\(354\) −16.9706 12.0000i −0.901975 0.637793i
\(355\) −2.00000 + 2.00000i −0.106149 + 0.106149i
\(356\) 1.41421 + 1.41421i 0.0749532 + 0.0749532i
\(357\) 2.34315 + 13.6569i 0.124012 + 0.722797i
\(358\) 10.0000i 0.528516i
\(359\) 22.6274i 1.19423i −0.802156 0.597115i \(-0.796314\pi\)
0.802156 0.597115i \(-0.203686\pi\)
\(360\) −2.82843 + 1.00000i −0.149071 + 0.0527046i
\(361\) 13.0000i 0.684211i
\(362\) −7.07107 + 7.07107i −0.371647 + 0.371647i
\(363\) 12.7279 + 9.00000i 0.668043 + 0.472377i
\(364\) −12.0000 12.0000i −0.628971 0.628971i
\(365\) 7.07107 7.07107i 0.370117 0.370117i
\(366\) −12.0000 8.48528i −0.627250 0.443533i
\(367\) −12.0000 −0.626395 −0.313197 0.949688i \(-0.601400\pi\)
−0.313197 + 0.949688i \(0.601400\pi\)
\(368\) −1.41421 1.41421i −0.0737210 0.0737210i
\(369\) −5.65685 16.0000i −0.294484 0.832927i
\(370\) 6.00000 + 1.00000i 0.311925 + 0.0519875i
\(371\) 11.3137i 0.587378i
\(372\) 7.24264 1.24264i 0.375513 0.0644279i
\(373\) 22.0000i 1.13912i 0.821951 + 0.569558i \(0.192886\pi\)
−0.821951 + 0.569558i \(0.807114\pi\)
\(374\) −2.82843 −0.146254
\(375\) 1.70711 0.292893i 0.0881546 0.0151249i
\(376\) 1.00000 1.00000i 0.0515711 0.0515711i
\(377\) 16.9706i 0.874028i
\(378\) −10.1421 18.1421i −0.521655 0.933131i
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) 5.65685i 0.290191i
\(381\) −22.6274 16.0000i −1.15924 0.819705i
\(382\) −24.0000 −1.22795
\(383\) −16.9706 16.9706i −0.867155 0.867155i 0.125001 0.992157i \(-0.460106\pi\)
−0.992157 + 0.125001i \(0.960106\pi\)
\(384\) 0.292893 + 1.70711i 0.0149466 + 0.0871154i
\(385\) −4.00000 4.00000i −0.203859 0.203859i
\(386\) 16.9706i 0.863779i
\(387\) 11.4853 + 5.48528i 0.583830 + 0.278833i
\(388\) −6.00000 6.00000i −0.304604 0.304604i
\(389\) −16.9706 16.9706i −0.860442 0.860442i 0.130948 0.991389i \(-0.458198\pi\)
−0.991389 + 0.130948i \(0.958198\pi\)
\(390\) −7.24264 + 1.24264i −0.366745 + 0.0629236i
\(391\) 4.00000i 0.202289i
\(392\) 6.36396 + 6.36396i 0.321429 + 0.321429i
\(393\) 6.82843 1.17157i 0.344449 0.0590980i
\(394\) −2.00000 2.00000i −0.100759 0.100759i
\(395\) 7.07107 0.355784
\(396\) 4.00000 1.41421i 0.201008 0.0710669i
\(397\) 22.0000i 1.10415i −0.833795 0.552074i \(-0.813837\pi\)
0.833795 0.552074i \(-0.186163\pi\)
\(398\) −1.41421 −0.0708881
\(399\) 38.6274 6.62742i 1.93379 0.331786i
\(400\) 1.00000i 0.0500000i
\(401\) 4.24264 4.24264i 0.211867 0.211867i −0.593193 0.805060i \(-0.702133\pi\)
0.805060 + 0.593193i \(0.202133\pi\)
\(402\) −1.75736 10.2426i −0.0876491 0.510856i
\(403\) 18.0000 0.896644
\(404\) 1.41421i 0.0703598i
\(405\) −8.94975 0.949747i −0.444717 0.0471933i
\(406\) 16.0000i 0.794067i
\(407\) −8.48528 1.41421i −0.420600 0.0701000i
\(408\) 2.00000 2.82843i 0.0990148 0.140028i
\(409\) −3.00000 3.00000i −0.148340 0.148340i 0.629036 0.777376i \(-0.283450\pi\)
−0.777376 + 0.629036i \(0.783450\pi\)
\(410\) 5.65685 0.279372
\(411\) −21.2132 + 30.0000i −1.04637 + 1.47979i
\(412\) 0 0
\(413\) 33.9411 + 33.9411i 1.67013 + 1.67013i
\(414\) −2.00000 5.65685i −0.0982946 0.278019i
\(415\) 2.00000 2.00000i 0.0981761 0.0981761i
\(416\) 4.24264i 0.208013i
\(417\) 0 0
\(418\) 8.00000i 0.391293i
\(419\) 32.5269i 1.58904i −0.607236 0.794522i \(-0.707722\pi\)
0.607236 0.794522i \(-0.292278\pi\)
\(420\) 6.82843 1.17157i 0.333193 0.0571669i
\(421\) 20.0000 + 20.0000i 0.974740 + 0.974740i 0.999689 0.0249484i \(-0.00794214\pi\)
−0.0249484 + 0.999689i \(0.507942\pi\)
\(422\) −5.65685 + 5.65685i −0.275371 + 0.275371i
\(423\) 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
\(427\) 24.0000 + 24.0000i 1.16144 + 1.16144i
\(428\) −8.48528 −0.410152
\(429\) 10.2426 1.75736i 0.494519 0.0848461i
\(430\) −3.00000 + 3.00000i −0.144673 + 0.144673i
\(431\) −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
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) −16.9706 −0.814613
\(435\) −5.65685 4.00000i −0.271225 0.191785i
\(436\) −14.0000 14.0000i −0.670478 0.670478i
\(437\) 11.3137 0.541208
\(438\) −2.92893 17.0711i −0.139950 0.815687i
\(439\) 9.00000 + 9.00000i 0.429547 + 0.429547i 0.888474 0.458927i \(-0.151766\pi\)
−0.458927 + 0.888474i \(0.651766\pi\)
\(440\) 1.41421i 0.0674200i
\(441\) 9.00000 + 25.4558i 0.428571 + 1.21218i
\(442\) 6.00000 6.00000i 0.285391 0.285391i
\(443\) 14.1421 0.671913 0.335957 0.941877i \(-0.390940\pi\)
0.335957 + 0.941877i \(0.390940\pi\)
\(444\) 7.41421 7.48528i 0.351863 0.355236i
\(445\) −2.00000 −0.0948091
\(446\) −5.65685 + 5.65685i −0.267860 + 0.267860i
\(447\) 18.3848 26.0000i 0.869570 1.22976i
\(448\) 4.00000i 0.188982i
\(449\) 15.5563 + 15.5563i 0.734150 + 0.734150i 0.971439 0.237289i \(-0.0762590\pi\)
−0.237289 + 0.971439i \(0.576259\pi\)
\(450\) 1.29289 2.70711i 0.0609476 0.127614i
\(451\) −8.00000 −0.376705
\(452\) −1.41421 1.41421i −0.0665190 0.0665190i
\(453\) 0 0
\(454\) 24.0000 1.12638
\(455\) 16.9706 0.795592
\(456\) −8.00000 5.65685i −0.374634 0.264906i
\(457\) −30.0000 + 30.0000i −1.40334 + 1.40334i −0.614157 + 0.789184i \(0.710504\pi\)
−0.789184 + 0.614157i \(0.789496\pi\)
\(458\) −7.07107 + 7.07107i −0.330409 + 0.330409i
\(459\) 9.07107 5.07107i 0.423401 0.236697i
\(460\) 2.00000 0.0932505
\(461\) 4.24264 + 4.24264i 0.197599 + 0.197599i 0.798970 0.601371i \(-0.205378\pi\)
−0.601371 + 0.798970i \(0.705378\pi\)
\(462\) −9.65685 + 1.65685i −0.449278 + 0.0770838i
\(463\) −4.00000 + 4.00000i −0.185896 + 0.185896i −0.793919 0.608023i \(-0.791963\pi\)
0.608023 + 0.793919i \(0.291963\pi\)
\(464\) −2.82843 + 2.82843i −0.131306 + 0.131306i
\(465\) −4.24264 + 6.00000i −0.196748 + 0.278243i
\(466\) 9.00000 9.00000i 0.416917 0.416917i
\(467\) 22.6274 + 22.6274i 1.04707 + 1.04707i 0.998836 + 0.0482360i \(0.0153600\pi\)
0.0482360 + 0.998836i \(0.484640\pi\)
\(468\) −5.48528 + 11.4853i −0.253557 + 0.530907i
\(469\) 24.0000i 1.10822i
\(470\) 1.41421i 0.0652328i
\(471\) 19.7990 + 14.0000i 0.912289 + 0.645086i
\(472\) 12.0000i 0.552345i
\(473\) 4.24264 4.24264i 0.195077 0.195077i
\(474\) 7.07107 10.0000i 0.324785 0.459315i
\(475\) 4.00000 + 4.00000i 0.183533 + 0.183533i
\(476\) −5.65685 + 5.65685i −0.259281 + 0.259281i
\(477\) −8.00000 + 2.82843i −0.366295 + 0.129505i
\(478\) 20.0000 0.914779
\(479\) −11.3137 11.3137i −0.516937 0.516937i 0.399707 0.916643i \(-0.369112\pi\)
−0.916643 + 0.399707i \(0.869112\pi\)
\(480\) −1.41421 1.00000i −0.0645497 0.0456435i
\(481\) 21.0000 15.0000i 0.957518 0.683941i
\(482\) 18.3848i 0.837404i
\(483\) 2.34315 + 13.6569i 0.106617 + 0.621408i
\(484\) 9.00000i 0.409091i
\(485\) 8.48528 0.385297
\(486\) −10.2929 + 11.7071i −0.466895 + 0.531045i
\(487\) 8.00000 8.00000i 0.362515 0.362515i −0.502223 0.864738i \(-0.667484\pi\)
0.864738 + 0.502223i \(0.167484\pi\)
\(488\) 8.48528i 0.384111i
\(489\) 6.21320 + 36.2132i 0.280971 + 1.63762i
\(490\) −9.00000 −0.406579
\(491\) 12.7279i 0.574403i −0.957870 0.287202i \(-0.907275\pi\)
0.957870 0.287202i \(-0.0927249\pi\)
\(492\) 5.65685 8.00000i 0.255031 0.360668i
\(493\) 8.00000 0.360302
\(494\) −16.9706 16.9706i −0.763542 0.763542i
\(495\) −1.82843 + 3.82843i −0.0821817 + 0.172075i
\(496\) 3.00000 + 3.00000i 0.134704 + 0.134704i
\(497\) 11.3137i 0.507489i
\(498\) −0.828427 4.82843i −0.0371227 0.216367i
\(499\) 6.00000 + 6.00000i 0.268597 + 0.268597i 0.828535 0.559938i \(-0.189175\pi\)
−0.559938 + 0.828535i \(0.689175\pi\)
\(500\) 0.707107 + 0.707107i 0.0316228 + 0.0316228i
\(501\) 0.585786 + 3.41421i 0.0261710 + 0.152536i
\(502\) 12.0000i 0.535586i
\(503\) 7.07107 + 7.07107i 0.315283 + 0.315283i 0.846952 0.531669i \(-0.178435\pi\)
−0.531669 + 0.846952i \(0.678435\pi\)
\(504\) 5.17157 10.8284i 0.230360 0.482336i
\(505\) 1.00000 + 1.00000i 0.0444994 + 0.0444994i
\(506\) −2.82843 −0.125739
\(507\) −5.00000 + 7.07107i −0.222058 + 0.314037i
\(508\) 16.0000i 0.709885i
\(509\) 1.41421 0.0626839 0.0313420 0.999509i \(-0.490022\pi\)
0.0313420 + 0.999509i \(0.490022\pi\)
\(510\) 0.585786 + 3.41421i 0.0259391 + 0.151184i
\(511\) 40.0000i 1.76950i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −14.3431 25.6569i −0.633265 1.13278i
\(514\) −24.0000 −1.05859
\(515\) 0 0
\(516\) 1.24264 + 7.24264i 0.0547042 + 0.318839i
\(517\) 2.00000i 0.0879599i
\(518\) −19.7990 + 14.1421i −0.869918 + 0.621370i
\(519\) −28.0000 19.7990i −1.22906 0.869079i
\(520\) −3.00000 3.00000i −0.131559 0.131559i
\(521\) 31.1127 1.36307 0.681536 0.731785i \(-0.261312\pi\)
0.681536 + 0.731785i \(0.261312\pi\)
\(522\) −11.3137 + 4.00000i −0.495188 + 0.175075i
\(523\) 21.0000 21.0000i 0.918266 0.918266i −0.0786374 0.996903i \(-0.525057\pi\)
0.996903 + 0.0786374i \(0.0250569\pi\)
\(524\) 2.82843 + 2.82843i 0.123560 + 0.123560i
\(525\) −4.00000 + 5.65685i −0.174574 + 0.246885i
\(526\) 19.0000 19.0000i 0.828439 0.828439i
\(527\) 8.48528i 0.369625i
\(528\) 2.00000 + 1.41421i 0.0870388 + 0.0615457i
\(529\) 19.0000i 0.826087i
\(530\) 2.82843i 0.122859i
\(531\) 15.5147 32.4853i 0.673281 1.40974i
\(532\) 16.0000 + 16.0000i 0.693688 + 0.693688i
\(533\) 16.9706 16.9706i 0.735077 0.735077i
\(534\) −2.00000 + 2.82843i −0.0865485 + 0.122398i
\(535\) 6.00000 6.00000i 0.259403 0.259403i
\(536\) 4.24264 4.24264i 0.183254 0.183254i
\(537\) −17.0711 + 2.92893i −0.736671 + 0.126393i
\(538\) −5.00000 5.00000i −0.215565 0.215565i
\(539\) 12.7279 0.548230
\(540\) −2.53553 4.53553i −0.109112 0.195178i
\(541\) −12.0000 + 12.0000i −0.515920 + 0.515920i −0.916334 0.400414i \(-0.868866\pi\)
0.400414 + 0.916334i \(0.368866\pi\)
\(542\) 11.3137 11.3137i 0.485965 0.485965i
\(543\) −14.1421 10.0000i −0.606897 0.429141i
\(544\) 2.00000 0.0857493
\(545\) 19.7990 0.848096
\(546\) 16.9706 24.0000i 0.726273 1.02711i
\(547\) −3.00000 3.00000i −0.128271 0.128271i 0.640057 0.768328i \(-0.278911\pi\)
−0.768328 + 0.640057i \(0.778911\pi\)
\(548\) −21.2132 −0.906183
\(549\) 10.9706 22.9706i 0.468212 0.980360i
\(550\) −1.00000 1.00000i −0.0426401 0.0426401i
\(551\) 22.6274i 0.963960i
\(552\) 2.00000 2.82843i 0.0851257 0.120386i
\(553\) −20.0000 + 20.0000i −0.850487 + 0.850487i
\(554\) −21.2132 −0.901263
\(555\) 0.0502525 + 10.5355i 0.00213310 + 0.447209i
\(556\) 0 0
\(557\) 1.41421 1.41421i 0.0599222 0.0599222i −0.676511 0.736433i \(-0.736509\pi\)
0.736433 + 0.676511i \(0.236509\pi\)
\(558\) 4.24264 + 12.0000i 0.179605 + 0.508001i
\(559\) 18.0000i 0.761319i
\(560\) 2.82843 + 2.82843i 0.119523 + 0.119523i
\(561\) −0.828427 4.82843i −0.0349762 0.203856i
\(562\) 6.00000 0.253095
\(563\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(564\) 2.00000 + 1.41421i 0.0842152 + 0.0595491i
\(565\) 2.00000 0.0841406
\(566\) 29.6985 1.24832
\(567\) 28.0000 22.6274i 1.17589 0.950262i
\(568\) −2.00000 + 2.00000i −0.0839181 + 0.0839181i
\(569\) −29.6985 + 29.6985i −1.24503 + 1.24503i −0.287135 + 0.957890i \(0.592703\pi\)
−0.957890 + 0.287135i \(0.907297\pi\)
\(570\) 9.65685 1.65685i 0.404481 0.0693980i
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 4.24264 + 4.24264i 0.177394 + 0.177394i
\(573\) −7.02944 40.9706i −0.293659 1.71157i
\(574\) −16.0000 + 16.0000i −0.667827 + 0.667827i
\(575\) −1.41421 + 1.41421i −0.0589768 + 0.0589768i
\(576\) −2.82843 + 1.00000i −0.117851 + 0.0416667i
\(577\) 10.0000 10.0000i 0.416305 0.416305i −0.467623 0.883928i \(-0.654889\pi\)
0.883928 + 0.467623i \(0.154889\pi\)
\(578\) 9.19239 + 9.19239i 0.382353 + 0.382353i
\(579\) 28.9706 4.97056i 1.20398 0.206570i
\(580\) 4.00000i 0.166091i
\(581\) 11.3137i 0.469372i
\(582\) 8.48528 12.0000i 0.351726 0.497416i
\(583\) 4.00000i 0.165663i
\(584\) 7.07107 7.07107i 0.292603 0.292603i
\(585\) −4.24264 12.0000i −0.175412 0.496139i
\(586\) 0 0
\(587\) 28.2843 28.2843i 1.16742 1.16742i 0.184604 0.982813i \(-0.440900\pi\)
0.982813 0.184604i \(-0.0591002\pi\)
\(588\) −9.00000 + 12.7279i −0.371154 + 0.524891i
\(589\) −24.0000 −0.988903
\(590\) 8.48528 + 8.48528i 0.349334 + 0.349334i
\(591\) 2.82843 4.00000i 0.116346 0.164538i
\(592\) 6.00000 + 1.00000i 0.246598 + 0.0410997i
\(593\) 24.0416i 0.987271i −0.869669 0.493636i \(-0.835668\pi\)
0.869669 0.493636i \(-0.164332\pi\)
\(594\) 3.58579 + 6.41421i 0.147127 + 0.263178i
\(595\) 8.00000i 0.327968i
\(596\) 18.3848 0.753070
\(597\) −0.414214 2.41421i −0.0169526 0.0988072i
\(598\) 6.00000 6.00000i 0.245358 0.245358i
\(599\) 22.6274i 0.924531i −0.886742 0.462266i \(-0.847037\pi\)
0.886742 0.462266i \(-0.152963\pi\)
\(600\) 1.70711 0.292893i 0.0696923 0.0119573i
\(601\) −42.0000 −1.71322 −0.856608 0.515968i \(-0.827432\pi\)
−0.856608 + 0.515968i \(0.827432\pi\)
\(602\) 16.9706i 0.691669i
\(603\) 16.9706 6.00000i 0.691095 0.244339i
\(604\) 0 0
\(605\) −6.36396 6.36396i −0.258732 0.258732i
\(606\) 2.41421 0.414214i 0.0980707 0.0168263i
\(607\) −8.00000 8.00000i −0.324710 0.324710i 0.525861 0.850571i \(-0.323743\pi\)
−0.850571 + 0.525861i \(0.823743\pi\)
\(608\) 5.65685i 0.229416i
\(609\) 27.3137 4.68629i 1.10681 0.189898i
\(610\) 6.00000 + 6.00000i 0.242933 + 0.242933i
\(611\) 4.24264 + 4.24264i 0.171639 + 0.171639i
\(612\) 5.41421 + 2.58579i 0.218857 + 0.104524i
\(613\) 16.0000i 0.646234i −0.946359 0.323117i \(-0.895269\pi\)
0.946359 0.323117i \(-0.104731\pi\)
\(614\) −19.7990 19.7990i −0.799022 0.799022i
\(615\) 1.65685 + 9.65685i 0.0668108 + 0.389402i
\(616\) −4.00000 4.00000i −0.161165 0.161165i
\(617\) 35.3553 1.42335 0.711676 0.702508i \(-0.247936\pi\)
0.711676 + 0.702508i \(0.247936\pi\)
\(618\) 0 0
\(619\) 20.0000i 0.803868i 0.915669 + 0.401934i \(0.131662\pi\)
−0.915669 + 0.401934i \(0.868338\pi\)
\(620\) −4.24264 −0.170389
\(621\) 9.07107 5.07107i 0.364009 0.203495i
\(622\) 20.0000i 0.801927i
\(623\) 5.65685 5.65685i 0.226637 0.226637i
\(624\) −7.24264 + 1.24264i −0.289938 + 0.0497454i
\(625\) −1.00000 −0.0400000
\(626\) 33.9411i 1.35656i
\(627\) −13.6569 + 2.34315i −0.545402 + 0.0935762i
\(628\) 14.0000i 0.558661i
\(629\) −7.07107 9.89949i −0.281942 0.394719i
\(630\) 4.00000 + 11.3137i 0.159364 + 0.450749i
\(631\) −11.0000 11.0000i −0.437903 0.437903i 0.453403 0.891306i \(-0.350210\pi\)
−0.891306 + 0.453403i \(0.850210\pi\)
\(632\) 7.07107 0.281272
\(633\) −11.3137 8.00000i −0.449680 0.317971i
\(634\) −18.0000 + 18.0000i −0.714871 + 0.714871i
\(635\) 11.3137 + 11.3137i 0.448971 + 0.448971i
\(636\) −4.00000 2.82843i −0.158610 0.112154i
\(637\) −27.0000 + 27.0000i −1.06978 + 1.06978i
\(638\) 5.65685i 0.223957i
\(639\) −8.00000 + 2.82843i −0.316475 + 0.111891i
\(640\) 1.00000i 0.0395285i
\(641\) 11.3137i 0.446865i 0.974719 + 0.223432i \(0.0717262\pi\)
−0.974719 + 0.223432i \(0.928274\pi\)
\(642\) −2.48528 14.4853i −0.0980862 0.571688i
\(643\) −25.0000 25.0000i −0.985904 0.985904i 0.0139983 0.999902i \(-0.495544\pi\)
−0.999902 + 0.0139983i \(0.995544\pi\)
\(644\) −5.65685 + 5.65685i −0.222911 + 0.222911i
\(645\) −6.00000 4.24264i −0.236250 0.167054i
\(646\) −8.00000 + 8.00000i −0.314756 + 0.314756i
\(647\) −5.65685 + 5.65685i −0.222394 + 0.222394i −0.809506 0.587112i \(-0.800265\pi\)
0.587112 + 0.809506i \(0.300265\pi\)
\(648\) −8.94975 0.949747i −0.351579 0.0373096i
\(649\) −12.0000 12.0000i −0.471041 0.471041i
\(650\) 4.24264 0.166410
\(651\) −4.97056 28.9706i −0.194812 1.13545i
\(652\) −15.0000 + 15.0000i −0.587445 + 0.587445i
\(653\) −12.7279 + 12.7279i −0.498082 + 0.498082i −0.910841 0.412758i \(-0.864565\pi\)
0.412758 + 0.910841i \(0.364565\pi\)
\(654\) 19.7990 28.0000i 0.774202 1.09489i
\(655\) −4.00000 −0.156293
\(656\) 5.65685 0.220863
\(657\) 28.2843 10.0000i 1.10347 0.390137i
\(658\) −4.00000 4.00000i −0.155936 0.155936i
\(659\) −26.8701 −1.04671 −0.523354 0.852115i \(-0.675320\pi\)
−0.523354 + 0.852115i \(0.675320\pi\)
\(660\) −2.41421 + 0.414214i −0.0939731 + 0.0161232i
\(661\) −28.0000 28.0000i −1.08907 1.08907i −0.995624 0.0934498i \(-0.970211\pi\)
−0.0934498 0.995624i \(-0.529789\pi\)
\(662\) 2.82843i 0.109930i
\(663\) 12.0000 + 8.48528i 0.466041 + 0.329541i
\(664\) 2.00000 2.00000i 0.0776151 0.0776151i
\(665\) −22.6274 −0.877454
\(666\) 14.9497 + 10.4645i 0.579291 + 0.405490i
\(667\) 8.00000 0.309761
\(668\) −1.41421 + 1.41421i −0.0547176 + 0.0547176i
\(669\) −11.3137 8.00000i −0.437413 0.309298i
\(670\) 6.00000i 0.231800i
\(671\) −8.48528 8.48528i −0.327571 0.327571i
\(672\) 6.82843 1.17157i 0.263412 0.0451944i
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) 18.3848 + 18.3848i 0.708155 + 0.708155i
\(675\) 5.00000 + 1.41421i 0.192450 + 0.0544331i
\(676\) −5.00000 −0.192308
\(677\) −45.2548 −1.73928 −0.869642 0.493682i \(-0.835651\pi\)
−0.869642 + 0.493682i \(0.835651\pi\)
\(678\) 2.00000 2.82843i 0.0768095 0.108625i
\(679\) −24.0000 + 24.0000i −0.921035 + 0.921035i
\(680\) −1.41421 + 1.41421i −0.0542326 + 0.0542326i
\(681\) 7.02944 + 40.9706i 0.269369 + 1.57000i
\(682\) 6.00000 0.229752
\(683\) −33.9411 33.9411i −1.29872 1.29872i −0.929237 0.369484i \(-0.879534\pi\)
−0.369484 0.929237i \(-0.620466\pi\)
\(684\) 7.31371 15.3137i 0.279647 0.585534i
\(685\) 15.0000 15.0000i 0.573121 0.573121i
\(686\) 5.65685 5.65685i 0.215980 0.215980i
\(687\) −14.1421 10.0000i −0.539556 0.381524i
\(688\) −3.00000 + 3.00000i −0.114374 + 0.114374i
\(689\) −8.48528 8.48528i −0.323263 0.323263i
\(690\) 0.585786 + 3.41421i 0.0223005 + 0.129977i
\(691\) 12.0000i 0.456502i 0.973602 + 0.228251i \(0.0733006\pi\)
−0.973602 + 0.228251i \(0.926699\pi\)
\(692\) 19.7990i 0.752645i
\(693\) −5.65685 16.0000i −0.214886 0.607790i
\(694\) 32.0000i 1.21470i
\(695\) 0 0
\(696\) −5.65685 4.00000i −0.214423 0.151620i
\(697\) −8.00000 8.00000i −0.303022 0.303022i
\(698\) −4.24264 + 4.24264i −0.160586 + 0.160586i
\(699\) 18.0000 + 12.7279i 0.680823 + 0.481414i
\(700\) −4.00000 −0.151186
\(701\) 21.2132 + 21.2132i 0.801212 + 0.801212i 0.983285 0.182073i \(-0.0582808\pi\)
−0.182073 + 0.983285i \(0.558281\pi\)
\(702\) −21.2132 6.00000i −0.800641 0.226455i
\(703\) −28.0000 + 20.0000i −1.05604 + 0.754314i
\(704\) 1.41421i 0.0533002i
\(705\) −2.41421 + 0.414214i −0.0909245 + 0.0156002i
\(706\) 26.0000i 0.978523i
\(707\) −5.65685 −0.212748
\(708\) 20.4853 3.51472i 0.769884 0.132091i
\(709\) −14.0000 + 14.0000i −0.525781 + 0.525781i −0.919312 0.393531i \(-0.871254\pi\)
0.393531 + 0.919312i \(0.371254\pi\)
\(710\) 2.82843i 0.106149i
\(711\) 19.1421 + 9.14214i 0.717886 + 0.342857i
\(712\) −2.00000 −0.0749532
\(713\) 8.48528i 0.317776i
\(714\) −11.3137 8.00000i −0.423405 0.299392i
\(715\) −6.00000 −0.224387
\(716\) −7.07107 7.07107i −0.264258 0.264258i
\(717\) 5.85786 + 34.1421i 0.218766 + 1.27506i
\(718\) 16.0000 + 16.0000i 0.597115 + 0.597115i
\(719\) 14.1421i 0.527413i 0.964603 + 0.263706i \(0.0849450\pi\)
−0.964603 + 0.263706i \(0.915055\pi\)
\(720\) 1.29289 2.70711i 0.0481833 0.100888i
\(721\) 0 0
\(722\) 9.19239 + 9.19239i 0.342105 + 0.342105i
\(723\) 31.3848 5.38478i 1.16721 0.200262i
\(724\) 10.0000i 0.371647i
\(725\) 2.82843 + 2.82843i 0.105045 + 0.105045i
\(726\) −15.3640 + 2.63604i −0.570210 + 0.0978326i
\(727\) −22.0000 22.0000i −0.815935 0.815935i 0.169581 0.985516i \(-0.445758\pi\)
−0.985516 + 0.169581i \(0.945758\pi\)
\(728\) 16.9706 0.628971
\(729\) −23.0000 14.1421i −0.851852 0.523783i
\(730\) 10.0000i 0.370117i
\(731\) 8.48528 0.313839
\(732\) 14.4853 2.48528i 0.535391 0.0918586i
\(733\) 40.0000i 1.47743i 0.674016 + 0.738717i \(0.264568\pi\)
−0.674016 + 0.738717i \(0.735432\pi\)
\(734\) 8.48528 8.48528i 0.313197 0.313197i
\(735\) −2.63604 15.3640i −0.0972318 0.566708i
\(736\) 2.00000 0.0737210
\(737\) 8.48528i 0.312559i
\(738\) 15.3137 + 7.31371i 0.563705 + 0.269221i
\(739\) 4.00000i 0.147142i 0.997290 + 0.0735712i \(0.0234396\pi\)
−0.997290 + 0.0735712i \(0.976560\pi\)
\(740\) −4.94975 + 3.53553i −0.181956 + 0.129969i
\(741\) 24.0000 33.9411i 0.881662 1.24686i
\(742\) 8.00000 + 8.00000i 0.293689 + 0.293689i
\(743\) −41.0122 −1.50459 −0.752296 0.658826i \(-0.771054\pi\)
−0.752296 + 0.658826i \(0.771054\pi\)
\(744\) −4.24264 + 6.00000i −0.155543 + 0.219971i
\(745\) −13.0000 + 13.0000i −0.476283 + 0.476283i
\(746\) −15.5563 15.5563i −0.569558 0.569558i
\(747\) 8.00000 2.82843i 0.292705 0.103487i
\(748\) 2.00000 2.00000i 0.0731272 0.0731272i
\(749\) 33.9411i 1.24018i
\(750\) −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
\(753\) 20.4853 3.51472i 0.746525 0.128083i
\(754\) −12.0000 12.0000i −0.437014 0.437014i
\(755\) 0 0
\(756\) 20.0000 + 5.65685i 0.727393 + 0.205738i
\(757\) 5.00000 5.00000i 0.181728 0.181728i −0.610380 0.792108i \(-0.708983\pi\)
0.792108 + 0.610380i \(0.208983\pi\)
\(758\) −19.7990 + 19.7990i −0.719132 + 0.719132i
\(759\) −0.828427 4.82843i −0.0300700 0.175261i
\(760\) 4.00000 + 4.00000i 0.145095 + 0.145095i
\(761\) −5.65685 −0.205061 −0.102530 0.994730i \(-0.532694\pi\)
−0.102530 + 0.994730i \(0.532694\pi\)
\(762\) 27.3137 4.68629i 0.989471 0.169766i
\(763\) −56.0000 + 56.0000i −2.02734 + 2.02734i
\(764\) 16.9706 16.9706i 0.613973 0.613973i
\(765\) −5.65685 + 2.00000i −0.204524 + 0.0723102i
\(766\) 24.0000 0.867155
\(767\) 50.9117 1.83831
\(768\) −1.41421 1.00000i −0.0510310 0.0360844i
\(769\) −5.00000 5.00000i −0.180305 0.180305i 0.611184 0.791489i \(-0.290694\pi\)
−0.791489 + 0.611184i \(0.790694\pi\)
\(770\) 5.65685 0.203859
\(771\) −7.02944 40.9706i −0.253159 1.47552i
\(772\) 12.0000 + 12.0000i 0.431889 + 0.431889i
\(773\) 28.2843i 1.01731i −0.860969 0.508657i \(-0.830142\pi\)
0.860969 0.508657i \(-0.169858\pi\)
\(774\) −12.0000 + 4.24264i −0.431331 + 0.152499i
\(775\) 3.00000 3.00000i 0.107763 0.107763i
\(776\) 8.48528