Properties

Label 930.2.j.a.497.2
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 497.2
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 930.497
Dual form 930.2.j.a.683.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(0.292893 - 1.70711i) q^{3} -1.00000i q^{4} +(-2.12132 - 0.707107i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(0.292893 - 1.70711i) 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} +(-1.70711 - 0.292893i) q^{12} +(-3.00000 + 3.00000i) q^{13} +(-1.82843 + 3.41421i) q^{15} -1.00000 q^{16} +(1.41421 - 1.41421i) q^{17} +(-2.70711 + 1.29289i) 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} +(-2.53553 + 4.53553i) q^{27} -2.82843 q^{29} +(1.12132 + 3.70711i) q^{30} -1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-7.24264 - 1.24264i) 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} +(5.29289 + 4.12132i) q^{45} +(-4.24264 + 4.24264i) q^{47} +(-0.292893 + 1.70711i) 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} +(6.82843 + 1.17157i) q^{57} +(-2.00000 + 2.00000i) q^{58} -5.65685 q^{59} +(3.41421 + 1.82843i) 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} +(1.29289 + 2.70711i) q^{72} +(2.00000 - 2.00000i) q^{73} -7.07107 q^{74} +(6.29289 - 5.94975i) q^{75} +4.00000 q^{76} +(7.24264 + 1.24264i) 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} +(-0.828427 + 4.82843i) q^{87} +(-3.00000 + 3.00000i) q^{88} -7.07107 q^{89} +(6.65685 - 0.828427i) q^{90} +(-0.292893 + 1.70711i) 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
\(3\) 0.292893 1.70711i 0.169102 0.985599i
\(4\) 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 \(-0.779099\pi\)
0.768706 0.639602i \(-0.220901\pi\)
\(12\) −1.70711 0.292893i −0.492799 0.0845510i
\(13\) −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
\(15\) −1.82843 + 3.41421i −0.472098 + 0.881546i
\(16\) −1.00000 −0.250000
\(17\) 1.41421 1.41421i 0.342997 0.342997i −0.514496 0.857493i \(-0.672021\pi\)
0.857493 + 0.514496i \(0.172021\pi\)
\(18\) −2.70711 + 1.29289i −0.638071 + 0.304738i
\(19\) 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
\(27\) −2.53553 + 4.53553i −0.487964 + 0.872864i
\(28\) 0 0
\(29\) −2.82843 −0.525226 −0.262613 0.964901i \(-0.584584\pi\)
−0.262613 + 0.964901i \(0.584584\pi\)
\(30\) 1.12132 + 3.70711i 0.204724 + 0.676822i
\(31\) −1.00000 −0.179605
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −7.24264 1.24264i −1.26078 0.216316i
\(34\) 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
\(45\) 5.29289 + 4.12132i 0.789018 + 0.614370i
\(46\) 0 0
\(47\) −4.24264 + 4.24264i −0.618853 + 0.618853i −0.945237 0.326384i \(-0.894170\pi\)
0.326384 + 0.945237i \(0.394170\pi\)
\(48\) −0.292893 + 1.70711i −0.0422755 + 0.246400i
\(49\) 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 0.352892 0.935664i \(-0.385198\pi\)
−0.935664 + 0.352892i \(0.885198\pi\)
\(54\) 1.41421 + 5.00000i 0.192450 + 0.680414i
\(55\) −3.00000 + 9.00000i −0.404520 + 1.21356i
\(56\) 0 0
\(57\) 6.82843 + 1.17157i 0.904447 + 0.155179i
\(58\) −2.00000 + 2.00000i −0.262613 + 0.262613i
\(59\) −5.65685 −0.736460 −0.368230 0.929735i \(-0.620036\pi\)
−0.368230 + 0.929735i \(0.620036\pi\)
\(60\) 3.41421 + 1.82843i 0.440773 + 0.236049i
\(61\) −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 \(0.0267434\pi\)
−0.996473 + 0.0839181i \(0.973257\pi\)
\(72\) 1.29289 + 2.70711i 0.152369 + 0.319036i
\(73\) 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
\(75\) 6.29289 5.94975i 0.726641 0.687018i
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) 7.24264 + 1.24264i 0.820068 + 0.140701i
\(79\) 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 \(0.200388\pi\)
0.588771 + 0.808300i \(0.299612\pi\)
\(84\) 0 0
\(85\) −4.00000 + 2.00000i −0.433861 + 0.216930i
\(86\) 11.3137i 1.21999i
\(87\) −0.828427 + 4.82843i −0.0888167 + 0.517662i
\(88\) −3.00000 + 3.00000i −0.319801 + 0.319801i
\(89\) −7.07107 −0.749532 −0.374766 0.927119i \(-0.622277\pi\)
−0.374766 + 0.927119i \(0.622277\pi\)
\(90\) 6.65685 0.828427i 0.701694 0.0873239i
\(91\) 0 0
\(92\) 0 0
\(93\) −0.292893 + 1.70711i −0.0303716 + 0.177019i
\(94\) 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 \(-0.632445\pi\)
0.404186 0.914677i \(-0.367555\pi\)
\(102\) −3.41421 0.585786i −0.338058 0.0580015i
\(103\) 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 −0.557047 0.830481i \(-0.688066\pi\)
0.830481 + 0.557047i \(0.188066\pi\)
\(108\) 4.53553 + 2.53553i 0.436432 + 0.243982i
\(109\) 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 0.877920 0.478806i \(-0.158930\pi\)
−0.478806 + 0.877920i \(0.658930\pi\)
\(114\) 5.65685 4.00000i 0.529813 0.374634i
\(115\) 0 0
\(116\) 2.82843i 0.262613i
\(117\) 11.4853 5.48528i 1.06181 0.507114i
\(118\) −4.00000 + 4.00000i −0.368230 + 0.368230i
\(119\) 0 0
\(120\) 3.70711 1.12132i 0.338411 0.102362i
\(121\) −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 \(-0.667367\pi\)
0.501905 0.864923i \(-0.332633\pi\)
\(132\) −1.24264 + 7.24264i −0.108158 + 0.630391i
\(133\) 0 0
\(134\) −1.41421 −0.122169
\(135\) 8.58579 7.82843i 0.738947 0.673764i
\(136\) −2.00000 −0.171499
\(137\) 12.7279 12.7279i 1.08742 1.08742i 0.0916263 0.995793i \(-0.470793\pi\)
0.995793 0.0916263i \(-0.0292065\pi\)
\(138\) 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
\(147\) −11.9497 2.05025i −0.985599 0.169102i
\(148\) −5.00000 + 5.00000i −0.410997 + 0.410997i
\(149\) −1.41421 −0.115857 −0.0579284 0.998321i \(-0.518450\pi\)
−0.0579284 + 0.998321i \(0.518450\pi\)
\(150\) 0.242641 8.65685i 0.0198115 0.706829i
\(151\) −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
\(153\) −5.41421 + 2.58579i −0.437713 + 0.209048i
\(154\) 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
\(162\) 8.94975 0.949747i 0.703159 0.0746192i
\(163\) −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
\(165\) 14.4853 + 7.75736i 1.12768 + 0.603910i
\(166\) 18.0000 1.39707
\(167\) −8.48528 + 8.48528i −0.656611 + 0.656611i −0.954577 0.297966i \(-0.903692\pi\)
0.297966 + 0.954577i \(0.403692\pi\)
\(168\) 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 0.951811 0.306687i \(-0.0992203\pi\)
−0.306687 + 0.951811i \(0.599220\pi\)
\(174\) 2.82843 + 4.00000i 0.214423 + 0.303239i
\(175\) 0 0
\(176\) 4.24264i 0.319801i
\(177\) −1.65685 + 9.65685i −0.124537 + 0.725854i
\(178\) −5.00000 + 5.00000i −0.374766 + 0.374766i
\(179\) −18.3848 −1.37414 −0.687071 0.726590i \(-0.741104\pi\)
−0.687071 + 0.726590i \(0.741104\pi\)
\(180\) 4.12132 5.29289i 0.307185 0.394509i
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) −2.34315 + 13.6569i −0.173210 + 1.00954i
\(184\) 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 \(0.0162933\pi\)
−0.998690 + 0.0511645i \(0.983707\pi\)
\(192\) 1.70711 + 0.292893i 0.123200 + 0.0211377i
\(193\) 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
\(195\) −4.75736 15.7279i −0.340682 1.12630i
\(196\) −7.00000 −0.500000
\(197\) 1.41421 1.41421i 0.100759 0.100759i −0.654931 0.755689i \(-0.727302\pi\)
0.755689 + 0.654931i \(0.227302\pi\)
\(198\) 5.48528 + 11.4853i 0.389822 + 0.816223i
\(199\) 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
\(213\) 2.41421 + 0.414214i 0.165419 + 0.0283814i
\(214\) 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
\(222\) −2.07107 + 12.0711i −0.139001 + 0.810157i
\(223\) −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
\(225\) −8.31371 12.4853i −0.554247 0.832352i
\(226\) 6.00000 0.399114
\(227\) 5.65685 5.65685i 0.375459 0.375459i −0.494002 0.869461i \(-0.664466\pi\)
0.869461 + 0.494002i \(0.164466\pi\)
\(228\) 1.17157 6.82843i 0.0775893 0.452224i
\(229\) 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 0.988039 0.154205i \(-0.0492816\pi\)
−0.154205 + 0.988039i \(0.549282\pi\)
\(234\) 4.24264 12.0000i 0.277350 0.784465i
\(235\) 12.0000 6.00000i 0.782794 0.391397i
\(236\) 5.65685i 0.368230i
\(237\) −17.0711 2.92893i −1.10889 0.190255i
\(238\) 0 0
\(239\) −11.3137 −0.731823 −0.365911 0.930650i \(-0.619243\pi\)
−0.365911 + 0.930650i \(0.619243\pi\)
\(240\) 1.82843 3.41421i 0.118024 0.220387i
\(241\) 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
\(243\) 11.7071 10.2929i 0.751011 0.660289i
\(244\) 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 \(0.233484\pi\)
−0.742828 + 0.669483i \(0.766516\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −12.7279 −0.798621
\(255\) 2.24264 + 7.41421i 0.140440 + 0.464296i
\(256\) 1.00000 0.0625000
\(257\) −4.24264 + 4.24264i −0.264649 + 0.264649i −0.826940 0.562291i \(-0.809920\pi\)
0.562291 + 0.826940i \(0.309920\pi\)
\(258\) −19.3137 3.31371i −1.20242 0.206302i
\(259\) 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 \(0.0815919\pi\)
0.253531 + 0.967327i \(0.418408\pi\)
\(264\) 4.24264 + 6.00000i 0.261116 + 0.369274i
\(265\) 6.00000 + 12.0000i 0.368577 + 0.737154i
\(266\) 0 0
\(267\) −2.07107 + 12.0711i −0.126747 + 0.738737i
\(268\) −1.00000 + 1.00000i −0.0610847 + 0.0610847i
\(269\) −2.82843 −0.172452 −0.0862261 0.996276i \(-0.527481\pi\)
−0.0862261 + 0.996276i \(0.527481\pi\)
\(270\) 0.535534 11.6066i 0.0325916 0.706355i
\(271\) 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 \(-0.764178\pi\)
0.737892 0.674919i \(-0.235822\pi\)
\(282\) 10.2426 + 1.75736i 0.609940 + 0.104649i
\(283\) −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
\(285\) −13.6569 7.31371i −0.808962 0.433227i
\(286\) 18.0000 1.06436
\(287\) 0 0
\(288\) 2.70711 1.29289i 0.159518 0.0761845i
\(289\) 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 0.852768 0.522291i \(-0.174922\pi\)
−0.522291 + 0.852768i \(0.674922\pi\)
\(294\) −9.89949 + 7.00000i −0.577350 + 0.408248i
\(295\) 12.0000 + 4.00000i 0.698667 + 0.232889i
\(296\) 7.07107i 0.410997i
\(297\) 19.2426 + 10.7574i 1.11657 + 0.624205i
\(298\) −1.00000 + 1.00000i −0.0579284 + 0.0579284i
\(299\) 0 0
\(300\) −5.94975 6.29289i −0.343509 0.363320i
\(301\) 0 0
\(302\) −11.3137 + 11.3137i −0.651031 + 0.651031i
\(303\) −31.3848 5.38478i −1.80301 0.309347i
\(304\) 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 \(0.117519\pi\)
−0.932617 + 0.360867i \(0.882481\pi\)
\(312\) 1.24264 7.24264i 0.0703507 0.410034i
\(313\) 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 −0.119145 0.992877i \(-0.538015\pi\)
0.992877 + 0.119145i \(0.0380154\pi\)
\(318\) −1.75736 + 10.2426i −0.0985478 + 0.574379i
\(319\) 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
\(327\) 10.2426 + 1.75736i 0.566419 + 0.0971822i
\(328\) 0 0
\(329\) 0 0
\(330\) 15.7279 4.75736i 0.865794 0.261884i
\(331\) −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
\(333\) 9.14214 + 19.1421i 0.500986 + 1.04898i
\(334\) 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
\(342\) −5.17157 10.8284i −0.279647 0.585534i
\(343\) 0 0
\(344\) −11.3137 −0.609994
\(345\) 0 0
\(346\) 12.0000 0.645124
\(347\) 1.41421 1.41421i 0.0759190 0.0759190i −0.668128 0.744047i \(-0.732904\pi\)
0.744047 + 0.668128i \(0.232904\pi\)
\(348\) 4.82843 + 0.828427i 0.258831 + 0.0444084i
\(349\) 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 0.778360 0.627818i \(-0.216052\pi\)
−0.627818 + 0.778360i \(0.716052\pi\)
\(354\) 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 \(-0.535713\pi\)
−0.111959 + 0.993713i \(0.535713\pi\)
\(360\) −0.828427 6.65685i −0.0436619 0.350847i
\(361\) 3.00000 0.157895
\(362\) 7.07107 7.07107i 0.371647 0.371647i
\(363\) −2.05025 + 11.9497i −0.107610 + 0.627199i
\(364\) 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
\(372\) 1.70711 + 0.292893i 0.0885094 + 0.0151858i
\(373\) −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
\(375\) −17.5563 + 8.17157i −0.906606 + 0.421978i
\(376\) 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 0.992157 0.125001i \(-0.0398935\pi\)
−0.125001 + 0.992157i \(0.539894\pi\)
\(384\) 1.41421 1.00000i 0.0721688 0.0510310i
\(385\) 0 0
\(386\) 21.2132i 1.07972i
\(387\) −30.6274 + 14.6274i −1.55688 + 0.743553i
\(388\) 3.00000 3.00000i 0.152302 0.152302i
\(389\) 22.6274 1.14726 0.573628 0.819116i \(-0.305536\pi\)
0.573628 + 0.819116i \(0.305536\pi\)
\(390\) −14.4853 7.75736i −0.733491 0.392809i
\(391\) 0 0
\(392\) −4.94975 + 4.94975i −0.250000 + 0.250000i
\(393\) −33.7990 5.79899i −1.70493 0.292520i
\(394\) 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 \(-0.765902\pi\)
0.741536 0.670913i \(-0.234098\pi\)
\(402\) −0.414214 + 2.41421i −0.0206591 + 0.120410i
\(403\) 3.00000 3.00000i 0.149441 0.149441i
\(404\) −18.3848 −0.914677
\(405\) −10.8492 16.9497i −0.539103 0.842240i
\(406\) 0 0
\(407\) −21.2132 + 21.2132i −1.05150 + 1.05150i
\(408\) −0.585786 + 3.41421i −0.0290008 + 0.169029i
\(409\) 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
\(417\) −13.6569 2.34315i −0.668779 0.114744i
\(418\) 12.0000 12.0000i 0.586939 0.586939i
\(419\) −22.6274 −1.10542 −0.552711 0.833373i \(-0.686407\pi\)
−0.552711 + 0.833373i \(0.686407\pi\)
\(420\) 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
\(423\) 16.2426 7.75736i 0.789744 0.377176i
\(424\) 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 \(0.0991717\pi\)
−0.951857 + 0.306541i \(0.900828\pi\)
\(432\) 2.53553 4.53553i 0.121991 0.218216i
\(433\) −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
\(435\) 5.17157 9.65685i 0.247958 0.463011i
\(436\) 6.00000 0.287348
\(437\) 0 0
\(438\) −4.82843 0.828427i −0.230711 0.0395838i
\(439\) 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 0.385272 0.922803i \(-0.374107\pi\)
−0.922803 + 0.385272i \(0.874107\pi\)
\(444\) 7.07107 + 10.0000i 0.335578 + 0.474579i
\(445\) 15.0000 + 5.00000i 0.711068 + 0.237023i
\(446\) 1.41421i 0.0669650i
\(447\) −0.414214 + 2.41421i −0.0195916 + 0.114188i
\(448\) 0 0
\(449\) 24.0416 1.13459 0.567297 0.823513i \(-0.307989\pi\)
0.567297 + 0.823513i \(0.307989\pi\)
\(450\) −14.7071 2.94975i −0.693300 0.139052i
\(451\) 0 0
\(452\) 4.24264 4.24264i 0.199557 0.199557i
\(453\) −4.68629 + 27.3137i −0.220181 + 1.28331i
\(454\) 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 \(-0.672779\pi\)
0.516538 0.856264i \(-0.327221\pi\)
\(462\) 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
\(465\) 1.82843 3.41421i 0.0847913 0.158330i
\(466\) 18.0000 0.833834
\(467\) −25.4558 + 25.4558i −1.17796 + 1.17796i −0.197692 + 0.980264i \(0.563345\pi\)
−0.980264 + 0.197692i \(0.936655\pi\)
\(468\) −5.48528 11.4853i −0.253557 0.530907i
\(469\) 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
\(477\) 7.75736 + 16.2426i 0.355185 + 0.743699i
\(478\) −8.00000 + 8.00000i −0.365911 + 0.365911i
\(479\) 7.07107 0.323085 0.161543 0.986866i \(-0.448353\pi\)
0.161543 + 0.986866i \(0.448353\pi\)
\(480\) −1.12132 3.70711i −0.0511810 0.169206i
\(481\) 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 \(-0.885834\pi\)
0.936366 0.351024i \(-0.114166\pi\)
\(492\) 0 0
\(493\) −4.00000 + 4.00000i −0.180151 + 0.180151i
\(494\) −16.9706 −0.763542
\(495\) 17.4853 22.4558i 0.785905 1.00932i
\(496\) 1.00000 0.0449013
\(497\) 0 0
\(498\) 5.27208 30.7279i 0.236247 1.37695i
\(499\) 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 0.963027 0.269404i \(-0.0868267\pi\)
−0.269404 + 0.963027i \(0.586827\pi\)
\(504\) 0 0
\(505\) −13.0000 + 39.0000i −0.578492 + 1.73548i
\(506\) 0 0
\(507\) −8.53553 1.46447i −0.379076 0.0650392i
\(508\) −9.00000 + 9.00000i −0.399310 + 0.399310i
\(509\) 39.5980 1.75515 0.877575 0.479440i \(-0.159160\pi\)
0.877575 + 0.479440i \(0.159160\pi\)
\(510\) 6.82843 + 3.65685i 0.302368 + 0.161928i
\(511\) 0 0
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −18.1421 10.1421i −0.800995 0.447786i
\(514\) 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 \(0.100258\pi\)
−0.950805 + 0.309789i \(0.899742\pi\)
\(522\) 7.65685 3.65685i 0.335131 0.160056i
\(523\) −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
\(528\) 7.24264 + 1.24264i 0.315195 + 0.0540790i
\(529\) 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
\(537\) −5.38478 + 31.3848i −0.232370 + 1.35435i
\(538\) −2.00000 + 2.00000i −0.0862261 + 0.0862261i
\(539\) −29.6985 −1.27920
\(540\) −7.82843 8.58579i −0.336882 0.369473i
\(541\) −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
\(543\) 2.92893 17.0711i 0.125693 0.732590i
\(544\) 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
\(555\) 26.2132 7.92893i 1.11269 0.336564i
\(556\) −8.00000 −0.339276
\(557\) −9.89949 + 9.89949i −0.419455 + 0.419455i −0.885016 0.465561i \(-0.845853\pi\)
0.465561 + 0.885016i \(0.345853\pi\)
\(558\) 2.70711 1.29289i 0.114601 0.0547325i
\(559\) 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 0.252399 0.967623i \(-0.418780\pi\)
−0.967623 + 0.252399i \(0.918780\pi\)
\(564\) 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 \(-0.528345\pi\)
−0.0889304 + 0.996038i \(0.528345\pi\)
\(570\) −14.8284 + 4.48528i −0.621094 + 0.187868i
\(571\) 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
\(573\) 2.41421 + 0.414214i 0.100855 + 0.0173040i
\(574\) 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
\(582\) 1.24264 7.24264i 0.0515091 0.300217i
\(583\) −18.0000 + 18.0000i −0.745484 + 0.745484i
\(584\) −2.82843 −0.117041
\(585\) −28.2426 + 3.51472i −1.16769 + 0.145316i
\(586\) 8.00000 0.330477
\(587\) 19.7990 19.7990i 0.817192 0.817192i −0.168508 0.985700i \(-0.553895\pi\)
0.985700 + 0.168508i \(0.0538950\pi\)
\(588\) −2.05025 + 11.9497i −0.0845510 + 0.492799i
\(589\) 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 0.0126486 0.999920i \(-0.495974\pi\)
−0.999920 + 0.0126486i \(0.995974\pi\)
\(594\) 21.2132 6.00000i 0.870388 0.246183i
\(595\) 0 0
\(596\) 1.41421i 0.0579284i
\(597\) −27.3137 4.68629i −1.11788 0.191797i
\(598\) 0 0
\(599\) −24.0416 −0.982314 −0.491157 0.871071i \(-0.663426\pi\)
−0.491157 + 0.871071i \(0.663426\pi\)
\(600\) −8.65685 0.242641i −0.353415 0.00990576i
\(601\) −30.0000 −1.22373 −0.611863 0.790964i \(-0.709580\pi\)
−0.611863 + 0.790964i \(0.709580\pi\)
\(602\) 0 0
\(603\) 1.82843 + 3.82843i 0.0744593 + 0.155906i
\(604\) 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
\(612\) 2.58579 + 5.41421i 0.104524 + 0.218857i
\(613\) −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 −0.915263 0.402856i \(-0.868017\pi\)
0.402856 + 0.915263i \(0.368017\pi\)
\(618\) −24.1421 4.14214i −0.971139 0.166621i
\(619\) 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
\(627\) 4.97056 28.9706i 0.198505 1.15697i
\(628\) −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
\(633\) −1.75736 + 10.2426i −0.0698488 + 0.407108i
\(634\) 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 \(0.300502\pi\)
−0.586510 + 0.809942i \(0.699498\pi\)
\(642\) −6.82843 1.17157i −0.269497 0.0462383i
\(643\) 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
\(645\) 12.6863 + 41.9411i 0.499522 + 1.65143i
\(646\) 8.00000 0.314756
\(647\) 5.65685 5.65685i 0.222394 0.222394i −0.587112 0.809506i \(-0.699735\pi\)
0.809506 + 0.587112i \(0.199735\pi\)
\(648\) −0.949747 8.94975i −0.0373096 0.351579i
\(649\) 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 0.998344 0.0575225i \(-0.0183201\pi\)
−0.0575225 + 0.998344i \(0.518320\pi\)
\(654\) 8.48528 6.00000i 0.331801 0.234619i
\(655\) −14.0000 + 42.0000i −0.547025 + 1.64108i
\(656\) 0 0
\(657\) −7.65685 + 3.65685i −0.298722 + 0.142667i
\(658\) 0 0
\(659\) −22.6274 −0.881439 −0.440720 0.897645i \(-0.645277\pi\)
−0.440720 + 0.897645i \(0.645277\pi\)
\(660\) 7.75736 14.4853i 0.301955 0.563839i
\(661\) −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
\(663\) 14.4853 + 2.48528i 0.562562 + 0.0965203i
\(664\) 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
\(675\) −23.7487 + 10.5355i −0.914089 + 0.405513i
\(676\) −5.00000 −0.192308
\(677\) −4.24264 + 4.24264i −0.163058 + 0.163058i −0.783920 0.620862i \(-0.786783\pi\)
0.620862 + 0.783920i \(0.286783\pi\)
\(678\) 1.75736 10.2426i 0.0674910 0.393366i
\(679\) 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 0.889616 0.456709i \(-0.150972\pi\)
−0.456709 + 0.889616i \(0.650972\pi\)
\(684\) −11.3137 4.00000i −0.432590 0.152944i
\(685\) −36.0000 + 18.0000i −1.37549 + 0.687745i
\(686\) 0 0
\(687\) −17.0711 2.92893i −0.651302 0.111746i
\(688\) −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 \(-0.717999\pi\)
0.632568 0.774505i \(-0.282001\pi\)
\(702\) −19.2426 10.7574i −0.726267 0.406010i
\(703\) 20.0000 20.0000i 0.754314 0.754314i
\(704\) 4.24264 0.159901
\(705\) −6.72792 22.2426i −0.253388 0.837706i
\(706\) 4.00000 0.150542
\(707\) 0 0
\(708\) 9.65685 + 1.65685i 0.362927 + 0.0622684i
\(709\) 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
\(717\) −3.31371 + 19.3137i −0.123753 + 0.721284i
\(718\) −3.00000 + 3.00000i −0.111959 + 0.111959i
\(719\) 22.6274 0.843860 0.421930 0.906628i \(-0.361353\pi\)
0.421930 + 0.906628i \(0.361353\pi\)
\(720\) −5.29289 4.12132i −0.197254 0.153593i
\(721\) 0 0
\(722\) 2.12132 2.12132i 0.0789474 0.0789474i
\(723\) 6.44365 37.5563i 0.239642 1.39674i
\(724\) 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
\(732\) 13.6569 + 2.34315i 0.504772 + 0.0866052i
\(733\) 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
\(735\) 23.8995 + 12.7990i 0.881546 + 0.472098i
\(736\) 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 0.323603 0.946193i \(-0.395106\pi\)
−0.946193 + 0.323603i \(0.895106\pi\)
\(744\) 1.41421 1.00000i 0.0518476 0.0366618i
\(745\) 3.00000 + 1.00000i 0.109911 + 0.0366372i
\(746\) 22.6274i 0.828449i
\(747\) −23.2721 48.7279i −0.851481 1.78286i
\(748\) −6.00000 + 6.00000i −0.219382 + 0.219382i
\(749\) 0 0
\(750\) −6.63604 + 18.1924i −0.242314 + 0.664292i
\(751\) −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
\(753\) 36.2132 + 6.21320i 1.31968 + 0.226422i
\(754\) 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 \(0.108136\pi\)
−0.942848 + 0.333224i \(0.891864\pi\)
\(762\) −3.72792 + 21.7279i −0.135048 + 0.787120i
\(763\) 0 0
\(764\) 1.41421 0.0511645
\(765\) 13.3137 1.65685i 0.481358 0.0599037i
\(766\) 24.0000 0.867155
\(767\) 16.9706 16.9706i 0.612772 0.612772i
\(768\) 0.292893 1.70711i 0.0105689 0.0615999i
\(769\) 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 0.0330063 0.999455i \(-0.489492\pi\)
−0.999455 + 0.0330063i \(0.989492\pi\)
\(774\) −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
\(780\) −15.7279 + 4.75736i −0.563150 + 0.170341i
\(781\) 6.00000 0.214697