Properties

Label 1110.2.x.d.751.3
Level $1110$
Weight $2$
Character 1110.751
Analytic conductor $8.863$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 60 x^{14} + 1362 x^{12} + 15028 x^{10} + 86441 x^{8} + 260376 x^{6} + 382684 x^{4} + 224224 x^{2} + 38416\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 751.3
Root \(0.871333i\) of defining polynomial
Character \(\chi\) \(=\) 1110.751
Dual form 1110.2.x.d.841.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(0.435667 - 0.754597i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(0.435667 - 0.754597i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +1.12820 q^{11} +(0.500000 + 0.866025i) q^{12} +(-5.16160 - 2.98005i) q^{13} +0.871333i q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.62062 + 0.935667i) q^{17} +(0.866025 + 0.500000i) q^{18} +(5.64541 + 3.25938i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(0.435667 + 0.754597i) q^{21} +(-0.977051 + 0.564101i) q^{22} +4.22805i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} +5.96011 q^{26} +1.00000 q^{27} +(-0.435667 - 0.754597i) q^{28} +4.16204i q^{29} +(-0.500000 + 0.866025i) q^{30} +5.15096i q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.564101 + 0.977051i) q^{33} +(0.935667 - 1.62062i) q^{34} +(-0.754597 + 0.435667i) q^{35} -1.00000 q^{36} +(-2.13754 - 5.69481i) q^{37} -6.51876 q^{38} +(5.16160 - 2.98005i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-5.31389 + 9.20392i) q^{41} +(-0.754597 - 0.435667i) q^{42} -9.37901i q^{43} +(0.564101 - 0.977051i) q^{44} +1.00000i q^{45} +(-2.11403 - 3.66160i) q^{46} +7.61359 q^{47} +1.00000 q^{48} +(3.12039 + 5.40467i) q^{49} +(-0.866025 - 0.500000i) q^{50} -1.87133i q^{51} +(-5.16160 + 2.98005i) q^{52} +(5.57432 + 9.65501i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.977051 - 0.564101i) q^{55} +(0.754597 + 0.435667i) q^{56} +(-5.64541 + 3.25938i) q^{57} +(-2.08102 - 3.60443i) q^{58} +(-1.96930 + 1.13698i) q^{59} -1.00000i q^{60} +(4.20441 + 2.42742i) q^{61} +(-2.57548 - 4.46086i) q^{62} -0.871333 q^{63} -1.00000 q^{64} +(2.98005 + 5.16160i) q^{65} -1.12820i q^{66} +(-7.07277 + 12.2504i) q^{67} +1.87133i q^{68} +(-3.66160 - 2.11403i) q^{69} +(0.435667 - 0.754597i) q^{70} +(-7.55813 + 13.0911i) q^{71} +(0.866025 - 0.500000i) q^{72} -4.43634 q^{73} +(4.69857 + 3.86308i) q^{74} -1.00000 q^{75} +(5.64541 - 3.25938i) q^{76} +(0.491520 - 0.851337i) q^{77} +(-2.98005 + 5.16160i) q^{78} +(-10.0774 - 5.81817i) q^{79} +1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -10.6278i q^{82} +(-2.47486 - 4.28659i) q^{83} +0.871333 q^{84} +1.87133 q^{85} +(4.68951 + 8.12246i) q^{86} +(-3.60443 - 2.08102i) q^{87} +1.12820i q^{88} +(7.87663 - 4.54758i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-4.49748 + 2.59662i) q^{91} +(3.66160 + 2.11403i) q^{92} +(-4.46086 - 2.57548i) q^{93} +(-6.59356 + 3.80679i) q^{94} +(-3.25938 - 5.64541i) q^{95} +(-0.866025 + 0.500000i) q^{96} +2.17225i q^{97} +(-5.40467 - 3.12039i) q^{98} +(-0.564101 - 0.977051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + O(q^{10}) \) \( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + 16q^{10} - 8q^{11} + 8q^{12} - 6q^{13} - 8q^{16} + 6q^{17} - 12q^{19} - 2q^{21} + 8q^{25} + 4q^{26} + 16q^{27} + 2q^{28} - 8q^{30} + 4q^{33} + 6q^{34} + 6q^{35} - 16q^{36} + 12q^{37} - 4q^{38} + 6q^{39} + 8q^{40} + 4q^{41} + 6q^{42} - 4q^{44} - 2q^{46} + 68q^{47} + 16q^{48} - 4q^{49} - 6q^{52} - 12q^{53} - 6q^{56} + 12q^{57} - 6q^{58} + 6q^{59} + 12q^{61} + 4q^{62} + 4q^{63} - 16q^{64} + 2q^{65} - 36q^{67} + 18q^{69} - 2q^{70} + 6q^{71} - 16q^{73} + 14q^{74} - 16q^{75} - 12q^{76} + 26q^{77} - 2q^{78} - 24q^{79} - 8q^{81} + 12q^{83} - 4q^{84} + 12q^{85} - 2q^{86} + 24q^{89} - 8q^{90} + 60q^{91} - 18q^{92} - 30q^{93} + 6q^{94} - 2q^{95} - 12q^{98} + 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −0.866025 0.500000i −0.387298 0.223607i
\(6\) 1.00000i 0.408248i
\(7\) 0.435667 0.754597i 0.164666 0.285211i −0.771870 0.635780i \(-0.780679\pi\)
0.936537 + 0.350569i \(0.114012\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.00000 0.316228
\(11\) 1.12820 0.340165 0.170083 0.985430i \(-0.445597\pi\)
0.170083 + 0.985430i \(0.445597\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −5.16160 2.98005i −1.43157 0.826518i −0.434330 0.900754i \(-0.643015\pi\)
−0.997241 + 0.0742358i \(0.976348\pi\)
\(14\) 0.871333i 0.232874i
\(15\) 0.866025 0.500000i 0.223607 0.129099i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.62062 + 0.935667i −0.393059 + 0.226932i −0.683485 0.729965i \(-0.739536\pi\)
0.290426 + 0.956897i \(0.406203\pi\)
\(18\) 0.866025 + 0.500000i 0.204124 + 0.117851i
\(19\) 5.64541 + 3.25938i 1.29515 + 0.747753i 0.979562 0.201144i \(-0.0644659\pi\)
0.315585 + 0.948897i \(0.397799\pi\)
\(20\) −0.866025 + 0.500000i −0.193649 + 0.111803i
\(21\) 0.435667 + 0.754597i 0.0950702 + 0.164666i
\(22\) −0.977051 + 0.564101i −0.208308 + 0.120267i
\(23\) 4.22805i 0.881610i 0.897603 + 0.440805i \(0.145307\pi\)
−0.897603 + 0.440805i \(0.854693\pi\)
\(24\) −0.866025 0.500000i −0.176777 0.102062i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 5.96011 1.16887
\(27\) 1.00000 0.192450
\(28\) −0.435667 0.754597i −0.0823332 0.142605i
\(29\) 4.16204i 0.772872i 0.922316 + 0.386436i \(0.126294\pi\)
−0.922316 + 0.386436i \(0.873706\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) 5.15096i 0.925140i 0.886583 + 0.462570i \(0.153073\pi\)
−0.886583 + 0.462570i \(0.846927\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) −0.564101 + 0.977051i −0.0981973 + 0.170083i
\(34\) 0.935667 1.62062i 0.160465 0.277934i
\(35\) −0.754597 + 0.435667i −0.127550 + 0.0736411i
\(36\) −1.00000 −0.166667
\(37\) −2.13754 5.69481i −0.351410 0.936222i
\(38\) −6.51876 −1.05748
\(39\) 5.16160 2.98005i 0.826518 0.477190i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) −5.31389 + 9.20392i −0.829890 + 1.43741i 0.0682345 + 0.997669i \(0.478263\pi\)
−0.898124 + 0.439742i \(0.855070\pi\)
\(42\) −0.754597 0.435667i −0.116437 0.0672248i
\(43\) 9.37901i 1.43029i −0.698978 0.715143i \(-0.746362\pi\)
0.698978 0.715143i \(-0.253638\pi\)
\(44\) 0.564101 0.977051i 0.0850414 0.147296i
\(45\) 1.00000i 0.149071i
\(46\) −2.11403 3.66160i −0.311696 0.539874i
\(47\) 7.61359 1.11056 0.555278 0.831665i \(-0.312612\pi\)
0.555278 + 0.831665i \(0.312612\pi\)
\(48\) 1.00000 0.144338
\(49\) 3.12039 + 5.40467i 0.445770 + 0.772096i
\(50\) −0.866025 0.500000i −0.122474 0.0707107i
\(51\) 1.87133i 0.262039i
\(52\) −5.16160 + 2.98005i −0.715786 + 0.413259i
\(53\) 5.57432 + 9.65501i 0.765692 + 1.32622i 0.939880 + 0.341505i \(0.110937\pi\)
−0.174188 + 0.984712i \(0.555730\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) −0.977051 0.564101i −0.131746 0.0760633i
\(56\) 0.754597 + 0.435667i 0.100837 + 0.0582184i
\(57\) −5.64541 + 3.25938i −0.747753 + 0.431716i
\(58\) −2.08102 3.60443i −0.273251 0.473285i
\(59\) −1.96930 + 1.13698i −0.256381 + 0.148022i −0.622683 0.782475i \(-0.713957\pi\)
0.366301 + 0.930496i \(0.380624\pi\)
\(60\) 1.00000i 0.129099i
\(61\) 4.20441 + 2.42742i 0.538319 + 0.310799i 0.744398 0.667737i \(-0.232737\pi\)
−0.206078 + 0.978536i \(0.566070\pi\)
\(62\) −2.57548 4.46086i −0.327086 0.566530i
\(63\) −0.871333 −0.109778
\(64\) −1.00000 −0.125000
\(65\) 2.98005 + 5.16160i 0.369630 + 0.640218i
\(66\) 1.12820i 0.138872i
\(67\) −7.07277 + 12.2504i −0.864076 + 1.49662i 0.00388486 + 0.999992i \(0.498763\pi\)
−0.867961 + 0.496632i \(0.834570\pi\)
\(68\) 1.87133i 0.226932i
\(69\) −3.66160 2.11403i −0.440805 0.254499i
\(70\) 0.435667 0.754597i 0.0520721 0.0901916i
\(71\) −7.55813 + 13.0911i −0.896985 + 1.55362i −0.0656567 + 0.997842i \(0.520914\pi\)
−0.831328 + 0.555782i \(0.812419\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) −4.43634 −0.519234 −0.259617 0.965712i \(-0.583596\pi\)
−0.259617 + 0.965712i \(0.583596\pi\)
\(74\) 4.69857 + 3.86308i 0.546198 + 0.449074i
\(75\) −1.00000 −0.115470
\(76\) 5.64541 3.25938i 0.647573 0.373877i
\(77\) 0.491520 0.851337i 0.0560139 0.0970188i
\(78\) −2.98005 + 5.16160i −0.337425 + 0.584436i
\(79\) −10.0774 5.81817i −1.13379 0.654596i −0.188907 0.981995i \(-0.560494\pi\)
−0.944886 + 0.327399i \(0.893828\pi\)
\(80\) 1.00000i 0.111803i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 10.6278i 1.17364i
\(83\) −2.47486 4.28659i −0.271652 0.470515i 0.697633 0.716455i \(-0.254237\pi\)
−0.969285 + 0.245941i \(0.920903\pi\)
\(84\) 0.871333 0.0950702
\(85\) 1.87133 0.202975
\(86\) 4.68951 + 8.12246i 0.505683 + 0.875868i
\(87\) −3.60443 2.08102i −0.386436 0.223109i
\(88\) 1.12820i 0.120267i
\(89\) 7.87663 4.54758i 0.834921 0.482042i −0.0206134 0.999788i \(-0.506562\pi\)
0.855535 + 0.517745i \(0.173229\pi\)
\(90\) −0.500000 0.866025i −0.0527046 0.0912871i
\(91\) −4.49748 + 2.59662i −0.471464 + 0.272200i
\(92\) 3.66160 + 2.11403i 0.381748 + 0.220403i
\(93\) −4.46086 2.57548i −0.462570 0.267065i
\(94\) −6.59356 + 3.80679i −0.680074 + 0.392641i
\(95\) −3.25938 5.64541i −0.334405 0.579207i
\(96\) −0.866025 + 0.500000i −0.0883883 + 0.0510310i
\(97\) 2.17225i 0.220558i 0.993901 + 0.110279i \(0.0351745\pi\)
−0.993901 + 0.110279i \(0.964826\pi\)
\(98\) −5.40467 3.12039i −0.545954 0.315207i
\(99\) −0.564101 0.977051i −0.0566942 0.0981973i
\(100\) 1.00000 0.100000
\(101\) −4.72751 −0.470405 −0.235202 0.971946i \(-0.575575\pi\)
−0.235202 + 0.971946i \(0.575575\pi\)
\(102\) 0.935667 + 1.62062i 0.0926448 + 0.160465i
\(103\) 5.43512i 0.535538i 0.963483 + 0.267769i \(0.0862864\pi\)
−0.963483 + 0.267769i \(0.913714\pi\)
\(104\) 2.98005 5.16160i 0.292218 0.506137i
\(105\) 0.871333i 0.0850334i
\(106\) −9.65501 5.57432i −0.937777 0.541426i
\(107\) −8.33163 + 14.4308i −0.805449 + 1.39508i 0.110539 + 0.993872i \(0.464742\pi\)
−0.915988 + 0.401206i \(0.868591\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 14.5230 8.38487i 1.39105 0.803125i 0.397622 0.917549i \(-0.369836\pi\)
0.993432 + 0.114424i \(0.0365023\pi\)
\(110\) 1.12820 0.107570
\(111\) 6.00063 + 0.996242i 0.569554 + 0.0945591i
\(112\) −0.871333 −0.0823332
\(113\) −7.42944 + 4.28939i −0.698903 + 0.403512i −0.806939 0.590635i \(-0.798877\pi\)
0.108036 + 0.994147i \(0.465544\pi\)
\(114\) 3.25938 5.64541i 0.305269 0.528741i
\(115\) 2.11403 3.66160i 0.197134 0.341446i
\(116\) 3.60443 + 2.08102i 0.334663 + 0.193218i
\(117\) 5.96011i 0.551012i
\(118\) 1.13698 1.96930i 0.104667 0.181289i
\(119\) 1.63055i 0.149473i
\(120\) 0.500000 + 0.866025i 0.0456435 + 0.0790569i
\(121\) −9.72716 −0.884287
\(122\) −4.85483 −0.439536
\(123\) −5.31389 9.20392i −0.479137 0.829890i
\(124\) 4.46086 + 2.57548i 0.400597 + 0.231285i
\(125\) 1.00000i 0.0894427i
\(126\) 0.754597 0.435667i 0.0672248 0.0388123i
\(127\) −8.08310 14.0003i −0.717259 1.24233i −0.962082 0.272761i \(-0.912063\pi\)
0.244823 0.969568i \(-0.421270\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 8.12246 + 4.68951i 0.715143 + 0.412888i
\(130\) −5.16160 2.98005i −0.452703 0.261368i
\(131\) −4.90282 + 2.83065i −0.428361 + 0.247315i −0.698648 0.715465i \(-0.746215\pi\)
0.270287 + 0.962780i \(0.412881\pi\)
\(132\) 0.564101 + 0.977051i 0.0490987 + 0.0850414i
\(133\) 4.91904 2.84001i 0.426535 0.246260i
\(134\) 14.1455i 1.22199i
\(135\) −0.866025 0.500000i −0.0745356 0.0430331i
\(136\) −0.935667 1.62062i −0.0802327 0.138967i
\(137\) −16.5057 −1.41018 −0.705088 0.709120i \(-0.749093\pi\)
−0.705088 + 0.709120i \(0.749093\pi\)
\(138\) 4.22805 0.359916
\(139\) 8.84982 + 15.3283i 0.750632 + 1.30013i 0.947517 + 0.319706i \(0.103584\pi\)
−0.196885 + 0.980427i \(0.563083\pi\)
\(140\) 0.871333i 0.0736411i
\(141\) −3.80679 + 6.59356i −0.320590 + 0.555278i
\(142\) 15.1163i 1.26853i
\(143\) −5.82333 3.36210i −0.486971 0.281153i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 2.08102 3.60443i 0.172819 0.299332i
\(146\) 3.84198 2.21817i 0.317964 0.183577i
\(147\) −6.24078 −0.514731
\(148\) −6.00063 0.996242i −0.493248 0.0818906i
\(149\) 16.5978 1.35975 0.679873 0.733330i \(-0.262035\pi\)
0.679873 + 0.733330i \(0.262035\pi\)
\(150\) 0.866025 0.500000i 0.0707107 0.0408248i
\(151\) 7.15224 12.3880i 0.582041 1.00812i −0.413196 0.910642i \(-0.635588\pi\)
0.995237 0.0974827i \(-0.0310791\pi\)
\(152\) −3.25938 + 5.64541i −0.264371 + 0.457903i
\(153\) 1.62062 + 0.935667i 0.131020 + 0.0756442i
\(154\) 0.983039i 0.0792156i
\(155\) 2.57548 4.46086i 0.206868 0.358305i
\(156\) 5.96011i 0.477190i
\(157\) 9.11409 + 15.7861i 0.727383 + 1.25986i 0.957985 + 0.286817i \(0.0925971\pi\)
−0.230602 + 0.973048i \(0.574070\pi\)
\(158\) 11.6363 0.925738
\(159\) −11.1486 −0.884145
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) 3.19048 + 1.84202i 0.251445 + 0.145172i
\(162\) 1.00000i 0.0785674i
\(163\) −5.43671 + 3.13889i −0.425836 + 0.245857i −0.697571 0.716516i \(-0.745736\pi\)
0.271735 + 0.962372i \(0.412403\pi\)
\(164\) 5.31389 + 9.20392i 0.414945 + 0.718706i
\(165\) 0.977051 0.564101i 0.0760633 0.0439152i
\(166\) 4.28659 + 2.47486i 0.332704 + 0.192087i
\(167\) 6.40836 + 3.69987i 0.495894 + 0.286304i 0.727016 0.686620i \(-0.240907\pi\)
−0.231123 + 0.972925i \(0.574240\pi\)
\(168\) −0.754597 + 0.435667i −0.0582184 + 0.0336124i
\(169\) 11.2614 + 19.5054i 0.866264 + 1.50041i
\(170\) −1.62062 + 0.935667i −0.124296 + 0.0717624i
\(171\) 6.51876i 0.498502i
\(172\) −8.12246 4.68951i −0.619332 0.357572i
\(173\) 5.21856 + 9.03881i 0.396760 + 0.687208i 0.993324 0.115357i \(-0.0368012\pi\)
−0.596564 + 0.802565i \(0.703468\pi\)
\(174\) 4.16204 0.315523
\(175\) 0.871333 0.0658666
\(176\) −0.564101 0.977051i −0.0425207 0.0736480i
\(177\) 2.27395i 0.170921i
\(178\) −4.54758 + 7.87663i −0.340855 + 0.590379i
\(179\) 8.74992i 0.653999i −0.945024 0.327000i \(-0.893962\pi\)
0.945024 0.327000i \(-0.106038\pi\)
\(180\) 0.866025 + 0.500000i 0.0645497 + 0.0372678i
\(181\) −7.65366 + 13.2565i −0.568892 + 0.985350i 0.427784 + 0.903881i \(0.359295\pi\)
−0.996676 + 0.0814692i \(0.974039\pi\)
\(182\) 2.59662 4.49748i 0.192474 0.333375i
\(183\) −4.20441 + 2.42742i −0.310799 + 0.179440i
\(184\) −4.22805 −0.311696
\(185\) −0.996242 + 6.00063i −0.0732452 + 0.441175i
\(186\) 5.15096 0.377687
\(187\) −1.82839 + 1.05562i −0.133705 + 0.0771946i
\(188\) 3.80679 6.59356i 0.277639 0.480885i
\(189\) 0.435667 0.754597i 0.0316901 0.0548888i
\(190\) 5.64541 + 3.25938i 0.409561 + 0.236460i
\(191\) 17.4079i 1.25959i −0.776761 0.629796i \(-0.783139\pi\)
0.776761 0.629796i \(-0.216861\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 18.8491i 1.35679i 0.734698 + 0.678395i \(0.237324\pi\)
−0.734698 + 0.678395i \(0.762676\pi\)
\(194\) −1.08612 1.88122i −0.0779791 0.135064i
\(195\) −5.96011 −0.426812
\(196\) 6.24078 0.445770
\(197\) 0.306829 + 0.531443i 0.0218607 + 0.0378638i 0.876749 0.480949i \(-0.159708\pi\)
−0.854888 + 0.518812i \(0.826374\pi\)
\(198\) 0.977051 + 0.564101i 0.0694360 + 0.0400889i
\(199\) 23.3952i 1.65844i −0.558920 0.829222i \(-0.688784\pi\)
0.558920 0.829222i \(-0.311216\pi\)
\(200\) −0.866025 + 0.500000i −0.0612372 + 0.0353553i
\(201\) −7.07277 12.2504i −0.498875 0.864076i
\(202\) 4.09414 2.36375i 0.288063 0.166313i
\(203\) 3.14066 + 1.81326i 0.220431 + 0.127266i
\(204\) −1.62062 0.935667i −0.113466 0.0655098i
\(205\) 9.20392 5.31389i 0.642830 0.371138i
\(206\) −2.71756 4.70695i −0.189341 0.327949i
\(207\) 3.66160 2.11403i 0.254499 0.146935i
\(208\) 5.96011i 0.413259i
\(209\) 6.36916 + 3.67724i 0.440564 + 0.254360i
\(210\) 0.435667 + 0.754597i 0.0300639 + 0.0520721i
\(211\) 21.1872 1.45859 0.729295 0.684199i \(-0.239848\pi\)
0.729295 + 0.684199i \(0.239848\pi\)
\(212\) 11.1486 0.765692
\(213\) −7.55813 13.0911i −0.517875 0.896985i
\(214\) 16.6633i 1.13908i
\(215\) −4.68951 + 8.12246i −0.319822 + 0.553947i
\(216\) 1.00000i 0.0680414i
\(217\) 3.88690 + 2.24410i 0.263860 + 0.152339i
\(218\) −8.38487 + 14.5230i −0.567895 + 0.983623i
\(219\) 2.21817 3.84198i 0.149890 0.259617i
\(220\) −0.977051 + 0.564101i −0.0658728 + 0.0380317i
\(221\) 11.1533 0.750255
\(222\) −5.69481 + 2.13754i −0.382211 + 0.143462i
\(223\) 15.4416 1.03405 0.517024 0.855971i \(-0.327040\pi\)
0.517024 + 0.855971i \(0.327040\pi\)
\(224\) 0.754597 0.435667i 0.0504186 0.0291092i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) 4.28939 7.42944i 0.285326 0.494199i
\(227\) 3.86623 + 2.23217i 0.256611 + 0.148154i 0.622788 0.782391i \(-0.286000\pi\)
−0.366177 + 0.930545i \(0.619333\pi\)
\(228\) 6.51876i 0.431716i
\(229\) 8.13293 14.0866i 0.537439 0.930872i −0.461602 0.887087i \(-0.652725\pi\)
0.999041 0.0437847i \(-0.0139416\pi\)
\(230\) 4.22805i 0.278790i
\(231\) 0.491520 + 0.851337i 0.0323396 + 0.0560139i
\(232\) −4.16204 −0.273251
\(233\) 3.64777 0.238973 0.119487 0.992836i \(-0.461875\pi\)
0.119487 + 0.992836i \(0.461875\pi\)
\(234\) −2.98005 5.16160i −0.194812 0.337425i
\(235\) −6.59356 3.80679i −0.430117 0.248328i
\(236\) 2.27395i 0.148022i
\(237\) 10.0774 5.81817i 0.654596 0.377931i
\(238\) −0.815277 1.41210i −0.0528466 0.0915330i
\(239\) 6.62403 3.82438i 0.428473 0.247379i −0.270223 0.962798i \(-0.587097\pi\)
0.698696 + 0.715419i \(0.253764\pi\)
\(240\) −0.866025 0.500000i −0.0559017 0.0322749i
\(241\) −18.8434 10.8793i −1.21381 0.700794i −0.250224 0.968188i \(-0.580504\pi\)
−0.963587 + 0.267394i \(0.913838\pi\)
\(242\) 8.42397 4.86358i 0.541513 0.312643i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 4.20441 2.42742i 0.269160 0.155399i
\(245\) 6.24078i 0.398709i
\(246\) 9.20392 + 5.31389i 0.586821 + 0.338801i
\(247\) −19.4263 33.6473i −1.23606 2.14092i
\(248\) −5.15096 −0.327086
\(249\) 4.94973 0.313676
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 0.241710i 0.0152566i −0.999971 0.00762829i \(-0.997572\pi\)
0.999971 0.00762829i \(-0.00242818\pi\)
\(252\) −0.435667 + 0.754597i −0.0274444 + 0.0475351i
\(253\) 4.77010i 0.299893i
\(254\) 14.0003 + 8.08310i 0.878459 + 0.507179i
\(255\) −0.935667 + 1.62062i −0.0585937 + 0.101487i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 21.5141 12.4212i 1.34201 0.774810i 0.354909 0.934901i \(-0.384512\pi\)
0.987102 + 0.160091i \(0.0511787\pi\)
\(258\) −9.37901 −0.583912
\(259\) −5.22854 0.868059i −0.324886 0.0539385i
\(260\) 5.96011 0.369630
\(261\) 3.60443 2.08102i 0.223109 0.128812i
\(262\) 2.83065 4.90282i 0.174878 0.302897i
\(263\) −1.71221 + 2.96564i −0.105580 + 0.182869i −0.913975 0.405771i \(-0.867003\pi\)
0.808395 + 0.588640i \(0.200336\pi\)
\(264\) −0.977051 0.564101i −0.0601333 0.0347180i
\(265\) 11.1486i 0.684856i
\(266\) −2.84001 + 4.91904i −0.174132 + 0.301605i
\(267\) 9.09515i 0.556614i
\(268\) 7.07277 + 12.2504i 0.432038 + 0.748312i
\(269\) 32.4772 1.98017 0.990084 0.140479i \(-0.0448644\pi\)
0.990084 + 0.140479i \(0.0448644\pi\)
\(270\) 1.00000 0.0608581
\(271\) −3.74795 6.49164i −0.227672 0.394339i 0.729446 0.684039i \(-0.239778\pi\)
−0.957118 + 0.289699i \(0.906445\pi\)
\(272\) 1.62062 + 0.935667i 0.0982646 + 0.0567331i
\(273\) 5.19324i 0.314309i
\(274\) 14.2943 8.25285i 0.863553 0.498573i
\(275\) 0.564101 + 0.977051i 0.0340165 + 0.0589184i
\(276\) −3.66160 + 2.11403i −0.220403 + 0.127249i
\(277\) −4.86420 2.80834i −0.292261 0.168737i 0.346700 0.937976i \(-0.387302\pi\)
−0.638961 + 0.769239i \(0.720636\pi\)
\(278\) −15.3283 8.84982i −0.919332 0.530777i
\(279\) 4.46086 2.57548i 0.267065 0.154190i
\(280\) −0.435667 0.754597i −0.0260361 0.0450958i
\(281\) −17.9392 + 10.3572i −1.07016 + 0.617860i −0.928226 0.372016i \(-0.878667\pi\)
−0.141938 + 0.989876i \(0.545333\pi\)
\(282\) 7.61359i 0.453383i
\(283\) 8.44311 + 4.87463i 0.501891 + 0.289767i 0.729494 0.683987i \(-0.239756\pi\)
−0.227603 + 0.973754i \(0.573089\pi\)
\(284\) 7.55813 + 13.0911i 0.448493 + 0.776812i
\(285\) 6.51876 0.386138
\(286\) 6.72420 0.397610
\(287\) 4.63017 + 8.01968i 0.273310 + 0.473387i
\(288\) 1.00000i 0.0589256i
\(289\) −6.74906 + 11.6897i −0.397003 + 0.687630i
\(290\) 4.16204i 0.244403i
\(291\) −1.88122 1.08612i −0.110279 0.0636697i
\(292\) −2.21817 + 3.84198i −0.129808 + 0.224835i
\(293\) 9.36994 16.2292i 0.547398 0.948121i −0.451054 0.892497i \(-0.648952\pi\)
0.998452 0.0556243i \(-0.0177149\pi\)
\(294\) 5.40467 3.12039i 0.315207 0.181985i
\(295\) 2.27395 0.132395
\(296\) 5.69481 2.13754i 0.331004 0.124242i
\(297\) 1.12820 0.0654649
\(298\) −14.3741 + 8.29891i −0.832671 + 0.480743i
\(299\) 12.5998 21.8235i 0.728667 1.26209i
\(300\) −0.500000 + 0.866025i −0.0288675 + 0.0500000i
\(301\) −7.07737 4.08612i −0.407933 0.235520i
\(302\) 14.3045i 0.823130i
\(303\) 2.36375 4.09414i 0.135794 0.235202i
\(304\) 6.51876i 0.373877i
\(305\) −2.42742 4.20441i −0.138993 0.240744i
\(306\) −1.87133 −0.106977
\(307\) 26.2743 1.49955 0.749776 0.661692i \(-0.230161\pi\)
0.749776 + 0.661692i \(0.230161\pi\)
\(308\) −0.491520 0.851337i −0.0280069 0.0485094i
\(309\) −4.70695 2.71756i −0.267769 0.154597i
\(310\) 5.15096i 0.292555i
\(311\) −28.9868 + 16.7355i −1.64369 + 0.948984i −0.664182 + 0.747571i \(0.731220\pi\)
−0.979506 + 0.201414i \(0.935446\pi\)
\(312\) 2.98005 + 5.16160i 0.168712 + 0.292218i
\(313\) −1.72710 + 0.997143i −0.0976216 + 0.0563619i −0.548016 0.836468i \(-0.684617\pi\)
0.450394 + 0.892830i \(0.351283\pi\)
\(314\) −15.7861 9.11409i −0.890859 0.514338i
\(315\) 0.754597 + 0.435667i 0.0425167 + 0.0245470i
\(316\) −10.0774 + 5.81817i −0.566897 + 0.327298i
\(317\) −2.99369 5.18523i −0.168143 0.291232i 0.769624 0.638497i \(-0.220444\pi\)
−0.937767 + 0.347266i \(0.887110\pi\)
\(318\) 9.65501 5.57432i 0.541426 0.312592i
\(319\) 4.69562i 0.262904i
\(320\) 0.866025 + 0.500000i 0.0484123 + 0.0279508i
\(321\) −8.33163 14.4308i −0.465026 0.805449i
\(322\) −3.68404 −0.205304
\(323\) −12.1988 −0.678758
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 5.96011i 0.330607i
\(326\) 3.13889 5.43671i 0.173847 0.301112i
\(327\) 16.7697i 0.927369i
\(328\) −9.20392 5.31389i −0.508202 0.293410i
\(329\) 3.31699 5.74519i 0.182871 0.316743i
\(330\) −0.564101 + 0.977051i −0.0310527 + 0.0537849i
\(331\) −16.1475 + 9.32279i −0.887549 + 0.512427i −0.873140 0.487470i \(-0.837920\pi\)
−0.0144090 + 0.999896i \(0.504587\pi\)
\(332\) −4.94973 −0.271652
\(333\) −3.86308 + 4.69857i −0.211696 + 0.257480i
\(334\) −7.39973 −0.404895
\(335\) 12.2504 7.07277i 0.669311 0.386427i
\(336\) 0.435667 0.754597i 0.0237676 0.0411666i
\(337\) 0.597607 1.03509i 0.0325538 0.0563848i −0.849290 0.527927i \(-0.822969\pi\)
0.881843 + 0.471543i \(0.156303\pi\)
\(338\) −19.5054 11.2614i −1.06095 0.612541i
\(339\) 8.57878i 0.465935i
\(340\) 0.935667 1.62062i 0.0507436 0.0878906i
\(341\) 5.81132i 0.314701i
\(342\) 3.25938 + 5.64541i 0.176247 + 0.305269i
\(343\) 11.5371 0.622946
\(344\) 9.37901 0.505683
\(345\) 2.11403 + 3.66160i 0.113815 + 0.197134i
\(346\) −9.03881 5.21856i −0.485930 0.280552i
\(347\) 5.89358i 0.316384i −0.987408 0.158192i \(-0.949434\pi\)
0.987408 0.158192i \(-0.0505665\pi\)
\(348\) −3.60443 + 2.08102i −0.193218 + 0.111554i
\(349\) 7.13276 + 12.3543i 0.381808 + 0.661311i 0.991321 0.131465i \(-0.0419682\pi\)
−0.609513 + 0.792776i \(0.708635\pi\)
\(350\) −0.754597 + 0.435667i −0.0403349 + 0.0232874i
\(351\) −5.16160 2.98005i −0.275506 0.159063i
\(352\) 0.977051 + 0.564101i 0.0520770 + 0.0300667i
\(353\) 14.6158 8.43844i 0.777921 0.449133i −0.0577722 0.998330i \(-0.518400\pi\)
0.835693 + 0.549197i \(0.185066\pi\)
\(354\) 1.13698 + 1.96930i 0.0604296 + 0.104667i
\(355\) 13.0911 7.55813i 0.694802 0.401144i
\(356\) 9.09515i 0.482042i
\(357\) −1.41210 0.815277i −0.0747364 0.0431491i
\(358\) 4.37496 + 7.57765i 0.231224 + 0.400491i
\(359\) −8.99932 −0.474966 −0.237483 0.971392i \(-0.576322\pi\)
−0.237483 + 0.971392i \(0.576322\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 11.7471 + 20.3466i 0.618270 + 1.07087i
\(362\) 15.3073i 0.804535i
\(363\) 4.86358 8.42397i 0.255272 0.442144i
\(364\) 5.19324i 0.272200i
\(365\) 3.84198 + 2.21817i 0.201098 + 0.116104i
\(366\) 2.42742 4.20441i 0.126883 0.219768i
\(367\) 6.20181 10.7419i 0.323732 0.560720i −0.657523 0.753435i \(-0.728396\pi\)
0.981255 + 0.192714i \(0.0617290\pi\)
\(368\) 3.66160 2.11403i 0.190874 0.110201i
\(369\) 10.6278 0.553260
\(370\) −2.13754 5.69481i −0.111126 0.296059i
\(371\) 9.71418 0.504335
\(372\) −4.46086 + 2.57548i −0.231285 + 0.133532i
\(373\) −5.45850 + 9.45441i −0.282631 + 0.489531i −0.972032 0.234849i \(-0.924540\pi\)
0.689401 + 0.724380i \(0.257874\pi\)
\(374\) 1.05562 1.82839i 0.0545848 0.0945437i
\(375\) 0.866025 + 0.500000i 0.0447214 + 0.0258199i
\(376\) 7.61359i 0.392641i
\(377\) 12.4031 21.4828i 0.638792 1.10642i
\(378\) 0.871333i 0.0448165i
\(379\) 11.4000 + 19.7454i 0.585578 + 1.01425i 0.994803 + 0.101818i \(0.0324659\pi\)
−0.409225 + 0.912434i \(0.634201\pi\)
\(380\) −6.51876 −0.334405
\(381\) 16.1662 0.828219
\(382\) 8.70395 + 15.0757i 0.445333 + 0.771339i
\(383\) −22.5335 13.0097i −1.15141 0.664767i −0.202180 0.979348i \(-0.564802\pi\)
−0.949230 + 0.314582i \(0.898136\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −0.851337 + 0.491520i −0.0433881 + 0.0250502i
\(386\) −9.42456 16.3238i −0.479697 0.830860i
\(387\) −8.12246 + 4.68951i −0.412888 + 0.238381i
\(388\) 1.88122 + 1.08612i 0.0955045 + 0.0551395i
\(389\) −31.1670 17.9943i −1.58023 0.912345i −0.994825 0.101602i \(-0.967603\pi\)
−0.585403 0.810743i \(-0.699064\pi\)
\(390\) 5.16160 2.98005i 0.261368 0.150901i
\(391\) −3.95605 6.85208i −0.200066 0.346525i
\(392\) −5.40467 + 3.12039i −0.272977 + 0.157603i
\(393\) 5.66129i 0.285574i
\(394\) −0.531443 0.306829i −0.0267737 0.0154578i
\(395\) 5.81817 + 10.0774i 0.292744 + 0.507048i
\(396\) −1.12820 −0.0566942
\(397\) −16.2648 −0.816306 −0.408153 0.912914i \(-0.633827\pi\)
−0.408153 + 0.912914i \(0.633827\pi\)
\(398\) 11.6976 + 20.2609i 0.586348 + 1.01559i
\(399\) 5.68001i 0.284356i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) 33.5429i 1.67505i 0.546397 + 0.837527i \(0.315999\pi\)
−0.546397 + 0.837527i \(0.684001\pi\)
\(402\) 12.2504 + 7.07277i 0.610994 + 0.352758i
\(403\) 15.3501 26.5872i 0.764644 1.32440i
\(404\) −2.36375 + 4.09414i −0.117601 + 0.203691i
\(405\) 0.866025 0.500000i 0.0430331 0.0248452i
\(406\) −3.62652 −0.179981
\(407\) −2.41158 6.42490i −0.119537 0.318470i
\(408\) 1.87133 0.0926448
\(409\) −9.51451 + 5.49320i −0.470462 + 0.271621i −0.716433 0.697656i \(-0.754227\pi\)
0.245971 + 0.969277i \(0.420893\pi\)
\(410\) −5.31389 + 9.20392i −0.262434 + 0.454549i
\(411\) 8.25285 14.2943i 0.407083 0.705088i
\(412\) 4.70695 + 2.71756i 0.231895 + 0.133885i
\(413\) 1.98137i 0.0974969i
\(414\) −2.11403 + 3.66160i −0.103899 + 0.179958i
\(415\) 4.94973i 0.242973i
\(416\) −2.98005 5.16160i −0.146109 0.253068i
\(417\) −17.6996 −0.866755
\(418\) −7.35448 −0.359719
\(419\) −16.6045 28.7598i −0.811181 1.40501i −0.912038 0.410105i \(-0.865492\pi\)
0.100858 0.994901i \(-0.467841\pi\)
\(420\) −0.754597 0.435667i −0.0368205 0.0212584i
\(421\) 17.5126i 0.853512i 0.904367 + 0.426756i \(0.140344\pi\)
−0.904367 + 0.426756i \(0.859656\pi\)
\(422\) −18.3487 + 10.5936i −0.893200 + 0.515689i
\(423\) −3.80679 6.59356i −0.185093 0.320590i
\(424\) −9.65501 + 5.57432i −0.468889 + 0.270713i
\(425\) −1.62062 0.935667i −0.0786117 0.0453865i
\(426\) 13.0911 + 7.55813i 0.634264 + 0.366193i
\(427\) 3.66344 2.11509i 0.177286 0.102356i
\(428\) 8.33163 + 14.4308i 0.402724 + 0.697539i
\(429\) 5.82333 3.36210i 0.281153 0.162324i
\(430\) 9.37901i 0.452296i
\(431\) −20.2700 11.7029i −0.976372 0.563709i −0.0751993 0.997169i \(-0.523959\pi\)
−0.901173 + 0.433460i \(0.857293\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 8.47827 0.407439 0.203720 0.979029i \(-0.434697\pi\)
0.203720 + 0.979029i \(0.434697\pi\)
\(434\) −4.48820 −0.215441
\(435\) 2.08102 + 3.60443i 0.0997773 + 0.172819i
\(436\) 16.7697i 0.803125i
\(437\) −13.7808 + 23.8691i −0.659227 + 1.14181i
\(438\) 4.43634i 0.211976i
\(439\) −2.06183 1.19040i −0.0984056 0.0568145i 0.449990 0.893034i \(-0.351428\pi\)
−0.548395 + 0.836219i \(0.684761\pi\)
\(440\) 0.564101 0.977051i 0.0268924 0.0465791i
\(441\) 3.12039 5.40467i 0.148590 0.257365i
\(442\) −9.65908 + 5.57667i −0.459436 + 0.265255i
\(443\) −3.83814 −0.182355 −0.0911777 0.995835i \(-0.529063\pi\)
−0.0911777 + 0.995835i \(0.529063\pi\)
\(444\) 3.86308 4.69857i 0.183334 0.222984i
\(445\) −9.09515 −0.431151
\(446\) −13.3728 + 7.72081i −0.633222 + 0.365591i
\(447\) −8.29891 + 14.3741i −0.392525 + 0.679873i
\(448\) −0.435667 + 0.754597i −0.0205833 + 0.0356513i
\(449\) −12.2708 7.08457i −0.579097 0.334342i 0.181678 0.983358i \(-0.441847\pi\)
−0.760774 + 0.649017i \(0.775181\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) −5.99513 + 10.3839i −0.282300 + 0.488958i
\(452\) 8.57878i 0.403512i
\(453\) 7.15224 + 12.3880i 0.336042 + 0.582041i
\(454\) −4.46434 −0.209522
\(455\) 5.19324 0.243463
\(456\) −3.25938 5.64541i −0.152634 0.264371i
\(457\) 10.7010 + 6.17825i 0.500574 + 0.289006i 0.728950 0.684566i \(-0.240008\pi\)
−0.228377 + 0.973573i \(0.573342\pi\)
\(458\) 16.2659i 0.760054i
\(459\) −1.62062 + 0.935667i −0.0756442 + 0.0436732i
\(460\) −2.11403 3.66160i −0.0985670 0.170723i
\(461\) 31.2722 18.0550i 1.45649 0.840905i 0.457654 0.889130i \(-0.348690\pi\)
0.998837 + 0.0482247i \(0.0153564\pi\)
\(462\) −0.851337 0.491520i −0.0396078 0.0228676i
\(463\) −21.4520 12.3853i −0.996960 0.575595i −0.0896122 0.995977i \(-0.528563\pi\)
−0.907347 + 0.420382i \(0.861896\pi\)
\(464\) 3.60443 2.08102i 0.167332 0.0966089i
\(465\) 2.57548 + 4.46086i 0.119435 + 0.206868i
\(466\) −3.15906 + 1.82389i −0.146341 + 0.0844899i
\(467\) 0.754892i 0.0349322i −0.999847 0.0174661i \(-0.994440\pi\)
0.999847 0.0174661i \(-0.00555992\pi\)
\(468\) 5.16160 + 2.98005i 0.238595 + 0.137753i
\(469\) 6.16274 + 10.6742i 0.284569 + 0.492888i
\(470\) 7.61359 0.351189
\(471\) −18.2282 −0.839910
\(472\) −1.13698 1.96930i −0.0523336 0.0906444i
\(473\) 10.5814i 0.486534i
\(474\) −5.81817 + 10.0774i −0.267238 + 0.462869i
\(475\) 6.51876i 0.299101i
\(476\) 1.41210 + 0.815277i 0.0647236 + 0.0373682i
\(477\) 5.57432 9.65501i 0.255231 0.442072i
\(478\) −3.82438 + 6.62403i −0.174923 + 0.302976i
\(479\) −13.3889 + 7.73007i −0.611753 + 0.353196i −0.773651 0.633611i \(-0.781572\pi\)
0.161898 + 0.986808i \(0.448238\pi\)
\(480\) 1.00000 0.0456435
\(481\) −5.93771 + 35.7644i −0.270736 + 1.63071i
\(482\) 21.7585 0.991073
\(483\) −3.19048 + 1.84202i −0.145172 + 0.0838149i
\(484\) −4.86358 + 8.42397i −0.221072 + 0.382908i
\(485\) 1.08612 1.88122i 0.0493183 0.0854218i
\(486\) 0.866025 + 0.500000i 0.0392837 + 0.0226805i
\(487\) 33.7547i 1.52957i 0.644283 + 0.764787i \(0.277156\pi\)
−0.644283 + 0.764787i \(0.722844\pi\)
\(488\) −2.42742 + 4.20441i −0.109884 + 0.190325i
\(489\) 6.27777i 0.283891i
\(490\) 3.12039 + 5.40467i 0.140965 + 0.244158i
\(491\) −9.71651 −0.438500 −0.219250 0.975669i \(-0.570361\pi\)
−0.219250 + 0.975669i \(0.570361\pi\)
\(492\) −10.6278 −0.479137
\(493\) −3.89428 6.74509i −0.175390 0.303784i
\(494\) 33.6473 + 19.4263i 1.51386 + 0.874029i
\(495\) 1.12820i 0.0507089i
\(496\) 4.46086 2.57548i 0.200299 0.115642i
\(497\) 6.58565 + 11.4067i 0.295407 + 0.511660i
\(498\) −4.28659 + 2.47486i −0.192087 + 0.110901i
\(499\) 8.26563 + 4.77216i 0.370020 + 0.213631i 0.673467 0.739217i \(-0.264804\pi\)
−0.303447 + 0.952848i \(0.598138\pi\)
\(500\) −0.866025 0.500000i −0.0387298 0.0223607i
\(501\) −6.40836 + 3.69987i −0.286304 + 0.165298i
\(502\) 0.120855 + 0.209327i 0.00539402 + 0.00934271i
\(503\) −6.69477 + 3.86523i −0.298505 + 0.172342i −0.641771 0.766896i \(-0.721800\pi\)
0.343266 + 0.939238i \(0.388467\pi\)
\(504\) 0.871333i 0.0388123i
\(505\) 4.09414 + 2.36375i 0.182187 + 0.105186i
\(506\) −2.38505 4.13102i −0.106028 0.183646i
\(507\) −22.5229 −1.00028
\(508\) −16.1662 −0.717259
\(509\) −10.0860 17.4694i −0.447052 0.774317i 0.551140 0.834412i \(-0.314193\pi\)
−0.998193 + 0.0600954i \(0.980859\pi\)
\(510\) 1.87133i 0.0828640i
\(511\) −1.93276 + 3.34764i −0.0855004 + 0.148091i
\(512\) 1.00000i 0.0441942i
\(513\) 5.64541 + 3.25938i 0.249251 + 0.143905i
\(514\) −12.4212 + 21.5141i −0.547874 + 0.948945i
\(515\) 2.71756 4.70695i 0.119750 0.207413i
\(516\) 8.12246 4.68951i 0.357572 0.206444i
\(517\) 8.58966 0.377773
\(518\) 4.96208 1.86251i 0.218021 0.0818340i
\(519\) −10.4371 −0.458139
\(520\) −5.16160 + 2.98005i −0.226351 + 0.130684i
\(521\) −6.83008 + 11.8301i −0.299231 + 0.518284i −0.975960 0.217948i \(-0.930064\pi\)
0.676729 + 0.736232i \(0.263397\pi\)
\(522\) −2.08102 + 3.60443i −0.0910838 + 0.157762i
\(523\) −16.6298 9.60120i −0.727169 0.419831i 0.0902166 0.995922i \(-0.471244\pi\)
−0.817386 + 0.576091i \(0.804577\pi\)
\(524\) 5.66129i 0.247315i
\(525\) −0.435667 + 0.754597i −0.0190140 + 0.0329333i
\(526\) 3.42443i 0.149312i
\(527\) −4.81958 8.34776i −0.209944 0.363634i
\(528\) 1.12820 0.0490987
\(529\) 5.12355 0.222763
\(530\) 5.57432 + 9.65501i 0.242133 + 0.419387i
\(531\) 1.96930 + 1.13698i 0.0854604 + 0.0493406i
\(532\) 5.68001i 0.246260i
\(533\) 54.8563 31.6713i 2.37609 1.37184i
\(534\) −4.54758 7.87663i −0.196793 0.340855i
\(535\) 14.4308 8.33163i 0.623898 0.360208i
\(536\) −12.2504 7.07277i −0.529137 0.305497i
\(537\) 7.57765 + 4.37496i 0.327000 + 0.188793i
\(538\) −28.1260 + 16.2386i −1.21260 + 0.700095i
\(539\) 3.52043 + 6.09756i 0.151636 + 0.262640i
\(540\) −0.866025 + 0.500000i −0.0372678 + 0.0215166i
\(541\) 29.5852i 1.27197i −0.771702 0.635984i \(-0.780594\pi\)
0.771702 0.635984i \(-0.219406\pi\)
\(542\) 6.49164 + 3.74795i 0.278840 + 0.160988i
\(543\) −7.65366 13.2565i −0.328450 0.568892i
\(544\) −1.87133 −0.0802327
\(545\) −16.7697 −0.718337
\(546\) 2.59662 + 4.49748i 0.111125 + 0.192474i
\(547\) 9.36718i 0.400512i −0.979744 0.200256i \(-0.935823\pi\)
0.979744 0.200256i \(-0.0641774\pi\)
\(548\) −8.25285 + 14.2943i −0.352544 + 0.610624i
\(549\) 4.85483i 0.207199i
\(550\) −0.977051 0.564101i −0.0416616 0.0240533i
\(551\) −13.5657 + 23.4964i −0.577917 + 1.00098i
\(552\) 2.11403 3.66160i 0.0899790 0.155848i
\(553\) −8.78075 + 5.06957i −0.373395 + 0.215580i
\(554\) 5.61669 0.238630
\(555\) −4.69857 3.86308i −0.199443 0.163979i
\(556\) 17.6996 0.750632
\(557\) −28.3100 + 16.3448i −1.19953 + 0.692551i −0.960451 0.278448i \(-0.910180\pi\)
−0.239082 + 0.970999i \(0.576847\pi\)
\(558\) −2.57548 + 4.46086i −0.109029 + 0.188843i
\(559\) −27.9500 + 48.4107i −1.18216 + 2.04756i
\(560\) 0.754597 + 0.435667i 0.0318875 + 0.0184103i
\(561\) 2.11124i 0.0891366i
\(562\) 10.3572 17.9392i 0.436893 0.756721i
\(563\) 29.2451i 1.23253i 0.787538 + 0.616267i \(0.211356\pi\)
−0.787538 + 0.616267i \(0.788644\pi\)
\(564\) 3.80679 + 6.59356i 0.160295 + 0.277639i
\(565\) 8.57878 0.360912
\(566\) −9.74927 −0.409792
\(567\) 0.435667 + 0.754597i 0.0182963 + 0.0316901i
\(568\) −13.0911 7.55813i −0.549289 0.317132i
\(569\) 2.76558i 0.115939i 0.998318 + 0.0579696i \(0.0184626\pi\)
−0.998318 + 0.0579696i \(0.981537\pi\)
\(570\) −5.64541 + 3.25938i −0.236460 + 0.136520i
\(571\) −8.17459 14.1588i −0.342096 0.592528i 0.642726 0.766096i \(-0.277804\pi\)
−0.984822 + 0.173569i \(0.944470\pi\)
\(572\) −5.82333 + 3.36210i −0.243486 + 0.140576i
\(573\) 15.0757 + 8.70395i 0.629796 + 0.363613i
\(574\) −8.01968 4.63017i −0.334735 0.193259i
\(575\) −3.66160 + 2.11403i −0.152699 + 0.0881610i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 14.5112 8.37802i 0.604107 0.348782i −0.166548 0.986033i \(-0.553262\pi\)
0.770656 + 0.637252i \(0.219929\pi\)
\(578\) 13.4981i 0.561447i
\(579\) −16.3238 9.42456i −0.678395 0.391671i
\(580\) −2.08102 3.60443i −0.0864097 0.149666i
\(581\) −4.31286 −0.178928
\(582\) 2.17225 0.0900425
\(583\) 6.28895 + 10.8928i 0.260462 + 0.451133i
\(584\) 4.43634i 0.183577i
\(585\) 2.98005 5.16160i 0.123210 0.213406i
\(586\) 18.7399i 0.774138i
\(587\) 9.82117 + 5.67026i 0.405363 + 0.234037i 0.688796 0.724956i \(-0.258140\pi\)
−0.283432 + 0.958992i \(0.591473\pi\)
\(588\) −3.12039 + 5.40467i −0.128683 + 0.222885i
\(589\) −16.7889 + 29.0793i −0.691776 + 1.19819i
\(590\) −1.96930 + 1.13698i −0.0810748 + 0.0468086i
\(591\) −0.613658 −0.0252425
\(592\) −3.86308 + 4.69857i −0.158772 + 0.193110i
\(593\) −37.1864 −1.52706 −0.763531 0.645771i \(-0.776536\pi\)
−0.763531 + 0.645771i \(0.776536\pi\)
\(594\) −0.977051 + 0.564101i −0.0400889 + 0.0231453i
\(595\) 0.815277 1.41210i 0.0334231 0.0578905i
\(596\) 8.29891 14.3741i 0.339937 0.588788i
\(597\) 20.2609 + 11.6976i 0.829222 + 0.478751i
\(598\) 25.1997i 1.03049i
\(599\) 7.12050 12.3331i 0.290936 0.503915i −0.683096 0.730329i \(-0.739367\pi\)
0.974031 + 0.226414i \(0.0727001\pi\)
\(600\) 1.00000i 0.0408248i
\(601\) −11.1396 19.2944i −0.454395 0.787036i 0.544258 0.838918i \(-0.316811\pi\)
−0.998653 + 0.0518822i \(0.983478\pi\)
\(602\) 8.17225 0.333076
\(603\) 14.1455 0.576051
\(604\) −7.15224 12.3880i −0.291021 0.504062i
\(605\) 8.42397 + 4.86358i 0.342483 + 0.197733i
\(606\) 4.72751i 0.192042i
\(607\) 20.6605 11.9284i 0.838585 0.484157i −0.0181978 0.999834i \(-0.505793\pi\)
0.856783 + 0.515677i \(0.172460\pi\)
\(608\) 3.25938 + 5.64541i 0.132185 + 0.228952i
\(609\) −3.14066 + 1.81326i −0.127266 + 0.0734771i
\(610\) 4.20441 + 2.42742i 0.170232 + 0.0982832i
\(611\) −39.2983 22.6889i −1.58984 0.917895i
\(612\) 1.62062 0.935667i 0.0655098 0.0378221i
\(613\) 16.6580 + 28.8526i 0.672812 + 1.16534i 0.977103 + 0.212765i \(0.0682470\pi\)
−0.304291 + 0.952579i \(0.598420\pi\)
\(614\) −22.7542 + 13.1371i −0.918284 + 0.530172i
\(615\) 10.6278i 0.428553i
\(616\) 0.851337 + 0.491520i 0.0343013 + 0.0198039i
\(617\) −0.0901992 0.156230i −0.00363128 0.00628956i 0.864204 0.503141i \(-0.167823\pi\)
−0.867835 + 0.496852i \(0.834489\pi\)
\(618\) 5.43512 0.218632
\(619\) 19.6346 0.789181 0.394590 0.918857i \(-0.370886\pi\)
0.394590 + 0.918857i \(0.370886\pi\)
\(620\) −2.57548 4.46086i −0.103434 0.179153i
\(621\) 4.22805i 0.169666i
\(622\) 16.7355 28.9868i 0.671033 1.16226i
\(623\) 7.92491i 0.317505i
\(624\) −5.16160 2.98005i −0.206629 0.119298i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0.997143 1.72710i 0.0398539 0.0690289i
\(627\) −6.36916 + 3.67724i −0.254360 + 0.146855i
\(628\) 18.2282 0.727383
\(629\) 8.79260 + 7.22912i 0.350584 + 0.288244i
\(630\) −0.871333 −0.0347147
\(631\) 26.8143 15.4812i 1.06746 0.616298i 0.139973 0.990155i \(-0.455298\pi\)
0.927486 + 0.373857i \(0.121965\pi\)
\(632\) 5.81817 10.0774i 0.231435 0.400856i
\(633\) −10.5936 + 18.3487i −0.421059 + 0.729295i
\(634\) 5.18523 + 2.99369i 0.205932 + 0.118895i
\(635\) 16.1662i 0.641536i
\(636\) −5.57432 + 9.65501i −0.221036 + 0.382846i
\(637\) 37.1957i 1.47375i
\(638\) −2.34781 4.06653i −0.0929507 0.160995i
\(639\) 15.1163 0.597990
\(640\) −1.00000 −0.0395285
\(641\) 5.04530 + 8.73872i 0.199277 + 0.345159i 0.948294 0.317392i \(-0.102807\pi\)
−0.749017 + 0.662551i \(0.769474\pi\)
\(642\) 14.4308 + 8.33163i 0.569538 + 0.328823i
\(643\) 19.4671i 0.767706i 0.923394 + 0.383853i \(0.125403\pi\)
−0.923394 + 0.383853i \(0.874597\pi\)
\(644\) 3.19048 1.84202i 0.125722 0.0725858i
\(645\) −4.68951 8.12246i −0.184649 0.319822i
\(646\) 10.5644 6.09939i 0.415653 0.239977i
\(647\) −11.4187 6.59257i −0.448914 0.259181i 0.258458 0.966023i \(-0.416786\pi\)
−0.707371 + 0.706842i \(0.750119\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) −2.22177 + 1.28274i −0.0872120 + 0.0503519i
\(650\) 2.98005 + 5.16160i 0.116887 + 0.202455i
\(651\) −3.88690 + 2.24410i −0.152339 + 0.0879532i
\(652\) 6.27777i 0.245857i
\(653\) −20.1410 11.6284i −0.788180 0.455056i 0.0511414 0.998691i \(-0.483714\pi\)
−0.839321 + 0.543635i \(0.817047\pi\)
\(654\) −8.38487 14.5230i −0.327874 0.567895i
\(655\) 5.66129 0.221205
\(656\) 10.6278 0.414945
\(657\) 2.21817 + 3.84198i 0.0865390 + 0.149890i
\(658\) 6.63397i 0.258619i
\(659\) 14.9905 25.9644i 0.583949 1.01143i −0.411057 0.911610i \(-0.634840\pi\)
0.995006 0.0998192i \(-0.0318265\pi\)
\(660\) 1.12820i 0.0439152i
\(661\) 11.5053 + 6.64256i 0.447503 + 0.258366i 0.706775 0.707439i \(-0.250149\pi\)
−0.259272 + 0.965804i \(0.583483\pi\)
\(662\) 9.32279 16.1475i 0.362340 0.627592i
\(663\) −5.57667 + 9.65908i −0.216580 + 0.375128i
\(664\) 4.28659 2.47486i 0.166352 0.0960434i
\(665\) −5.68001 −0.220261
\(666\) 0.996242 6.00063i 0.0386036 0.232520i
\(667\) −17.5973 −0.681372
\(668\) 6.40836 3.69987i 0.247947 0.143152i
\(669\) −7.72081 + 13.3728i −0.298504 + 0.517024i
\(670\) −7.07277 + 12.2504i −0.273245 + 0.473274i
\(671\) 4.74342 + 2.73861i 0.183118 + 0.105723i
\(672\) 0.871333i 0.0336124i
\(673\) −6.35737 + 11.0113i −0.245058 + 0.424454i −0.962148 0.272527i \(-0.912140\pi\)
0.717090 + 0.696981i \(0.245474\pi\)
\(674\) 1.19521i 0.0460380i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) 22.5229 0.866264
\(677\) −12.3800 −0.475801 −0.237901 0.971290i \(-0.576459\pi\)
−0.237901 + 0.971290i \(0.576459\pi\)
\(678\) 4.28939 + 7.42944i 0.164733 + 0.285326i
\(679\) 1.63917 + 0.946375i 0.0629056 + 0.0363185i
\(680\) 1.87133i 0.0717624i
\(681\) −3.86623 + 2.23217i −0.148154 + 0.0855370i
\(682\) −2.90566 5.03275i −0.111263 0.192714i
\(683\) −8.49785 + 4.90623i −0.325161 + 0.187732i −0.653691 0.756762i \(-0.726780\pi\)
0.328530 + 0.944494i \(0.393447\pi\)
\(684\) −5.64541 3.25938i −0.215858 0.124626i
\(685\) 14.2943 + 8.25285i 0.546159 + 0.315325i
\(686\) −9.99145 + 5.76856i −0.381475 + 0.220245i
\(687\) 8.13293 + 14.0866i 0.310291 + 0.537439i
\(688\) −8.12246 + 4.68951i −0.309666 + 0.178786i
\(689\) 66.4471i 2.53143i
\(690\) −3.66160 2.11403i −0.139395 0.0804796i
\(691\) 10.7731 + 18.6595i 0.409828 + 0.709842i 0.994870 0.101160i \(-0.0322555\pi\)
−0.585043 + 0.811003i \(0.698922\pi\)
\(692\) 10.4371 0.396760
\(693\) −0.983039 −0.0373426
\(694\) 2.94679 + 5.10399i 0.111859 + 0.193745i
\(695\) 17.6996i 0.671385i
\(696\) 2.08102 3.60443i 0.0788809 0.136626i
\(697\) 19.8881i 0.753316i
\(698\) −12.3543 7.13276i −0.467617 0.269979i
\(699\) −1.82389 + 3.15906i −0.0689857 + 0.119487i
\(700\) 0.435667 0.754597i 0.0164666 0.0285211i
\(701\) 38.8616 22.4368i 1.46778 0.847426i 0.468435 0.883498i \(-0.344818\pi\)
0.999349 + 0.0360723i \(0.0114847\pi\)
\(702\) 5.96011 0.224950
\(703\) 6.49426 39.1166i 0.244936 1.47531i
\(704\) −1.12820 −0.0425207
\(705\) 6.59356 3.80679i 0.248328 0.143372i
\(706\) −8.43844 + 14.6158i −0.317585 + 0.550073i
\(707\) −2.05962 + 3.56736i −0.0774599 + 0.134164i
\(708\) −1.96930 1.13698i −0.0740109 0.0427302i
\(709\) 23.4849i 0.881995i −0.897508 0.440998i \(-0.854625\pi\)
0.897508 0.440998i \(-0.145375\pi\)
\(710\) −7.55813 + 13.0911i −0.283652 + 0.491299i
\(711\) 11.6363i 0.436397i
\(712\) 4.54758 + 7.87663i 0.170428 + 0.295189i
\(713\) −21.7785 −0.815613
\(714\) 1.63055 0.0610220
\(715\) 3.36210 + 5.82333i 0.125735 + 0.217780i
\(716\) −7.57765 4.37496i −0.283190 0.163500i
\(717\) 7.64877i 0.285648i
\(718\) 7.79364 4.49966i 0.290856 0.167926i
\(719\) −14.6060 25.2983i −0.544710 0.943466i −0.998625 0.0524210i \(-0.983306\pi\)
0.453915 0.891045i \(-0.350027\pi\)
\(720\) 0.866025 0.500000i 0.0322749 0.0186339i
\(721\) 4.10132 + 2.36790i 0.152741 + 0.0881852i
\(722\) −20.3466 11.7471i −0.757223 0.437183i
\(723\) 18.8434 10.8793i 0.700794 0.404604i
\(724\) 7.65366 + 13.2565i 0.284446 + 0.492675i
\(725\) −3.60443 + 2.08102i −0.133865 + 0.0772872i
\(726\) 9.72716i 0.361009i
\(727\) 23.3477 + 13.4798i 0.865917 + 0.499938i 0.865989 0.500062i \(-0.166690\pi\)
−7.19505e−5 1.00000i \(0.500023\pi\)
\(728\) −2.59662 4.49748i −0.0962371 0.166688i
\(729\) 1.00000 0.0370370
\(730\) −4.43634 −0.164196
\(731\) 8.77563 + 15.1998i 0.324578 + 0.562186i
\(732\) 4.85483i 0.179440i
\(733\) −15.1833 + 26.2982i −0.560806 + 0.971345i 0.436620 + 0.899646i \(0.356175\pi\)
−0.997426 + 0.0716990i \(0.977158\pi\)
\(734\) 12.4036i 0.457826i
\(735\) 5.40467 + 3.12039i 0.199354 + 0.115097i
\(736\) −2.11403 + 3.66160i −0.0779241 + 0.134968i
\(737\) −7.97951 + 13.8209i −0.293929 + 0.509100i
\(738\) −9.20392 + 5.31389i −0.338801 + 0.195607i
\(739\) −13.9985 −0.514942 −0.257471 0.966286i \(-0.582889\pi\)
−0.257471 + 0.966286i \(0.582889\pi\)
\(740\) 4.69857 + 3.86308i 0.172723 + 0.142010i
\(741\) 38.8525 1.42728
\(742\) −8.41273 + 4.85709i −0.308841 + 0.178309i
\(743\) 10.1124 17.5151i 0.370986 0.642567i −0.618731 0.785603i \(-0.712353\pi\)
0.989718 + 0.143036i \(0.0456864\pi\)
\(744\) 2.57548 4.46086i 0.0944217 0.163543i
\(745\) −14.3741 8.29891i −0.526628 0.304049i
\(746\) 10.9170i 0.399700i
\(747\) −2.47486 + 4.28659i −0.0905506 + 0.156838i
\(748\) 2.11124i 0.0771946i
\(749\) 7.25962 + 12.5740i 0.265261 + 0.459445i
\(750\) −1.00000 −0.0365148
\(751\) −48.7420 −1.77862 −0.889311 0.457302i \(-0.848816\pi\)
−0.889311 + 0.457302i \(0.848816\pi\)
\(752\) −3.80679 6.59356i −0.138820 0.240442i
\(753\) 0.209327 + 0.120855i 0.00762829 + 0.00440420i
\(754\) 24.8062i 0.903389i
\(755\) −12.3880 + 7.15224i −0.450847 + 0.260297i
\(756\) −0.435667 0.754597i −0.0158450 0.0274444i
\(757\) −24.5161 + 14.1544i −0.891051 + 0.514449i −0.874286 0.485411i \(-0.838670\pi\)
−0.0167650 + 0.999859i \(0.505337\pi\)
\(758\) −19.7454 11.4000i −0.717184 0.414067i
\(759\) −4.13102 2.38505i −0.149947 0.0865718i
\(760\) 5.64541 3.25938i 0.204781 0.118230i
\(761\) 14.3149 + 24.7942i 0.518916 + 0.898790i 0.999758 + 0.0219824i \(0.00699777\pi\)
−0.480842 + 0.876807i \(0.659669\pi\)
\(762\) −14.0003 + 8.08310i −0.507179 + 0.292820i
\(763\) 14.6120i 0.528991i
\(764\) −15.0757 8.70395i −0.545419 0.314898i
\(765\) −0.935667 1.62062i −0.0338291 0.0585937i
\(766\) 26.0195 0.940122
\(767\) 13.5530 0.489370
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 53.0077i 1.91151i 0.294168 + 0.955754i \(0.404957\pi\)
−0.294168 + 0.955754i \(0.595043\pi\)
\(770\) 0.491520 0.851337i 0.0177131 0.0306801i
\(771\) 24.8423i 0.894674i
\(772\) 16.3238 + 9.42456i 0.587507 + 0.339197i
\(773\) 4.26473 7.38673i 0.153392 0.265682i −0.779080 0.626924i \(-0.784314\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(774\) 4.68951 8.12246i 0.168561 0.291956i
\(775\) −4.46086 + 2.57548i −0.160239 + 0.0925140i
\(776\) −2.17225 −0.0779791
\(777\) 3.36603