Properties

Label 370.2.h.c.117.1
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 117.1
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 370.117
Dual form 370.2.h.c.253.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-1.41421 - 1.41421i) q^{3} +1.00000 q^{4} +(-0.707107 + 2.12132i) q^{5} +(-1.41421 - 1.41421i) q^{6} +(2.70711 + 2.70711i) q^{7} +1.00000 q^{8} +1.00000i q^{9} +O(q^{10})\) \(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} +(2.70711 + 2.70711i) q^{7} +1.00000 q^{8} +1.00000i q^{9} +(-0.707107 + 2.12132i) q^{10} +3.82843i q^{11} +(-1.41421 - 1.41421i) q^{12} +2.24264 q^{13} +(2.70711 + 2.70711i) q^{14} +(4.00000 - 2.00000i) q^{15} +1.00000 q^{16} -1.82843i q^{17} +1.00000i q^{18} +(5.82843 - 5.82843i) q^{19} +(-0.707107 + 2.12132i) q^{20} -7.65685i q^{21} +3.82843i q^{22} -2.58579 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} +1.00000 q^{32} +(5.41421 - 5.41421i) q^{33} -1.82843i q^{34} +(-7.65685 + 3.82843i) q^{35} +1.00000i q^{36} +(3.53553 - 4.94975i) q^{37} +(5.82843 - 5.82843i) q^{38} +(-3.17157 - 3.17157i) q^{39} +(-0.707107 + 2.12132i) q^{40} +7.00000i q^{41} -7.65685i q^{42} -7.00000 q^{43} +3.82843i q^{44} +(-2.12132 - 0.707107i) q^{45} -2.58579 q^{46} +(-8.24264 - 8.24264i) q^{47} +(-1.41421 - 1.41421i) q^{48} +7.65685i q^{49} +(-4.00000 - 3.00000i) q^{50} +(-2.58579 + 2.58579i) q^{51} +2.24264 q^{52} +(2.12132 - 2.12132i) q^{53} +(-2.82843 + 2.82843i) q^{54} +(-8.12132 - 2.70711i) q^{55} +(2.70711 + 2.70711i) q^{56} -16.4853 q^{57} +(6.70711 + 6.70711i) q^{58} +(1.17157 - 1.17157i) q^{59} +(4.00000 - 2.00000i) 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} -1.82843i q^{68} +(3.65685 + 3.65685i) q^{69} +(-7.65685 + 3.82843i) q^{70} -0.343146 q^{71} +1.00000i 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} +(-0.707107 + 2.12132i) q^{80} +11.0000 q^{81} +7.00000i q^{82} +(-0.828427 + 0.828427i) q^{83} -7.65685i q^{84} +(3.87868 + 1.29289i) q^{85} -7.00000 q^{86} -18.9706i q^{87} +3.82843i q^{88} +(-7.41421 - 7.41421i) q^{89} +(-2.12132 - 0.707107i) q^{90} +(6.07107 + 6.07107i) q^{91} -2.58579 q^{92} +11.6569 q^{93} +(-8.24264 - 8.24264i) q^{94} +(8.24264 + 16.4853i) q^{95} +(-1.41421 - 1.41421i) q^{96} -7.00000i q^{97} +7.65685i q^{98} -3.82843 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 0.169102 0.985599i \(-0.445913\pi\)
−0.985599 + 0.169102i \(0.945913\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.707107 + 2.12132i −0.316228 + 0.948683i
\(6\) −1.41421 1.41421i −0.577350 0.577350i
\(7\) 2.70711 + 2.70711i 1.02319 + 1.02319i 0.999725 + 0.0234655i \(0.00747000\pi\)
0.0234655 + 0.999725i \(0.492530\pi\)
\(8\) 1.00000 0.353553
\(9\) 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
\(13\) 2.24264 0.621997 0.310998 0.950410i \(-0.399337\pi\)
0.310998 + 0.950410i \(0.399337\pi\)
\(14\) 2.70711 + 2.70711i 0.723505 + 0.723505i
\(15\) 4.00000 2.00000i 1.03280 0.516398i
\(16\) 1.00000 0.250000
\(17\) 1.82843i 0.443459i −0.975108 0.221729i \(-0.928830\pi\)
0.975108 0.221729i \(-0.0711701\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 5.82843 5.82843i 1.33713 1.33713i 0.438308 0.898825i \(-0.355578\pi\)
0.898825 0.438308i \(-0.144422\pi\)
\(20\) −0.707107 + 2.12132i −0.158114 + 0.474342i
\(21\) 7.65685i 1.67086i
\(22\) 3.82843i 0.816223i
\(23\) −2.58579 −0.539174 −0.269587 0.962976i \(-0.586887\pi\)
−0.269587 + 0.962976i \(0.586887\pi\)
\(24\) −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 \(0.0929181\pi\)
0.287783 + 0.957696i \(0.407082\pi\)
\(30\) 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 \(0.425340\pi\)
\(32\) 1.00000 0.176777
\(33\) 5.41421 5.41421i 0.942494 0.942494i
\(34\) 1.82843i 0.313573i
\(35\) −7.65685 + 3.82843i −1.29424 + 0.647122i
\(36\) 1.00000i 0.166667i
\(37\) 3.53553 4.94975i 0.581238 0.813733i
\(38\) 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 \(0.815919\pi\)
\(42\) 7.65685i 1.18148i
\(43\) −7.00000 −1.06749 −0.533745 0.845645i \(-0.679216\pi\)
−0.533745 + 0.845645i \(0.679216\pi\)
\(44\) 3.82843i 0.577157i
\(45\) −2.12132 0.707107i −0.316228 0.105409i
\(46\) −2.58579 −0.381253
\(47\) −8.24264 8.24264i −1.20231 1.20231i −0.973461 0.228851i \(-0.926503\pi\)
−0.228851 0.973461i \(-0.573497\pi\)
\(48\) −1.41421 1.41421i −0.204124 0.204124i
\(49\) 7.65685i 1.09384i
\(50\) −4.00000 3.00000i −0.565685 0.424264i
\(51\) −2.58579 + 2.58579i −0.362083 + 0.362083i
\(52\) 2.24264 0.310998
\(53\) 2.12132 2.12132i 0.291386 0.291386i −0.546242 0.837628i \(-0.683942\pi\)
0.837628 + 0.546242i \(0.183942\pi\)
\(54\) −2.82843 + 2.82843i −0.384900 + 0.384900i
\(55\) −8.12132 2.70711i −1.09508 0.365026i
\(56\) 2.70711 + 2.70711i 0.361752 + 0.361752i
\(57\) −16.4853 −2.18353
\(58\) 6.70711 + 6.70711i 0.880686 + 0.880686i
\(59\) 1.17157 1.17157i 0.152526 0.152526i −0.626719 0.779245i \(-0.715603\pi\)
0.779245 + 0.626719i \(0.215603\pi\)
\(60\) 4.00000 2.00000i 0.516398 0.258199i
\(61\) 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 \(-0.784236\pi\)
0.627114 + 0.778927i \(0.284236\pi\)
\(68\) 1.82843i 0.221729i
\(69\) 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 \(0.506482\pi\)
\(72\) 1.00000i 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
\(76\) 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 \(0.528876\pi\)
−0.995888 + 0.0905930i \(0.971124\pi\)
\(80\) −0.707107 + 2.12132i −0.0790569 + 0.237171i
\(81\) 11.0000 1.22222
\(82\) 7.00000i 0.773021i
\(83\) −0.828427 + 0.828427i −0.0909317 + 0.0909317i −0.751109 0.660178i \(-0.770481\pi\)
0.660178 + 0.751109i \(0.270481\pi\)
\(84\) 7.65685i 0.835431i
\(85\) 3.87868 + 1.29289i 0.420702 + 0.140234i
\(86\) −7.00000 −0.754829
\(87\) 18.9706i 2.03386i
\(88\) 3.82843i 0.408112i
\(89\) −7.41421 7.41421i −0.785905 0.785905i 0.194915 0.980820i \(-0.437557\pi\)
−0.980820 + 0.194915i \(0.937557\pi\)
\(90\) −2.12132 0.707107i −0.223607 0.0745356i
\(91\) 6.07107 + 6.07107i 0.636421 + 0.636421i
\(92\) −2.58579 −0.269587
\(93\) 11.6569 1.20876
\(94\) −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
\(97\) 7.00000i 0.710742i −0.934725 0.355371i \(-0.884354\pi\)
0.934725 0.355371i \(-0.115646\pi\)
\(98\) 7.65685i 0.773459i
\(99\) −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
\(103\) 13.5563i 1.33575i −0.744275 0.667873i \(-0.767205\pi\)
0.744275 0.667873i \(-0.232795\pi\)
\(104\) 2.24264 0.219909
\(105\) 16.2426 + 5.41421i 1.58512 + 0.528373i
\(106\) 2.12132 2.12132i 0.206041 0.206041i
\(107\) −9.07107 9.07107i −0.876933 0.876933i 0.116283 0.993216i \(-0.462902\pi\)
−0.993216 + 0.116283i \(0.962902\pi\)
\(108\) −2.82843 + 2.82843i −0.272166 + 0.272166i
\(109\) 0.949747 0.949747i 0.0909693 0.0909693i −0.660158 0.751127i \(-0.729511\pi\)
0.751127 + 0.660158i \(0.229511\pi\)
\(110\) −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
\(113\) 3.82843i 0.360148i 0.983653 + 0.180074i \(0.0576337\pi\)
−0.983653 + 0.180074i \(0.942366\pi\)
\(114\) −16.4853 −1.54399
\(115\) 1.82843 5.48528i 0.170502 0.511505i
\(116\) 6.70711 + 6.70711i 0.622739 + 0.622739i
\(117\) 2.24264i 0.207332i
\(118\) 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
\(125\) 9.19239 6.36396i 0.822192 0.569210i
\(126\) −2.70711 + 2.70711i −0.241168 + 0.241168i
\(127\) 2.58579 + 2.58579i 0.229451 + 0.229451i 0.812464 0.583012i \(-0.198126\pi\)
−0.583012 + 0.812464i \(0.698126\pi\)
\(128\) 1.00000 0.0883883
\(129\) 9.89949 + 9.89949i 0.871602 + 0.871602i
\(130\) −1.58579 + 4.75736i −0.139083 + 0.417248i
\(131\) 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
\(133\) 31.5563 2.73628
\(134\) −1.24264 + 1.24264i −0.107348 + 0.107348i
\(135\) −4.00000 8.00000i −0.344265 0.688530i
\(136\) 1.82843i 0.156786i
\(137\) 8.41421 + 8.41421i 0.718875 + 0.718875i 0.968375 0.249500i \(-0.0802663\pi\)
−0.249500 + 0.968375i \(0.580266\pi\)
\(138\) 3.65685 + 3.65685i 0.311292 + 0.311292i
\(139\) 6.17157 0.523466 0.261733 0.965140i \(-0.415706\pi\)
0.261733 + 0.965140i \(0.415706\pi\)
\(140\) −7.65685 + 3.82843i −0.647122 + 0.323561i
\(141\) 23.3137i 1.96337i
\(142\) −0.343146 −0.0287962
\(143\) 8.58579i 0.717980i
\(144\) 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
\(148\) 3.53553 4.94975i 0.290619 0.406867i
\(149\) 8.24264i 0.675263i −0.941278 0.337632i \(-0.890374\pi\)
0.941278 0.337632i \(-0.109626\pi\)
\(150\) 1.41421 + 9.89949i 0.115470 + 0.808290i
\(151\) 12.0000i 0.976546i −0.872691 0.488273i \(-0.837627\pi\)
0.872691 0.488273i \(-0.162373\pi\)
\(152\) 5.82843 5.82843i 0.472748 0.472748i
\(153\) 1.82843 0.147820
\(154\) −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 0.901646 0.432476i \(-0.142360\pi\)
−0.432476 + 0.901646i \(0.642360\pi\)
\(158\) −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
\(162\) 11.0000 0.864242
\(163\) 14.6569i 1.14801i 0.818851 + 0.574007i \(0.194612\pi\)
−0.818851 + 0.574007i \(0.805388\pi\)
\(164\) 7.00000i 0.546608i
\(165\) 7.65685 + 15.3137i 0.596085 + 1.19217i
\(166\) −0.828427 + 0.828427i −0.0642984 + 0.0642984i
\(167\) 1.17157i 0.0906590i −0.998972 0.0453295i \(-0.985566\pi\)
0.998972 0.0453295i \(-0.0144338\pi\)
\(168\) 7.65685i 0.590739i
\(169\) −7.97056 −0.613120
\(170\) 3.87868 + 1.29289i 0.297481 + 0.0991604i
\(171\) 5.82843 + 5.82843i 0.445711 + 0.445711i
\(172\) −7.00000 −0.533745
\(173\) −6.02082 6.02082i −0.457754 0.457754i 0.440164 0.897918i \(-0.354920\pi\)
−0.897918 + 0.440164i \(0.854920\pi\)
\(174\) 18.9706i 1.43815i
\(175\) −2.70711 18.9497i −0.204638 1.43247i
\(176\) 3.82843i 0.288579i
\(177\) −3.31371 −0.249074
\(178\) −7.41421 7.41421i −0.555719 0.555719i
\(179\) 14.4853 + 14.4853i 1.08268 + 1.08268i 0.996259 + 0.0864222i \(0.0275434\pi\)
0.0864222 + 0.996259i \(0.472457\pi\)
\(180\) −2.12132 0.707107i −0.158114 0.0527046i
\(181\) 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
\(183\) −26.2843 −1.94299
\(184\) −2.58579 −0.190627
\(185\) 8.00000 + 11.0000i 0.588172 + 0.808736i
\(186\) 11.6569 0.854722
\(187\) 7.00000 0.511891
\(188\) −8.24264 8.24264i −0.601156 0.601156i
\(189\) −15.3137 −1.11391
\(190\) 8.24264 + 16.4853i 0.597984 + 1.19597i
\(191\) 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
\(193\) −20.4853 −1.47456 −0.737281 0.675586i \(-0.763891\pi\)
−0.737281 + 0.675586i \(0.763891\pi\)
\(194\) 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 0.632261 0.774755i \(-0.282127\pi\)
−0.774755 + 0.632261i \(0.782127\pi\)
\(198\) −3.82843 −0.272074
\(199\) 3.89949 + 3.89949i 0.276428 + 0.276428i 0.831681 0.555253i \(-0.187379\pi\)
−0.555253 + 0.831681i \(0.687379\pi\)
\(200\) −4.00000 3.00000i −0.282843 0.212132i
\(201\) 3.51472 0.247909
\(202\) 11.0711i 0.778958i
\(203\) 36.3137i 2.54872i
\(204\) −2.58579 + 2.58579i −0.181041 + 0.181041i
\(205\) −14.8492 4.94975i −1.03712 0.345705i
\(206\) 13.5563i 0.944516i
\(207\) 2.58579i 0.179725i
\(208\) 2.24264 0.155499
\(209\) 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
\(217\) −22.3137 −1.51475
\(218\) 0.949747 0.949747i 0.0643250 0.0643250i
\(219\) 16.9706i 1.14676i
\(220\) −8.12132 2.70711i −0.547539 0.182513i
\(221\) 4.10051i 0.275830i
\(222\) −12.0000 + 2.00000i −0.805387 + 0.134231i
\(223\) 13.8787 13.8787i 0.929385 0.929385i −0.0682810 0.997666i \(-0.521751\pi\)
0.997666 + 0.0682810i \(0.0217514\pi\)
\(224\) 2.70711 + 2.70711i 0.180876 + 0.180876i
\(225\) 3.00000 4.00000i 0.200000 0.266667i
\(226\) 3.82843i 0.254663i
\(227\) 7.48528i 0.496816i −0.968656 0.248408i \(-0.920093\pi\)
0.968656 0.248408i \(-0.0799073\pi\)
\(228\) −16.4853 −1.09176
\(229\) 1.41421i 0.0934539i 0.998908 + 0.0467269i \(0.0148791\pi\)
−0.998908 + 0.0467269i \(0.985121\pi\)
\(230\) 1.82843 5.48528i 0.120563 0.361689i
\(231\) 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 \(-0.251048\pi\)
−0.709431 + 0.704775i \(0.751048\pi\)
\(234\) 2.24264i 0.146606i
\(235\) 23.3137 11.6569i 1.52082 0.760409i
\(236\) 1.17157 1.17157i 0.0762629 0.0762629i
\(237\) 27.3137 1.77422
\(238\) 4.94975 4.94975i 0.320844 0.320844i
\(239\) −7.05025 + 7.05025i −0.456043 + 0.456043i −0.897354 0.441311i \(-0.854513\pi\)
0.441311 + 0.897354i \(0.354513\pi\)
\(240\) 4.00000 2.00000i 0.258199 0.129099i
\(241\) 0.757359 + 0.757359i 0.0487858 + 0.0487858i 0.731079 0.682293i \(-0.239017\pi\)
−0.682293 + 0.731079i \(0.739017\pi\)
\(242\) −3.65685 −0.235071
\(243\) −7.07107 7.07107i −0.453609 0.453609i
\(244\) 9.29289 9.29289i 0.594917 0.594917i
\(245\) −16.2426 5.41421i −1.03770 0.345901i
\(246\) 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
\(253\) 9.89949i 0.622376i
\(254\) 2.58579 + 2.58579i 0.162247 + 0.162247i
\(255\) −3.65685 7.31371i −0.229001 0.458002i
\(256\) 1.00000 0.0625000
\(257\) 18.8284i 1.17449i 0.809411 + 0.587243i \(0.199787\pi\)
−0.809411 + 0.587243i \(0.800213\pi\)
\(258\) 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 \(-0.0302254\pi\)
−0.0948134 + 0.995495i \(0.530225\pi\)
\(264\) 5.41421 5.41421i 0.333222 0.333222i
\(265\) 3.00000 + 6.00000i 0.184289 + 0.368577i
\(266\) 31.5563 1.93484
\(267\) 20.9706i 1.28338i
\(268\) −1.24264 + 1.24264i −0.0759064 + 0.0759064i
\(269\) 17.7990i 1.08522i −0.839984 0.542612i \(-0.817435\pi\)
0.839984 0.542612i \(-0.182565\pi\)
\(270\) −4.00000 8.00000i −0.243432 0.486864i
\(271\) −3.07107 −0.186554 −0.0932770 0.995640i \(-0.529734\pi\)
−0.0932770 + 0.995640i \(0.529734\pi\)
\(272\) 1.82843i 0.110865i
\(273\) 17.1716i 1.03927i
\(274\) 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
\(277\) 7.79899 0.468596 0.234298 0.972165i \(-0.424721\pi\)
0.234298 + 0.972165i \(0.424721\pi\)
\(278\) 6.17157 0.370146
\(279\) −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 \(0.696033\pi\)
\(282\) 23.3137i 1.38831i
\(283\) 28.0000i 1.66443i −0.554455 0.832214i \(-0.687073\pi\)
0.554455 0.832214i \(-0.312927\pi\)
\(284\) −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
\(288\) 1.00000i 0.0589256i
\(289\) 13.6569 0.803344
\(290\) −18.9706 + 9.48528i −1.11399 + 0.556995i
\(291\) −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 −0.757138 0.653255i \(-0.773403\pi\)
0.653255 + 0.757138i \(0.273403\pi\)
\(294\) 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
\(298\) 8.24264i 0.477483i
\(299\) −5.79899 −0.335364
\(300\) 1.41421 + 9.89949i 0.0816497 + 0.571548i
\(301\) −18.9497 18.9497i −1.09225 1.09225i
\(302\) 12.0000i 0.690522i
\(303\) −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 \(-0.725575\pi\)
0.759231 + 0.650821i \(0.225575\pi\)
\(308\) −10.3640 + 10.3640i −0.590541 + 0.590541i
\(309\) −19.1716 + 19.1716i −1.09063 + 1.09063i
\(310\) −5.82843 11.6569i −0.331032 0.662065i
\(311\) −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
\(313\) −0.686292 −0.0387915 −0.0193957 0.999812i \(-0.506174\pi\)
−0.0193957 + 0.999812i \(0.506174\pi\)
\(314\) 5.87868 + 5.87868i 0.331753 + 0.331753i
\(315\) −3.82843 7.65685i −0.215707 0.431415i
\(316\) −9.65685 + 9.65685i −0.543240 + 0.543240i
\(317\) −15.5355 + 15.5355i −0.872563 + 0.872563i −0.992751 0.120189i \(-0.961650\pi\)
0.120189 + 0.992751i \(0.461650\pi\)
\(318\) −6.00000 −0.336463
\(319\) −25.6777 + 25.6777i −1.43767 + 1.43767i
\(320\) −0.707107 + 2.12132i −0.0395285 + 0.118585i
\(321\) 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
\(325\) −8.97056 6.72792i −0.497597 0.373198i
\(326\) 14.6569i 0.811768i
\(327\) −2.68629 −0.148552
\(328\) 7.00000i 0.386510i
\(329\) 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
\(333\) 4.94975 + 3.53553i 0.271244 + 0.193746i
\(334\) 1.17157i 0.0641056i
\(335\) −1.75736 3.51472i −0.0960148 0.192030i
\(336\) 7.65685i 0.417716i
\(337\) −5.65685 + 5.65685i −0.308148 + 0.308148i −0.844191 0.536043i \(-0.819919\pi\)
0.536043 + 0.844191i \(0.319919\pi\)
\(338\) −7.97056 −0.433541
\(339\) 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
\(347\) −17.3137 −0.929449 −0.464724 0.885455i \(-0.653847\pi\)
−0.464724 + 0.885455i \(0.653847\pi\)
\(348\) 18.9706i 1.01693i
\(349\) 4.14214i 0.221723i 0.993836 + 0.110862i \(0.0353611\pi\)
−0.993836 + 0.110862i \(0.964639\pi\)
\(350\) −2.70711 18.9497i −0.144701 1.01291i
\(351\) −6.34315 + 6.34315i −0.338572 + 0.338572i
\(352\) 3.82843i 0.204056i
\(353\) 7.34315i 0.390836i −0.980720 0.195418i \(-0.937394\pi\)
0.980720 0.195418i \(-0.0626064\pi\)
\(354\) −3.31371 −0.176122
\(355\) 0.242641 0.727922i 0.0128780 0.0386341i
\(356\) −7.41421 7.41421i −0.392953 0.392953i
\(357\) −14.0000 −0.740959
\(358\) 14.4853 + 14.4853i 0.765571 + 0.765571i
\(359\) 30.5269i 1.61115i −0.592495 0.805574i \(-0.701857\pi\)
0.592495 0.805574i \(-0.298143\pi\)
\(360\) −2.12132 0.707107i −0.111803 0.0372678i
\(361\) 48.9411i 2.57585i
\(362\) 7.65685 0.402435
\(363\) 5.17157 + 5.17157i 0.271437 + 0.271437i
\(364\) 6.07107 + 6.07107i 0.318210 + 0.318210i
\(365\) 16.9706 8.48528i 0.888280 0.444140i
\(366\) −26.2843 −1.37390
\(367\) 13.0919 + 13.0919i 0.683391 + 0.683391i 0.960763 0.277372i \(-0.0894634\pi\)
−0.277372 + 0.960763i \(0.589463\pi\)
\(368\) −2.58579 −0.134793
\(369\) −7.00000 −0.364405
\(370\) 8.00000 + 11.0000i 0.415900 + 0.571863i
\(371\) 11.4853 0.596286
\(372\) 11.6569 0.604380
\(373\) 10.8284 + 10.8284i 0.560675 + 0.560675i 0.929499 0.368824i \(-0.120240\pi\)
−0.368824 + 0.929499i \(0.620240\pi\)
\(374\) 7.00000 0.361961
\(375\) −22.0000 4.00000i −1.13608 0.206559i
\(376\) −8.24264 8.24264i −0.425082 0.425082i
\(377\) 15.0416 + 15.0416i 0.774683 + 0.774683i
\(378\) −15.3137 −0.787652
\(379\) 18.0000i 0.924598i −0.886724 0.462299i \(-0.847025\pi\)
0.886724 0.462299i \(-0.152975\pi\)
\(380\) 8.24264 + 16.4853i 0.422839 + 0.845677i
\(381\) 7.31371i 0.374693i
\(382\) 1.53553 + 1.53553i 0.0785647 + 0.0785647i
\(383\) −16.5858 −0.847494 −0.423747 0.905781i \(-0.639285\pi\)
−0.423747 + 0.905781i \(0.639285\pi\)
\(384\) −1.41421 1.41421i −0.0721688 0.0721688i
\(385\) −14.6569 29.3137i −0.746982 1.49396i
\(386\) −20.4853 −1.04267
\(387\) 7.00000i 0.355830i
\(388\) 7.00000i 0.355371i
\(389\) 3.77817 3.77817i 0.191561 0.191561i −0.604809 0.796370i \(-0.706751\pi\)
0.796370 + 0.604809i \(0.206751\pi\)
\(390\) 8.97056 4.48528i 0.454242 0.227121i
\(391\) 4.72792i 0.239101i
\(392\) 7.65685i 0.386730i
\(393\) −1.17157 −0.0590980
\(394\) −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 \(-0.847364\pi\)
0.461353 + 0.887217i \(0.347364\pi\)
\(398\) 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 \(0.330328\pi\)
\(402\) 3.51472 0.175298
\(403\) −9.24264 + 9.24264i −0.460409 + 0.460409i
\(404\) 11.0711i 0.550806i
\(405\) −7.77817 + 23.3345i −0.386501 + 1.15950i
\(406\) 36.3137i 1.80222i
\(407\) 18.9497 + 13.5355i 0.939304 + 0.670932i
\(408\) −2.58579 + 2.58579i −0.128016 + 0.128016i
\(409\) 19.7990 + 19.7990i 0.978997 + 0.978997i 0.999784 0.0207869i \(-0.00661715\pi\)
−0.0207869 + 0.999784i \(0.506617\pi\)
\(410\) −14.8492 4.94975i −0.733352 0.244451i
\(411\) 23.7990i 1.17392i
\(412\) 13.5563i 0.667873i
\(413\) 6.34315 0.312126
\(414\) 2.58579i 0.127084i
\(415\) −1.17157 2.34315i −0.0575103 0.115021i
\(416\) 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 \(0.228935\pi\)
−0.752319 + 0.658799i \(0.771065\pi\)
\(420\) 16.2426 + 5.41421i 0.792560 + 0.264187i
\(421\) −25.3137 + 25.3137i −1.23371 + 1.23371i −0.271188 + 0.962526i \(0.587417\pi\)
−0.962526 + 0.271188i \(0.912583\pi\)
\(422\) −9.00000 −0.438113
\(423\) 8.24264 8.24264i 0.400771 0.400771i
\(424\) 2.12132 2.12132i 0.103020 0.103020i
\(425\) −5.48528 + 7.31371i −0.266075 + 0.354767i
\(426\) 0.485281 + 0.485281i 0.0235120 + 0.0235120i
\(427\) 50.3137 2.43485
\(428\) −9.07107 9.07107i −0.438467 0.438467i
\(429\) 12.1421 12.1421i 0.586228 0.586228i
\(430\) 4.94975 14.8492i 0.238698 0.716094i
\(431\) −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 −0.572670 0.819786i \(-0.694093\pi\)
0.819786 + 0.572670i \(0.194093\pi\)
\(434\) −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
\(438\) 16.9706i 0.810885i
\(439\) −2.22183 2.22183i −0.106042 0.106042i 0.652095 0.758137i \(-0.273890\pi\)
−0.758137 + 0.652095i \(0.773890\pi\)
\(440\) −8.12132 2.70711i −0.387169 0.129056i
\(441\) −7.65685 −0.364612
\(442\) 4.10051i 0.195041i
\(443\) 5.34315 + 5.34315i 0.253861 + 0.253861i 0.822551 0.568691i \(-0.192550\pi\)
−0.568691 + 0.822551i \(0.692550\pi\)
\(444\) −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 \(-0.423435\pi\)
0.971211 0.238222i \(-0.0765645\pi\)
\(450\) 3.00000 4.00000i 0.141421 0.188562i
\(451\) −26.7990 −1.26192
\(452\) 3.82843i 0.180074i
\(453\) −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
\(457\) 3.68629i 0.172437i −0.996276 0.0862187i \(-0.972522\pi\)
0.996276 0.0862187i \(-0.0274784\pi\)
\(458\) 1.41421i 0.0660819i
\(459\) 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 \(0.638005\pi\)
\(462\) 29.3137 1.36380
\(463\) 29.9411 1.39148 0.695741 0.718293i \(-0.255076\pi\)
0.695741 + 0.718293i \(0.255076\pi\)
\(464\) 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
\(467\) 2.31371i 0.107066i 0.998566 + 0.0535328i \(0.0170482\pi\)
−0.998566 + 0.0535328i \(0.982952\pi\)
\(468\) 2.24264i 0.103666i
\(469\) −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
\(473\) 26.7990i 1.23222i
\(474\) 27.3137 1.25456
\(475\) −40.7990 + 5.82843i −1.87199 + 0.267427i
\(476\) 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 −0.966700 0.255912i \(-0.917624\pi\)
0.255912 + 0.966700i \(0.417624\pi\)
\(480\) 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
\(483\) 19.7990i 0.900885i
\(484\) −3.65685 −0.166221
\(485\) 14.8492 + 4.94975i 0.674269 + 0.224756i
\(486\) −7.07107 7.07107i −0.320750 0.320750i
\(487\) 26.9706i 1.22215i 0.791572 + 0.611076i \(0.209263\pi\)
−0.791572 + 0.611076i \(0.790737\pi\)
\(488\) 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
\(495\) 2.70711 8.12132i 0.121675 0.365026i
\(496\) −4.12132 + 4.12132i −0.185053 + 0.185053i
\(497\) −0.928932 0.928932i −0.0416683 0.0416683i
\(498\) 2.34315 0.104999
\(499\) 10.2426 + 10.2426i 0.458524 + 0.458524i 0.898171 0.439647i \(-0.144896\pi\)
−0.439647 + 0.898171i \(0.644896\pi\)
\(500\) 9.19239 6.36396i 0.411096 0.284605i
\(501\) −1.65685 + 1.65685i −0.0740228 + 0.0740228i
\(502\) −17.8995 + 17.8995i −0.798894 + 0.798894i
\(503\) −32.5858 −1.45293 −0.726464 0.687204i \(-0.758838\pi\)
−0.726464 + 0.687204i \(0.758838\pi\)
\(504\) −2.70711 + 2.70711i −0.120584 + 0.120584i
\(505\) 23.4853 + 7.82843i 1.04508 + 0.348360i
\(506\) 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 \(-0.508975\pi\)
−0.0281919 + 0.999603i \(0.508975\pi\)
\(510\) −3.65685 7.31371i −0.161928 0.323856i
\(511\) 32.4853i 1.43706i
\(512\) 1.00000 0.0441942
\(513\) 32.9706i 1.45569i
\(514\) 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
\(518\) 22.9706 3.82843i 1.00927 0.168211i
\(519\) 17.0294i 0.747509i
\(520\) −1.58579 + 4.75736i −0.0695413 + 0.208624i
\(521\) 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
\(523\) 43.6569 1.90898 0.954490 0.298241i \(-0.0964000\pi\)
0.954490 + 0.298241i \(0.0964000\pi\)
\(524\) 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
\(532\) 31.5563 1.36814
\(533\) 15.6985i 0.679977i
\(534\) 20.9706i 0.907485i
\(535\) 25.6569 12.8284i 1.10924 0.554621i
\(536\) −1.24264 + 1.24264i −0.0536739 + 0.0536739i
\(537\) 40.9706i 1.76801i
\(538\) 17.7990i 0.767369i
\(539\) −29.3137 −1.26263
\(540\) −4.00000 8.00000i −0.172133 0.344265i
\(541\) −27.7990 27.7990i −1.19517 1.19517i −0.975595 0.219577i \(-0.929532\pi\)
−0.219577 0.975595i \(-0.570468\pi\)
\(542\) −3.07107 −0.131914
\(543\) −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
\(547\) −27.8284 −1.18986 −0.594929 0.803778i \(-0.702820\pi\)
−0.594929 + 0.803778i \(0.702820\pi\)
\(548\) 8.41421 + 8.41421i 0.359437 + 0.359437i
\(549\) 9.29289 + 9.29289i 0.396611 + 0.396611i
\(550\) 11.4853 15.3137i 0.489734 0.652979i
\(551\) 78.1838 3.33074
\(552\) 3.65685 + 3.65685i 0.155646 + 0.155646i
\(553\) −52.2843 −2.22335
\(554\) 7.79899 0.331347
\(555\) 4.24264 26.8701i 0.180090 1.14057i
\(556\) 6.17157 0.261733
\(557\) 23.2132 0.983575 0.491787 0.870715i \(-0.336344\pi\)
0.491787 + 0.870715i \(0.336344\pi\)
\(558\) −4.12132 4.12132i −0.174469 0.174469i
\(559\) −15.6985 −0.663975
\(560\) −7.65685 + 3.82843i −0.323561 + 0.161781i
\(561\) −9.89949 9.89949i −0.417957 0.417957i
\(562\) 4.00000 + 4.00000i 0.168730 + 0.168730i
\(563\) −24.1127 −1.01623 −0.508115 0.861290i \(-0.669657\pi\)
−0.508115 + 0.861290i \(0.669657\pi\)
\(564\) 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
\(568\) −0.343146 −0.0143981
\(569\) 1.68629 + 1.68629i 0.0706930 + 0.0706930i 0.741569 0.670876i \(-0.234082\pi\)
−0.670876 + 0.741569i \(0.734082\pi\)
\(570\) 11.6569 34.9706i 0.488252 1.46476i
\(571\) 46.7990 1.95848 0.979238 0.202712i \(-0.0649755\pi\)
0.979238 + 0.202712i \(0.0649755\pi\)
\(572\) 8.58579i 0.358990i
\(573\) 4.34315i 0.181438i
\(574\) −18.9497 + 18.9497i −0.790947 + 0.790947i
\(575\) 10.3431 + 7.75736i 0.431339 + 0.323504i
\(576\) 1.00000i 0.0416667i
\(577\) 21.6569i 0.901587i 0.892628 + 0.450793i \(0.148859\pi\)
−0.892628 + 0.450793i \(0.851141\pi\)
\(578\) 13.6569 0.568050
\(579\) 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
\(587\) −4.45584 −0.183912 −0.0919562 0.995763i \(-0.529312\pi\)
−0.0919562 + 0.995763i \(0.529312\pi\)
\(588\) 10.8284 10.8284i 0.446557 0.446557i
\(589\) 48.0416i 1.97952i
\(590\) 1.65685 + 3.31371i 0.0682116 + 0.136423i
\(591\) 5.65685i 0.232692i
\(592\) 3.53553 4.94975i 0.145310 0.203433i
\(593\) −26.1421 + 26.1421i −1.07353 + 1.07353i −0.0764559 + 0.997073i \(0.524360\pi\)
−0.997073 + 0.0764559i \(0.975640\pi\)
\(594\) −10.8284 10.8284i −0.444296 0.444296i
\(595\) 7.00000 + 14.0000i 0.286972 + 0.573944i
\(596\) 8.24264i 0.337632i
\(597\) 11.0294i 0.451405i
\(598\) −5.79899 −0.237138
\(599\) 33.7574i 1.37929i −0.724148 0.689644i \(-0.757767\pi\)
0.724148 0.689644i \(-0.242233\pi\)
\(600\) 1.41421 + 9.89949i 0.0577350 + 0.404145i
\(601\) −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
\(605\) 2.58579 7.75736i 0.105127 0.315382i
\(606\) −15.6569 + 15.6569i −0.636016 + 0.636016i
\(607\) −34.1838 −1.38748 −0.693738 0.720227i \(-0.744037\pi\)
−0.693738 + 0.720227i \(0.744037\pi\)
\(608\) 5.82843 5.82843i 0.236374 0.236374i
\(609\) 51.3553 51.3553i 2.08102 2.08102i
\(610\) 13.1421 + 26.2843i 0.532110 + 1.06422i
\(611\) −18.4853 18.4853i −0.747834 0.747834i
\(612\) 1.82843 0.0739098
\(613\) 12.1213 + 12.1213i 0.489576 + 0.489576i 0.908172 0.418597i \(-0.137478\pi\)
−0.418597 + 0.908172i \(0.637478\pi\)
\(614\) 1.89949 1.89949i 0.0766574 0.0766574i
\(615\) 14.0000 + 28.0000i 0.564534 + 1.12907i
\(616\) −10.3640 + 10.3640i −0.417576 + 0.417576i
\(617\) 27.7279 27.7279i 1.11628 1.11628i 0.124002 0.992282i \(-0.460427\pi\)
0.992282 0.124002i \(-0.0395730\pi\)
\(618\) −19.1716 + 19.1716i −0.771194 + 0.771194i
\(619\) −46.5980 −1.87293 −0.936465 0.350760i \(-0.885923\pi\)
−0.936465 + 0.350760i \(0.885923\pi\)
\(620\) −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
\(623\) 40.1421i 1.60826i
\(624\) −3.17157 3.17157i −0.126965 0.126965i
\(625\) 7.00000 + 24.0000i 0.280000 + 0.960000i
\(626\) −0.686292 −0.0274297
\(627\) 63.1127i 2.52048i
\(628\) 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
\(635\) −7.31371 + 3.65685i −0.290236 + 0.145118i
\(636\) −6.00000 −0.237915
\(637\) 17.1716i 0.680362i
\(638\) −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 \(0.333578\pi\)
\(642\) 25.6569i 1.01260i
\(643\) 24.5147i 0.966766i 0.875409 + 0.483383i \(0.160592\pi\)
−0.875409 + 0.483383i \(0.839408\pi\)
\(644\) −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
\(647\) 27.3137 1.07381 0.536906 0.843642i \(-0.319593\pi\)
0.536906 + 0.843642i \(0.319593\pi\)
\(648\) 11.0000 0.432121
\(649\) 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
\(652\) 14.6569i 0.574007i
\(653\) 19.6569i 0.769232i 0.923077 + 0.384616i \(0.125666\pi\)
−0.923077 + 0.384616i \(0.874334\pi\)
\(654\) −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
\(658\) 44.6274i 1.73976i
\(659\) 20.1421 0.784626 0.392313 0.919832i \(-0.371675\pi\)
0.392313 + 0.919832i \(0.371675\pi\)
\(660\) 7.65685 + 15.3137i 0.298043 + 0.596085i
\(661\) −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
\(668\) 1.17157i 0.0453295i
\(669\) −39.2548 −1.51768
\(670\) −1.75736 3.51472i −0.0678927 0.135785i
\(671\) 35.5772 + 35.5772i 1.37344 + 1.37344i
\(672\) 7.65685i 0.295370i
\(673\) −10.5147 + 10.5147i −0.405313 + 0.405313i −0.880100 0.474788i \(-0.842525\pi\)
0.474788 + 0.880100i \(0.342525\pi\)
\(674\) −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 \(-0.630289\pi\)
0.917394 + 0.397981i \(0.130289\pi\)
\(678\) 5.41421 5.41421i 0.207932 0.207932i
\(679\) 18.9497 18.9497i 0.727225 0.727225i
\(680\) 3.87868 + 1.29289i 0.148741 + 0.0495802i
\(681\) −10.5858 + 10.5858i −0.405648 + 0.405648i
\(682\) −15.7782 15.7782i −0.604178 0.604178i
\(683\) 12.3137 0.471171 0.235585 0.971854i \(-0.424299\pi\)
0.235585 + 0.971854i \(0.424299\pi\)
\(684\) 5.82843 + 5.82843i 0.222855 + 0.222855i
\(685\) −23.7990 + 11.8995i −0.909313 + 0.454656i
\(686\) −1.77817 + 1.77817i −0.0678910 + 0.0678910i
\(687\) 2.00000 2.00000i 0.0763048 0.0763048i
\(688\) −7.00000 −0.266872
\(689\) 4.75736 4.75736i 0.181241 0.181241i
\(690\) −10.3431 + 5.17157i −0.393757 + 0.196878i
\(691\) 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
\(695\) −4.36396 + 13.0919i −0.165534 + 0.496603i
\(696\) 18.9706i 0.719077i
\(697\) 12.7990 0.484796
\(698\) 4.14214i 0.156782i
\(699\) 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
\(703\) −8.24264 49.4558i −0.310877 1.86526i
\(704\) 3.82843i 0.144289i
\(705\) −49.4558 16.4853i −1.86261 0.620872i
\(706\) 7.34315i 0.276363i
\(707\) 29.9706 29.9706i 1.12716 1.12716i
\(708\) −3.31371 −0.124537
\(709\) −10.7071 + 10.7071i −0.402114 + 0.402114i −0.878977 0.476864i \(-0.841774\pi\)
0.476864 + 0.878977i \(0.341774\pi\)
\(710\) 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
\(717\) 19.9411 0.744715
\(718\) 30.5269i 1.13925i
\(719\) 24.1421i 0.900350i −0.892940 0.450175i \(-0.851362\pi\)
0.892940 0.450175i \(-0.148638\pi\)
\(720\) −2.12132 0.707107i −0.0790569 0.0263523i
\(721\) 36.6985 36.6985i 1.36672 1.36672i
\(722\) 48.9411i 1.82140i
\(723\) 2.14214i 0.0796669i
\(724\) 7.65685 0.284565
\(725\) −6.70711 46.9497i −0.249096 1.74367i
\(726\) 5.17157 + 5.17157i 0.191935 + 0.191935i
\(727\) −13.8579 −0.513960 −0.256980 0.966417i \(-0.582727\pi\)
−0.256980 + 0.966417i \(0.582727\pi\)
\(728\) 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
\(732\) −26.2843 −0.971495
\(733\) 22.7487 + 22.7487i 0.840244 + 0.840244i 0.988890 0.148647i \(-0.0474917\pi\)
−0.148647 + 0.988890i \(0.547492\pi\)
\(734\) 13.0919 + 13.0919i 0.483230 + 0.483230i
\(735\) 15.3137 + 30.6274i 0.564855 + 1.12971i
\(736\) −2.58579 −0.0953134
\(737\) −4.75736 4.75736i −0.175240 0.175240i
\(738\) −7.00000 −0.257674
\(739\) 10.7990 0.397247 0.198624 0.980076i \(-0.436353\pi\)
0.198624 + 0.980076i \(0.436353\pi\)
\(740\) 8.00000 + 11.0000i 0.294086 + 0.404368i
\(741\) −36.9706 −1.35815
\(742\) 11.4853 0.421638
\(743\) −5.05025 5.05025i −0.185276 0.185276i 0.608374 0.793650i \(-0.291822\pi\)
−0.793650 + 0.608374i \(0.791822\pi\)
\(744\) 11.6569 0.427361
\(745\) 17.4853 + 5.82843i 0.640611 + 0.213537i
\(746\) 10.8284 + 10.8284i 0.396457 + 0.396457i
\(747\) −0.828427 0.828427i −0.0303106 0.0303106i
\(748\) 7.00000 0.255945
\(749\) 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
\(753\) 50.6274 1.84497
\(754\) 15.0416 + 15.0416i 0.547784 + 0.547784i
\(755\) 25.4558 + 8.48528i 0.926433 + 0.308811i
\(756\) −15.3137 −0.556954
\(757\) 27.6569i 1.00521i 0.864517 + 0.502603i \(0.167624\pi\)
−0.864517 + 0.502603i \(0.832376\pi\)
\(758\) 18.0000i 0.653789i
\(759\) −14.0000 + 14.0000i −0.508168 + 0.508168i
\(760\) 8.24264 + 16.4853i 0.298992 + 0.597984i
\(761\) 11.6863i 0.423628i −0.977310 0.211814i \(-0.932063\pi\)
0.977310 0.211814i \(-0.0679371\pi\)
\(762\) 7.31371i 0.264948i
\(763\) 5.14214 0.186158
\(764\) 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 0.962528 0.271183i \(-0.0874149\pi\)
−0.271183 + 0.962528i \(0.587415\pi\)
\(770\) −14.6569 29.3137i −0.528196 1.05639i
\(771\) 26.6274 26.6274i 0.958963 0.958963i
\(772\) −20.4853 −0.737281
\(773\) 10.1213 10.1213i 0.364039 0.364039i −0.501259 0.865297i \(-0.667130\pi\)
0.865297 + 0.501259i \(0.167130\pi\)
\(774\) 7.00000i 0.251610i
\(775\) 28.8492 4.12132i 1.03630 0.148042i
\(776\) 7.00000i 0.251285i
\(777\) −37.8995 27.0711i −1.35964