Properties

Label 370.2.h.c.117.2
Level $370$
Weight $2$
Character 370.117
Analytic conductor $2.954$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.h (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 117.2
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 370.117
Dual form 370.2.h.c.253.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(1.41421 + 1.41421i) q^{3} +1.00000 q^{4} +(0.707107 - 2.12132i) q^{5} +(1.41421 + 1.41421i) q^{6} +(1.29289 + 1.29289i) q^{7} +1.00000 q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(1.41421 + 1.41421i) q^{3} +1.00000 q^{4} +(0.707107 - 2.12132i) q^{5} +(1.41421 + 1.41421i) q^{6} +(1.29289 + 1.29289i) q^{7} +1.00000 q^{8} +1.00000i q^{9} +(0.707107 - 2.12132i) q^{10} -1.82843i q^{11} +(1.41421 + 1.41421i) q^{12} -6.24264 q^{13} +(1.29289 + 1.29289i) q^{14} +(4.00000 - 2.00000i) q^{15} +1.00000 q^{16} +3.82843i q^{17} +1.00000i q^{18} +(0.171573 - 0.171573i) q^{19} +(0.707107 - 2.12132i) q^{20} +3.65685i q^{21} -1.82843i q^{22} -5.41421 q^{23} +(1.41421 + 1.41421i) q^{24} +(-4.00000 - 3.00000i) q^{25} -6.24264 q^{26} +(2.82843 - 2.82843i) q^{27} +(1.29289 + 1.29289i) q^{28} +(5.29289 + 5.29289i) q^{29} +(4.00000 - 2.00000i) q^{30} +(0.121320 - 0.121320i) q^{31} +1.00000 q^{32} +(2.58579 - 2.58579i) q^{33} +3.82843i q^{34} +(3.65685 - 1.82843i) q^{35} +1.00000i q^{36} +(-3.53553 + 4.94975i) q^{37} +(0.171573 - 0.171573i) q^{38} +(-8.82843 - 8.82843i) q^{39} +(0.707107 - 2.12132i) q^{40} +7.00000i q^{41} +3.65685i q^{42} -7.00000 q^{43} -1.82843i q^{44} +(2.12132 + 0.707107i) q^{45} -5.41421 q^{46} +(0.242641 + 0.242641i) q^{47} +(1.41421 + 1.41421i) q^{48} -3.65685i q^{49} +(-4.00000 - 3.00000i) q^{50} +(-5.41421 + 5.41421i) q^{51} -6.24264 q^{52} +(-2.12132 + 2.12132i) q^{53} +(2.82843 - 2.82843i) q^{54} +(-3.87868 - 1.29289i) q^{55} +(1.29289 + 1.29289i) q^{56} +0.485281 q^{57} +(5.29289 + 5.29289i) q^{58} +(6.82843 - 6.82843i) q^{59} +(4.00000 - 2.00000i) q^{60} +(10.7071 - 10.7071i) q^{61} +(0.121320 - 0.121320i) q^{62} +(-1.29289 + 1.29289i) q^{63} +1.00000 q^{64} +(-4.41421 + 13.2426i) q^{65} +(2.58579 - 2.58579i) q^{66} +(7.24264 - 7.24264i) q^{67} +3.82843i q^{68} +(-7.65685 - 7.65685i) q^{69} +(3.65685 - 1.82843i) q^{70} -11.6569 q^{71} +1.00000i q^{72} +(-6.00000 - 6.00000i) q^{73} +(-3.53553 + 4.94975i) q^{74} +(-1.41421 - 9.89949i) q^{75} +(0.171573 - 0.171573i) q^{76} +(2.36396 - 2.36396i) q^{77} +(-8.82843 - 8.82843i) q^{78} +(1.65685 - 1.65685i) q^{79} +(0.707107 - 2.12132i) q^{80} +11.0000 q^{81} +7.00000i q^{82} +(4.82843 - 4.82843i) q^{83} +3.65685i q^{84} +(8.12132 + 2.70711i) q^{85} -7.00000 q^{86} +14.9706i q^{87} -1.82843i q^{88} +(-4.58579 - 4.58579i) q^{89} +(2.12132 + 0.707107i) q^{90} +(-8.07107 - 8.07107i) q^{91} -5.41421 q^{92} +0.343146 q^{93} +(0.242641 + 0.242641i) q^{94} +(-0.242641 - 0.485281i) q^{95} +(1.41421 + 1.41421i) q^{96} -7.00000i q^{97} -3.65685i q^{98} +1.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} + 4q^{4} + 8q^{7} + 4q^{8} + O(q^{10}) \) \( 4q + 4q^{2} + 4q^{4} + 8q^{7} + 4q^{8} - 8q^{13} + 8q^{14} + 16q^{15} + 4q^{16} + 12q^{19} - 16q^{23} - 16q^{25} - 8q^{26} + 8q^{28} + 24q^{29} + 16q^{30} - 8q^{31} + 4q^{32} + 16q^{33} - 8q^{35} + 12q^{38} - 24q^{39} - 28q^{43} - 16q^{46} - 16q^{47} - 16q^{50} - 16q^{51} - 8q^{52} - 24q^{55} + 8q^{56} - 32q^{57} + 24q^{58} + 16q^{59} + 16q^{60} + 40q^{61} - 8q^{62} - 8q^{63} + 4q^{64} - 12q^{65} + 16q^{66} + 12q^{67} - 8q^{69} - 8q^{70} - 24q^{71} - 24q^{73} + 12q^{76} - 16q^{77} - 24q^{78} - 16q^{79} + 44q^{81} + 8q^{83} + 24q^{85} - 28q^{86} - 24q^{89} - 4q^{91} - 16q^{92} + 24q^{93} - 16q^{94} + 16q^{95} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.41421 + 1.41421i 0.816497 + 0.816497i 0.985599 0.169102i \(-0.0540867\pi\)
−0.169102 + 0.985599i \(0.554087\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.707107 2.12132i 0.316228 0.948683i
\(6\) 1.41421 + 1.41421i 0.577350 + 0.577350i
\(7\) 1.29289 + 1.29289i 0.488668 + 0.488668i 0.907886 0.419218i \(-0.137696\pi\)
−0.419218 + 0.907886i \(0.637696\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000i 0.333333i
\(10\) 0.707107 2.12132i 0.223607 0.670820i
\(11\) 1.82843i 0.551292i −0.961259 0.275646i \(-0.911108\pi\)
0.961259 0.275646i \(-0.0888917\pi\)
\(12\) 1.41421 + 1.41421i 0.408248 + 0.408248i
\(13\) −6.24264 −1.73140 −0.865699 0.500566i \(-0.833125\pi\)
−0.865699 + 0.500566i \(0.833125\pi\)
\(14\) 1.29289 + 1.29289i 0.345540 + 0.345540i
\(15\) 4.00000 2.00000i 1.03280 0.516398i
\(16\) 1.00000 0.250000
\(17\) 3.82843i 0.928530i 0.885696 + 0.464265i \(0.153681\pi\)
−0.885696 + 0.464265i \(0.846319\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 0.171573 0.171573i 0.0393615 0.0393615i −0.687152 0.726514i \(-0.741139\pi\)
0.726514 + 0.687152i \(0.241139\pi\)
\(20\) 0.707107 2.12132i 0.158114 0.474342i
\(21\) 3.65685i 0.797991i
\(22\) 1.82843i 0.389822i
\(23\) −5.41421 −1.12894 −0.564471 0.825453i \(-0.690920\pi\)
−0.564471 + 0.825453i \(0.690920\pi\)
\(24\) 1.41421 + 1.41421i 0.288675 + 0.288675i
\(25\) −4.00000 3.00000i −0.800000 0.600000i
\(26\) −6.24264 −1.22428
\(27\) 2.82843 2.82843i 0.544331 0.544331i
\(28\) 1.29289 + 1.29289i 0.244334 + 0.244334i
\(29\) 5.29289 + 5.29289i 0.982866 + 0.982866i 0.999856 0.0169901i \(-0.00540837\pi\)
−0.0169901 + 0.999856i \(0.505408\pi\)
\(30\) 4.00000 2.00000i 0.730297 0.365148i
\(31\) 0.121320 0.121320i 0.0217898 0.0217898i −0.696128 0.717918i \(-0.745095\pi\)
0.717918 + 0.696128i \(0.245095\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.58579 2.58579i 0.450128 0.450128i
\(34\) 3.82843i 0.656570i
\(35\) 3.65685 1.82843i 0.618121 0.309061i
\(36\) 1.00000i 0.166667i
\(37\) −3.53553 + 4.94975i −0.581238 + 0.813733i
\(38\) 0.171573 0.171573i 0.0278328 0.0278328i
\(39\) −8.82843 8.82843i −1.41368 1.41368i
\(40\) 0.707107 2.12132i 0.111803 0.335410i
\(41\) 7.00000i 1.09322i 0.837389 + 0.546608i \(0.184081\pi\)
−0.837389 + 0.546608i \(0.815919\pi\)
\(42\) 3.65685i 0.564265i
\(43\) −7.00000 −1.06749 −0.533745 0.845645i \(-0.679216\pi\)
−0.533745 + 0.845645i \(0.679216\pi\)
\(44\) 1.82843i 0.275646i
\(45\) 2.12132 + 0.707107i 0.316228 + 0.105409i
\(46\) −5.41421 −0.798282
\(47\) 0.242641 + 0.242641i 0.0353928 + 0.0353928i 0.724582 0.689189i \(-0.242033\pi\)
−0.689189 + 0.724582i \(0.742033\pi\)
\(48\) 1.41421 + 1.41421i 0.204124 + 0.204124i
\(49\) 3.65685i 0.522408i
\(50\) −4.00000 3.00000i −0.565685 0.424264i
\(51\) −5.41421 + 5.41421i −0.758142 + 0.758142i
\(52\) −6.24264 −0.865699
\(53\) −2.12132 + 2.12132i −0.291386 + 0.291386i −0.837628 0.546242i \(-0.816058\pi\)
0.546242 + 0.837628i \(0.316058\pi\)
\(54\) 2.82843 2.82843i 0.384900 0.384900i
\(55\) −3.87868 1.29289i −0.523001 0.174334i
\(56\) 1.29289 + 1.29289i 0.172770 + 0.172770i
\(57\) 0.485281 0.0642771
\(58\) 5.29289 + 5.29289i 0.694991 + 0.694991i
\(59\) 6.82843 6.82843i 0.888985 0.888985i −0.105440 0.994426i \(-0.533625\pi\)
0.994426 + 0.105440i \(0.0336251\pi\)
\(60\) 4.00000 2.00000i 0.516398 0.258199i
\(61\) 10.7071 10.7071i 1.37090 1.37090i 0.511800 0.859105i \(-0.328979\pi\)
0.859105 0.511800i \(-0.171021\pi\)
\(62\) 0.121320 0.121320i 0.0154077 0.0154077i
\(63\) −1.29289 + 1.29289i −0.162889 + 0.162889i
\(64\) 1.00000 0.125000
\(65\) −4.41421 + 13.2426i −0.547516 + 1.64255i
\(66\) 2.58579 2.58579i 0.318288 0.318288i
\(67\) 7.24264 7.24264i 0.884829 0.884829i −0.109191 0.994021i \(-0.534826\pi\)
0.994021 + 0.109191i \(0.0348261\pi\)
\(68\) 3.82843i 0.464265i
\(69\) −7.65685 7.65685i −0.921777 0.921777i
\(70\) 3.65685 1.82843i 0.437078 0.218539i
\(71\) −11.6569 −1.38341 −0.691707 0.722178i \(-0.743141\pi\)
−0.691707 + 0.722178i \(0.743141\pi\)
\(72\) 1.00000i 0.117851i
\(73\) −6.00000 6.00000i −0.702247 0.702247i 0.262646 0.964892i \(-0.415405\pi\)
−0.964892 + 0.262646i \(0.915405\pi\)
\(74\) −3.53553 + 4.94975i −0.410997 + 0.575396i
\(75\) −1.41421 9.89949i −0.163299 1.14310i
\(76\) 0.171573 0.171573i 0.0196808 0.0196808i
\(77\) 2.36396 2.36396i 0.269398 0.269398i
\(78\) −8.82843 8.82843i −0.999623 0.999623i
\(79\) 1.65685 1.65685i 0.186411 0.186411i −0.607732 0.794142i \(-0.707920\pi\)
0.794142 + 0.607732i \(0.207920\pi\)
\(80\) 0.707107 2.12132i 0.0790569 0.237171i
\(81\) 11.0000 1.22222
\(82\) 7.00000i 0.773021i
\(83\) 4.82843 4.82843i 0.529989 0.529989i −0.390580 0.920569i \(-0.627726\pi\)
0.920569 + 0.390580i \(0.127726\pi\)
\(84\) 3.65685i 0.398996i
\(85\) 8.12132 + 2.70711i 0.880881 + 0.293627i
\(86\) −7.00000 −0.754829
\(87\) 14.9706i 1.60501i
\(88\) 1.82843i 0.194911i
\(89\) −4.58579 4.58579i −0.486092 0.486092i 0.420978 0.907071i \(-0.361687\pi\)
−0.907071 + 0.420978i \(0.861687\pi\)
\(90\) 2.12132 + 0.707107i 0.223607 + 0.0745356i
\(91\) −8.07107 8.07107i −0.846078 0.846078i
\(92\) −5.41421 −0.564471
\(93\) 0.343146 0.0355826
\(94\) 0.242641 + 0.242641i 0.0250265 + 0.0250265i
\(95\) −0.242641 0.485281i −0.0248944 0.0497888i
\(96\) 1.41421 + 1.41421i 0.144338 + 0.144338i
\(97\) 7.00000i 0.710742i −0.934725 0.355371i \(-0.884354\pi\)
0.934725 0.355371i \(-0.115646\pi\)
\(98\) 3.65685i 0.369398i
\(99\) 1.82843 0.183764
\(100\) −4.00000 3.00000i −0.400000 0.300000i
\(101\) 3.07107i 0.305583i 0.988258 + 0.152791i \(0.0488262\pi\)
−0.988258 + 0.152791i \(0.951174\pi\)
\(102\) −5.41421 + 5.41421i −0.536087 + 0.536087i
\(103\) 17.5563i 1.72988i 0.501877 + 0.864939i \(0.332643\pi\)
−0.501877 + 0.864939i \(0.667357\pi\)
\(104\) −6.24264 −0.612141
\(105\) 7.75736 + 2.58579i 0.757041 + 0.252347i
\(106\) −2.12132 + 2.12132i −0.206041 + 0.206041i
\(107\) 5.07107 + 5.07107i 0.490239 + 0.490239i 0.908381 0.418143i \(-0.137319\pi\)
−0.418143 + 0.908381i \(0.637319\pi\)
\(108\) 2.82843 2.82843i 0.272166 0.272166i
\(109\) −8.94975 + 8.94975i −0.857230 + 0.857230i −0.991011 0.133781i \(-0.957288\pi\)
0.133781 + 0.991011i \(0.457288\pi\)
\(110\) −3.87868 1.29289i −0.369818 0.123273i
\(111\) −12.0000 + 2.00000i −1.13899 + 0.189832i
\(112\) 1.29289 + 1.29289i 0.122167 + 0.122167i
\(113\) 1.82843i 0.172004i −0.996295 0.0860020i \(-0.972591\pi\)
0.996295 0.0860020i \(-0.0274091\pi\)
\(114\) 0.485281 0.0454508
\(115\) −3.82843 + 11.4853i −0.357003 + 1.07101i
\(116\) 5.29289 + 5.29289i 0.491433 + 0.491433i
\(117\) 6.24264i 0.577132i
\(118\) 6.82843 6.82843i 0.628608 0.628608i
\(119\) −4.94975 + 4.94975i −0.453743 + 0.453743i
\(120\) 4.00000 2.00000i 0.365148 0.182574i
\(121\) 7.65685 0.696078
\(122\) 10.7071 10.7071i 0.969376 0.969376i
\(123\) −9.89949 + 9.89949i −0.892607 + 0.892607i
\(124\) 0.121320 0.121320i 0.0108949 0.0108949i
\(125\) −9.19239 + 6.36396i −0.822192 + 0.569210i
\(126\) −1.29289 + 1.29289i −0.115180 + 0.115180i
\(127\) 5.41421 + 5.41421i 0.480434 + 0.480434i 0.905270 0.424836i \(-0.139668\pi\)
−0.424836 + 0.905270i \(0.639668\pi\)
\(128\) 1.00000 0.0883883
\(129\) −9.89949 9.89949i −0.871602 0.871602i
\(130\) −4.41421 + 13.2426i −0.387152 + 1.16146i
\(131\) −2.41421 + 2.41421i −0.210931 + 0.210931i −0.804663 0.593732i \(-0.797654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(132\) 2.58579 2.58579i 0.225064 0.225064i
\(133\) 0.443651 0.0384694
\(134\) 7.24264 7.24264i 0.625669 0.625669i
\(135\) −4.00000 8.00000i −0.344265 0.688530i
\(136\) 3.82843i 0.328285i
\(137\) 5.58579 + 5.58579i 0.477226 + 0.477226i 0.904243 0.427017i \(-0.140436\pi\)
−0.427017 + 0.904243i \(0.640436\pi\)
\(138\) −7.65685 7.65685i −0.651795 0.651795i
\(139\) 11.8284 1.00327 0.501637 0.865078i \(-0.332731\pi\)
0.501637 + 0.865078i \(0.332731\pi\)
\(140\) 3.65685 1.82843i 0.309061 0.154530i
\(141\) 0.686292i 0.0577962i
\(142\) −11.6569 −0.978221
\(143\) 11.4142i 0.954504i
\(144\) 1.00000i 0.0833333i
\(145\) 14.9706 7.48528i 1.24324 0.621619i
\(146\) −6.00000 6.00000i −0.496564 0.496564i
\(147\) 5.17157 5.17157i 0.426544 0.426544i
\(148\) −3.53553 + 4.94975i −0.290619 + 0.406867i
\(149\) 0.242641i 0.0198779i 0.999951 + 0.00993895i \(0.00316372\pi\)
−0.999951 + 0.00993895i \(0.996836\pi\)
\(150\) −1.41421 9.89949i −0.115470 0.808290i
\(151\) 12.0000i 0.976546i −0.872691 0.488273i \(-0.837627\pi\)
0.872691 0.488273i \(-0.162373\pi\)
\(152\) 0.171573 0.171573i 0.0139164 0.0139164i
\(153\) −3.82843 −0.309510
\(154\) 2.36396 2.36396i 0.190493 0.190493i
\(155\) −0.171573 0.343146i −0.0137811 0.0275621i
\(156\) −8.82843 8.82843i −0.706840 0.706840i
\(157\) 10.1213 + 10.1213i 0.807769 + 0.807769i 0.984296 0.176527i \(-0.0564862\pi\)
−0.176527 + 0.984296i \(0.556486\pi\)
\(158\) 1.65685 1.65685i 0.131812 0.131812i
\(159\) −6.00000 −0.475831
\(160\) 0.707107 2.12132i 0.0559017 0.167705i
\(161\) −7.00000 7.00000i −0.551677 0.551677i
\(162\) 11.0000 0.864242
\(163\) 3.34315i 0.261855i 0.991392 + 0.130928i \(0.0417956\pi\)
−0.991392 + 0.130928i \(0.958204\pi\)
\(164\) 7.00000i 0.546608i
\(165\) −3.65685 7.31371i −0.284686 0.569371i
\(166\) 4.82843 4.82843i 0.374759 0.374759i
\(167\) 6.82843i 0.528400i −0.964468 0.264200i \(-0.914892\pi\)
0.964468 0.264200i \(-0.0851078\pi\)
\(168\) 3.65685i 0.282132i
\(169\) 25.9706 1.99774
\(170\) 8.12132 + 2.70711i 0.622877 + 0.207626i
\(171\) 0.171573 + 0.171573i 0.0131205 + 0.0131205i
\(172\) −7.00000 −0.533745
\(173\) 18.0208 + 18.0208i 1.37010 + 1.37010i 0.860287 + 0.509810i \(0.170284\pi\)
0.509810 + 0.860287i \(0.329716\pi\)
\(174\) 14.9706i 1.13492i
\(175\) −1.29289 9.05025i −0.0977335 0.684135i
\(176\) 1.82843i 0.137823i
\(177\) 19.3137 1.45171
\(178\) −4.58579 4.58579i −0.343719 0.343719i
\(179\) −2.48528 2.48528i −0.185759 0.185759i 0.608101 0.793860i \(-0.291932\pi\)
−0.793860 + 0.608101i \(0.791932\pi\)
\(180\) 2.12132 + 0.707107i 0.158114 + 0.0527046i
\(181\) −3.65685 −0.271812 −0.135906 0.990722i \(-0.543394\pi\)
−0.135906 + 0.990722i \(0.543394\pi\)
\(182\) −8.07107 8.07107i −0.598267 0.598267i
\(183\) 30.2843 2.23868
\(184\) −5.41421 −0.399141
\(185\) 8.00000 + 11.0000i 0.588172 + 0.808736i
\(186\) 0.343146 0.0251607
\(187\) 7.00000 0.511891
\(188\) 0.242641 + 0.242641i 0.0176964 + 0.0176964i
\(189\) 7.31371 0.531994
\(190\) −0.242641 0.485281i −0.0176030 0.0352060i
\(191\) −5.53553 5.53553i −0.400537 0.400537i 0.477885 0.878422i \(-0.341404\pi\)
−0.878422 + 0.477885i \(0.841404\pi\)
\(192\) 1.41421 + 1.41421i 0.102062 + 0.102062i
\(193\) −3.51472 −0.252995 −0.126497 0.991967i \(-0.540374\pi\)
−0.126497 + 0.991967i \(0.540374\pi\)
\(194\) 7.00000i 0.502571i
\(195\) −24.9706 + 12.4853i −1.78818 + 0.894090i
\(196\) 3.65685i 0.261204i
\(197\) −2.00000 2.00000i −0.142494 0.142494i 0.632261 0.774755i \(-0.282127\pi\)
−0.774755 + 0.632261i \(0.782127\pi\)
\(198\) 1.82843 0.129941
\(199\) −15.8995 15.8995i −1.12709 1.12709i −0.990649 0.136436i \(-0.956435\pi\)
−0.136436 0.990649i \(-0.543565\pi\)
\(200\) −4.00000 3.00000i −0.282843 0.212132i
\(201\) 20.4853 1.44492
\(202\) 3.07107i 0.216080i
\(203\) 13.6863i 0.960589i
\(204\) −5.41421 + 5.41421i −0.379071 + 0.379071i
\(205\) 14.8492 + 4.94975i 1.03712 + 0.345705i
\(206\) 17.5563i 1.22321i
\(207\) 5.41421i 0.376314i
\(208\) −6.24264 −0.432849
\(209\) −0.313708 0.313708i −0.0216997 0.0216997i
\(210\) 7.75736 + 2.58579i 0.535309 + 0.178436i
\(211\) −9.00000 −0.619586 −0.309793 0.950804i \(-0.600260\pi\)
−0.309793 + 0.950804i \(0.600260\pi\)
\(212\) −2.12132 + 2.12132i −0.145693 + 0.145693i
\(213\) −16.4853 16.4853i −1.12955 1.12955i
\(214\) 5.07107 + 5.07107i 0.346651 + 0.346651i
\(215\) −4.94975 + 14.8492i −0.337570 + 1.01271i
\(216\) 2.82843 2.82843i 0.192450 0.192450i
\(217\) 0.313708 0.0212959
\(218\) −8.94975 + 8.94975i −0.606153 + 0.606153i
\(219\) 16.9706i 1.14676i
\(220\) −3.87868 1.29289i −0.261501 0.0871668i
\(221\) 23.8995i 1.60765i
\(222\) −12.0000 + 2.00000i −0.805387 + 0.134231i
\(223\) 18.1213 18.1213i 1.21349 1.21349i 0.243623 0.969870i \(-0.421664\pi\)
0.969870 0.243623i \(-0.0783361\pi\)
\(224\) 1.29289 + 1.29289i 0.0863851 + 0.0863851i
\(225\) 3.00000 4.00000i 0.200000 0.266667i
\(226\) 1.82843i 0.121625i
\(227\) 9.48528i 0.629560i 0.949165 + 0.314780i \(0.101931\pi\)
−0.949165 + 0.314780i \(0.898069\pi\)
\(228\) 0.485281 0.0321385
\(229\) 1.41421i 0.0934539i −0.998908 0.0467269i \(-0.985121\pi\)
0.998908 0.0467269i \(-0.0148791\pi\)
\(230\) −3.82843 + 11.4853i −0.252439 + 0.757317i
\(231\) 6.68629 0.439926
\(232\) 5.29289 + 5.29289i 0.347495 + 0.347495i
\(233\) 14.0711 + 14.0711i 0.921826 + 0.921826i 0.997158 0.0753322i \(-0.0240017\pi\)
−0.0753322 + 0.997158i \(0.524002\pi\)
\(234\) 6.24264i 0.408094i
\(235\) 0.686292 0.343146i 0.0447687 0.0223844i
\(236\) 6.82843 6.82843i 0.444493 0.444493i
\(237\) 4.68629 0.304407
\(238\) −4.94975 + 4.94975i −0.320844 + 0.320844i
\(239\) −16.9497 + 16.9497i −1.09639 + 1.09639i −0.101558 + 0.994830i \(0.532383\pi\)
−0.994830 + 0.101558i \(0.967617\pi\)
\(240\) 4.00000 2.00000i 0.258199 0.129099i
\(241\) 9.24264 + 9.24264i 0.595371 + 0.595371i 0.939077 0.343706i \(-0.111682\pi\)
−0.343706 + 0.939077i \(0.611682\pi\)
\(242\) 7.65685 0.492201
\(243\) 7.07107 + 7.07107i 0.453609 + 0.453609i
\(244\) 10.7071 10.7071i 0.685452 0.685452i
\(245\) −7.75736 2.58579i −0.495600 0.165200i
\(246\) −9.89949 + 9.89949i −0.631169 + 0.631169i
\(247\) −1.07107 + 1.07107i −0.0681504 + 0.0681504i
\(248\) 0.121320 0.121320i 0.00770385 0.00770385i
\(249\) 13.6569 0.865468
\(250\) −9.19239 + 6.36396i −0.581378 + 0.402492i
\(251\) 1.89949 1.89949i 0.119895 0.119895i −0.644614 0.764509i \(-0.722982\pi\)
0.764509 + 0.644614i \(0.222982\pi\)
\(252\) −1.29289 + 1.29289i −0.0814446 + 0.0814446i
\(253\) 9.89949i 0.622376i
\(254\) 5.41421 + 5.41421i 0.339718 + 0.339718i
\(255\) 7.65685 + 15.3137i 0.479491 + 0.958982i
\(256\) 1.00000 0.0625000
\(257\) 13.1716i 0.821620i 0.911721 + 0.410810i \(0.134754\pi\)
−0.911721 + 0.410810i \(0.865246\pi\)
\(258\) −9.89949 9.89949i −0.616316 0.616316i
\(259\) −10.9706 + 1.82843i −0.681678 + 0.113613i
\(260\) −4.41421 + 13.2426i −0.273758 + 0.821274i
\(261\) −5.29289 + 5.29289i −0.327622 + 0.327622i
\(262\) −2.41421 + 2.41421i −0.149151 + 0.149151i
\(263\) −6.60660 6.60660i −0.407381 0.407381i 0.473444 0.880824i \(-0.343011\pi\)
−0.880824 + 0.473444i \(0.843011\pi\)
\(264\) 2.58579 2.58579i 0.159144 0.159144i
\(265\) 3.00000 + 6.00000i 0.184289 + 0.368577i
\(266\) 0.443651 0.0272020
\(267\) 12.9706i 0.793786i
\(268\) 7.24264 7.24264i 0.442415 0.442415i
\(269\) 21.7990i 1.32911i 0.747240 + 0.664554i \(0.231378\pi\)
−0.747240 + 0.664554i \(0.768622\pi\)
\(270\) −4.00000 8.00000i −0.243432 0.486864i
\(271\) 11.0711 0.672519 0.336260 0.941769i \(-0.390838\pi\)
0.336260 + 0.941769i \(0.390838\pi\)
\(272\) 3.82843i 0.232132i
\(273\) 22.8284i 1.38164i
\(274\) 5.58579 + 5.58579i 0.337450 + 0.337450i
\(275\) −5.48528 + 7.31371i −0.330775 + 0.441033i
\(276\) −7.65685 7.65685i −0.460888 0.460888i
\(277\) −31.7990 −1.91062 −0.955308 0.295612i \(-0.904476\pi\)
−0.955308 + 0.295612i \(0.904476\pi\)
\(278\) 11.8284 0.709422
\(279\) 0.121320 + 0.121320i 0.00726326 + 0.00726326i
\(280\) 3.65685 1.82843i 0.218539 0.109269i
\(281\) 4.00000 + 4.00000i 0.238620 + 0.238620i 0.816279 0.577659i \(-0.196033\pi\)
−0.577659 + 0.816279i \(0.696033\pi\)
\(282\) 0.686292i 0.0408681i
\(283\) 28.0000i 1.66443i −0.554455 0.832214i \(-0.687073\pi\)
0.554455 0.832214i \(-0.312927\pi\)
\(284\) −11.6569 −0.691707
\(285\) 0.343146 1.02944i 0.0203262 0.0609786i
\(286\) 11.4142i 0.674937i
\(287\) −9.05025 + 9.05025i −0.534220 + 0.534220i
\(288\) 1.00000i 0.0589256i
\(289\) 2.34315 0.137832
\(290\) 14.9706 7.48528i 0.879102 0.439551i
\(291\) 9.89949 9.89949i 0.580319 0.580319i
\(292\) −6.00000 6.00000i −0.351123 0.351123i
\(293\) 13.7782 13.7782i 0.804930 0.804930i −0.178932 0.983861i \(-0.557264\pi\)
0.983861 + 0.178932i \(0.0572642\pi\)
\(294\) 5.17157 5.17157i 0.301612 0.301612i
\(295\) −9.65685 19.3137i −0.562244 1.12449i
\(296\) −3.53553 + 4.94975i −0.205499 + 0.287698i
\(297\) −5.17157 5.17157i −0.300085 0.300085i
\(298\) 0.242641i 0.0140558i
\(299\) 33.7990 1.95465
\(300\) −1.41421 9.89949i −0.0816497 0.571548i
\(301\) −9.05025 9.05025i −0.521648 0.521648i
\(302\) 12.0000i 0.690522i
\(303\) −4.34315 + 4.34315i −0.249507 + 0.249507i
\(304\) 0.171573 0.171573i 0.00984038 0.00984038i
\(305\) −15.1421 30.2843i −0.867036 1.73407i
\(306\) −3.82843 −0.218857
\(307\) −17.8995 + 17.8995i −1.02158 + 1.02158i −0.0218161 + 0.999762i \(0.506945\pi\)
−0.999762 + 0.0218161i \(0.993055\pi\)
\(308\) 2.36396 2.36396i 0.134699 0.134699i
\(309\) −24.8284 + 24.8284i −1.41244 + 1.41244i
\(310\) −0.171573 0.343146i −0.00974468 0.0194894i
\(311\) 3.77817 3.77817i 0.214241 0.214241i −0.591825 0.806066i \(-0.701593\pi\)
0.806066 + 0.591825i \(0.201593\pi\)
\(312\) −8.82843 8.82843i −0.499811 0.499811i
\(313\) −23.3137 −1.31777 −0.658884 0.752244i \(-0.728971\pi\)
−0.658884 + 0.752244i \(0.728971\pi\)
\(314\) 10.1213 + 10.1213i 0.571179 + 0.571179i
\(315\) 1.82843 + 3.65685i 0.103020 + 0.206040i
\(316\) 1.65685 1.65685i 0.0932053 0.0932053i
\(317\) −8.46447 + 8.46447i −0.475412 + 0.475412i −0.903661 0.428249i \(-0.859131\pi\)
0.428249 + 0.903661i \(0.359131\pi\)
\(318\) −6.00000 −0.336463
\(319\) 9.67767 9.67767i 0.541845 0.541845i
\(320\) 0.707107 2.12132i 0.0395285 0.118585i
\(321\) 14.3431i 0.800556i
\(322\) −7.00000 7.00000i −0.390095 0.390095i
\(323\) 0.656854 + 0.656854i 0.0365483 + 0.0365483i
\(324\) 11.0000 0.611111
\(325\) 24.9706 + 18.7279i 1.38512 + 1.03884i
\(326\) 3.34315i 0.185160i
\(327\) −25.3137 −1.39985
\(328\) 7.00000i 0.386510i
\(329\) 0.627417i 0.0345906i
\(330\) −3.65685 7.31371i −0.201303 0.402606i
\(331\) 5.41421 + 5.41421i 0.297592 + 0.297592i 0.840070 0.542478i \(-0.182514\pi\)
−0.542478 + 0.840070i \(0.682514\pi\)
\(332\) 4.82843 4.82843i 0.264994 0.264994i
\(333\) −4.94975 3.53553i −0.271244 0.193746i
\(334\) 6.82843i 0.373635i
\(335\) −10.2426 20.4853i −0.559615 1.11923i
\(336\) 3.65685i 0.199498i
\(337\) 5.65685 5.65685i 0.308148 0.308148i −0.536043 0.844191i \(-0.680081\pi\)
0.844191 + 0.536043i \(0.180081\pi\)
\(338\) 25.9706 1.41261
\(339\) 2.58579 2.58579i 0.140441 0.140441i
\(340\) 8.12132 + 2.70711i 0.440440 + 0.146813i
\(341\) −0.221825 0.221825i −0.0120125 0.0120125i
\(342\) 0.171573 + 0.171573i 0.00927760 + 0.00927760i
\(343\) 13.7782 13.7782i 0.743951 0.743951i
\(344\) −7.00000 −0.377415
\(345\) −21.6569 + 10.8284i −1.16597 + 0.582983i
\(346\) 18.0208 + 18.0208i 0.968805 + 0.968805i
\(347\) 5.31371 0.285255 0.142627 0.989776i \(-0.454445\pi\)
0.142627 + 0.989776i \(0.454445\pi\)
\(348\) 14.9706i 0.802506i
\(349\) 24.1421i 1.29230i −0.763211 0.646149i \(-0.776378\pi\)
0.763211 0.646149i \(-0.223622\pi\)
\(350\) −1.29289 9.05025i −0.0691080 0.483756i
\(351\) −17.6569 + 17.6569i −0.942453 + 0.942453i
\(352\) 1.82843i 0.0974555i
\(353\) 18.6569i 0.993004i −0.868036 0.496502i \(-0.834618\pi\)
0.868036 0.496502i \(-0.165382\pi\)
\(354\) 19.3137 1.02651
\(355\) −8.24264 + 24.7279i −0.437474 + 1.31242i
\(356\) −4.58579 4.58579i −0.243046 0.243046i
\(357\) −14.0000 −0.740959
\(358\) −2.48528 2.48528i −0.131351 0.131351i
\(359\) 34.5269i 1.82226i 0.412118 + 0.911130i \(0.364789\pi\)
−0.412118 + 0.911130i \(0.635211\pi\)
\(360\) 2.12132 + 0.707107i 0.111803 + 0.0372678i
\(361\) 18.9411i 0.996901i
\(362\) −3.65685 −0.192200
\(363\) 10.8284 + 10.8284i 0.568345 + 0.568345i
\(364\) −8.07107 8.07107i −0.423039 0.423039i
\(365\) −16.9706 + 8.48528i −0.888280 + 0.444140i
\(366\) 30.2843 1.58298
\(367\) −25.0919 25.0919i −1.30979 1.30979i −0.921568 0.388218i \(-0.873091\pi\)
−0.388218 0.921568i \(-0.626909\pi\)
\(368\) −5.41421 −0.282235
\(369\) −7.00000 −0.364405
\(370\) 8.00000 + 11.0000i 0.415900 + 0.571863i
\(371\) −5.48528 −0.284782
\(372\) 0.343146 0.0177913
\(373\) 5.17157 + 5.17157i 0.267774 + 0.267774i 0.828203 0.560429i \(-0.189364\pi\)
−0.560429 + 0.828203i \(0.689364\pi\)
\(374\) 7.00000 0.361961
\(375\) −22.0000 4.00000i −1.13608 0.206559i
\(376\) 0.242641 + 0.242641i 0.0125132 + 0.0125132i
\(377\) −33.0416 33.0416i −1.70173 1.70173i
\(378\) 7.31371 0.376177
\(379\) 18.0000i 0.924598i −0.886724 0.462299i \(-0.847025\pi\)
0.886724 0.462299i \(-0.152975\pi\)
\(380\) −0.242641 0.485281i −0.0124472 0.0248944i
\(381\) 15.3137i 0.784545i
\(382\) −5.53553 5.53553i −0.283223 0.283223i
\(383\) −19.4142 −0.992020 −0.496010 0.868317i \(-0.665202\pi\)
−0.496010 + 0.868317i \(0.665202\pi\)
\(384\) 1.41421 + 1.41421i 0.0721688 + 0.0721688i
\(385\) −3.34315 6.68629i −0.170382 0.340765i
\(386\) −3.51472 −0.178894
\(387\) 7.00000i 0.355830i
\(388\) 7.00000i 0.355371i
\(389\) −11.7782 + 11.7782i −0.597177 + 0.597177i −0.939560 0.342383i \(-0.888766\pi\)
0.342383 + 0.939560i \(0.388766\pi\)
\(390\) −24.9706 + 12.4853i −1.26443 + 0.632217i
\(391\) 20.7279i 1.04826i
\(392\) 3.65685i 0.184699i
\(393\) −6.82843 −0.344449
\(394\) −2.00000 2.00000i −0.100759 0.100759i
\(395\) −2.34315 4.68629i −0.117896 0.235793i
\(396\) 1.82843 0.0918819
\(397\) 8.48528 8.48528i 0.425864 0.425864i −0.461353 0.887217i \(-0.652636\pi\)
0.887217 + 0.461353i \(0.152636\pi\)
\(398\) −15.8995 15.8995i −0.796970 0.796970i
\(399\) 0.627417 + 0.627417i 0.0314101 + 0.0314101i
\(400\) −4.00000 3.00000i −0.200000 0.150000i
\(401\) 7.07107 7.07107i 0.353112 0.353112i −0.508154 0.861266i \(-0.669672\pi\)
0.861266 + 0.508154i \(0.169672\pi\)
\(402\) 20.4853 1.02171
\(403\) −0.757359 + 0.757359i −0.0377268 + 0.0377268i
\(404\) 3.07107i 0.152791i
\(405\) 7.77817 23.3345i 0.386501 1.15950i
\(406\) 13.6863i 0.679239i
\(407\) 9.05025 + 6.46447i 0.448604 + 0.320432i
\(408\) −5.41421 + 5.41421i −0.268044 + 0.268044i
\(409\) −19.7990 19.7990i −0.978997 0.978997i 0.0207869 0.999784i \(-0.493383\pi\)
−0.999784 + 0.0207869i \(0.993383\pi\)
\(410\) 14.8492 + 4.94975i 0.733352 + 0.244451i
\(411\) 15.7990i 0.779307i
\(412\) 17.5563i 0.864939i
\(413\) 17.6569 0.868837
\(414\) 5.41421i 0.266094i
\(415\) −6.82843 13.6569i −0.335194 0.670389i
\(416\) −6.24264 −0.306071
\(417\) 16.7279 + 16.7279i 0.819170 + 0.819170i
\(418\) −0.313708 0.313708i −0.0153440 0.0153440i
\(419\) 6.97056i 0.340534i −0.985398 0.170267i \(-0.945537\pi\)
0.985398 0.170267i \(-0.0544631\pi\)
\(420\) 7.75736 + 2.58579i 0.378520 + 0.126173i
\(421\) −2.68629 + 2.68629i −0.130922 + 0.130922i −0.769531 0.638609i \(-0.779510\pi\)
0.638609 + 0.769531i \(0.279510\pi\)
\(422\) −9.00000 −0.438113
\(423\) −0.242641 + 0.242641i −0.0117976 + 0.0117976i
\(424\) −2.12132 + 2.12132i −0.103020 + 0.103020i
\(425\) 11.4853 15.3137i 0.557118 0.742824i
\(426\) −16.4853 16.4853i −0.798714 0.798714i
\(427\) 27.6863 1.33983
\(428\) 5.07107 + 5.07107i 0.245119 + 0.245119i
\(429\) −16.1421 + 16.1421i −0.779350 + 0.779350i
\(430\) −4.94975 + 14.8492i −0.238698 + 0.716094i
\(431\) 20.5061 20.5061i 0.987744 0.987744i −0.0121819 0.999926i \(-0.503878\pi\)
0.999926 + 0.0121819i \(0.00387771\pi\)
\(432\) 2.82843 2.82843i 0.136083 0.136083i
\(433\) −23.1421 + 23.1421i −1.11214 + 1.11214i −0.119279 + 0.992861i \(0.538058\pi\)
−0.992861 + 0.119279i \(0.961942\pi\)
\(434\) 0.313708 0.0150585
\(435\) 31.7574 + 10.5858i 1.52265 + 0.507550i
\(436\) −8.94975 + 8.94975i −0.428615 + 0.428615i
\(437\) −0.928932 + 0.928932i −0.0444369 + 0.0444369i
\(438\) 16.9706i 0.810885i
\(439\) −17.7782 17.7782i −0.848506 0.848506i 0.141441 0.989947i \(-0.454827\pi\)
−0.989947 + 0.141441i \(0.954827\pi\)
\(440\) −3.87868 1.29289i −0.184909 0.0616363i
\(441\) 3.65685 0.174136
\(442\) 23.8995i 1.13678i
\(443\) 16.6569 + 16.6569i 0.791391 + 0.791391i 0.981720 0.190329i \(-0.0609556\pi\)
−0.190329 + 0.981720i \(0.560956\pi\)
\(444\) −12.0000 + 2.00000i −0.569495 + 0.0949158i
\(445\) −12.9706 + 6.48528i −0.614864 + 0.307432i
\(446\) 18.1213 18.1213i 0.858069 0.858069i
\(447\) −0.343146 + 0.343146i −0.0162302 + 0.0162302i
\(448\) 1.29289 + 1.29289i 0.0610835 + 0.0610835i
\(449\) −19.6274 + 19.6274i −0.926275 + 0.926275i −0.997463 0.0711878i \(-0.977321\pi\)
0.0711878 + 0.997463i \(0.477321\pi\)
\(450\) 3.00000 4.00000i 0.141421 0.188562i
\(451\) 12.7990 0.602681
\(452\) 1.82843i 0.0860020i
\(453\) 16.9706 16.9706i 0.797347 0.797347i
\(454\) 9.48528i 0.445166i
\(455\) −22.8284 + 11.4142i −1.07021 + 0.535107i
\(456\) 0.485281 0.0227254
\(457\) 26.3137i 1.23090i −0.788175 0.615452i \(-0.788974\pi\)
0.788175 0.615452i \(-0.211026\pi\)
\(458\) 1.41421i 0.0660819i
\(459\) 10.8284 + 10.8284i 0.505428 + 0.505428i
\(460\) −3.82843 + 11.4853i −0.178501 + 0.535504i
\(461\) 17.5355 + 17.5355i 0.816711 + 0.816711i 0.985630 0.168919i \(-0.0540275\pi\)
−0.168919 + 0.985630i \(0.554028\pi\)
\(462\) 6.68629 0.311074
\(463\) −37.9411 −1.76327 −0.881637 0.471929i \(-0.843558\pi\)
−0.881637 + 0.471929i \(0.843558\pi\)
\(464\) 5.29289 + 5.29289i 0.245716 + 0.245716i
\(465\) 0.242641 0.727922i 0.0112522 0.0337566i
\(466\) 14.0711 + 14.0711i 0.651830 + 0.651830i
\(467\) 20.3137i 0.940006i −0.882665 0.470003i \(-0.844253\pi\)
0.882665 0.470003i \(-0.155747\pi\)
\(468\) 6.24264i 0.288566i
\(469\) 18.7279 0.864775
\(470\) 0.686292 0.343146i 0.0316563 0.0158281i
\(471\) 28.6274i 1.31908i
\(472\) 6.82843 6.82843i 0.314304 0.314304i
\(473\) 12.7990i 0.588498i
\(474\) 4.68629 0.215248
\(475\) −1.20101 + 0.171573i −0.0551061 + 0.00787230i
\(476\) −4.94975 + 4.94975i −0.226871 + 0.226871i
\(477\) −2.12132 2.12132i −0.0971286 0.0971286i
\(478\) −16.9497 + 16.9497i −0.775263 + 0.775263i
\(479\) 15.5563 15.5563i 0.710788 0.710788i −0.255912 0.966700i \(-0.582376\pi\)
0.966700 + 0.255912i \(0.0823758\pi\)
\(480\) 4.00000 2.00000i 0.182574 0.0912871i
\(481\) 22.0711 30.8995i 1.00635 1.40890i
\(482\) 9.24264 + 9.24264i 0.420991 + 0.420991i
\(483\) 19.7990i 0.900885i
\(484\) 7.65685 0.348039
\(485\) −14.8492 4.94975i −0.674269 0.224756i
\(486\) 7.07107 + 7.07107i 0.320750 + 0.320750i
\(487\) 6.97056i 0.315866i −0.987450 0.157933i \(-0.949517\pi\)
0.987450 0.157933i \(-0.0504831\pi\)
\(488\) 10.7071 10.7071i 0.484688 0.484688i
\(489\) −4.72792 + 4.72792i −0.213804 + 0.213804i
\(490\) −7.75736 2.58579i −0.350442 0.116814i
\(491\) −21.7990 −0.983775 −0.491887 0.870659i \(-0.663693\pi\)
−0.491887 + 0.870659i \(0.663693\pi\)
\(492\) −9.89949 + 9.89949i −0.446304 + 0.446304i
\(493\) −20.2635 + 20.2635i −0.912620 + 0.912620i
\(494\) −1.07107 + 1.07107i −0.0481896 + 0.0481896i
\(495\) 1.29289 3.87868i 0.0581112 0.174334i
\(496\) 0.121320 0.121320i 0.00544744 0.00544744i
\(497\) −15.0711 15.0711i −0.676030 0.676030i
\(498\) 13.6569 0.611978
\(499\) 1.75736 + 1.75736i 0.0786702 + 0.0786702i 0.745347 0.666677i \(-0.232284\pi\)
−0.666677 + 0.745347i \(0.732284\pi\)
\(500\) −9.19239 + 6.36396i −0.411096 + 0.284605i
\(501\) 9.65685 9.65685i 0.431436 0.431436i
\(502\) 1.89949 1.89949i 0.0847786 0.0847786i
\(503\) −35.4142 −1.57904 −0.789521 0.613724i \(-0.789671\pi\)
−0.789521 + 0.613724i \(0.789671\pi\)
\(504\) −1.29289 + 1.29289i −0.0575900 + 0.0575900i
\(505\) 6.51472 + 2.17157i 0.289901 + 0.0966337i
\(506\) 9.89949i 0.440086i
\(507\) 36.7279 + 36.7279i 1.63114 + 1.63114i
\(508\) 5.41421 + 5.41421i 0.240217 + 0.240217i
\(509\) −26.7279 −1.18469 −0.592347 0.805683i \(-0.701799\pi\)
−0.592347 + 0.805683i \(0.701799\pi\)
\(510\) 7.65685 + 15.3137i 0.339051 + 0.678102i
\(511\) 15.5147i 0.686331i
\(512\) 1.00000 0.0441942
\(513\) 0.970563i 0.0428514i
\(514\) 13.1716i 0.580973i
\(515\) 37.2426 + 12.4142i 1.64111 + 0.547036i
\(516\) −9.89949 9.89949i −0.435801 0.435801i
\(517\) 0.443651 0.443651i 0.0195117 0.0195117i
\(518\) −10.9706 + 1.82843i −0.482019 + 0.0803365i
\(519\) 50.9706i 2.23736i
\(520\) −4.41421 + 13.2426i −0.193576 + 0.580728i
\(521\) 17.6274i 0.772271i 0.922442 + 0.386136i \(0.126190\pi\)
−0.922442 + 0.386136i \(0.873810\pi\)
\(522\) −5.29289 + 5.29289i −0.231664 + 0.231664i
\(523\) 32.3431 1.41427 0.707134 0.707080i \(-0.249988\pi\)
0.707134 + 0.707080i \(0.249988\pi\)
\(524\) −2.41421 + 2.41421i −0.105465 + 0.105465i
\(525\) 10.9706 14.6274i 0.478795 0.638393i
\(526\) −6.60660 6.60660i −0.288062 0.288062i
\(527\) 0.464466 + 0.464466i 0.0202325 + 0.0202325i
\(528\) 2.58579 2.58579i 0.112532 0.112532i
\(529\) 6.31371 0.274509
\(530\) 3.00000 + 6.00000i 0.130312 + 0.260623i
\(531\) 6.82843 + 6.82843i 0.296328 + 0.296328i
\(532\) 0.443651 0.0192347
\(533\) 43.6985i 1.89279i
\(534\) 12.9706i 0.561291i
\(535\) 14.3431 7.17157i 0.620108 0.310054i
\(536\) 7.24264 7.24264i 0.312834 0.312834i
\(537\) 7.02944i 0.303343i
\(538\) 21.7990i 0.939821i
\(539\) −6.68629 −0.287999
\(540\) −4.00000 8.00000i −0.172133 0.344265i
\(541\) 11.7990 + 11.7990i 0.507278 + 0.507278i 0.913690 0.406412i \(-0.133220\pi\)
−0.406412 + 0.913690i \(0.633220\pi\)
\(542\) 11.0711 0.475543
\(543\) −5.17157 5.17157i −0.221933 0.221933i
\(544\) 3.82843i 0.164142i
\(545\) 12.6569 + 25.3137i 0.542160 + 1.08432i
\(546\) 22.8284i 0.976966i
\(547\) −22.1716 −0.947988 −0.473994 0.880528i \(-0.657188\pi\)
−0.473994 + 0.880528i \(0.657188\pi\)
\(548\) 5.58579 + 5.58579i 0.238613 + 0.238613i
\(549\) 10.7071 + 10.7071i 0.456968 + 0.456968i
\(550\) −5.48528 + 7.31371i −0.233893 + 0.311858i
\(551\) 1.81623 0.0773742
\(552\) −7.65685 7.65685i −0.325897 0.325897i
\(553\) 4.28427 0.182186
\(554\) −31.7990 −1.35101
\(555\) −4.24264 + 26.8701i −0.180090 + 1.14057i
\(556\) 11.8284 0.501637
\(557\) −19.2132 −0.814090 −0.407045 0.913408i \(-0.633441\pi\)
−0.407045 + 0.913408i \(0.633441\pi\)
\(558\) 0.121320 + 0.121320i 0.00513590 + 0.00513590i
\(559\) 43.6985 1.84825
\(560\) 3.65685 1.82843i 0.154530 0.0772651i
\(561\) 9.89949 + 9.89949i 0.417957 + 0.417957i
\(562\) 4.00000 + 4.00000i 0.168730 + 0.168730i
\(563\) 38.1127 1.60626 0.803129 0.595805i \(-0.203167\pi\)
0.803129 + 0.595805i \(0.203167\pi\)
\(564\) 0.686292i 0.0288981i
\(565\) −3.87868 1.29289i −0.163177 0.0543924i
\(566\) 28.0000i 1.17693i
\(567\) 14.2218 + 14.2218i 0.597261 + 0.597261i
\(568\) −11.6569 −0.489111
\(569\) 24.3137 + 24.3137i 1.01928 + 1.01928i 0.999810 + 0.0194733i \(0.00619894\pi\)
0.0194733 + 0.999810i \(0.493801\pi\)
\(570\) 0.343146 1.02944i 0.0143728 0.0431184i
\(571\) 7.20101 0.301353 0.150676 0.988583i \(-0.451855\pi\)
0.150676 + 0.988583i \(0.451855\pi\)
\(572\) 11.4142i 0.477252i
\(573\) 15.6569i 0.654074i
\(574\) −9.05025 + 9.05025i −0.377750 + 0.377750i
\(575\) 21.6569 + 16.2426i 0.903153 + 0.677365i
\(576\) 1.00000i 0.0416667i
\(577\) 10.3431i 0.430591i 0.976549 + 0.215295i \(0.0690714\pi\)
−0.976549 + 0.215295i \(0.930929\pi\)
\(578\) 2.34315 0.0974620
\(579\) −4.97056 4.97056i −0.206570 0.206570i
\(580\) 14.9706 7.48528i 0.621619 0.310809i
\(581\) 12.4853 0.517977
\(582\) 9.89949 9.89949i 0.410347 0.410347i
\(583\) 3.87868 + 3.87868i 0.160638 + 0.160638i
\(584\) −6.00000 6.00000i −0.248282 0.248282i
\(585\) −13.2426 4.41421i −0.547516 0.182505i
\(586\) 13.7782 13.7782i 0.569171 0.569171i
\(587\) 46.4558 1.91744 0.958719 0.284355i \(-0.0917796\pi\)
0.958719 + 0.284355i \(0.0917796\pi\)
\(588\) 5.17157 5.17157i 0.213272 0.213272i
\(589\) 0.0416306i 0.00171536i
\(590\) −9.65685 19.3137i −0.397566 0.795133i
\(591\) 5.65685i 0.232692i
\(592\) −3.53553 + 4.94975i −0.145310 + 0.203433i
\(593\) 2.14214 2.14214i 0.0879670 0.0879670i −0.661754 0.749721i \(-0.730188\pi\)
0.749721 + 0.661754i \(0.230188\pi\)
\(594\) −5.17157 5.17157i −0.212192 0.212192i
\(595\) 7.00000 + 14.0000i 0.286972 + 0.573944i
\(596\) 0.242641i 0.00993895i
\(597\) 44.9706i 1.84052i
\(598\) 33.7990 1.38214
\(599\) 42.2426i 1.72599i −0.505215 0.862994i \(-0.668587\pi\)
0.505215 0.862994i \(-0.331413\pi\)
\(600\) −1.41421 9.89949i −0.0577350 0.404145i
\(601\) −33.4853 −1.36589 −0.682947 0.730468i \(-0.739302\pi\)
−0.682947 + 0.730468i \(0.739302\pi\)
\(602\) −9.05025 9.05025i −0.368861 0.368861i
\(603\) 7.24264 + 7.24264i 0.294943 + 0.294943i
\(604\) 12.0000i 0.488273i
\(605\) 5.41421 16.2426i 0.220119 0.660357i
\(606\) −4.34315 + 4.34315i −0.176428 + 0.176428i
\(607\) 42.1838 1.71219 0.856093 0.516822i \(-0.172885\pi\)
0.856093 + 0.516822i \(0.172885\pi\)
\(608\) 0.171573 0.171573i 0.00695820 0.00695820i
\(609\) −19.3553 + 19.3553i −0.784318 + 0.784318i
\(610\) −15.1421 30.2843i −0.613087 1.22617i
\(611\) −1.51472 1.51472i −0.0612790 0.0612790i
\(612\) −3.82843 −0.154755
\(613\) 7.87868 + 7.87868i 0.318217 + 0.318217i 0.848082 0.529865i \(-0.177757\pi\)
−0.529865 + 0.848082i \(0.677757\pi\)
\(614\) −17.8995 + 17.8995i −0.722365 + 0.722365i
\(615\) 14.0000 + 28.0000i 0.564534 + 1.12907i
\(616\) 2.36396 2.36396i 0.0952467 0.0952467i
\(617\) 2.27208 2.27208i 0.0914704 0.0914704i −0.659891 0.751361i \(-0.729398\pi\)
0.751361 + 0.659891i \(0.229398\pi\)
\(618\) −24.8284 + 24.8284i −0.998746 + 0.998746i
\(619\) 32.5980 1.31022 0.655112 0.755532i \(-0.272622\pi\)
0.655112 + 0.755532i \(0.272622\pi\)
\(620\) −0.171573 0.343146i −0.00689053 0.0137811i
\(621\) −15.3137 + 15.3137i −0.614518 + 0.614518i
\(622\) 3.77817 3.77817i 0.151491 0.151491i
\(623\) 11.8579i 0.475075i
\(624\) −8.82843 8.82843i −0.353420 0.353420i
\(625\) 7.00000 + 24.0000i 0.280000 + 0.960000i
\(626\) −23.3137 −0.931803
\(627\) 0.887302i 0.0354354i
\(628\) 10.1213 + 10.1213i 0.403885 + 0.403885i
\(629\) −18.9497 13.5355i −0.755576 0.539697i
\(630\) 1.82843 + 3.65685i 0.0728463 + 0.145693i
\(631\) 10.8492 10.8492i 0.431902 0.431902i −0.457373 0.889275i \(-0.651210\pi\)
0.889275 + 0.457373i \(0.151210\pi\)
\(632\) 1.65685 1.65685i 0.0659061 0.0659061i
\(633\) −12.7279 12.7279i −0.505889 0.505889i
\(634\) −8.46447 + 8.46447i −0.336167 + 0.336167i
\(635\) 15.3137 7.65685i 0.607706 0.303853i
\(636\) −6.00000 −0.237915
\(637\) 22.8284i 0.904495i
\(638\) 9.67767 9.67767i 0.383143 0.383143i
\(639\) 11.6569i 0.461138i
\(640\) 0.707107 2.12132i 0.0279508 0.0838525i
\(641\) −31.2843 −1.23565 −0.617827 0.786314i \(-0.711987\pi\)
−0.617827 + 0.786314i \(0.711987\pi\)
\(642\) 14.3431i 0.566079i
\(643\) 41.4853i 1.63602i 0.575204 + 0.818010i \(0.304923\pi\)
−0.575204 + 0.818010i \(0.695077\pi\)
\(644\) −7.00000 7.00000i −0.275839 0.275839i
\(645\) −28.0000 + 14.0000i −1.10250 + 0.551249i
\(646\) 0.656854 + 0.656854i 0.0258436 + 0.0258436i
\(647\) 4.68629 0.184237 0.0921186 0.995748i \(-0.470636\pi\)
0.0921186 + 0.995748i \(0.470636\pi\)
\(648\) 11.0000 0.432121
\(649\) −12.4853 12.4853i −0.490090 0.490090i
\(650\) 24.9706 + 18.7279i 0.979426 + 0.734570i
\(651\) 0.443651 + 0.443651i 0.0173880 + 0.0173880i
\(652\) 3.34315i 0.130928i
\(653\) 8.34315i 0.326493i 0.986585 + 0.163246i \(0.0521965\pi\)
−0.986585 + 0.163246i \(0.947803\pi\)
\(654\) −25.3137 −0.989844
\(655\) 3.41421 + 6.82843i 0.133404 + 0.266809i
\(656\) 7.00000i 0.273304i
\(657\) 6.00000 6.00000i 0.234082 0.234082i
\(658\) 0.627417i 0.0244593i
\(659\) −8.14214 −0.317173 −0.158586 0.987345i \(-0.550694\pi\)
−0.158586 + 0.987345i \(0.550694\pi\)
\(660\) −3.65685 7.31371i −0.142343 0.284686i
\(661\) 12.2635 12.2635i 0.476993 0.476993i −0.427176 0.904169i \(-0.640491\pi\)
0.904169 + 0.427176i \(0.140491\pi\)
\(662\) 5.41421 + 5.41421i 0.210429 + 0.210429i
\(663\) 33.7990 33.7990i 1.31264 1.31264i
\(664\) 4.82843 4.82843i 0.187379 0.187379i
\(665\) 0.313708 0.941125i 0.0121651 0.0364953i
\(666\) −4.94975 3.53553i −0.191799 0.136999i
\(667\) −28.6569 28.6569i −1.10960 1.10960i
\(668\) 6.82843i 0.264200i
\(669\) 51.2548 1.98163
\(670\) −10.2426 20.4853i −0.395708 0.791415i
\(671\) −19.5772 19.5772i −0.755768 0.755768i
\(672\) 3.65685i 0.141066i
\(673\) −27.4853 + 27.4853i −1.05948 + 1.05948i −0.0613643 + 0.998115i \(0.519545\pi\)
−0.998115 + 0.0613643i \(0.980455\pi\)
\(674\) 5.65685 5.65685i 0.217894 0.217894i
\(675\) −19.7990 + 2.82843i −0.762063 + 0.108866i
\(676\) 25.9706 0.998868
\(677\) 30.4853 30.4853i 1.17164 1.17164i 0.189827 0.981818i \(-0.439207\pi\)
0.981818 0.189827i \(-0.0607927\pi\)
\(678\) 2.58579 2.58579i 0.0993065 0.0993065i
\(679\) 9.05025 9.05025i 0.347317 0.347317i
\(680\) 8.12132 + 2.70711i 0.311438 + 0.103813i
\(681\) −13.4142 + 13.4142i −0.514034 + 0.514034i
\(682\) −0.221825 0.221825i −0.00849413 0.00849413i
\(683\) −10.3137 −0.394643 −0.197322 0.980339i \(-0.563224\pi\)
−0.197322 + 0.980339i \(0.563224\pi\)
\(684\) 0.171573 + 0.171573i 0.00656025 + 0.00656025i
\(685\) 15.7990 7.89949i 0.603648 0.301824i
\(686\) 13.7782 13.7782i 0.526053 0.526053i
\(687\) 2.00000 2.00000i 0.0763048 0.0763048i
\(688\) −7.00000 −0.266872
\(689\) 13.2426 13.2426i 0.504504 0.504504i
\(690\) −21.6569 + 10.8284i −0.824462 + 0.412231i
\(691\) 23.9706i 0.911883i −0.890010 0.455942i \(-0.849303\pi\)
0.890010 0.455942i \(-0.150697\pi\)
\(692\) 18.0208 + 18.0208i 0.685049 + 0.685049i
\(693\) 2.36396 + 2.36396i 0.0897995 + 0.0897995i
\(694\) 5.31371 0.201706
\(695\) 8.36396 25.0919i 0.317263 0.951789i
\(696\) 14.9706i 0.567458i
\(697\) −26.7990 −1.01508
\(698\) 24.1421i 0.913793i
\(699\) 39.7990i 1.50534i
\(700\) −1.29289 9.05025i −0.0488668 0.342067i
\(701\) 15.6569 + 15.6569i 0.591351 + 0.591351i 0.937996 0.346645i \(-0.112679\pi\)
−0.346645 + 0.937996i \(0.612679\pi\)
\(702\) −17.6569 + 17.6569i −0.666415 + 0.666415i
\(703\) 0.242641 + 1.45584i 0.00915137 + 0.0549082i
\(704\) 1.82843i 0.0689114i
\(705\) 1.45584 + 0.485281i 0.0548303 + 0.0182768i
\(706\) 18.6569i 0.702160i
\(707\) −3.97056 + 3.97056i −0.149328 + 0.149328i
\(708\) 19.3137 0.725854
\(709\) −9.29289 + 9.29289i −0.349002 + 0.349002i −0.859738 0.510736i \(-0.829373\pi\)
0.510736 + 0.859738i \(0.329373\pi\)
\(710\) −8.24264 + 24.7279i −0.309341 + 0.928022i
\(711\) 1.65685 + 1.65685i 0.0621369 + 0.0621369i
\(712\) −4.58579 4.58579i −0.171860 0.171860i
\(713\) −0.656854 + 0.656854i −0.0245994 + 0.0245994i
\(714\) −14.0000 −0.523937
\(715\) 24.2132 + 8.07107i 0.905522 + 0.301841i
\(716\) −2.48528 2.48528i −0.0928793 0.0928793i
\(717\) −47.9411 −1.79039
\(718\) 34.5269i 1.28853i
\(719\) 4.14214i 0.154476i 0.997013 + 0.0772378i \(0.0246101\pi\)
−0.997013 + 0.0772378i \(0.975390\pi\)
\(720\) 2.12132 + 0.707107i 0.0790569 + 0.0263523i
\(721\) −22.6985 + 22.6985i −0.845336 + 0.845336i
\(722\) 18.9411i 0.704916i
\(723\) 26.1421i 0.972236i
\(724\) −3.65685 −0.135906
\(725\) −5.29289 37.0503i −0.196573 1.37601i
\(726\) 10.8284 + 10.8284i 0.401881 + 0.401881i
\(727\) −42.1421 −1.56297 −0.781483 0.623927i \(-0.785536\pi\)
−0.781483 + 0.623927i \(0.785536\pi\)
\(728\) −8.07107 8.07107i −0.299134 0.299134i
\(729\) 13.0000i 0.481481i
\(730\) −16.9706 + 8.48528i −0.628109 + 0.314054i
\(731\) 26.7990i 0.991196i
\(732\) 30.2843 1.11934
\(733\) −26.7487 26.7487i −0.987987 0.987987i 0.0119415 0.999929i \(-0.496199\pi\)
−0.999929 + 0.0119415i \(0.996199\pi\)
\(734\) −25.0919 25.0919i −0.926158 0.926158i
\(735\) −7.31371 14.6274i −0.269770 0.539540i
\(736\) −5.41421 −0.199571
\(737\) −13.2426 13.2426i −0.487799 0.487799i
\(738\) −7.00000 −0.257674
\(739\) −28.7990 −1.05939 −0.529694 0.848189i \(-0.677693\pi\)
−0.529694 + 0.848189i \(0.677693\pi\)
\(740\) 8.00000 + 11.0000i 0.294086 + 0.404368i
\(741\) −3.02944 −0.111289
\(742\) −5.48528 −0.201371
\(743\) −14.9497 14.9497i −0.548453 0.548453i 0.377540 0.925993i \(-0.376770\pi\)
−0.925993 + 0.377540i \(0.876770\pi\)
\(744\) 0.343146 0.0125803
\(745\) 0.514719 + 0.171573i 0.0188578 + 0.00628594i
\(746\) 5.17157 + 5.17157i 0.189345 + 0.189345i
\(747\) 4.82843 + 4.82843i 0.176663 + 0.176663i
\(748\) 7.00000 0.255945
\(749\) 13.1127i 0.479128i
\(750\) −22.0000 4.00000i −0.803326 0.146059i
\(751\) 32.0416i 1.16922i 0.811316 + 0.584608i \(0.198752\pi\)
−0.811316 + 0.584608i \(0.801248\pi\)
\(752\) 0.242641 + 0.242641i 0.00884820 + 0.00884820i
\(753\) 5.37258 0.195788
\(754\) −33.0416 33.0416i −1.20331 1.20331i
\(755\) −25.4558 8.48528i −0.926433 0.308811i
\(756\) 7.31371 0.265997
\(757\) 16.3431i 0.594002i 0.954877 + 0.297001i \(0.0959864\pi\)
−0.954877 + 0.297001i \(0.904014\pi\)
\(758\) 18.0000i 0.653789i
\(759\) −14.0000 + 14.0000i −0.508168 + 0.508168i
\(760\) −0.242641 0.485281i −0.00880150 0.0176030i
\(761\) 34.3137i 1.24387i −0.783068 0.621935i \(-0.786347\pi\)
0.783068 0.621935i \(-0.213653\pi\)
\(762\) 15.3137i 0.554757i
\(763\) −23.1421 −0.837802
\(764\) −5.53553 5.53553i −0.200269 0.200269i
\(765\) −2.70711 + 8.12132i −0.0978757 + 0.293627i
\(766\) −19.4142 −0.701464
\(767\) −42.6274 + 42.6274i −1.53919 + 1.53919i
\(768\) 1.41421 + 1.41421i 0.0510310 + 0.0510310i
\(769\) 24.8284 + 24.8284i 0.895336 + 0.895336i 0.995019 0.0996832i \(-0.0317829\pi\)
−0.0996832 + 0.995019i \(0.531783\pi\)
\(770\) −3.34315 6.68629i −0.120479 0.240957i
\(771\) −18.6274 + 18.6274i −0.670850 + 0.670850i
\(772\) −3.51472 −0.126497
\(773\) 5.87868 5.87868i 0.211441 0.211441i −0.593438 0.804880i \(-0.702230\pi\)
0.804880 + 0.593438i \(0.202230\pi\)
\(774\) 7.00000i 0.251610i
\(775\) −0.849242 + 0.121320i −0.0305057 + 0.00435796i
\(776\) 7.00000i 0.251285i
\(777\) −18.1005 12.9289i −0.649352