Properties

Label 731.2.m.c.87.20
Level 731
Weight 2
Character 731.87
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.m (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 87.20
Character \(\chi\) = 731.87
Dual form 731.2.m.c.689.20

$q$-expansion

\(f(q)\) \(=\) \(q+(0.810350 + 0.810350i) q^{2} +(3.13521 - 1.29865i) q^{3} -0.686666i q^{4} +(1.23003 + 2.96956i) q^{5} +(3.59298 + 1.48826i) q^{6} +(-0.604922 + 1.46041i) q^{7} +(2.17714 - 2.17714i) q^{8} +(6.02174 - 6.02174i) q^{9} +O(q^{10})\) \(q+(0.810350 + 0.810350i) q^{2} +(3.13521 - 1.29865i) q^{3} -0.686666i q^{4} +(1.23003 + 2.96956i) q^{5} +(3.59298 + 1.48826i) q^{6} +(-0.604922 + 1.46041i) q^{7} +(2.17714 - 2.17714i) q^{8} +(6.02174 - 6.02174i) q^{9} +(-1.40963 + 3.40314i) q^{10} +(-4.91459 - 2.03569i) q^{11} +(-0.891736 - 2.15284i) q^{12} +1.77520i q^{13} +(-1.67364 + 0.693246i) q^{14} +(7.71281 + 7.71281i) q^{15} +2.15516 q^{16} +(-4.01260 + 0.948189i) q^{17} +9.75943 q^{18} +(-2.37035 - 2.37035i) q^{19} +(2.03909 - 0.844620i) q^{20} +5.36428i q^{21} +(-2.33292 - 5.63216i) q^{22} +(3.32148 + 1.37580i) q^{23} +(3.99846 - 9.65312i) q^{24} +(-3.76976 + 3.76976i) q^{25} +(-1.43853 + 1.43853i) q^{26} +(7.16337 - 17.2939i) q^{27} +(1.00281 + 0.415379i) q^{28} +(3.17390 + 7.66248i) q^{29} +12.5002i q^{30} +(-7.90431 + 3.27407i) q^{31} +(-2.60785 - 2.60785i) q^{32} -18.0519 q^{33} +(-4.01997 - 2.48324i) q^{34} -5.08085 q^{35} +(-4.13492 - 4.13492i) q^{36} +(-3.49145 + 1.44620i) q^{37} -3.84163i q^{38} +(2.30536 + 5.56563i) q^{39} +(9.14309 + 3.78719i) q^{40} +(1.94976 - 4.70713i) q^{41} +(-4.34694 + 4.34694i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(-1.39784 + 3.37468i) q^{44} +(25.2888 + 10.4750i) q^{45} +(1.57668 + 3.80645i) q^{46} +1.99825i q^{47} +(6.75688 - 2.79879i) q^{48} +(3.18288 + 3.18288i) q^{49} -6.10965 q^{50} +(-11.3490 + 8.18372i) q^{51} +1.21897 q^{52} +(-5.93359 - 5.93359i) q^{53} +(19.8189 - 8.20927i) q^{54} -17.0981i q^{55} +(1.86252 + 4.49652i) q^{56} +(-10.5098 - 4.35330i) q^{57} +(-3.63732 + 8.78126i) q^{58} +(2.04099 - 2.04099i) q^{59} +(5.29612 - 5.29612i) q^{60} +(0.209778 - 0.506448i) q^{61} +(-9.05840 - 3.75211i) q^{62} +(5.15153 + 12.4369i) q^{63} -8.53685i q^{64} +(-5.27156 + 2.18355i) q^{65} +(-14.6284 - 14.6284i) q^{66} +4.80863 q^{67} +(0.651089 + 2.75531i) q^{68} +12.2002 q^{69} +(-4.11727 - 4.11727i) q^{70} +(7.00308 - 2.90077i) q^{71} -26.2203i q^{72} +(-1.29534 - 3.12722i) q^{73} +(-4.00122 - 1.65736i) q^{74} +(-6.92340 + 16.7146i) q^{75} +(-1.62764 + 1.62764i) q^{76} +(5.94589 - 5.94589i) q^{77} +(-2.64196 + 6.37825i) q^{78} +(6.79229 + 2.81346i) q^{79} +(2.65091 + 6.39987i) q^{80} -37.9746i q^{81} +(5.39441 - 2.23444i) q^{82} +(-1.85608 - 1.85608i) q^{83} +3.68347 q^{84} +(-7.75132 - 10.7493i) q^{85} -1.14601 q^{86} +(19.9017 + 19.9017i) q^{87} +(-15.1317 + 6.26777i) q^{88} -9.53974i q^{89} +(12.0044 + 28.9812i) q^{90} +(-2.59252 - 1.07386i) q^{91} +(0.944717 - 2.28075i) q^{92} +(-20.5298 + 20.5298i) q^{93} +(-1.61928 + 1.61928i) q^{94} +(4.12329 - 9.95449i) q^{95} +(-11.5628 - 4.78948i) q^{96} +(4.96439 + 11.9851i) q^{97} +5.15849i q^{98} +(-41.8528 + 17.3360i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q + 4q^{2} + 4q^{3} + 8q^{5} - 12q^{6} + 4q^{7} - 4q^{8} + 8q^{9} + O(q^{10}) \) \( 128q + 4q^{2} + 4q^{3} + 8q^{5} - 12q^{6} + 4q^{7} - 4q^{8} + 8q^{9} - 8q^{10} - 4q^{11} + 12q^{12} + 12q^{14} - 12q^{15} - 144q^{16} - 12q^{17} + 64q^{18} - 28q^{19} - 8q^{20} - 12q^{22} + 16q^{23} - 16q^{24} - 20q^{25} + 16q^{26} - 8q^{27} + 20q^{28} + 12q^{31} - 4q^{32} - 104q^{33} + 20q^{34} + 32q^{35} - 96q^{36} - 12q^{37} + 8q^{39} + 216q^{40} + 24q^{41} - 4q^{42} + 24q^{44} - 28q^{45} - 48q^{46} + 28q^{48} - 80q^{50} - 20q^{51} + 56q^{52} - 36q^{53} - 12q^{54} - 8q^{56} + 72q^{57} - 32q^{58} + 48q^{59} - 40q^{60} - 76q^{61} - 44q^{62} + 36q^{65} - 68q^{66} - 48q^{67} + 32q^{68} + 216q^{69} - 196q^{70} + 4q^{71} + 20q^{73} + 88q^{74} + 80q^{75} + 72q^{76} + 28q^{77} - 120q^{78} + 68q^{79} - 68q^{80} + 28q^{82} - 36q^{83} - 152q^{84} + 28q^{85} - 24q^{86} - 56q^{87} + 20q^{88} - 112q^{90} + 96q^{91} - 28q^{92} + 24q^{93} - 36q^{94} - 108q^{95} + 272q^{96} + 8q^{97} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.810350 + 0.810350i 0.573004 + 0.573004i 0.932967 0.359963i \(-0.117211\pi\)
−0.359963 + 0.932967i \(0.617211\pi\)
\(3\) 3.13521 1.29865i 1.81011 0.749774i 0.828204 0.560427i \(-0.189363\pi\)
0.981910 0.189347i \(-0.0606372\pi\)
\(4\) 0.686666i 0.343333i
\(5\) 1.23003 + 2.96956i 0.550086 + 1.32803i 0.917414 + 0.397935i \(0.130273\pi\)
−0.367327 + 0.930092i \(0.619727\pi\)
\(6\) 3.59298 + 1.48826i 1.46683 + 0.607579i
\(7\) −0.604922 + 1.46041i −0.228639 + 0.551984i −0.996012 0.0892172i \(-0.971563\pi\)
0.767373 + 0.641201i \(0.221563\pi\)
\(8\) 2.17714 2.17714i 0.769735 0.769735i
\(9\) 6.02174 6.02174i 2.00725 2.00725i
\(10\) −1.40963 + 3.40314i −0.445763 + 1.07617i
\(11\) −4.91459 2.03569i −1.48180 0.613783i −0.512289 0.858813i \(-0.671202\pi\)
−0.969516 + 0.245030i \(0.921202\pi\)
\(12\) −0.891736 2.15284i −0.257422 0.621472i
\(13\) 1.77520i 0.492352i 0.969225 + 0.246176i \(0.0791742\pi\)
−0.969225 + 0.246176i \(0.920826\pi\)
\(14\) −1.67364 + 0.693246i −0.447300 + 0.185278i
\(15\) 7.71281 + 7.71281i 1.99144 + 1.99144i
\(16\) 2.15516 0.538790
\(17\) −4.01260 + 0.948189i −0.973198 + 0.229970i
\(18\) 9.75943 2.30032
\(19\) −2.37035 2.37035i −0.543796 0.543796i 0.380844 0.924639i \(-0.375634\pi\)
−0.924639 + 0.380844i \(0.875634\pi\)
\(20\) 2.03909 0.844620i 0.455955 0.188863i
\(21\) 5.36428i 1.17058i
\(22\) −2.33292 5.63216i −0.497379 1.20078i
\(23\) 3.32148 + 1.37580i 0.692577 + 0.286875i 0.701074 0.713089i \(-0.252704\pi\)
−0.00849611 + 0.999964i \(0.502704\pi\)
\(24\) 3.99846 9.65312i 0.816181 1.97044i
\(25\) −3.76976 + 3.76976i −0.753952 + 0.753952i
\(26\) −1.43853 + 1.43853i −0.282120 + 0.282120i
\(27\) 7.16337 17.2939i 1.37859 3.32821i
\(28\) 1.00281 + 0.415379i 0.189514 + 0.0784993i
\(29\) 3.17390 + 7.66248i 0.589379 + 1.42289i 0.884098 + 0.467302i \(0.154774\pi\)
−0.294719 + 0.955584i \(0.595226\pi\)
\(30\) 12.5002i 2.28220i
\(31\) −7.90431 + 3.27407i −1.41966 + 0.588040i −0.954774 0.297333i \(-0.903903\pi\)
−0.464881 + 0.885373i \(0.653903\pi\)
\(32\) −2.60785 2.60785i −0.461006 0.461006i
\(33\) −18.0519 −3.14243
\(34\) −4.01997 2.48324i −0.689420 0.425873i
\(35\) −5.08085 −0.858820
\(36\) −4.13492 4.13492i −0.689154 0.689154i
\(37\) −3.49145 + 1.44620i −0.573990 + 0.237754i −0.650746 0.759295i \(-0.725544\pi\)
0.0767560 + 0.997050i \(0.475544\pi\)
\(38\) 3.84163i 0.623194i
\(39\) 2.30536 + 5.56563i 0.369153 + 0.891214i
\(40\) 9.14309 + 3.78719i 1.44565 + 0.598808i
\(41\) 1.94976 4.70713i 0.304501 0.735131i −0.695363 0.718658i \(-0.744757\pi\)
0.999864 0.0164722i \(-0.00524349\pi\)
\(42\) −4.34694 + 4.34694i −0.670748 + 0.670748i
\(43\) −0.707107 + 0.707107i −0.107833 + 0.107833i
\(44\) −1.39784 + 3.37468i −0.210732 + 0.508752i
\(45\) 25.2888 + 10.4750i 3.76983 + 1.56152i
\(46\) 1.57668 + 3.80645i 0.232469 + 0.561230i
\(47\) 1.99825i 0.291475i 0.989323 + 0.145737i \(0.0465555\pi\)
−0.989323 + 0.145737i \(0.953445\pi\)
\(48\) 6.75688 2.79879i 0.975271 0.403970i
\(49\) 3.18288 + 3.18288i 0.454697 + 0.454697i
\(50\) −6.10965 −0.864035
\(51\) −11.3490 + 8.18372i −1.58917 + 1.14595i
\(52\) 1.21897 0.169041
\(53\) −5.93359 5.93359i −0.815041 0.815041i 0.170343 0.985385i \(-0.445512\pi\)
−0.985385 + 0.170343i \(0.945512\pi\)
\(54\) 19.8189 8.20927i 2.69702 1.11714i
\(55\) 17.0981i 2.30551i
\(56\) 1.86252 + 4.49652i 0.248890 + 0.600873i
\(57\) −10.5098 4.35330i −1.39206 0.576608i
\(58\) −3.63732 + 8.78126i −0.477603 + 1.15304i
\(59\) 2.04099 2.04099i 0.265715 0.265715i −0.561656 0.827371i \(-0.689836\pi\)
0.827371 + 0.561656i \(0.189836\pi\)
\(60\) 5.29612 5.29612i 0.683726 0.683726i
\(61\) 0.209778 0.506448i 0.0268593 0.0648440i −0.909881 0.414870i \(-0.863827\pi\)
0.936740 + 0.350026i \(0.113827\pi\)
\(62\) −9.05840 3.75211i −1.15042 0.476519i
\(63\) 5.15153 + 12.4369i 0.649032 + 1.56690i
\(64\) 8.53685i 1.06711i
\(65\) −5.27156 + 2.18355i −0.653857 + 0.270836i
\(66\) −14.6284 14.6284i −1.80063 1.80063i
\(67\) 4.80863 0.587468 0.293734 0.955887i \(-0.405102\pi\)
0.293734 + 0.955887i \(0.405102\pi\)
\(68\) 0.651089 + 2.75531i 0.0789561 + 0.334131i
\(69\) 12.2002 1.46874
\(70\) −4.11727 4.11727i −0.492107 0.492107i
\(71\) 7.00308 2.90077i 0.831113 0.344258i 0.0737696 0.997275i \(-0.476497\pi\)
0.757343 + 0.653017i \(0.226497\pi\)
\(72\) 26.2203i 3.09010i
\(73\) −1.29534 3.12722i −0.151608 0.366013i 0.829769 0.558107i \(-0.188472\pi\)
−0.981377 + 0.192094i \(0.938472\pi\)
\(74\) −4.00122 1.65736i −0.465133 0.192664i
\(75\) −6.92340 + 16.7146i −0.799446 + 1.93003i
\(76\) −1.62764 + 1.62764i −0.186703 + 0.186703i
\(77\) 5.94589 5.94589i 0.677597 0.677597i
\(78\) −2.64196 + 6.37825i −0.299143 + 0.722195i
\(79\) 6.79229 + 2.81346i 0.764192 + 0.316539i 0.730517 0.682894i \(-0.239279\pi\)
0.0336749 + 0.999433i \(0.489279\pi\)
\(80\) 2.65091 + 6.39987i 0.296381 + 0.715527i
\(81\) 37.9746i 4.21940i
\(82\) 5.39441 2.23444i 0.595713 0.246752i
\(83\) −1.85608 1.85608i −0.203731 0.203731i 0.597866 0.801596i \(-0.296016\pi\)
−0.801596 + 0.597866i \(0.796016\pi\)
\(84\) 3.68347 0.401899
\(85\) −7.75132 10.7493i −0.840749 1.16593i
\(86\) −1.14601 −0.123577
\(87\) 19.9017 + 19.9017i 2.13369 + 2.13369i
\(88\) −15.1317 + 6.26777i −1.61305 + 0.668146i
\(89\) 9.53974i 1.01121i −0.862765 0.505605i \(-0.831269\pi\)
0.862765 0.505605i \(-0.168731\pi\)
\(90\) 12.0044 + 28.9812i 1.26537 + 3.05489i
\(91\) −2.59252 1.07386i −0.271770 0.112571i
\(92\) 0.944717 2.28075i 0.0984936 0.237785i
\(93\) −20.5298 + 20.5298i −2.12884 + 2.12884i
\(94\) −1.61928 + 1.61928i −0.167016 + 0.167016i
\(95\) 4.12329 9.95449i 0.423040 1.02131i
\(96\) −11.5628 4.78948i −1.18012 0.488824i
\(97\) 4.96439 + 11.9851i 0.504057 + 1.21690i 0.947256 + 0.320479i \(0.103844\pi\)
−0.443198 + 0.896424i \(0.646156\pi\)
\(98\) 5.15849i 0.521086i
\(99\) −41.8528 + 17.3360i −4.20636 + 1.74233i
\(100\) 2.58856 + 2.58856i 0.258856 + 0.258856i
\(101\) −11.1739 −1.11185 −0.555923 0.831234i \(-0.687635\pi\)
−0.555923 + 0.831234i \(0.687635\pi\)
\(102\) −15.8283 2.56497i −1.56724 0.253970i
\(103\) 13.3054 1.31102 0.655508 0.755188i \(-0.272454\pi\)
0.655508 + 0.755188i \(0.272454\pi\)
\(104\) 3.86486 + 3.86486i 0.378981 + 0.378981i
\(105\) −15.9295 + 6.59823i −1.55456 + 0.643921i
\(106\) 9.61657i 0.934044i
\(107\) 1.70378 + 4.11330i 0.164711 + 0.397648i 0.984587 0.174893i \(-0.0559579\pi\)
−0.819876 + 0.572540i \(0.805958\pi\)
\(108\) −11.8751 4.91884i −1.14268 0.473315i
\(109\) −2.78980 + 6.73516i −0.267214 + 0.645112i −0.999350 0.0360466i \(-0.988524\pi\)
0.732136 + 0.681158i \(0.238524\pi\)
\(110\) 13.8555 13.8555i 1.32107 1.32107i
\(111\) −9.06831 + 9.06831i −0.860726 + 0.860726i
\(112\) −1.30370 + 3.14742i −0.123188 + 0.297403i
\(113\) −1.71581 0.710712i −0.161410 0.0668581i 0.300516 0.953777i \(-0.402841\pi\)
−0.461925 + 0.886919i \(0.652841\pi\)
\(114\) −4.98891 12.0443i −0.467255 1.12805i
\(115\) 11.5556i 1.07757i
\(116\) 5.26156 2.17941i 0.488524 0.202353i
\(117\) 10.6898 + 10.6898i 0.988272 + 0.988272i
\(118\) 3.30784 0.304511
\(119\) 1.04256 6.43362i 0.0955717 0.589769i
\(120\) 33.5837 3.06576
\(121\) 12.2310 + 12.2310i 1.11191 + 1.11191i
\(122\) 0.580393 0.240407i 0.0525464 0.0217654i
\(123\) 17.2899i 1.55898i
\(124\) 2.24819 + 5.42762i 0.201894 + 0.487414i
\(125\) −0.983649 0.407441i −0.0879802 0.0364426i
\(126\) −5.90370 + 14.2528i −0.525943 + 1.26974i
\(127\) −5.58303 + 5.58303i −0.495414 + 0.495414i −0.910007 0.414593i \(-0.863924\pi\)
0.414593 + 0.910007i \(0.363924\pi\)
\(128\) 1.70215 1.70215i 0.150450 0.150450i
\(129\) −1.29865 + 3.13521i −0.114339 + 0.276040i
\(130\) −6.04125 2.50237i −0.529853 0.219472i
\(131\) −3.81481 9.20978i −0.333302 0.804662i −0.998326 0.0578398i \(-0.981579\pi\)
0.665024 0.746822i \(-0.268421\pi\)
\(132\) 12.3956i 1.07890i
\(133\) 4.89556 2.02781i 0.424499 0.175833i
\(134\) 3.89667 + 3.89667i 0.336621 + 0.336621i
\(135\) 60.1664 5.17830
\(136\) −6.67165 + 10.8003i −0.572089 + 0.926120i
\(137\) −17.8433 −1.52446 −0.762228 0.647309i \(-0.775895\pi\)
−0.762228 + 0.647309i \(0.775895\pi\)
\(138\) 9.88646 + 9.88646i 0.841591 + 0.841591i
\(139\) 3.15629 1.30738i 0.267713 0.110890i −0.244789 0.969576i \(-0.578719\pi\)
0.512502 + 0.858686i \(0.328719\pi\)
\(140\) 3.48884i 0.294861i
\(141\) 2.59502 + 6.26493i 0.218540 + 0.527603i
\(142\) 8.02559 + 3.32431i 0.673492 + 0.278970i
\(143\) 3.61376 8.72438i 0.302198 0.729570i
\(144\) 12.9778 12.9778i 1.08148 1.08148i
\(145\) −18.8502 + 18.8502i −1.56542 + 1.56542i
\(146\) 1.48447 3.58382i 0.122855 0.296599i
\(147\) 14.1124 + 5.84555i 1.16397 + 0.482133i
\(148\) 0.993059 + 2.39746i 0.0816289 + 0.197070i
\(149\) 5.74817i 0.470908i −0.971885 0.235454i \(-0.924342\pi\)
0.971885 0.235454i \(-0.0756578\pi\)
\(150\) −19.1550 + 7.93427i −1.56400 + 0.647831i
\(151\) −6.93901 6.93901i −0.564689 0.564689i 0.365947 0.930636i \(-0.380745\pi\)
−0.930636 + 0.365947i \(0.880745\pi\)
\(152\) −10.3212 −0.837157
\(153\) −18.4531 + 29.8726i −1.49184 + 2.41505i
\(154\) 9.63650 0.776531
\(155\) −19.4451 19.4451i −1.56187 1.56187i
\(156\) 3.82173 1.58301i 0.305983 0.126742i
\(157\) 17.9634i 1.43363i 0.697262 + 0.716816i \(0.254401\pi\)
−0.697262 + 0.716816i \(0.745599\pi\)
\(158\) 3.22425 + 7.78402i 0.256507 + 0.619263i
\(159\) −26.3087 10.8974i −2.08641 0.864221i
\(160\) 4.53642 10.9519i 0.358635 0.865822i
\(161\) −4.01848 + 4.01848i −0.316701 + 0.316701i
\(162\) 30.7727 30.7727i 2.41773 2.41773i
\(163\) 7.41463 17.9005i 0.580759 1.40208i −0.311368 0.950289i \(-0.600787\pi\)
0.892126 0.451786i \(-0.149213\pi\)
\(164\) −3.23223 1.33883i −0.252394 0.104545i
\(165\) −22.2044 53.6062i −1.72861 4.17323i
\(166\) 3.00814i 0.233477i
\(167\) −21.6131 + 8.95243i −1.67247 + 0.692759i −0.998924 0.0463860i \(-0.985230\pi\)
−0.673546 + 0.739146i \(0.735230\pi\)
\(168\) 11.6788 + 11.6788i 0.901037 + 0.901037i
\(169\) 9.84866 0.757589
\(170\) 2.42944 14.9920i 0.186330 1.14983i
\(171\) −28.5473 −2.18306
\(172\) 0.485546 + 0.485546i 0.0370225 + 0.0370225i
\(173\) 13.7539 5.69706i 1.04569 0.433139i 0.207339 0.978269i \(-0.433520\pi\)
0.838352 + 0.545130i \(0.183520\pi\)
\(174\) 32.2547i 2.44522i
\(175\) −3.22499 7.78581i −0.243786 0.588552i
\(176\) −10.5917 4.38723i −0.798381 0.330700i
\(177\) 3.74841 9.04947i 0.281748 0.680200i
\(178\) 7.73053 7.73053i 0.579428 0.579428i
\(179\) 8.99052 8.99052i 0.671983 0.671983i −0.286190 0.958173i \(-0.592389\pi\)
0.958173 + 0.286190i \(0.0923887\pi\)
\(180\) 7.19280 17.3650i 0.536120 1.29431i
\(181\) −14.1593 5.86496i −1.05245 0.435939i −0.211685 0.977338i \(-0.567895\pi\)
−0.840766 + 0.541399i \(0.817895\pi\)
\(182\) −1.23065 2.97105i −0.0912219 0.220229i
\(183\) 1.86025i 0.137513i
\(184\) 10.2267 4.23602i 0.753919 0.312283i
\(185\) −8.58917 8.58917i −0.631488 0.631488i
\(186\) −33.2726 −2.43967
\(187\) 21.6505 + 3.50844i 1.58324 + 0.256563i
\(188\) 1.37213 0.100073
\(189\) 20.9229 + 20.9229i 1.52192 + 1.52192i
\(190\) 11.4079 4.72532i 0.827618 0.342811i
\(191\) 0.444488i 0.0321620i 0.999871 + 0.0160810i \(0.00511897\pi\)
−0.999871 + 0.0160810i \(0.994881\pi\)
\(192\) −11.0864 26.7648i −0.800089 1.93159i
\(193\) 0.537629 + 0.222693i 0.0386994 + 0.0160298i 0.401949 0.915662i \(-0.368333\pi\)
−0.363250 + 0.931692i \(0.618333\pi\)
\(194\) −5.68923 + 13.7350i −0.408463 + 0.986117i
\(195\) −13.6918 + 13.6918i −0.980489 + 0.980489i
\(196\) 2.18557 2.18557i 0.156112 0.156112i
\(197\) −2.75232 + 6.64468i −0.196094 + 0.473414i −0.991089 0.133203i \(-0.957474\pi\)
0.794994 + 0.606617i \(0.207474\pi\)
\(198\) −47.9636 19.8672i −3.40862 1.41190i
\(199\) 5.39773 + 13.0313i 0.382635 + 0.923762i 0.991454 + 0.130453i \(0.0416433\pi\)
−0.608820 + 0.793309i \(0.708357\pi\)
\(200\) 16.4146i 1.16069i
\(201\) 15.0761 6.24471i 1.06338 0.440468i
\(202\) −9.05478 9.05478i −0.637092 0.637092i
\(203\) −13.1103 −0.920165
\(204\) 5.61948 + 7.79295i 0.393442 + 0.545616i
\(205\) 16.3764 1.14377
\(206\) 10.7820 + 10.7820i 0.751218 + 0.751218i
\(207\) 28.2858 11.7164i 1.96600 0.814345i
\(208\) 3.82584i 0.265274i
\(209\) 6.82400 + 16.4746i 0.472026 + 1.13957i
\(210\) −18.2554 7.56162i −1.25974 0.521801i
\(211\) −1.74586 + 4.21488i −0.120190 + 0.290164i −0.972512 0.232853i \(-0.925194\pi\)
0.852322 + 0.523018i \(0.175194\pi\)
\(212\) −4.07439 + 4.07439i −0.279830 + 0.279830i
\(213\) 18.1890 18.1890i 1.24629 1.24629i
\(214\) −1.95255 + 4.71387i −0.133474 + 0.322234i
\(215\) −2.96956 1.23003i −0.202522 0.0838874i
\(216\) −22.0556 53.2469i −1.50069 3.62299i
\(217\) 13.5241i 0.918076i
\(218\) −7.71855 + 3.19713i −0.522766 + 0.216537i
\(219\) −8.12230 8.12230i −0.548854 0.548854i
\(220\) −11.7407 −0.791557
\(221\) −1.68323 7.12317i −0.113226 0.479156i
\(222\) −14.6970 −0.986398
\(223\) −3.27691 3.27691i −0.219438 0.219438i 0.588823 0.808262i \(-0.299591\pi\)
−0.808262 + 0.588823i \(0.799591\pi\)
\(224\) 5.38607 2.23098i 0.359872 0.149064i
\(225\) 45.4010i 3.02673i
\(226\) −0.814481 1.96633i −0.0541785 0.130798i
\(227\) −8.50128 3.52135i −0.564250 0.233720i 0.0822792 0.996609i \(-0.473780\pi\)
−0.646529 + 0.762889i \(0.723780\pi\)
\(228\) −2.98926 + 7.21671i −0.197969 + 0.477938i
\(229\) 15.3361 15.3361i 1.01344 1.01344i 0.0135301 0.999908i \(-0.495693\pi\)
0.999908 0.0135301i \(-0.00430691\pi\)
\(230\) −9.36410 + 9.36410i −0.617450 + 0.617450i
\(231\) 10.9200 26.3632i 0.718483 1.73457i
\(232\) 23.5923 + 9.77225i 1.54891 + 0.641580i
\(233\) 9.13752 + 22.0599i 0.598619 + 1.44519i 0.874989 + 0.484142i \(0.160868\pi\)
−0.276370 + 0.961051i \(0.589132\pi\)
\(234\) 17.3250i 1.13257i
\(235\) −5.93392 + 2.45791i −0.387086 + 0.160336i
\(236\) −1.40148 1.40148i −0.0912286 0.0912286i
\(237\) 24.9489 1.62061
\(238\) 6.05833 4.36865i 0.392703 0.283177i
\(239\) 4.66754 0.301918 0.150959 0.988540i \(-0.451764\pi\)
0.150959 + 0.988540i \(0.451764\pi\)
\(240\) 16.6223 + 16.6223i 1.07297 + 1.07297i
\(241\) −3.60404 + 1.49284i −0.232157 + 0.0961624i −0.495729 0.868477i \(-0.665099\pi\)
0.263573 + 0.964640i \(0.415099\pi\)
\(242\) 19.8227i 1.27425i
\(243\) −27.8255 67.1766i −1.78501 4.30938i
\(244\) −0.347760 0.144047i −0.0222631 0.00922167i
\(245\) −5.53670 + 13.3668i −0.353727 + 0.853972i
\(246\) 14.0109 14.0109i 0.893300 0.893300i
\(247\) 4.20785 4.20785i 0.267739 0.267739i
\(248\) −10.0807 + 24.3369i −0.640123 + 1.54539i
\(249\) −8.22958 3.40880i −0.521528 0.216024i
\(250\) −0.466930 1.12727i −0.0295313 0.0712948i
\(251\) 16.3442i 1.03163i −0.856699 0.515817i \(-0.827488\pi\)
0.856699 0.515817i \(-0.172512\pi\)
\(252\) 8.53999 3.53738i 0.537969 0.222834i
\(253\) −13.5230 13.5230i −0.850185 0.850185i
\(254\) −9.04841 −0.567748
\(255\) −38.2616 23.6352i −2.39603 1.48009i
\(256\) −14.3150 −0.894690
\(257\) 10.7528 + 10.7528i 0.670742 + 0.670742i 0.957887 0.287145i \(-0.0927062\pi\)
−0.287145 + 0.957887i \(0.592706\pi\)
\(258\) −3.59298 + 1.48826i −0.223689 + 0.0926550i
\(259\) 5.97379i 0.371193i
\(260\) 1.49937 + 3.61980i 0.0929870 + 0.224490i
\(261\) 65.2538 + 27.0290i 4.03911 + 1.67305i
\(262\) 4.37181 10.5545i 0.270091 0.652058i
\(263\) 15.2689 15.2689i 0.941519 0.941519i −0.0568626 0.998382i \(-0.518110\pi\)
0.998382 + 0.0568626i \(0.0181097\pi\)
\(264\) −39.3015 + 39.3015i −2.41884 + 2.41884i
\(265\) 10.3216 24.9186i 0.634053 1.53074i
\(266\) 5.61036 + 2.32389i 0.343993 + 0.142487i
\(267\) −12.3887 29.9091i −0.758179 1.83041i
\(268\) 3.30192i 0.201697i
\(269\) 14.0934 5.83768i 0.859290 0.355929i 0.0908599 0.995864i \(-0.471038\pi\)
0.768430 + 0.639934i \(0.221038\pi\)
\(270\) 48.7558 + 48.7558i 2.96718 + 2.96718i
\(271\) 6.00809 0.364965 0.182483 0.983209i \(-0.441587\pi\)
0.182483 + 0.983209i \(0.441587\pi\)
\(272\) −8.64778 + 2.04350i −0.524349 + 0.123905i
\(273\) −9.52267 −0.576338
\(274\) −14.4593 14.4593i −0.873519 0.873519i
\(275\) 26.2009 10.8528i 1.57997 0.654446i
\(276\) 8.37748i 0.504265i
\(277\) 7.18164 + 17.3380i 0.431503 + 1.04174i 0.978803 + 0.204804i \(0.0656556\pi\)
−0.547300 + 0.836936i \(0.684344\pi\)
\(278\) 3.61714 + 1.49827i 0.216941 + 0.0898601i
\(279\) −27.8821 + 67.3133i −1.66926 + 4.02994i
\(280\) −11.0617 + 11.0617i −0.661064 + 0.661064i
\(281\) −13.8956 + 13.8956i −0.828941 + 0.828941i −0.987370 0.158429i \(-0.949357\pi\)
0.158429 + 0.987370i \(0.449357\pi\)
\(282\) −2.97391 + 7.17967i −0.177094 + 0.427543i
\(283\) 6.05053 + 2.50621i 0.359666 + 0.148979i 0.555197 0.831719i \(-0.312643\pi\)
−0.195531 + 0.980698i \(0.562643\pi\)
\(284\) −1.99186 4.80877i −0.118195 0.285348i
\(285\) 36.5641i 2.16587i
\(286\) 9.99821 4.14140i 0.591207 0.244886i
\(287\) 5.69490 + 5.69490i 0.336159 + 0.336159i
\(288\) −31.4075 −1.85071
\(289\) 15.2019 7.60940i 0.894228 0.447612i
\(290\) −30.5505 −1.79398
\(291\) 31.1288 + 31.1288i 1.82480 + 1.82480i
\(292\) −2.14735 + 0.889463i −0.125664 + 0.0520519i
\(293\) 15.9670i 0.932803i 0.884573 + 0.466402i \(0.154450\pi\)
−0.884573 + 0.466402i \(0.845550\pi\)
\(294\) 6.69905 + 16.1729i 0.390697 + 0.943225i
\(295\) 8.57133 + 3.55036i 0.499042 + 0.206710i
\(296\) −4.45278 + 10.7500i −0.258812 + 0.624828i
\(297\) −70.4100 + 70.4100i −4.08560 + 4.08560i
\(298\) 4.65803 4.65803i 0.269832 0.269832i
\(299\) −2.44233 + 5.89630i −0.141244 + 0.340992i
\(300\) 11.4773 + 4.75406i 0.662643 + 0.274476i
\(301\) −0.604922 1.46041i −0.0348671 0.0841767i
\(302\) 11.2461i 0.647138i
\(303\) −35.0326 + 14.5110i −2.01257 + 0.833633i
\(304\) −5.10848 5.10848i −0.292991 0.292991i
\(305\) 1.76196 0.100889
\(306\) −39.1607 + 9.25378i −2.23867 + 0.529004i
\(307\) 15.3519 0.876179 0.438089 0.898931i \(-0.355655\pi\)
0.438089 + 0.898931i \(0.355655\pi\)
\(308\) −4.08284 4.08284i −0.232641 0.232641i
\(309\) 41.7151 17.2790i 2.37309 0.982966i
\(310\) 31.5146i 1.78991i
\(311\) −6.78506 16.3806i −0.384745 0.928858i −0.991034 0.133613i \(-0.957342\pi\)
0.606288 0.795245i \(-0.292658\pi\)
\(312\) 17.1362 + 7.09806i 0.970148 + 0.401849i
\(313\) −6.42256 + 15.5054i −0.363025 + 0.876419i 0.631830 + 0.775107i \(0.282304\pi\)
−0.994855 + 0.101312i \(0.967696\pi\)
\(314\) −14.5566 + 14.5566i −0.821477 + 0.821477i
\(315\) −30.5955 + 30.5955i −1.72386 + 1.72386i
\(316\) 1.93191 4.66403i 0.108678 0.262372i
\(317\) −12.0607 4.99570i −0.677395 0.280586i 0.0173424 0.999850i \(-0.494479\pi\)
−0.694738 + 0.719263i \(0.744479\pi\)
\(318\) −12.4885 30.1500i −0.700322 1.69073i
\(319\) 44.1190i 2.47019i
\(320\) 25.3507 10.5006i 1.41715 0.587001i
\(321\) 10.6834 + 10.6834i 0.596291 + 0.596291i
\(322\) −6.51275 −0.362941
\(323\) 11.7588 + 7.26372i 0.654277 + 0.404164i
\(324\) −26.0759 −1.44866
\(325\) −6.69208 6.69208i −0.371210 0.371210i
\(326\) 20.5141 8.49722i 1.13617 0.470618i
\(327\) 24.7391i 1.36808i
\(328\) −6.00319 14.4930i −0.331471 0.800241i
\(329\) −2.91827 1.20879i −0.160889 0.0666425i
\(330\) 25.4464 61.4331i 1.40078 3.38178i
\(331\) 22.4116 22.4116i 1.23185 1.23185i 0.268600 0.963252i \(-0.413439\pi\)
0.963252 0.268600i \(-0.0865609\pi\)
\(332\) −1.27450 + 1.27450i −0.0699475 + 0.0699475i
\(333\) −12.3159 + 29.7332i −0.674908 + 1.62937i
\(334\) −24.7687 10.2596i −1.35529 0.561378i
\(335\) 5.91476 + 14.2795i 0.323158 + 0.780172i
\(336\) 11.5609i 0.630697i
\(337\) 22.9751 9.51659i 1.25153 0.518402i 0.344232 0.938885i \(-0.388139\pi\)
0.907301 + 0.420483i \(0.138139\pi\)
\(338\) 7.98086 + 7.98086i 0.434102 + 0.434102i
\(339\) −6.30239 −0.342299
\(340\) −7.38120 + 5.32256i −0.400302 + 0.288657i
\(341\) 45.5114 2.46458
\(342\) −23.1333 23.1333i −1.25090 1.25090i
\(343\) −16.7966 + 6.95737i −0.906930 + 0.375663i
\(344\) 3.07894i 0.166005i
\(345\) 15.0067 + 36.2293i 0.807932 + 1.95052i
\(346\) 15.7621 + 6.52888i 0.847376 + 0.350995i
\(347\) 9.15919 22.1123i 0.491691 1.18705i −0.462168 0.886793i \(-0.652928\pi\)
0.953859 0.300255i \(-0.0970719\pi\)
\(348\) 13.6658 13.6658i 0.732564 0.732564i
\(349\) −24.8433 + 24.8433i −1.32983 + 1.32983i −0.424317 + 0.905514i \(0.639486\pi\)
−0.905514 + 0.424317i \(0.860514\pi\)
\(350\) 3.69586 8.92260i 0.197552 0.476933i
\(351\) 30.7001 + 12.7164i 1.63865 + 0.678752i
\(352\) 7.50773 + 18.1253i 0.400163 + 0.966079i
\(353\) 20.1046i 1.07006i 0.844832 + 0.535031i \(0.179700\pi\)
−0.844832 + 0.535031i \(0.820300\pi\)
\(354\) 10.3708 4.29571i 0.551200 0.228315i
\(355\) 17.2280 + 17.2280i 0.914368 + 0.914368i
\(356\) −6.55061 −0.347182
\(357\) −5.08635 21.5247i −0.269198 1.13921i
\(358\) 14.5709 0.770098
\(359\) −8.38382 8.38382i −0.442481 0.442481i 0.450364 0.892845i \(-0.351294\pi\)
−0.892845 + 0.450364i \(0.851294\pi\)
\(360\) 77.8628 32.2518i 4.10373 1.69982i
\(361\) 7.76288i 0.408573i
\(362\) −6.72129 16.2266i −0.353263 0.852853i
\(363\) 54.2304 + 22.4630i 2.84636 + 1.17900i
\(364\) −0.737382 + 1.78020i −0.0386493 + 0.0933077i
\(365\) 7.69315 7.69315i 0.402678 0.402678i
\(366\) 1.50745 1.50745i 0.0787958 0.0787958i
\(367\) 6.20252 14.9742i 0.323769 0.781647i −0.675260 0.737580i \(-0.735968\pi\)
0.999029 0.0440670i \(-0.0140315\pi\)
\(368\) 7.15833 + 2.96508i 0.373154 + 0.154565i
\(369\) −16.6042 40.0861i −0.864379 2.08680i
\(370\) 13.9205i 0.723691i
\(371\) 12.2548 5.07612i 0.636240 0.263539i
\(372\) 14.0971 + 14.0971i 0.730901 + 0.730901i
\(373\) −26.9809 −1.39702 −0.698510 0.715601i \(-0.746153\pi\)
−0.698510 + 0.715601i \(0.746153\pi\)
\(374\) 14.7014 + 20.3875i 0.760191 + 1.05421i
\(375\) −3.61307 −0.186578
\(376\) 4.35047 + 4.35047i 0.224358 + 0.224358i
\(377\) −13.6024 + 5.63431i −0.700561 + 0.290182i
\(378\) 33.9098i 1.74413i
\(379\) 8.44037 + 20.3769i 0.433553 + 1.04669i 0.978133 + 0.207980i \(0.0666889\pi\)
−0.544580 + 0.838709i \(0.683311\pi\)
\(380\) −6.83541 2.83132i −0.350649 0.145244i
\(381\) −10.2536 + 24.7543i −0.525307 + 1.26820i
\(382\) −0.360191 + 0.360191i −0.0184290 + 0.0184290i
\(383\) −10.7058 + 10.7058i −0.547039 + 0.547039i −0.925583 0.378544i \(-0.876425\pi\)
0.378544 + 0.925583i \(0.376425\pi\)
\(384\) 3.12610 7.54708i 0.159528 0.385135i
\(385\) 24.9703 + 10.3430i 1.27260 + 0.527130i
\(386\) 0.255208 + 0.616127i 0.0129898 + 0.0313600i
\(387\) 8.51602i 0.432894i
\(388\) 8.22975 3.40888i 0.417802 0.173059i
\(389\) −12.2839 12.2839i −0.622818 0.622818i 0.323433 0.946251i \(-0.395163\pi\)
−0.946251 + 0.323433i \(0.895163\pi\)
\(390\) −22.1903 −1.12365
\(391\) −14.6323 2.37115i −0.739987 0.119914i
\(392\) 13.8591 0.699992
\(393\) −23.9205 23.9205i −1.20663 1.20663i
\(394\) −7.61486 + 3.15418i −0.383631 + 0.158905i
\(395\) 23.6307i 1.18899i
\(396\) 11.9040 + 28.7389i 0.598200 + 1.44418i
\(397\) −25.9904 10.7656i −1.30442 0.540309i −0.381169 0.924505i \(-0.624479\pi\)
−0.923251 + 0.384196i \(0.874479\pi\)
\(398\) −6.18584 + 14.9339i −0.310068 + 0.748571i
\(399\) 12.7152 12.7152i 0.636557 0.636557i
\(400\) −8.12443 + 8.12443i −0.406221 + 0.406221i
\(401\) −4.63547 + 11.1910i −0.231484 + 0.558853i −0.996352 0.0853344i \(-0.972804\pi\)
0.764868 + 0.644187i \(0.222804\pi\)
\(402\) 17.2773 + 7.15649i 0.861713 + 0.356933i
\(403\) −5.81213 14.0317i −0.289523 0.698970i
\(404\) 7.67275i 0.381733i
\(405\) 112.768 46.7099i 5.60347 2.32103i
\(406\) −10.6240 10.6240i −0.527258 0.527258i
\(407\) 20.1030 0.996471
\(408\) −6.89121 + 42.5254i −0.341166 + 2.10532i
\(409\) 33.6685 1.66480 0.832401 0.554174i \(-0.186966\pi\)
0.832401 + 0.554174i \(0.186966\pi\)
\(410\) 13.2706 + 13.2706i 0.655387 + 0.655387i
\(411\) −55.9425 + 23.1721i −2.75944 + 1.14300i
\(412\) 9.13634i 0.450115i
\(413\) 1.74605 + 4.21533i 0.0859174 + 0.207423i
\(414\) 32.4158 + 13.4271i 1.59315 + 0.659904i
\(415\) 3.22869 7.79476i 0.158490 0.382630i
\(416\) 4.62945 4.62945i 0.226978 0.226978i
\(417\) 8.19782 8.19782i 0.401449 0.401449i
\(418\) −7.82036 + 18.8800i −0.382506 + 0.923452i
\(419\) 15.5959 + 6.46004i 0.761910 + 0.315594i 0.729591 0.683884i \(-0.239711\pi\)
0.0323196 + 0.999478i \(0.489711\pi\)
\(420\) 4.53078 + 10.9383i 0.221079 + 0.533732i
\(421\) 6.97939i 0.340155i −0.985431 0.170077i \(-0.945598\pi\)
0.985431 0.170077i \(-0.0544018\pi\)
\(422\) −4.83028 + 2.00077i −0.235135 + 0.0973959i
\(423\) 12.0329 + 12.0329i 0.585062 + 0.585062i
\(424\) −25.8365 −1.25473
\(425\) 11.5521 18.7010i 0.560358 0.907130i
\(426\) 29.4790 1.42826
\(427\) 0.612723 + 0.612723i 0.0296518 + 0.0296518i
\(428\) 2.82446 1.16993i 0.136525 0.0565507i
\(429\) 32.0458i 1.54718i
\(430\) −1.40963 3.40314i −0.0679782 0.164114i
\(431\) −11.0654 4.58343i −0.533000 0.220776i 0.0999163 0.994996i \(-0.468142\pi\)
−0.632917 + 0.774220i \(0.718142\pi\)
\(432\) 15.4382 37.2711i 0.742770 1.79321i
\(433\) −11.3846 + 11.3846i −0.547107 + 0.547107i −0.925603 0.378496i \(-0.876441\pi\)
0.378496 + 0.925603i \(0.376441\pi\)
\(434\) 10.9593 10.9593i 0.526061 0.526061i
\(435\) −34.6195 + 83.5789i −1.65988 + 4.00730i
\(436\) 4.62481 + 1.91566i 0.221488 + 0.0917434i
\(437\) −4.61194 11.1342i −0.220619 0.532622i
\(438\) 13.1638i 0.628991i
\(439\) 18.8575 7.81102i 0.900018 0.372800i 0.115791 0.993274i \(-0.463060\pi\)
0.784227 + 0.620474i \(0.213060\pi\)
\(440\) −37.2250 37.2250i −1.77463 1.77463i
\(441\) 38.3329 1.82538
\(442\) 4.40826 7.13626i 0.209679 0.339437i
\(443\) 28.7154 1.36431 0.682154 0.731209i \(-0.261043\pi\)
0.682154 + 0.731209i \(0.261043\pi\)
\(444\) 6.22689 + 6.22689i 0.295515 + 0.295515i
\(445\) 28.3288 11.7342i 1.34291 0.556253i
\(446\) 5.31089i 0.251478i
\(447\) −7.46484 18.0217i −0.353075 0.852398i
\(448\) 12.4673 + 5.16413i 0.589026 + 0.243982i
\(449\) 5.27334 12.7310i 0.248864 0.600811i −0.749244 0.662294i \(-0.769583\pi\)
0.998108 + 0.0614828i \(0.0195829\pi\)
\(450\) −36.7907 + 36.7907i −1.73433 + 1.73433i
\(451\) −19.1645 + 19.1645i −0.902422 + 0.902422i
\(452\) −0.488021 + 1.17819i −0.0229546 + 0.0554173i
\(453\) −30.7666 12.7439i −1.44554 0.598762i
\(454\) −4.03549 9.74253i −0.189395 0.457240i
\(455\) 9.01953i 0.422842i
\(456\) −32.3590 + 13.4035i −1.51535 + 0.627678i
\(457\) −2.40110 2.40110i −0.112319 0.112319i 0.648714 0.761032i \(-0.275307\pi\)
−0.761032 + 0.648714i \(0.775307\pi\)
\(458\) 24.8552 1.16141
\(459\) −12.3458 + 76.1857i −0.576254 + 3.55604i
\(460\) 7.93485 0.369964
\(461\) 8.25353 + 8.25353i 0.384405 + 0.384405i 0.872686 0.488281i \(-0.162376\pi\)
−0.488281 + 0.872686i \(0.662376\pi\)
\(462\) 30.2125 12.5144i 1.40561 0.582223i
\(463\) 19.5438i 0.908277i −0.890931 0.454139i \(-0.849947\pi\)
0.890931 0.454139i \(-0.150053\pi\)
\(464\) 6.84026 + 16.5139i 0.317551 + 0.766636i
\(465\) −86.2167 35.7121i −3.99820 1.65611i
\(466\) −10.4717 + 25.2808i −0.485091 + 1.17111i
\(467\) −4.61711 + 4.61711i −0.213655 + 0.213655i −0.805818 0.592163i \(-0.798274\pi\)
0.592163 + 0.805818i \(0.298274\pi\)
\(468\) 7.34032 7.34032i 0.339306 0.339306i
\(469\) −2.90885 + 7.02258i −0.134318 + 0.324273i
\(470\) −6.80032 2.81678i −0.313675 0.129929i
\(471\) 23.3281 + 56.3189i 1.07490 + 2.59504i
\(472\) 8.88705i 0.409060i
\(473\) 4.91459 2.03569i 0.225973 0.0936011i
\(474\) 20.2174 + 20.2174i 0.928615 + 0.928615i
\(475\) 17.8713 0.819991
\(476\) −4.41775 0.715893i −0.202487 0.0328129i
\(477\) −71.4611 −3.27198
\(478\) 3.78234 + 3.78234i 0.173000 + 0.173000i
\(479\) −0.881094 + 0.364961i −0.0402582 + 0.0166755i −0.402722 0.915322i \(-0.631936\pi\)
0.362463 + 0.931998i \(0.381936\pi\)
\(480\) 40.2276i 1.83613i
\(481\) −2.56730 6.19802i −0.117059 0.282605i
\(482\) −4.13026 1.71081i −0.188128 0.0779252i
\(483\) −7.38019 + 17.8174i −0.335810 + 0.810718i
\(484\) 8.39859 8.39859i 0.381754 0.381754i
\(485\) −29.4841 + 29.4841i −1.33880 + 1.33880i
\(486\) 31.8882 76.9850i 1.44648 3.49211i
\(487\) −8.72830 3.61538i −0.395517 0.163829i 0.176055 0.984380i \(-0.443666\pi\)
−0.571572 + 0.820552i \(0.693666\pi\)
\(488\) −0.645893 1.55932i −0.0292382 0.0705872i
\(489\) 65.7508i 2.97335i
\(490\) −15.3184 + 6.34510i −0.692016 + 0.286642i
\(491\) −18.3353 18.3353i −0.827461 0.827461i 0.159704 0.987165i \(-0.448946\pi\)
−0.987165 + 0.159704i \(0.948946\pi\)
\(492\) −11.8724 −0.535248
\(493\) −20.0011 27.7370i −0.900803 1.24921i
\(494\) 6.81966 0.306831
\(495\) −102.960 102.960i −4.62772 4.62772i
\(496\) −17.0350 + 7.05614i −0.764896 + 0.316830i
\(497\) 11.9821i 0.537472i
\(498\) −3.90651 9.43116i −0.175055 0.422620i
\(499\) 38.7209 + 16.0387i 1.73339 + 0.717992i 0.999239 + 0.0390019i \(0.0124178\pi\)
0.734147 + 0.678990i \(0.237582\pi\)
\(500\) −0.279776 + 0.675438i −0.0125119 + 0.0302065i
\(501\) −56.1355 + 56.1355i −2.50795 + 2.50795i
\(502\) 13.2445 13.2445i 0.591131 0.591131i
\(503\) −13.9777 + 33.7452i −0.623237 + 1.50463i 0.224645 + 0.974441i \(0.427878\pi\)
−0.847882 + 0.530185i \(0.822122\pi\)
\(504\) 38.2925 + 15.8613i 1.70568 + 0.706517i
\(505\) −13.7443 33.1816i −0.611612 1.47656i
\(506\) 21.9168i 0.974319i
\(507\) 30.8776 12.7899i 1.37132 0.568021i
\(508\) 3.83367 + 3.83367i 0.170092 + 0.170092i
\(509\) −7.10896 −0.315099 −0.157550 0.987511i \(-0.550359\pi\)
−0.157550 + 0.987511i \(0.550359\pi\)
\(510\) −11.8525 50.1581i −0.524838 2.22104i
\(511\) 5.35060 0.236697
\(512\) −15.0045 15.0045i −0.663111 0.663111i
\(513\) −57.9723 + 24.0129i −2.55954 + 1.06020i
\(514\) 17.4271i 0.768676i
\(515\) 16.3660 + 39.5110i 0.721172 + 1.74106i
\(516\) 2.15284 + 0.891736i 0.0947735 + 0.0392565i
\(517\) 4.06782 9.82058i 0.178902 0.431909i
\(518\) 4.84086 4.84086i 0.212695 0.212695i
\(519\) 35.7230 35.7230i 1.56806 1.56806i
\(520\) −6.72303 + 16.2308i −0.294824 + 0.711769i
\(521\) 17.0798 + 7.07469i 0.748280 + 0.309948i 0.724040 0.689758i \(-0.242283\pi\)
0.0242405 + 0.999706i \(0.492283\pi\)
\(522\) 30.9755 + 74.7814i 1.35576 + 3.27309i
\(523\) 20.0606i 0.877190i 0.898685 + 0.438595i \(0.144524\pi\)
−0.898685 + 0.438595i \(0.855476\pi\)
\(524\) −6.32404 + 2.61950i −0.276267 + 0.114433i
\(525\) −20.2220 20.2220i −0.882562 0.882562i
\(526\) 24.7463 1.07899
\(527\) 28.6124 20.6323i 1.24637 0.898757i
\(528\) −38.9047 −1.69311
\(529\) −7.12403 7.12403i −0.309740 0.309740i
\(530\) 28.5570 11.8287i 1.24043 0.513805i
\(531\) 24.5807i 1.06671i
\(532\) −1.39243 3.36162i −0.0603694 0.145745i
\(533\) 8.35611 + 3.46121i 0.361943 + 0.149922i
\(534\) 14.1976 34.2760i 0.614390 1.48327i
\(535\) −10.1190 + 10.1190i −0.437481 + 0.437481i
\(536\) 10.4691 10.4691i 0.452194 0.452194i
\(537\) 16.5117 39.8627i 0.712531 1.72020i
\(538\) 16.1511 + 6.69002i 0.696325 + 0.288427i
\(539\) −9.16318 22.1219i −0.394686 0.952857i
\(540\) 41.3142i 1.77788i
\(541\) −16.9187 + 7.00796i −0.727392 + 0.301296i −0.715480 0.698633i \(-0.753792\pi\)
−0.0119121 + 0.999929i \(0.503792\pi\)
\(542\) 4.86865 + 4.86865i 0.209127 + 0.209127i
\(543\) −52.0088 −2.23191
\(544\) 12.9370 + 7.99151i 0.554668 + 0.342633i
\(545\) −23.4320 −1.00372
\(546\) −7.71670 7.71670i −0.330244 0.330244i
\(547\) −20.9107 + 8.66150i −0.894078 + 0.370339i −0.781940 0.623354i \(-0.785770\pi\)
−0.112138 + 0.993693i \(0.535770\pi\)
\(548\) 12.2524i 0.523396i
\(549\) −1.78647 4.31292i −0.0762447 0.184071i
\(550\) 30.0264 + 12.4373i 1.28033 + 0.530330i
\(551\) 10.6395 25.6860i 0.453258 1.09426i
\(552\) 26.5616 26.5616i 1.13054 1.13054i
\(553\) −8.21762 + 8.21762i −0.349449 + 0.349449i
\(554\) −8.23022 + 19.8695i −0.349668 + 0.844174i
\(555\) −38.0831 15.7746i −1.61654 0.669593i
\(556\) −0.897732 2.16732i −0.0380723 0.0919148i
\(557\) 9.37961i 0.397427i −0.980058 0.198713i \(-0.936324\pi\)
0.980058 0.198713i \(-0.0636763\pi\)
\(558\) −77.1415 + 31.9531i −3.26566 + 1.35268i
\(559\) −1.25526 1.25526i −0.0530917 0.0530917i
\(560\) −10.9500 −0.462723
\(561\) 72.4350 17.1166i 3.05821 0.722664i
\(562\) −22.5206 −0.949973
\(563\) −10.4100 10.4100i −0.438728 0.438728i 0.452856 0.891584i \(-0.350405\pi\)
−0.891584 + 0.452856i \(0.850405\pi\)
\(564\) 4.30192 1.78191i 0.181143 0.0750320i
\(565\) 5.96939i 0.251134i
\(566\) 2.87214 + 6.93395i 0.120725 + 0.291456i
\(567\) 55.4585 + 22.9717i 2.32904 + 0.964720i
\(568\) 8.93130 21.5621i 0.374749 0.904724i
\(569\) 9.59991 9.59991i 0.402449 0.402449i −0.476646 0.879095i \(-0.658148\pi\)
0.879095 + 0.476646i \(0.158148\pi\)
\(570\) 29.6297 29.6297i 1.24105 1.24105i
\(571\) 7.40989 17.8891i 0.310094 0.748633i −0.689607 0.724184i \(-0.742217\pi\)
0.999701 0.0244496i \(-0.00778332\pi\)
\(572\) −5.99074 2.48144i −0.250485 0.103754i
\(573\) 0.577233 + 1.39356i 0.0241142 + 0.0582169i
\(574\) 9.22972i 0.385241i
\(575\) −17.7076 + 7.33475i −0.738460 + 0.305880i
\(576\) −51.4067 51.4067i −2.14195 2.14195i
\(577\) 3.21303 0.133760 0.0668801 0.997761i \(-0.478695\pi\)
0.0668801 + 0.997761i \(0.478695\pi\)
\(578\) 18.4851 + 6.15256i 0.768880 + 0.255913i
\(579\) 1.97478 0.0820690
\(580\) 12.9438 + 12.9438i 0.537460 + 0.537460i
\(581\) 3.83342 1.58785i 0.159037 0.0658753i
\(582\) 50.4505i 2.09124i
\(583\) 17.0822 + 41.2401i 0.707473 + 1.70799i
\(584\) −9.62852 3.98826i −0.398431 0.165035i
\(585\) −18.5952 + 44.8927i −0.768816 + 1.85609i
\(586\) −12.9389 + 12.9389i −0.534500 + 0.534500i
\(587\) −23.0027 + 23.0027i −0.949425 + 0.949425i −0.998781 0.0493564i \(-0.984283\pi\)
0.0493564 + 0.998781i \(0.484283\pi\)
\(588\) 4.01394 9.69051i 0.165532 0.399630i
\(589\) 26.4967 + 10.9753i 1.09178 + 0.452228i
\(590\) 4.06874 + 9.82281i 0.167507 + 0.404399i
\(591\) 24.4068i 1.00396i
\(592\) −7.52462 + 3.11680i −0.309260 + 0.128100i
\(593\) 8.34611 + 8.34611i 0.342734 + 0.342734i 0.857394 0.514660i \(-0.172082\pi\)
−0.514660 + 0.857394i \(0.672082\pi\)
\(594\) −114.113 −4.68213
\(595\) 20.3874 4.81760i 0.835802 0.197502i
\(596\) −3.94707 −0.161678
\(597\) 33.8460 + 33.8460i 1.38523 + 1.38523i
\(598\) −6.75721 + 2.79893i −0.276323 + 0.114457i
\(599\) 21.5156i 0.879103i −0.898217 0.439551i \(-0.855137\pi\)
0.898217 0.439551i \(-0.144863\pi\)
\(600\) 21.3167 + 51.4632i 0.870252 + 2.10097i
\(601\) 3.40944 + 1.41224i 0.139074 + 0.0576064i 0.451135 0.892456i \(-0.351019\pi\)
−0.312061 + 0.950062i \(0.601019\pi\)
\(602\) 0.693246 1.67364i 0.0282546 0.0682126i
\(603\) 28.9563 28.9563i 1.17919 1.17919i
\(604\) −4.76478 + 4.76478i −0.193876 + 0.193876i
\(605\) −21.2761 + 51.3651i −0.864997 + 2.08829i
\(606\) −40.1476 16.6297i −1.63089 0.675535i
\(607\) 14.7555 + 35.6229i 0.598907 + 1.44589i 0.874696 + 0.484671i \(0.161061\pi\)
−0.275790 + 0.961218i \(0.588939\pi\)
\(608\) 12.3630i 0.501386i
\(609\) −41.1036 + 17.0257i −1.66560 + 0.689916i
\(610\) 1.42780 + 1.42780i 0.0578101 + 0.0578101i
\(611\) −3.54730 −0.143508
\(612\) 20.5125 + 12.6711i 0.829167 + 0.512198i
\(613\) −7.68277 −0.310304 −0.155152 0.987891i \(-0.549587\pi\)
−0.155152 + 0.987891i \(0.549587\pi\)
\(614\) 12.4404 + 12.4404i 0.502054 + 0.502054i
\(615\) 51.3433 21.2671i 2.07036 0.857572i
\(616\) 25.8901i 1.04314i
\(617\) 5.33140 + 12.8711i 0.214634 + 0.518172i 0.994125 0.108242i \(-0.0345220\pi\)
−0.779491 + 0.626414i \(0.784522\pi\)
\(618\) 47.8058 + 19.8018i 1.92303 + 0.796546i
\(619\) −2.09066 + 5.04730i −0.0840308 + 0.202868i −0.960310 0.278936i \(-0.910018\pi\)
0.876279 + 0.481804i \(0.160018\pi\)
\(620\) −13.3523 + 13.3523i −0.536240 + 0.536240i
\(621\) 47.5860 47.5860i 1.90956 1.90956i
\(622\) 7.77573 18.7723i 0.311778 0.752700i
\(623\) 13.9319 + 5.77080i 0.558172 + 0.231202i
\(624\) 4.96841 + 11.9948i 0.198896 + 0.480177i
\(625\) 23.2341i 0.929362i
\(626\) −17.7694 + 7.36031i −0.710206 + 0.294177i
\(627\) 42.7893 + 42.7893i 1.70884 + 1.70884i
\(628\) 12.3348 0.492213
\(629\) 12.6385 9.11358i 0.503930 0.363382i
\(630\) −49.5862 −1.97556
\(631\) 17.6233 + 17.6233i 0.701572 + 0.701572i 0.964748 0.263176i \(-0.0847701\pi\)
−0.263176 + 0.964748i \(0.584770\pi\)
\(632\) 20.9131 8.66247i 0.831877 0.344575i
\(633\) 15.4818i 0.615346i
\(634\) −5.72511 13.8216i −0.227373 0.548927i
\(635\) −23.4464 9.71182i −0.930443 0.385402i
\(636\) −7.48288 + 18.0653i −0.296716 + 0.716335i
\(637\) −5.65025 + 5.65025i −0.223871 + 0.223871i
\(638\) 35.7518 35.7518i 1.41543 1.41543i
\(639\) 24.7030 59.6384i 0.977237 2.35926i
\(640\) 7.14832 + 2.96093i 0.282562 + 0.117041i
\(641\) −12.2981 29.6903i −0.485746 1.17270i −0.956841 0.290612i \(-0.906141\pi\)
0.471095 0.882083i \(-0.343859\pi\)
\(642\) 17.3147i 0.683355i
\(643\) 44.1993 18.3080i 1.74305 0.721995i 0.744532 0.667587i \(-0.232673\pi\)
0.998519 0.0544084i \(-0.0173273\pi\)
\(644\) 2.75935 + 2.75935i 0.108734 + 0.108734i
\(645\) −10.9076 −0.429485
\(646\) 3.64259 + 15.4149i 0.143316 + 0.606491i
\(647\) −43.4177 −1.70693 −0.853463 0.521153i \(-0.825502\pi\)
−0.853463 + 0.521153i \(0.825502\pi\)
\(648\) −82.6760 82.6760i −3.24782 3.24782i
\(649\) −14.1855 + 5.87581i −0.556828 + 0.230646i
\(650\) 10.8459i 0.425409i
\(651\) −17.5630 42.4009i −0.688349 1.66182i
\(652\) −12.2917 5.09137i −0.481379 0.199394i
\(653\) −1.48976 + 3.59659i −0.0582987 + 0.140746i −0.950345 0.311199i \(-0.899269\pi\)
0.892046 + 0.451944i \(0.149269\pi\)
\(654\) −20.0473 + 20.0473i −0.783913 + 0.783913i
\(655\) 22.6566 22.6566i 0.885267 0.885267i
\(656\) 4.20204 10.1446i 0.164062 0.396081i
\(657\) −26.6315 11.0311i −1.03899 0.430365i
\(658\) −1.38528 3.34436i −0.0540038 0.130377i
\(659\) 11.0855i 0.431829i −0.976412 0.215914i \(-0.930727\pi\)
0.976412 0.215914i \(-0.0692732\pi\)
\(660\) −36.8095 + 15.2470i −1.43281 + 0.593489i
\(661\) 12.0407 + 12.0407i 0.468327 + 0.468327i 0.901372 0.433045i \(-0.142561\pi\)
−0.433045 + 0.901372i \(0.642561\pi\)
\(662\) 36.3224 1.41171
\(663\) −14.5277 20.1467i −0.564211 0.782433i
\(664\) −8.08188 −0.313638
\(665\) 12.0434 + 12.0434i 0.467023 + 0.467023i
\(666\) −34.0745 + 14.1141i −1.32036 + 0.546911i
\(667\) 29.8175i 1.15454i
\(668\) 6.14732 + 14.8410i 0.237847 + 0.574214i
\(669\) −14.5294 6.01826i −0.561738 0.232679i
\(670\) −6.77836 + 16.3644i −0.261871 + 0.632213i
\(671\) −2.06194 + 2.06194i −0.0796004 + 0.0796004i
\(672\) 13.9892 13.9892i 0.539645 0.539645i
\(673\) 7.46818 18.0298i 0.287877 0.694997i −0.712098 0.702080i \(-0.752255\pi\)
0.999975 + 0.00708318i \(0.00225467\pi\)
\(674\) 26.3296 + 10.9061i 1.01418 + 0.420087i
\(675\) 38.1897 + 92.1980i 1.46992 + 3.54870i
\(676\) 6.76274i 0.260105i
\(677\) 26.8514 11.1222i 1.03198 0.427462i 0.198556 0.980090i \(-0.436375\pi\)
0.833428 + 0.552628i \(0.186375\pi\)
\(678\) −5.10714 5.10714i −0.196139 0.196139i
\(679\) −20.5062 −0.786957
\(680\) −40.2785 6.52710i −1.54461 0.250303i
\(681\) −31.2263 −1.19659
\(682\) 36.8802 + 36.8802i 1.41221 + 1.41221i
\(683\) −32.0395 + 13.2712i −1.22596 + 0.507808i −0.899299 0.437335i \(-0.855922\pi\)
−0.326658 + 0.945143i \(0.605922\pi\)
\(684\) 19.6024i 0.749517i
\(685\) −21.9478 52.9867i −0.838583 2.02452i
\(686\) −19.2490 7.97320i −0.734931 0.304418i
\(687\) 28.1657 67.9981i 1.07459 2.59429i
\(688\) −1.52393 + 1.52393i −0.0580992 + 0.0580992i
\(689\) 10.5333 10.5333i 0.401287 0.401287i
\(690\) −17.1978 + 41.5191i −0.654707 + 1.58060i
\(691\) 30.8116 + 12.7626i 1.17213 + 0.485511i 0.881895 0.471446i \(-0.156268\pi\)
0.290232 + 0.956956i \(0.406268\pi\)
\(692\) −3.91198 9.44434i −0.148711 0.359020i
\(693\) 71.6092i 2.72021i
\(694\) 25.3408 10.4965i 0.961924 0.398442i
\(695\) 7.76467 + 7.76467i 0.294531 + 0.294531i
\(696\) 86.6575 3.28475
\(697\) −3.36034 + 20.7366i −0.127282 + 0.785453i
\(698\) −40.2635 −1.52400
\(699\) 57.2961 + 57.2961i 2.16714 + 2.16714i
\(700\) −5.34625 + 2.21449i −0.202069 + 0.0836998i
\(701\) 7.43050i 0.280646i 0.990106 + 0.140323i \(0.0448141\pi\)
−0.990106 + 0.140323i \(0.955186\pi\)
\(702\) 14.5731 + 35.1826i 0.550027 + 1.32788i
\(703\) 11.7040 + 4.84794i 0.441423 + 0.182843i
\(704\) −17.3784 + 41.9551i −0.654972 + 1.58124i
\(705\) −15.4121 + 15.4121i −0.580454 + 0.580454i
\(706\) −16.2918 + 16.2918i −0.613150 + 0.613150i
\(707\) 6.75935 16.3185i 0.254212 0.613721i
\(708\) −6.21396 2.57391i −0.233535 0.0967334i
\(709\) −6.71448 16.2102i −0.252168 0.608787i 0.746211 0.665710i \(-0.231871\pi\)
−0.998379 + 0.0569229i \(0.981871\pi\)
\(710\) 27.9214i 1.04787i
\(711\) 57.8433 23.9595i 2.16929 0.898551i
\(712\) −20.7693 20.7693i −0.778364 0.778364i
\(713\) −30.7585 −1.15192
\(714\) 13.3208 21.5642i 0.498519 0.807022i
\(715\) 30.3526 1.13512
\(716\) −6.17348 6.17348i −0.230714 0.230714i
\(717\) 14.6337 6.06148i 0.546506 0.226370i
\(718\) 13.5877i 0.507087i
\(719\) −5.63222 13.5974i −0.210046 0.507097i 0.783384 0.621539i \(-0.213492\pi\)
−0.993430 + 0.114442i \(0.963492\pi\)
\(720\) 54.5014 + 22.5752i 2.03115 + 0.841329i
\(721\) −8.04871 + 19.4313i −0.299750 + 0.723660i
\(722\) 6.29065 6.29065i 0.234114 0.234114i
\(723\) −9.36075 + 9.36075i −0.348130 + 0.348130i
\(724\) −4.02727 + 9.72269i −0.149672 + 0.361341i
\(725\) −40.8505 16.9208i −1.51715 0.628424i
\(726\) 25.7427 + 62.1485i 0.955403 + 2.30655i
\(727\) 26.0781i 0.967182i −0.875294 0.483591i \(-0.839332\pi\)
0.875294 0.483591i \(-0.160668\pi\)
\(728\) −7.98223 + 3.30635i −0.295841 + 0.122541i
\(729\) −93.9211 93.9211i −3.47856 3.47856i
\(730\) 12.4683 0.461472
\(731\) 2.16686 3.50781i 0.0801444 0.129741i
\(732\) −1.27737 −0.0472129
\(733\) −12.7631 12.7631i −0.471417 0.471417i 0.430956 0.902373i \(-0.358177\pi\)
−0.902373 + 0.430956i \(0.858177\pi\)
\(734\) 17.1606 7.10813i 0.633408 0.262366i
\(735\) 49.0978i 1.81100i
\(736\) −5.07404 12.2498i −0.187031 0.451534i
\(737\) −23.6324 9.78888i −0.870512 0.360578i
\(738\) 19.0285 45.9389i 0.700450 1.69104i
\(739\) −24.8634 + 24.8634i −0.914615 + 0.914615i −0.996631 0.0820156i \(-0.973864\pi\)
0.0820156 + 0.996631i \(0.473864\pi\)
\(740\) −5.89789 + 5.89789i −0.216811 + 0.216811i
\(741\) 7.72798 18.6570i 0.283894 0.685382i
\(742\) 14.0442 + 5.81728i 0.515577 + 0.213559i
\(743\) −8.38588 20.2453i −0.307648 0.742728i −0.999780 0.0209575i \(-0.993329\pi\)
0.692132 0.721771i \(-0.256671\pi\)
\(744\) 89.3925i 3.27729i
\(745\) 17.0695 7.07043i 0.625379 0.259040i
\(746\) −21.8640 21.8640i −0.800498 0.800498i
\(747\) −22.3536 −0.817876
\(748\) 2.40913 14.8666i 0.0880865 0.543578i
\(749\) −7.03776 −0.257154
\(750\) −2.92785 2.92785i −0.106910 0.106910i
\(751\) −46.6377 + 19.3180i −1.70183 + 0.704922i −0.999973 0.00739212i \(-0.997647\pi\)
−0.701860 + 0.712314i \(0.747647\pi\)
\(752\) 4.30655i 0.157044i
\(753\) −21.2253 51.2424i −0.773493 1.86738i
\(754\) −15.5885 6.45697i −0.567700 0.235149i
\(755\) 12.0706 29.1410i 0.439294 1.06055i
\(756\) 14.3671 14.3671i 0.522525 0.522525i
\(757\) 1.16834 1.16834i 0.0424641 0.0424641i −0.685556 0.728020i \(-0.740441\pi\)
0.728020 + 0.685556i \(0.240441\pi\)
\(758\) −9.67273 + 23.3520i −0.351329 + 0.848184i
\(759\) −59.9591 24.8359i −2.17638 0.901486i
\(760\) −12.6954 30.6493i −0.460509 1.11177i
\(761\) 3.89048i 0.141030i