Properties

Label 1110.2.u.d.401.2
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 401.2
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.d.191.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(1.41421 + 1.00000i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(1.70711 - 0.292893i) q^{6} +2.00000 q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(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} +2.00000 q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +1.00000 q^{10} +(1.00000 - 1.41421i) q^{12} +(1.00000 - 1.00000i) q^{13} +(1.41421 - 1.41421i) q^{14} +(0.292893 + 1.70711i) q^{15} -1.00000 q^{16} +(4.24264 + 4.24264i) q^{17} +(2.70711 + 1.29289i) q^{18} +(-3.00000 + 3.00000i) q^{19} +(0.707107 - 0.707107i) q^{20} +(2.82843 + 2.00000i) q^{21} +(-2.82843 - 2.82843i) q^{23} +(-0.292893 - 1.70711i) q^{24} +1.00000i q^{25} -1.41421i q^{26} +(-1.41421 + 5.00000i) q^{27} -2.00000i q^{28} +(4.24264 - 4.24264i) q^{29} +(1.41421 + 1.00000i) q^{30} +(-7.00000 - 7.00000i) q^{31} +(-0.707107 + 0.707107i) q^{32} +6.00000 q^{34} +(1.41421 + 1.41421i) q^{35} +(2.82843 - 1.00000i) q^{36} +(-1.00000 + 6.00000i) q^{37} +4.24264i q^{38} +(2.41421 - 0.414214i) q^{39} -1.00000i q^{40} +5.65685 q^{41} +(3.41421 - 0.585786i) q^{42} +(7.00000 - 7.00000i) q^{43} +(-1.29289 + 2.70711i) q^{45} -4.00000 q^{46} -2.82843i q^{47} +(-1.41421 - 1.00000i) q^{48} -3.00000 q^{49} +(0.707107 + 0.707107i) q^{50} +(1.75736 + 10.2426i) q^{51} +(-1.00000 - 1.00000i) q^{52} +5.65685i q^{53} +(2.53553 + 4.53553i) q^{54} +(-1.41421 - 1.41421i) q^{56} +(-7.24264 + 1.24264i) q^{57} -6.00000i q^{58} +(5.65685 + 5.65685i) q^{59} +(1.70711 - 0.292893i) q^{60} +(-9.00000 - 9.00000i) q^{61} -9.89949 q^{62} +(2.00000 + 5.65685i) q^{63} +1.00000i q^{64} +1.41421 q^{65} +4.00000i q^{67} +(4.24264 - 4.24264i) q^{68} +(-1.17157 - 6.82843i) q^{69} +2.00000 q^{70} +2.82843i q^{71} +(1.29289 - 2.70711i) q^{72} -6.00000i q^{73} +(3.53553 + 4.94975i) q^{74} +(-1.00000 + 1.41421i) q^{75} +(3.00000 + 3.00000i) q^{76} +(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} +(2.00000 - 2.82843i) q^{84} +6.00000i q^{85} -9.89949i q^{86} +(10.2426 - 1.75736i) q^{87} +(-1.41421 + 1.41421i) q^{89} +(1.00000 + 2.82843i) q^{90} +(2.00000 - 2.00000i) q^{91} +(-2.82843 + 2.82843i) q^{92} +(-2.89949 - 16.8995i) q^{93} +(-2.00000 - 2.00000i) q^{94} -4.24264 q^{95} +(-1.70711 + 0.292893i) q^{96} +(7.00000 - 7.00000i) q^{97} +(-2.12132 + 2.12132i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{6} + 8q^{7} + 4q^{9} + O(q^{10}) \) \( 4q + 4q^{6} + 8q^{7} + 4q^{9} + 4q^{10} + 4q^{12} + 4q^{13} + 4q^{15} - 4q^{16} + 8q^{18} - 12q^{19} - 4q^{24} - 28q^{31} + 24q^{34} - 4q^{37} + 4q^{39} + 8q^{42} + 28q^{43} - 8q^{45} - 16q^{46} - 12q^{49} + 24q^{51} - 4q^{52} - 4q^{54} - 12q^{57} + 4q^{60} - 36q^{61} + 8q^{63} - 16q^{69} + 8q^{70} + 8q^{72} - 4q^{75} + 12q^{76} + 12q^{79} - 28q^{81} + 16q^{82} + 8q^{84} + 24q^{87} + 4q^{90} + 8q^{91} + 28q^{93} - 8q^{94} - 4q^{96} + 28q^{97} + O(q^{100}) \)

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
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 1.00000 + 2.82843i 0.333333 + 0.942809i
\(10\) 1.00000 0.316228
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.00000 1.41421i 0.288675 0.408248i
\(13\) 1.00000 1.00000i 0.277350 0.277350i −0.554700 0.832050i \(-0.687167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 1.41421 1.41421i 0.377964 0.377964i
\(15\) 0.292893 + 1.70711i 0.0756247 + 0.440773i
\(16\) −1.00000 −0.250000
\(17\) 4.24264 + 4.24264i 1.02899 + 1.02899i 0.999567 + 0.0294245i \(0.00936746\pi\)
0.0294245 + 0.999567i \(0.490633\pi\)
\(18\) 2.70711 + 1.29289i 0.638071 + 0.304738i
\(19\) −3.00000 + 3.00000i −0.688247 + 0.688247i −0.961844 0.273597i \(-0.911786\pi\)
0.273597 + 0.961844i \(0.411786\pi\)
\(20\) 0.707107 0.707107i 0.158114 0.158114i
\(21\) 2.82843 + 2.00000i 0.617213 + 0.436436i
\(22\) 0 0
\(23\) −2.82843 2.82843i −0.589768 0.589768i 0.347801 0.937568i \(-0.386929\pi\)
−0.937568 + 0.347801i \(0.886929\pi\)
\(24\) −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
\(28\) 2.00000i 0.377964i
\(29\) 4.24264 4.24264i 0.787839 0.787839i −0.193301 0.981140i \(-0.561919\pi\)
0.981140 + 0.193301i \(0.0619194\pi\)
\(30\) 1.41421 + 1.00000i 0.258199 + 0.182574i
\(31\) −7.00000 7.00000i −1.25724 1.25724i −0.952407 0.304830i \(-0.901400\pi\)
−0.304830 0.952407i \(-0.598600\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 1.41421 + 1.41421i 0.239046 + 0.239046i
\(36\) 2.82843 1.00000i 0.471405 0.166667i
\(37\) −1.00000 + 6.00000i −0.164399 + 0.986394i
\(38\) 4.24264i 0.688247i
\(39\) 2.41421 0.414214i 0.386584 0.0663273i
\(40\) 1.00000i 0.158114i
\(41\) 5.65685 0.883452 0.441726 0.897150i \(-0.354366\pi\)
0.441726 + 0.897150i \(0.354366\pi\)
\(42\) 3.41421 0.585786i 0.526825 0.0903888i
\(43\) 7.00000 7.00000i 1.06749 1.06749i 0.0699387 0.997551i \(-0.477720\pi\)
0.997551 0.0699387i \(-0.0222804\pi\)
\(44\) 0 0
\(45\) −1.29289 + 2.70711i −0.192733 + 0.403552i
\(46\) −4.00000 −0.589768
\(47\) 2.82843i 0.412568i −0.978492 0.206284i \(-0.933863\pi\)
0.978492 0.206284i \(-0.0661372\pi\)
\(48\) −1.41421 1.00000i −0.204124 0.144338i
\(49\) −3.00000 −0.428571
\(50\) 0.707107 + 0.707107i 0.100000 + 0.100000i
\(51\) 1.75736 + 10.2426i 0.246080 + 1.43426i
\(52\) −1.00000 1.00000i −0.138675 0.138675i
\(53\) 5.65685i 0.777029i 0.921443 + 0.388514i \(0.127012\pi\)
−0.921443 + 0.388514i \(0.872988\pi\)
\(54\) 2.53553 + 4.53553i 0.345042 + 0.617208i
\(55\) 0 0
\(56\) −1.41421 1.41421i −0.188982 0.188982i
\(57\) −7.24264 + 1.24264i −0.959311 + 0.164592i
\(58\) 6.00000i 0.787839i
\(59\) 5.65685 + 5.65685i 0.736460 + 0.736460i 0.971891 0.235431i \(-0.0756503\pi\)
−0.235431 + 0.971891i \(0.575650\pi\)
\(60\) 1.70711 0.292893i 0.220387 0.0378124i
\(61\) −9.00000 9.00000i −1.15233 1.15233i −0.986084 0.166248i \(-0.946835\pi\)
−0.166248 0.986084i \(-0.553165\pi\)
\(62\) −9.89949 −1.25724
\(63\) 2.00000 + 5.65685i 0.251976 + 0.712697i
\(64\) 1.00000i 0.125000i
\(65\) 1.41421 0.175412
\(66\) 0 0
\(67\) 4.00000i 0.488678i 0.969690 + 0.244339i \(0.0785709\pi\)
−0.969690 + 0.244339i \(0.921429\pi\)
\(68\) 4.24264 4.24264i 0.514496 0.514496i
\(69\) −1.17157 6.82843i −0.141041 0.822046i
\(70\) 2.00000 0.239046
\(71\) 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
\(73\) 6.00000i 0.702247i −0.936329 0.351123i \(-0.885800\pi\)
0.936329 0.351123i \(-0.114200\pi\)
\(74\) 3.53553 + 4.94975i 0.410997 + 0.575396i
\(75\) −1.00000 + 1.41421i −0.115470 + 0.163299i
\(76\) 3.00000 + 3.00000i 0.344124 + 0.344124i
\(77\) 0 0
\(78\) 1.41421 2.00000i 0.160128 0.226455i
\(79\) 3.00000 3.00000i 0.337526 0.337526i −0.517909 0.855436i \(-0.673290\pi\)
0.855436 + 0.517909i \(0.173290\pi\)
\(80\) −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 \(0.0496119\pi\)
−0.987878 + 0.155230i \(0.950388\pi\)
\(84\) 2.00000 2.82843i 0.218218 0.308607i
\(85\) 6.00000i 0.650791i
\(86\) 9.89949i 1.06749i
\(87\) 10.2426 1.75736i 1.09813 0.188409i
\(88\) 0 0
\(89\) −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
\(91\) 2.00000 2.00000i 0.209657 0.209657i
\(92\) −2.82843 + 2.82843i −0.294884 + 0.294884i
\(93\) −2.89949 16.8995i −0.300664 1.75240i
\(94\) −2.00000 2.00000i −0.206284 0.206284i
\(95\) −4.24264 −0.435286
\(96\) −1.70711 + 0.292893i −0.174231 + 0.0298933i
\(97\) 7.00000 7.00000i 0.710742 0.710742i −0.255948 0.966691i \(-0.582388\pi\)
0.966691 + 0.255948i \(0.0823876\pi\)
\(98\) −2.12132 + 2.12132i −0.214286 + 0.214286i
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −2.82843 −0.281439 −0.140720 0.990050i \(-0.544942\pi\)
−0.140720 + 0.990050i \(0.544942\pi\)
\(102\) 8.48528 + 6.00000i 0.840168 + 0.594089i
\(103\) −5.00000 5.00000i −0.492665 0.492665i 0.416480 0.909145i \(-0.363264\pi\)
−0.909145 + 0.416480i \(0.863264\pi\)
\(104\) −1.41421 −0.138675
\(105\) 0.585786 + 3.41421i 0.0571669 + 0.333193i
\(106\) 4.00000 + 4.00000i 0.388514 + 0.388514i
\(107\) 11.3137i 1.09374i −0.837218 0.546869i \(-0.815820\pi\)
0.837218 0.546869i \(-0.184180\pi\)
\(108\) 5.00000 + 1.41421i 0.481125 + 0.136083i
\(109\) −3.00000 + 3.00000i −0.287348 + 0.287348i −0.836031 0.548683i \(-0.815129\pi\)
0.548683 + 0.836031i \(0.315129\pi\)
\(110\) 0 0
\(111\) −7.41421 + 7.48528i −0.703726 + 0.710471i
\(112\) −2.00000 −0.188982
\(113\) −1.41421 + 1.41421i −0.133038 + 0.133038i −0.770490 0.637452i \(-0.779988\pi\)
0.637452 + 0.770490i \(0.279988\pi\)
\(114\) −4.24264 + 6.00000i −0.397360 + 0.561951i
\(115\) 4.00000i 0.373002i
\(116\) −4.24264 4.24264i −0.393919 0.393919i
\(117\) 3.82843 + 1.82843i 0.353938 + 0.169038i
\(118\) 8.00000 0.736460
\(119\) 8.48528 + 8.48528i 0.777844 + 0.777844i
\(120\) 1.00000 1.41421i 0.0912871 0.129099i
\(121\) −11.0000 −1.00000
\(122\) −12.7279 −1.15233
\(123\) 8.00000 + 5.65685i 0.721336 + 0.510061i
\(124\) −7.00000 + 7.00000i −0.628619 + 0.628619i
\(125\) −0.707107 + 0.707107i −0.0632456 + 0.0632456i
\(126\) 5.41421 + 2.58579i 0.482336 + 0.230360i
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 16.8995 2.89949i 1.48792 0.255286i
\(130\) 1.00000 1.00000i 0.0877058 0.0877058i
\(131\) −11.3137 + 11.3137i −0.988483 + 0.988483i −0.999934 0.0114511i \(-0.996355\pi\)
0.0114511 + 0.999934i \(0.496355\pi\)
\(132\) 0 0
\(133\) −6.00000 + 6.00000i −0.520266 + 0.520266i
\(134\) 2.82843 + 2.82843i 0.244339 + 0.244339i
\(135\) −4.53553 + 2.53553i −0.390357 + 0.218224i
\(136\) 6.00000i 0.514496i
\(137\) 2.82843i 0.241649i 0.992674 + 0.120824i \(0.0385538\pi\)
−0.992674 + 0.120824i \(0.961446\pi\)
\(138\) −5.65685 4.00000i −0.481543 0.340503i
\(139\) 4.00000i 0.339276i 0.985506 + 0.169638i \(0.0542598\pi\)
−0.985506 + 0.169638i \(0.945740\pi\)
\(140\) 1.41421 1.41421i 0.119523 0.119523i
\(141\) 2.82843 4.00000i 0.238197 0.336861i
\(142\) 2.00000 + 2.00000i 0.167836 + 0.167836i
\(143\) 0 0
\(144\) −1.00000 2.82843i −0.0833333 0.235702i
\(145\) 6.00000 0.498273
\(146\) −4.24264 4.24264i −0.351123 0.351123i
\(147\) −4.24264 3.00000i −0.349927 0.247436i
\(148\) 6.00000 + 1.00000i 0.493197 + 0.0821995i
\(149\) 19.7990i 1.62200i −0.585049 0.810998i \(-0.698925\pi\)
0.585049 0.810998i \(-0.301075\pi\)
\(150\) 0.292893 + 1.70711i 0.0239146 + 0.139385i
\(151\) 18.0000i 1.46482i −0.680864 0.732410i \(-0.738396\pi\)
0.680864 0.732410i \(-0.261604\pi\)
\(152\) 4.24264 0.344124
\(153\) −7.75736 + 16.2426i −0.627145 + 1.31314i
\(154\) 0 0
\(155\) 9.89949i 0.795147i
\(156\) −0.414214 2.41421i −0.0331636 0.193292i
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) 4.24264i 0.337526i
\(159\) −5.65685 + 8.00000i −0.448618 + 0.634441i
\(160\) −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 0
\(166\) 2.00000 + 2.00000i 0.155230 + 0.155230i
\(167\) 11.3137 + 11.3137i 0.875481 + 0.875481i 0.993063 0.117582i \(-0.0375143\pi\)
−0.117582 + 0.993063i \(0.537514\pi\)
\(168\) −0.585786 3.41421i −0.0451944 0.263412i
\(169\) 11.0000i 0.846154i
\(170\) 4.24264 + 4.24264i 0.325396 + 0.325396i
\(171\) −11.4853 5.48528i −0.878301 0.419470i
\(172\) −7.00000 7.00000i −0.533745 0.533745i
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 6.00000 8.48528i 0.454859 0.643268i
\(175\) 2.00000i 0.151186i
\(176\) 0 0
\(177\) 2.34315 + 13.6569i 0.176122 + 1.02651i
\(178\) 2.00000i 0.149906i
\(179\) 11.3137 11.3137i 0.845626 0.845626i −0.143958 0.989584i \(-0.545983\pi\)
0.989584 + 0.143958i \(0.0459829\pi\)
\(180\) 2.70711 + 1.29289i 0.201776 + 0.0963666i
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 2.82843i 0.209657i
\(183\) −3.72792 21.7279i −0.275576 1.60617i
\(184\) 4.00000i 0.294884i
\(185\) −4.94975 + 3.53553i −0.363913 + 0.259938i
\(186\) −14.0000 9.89949i −1.02653 0.725866i
\(187\) 0 0
\(188\) −2.82843 −0.206284
\(189\) −2.82843 + 10.0000i −0.205738 + 0.727393i
\(190\) −3.00000 + 3.00000i −0.217643 + 0.217643i
\(191\) −5.65685 5.65685i −0.409316 0.409316i 0.472184 0.881500i \(-0.343466\pi\)
−0.881500 + 0.472184i \(0.843466\pi\)
\(192\) −1.00000 + 1.41421i −0.0721688 + 0.102062i
\(193\) −1.00000 + 1.00000i −0.0719816 + 0.0719816i −0.742181 0.670199i \(-0.766209\pi\)
0.670199 + 0.742181i \(0.266209\pi\)
\(194\) 9.89949i 0.710742i
\(195\) 2.00000 + 1.41421i 0.143223 + 0.101274i
\(196\) 3.00000i 0.214286i
\(197\) 2.82843i 0.201517i 0.994911 + 0.100759i \(0.0321270\pi\)
−0.994911 + 0.100759i \(0.967873\pi\)
\(198\) 0 0
\(199\) 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
\(201\) −4.00000 + 5.65685i −0.282138 + 0.399004i
\(202\) −2.00000 + 2.00000i −0.140720 + 0.140720i
\(203\) 8.48528 8.48528i 0.595550 0.595550i
\(204\) 10.2426 1.75736i 0.717128 0.123040i
\(205\) 4.00000 + 4.00000i 0.279372 + 0.279372i
\(206\) −7.07107 −0.492665
\(207\) 5.17157 10.8284i 0.359449 0.752628i
\(208\) −1.00000 + 1.00000i −0.0693375 + 0.0693375i
\(209\) 0 0
\(210\) 2.82843 + 2.00000i 0.195180 + 0.138013i
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 5.65685 0.388514
\(213\) −2.82843 + 4.00000i −0.193801 + 0.274075i
\(214\) −8.00000 8.00000i −0.546869 0.546869i
\(215\) 9.89949 0.675140
\(216\) 4.53553 2.53553i 0.308604 0.172521i
\(217\) −14.0000 14.0000i −0.950382 0.950382i
\(218\) 4.24264i 0.287348i
\(219\) 6.00000 8.48528i 0.405442 0.573382i
\(220\) 0 0
\(221\) 8.48528 0.570782
\(222\) 0.0502525 + 10.5355i 0.00337273 + 0.707099i
\(223\) −24.0000 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) −1.41421 + 1.41421i −0.0944911 + 0.0944911i
\(225\) −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 \(-0.543301\pi\)
\(228\) 1.24264 + 7.24264i 0.0822959 + 0.479656i
\(229\) −26.0000 −1.71813 −0.859064 0.511868i \(-0.828954\pi\)
−0.859064 + 0.511868i \(0.828954\pi\)
\(230\) −2.82843 2.82843i −0.186501 0.186501i
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) 28.2843 1.85296 0.926482 0.376339i \(-0.122817\pi\)
0.926482 + 0.376339i \(0.122817\pi\)
\(234\) 4.00000 1.41421i 0.261488 0.0924500i
\(235\) 2.00000 2.00000i 0.130466 0.130466i
\(236\) 5.65685 5.65685i 0.368230 0.368230i
\(237\) 7.24264 1.24264i 0.470460 0.0807182i
\(238\) 12.0000 0.777844
\(239\) 14.1421 + 14.1421i 0.914779 + 0.914779i 0.996643 0.0818647i \(-0.0260876\pi\)
−0.0818647 + 0.996643i \(0.526088\pi\)
\(240\) −0.292893 1.70711i −0.0189062 0.110193i
\(241\) −11.0000 + 11.0000i −0.708572 + 0.708572i −0.966235 0.257663i \(-0.917048\pi\)
0.257663 + 0.966235i \(0.417048\pi\)
\(242\) −7.77817 + 7.77817i −0.500000 + 0.500000i
\(243\) −15.5563 + 1.00000i −0.997940 + 0.0641500i
\(244\) −9.00000 + 9.00000i −0.576166 + 0.576166i
\(245\) −2.12132 2.12132i −0.135526 0.135526i
\(246\) 9.65685 1.65685i 0.615699 0.105637i
\(247\) 6.00000i 0.381771i
\(248\) 9.89949i 0.628619i
\(249\) −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 \(0.373635\pi\)
\(252\) 5.65685 2.00000i 0.356348 0.125988i
\(253\) 0 0
\(254\) −11.3137 + 11.3137i −0.709885 + 0.709885i
\(255\) −6.00000 + 8.48528i −0.375735 + 0.531369i
\(256\) 1.00000 0.0625000
\(257\) −9.89949 9.89949i −0.617514 0.617514i 0.327379 0.944893i \(-0.393834\pi\)
−0.944893 + 0.327379i \(0.893834\pi\)
\(258\) 9.89949 14.0000i 0.616316 0.871602i
\(259\) −2.00000 + 12.0000i −0.124274 + 0.745644i
\(260\) 1.41421i 0.0877058i
\(261\) 16.2426 + 7.75736i 1.00539 + 0.480168i
\(262\) 16.0000i 0.988483i
\(263\) −31.1127 −1.91849 −0.959246 0.282574i \(-0.908812\pi\)
−0.959246 + 0.282574i \(0.908812\pi\)
\(264\) 0 0
\(265\) −4.00000 + 4.00000i −0.245718 + 0.245718i
\(266\) 8.48528i 0.520266i
\(267\) −3.41421 + 0.585786i −0.208946 + 0.0358495i
\(268\) 4.00000 0.244339
\(269\) 19.7990i 1.20717i 0.797300 + 0.603583i \(0.206261\pi\)
−0.797300 + 0.603583i \(0.793739\pi\)
\(270\) −1.41421 + 5.00000i −0.0860663 + 0.304290i
\(271\) 10.0000 0.607457 0.303728 0.952759i \(-0.401768\pi\)
0.303728 + 0.952759i \(0.401768\pi\)
\(272\) −4.24264 4.24264i −0.257248 0.257248i
\(273\) 4.82843 0.828427i 0.292230 0.0501387i
\(274\) 2.00000 + 2.00000i 0.120824 + 0.120824i
\(275\) 0 0
\(276\) −6.82843 + 1.17157i −0.411023 + 0.0705204i
\(277\) 11.0000 + 11.0000i 0.660926 + 0.660926i 0.955598 0.294672i \(-0.0952105\pi\)
−0.294672 + 0.955598i \(0.595211\pi\)
\(278\) 2.82843 + 2.82843i 0.169638 + 0.169638i
\(279\) 12.7990 26.7990i 0.766255 1.60441i
\(280\) 2.00000i 0.119523i
\(281\) 12.7279 + 12.7279i 0.759284 + 0.759284i 0.976192 0.216908i \(-0.0695971\pi\)
−0.216908 + 0.976192i \(0.569597\pi\)
\(282\) −0.828427 4.82843i −0.0493321 0.287529i
\(283\) 3.00000 + 3.00000i 0.178331 + 0.178331i 0.790628 0.612297i \(-0.209754\pi\)
−0.612297 + 0.790628i \(0.709754\pi\)
\(284\) 2.82843 0.167836
\(285\) −6.00000 4.24264i −0.355409 0.251312i
\(286\) 0 0
\(287\) 11.3137 0.667827
\(288\) −2.70711 1.29289i −0.159518 0.0761845i
\(289\) 19.0000i 1.11765i
\(290\) 4.24264 4.24264i 0.249136 0.249136i
\(291\) 16.8995 2.89949i 0.990666 0.169971i
\(292\) −6.00000 −0.351123
\(293\) 22.6274i 1.32191i −0.750426 0.660954i \(-0.770152\pi\)
0.750426 0.660954i \(-0.229848\pi\)
\(294\) −5.12132 + 0.878680i −0.298681 + 0.0512456i
\(295\) 8.00000i 0.465778i
\(296\) 4.94975 3.53553i 0.287698 0.205499i
\(297\) 0 0
\(298\) −14.0000 14.0000i −0.810998 0.810998i
\(299\) −5.65685 −0.327144
\(300\) 1.41421 + 1.00000i 0.0816497 + 0.0577350i
\(301\) 14.0000 14.0000i 0.806947 0.806947i
\(302\) −12.7279 12.7279i −0.732410 0.732410i
\(303\) −4.00000 2.82843i −0.229794 0.162489i
\(304\) 3.00000 3.00000i 0.172062 0.172062i
\(305\) 12.7279i 0.728799i
\(306\) 6.00000 + 16.9706i 0.342997 + 0.970143i
\(307\) 10.0000i 0.570730i −0.958419 0.285365i \(-0.907885\pi\)
0.958419 0.285365i \(-0.0921148\pi\)
\(308\) 0 0
\(309\) −2.07107 12.0711i −0.117819 0.686699i
\(310\) −7.00000 7.00000i −0.397573 0.397573i
\(311\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(312\) −2.00000 1.41421i −0.113228 0.0800641i
\(313\) 1.00000 1.00000i 0.0565233 0.0565233i −0.678280 0.734803i \(-0.737274\pi\)
0.734803 + 0.678280i \(0.237274\pi\)
\(314\) −2.82843 + 2.82843i −0.159617 + 0.159617i
\(315\) −2.58579 + 5.41421i −0.145693 + 0.305056i
\(316\) −3.00000 3.00000i −0.168763 0.168763i
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 1.65685 + 9.65685i 0.0929118 + 0.541529i
\(319\) 0 0
\(320\) −0.707107 + 0.707107i −0.0395285 + 0.0395285i
\(321\) 11.3137 16.0000i 0.631470 0.893033i
\(322\) −8.00000 −0.445823
\(323\) −25.4558 −1.41640
\(324\) 5.65685 + 7.00000i 0.314270 + 0.388889i
\(325\) 1.00000 + 1.00000i 0.0554700 + 0.0554700i
\(326\) −21.2132 −1.17489
\(327\) −7.24264 + 1.24264i −0.400519 + 0.0687182i
\(328\) −4.00000 4.00000i −0.220863 0.220863i
\(329\) 5.65685i 0.311872i
\(330\) 0 0
\(331\) 15.0000 15.0000i 0.824475 0.824475i −0.162272 0.986746i \(-0.551882\pi\)
0.986746 + 0.162272i \(0.0518821\pi\)
\(332\) 2.82843 0.155230
\(333\) −17.9706 + 3.17157i −0.984781 + 0.173801i
\(334\) 16.0000 0.875481
\(335\) −2.82843 + 2.82843i −0.154533 + 0.154533i
\(336\) −2.82843 2.00000i −0.154303 0.109109i
\(337\) 20.0000i 1.08947i 0.838608 + 0.544735i \(0.183370\pi\)
−0.838608 + 0.544735i \(0.816630\pi\)
\(338\) 7.77817 + 7.77817i 0.423077 + 0.423077i
\(339\) −3.41421 + 0.585786i −0.185435 + 0.0318156i
\(340\) 6.00000 0.325396
\(341\) 0 0
\(342\) −12.0000 + 4.24264i −0.648886 + 0.229416i
\(343\) −20.0000 −1.07990
\(344\) −9.89949 −0.533745
\(345\) 4.00000 5.65685i 0.215353 0.304555i
\(346\) 0 0
\(347\) −5.65685 + 5.65685i −0.303676 + 0.303676i −0.842450 0.538774i \(-0.818888\pi\)
0.538774 + 0.842450i \(0.318888\pi\)
\(348\) −1.75736 10.2426i −0.0942043 0.549063i
\(349\) 32.0000 1.71292 0.856460 0.516213i \(-0.172659\pi\)
0.856460 + 0.516213i \(0.172659\pi\)
\(350\) 1.41421 + 1.41421i 0.0755929 + 0.0755929i
\(351\) 3.58579 + 6.41421i 0.191395 + 0.342365i
\(352\) 0 0
\(353\) −18.3848 + 18.3848i −0.978523 + 0.978523i −0.999774 0.0212513i \(-0.993235\pi\)
0.0212513 + 0.999774i \(0.493235\pi\)
\(354\) 11.3137 + 8.00000i 0.601317 + 0.425195i
\(355\) −2.00000 + 2.00000i −0.106149 + 0.106149i
\(356\) 1.41421 + 1.41421i 0.0749532 + 0.0749532i
\(357\) 3.51472 + 20.4853i 0.186019 + 1.08420i
\(358\) 16.0000i 0.845626i
\(359\) 5.65685i 0.298557i 0.988795 + 0.149279i \(0.0476951\pi\)
−0.988795 + 0.149279i \(0.952305\pi\)
\(360\) 2.82843 1.00000i 0.149071 0.0527046i
\(361\) 1.00000i 0.0526316i
\(362\) 0 0
\(363\) −15.5563 11.0000i −0.816497 0.577350i
\(364\) −2.00000 2.00000i −0.104828 0.104828i
\(365\) 4.24264 4.24264i 0.222070 0.222070i
\(366\) −18.0000 12.7279i −0.940875 0.665299i
\(367\) 32.0000 1.67039 0.835193 0.549957i \(-0.185356\pi\)
0.835193 + 0.549957i \(0.185356\pi\)
\(368\) 2.82843 + 2.82843i 0.147442 + 0.147442i
\(369\) 5.65685 + 16.0000i 0.294484 + 0.832927i
\(370\) −1.00000 + 6.00000i −0.0519875 + 0.311925i
\(371\) 11.3137i 0.587378i
\(372\) −16.8995 + 2.89949i −0.876198 + 0.150332i
\(373\) 10.0000i 0.517780i 0.965907 + 0.258890i \(0.0833568\pi\)
−0.965907 + 0.258890i \(0.916643\pi\)
\(374\) 0 0
\(375\) −1.70711 + 0.292893i −0.0881546 + 0.0151249i
\(376\) −2.00000 + 2.00000i −0.103142 + 0.103142i
\(377\) 8.48528i 0.437014i
\(378\) 5.07107 + 9.07107i 0.260828 + 0.466565i
\(379\) −6.00000 −0.308199 −0.154100 0.988055i \(-0.549248\pi\)
−0.154100 + 0.988055i \(0.549248\pi\)
\(380\) 4.24264i 0.217643i
\(381\) −22.6274 16.0000i −1.15924 0.819705i
\(382\) −8.00000 −0.409316
\(383\) −25.4558 25.4558i −1.30073 1.30073i −0.927898 0.372835i \(-0.878386\pi\)
−0.372835 0.927898i \(-0.621614\pi\)
\(384\) 0.292893 + 1.70711i 0.0149466 + 0.0871154i
\(385\) 0 0
\(386\) 1.41421i 0.0719816i
\(387\) 26.7990 + 12.7990i 1.36227 + 0.650609i
\(388\) −7.00000 7.00000i −0.355371 0.355371i
\(389\) 18.3848 + 18.3848i 0.932145 + 0.932145i 0.997840 0.0656946i \(-0.0209263\pi\)
−0.0656946 + 0.997840i \(0.520926\pi\)
\(390\) 2.41421 0.414214i 0.122248 0.0209745i
\(391\) 24.0000i 1.21373i
\(392\) 2.12132 + 2.12132i 0.107143 + 0.107143i
\(393\) −27.3137 + 4.68629i −1.37779 + 0.236392i
\(394\) 2.00000 + 2.00000i 0.100759 + 0.100759i
\(395\) 4.24264 0.213470
\(396\) 0 0
\(397\) 18.0000i 0.903394i 0.892171 + 0.451697i \(0.149181\pi\)
−0.892171 + 0.451697i \(0.850819\pi\)
\(398\) 1.41421 0.0708881
\(399\) −14.4853 + 2.48528i −0.725171 + 0.124420i
\(400\) 1.00000i 0.0500000i
\(401\) 12.7279 12.7279i 0.635602 0.635602i −0.313865 0.949467i \(-0.601624\pi\)
0.949467 + 0.313865i \(0.101624\pi\)
\(402\) 1.17157 + 6.82843i 0.0584327 + 0.340571i
\(403\) −14.0000 −0.697390
\(404\) 2.82843i 0.140720i
\(405\) −8.94975 0.949747i −0.444717 0.0471933i
\(406\) 12.0000i 0.595550i
\(407\) 0 0
\(408\) 6.00000 8.48528i 0.297044 0.420084i
\(409\) −5.00000 5.00000i −0.247234 0.247234i 0.572600 0.819835i \(-0.305935\pi\)
−0.819835 + 0.572600i \(0.805935\pi\)
\(410\) 5.65685 0.279372
\(411\) −2.82843 + 4.00000i −0.139516 + 0.197305i
\(412\) −5.00000 + 5.00000i −0.246332 + 0.246332i
\(413\) 11.3137 + 11.3137i 0.556711 + 0.556711i
\(414\) −4.00000 11.3137i −0.196589 0.556038i
\(415\) −2.00000 + 2.00000i −0.0981761 + 0.0981761i
\(416\) 1.41421i 0.0693375i
\(417\) −4.00000 + 5.65685i −0.195881 + 0.277017i
\(418\) 0 0
\(419\) 25.4558i 1.24360i 0.783176 + 0.621800i \(0.213598\pi\)
−0.783176 + 0.621800i \(0.786402\pi\)
\(420\) 3.41421 0.585786i 0.166597 0.0285835i
\(421\) 9.00000 + 9.00000i 0.438633 + 0.438633i 0.891552 0.452919i \(-0.149617\pi\)
−0.452919 + 0.891552i \(0.649617\pi\)
\(422\) 14.1421 14.1421i 0.688428 0.688428i
\(423\) 8.00000 2.82843i 0.388973 0.137523i
\(424\) 4.00000 4.00000i 0.194257 0.194257i
\(425\) −4.24264 + 4.24264i −0.205798 + 0.205798i
\(426\) 0.828427 + 4.82843i 0.0401374 + 0.233938i
\(427\) −18.0000 18.0000i −0.871081 0.871081i
\(428\) −11.3137 −0.546869
\(429\) 0 0
\(430\) 7.00000 7.00000i 0.337570 0.337570i
\(431\) 5.65685 5.65685i 0.272481 0.272481i −0.557617 0.830098i \(-0.688284\pi\)
0.830098 + 0.557617i \(0.188284\pi\)
\(432\) 1.41421 5.00000i 0.0680414 0.240563i
\(433\) −24.0000 −1.15337 −0.576683 0.816968i \(-0.695653\pi\)
−0.576683 + 0.816968i \(0.695653\pi\)
\(434\) −19.7990 −0.950382
\(435\) 8.48528 + 6.00000i 0.406838 + 0.287678i
\(436\) 3.00000 + 3.00000i 0.143674 + 0.143674i
\(437\) 16.9706 0.811812
\(438\) −1.75736 10.2426i −0.0839699 0.489412i
\(439\) 27.0000 + 27.0000i 1.28864 + 1.28864i 0.935613 + 0.353026i \(0.114847\pi\)
0.353026 + 0.935613i \(0.385153\pi\)
\(440\) 0 0
\(441\) −3.00000 8.48528i −0.142857 0.404061i
\(442\) 6.00000 6.00000i 0.285391 0.285391i
\(443\) 14.1421 0.671913 0.335957 0.941877i \(-0.390940\pi\)
0.335957 + 0.941877i \(0.390940\pi\)
\(444\) 7.48528 + 7.41421i 0.355236 + 0.351863i
\(445\) −2.00000 −0.0948091
\(446\) −16.9706 + 16.9706i −0.803579 + 0.803579i
\(447\) 19.7990 28.0000i 0.936460 1.32435i
\(448\) 2.00000i 0.0944911i
\(449\) 18.3848 + 18.3848i 0.867631 + 0.867631i 0.992210 0.124579i \(-0.0397579\pi\)
−0.124579 + 0.992210i \(0.539758\pi\)
\(450\) −1.29289 + 2.70711i −0.0609476 + 0.127614i
\(451\) 0 0
\(452\) 1.41421 + 1.41421i 0.0665190 + 0.0665190i
\(453\) 18.0000 25.4558i 0.845714 1.19602i
\(454\) −24.0000 −1.12638
\(455\) 2.82843 0.132599
\(456\) 6.00000 + 4.24264i 0.280976 + 0.198680i
\(457\) −7.00000 + 7.00000i −0.327446 + 0.327446i −0.851615 0.524168i \(-0.824376\pi\)
0.524168 + 0.851615i \(0.324376\pi\)
\(458\) −18.3848 + 18.3848i −0.859064 + 0.859064i
\(459\) −27.2132 + 15.2132i −1.27020 + 0.710092i
\(460\) −4.00000 −0.186501
\(461\) 21.2132 + 21.2132i 0.987997 + 0.987997i 0.999929 0.0119314i \(-0.00379798\pi\)
−0.0119314 + 0.999929i \(0.503798\pi\)
\(462\) 0 0
\(463\) 11.0000 11.0000i 0.511213 0.511213i −0.403685 0.914898i \(-0.632271\pi\)
0.914898 + 0.403685i \(0.132271\pi\)
\(464\) −4.24264 + 4.24264i −0.196960 + 0.196960i
\(465\) 9.89949 14.0000i 0.459078 0.649234i
\(466\) 20.0000 20.0000i 0.926482 0.926482i
\(467\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(468\) 1.82843 3.82843i 0.0845191 0.176969i
\(469\) 8.00000i 0.369406i
\(470\) 2.82843i 0.130466i
\(471\) −5.65685 4.00000i −0.260654 0.184310i
\(472\) 8.00000i 0.368230i
\(473\) 0 0
\(474\) 4.24264 6.00000i 0.194871 0.275589i
\(475\) −3.00000 3.00000i −0.137649 0.137649i
\(476\) 8.48528 8.48528i 0.388922 0.388922i
\(477\) −16.0000 + 5.65685i −0.732590 + 0.259010i
\(478\) 20.0000 0.914779
\(479\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(480\) −1.41421 1.00000i −0.0645497 0.0456435i
\(481\) 5.00000 + 7.00000i 0.227980 + 0.319173i
\(482\) 15.5563i 0.708572i
\(483\) −2.34315 13.6569i −0.106617 0.621408i
\(484\) 11.0000i 0.500000i
\(485\) 9.89949 0.449513
\(486\) −10.2929 + 11.7071i −0.466895 + 0.531045i
\(487\) 17.0000 17.0000i 0.770344 0.770344i −0.207823 0.978166i \(-0.566638\pi\)
0.978166 + 0.207823i \(0.0666378\pi\)
\(488\) 12.7279i 0.576166i
\(489\) −6.21320 36.2132i −0.280971 1.63762i
\(490\) −3.00000 −0.135526
\(491\) 14.1421i 0.638226i −0.947717 0.319113i \(-0.896615\pi\)
0.947717 0.319113i \(-0.103385\pi\)
\(492\) 5.65685 8.00000i 0.255031 0.360668i
\(493\) 36.0000 1.62136
\(494\) 4.24264 + 4.24264i 0.190885 + 0.190885i
\(495\) 0 0
\(496\) 7.00000 + 7.00000i 0.314309 + 0.314309i
\(497\) 5.65685i 0.253745i
\(498\) 0.828427 + 4.82843i 0.0371227 + 0.216367i
\(499\) 3.00000 + 3.00000i 0.134298 + 0.134298i 0.771060 0.636762i \(-0.219727\pi\)
−0.636762 + 0.771060i \(0.719727\pi\)
\(500\) 0.707107 + 0.707107i 0.0316228 + 0.0316228i
\(501\) 4.68629 + 27.3137i 0.209368 + 1.22029i
\(502\) 12.0000i 0.535586i
\(503\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(504\) 2.58579 5.41421i 0.115180 0.241168i
\(505\) −2.00000 2.00000i −0.0889988 0.0889988i
\(506\) 0 0
\(507\) −11.0000 + 15.5563i −0.488527 + 0.690882i
\(508\) 16.0000i 0.709885i
\(509\) −5.65685 −0.250736 −0.125368 0.992110i \(-0.540011\pi\)
−0.125368 + 0.992110i \(0.540011\pi\)
\(510\) 1.75736 + 10.2426i 0.0778172 + 0.453552i
\(511\) 12.0000i 0.530849i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −10.7574 19.2426i −0.474949 0.849583i
\(514\) −14.0000 −0.617514
\(515\) 7.07107i 0.311588i
\(516\) −2.89949 16.8995i −0.127643 0.743959i
\(517\) 0 0
\(518\) 7.07107 + 9.89949i 0.310685 + 0.434959i
\(519\) 0 0
\(520\) −1.00000 1.00000i −0.0438529 0.0438529i
\(521\) −16.9706 −0.743494 −0.371747 0.928334i \(-0.621241\pi\)
−0.371747 + 0.928334i \(0.621241\pi\)
\(522\) 16.9706 6.00000i 0.742781 0.262613i
\(523\) 3.00000 3.00000i 0.131181 0.131181i −0.638468 0.769649i \(-0.720431\pi\)
0.769649 + 0.638468i \(0.220431\pi\)
\(524\) 11.3137 + 11.3137i 0.494242 + 0.494242i
\(525\) −2.00000 + 2.82843i −0.0872872 + 0.123443i
\(526\) −22.0000 + 22.0000i −0.959246 + 0.959246i
\(527\) 59.3970i 2.58737i
\(528\) 0 0
\(529\) 7.00000i 0.304348i
\(530\) 5.65685i 0.245718i
\(531\) −10.3431 + 21.6569i −0.448854 + 0.939827i
\(532\) 6.00000 + 6.00000i 0.260133 + 0.260133i
\(533\) 5.65685 5.65685i 0.245026 0.245026i
\(534\) −2.00000 + 2.82843i −0.0865485 + 0.122398i
\(535\) 8.00000 8.00000i 0.345870 0.345870i
\(536\) 2.82843 2.82843i 0.122169 0.122169i
\(537\) 27.3137 4.68629i 1.17867 0.202228i
\(538\) 14.0000 + 14.0000i 0.603583 + 0.603583i
\(539\) 0 0
\(540\) 2.53553 + 4.53553i 0.109112 + 0.195178i
\(541\) 21.0000 21.0000i 0.902861 0.902861i −0.0928222 0.995683i \(-0.529589\pi\)
0.995683 + 0.0928222i \(0.0295888\pi\)
\(542\) 7.07107 7.07107i 0.303728 0.303728i
\(543\) 0 0
\(544\) −6.00000 −0.257248
\(545\) −4.24264 −0.181735
\(546\) 2.82843 4.00000i 0.121046 0.171184i
\(547\) 7.00000 + 7.00000i 0.299298 + 0.299298i 0.840739 0.541441i \(-0.182121\pi\)
−0.541441 + 0.840739i \(0.682121\pi\)
\(548\) 2.82843 0.120824
\(549\) 16.4558 34.4558i 0.702318 1.47054i
\(550\) 0 0
\(551\) 25.4558i 1.08446i
\(552\) −4.00000 + 5.65685i −0.170251 + 0.240772i
\(553\) 6.00000 6.00000i 0.255146 0.255146i
\(554\) 15.5563 0.660926
\(555\) −10.5355 + 0.0502525i −0.447209 + 0.00213310i
\(556\) 4.00000 0.169638
\(557\) 7.07107 7.07107i 0.299611 0.299611i −0.541251 0.840861i \(-0.682049\pi\)
0.840861 + 0.541251i \(0.182049\pi\)
\(558\) −9.89949 28.0000i −0.419079 1.18533i
\(559\) 14.0000i 0.592137i
\(560\) −1.41421 1.41421i −0.0597614 0.0597614i
\(561\) 0 0
\(562\) 18.0000 0.759284
\(563\) −8.48528 8.48528i −0.357612 0.357612i 0.505320 0.862932i \(-0.331374\pi\)
−0.862932 + 0.505320i \(0.831374\pi\)
\(564\) −4.00000 2.82843i −0.168430 0.119098i
\(565\) −2.00000 −0.0841406
\(566\) 4.24264 0.178331
\(567\) −14.0000 + 11.3137i −0.587945 + 0.475131i
\(568\) 2.00000 2.00000i 0.0839181 0.0839181i
\(569\) 32.5269 32.5269i 1.36360 1.36360i 0.494318 0.869281i \(-0.335418\pi\)
0.869281 0.494318i \(-0.164582\pi\)
\(570\) −7.24264 + 1.24264i −0.303361 + 0.0520485i
\(571\) 30.0000 1.25546 0.627730 0.778431i \(-0.283984\pi\)
0.627730 + 0.778431i \(0.283984\pi\)
\(572\) 0 0
\(573\) −2.34315 13.6569i −0.0978863 0.570523i
\(574\) 8.00000 8.00000i 0.333914 0.333914i
\(575\) 2.82843 2.82843i 0.117954 0.117954i
\(576\) −2.82843 + 1.00000i −0.117851 + 0.0416667i
\(577\) 27.0000 27.0000i 1.12402 1.12402i 0.132895 0.991130i \(-0.457573\pi\)
0.991130 0.132895i \(-0.0424272\pi\)
\(578\) 13.4350 + 13.4350i 0.558824 + 0.558824i
\(579\) −2.41421 + 0.414214i −0.100331 + 0.0172141i
\(580\) 6.00000i 0.249136i
\(581\) 5.65685i 0.234686i
\(582\) 9.89949 14.0000i 0.410347 0.580319i
\(583\) 0 0
\(584\) −4.24264 + 4.24264i −0.175562 + 0.175562i
\(585\) 1.41421 + 4.00000i 0.0584705 + 0.165380i
\(586\) −16.0000 16.0000i −0.660954 0.660954i
\(587\) 25.4558 25.4558i 1.05068 1.05068i 0.0520296 0.998646i \(-0.483431\pi\)
0.998646 0.0520296i \(-0.0165690\pi\)
\(588\) −3.00000 + 4.24264i −0.123718 + 0.174964i
\(589\) 42.0000 1.73058
\(590\) 5.65685 + 5.65685i 0.232889 + 0.232889i
\(591\) −2.82843 + 4.00000i −0.116346 + 0.164538i
\(592\) 1.00000 6.00000i 0.0410997 0.246598i
\(593\) 39.5980i 1.62609i 0.582198 + 0.813047i \(0.302193\pi\)
−0.582198 + 0.813047i \(0.697807\pi\)
\(594\) 0 0
\(595\) 12.0000i 0.491952i
\(596\) −19.7990 −0.810998
\(597\) 0.414214 + 2.41421i 0.0169526 + 0.0988072i
\(598\) −4.00000 + 4.00000i −0.163572 + 0.163572i
\(599\) 8.48528i 0.346699i 0.984860 + 0.173350i \(0.0554591\pi\)
−0.984860 + 0.173350i \(0.944541\pi\)
\(600\) 1.70711 0.292893i 0.0696923 0.0119573i
\(601\) 12.0000 0.489490 0.244745 0.969587i \(-0.421296\pi\)
0.244745 + 0.969587i \(0.421296\pi\)
\(602\) 19.7990i 0.806947i
\(603\) −11.3137 + 4.00000i −0.460730 + 0.162893i
\(604\) −18.0000 −0.732410
\(605\) −7.77817 7.77817i −0.316228 0.316228i
\(606\) −4.82843 + 0.828427i −0.196141 + 0.0336526i
\(607\) −9.00000 9.00000i −0.365299 0.365299i 0.500461 0.865759i \(-0.333164\pi\)
−0.865759 + 0.500461i \(0.833164\pi\)
\(608\) 4.24264i 0.172062i
\(609\) 20.4853 3.51472i 0.830105 0.142424i
\(610\) −9.00000 9.00000i −0.364399 0.364399i
\(611\) −2.82843 2.82843i −0.114426 0.114426i
\(612\) 16.2426 + 7.75736i 0.656570 + 0.313573i
\(613\) 4.00000i 0.161558i −0.996732 0.0807792i \(-0.974259\pi\)
0.996732 0.0807792i \(-0.0257409\pi\)
\(614\) −7.07107 7.07107i −0.285365 0.285365i
\(615\) 1.65685 + 9.65685i 0.0668108 + 0.389402i
\(616\) 0 0
\(617\) −14.1421 −0.569341 −0.284670 0.958625i \(-0.591884\pi\)
−0.284670 + 0.958625i \(0.591884\pi\)
\(618\) −10.0000 7.07107i −0.402259 0.284440i
\(619\) 14.0000i 0.562708i 0.959604 + 0.281354i \(0.0907834\pi\)
−0.959604 + 0.281354i \(0.909217\pi\)
\(620\) −9.89949 −0.397573
\(621\) 18.1421 10.1421i 0.728019 0.406990i
\(622\) 0 0
\(623\) −2.82843 + 2.82843i −0.113319 + 0.113319i
\(624\) −2.41421 + 0.414214i −0.0966459 + 0.0165818i
\(625\) −1.00000 −0.0400000
\(626\) 1.41421i 0.0565233i
\(627\) 0 0
\(628\) 4.00000i 0.159617i
\(629\) −29.6985 + 21.2132i −1.18416 + 0.845826i
\(630\) 2.00000 + 5.65685i 0.0796819 + 0.225374i
\(631\) −19.0000 19.0000i −0.756378 0.756378i 0.219283 0.975661i \(-0.429628\pi\)
−0.975661 + 0.219283i \(0.929628\pi\)
\(632\) −4.24264 −0.168763
\(633\) 28.2843 + 20.0000i 1.12420 + 0.794929i
\(634\) 0 0
\(635\) −11.3137 11.3137i −0.448971 0.448971i
\(636\) 8.00000 + 5.65685i 0.317221 + 0.224309i
\(637\) −3.00000 + 3.00000i −0.118864 + 0.118864i
\(638\) 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 \(0.147459\pi\)
−0.894602 + 0.446865i \(0.852541\pi\)
\(642\) −3.31371 19.3137i −0.130782 0.762251i
\(643\) 27.0000 + 27.0000i 1.06478 + 1.06478i 0.997751 + 0.0670247i \(0.0213506\pi\)
0.0670247 + 0.997751i \(0.478649\pi\)
\(644\) −5.65685 + 5.65685i −0.222911 + 0.222911i
\(645\) 14.0000 + 9.89949i 0.551249 + 0.389792i
\(646\) −18.0000 + 18.0000i −0.708201 + 0.708201i
\(647\) 25.4558 25.4558i 1.00077 1.00077i 0.000772798 1.00000i \(-0.499754\pi\)
1.00000 0.000772798i \(-0.000245989\pi\)
\(648\) 8.94975 + 0.949747i 0.351579 + 0.0373096i
\(649\) 0 0
\(650\) 1.41421 0.0554700
\(651\) −5.79899 33.7990i −0.227280 1.32469i
\(652\) −15.0000 + 15.0000i −0.587445 + 0.587445i
\(653\) 24.0416 24.0416i 0.940822 0.940822i −0.0575225 0.998344i \(-0.518320\pi\)
0.998344 + 0.0575225i \(0.0183201\pi\)
\(654\) −4.24264 + 6.00000i −0.165900 + 0.234619i
\(655\) −16.0000 −0.625172
\(656\) −5.65685 −0.220863
\(657\) 16.9706 6.00000i 0.662085 0.234082i
\(658\) −4.00000 4.00000i −0.155936 0.155936i
\(659\) 16.9706 0.661079 0.330540 0.943792i \(-0.392769\pi\)
0.330540 + 0.943792i \(0.392769\pi\)
\(660\) 0 0
\(661\) 11.0000 + 11.0000i 0.427850 + 0.427850i 0.887896 0.460045i \(-0.152167\pi\)
−0.460045 + 0.887896i \(0.652167\pi\)
\(662\) 21.2132i 0.824475i
\(663\) 12.0000 + 8.48528i 0.466041 + 0.329541i
\(664\) 2.00000 2.00000i 0.0776151 0.0776151i
\(665\) −8.48528 −0.329045
\(666\) −10.4645 + 14.9497i −0.405490 + 0.579291i
\(667\) −24.0000 −0.929284
\(668\) 11.3137 11.3137i 0.437741 0.437741i
\(669\) −33.9411 24.0000i −1.31224 0.927894i
\(670\) 4.00000i 0.154533i
\(671\) 0 0
\(672\) −3.41421 + 0.585786i −0.131706 + 0.0225972i
\(673\) −4.00000 −0.154189 −0.0770943 0.997024i \(-0.524564\pi\)
−0.0770943 + 0.997024i \(0.524564\pi\)
\(674\) 14.1421 + 14.1421i 0.544735 + 0.544735i
\(675\) −5.00000 1.41421i −0.192450 0.0544331i
\(676\) 11.0000 0.423077
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) −2.00000 + 2.82843i −0.0768095 + 0.108625i
\(679\) 14.0000 14.0000i 0.537271 0.537271i
\(680\) 4.24264 4.24264i 0.162698 0.162698i
\(681\) −7.02944 40.9706i −0.269369 1.57000i
\(682\) 0 0
\(683\) 2.82843 + 2.82843i 0.108227 + 0.108227i 0.759147 0.650920i \(-0.225617\pi\)
−0.650920 + 0.759147i \(0.725617\pi\)
\(684\) −5.48528 + 11.4853i −0.209735 + 0.439151i
\(685\) −2.00000 + 2.00000i −0.0764161 + 0.0764161i
\(686\) −14.1421 + 14.1421i −0.539949 + 0.539949i
\(687\) −36.7696 26.0000i −1.40285 0.991962i
\(688\) −7.00000 + 7.00000i −0.266872 + 0.266872i
\(689\) 5.65685 + 5.65685i 0.215509 + 0.215509i
\(690\) −1.17157 6.82843i −0.0446010 0.259954i
\(691\) 20.0000i 0.760836i 0.924815 + 0.380418i \(0.124220\pi\)
−0.924815 + 0.380418i \(0.875780\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 8.00000i 0.303676i
\(695\) −2.82843 + 2.82843i −0.107288 + 0.107288i
\(696\) −8.48528 6.00000i −0.321634 0.227429i
\(697\) 24.0000 + 24.0000i 0.909065 + 0.909065i
\(698\) 22.6274 22.6274i 0.856460 0.856460i
\(699\) 40.0000 + 28.2843i 1.51294 + 1.06981i
\(700\) 2.00000 0.0755929
\(701\) 18.3848 + 18.3848i 0.694383 + 0.694383i 0.963193 0.268810i \(-0.0866303\pi\)
−0.268810 + 0.963193i \(0.586630\pi\)
\(702\) 7.07107 + 2.00000i 0.266880 + 0.0754851i
\(703\) −15.0000 21.0000i −0.565736 0.792030i
\(704\) 0 0
\(705\) 4.82843 0.828427i 0.181849 0.0312004i
\(706\) 26.0000i 0.978523i
\(707\) −5.65685 −0.212748
\(708\) 13.6569 2.34315i 0.513256 0.0880608i
\(709\) 15.0000 15.0000i 0.563337 0.563337i −0.366917 0.930254i \(-0.619587\pi\)
0.930254 + 0.366917i \(0.119587\pi\)
\(710\) 2.82843i 0.106149i
\(711\) 11.4853 + 5.48528i 0.430732 + 0.205714i
\(712\) 2.00000 0.0749532
\(713\) 39.5980i 1.48296i
\(714\) 16.9706 + 12.0000i 0.635107 + 0.449089i
\(715\) 0 0
\(716\) −11.3137 11.3137i −0.422813 0.422813i
\(717\) 5.85786 + 34.1421i 0.218766 + 1.27506i
\(718\) 4.00000 + 4.00000i 0.149279 + 0.149279i
\(719\) 11.3137i 0.421930i 0.977494 + 0.210965i \(0.0676606\pi\)
−0.977494 + 0.210965i \(0.932339\pi\)
\(720\) 1.29289 2.70711i 0.0481833 0.100888i
\(721\) −10.0000 10.0000i −0.372419 0.372419i
\(722\) 0.707107 + 0.707107i 0.0263158 + 0.0263158i
\(723\) −26.5563 + 4.55635i −0.987641 + 0.169452i
\(724\) 0 0
\(725\) 4.24264 + 4.24264i 0.157568 + 0.157568i
\(726\) −18.7782 + 3.22183i −0.696923 + 0.119573i
\(727\) −27.0000 27.0000i −1.00137 1.00137i −0.999999 0.00137552i \(-0.999562\pi\)
−0.00137552 0.999999i \(-0.500438\pi\)
\(728\) −2.82843 −0.104828
\(729\) −23.0000 14.1421i −0.851852 0.523783i
\(730\) 6.00000i 0.222070i
\(731\) 59.3970 2.19688
\(732\) −21.7279 + 3.72792i −0.803087 + 0.137788i
\(733\) 4.00000i 0.147743i −0.997268 0.0738717i \(-0.976464\pi\)
0.997268 0.0738717i \(-0.0235355\pi\)
\(734\) 22.6274 22.6274i 0.835193 0.835193i
\(735\) −0.878680 5.12132i −0.0324106 0.188903i
\(736\) 4.00000 0.147442
\(737\) 0 0
\(738\) 15.3137 + 7.31371i 0.563705 + 0.269221i
\(739\) 22.0000i 0.809283i 0.914475 + 0.404642i \(0.132604\pi\)
−0.914475 + 0.404642i \(0.867396\pi\)
\(740\) 3.53553 + 4.94975i 0.129969 + 0.181956i
\(741\) −6.00000 + 8.48528i −0.220416 + 0.311715i
\(742\) 8.00000 + 8.00000i 0.293689 + 0.293689i
\(743\) −31.1127 −1.14141 −0.570707 0.821154i \(-0.693331\pi\)
−0.570707 + 0.821154i \(0.693331\pi\)
\(744\) −9.89949 + 14.0000i −0.362933 + 0.513265i
\(745\) 14.0000 14.0000i 0.512920 0.512920i
\(746\) 7.07107 + 7.07107i 0.258890 + 0.258890i
\(747\) −8.00000 + 2.82843i −0.292705 + 0.103487i
\(748\) 0 0
\(749\) 22.6274i 0.826788i
\(750\) −1.00000 + 1.41421i −0.0365148 + 0.0516398i
\(751\) 40.0000i 1.45962i 0.683650 + 0.729810i \(0.260392\pi\)
−0.683650 + 0.729810i \(0.739608\pi\)
\(752\) 2.82843i 0.103142i
\(753\) −20.4853 + 3.51472i −0.746525 + 0.128083i
\(754\) −6.00000 6.00000i −0.218507 0.218507i
\(755\) 12.7279 12.7279i 0.463217 0.463217i
\(756\) 10.0000 + 2.82843i 0.363696 + 0.102869i
\(757\) 3.00000 3.00000i 0.109037 0.109037i −0.650484 0.759520i \(-0.725434\pi\)
0.759520 + 0.650484i \(0.225434\pi\)
\(758\) −4.24264 + 4.24264i −0.154100 + 0.154100i
\(759\) 0 0
\(760\) 3.00000 + 3.00000i 0.108821 + 0.108821i
\(761\) 2.82843 0.102530 0.0512652 0.998685i \(-0.483675\pi\)
0.0512652 + 0.998685i \(0.483675\pi\)
\(762\) −27.3137 + 4.68629i −0.989471 + 0.169766i
\(763\) −6.00000 + 6.00000i −0.217215 + 0.217215i
\(764\) −5.65685 + 5.65685i −0.204658 + 0.204658i
\(765\) −16.9706 + 6.00000i −0.613572 + 0.216930i
\(766\) −36.0000 −1.30073
\(767\) 11.3137 0.408514
\(768\) 1.41421 + 1.00000i 0.0510310 + 0.0360844i
\(769\) 3.00000 + 3.00000i 0.108183 + 0.108183i 0.759126 0.650943i \(-0.225627\pi\)
−0.650943 + 0.759126i \(0.725627\pi\)
\(770\) 0 0
\(771\) −4.10051 23.8995i −0.147676 0.860719i
\(772\) 1.00000 + 1.00000i 0.0359908 + 0.0359908i
\(773\) 8.48528i 0.305194i 0.988288 + 0.152597i \(0.0487637\pi\)
−0.988288 + 0.152597i \(0.951236\pi\)
\(774\) 28.0000 9.89949i 1.00644 0.355830i
\(775\) 7.00000 7.00000i 0.251447 0.251447i
\(776\) −9.89949 −0.355371
\(777\) −14.8284 + 14.9706i −0.531967 + 0.537066i
\(778\) 26.0000 0.932145
\(779\) −16.9706 + 16.9706i −0.608034 + 0.608034i
\(780\) 1.41421 2.00000i 0.0506370 0.0716115i
\(781\) 0