Properties

Label 930.2.j.a.497.1
Level $930$
Weight $2$
Character 930.497
Analytic conductor $7.426$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
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 497.1
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 930.497
Dual form 930.2.j.a.683.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.70711 - 0.292893i) q^{3} -1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(0.707107 + 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.70711 - 0.292893i) q^{3} -1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(0.707107 + 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +(-2.00000 + 1.00000i) q^{10} +4.24264i q^{11} +(-0.292893 - 1.70711i) q^{12} +(-3.00000 + 3.00000i) q^{13} +(3.82843 + 0.585786i) q^{15} -1.00000 q^{16} +(-1.41421 + 1.41421i) q^{17} +(-1.29289 + 2.70711i) q^{18} +4.00000i q^{19} +(0.707107 - 2.12132i) q^{20} +(-3.00000 - 3.00000i) q^{22} +(1.41421 + 1.00000i) q^{24} +(4.00000 + 3.00000i) q^{25} -4.24264i q^{26} +(4.53553 - 2.53553i) q^{27} +2.82843 q^{29} +(-3.12132 + 2.29289i) q^{30} -1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(1.24264 + 7.24264i) q^{33} -2.00000i q^{34} +(-1.00000 - 2.82843i) q^{36} +(-5.00000 - 5.00000i) q^{37} +(-2.82843 - 2.82843i) q^{38} +(-4.24264 + 6.00000i) q^{39} +(1.00000 + 2.00000i) q^{40} +(8.00000 - 8.00000i) q^{43} +4.24264 q^{44} +(6.70711 - 0.121320i) q^{45} +(4.24264 - 4.24264i) q^{47} +(-1.70711 + 0.292893i) q^{48} -7.00000i q^{49} +(-4.94975 + 0.707107i) q^{50} +(-2.00000 + 2.82843i) q^{51} +(3.00000 + 3.00000i) q^{52} +(4.24264 + 4.24264i) q^{53} +(-1.41421 + 5.00000i) q^{54} +(-3.00000 + 9.00000i) q^{55} +(1.17157 + 6.82843i) q^{57} +(-2.00000 + 2.00000i) q^{58} +5.65685 q^{59} +(0.585786 - 3.82843i) q^{60} -8.00000 q^{61} +(0.707107 - 0.707107i) q^{62} +1.00000i q^{64} +(-8.48528 + 4.24264i) q^{65} +(-6.00000 - 4.24264i) q^{66} +(-1.00000 - 1.00000i) q^{67} +(1.41421 + 1.41421i) q^{68} -1.41421i q^{71} +(2.70711 + 1.29289i) q^{72} +(2.00000 - 2.00000i) q^{73} +7.07107 q^{74} +(7.70711 + 3.94975i) q^{75} +4.00000 q^{76} +(-1.24264 - 7.24264i) q^{78} -10.0000i q^{79} +(-2.12132 - 0.707107i) q^{80} +(7.00000 - 5.65685i) q^{81} +(-12.7279 - 12.7279i) q^{83} +(-4.00000 + 2.00000i) q^{85} +11.3137i q^{86} +(4.82843 - 0.828427i) q^{87} +(-3.00000 + 3.00000i) q^{88} +7.07107 q^{89} +(-4.65685 + 4.82843i) q^{90} +(-1.70711 + 0.292893i) q^{93} +6.00000i q^{94} +(-2.82843 + 8.48528i) q^{95} +(1.00000 - 1.41421i) q^{96} +(3.00000 + 3.00000i) q^{97} +(4.94975 + 4.94975i) q^{98} +(4.24264 + 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{3} - 4 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{3} - 4 q^{6} - 8 q^{10} - 4 q^{12} - 12 q^{13} + 4 q^{15} - 4 q^{16} - 8 q^{18} - 12 q^{22} + 16 q^{25} + 4 q^{27} - 4 q^{30} - 4 q^{31} - 12 q^{33} - 4 q^{36} - 20 q^{37} + 4 q^{40} + 32 q^{43} + 24 q^{45} - 4 q^{48} - 8 q^{51} + 12 q^{52} - 12 q^{55} + 16 q^{57} - 8 q^{58} + 8 q^{60} - 32 q^{61} - 24 q^{66} - 4 q^{67} + 8 q^{72} + 8 q^{73} + 28 q^{75} + 16 q^{76} + 12 q^{78} + 28 q^{81} - 16 q^{85} + 8 q^{87} - 12 q^{88} + 4 q^{90} - 4 q^{93} + 4 q^{96} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 1.70711 0.292893i 0.985599 0.169102i
\(4\) 1.00000i 0.500000i
\(5\) 2.12132 + 0.707107i 0.948683 + 0.316228i
\(6\) −1.00000 + 1.41421i −0.408248 + 0.577350i
\(7\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 2.82843 1.00000i 0.942809 0.333333i
\(10\) −2.00000 + 1.00000i −0.632456 + 0.316228i
\(11\) 4.24264i 1.27920i 0.768706 + 0.639602i \(0.220901\pi\)
−0.768706 + 0.639602i \(0.779099\pi\)
\(12\) −0.292893 1.70711i −0.0845510 0.492799i
\(13\) −3.00000 + 3.00000i −0.832050 + 0.832050i −0.987797 0.155747i \(-0.950222\pi\)
0.155747 + 0.987797i \(0.450222\pi\)
\(14\) 0 0
\(15\) 3.82843 + 0.585786i 0.988496 + 0.151249i
\(16\) −1.00000 −0.250000
\(17\) −1.41421 + 1.41421i −0.342997 + 0.342997i −0.857493 0.514496i \(-0.827979\pi\)
0.514496 + 0.857493i \(0.327979\pi\)
\(18\) −1.29289 + 2.70711i −0.304738 + 0.638071i
\(19\) 4.00000i 0.917663i 0.888523 + 0.458831i \(0.151732\pi\)
−0.888523 + 0.458831i \(0.848268\pi\)
\(20\) 0.707107 2.12132i 0.158114 0.474342i
\(21\) 0 0
\(22\) −3.00000 3.00000i −0.639602 0.639602i
\(23\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(24\) 1.41421 + 1.00000i 0.288675 + 0.204124i
\(25\) 4.00000 + 3.00000i 0.800000 + 0.600000i
\(26\) 4.24264i 0.832050i
\(27\) 4.53553 2.53553i 0.872864 0.487964i
\(28\) 0 0
\(29\) 2.82843 0.525226 0.262613 0.964901i \(-0.415416\pi\)
0.262613 + 0.964901i \(0.415416\pi\)
\(30\) −3.12132 + 2.29289i −0.569873 + 0.418623i
\(31\) −1.00000 −0.179605
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 1.24264 + 7.24264i 0.216316 + 1.26078i
\(34\) 2.00000i 0.342997i
\(35\) 0 0
\(36\) −1.00000 2.82843i −0.166667 0.471405i
\(37\) −5.00000 5.00000i −0.821995 0.821995i 0.164399 0.986394i \(-0.447432\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(38\) −2.82843 2.82843i −0.458831 0.458831i
\(39\) −4.24264 + 6.00000i −0.679366 + 0.960769i
\(40\) 1.00000 + 2.00000i 0.158114 + 0.316228i
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 8.00000 8.00000i 1.21999 1.21999i 0.252353 0.967635i \(-0.418795\pi\)
0.967635 0.252353i \(-0.0812046\pi\)
\(44\) 4.24264 0.639602
\(45\) 6.70711 0.121320i 0.999836 0.0180854i
\(46\) 0 0
\(47\) 4.24264 4.24264i 0.618853 0.618853i −0.326384 0.945237i \(-0.605830\pi\)
0.945237 + 0.326384i \(0.105830\pi\)
\(48\) −1.70711 + 0.292893i −0.246400 + 0.0422755i
\(49\) 7.00000i 1.00000i
\(50\) −4.94975 + 0.707107i −0.700000 + 0.100000i
\(51\) −2.00000 + 2.82843i −0.280056 + 0.396059i
\(52\) 3.00000 + 3.00000i 0.416025 + 0.416025i
\(53\) 4.24264 + 4.24264i 0.582772 + 0.582772i 0.935664 0.352892i \(-0.114802\pi\)
−0.352892 + 0.935664i \(0.614802\pi\)
\(54\) −1.41421 + 5.00000i −0.192450 + 0.680414i
\(55\) −3.00000 + 9.00000i −0.404520 + 1.21356i
\(56\) 0 0
\(57\) 1.17157 + 6.82843i 0.155179 + 0.904447i
\(58\) −2.00000 + 2.00000i −0.262613 + 0.262613i
\(59\) 5.65685 0.736460 0.368230 0.929735i \(-0.379964\pi\)
0.368230 + 0.929735i \(0.379964\pi\)
\(60\) 0.585786 3.82843i 0.0756247 0.494248i
\(61\) −8.00000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 0.707107 0.707107i 0.0898027 0.0898027i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −8.48528 + 4.24264i −1.05247 + 0.526235i
\(66\) −6.00000 4.24264i −0.738549 0.522233i
\(67\) −1.00000 1.00000i −0.122169 0.122169i 0.643379 0.765548i \(-0.277532\pi\)
−0.765548 + 0.643379i \(0.777532\pi\)
\(68\) 1.41421 + 1.41421i 0.171499 + 0.171499i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.41421i 0.167836i −0.996473 0.0839181i \(-0.973257\pi\)
0.996473 0.0839181i \(-0.0267434\pi\)
\(72\) 2.70711 + 1.29289i 0.319036 + 0.152369i
\(73\) 2.00000 2.00000i 0.234082 0.234082i −0.580312 0.814394i \(-0.697069\pi\)
0.814394 + 0.580312i \(0.197069\pi\)
\(74\) 7.07107 0.821995
\(75\) 7.70711 + 3.94975i 0.889940 + 0.456078i
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) −1.24264 7.24264i −0.140701 0.820068i
\(79\) 10.0000i 1.12509i −0.826767 0.562544i \(-0.809823\pi\)
0.826767 0.562544i \(-0.190177\pi\)
\(80\) −2.12132 0.707107i −0.237171 0.0790569i
\(81\) 7.00000 5.65685i 0.777778 0.628539i
\(82\) 0 0
\(83\) −12.7279 12.7279i −1.39707 1.39707i −0.808300 0.588771i \(-0.799612\pi\)
−0.588771 0.808300i \(-0.700388\pi\)
\(84\) 0 0
\(85\) −4.00000 + 2.00000i −0.433861 + 0.216930i
\(86\) 11.3137i 1.21999i
\(87\) 4.82843 0.828427i 0.517662 0.0888167i
\(88\) −3.00000 + 3.00000i −0.319801 + 0.319801i
\(89\) 7.07107 0.749532 0.374766 0.927119i \(-0.377723\pi\)
0.374766 + 0.927119i \(0.377723\pi\)
\(90\) −4.65685 + 4.82843i −0.490876 + 0.508961i
\(91\) 0 0
\(92\) 0 0
\(93\) −1.70711 + 0.292893i −0.177019 + 0.0303716i
\(94\) 6.00000i 0.618853i
\(95\) −2.82843 + 8.48528i −0.290191 + 0.870572i
\(96\) 1.00000 1.41421i 0.102062 0.144338i
\(97\) 3.00000 + 3.00000i 0.304604 + 0.304604i 0.842812 0.538208i \(-0.180899\pi\)
−0.538208 + 0.842812i \(0.680899\pi\)
\(98\) 4.94975 + 4.94975i 0.500000 + 0.500000i
\(99\) 4.24264 + 12.0000i 0.426401 + 1.20605i
\(100\) 3.00000 4.00000i 0.300000 0.400000i
\(101\) 18.3848i 1.82935i 0.404186 + 0.914677i \(0.367555\pi\)
−0.404186 + 0.914677i \(0.632445\pi\)
\(102\) −0.585786 3.41421i −0.0580015 0.338058i
\(103\) 10.0000 10.0000i 0.985329 0.985329i −0.0145647 0.999894i \(-0.504636\pi\)
0.999894 + 0.0145647i \(0.00463624\pi\)
\(104\) −4.24264 −0.416025
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) −2.82843 + 2.82843i −0.273434 + 0.273434i −0.830481 0.557047i \(-0.811934\pi\)
0.557047 + 0.830481i \(0.311934\pi\)
\(108\) −2.53553 4.53553i −0.243982 0.436432i
\(109\) 6.00000i 0.574696i 0.957826 + 0.287348i \(0.0927736\pi\)
−0.957826 + 0.287348i \(0.907226\pi\)
\(110\) −4.24264 8.48528i −0.404520 0.809040i
\(111\) −10.0000 7.07107i −0.949158 0.671156i
\(112\) 0 0
\(113\) −4.24264 4.24264i −0.399114 0.399114i 0.478806 0.877920i \(-0.341070\pi\)
−0.877920 + 0.478806i \(0.841070\pi\)
\(114\) −5.65685 4.00000i −0.529813 0.374634i
\(115\) 0 0
\(116\) 2.82843i 0.262613i
\(117\) −5.48528 + 11.4853i −0.507114 + 1.06181i
\(118\) −4.00000 + 4.00000i −0.368230 + 0.368230i
\(119\) 0 0
\(120\) 2.29289 + 3.12132i 0.209312 + 0.284936i
\(121\) −7.00000 −0.636364
\(122\) 5.65685 5.65685i 0.512148 0.512148i
\(123\) 0 0
\(124\) 1.00000i 0.0898027i
\(125\) 6.36396 + 9.19239i 0.569210 + 0.822192i
\(126\) 0 0
\(127\) −9.00000 9.00000i −0.798621 0.798621i 0.184257 0.982878i \(-0.441012\pi\)
−0.982878 + 0.184257i \(0.941012\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 11.3137 16.0000i 0.996116 1.40872i
\(130\) 3.00000 9.00000i 0.263117 0.789352i
\(131\) 19.7990i 1.72985i 0.501905 + 0.864923i \(0.332633\pi\)
−0.501905 + 0.864923i \(0.667367\pi\)
\(132\) 7.24264 1.24264i 0.630391 0.108158i
\(133\) 0 0
\(134\) 1.41421 0.122169
\(135\) 11.4142 2.17157i 0.982379 0.186899i
\(136\) −2.00000 −0.171499
\(137\) −12.7279 + 12.7279i −1.08742 + 1.08742i −0.0916263 + 0.995793i \(0.529207\pi\)
−0.995793 + 0.0916263i \(0.970793\pi\)
\(138\) 0 0
\(139\) 8.00000i 0.678551i −0.940687 0.339276i \(-0.889818\pi\)
0.940687 0.339276i \(-0.110182\pi\)
\(140\) 0 0
\(141\) 6.00000 8.48528i 0.505291 0.714590i
\(142\) 1.00000 + 1.00000i 0.0839181 + 0.0839181i
\(143\) −12.7279 12.7279i −1.06436 1.06436i
\(144\) −2.82843 + 1.00000i −0.235702 + 0.0833333i
\(145\) 6.00000 + 2.00000i 0.498273 + 0.166091i
\(146\) 2.82843i 0.234082i
\(147\) −2.05025 11.9497i −0.169102 0.985599i
\(148\) −5.00000 + 5.00000i −0.410997 + 0.410997i
\(149\) 1.41421 0.115857 0.0579284 0.998321i \(-0.481550\pi\)
0.0579284 + 0.998321i \(0.481550\pi\)
\(150\) −8.24264 + 2.65685i −0.673009 + 0.216931i
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) −2.82843 + 2.82843i −0.229416 + 0.229416i
\(153\) −2.58579 + 5.41421i −0.209048 + 0.437713i
\(154\) 0 0
\(155\) −2.12132 0.707107i −0.170389 0.0567962i
\(156\) 6.00000 + 4.24264i 0.480384 + 0.339683i
\(157\) −4.00000 4.00000i −0.319235 0.319235i 0.529238 0.848473i \(-0.322478\pi\)
−0.848473 + 0.529238i \(0.822478\pi\)
\(158\) 7.07107 + 7.07107i 0.562544 + 0.562544i
\(159\) 8.48528 + 6.00000i 0.672927 + 0.475831i
\(160\) 2.00000 1.00000i 0.158114 0.0790569i
\(161\) 0 0
\(162\) −0.949747 + 8.94975i −0.0746192 + 0.703159i
\(163\) −11.0000 + 11.0000i −0.861586 + 0.861586i −0.991522 0.129936i \(-0.958523\pi\)
0.129936 + 0.991522i \(0.458523\pi\)
\(164\) 0 0
\(165\) −2.48528 + 16.2426i −0.193479 + 1.26449i
\(166\) 18.0000 1.39707
\(167\) 8.48528 8.48528i 0.656611 0.656611i −0.297966 0.954577i \(-0.596308\pi\)
0.954577 + 0.297966i \(0.0963081\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) 1.41421 4.24264i 0.108465 0.325396i
\(171\) 4.00000 + 11.3137i 0.305888 + 0.865181i
\(172\) −8.00000 8.00000i −0.609994 0.609994i
\(173\) −8.48528 8.48528i −0.645124 0.645124i 0.306687 0.951811i \(-0.400780\pi\)
−0.951811 + 0.306687i \(0.900780\pi\)
\(174\) −2.82843 + 4.00000i −0.214423 + 0.303239i
\(175\) 0 0
\(176\) 4.24264i 0.319801i
\(177\) 9.65685 1.65685i 0.725854 0.124537i
\(178\) −5.00000 + 5.00000i −0.374766 + 0.374766i
\(179\) 18.3848 1.37414 0.687071 0.726590i \(-0.258896\pi\)
0.687071 + 0.726590i \(0.258896\pi\)
\(180\) −0.121320 6.70711i −0.00904268 0.499918i
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) −13.6569 + 2.34315i −1.00954 + 0.173210i
\(184\) 0 0
\(185\) −7.07107 14.1421i −0.519875 1.03975i
\(186\) 1.00000 1.41421i 0.0733236 0.103695i
\(187\) −6.00000 6.00000i −0.438763 0.438763i
\(188\) −4.24264 4.24264i −0.309426 0.309426i
\(189\) 0 0
\(190\) −4.00000 8.00000i −0.290191 0.580381i
\(191\) 1.41421i 0.102329i −0.998690 0.0511645i \(-0.983707\pi\)
0.998690 0.0511645i \(-0.0162933\pi\)
\(192\) 0.292893 + 1.70711i 0.0211377 + 0.123200i
\(193\) 15.0000 15.0000i 1.07972 1.07972i 0.0831899 0.996534i \(-0.473489\pi\)
0.996534 0.0831899i \(-0.0265108\pi\)
\(194\) −4.24264 −0.304604
\(195\) −13.2426 + 9.72792i −0.948325 + 0.696631i
\(196\) −7.00000 −0.500000
\(197\) −1.41421 + 1.41421i −0.100759 + 0.100759i −0.755689 0.654931i \(-0.772698\pi\)
0.654931 + 0.755689i \(0.272698\pi\)
\(198\) −11.4853 5.48528i −0.816223 0.389822i
\(199\) 16.0000i 1.13421i −0.823646 0.567105i \(-0.808063\pi\)
0.823646 0.567105i \(-0.191937\pi\)
\(200\) 0.707107 + 4.94975i 0.0500000 + 0.350000i
\(201\) −2.00000 1.41421i −0.141069 0.0997509i
\(202\) −13.0000 13.0000i −0.914677 0.914677i
\(203\) 0 0
\(204\) 2.82843 + 2.00000i 0.198030 + 0.140028i
\(205\) 0 0
\(206\) 14.1421i 0.985329i
\(207\) 0 0
\(208\) 3.00000 3.00000i 0.208013 0.208013i
\(209\) −16.9706 −1.17388
\(210\) 0 0
\(211\) −6.00000 −0.413057 −0.206529 0.978441i \(-0.566217\pi\)
−0.206529 + 0.978441i \(0.566217\pi\)
\(212\) 4.24264 4.24264i 0.291386 0.291386i
\(213\) −0.414214 2.41421i −0.0283814 0.165419i
\(214\) 4.00000i 0.273434i
\(215\) 22.6274 11.3137i 1.54318 0.771589i
\(216\) 5.00000 + 1.41421i 0.340207 + 0.0962250i
\(217\) 0 0
\(218\) −4.24264 4.24264i −0.287348 0.287348i
\(219\) 2.82843 4.00000i 0.191127 0.270295i
\(220\) 9.00000 + 3.00000i 0.606780 + 0.202260i
\(221\) 8.48528i 0.570782i
\(222\) 12.0711 2.07107i 0.810157 0.139001i
\(223\) −1.00000 + 1.00000i −0.0669650 + 0.0669650i −0.739796 0.672831i \(-0.765078\pi\)
0.672831 + 0.739796i \(0.265078\pi\)
\(224\) 0 0
\(225\) 14.3137 + 4.48528i 0.954247 + 0.299019i
\(226\) 6.00000 0.399114
\(227\) −5.65685 + 5.65685i −0.375459 + 0.375459i −0.869461 0.494002i \(-0.835534\pi\)
0.494002 + 0.869461i \(0.335534\pi\)
\(228\) 6.82843 1.17157i 0.452224 0.0775893i
\(229\) 10.0000i 0.660819i −0.943838 0.330409i \(-0.892813\pi\)
0.943838 0.330409i \(-0.107187\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 2.00000 + 2.00000i 0.131306 + 0.131306i
\(233\) −12.7279 12.7279i −0.833834 0.833834i 0.154205 0.988039i \(-0.450718\pi\)
−0.988039 + 0.154205i \(0.950718\pi\)
\(234\) −4.24264 12.0000i −0.277350 0.784465i
\(235\) 12.0000 6.00000i 0.782794 0.391397i
\(236\) 5.65685i 0.368230i
\(237\) −2.92893 17.0711i −0.190255 1.10889i
\(238\) 0 0
\(239\) 11.3137 0.731823 0.365911 0.930650i \(-0.380757\pi\)
0.365911 + 0.930650i \(0.380757\pi\)
\(240\) −3.82843 0.585786i −0.247124 0.0378124i
\(241\) 22.0000 1.41714 0.708572 0.705638i \(-0.249340\pi\)
0.708572 + 0.705638i \(0.249340\pi\)
\(242\) 4.94975 4.94975i 0.318182 0.318182i
\(243\) 10.2929 11.7071i 0.660289 0.751011i
\(244\) 8.00000i 0.512148i
\(245\) 4.94975 14.8492i 0.316228 0.948683i
\(246\) 0 0
\(247\) −12.0000 12.0000i −0.763542 0.763542i
\(248\) −0.707107 0.707107i −0.0449013 0.0449013i
\(249\) −25.4558 18.0000i −1.61320 1.14070i
\(250\) −11.0000 2.00000i −0.695701 0.126491i
\(251\) 21.2132i 1.33897i −0.742828 0.669483i \(-0.766516\pi\)
0.742828 0.669483i \(-0.233484\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 12.7279 0.798621
\(255\) −6.24264 + 4.58579i −0.390929 + 0.287173i
\(256\) 1.00000 0.0625000
\(257\) 4.24264 4.24264i 0.264649 0.264649i −0.562291 0.826940i \(-0.690080\pi\)
0.826940 + 0.562291i \(0.190080\pi\)
\(258\) 3.31371 + 19.3137i 0.206302 + 1.20242i
\(259\) 0 0
\(260\) 4.24264 + 8.48528i 0.263117 + 0.526235i
\(261\) 8.00000 2.82843i 0.495188 0.175075i
\(262\) −14.0000 14.0000i −0.864923 0.864923i
\(263\) −19.7990 19.7990i −1.22086 1.22086i −0.967327 0.253531i \(-0.918408\pi\)
−0.253531 0.967327i \(-0.581592\pi\)
\(264\) −4.24264 + 6.00000i −0.261116 + 0.369274i
\(265\) 6.00000 + 12.0000i 0.368577 + 0.737154i
\(266\) 0 0
\(267\) 12.0711 2.07107i 0.738737 0.126747i
\(268\) −1.00000 + 1.00000i −0.0610847 + 0.0610847i
\(269\) 2.82843 0.172452 0.0862261 0.996276i \(-0.472519\pi\)
0.0862261 + 0.996276i \(0.472519\pi\)
\(270\) −6.53553 + 9.60660i −0.397740 + 0.584639i
\(271\) 22.0000 1.33640 0.668202 0.743980i \(-0.267064\pi\)
0.668202 + 0.743980i \(0.267064\pi\)
\(272\) 1.41421 1.41421i 0.0857493 0.0857493i
\(273\) 0 0
\(274\) 18.0000i 1.08742i
\(275\) −12.7279 + 16.9706i −0.767523 + 1.02336i
\(276\) 0 0
\(277\) −21.0000 21.0000i −1.26177 1.26177i −0.950236 0.311532i \(-0.899158\pi\)
−0.311532 0.950236i \(-0.600842\pi\)
\(278\) 5.65685 + 5.65685i 0.339276 + 0.339276i
\(279\) −2.82843 + 1.00000i −0.169334 + 0.0598684i
\(280\) 0 0
\(281\) 22.6274i 1.34984i 0.737892 + 0.674919i \(0.235822\pi\)
−0.737892 + 0.674919i \(0.764178\pi\)
\(282\) 1.75736 + 10.2426i 0.104649 + 0.609940i
\(283\) −3.00000 + 3.00000i −0.178331 + 0.178331i −0.790628 0.612297i \(-0.790246\pi\)
0.612297 + 0.790628i \(0.290246\pi\)
\(284\) −1.41421 −0.0839181
\(285\) −2.34315 + 15.3137i −0.138796 + 0.907106i
\(286\) 18.0000 1.06436
\(287\) 0 0
\(288\) 1.29289 2.70711i 0.0761845 0.159518i
\(289\) 13.0000i 0.764706i
\(290\) −5.65685 + 2.82843i −0.332182 + 0.166091i
\(291\) 6.00000 + 4.24264i 0.351726 + 0.248708i
\(292\) −2.00000 2.00000i −0.117041 0.117041i
\(293\) −5.65685 5.65685i −0.330477 0.330477i 0.522291 0.852768i \(-0.325078\pi\)
−0.852768 + 0.522291i \(0.825078\pi\)
\(294\) 9.89949 + 7.00000i 0.577350 + 0.408248i
\(295\) 12.0000 + 4.00000i 0.698667 + 0.232889i
\(296\) 7.07107i 0.410997i
\(297\) 10.7574 + 19.2426i 0.624205 + 1.11657i
\(298\) −1.00000 + 1.00000i −0.0579284 + 0.0579284i
\(299\) 0 0
\(300\) 3.94975 7.70711i 0.228039 0.444970i
\(301\) 0 0
\(302\) 11.3137 11.3137i 0.651031 0.651031i
\(303\) 5.38478 + 31.3848i 0.309347 + 1.80301i
\(304\) 4.00000i 0.229416i
\(305\) −16.9706 5.65685i −0.971732 0.323911i
\(306\) −2.00000 5.65685i −0.114332 0.323381i
\(307\) 5.00000 + 5.00000i 0.285365 + 0.285365i 0.835244 0.549879i \(-0.185326\pi\)
−0.549879 + 0.835244i \(0.685326\pi\)
\(308\) 0 0
\(309\) 14.1421 20.0000i 0.804518 1.13776i
\(310\) 2.00000 1.00000i 0.113592 0.0567962i
\(311\) 12.7279i 0.721734i −0.932617 0.360867i \(-0.882481\pi\)
0.932617 0.360867i \(-0.117519\pi\)
\(312\) −7.24264 + 1.24264i −0.410034 + 0.0703507i
\(313\) 14.0000 14.0000i 0.791327 0.791327i −0.190383 0.981710i \(-0.560973\pi\)
0.981710 + 0.190383i \(0.0609730\pi\)
\(314\) 5.65685 0.319235
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) −15.5563 + 15.5563i −0.873732 + 0.873732i −0.992877 0.119145i \(-0.961985\pi\)
0.119145 + 0.992877i \(0.461985\pi\)
\(318\) −10.2426 + 1.75736i −0.574379 + 0.0985478i
\(319\) 12.0000i 0.671871i
\(320\) −0.707107 + 2.12132i −0.0395285 + 0.118585i
\(321\) −4.00000 + 5.65685i −0.223258 + 0.315735i
\(322\) 0 0
\(323\) −5.65685 5.65685i −0.314756 0.314756i
\(324\) −5.65685 7.00000i −0.314270 0.388889i
\(325\) −21.0000 + 3.00000i −1.16487 + 0.166410i
\(326\) 15.5563i 0.861586i
\(327\) 1.75736 + 10.2426i 0.0971822 + 0.566419i
\(328\) 0 0
\(329\) 0 0
\(330\) −9.72792 13.2426i −0.535504 0.728983i
\(331\) −28.0000 −1.53902 −0.769510 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) −12.7279 + 12.7279i −0.698535 + 0.698535i
\(333\) −19.1421 9.14214i −1.04898 0.500986i
\(334\) 12.0000i 0.656611i
\(335\) −1.41421 2.82843i −0.0772667 0.154533i
\(336\) 0 0
\(337\) 24.0000 + 24.0000i 1.30736 + 1.30736i 0.923312 + 0.384052i \(0.125472\pi\)
0.384052 + 0.923312i \(0.374528\pi\)
\(338\) 3.53553 + 3.53553i 0.192308 + 0.192308i
\(339\) −8.48528 6.00000i −0.460857 0.325875i
\(340\) 2.00000 + 4.00000i 0.108465 + 0.216930i
\(341\) 4.24264i 0.229752i
\(342\) −10.8284 5.17157i −0.585534 0.279647i
\(343\) 0 0
\(344\) 11.3137 0.609994
\(345\) 0 0
\(346\) 12.0000 0.645124
\(347\) −1.41421 + 1.41421i −0.0759190 + 0.0759190i −0.744047 0.668128i \(-0.767096\pi\)
0.668128 + 0.744047i \(0.267096\pi\)
\(348\) −0.828427 4.82843i −0.0444084 0.258831i
\(349\) 14.0000i 0.749403i 0.927146 + 0.374701i \(0.122255\pi\)
−0.927146 + 0.374701i \(0.877745\pi\)
\(350\) 0 0
\(351\) −6.00000 + 21.2132i −0.320256 + 1.13228i
\(352\) 3.00000 + 3.00000i 0.159901 + 0.159901i
\(353\) −2.82843 2.82843i −0.150542 0.150542i 0.627818 0.778360i \(-0.283948\pi\)
−0.778360 + 0.627818i \(0.783948\pi\)
\(354\) −5.65685 + 8.00000i −0.300658 + 0.425195i
\(355\) 1.00000 3.00000i 0.0530745 0.159223i
\(356\) 7.07107i 0.374766i
\(357\) 0 0
\(358\) −13.0000 + 13.0000i −0.687071 + 0.687071i
\(359\) 4.24264 0.223918 0.111959 0.993713i \(-0.464287\pi\)
0.111959 + 0.993713i \(0.464287\pi\)
\(360\) 4.82843 + 4.65685i 0.254480 + 0.245438i
\(361\) 3.00000 0.157895
\(362\) −7.07107 + 7.07107i −0.371647 + 0.371647i
\(363\) −11.9497 + 2.05025i −0.627199 + 0.107610i
\(364\) 0 0
\(365\) 5.65685 2.82843i 0.296093 0.148047i
\(366\) 8.00000 11.3137i 0.418167 0.591377i
\(367\) 3.00000 + 3.00000i 0.156599 + 0.156599i 0.781058 0.624459i \(-0.214680\pi\)
−0.624459 + 0.781058i \(0.714680\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 15.0000 + 5.00000i 0.779813 + 0.259938i
\(371\) 0 0
\(372\) 0.292893 + 1.70711i 0.0151858 + 0.0885094i
\(373\) −16.0000 + 16.0000i −0.828449 + 0.828449i −0.987302 0.158854i \(-0.949220\pi\)
0.158854 + 0.987302i \(0.449220\pi\)
\(374\) 8.48528 0.438763
\(375\) 13.5563 + 13.8284i 0.700047 + 0.714097i
\(376\) 6.00000 0.309426
\(377\) −8.48528 + 8.48528i −0.437014 + 0.437014i
\(378\) 0 0
\(379\) 6.00000i 0.308199i 0.988055 + 0.154100i \(0.0492477\pi\)
−0.988055 + 0.154100i \(0.950752\pi\)
\(380\) 8.48528 + 2.82843i 0.435286 + 0.145095i
\(381\) −18.0000 12.7279i −0.922168 0.652071i
\(382\) 1.00000 + 1.00000i 0.0511645 + 0.0511645i
\(383\) −16.9706 16.9706i −0.867155 0.867155i 0.125001 0.992157i \(-0.460106\pi\)
−0.992157 + 0.125001i \(0.960106\pi\)
\(384\) −1.41421 1.00000i −0.0721688 0.0510310i
\(385\) 0 0
\(386\) 21.2132i 1.07972i
\(387\) 14.6274 30.6274i 0.743553 1.55688i
\(388\) 3.00000 3.00000i 0.152302 0.152302i
\(389\) −22.6274 −1.14726 −0.573628 0.819116i \(-0.694464\pi\)
−0.573628 + 0.819116i \(0.694464\pi\)
\(390\) 2.48528 16.2426i 0.125847 0.822478i
\(391\) 0 0
\(392\) 4.94975 4.94975i 0.250000 0.250000i
\(393\) 5.79899 + 33.7990i 0.292520 + 1.70493i
\(394\) 2.00000i 0.100759i
\(395\) 7.07107 21.2132i 0.355784 1.06735i
\(396\) 12.0000 4.24264i 0.603023 0.213201i
\(397\) 12.0000 + 12.0000i 0.602263 + 0.602263i 0.940913 0.338650i \(-0.109970\pi\)
−0.338650 + 0.940913i \(0.609970\pi\)
\(398\) 11.3137 + 11.3137i 0.567105 + 0.567105i
\(399\) 0 0
\(400\) −4.00000 3.00000i −0.200000 0.150000i
\(401\) 26.8701i 1.34183i 0.741536 + 0.670913i \(0.234098\pi\)
−0.741536 + 0.670913i \(0.765902\pi\)
\(402\) 2.41421 0.414214i 0.120410 0.0206591i
\(403\) 3.00000 3.00000i 0.149441 0.149441i
\(404\) 18.3848 0.914677
\(405\) 18.8492 7.05025i 0.936626 0.350330i
\(406\) 0 0
\(407\) 21.2132 21.2132i 1.05150 1.05150i
\(408\) −3.41421 + 0.585786i −0.169029 + 0.0290008i
\(409\) 30.0000i 1.48340i 0.670729 + 0.741702i \(0.265981\pi\)
−0.670729 + 0.741702i \(0.734019\pi\)
\(410\) 0 0
\(411\) −18.0000 + 25.4558i −0.887875 + 1.25564i
\(412\) −10.0000 10.0000i −0.492665 0.492665i
\(413\) 0 0
\(414\) 0 0
\(415\) −18.0000 36.0000i −0.883585 1.76717i
\(416\) 4.24264i 0.208013i
\(417\) −2.34315 13.6569i −0.114744 0.668779i
\(418\) 12.0000 12.0000i 0.586939 0.586939i
\(419\) 22.6274 1.10542 0.552711 0.833373i \(-0.313593\pi\)
0.552711 + 0.833373i \(0.313593\pi\)
\(420\) 0 0
\(421\) −6.00000 −0.292422 −0.146211 0.989253i \(-0.546708\pi\)
−0.146211 + 0.989253i \(0.546708\pi\)
\(422\) 4.24264 4.24264i 0.206529 0.206529i
\(423\) 7.75736 16.2426i 0.377176 0.789744i
\(424\) 6.00000i 0.291386i
\(425\) −9.89949 + 1.41421i −0.480196 + 0.0685994i
\(426\) 2.00000 + 1.41421i 0.0969003 + 0.0685189i
\(427\) 0 0
\(428\) 2.82843 + 2.82843i 0.136717 + 0.136717i
\(429\) −25.4558 18.0000i −1.22902 0.869048i
\(430\) −8.00000 + 24.0000i −0.385794 + 1.15738i
\(431\) 12.7279i 0.613082i −0.951857 0.306541i \(-0.900828\pi\)
0.951857 0.306541i \(-0.0991717\pi\)
\(432\) −4.53553 + 2.53553i −0.218216 + 0.121991i
\(433\) −26.0000 + 26.0000i −1.24948 + 1.24948i −0.293531 + 0.955950i \(0.594830\pi\)
−0.955950 + 0.293531i \(0.905170\pi\)
\(434\) 0 0
\(435\) 10.8284 + 1.65685i 0.519183 + 0.0794401i
\(436\) 6.00000 0.287348
\(437\) 0 0
\(438\) 0.828427 + 4.82843i 0.0395838 + 0.230711i
\(439\) 16.0000i 0.763638i 0.924237 + 0.381819i \(0.124702\pi\)
−0.924237 + 0.381819i \(0.875298\pi\)
\(440\) −8.48528 + 4.24264i −0.404520 + 0.202260i
\(441\) −7.00000 19.7990i −0.333333 0.942809i
\(442\) 6.00000 + 6.00000i 0.285391 + 0.285391i
\(443\) 11.3137 + 11.3137i 0.537531 + 0.537531i 0.922803 0.385272i \(-0.125893\pi\)
−0.385272 + 0.922803i \(0.625893\pi\)
\(444\) −7.07107 + 10.0000i −0.335578 + 0.474579i
\(445\) 15.0000 + 5.00000i 0.711068 + 0.237023i
\(446\) 1.41421i 0.0669650i
\(447\) 2.41421 0.414214i 0.114188 0.0195916i
\(448\) 0 0
\(449\) −24.0416 −1.13459 −0.567297 0.823513i \(-0.692011\pi\)
−0.567297 + 0.823513i \(0.692011\pi\)
\(450\) −13.2929 + 6.94975i −0.626633 + 0.327614i
\(451\) 0 0
\(452\) −4.24264 + 4.24264i −0.199557 + 0.199557i
\(453\) −27.3137 + 4.68629i −1.28331 + 0.220181i
\(454\) 8.00000i 0.375459i
\(455\) 0 0
\(456\) −4.00000 + 5.65685i −0.187317 + 0.264906i
\(457\) −8.00000 8.00000i −0.374224 0.374224i 0.494789 0.869013i \(-0.335245\pi\)
−0.869013 + 0.494789i \(0.835245\pi\)
\(458\) 7.07107 + 7.07107i 0.330409 + 0.330409i
\(459\) −2.82843 + 10.0000i −0.132020 + 0.466760i
\(460\) 0 0
\(461\) 36.7696i 1.71253i 0.516538 + 0.856264i \(0.327221\pi\)
−0.516538 + 0.856264i \(0.672779\pi\)
\(462\) 0 0
\(463\) 3.00000 3.00000i 0.139422 0.139422i −0.633951 0.773373i \(-0.718568\pi\)
0.773373 + 0.633951i \(0.218568\pi\)
\(464\) −2.82843 −0.131306
\(465\) −3.82843 0.585786i −0.177539 0.0271652i
\(466\) 18.0000 0.833834
\(467\) 25.4558 25.4558i 1.17796 1.17796i 0.197692 0.980264i \(-0.436655\pi\)
0.980264 0.197692i \(-0.0633445\pi\)
\(468\) 11.4853 + 5.48528i 0.530907 + 0.253557i
\(469\) 0 0
\(470\) −4.24264 + 12.7279i −0.195698 + 0.587095i
\(471\) −8.00000 5.65685i −0.368621 0.260654i
\(472\) 4.00000 + 4.00000i 0.184115 + 0.184115i
\(473\) 33.9411 + 33.9411i 1.56061 + 1.56061i
\(474\) 14.1421 + 10.0000i 0.649570 + 0.459315i
\(475\) −12.0000 + 16.0000i −0.550598 + 0.734130i
\(476\) 0 0
\(477\) 16.2426 + 7.75736i 0.743699 + 0.355185i
\(478\) −8.00000 + 8.00000i −0.365911 + 0.365911i
\(479\) −7.07107 −0.323085 −0.161543 0.986866i \(-0.551647\pi\)
−0.161543 + 0.986866i \(0.551647\pi\)
\(480\) 3.12132 2.29289i 0.142468 0.104656i
\(481\) 30.0000 1.36788
\(482\) −15.5563 + 15.5563i −0.708572 + 0.708572i
\(483\) 0 0
\(484\) 7.00000i 0.318182i
\(485\) 4.24264 + 8.48528i 0.192648 + 0.385297i
\(486\) 1.00000 + 15.5563i 0.0453609 + 0.705650i
\(487\) 15.0000 + 15.0000i 0.679715 + 0.679715i 0.959936 0.280221i \(-0.0904077\pi\)
−0.280221 + 0.959936i \(0.590408\pi\)
\(488\) −5.65685 5.65685i −0.256074 0.256074i
\(489\) −15.5563 + 22.0000i −0.703482 + 0.994874i
\(490\) 7.00000 + 14.0000i 0.316228 + 0.632456i
\(491\) 15.5563i 0.702048i 0.936366 + 0.351024i \(0.114166\pi\)
−0.936366 + 0.351024i \(0.885834\pi\)
\(492\) 0 0
\(493\) −4.00000 + 4.00000i −0.180151 + 0.180151i
\(494\) 16.9706 0.763542
\(495\) 0.514719 + 28.4558i 0.0231349 + 1.27900i
\(496\) 1.00000 0.0449013
\(497\) 0 0
\(498\) 30.7279 5.27208i 1.37695 0.236247i
\(499\) 40.0000i 1.79065i −0.445418 0.895323i \(-0.646945\pi\)
0.445418 0.895323i \(-0.353055\pi\)
\(500\) 9.19239 6.36396i 0.411096 0.284605i
\(501\) 12.0000 16.9706i 0.536120 0.758189i
\(502\) 15.0000 + 15.0000i 0.669483 + 0.669483i
\(503\) −15.5563 15.5563i −0.693623 0.693623i 0.269404 0.963027i \(-0.413173\pi\)
−0.963027 + 0.269404i \(0.913173\pi\)
\(504\) 0 0
\(505\) −13.0000 + 39.0000i −0.578492 + 1.73548i
\(506\) 0 0
\(507\) −1.46447 8.53553i −0.0650392 0.379076i
\(508\) −9.00000 + 9.00000i −0.399310 + 0.399310i
\(509\) −39.5980 −1.75515 −0.877575 0.479440i \(-0.840840\pi\)
−0.877575 + 0.479440i \(0.840840\pi\)
\(510\) 1.17157 7.65685i 0.0518781 0.339051i
\(511\) 0 0
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 10.1421 + 18.1421i 0.447786 + 0.800995i
\(514\) 6.00000i 0.264649i
\(515\) 28.2843 14.1421i 1.24635 0.623177i
\(516\) −16.0000 11.3137i −0.704361 0.498058i
\(517\) 18.0000 + 18.0000i 0.791639 + 0.791639i
\(518\) 0 0
\(519\) −16.9706 12.0000i −0.744925 0.526742i
\(520\) −9.00000 3.00000i −0.394676 0.131559i
\(521\) 14.1421i 0.619578i −0.950805 0.309789i \(-0.899742\pi\)
0.950805 0.309789i \(-0.100258\pi\)
\(522\) −3.65685 + 7.65685i −0.160056 + 0.335131i
\(523\) −6.00000 + 6.00000i −0.262362 + 0.262362i −0.826013 0.563651i \(-0.809396\pi\)
0.563651 + 0.826013i \(0.309396\pi\)
\(524\) 19.7990 0.864923
\(525\) 0 0
\(526\) 28.0000 1.22086
\(527\) 1.41421 1.41421i 0.0616041 0.0616041i
\(528\) −1.24264 7.24264i −0.0540790 0.315195i
\(529\) 23.0000i 1.00000i
\(530\) −12.7279 4.24264i −0.552866 0.184289i
\(531\) 16.0000 5.65685i 0.694341 0.245487i
\(532\) 0 0
\(533\) 0 0
\(534\) −7.07107 + 10.0000i −0.305995 + 0.432742i
\(535\) −8.00000 + 4.00000i −0.345870 + 0.172935i
\(536\) 1.41421i 0.0610847i
\(537\) 31.3848 5.38478i 1.35435 0.232370i
\(538\) −2.00000 + 2.00000i −0.0862261 + 0.0862261i
\(539\) 29.6985 1.27920
\(540\) −2.17157 11.4142i −0.0934496 0.491190i
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) −15.5563 + 15.5563i −0.668202 + 0.668202i
\(543\) 17.0711 2.92893i 0.732590 0.125693i
\(544\) 2.00000i 0.0857493i
\(545\) −4.24264 + 12.7279i −0.181735 + 0.545204i
\(546\) 0 0
\(547\) 3.00000 + 3.00000i 0.128271 + 0.128271i 0.768328 0.640057i \(-0.221089\pi\)
−0.640057 + 0.768328i \(0.721089\pi\)
\(548\) 12.7279 + 12.7279i 0.543710 + 0.543710i
\(549\) −22.6274 + 8.00000i −0.965715 + 0.341432i
\(550\) −3.00000 21.0000i −0.127920 0.895443i
\(551\) 11.3137i 0.481980i
\(552\) 0 0
\(553\) 0 0
\(554\) 29.6985 1.26177
\(555\) −16.2132 22.0711i −0.688212 0.936865i
\(556\) −8.00000 −0.339276
\(557\) 9.89949 9.89949i 0.419455 0.419455i −0.465561 0.885016i \(-0.654147\pi\)
0.885016 + 0.465561i \(0.154147\pi\)
\(558\) 1.29289 2.70711i 0.0547325 0.114601i
\(559\) 48.0000i 2.03018i
\(560\) 0 0
\(561\) −12.0000 8.48528i −0.506640 0.358249i
\(562\) −16.0000 16.0000i −0.674919 0.674919i
\(563\) 16.9706 + 16.9706i 0.715224 + 0.715224i 0.967623 0.252399i \(-0.0812196\pi\)
−0.252399 + 0.967623i \(0.581220\pi\)
\(564\) −8.48528 6.00000i −0.357295 0.252646i
\(565\) −6.00000 12.0000i −0.252422 0.504844i
\(566\) 4.24264i 0.178331i
\(567\) 0 0
\(568\) 1.00000 1.00000i 0.0419591 0.0419591i
\(569\) 4.24264 0.177861 0.0889304 0.996038i \(-0.471655\pi\)
0.0889304 + 0.996038i \(0.471655\pi\)
\(570\) −9.17157 12.4853i −0.384155 0.522951i
\(571\) 36.0000 1.50655 0.753277 0.657704i \(-0.228472\pi\)
0.753277 + 0.657704i \(0.228472\pi\)
\(572\) −12.7279 + 12.7279i −0.532181 + 0.532181i
\(573\) −0.414214 2.41421i −0.0173040 0.100855i
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 + 2.82843i 0.0416667 + 0.117851i
\(577\) 13.0000 + 13.0000i 0.541197 + 0.541197i 0.923880 0.382683i \(-0.125000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(578\) −9.19239 9.19239i −0.382353 0.382353i
\(579\) 21.2132 30.0000i 0.881591 1.24676i
\(580\) 2.00000 6.00000i 0.0830455 0.249136i
\(581\) 0 0
\(582\) −7.24264 + 1.24264i −0.300217 + 0.0515091i
\(583\) −18.0000 + 18.0000i −0.745484 + 0.745484i
\(584\) 2.82843 0.117041
\(585\) −19.7574 + 20.4853i −0.816866 + 0.846962i
\(586\) 8.00000 0.330477
\(587\) −19.7990 + 19.7990i −0.817192 + 0.817192i −0.985700 0.168508i \(-0.946105\pi\)
0.168508 + 0.985700i \(0.446105\pi\)
\(588\) −11.9497 + 2.05025i −0.492799 + 0.0845510i
\(589\) 4.00000i 0.164817i
\(590\) −11.3137 + 5.65685i −0.465778 + 0.232889i
\(591\) −2.00000 + 2.82843i −0.0822690 + 0.116346i
\(592\) 5.00000 + 5.00000i 0.205499 + 0.205499i
\(593\) 24.0416 + 24.0416i 0.987271 + 0.987271i 0.999920 0.0126486i \(-0.00402627\pi\)
−0.0126486 + 0.999920i \(0.504026\pi\)
\(594\) −21.2132 6.00000i −0.870388 0.246183i
\(595\) 0 0
\(596\) 1.41421i 0.0579284i
\(597\) −4.68629 27.3137i −0.191797 1.11788i
\(598\) 0 0
\(599\) 24.0416 0.982314 0.491157 0.871071i \(-0.336574\pi\)
0.491157 + 0.871071i \(0.336574\pi\)
\(600\) 2.65685 + 8.24264i 0.108466 + 0.336504i
\(601\) −30.0000 −1.22373 −0.611863 0.790964i \(-0.709580\pi\)
−0.611863 + 0.790964i \(0.709580\pi\)
\(602\) 0 0
\(603\) −3.82843 1.82843i −0.155906 0.0744593i
\(604\) 16.0000i 0.651031i
\(605\) −14.8492 4.94975i −0.603708 0.201236i
\(606\) −26.0000 18.3848i −1.05618 0.746830i
\(607\) −16.0000 16.0000i −0.649420 0.649420i 0.303433 0.952853i \(-0.401867\pi\)
−0.952853 + 0.303433i \(0.901867\pi\)
\(608\) 2.82843 + 2.82843i 0.114708 + 0.114708i
\(609\) 0 0
\(610\) 16.0000 8.00000i 0.647821 0.323911i
\(611\) 25.4558i 1.02983i
\(612\) 5.41421 + 2.58579i 0.218857 + 0.104524i
\(613\) −19.0000 + 19.0000i −0.767403 + 0.767403i −0.977649 0.210246i \(-0.932574\pi\)
0.210246 + 0.977649i \(0.432574\pi\)
\(614\) −7.07107 −0.285365
\(615\) 0 0
\(616\) 0 0
\(617\) 12.7279 12.7279i 0.512407 0.512407i −0.402856 0.915263i \(-0.631983\pi\)
0.915263 + 0.402856i \(0.131983\pi\)
\(618\) 4.14214 + 24.1421i 0.166621 + 0.971139i
\(619\) 32.0000i 1.28619i −0.765787 0.643094i \(-0.777650\pi\)
0.765787 0.643094i \(-0.222350\pi\)
\(620\) −0.707107 + 2.12132i −0.0283981 + 0.0851943i
\(621\) 0 0
\(622\) 9.00000 + 9.00000i 0.360867 + 0.360867i
\(623\) 0 0
\(624\) 4.24264 6.00000i 0.169842 0.240192i
\(625\) 7.00000 + 24.0000i 0.280000 + 0.960000i
\(626\) 19.7990i 0.791327i
\(627\) −28.9706 + 4.97056i −1.15697 + 0.198505i
\(628\) −4.00000 + 4.00000i −0.159617 + 0.159617i
\(629\) 14.1421 0.563884
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 7.07107 7.07107i 0.281272 0.281272i
\(633\) −10.2426 + 1.75736i −0.407108 + 0.0698488i
\(634\) 22.0000i 0.873732i
\(635\) −12.7279 25.4558i −0.505092 1.01018i
\(636\) 6.00000 8.48528i 0.237915 0.336463i
\(637\) 21.0000 + 21.0000i 0.832050 + 0.832050i
\(638\) −8.48528 8.48528i −0.335936 0.335936i
\(639\) −1.41421 4.00000i −0.0559454 0.158238i
\(640\) −1.00000 2.00000i −0.0395285 0.0790569i
\(641\) 41.0122i 1.61988i −0.586510 0.809942i \(-0.699498\pi\)
0.586510 0.809942i \(-0.300502\pi\)
\(642\) −1.17157 6.82843i −0.0462383 0.269497i
\(643\) 30.0000 30.0000i 1.18308 1.18308i 0.204144 0.978941i \(-0.434559\pi\)
0.978941 0.204144i \(-0.0654409\pi\)
\(644\) 0 0
\(645\) 35.3137 25.9411i 1.39048 1.02143i
\(646\) 8.00000 0.314756
\(647\) −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
\(649\) 24.0000i 0.942082i
\(650\) 12.7279 16.9706i 0.499230 0.665640i
\(651\) 0 0
\(652\) 11.0000 + 11.0000i 0.430793 + 0.430793i
\(653\) −24.0416 24.0416i −0.940822 0.940822i 0.0575225 0.998344i \(-0.481680\pi\)
−0.998344 + 0.0575225i \(0.981680\pi\)
\(654\) −8.48528 6.00000i −0.331801 0.234619i
\(655\) −14.0000 + 42.0000i −0.547025 + 1.64108i
\(656\) 0 0
\(657\) 3.65685 7.65685i 0.142667 0.298722i
\(658\) 0 0
\(659\) 22.6274 0.881439 0.440720 0.897645i \(-0.354723\pi\)
0.440720 + 0.897645i \(0.354723\pi\)
\(660\) 16.2426 + 2.48528i 0.632244 + 0.0967394i
\(661\) −2.00000 −0.0777910 −0.0388955 0.999243i \(-0.512384\pi\)
−0.0388955 + 0.999243i \(0.512384\pi\)
\(662\) 19.7990 19.7990i 0.769510 0.769510i
\(663\) −2.48528 14.4853i −0.0965203 0.562562i
\(664\) 18.0000i 0.698535i
\(665\) 0 0
\(666\) 20.0000 7.07107i 0.774984 0.273998i
\(667\) 0 0
\(668\) −8.48528 8.48528i −0.328305 0.328305i
\(669\) −1.41421 + 2.00000i −0.0546767 + 0.0773245i
\(670\) 3.00000 + 1.00000i 0.115900 + 0.0386334i
\(671\) 33.9411i 1.31028i
\(672\) 0 0
\(673\) 12.0000 12.0000i 0.462566 0.462566i −0.436930 0.899496i \(-0.643934\pi\)
0.899496 + 0.436930i \(0.143934\pi\)
\(674\) −33.9411 −1.30736
\(675\) 25.7487 + 3.46447i 0.991069 + 0.133347i
\(676\) −5.00000 −0.192308
\(677\) 4.24264 4.24264i 0.163058 0.163058i −0.620862 0.783920i \(-0.713217\pi\)
0.783920 + 0.620862i \(0.213217\pi\)
\(678\) 10.2426 1.75736i 0.393366 0.0674910i
\(679\) 0 0
\(680\) −4.24264 1.41421i −0.162698 0.0542326i
\(681\) −8.00000 + 11.3137i −0.306561 + 0.433542i
\(682\) 3.00000 + 3.00000i 0.114876 + 0.114876i
\(683\) −11.3137 11.3137i −0.432907 0.432907i 0.456709 0.889616i \(-0.349028\pi\)
−0.889616 + 0.456709i \(0.849028\pi\)
\(684\) 11.3137 4.00000i 0.432590 0.152944i
\(685\) −36.0000 + 18.0000i −1.37549 + 0.687745i
\(686\) 0 0
\(687\) −2.92893 17.0711i −0.111746 0.651302i
\(688\) −8.00000 + 8.00000i −0.304997 + 0.304997i
\(689\) −25.4558 −0.969790
\(690\) 0 0
\(691\) −46.0000 −1.74992 −0.874961 0.484193i \(-0.839113\pi\)
−0.874961 + 0.484193i \(0.839113\pi\)
\(692\) −8.48528 + 8.48528i −0.322562 + 0.322562i
\(693\) 0 0
\(694\) 2.00000i 0.0759190i
\(695\) 5.65685 16.9706i 0.214577 0.643730i
\(696\) 4.00000 + 2.82843i 0.151620 + 0.107211i
\(697\) 0 0
\(698\) −9.89949 9.89949i −0.374701 0.374701i
\(699\) −25.4558 18.0000i −0.962828 0.680823i
\(700\) 0 0
\(701\) 41.0122i 1.54901i 0.632568 + 0.774505i \(0.282001\pi\)
−0.632568 + 0.774505i \(0.717999\pi\)
\(702\) −10.7574 19.2426i −0.406010 0.726267i
\(703\) 20.0000 20.0000i 0.754314 0.754314i
\(704\) −4.24264 −0.159901
\(705\) 18.7279 13.7574i 0.705334 0.518132i
\(706\) 4.00000 0.150542
\(707\) 0 0
\(708\) −1.65685 9.65685i −0.0622684 0.362927i
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 1.41421 + 2.82843i 0.0530745 + 0.106149i
\(711\) −10.0000 28.2843i −0.375029 1.06074i
\(712\) 5.00000 + 5.00000i 0.187383 + 0.187383i
\(713\) 0 0
\(714\) 0 0
\(715\) −18.0000 36.0000i −0.673162 1.34632i
\(716\) 18.3848i 0.687071i
\(717\) 19.3137 3.31371i 0.721284 0.123753i
\(718\) −3.00000 + 3.00000i −0.111959 + 0.111959i
\(719\) −22.6274 −0.843860 −0.421930 0.906628i \(-0.638647\pi\)
−0.421930 + 0.906628i \(0.638647\pi\)
\(720\) −6.70711 + 0.121320i −0.249959 + 0.00452134i
\(721\) 0 0
\(722\) −2.12132 + 2.12132i −0.0789474 + 0.0789474i
\(723\) 37.5563 6.44365i 1.39674 0.239642i
\(724\) 10.0000i 0.371647i
\(725\) 11.3137 + 8.48528i 0.420181 + 0.315135i
\(726\) 7.00000 9.89949i 0.259794 0.367405i
\(727\) −14.0000 14.0000i −0.519231 0.519231i 0.398108 0.917339i \(-0.369667\pi\)
−0.917339 + 0.398108i \(0.869667\pi\)
\(728\) 0 0
\(729\) 14.1421 23.0000i 0.523783 0.851852i
\(730\) −2.00000 + 6.00000i −0.0740233 + 0.222070i
\(731\) 22.6274i 0.836905i
\(732\) 2.34315 + 13.6569i 0.0866052 + 0.504772i
\(733\) 28.0000 28.0000i 1.03420 1.03420i 0.0348096 0.999394i \(-0.488918\pi\)
0.999394 0.0348096i \(-0.0110825\pi\)
\(734\) −4.24264 −0.156599
\(735\) 4.10051 26.7990i 0.151249 0.988496i
\(736\) 0 0
\(737\) 4.24264 4.24264i 0.156280 0.156280i
\(738\) 0 0
\(739\) 20.0000i 0.735712i 0.929883 + 0.367856i \(0.119908\pi\)
−0.929883 + 0.367856i \(0.880092\pi\)
\(740\) −14.1421 + 7.07107i −0.519875 + 0.259938i
\(741\) −24.0000 16.9706i −0.881662 0.623429i
\(742\) 0 0
\(743\) 16.9706 + 16.9706i 0.622590 + 0.622590i 0.946193 0.323603i \(-0.104894\pi\)
−0.323603 + 0.946193i \(0.604894\pi\)
\(744\) −1.41421 1.00000i −0.0518476 0.0366618i
\(745\) 3.00000 + 1.00000i 0.109911 + 0.0366372i
\(746\) 22.6274i 0.828449i
\(747\) −48.7279 23.2721i −1.78286 0.851481i
\(748\) −6.00000 + 6.00000i −0.219382 + 0.219382i
\(749\) 0 0
\(750\) −19.3640 0.192388i −0.707072 0.00702502i
\(751\) −12.0000 −0.437886 −0.218943 0.975738i \(-0.570261\pi\)
−0.218943 + 0.975738i \(0.570261\pi\)
\(752\) −4.24264 + 4.24264i −0.154713 + 0.154713i
\(753\) −6.21320 36.2132i −0.226422 1.31968i
\(754\) 12.0000i 0.437014i
\(755\) −33.9411 11.3137i −1.23524 0.411748i
\(756\) 0 0
\(757\) −21.0000 21.0000i −0.763258 0.763258i 0.213652 0.976910i \(-0.431464\pi\)
−0.976910 + 0.213652i \(0.931464\pi\)
\(758\) −4.24264 4.24264i −0.154100 0.154100i
\(759\) 0 0
\(760\) −8.00000 + 4.00000i −0.290191 + 0.145095i
\(761\) 18.3848i 0.666448i −0.942848 0.333224i \(-0.891864\pi\)
0.942848 0.333224i \(-0.108136\pi\)
\(762\) 21.7279 3.72792i 0.787120 0.135048i
\(763\) 0 0
\(764\) −1.41421 −0.0511645
\(765\) −9.31371 + 9.65685i −0.336738 + 0.349144i
\(766\) 24.0000 0.867155
\(767\) −16.9706 + 16.9706i −0.612772 + 0.612772i
\(768\) 1.70711 0.292893i 0.0615999 0.0105689i
\(769\) 32.0000i 1.15395i −0.816762 0.576975i \(-0.804233\pi\)
0.816762 0.576975i \(-0.195767\pi\)
\(770\) 0 0
\(771\) 6.00000 8.48528i 0.216085 0.305590i
\(772\) −15.0000 15.0000i −0.539862 0.539862i
\(773\) 26.8701 + 26.8701i 0.966449 + 0.966449i 0.999455 0.0330063i \(-0.0105082\pi\)
−0.0330063 + 0.999455i \(0.510508\pi\)
\(774\) 11.3137 + 32.0000i 0.406663 + 1.15022i
\(775\) −4.00000 3.00000i −0.143684 0.107763i
\(776\) 4.24264i 0.152302i
\(777\) 0 0
\(778\) 16.0000 16.0000i 0.573628 0.573628i
\(779\) 0 0
\(780\) 9.72792 + 13.2426i 0.348315 + 0.474163i
\(781\) 6.00000 0.214697