Properties

Label 370.2.g.c.43.2
Level $370$
Weight $2$
Character 370.43
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.g (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 43.2
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 370.43
Dual form 370.2.g.c.327.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(1.41421 - 1.41421i) q^{3} -1.00000 q^{4} +(2.12132 - 0.707107i) q^{5} +(-1.41421 - 1.41421i) q^{6} +(2.70711 - 2.70711i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(1.41421 - 1.41421i) q^{3} -1.00000 q^{4} +(2.12132 - 0.707107i) q^{5} +(-1.41421 - 1.41421i) q^{6} +(2.70711 - 2.70711i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-0.707107 - 2.12132i) q^{10} +3.82843i q^{11} +(-1.41421 + 1.41421i) q^{12} +2.24264i q^{13} +(-2.70711 - 2.70711i) q^{14} +(2.00000 - 4.00000i) q^{15} +1.00000 q^{16} -1.82843 q^{17} -1.00000 q^{18} +(-5.82843 + 5.82843i) q^{19} +(-2.12132 + 0.707107i) q^{20} -7.65685i q^{21} +3.82843 q^{22} -2.58579i q^{23} +(1.41421 + 1.41421i) q^{24} +(4.00000 - 3.00000i) q^{25} +2.24264 q^{26} +(2.82843 + 2.82843i) q^{27} +(-2.70711 + 2.70711i) q^{28} +(-6.70711 - 6.70711i) q^{29} +(-4.00000 - 2.00000i) q^{30} +(-4.12132 + 4.12132i) q^{31} -1.00000i q^{32} +(5.41421 + 5.41421i) q^{33} +1.82843i q^{34} +(3.82843 - 7.65685i) q^{35} +1.00000i q^{36} +(-4.94975 - 3.53553i) q^{37} +(5.82843 + 5.82843i) q^{38} +(3.17157 + 3.17157i) q^{39} +(0.707107 + 2.12132i) q^{40} +7.00000i q^{41} -7.65685 q^{42} -7.00000i q^{43} -3.82843i q^{44} +(-0.707107 - 2.12132i) q^{45} -2.58579 q^{46} +(-8.24264 + 8.24264i) q^{47} +(1.41421 - 1.41421i) q^{48} -7.65685i q^{49} +(-3.00000 - 4.00000i) q^{50} +(-2.58579 + 2.58579i) q^{51} -2.24264i q^{52} +(2.12132 + 2.12132i) q^{53} +(2.82843 - 2.82843i) q^{54} +(2.70711 + 8.12132i) q^{55} +(2.70711 + 2.70711i) q^{56} +16.4853i q^{57} +(-6.70711 + 6.70711i) q^{58} +(-1.17157 + 1.17157i) q^{59} +(-2.00000 + 4.00000i) q^{60} +(9.29289 - 9.29289i) q^{61} +(4.12132 + 4.12132i) q^{62} +(-2.70711 - 2.70711i) q^{63} -1.00000 q^{64} +(1.58579 + 4.75736i) q^{65} +(5.41421 - 5.41421i) q^{66} +(1.24264 + 1.24264i) q^{67} +1.82843 q^{68} +(-3.65685 - 3.65685i) q^{69} +(-7.65685 - 3.82843i) q^{70} -0.343146 q^{71} +1.00000 q^{72} +(6.00000 - 6.00000i) q^{73} +(-3.53553 + 4.94975i) q^{74} +(1.41421 - 9.89949i) q^{75} +(5.82843 - 5.82843i) q^{76} +(10.3640 + 10.3640i) q^{77} +(3.17157 - 3.17157i) q^{78} +(9.65685 - 9.65685i) q^{79} +(2.12132 - 0.707107i) q^{80} +11.0000 q^{81} +7.00000 q^{82} +(-0.828427 - 0.828427i) q^{83} +7.65685i q^{84} +(-3.87868 + 1.29289i) q^{85} -7.00000 q^{86} -18.9706 q^{87} -3.82843 q^{88} +(7.41421 + 7.41421i) q^{89} +(-2.12132 + 0.707107i) q^{90} +(6.07107 + 6.07107i) q^{91} +2.58579i q^{92} +11.6569i q^{93} +(8.24264 + 8.24264i) q^{94} +(-8.24264 + 16.4853i) q^{95} +(-1.41421 - 1.41421i) q^{96} -7.00000 q^{97} -7.65685 q^{98} +3.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{4} + 8q^{7} + O(q^{10}) \) \( 4q - 4q^{4} + 8q^{7} - 8q^{14} + 8q^{15} + 4q^{16} + 4q^{17} - 4q^{18} - 12q^{19} + 4q^{22} + 16q^{25} - 8q^{26} - 8q^{28} - 24q^{29} - 16q^{30} - 8q^{31} + 16q^{33} + 4q^{35} + 12q^{38} + 24q^{39} - 8q^{42} - 16q^{46} - 16q^{47} - 12q^{50} - 16q^{51} + 8q^{55} + 8q^{56} - 24q^{58} - 16q^{59} - 8q^{60} + 40q^{61} + 8q^{62} - 8q^{63} - 4q^{64} + 12q^{65} + 16q^{66} - 12q^{67} - 4q^{68} + 8q^{69} - 8q^{70} - 24q^{71} + 4q^{72} + 24q^{73} + 12q^{76} + 16q^{77} + 24q^{78} + 16q^{79} + 44q^{81} + 28q^{82} + 8q^{83} - 24q^{85} - 28q^{86} - 8q^{87} - 4q^{88} + 24q^{89} - 4q^{91} + 16q^{94} - 16q^{95} - 28q^{97} - 8q^{98} + 4q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.41421 1.41421i 0.816497 0.816497i −0.169102 0.985599i \(-0.554087\pi\)
0.985599 + 0.169102i \(0.0540867\pi\)
\(4\) −1.00000 −0.500000
\(5\) 2.12132 0.707107i 0.948683 0.316228i
\(6\) −1.41421 1.41421i −0.577350 0.577350i
\(7\) 2.70711 2.70711i 1.02319 1.02319i 0.0234655 0.999725i \(-0.492530\pi\)
0.999725 0.0234655i \(-0.00747000\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) −0.707107 2.12132i −0.223607 0.670820i
\(11\) 3.82843i 1.15431i 0.816633 + 0.577157i \(0.195838\pi\)
−0.816633 + 0.577157i \(0.804162\pi\)
\(12\) −1.41421 + 1.41421i −0.408248 + 0.408248i
\(13\) 2.24264i 0.621997i 0.950410 + 0.310998i \(0.100663\pi\)
−0.950410 + 0.310998i \(0.899337\pi\)
\(14\) −2.70711 2.70711i −0.723505 0.723505i
\(15\) 2.00000 4.00000i 0.516398 1.03280i
\(16\) 1.00000 0.250000
\(17\) −1.82843 −0.443459 −0.221729 0.975108i \(-0.571170\pi\)
−0.221729 + 0.975108i \(0.571170\pi\)
\(18\) −1.00000 −0.235702
\(19\) −5.82843 + 5.82843i −1.33713 + 1.33713i −0.438308 + 0.898825i \(0.644422\pi\)
−0.898825 + 0.438308i \(0.855578\pi\)
\(20\) −2.12132 + 0.707107i −0.474342 + 0.158114i
\(21\) 7.65685i 1.67086i
\(22\) 3.82843 0.816223
\(23\) 2.58579i 0.539174i −0.962976 0.269587i \(-0.913113\pi\)
0.962976 0.269587i \(-0.0868871\pi\)
\(24\) 1.41421 + 1.41421i 0.288675 + 0.288675i
\(25\) 4.00000 3.00000i 0.800000 0.600000i
\(26\) 2.24264 0.439818
\(27\) 2.82843 + 2.82843i 0.544331 + 0.544331i
\(28\) −2.70711 + 2.70711i −0.511595 + 0.511595i
\(29\) −6.70711 6.70711i −1.24548 1.24548i −0.957696 0.287783i \(-0.907082\pi\)
−0.287783 0.957696i \(-0.592918\pi\)
\(30\) −4.00000 2.00000i −0.730297 0.365148i
\(31\) −4.12132 + 4.12132i −0.740211 + 0.740211i −0.972619 0.232408i \(-0.925340\pi\)
0.232408 + 0.972619i \(0.425340\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 5.41421 + 5.41421i 0.942494 + 0.942494i
\(34\) 1.82843i 0.313573i
\(35\) 3.82843 7.65685i 0.647122 1.29424i
\(36\) 1.00000i 0.166667i
\(37\) −4.94975 3.53553i −0.813733 0.581238i
\(38\) 5.82843 + 5.82843i 0.945496 + 0.945496i
\(39\) 3.17157 + 3.17157i 0.507858 + 0.507858i
\(40\) 0.707107 + 2.12132i 0.111803 + 0.335410i
\(41\) 7.00000i 1.09322i 0.837389 + 0.546608i \(0.184081\pi\)
−0.837389 + 0.546608i \(0.815919\pi\)
\(42\) −7.65685 −1.18148
\(43\) 7.00000i 1.06749i −0.845645 0.533745i \(-0.820784\pi\)
0.845645 0.533745i \(-0.179216\pi\)
\(44\) 3.82843i 0.577157i
\(45\) −0.707107 2.12132i −0.105409 0.316228i
\(46\) −2.58579 −0.381253
\(47\) −8.24264 + 8.24264i −1.20231 + 1.20231i −0.228851 + 0.973461i \(0.573497\pi\)
−0.973461 + 0.228851i \(0.926503\pi\)
\(48\) 1.41421 1.41421i 0.204124 0.204124i
\(49\) 7.65685i 1.09384i
\(50\) −3.00000 4.00000i −0.424264 0.565685i
\(51\) −2.58579 + 2.58579i −0.362083 + 0.362083i
\(52\) 2.24264i 0.310998i
\(53\) 2.12132 + 2.12132i 0.291386 + 0.291386i 0.837628 0.546242i \(-0.183942\pi\)
−0.546242 + 0.837628i \(0.683942\pi\)
\(54\) 2.82843 2.82843i 0.384900 0.384900i
\(55\) 2.70711 + 8.12132i 0.365026 + 1.09508i
\(56\) 2.70711 + 2.70711i 0.361752 + 0.361752i
\(57\) 16.4853i 2.18353i
\(58\) −6.70711 + 6.70711i −0.880686 + 0.880686i
\(59\) −1.17157 + 1.17157i −0.152526 + 0.152526i −0.779245 0.626719i \(-0.784397\pi\)
0.626719 + 0.779245i \(0.284397\pi\)
\(60\) −2.00000 + 4.00000i −0.258199 + 0.516398i
\(61\) 9.29289 9.29289i 1.18983 1.18983i 0.212720 0.977113i \(-0.431768\pi\)
0.977113 0.212720i \(-0.0682322\pi\)
\(62\) 4.12132 + 4.12132i 0.523408 + 0.523408i
\(63\) −2.70711 2.70711i −0.341063 0.341063i
\(64\) −1.00000 −0.125000
\(65\) 1.58579 + 4.75736i 0.196693 + 0.590078i
\(66\) 5.41421 5.41421i 0.666444 0.666444i
\(67\) 1.24264 + 1.24264i 0.151813 + 0.151813i 0.778927 0.627114i \(-0.215764\pi\)
−0.627114 + 0.778927i \(0.715764\pi\)
\(68\) 1.82843 0.221729
\(69\) −3.65685 3.65685i −0.440234 0.440234i
\(70\) −7.65685 3.82843i −0.915169 0.457585i
\(71\) −0.343146 −0.0407239 −0.0203620 0.999793i \(-0.506482\pi\)
−0.0203620 + 0.999793i \(0.506482\pi\)
\(72\) 1.00000 0.117851
\(73\) 6.00000 6.00000i 0.702247 0.702247i −0.262646 0.964892i \(-0.584595\pi\)
0.964892 + 0.262646i \(0.0845950\pi\)
\(74\) −3.53553 + 4.94975i −0.410997 + 0.575396i
\(75\) 1.41421 9.89949i 0.163299 1.14310i
\(76\) 5.82843 5.82843i 0.668566 0.668566i
\(77\) 10.3640 + 10.3640i 1.18108 + 1.18108i
\(78\) 3.17157 3.17157i 0.359110 0.359110i
\(79\) 9.65685 9.65685i 1.08648 1.08648i 0.0905930 0.995888i \(-0.471124\pi\)
0.995888 0.0905930i \(-0.0288762\pi\)
\(80\) 2.12132 0.707107i 0.237171 0.0790569i
\(81\) 11.0000 1.22222
\(82\) 7.00000 0.773021
\(83\) −0.828427 0.828427i −0.0909317 0.0909317i 0.660178 0.751109i \(-0.270481\pi\)
−0.751109 + 0.660178i \(0.770481\pi\)
\(84\) 7.65685i 0.835431i
\(85\) −3.87868 + 1.29289i −0.420702 + 0.140234i
\(86\) −7.00000 −0.754829
\(87\) −18.9706 −2.03386
\(88\) −3.82843 −0.408112
\(89\) 7.41421 + 7.41421i 0.785905 + 0.785905i 0.980820 0.194915i \(-0.0624431\pi\)
−0.194915 + 0.980820i \(0.562443\pi\)
\(90\) −2.12132 + 0.707107i −0.223607 + 0.0745356i
\(91\) 6.07107 + 6.07107i 0.636421 + 0.636421i
\(92\) 2.58579i 0.269587i
\(93\) 11.6569i 1.20876i
\(94\) 8.24264 + 8.24264i 0.850163 + 0.850163i
\(95\) −8.24264 + 16.4853i −0.845677 + 1.69135i
\(96\) −1.41421 1.41421i −0.144338 0.144338i
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) −7.65685 −0.773459
\(99\) 3.82843 0.384771
\(100\) −4.00000 + 3.00000i −0.400000 + 0.300000i
\(101\) 11.0711i 1.10161i −0.834633 0.550806i \(-0.814320\pi\)
0.834633 0.550806i \(-0.185680\pi\)
\(102\) 2.58579 + 2.58579i 0.256031 + 0.256031i
\(103\) 13.5563 1.33575 0.667873 0.744275i \(-0.267205\pi\)
0.667873 + 0.744275i \(0.267205\pi\)
\(104\) −2.24264 −0.219909
\(105\) −5.41421 16.2426i −0.528373 1.58512i
\(106\) 2.12132 2.12132i 0.206041 0.206041i
\(107\) −9.07107 + 9.07107i −0.876933 + 0.876933i −0.993216 0.116283i \(-0.962902\pi\)
0.116283 + 0.993216i \(0.462902\pi\)
\(108\) −2.82843 2.82843i −0.272166 0.272166i
\(109\) −0.949747 + 0.949747i −0.0909693 + 0.0909693i −0.751127 0.660158i \(-0.770489\pi\)
0.660158 + 0.751127i \(0.270489\pi\)
\(110\) 8.12132 2.70711i 0.774338 0.258113i
\(111\) −12.0000 + 2.00000i −1.13899 + 0.189832i
\(112\) 2.70711 2.70711i 0.255798 0.255798i
\(113\) −3.82843 −0.360148 −0.180074 0.983653i \(-0.557634\pi\)
−0.180074 + 0.983653i \(0.557634\pi\)
\(114\) 16.4853 1.54399
\(115\) −1.82843 5.48528i −0.170502 0.511505i
\(116\) 6.70711 + 6.70711i 0.622739 + 0.622739i
\(117\) 2.24264 0.207332
\(118\) 1.17157 + 1.17157i 0.107852 + 0.107852i
\(119\) −4.94975 + 4.94975i −0.453743 + 0.453743i
\(120\) 4.00000 + 2.00000i 0.365148 + 0.182574i
\(121\) −3.65685 −0.332441
\(122\) −9.29289 9.29289i −0.841339 0.841339i
\(123\) 9.89949 + 9.89949i 0.892607 + 0.892607i
\(124\) 4.12132 4.12132i 0.370105 0.370105i
\(125\) 6.36396 9.19239i 0.569210 0.822192i
\(126\) −2.70711 + 2.70711i −0.241168 + 0.241168i
\(127\) 2.58579 2.58579i 0.229451 0.229451i −0.583012 0.812464i \(-0.698126\pi\)
0.812464 + 0.583012i \(0.198126\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −9.89949 9.89949i −0.871602 0.871602i
\(130\) 4.75736 1.58579i 0.417248 0.139083i
\(131\) 0.414214 0.414214i 0.0361900 0.0361900i −0.688780 0.724970i \(-0.741853\pi\)
0.724970 + 0.688780i \(0.241853\pi\)
\(132\) −5.41421 5.41421i −0.471247 0.471247i
\(133\) 31.5563i 2.73628i
\(134\) 1.24264 1.24264i 0.107348 0.107348i
\(135\) 8.00000 + 4.00000i 0.688530 + 0.344265i
\(136\) 1.82843i 0.156786i
\(137\) 8.41421 8.41421i 0.718875 0.718875i −0.249500 0.968375i \(-0.580266\pi\)
0.968375 + 0.249500i \(0.0802663\pi\)
\(138\) −3.65685 + 3.65685i −0.311292 + 0.311292i
\(139\) −6.17157 −0.523466 −0.261733 0.965140i \(-0.584294\pi\)
−0.261733 + 0.965140i \(0.584294\pi\)
\(140\) −3.82843 + 7.65685i −0.323561 + 0.647122i
\(141\) 23.3137i 1.96337i
\(142\) 0.343146i 0.0287962i
\(143\) −8.58579 −0.717980
\(144\) 1.00000i 0.0833333i
\(145\) −18.9706 9.48528i −1.57542 0.787710i
\(146\) −6.00000 6.00000i −0.496564 0.496564i
\(147\) −10.8284 10.8284i −0.893114 0.893114i
\(148\) 4.94975 + 3.53553i 0.406867 + 0.290619i
\(149\) 8.24264i 0.675263i 0.941278 + 0.337632i \(0.109626\pi\)
−0.941278 + 0.337632i \(0.890374\pi\)
\(150\) −9.89949 1.41421i −0.808290 0.115470i
\(151\) 12.0000i 0.976546i −0.872691 0.488273i \(-0.837627\pi\)
0.872691 0.488273i \(-0.162373\pi\)
\(152\) −5.82843 5.82843i −0.472748 0.472748i
\(153\) 1.82843i 0.147820i
\(154\) 10.3640 10.3640i 0.835152 0.835152i
\(155\) −5.82843 + 11.6569i −0.468151 + 0.936301i
\(156\) −3.17157 3.17157i −0.253929 0.253929i
\(157\) 5.87868 5.87868i 0.469170 0.469170i −0.432476 0.901646i \(-0.642360\pi\)
0.901646 + 0.432476i \(0.142360\pi\)
\(158\) −9.65685 9.65685i −0.768258 0.768258i
\(159\) 6.00000 0.475831
\(160\) −0.707107 2.12132i −0.0559017 0.167705i
\(161\) −7.00000 7.00000i −0.551677 0.551677i
\(162\) 11.0000i 0.864242i
\(163\) −14.6569 −1.14801 −0.574007 0.818851i \(-0.694612\pi\)
−0.574007 + 0.818851i \(0.694612\pi\)
\(164\) 7.00000i 0.546608i
\(165\) 15.3137 + 7.65685i 1.19217 + 0.596085i
\(166\) −0.828427 + 0.828427i −0.0642984 + 0.0642984i
\(167\) −1.17157 −0.0906590 −0.0453295 0.998972i \(-0.514434\pi\)
−0.0453295 + 0.998972i \(0.514434\pi\)
\(168\) 7.65685 0.590739
\(169\) 7.97056 0.613120
\(170\) 1.29289 + 3.87868i 0.0991604 + 0.297481i
\(171\) 5.82843 + 5.82843i 0.445711 + 0.445711i
\(172\) 7.00000i 0.533745i
\(173\) 6.02082 6.02082i 0.457754 0.457754i −0.440164 0.897918i \(-0.645080\pi\)
0.897918 + 0.440164i \(0.145080\pi\)
\(174\) 18.9706i 1.43815i
\(175\) 2.70711 18.9497i 0.204638 1.43247i
\(176\) 3.82843i 0.288579i
\(177\) 3.31371i 0.249074i
\(178\) 7.41421 7.41421i 0.555719 0.555719i
\(179\) −14.4853 14.4853i −1.08268 1.08268i −0.996259 0.0864222i \(-0.972457\pi\)
−0.0864222 0.996259i \(-0.527543\pi\)
\(180\) 0.707107 + 2.12132i 0.0527046 + 0.158114i
\(181\) 7.65685 0.569129 0.284565 0.958657i \(-0.408151\pi\)
0.284565 + 0.958657i \(0.408151\pi\)
\(182\) 6.07107 6.07107i 0.450017 0.450017i
\(183\) 26.2843i 1.94299i
\(184\) 2.58579 0.190627
\(185\) −13.0000 4.00000i −0.955779 0.294086i
\(186\) 11.6569 0.854722
\(187\) 7.00000i 0.511891i
\(188\) 8.24264 8.24264i 0.601156 0.601156i
\(189\) 15.3137 1.11391
\(190\) 16.4853 + 8.24264i 1.19597 + 0.597984i
\(191\) 1.53553 + 1.53553i 0.111107 + 0.111107i 0.760475 0.649367i \(-0.224966\pi\)
−0.649367 + 0.760475i \(0.724966\pi\)
\(192\) −1.41421 + 1.41421i −0.102062 + 0.102062i
\(193\) 20.4853i 1.47456i −0.675586 0.737281i \(-0.736109\pi\)
0.675586 0.737281i \(-0.263891\pi\)
\(194\) 7.00000i 0.502571i
\(195\) 8.97056 + 4.48528i 0.642395 + 0.321198i
\(196\) 7.65685i 0.546918i
\(197\) −2.00000 + 2.00000i −0.142494 + 0.142494i −0.774755 0.632261i \(-0.782127\pi\)
0.632261 + 0.774755i \(0.282127\pi\)
\(198\) 3.82843i 0.272074i
\(199\) −3.89949 3.89949i −0.276428 0.276428i 0.555253 0.831681i \(-0.312621\pi\)
−0.831681 + 0.555253i \(0.812621\pi\)
\(200\) 3.00000 + 4.00000i 0.212132 + 0.282843i
\(201\) 3.51472 0.247909
\(202\) −11.0711 −0.778958
\(203\) −36.3137 −2.54872
\(204\) 2.58579 2.58579i 0.181041 0.181041i
\(205\) 4.94975 + 14.8492i 0.345705 + 1.03712i
\(206\) 13.5563i 0.944516i
\(207\) −2.58579 −0.179725
\(208\) 2.24264i 0.155499i
\(209\) −22.3137 22.3137i −1.54347 1.54347i
\(210\) −16.2426 + 5.41421i −1.12085 + 0.373616i
\(211\) −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
\(213\) −0.485281 + 0.485281i −0.0332509 + 0.0332509i
\(214\) 9.07107 + 9.07107i 0.620085 + 0.620085i
\(215\) −4.94975 14.8492i −0.337570 1.01271i
\(216\) −2.82843 + 2.82843i −0.192450 + 0.192450i
\(217\) 22.3137i 1.51475i
\(218\) 0.949747 + 0.949747i 0.0643250 + 0.0643250i
\(219\) 16.9706i 1.14676i
\(220\) −2.70711 8.12132i −0.182513 0.547539i
\(221\) 4.10051i 0.275830i
\(222\) 2.00000 + 12.0000i 0.134231 + 0.805387i
\(223\) 13.8787 + 13.8787i 0.929385 + 0.929385i 0.997666 0.0682810i \(-0.0217514\pi\)
−0.0682810 + 0.997666i \(0.521751\pi\)
\(224\) −2.70711 2.70711i −0.180876 0.180876i
\(225\) −3.00000 4.00000i −0.200000 0.266667i
\(226\) 3.82843i 0.254663i
\(227\) −7.48528 −0.496816 −0.248408 0.968656i \(-0.579907\pi\)
−0.248408 + 0.968656i \(0.579907\pi\)
\(228\) 16.4853i 1.09176i
\(229\) 1.41421i 0.0934539i −0.998908 0.0467269i \(-0.985121\pi\)
0.998908 0.0467269i \(-0.0148791\pi\)
\(230\) −5.48528 + 1.82843i −0.361689 + 0.120563i
\(231\) 29.3137 1.92870
\(232\) 6.70711 6.70711i 0.440343 0.440343i
\(233\) 0.0710678 0.0710678i 0.00465581 0.00465581i −0.704775 0.709431i \(-0.748952\pi\)
0.709431 + 0.704775i \(0.248952\pi\)
\(234\) 2.24264i 0.146606i
\(235\) −11.6569 + 23.3137i −0.760409 + 1.52082i
\(236\) 1.17157 1.17157i 0.0762629 0.0762629i
\(237\) 27.3137i 1.77422i
\(238\) 4.94975 + 4.94975i 0.320844 + 0.320844i
\(239\) 7.05025 7.05025i 0.456043 0.456043i −0.441311 0.897354i \(-0.645487\pi\)
0.897354 + 0.441311i \(0.145487\pi\)
\(240\) 2.00000 4.00000i 0.129099 0.258199i
\(241\) 0.757359 + 0.757359i 0.0487858 + 0.0487858i 0.731079 0.682293i \(-0.239017\pi\)
−0.682293 + 0.731079i \(0.739017\pi\)
\(242\) 3.65685i 0.235071i
\(243\) 7.07107 7.07107i 0.453609 0.453609i
\(244\) −9.29289 + 9.29289i −0.594917 + 0.594917i
\(245\) −5.41421 16.2426i −0.345901 1.03770i
\(246\) 9.89949 9.89949i 0.631169 0.631169i
\(247\) −13.0711 13.0711i −0.831692 0.831692i
\(248\) −4.12132 4.12132i −0.261704 0.261704i
\(249\) −2.34315 −0.148491
\(250\) −9.19239 6.36396i −0.581378 0.402492i
\(251\) −17.8995 + 17.8995i −1.12981 + 1.12981i −0.139598 + 0.990208i \(0.544581\pi\)
−0.990208 + 0.139598i \(0.955419\pi\)
\(252\) 2.70711 + 2.70711i 0.170532 + 0.170532i
\(253\) 9.89949 0.622376
\(254\) −2.58579 2.58579i −0.162247 0.162247i
\(255\) −3.65685 + 7.31371i −0.229001 + 0.458002i
\(256\) 1.00000 0.0625000
\(257\) 18.8284 1.17449 0.587243 0.809411i \(-0.300213\pi\)
0.587243 + 0.809411i \(0.300213\pi\)
\(258\) −9.89949 + 9.89949i −0.616316 + 0.616316i
\(259\) −22.9706 + 3.82843i −1.42732 + 0.237887i
\(260\) −1.58579 4.75736i −0.0983463 0.295039i
\(261\) −6.70711 + 6.70711i −0.415159 + 0.415159i
\(262\) −0.414214 0.414214i −0.0255902 0.0255902i
\(263\) −14.6066 + 14.6066i −0.900682 + 0.900682i −0.995495 0.0948134i \(-0.969775\pi\)
0.0948134 + 0.995495i \(0.469775\pi\)
\(264\) −5.41421 + 5.41421i −0.333222 + 0.333222i
\(265\) 6.00000 + 3.00000i 0.368577 + 0.184289i
\(266\) 31.5563 1.93484
\(267\) 20.9706 1.28338
\(268\) −1.24264 1.24264i −0.0759064 0.0759064i
\(269\) 17.7990i 1.08522i 0.839984 + 0.542612i \(0.182565\pi\)
−0.839984 + 0.542612i \(0.817435\pi\)
\(270\) 4.00000 8.00000i 0.243432 0.486864i
\(271\) −3.07107 −0.186554 −0.0932770 0.995640i \(-0.529734\pi\)
−0.0932770 + 0.995640i \(0.529734\pi\)
\(272\) −1.82843 −0.110865
\(273\) 17.1716 1.03927
\(274\) −8.41421 8.41421i −0.508321 0.508321i
\(275\) 11.4853 + 15.3137i 0.692589 + 0.923451i
\(276\) 3.65685 + 3.65685i 0.220117 + 0.220117i
\(277\) 7.79899i 0.468596i −0.972165 0.234298i \(-0.924721\pi\)
0.972165 0.234298i \(-0.0752791\pi\)
\(278\) 6.17157i 0.370146i
\(279\) 4.12132 + 4.12132i 0.246737 + 0.246737i
\(280\) 7.65685 + 3.82843i 0.457585 + 0.228792i
\(281\) 4.00000 + 4.00000i 0.238620 + 0.238620i 0.816279 0.577659i \(-0.196033\pi\)
−0.577659 + 0.816279i \(0.696033\pi\)
\(282\) 23.3137 1.38831
\(283\) 28.0000 1.66443 0.832214 0.554455i \(-0.187073\pi\)
0.832214 + 0.554455i \(0.187073\pi\)
\(284\) 0.343146 0.0203620
\(285\) 11.6569 + 34.9706i 0.690492 + 2.07148i
\(286\) 8.58579i 0.507688i
\(287\) 18.9497 + 18.9497i 1.11857 + 1.11857i
\(288\) −1.00000 −0.0589256
\(289\) −13.6569 −0.803344
\(290\) −9.48528 + 18.9706i −0.556995 + 1.11399i
\(291\) −9.89949 + 9.89949i −0.580319 + 0.580319i
\(292\) −6.00000 + 6.00000i −0.351123 + 0.351123i
\(293\) −1.77817 1.77817i −0.103882 0.103882i 0.653255 0.757138i \(-0.273403\pi\)
−0.757138 + 0.653255i \(0.773403\pi\)
\(294\) −10.8284 + 10.8284i −0.631527 + 0.631527i
\(295\) −1.65685 + 3.31371i −0.0964658 + 0.192932i
\(296\) 3.53553 4.94975i 0.205499 0.287698i
\(297\) −10.8284 + 10.8284i −0.628329 + 0.628329i
\(298\) 8.24264 0.477483
\(299\) 5.79899 0.335364
\(300\) −1.41421 + 9.89949i −0.0816497 + 0.571548i
\(301\) −18.9497 18.9497i −1.09225 1.09225i
\(302\) −12.0000 −0.690522
\(303\) −15.6569 15.6569i −0.899463 0.899463i
\(304\) −5.82843 + 5.82843i −0.334283 + 0.334283i
\(305\) 13.1421 26.2843i 0.752516 1.50503i
\(306\) 1.82843 0.104524
\(307\) −1.89949 1.89949i −0.108410 0.108410i 0.650821 0.759231i \(-0.274425\pi\)
−0.759231 + 0.650821i \(0.774425\pi\)
\(308\) −10.3640 10.3640i −0.590541 0.590541i
\(309\) 19.1716 19.1716i 1.09063 1.09063i
\(310\) 11.6569 + 5.82843i 0.662065 + 0.331032i
\(311\) −11.7782 + 11.7782i −0.667879 + 0.667879i −0.957225 0.289346i \(-0.906562\pi\)
0.289346 + 0.957225i \(0.406562\pi\)
\(312\) −3.17157 + 3.17157i −0.179555 + 0.179555i
\(313\) 0.686292i 0.0387915i −0.999812 0.0193957i \(-0.993826\pi\)
0.999812 0.0193957i \(-0.00617424\pi\)
\(314\) −5.87868 5.87868i −0.331753 0.331753i
\(315\) −7.65685 3.82843i −0.431415 0.215707i
\(316\) −9.65685 + 9.65685i −0.543240 + 0.543240i
\(317\) 15.5355 + 15.5355i 0.872563 + 0.872563i 0.992751 0.120189i \(-0.0383499\pi\)
−0.120189 + 0.992751i \(0.538350\pi\)
\(318\) 6.00000i 0.336463i
\(319\) 25.6777 25.6777i 1.43767 1.43767i
\(320\) −2.12132 + 0.707107i −0.118585 + 0.0395285i
\(321\) 25.6569i 1.43203i
\(322\) −7.00000 + 7.00000i −0.390095 + 0.390095i
\(323\) 10.6569 10.6569i 0.592963 0.592963i
\(324\) −11.0000 −0.611111
\(325\) 6.72792 + 8.97056i 0.373198 + 0.497597i
\(326\) 14.6569i 0.811768i
\(327\) 2.68629i 0.148552i
\(328\) −7.00000 −0.386510
\(329\) 44.6274i 2.46039i
\(330\) 7.65685 15.3137i 0.421496 0.842992i
\(331\) 2.58579 + 2.58579i 0.142128 + 0.142128i 0.774591 0.632463i \(-0.217956\pi\)
−0.632463 + 0.774591i \(0.717956\pi\)
\(332\) 0.828427 + 0.828427i 0.0454658 + 0.0454658i
\(333\) −3.53553 + 4.94975i −0.193746 + 0.271244i
\(334\) 1.17157i 0.0641056i
\(335\) 3.51472 + 1.75736i 0.192030 + 0.0960148i
\(336\) 7.65685i 0.417716i
\(337\) 5.65685 + 5.65685i 0.308148 + 0.308148i 0.844191 0.536043i \(-0.180081\pi\)
−0.536043 + 0.844191i \(0.680081\pi\)
\(338\) 7.97056i 0.433541i
\(339\) −5.41421 + 5.41421i −0.294060 + 0.294060i
\(340\) 3.87868 1.29289i 0.210351 0.0701170i
\(341\) −15.7782 15.7782i −0.854436 0.854436i
\(342\) 5.82843 5.82843i 0.315165 0.315165i
\(343\) −1.77817 1.77817i −0.0960124 0.0960124i
\(344\) 7.00000 0.377415
\(345\) −10.3431 5.17157i −0.556856 0.278428i
\(346\) −6.02082 6.02082i −0.323681 0.323681i
\(347\) 17.3137i 0.929449i 0.885455 + 0.464724i \(0.153847\pi\)
−0.885455 + 0.464724i \(0.846153\pi\)
\(348\) 18.9706 1.01693
\(349\) 4.14214i 0.221723i −0.993836 0.110862i \(-0.964639\pi\)
0.993836 0.110862i \(-0.0353611\pi\)
\(350\) −18.9497 2.70711i −1.01291 0.144701i
\(351\) −6.34315 + 6.34315i −0.338572 + 0.338572i
\(352\) 3.82843 0.204056
\(353\) 7.34315 0.390836 0.195418 0.980720i \(-0.437394\pi\)
0.195418 + 0.980720i \(0.437394\pi\)
\(354\) 3.31371 0.176122
\(355\) −0.727922 + 0.242641i −0.0386341 + 0.0128780i
\(356\) −7.41421 7.41421i −0.392953 0.392953i
\(357\) 14.0000i 0.740959i
\(358\) −14.4853 + 14.4853i −0.765571 + 0.765571i
\(359\) 30.5269i 1.61115i 0.592495 + 0.805574i \(0.298143\pi\)
−0.592495 + 0.805574i \(0.701857\pi\)
\(360\) 2.12132 0.707107i 0.111803 0.0372678i
\(361\) 48.9411i 2.57585i
\(362\) 7.65685i 0.402435i
\(363\) −5.17157 + 5.17157i −0.271437 + 0.271437i
\(364\) −6.07107 6.07107i −0.318210 0.318210i
\(365\) 8.48528 16.9706i 0.444140 0.888280i
\(366\) −26.2843 −1.37390
\(367\) 13.0919 13.0919i 0.683391 0.683391i −0.277372 0.960763i \(-0.589463\pi\)
0.960763 + 0.277372i \(0.0894634\pi\)
\(368\) 2.58579i 0.134793i
\(369\) 7.00000 0.364405
\(370\) −4.00000 + 13.0000i −0.207950 + 0.675838i
\(371\) 11.4853 0.596286
\(372\) 11.6569i 0.604380i
\(373\) −10.8284 + 10.8284i −0.560675 + 0.560675i −0.929499 0.368824i \(-0.879760\pi\)
0.368824 + 0.929499i \(0.379760\pi\)
\(374\) −7.00000 −0.361961
\(375\) −4.00000 22.0000i −0.206559 1.13608i
\(376\) −8.24264 8.24264i −0.425082 0.425082i
\(377\) 15.0416 15.0416i 0.774683 0.774683i
\(378\) 15.3137i 0.787652i
\(379\) 18.0000i 0.924598i 0.886724 + 0.462299i \(0.152975\pi\)
−0.886724 + 0.462299i \(0.847025\pi\)
\(380\) 8.24264 16.4853i 0.422839 0.845677i
\(381\) 7.31371i 0.374693i
\(382\) 1.53553 1.53553i 0.0785647 0.0785647i
\(383\) 16.5858i 0.847494i −0.905781 0.423747i \(-0.860715\pi\)
0.905781 0.423747i \(-0.139285\pi\)
\(384\) 1.41421 + 1.41421i 0.0721688 + 0.0721688i
\(385\) 29.3137 + 14.6569i 1.49396 + 0.746982i
\(386\) −20.4853 −1.04267
\(387\) −7.00000 −0.355830
\(388\) 7.00000 0.355371
\(389\) −3.77817 + 3.77817i −0.191561 + 0.191561i −0.796370 0.604809i \(-0.793249\pi\)
0.604809 + 0.796370i \(0.293249\pi\)
\(390\) 4.48528 8.97056i 0.227121 0.454242i
\(391\) 4.72792i 0.239101i
\(392\) 7.65685 0.386730
\(393\) 1.17157i 0.0590980i
\(394\) 2.00000 + 2.00000i 0.100759 + 0.100759i
\(395\) 13.6569 27.3137i 0.687151 1.37430i
\(396\) −3.82843 −0.192386
\(397\) 8.48528 + 8.48528i 0.425864 + 0.425864i 0.887217 0.461353i \(-0.152636\pi\)
−0.461353 + 0.887217i \(0.652636\pi\)
\(398\) −3.89949 + 3.89949i −0.195464 + 0.195464i
\(399\) 44.6274 + 44.6274i 2.23417 + 2.23417i
\(400\) 4.00000 3.00000i 0.200000 0.150000i
\(401\) −7.07107 + 7.07107i −0.353112 + 0.353112i −0.861266 0.508154i \(-0.830328\pi\)
0.508154 + 0.861266i \(0.330328\pi\)
\(402\) 3.51472i 0.175298i
\(403\) −9.24264 9.24264i −0.460409 0.460409i
\(404\) 11.0711i 0.550806i
\(405\) 23.3345 7.77817i 1.15950 0.386501i
\(406\) 36.3137i 1.80222i
\(407\) 13.5355 18.9497i 0.670932 0.939304i
\(408\) −2.58579 2.58579i −0.128016 0.128016i
\(409\) −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
\(411\) 23.7990i 1.17392i
\(412\) −13.5563 −0.667873
\(413\) 6.34315i 0.312126i
\(414\) 2.58579i 0.127084i
\(415\) −2.34315 1.17157i −0.115021 0.0575103i
\(416\) 2.24264 0.109955
\(417\) −8.72792 + 8.72792i −0.427408 + 0.427408i
\(418\) −22.3137 + 22.3137i −1.09140 + 1.09140i
\(419\) 26.9706i 1.31760i −0.752319 0.658799i \(-0.771065\pi\)
0.752319 0.658799i \(-0.228935\pi\)
\(420\) 5.41421 + 16.2426i 0.264187 + 0.792560i
\(421\) −25.3137 + 25.3137i −1.23371 + 1.23371i −0.271188 + 0.962526i \(0.587417\pi\)
−0.962526 + 0.271188i \(0.912583\pi\)
\(422\) 9.00000i 0.438113i
\(423\) 8.24264 + 8.24264i 0.400771 + 0.400771i
\(424\) −2.12132 + 2.12132i −0.103020 + 0.103020i
\(425\) −7.31371 + 5.48528i −0.354767 + 0.266075i
\(426\) 0.485281 + 0.485281i 0.0235120 + 0.0235120i
\(427\) 50.3137i 2.43485i
\(428\) 9.07107 9.07107i 0.438467 0.438467i
\(429\) −12.1421 + 12.1421i −0.586228 + 0.586228i
\(430\) −14.8492 + 4.94975i −0.716094 + 0.238698i
\(431\) −20.5061 + 20.5061i −0.987744 + 0.987744i −0.999926 0.0121819i \(-0.996122\pi\)
0.0121819 + 0.999926i \(0.496122\pi\)
\(432\) 2.82843 + 2.82843i 0.136083 + 0.136083i
\(433\) 5.14214 + 5.14214i 0.247115 + 0.247115i 0.819786 0.572670i \(-0.194093\pi\)
−0.572670 + 0.819786i \(0.694093\pi\)
\(434\) 22.3137 1.07109
\(435\) −40.2426 + 13.4142i −1.92949 + 0.643162i
\(436\) 0.949747 0.949747i 0.0454847 0.0454847i
\(437\) 15.0711 + 15.0711i 0.720947 + 0.720947i
\(438\) −16.9706 −0.810885
\(439\) 2.22183 + 2.22183i 0.106042 + 0.106042i 0.758137 0.652095i \(-0.226110\pi\)
−0.652095 + 0.758137i \(0.726110\pi\)
\(440\) −8.12132 + 2.70711i −0.387169 + 0.129056i
\(441\) −7.65685 −0.364612
\(442\) −4.10051 −0.195041
\(443\) −5.34315 + 5.34315i −0.253861 + 0.253861i −0.822551 0.568691i \(-0.807450\pi\)
0.568691 + 0.822551i \(0.307450\pi\)
\(444\) 12.0000 2.00000i 0.569495 0.0949158i
\(445\) 20.9706 + 10.4853i 0.994100 + 0.497050i
\(446\) 13.8787 13.8787i 0.657175 0.657175i
\(447\) 11.6569 + 11.6569i 0.551350 + 0.551350i
\(448\) −2.70711 + 2.70711i −0.127899 + 0.127899i
\(449\) −25.6274 + 25.6274i −1.20943 + 1.20943i −0.238222 + 0.971211i \(0.576565\pi\)
−0.971211 + 0.238222i \(0.923435\pi\)
\(450\) −4.00000 + 3.00000i −0.188562 + 0.141421i
\(451\) −26.7990 −1.26192
\(452\) 3.82843 0.180074
\(453\) −16.9706 16.9706i −0.797347 0.797347i
\(454\) 7.48528i 0.351302i
\(455\) 17.1716 + 8.58579i 0.805016 + 0.402508i
\(456\) −16.4853 −0.771994
\(457\) −3.68629 −0.172437 −0.0862187 0.996276i \(-0.527478\pi\)
−0.0862187 + 0.996276i \(0.527478\pi\)
\(458\) −1.41421 −0.0660819
\(459\) −5.17157 5.17157i −0.241388 0.241388i
\(460\) 1.82843 + 5.48528i 0.0852509 + 0.255753i
\(461\) 10.4645 + 10.4645i 0.487379 + 0.487379i 0.907478 0.420099i \(-0.138005\pi\)
−0.420099 + 0.907478i \(0.638005\pi\)
\(462\) 29.3137i 1.36380i
\(463\) 29.9411i 1.39148i 0.718293 + 0.695741i \(0.244924\pi\)
−0.718293 + 0.695741i \(0.755076\pi\)
\(464\) −6.70711 6.70711i −0.311370 0.311370i
\(465\) 8.24264 + 24.7279i 0.382243 + 1.14673i
\(466\) −0.0710678 0.0710678i −0.00329215 0.00329215i
\(467\) 2.31371 0.107066 0.0535328 0.998566i \(-0.482952\pi\)
0.0535328 + 0.998566i \(0.482952\pi\)
\(468\) −2.24264 −0.103666
\(469\) 6.72792 0.310667
\(470\) 23.3137 + 11.6569i 1.07538 + 0.537691i
\(471\) 16.6274i 0.766151i
\(472\) −1.17157 1.17157i −0.0539260 0.0539260i
\(473\) 26.7990 1.23222
\(474\) −27.3137 −1.25456
\(475\) −5.82843 + 40.7990i −0.267427 + 1.87199i
\(476\) 4.94975 4.94975i 0.226871 0.226871i
\(477\) 2.12132 2.12132i 0.0971286 0.0971286i
\(478\) −7.05025 7.05025i −0.322471 0.322471i
\(479\) 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
\(481\) 7.92893 11.1005i 0.361528 0.506139i
\(482\) 0.757359 0.757359i 0.0344968 0.0344968i
\(483\) −19.7990 −0.900885
\(484\) 3.65685 0.166221
\(485\) −14.8492 + 4.94975i −0.674269 + 0.224756i
\(486\) −7.07107 7.07107i −0.320750 0.320750i
\(487\) 26.9706 1.22215 0.611076 0.791572i \(-0.290737\pi\)
0.611076 + 0.791572i \(0.290737\pi\)
\(488\) 9.29289 + 9.29289i 0.420670 + 0.420670i
\(489\) −20.7279 + 20.7279i −0.937349 + 0.937349i
\(490\) −16.2426 + 5.41421i −0.733768 + 0.244589i
\(491\) 17.7990 0.803257 0.401629 0.915803i \(-0.368444\pi\)
0.401629 + 0.915803i \(0.368444\pi\)
\(492\) −9.89949 9.89949i −0.446304 0.446304i
\(493\) 12.2635 + 12.2635i 0.552318 + 0.552318i
\(494\) −13.0711 + 13.0711i −0.588095 + 0.588095i
\(495\) 8.12132 2.70711i 0.365026 0.121675i
\(496\) −4.12132 + 4.12132i −0.185053 + 0.185053i
\(497\) −0.928932 + 0.928932i −0.0416683 + 0.0416683i
\(498\) 2.34315i 0.104999i
\(499\) −10.2426 10.2426i −0.458524 0.458524i 0.439647 0.898171i \(-0.355104\pi\)
−0.898171 + 0.439647i \(0.855104\pi\)
\(500\) −6.36396 + 9.19239i −0.284605 + 0.411096i
\(501\) −1.65685 + 1.65685i −0.0740228 + 0.0740228i
\(502\) 17.8995 + 17.8995i 0.798894 + 0.798894i
\(503\) 32.5858i 1.45293i −0.687204 0.726464i \(-0.741162\pi\)
0.687204 0.726464i \(-0.258838\pi\)
\(504\) 2.70711 2.70711i 0.120584 0.120584i
\(505\) −7.82843 23.4853i −0.348360 1.04508i
\(506\) 9.89949i 0.440086i
\(507\) 11.2721 11.2721i 0.500611 0.500611i
\(508\) −2.58579 + 2.58579i −0.114726 + 0.114726i
\(509\) 1.27208 0.0563839 0.0281919 0.999603i \(-0.491025\pi\)
0.0281919 + 0.999603i \(0.491025\pi\)
\(510\) 7.31371 + 3.65685i 0.323856 + 0.161928i
\(511\) 32.4853i 1.43706i
\(512\) 1.00000i 0.0441942i
\(513\) −32.9706 −1.45569
\(514\) 18.8284i 0.830486i
\(515\) 28.7574 9.58579i 1.26720 0.422400i
\(516\) 9.89949 + 9.89949i 0.435801 + 0.435801i
\(517\) −31.5563 31.5563i −1.38785 1.38785i
\(518\) 3.82843 + 22.9706i 0.168211 + 1.00927i
\(519\) 17.0294i 0.747509i
\(520\) −4.75736 + 1.58579i −0.208624 + 0.0695413i
\(521\) 27.6274i 1.21038i −0.796081 0.605190i \(-0.793097\pi\)
0.796081 0.605190i \(-0.206903\pi\)
\(522\) 6.70711 + 6.70711i 0.293562 + 0.293562i
\(523\) 43.6569i 1.90898i 0.298241 + 0.954490i \(0.403600\pi\)
−0.298241 + 0.954490i \(0.596400\pi\)
\(524\) −0.414214 + 0.414214i −0.0180950 + 0.0180950i
\(525\) −22.9706 30.6274i −1.00252 1.33669i
\(526\) 14.6066 + 14.6066i 0.636878 + 0.636878i
\(527\) 7.53553 7.53553i 0.328253 0.328253i
\(528\) 5.41421 + 5.41421i 0.235623 + 0.235623i
\(529\) 16.3137 0.709292
\(530\) 3.00000 6.00000i 0.130312 0.260623i
\(531\) 1.17157 + 1.17157i 0.0508419 + 0.0508419i
\(532\) 31.5563i 1.36814i
\(533\) −15.6985 −0.679977
\(534\) 20.9706i 0.907485i
\(535\) −12.8284 + 25.6569i −0.554621 + 1.10924i
\(536\) −1.24264 + 1.24264i −0.0536739 + 0.0536739i
\(537\) −40.9706 −1.76801
\(538\) 17.7990 0.767369
\(539\) 29.3137 1.26263
\(540\) −8.00000 4.00000i −0.344265 0.172133i
\(541\) −27.7990 27.7990i −1.19517 1.19517i −0.975595 0.219577i \(-0.929532\pi\)
−0.219577 0.975595i \(-0.570468\pi\)
\(542\) 3.07107i 0.131914i
\(543\) 10.8284 10.8284i 0.464692 0.464692i
\(544\) 1.82843i 0.0783932i
\(545\) −1.34315 + 2.68629i −0.0575340 + 0.115068i
\(546\) 17.1716i 0.734875i
\(547\) 27.8284i 1.18986i 0.803778 + 0.594929i \(0.202820\pi\)
−0.803778 + 0.594929i \(0.797180\pi\)
\(548\) −8.41421 + 8.41421i −0.359437 + 0.359437i
\(549\) −9.29289 9.29289i −0.396611 0.396611i
\(550\) 15.3137 11.4853i 0.652979 0.489734i
\(551\) 78.1838 3.33074
\(552\) 3.65685 3.65685i 0.155646 0.155646i
\(553\) 52.2843i 2.22335i
\(554\) −7.79899 −0.331347
\(555\) −24.0416 + 12.7279i −1.02051 + 0.540270i
\(556\) 6.17157 0.261733
\(557\) 23.2132i 0.983575i −0.870715 0.491787i \(-0.836344\pi\)
0.870715 0.491787i \(-0.163656\pi\)
\(558\) 4.12132 4.12132i 0.174469 0.174469i
\(559\) 15.6985 0.663975
\(560\) 3.82843 7.65685i 0.161781 0.323561i
\(561\) −9.89949 9.89949i −0.417957 0.417957i
\(562\) 4.00000 4.00000i 0.168730 0.168730i
\(563\) 24.1127i 1.01623i −0.861290 0.508115i \(-0.830343\pi\)
0.861290 0.508115i \(-0.169657\pi\)
\(564\) 23.3137i 0.981684i
\(565\) −8.12132 + 2.70711i −0.341667 + 0.113889i
\(566\) 28.0000i 1.17693i
\(567\) 29.7782 29.7782i 1.25057 1.25057i
\(568\) 0.343146i 0.0143981i
\(569\) −1.68629 1.68629i −0.0706930 0.0706930i 0.670876 0.741569i \(-0.265918\pi\)
−0.741569 + 0.670876i \(0.765918\pi\)
\(570\) 34.9706 11.6569i 1.46476 0.488252i
\(571\) 46.7990 1.95848 0.979238 0.202712i \(-0.0649755\pi\)
0.979238 + 0.202712i \(0.0649755\pi\)
\(572\) 8.58579 0.358990
\(573\) 4.34315 0.181438
\(574\) 18.9497 18.9497i 0.790947 0.790947i
\(575\) −7.75736 10.3431i −0.323504 0.431339i
\(576\) 1.00000i 0.0416667i
\(577\) 21.6569 0.901587 0.450793 0.892628i \(-0.351141\pi\)
0.450793 + 0.892628i \(0.351141\pi\)
\(578\) 13.6569i 0.568050i
\(579\) −28.9706 28.9706i −1.20398 1.20398i
\(580\) 18.9706 + 9.48528i 0.787710 + 0.393855i
\(581\) −4.48528 −0.186081
\(582\) 9.89949 + 9.89949i 0.410347 + 0.410347i
\(583\) −8.12132 + 8.12132i −0.336351 + 0.336351i
\(584\) 6.00000 + 6.00000i 0.248282 + 0.248282i
\(585\) 4.75736 1.58579i 0.196693 0.0655642i
\(586\) −1.77817 + 1.77817i −0.0734557 + 0.0734557i
\(587\) 4.45584i 0.183912i 0.995763 + 0.0919562i \(0.0293120\pi\)
−0.995763 + 0.0919562i \(0.970688\pi\)
\(588\) 10.8284 + 10.8284i 0.446557 + 0.446557i
\(589\) 48.0416i 1.97952i
\(590\) 3.31371 + 1.65685i 0.136423 + 0.0682116i
\(591\) 5.65685i 0.232692i
\(592\) −4.94975 3.53553i −0.203433 0.145310i
\(593\) −26.1421 26.1421i −1.07353 1.07353i −0.997073 0.0764559i \(-0.975640\pi\)
−0.0764559 0.997073i \(-0.524360\pi\)
\(594\) 10.8284 + 10.8284i 0.444296 + 0.444296i
\(595\) −7.00000 + 14.0000i −0.286972 + 0.573944i
\(596\) 8.24264i 0.337632i
\(597\) −11.0294 −0.451405
\(598\) 5.79899i 0.237138i
\(599\) 33.7574i 1.37929i 0.724148 + 0.689644i \(0.242233\pi\)
−0.724148 + 0.689644i \(0.757767\pi\)
\(600\) 9.89949 + 1.41421i 0.404145 + 0.0577350i
\(601\) −16.5147 −0.673649 −0.336825 0.941567i \(-0.609353\pi\)
−0.336825 + 0.941567i \(0.609353\pi\)
\(602\) −18.9497 + 18.9497i −0.772334 + 0.772334i
\(603\) 1.24264 1.24264i 0.0506042 0.0506042i
\(604\) 12.0000i 0.488273i
\(605\) −7.75736 + 2.58579i −0.315382 + 0.105127i
\(606\) −15.6569 + 15.6569i −0.636016 + 0.636016i
\(607\) 34.1838i 1.38748i 0.720227 + 0.693738i \(0.244037\pi\)
−0.720227 + 0.693738i \(0.755963\pi\)
\(608\) 5.82843 + 5.82843i 0.236374 + 0.236374i
\(609\) −51.3553 + 51.3553i −2.08102 + 2.08102i
\(610\) −26.2843 13.1421i −1.06422 0.532110i
\(611\) −18.4853 18.4853i −0.747834 0.747834i
\(612\) 1.82843i 0.0739098i
\(613\) −12.1213 + 12.1213i −0.489576 + 0.489576i −0.908172 0.418597i \(-0.862522\pi\)
0.418597 + 0.908172i \(0.362522\pi\)
\(614\) −1.89949 + 1.89949i −0.0766574 + 0.0766574i
\(615\) 28.0000 + 14.0000i 1.12907 + 0.564534i
\(616\) −10.3640 + 10.3640i −0.417576 + 0.417576i
\(617\) −27.7279 27.7279i −1.11628 1.11628i −0.992282 0.124002i \(-0.960427\pi\)
−0.124002 0.992282i \(-0.539573\pi\)
\(618\) −19.1716 19.1716i −0.771194 0.771194i
\(619\) 46.5980 1.87293 0.936465 0.350760i \(-0.114077\pi\)
0.936465 + 0.350760i \(0.114077\pi\)
\(620\) 5.82843 11.6569i 0.234075 0.468151i
\(621\) 7.31371 7.31371i 0.293489 0.293489i
\(622\) 11.7782 + 11.7782i 0.472262 + 0.472262i
\(623\) 40.1421 1.60826
\(624\) 3.17157 + 3.17157i 0.126965 + 0.126965i
\(625\) 7.00000 24.0000i 0.280000 0.960000i
\(626\) −0.686292 −0.0274297
\(627\) −63.1127 −2.52048
\(628\) −5.87868 + 5.87868i −0.234585 + 0.234585i
\(629\) 9.05025 + 6.46447i 0.360857 + 0.257755i
\(630\) −3.82843 + 7.65685i −0.152528 + 0.305056i
\(631\) −18.8492 + 18.8492i −0.750376 + 0.750376i −0.974549 0.224173i \(-0.928032\pi\)
0.224173 + 0.974549i \(0.428032\pi\)
\(632\) 9.65685 + 9.65685i 0.384129 + 0.384129i
\(633\) −12.7279 + 12.7279i −0.505889 + 0.505889i
\(634\) 15.5355 15.5355i 0.616995 0.616995i
\(635\) 3.65685 7.31371i 0.145118 0.290236i
\(636\) −6.00000 −0.237915
\(637\) 17.1716 0.680362
\(638\) −25.6777 25.6777i −1.01659 1.01659i
\(639\) 0.343146i 0.0135746i
\(640\) 0.707107 + 2.12132i 0.0279508 + 0.0838525i
\(641\) 25.2843 0.998669 0.499334 0.866409i \(-0.333578\pi\)
0.499334 + 0.866409i \(0.333578\pi\)
\(642\) 25.6569 1.01260
\(643\) −24.5147 −0.966766 −0.483383 0.875409i \(-0.660592\pi\)
−0.483383 + 0.875409i \(0.660592\pi\)
\(644\) 7.00000 + 7.00000i 0.275839 + 0.275839i
\(645\) −28.0000 14.0000i −1.10250 0.551249i
\(646\) −10.6569 10.6569i −0.419288 0.419288i
\(647\) 27.3137i 1.07381i −0.843642 0.536906i \(-0.819593\pi\)
0.843642 0.536906i \(-0.180407\pi\)
\(648\) 11.0000i 0.432121i
\(649\) −4.48528 4.48528i −0.176063 0.176063i
\(650\) 8.97056 6.72792i 0.351854 0.263891i
\(651\) 31.5563 + 31.5563i 1.23679 + 1.23679i
\(652\) 14.6569 0.574007
\(653\) −19.6569 −0.769232 −0.384616 0.923077i \(-0.625666\pi\)
−0.384616 + 0.923077i \(0.625666\pi\)
\(654\) 2.68629 0.105042
\(655\) 0.585786 1.17157i 0.0228886 0.0457771i
\(656\) 7.00000i 0.273304i
\(657\) −6.00000 6.00000i −0.234082 0.234082i
\(658\) 44.6274 1.73976
\(659\) −20.1421 −0.784626 −0.392313 0.919832i \(-0.628325\pi\)
−0.392313 + 0.919832i \(0.628325\pi\)
\(660\) −15.3137 7.65685i −0.596085 0.298043i
\(661\) −20.2635 + 20.2635i −0.788157 + 0.788157i −0.981192 0.193035i \(-0.938167\pi\)
0.193035 + 0.981192i \(0.438167\pi\)
\(662\) 2.58579 2.58579i 0.100499 0.100499i
\(663\) −5.79899 5.79899i −0.225214 0.225214i
\(664\) 0.828427 0.828427i 0.0321492 0.0321492i
\(665\) 22.3137 + 66.9411i 0.865289 + 2.59587i
\(666\) 4.94975 + 3.53553i 0.191799 + 0.136999i
\(667\) −17.3431 + 17.3431i −0.671529 + 0.671529i
\(668\) 1.17157 0.0453295
\(669\) 39.2548 1.51768
\(670\) 1.75736 3.51472i 0.0678927 0.135785i
\(671\) 35.5772 + 35.5772i 1.37344 + 1.37344i
\(672\) −7.65685 −0.295370
\(673\) −10.5147 10.5147i −0.405313 0.405313i 0.474788 0.880100i \(-0.342525\pi\)
−0.880100 + 0.474788i \(0.842525\pi\)
\(674\) 5.65685 5.65685i 0.217894 0.217894i
\(675\) 19.7990 + 2.82843i 0.762063 + 0.108866i
\(676\) −7.97056 −0.306560
\(677\) −13.5147 13.5147i −0.519413 0.519413i 0.397981 0.917394i \(-0.369711\pi\)
−0.917394 + 0.397981i \(0.869711\pi\)
\(678\) 5.41421 + 5.41421i 0.207932 + 0.207932i
\(679\) −18.9497 + 18.9497i −0.727225 + 0.727225i
\(680\) −1.29289 3.87868i −0.0495802 0.148741i
\(681\) −10.5858 + 10.5858i −0.405648 + 0.405648i
\(682\) −15.7782 + 15.7782i −0.604178 + 0.604178i
\(683\) 12.3137i 0.471171i 0.971854 + 0.235585i \(0.0757008\pi\)
−0.971854 + 0.235585i \(0.924299\pi\)
\(684\) −5.82843 5.82843i −0.222855 0.222855i
\(685\) 11.8995 23.7990i 0.454656 0.909313i
\(686\) −1.77817 + 1.77817i −0.0678910 + 0.0678910i
\(687\) −2.00000 2.00000i −0.0763048 0.0763048i
\(688\) 7.00000i 0.266872i
\(689\) −4.75736 + 4.75736i −0.181241 + 0.181241i
\(690\) −5.17157 + 10.3431i −0.196878 + 0.393757i
\(691\) 9.97056i 0.379298i 0.981852 + 0.189649i \(0.0607350\pi\)
−0.981852 + 0.189649i \(0.939265\pi\)
\(692\) −6.02082 + 6.02082i −0.228877 + 0.228877i
\(693\) 10.3640 10.3640i 0.393694 0.393694i
\(694\) 17.3137 0.657219
\(695\) −13.0919 + 4.36396i −0.496603 + 0.165534i
\(696\) 18.9706i 0.719077i
\(697\) 12.7990i 0.484796i
\(698\) −4.14214 −0.156782
\(699\) 0.201010i 0.00760290i
\(700\) −2.70711 + 18.9497i −0.102319 + 0.716233i
\(701\) 4.34315 + 4.34315i 0.164038 + 0.164038i 0.784353 0.620315i \(-0.212995\pi\)
−0.620315 + 0.784353i \(0.712995\pi\)
\(702\) 6.34315 + 6.34315i 0.239407 + 0.239407i
\(703\) 49.4558 8.24264i 1.86526 0.310877i
\(704\) 3.82843i 0.144289i
\(705\) 16.4853 + 49.4558i 0.620872 + 1.86261i
\(706\) 7.34315i 0.276363i
\(707\) −29.9706 29.9706i −1.12716 1.12716i
\(708\) 3.31371i 0.124537i
\(709\) 10.7071 10.7071i 0.402114 0.402114i −0.476864 0.878977i \(-0.658226\pi\)
0.878977 + 0.476864i \(0.158226\pi\)
\(710\) 0.242641 + 0.727922i 0.00910614 + 0.0273184i
\(711\) −9.65685 9.65685i −0.362160 0.362160i
\(712\) −7.41421 + 7.41421i −0.277859 + 0.277859i
\(713\) 10.6569 + 10.6569i 0.399102 + 0.399102i
\(714\) 14.0000 0.523937
\(715\) −18.2132 + 6.07107i −0.681135 + 0.227045i
\(716\) 14.4853 + 14.4853i 0.541340 + 0.541340i
\(717\) 19.9411i 0.744715i
\(718\) 30.5269 1.13925
\(719\) 24.1421i 0.900350i 0.892940 + 0.450175i \(0.148638\pi\)
−0.892940 + 0.450175i \(0.851362\pi\)
\(720\) −0.707107 2.12132i −0.0263523 0.0790569i
\(721\) 36.6985 36.6985i 1.36672 1.36672i
\(722\) −48.9411 −1.82140
\(723\) 2.14214 0.0796669
\(724\) −7.65685 −0.284565
\(725\) −46.9497 6.70711i −1.74367 0.249096i
\(726\) 5.17157 + 5.17157i 0.191935 + 0.191935i
\(727\) 13.8579i 0.513960i 0.966417 + 0.256980i \(0.0827274\pi\)
−0.966417 + 0.256980i \(0.917273\pi\)
\(728\) −6.07107 + 6.07107i −0.225009 + 0.225009i
\(729\) 13.0000i 0.481481i
\(730\) −16.9706 8.48528i −0.628109 0.314054i
\(731\) 12.7990i 0.473388i
\(732\) 26.2843i 0.971495i
\(733\) −22.7487 + 22.7487i −0.840244 + 0.840244i −0.988890 0.148647i \(-0.952508\pi\)
0.148647 + 0.988890i \(0.452508\pi\)
\(734\) −13.0919 13.0919i −0.483230 0.483230i
\(735\) −30.6274 15.3137i −1.12971 0.564855i
\(736\) −2.58579 −0.0953134
\(737\) −4.75736 + 4.75736i −0.175240 + 0.175240i
\(738\) 7.00000i 0.257674i
\(739\) −10.7990 −0.397247 −0.198624 0.980076i \(-0.563647\pi\)
−0.198624 + 0.980076i \(0.563647\pi\)
\(740\) 13.0000 + 4.00000i 0.477890 + 0.147043i
\(741\) −36.9706 −1.35815
\(742\) 11.4853i 0.421638i
\(743\) 5.05025 5.05025i 0.185276 0.185276i −0.608374 0.793650i \(-0.708178\pi\)
0.793650 + 0.608374i \(0.208178\pi\)
\(744\) −11.6569 −0.427361
\(745\) 5.82843 + 17.4853i 0.213537 + 0.640611i
\(746\) 10.8284 + 10.8284i 0.396457 + 0.396457i
\(747\) −0.828427 + 0.828427i −0.0303106 + 0.0303106i
\(748\) 7.00000i 0.255945i
\(749\) 49.1127i 1.79454i
\(750\) −22.0000 + 4.00000i −0.803326 + 0.146059i
\(751\) 16.0416i 0.585367i −0.956209 0.292684i \(-0.905452\pi\)
0.956209 0.292684i \(-0.0945483\pi\)
\(752\) −8.24264 + 8.24264i −0.300578 + 0.300578i
\(753\) 50.6274i 1.84497i
\(754\) −15.0416 15.0416i −0.547784 0.547784i
\(755\) −8.48528 25.4558i −0.308811 0.926433i
\(756\) −15.3137 −0.556954
\(757\) 27.6569 1.00521 0.502603 0.864517i \(-0.332376\pi\)
0.502603 + 0.864517i \(0.332376\pi\)
\(758\) 18.0000 0.653789
\(759\) 14.0000 14.0000i 0.508168 0.508168i
\(760\) −16.4853 8.24264i −0.597984 0.298992i
\(761\) 11.6863i 0.423628i −0.977310 0.211814i \(-0.932063\pi\)
0.977310 0.211814i \(-0.0679371\pi\)
\(762\) −7.31371 −0.264948
\(763\) 5.14214i 0.186158i
\(764\) −1.53553 1.53553i −0.0555537 0.0555537i
\(765\) 1.29289 + 3.87868i 0.0467447 + 0.140234i
\(766\) −16.5858 −0.599269
\(767\) −2.62742 2.62742i −0.0948705 0.0948705i
\(768\) 1.41421 1.41421i 0.0510310 0.0510310i
\(769\) −19.1716 19.1716i −0.691345 0.691345i 0.271183 0.962528i \(-0.412585\pi\)
−0.962528 + 0.271183i \(0.912585\pi\)
\(770\) 14.6569 29.3137i 0.528196 1.05639i
\(771\) 26.6274 26.6274i 0.958963 0.958963i
\(772\) 20.4853i 0.737281i
\(773\) 10.1213 + 10.1213i 0.364039 + 0.364039i 0.865297 0.501259i \(-0.167130\pi\)
−0.501259 + 0.865297i \(0.667130\pi\)
\(774\) 7.00000i 0.251610i
\(775\) −4.12132 + 28.8492i −0.148042 + 1.03630i
\(776\) 7.00000i 0.251285i
\(777\) −27.0711 + 37.8995i −0.971169 + 1.35964i
\(778\) 3.77817 + 3.77817i 0.135454