Properties

Label 390.2.p.e.281.2
Level $390$
Weight $2$
Character 390.281
Analytic conductor $3.114$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.p (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 281.2
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 390.281
Dual form 390.2.p.e.161.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(0.292893 - 1.70711i) q^{3} -1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(2.00000 - 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(0.292893 - 1.70711i) q^{3} -1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(2.00000 - 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +1.00000i q^{10} +(-2.00000 - 2.00000i) q^{11} +(-1.70711 - 0.292893i) q^{12} +(3.53553 + 0.707107i) q^{13} -2.82843i q^{14} +(1.00000 + 1.41421i) q^{15} -1.00000 q^{16} -4.82843 q^{17} +(-2.70711 + 1.29289i) q^{18} +(0.707107 + 0.707107i) q^{20} +(-2.82843 - 4.00000i) q^{21} -2.82843 q^{22} +6.82843 q^{23} +(-1.41421 + 1.00000i) q^{24} -1.00000i q^{25} +(3.00000 - 2.00000i) q^{26} +(-2.53553 + 4.53553i) q^{27} +(-2.00000 - 2.00000i) q^{28} -3.65685i q^{29} +(1.70711 + 0.292893i) q^{30} +(4.41421 + 4.41421i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-4.00000 + 2.82843i) q^{33} +(-3.41421 + 3.41421i) q^{34} +2.82843i q^{35} +(-1.00000 + 2.82843i) q^{36} +(-4.00000 + 4.00000i) q^{37} +(2.24264 - 5.82843i) q^{39} +1.00000 q^{40} +(2.17157 - 2.17157i) q^{41} +(-4.82843 - 0.828427i) q^{42} -5.07107i q^{43} +(-2.00000 + 2.00000i) q^{44} +(2.70711 - 1.29289i) q^{45} +(4.82843 - 4.82843i) q^{46} +(2.00000 + 2.00000i) q^{47} +(-0.292893 + 1.70711i) q^{48} -1.00000i q^{49} +(-0.707107 - 0.707107i) q^{50} +(-1.41421 + 8.24264i) q^{51} +(0.707107 - 3.53553i) q^{52} +9.41421i q^{53} +(1.41421 + 5.00000i) q^{54} +2.82843 q^{55} -2.82843 q^{56} +(-2.58579 - 2.58579i) q^{58} +(4.00000 + 4.00000i) q^{59} +(1.41421 - 1.00000i) q^{60} +12.8284 q^{61} +6.24264 q^{62} +(-7.65685 + 3.65685i) q^{63} +1.00000i q^{64} +(-3.00000 + 2.00000i) q^{65} +(-0.828427 + 4.82843i) q^{66} +(2.24264 + 2.24264i) q^{67} +4.82843i q^{68} +(2.00000 - 11.6569i) q^{69} +(2.00000 + 2.00000i) q^{70} +(10.4142 - 10.4142i) q^{71} +(1.29289 + 2.70711i) q^{72} +(9.89949 - 9.89949i) q^{73} +5.65685i q^{74} +(-1.70711 - 0.292893i) q^{75} -8.00000 q^{77} +(-2.53553 - 5.70711i) q^{78} -8.82843 q^{79} +(0.707107 - 0.707107i) q^{80} +(7.00000 + 5.65685i) q^{81} -3.07107i q^{82} +(-1.17157 + 1.17157i) q^{83} +(-4.00000 + 2.82843i) q^{84} +(3.41421 - 3.41421i) q^{85} +(-3.58579 - 3.58579i) q^{86} +(-6.24264 - 1.07107i) q^{87} +2.82843i q^{88} +(2.65685 + 2.65685i) q^{89} +(1.00000 - 2.82843i) q^{90} +(8.48528 - 5.65685i) q^{91} -6.82843i q^{92} +(8.82843 - 6.24264i) q^{93} +2.82843 q^{94} +(1.00000 + 1.41421i) q^{96} +(-8.58579 - 8.58579i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(3.65685 + 7.65685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{3} - 4 q^{6} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{3} - 4 q^{6} + 8 q^{7} - 8 q^{11} - 4 q^{12} + 4 q^{15} - 4 q^{16} - 8 q^{17} - 8 q^{18} + 16 q^{23} + 12 q^{26} + 4 q^{27} - 8 q^{28} + 4 q^{30} + 12 q^{31} - 16 q^{33} - 8 q^{34} - 4 q^{36} - 16 q^{37} - 8 q^{39} + 4 q^{40} + 20 q^{41} - 8 q^{42} - 8 q^{44} + 8 q^{45} + 8 q^{46} + 8 q^{47} - 4 q^{48} - 16 q^{58} + 16 q^{59} + 40 q^{61} + 8 q^{62} - 8 q^{63} - 12 q^{65} + 8 q^{66} - 8 q^{67} + 8 q^{69} + 8 q^{70} + 36 q^{71} + 8 q^{72} - 4 q^{75} - 32 q^{77} + 4 q^{78} - 24 q^{79} + 28 q^{81} - 16 q^{83} - 16 q^{84} + 8 q^{85} - 20 q^{86} - 8 q^{87} - 12 q^{89} + 4 q^{90} + 24 q^{93} + 4 q^{96} - 40 q^{97} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 0.292893 1.70711i 0.169102 0.985599i
\(4\) 1.00000i 0.500000i
\(5\) −0.707107 + 0.707107i −0.316228 + 0.316228i
\(6\) −1.00000 1.41421i −0.408248 0.577350i
\(7\) 2.00000 2.00000i 0.755929 0.755929i −0.219650 0.975579i \(-0.570491\pi\)
0.975579 + 0.219650i \(0.0704915\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −2.82843 1.00000i −0.942809 0.333333i
\(10\) 1.00000i 0.316228i
\(11\) −2.00000 2.00000i −0.603023 0.603023i 0.338091 0.941113i \(-0.390219\pi\)
−0.941113 + 0.338091i \(0.890219\pi\)
\(12\) −1.70711 0.292893i −0.492799 0.0845510i
\(13\) 3.53553 + 0.707107i 0.980581 + 0.196116i
\(14\) 2.82843i 0.755929i
\(15\) 1.00000 + 1.41421i 0.258199 + 0.365148i
\(16\) −1.00000 −0.250000
\(17\) −4.82843 −1.17107 −0.585533 0.810649i \(-0.699115\pi\)
−0.585533 + 0.810649i \(0.699115\pi\)
\(18\) −2.70711 + 1.29289i −0.638071 + 0.304738i
\(19\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(20\) 0.707107 + 0.707107i 0.158114 + 0.158114i
\(21\) −2.82843 4.00000i −0.617213 0.872872i
\(22\) −2.82843 −0.603023
\(23\) 6.82843 1.42383 0.711913 0.702268i \(-0.247829\pi\)
0.711913 + 0.702268i \(0.247829\pi\)
\(24\) −1.41421 + 1.00000i −0.288675 + 0.204124i
\(25\) 1.00000i 0.200000i
\(26\) 3.00000 2.00000i 0.588348 0.392232i
\(27\) −2.53553 + 4.53553i −0.487964 + 0.872864i
\(28\) −2.00000 2.00000i −0.377964 0.377964i
\(29\) 3.65685i 0.679061i −0.940595 0.339530i \(-0.889732\pi\)
0.940595 0.339530i \(-0.110268\pi\)
\(30\) 1.70711 + 0.292893i 0.311674 + 0.0534747i
\(31\) 4.41421 + 4.41421i 0.792816 + 0.792816i 0.981951 0.189135i \(-0.0605684\pi\)
−0.189135 + 0.981951i \(0.560568\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −4.00000 + 2.82843i −0.696311 + 0.492366i
\(34\) −3.41421 + 3.41421i −0.585533 + 0.585533i
\(35\) 2.82843i 0.478091i
\(36\) −1.00000 + 2.82843i −0.166667 + 0.471405i
\(37\) −4.00000 + 4.00000i −0.657596 + 0.657596i −0.954811 0.297215i \(-0.903942\pi\)
0.297215 + 0.954811i \(0.403942\pi\)
\(38\) 0 0
\(39\) 2.24264 5.82843i 0.359110 0.933295i
\(40\) 1.00000 0.158114
\(41\) 2.17157 2.17157i 0.339143 0.339143i −0.516902 0.856045i \(-0.672915\pi\)
0.856045 + 0.516902i \(0.172915\pi\)
\(42\) −4.82843 0.828427i −0.745042 0.127829i
\(43\) 5.07107i 0.773331i −0.922220 0.386665i \(-0.873627\pi\)
0.922220 0.386665i \(-0.126373\pi\)
\(44\) −2.00000 + 2.00000i −0.301511 + 0.301511i
\(45\) 2.70711 1.29289i 0.403552 0.192733i
\(46\) 4.82843 4.82843i 0.711913 0.711913i
\(47\) 2.00000 + 2.00000i 0.291730 + 0.291730i 0.837763 0.546033i \(-0.183863\pi\)
−0.546033 + 0.837763i \(0.683863\pi\)
\(48\) −0.292893 + 1.70711i −0.0422755 + 0.246400i
\(49\) 1.00000i 0.142857i
\(50\) −0.707107 0.707107i −0.100000 0.100000i
\(51\) −1.41421 + 8.24264i −0.198030 + 1.15420i
\(52\) 0.707107 3.53553i 0.0980581 0.490290i
\(53\) 9.41421i 1.29314i 0.762854 + 0.646571i \(0.223798\pi\)
−0.762854 + 0.646571i \(0.776202\pi\)
\(54\) 1.41421 + 5.00000i 0.192450 + 0.680414i
\(55\) 2.82843 0.381385
\(56\) −2.82843 −0.377964
\(57\) 0 0
\(58\) −2.58579 2.58579i −0.339530 0.339530i
\(59\) 4.00000 + 4.00000i 0.520756 + 0.520756i 0.917800 0.397044i \(-0.129964\pi\)
−0.397044 + 0.917800i \(0.629964\pi\)
\(60\) 1.41421 1.00000i 0.182574 0.129099i
\(61\) 12.8284 1.64251 0.821256 0.570560i \(-0.193274\pi\)
0.821256 + 0.570560i \(0.193274\pi\)
\(62\) 6.24264 0.792816
\(63\) −7.65685 + 3.65685i −0.964673 + 0.460720i
\(64\) 1.00000i 0.125000i
\(65\) −3.00000 + 2.00000i −0.372104 + 0.248069i
\(66\) −0.828427 + 4.82843i −0.101972 + 0.594338i
\(67\) 2.24264 + 2.24264i 0.273982 + 0.273982i 0.830701 0.556719i \(-0.187940\pi\)
−0.556719 + 0.830701i \(0.687940\pi\)
\(68\) 4.82843i 0.585533i
\(69\) 2.00000 11.6569i 0.240772 1.40332i
\(70\) 2.00000 + 2.00000i 0.239046 + 0.239046i
\(71\) 10.4142 10.4142i 1.23594 1.23594i 0.274294 0.961646i \(-0.411556\pi\)
0.961646 0.274294i \(-0.0884441\pi\)
\(72\) 1.29289 + 2.70711i 0.152369 + 0.319036i
\(73\) 9.89949 9.89949i 1.15865 1.15865i 0.173882 0.984767i \(-0.444369\pi\)
0.984767 0.173882i \(-0.0556310\pi\)
\(74\) 5.65685i 0.657596i
\(75\) −1.70711 0.292893i −0.197120 0.0338204i
\(76\) 0 0
\(77\) −8.00000 −0.911685
\(78\) −2.53553 5.70711i −0.287093 0.646203i
\(79\) −8.82843 −0.993276 −0.496638 0.867958i \(-0.665432\pi\)
−0.496638 + 0.867958i \(0.665432\pi\)
\(80\) 0.707107 0.707107i 0.0790569 0.0790569i
\(81\) 7.00000 + 5.65685i 0.777778 + 0.628539i
\(82\) 3.07107i 0.339143i
\(83\) −1.17157 + 1.17157i −0.128597 + 0.128597i −0.768476 0.639879i \(-0.778984\pi\)
0.639879 + 0.768476i \(0.278984\pi\)
\(84\) −4.00000 + 2.82843i −0.436436 + 0.308607i
\(85\) 3.41421 3.41421i 0.370323 0.370323i
\(86\) −3.58579 3.58579i −0.386665 0.386665i
\(87\) −6.24264 1.07107i −0.669281 0.114831i
\(88\) 2.82843i 0.301511i
\(89\) 2.65685 + 2.65685i 0.281626 + 0.281626i 0.833757 0.552131i \(-0.186185\pi\)
−0.552131 + 0.833757i \(0.686185\pi\)
\(90\) 1.00000 2.82843i 0.105409 0.298142i
\(91\) 8.48528 5.65685i 0.889499 0.592999i
\(92\) 6.82843i 0.711913i
\(93\) 8.82843 6.24264i 0.915465 0.647332i
\(94\) 2.82843 0.291730
\(95\) 0 0
\(96\) 1.00000 + 1.41421i 0.102062 + 0.144338i
\(97\) −8.58579 8.58579i −0.871755 0.871755i 0.120909 0.992664i \(-0.461419\pi\)
−0.992664 + 0.120909i \(0.961419\pi\)
\(98\) −0.707107 0.707107i −0.0714286 0.0714286i
\(99\) 3.65685 + 7.65685i 0.367528 + 0.769543i
\(100\) −1.00000 −0.100000
\(101\) −7.17157 −0.713598 −0.356799 0.934181i \(-0.616132\pi\)
−0.356799 + 0.934181i \(0.616132\pi\)
\(102\) 4.82843 + 6.82843i 0.478086 + 0.676115i
\(103\) 14.8284i 1.46109i 0.682865 + 0.730544i \(0.260734\pi\)
−0.682865 + 0.730544i \(0.739266\pi\)
\(104\) −2.00000 3.00000i −0.196116 0.294174i
\(105\) 4.82843 + 0.828427i 0.471206 + 0.0808462i
\(106\) 6.65685 + 6.65685i 0.646571 + 0.646571i
\(107\) 12.5858i 1.21671i 0.793664 + 0.608357i \(0.208171\pi\)
−0.793664 + 0.608357i \(0.791829\pi\)
\(108\) 4.53553 + 2.53553i 0.436432 + 0.243982i
\(109\) −8.24264 8.24264i −0.789502 0.789502i 0.191911 0.981412i \(-0.438532\pi\)
−0.981412 + 0.191911i \(0.938532\pi\)
\(110\) 2.00000 2.00000i 0.190693 0.190693i
\(111\) 5.65685 + 8.00000i 0.536925 + 0.759326i
\(112\) −2.00000 + 2.00000i −0.188982 + 0.188982i
\(113\) 18.4853i 1.73895i 0.493978 + 0.869474i \(0.335542\pi\)
−0.493978 + 0.869474i \(0.664458\pi\)
\(114\) 0 0
\(115\) −4.82843 + 4.82843i −0.450253 + 0.450253i
\(116\) −3.65685 −0.339530
\(117\) −9.29289 5.53553i −0.859128 0.511760i
\(118\) 5.65685 0.520756
\(119\) −9.65685 + 9.65685i −0.885242 + 0.885242i
\(120\) 0.292893 1.70711i 0.0267374 0.155837i
\(121\) 3.00000i 0.272727i
\(122\) 9.07107 9.07107i 0.821256 0.821256i
\(123\) −3.07107 4.34315i −0.276909 0.391608i
\(124\) 4.41421 4.41421i 0.396408 0.396408i
\(125\) 0.707107 + 0.707107i 0.0632456 + 0.0632456i
\(126\) −2.82843 + 8.00000i −0.251976 + 0.712697i
\(127\) 1.65685i 0.147022i 0.997294 + 0.0735110i \(0.0234204\pi\)
−0.997294 + 0.0735110i \(0.976580\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −8.65685 1.48528i −0.762194 0.130772i
\(130\) −0.707107 + 3.53553i −0.0620174 + 0.310087i
\(131\) 11.3137i 0.988483i 0.869325 + 0.494242i \(0.164554\pi\)
−0.869325 + 0.494242i \(0.835446\pi\)
\(132\) 2.82843 + 4.00000i 0.246183 + 0.348155i
\(133\) 0 0
\(134\) 3.17157 0.273982
\(135\) −1.41421 5.00000i −0.121716 0.430331i
\(136\) 3.41421 + 3.41421i 0.292766 + 0.292766i
\(137\) −6.58579 6.58579i −0.562662 0.562662i 0.367401 0.930063i \(-0.380248\pi\)
−0.930063 + 0.367401i \(0.880248\pi\)
\(138\) −6.82843 9.65685i −0.581274 0.822046i
\(139\) −7.31371 −0.620341 −0.310170 0.950681i \(-0.600386\pi\)
−0.310170 + 0.950681i \(0.600386\pi\)
\(140\) 2.82843 0.239046
\(141\) 4.00000 2.82843i 0.336861 0.238197i
\(142\) 14.7279i 1.23594i
\(143\) −5.65685 8.48528i −0.473050 0.709575i
\(144\) 2.82843 + 1.00000i 0.235702 + 0.0833333i
\(145\) 2.58579 + 2.58579i 0.214738 + 0.214738i
\(146\) 14.0000i 1.15865i
\(147\) −1.70711 0.292893i −0.140800 0.0241574i
\(148\) 4.00000 + 4.00000i 0.328798 + 0.328798i
\(149\) 11.8995 11.8995i 0.974845 0.974845i −0.0248467 0.999691i \(-0.507910\pi\)
0.999691 + 0.0248467i \(0.00790975\pi\)
\(150\) −1.41421 + 1.00000i −0.115470 + 0.0816497i
\(151\) −12.4142 + 12.4142i −1.01025 + 1.01025i −0.0103075 + 0.999947i \(0.503281\pi\)
−0.999947 + 0.0103075i \(0.996719\pi\)
\(152\) 0 0
\(153\) 13.6569 + 4.82843i 1.10409 + 0.390355i
\(154\) −5.65685 + 5.65685i −0.455842 + 0.455842i
\(155\) −6.24264 −0.501421
\(156\) −5.82843 2.24264i −0.466648 0.179555i
\(157\) −20.7279 −1.65427 −0.827134 0.562005i \(-0.810030\pi\)
−0.827134 + 0.562005i \(0.810030\pi\)
\(158\) −6.24264 + 6.24264i −0.496638 + 0.496638i
\(159\) 16.0711 + 2.75736i 1.27452 + 0.218673i
\(160\) 1.00000i 0.0790569i
\(161\) 13.6569 13.6569i 1.07631 1.07631i
\(162\) 8.94975 0.949747i 0.703159 0.0746192i
\(163\) −4.48528 + 4.48528i −0.351314 + 0.351314i −0.860598 0.509284i \(-0.829910\pi\)
0.509284 + 0.860598i \(0.329910\pi\)
\(164\) −2.17157 2.17157i −0.169571 0.169571i
\(165\) 0.828427 4.82843i 0.0644930 0.375893i
\(166\) 1.65685i 0.128597i
\(167\) −9.31371 9.31371i −0.720716 0.720716i 0.248035 0.968751i \(-0.420215\pi\)
−0.968751 + 0.248035i \(0.920215\pi\)
\(168\) −0.828427 + 4.82843i −0.0639145 + 0.372521i
\(169\) 12.0000 + 5.00000i 0.923077 + 0.384615i
\(170\) 4.82843i 0.370323i
\(171\) 0 0
\(172\) −5.07107 −0.386665
\(173\) −14.5858 −1.10894 −0.554468 0.832205i \(-0.687078\pi\)
−0.554468 + 0.832205i \(0.687078\pi\)
\(174\) −5.17157 + 3.65685i −0.392056 + 0.277225i
\(175\) −2.00000 2.00000i −0.151186 0.151186i
\(176\) 2.00000 + 2.00000i 0.150756 + 0.150756i
\(177\) 8.00000 5.65685i 0.601317 0.425195i
\(178\) 3.75736 0.281626
\(179\) 2.34315 0.175135 0.0875675 0.996159i \(-0.472091\pi\)
0.0875675 + 0.996159i \(0.472091\pi\)
\(180\) −1.29289 2.70711i −0.0963666 0.201776i
\(181\) 11.6569i 0.866447i −0.901286 0.433224i \(-0.857376\pi\)
0.901286 0.433224i \(-0.142624\pi\)
\(182\) 2.00000 10.0000i 0.148250 0.741249i
\(183\) 3.75736 21.8995i 0.277752 1.61886i
\(184\) −4.82843 4.82843i −0.355956 0.355956i
\(185\) 5.65685i 0.415900i
\(186\) 1.82843 10.6569i 0.134067 0.781398i
\(187\) 9.65685 + 9.65685i 0.706179 + 0.706179i
\(188\) 2.00000 2.00000i 0.145865 0.145865i
\(189\) 4.00000 + 14.1421i 0.290957 + 1.02869i
\(190\) 0 0
\(191\) 12.8284i 0.928232i 0.885774 + 0.464116i \(0.153628\pi\)
−0.885774 + 0.464116i \(0.846372\pi\)
\(192\) 1.70711 + 0.292893i 0.123200 + 0.0211377i
\(193\) −1.07107 + 1.07107i −0.0770971 + 0.0770971i −0.744604 0.667507i \(-0.767362\pi\)
0.667507 + 0.744604i \(0.267362\pi\)
\(194\) −12.1421 −0.871755
\(195\) 2.53553 + 5.70711i 0.181573 + 0.408694i
\(196\) −1.00000 −0.0714286
\(197\) −9.17157 + 9.17157i −0.653448 + 0.653448i −0.953822 0.300374i \(-0.902889\pi\)
0.300374 + 0.953822i \(0.402889\pi\)
\(198\) 8.00000 + 2.82843i 0.568535 + 0.201008i
\(199\) 0.828427i 0.0587256i 0.999569 + 0.0293628i \(0.00934782\pi\)
−0.999569 + 0.0293628i \(0.990652\pi\)
\(200\) −0.707107 + 0.707107i −0.0500000 + 0.0500000i
\(201\) 4.48528 3.17157i 0.316367 0.223706i
\(202\) −5.07107 + 5.07107i −0.356799 + 0.356799i
\(203\) −7.31371 7.31371i −0.513322 0.513322i
\(204\) 8.24264 + 1.41421i 0.577100 + 0.0990148i
\(205\) 3.07107i 0.214493i
\(206\) 10.4853 + 10.4853i 0.730544 + 0.730544i
\(207\) −19.3137 6.82843i −1.34240 0.474608i
\(208\) −3.53553 0.707107i −0.245145 0.0490290i
\(209\) 0 0
\(210\) 4.00000 2.82843i 0.276026 0.195180i
\(211\) −16.9706 −1.16830 −0.584151 0.811645i \(-0.698572\pi\)
−0.584151 + 0.811645i \(0.698572\pi\)
\(212\) 9.41421 0.646571
\(213\) −14.7279 20.8284i −1.00914 1.42714i
\(214\) 8.89949 + 8.89949i 0.608357 + 0.608357i
\(215\) 3.58579 + 3.58579i 0.244549 + 0.244549i
\(216\) 5.00000 1.41421i 0.340207 0.0962250i
\(217\) 17.6569 1.19863
\(218\) −11.6569 −0.789502
\(219\) −14.0000 19.7990i −0.946032 1.33789i
\(220\) 2.82843i 0.190693i
\(221\) −17.0711 3.41421i −1.14832 0.229665i
\(222\) 9.65685 + 1.65685i 0.648126 + 0.111201i
\(223\) −13.6569 13.6569i −0.914531 0.914531i 0.0820940 0.996625i \(-0.473839\pi\)
−0.996625 + 0.0820940i \(0.973839\pi\)
\(224\) 2.82843i 0.188982i
\(225\) −1.00000 + 2.82843i −0.0666667 + 0.188562i
\(226\) 13.0711 + 13.0711i 0.869474 + 0.869474i
\(227\) 11.4142 11.4142i 0.757588 0.757588i −0.218295 0.975883i \(-0.570049\pi\)
0.975883 + 0.218295i \(0.0700495\pi\)
\(228\) 0 0
\(229\) −15.8995 + 15.8995i −1.05067 + 1.05067i −0.0520223 + 0.998646i \(0.516567\pi\)
−0.998646 + 0.0520223i \(0.983433\pi\)
\(230\) 6.82843i 0.450253i
\(231\) −2.34315 + 13.6569i −0.154168 + 0.898555i
\(232\) −2.58579 + 2.58579i −0.169765 + 0.169765i
\(233\) 0.142136 0.00931161 0.00465581 0.999989i \(-0.498518\pi\)
0.00465581 + 0.999989i \(0.498518\pi\)
\(234\) −10.4853 + 2.65685i −0.685444 + 0.173684i
\(235\) −2.82843 −0.184506
\(236\) 4.00000 4.00000i 0.260378 0.260378i
\(237\) −2.58579 + 15.0711i −0.167965 + 0.978971i
\(238\) 13.6569i 0.885242i
\(239\) 12.0711 12.0711i 0.780812 0.780812i −0.199155 0.979968i \(-0.563820\pi\)
0.979968 + 0.199155i \(0.0638199\pi\)
\(240\) −1.00000 1.41421i −0.0645497 0.0912871i
\(241\) −2.65685 + 2.65685i −0.171143 + 0.171143i −0.787481 0.616338i \(-0.788615\pi\)
0.616338 + 0.787481i \(0.288615\pi\)
\(242\) −2.12132 2.12132i −0.136364 0.136364i
\(243\) 11.7071 10.2929i 0.751011 0.660289i
\(244\) 12.8284i 0.821256i
\(245\) 0.707107 + 0.707107i 0.0451754 + 0.0451754i
\(246\) −5.24264 0.899495i −0.334259 0.0573497i
\(247\) 0 0
\(248\) 6.24264i 0.396408i
\(249\) 1.65685 + 2.34315i 0.104999 + 0.148491i
\(250\) 1.00000 0.0632456
\(251\) −4.97056 −0.313739 −0.156870 0.987619i \(-0.550140\pi\)
−0.156870 + 0.987619i \(0.550140\pi\)
\(252\) 3.65685 + 7.65685i 0.230360 + 0.482336i
\(253\) −13.6569 13.6569i −0.858599 0.858599i
\(254\) 1.17157 + 1.17157i 0.0735110 + 0.0735110i
\(255\) −4.82843 6.82843i −0.302368 0.427613i
\(256\) 1.00000 0.0625000
\(257\) 26.4853 1.65211 0.826053 0.563592i \(-0.190581\pi\)
0.826053 + 0.563592i \(0.190581\pi\)
\(258\) −7.17157 + 5.07107i −0.446483 + 0.315711i
\(259\) 16.0000i 0.994192i
\(260\) 2.00000 + 3.00000i 0.124035 + 0.186052i
\(261\) −3.65685 + 10.3431i −0.226354 + 0.640225i
\(262\) 8.00000 + 8.00000i 0.494242 + 0.494242i
\(263\) 7.51472i 0.463377i 0.972790 + 0.231689i \(0.0744251\pi\)
−0.972790 + 0.231689i \(0.925575\pi\)
\(264\) 4.82843 + 0.828427i 0.297169 + 0.0509862i
\(265\) −6.65685 6.65685i −0.408927 0.408927i
\(266\) 0 0
\(267\) 5.31371 3.75736i 0.325194 0.229947i
\(268\) 2.24264 2.24264i 0.136991 0.136991i
\(269\) 12.8284i 0.782163i −0.920356 0.391082i \(-0.872101\pi\)
0.920356 0.391082i \(-0.127899\pi\)
\(270\) −4.53553 2.53553i −0.276024 0.154308i
\(271\) 12.5563 12.5563i 0.762744 0.762744i −0.214074 0.976818i \(-0.568673\pi\)
0.976818 + 0.214074i \(0.0686733\pi\)
\(272\) 4.82843 0.292766
\(273\) −7.17157 16.1421i −0.434043 0.976966i
\(274\) −9.31371 −0.562662
\(275\) −2.00000 + 2.00000i −0.120605 + 0.120605i
\(276\) −11.6569 2.00000i −0.701660 0.120386i
\(277\) 8.72792i 0.524410i 0.965012 + 0.262205i \(0.0844497\pi\)
−0.965012 + 0.262205i \(0.915550\pi\)
\(278\) −5.17157 + 5.17157i −0.310170 + 0.310170i
\(279\) −8.07107 16.8995i −0.483202 1.01175i
\(280\) 2.00000 2.00000i 0.119523 0.119523i
\(281\) −15.0000 15.0000i −0.894825 0.894825i 0.100148 0.994973i \(-0.468068\pi\)
−0.994973 + 0.100148i \(0.968068\pi\)
\(282\) 0.828427 4.82843i 0.0493321 0.287529i
\(283\) 9.75736i 0.580015i −0.957024 0.290007i \(-0.906342\pi\)
0.957024 0.290007i \(-0.0936578\pi\)
\(284\) −10.4142 10.4142i −0.617970 0.617970i
\(285\) 0 0
\(286\) −10.0000 2.00000i −0.591312 0.118262i
\(287\) 8.68629i 0.512736i
\(288\) 2.70711 1.29289i 0.159518 0.0761845i
\(289\) 6.31371 0.371395
\(290\) 3.65685 0.214738
\(291\) −17.1716 + 12.1421i −1.00662 + 0.711785i
\(292\) −9.89949 9.89949i −0.579324 0.579324i
\(293\) 16.4853 + 16.4853i 0.963080 + 0.963080i 0.999342 0.0362619i \(-0.0115451\pi\)
−0.0362619 + 0.999342i \(0.511545\pi\)
\(294\) −1.41421 + 1.00000i −0.0824786 + 0.0583212i
\(295\) −5.65685 −0.329355
\(296\) 5.65685 0.328798
\(297\) 14.1421 4.00000i 0.820610 0.232104i
\(298\) 16.8284i 0.974845i
\(299\) 24.1421 + 4.82843i 1.39618 + 0.279235i
\(300\) −0.292893 + 1.70711i −0.0169102 + 0.0985599i
\(301\) −10.1421 10.1421i −0.584583 0.584583i
\(302\) 17.5563i 1.01025i
\(303\) −2.10051 + 12.2426i −0.120671 + 0.703321i
\(304\) 0 0
\(305\) −9.07107 + 9.07107i −0.519408 + 0.519408i
\(306\) 13.0711 6.24264i 0.747223 0.356868i
\(307\) −8.58579 + 8.58579i −0.490017 + 0.490017i −0.908311 0.418295i \(-0.862628\pi\)
0.418295 + 0.908311i \(0.362628\pi\)
\(308\) 8.00000i 0.455842i
\(309\) 25.3137 + 4.34315i 1.44005 + 0.247073i
\(310\) −4.41421 + 4.41421i −0.250710 + 0.250710i
\(311\) 30.6274 1.73672 0.868361 0.495933i \(-0.165174\pi\)
0.868361 + 0.495933i \(0.165174\pi\)
\(312\) −5.70711 + 2.53553i −0.323101 + 0.143546i
\(313\) 18.9706 1.07228 0.536140 0.844129i \(-0.319882\pi\)
0.536140 + 0.844129i \(0.319882\pi\)
\(314\) −14.6569 + 14.6569i −0.827134 + 0.827134i
\(315\) 2.82843 8.00000i 0.159364 0.450749i
\(316\) 8.82843i 0.496638i
\(317\) −16.9706 + 16.9706i −0.953162 + 0.953162i −0.998951 0.0457894i \(-0.985420\pi\)
0.0457894 + 0.998951i \(0.485420\pi\)
\(318\) 13.3137 9.41421i 0.746596 0.527923i
\(319\) −7.31371 + 7.31371i −0.409489 + 0.409489i
\(320\) −0.707107 0.707107i −0.0395285 0.0395285i
\(321\) 21.4853 + 3.68629i 1.19919 + 0.205749i
\(322\) 19.3137i 1.07631i
\(323\) 0 0
\(324\) 5.65685 7.00000i 0.314270 0.388889i
\(325\) 0.707107 3.53553i 0.0392232 0.196116i
\(326\) 6.34315i 0.351314i
\(327\) −16.4853 + 11.6569i −0.911638 + 0.644626i
\(328\) −3.07107 −0.169571
\(329\) 8.00000 0.441054
\(330\) −2.82843 4.00000i −0.155700 0.220193i
\(331\) −6.00000 6.00000i −0.329790 0.329790i 0.522717 0.852506i \(-0.324919\pi\)
−0.852506 + 0.522717i \(0.824919\pi\)
\(332\) 1.17157 + 1.17157i 0.0642984 + 0.0642984i
\(333\) 15.3137 7.31371i 0.839186 0.400789i
\(334\) −13.1716 −0.720716
\(335\) −3.17157 −0.173282
\(336\) 2.82843 + 4.00000i 0.154303 + 0.218218i
\(337\) 25.3137i 1.37893i 0.724321 + 0.689463i \(0.242153\pi\)
−0.724321 + 0.689463i \(0.757847\pi\)
\(338\) 12.0208 4.94975i 0.653846 0.269231i
\(339\) 31.5563 + 5.41421i 1.71391 + 0.294060i
\(340\) −3.41421 3.41421i −0.185162 0.185162i
\(341\) 17.6569i 0.956172i
\(342\) 0 0
\(343\) 12.0000 + 12.0000i 0.647939 + 0.647939i
\(344\) −3.58579 + 3.58579i −0.193333 + 0.193333i
\(345\) 6.82843 + 9.65685i 0.367630 + 0.519908i
\(346\) −10.3137 + 10.3137i −0.554468 + 0.554468i
\(347\) 31.6985i 1.70166i 0.525438 + 0.850832i \(0.323901\pi\)
−0.525438 + 0.850832i \(0.676099\pi\)
\(348\) −1.07107 + 6.24264i −0.0574153 + 0.334641i
\(349\) 18.3848 18.3848i 0.984115 0.984115i −0.0157613 0.999876i \(-0.505017\pi\)
0.999876 + 0.0157613i \(0.00501718\pi\)
\(350\) −2.82843 −0.151186
\(351\) −12.1716 + 14.2426i −0.649670 + 0.760216i
\(352\) 2.82843 0.150756
\(353\) −3.89949 + 3.89949i −0.207549 + 0.207549i −0.803225 0.595676i \(-0.796884\pi\)
0.595676 + 0.803225i \(0.296884\pi\)
\(354\) 1.65685 9.65685i 0.0880608 0.513256i
\(355\) 14.7279i 0.781677i
\(356\) 2.65685 2.65685i 0.140813 0.140813i
\(357\) 13.6569 + 19.3137i 0.722797 + 1.02219i
\(358\) 1.65685 1.65685i 0.0875675 0.0875675i
\(359\) −2.41421 2.41421i −0.127417 0.127417i 0.640522 0.767940i \(-0.278718\pi\)
−0.767940 + 0.640522i \(0.778718\pi\)
\(360\) −2.82843 1.00000i −0.149071 0.0527046i
\(361\) 19.0000i 1.00000i
\(362\) −8.24264 8.24264i −0.433224 0.433224i
\(363\) −5.12132 0.878680i −0.268800 0.0461187i
\(364\) −5.65685 8.48528i −0.296500 0.444750i
\(365\) 14.0000i 0.732793i
\(366\) −12.8284 18.1421i −0.670553 0.948305i
\(367\) 37.4558 1.95518 0.977590 0.210520i \(-0.0675157\pi\)
0.977590 + 0.210520i \(0.0675157\pi\)
\(368\) −6.82843 −0.355956
\(369\) −8.31371 + 3.97056i −0.432794 + 0.206699i
\(370\) −4.00000 4.00000i −0.207950 0.207950i
\(371\) 18.8284 + 18.8284i 0.977523 + 0.977523i
\(372\) −6.24264 8.82843i −0.323666 0.457733i
\(373\) −28.7279 −1.48748 −0.743738 0.668472i \(-0.766949\pi\)
−0.743738 + 0.668472i \(0.766949\pi\)
\(374\) 13.6569 0.706179
\(375\) 1.41421 1.00000i 0.0730297 0.0516398i
\(376\) 2.82843i 0.145865i
\(377\) 2.58579 12.9289i 0.133175 0.665874i
\(378\) 12.8284 + 7.17157i 0.659823 + 0.368866i
\(379\) 7.51472 + 7.51472i 0.386005 + 0.386005i 0.873260 0.487255i \(-0.162002\pi\)
−0.487255 + 0.873260i \(0.662002\pi\)
\(380\) 0 0
\(381\) 2.82843 + 0.485281i 0.144905 + 0.0248617i
\(382\) 9.07107 + 9.07107i 0.464116 + 0.464116i
\(383\) 4.00000 4.00000i 0.204390 0.204390i −0.597488 0.801878i \(-0.703834\pi\)
0.801878 + 0.597488i \(0.203834\pi\)
\(384\) 1.41421 1.00000i 0.0721688 0.0510310i
\(385\) 5.65685 5.65685i 0.288300 0.288300i
\(386\) 1.51472i 0.0770971i
\(387\) −5.07107 + 14.3431i −0.257777 + 0.729103i
\(388\) −8.58579 + 8.58579i −0.435877 + 0.435877i
\(389\) −31.6569 −1.60507 −0.802533 0.596608i \(-0.796515\pi\)
−0.802533 + 0.596608i \(0.796515\pi\)
\(390\) 5.82843 + 2.24264i 0.295134 + 0.113561i
\(391\) −32.9706 −1.66739
\(392\) −0.707107 + 0.707107i −0.0357143 + 0.0357143i
\(393\) 19.3137 + 3.31371i 0.974248 + 0.167154i
\(394\) 12.9706i 0.653448i
\(395\) 6.24264 6.24264i 0.314101 0.314101i
\(396\) 7.65685 3.65685i 0.384771 0.183764i
\(397\) 6.58579 6.58579i 0.330531 0.330531i −0.522257 0.852788i \(-0.674910\pi\)
0.852788 + 0.522257i \(0.174910\pi\)
\(398\) 0.585786 + 0.585786i 0.0293628 + 0.0293628i
\(399\) 0 0
\(400\) 1.00000i 0.0500000i
\(401\) −21.6274 21.6274i −1.08002 1.08002i −0.996507 0.0835152i \(-0.973385\pi\)
−0.0835152 0.996507i \(-0.526615\pi\)
\(402\) 0.928932 5.41421i 0.0463309 0.270036i
\(403\) 12.4853 + 18.7279i 0.621936 + 0.932904i
\(404\) 7.17157i 0.356799i
\(405\) −8.94975 + 0.949747i −0.444717 + 0.0471933i
\(406\) −10.3431 −0.513322
\(407\) 16.0000 0.793091
\(408\) 6.82843 4.82843i 0.338058 0.239043i
\(409\) 13.4853 + 13.4853i 0.666804 + 0.666804i 0.956975 0.290171i \(-0.0937121\pi\)
−0.290171 + 0.956975i \(0.593712\pi\)
\(410\) 2.17157 + 2.17157i 0.107246 + 0.107246i
\(411\) −13.1716 + 9.31371i −0.649706 + 0.459411i
\(412\) 14.8284 0.730544
\(413\) 16.0000 0.787309
\(414\) −18.4853 + 8.82843i −0.908502 + 0.433894i
\(415\) 1.65685i 0.0813318i
\(416\) −3.00000 + 2.00000i −0.147087 + 0.0980581i
\(417\) −2.14214 + 12.4853i −0.104901 + 0.611407i
\(418\) 0 0
\(419\) 5.17157i 0.252648i −0.991989 0.126324i \(-0.959682\pi\)
0.991989 0.126324i \(-0.0403179\pi\)
\(420\) 0.828427 4.82843i 0.0404231 0.235603i
\(421\) −5.89949 5.89949i −0.287524 0.287524i 0.548577 0.836100i \(-0.315170\pi\)
−0.836100 + 0.548577i \(0.815170\pi\)
\(422\) −12.0000 + 12.0000i −0.584151 + 0.584151i
\(423\) −3.65685 7.65685i −0.177802 0.372289i
\(424\) 6.65685 6.65685i 0.323285 0.323285i
\(425\) 4.82843i 0.234213i
\(426\) −25.1421 4.31371i −1.21814 0.209000i
\(427\) 25.6569 25.6569i 1.24162 1.24162i
\(428\) 12.5858 0.608357
\(429\) −16.1421 + 7.17157i −0.779350 + 0.346247i
\(430\) 5.07107 0.244549
\(431\) 15.2426 15.2426i 0.734212 0.734212i −0.237239 0.971451i \(-0.576242\pi\)
0.971451 + 0.237239i \(0.0762425\pi\)
\(432\) 2.53553 4.53553i 0.121991 0.218216i
\(433\) 35.6569i 1.71356i 0.515683 + 0.856780i \(0.327538\pi\)
−0.515683 + 0.856780i \(0.672462\pi\)
\(434\) 12.4853 12.4853i 0.599313 0.599313i
\(435\) 5.17157 3.65685i 0.247958 0.175333i
\(436\) −8.24264 + 8.24264i −0.394751 + 0.394751i
\(437\) 0 0
\(438\) −23.8995 4.10051i −1.14196 0.195930i
\(439\) 24.0000i 1.14546i −0.819745 0.572729i \(-0.805885\pi\)
0.819745 0.572729i \(-0.194115\pi\)
\(440\) −2.00000 2.00000i −0.0953463 0.0953463i
\(441\) −1.00000 + 2.82843i −0.0476190 + 0.134687i
\(442\) −14.4853 + 9.65685i −0.688995 + 0.459330i
\(443\) 23.8995i 1.13550i 0.823201 + 0.567750i \(0.192186\pi\)
−0.823201 + 0.567750i \(0.807814\pi\)
\(444\) 8.00000 5.65685i 0.379663 0.268462i
\(445\) −3.75736 −0.178116
\(446\) −19.3137 −0.914531
\(447\) −16.8284 23.7990i −0.795957 1.12565i
\(448\) 2.00000 + 2.00000i 0.0944911 + 0.0944911i
\(449\) −7.34315 7.34315i −0.346544 0.346544i 0.512276 0.858821i \(-0.328802\pi\)
−0.858821 + 0.512276i \(0.828802\pi\)
\(450\) 1.29289 + 2.70711i 0.0609476 + 0.127614i
\(451\) −8.68629 −0.409021
\(452\) 18.4853 0.869474
\(453\) 17.5563 + 24.8284i 0.824869 + 1.16654i
\(454\) 16.1421i 0.757588i
\(455\) −2.00000 + 10.0000i −0.0937614 + 0.468807i
\(456\) 0 0
\(457\) 11.4142 + 11.4142i 0.533934 + 0.533934i 0.921741 0.387806i \(-0.126767\pi\)
−0.387806 + 0.921741i \(0.626767\pi\)
\(458\) 22.4853i 1.05067i
\(459\) 12.2426 21.8995i 0.571438 1.02218i
\(460\) 4.82843 + 4.82843i 0.225127 + 0.225127i
\(461\) 8.72792 8.72792i 0.406500 0.406500i −0.474016 0.880516i \(-0.657196\pi\)
0.880516 + 0.474016i \(0.157196\pi\)
\(462\) 8.00000 + 11.3137i 0.372194 + 0.526361i
\(463\) 12.0000 12.0000i 0.557687 0.557687i −0.370961 0.928648i \(-0.620972\pi\)
0.928648 + 0.370961i \(0.120972\pi\)
\(464\) 3.65685i 0.169765i
\(465\) −1.82843 + 10.6569i −0.0847913 + 0.494200i
\(466\) 0.100505 0.100505i 0.00465581 0.00465581i
\(467\) 2.24264 0.103777 0.0518885 0.998653i \(-0.483476\pi\)
0.0518885 + 0.998653i \(0.483476\pi\)
\(468\) −5.53553 + 9.29289i −0.255880 + 0.429564i
\(469\) 8.97056 0.414222
\(470\) −2.00000 + 2.00000i −0.0922531 + 0.0922531i
\(471\) −6.07107 + 35.3848i −0.279740 + 1.63044i
\(472\) 5.65685i 0.260378i
\(473\) −10.1421 + 10.1421i −0.466336 + 0.466336i
\(474\) 8.82843 + 12.4853i 0.405503 + 0.573468i
\(475\) 0 0
\(476\) 9.65685 + 9.65685i 0.442621 + 0.442621i
\(477\) 9.41421 26.6274i 0.431047 1.21919i
\(478\) 17.0711i 0.780812i
\(479\) −2.41421 2.41421i −0.110308 0.110308i 0.649798 0.760107i \(-0.274853\pi\)
−0.760107 + 0.649798i \(0.774853\pi\)
\(480\) −1.70711 0.292893i −0.0779184 0.0133687i
\(481\) −16.9706 + 11.3137i −0.773791 + 0.515861i
\(482\) 3.75736i 0.171143i
\(483\) −19.3137 27.3137i −0.878804 1.24282i
\(484\) −3.00000 −0.136364
\(485\) 12.1421 0.551346
\(486\) 1.00000 15.5563i 0.0453609 0.705650i
\(487\) 23.4558 + 23.4558i 1.06289 + 1.06289i 0.997885 + 0.0650005i \(0.0207049\pi\)
0.0650005 + 0.997885i \(0.479295\pi\)
\(488\) −9.07107 9.07107i −0.410628 0.410628i
\(489\) 6.34315 + 8.97056i 0.286847 + 0.405663i
\(490\) 1.00000 0.0451754
\(491\) −9.85786 −0.444879 −0.222440 0.974946i \(-0.571402\pi\)
−0.222440 + 0.974946i \(0.571402\pi\)
\(492\) −4.34315 + 3.07107i −0.195804 + 0.138454i
\(493\) 17.6569i 0.795225i
\(494\) 0 0
\(495\) −8.00000 2.82843i −0.359573 0.127128i
\(496\) −4.41421 4.41421i −0.198204 0.198204i
\(497\) 41.6569i 1.86857i
\(498\) 2.82843 + 0.485281i 0.126745 + 0.0217460i
\(499\) 22.4853 + 22.4853i 1.00658 + 1.00658i 0.999978 + 0.00660122i \(0.00210125\pi\)
0.00660122 + 0.999978i \(0.497899\pi\)
\(500\) 0.707107 0.707107i 0.0316228 0.0316228i
\(501\) −18.6274 + 13.1716i −0.832212 + 0.588462i
\(502\) −3.51472 + 3.51472i −0.156870 + 0.156870i
\(503\) 8.68629i 0.387303i −0.981070 0.193651i \(-0.937967\pi\)
0.981070 0.193651i \(-0.0620330\pi\)
\(504\) 8.00000 + 2.82843i 0.356348 + 0.125988i
\(505\) 5.07107 5.07107i 0.225660 0.225660i
\(506\) −19.3137 −0.858599
\(507\) 12.0503 19.0208i 0.535171 0.844744i
\(508\) 1.65685 0.0735110
\(509\) −18.7279 + 18.7279i −0.830101 + 0.830101i −0.987530 0.157430i \(-0.949679\pi\)
0.157430 + 0.987530i \(0.449679\pi\)
\(510\) −8.24264 1.41421i −0.364990 0.0626224i
\(511\) 39.5980i 1.75171i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) 18.7279 18.7279i 0.826053 0.826053i
\(515\) −10.4853 10.4853i −0.462037 0.462037i
\(516\) −1.48528 + 8.65685i −0.0653859 + 0.381097i
\(517\) 8.00000i 0.351840i
\(518\) 11.3137 + 11.3137i 0.497096 + 0.497096i
\(519\) −4.27208 + 24.8995i −0.187523 + 1.09297i
\(520\) 3.53553 + 0.707107i 0.155043 + 0.0310087i
\(521\) 2.68629i 0.117689i −0.998267 0.0588443i \(-0.981258\pi\)
0.998267 0.0588443i \(-0.0187415\pi\)
\(522\) 4.72792 + 9.89949i 0.206936 + 0.433289i
\(523\) 11.8995 0.520329 0.260164 0.965564i \(-0.416223\pi\)
0.260164 + 0.965564i \(0.416223\pi\)
\(524\) 11.3137 0.494242
\(525\) −4.00000 + 2.82843i −0.174574 + 0.123443i
\(526\) 5.31371 + 5.31371i 0.231689 + 0.231689i
\(527\) −21.3137 21.3137i −0.928440 0.928440i
\(528\) 4.00000 2.82843i 0.174078 0.123091i
\(529\) 23.6274 1.02728
\(530\) −9.41421 −0.408927
\(531\) −7.31371 15.3137i −0.317388 0.664558i
\(532\) 0 0
\(533\) 9.21320 6.14214i 0.399068 0.266045i
\(534\) 1.10051 6.41421i 0.0476235 0.277570i
\(535\) −8.89949 8.89949i −0.384759 0.384759i
\(536\) 3.17157i 0.136991i
\(537\) 0.686292 4.00000i 0.0296157 0.172613i
\(538\) −9.07107 9.07107i −0.391082 0.391082i
\(539\) −2.00000 + 2.00000i −0.0861461 + 0.0861461i
\(540\) −5.00000 + 1.41421i −0.215166 + 0.0608581i
\(541\) −25.0711 + 25.0711i −1.07789 + 1.07789i −0.0811908 + 0.996699i \(0.525872\pi\)
−0.996699 + 0.0811908i \(0.974128\pi\)
\(542\) 17.7574i 0.762744i
\(543\) −19.8995 3.41421i −0.853969 0.146518i
\(544\) 3.41421 3.41421i 0.146383 0.146383i
\(545\) 11.6569 0.499325
\(546\) −16.4853 6.34315i −0.705505 0.271462i
\(547\) −35.8995 −1.53495 −0.767476 0.641078i \(-0.778488\pi\)
−0.767476 + 0.641078i \(0.778488\pi\)
\(548\) −6.58579 + 6.58579i −0.281331 + 0.281331i
\(549\) −36.2843 12.8284i −1.54857 0.547504i
\(550\) 2.82843i 0.120605i
\(551\) 0 0
\(552\) −9.65685 + 6.82843i −0.411023 + 0.290637i
\(553\) −17.6569 + 17.6569i −0.750846 + 0.750846i
\(554\) 6.17157 + 6.17157i 0.262205 + 0.262205i
\(555\) −9.65685 1.65685i −0.409911 0.0703295i
\(556\) 7.31371i 0.310170i
\(557\) −15.7990 15.7990i −0.669425 0.669425i 0.288158 0.957583i \(-0.406957\pi\)
−0.957583 + 0.288158i \(0.906957\pi\)
\(558\) −17.6569 6.24264i −0.747474 0.264272i
\(559\) 3.58579 17.9289i 0.151663 0.758313i
\(560\) 2.82843i 0.119523i
\(561\) 19.3137 13.6569i 0.815425 0.576593i
\(562\) −21.2132 −0.894825
\(563\) −15.8995 −0.670084 −0.335042 0.942203i \(-0.608750\pi\)
−0.335042 + 0.942203i \(0.608750\pi\)
\(564\) −2.82843 4.00000i −0.119098 0.168430i
\(565\) −13.0711 13.0711i −0.549904 0.549904i
\(566\) −6.89949 6.89949i −0.290007 0.290007i
\(567\) 25.3137 2.68629i 1.06308 0.112814i
\(568\) −14.7279 −0.617970
\(569\) −31.9411 −1.33904 −0.669521 0.742793i \(-0.733501\pi\)
−0.669521 + 0.742793i \(0.733501\pi\)
\(570\) 0 0
\(571\) 1.17157i 0.0490288i −0.999699 0.0245144i \(-0.992196\pi\)
0.999699 0.0245144i \(-0.00780396\pi\)
\(572\) −8.48528 + 5.65685i −0.354787 + 0.236525i
\(573\) 21.8995 + 3.75736i 0.914865 + 0.156966i
\(574\) −6.14214 6.14214i −0.256368 0.256368i
\(575\) 6.82843i 0.284765i
\(576\) 1.00000 2.82843i 0.0416667 0.117851i
\(577\) −0.727922 0.727922i −0.0303038 0.0303038i 0.691793 0.722096i \(-0.256821\pi\)
−0.722096 + 0.691793i \(0.756821\pi\)
\(578\) 4.46447 4.46447i 0.185697 0.185697i
\(579\) 1.51472 + 2.14214i 0.0629496 + 0.0890241i
\(580\) 2.58579 2.58579i 0.107369 0.107369i
\(581\) 4.68629i 0.194420i
\(582\) −3.55635 + 20.7279i −0.147415 + 0.859200i
\(583\) 18.8284 18.8284i 0.779794 0.779794i
\(584\) −14.0000 −0.579324
\(585\) 10.4853 2.65685i 0.433513 0.109847i
\(586\) 23.3137 0.963080
\(587\) 27.7990 27.7990i 1.14739 1.14739i 0.160322 0.987065i \(-0.448747\pi\)
0.987065 0.160322i \(-0.0512534\pi\)
\(588\) −0.292893 + 1.70711i −0.0120787 + 0.0703999i
\(589\) 0 0
\(590\) −4.00000 + 4.00000i −0.164677 + 0.164677i
\(591\) 12.9706 + 18.3431i 0.533538 + 0.754536i
\(592\) 4.00000 4.00000i 0.164399 0.164399i
\(593\) −11.8995 11.8995i −0.488654 0.488654i 0.419228 0.907881i \(-0.362301\pi\)
−0.907881 + 0.419228i \(0.862301\pi\)
\(594\) 7.17157 12.8284i 0.294253 0.526357i
\(595\) 13.6569i 0.559876i
\(596\) −11.8995 11.8995i −0.487422 0.487422i
\(597\) 1.41421 + 0.242641i 0.0578799 + 0.00993062i
\(598\) 20.4853 13.6569i 0.837705 0.558470i
\(599\) 21.5147i 0.879068i −0.898226 0.439534i \(-0.855144\pi\)
0.898226 0.439534i \(-0.144856\pi\)
\(600\) 1.00000 + 1.41421i 0.0408248 + 0.0577350i
\(601\) −8.28427 −0.337922 −0.168961 0.985623i \(-0.554041\pi\)
−0.168961 + 0.985623i \(0.554041\pi\)
\(602\) −14.3431 −0.584583
\(603\) −4.10051 8.58579i −0.166985 0.349640i
\(604\) 12.4142 + 12.4142i 0.505127 + 0.505127i
\(605\) 2.12132 + 2.12132i 0.0862439 + 0.0862439i
\(606\) 7.17157 + 10.1421i 0.291325 + 0.411996i
\(607\) 0.686292 0.0278557 0.0139279 0.999903i \(-0.495566\pi\)
0.0139279 + 0.999903i \(0.495566\pi\)
\(608\) 0 0
\(609\) −14.6274 + 10.3431i −0.592733 + 0.419125i
\(610\) 12.8284i 0.519408i
\(611\) 5.65685 + 8.48528i 0.228852 + 0.343278i
\(612\) 4.82843 13.6569i 0.195178 0.552046i
\(613\) 18.6274 + 18.6274i 0.752354 + 0.752354i 0.974918 0.222564i \(-0.0714426\pi\)
−0.222564 + 0.974918i \(0.571443\pi\)
\(614\) 12.1421i 0.490017i
\(615\) 5.24264 + 0.899495i 0.211404 + 0.0362711i
\(616\) 5.65685 + 5.65685i 0.227921 + 0.227921i
\(617\) 2.72792 2.72792i 0.109822 0.109822i −0.650060 0.759882i \(-0.725256\pi\)
0.759882 + 0.650060i \(0.225256\pi\)
\(618\) 20.9706 14.8284i 0.843560 0.596487i
\(619\) 21.3137 21.3137i 0.856670 0.856670i −0.134274 0.990944i \(-0.542870\pi\)
0.990944 + 0.134274i \(0.0428702\pi\)
\(620\) 6.24264i 0.250710i
\(621\) −17.3137 + 30.9706i −0.694775 + 1.24281i
\(622\) 21.6569 21.6569i 0.868361 0.868361i
\(623\) 10.6274 0.425778
\(624\) −2.24264 + 5.82843i −0.0897775 + 0.233324i
\(625\) −1.00000 −0.0400000
\(626\) 13.4142 13.4142i 0.536140 0.536140i
\(627\) 0 0
\(628\) 20.7279i 0.827134i
\(629\) 19.3137 19.3137i 0.770088 0.770088i
\(630\) −3.65685 7.65685i −0.145693 0.305056i
\(631\) 34.2132 34.2132i 1.36201 1.36201i 0.490649 0.871358i \(-0.336760\pi\)
0.871358 0.490649i \(-0.163240\pi\)
\(632\) 6.24264 + 6.24264i 0.248319 + 0.248319i
\(633\) −4.97056 + 28.9706i −0.197562 + 1.15148i
\(634\) 24.0000i 0.953162i
\(635\) −1.17157 1.17157i −0.0464925 0.0464925i
\(636\) 2.75736 16.0711i 0.109336 0.637259i
\(637\) 0.707107 3.53553i 0.0280166 0.140083i
\(638\) 10.3431i 0.409489i
\(639\) −39.8701 + 19.0416i −1.57724 + 0.753275i
\(640\) −1.00000 −0.0395285
\(641\) −16.9706 −0.670297 −0.335148 0.942165i \(-0.608786\pi\)
−0.335148 + 0.942165i \(0.608786\pi\)
\(642\) 17.7990 12.5858i 0.702470 0.496721i
\(643\) −23.7990 23.7990i −0.938541 0.938541i 0.0596772 0.998218i \(-0.480993\pi\)
−0.998218 + 0.0596772i \(0.980993\pi\)
\(644\) −13.6569 13.6569i −0.538155 0.538155i
\(645\) 7.17157 5.07107i 0.282380 0.199673i
\(646\) 0 0
\(647\) 5.65685 0.222394 0.111197 0.993798i \(-0.464532\pi\)
0.111197 + 0.993798i \(0.464532\pi\)
\(648\) −0.949747 8.94975i −0.0373096 0.351579i
\(649\) 16.0000i 0.628055i
\(650\) −2.00000 3.00000i −0.0784465 0.117670i
\(651\) 5.17157 30.1421i 0.202690 1.18136i
\(652\) 4.48528 + 4.48528i 0.175657 + 0.175657i
\(653\) 9.21320i 0.360541i −0.983617 0.180270i \(-0.942303\pi\)
0.983617 0.180270i \(-0.0576972\pi\)
\(654\) −3.41421 + 19.8995i −0.133506 + 0.778132i
\(655\) −8.00000 8.00000i −0.312586 0.312586i
\(656\) −2.17157 + 2.17157i −0.0847857 + 0.0847857i
\(657\) −37.8995 + 18.1005i −1.47860 + 0.706168i
\(658\) 5.65685 5.65685i 0.220527 0.220527i
\(659\) 17.1716i 0.668910i 0.942412 + 0.334455i \(0.108552\pi\)
−0.942412 + 0.334455i \(0.891448\pi\)
\(660\) −4.82843 0.828427i −0.187946 0.0322465i
\(661\) 10.9289 10.9289i 0.425086 0.425086i −0.461864 0.886951i \(-0.652819\pi\)
0.886951 + 0.461864i \(0.152819\pi\)
\(662\) −8.48528 −0.329790
\(663\) −10.8284 + 28.1421i −0.420541 + 1.09295i
\(664\) 1.65685 0.0642984
\(665\) 0 0
\(666\) 5.65685 16.0000i 0.219199 0.619987i
\(667\) 24.9706i 0.966864i
\(668\) −9.31371 + 9.31371i −0.360358 + 0.360358i
\(669\) −27.3137 + 19.3137i −1.05601 + 0.746711i
\(670\) −2.24264 + 2.24264i −0.0866408 + 0.0866408i
\(671\) −25.6569 25.6569i −0.990472 0.990472i
\(672\) 4.82843 + 0.828427i 0.186261 + 0.0319573i
\(673\) 45.1127i 1.73897i −0.493962 0.869483i \(-0.664452\pi\)
0.493962 0.869483i \(-0.335548\pi\)
\(674\) 17.8995 + 17.8995i 0.689463 + 0.689463i
\(675\) 4.53553 + 2.53553i 0.174573 + 0.0975927i
\(676\) 5.00000 12.0000i 0.192308 0.461538i
\(677\) 13.8995i 0.534201i −0.963669 0.267100i \(-0.913934\pi\)
0.963669 0.267100i \(-0.0860656\pi\)
\(678\) 26.1421 18.4853i 1.00398 0.709923i
\(679\) −34.3431 −1.31797
\(680\) −4.82843 −0.185162
\(681\) −16.1421 22.8284i −0.618568 0.874787i
\(682\) −12.4853 12.4853i −0.478086 0.478086i
\(683\) −23.4142 23.4142i −0.895920 0.895920i 0.0991523 0.995072i \(-0.468387\pi\)
−0.995072 + 0.0991523i \(0.968387\pi\)
\(684\) 0 0
\(685\) 9.31371 0.355859
\(686\) 16.9706 0.647939
\(687\) 22.4853 + 31.7990i 0.857867 + 1.21321i
\(688\) 5.07107i 0.193333i
\(689\) −6.65685 + 33.2843i −0.253606 + 1.26803i
\(690\) 11.6569 + 2.00000i 0.443769 + 0.0761387i
\(691\) 8.14214 + 8.14214i 0.309741 + 0.309741i 0.844809 0.535068i \(-0.179714\pi\)
−0.535068 + 0.844809i \(0.679714\pi\)
\(692\) 14.5858i 0.554468i
\(693\) 22.6274 + 8.00000i 0.859544 + 0.303895i
\(694\) 22.4142 + 22.4142i 0.850832 + 0.850832i
\(695\) 5.17157 5.17157i 0.196169 0.196169i
\(696\) 3.65685 + 5.17157i 0.138613 + 0.196028i
\(697\) −10.4853 + 10.4853i −0.397158 + 0.397158i
\(698\) 26.0000i 0.984115i
\(699\) 0.0416306 0.242641i 0.00157461 0.00917751i
\(700\) −2.00000 + 2.00000i −0.0755929 + 0.0755929i
\(701\) −0.142136 −0.00536839 −0.00268419 0.999996i \(-0.500854\pi\)
−0.00268419 + 0.999996i \(0.500854\pi\)
\(702\) 1.46447 + 18.6777i 0.0552727 + 0.704943i
\(703\) 0 0
\(704\) 2.00000 2.00000i 0.0753778 0.0753778i
\(705\) −0.828427 + 4.82843i −0.0312004 + 0.181849i
\(706\) 5.51472i 0.207549i
\(707\) −14.3431 + 14.3431i −0.539430 + 0.539430i
\(708\) −5.65685 8.00000i −0.212598 0.300658i
\(709\) −8.58579 + 8.58579i −0.322446 + 0.322446i −0.849705 0.527259i \(-0.823220\pi\)
0.527259 + 0.849705i \(0.323220\pi\)
\(710\) 10.4142 + 10.4142i 0.390838 + 0.390838i
\(711\) 24.9706 + 8.82843i 0.936469 + 0.331092i
\(712\) 3.75736i 0.140813i
\(713\) 30.1421 + 30.1421i 1.12883 + 1.12883i
\(714\) 23.3137 + 4.00000i 0.872494 + 0.149696i
\(715\) 10.0000 + 2.00000i 0.373979 + 0.0747958i
\(716\) 2.34315i 0.0875675i
\(717\) −17.0711 24.1421i −0.637531 0.901605i
\(718\) −3.41421 −0.127417
\(719\) 5.51472 0.205664 0.102832 0.994699i \(-0.467210\pi\)
0.102832 + 0.994699i \(0.467210\pi\)
\(720\) −2.70711 + 1.29289i −0.100888 + 0.0481833i
\(721\) 29.6569 + 29.6569i 1.10448 + 1.10448i
\(722\) −13.4350 13.4350i −0.500000 0.500000i
\(723\) 3.75736 + 5.31371i 0.139738 + 0.197619i
\(724\) −11.6569 −0.433224
\(725\) −3.65685 −0.135812
\(726\) −4.24264 + 3.00000i −0.157459 + 0.111340i
\(727\) 40.0000i 1.48352i 0.670667 + 0.741759i \(0.266008\pi\)
−0.670667 + 0.741759i \(0.733992\pi\)
\(728\) −10.0000 2.00000i −0.370625 0.0741249i
\(729\) −14.1421 23.0000i −0.523783 0.851852i
\(730\) 9.89949 + 9.89949i 0.366397 + 0.366397i
\(731\) 24.4853i 0.905621i
\(732\) −21.8995 3.75736i −0.809429 0.138876i
\(733\) −15.5563 15.5563i −0.574587 0.574587i 0.358820 0.933407i \(-0.383179\pi\)
−0.933407 + 0.358820i \(0.883179\pi\)
\(734\) 26.4853 26.4853i 0.977590 0.977590i
\(735\) 1.41421 1.00000i 0.0521641 0.0368856i
\(736\) −4.82843 + 4.82843i −0.177978 + 0.177978i
\(737\) 8.97056i 0.330435i
\(738\) −3.07107 + 8.68629i −0.113048 + 0.319747i
\(739\) −5.65685 + 5.65685i −0.208091 + 0.208091i −0.803456 0.595365i \(-0.797008\pi\)
0.595365 + 0.803456i \(0.297008\pi\)
\(740\) −5.65685 −0.207950
\(741\) 0 0
\(742\) 26.6274 0.977523
\(743\) 23.3137 23.3137i 0.855297 0.855297i −0.135483 0.990780i \(-0.543259\pi\)
0.990780 + 0.135483i \(0.0432585\pi\)
\(744\) −10.6569 1.82843i −0.390699 0.0670334i
\(745\) 16.8284i 0.616546i
\(746\) −20.3137 + 20.3137i −0.743738 + 0.743738i
\(747\) 4.48528 2.14214i 0.164108 0.0783766i
\(748\) 9.65685 9.65685i 0.353090 0.353090i
\(749\) 25.1716 + 25.1716i 0.919749 + 0.919749i
\(750\) 0.292893 1.70711i 0.0106949 0.0623347i
\(751\) 21.6569i 0.790270i 0.918623 + 0.395135i \(0.129302\pi\)
−0.918623 + 0.395135i \(0.870698\pi\)
\(752\) −2.00000 2.00000i −0.0729325 0.0729325i
\(753\) −1.45584 + 8.48528i −0.0530539 + 0.309221i
\(754\) −7.31371 10.9706i −0.266350 0.399524i
\(755\) 17.5563i 0.638941i
\(756\) 14.1421 4.00000i 0.514344 0.145479i
\(757\) −35.0711 −1.27468 −0.637340 0.770583i \(-0.719965\pi\)
−0.637340 + 0.770583i \(0.719965\pi\)
\(758\) 10.6274 0.386005
\(759\) −27.3137 + 19.3137i −0.991425 + 0.701043i
\(760\) 0 0
\(761\) 17.9706 + 17.9706i 0.651432 + 0.651432i 0.953338 0.301905i \(-0.0976227\pi\)
−0.301905 + 0.953338i \(0.597623\pi\)
\(762\) 2.34315 1.65685i 0.0848832 0.0600215i
\(763\) −32.9706 −1.19361
\(764\) 12.8284 0.464116
\(765\) −13.0711 + 6.24264i −0.472585 + 0.225703i
\(766\) 5.65685i 0.204390i
\(767\) 11.3137 + 16.9706i 0.408514 + 0.612772i
\(768\) 0.292893 1.70711i 0.0105689 0.0615999i
\(769\) 7.97056 + 7.97056i 0.287426 + 0.287426i 0.836062 0.548636i \(-0.184853\pi\)
−0.548636 + 0.836062i \(0.684853\pi\)
\(770\) 8.00000i 0.288300i
\(771\) 7.75736 45.2132i 0.279374 1.62831i
\(772\) 1.07107 + 1.07107i 0.0385486 + 0.0385486i
\(773\) −22.6274 + 22.6274i −0.813852 + 0.813852i −0.985209 0.171357i \(-0.945185\pi\)
0.171357 + 0.985209i \(0.445185\pi\)
\(774\) 6.55635 + 13.7279i 0.235663 + 0.493440i
\(775\) 4.41421 4.41421i 0.158563 0.158563i