Properties

Label 65.2.m.a.36.3
Level $65$
Weight $2$
Character 65.36
Analytic conductor $0.519$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 65 = 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 65.m (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.519027613138\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.22581504.2
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 2 x^{5} - 11 x^{4} + 4 x^{3} + 20 x^{2} - 32 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 36.3
Root \(1.40994 - 0.109843i\) of defining polynomial
Character \(\chi\) \(=\) 65.36
Dual form 65.2.m.a.56.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.05628 - 0.609843i) q^{2} +(-1.16612 - 2.01978i) q^{3} +(-0.256182 + 0.443720i) q^{4} -1.00000i q^{5} +(-2.46350 - 1.42231i) q^{6} +(3.11786 + 1.80010i) q^{7} +3.06430i q^{8} +(-1.21969 + 2.11256i) q^{9} +O(q^{10})\) \(q+(1.05628 - 0.609843i) q^{2} +(-1.16612 - 2.01978i) q^{3} +(-0.256182 + 0.443720i) q^{4} -1.00000i q^{5} +(-2.46350 - 1.42231i) q^{6} +(3.11786 + 1.80010i) q^{7} +3.06430i q^{8} +(-1.21969 + 2.11256i) q^{9} +(-0.609843 - 1.05628i) q^{10} +(-4.65213 + 2.68591i) q^{11} +1.19496 q^{12} +(1.81988 - 3.11256i) q^{13} +4.39111 q^{14} +(-2.01978 + 1.16612i) q^{15} +(1.35638 + 2.34932i) q^{16} +(-0.565928 + 0.980215i) q^{17} +2.97527i q^{18} +(-1.96410 - 1.13397i) q^{19} +(0.443720 + 0.256182i) q^{20} -8.39654i q^{21} +(-3.27597 + 5.67414i) q^{22} +(-1.94644 - 3.37133i) q^{23} +(6.18922 - 3.57335i) q^{24} -1.00000 q^{25} +(0.0241312 - 4.39758i) q^{26} -1.30752 q^{27} +(-1.59748 + 0.922305i) q^{28} +(0.0123639 + 0.0214150i) q^{29} +(-1.42231 + 2.46350i) q^{30} +5.46410i q^{31} +(-2.44209 - 1.40994i) q^{32} +(10.8499 + 6.26420i) q^{33} +1.38051i q^{34} +(1.80010 - 3.11786i) q^{35} +(-0.624924 - 1.08240i) q^{36} +(7.53794 - 4.35203i) q^{37} -2.76619 q^{38} +(-8.40891 - 0.0461428i) q^{39} +3.06430 q^{40} +(3.23205 - 1.86603i) q^{41} +(-5.12058 - 8.86910i) q^{42} +(-0.565928 + 0.980215i) q^{43} -2.75232i q^{44} +(2.11256 + 1.21969i) q^{45} +(-4.11196 - 2.37404i) q^{46} -2.58535i q^{47} +(3.16341 - 5.47918i) q^{48} +(2.98070 + 5.16273i) q^{49} +(-1.05628 + 0.609843i) q^{50} +2.63977 q^{51} +(0.914884 + 1.60490i) q^{52} -4.43937 q^{53} +(-1.38111 + 0.797382i) q^{54} +(2.68591 + 4.65213i) q^{55} +(-5.51603 + 9.55405i) q^{56} +5.28942i q^{57} +(0.0261196 + 0.0150801i) q^{58} +(-0.148458 - 0.0857123i) q^{59} -1.19496i q^{60} +(-1.68012 + 2.91005i) q^{61} +(3.33225 + 5.77162i) q^{62} +(-7.60563 + 4.39111i) q^{63} -8.86488 q^{64} +(-3.11256 - 1.81988i) q^{65} +15.2807 q^{66} +(5.54239 - 3.19990i) q^{67} +(-0.289961 - 0.502227i) q^{68} +(-4.53957 + 7.86276i) q^{69} -4.39111i q^{70} +(9.35076 + 5.39866i) q^{71} +(-6.47351 - 3.73748i) q^{72} +4.70308i q^{73} +(5.30812 - 9.19393i) q^{74} +(1.16612 + 2.01978i) q^{75} +(1.00633 - 0.581008i) q^{76} -19.3396 q^{77} +(-8.91030 + 5.07938i) q^{78} -11.9826 q^{79} +(2.34932 - 1.35638i) q^{80} +(5.18379 + 8.97859i) q^{81} +(2.27597 - 3.94209i) q^{82} -12.1286i q^{83} +(3.72572 + 2.15104i) q^{84} +(0.980215 + 0.565928i) q^{85} +1.38051i q^{86} +(0.0288357 - 0.0499450i) q^{87} +(-8.23042 - 14.2555i) q^{88} +(13.9898 - 8.07702i) q^{89} +2.97527 q^{90} +(11.2771 - 6.42856i) q^{91} +1.99457 q^{92} +(11.0363 - 6.37182i) q^{93} +(-1.57666 - 2.73086i) q^{94} +(-1.13397 + 1.96410i) q^{95} +6.57666i q^{96} +(-10.5379 - 6.08408i) q^{97} +(6.29692 + 3.63553i) q^{98} -13.1039i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{3} + 2q^{4} - 18q^{6} - 6q^{7} - 4q^{9} + O(q^{10}) \) \( 8q + 2q^{3} + 2q^{4} - 18q^{6} - 6q^{7} - 4q^{9} - 2q^{10} + 20q^{12} + 4q^{14} - 6q^{15} - 2q^{16} - 2q^{17} + 12q^{19} + 12q^{20} - 12q^{22} - 10q^{23} - 12q^{24} - 8q^{25} + 10q^{26} - 4q^{27} - 18q^{28} - 8q^{29} + 4q^{30} + 6q^{32} + 42q^{33} + 10q^{35} + 20q^{36} + 6q^{37} - 16q^{38} - 12q^{40} + 12q^{41} + 4q^{42} - 2q^{43} - 42q^{46} + 28q^{48} + 12q^{49} - 8q^{51} - 6q^{52} - 24q^{53} + 18q^{54} + 12q^{56} + 36q^{58} - 12q^{59} - 28q^{61} + 4q^{62} - 24q^{63} - 8q^{64} - 8q^{65} + 12q^{66} + 6q^{67} - 14q^{68} - 16q^{69} - 48q^{72} + 10q^{74} - 2q^{75} + 54q^{76} - 36q^{77} - 56q^{78} - 16q^{79} + 8q^{81} + 4q^{82} - 30q^{84} + 18q^{85} + 22q^{87} - 18q^{88} + 24q^{89} + 40q^{90} + 28q^{91} + 44q^{92} + 32q^{94} - 16q^{95} - 30q^{97} + 72q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.05628 0.609843i 0.746903 0.431224i −0.0776710 0.996979i \(-0.524748\pi\)
0.824574 + 0.565755i \(0.191415\pi\)
\(3\) −1.16612 2.01978i −0.673262 1.16612i −0.976974 0.213359i \(-0.931559\pi\)
0.303712 0.952764i \(-0.401774\pi\)
\(4\) −0.256182 + 0.443720i −0.128091 + 0.221860i
\(5\) 1.00000i 0.447214i
\(6\) −2.46350 1.42231i −1.00572 0.580654i
\(7\) 3.11786 + 1.80010i 1.17844 + 0.680373i 0.955653 0.294494i \(-0.0951511\pi\)
0.222787 + 0.974867i \(0.428484\pi\)
\(8\) 3.06430i 1.08339i
\(9\) −1.21969 + 2.11256i −0.406562 + 0.704187i
\(10\) −0.609843 1.05628i −0.192849 0.334025i
\(11\) −4.65213 + 2.68591i −1.40267 + 0.809832i −0.994666 0.103149i \(-0.967108\pi\)
−0.408004 + 0.912980i \(0.633775\pi\)
\(12\) 1.19496 0.344955
\(13\) 1.81988 3.11256i 0.504745 0.863269i
\(14\) 4.39111 1.17357
\(15\) −2.01978 + 1.16612i −0.521506 + 0.301092i
\(16\) 1.35638 + 2.34932i 0.339094 + 0.587329i
\(17\) −0.565928 + 0.980215i −0.137258 + 0.237737i −0.926458 0.376399i \(-0.877162\pi\)
0.789200 + 0.614136i \(0.210495\pi\)
\(18\) 2.97527i 0.701278i
\(19\) −1.96410 1.13397i −0.450596 0.260152i 0.257486 0.966282i \(-0.417106\pi\)
−0.708082 + 0.706130i \(0.750439\pi\)
\(20\) 0.443720 + 0.256182i 0.0992188 + 0.0572840i
\(21\) 8.39654i 1.83228i
\(22\) −3.27597 + 5.67414i −0.698438 + 1.20973i
\(23\) −1.94644 3.37133i −0.405860 0.702970i 0.588561 0.808453i \(-0.299695\pi\)
−0.994421 + 0.105483i \(0.966361\pi\)
\(24\) 6.18922 3.57335i 1.26337 0.729407i
\(25\) −1.00000 −0.200000
\(26\) 0.0241312 4.39758i 0.00473251 0.862436i
\(27\) −1.30752 −0.251632
\(28\) −1.59748 + 0.922305i −0.301895 + 0.174299i
\(29\) 0.0123639 + 0.0214150i 0.00229593 + 0.00397666i 0.867171 0.498010i \(-0.165936\pi\)
−0.864875 + 0.501987i \(0.832603\pi\)
\(30\) −1.42231 + 2.46350i −0.259676 + 0.449772i
\(31\) 5.46410i 0.981382i 0.871334 + 0.490691i \(0.163256\pi\)
−0.871334 + 0.490691i \(0.836744\pi\)
\(32\) −2.44209 1.40994i −0.431705 0.249245i
\(33\) 10.8499 + 6.26420i 1.88873 + 1.09046i
\(34\) 1.38051i 0.236755i
\(35\) 1.80010 3.11786i 0.304272 0.527015i
\(36\) −0.624924 1.08240i −0.104154 0.180400i
\(37\) 7.53794 4.35203i 1.23923 0.715470i 0.270293 0.962778i \(-0.412879\pi\)
0.968937 + 0.247309i \(0.0795462\pi\)
\(38\) −2.76619 −0.448735
\(39\) −8.40891 0.0461428i −1.34650 0.00738877i
\(40\) 3.06430 0.484508
\(41\) 3.23205 1.86603i 0.504762 0.291424i −0.225916 0.974147i \(-0.572538\pi\)
0.730678 + 0.682723i \(0.239204\pi\)
\(42\) −5.12058 8.86910i −0.790122 1.36853i
\(43\) −0.565928 + 0.980215i −0.0863031 + 0.149481i −0.905946 0.423394i \(-0.860839\pi\)
0.819643 + 0.572875i \(0.194172\pi\)
\(44\) 2.75232i 0.414929i
\(45\) 2.11256 + 1.21969i 0.314922 + 0.181820i
\(46\) −4.11196 2.37404i −0.606276 0.350034i
\(47\) 2.58535i 0.377113i −0.982062 0.188556i \(-0.939619\pi\)
0.982062 0.188556i \(-0.0603808\pi\)
\(48\) 3.16341 5.47918i 0.456598 0.790852i
\(49\) 2.98070 + 5.16273i 0.425815 + 0.737533i
\(50\) −1.05628 + 0.609843i −0.149381 + 0.0862449i
\(51\) 2.63977 0.369641
\(52\) 0.914884 + 1.60490i 0.126872 + 0.222560i
\(53\) −4.43937 −0.609795 −0.304897 0.952385i \(-0.598622\pi\)
−0.304897 + 0.952385i \(0.598622\pi\)
\(54\) −1.38111 + 0.797382i −0.187945 + 0.108510i
\(55\) 2.68591 + 4.65213i 0.362168 + 0.627293i
\(56\) −5.51603 + 9.55405i −0.737111 + 1.27671i
\(57\) 5.28942i 0.700600i
\(58\) 0.0261196 + 0.0150801i 0.00342967 + 0.00198012i
\(59\) −0.148458 0.0857123i −0.0193276 0.0111588i 0.490305 0.871551i \(-0.336885\pi\)
−0.509633 + 0.860392i \(0.670219\pi\)
\(60\) 1.19496i 0.154269i
\(61\) −1.68012 + 2.91005i −0.215117 + 0.372594i −0.953309 0.301997i \(-0.902347\pi\)
0.738192 + 0.674591i \(0.235680\pi\)
\(62\) 3.33225 + 5.77162i 0.423196 + 0.732997i
\(63\) −7.60563 + 4.39111i −0.958219 + 0.553228i
\(64\) −8.86488 −1.10811
\(65\) −3.11256 1.81988i −0.386066 0.225729i
\(66\) 15.2807 1.88093
\(67\) 5.54239 3.19990i 0.677111 0.390930i −0.121655 0.992572i \(-0.538820\pi\)
0.798766 + 0.601642i \(0.205487\pi\)
\(68\) −0.289961 0.502227i −0.0351629 0.0609040i
\(69\) −4.53957 + 7.86276i −0.546500 + 0.946566i
\(70\) 4.39111i 0.524838i
\(71\) 9.35076 + 5.39866i 1.10973 + 0.640703i 0.938760 0.344573i \(-0.111976\pi\)
0.170971 + 0.985276i \(0.445309\pi\)
\(72\) −6.47351 3.73748i −0.762911 0.440467i
\(73\) 4.70308i 0.550454i 0.961379 + 0.275227i \(0.0887531\pi\)
−0.961379 + 0.275227i \(0.911247\pi\)
\(74\) 5.30812 9.19393i 0.617056 1.06877i
\(75\) 1.16612 + 2.01978i 0.134652 + 0.233225i
\(76\) 1.00633 0.581008i 0.115435 0.0666462i
\(77\) −19.3396 −2.20395
\(78\) −8.91030 + 5.07938i −1.00889 + 0.575126i
\(79\) −11.9826 −1.34815 −0.674075 0.738663i \(-0.735457\pi\)
−0.674075 + 0.738663i \(0.735457\pi\)
\(80\) 2.34932 1.35638i 0.262661 0.151648i
\(81\) 5.18379 + 8.97859i 0.575976 + 0.997621i
\(82\) 2.27597 3.94209i 0.251338 0.435331i
\(83\) 12.1286i 1.33129i −0.746270 0.665643i \(-0.768157\pi\)
0.746270 0.665643i \(-0.231843\pi\)
\(84\) 3.72572 + 2.15104i 0.406509 + 0.234698i
\(85\) 0.980215 + 0.565928i 0.106319 + 0.0613835i
\(86\) 1.38051i 0.148864i
\(87\) 0.0288357 0.0499450i 0.00309152 0.00535466i
\(88\) −8.23042 14.2555i −0.877366 1.51964i
\(89\) 13.9898 8.07702i 1.48292 0.856162i 0.483105 0.875562i \(-0.339509\pi\)
0.999812 + 0.0194001i \(0.00617565\pi\)
\(90\) 2.97527 0.313621
\(91\) 11.2771 6.42856i 1.18216 0.673896i
\(92\) 1.99457 0.207948
\(93\) 11.0363 6.37182i 1.14441 0.660727i
\(94\) −1.57666 2.73086i −0.162620 0.281666i
\(95\) −1.13397 + 1.96410i −0.116343 + 0.201513i
\(96\) 6.57666i 0.671228i
\(97\) −10.5379 6.08408i −1.06997 0.617745i −0.141794 0.989896i \(-0.545287\pi\)
−0.928172 + 0.372151i \(0.878620\pi\)
\(98\) 6.29692 + 3.63553i 0.636085 + 0.367244i
\(99\) 13.1039i 1.31699i
\(100\) 0.256182 0.443720i 0.0256182 0.0443720i
\(101\) −2.02721 3.51122i −0.201714 0.349380i 0.747366 0.664412i \(-0.231318\pi\)
−0.949081 + 0.315032i \(0.897985\pi\)
\(102\) 2.78833 1.60984i 0.276086 0.159398i
\(103\) 17.9035 1.76408 0.882041 0.471173i \(-0.156169\pi\)
0.882041 + 0.471173i \(0.156169\pi\)
\(104\) 9.53781 + 5.57666i 0.935259 + 0.546837i
\(105\) −8.39654 −0.819419
\(106\) −4.68922 + 2.70732i −0.455457 + 0.262958i
\(107\) 4.56593 + 7.90842i 0.441405 + 0.764536i 0.997794 0.0663862i \(-0.0211469\pi\)
−0.556389 + 0.830922i \(0.687814\pi\)
\(108\) 0.334963 0.580172i 0.0322318 0.0558271i
\(109\) 7.37605i 0.706498i 0.935529 + 0.353249i \(0.114923\pi\)
−0.935529 + 0.353249i \(0.885077\pi\)
\(110\) 5.67414 + 3.27597i 0.541008 + 0.312351i
\(111\) −17.5803 10.1500i −1.66865 0.963396i
\(112\) 9.76645i 0.922843i
\(113\) −3.53794 + 6.12789i −0.332821 + 0.576463i −0.983064 0.183263i \(-0.941334\pi\)
0.650243 + 0.759727i \(0.274667\pi\)
\(114\) 3.22572 + 5.58710i 0.302116 + 0.523280i
\(115\) −3.37133 + 1.94644i −0.314378 + 0.181506i
\(116\) −0.0126697 −0.00117635
\(117\) 4.35578 + 7.64096i 0.402692 + 0.706407i
\(118\) −0.209084 −0.0192478
\(119\) −3.52897 + 2.03745i −0.323500 + 0.186773i
\(120\) −3.57335 6.18922i −0.326201 0.564996i
\(121\) 8.92820 15.4641i 0.811655 1.40583i
\(122\) 4.09843i 0.371055i
\(123\) −7.53794 4.35203i −0.679673 0.392409i
\(124\) −2.42453 1.39980i −0.217729 0.125706i
\(125\) 1.00000i 0.0894427i
\(126\) −5.35578 + 9.27648i −0.477131 + 0.826415i
\(127\) −5.71806 9.90396i −0.507395 0.878835i −0.999963 0.00856072i \(-0.997275\pi\)
0.492568 0.870274i \(-0.336058\pi\)
\(128\) −4.47962 + 2.58631i −0.395946 + 0.228600i
\(129\) 2.63977 0.232418
\(130\) −4.39758 0.0241312i −0.385693 0.00211644i
\(131\) −10.5680 −0.923328 −0.461664 0.887055i \(-0.652747\pi\)
−0.461664 + 0.887055i \(0.652747\pi\)
\(132\) −5.55910 + 3.20955i −0.483858 + 0.279355i
\(133\) −4.08253 7.07115i −0.354000 0.613146i
\(134\) 3.90288 6.75998i 0.337157 0.583974i
\(135\) 1.30752i 0.112533i
\(136\) −3.00367 1.73417i −0.257563 0.148704i
\(137\) 3.27940 + 1.89336i 0.280178 + 0.161761i 0.633504 0.773739i \(-0.281616\pi\)
−0.353326 + 0.935500i \(0.614949\pi\)
\(138\) 11.0737i 0.942656i
\(139\) −1.00693 + 1.74406i −0.0854068 + 0.147929i −0.905564 0.424209i \(-0.860552\pi\)
0.820158 + 0.572138i \(0.193886\pi\)
\(140\) 0.922305 + 1.59748i 0.0779490 + 0.135012i
\(141\) −5.22186 + 3.01484i −0.439760 + 0.253895i
\(142\) 13.1694 1.10515
\(143\) −0.106280 + 19.3681i −0.00888757 + 1.61964i
\(144\) −6.61742 −0.551452
\(145\) 0.0214150 0.0123639i 0.00177842 0.00102677i
\(146\) 2.86814 + 4.96777i 0.237369 + 0.411136i
\(147\) 6.95174 12.0408i 0.573370 0.993105i
\(148\) 4.45965i 0.366581i
\(149\) 4.77855 + 2.75890i 0.391474 + 0.226018i 0.682799 0.730607i \(-0.260763\pi\)
−0.291324 + 0.956624i \(0.594096\pi\)
\(150\) 2.46350 + 1.42231i 0.201144 + 0.116131i
\(151\) 4.88961i 0.397911i 0.980009 + 0.198956i \(0.0637549\pi\)
−0.980009 + 0.198956i \(0.936245\pi\)
\(152\) 3.47484 6.01859i 0.281846 0.488172i
\(153\) −1.38051 2.39111i −0.111608 0.193310i
\(154\) −20.4280 + 11.7941i −1.64614 + 0.950397i
\(155\) 5.46410 0.438887
\(156\) 2.17469 3.71938i 0.174114 0.297789i
\(157\) 10.0405 0.801323 0.400661 0.916226i \(-0.368780\pi\)
0.400661 + 0.916226i \(0.368780\pi\)
\(158\) −12.6570 + 7.30752i −1.00694 + 0.581355i
\(159\) 5.17686 + 8.96658i 0.410551 + 0.711096i
\(160\) −1.40994 + 2.44209i −0.111466 + 0.193064i
\(161\) 14.0151i 1.10454i
\(162\) 10.9511 + 6.32260i 0.860397 + 0.496750i
\(163\) 5.87273 + 3.39062i 0.459988 + 0.265574i 0.712039 0.702140i \(-0.247772\pi\)
−0.252051 + 0.967714i \(0.581105\pi\)
\(164\) 1.91217i 0.149315i
\(165\) 6.26420 10.8499i 0.487667 0.844664i
\(166\) −7.39654 12.8112i −0.574083 0.994341i
\(167\) −9.08444 + 5.24490i −0.702975 + 0.405863i −0.808455 0.588559i \(-0.799696\pi\)
0.105479 + 0.994421i \(0.466362\pi\)
\(168\) 25.7295 1.98507
\(169\) −6.37605 11.3290i −0.490466 0.871460i
\(170\) 1.38051 0.105880
\(171\) 4.79118 2.76619i 0.366391 0.211536i
\(172\) −0.289961 0.502227i −0.0221093 0.0382944i
\(173\) −2.22923 + 3.86113i −0.169485 + 0.293557i −0.938239 0.345988i \(-0.887544\pi\)
0.768754 + 0.639545i \(0.220877\pi\)
\(174\) 0.0703412i 0.00533255i
\(175\) −3.11786 1.80010i −0.235688 0.136075i
\(176\) −12.6201 7.28621i −0.951275 0.549219i
\(177\) 0.399804i 0.0300511i
\(178\) 9.85143 17.0632i 0.738396 1.27894i
\(179\) 9.31564 + 16.1352i 0.696284 + 1.20600i 0.969746 + 0.244116i \(0.0784979\pi\)
−0.273462 + 0.961883i \(0.588169\pi\)
\(180\) −1.08240 + 0.624924i −0.0806773 + 0.0465791i
\(181\) −18.0900 −1.34462 −0.672310 0.740270i \(-0.734698\pi\)
−0.672310 + 0.740270i \(0.734698\pi\)
\(182\) 7.99131 13.6676i 0.592355 1.01311i
\(183\) 7.83690 0.579320
\(184\) 10.3307 5.96446i 0.761593 0.439706i
\(185\) −4.35203 7.53794i −0.319968 0.554200i
\(186\) 7.77162 13.4608i 0.569843 0.986997i
\(187\) 6.08012i 0.444622i
\(188\) 1.14717 + 0.662321i 0.0836662 + 0.0483047i
\(189\) −4.07666 2.35366i −0.296533 0.171204i
\(190\) 2.76619i 0.200680i
\(191\) −13.6682 + 23.6740i −0.988994 + 1.71299i −0.366361 + 0.930473i \(0.619397\pi\)
−0.622632 + 0.782515i \(0.713937\pi\)
\(192\) 10.3375 + 17.9052i 0.746048 + 1.29219i
\(193\) −18.8511 + 10.8837i −1.35693 + 0.783425i −0.989209 0.146510i \(-0.953196\pi\)
−0.367723 + 0.929935i \(0.619863\pi\)
\(194\) −14.8413 −1.06555
\(195\) −0.0461428 + 8.40891i −0.00330436 + 0.602174i
\(196\) −3.05441 −0.218172
\(197\) −1.46940 + 0.848360i −0.104691 + 0.0604432i −0.551431 0.834220i \(-0.685918\pi\)
0.446741 + 0.894664i \(0.352585\pi\)
\(198\) −7.99131 13.8413i −0.567917 0.983662i
\(199\) 12.6627 21.9325i 0.897637 1.55475i 0.0671309 0.997744i \(-0.478615\pi\)
0.830506 0.557009i \(-0.188051\pi\)
\(200\) 3.06430i 0.216679i
\(201\) −12.9262 7.46296i −0.911746 0.526397i
\(202\) −4.28259 2.47256i −0.301322 0.173968i
\(203\) 0.0890252i 0.00624834i
\(204\) −0.676260 + 1.17132i −0.0473477 + 0.0820086i
\(205\) −1.86603 3.23205i −0.130329 0.225736i
\(206\) 18.9111 10.9183i 1.31760 0.760715i
\(207\) 9.49617 0.660030
\(208\) 9.78083 + 0.0536711i 0.678179 + 0.00372142i
\(209\) 12.1830 0.842716
\(210\) −8.86910 + 5.12058i −0.612026 + 0.353353i
\(211\) 0.167753 + 0.290558i 0.0115486 + 0.0200028i 0.871742 0.489965i \(-0.162991\pi\)
−0.860193 + 0.509968i \(0.829657\pi\)
\(212\) 1.13729 1.96984i 0.0781092 0.135289i
\(213\) 25.1820i 1.72544i
\(214\) 9.64579 + 5.56900i 0.659373 + 0.380689i
\(215\) 0.980215 + 0.565928i 0.0668501 + 0.0385959i
\(216\) 4.00663i 0.272616i
\(217\) −9.83592 + 17.0363i −0.667706 + 1.15650i
\(218\) 4.49824 + 7.79118i 0.304659 + 0.527685i
\(219\) 9.49922 5.48438i 0.641898 0.370600i
\(220\) −2.75232 −0.185562
\(221\) 2.02106 + 3.54536i 0.135951 + 0.238487i
\(222\) −24.7597 −1.66176
\(223\) −10.6493 + 6.14838i −0.713130 + 0.411726i −0.812219 0.583353i \(-0.801741\pi\)
0.0990887 + 0.995079i \(0.468407\pi\)
\(224\) −5.07606 8.79200i −0.339159 0.587440i
\(225\) 1.21969 2.11256i 0.0813125 0.140837i
\(226\) 8.63036i 0.574083i
\(227\) 6.60974 + 3.81613i 0.438704 + 0.253286i 0.703048 0.711143i \(-0.251822\pi\)
−0.264344 + 0.964428i \(0.585155\pi\)
\(228\) −2.34702 1.35505i −0.155435 0.0897406i
\(229\) 14.4008i 0.951631i 0.879545 + 0.475815i \(0.157847\pi\)
−0.879545 + 0.475815i \(0.842153\pi\)
\(230\) −2.37404 + 4.11196i −0.156540 + 0.271135i
\(231\) 22.5523 + 39.0618i 1.48384 + 2.57008i
\(232\) −0.0656218 + 0.0378868i −0.00430828 + 0.00248739i
\(233\) −9.49617 −0.622115 −0.311057 0.950391i \(-0.600683\pi\)
−0.311057 + 0.950391i \(0.600683\pi\)
\(234\) 9.26071 + 5.41465i 0.605392 + 0.353966i
\(235\) −2.58535 −0.168650
\(236\) 0.0760645 0.0439159i 0.00495138 0.00285868i
\(237\) 13.9732 + 24.2023i 0.907657 + 1.57211i
\(238\) −2.48505 + 4.30423i −0.161082 + 0.279002i
\(239\) 19.9143i 1.28815i −0.764962 0.644076i \(-0.777242\pi\)
0.764962 0.644076i \(-0.222758\pi\)
\(240\) −5.47918 3.16341i −0.353680 0.204197i
\(241\) 20.1493 + 11.6332i 1.29793 + 0.749360i 0.980046 0.198770i \(-0.0636947\pi\)
0.317883 + 0.948130i \(0.397028\pi\)
\(242\) 21.7792i 1.40002i
\(243\) 10.1286 17.5432i 0.649750 1.12540i
\(244\) −0.860832 1.49100i −0.0551091 0.0954518i
\(245\) 5.16273 2.98070i 0.329835 0.190430i
\(246\) −10.6162 −0.676866
\(247\) −7.10400 + 4.04968i −0.452017 + 0.257675i
\(248\) −16.7436 −1.06322
\(249\) −24.4972 + 14.1434i −1.55244 + 0.896304i
\(250\) 0.609843 + 1.05628i 0.0385699 + 0.0668050i
\(251\) 5.92008 10.2539i 0.373672 0.647219i −0.616455 0.787390i \(-0.711432\pi\)
0.990127 + 0.140171i \(0.0447652\pi\)
\(252\) 4.49969i 0.283454i
\(253\) 18.1101 + 10.4559i 1.13858 + 0.657357i
\(254\) −12.0797 6.97424i −0.757950 0.437603i
\(255\) 2.63977i 0.165309i
\(256\) 5.71040 9.89070i 0.356900 0.618169i
\(257\) −2.77501 4.80646i −0.173100 0.299819i 0.766402 0.642361i \(-0.222045\pi\)
−0.939502 + 0.342543i \(0.888712\pi\)
\(258\) 2.78833 1.60984i 0.173594 0.100224i
\(259\) 31.3363 1.94714
\(260\) 1.60490 0.914884i 0.0995317 0.0567387i
\(261\) −0.0603205 −0.00373375
\(262\) −11.1627 + 6.44481i −0.689636 + 0.398161i
\(263\) −3.42983 5.94065i −0.211493 0.366316i 0.740689 0.671848i \(-0.234499\pi\)
−0.952182 + 0.305532i \(0.901166\pi\)
\(264\) −19.1954 + 33.2474i −1.18139 + 2.04623i
\(265\) 4.43937i 0.272709i
\(266\) −8.62459 4.97941i −0.528807 0.305307i
\(267\) −32.6277 18.8376i −1.99678 1.15284i
\(268\) 3.27903i 0.200299i
\(269\) 0.710994 1.23148i 0.0433501 0.0750845i −0.843536 0.537072i \(-0.819530\pi\)
0.886886 + 0.461988i \(0.152864\pi\)
\(270\) 0.797382 + 1.38111i 0.0485271 + 0.0840514i
\(271\) 8.63381 4.98473i 0.524467 0.302801i −0.214294 0.976769i \(-0.568745\pi\)
0.738760 + 0.673968i \(0.235412\pi\)
\(272\) −3.07045 −0.186173
\(273\) −26.1347 15.2807i −1.58175 0.924831i
\(274\) 4.61862 0.279021
\(275\) 4.65213 2.68591i 0.280534 0.161966i
\(276\) −2.32591 4.02860i −0.140003 0.242493i
\(277\) −8.76187 + 15.1760i −0.526449 + 0.911837i 0.473076 + 0.881022i \(0.343144\pi\)
−0.999525 + 0.0308154i \(0.990190\pi\)
\(278\) 2.45628i 0.147318i
\(279\) −11.5432 6.66449i −0.691076 0.398993i
\(280\) 9.55405 + 5.51603i 0.570964 + 0.329646i
\(281\) 10.7352i 0.640406i −0.947349 0.320203i \(-0.896249\pi\)
0.947349 0.320203i \(-0.103751\pi\)
\(282\) −3.67716 + 6.36903i −0.218972 + 0.379270i
\(283\) 0.659192 + 1.14175i 0.0391849 + 0.0678702i 0.884953 0.465681i \(-0.154191\pi\)
−0.845768 + 0.533551i \(0.820857\pi\)
\(284\) −4.79099 + 2.76608i −0.284293 + 0.164137i
\(285\) 5.28942 0.313318
\(286\) 11.6992 + 20.5229i 0.691790 + 1.21355i
\(287\) 13.4361 0.793109
\(288\) 5.95717 3.43937i 0.351030 0.202667i
\(289\) 7.85945 + 13.6130i 0.462321 + 0.800763i
\(290\) 0.0150801 0.0261196i 0.000885536 0.00153379i
\(291\) 28.3792i 1.66362i
\(292\) −2.08685 1.20485i −0.122124 0.0705082i
\(293\) 16.2316 + 9.37133i 0.948261 + 0.547479i 0.892540 0.450968i \(-0.148921\pi\)
0.0557207 + 0.998446i \(0.482254\pi\)
\(294\) 16.9579i 0.989004i
\(295\) −0.0857123 + 0.148458i −0.00499036 + 0.00864356i
\(296\) 13.3359 + 23.0985i 0.775134 + 1.34257i
\(297\) 6.08275 3.51187i 0.352957 0.203780i
\(298\) 6.72998 0.389857
\(299\) −14.0357 0.0770194i −0.811708 0.00445415i
\(300\) −1.19496 −0.0689910
\(301\) −3.52897 + 2.03745i −0.203406 + 0.117437i
\(302\) 2.98190 + 5.16480i 0.171589 + 0.297201i
\(303\) −4.72794 + 8.18904i −0.271613 + 0.470448i
\(304\) 6.15239i 0.352864i
\(305\) 2.91005 + 1.68012i 0.166629 + 0.0962032i
\(306\) −2.91641 1.68379i −0.166720 0.0962558i
\(307\) 14.3043i 0.816387i −0.912895 0.408194i \(-0.866159\pi\)
0.912895 0.408194i \(-0.133841\pi\)
\(308\) 4.95445 8.58137i 0.282306 0.488969i
\(309\) −20.8777 36.1612i −1.18769 2.05714i
\(310\) 5.77162 3.33225i 0.327806 0.189259i
\(311\) −2.76102 −0.156563 −0.0782815 0.996931i \(-0.524943\pi\)
−0.0782815 + 0.996931i \(0.524943\pi\)
\(312\) 0.141395 25.7674i 0.00800494 1.45879i
\(313\) −16.3858 −0.926179 −0.463090 0.886311i \(-0.653259\pi\)
−0.463090 + 0.886311i \(0.653259\pi\)
\(314\) 10.6056 6.12316i 0.598510 0.345550i
\(315\) 4.39111 + 7.60563i 0.247411 + 0.428529i
\(316\) 3.06973 5.31693i 0.172686 0.299101i
\(317\) 1.78575i 0.100297i 0.998742 + 0.0501487i \(0.0159695\pi\)
−0.998742 + 0.0501487i \(0.984030\pi\)
\(318\) 10.9364 + 6.31414i 0.613284 + 0.354080i
\(319\) −0.115037 0.0664168i −0.00644085 0.00371863i
\(320\) 8.86488i 0.495562i
\(321\) 10.6489 18.4444i 0.594362 1.02946i
\(322\) −8.54702 14.8039i −0.476307 0.824987i
\(323\) 2.22308 1.28349i 0.123695 0.0714156i
\(324\) −5.31197 −0.295110
\(325\) −1.81988 + 3.11256i −0.100949 + 0.172654i
\(326\) 8.27099 0.458088
\(327\) 14.8980 8.60139i 0.823864 0.475658i
\(328\) 5.71806 + 9.90396i 0.315727 + 0.546855i
\(329\) 4.65389 8.06077i 0.256577 0.444405i
\(330\) 15.2807i 0.841176i
\(331\) −6.25652 3.61220i −0.343889 0.198545i 0.318101 0.948057i \(-0.396955\pi\)
−0.661991 + 0.749512i \(0.730288\pi\)
\(332\) 5.38170 + 3.10713i 0.295359 + 0.170526i
\(333\) 21.2325i 1.16353i
\(334\) −6.39714 + 11.0802i −0.350036 + 0.606280i
\(335\) −3.19990 5.54239i −0.174829 0.302813i
\(336\) 19.7261 11.3889i 1.07615 0.621315i
\(337\) 4.36219 0.237624 0.118812 0.992917i \(-0.462091\pi\)
0.118812 + 0.992917i \(0.462091\pi\)
\(338\) −13.6438 8.07818i −0.742125 0.439395i
\(339\) 16.5027 0.896303
\(340\) −0.502227 + 0.289961i −0.0272371 + 0.0157253i
\(341\) −14.6761 25.4197i −0.794754 1.37655i
\(342\) 3.37388 5.84374i 0.182439 0.315993i
\(343\) 3.73913i 0.201894i
\(344\) −3.00367 1.73417i −0.161947 0.0935002i
\(345\) 7.86276 + 4.53957i 0.423317 + 0.244402i
\(346\) 5.43792i 0.292344i
\(347\) 13.3536 23.1291i 0.716858 1.24163i −0.245381 0.969427i \(-0.578913\pi\)
0.962239 0.272207i \(-0.0877537\pi\)
\(348\) 0.0147744 + 0.0255900i 0.000791991 + 0.00137177i
\(349\) −20.4131 + 11.7855i −1.09269 + 0.630865i −0.934292 0.356510i \(-0.883967\pi\)
−0.158399 + 0.987375i \(0.550633\pi\)
\(350\) −4.39111 −0.234715
\(351\) −2.37953 + 4.06973i −0.127010 + 0.217226i
\(352\) 15.1479 0.807385
\(353\) 4.96862 2.86863i 0.264453 0.152682i −0.361911 0.932213i \(-0.617876\pi\)
0.626364 + 0.779531i \(0.284542\pi\)
\(354\) 0.243818 + 0.422305i 0.0129588 + 0.0224453i
\(355\) 5.39866 9.35076i 0.286531 0.496287i
\(356\) 8.27675i 0.438667i
\(357\) 8.23042 + 4.75184i 0.435600 + 0.251494i
\(358\) 19.6799 + 11.3622i 1.04011 + 0.600509i
\(359\) 24.7583i 1.30669i 0.757059 + 0.653347i \(0.226636\pi\)
−0.757059 + 0.653347i \(0.773364\pi\)
\(360\) −3.73748 + 6.47351i −0.196983 + 0.341184i
\(361\) −6.92820 12.0000i −0.364642 0.631579i
\(362\) −19.1081 + 11.0321i −1.00430 + 0.579833i
\(363\) −41.6455 −2.18582
\(364\) −0.0364951 + 6.65074i −0.00191286 + 0.348593i
\(365\) 4.70308 0.246171
\(366\) 8.27796 4.77928i 0.432696 0.249817i
\(367\) −13.0268 22.5630i −0.679992 1.17778i −0.974983 0.222280i \(-0.928650\pi\)
0.294991 0.955500i \(-0.404683\pi\)
\(368\) 5.28021 9.14558i 0.275250 0.476747i
\(369\) 9.10387i 0.473928i
\(370\) −9.19393 5.30812i −0.477969 0.275956i
\(371\) −13.8413 7.99131i −0.718607 0.414888i
\(372\) 6.52938i 0.338532i
\(373\) −6.60224 + 11.4354i −0.341851 + 0.592103i −0.984776 0.173826i \(-0.944387\pi\)
0.642926 + 0.765929i \(0.277720\pi\)
\(374\) −3.70792 6.42231i −0.191732 0.332089i
\(375\) 2.01978 1.16612i 0.104301 0.0602183i
\(376\) 7.92229 0.408561
\(377\) 0.0891563 0.000489234i 0.00459178 2.51968e-5i
\(378\) −5.74146 −0.295309
\(379\) 22.5147 12.9989i 1.15650 0.667707i 0.206039 0.978544i \(-0.433943\pi\)
0.950463 + 0.310837i \(0.100609\pi\)
\(380\) −0.581008 1.00633i −0.0298051 0.0516239i
\(381\) −13.3359 + 23.0985i −0.683220 + 1.18337i
\(382\) 33.3418i 1.70591i
\(383\) 8.31401 + 4.80010i 0.424826 + 0.245274i 0.697140 0.716935i \(-0.254456\pi\)
−0.272314 + 0.962208i \(0.587789\pi\)
\(384\) 10.4476 + 6.03191i 0.533151 + 0.307815i
\(385\) 19.3396i 0.985637i
\(386\) −13.2747 + 22.9924i −0.675664 + 1.17028i
\(387\) −1.38051 2.39111i −0.0701752 0.121547i
\(388\) 5.39926 3.11726i 0.274106 0.158255i
\(389\) −5.63129 −0.285518 −0.142759 0.989758i \(-0.545597\pi\)
−0.142759 + 0.989758i \(0.545597\pi\)
\(390\) 5.07938 + 8.91030i 0.257204 + 0.451191i
\(391\) 4.40617 0.222829
\(392\) −15.8201 + 9.13376i −0.799038 + 0.461325i
\(393\) 12.3236 + 21.3450i 0.621641 + 1.07671i
\(394\) −1.03473 + 1.79221i −0.0521291 + 0.0902903i
\(395\) 11.9826i 0.602911i
\(396\) 5.81445 + 3.35697i 0.292187 + 0.168694i
\(397\) −14.5196 8.38291i −0.728719 0.420726i 0.0892344 0.996011i \(-0.471558\pi\)
−0.817953 + 0.575285i \(0.804891\pi\)
\(398\) 30.8891i 1.54833i
\(399\) −9.52147 + 16.4917i −0.476670 + 0.825616i
\(400\) −1.35638 2.34932i −0.0678189 0.117466i
\(401\) 12.0187 6.93902i 0.600187 0.346518i −0.168928 0.985628i \(-0.554031\pi\)
0.769115 + 0.639110i \(0.220697\pi\)
\(402\) −18.2050 −0.907980
\(403\) 17.0073 + 9.94402i 0.847196 + 0.495347i
\(404\) 2.07733 0.103351
\(405\) 8.97859 5.18379i 0.446149 0.257585i
\(406\) 0.0542914 + 0.0940355i 0.00269444 + 0.00466690i
\(407\) −23.3783 + 40.4924i −1.15882 + 2.00713i
\(408\) 8.08903i 0.400466i
\(409\) −25.4829 14.7125i −1.26005 0.727489i −0.286964 0.957941i \(-0.592646\pi\)
−0.973083 + 0.230453i \(0.925979\pi\)
\(410\) −3.94209 2.27597i −0.194686 0.112402i
\(411\) 8.83157i 0.435629i
\(412\) −4.58655 + 7.94413i −0.225963 + 0.391379i
\(413\) −0.308581 0.534478i −0.0151843 0.0262999i
\(414\) 10.0306 5.79118i 0.492978 0.284621i
\(415\) −12.1286 −0.595369
\(416\) −8.83284 + 5.03522i −0.433066 + 0.246872i
\(417\) 4.69683 0.230005
\(418\) 12.8687 7.42973i 0.629427 0.363400i
\(419\) −3.48397 6.03440i −0.170203 0.294800i 0.768288 0.640104i \(-0.221109\pi\)
−0.938491 + 0.345305i \(0.887776\pi\)
\(420\) 2.15104 3.72572i 0.104960 0.181796i
\(421\) 7.12125i 0.347069i 0.984828 + 0.173534i \(0.0555188\pi\)
−0.984828 + 0.173534i \(0.944481\pi\)
\(422\) 0.354389 + 0.204607i 0.0172514 + 0.00996010i
\(423\) 5.46171 + 3.15332i 0.265558 + 0.153320i
\(424\) 13.6036i 0.660647i
\(425\) 0.565928 0.980215i 0.0274515 0.0475474i
\(426\) −15.3571 26.5993i −0.744054 1.28874i
\(427\) −10.4767 + 6.04875i −0.507005 + 0.292720i
\(428\) −4.67883 −0.226160
\(429\) 39.2433 22.3709i 1.89468 1.08008i
\(430\) 1.38051 0.0665740
\(431\) 26.1664 15.1072i 1.26039 0.727687i 0.287241 0.957858i \(-0.407262\pi\)
0.973150 + 0.230171i \(0.0739286\pi\)
\(432\) −1.77349 3.07177i −0.0853270 0.147791i
\(433\) 0.600065 1.03934i 0.0288373 0.0499476i −0.851247 0.524766i \(-0.824153\pi\)
0.880084 + 0.474818i \(0.157486\pi\)
\(434\) 23.9935i 1.15172i
\(435\) −0.0499450 0.0288357i −0.00239468 0.00138257i
\(436\) −3.27290 1.88961i −0.156744 0.0904960i
\(437\) 8.82884i 0.422341i
\(438\) 6.68922 11.5861i 0.319623 0.553604i
\(439\) −8.27705 14.3363i −0.395042 0.684233i 0.598064 0.801448i \(-0.295937\pi\)
−0.993107 + 0.117215i \(0.962603\pi\)
\(440\) −14.2555 + 8.23042i −0.679605 + 0.392370i
\(441\) −14.5421 −0.692481
\(442\) 4.29692 + 2.51236i 0.204383 + 0.119501i
\(443\) 4.55949 0.216628 0.108314 0.994117i \(-0.465455\pi\)
0.108314 + 0.994117i \(0.465455\pi\)
\(444\) 9.00753 5.20050i 0.427478 0.246805i
\(445\) −8.07702 13.9898i −0.382887 0.663180i
\(446\) −7.49910 + 12.9888i −0.355093 + 0.615038i
\(447\) 12.8689i 0.608676i
\(448\) −27.6395 15.9577i −1.30584 0.753929i
\(449\) 11.9963 + 6.92608i 0.566142 + 0.326862i 0.755607 0.655025i \(-0.227342\pi\)
−0.189465 + 0.981887i \(0.560675\pi\)
\(450\) 2.97527i 0.140256i
\(451\) −10.0239 + 17.3620i −0.472009 + 0.817544i
\(452\) −1.81271 3.13971i −0.0852628 0.147680i
\(453\) 9.87596 5.70189i 0.464013 0.267898i
\(454\) 9.30897 0.436892
\(455\) −6.42856 11.2771i −0.301376 0.528676i
\(456\) −16.2083 −0.759025
\(457\) 34.7402 20.0573i 1.62508 0.938240i 0.639548 0.768751i \(-0.279122\pi\)
0.985532 0.169489i \(-0.0542117\pi\)
\(458\) 8.78222 + 15.2113i 0.410366 + 0.710775i
\(459\) 0.739961 1.28165i 0.0345384 0.0598223i
\(460\) 1.99457i 0.0929972i
\(461\) 6.52897 + 3.76950i 0.304084 + 0.175563i 0.644276 0.764793i \(-0.277159\pi\)
−0.340192 + 0.940356i \(0.610492\pi\)
\(462\) 47.6432 + 27.5068i 2.21656 + 1.27973i
\(463\) 23.3031i 1.08299i −0.840705 0.541494i \(-0.817859\pi\)
0.840705 0.541494i \(-0.182141\pi\)
\(464\) −0.0335403 + 0.0580936i −0.00155707 + 0.00269693i
\(465\) −6.37182 11.0363i −0.295486 0.511797i
\(466\) −10.0306 + 5.79118i −0.464659 + 0.268271i
\(467\) 22.6297 1.04718 0.523589 0.851971i \(-0.324593\pi\)
0.523589 + 0.851971i \(0.324593\pi\)
\(468\) −4.50632 0.0247279i −0.208305 0.00114305i
\(469\) 23.0405 1.06391
\(470\) −2.73086 + 1.57666i −0.125965 + 0.0727260i
\(471\) −11.7085 20.2797i −0.539500 0.934441i
\(472\) 0.262648 0.454919i 0.0120893 0.0209394i
\(473\) 6.08012i 0.279564i
\(474\) 29.5192 + 17.0429i 1.35586 + 0.782808i
\(475\) 1.96410 + 1.13397i 0.0901192 + 0.0520303i
\(476\) 2.08783i 0.0956956i
\(477\) 5.41465 9.37844i 0.247920 0.429409i
\(478\) −12.1446 21.0351i −0.555482 0.962124i
\(479\) −17.8789 + 10.3224i −0.816910 + 0.471643i −0.849350 0.527831i \(-0.823006\pi\)
0.0324399 + 0.999474i \(0.489672\pi\)
\(480\) 6.57666 0.300182
\(481\) 0.172207 31.3825i 0.00785198 1.43092i
\(482\) 28.3777 1.29257
\(483\) −28.3075 + 16.3433i −1.28804 + 0.743648i
\(484\) 4.57449 + 7.92325i 0.207931 + 0.360148i
\(485\) −6.08408 + 10.5379i −0.276264 + 0.478503i
\(486\) 24.7074i 1.12075i
\(487\) −2.62929 1.51802i −0.119145 0.0687882i 0.439243 0.898368i \(-0.355247\pi\)
−0.558388 + 0.829580i \(0.688580\pi\)
\(488\) −8.91725 5.14838i −0.403665 0.233056i
\(489\) 15.8155i 0.715203i
\(490\) 3.63553 6.29692i 0.164236 0.284466i
\(491\) 5.33401 + 9.23877i 0.240720 + 0.416940i 0.960920 0.276827i \(-0.0892830\pi\)
−0.720199 + 0.693767i \(0.755950\pi\)
\(492\) 3.86217 2.22982i 0.174120 0.100528i
\(493\) −0.0279884 −0.00126053
\(494\) −5.03414 + 8.60992i −0.226497 + 0.387379i
\(495\) −13.1039 −0.588975
\(496\) −12.8369 + 7.41139i −0.576394 + 0.332781i
\(497\) 19.4362 + 33.6646i 0.871835 + 1.51006i
\(498\) −17.2506 + 29.8789i −0.773016 + 1.33890i
\(499\) 33.9143i 1.51821i 0.650966 + 0.759107i \(0.274364\pi\)
−0.650966 + 0.759107i \(0.725636\pi\)
\(500\) −0.443720 0.256182i −0.0198438 0.0114568i
\(501\) 21.1872 + 12.2324i 0.946572 + 0.546504i
\(502\) 14.4413i 0.644546i
\(503\) 6.31380 10.9358i 0.281518 0.487604i −0.690241 0.723580i \(-0.742495\pi\)
0.971759 + 0.235976i \(0.0758286\pi\)
\(504\) −13.4557 23.3059i −0.599363 1.03813i
\(505\) −3.51122 + 2.02721i −0.156247 + 0.0902095i
\(506\) 25.5058 1.13387
\(507\) −15.4468 + 26.0893i −0.686019 + 1.15866i
\(508\) 5.85945 0.259971
\(509\) −20.9168 + 12.0763i −0.927120 + 0.535273i −0.885899 0.463877i \(-0.846458\pi\)
−0.0412201 + 0.999150i \(0.513124\pi\)
\(510\) −1.60984 2.78833i −0.0712851 0.123469i
\(511\) −8.46601 + 14.6636i −0.374514 + 0.648678i
\(512\) 24.2750i 1.07281i
\(513\) 2.56810 + 1.48269i 0.113384 + 0.0654625i
\(514\) −5.86238 3.38465i −0.258578 0.149290i
\(515\) 17.9035i 0.788921i
\(516\) −0.676260 + 1.17132i −0.0297707 + 0.0515644i
\(517\) 6.94402 + 12.0274i 0.305398 + 0.528964i
\(518\) 33.0999 19.1103i 1.45433 0.839656i
\(519\) 10.3982 0.456431
\(520\) 5.57666 9.53781i 0.244553 0.418261i
\(521\) −24.7521 −1.08441 −0.542205 0.840246i \(-0.682410\pi\)
−0.542205 + 0.840246i \(0.682410\pi\)
\(522\) −0.0637154 + 0.0367861i −0.00278875 + 0.00161008i
\(523\) −18.5163 32.0712i −0.809662 1.40238i −0.913098 0.407739i \(-0.866317\pi\)
0.103436 0.994636i \(-0.467016\pi\)
\(524\) 2.70732 4.68922i 0.118270 0.204850i
\(525\) 8.39654i 0.366455i
\(526\) −7.24573 4.18332i −0.315929 0.182402i
\(527\) −5.35600 3.09229i −0.233311 0.134702i
\(528\) 33.9865i 1.47907i
\(529\) 3.92277 6.79444i 0.170555 0.295410i
\(530\) 2.70732 + 4.68922i 0.117599 + 0.203687i
\(531\) 0.362145 0.209084i 0.0157157 0.00907348i
\(532\) 4.18348 0.181377
\(533\) 0.0738376 13.4559i 0.00319826 0.582840i
\(534\) −45.9519 −1.98854
\(535\) 7.90842 4.56593i 0.341911 0.197402i
\(536\) 9.80545 + 16.9835i 0.423531 + 0.733577i
\(537\) 21.7264 37.6312i 0.937562 1.62391i
\(538\) 1.73438i 0.0747744i
\(539\) −27.7332 16.0118i −1.19456 0.689677i
\(540\) −0.580172 0.334963i −0.0249666 0.0144145i
\(541\) 8.38144i 0.360346i 0.983635 + 0.180173i \(0.0576658\pi\)
−0.983635 + 0.180173i \(0.942334\pi\)
\(542\) 6.07981 10.5305i 0.261150 0.452326i
\(543\) 21.0952 + 36.5379i 0.905281 + 1.56799i
\(544\) 2.76409 1.59585i 0.118509 0.0684215i
\(545\) 7.37605 0.315955
\(546\) −36.9245 0.202618i −1.58022 0.00867126i
\(547\) −22.7842 −0.974181 −0.487091 0.873351i \(-0.661942\pi\)
−0.487091 + 0.873351i \(0.661942\pi\)
\(548\) −1.68025 + 0.970090i −0.0717765 + 0.0414402i
\(549\) −4.09843 7.09870i −0.174917 0.302965i
\(550\) 3.27597 5.67414i 0.139688 0.241946i
\(551\) 0.0560816i 0.00238915i
\(552\) −24.0938 13.9106i −1.02550 0.592074i
\(553\) −37.3601 21.5699i −1.58871 0.917245i
\(554\) 21.3735i 0.908071i
\(555\) −10.1500 + 17.5803i −0.430844 + 0.746244i
\(556\) −0.515915 0.893592i −0.0218797 0.0378967i
\(557\) 24.3810 14.0764i 1.03306 0.596435i 0.115197 0.993343i \(-0.463250\pi\)
0.917858 + 0.396908i \(0.129917\pi\)
\(558\) −16.2572 −0.688222
\(559\) 2.02106 + 3.54536i 0.0854816 + 0.149953i
\(560\) 9.76645 0.412708
\(561\) −12.2805 + 7.09017i −0.518484 + 0.299347i
\(562\) −6.54676 11.3393i −0.276159 0.478321i
\(563\) −9.06514 + 15.7013i −0.382050 + 0.661731i −0.991355 0.131206i \(-0.958115\pi\)
0.609305 + 0.792936i \(0.291449\pi\)
\(564\) 3.08939i 0.130087i
\(565\) 6.12789 + 3.53794i 0.257802 + 0.148842i
\(566\) 1.39258 + 0.804007i 0.0585346 + 0.0337950i
\(567\) 37.3253i 1.56752i
\(568\) −16.5431 + 28.6535i −0.694133 + 1.20227i
\(569\) 20.2992 + 35.1593i 0.850988 + 1.47395i 0.880317 + 0.474385i \(0.157330\pi\)
−0.0293292 + 0.999570i \(0.509337\pi\)
\(570\) 5.58710 3.22572i 0.234018 0.135110i
\(571\) −24.7159 −1.03433 −0.517164 0.855886i \(-0.673012\pi\)
−0.517164 + 0.855886i \(0.673012\pi\)
\(572\) −8.56677 5.00891i −0.358195 0.209433i
\(573\) 63.7551 2.66341
\(574\) 14.1923 8.19393i 0.592375 0.342008i
\(575\) 1.94644 + 3.37133i 0.0811720 + 0.140594i
\(576\) 10.8124 18.7276i 0.450516 0.780317i
\(577\) 23.0691i 0.960379i 0.877165 + 0.480189i \(0.159432\pi\)
−0.877165 + 0.480189i \(0.840568\pi\)
\(578\) 16.6036 + 9.58607i 0.690617 + 0.398728i
\(579\) 43.9654 + 25.3834i 1.82714 + 1.05490i
\(580\) 0.0126697i 0.000526079i
\(581\) 21.8327 37.8153i 0.905771 1.56884i
\(582\) 17.3068 + 29.9763i 0.717392 + 1.24256i
\(583\) 20.6525 11.9237i 0.855341 0.493831i
\(584\) −14.4116 −0.596358
\(585\) 7.64096 4.35578i 0.315915 0.180089i
\(586\) 22.8602 0.944345
\(587\) −17.6256 + 10.1762i −0.727487 + 0.420015i −0.817502 0.575926i \(-0.804642\pi\)
0.0900152 + 0.995940i \(0.471308\pi\)
\(588\) 3.56182 + 6.16925i 0.146887 + 0.254416i
\(589\) 6.19615 10.7321i 0.255308 0.442206i
\(590\) 0.209084i 0.00860786i
\(591\) 3.42701 + 1.97859i 0.140968 + 0.0813881i
\(592\) 20.4486 + 11.8060i 0.840432 + 0.485223i
\(593\) 10.3834i 0.426395i −0.977009 0.213198i \(-0.931612\pi\)
0.977009 0.213198i \(-0.0683878\pi\)
\(594\) 4.28339 7.41904i 0.175750 0.304407i
\(595\) 2.03745 + 3.52897i 0.0835273 + 0.144674i
\(596\) −2.44836 + 1.41356i −0.100289 + 0.0579017i
\(597\) −59.0652 −2.41738
\(598\) −14.8726 + 8.47825i −0.608187 + 0.346701i
\(599\) −31.5965 −1.29100 −0.645499 0.763761i \(-0.723351\pi\)
−0.645499 + 0.763761i \(0.723351\pi\)
\(600\) −6.18922 + 3.57335i −0.252674 + 0.145881i
\(601\) 21.9423 + 38.0051i 0.895044 + 1.55026i 0.833751 + 0.552141i \(0.186189\pi\)
0.0612928 + 0.998120i \(0.480478\pi\)
\(602\) −2.48505 + 4.30423i −0.101283 + 0.175428i
\(603\) 15.6115i 0.635750i
\(604\) −2.16962 1.25263i −0.0882806 0.0509688i
\(605\) −15.4641 8.92820i −0.628705 0.362983i
\(606\) 11.5332i 0.468505i
\(607\) −1.08770 + 1.88395i −0.0441484 + 0.0764673i −0.887255 0.461279i \(-0.847391\pi\)
0.843107 + 0.537746i \(0.180724\pi\)
\(608\) 3.19768 + 5.53854i 0.129683 + 0.224617i
\(609\) 0.179812 0.103814i 0.00728634 0.00420677i
\(610\) 4.09843 0.165941
\(611\) −8.04707 4.70504i −0.325550 0.190346i
\(612\) 1.41465 0.0571837
\(613\) −12.7843 + 7.38100i −0.516352 + 0.298116i −0.735441 0.677589i \(-0.763025\pi\)
0.219089 + 0.975705i \(0.429691\pi\)
\(614\) −8.72336 15.1093i −0.352046 0.609762i
\(615\) −4.35203 + 7.53794i −0.175491 + 0.303959i
\(616\) 59.2622i 2.38774i
\(617\) 17.5779 + 10.1486i 0.707659 + 0.408567i 0.810194 0.586162i \(-0.199362\pi\)
−0.102535 + 0.994729i \(0.532695\pi\)
\(618\) −44.1053 25.4642i −1.77418 1.02432i
\(619\) 9.94207i 0.399605i −0.979836 0.199803i \(-0.935970\pi\)
0.979836 0.199803i \(-0.0640301\pi\)
\(620\) −1.39980 + 2.42453i −0.0562175 + 0.0973716i
\(621\) 2.54500 + 4.40807i 0.102127 + 0.176890i
\(622\) −2.91641 + 1.68379i −0.116937 + 0.0675138i
\(623\) 58.1577 2.33004
\(624\) −11.2973 19.8178i −0.452252 0.793345i
\(625\) 1.00000 0.0400000
\(626\) −17.3080 + 9.99276i −0.691766 + 0.399391i
\(627\) −14.2069 24.6070i −0.567368 0.982711i
\(628\) −2.57221 + 4.45519i −0.102642 + 0.177782i
\(629\) 9.85174i 0.392815i
\(630\) 9.27648 + 5.35578i 0.369584 + 0.213379i
\(631\) 0.843006 + 0.486710i 0.0335596 + 0.0193756i 0.516686 0.856175i \(-0.327165\pi\)
−0.483126 + 0.875551i \(0.660499\pi\)
\(632\) 36.7183i 1.46058i
\(633\) 0.391243 0.677652i 0.0155505 0.0269342i
\(634\) 1.08903 + 1.88625i 0.0432507 + 0.0749124i
\(635\) −9.90396 + 5.71806i −0.393027 + 0.226914i
\(636\) −5.30487 −0.210352
\(637\) 21.4938 + 0.117945i 0.851617 + 0.00467314i
\(638\) −0.162015 −0.00641425
\(639\) −22.8100 + 13.1694i −0.902350 + 0.520972i
\(640\) 2.58631 + 4.47962i 0.102233 + 0.177072i
\(641\) −6.31047 + 10.9301i −0.249249 + 0.431711i −0.963318 0.268364i \(-0.913517\pi\)
0.714069 + 0.700075i \(0.246850\pi\)
\(642\) 25.9766i 1.02521i
\(643\) −8.62599 4.98022i −0.340176 0.196401i 0.320174 0.947359i \(-0.396259\pi\)
−0.660350 + 0.750958i \(0.729592\pi\)
\(644\) 6.21878 + 3.59042i 0.245054 + 0.141482i
\(645\) 2.63977i 0.103941i
\(646\) 1.56546 2.71146i 0.0615923 0.106681i
\(647\) −18.1381 31.4162i −0.713084 1.23510i −0.963694 0.267009i \(-0.913965\pi\)
0.250610 0.968088i \(-0.419369\pi\)
\(648\) −27.5131 + 15.8847i −1.08081 + 0.624009i
\(649\) 0.920861 0.0361470
\(650\) −0.0241312 + 4.39758i −0.000946502 + 0.172487i
\(651\) 45.8796 1.79816
\(652\) −3.00898 + 1.73723i −0.117841 + 0.0680353i
\(653\) −6.87769 11.9125i −0.269145 0.466172i 0.699497 0.714636i \(-0.253408\pi\)
−0.968641 + 0.248464i \(0.920074\pi\)
\(654\) 10.4910 18.1709i 0.410231 0.710540i
\(655\) 10.5680i 0.412925i
\(656\) 8.76776 + 5.06207i 0.342324 + 0.197641i
\(657\) −9.93555 5.73629i −0.387623 0.223794i
\(658\) 11.3526i 0.442570i
\(659\) 1.29092 2.23593i 0.0502869 0.0870995i −0.839786 0.542917i \(-0.817320\pi\)
0.890073 + 0.455818i \(0.150653\pi\)
\(660\) 3.20955 + 5.55910i 0.124932 + 0.216388i
\(661\) −21.5437 + 12.4382i −0.837951 + 0.483791i −0.856567 0.516036i \(-0.827407\pi\)
0.0186163 + 0.999827i \(0.494074\pi\)
\(662\) −8.81151 −0.342469
\(663\) 4.80406 8.21643i 0.186574 0.319100i
\(664\) 37.1656 1.44231
\(665\) −7.07115 + 4.08253i −0.274207 + 0.158314i
\(666\) 12.9485 + 22.4274i 0.501743 + 0.869045i
\(667\) 0.0481312 0.0833657i 0.00186365 0.00322793i
\(668\) 5.37460i 0.207949i
\(669\) 24.8368 + 14.3395i 0.960246 + 0.554398i
\(670\) −6.75998 3.90288i −0.261161 0.150781i
\(671\) 18.0506i 0.696834i
\(672\) −11.8386 + 20.5051i −0.456685 + 0.791002i
\(673\) 21.6611 + 37.5181i 0.834974 + 1.44622i 0.894052 + 0.447964i \(0.147851\pi\)
−0.0590774 + 0.998253i \(0.518816\pi\)
\(674\) 4.60770 2.66025i 0.177482 0.102469i
\(675\) 1.30752 0.0503264
\(676\) 6.66033 + 0.0730977i 0.256167 + 0.00281145i
\(677\) −41.3625 −1.58969 −0.794845 0.606813i \(-0.792448\pi\)
−0.794845 + 0.606813i \(0.792448\pi\)
\(678\) 17.4315 10.0641i 0.669451 0.386508i
\(679\) −21.9039 37.9386i −0.840594 1.45595i
\(680\) −1.73417 + 3.00367i −0.0665024 + 0.115186i
\(681\) 17.8003i 0.682110i
\(682\) −31.0041 17.9002i −1.18721 0.685435i
\(683\) 2.27495 + 1.31344i 0.0870484 + 0.0502574i 0.542892 0.839802i \(-0.317329\pi\)
−0.455844 + 0.890060i \(0.650662\pi\)
\(684\) 2.83459i 0.108383i
\(685\) 1.89336 3.27940i 0.0723416 0.125299i
\(686\) −2.28028 3.94957i −0.0870617 0.150795i
\(687\) 29.0865 16.7931i 1.10972 0.640696i
\(688\) −3.07045 −0.117060
\(689\) −8.07914 + 13.8178i −0.307791 + 0.526417i
\(690\) 11.0737 0.421569
\(691\) −13.2288 + 7.63765i −0.503247 + 0.290550i −0.730053 0.683390i \(-0.760505\pi\)
0.226806 + 0.973940i \(0.427172\pi\)
\(692\) −1.14218 1.97831i −0.0434190 0.0752039i
\(693\) 23.5882 40.8560i 0.896043 1.55199i
\(694\) 32.5744i 1.23651i
\(695\) 1.74406 + 1.00693i 0.0661558 + 0.0381951i
\(696\) 0.153046 + 0.0883613i 0.00580120 + 0.00334933i
\(697\) 4.22414i 0.160001i
\(698\) −14.3747 + 24.8976i −0.544089 + 0.942390i
\(699\) 11.0737 + 19.1802i 0.418846 + 0.725463i
\(700\) 1.59748 0.922305i 0.0603790 0.0348599i
\(701\) 48.1947 1.82029 0.910144 0.414292i \(-0.135971\pi\)
0.910144 + 0.414292i \(0.135971\pi\)
\(702\) −0.0315519 + 5.74991i −0.00119085 + 0.217017i
\(703\) −19.7404 −0.744522
\(704\) 41.2406 23.8103i 1.55431 0.897383i
\(705\) 3.01484 + 5.22186i 0.113546 + 0.196667i
\(706\) 3.49884 6.06016i 0.131680 0.228077i
\(707\) 14.5967i 0.548964i
\(708\) −0.177401 0.102423i −0.00666715 0.00384928i
\(709\) −33.6624 19.4350i −1.26422 0.729896i −0.290329 0.956927i \(-0.593765\pi\)
−0.973887 + 0.227031i \(0.927098\pi\)
\(710\) 13.1694i 0.494237i
\(711\) 14.6150 25.3140i 0.548107 0.949349i
\(712\) 24.7504 + 42.8689i 0.927560 + 1.60658i
\(713\) 18.4213 10.6355i 0.689882 0.398304i
\(714\) 11.5915 0.433801
\(715\) 19.3681 + 0.106280i 0.724325 + 0.00397464i
\(716\) −9.54600 −0.356751
\(717\) −40.2227 + 23.2226i −1.50214 + 0.867263i
\(718\) 15.0987 + 26.1517i 0.563478 + 0.975973i
\(719\) 3.30830 5.73015i 0.123379 0.213698i −0.797719 0.603029i \(-0.793960\pi\)
0.921098 + 0.389331i \(0.127294\pi\)
\(720\) 6.61742i 0.246617i
\(721\) 55.8205 + 32.2280i 2.07887 + 1.20023i
\(722\) −14.6362 8.45024i −0.544705 0.314485i
\(723\) 54.2629i 2.01806i
\(724\) 4.63433 8.02690i 0.172234 0.298317i
\(725\) −0.0123639 0.0214150i −0.000459185 0.000795332i
\(726\) −43.9893 + 25.3973i −1.63260 + 0.942581i
\(727\) 18.3735 0.681435 0.340717 0.940166i \(-0.389330\pi\)
0.340717 + 0.940166i \(0.389330\pi\)
\(728\) 19.6990 + 34.5562i 0.730094 + 1.28074i
\(729\) −16.1420 −0.597853
\(730\) 4.96777 2.86814i 0.183866 0.106155i
\(731\) −0.640548 1.10946i −0.0236915 0.0410349i
\(732\) −2.00767 + 3.47739i −0.0742057 + 0.128528i
\(733\) 0.791131i 0.0292211i 0.999893 + 0.0146105i \(0.00465084\pi\)
−0.999893 + 0.0146105i \(0.995349\pi\)
\(734\) −27.5198 15.8886i −1.01578 0.586458i
\(735\) −12.0408 6.95174i −0.444130 0.256419i
\(736\) 10.9774i 0.404634i
\(737\) −17.1893 + 29.7727i −0.633175 + 1.09669i
\(738\) 5.55193 + 9.61623i 0.204369 + 0.353978i
\(739\) −27.0073 + 15.5926i −0.993478 + 0.573585i −0.906312 0.422609i \(-0.861114\pi\)
−0.0871658 + 0.996194i \(0.527781\pi\)
\(740\) 4.45965 0.163940
\(741\) 16.4636 + 9.62612i 0.604806 + 0.353624i
\(742\) −19.4938 −0.715639
\(743\) 4.81773 2.78152i 0.176745 0.102044i −0.409017 0.912527i \(-0.634128\pi\)
0.585763 + 0.810483i \(0.300795\pi\)
\(744\) 19.5251 + 33.8185i 0.715826 + 1.23985i
\(745\) 2.75890 4.77855i 0.101078 0.175073i
\(746\) 16.1053i 0.589658i
\(747\) 25.6224 + 14.7931i 0.937474 + 0.541251i
\(748\) 2.69787 + 1.55762i 0.0986439 + 0.0569521i
\(749\) 32.8765i 1.20128i
\(750\) 1.42231 2.46350i 0.0519352 0.0899545i
\(751\) −17.6048 30.4925i −0.642410 1.11269i −0.984893 0.173163i \(-0.944601\pi\)
0.342483 0.939524i \(-0.388732\pi\)
\(752\) 6.07381 3.50672i 0.221489 0.127877i
\(753\) −27.6142 −1.00632
\(754\) 0.0944723 0.0538546i 0.00344048 0.00196127i
\(755\) 4.88961 0.177951
\(756\) 2.08873 1.20593i 0.0759665 0.0438593i
\(757\) −25.0223 43.3399i −0.909451 1.57522i −0.814828 0.579703i \(-0.803169\pi\)
−0.0946237 0.995513i \(-0.530165\pi\)
\(758\) 15.8545 27.4609i 0.575863 0.997424i
\(759\) 48.7715i 1.77029i
\(760\) −6.01859 3.47484i −0.218317 0.126046i
\(761\) 38.8161 + 22.4105i 1.40708 + 0.812379i 0.995106 0.0988165i \(-0.0315057\pi\)
0.411975 + 0.911195i \(0.364839\pi\)
\(762\) 32.5313i 1.17848i
\(763\) −13.2776 + 22.9975i −0.480682 + 0.832566i
\(764\) −7.00307 12.1297i −0.253362 0.438836i
\(765\) −2.39111 + 1.38051i −0.0864508 + 0.0499124i
\(766\) 11.7092 0.423072
\(767\) −0.536961 + 0.306098i −0.0193885 + 0.0110526i
\(768\) −26.6361 −0.961148
\(769\) −34.0897 + 19.6817i −1.22930 + 0.709739i −0.966884 0.255215i \(-0.917854\pi\)
−0.262420 + 0.964954i \(0.584521\pi\)
\(770\) 11.7941 + 20.4280i 0.425031 + 0.736175i
\(771\) −6.47201 + 11.2099i −0.233084 + 0.403713i
\(772\) 11.1528i 0.401399i
\(773\) −42.2452 24.3902i −1.51945 0.877256i −0.999737 0.0229167i \(-0.992705\pi\)
−0.519715 0.854340i \(-0.673962\pi\)
\(774\) −2.91641 1.68379i −0.104828 0.0605225i
\(775\) 5.46410i