Properties

Label 605.2.g.e.251.2
Level $605$
Weight $2$
Character 605.251
Analytic conductor $4.831$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
Defining polynomial: \(x^{8} - 3 x^{7} + 5 x^{6} - 3 x^{5} + 4 x^{4} + 3 x^{3} + 5 x^{2} + 3 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 251.2
Root \(-0.227943 - 0.701538i\) of defining polynomial
Character \(\chi\) \(=\) 605.251
Dual form 605.2.g.e.511.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.227943 - 0.701538i) q^{2} +(2.27460 - 1.65259i) q^{3} +(1.17784 + 0.855749i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.640877 - 1.97242i) q^{6} +(0.834404 + 0.606230i) q^{7} +(2.06235 - 1.49838i) q^{8} +(1.51569 - 4.66481i) q^{9} +O(q^{10})\) \(q+(0.227943 - 0.701538i) q^{2} +(2.27460 - 1.65259i) q^{3} +(1.17784 + 0.855749i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.640877 - 1.97242i) q^{6} +(0.834404 + 0.606230i) q^{7} +(2.06235 - 1.49838i) q^{8} +(1.51569 - 4.66481i) q^{9} -0.737640 q^{10} +4.09331 q^{12} +(-1.06580 + 3.28018i) q^{13} +(0.615490 - 0.447180i) q^{14} +(-2.27460 - 1.65259i) q^{15} +(0.318714 + 0.980901i) q^{16} +(-0.741089 - 2.28084i) q^{17} +(-2.92705 - 2.12663i) q^{18} +(-6.20420 + 4.50761i) q^{19} +(0.449894 - 1.38463i) q^{20} +2.89979 q^{21} +2.45589 q^{23} +(2.21480 - 6.81645i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(2.05823 + 1.49539i) q^{26} +(-1.65499 - 5.09355i) q^{27} +(0.464011 + 1.42808i) q^{28} +(-4.81714 - 3.49986i) q^{29} +(-1.67784 + 1.21902i) q^{30} +(-1.13972 + 3.50769i) q^{31} +5.85919 q^{32} -1.76902 q^{34} +(0.318714 - 0.980901i) q^{35} +(5.77714 - 4.19734i) q^{36} +(-4.82059 - 3.50236i) q^{37} +(1.74805 + 5.37996i) q^{38} +(2.99655 + 9.22244i) q^{39} +(-2.06235 - 1.49838i) q^{40} +(3.18450 - 2.31367i) q^{41} +(0.660987 - 2.03431i) q^{42} +7.64941 q^{43} -4.90488 q^{45} +(0.559803 - 1.72290i) q^{46} +(-4.72704 + 3.43439i) q^{47} +(2.34598 + 1.70445i) q^{48} +(-1.83440 - 5.64571i) q^{49} +(0.227943 + 0.701538i) q^{50} +(-5.45498 - 3.96328i) q^{51} +(-4.06235 + 2.95147i) q^{52} +(-3.66124 + 11.2681i) q^{53} -3.95056 q^{54} +2.62920 q^{56} +(-6.66281 + 20.5060i) q^{57} +(-3.55332 + 2.58164i) q^{58} +(-2.38361 - 1.73179i) q^{59} +(-1.26490 - 3.89297i) q^{60} +(-0.766476 - 2.35897i) q^{61} +(2.20098 + 1.59911i) q^{62} +(4.09265 - 2.97348i) q^{63} +(0.698136 - 2.14864i) q^{64} +3.44899 q^{65} -6.14702 q^{67} +(1.07894 - 3.32064i) q^{68} +(5.58616 - 4.05858i) q^{69} +(-0.615490 - 0.447180i) q^{70} +(0.625187 + 1.92413i) q^{71} +(-3.86380 - 11.8916i) q^{72} +(-0.668140 - 0.485432i) q^{73} +(-3.55586 + 2.58348i) q^{74} +(-0.868820 + 2.67395i) q^{75} -11.1649 q^{76} +7.15293 q^{78} +(3.73236 - 11.4870i) q^{79} +(0.834404 - 0.606230i) q^{80} +(-0.277637 - 0.201715i) q^{81} +(-0.897243 - 2.76143i) q^{82} +(-0.497523 - 1.53122i) q^{83} +(3.41548 + 2.48149i) q^{84} +(-1.94020 + 1.40964i) q^{85} +(1.74363 - 5.36635i) q^{86} -16.7409 q^{87} +8.16116 q^{89} +(-1.11803 + 3.44095i) q^{90} +(-2.87785 + 2.09088i) q^{91} +(2.89263 + 2.10162i) q^{92} +(3.20438 + 9.86208i) q^{93} +(1.33186 + 4.09904i) q^{94} +(6.20420 + 4.50761i) q^{95} +(13.3273 - 9.68286i) q^{96} +(0.754861 - 2.32322i) q^{97} -4.37882 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 3q^{2} + 5q^{3} + 3q^{4} + 2q^{5} - 8q^{6} - 4q^{7} + q^{8} + 5q^{9} + O(q^{10}) \) \( 8q - 3q^{2} + 5q^{3} + 3q^{4} + 2q^{5} - 8q^{6} - 4q^{7} + q^{8} + 5q^{9} - 2q^{10} + 16q^{12} - 3q^{13} + 14q^{14} - 5q^{15} - q^{16} - 12q^{17} - 10q^{18} - 5q^{19} + 2q^{20} + 20q^{21} + 10q^{23} + 2q^{24} - 2q^{25} + 5q^{26} + 5q^{27} - 19q^{28} - 21q^{29} - 7q^{30} + 15q^{31} - 16q^{32} + 4q^{34} - q^{35} + 15q^{36} - 31q^{37} - 20q^{38} + 14q^{39} - q^{40} - 3q^{41} - 21q^{42} + 38q^{43} + 7q^{46} - 5q^{47} + 5q^{48} - 4q^{49} - 3q^{50} - 6q^{51} - 17q^{52} - 2q^{53} - 16q^{54} + 22q^{56} - 40q^{57} + 2q^{58} + 18q^{59} + 4q^{60} - 6q^{61} + 5q^{62} + 30q^{63} + 29q^{64} - 2q^{65} - 38q^{67} + 14q^{68} + 9q^{69} - 14q^{70} + 15q^{71} - 5q^{72} + 2q^{73} + 20q^{74} - 5q^{75} - 16q^{78} + 3q^{79} - 4q^{80} - 12q^{81} - 22q^{82} + 38q^{83} + 17q^{84} - 13q^{85} + 2q^{86} - 38q^{87} - 16q^{89} - 36q^{91} + q^{92} + 40q^{93} + 18q^{94} + 5q^{95} + 17q^{96} - 56q^{97} - 16q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.227943 0.701538i 0.161180 0.496062i −0.837554 0.546354i \(-0.816015\pi\)
0.998735 + 0.0502922i \(0.0160153\pi\)
\(3\) 2.27460 1.65259i 1.31324 0.954126i 0.313251 0.949670i \(-0.398582\pi\)
0.999990 0.00445538i \(-0.00141820\pi\)
\(4\) 1.17784 + 0.855749i 0.588919 + 0.427874i
\(5\) −0.309017 0.951057i −0.138197 0.425325i
\(6\) −0.640877 1.97242i −0.261637 0.805235i
\(7\) 0.834404 + 0.606230i 0.315375 + 0.229133i 0.734199 0.678934i \(-0.237558\pi\)
−0.418824 + 0.908067i \(0.637558\pi\)
\(8\) 2.06235 1.49838i 0.729150 0.529758i
\(9\) 1.51569 4.66481i 0.505230 1.55494i
\(10\) −0.737640 −0.233262
\(11\) 0 0
\(12\) 4.09331 1.18164
\(13\) −1.06580 + 3.28018i −0.295599 + 0.909759i 0.687421 + 0.726259i \(0.258743\pi\)
−0.983020 + 0.183500i \(0.941257\pi\)
\(14\) 0.615490 0.447180i 0.164497 0.119514i
\(15\) −2.27460 1.65259i −0.587299 0.426698i
\(16\) 0.318714 + 0.980901i 0.0796785 + 0.245225i
\(17\) −0.741089 2.28084i −0.179741 0.553185i 0.820078 0.572252i \(-0.193930\pi\)
−0.999818 + 0.0190677i \(0.993930\pi\)
\(18\) −2.92705 2.12663i −0.689913 0.501251i
\(19\) −6.20420 + 4.50761i −1.42334 + 1.03412i −0.432131 + 0.901811i \(0.642238\pi\)
−0.991209 + 0.132306i \(0.957762\pi\)
\(20\) 0.449894 1.38463i 0.100599 0.309613i
\(21\) 2.89979 0.632786
\(22\) 0 0
\(23\) 2.45589 0.512088 0.256044 0.966665i \(-0.417581\pi\)
0.256044 + 0.966665i \(0.417581\pi\)
\(24\) 2.21480 6.81645i 0.452094 1.39140i
\(25\) −0.809017 + 0.587785i −0.161803 + 0.117557i
\(26\) 2.05823 + 1.49539i 0.403652 + 0.293271i
\(27\) −1.65499 5.09355i −0.318504 0.980254i
\(28\) 0.464011 + 1.42808i 0.0876899 + 0.269882i
\(29\) −4.81714 3.49986i −0.894521 0.649907i 0.0425320 0.999095i \(-0.486458\pi\)
−0.937053 + 0.349188i \(0.886458\pi\)
\(30\) −1.67784 + 1.21902i −0.306330 + 0.222562i
\(31\) −1.13972 + 3.50769i −0.204699 + 0.629999i 0.795026 + 0.606575i \(0.207457\pi\)
−0.999726 + 0.0234246i \(0.992543\pi\)
\(32\) 5.85919 1.03577
\(33\) 0 0
\(34\) −1.76902 −0.303384
\(35\) 0.318714 0.980901i 0.0538725 0.165802i
\(36\) 5.77714 4.19734i 0.962857 0.699557i
\(37\) −4.82059 3.50236i −0.792500 0.575785i 0.116204 0.993225i \(-0.462927\pi\)
−0.908704 + 0.417440i \(0.862927\pi\)
\(38\) 1.74805 + 5.37996i 0.283572 + 0.872744i
\(39\) 2.99655 + 9.22244i 0.479832 + 1.47677i
\(40\) −2.06235 1.49838i −0.326086 0.236915i
\(41\) 3.18450 2.31367i 0.497335 0.361335i −0.310663 0.950520i \(-0.600551\pi\)
0.807998 + 0.589185i \(0.200551\pi\)
\(42\) 0.660987 2.03431i 0.101993 0.313901i
\(43\) 7.64941 1.16652 0.583262 0.812284i \(-0.301776\pi\)
0.583262 + 0.812284i \(0.301776\pi\)
\(44\) 0 0
\(45\) −4.90488 −0.731176
\(46\) 0.559803 1.72290i 0.0825385 0.254027i
\(47\) −4.72704 + 3.43439i −0.689509 + 0.500958i −0.876499 0.481404i \(-0.840127\pi\)
0.186989 + 0.982362i \(0.440127\pi\)
\(48\) 2.34598 + 1.70445i 0.338613 + 0.246017i
\(49\) −1.83440 5.64571i −0.262058 0.806531i
\(50\) 0.227943 + 0.701538i 0.0322361 + 0.0992124i
\(51\) −5.45498 3.96328i −0.763850 0.554970i
\(52\) −4.06235 + 2.95147i −0.563346 + 0.409295i
\(53\) −3.66124 + 11.2681i −0.502910 + 1.54780i 0.301345 + 0.953515i \(0.402564\pi\)
−0.804256 + 0.594284i \(0.797436\pi\)
\(54\) −3.95056 −0.537603
\(55\) 0 0
\(56\) 2.62920 0.351341
\(57\) −6.66281 + 20.5060i −0.882511 + 2.71609i
\(58\) −3.55332 + 2.58164i −0.466573 + 0.338985i
\(59\) −2.38361 1.73179i −0.310319 0.225460i 0.421714 0.906729i \(-0.361428\pi\)
−0.732033 + 0.681269i \(0.761428\pi\)
\(60\) −1.26490 3.89297i −0.163298 0.502581i
\(61\) −0.766476 2.35897i −0.0981372 0.302035i 0.889921 0.456114i \(-0.150759\pi\)
−0.988059 + 0.154079i \(0.950759\pi\)
\(62\) 2.20098 + 1.59911i 0.279525 + 0.203087i
\(63\) 4.09265 2.97348i 0.515625 0.374624i
\(64\) 0.698136 2.14864i 0.0872670 0.268580i
\(65\) 3.44899 0.427794
\(66\) 0 0
\(67\) −6.14702 −0.750978 −0.375489 0.926827i \(-0.622525\pi\)
−0.375489 + 0.926827i \(0.622525\pi\)
\(68\) 1.07894 3.32064i 0.130841 0.402687i
\(69\) 5.58616 4.05858i 0.672495 0.488596i
\(70\) −0.615490 0.447180i −0.0735651 0.0534482i
\(71\) 0.625187 + 1.92413i 0.0741960 + 0.228352i 0.981276 0.192606i \(-0.0616940\pi\)
−0.907080 + 0.420958i \(0.861694\pi\)
\(72\) −3.86380 11.8916i −0.455353 1.40143i
\(73\) −0.668140 0.485432i −0.0781999 0.0568156i 0.547998 0.836479i \(-0.315390\pi\)
−0.626198 + 0.779664i \(0.715390\pi\)
\(74\) −3.55586 + 2.58348i −0.413361 + 0.300324i
\(75\) −0.868820 + 2.67395i −0.100323 + 0.308762i
\(76\) −11.1649 −1.28070
\(77\) 0 0
\(78\) 7.15293 0.809910
\(79\) 3.73236 11.4870i 0.419924 1.29239i −0.487848 0.872928i \(-0.662218\pi\)
0.907772 0.419464i \(-0.137782\pi\)
\(80\) 0.834404 0.606230i 0.0932892 0.0677786i
\(81\) −0.277637 0.201715i −0.0308486 0.0224128i
\(82\) −0.897243 2.76143i −0.0990840 0.304949i
\(83\) −0.497523 1.53122i −0.0546102 0.168073i 0.920031 0.391845i \(-0.128163\pi\)
−0.974642 + 0.223772i \(0.928163\pi\)
\(84\) 3.41548 + 2.48149i 0.372659 + 0.270753i
\(85\) −1.94020 + 1.40964i −0.210444 + 0.152896i
\(86\) 1.74363 5.36635i 0.188021 0.578669i
\(87\) −16.7409 −1.79481
\(88\) 0 0
\(89\) 8.16116 0.865081 0.432541 0.901614i \(-0.357617\pi\)
0.432541 + 0.901614i \(0.357617\pi\)
\(90\) −1.11803 + 3.44095i −0.117851 + 0.362708i
\(91\) −2.87785 + 2.09088i −0.301681 + 0.219184i
\(92\) 2.89263 + 2.10162i 0.301578 + 0.219109i
\(93\) 3.20438 + 9.86208i 0.332279 + 1.02265i
\(94\) 1.33186 + 4.09904i 0.137371 + 0.422784i
\(95\) 6.20420 + 4.50761i 0.636537 + 0.462471i
\(96\) 13.3273 9.68286i 1.36021 0.988253i
\(97\) 0.754861 2.32322i 0.0766445 0.235888i −0.905393 0.424575i \(-0.860423\pi\)
0.982037 + 0.188688i \(0.0604234\pi\)
\(98\) −4.37882 −0.442328
\(99\) 0 0
\(100\) −1.45589 −0.145589
\(101\) 2.32496 7.15550i 0.231342 0.711999i −0.766243 0.642551i \(-0.777876\pi\)
0.997586 0.0694479i \(-0.0221238\pi\)
\(102\) −4.02381 + 2.92347i −0.398417 + 0.289467i
\(103\) 7.67135 + 5.57356i 0.755881 + 0.549180i 0.897644 0.440721i \(-0.145277\pi\)
−0.141763 + 0.989901i \(0.545277\pi\)
\(104\) 2.71693 + 8.36185i 0.266417 + 0.819947i
\(105\) −0.896084 2.75786i −0.0874488 0.269140i
\(106\) 7.07047 + 5.13700i 0.686745 + 0.498949i
\(107\) −3.75932 + 2.73131i −0.363427 + 0.264046i −0.754480 0.656323i \(-0.772111\pi\)
0.391053 + 0.920368i \(0.372111\pi\)
\(108\) 2.40948 7.41563i 0.231853 0.713569i
\(109\) 5.32826 0.510355 0.255178 0.966894i \(-0.417866\pi\)
0.255178 + 0.966894i \(0.417866\pi\)
\(110\) 0 0
\(111\) −16.7529 −1.59012
\(112\) −0.328715 + 1.01168i −0.0310607 + 0.0955949i
\(113\) −0.246670 + 0.179216i −0.0232047 + 0.0168592i −0.599327 0.800504i \(-0.704565\pi\)
0.576122 + 0.817363i \(0.304565\pi\)
\(114\) 12.8670 + 9.34843i 1.20511 + 0.875561i
\(115\) −0.758911 2.33569i −0.0707688 0.217804i
\(116\) −2.67881 8.24453i −0.248721 0.765485i
\(117\) 13.6860 + 9.94348i 1.26527 + 0.919275i
\(118\) −1.75824 + 1.27744i −0.161859 + 0.117598i
\(119\) 0.764345 2.35241i 0.0700673 0.215645i
\(120\) −7.16724 −0.654276
\(121\) 0 0
\(122\) −1.82962 −0.165646
\(123\) 3.41990 10.5254i 0.308362 0.949040i
\(124\) −4.34410 + 3.15617i −0.390112 + 0.283433i
\(125\) 0.809017 + 0.587785i 0.0723607 + 0.0525731i
\(126\) −1.15312 3.54893i −0.102728 0.316164i
\(127\) 3.68038 + 11.3270i 0.326581 + 1.00511i 0.970722 + 0.240206i \(0.0772150\pi\)
−0.644141 + 0.764907i \(0.722785\pi\)
\(128\) 8.13215 + 5.90835i 0.718787 + 0.522230i
\(129\) 17.3994 12.6414i 1.53193 1.11301i
\(130\) 0.786174 2.41960i 0.0689520 0.212213i
\(131\) 11.1875 0.977452 0.488726 0.872437i \(-0.337462\pi\)
0.488726 + 0.872437i \(0.337462\pi\)
\(132\) 0 0
\(133\) −7.90945 −0.685837
\(134\) −1.40117 + 4.31236i −0.121043 + 0.372531i
\(135\) −4.33283 + 3.14799i −0.372911 + 0.270936i
\(136\) −4.94595 3.59344i −0.424112 0.308135i
\(137\) −1.32298 4.07170i −0.113030 0.347869i 0.878501 0.477740i \(-0.158544\pi\)
−0.991531 + 0.129871i \(0.958544\pi\)
\(138\) −1.57392 4.84403i −0.133981 0.412351i
\(139\) −4.81624 3.49920i −0.408508 0.296798i 0.364490 0.931207i \(-0.381243\pi\)
−0.772997 + 0.634409i \(0.781243\pi\)
\(140\) 1.21480 0.882602i 0.102669 0.0745935i
\(141\) −5.07646 + 15.6238i −0.427515 + 1.31576i
\(142\) 1.49235 0.125236
\(143\) 0 0
\(144\) 5.05879 0.421566
\(145\) −1.83998 + 5.66289i −0.152802 + 0.470277i
\(146\) −0.492847 + 0.358074i −0.0407883 + 0.0296345i
\(147\) −13.5026 9.81022i −1.11368 0.809133i
\(148\) −2.68073 8.25043i −0.220354 0.678181i
\(149\) 1.16946 + 3.59922i 0.0958057 + 0.294860i 0.987463 0.157852i \(-0.0504568\pi\)
−0.891657 + 0.452711i \(0.850457\pi\)
\(150\) 1.67784 + 1.21902i 0.136995 + 0.0995326i
\(151\) −19.7049 + 14.3165i −1.60356 + 1.16506i −0.723350 + 0.690481i \(0.757399\pi\)
−0.880214 + 0.474576i \(0.842601\pi\)
\(152\) −6.04108 + 18.5925i −0.489996 + 1.50805i
\(153\) −11.7629 −0.950978
\(154\) 0 0
\(155\) 3.68820 0.296243
\(156\) −4.36264 + 13.4268i −0.349291 + 1.07501i
\(157\) −5.85089 + 4.25092i −0.466952 + 0.339260i −0.796252 0.604965i \(-0.793187\pi\)
0.329300 + 0.944225i \(0.393187\pi\)
\(158\) −7.20782 5.23679i −0.573423 0.416616i
\(159\) 10.2938 + 31.6811i 0.816352 + 2.51247i
\(160\) −1.81059 5.57242i −0.143140 0.440539i
\(161\) 2.04920 + 1.48883i 0.161500 + 0.117336i
\(162\) −0.204796 + 0.148793i −0.0160903 + 0.0116903i
\(163\) 5.77527 17.7744i 0.452354 1.39220i −0.421860 0.906661i \(-0.638623\pi\)
0.874214 0.485541i \(-0.161377\pi\)
\(164\) 5.73074 0.447496
\(165\) 0 0
\(166\) −1.18761 −0.0921767
\(167\) −2.42680 + 7.46891i −0.187791 + 0.577962i −0.999985 0.00542559i \(-0.998273\pi\)
0.812194 + 0.583387i \(0.198273\pi\)
\(168\) 5.98037 4.34499i 0.461395 0.335223i
\(169\) 0.893540 + 0.649194i 0.0687338 + 0.0499380i
\(170\) 0.546657 + 1.68244i 0.0419267 + 0.129037i
\(171\) 11.6235 + 35.7736i 0.888874 + 2.73567i
\(172\) 9.00976 + 6.54598i 0.686988 + 0.499126i
\(173\) 9.06478 6.58595i 0.689183 0.500721i −0.187209 0.982320i \(-0.559944\pi\)
0.876391 + 0.481600i \(0.159944\pi\)
\(174\) −3.81598 + 11.7444i −0.289289 + 0.890339i
\(175\) −1.03138 −0.0779650
\(176\) 0 0
\(177\) −8.28370 −0.622641
\(178\) 1.86028 5.72536i 0.139434 0.429134i
\(179\) −1.18491 + 0.860888i −0.0885643 + 0.0643458i −0.631186 0.775631i \(-0.717432\pi\)
0.542622 + 0.839977i \(0.317432\pi\)
\(180\) −5.77714 4.19734i −0.430603 0.312851i
\(181\) 2.87046 + 8.83437i 0.213360 + 0.656653i 0.999266 + 0.0383078i \(0.0121967\pi\)
−0.785906 + 0.618345i \(0.787803\pi\)
\(182\) 0.810844 + 2.49552i 0.0601038 + 0.184980i
\(183\) −5.64185 4.09904i −0.417057 0.303010i
\(184\) 5.06489 3.67986i 0.373389 0.271283i
\(185\) −1.84130 + 5.66694i −0.135375 + 0.416642i
\(186\) 7.64904 0.560855
\(187\) 0 0
\(188\) −8.50666 −0.620412
\(189\) 1.70693 5.25338i 0.124161 0.382127i
\(190\) 4.57646 3.32500i 0.332012 0.241221i
\(191\) 3.61870 + 2.62914i 0.261840 + 0.190238i 0.710958 0.703235i \(-0.248262\pi\)
−0.449118 + 0.893473i \(0.648262\pi\)
\(192\) −1.96285 6.04104i −0.141657 0.435974i
\(193\) 7.00418 + 21.5567i 0.504172 + 1.55168i 0.802158 + 0.597112i \(0.203685\pi\)
−0.297986 + 0.954570i \(0.596315\pi\)
\(194\) −1.45776 1.05913i −0.104661 0.0760409i
\(195\) 7.84507 5.69978i 0.561797 0.408170i
\(196\) 2.67068 8.21952i 0.190763 0.587109i
\(197\) 11.2080 0.798535 0.399267 0.916835i \(-0.369265\pi\)
0.399267 + 0.916835i \(0.369265\pi\)
\(198\) 0 0
\(199\) −7.81979 −0.554330 −0.277165 0.960822i \(-0.589395\pi\)
−0.277165 + 0.960822i \(0.589395\pi\)
\(200\) −0.787747 + 2.42443i −0.0557021 + 0.171433i
\(201\) −13.9820 + 10.1585i −0.986215 + 0.716527i
\(202\) −4.48989 3.26210i −0.315908 0.229520i
\(203\) −1.89772 5.84059i −0.133194 0.409929i
\(204\) −3.03351 9.33619i −0.212388 0.653664i
\(205\) −3.18450 2.31367i −0.222415 0.161594i
\(206\) 5.65870 4.11128i 0.394260 0.286447i
\(207\) 3.72236 11.4563i 0.258722 0.796265i
\(208\) −3.55722 −0.246649
\(209\) 0 0
\(210\) −2.13900 −0.147605
\(211\) 7.03539 21.6527i 0.484336 1.49063i −0.348604 0.937270i \(-0.613344\pi\)
0.832940 0.553363i \(-0.186656\pi\)
\(212\) −13.9550 + 10.1389i −0.958437 + 0.696345i
\(213\) 4.60185 + 3.34344i 0.315314 + 0.229089i
\(214\) 1.05920 + 3.25989i 0.0724056 + 0.222842i
\(215\) −2.36380 7.27502i −0.161210 0.496153i
\(216\) −11.0453 8.02485i −0.751535 0.546022i
\(217\) −3.07745 + 2.23590i −0.208911 + 0.151783i
\(218\) 1.21454 3.73798i 0.0822592 0.253168i
\(219\) −2.32197 −0.156905
\(220\) 0 0
\(221\) 8.27142 0.556396
\(222\) −3.81871 + 11.7528i −0.256295 + 0.788796i
\(223\) 12.9788 9.42965i 0.869124 0.631456i −0.0612274 0.998124i \(-0.519501\pi\)
0.930352 + 0.366668i \(0.119501\pi\)
\(224\) 4.88893 + 3.55202i 0.326655 + 0.237329i
\(225\) 1.51569 + 4.66481i 0.101046 + 0.310988i
\(226\) 0.0695001 + 0.213899i 0.00462308 + 0.0142284i
\(227\) −19.5428 14.1987i −1.29710 0.942398i −0.297177 0.954822i \(-0.596045\pi\)
−0.999923 + 0.0124240i \(0.996045\pi\)
\(228\) −25.3957 + 18.4511i −1.68187 + 1.22195i
\(229\) −4.63967 + 14.2794i −0.306598 + 0.943611i 0.672478 + 0.740117i \(0.265230\pi\)
−0.979076 + 0.203494i \(0.934770\pi\)
\(230\) −1.81156 −0.119451
\(231\) 0 0
\(232\) −15.1787 −0.996534
\(233\) −3.53081 + 10.8667i −0.231311 + 0.711902i 0.766278 + 0.642509i \(0.222106\pi\)
−0.997589 + 0.0693934i \(0.977894\pi\)
\(234\) 10.0954 7.33471i 0.659955 0.479485i
\(235\) 4.72704 + 3.43439i 0.308358 + 0.224035i
\(236\) −1.32552 4.07953i −0.0862841 0.265555i
\(237\) −10.4938 32.2965i −0.681644 2.09788i
\(238\) −1.47608 1.07243i −0.0956799 0.0695155i
\(239\) 22.1725 16.1093i 1.43422 1.04202i 0.445008 0.895526i \(-0.353201\pi\)
0.989211 0.146495i \(-0.0467993\pi\)
\(240\) 0.896084 2.75786i 0.0578419 0.178019i
\(241\) −10.9387 −0.704624 −0.352312 0.935883i \(-0.614604\pi\)
−0.352312 + 0.935883i \(0.614604\pi\)
\(242\) 0 0
\(243\) 15.1022 0.968804
\(244\) 1.11590 3.43439i 0.0714383 0.219865i
\(245\) −4.80253 + 3.48924i −0.306822 + 0.222920i
\(246\) −6.60440 4.79837i −0.421081 0.305933i
\(247\) −8.17339 25.1551i −0.520060 1.60058i
\(248\) 2.90537 + 8.94180i 0.184491 + 0.567805i
\(249\) −3.66215 2.66071i −0.232079 0.168615i
\(250\) 0.596764 0.433574i 0.0377426 0.0274216i
\(251\) 5.32471 16.3878i 0.336093 1.03439i −0.630089 0.776523i \(-0.716982\pi\)
0.966181 0.257863i \(-0.0830184\pi\)
\(252\) 7.36503 0.463953
\(253\) 0 0
\(254\) 8.78527 0.551237
\(255\) −2.08362 + 6.41272i −0.130481 + 0.401580i
\(256\) 9.65409 7.01411i 0.603381 0.438382i
\(257\) −14.9631 10.8713i −0.933373 0.678135i 0.0134434 0.999910i \(-0.495721\pi\)
−0.946816 + 0.321774i \(0.895721\pi\)
\(258\) −4.90233 15.0878i −0.305206 0.939327i
\(259\) −1.89908 5.84477i −0.118003 0.363176i
\(260\) 4.06235 + 2.95147i 0.251936 + 0.183042i
\(261\) −23.6275 + 17.1664i −1.46250 + 1.06257i
\(262\) 2.55011 7.84842i 0.157546 0.484877i
\(263\) −3.69135 −0.227618 −0.113809 0.993503i \(-0.536305\pi\)
−0.113809 + 0.993503i \(0.536305\pi\)
\(264\) 0 0
\(265\) 11.8480 0.727819
\(266\) −1.80291 + 5.54878i −0.110543 + 0.340217i
\(267\) 18.5634 13.4871i 1.13606 0.825396i
\(268\) −7.24018 5.26030i −0.442265 0.321324i
\(269\) −3.07320 9.45835i −0.187377 0.576686i 0.812605 0.582815i \(-0.198049\pi\)
−0.999981 + 0.00612956i \(0.998049\pi\)
\(270\) 1.22079 + 3.75721i 0.0742949 + 0.228656i
\(271\) 1.01423 + 0.736878i 0.0616098 + 0.0447622i 0.618164 0.786049i \(-0.287877\pi\)
−0.556554 + 0.830811i \(0.687877\pi\)
\(272\) 2.00108 1.45387i 0.121333 0.0881538i
\(273\) −3.09058 + 9.51183i −0.187051 + 0.575682i
\(274\) −3.15802 −0.190783
\(275\) 0 0
\(276\) 10.0527 0.605102
\(277\) 2.50097 7.69720i 0.150269 0.462480i −0.847382 0.530984i \(-0.821823\pi\)
0.997651 + 0.0685038i \(0.0218225\pi\)
\(278\) −3.55265 + 2.58115i −0.213074 + 0.154807i
\(279\) 14.6353 + 10.6331i 0.876190 + 0.636589i
\(280\) −0.812466 2.50051i −0.0485541 0.149434i
\(281\) −7.83984 24.1285i −0.467686 1.43939i −0.855573 0.517681i \(-0.826795\pi\)
0.387888 0.921707i \(-0.373205\pi\)
\(282\) 9.80350 + 7.12266i 0.583790 + 0.424148i
\(283\) −16.5383 + 12.0157i −0.983097 + 0.714262i −0.958399 0.285433i \(-0.907863\pi\)
−0.0246985 + 0.999695i \(0.507863\pi\)
\(284\) −0.910201 + 2.80131i −0.0540105 + 0.166227i
\(285\) 21.5613 1.27718
\(286\) 0 0
\(287\) 4.05977 0.239641
\(288\) 8.88072 27.3320i 0.523301 1.61056i
\(289\) 9.10028 6.61174i 0.535311 0.388926i
\(290\) 3.55332 + 2.58164i 0.208658 + 0.151599i
\(291\) −2.12234 6.53189i −0.124414 0.382906i
\(292\) −0.371552 1.14352i −0.0217435 0.0669195i
\(293\) 2.06224 + 1.49830i 0.120477 + 0.0875319i 0.646392 0.763005i \(-0.276277\pi\)
−0.525915 + 0.850537i \(0.676277\pi\)
\(294\) −9.96007 + 7.23641i −0.580883 + 0.422036i
\(295\) −0.910456 + 2.80210i −0.0530088 + 0.163144i
\(296\) −15.1896 −0.882878
\(297\) 0 0
\(298\) 2.79156 0.161711
\(299\) −2.61747 + 8.05576i −0.151372 + 0.465877i
\(300\) −3.31156 + 2.40599i −0.191193 + 0.138910i
\(301\) 6.38270 + 4.63730i 0.367893 + 0.267290i
\(302\) 5.55193 + 17.0871i 0.319478 + 0.983252i
\(303\) −6.53677 20.1181i −0.375528 1.15576i
\(304\) −6.39888 4.64906i −0.367001 0.266642i
\(305\) −2.00666 + 1.45792i −0.114901 + 0.0834805i
\(306\) −2.68129 + 8.25215i −0.153279 + 0.471744i
\(307\) −8.99273 −0.513242 −0.256621 0.966512i \(-0.582609\pi\)
−0.256621 + 0.966512i \(0.582609\pi\)
\(308\) 0 0
\(309\) 26.6601 1.51664
\(310\) 0.840701 2.58741i 0.0477486 0.146955i
\(311\) 16.2800 11.8281i 0.923154 0.670710i −0.0211533 0.999776i \(-0.506734\pi\)
0.944307 + 0.329066i \(0.106734\pi\)
\(312\) 19.9987 + 14.5299i 1.13220 + 0.822593i
\(313\) 2.19551 + 6.75709i 0.124098 + 0.381933i 0.993736 0.111757i \(-0.0356477\pi\)
−0.869638 + 0.493690i \(0.835648\pi\)
\(314\) 1.64851 + 5.07359i 0.0930307 + 0.286319i
\(315\) −4.09265 2.97348i −0.230595 0.167537i
\(316\) 14.2261 10.3359i 0.800283 0.581439i
\(317\) 0.708647 2.18099i 0.0398016 0.122497i −0.929181 0.369624i \(-0.879487\pi\)
0.968983 + 0.247127i \(0.0794865\pi\)
\(318\) 24.5719 1.37792
\(319\) 0 0
\(320\) −2.25922 −0.126294
\(321\) −4.03722 + 12.4253i −0.225335 + 0.693511i
\(322\) 1.51157 1.09822i 0.0842367 0.0612015i
\(323\) 14.8790 + 10.8102i 0.827890 + 0.601497i
\(324\) −0.154394 0.475175i −0.00857743 0.0263986i
\(325\) −1.06580 3.28018i −0.0591197 0.181952i
\(326\) −11.1530 8.10314i −0.617708 0.448791i
\(327\) 12.1197 8.80546i 0.670219 0.486943i
\(328\) 3.10077 9.54319i 0.171211 0.526935i
\(329\) −6.02629 −0.332240
\(330\) 0 0
\(331\) 15.3951 0.846192 0.423096 0.906085i \(-0.360943\pi\)
0.423096 + 0.906085i \(0.360943\pi\)
\(332\) 0.724337 2.22928i 0.0397532 0.122348i
\(333\) −23.6444 + 17.1787i −1.29570 + 0.941385i
\(334\) 4.68655 + 3.40498i 0.256437 + 0.186312i
\(335\) 1.89953 + 5.84616i 0.103783 + 0.319410i
\(336\) 0.924203 + 2.84440i 0.0504194 + 0.155175i
\(337\) −15.7733 11.4600i −0.859225 0.624263i 0.0684492 0.997655i \(-0.478195\pi\)
−0.927674 + 0.373391i \(0.878195\pi\)
\(338\) 0.659111 0.478872i 0.0358509 0.0260472i
\(339\) −0.264904 + 0.815290i −0.0143876 + 0.0442805i
\(340\) −3.49153 −0.189355
\(341\) 0 0
\(342\) 27.7460 1.50033
\(343\) 4.12296 12.6892i 0.222619 0.685151i
\(344\) 15.7757 11.4618i 0.850571 0.617976i
\(345\) −5.58616 4.05858i −0.300749 0.218507i
\(346\) −2.55403 7.86051i −0.137306 0.422584i
\(347\) 0.670272 + 2.06288i 0.0359821 + 0.110741i 0.967434 0.253122i \(-0.0814574\pi\)
−0.931452 + 0.363864i \(0.881457\pi\)
\(348\) −19.7181 14.3260i −1.05700 0.767955i
\(349\) −20.2675 + 14.7252i −1.08490 + 0.788222i −0.978530 0.206105i \(-0.933921\pi\)
−0.106365 + 0.994327i \(0.533921\pi\)
\(350\) −0.235096 + 0.723552i −0.0125664 + 0.0386755i
\(351\) 18.4717 0.985944
\(352\) 0 0
\(353\) −23.2532 −1.23764 −0.618821 0.785532i \(-0.712389\pi\)
−0.618821 + 0.785532i \(0.712389\pi\)
\(354\) −1.88821 + 5.81133i −0.100357 + 0.308868i
\(355\) 1.63676 1.18918i 0.0868702 0.0631149i
\(356\) 9.61252 + 6.98390i 0.509463 + 0.370146i
\(357\) −2.14900 6.61395i −0.113737 0.350047i
\(358\) 0.333853 + 1.02749i 0.0176447 + 0.0543047i
\(359\) 8.18917 + 5.94978i 0.432208 + 0.314018i 0.782531 0.622611i \(-0.213928\pi\)
−0.350323 + 0.936629i \(0.613928\pi\)
\(360\) −10.1156 + 7.34938i −0.533137 + 0.387346i
\(361\) 12.3022 37.8621i 0.647482 1.99274i
\(362\) 6.85194 0.360130
\(363\) 0 0
\(364\) −5.17891 −0.271448
\(365\) −0.255207 + 0.785446i −0.0133581 + 0.0411121i
\(366\) −4.16165 + 3.02362i −0.217533 + 0.158047i
\(367\) −3.00084 2.18024i −0.156643 0.113808i 0.506703 0.862121i \(-0.330864\pi\)
−0.663346 + 0.748313i \(0.730864\pi\)
\(368\) 0.782725 + 2.40898i 0.0408024 + 0.125577i
\(369\) −5.96614 18.3619i −0.310585 0.955882i
\(370\) 3.55586 + 2.58348i 0.184860 + 0.134309i
\(371\) −9.88604 + 7.18263i −0.513258 + 0.372904i
\(372\) −4.66522 + 14.3581i −0.241880 + 0.744431i
\(373\) 9.34017 0.483616 0.241808 0.970324i \(-0.422260\pi\)
0.241808 + 0.970324i \(0.422260\pi\)
\(374\) 0 0
\(375\) 2.81156 0.145188
\(376\) −4.60276 + 14.1658i −0.237369 + 0.730547i
\(377\) 16.6143 12.0710i 0.855678 0.621687i
\(378\) −3.29636 2.39495i −0.169547 0.123183i
\(379\) −3.03198 9.33148i −0.155742 0.479326i 0.842493 0.538707i \(-0.181087\pi\)
−0.998235 + 0.0593816i \(0.981087\pi\)
\(380\) 3.45015 + 10.6185i 0.176989 + 0.544716i
\(381\) 27.0904 + 19.6823i 1.38788 + 1.00836i
\(382\) 2.66930 1.93936i 0.136573 0.0992263i
\(383\) −5.57677 + 17.1635i −0.284960 + 0.877015i 0.701451 + 0.712718i \(0.252536\pi\)
−0.986411 + 0.164298i \(0.947464\pi\)
\(384\) 28.2615 1.44221
\(385\) 0 0
\(386\) 16.7194 0.850993
\(387\) 11.5941 35.6831i 0.589363 1.81387i
\(388\) 2.87720 2.09041i 0.146068 0.106124i
\(389\) −25.2345 18.3339i −1.27944 0.929567i −0.279903 0.960028i \(-0.590302\pi\)
−0.999536 + 0.0304614i \(0.990302\pi\)
\(390\) −2.21038 6.80284i −0.111927 0.344475i
\(391\) −1.82003 5.60148i −0.0920429 0.283279i
\(392\) −12.2426 8.89478i −0.618346 0.449254i
\(393\) 25.4470 18.4883i 1.28363 0.932612i
\(394\) 2.55478 7.86281i 0.128708 0.396123i
\(395\) −12.0782 −0.607719
\(396\) 0 0
\(397\) −10.6212 −0.533062 −0.266531 0.963826i \(-0.585877\pi\)
−0.266531 + 0.963826i \(0.585877\pi\)
\(398\) −1.78247 + 5.48588i −0.0893472 + 0.274982i
\(399\) −17.9908 + 13.0711i −0.900669 + 0.654374i
\(400\) −0.834404 0.606230i −0.0417202 0.0303115i
\(401\) −8.51895 26.2186i −0.425416 1.30930i −0.902595 0.430490i \(-0.858341\pi\)
0.477179 0.878806i \(-0.341659\pi\)
\(402\) 3.93948 + 12.1245i 0.196483 + 0.604714i
\(403\) −10.2912 7.47696i −0.512639 0.372454i
\(404\) 8.86173 6.43843i 0.440888 0.320324i
\(405\) −0.106048 + 0.326382i −0.00526956 + 0.0162181i
\(406\) −4.52997 −0.224818
\(407\) 0 0
\(408\) −17.1886 −0.850961
\(409\) −4.44001 + 13.6649i −0.219544 + 0.675688i 0.779255 + 0.626707i \(0.215598\pi\)
−0.998800 + 0.0489814i \(0.984402\pi\)
\(410\) −2.34901 + 1.70666i −0.116010 + 0.0842859i
\(411\) −9.73812 7.07516i −0.480346 0.348992i
\(412\) 4.26603 + 13.1295i 0.210172 + 0.646844i
\(413\) −0.939026 2.89003i −0.0462065 0.142209i
\(414\) −7.18851 5.22276i −0.353296 0.256684i
\(415\) −1.30253 + 0.946345i −0.0639388 + 0.0464542i
\(416\) −6.24470 + 19.2192i −0.306172 + 0.942300i
\(417\) −16.7378 −0.819652
\(418\) 0 0
\(419\) −31.4707 −1.53744 −0.768722 0.639584i \(-0.779107\pi\)
−0.768722 + 0.639584i \(0.779107\pi\)
\(420\) 1.30460 4.01513i 0.0636578 0.195919i
\(421\) −21.4965 + 15.6181i −1.04768 + 0.761182i −0.971769 0.235933i \(-0.924185\pi\)
−0.0759078 + 0.997115i \(0.524185\pi\)
\(422\) −13.5865 9.87118i −0.661381 0.480521i
\(423\) 8.85609 + 27.2562i 0.430598 + 1.32524i
\(424\) 9.33324 + 28.7248i 0.453262 + 1.39500i
\(425\) 1.94020 + 1.40964i 0.0941134 + 0.0683774i
\(426\) 3.39451 2.46626i 0.164465 0.119491i
\(427\) 0.790528 2.43300i 0.0382563 0.117741i
\(428\) −6.76518 −0.327008
\(429\) 0 0
\(430\) −5.64252 −0.272106
\(431\) 1.19549 3.67935i 0.0575849 0.177228i −0.918127 0.396287i \(-0.870299\pi\)
0.975712 + 0.219059i \(0.0702986\pi\)
\(432\) 4.46880 3.24677i 0.215005 0.156210i
\(433\) −32.4730 23.5930i −1.56055 1.13381i −0.935556 0.353178i \(-0.885101\pi\)
−0.624995 0.780629i \(-0.714899\pi\)
\(434\) 0.867082 + 2.66860i 0.0416213 + 0.128097i
\(435\) 5.17323 + 15.9216i 0.248037 + 0.763380i
\(436\) 6.27583 + 4.55966i 0.300558 + 0.218368i
\(437\) −15.2368 + 11.0702i −0.728875 + 0.529559i
\(438\) −0.529279 + 1.62895i −0.0252899 + 0.0778344i
\(439\) −1.02336 −0.0488425 −0.0244212 0.999702i \(-0.507774\pi\)
−0.0244212 + 0.999702i \(0.507774\pi\)
\(440\) 0 0
\(441\) −29.1166 −1.38650
\(442\) 1.88541 5.80271i 0.0896800 0.276007i
\(443\) 13.0032 9.44738i 0.617801 0.448858i −0.234352 0.972152i \(-0.575297\pi\)
0.852153 + 0.523293i \(0.175297\pi\)
\(444\) −19.7322 14.3363i −0.936448 0.680370i
\(445\) −2.52194 7.76173i −0.119551 0.367941i
\(446\) −3.65682 11.2545i −0.173156 0.532918i
\(447\) 8.60810 + 6.25415i 0.407149 + 0.295811i
\(448\) 1.88510 1.36960i 0.0890625 0.0647077i
\(449\) 11.0758 34.0879i 0.522700 1.60871i −0.246120 0.969239i \(-0.579156\pi\)
0.768820 0.639466i \(-0.220844\pi\)
\(450\) 3.61803 0.170556
\(451\) 0 0
\(452\) −0.443901 −0.0208793
\(453\) −21.1615 + 65.1285i −0.994256 + 3.06000i
\(454\) −14.4155 + 10.4735i −0.676555 + 0.491546i
\(455\) 2.87785 + 2.09088i 0.134916 + 0.0980220i
\(456\) 16.9849 + 52.2740i 0.795389 + 2.44795i
\(457\) 7.77254 + 23.9214i 0.363584 + 1.11900i 0.950863 + 0.309612i \(0.100199\pi\)
−0.587279 + 0.809384i \(0.699801\pi\)
\(458\) 8.95997 + 6.50980i 0.418672 + 0.304183i
\(459\) −10.3911 + 7.54955i −0.485013 + 0.352383i
\(460\) 1.10489 3.40050i 0.0515157 0.158549i
\(461\) −6.65631 −0.310015 −0.155008 0.987913i \(-0.549540\pi\)
−0.155008 + 0.987913i \(0.549540\pi\)
\(462\) 0 0
\(463\) 38.7730 1.80194 0.900968 0.433886i \(-0.142858\pi\)
0.900968 + 0.433886i \(0.142858\pi\)
\(464\) 1.89772 5.84059i 0.0880996 0.271143i
\(465\) 8.38919 6.09510i 0.389039 0.282654i
\(466\) 6.81858 + 4.95399i 0.315865 + 0.229489i
\(467\) 6.96815 + 21.4458i 0.322448 + 0.992392i 0.972580 + 0.232571i \(0.0747136\pi\)
−0.650132 + 0.759821i \(0.725286\pi\)
\(468\) 7.61079 + 23.4236i 0.351809 + 1.08276i
\(469\) −5.12909 3.72651i −0.236840 0.172074i
\(470\) 3.48685 2.53335i 0.160837 0.116855i
\(471\) −6.28339 + 19.3383i −0.289523 + 0.891062i
\(472\) −7.51071 −0.345708
\(473\) 0 0
\(474\) −25.0492 −1.15055
\(475\) 2.36979 7.29347i 0.108734 0.334647i
\(476\) 2.91335 2.11667i 0.133533 0.0970174i
\(477\) 47.0145 + 34.1580i 2.15265 + 1.56399i
\(478\) −6.24718 19.2268i −0.285739 0.879415i
\(479\) 0.504274 + 1.55200i 0.0230409 + 0.0709125i 0.961916 0.273346i \(-0.0881304\pi\)
−0.938875 + 0.344258i \(0.888130\pi\)
\(480\) −13.3273 9.68286i −0.608306 0.441960i
\(481\) 16.6262 12.0796i 0.758088 0.550783i
\(482\) −2.49341 + 7.67392i −0.113572 + 0.349537i
\(483\) 7.12155 0.324042
\(484\) 0 0
\(485\) −2.44278 −0.110921
\(486\) 3.44244 10.5947i 0.156152 0.480587i
\(487\) −0.849710 + 0.617350i −0.0385040 + 0.0279748i −0.606871 0.794800i \(-0.707575\pi\)
0.568367 + 0.822775i \(0.307575\pi\)
\(488\) −5.11538 3.71654i −0.231562 0.168240i
\(489\) −16.2375 49.9739i −0.734286 2.25990i
\(490\) 1.35313 + 4.16451i 0.0611282 + 0.188133i
\(491\) −11.2567 8.17850i −0.508009 0.369090i 0.304058 0.952653i \(-0.401658\pi\)
−0.812068 + 0.583563i \(0.801658\pi\)
\(492\) 13.0352 9.47059i 0.587670 0.426967i
\(493\) −4.41268 + 13.5808i −0.198737 + 0.611650i
\(494\) −19.5103 −0.877811
\(495\) 0 0
\(496\) −3.80394 −0.170802
\(497\) −0.644805 + 1.98451i −0.0289235 + 0.0890173i
\(498\) −2.70135 + 1.96264i −0.121050 + 0.0879482i
\(499\) −14.0504 10.2082i −0.628984 0.456983i 0.227064 0.973880i \(-0.427087\pi\)
−0.856048 + 0.516896i \(0.827087\pi\)
\(500\) 0.449894 + 1.38463i 0.0201199 + 0.0619226i
\(501\) 6.82309 + 20.9993i 0.304833 + 0.938179i
\(502\) −10.2829 7.47096i −0.458948 0.333445i
\(503\) 29.0062 21.0742i 1.29332 0.939653i 0.293454 0.955973i \(-0.405195\pi\)
0.999867 + 0.0163204i \(0.00519519\pi\)
\(504\) 3.98504 12.2647i 0.177508 0.546313i
\(505\) −7.52373 −0.334802
\(506\) 0 0
\(507\) 3.10530 0.137911
\(508\) −5.35822 + 16.4909i −0.237732 + 0.731665i
\(509\) −1.73031 + 1.25715i −0.0766947 + 0.0557220i −0.625472 0.780247i \(-0.715094\pi\)
0.548777 + 0.835969i \(0.315094\pi\)
\(510\) 4.02381 + 2.92347i 0.178178 + 0.129454i
\(511\) −0.263215 0.810093i −0.0116440 0.0358364i
\(512\) 3.49234 + 10.7483i 0.154341 + 0.475013i
\(513\) 33.2277 + 24.1413i 1.46704 + 1.06586i
\(514\) −11.0374 + 8.01913i −0.486838 + 0.353709i
\(515\) 2.93020 9.01821i 0.129120 0.397390i
\(516\) 31.3115 1.37841
\(517\) 0 0
\(518\) −4.53321 −0.199178
\(519\) 9.73486 29.9608i 0.427313 1.31513i
\(520\) 7.11301 5.16791i 0.311926 0.226628i
\(521\) 10.3030 + 7.48558i 0.451383 + 0.327949i 0.790142 0.612924i \(-0.210007\pi\)
−0.338758 + 0.940873i \(0.610007\pi\)
\(522\) 6.65713 + 20.4885i 0.291374 + 0.896758i
\(523\) −7.38821 22.7386i −0.323064 0.994289i −0.972307 0.233708i \(-0.924914\pi\)
0.649243 0.760581i \(-0.275086\pi\)
\(524\) 13.1770 + 9.57365i 0.575640 + 0.418227i
\(525\) −2.34598 + 1.70445i −0.102387 + 0.0743884i
\(526\) −0.841418 + 2.58962i −0.0366876 + 0.112913i
\(527\) 8.84510 0.385299
\(528\) 0 0
\(529\) −16.9686 −0.737766
\(530\) 2.70068 8.31184i 0.117310 0.361043i
\(531\) −11.6913 + 8.49422i −0.507359 + 0.368618i
\(532\) −9.31605 6.76851i −0.403902 0.293452i
\(533\) 4.19525 + 12.9116i 0.181716 + 0.559265i
\(534\) −5.23030 16.0972i −0.226337 0.696594i
\(535\) 3.75932 + 2.73131i 0.162530 + 0.118085i
\(536\) −12.6773 + 9.21058i −0.547575 + 0.397837i
\(537\) −1.27250 + 3.91635i −0.0549124 + 0.169003i
\(538\) −7.33590 −0.316273
\(539\) 0 0
\(540\) −7.79726 −0.335540
\(541\) −0.407657 + 1.25464i −0.0175265 + 0.0539412i −0.959437 0.281922i \(-0.909028\pi\)
0.941911 + 0.335863i \(0.109028\pi\)
\(542\) 0.748134 0.543551i 0.0321351 0.0233475i
\(543\) 21.1288 + 15.3509i 0.906722 + 0.658772i
\(544\) −4.34218 13.3639i −0.186170 0.572971i
\(545\) −1.64652 5.06748i −0.0705293 0.217067i
\(546\) 5.96843 + 4.33632i 0.255425 + 0.185577i
\(547\) 7.54108 5.47891i 0.322433 0.234261i −0.414780 0.909922i \(-0.636141\pi\)
0.737213 + 0.675660i \(0.236141\pi\)
\(548\) 1.92610 5.92794i 0.0822791 0.253229i
\(549\) −12.1659 −0.519228
\(550\) 0 0
\(551\) 45.6625 1.94529
\(552\) 5.43929 16.7404i 0.231512 0.712520i
\(553\) 10.0781 7.32216i 0.428564 0.311370i
\(554\) −4.82980 3.50905i −0.205198 0.149085i
\(555\) 5.17693 + 15.9330i 0.219749 + 0.676316i
\(556\) −2.67831 8.24298i −0.113585 0.349580i
\(557\) 31.8083 + 23.1101i 1.34776 + 0.979205i 0.999120 + 0.0419481i \(0.0133564\pi\)
0.348640 + 0.937257i \(0.386644\pi\)
\(558\) 10.7956 7.84343i 0.457012 0.332039i
\(559\) −8.15272 + 25.0915i −0.344823 + 1.06126i
\(560\) 1.06374 0.0449514
\(561\) 0 0
\(562\) −18.7141 −0.789407
\(563\) −6.17446 + 19.0030i −0.260222 + 0.800882i 0.732533 + 0.680731i \(0.238338\pi\)
−0.992756 + 0.120151i \(0.961662\pi\)
\(564\) −19.3493 + 14.0581i −0.814751 + 0.591951i
\(565\) 0.246670 + 0.179216i 0.0103775 + 0.00753968i
\(566\) 4.65971 + 14.3411i 0.195862 + 0.602802i
\(567\) −0.109376 0.336624i −0.00459335 0.0141369i
\(568\) 4.17243 + 3.03145i 0.175071 + 0.127197i
\(569\) −27.9635 + 20.3166i −1.17229 + 0.851718i −0.991281 0.131764i \(-0.957936\pi\)
−0.181008 + 0.983482i \(0.557936\pi\)
\(570\) 4.91476 15.1261i 0.205857 0.633562i
\(571\) −3.15090 −0.131861 −0.0659306 0.997824i \(-0.521002\pi\)
−0.0659306 + 0.997824i \(0.521002\pi\)
\(572\) 0 0
\(573\) 12.5760 0.525370
\(574\) 0.925399 2.84808i 0.0386254 0.118877i
\(575\) −1.98685 + 1.44353i −0.0828575 + 0.0601995i
\(576\) −8.96485 6.51335i −0.373536 0.271389i
\(577\) 8.44314 + 25.9853i 0.351493 + 1.08178i 0.958015 + 0.286717i \(0.0925639\pi\)
−0.606523 + 0.795066i \(0.707436\pi\)
\(578\) −2.56404 7.89129i −0.106650 0.328234i
\(579\) 51.5561 + 37.4577i 2.14260 + 1.55669i
\(580\) −7.01321 + 5.09540i −0.291208 + 0.211575i
\(581\) 0.513135 1.57927i 0.0212884 0.0655190i
\(582\) −5.06614 −0.209998
\(583\) 0 0
\(584\) −2.10530 −0.0871180
\(585\) 5.22760 16.0889i 0.216135 0.665194i
\(586\) 1.52119 1.10521i 0.0628398 0.0456558i
\(587\) 37.3506 + 27.1368i 1.54162 + 1.12005i 0.949307 + 0.314349i \(0.101786\pi\)
0.592316 + 0.805706i \(0.298214\pi\)
\(588\) −7.50879 23.1097i −0.309657 0.953027i
\(589\) −8.74027 26.8998i −0.360137 1.10839i
\(590\) 1.75824 + 1.27744i 0.0723857 + 0.0525913i
\(591\) 25.4936 18.5222i 1.04867 0.761902i
\(592\) 1.89908 5.84477i 0.0780518 0.240219i
\(593\) −39.4265 −1.61905 −0.809525 0.587085i \(-0.800275\pi\)
−0.809525 + 0.587085i \(0.800275\pi\)
\(594\) 0 0
\(595\) −2.47347 −0.101402
\(596\) −1.70260 + 5.24006i −0.0697411 + 0.214641i
\(597\) −17.7869 + 12.9229i −0.727970 + 0.528901i
\(598\) 5.05478 + 3.67251i 0.206705 + 0.150180i
\(599\) 0.324081 + 0.997418i 0.0132416 + 0.0407534i 0.957459 0.288569i \(-0.0931796\pi\)
−0.944217 + 0.329323i \(0.893180\pi\)
\(600\) 2.21480 + 6.81645i 0.0904187 + 0.278280i
\(601\) 22.0455 + 16.0170i 0.899256 + 0.653348i 0.938275 0.345891i \(-0.112423\pi\)
−0.0390187 + 0.999238i \(0.512423\pi\)
\(602\) 4.70814 3.42066i 0.191889 0.139416i
\(603\) −9.31697 + 28.6747i −0.379416 + 1.16772i
\(604\) −35.4605 −1.44287
\(605\) 0 0
\(606\) −15.6036 −0.633854
\(607\) −6.77418 + 20.8488i −0.274955 + 0.846225i 0.714276 + 0.699864i \(0.246756\pi\)
−0.989231 + 0.146361i \(0.953244\pi\)
\(608\) −36.3516 + 26.4110i −1.47425 + 1.07111i
\(609\) −13.9687 10.1488i −0.566040 0.411252i
\(610\) 0.565384 + 1.74007i 0.0228917 + 0.0704535i
\(611\) −6.22738 19.1659i −0.251933 0.775370i
\(612\) −13.8548 10.0661i −0.560049 0.406899i
\(613\) 8.56915 6.22586i 0.346105 0.251460i −0.401128 0.916022i \(-0.631382\pi\)
0.747233 + 0.664562i \(0.231382\pi\)
\(614\) −2.04983 + 6.30874i −0.0827245 + 0.254600i
\(615\) −11.0670 −0.446265
\(616\) 0 0
\(617\) 4.60402 0.185351 0.0926755 0.995696i \(-0.470458\pi\)
0.0926755 + 0.995696i \(0.470458\pi\)
\(618\) 6.07699 18.7031i 0.244453 0.752348i
\(619\) −29.9366 + 21.7502i −1.20326 + 0.874216i −0.994601 0.103773i \(-0.966908\pi\)
−0.208654 + 0.977989i \(0.566908\pi\)
\(620\) 4.34410 + 3.15617i 0.174463 + 0.126755i
\(621\) −4.06448 12.5092i −0.163102 0.501976i
\(622\) −4.58695 14.1172i −0.183920 0.566047i
\(623\) 6.80971 + 4.94754i 0.272825 + 0.198219i
\(624\) −8.09125 + 5.87864i −0.323909 + 0.235334i
\(625\) 0.309017 0.951057i 0.0123607 0.0380423i
\(626\) 5.24081 0.209465
\(627\) 0 0
\(628\) −10.5291 −0.420157
\(629\) −4.41584 + 13.5906i −0.176071 + 0.541891i
\(630\) −3.01890 + 2.19336i −0.120276 + 0.0873856i
\(631\) 20.0965 + 14.6009i 0.800028 + 0.581254i 0.910922 0.412578i \(-0.135372\pi\)
−0.110895 + 0.993832i \(0.535372\pi\)
\(632\) −9.51455 29.2828i −0.378468 1.16481i
\(633\) −19.7804 60.8779i −0.786201 2.41968i
\(634\) −1.36852 0.994285i −0.0543507 0.0394881i
\(635\) 9.63536 7.00050i 0.382368 0.277806i
\(636\) −14.9866 + 46.1241i −0.594258 + 1.82894i
\(637\) 20.4741 0.811213
\(638\) 0 0
\(639\) 9.92328 0.392559
\(640\) 3.10621 9.55992i 0.122784 0.377889i
\(641\) 35.9440 26.1149i 1.41970 1.03147i 0.427883 0.903834i \(-0.359260\pi\)
0.991820 0.127641i \(-0.0407405\pi\)
\(642\) 7.79654 + 5.66452i 0.307705 + 0.223561i
\(643\) 7.99148 + 24.5952i 0.315153 + 0.969942i 0.975691 + 0.219149i \(0.0703282\pi\)
−0.660538 + 0.750793i \(0.729672\pi\)
\(644\) 1.13956 + 3.50720i 0.0449049 + 0.138203i
\(645\) −17.3994 12.6414i −0.685099 0.497754i
\(646\) 10.9753 7.97406i 0.431819 0.313735i
\(647\) 6.02166 18.5328i 0.236736 0.728598i −0.760151 0.649747i \(-0.774875\pi\)
0.996886 0.0788509i \(-0.0251251\pi\)
\(648\) −0.874831 −0.0343666
\(649\) 0 0
\(650\) −2.54411 −0.0997883
\(651\) −3.30494 + 10.1716i −0.129531 + 0.398654i
\(652\) 22.0128 15.9932i 0.862087 0.626343i
\(653\) 13.5347 + 9.83353i 0.529653 + 0.384816i 0.820228 0.572037i \(-0.193847\pi\)
−0.290575 + 0.956852i \(0.593847\pi\)
\(654\) −3.41476 10.5096i −0.133528 0.410956i
\(655\) −3.45711 10.6399i −0.135081 0.415735i
\(656\) 3.28443 + 2.38628i 0.128235 + 0.0931684i
\(657\) −3.27714 + 2.38099i −0.127854 + 0.0928911i
\(658\) −1.37365 + 4.22767i −0.0535506 + 0.164812i
\(659\) 1.66127 0.0647137 0.0323569 0.999476i \(-0.489699\pi\)
0.0323569 + 0.999476i \(0.489699\pi\)
\(660\) 0 0
\(661\) −44.0130 −1.71191 −0.855953 0.517053i \(-0.827029\pi\)
−0.855953 + 0.517053i \(0.827029\pi\)
\(662\) 3.50921 10.8002i 0.136389 0.419763i
\(663\) 18.8142 13.6693i 0.730682 0.530871i
\(664\) −3.32042 2.41242i −0.128857 0.0936202i
\(665\) 2.44416 + 7.52234i 0.0947803 + 0.291704i
\(666\) 6.66189 + 20.5032i 0.258143 + 0.794483i
\(667\) −11.8304 8.59526i −0.458073 0.332810i
\(668\) −9.24988 + 6.72043i −0.357889 + 0.260021i
\(669\) 13.9382 42.8974i 0.538882 1.65851i
\(670\) 4.53429 0.175175
\(671\) 0 0
\(672\) 16.9904 0.655419
\(673\) 11.9265 36.7059i 0.459732 1.41491i −0.405757 0.913981i \(-0.632992\pi\)
0.865489 0.500928i \(-0.167008\pi\)
\(674\) −11.6350 + 8.45332i −0.448163 + 0.325610i
\(675\) 4.33283 + 3.14799i 0.166771 + 0.121166i
\(676\) 0.496897 + 1.52929i 0.0191114 + 0.0588189i
\(677\) 11.9277 + 36.7097i 0.458419 + 1.41087i 0.867074 + 0.498179i \(0.165998\pi\)
−0.408656 + 0.912689i \(0.634002\pi\)
\(678\) 0.511574 + 0.371680i 0.0196469 + 0.0142743i
\(679\) 2.03827 1.48089i 0.0782215 0.0568313i
\(680\) −1.88919 + 5.81432i −0.0724470 + 0.222969i
\(681\) −67.9167 −2.60257
\(682\) 0 0
\(683\) −0.748158 −0.0286275 −0.0143137 0.999898i \(-0.504556\pi\)
−0.0143137 + 0.999898i \(0.504556\pi\)
\(684\) −16.9226 + 52.0823i −0.647050 + 1.99141i
\(685\) −3.46360 + 2.51645i −0.132337 + 0.0961487i
\(686\) −7.96213 5.78483i −0.303996 0.220866i
\(687\) 13.0447 + 40.1475i 0.497687 + 1.53172i
\(688\) 2.43797 + 7.50331i 0.0929469 + 0.286061i
\(689\) −33.0594 24.0191i −1.25946 0.915055i
\(690\) −4.12058 + 2.99378i −0.156868 + 0.113971i
\(691\) 1.61364 4.96627i 0.0613857 0.188926i −0.915661 0.401952i \(-0.868332\pi\)
0.977047 + 0.213026i \(0.0683319\pi\)
\(692\) 16.3128 0.620118
\(693\) 0 0
\(694\) 1.59998 0.0607342
\(695\) −1.83964 + 5.66183i −0.0697815 + 0.214765i
\(696\) −34.5256 + 25.0843i −1.30869 + 0.950818i
\(697\) −7.63711 5.54869i −0.289276 0.210171i
\(698\) 5.71044 + 17.5749i 0.216143 + 0.665221i
\(699\) 9.92709 + 30.5524i 0.375477 + 1.15560i
\(700\) −1.21480 0.882602i −0.0459150 0.0333592i
\(701\) −11.4540 + 8.32185i −0.432613 + 0.314312i −0.782693 0.622408i \(-0.786155\pi\)
0.350080 + 0.936720i \(0.386155\pi\)
\(702\) 4.21049 12.9586i 0.158915 0.489090i
\(703\) 45.6952 1.72343
\(704\) 0 0
\(705\) 16.4278 0.618706
\(706\) −5.30041 + 16.3130i −0.199483 + 0.613947i
\(707\) 6.27783 4.56111i 0.236102 0.171538i
\(708\) −9.75685 7.08876i −0.366685 0.266412i
\(709\) −5.31953 16.3718i −0.199779 0.614857i −0.999887 0.0150013i \(-0.995225\pi\)
0.800108 0.599855i \(-0.204775\pi\)
\(710\) −0.461163 1.41931i −0.0173071 0.0532659i
\(711\) −47.9278 34.8216i −1.79743 1.30591i
\(712\) 16.8312 12.2285i 0.630774 0.458284i
\(713\) −2.79902 + 8.61448i −0.104824 + 0.322615i
\(714\) −5.12978 −0.191977
\(715\) 0 0
\(716\) −2.13233 −0.0796891
\(717\) 23.8115 73.2843i 0.889257 2.73685i
\(718\) 6.04066 4.38880i 0.225436 0.163789i
\(719\) 21.4842 + 15.6092i 0.801226 + 0.582125i 0.911273 0.411802i \(-0.135100\pi\)
−0.110048 + 0.993926i \(0.535100\pi\)
\(720\) −1.56325 4.81120i −0.0582590 0.179303i
\(721\) 3.02214 + 9.30121i 0.112551 + 0.346395i
\(722\) −23.7575 17.2608i −0.884163 0.642382i
\(723\) −24.8812 + 18.0772i −0.925342 + 0.672300i
\(724\) −4.17906 + 12.8618i −0.155314 + 0.478006i
\(725\) 5.95431 0.221138
\(726\) 0 0
\(727\) 44.1917 1.63898 0.819490 0.573094i \(-0.194257\pi\)
0.819490 + 0.573094i \(0.194257\pi\)
\(728\) −2.80219 + 8.62424i −0.103856 + 0.319636i
\(729\) 35.1843 25.5629i 1.30312 0.946773i
\(730\) 0.492847 + 0.358074i 0.0182411 + 0.0132529i
\(731\) −5.66890 17.4471i −0.209672 0.645303i
\(732\) −3.13743 9.65601i −0.115963 0.356896i
\(733\) 20.1934 + 14.6714i 0.745861 + 0.541900i 0.894541 0.446986i \(-0.147502\pi\)
−0.148680 + 0.988885i \(0.547502\pi\)
\(734\) −2.21354 + 1.60823i −0.0817033 + 0.0593610i
\(735\) −5.15754 + 15.8733i −0.190239 + 0.585494i
\(736\) 14.3895 0.530404
\(737\) 0 0
\(738\) −14.2415 −0.524237
\(739\) −6.56174 + 20.1950i −0.241377 + 0.742883i 0.754834 + 0.655916i \(0.227718\pi\)
−0.996211 + 0.0869672i \(0.972282\pi\)
\(740\) −7.01823 + 5.09905i −0.257995 + 0.187445i
\(741\) −60.1624 43.7105i −2.21012 1.60575i
\(742\) 2.78543 + 8.57266i 0.102256 + 0.314712i
\(743\) 9.47222 + 29.1525i 0.347502 + 1.06950i 0.960231 + 0.279208i \(0.0900718\pi\)
−0.612729 + 0.790293i \(0.709928\pi\)
\(744\) 21.3857 + 15.5376i 0.784039 + 0.569637i
\(745\) 3.06168 2.22444i 0.112171 0.0814972i
\(746\) 2.12903 6.55248i 0.0779493 0.239903i
\(747\) −7.89694 −0.288934
\(748\) 0 0
\(749\) −4.79259 −0.175118
\(750\) 0.640877 1.97242i 0.0234015 0.0720224i
\(751\) 24.5191 17.8142i 0.894716 0.650049i −0.0423872 0.999101i \(-0.513496\pi\)
0.937103 + 0.349052i \(0.113496\pi\)
\(752\) −4.87537 3.54217i −0.177787 0.129169i
\(753\) −14.9707 46.0752i −0.545564 1.67907i
\(754\) −4.68113 14.4070i −0.170477 0.524673i
\(755\) 19.7049 + 14.3165i 0.717136 + 0.521030i
\(756\) 6.50606 4.72693i 0.236623 0.171917i
\(757\) −10.7752 + 33.1627i −0.391632 + 1.20532i 0.539921 + 0.841716i \(0.318454\pi\)
−0.931553 + 0.363605i \(0.881546\pi\)
\(758\) −7.23750 −0.262878
\(759\) 0 0
\(760\) 19.5493 0.709129
\(761\) 0.831169 2.55807i 0.0301298 0.0927301i −0.934861 0.355015i \(-0.884476\pi\)
0.964991 + 0.262285i \(0.0844759\pi\)
\(762\) 19.9830 14.5185i 0.723907 0.525949i
\(763\) 4.44592 + 3.23015i 0.160953 + 0.116939i
\(764\) 2.01236 + 6.19340i 0.0728045 + 0.224069i
\(765\) 3.63495 + 11.1872i 0.131422 + 0.404475i
\(766\) 10.7697 + 7.82463i 0.389124 + 0.282715i
\(767\) 8.22103 5.97293i 0.296844 0.215670i
\(768\) 10.3677 31.9086i 0.374113 1.15140i
\(769\) 32.5735 1.17463 0.587315 0.809359i \(-0.300185\pi\)
0.587315 + 0.809359i \(0.300185\pi\)
\(770\) 0 0
\(771\) −52.0010 −1.87277
\(772\) −10.1973 + 31.3841i −0.367009 + 1.12954i
\(773\) −33.7067 + 24.4893i −1.21234 + 0.880820i −0.995442 0.0953734i \(-0.969595\pi\)
−0.216903 + 0.976193i \(0.569595\pi\)
\(774\) −22.3902 16.2675i −0.804800 0.584721i
\(775\) −1.13972 3.50769i −0.0409398 0.126000i
\(776\) −1.92429 5.92237i −0.0690781 0.212601i
\(777\) −13.9787 10.1561i −0.501483 0.364348i
\(778\) −18.6140 + 13.5238i −0.667343 + 0.484853i