Properties

Label 403.2.l.c.25.13
Level 403
Weight 2
Character 403.25
Analytic conductor 3.218
Analytic rank 0
Dimension 68
CM No

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Newspace parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.l (of order \(6\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(68\)
Relative dimension: \(34\) over \(\Q(\zeta_{6})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 25.13
Character \(\chi\) = 403.25
Dual form 403.2.l.c.129.22

$q$-expansion

\(f(q)\) \(=\) \(q-0.909522i q^{2} +(0.193979 + 0.335982i) q^{3} +1.17277 q^{4} +(3.26453 + 1.88478i) q^{5} +(0.305583 - 0.176429i) q^{6} +(-3.57672 + 2.06502i) q^{7} -2.88570i q^{8} +(1.42474 - 2.46773i) q^{9} +O(q^{10})\) \(q-0.909522i q^{2} +(0.193979 + 0.335982i) q^{3} +1.17277 q^{4} +(3.26453 + 1.88478i) q^{5} +(0.305583 - 0.176429i) q^{6} +(-3.57672 + 2.06502i) q^{7} -2.88570i q^{8} +(1.42474 - 2.46773i) q^{9} +(1.71425 - 2.96916i) q^{10} +(-0.310190 - 0.179088i) q^{11} +(0.227493 + 0.394029i) q^{12} +(2.94922 + 2.07415i) q^{13} +(1.87818 + 3.25311i) q^{14} +1.46243i q^{15} -0.279074 q^{16} +(-0.359393 - 0.622486i) q^{17} +(-2.24445 - 1.29584i) q^{18} +(-5.27077 + 3.04308i) q^{19} +(3.82854 + 2.21041i) q^{20} +(-1.38762 - 0.801142i) q^{21} +(-0.162885 + 0.282124i) q^{22} +5.38696 q^{23} +(0.969545 - 0.559767i) q^{24} +(4.60478 + 7.97571i) q^{25} +(1.88648 - 2.68238i) q^{26} +2.26936 q^{27} +(-4.19467 + 2.42179i) q^{28} -5.79655 q^{29} +1.33011 q^{30} +(-2.82668 - 4.79686i) q^{31} -5.51758i q^{32} -0.138957i q^{33} +(-0.566165 + 0.326876i) q^{34} -15.5684 q^{35} +(1.67090 - 2.89408i) q^{36} +(5.77708 - 3.33540i) q^{37} +(2.76775 + 4.79389i) q^{38} +(-0.124788 + 1.39323i) q^{39} +(5.43891 - 9.42047i) q^{40} +(-0.227336 - 0.131253i) q^{41} +(-0.728657 + 1.26207i) q^{42} +(-1.36823 - 2.36984i) q^{43} +(-0.363781 - 0.210029i) q^{44} +(9.30224 - 5.37065i) q^{45} -4.89956i q^{46} -3.52717i q^{47} +(-0.0541346 - 0.0937638i) q^{48} +(5.02862 - 8.70982i) q^{49} +(7.25408 - 4.18815i) q^{50} +(0.139429 - 0.241499i) q^{51} +(3.45876 + 2.43250i) q^{52} +(-1.14813 + 1.98862i) q^{53} -2.06403i q^{54} +(-0.675082 - 1.16928i) q^{55} +(5.95904 + 10.3214i) q^{56} +(-2.04484 - 1.18059i) q^{57} +5.27209i q^{58} +(-3.44943 + 1.99153i) q^{59} +1.71510i q^{60} -11.6253 q^{61} +(-4.36285 + 2.57093i) q^{62} +11.7685i q^{63} -5.57651 q^{64} +(5.71852 + 12.3297i) q^{65} -0.126385 q^{66} +(-7.25205 - 4.18697i) q^{67} +(-0.421485 - 0.730033i) q^{68} +(1.04496 + 1.80992i) q^{69} +14.1598i q^{70} +(-8.34100 - 4.81568i) q^{71} +(-7.12114 - 4.11139i) q^{72} +(1.72044 + 0.993294i) q^{73} +(-3.03362 - 5.25439i) q^{74} +(-1.78646 + 3.09424i) q^{75} +(-6.18140 + 3.56883i) q^{76} +1.47928 q^{77} +(1.26717 + 0.113497i) q^{78} +(-3.43571 - 5.95083i) q^{79} +(-0.911045 - 0.525992i) q^{80} +(-3.83402 - 6.64072i) q^{81} +(-0.119377 + 0.206767i) q^{82} +(11.1050 + 6.41147i) q^{83} +(-1.62736 - 0.939555i) q^{84} -2.70950i q^{85} +(-2.15542 + 1.24443i) q^{86} +(-1.12441 - 1.94754i) q^{87} +(-0.516795 + 0.895115i) q^{88} +10.6987i q^{89} +(-4.88473 - 8.46060i) q^{90} +(-14.8317 - 1.32844i) q^{91} +6.31766 q^{92} +(1.06334 - 1.88021i) q^{93} -3.20804 q^{94} -22.9421 q^{95} +(1.85381 - 1.07030i) q^{96} +2.44420i q^{97} +(-7.92177 - 4.57364i) q^{98} +(-0.883881 + 0.510309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68q - 6q^{3} - 76q^{4} - 40q^{9} + O(q^{10}) \) \( 68q - 6q^{3} - 76q^{4} - 40q^{9} + 8q^{10} - 10q^{12} - 3q^{13} + 10q^{14} + 84q^{16} + 6q^{17} + 4q^{22} - 44q^{23} + 30q^{25} - 3q^{26} - 12q^{27} + 48q^{29} - 4q^{30} - 48q^{35} + 40q^{36} + 60q^{38} - 14q^{39} + 20q^{40} - 10q^{42} - 12q^{43} + 32q^{48} + 58q^{49} + 20q^{51} - 27q^{52} + 8q^{53} - 36q^{55} - 50q^{56} - 12q^{61} - 74q^{62} - 15q^{65} + 164q^{66} + 4q^{68} - 34q^{69} - 4q^{74} + 20q^{75} - 200q^{77} - 58q^{78} - 80q^{79} - 82q^{81} - 66q^{82} + 52q^{87} + 16q^{88} - 14q^{90} - 70q^{91} + 108q^{92} - 4q^{94} + 76q^{95} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.909522i 0.643129i −0.946888 0.321565i \(-0.895791\pi\)
0.946888 0.321565i \(-0.104209\pi\)
\(3\) 0.193979 + 0.335982i 0.111994 + 0.193979i 0.916574 0.399865i \(-0.130943\pi\)
−0.804580 + 0.593844i \(0.797610\pi\)
\(4\) 1.17277 0.586385
\(5\) 3.26453 + 1.88478i 1.45994 + 0.842898i 0.999008 0.0445356i \(-0.0141808\pi\)
0.460935 + 0.887434i \(0.347514\pi\)
\(6\) 0.305583 0.176429i 0.124754 0.0720266i
\(7\) −3.57672 + 2.06502i −1.35187 + 0.780504i −0.988512 0.151144i \(-0.951704\pi\)
−0.363361 + 0.931648i \(0.618371\pi\)
\(8\) 2.88570i 1.02025i
\(9\) 1.42474 2.46773i 0.474915 0.822576i
\(10\) 1.71425 2.96916i 0.542093 0.938932i
\(11\) −0.310190 0.179088i −0.0935257 0.0539971i 0.452508 0.891760i \(-0.350529\pi\)
−0.546033 + 0.837763i \(0.683863\pi\)
\(12\) 0.227493 + 0.394029i 0.0656716 + 0.113746i
\(13\) 2.94922 + 2.07415i 0.817967 + 0.575265i
\(14\) 1.87818 + 3.25311i 0.501965 + 0.869429i
\(15\) 1.46243i 0.377598i
\(16\) −0.279074 −0.0697685
\(17\) −0.359393 0.622486i −0.0871655 0.150975i 0.819146 0.573584i \(-0.194448\pi\)
−0.906312 + 0.422609i \(0.861114\pi\)
\(18\) −2.24445 1.29584i −0.529023 0.305432i
\(19\) −5.27077 + 3.04308i −1.20920 + 0.698131i −0.962584 0.270983i \(-0.912651\pi\)
−0.246614 + 0.969114i \(0.579318\pi\)
\(20\) 3.82854 + 2.21041i 0.856088 + 0.494263i
\(21\) −1.38762 0.801142i −0.302803 0.174824i
\(22\) −0.162885 + 0.282124i −0.0347271 + 0.0601491i
\(23\) 5.38696 1.12326 0.561630 0.827389i \(-0.310175\pi\)
0.561630 + 0.827389i \(0.310175\pi\)
\(24\) 0.969545 0.559767i 0.197908 0.114262i
\(25\) 4.60478 + 7.97571i 0.920955 + 1.59514i
\(26\) 1.88648 2.68238i 0.369970 0.526059i
\(27\) 2.26936 0.436738
\(28\) −4.19467 + 2.42179i −0.792718 + 0.457676i
\(29\) −5.79655 −1.07639 −0.538196 0.842820i \(-0.680894\pi\)
−0.538196 + 0.842820i \(0.680894\pi\)
\(30\) 1.33011 0.242845
\(31\) −2.82668 4.79686i −0.507687 0.861541i
\(32\) 5.51758i 0.975380i
\(33\) 0.138957i 0.0241894i
\(34\) −0.566165 + 0.326876i −0.0970965 + 0.0560587i
\(35\) −15.5684 −2.63154
\(36\) 1.67090 2.89408i 0.278483 0.482346i
\(37\) 5.77708 3.33540i 0.949747 0.548336i 0.0567444 0.998389i \(-0.481928\pi\)
0.893002 + 0.450052i \(0.148595\pi\)
\(38\) 2.76775 + 4.79389i 0.448989 + 0.777671i
\(39\) −0.124788 + 1.39323i −0.0199820 + 0.223095i
\(40\) 5.43891 9.42047i 0.859967 1.48951i
\(41\) −0.227336 0.131253i −0.0355039 0.0204982i 0.482143 0.876093i \(-0.339859\pi\)
−0.517647 + 0.855594i \(0.673192\pi\)
\(42\) −0.728657 + 1.26207i −0.112434 + 0.194742i
\(43\) −1.36823 2.36984i −0.208653 0.361397i 0.742638 0.669693i \(-0.233574\pi\)
−0.951290 + 0.308296i \(0.900241\pi\)
\(44\) −0.363781 0.210029i −0.0548420 0.0316630i
\(45\) 9.30224 5.37065i 1.38670 0.800610i
\(46\) 4.89956i 0.722401i
\(47\) 3.52717i 0.514491i −0.966346 0.257245i \(-0.917185\pi\)
0.966346 0.257245i \(-0.0828148\pi\)
\(48\) −0.0541346 0.0937638i −0.00781365 0.0135336i
\(49\) 5.02862 8.70982i 0.718374 1.24426i
\(50\) 7.25408 4.18815i 1.02588 0.592293i
\(51\) 0.139429 0.241499i 0.0195240 0.0338166i
\(52\) 3.45876 + 2.43250i 0.479643 + 0.337326i
\(53\) −1.14813 + 1.98862i −0.157708 + 0.273158i −0.934042 0.357164i \(-0.883744\pi\)
0.776334 + 0.630322i \(0.217077\pi\)
\(54\) 2.06403i 0.280879i
\(55\) −0.675082 1.16928i −0.0910281 0.157665i
\(56\) 5.95904 + 10.3214i 0.796310 + 1.37925i
\(57\) −2.04484 1.18059i −0.270846 0.156373i
\(58\) 5.27209i 0.692259i
\(59\) −3.44943 + 1.99153i −0.449077 + 0.259275i −0.707440 0.706773i \(-0.750150\pi\)
0.258363 + 0.966048i \(0.416817\pi\)
\(60\) 1.71510i 0.221418i
\(61\) −11.6253 −1.48847 −0.744233 0.667920i \(-0.767185\pi\)
−0.744233 + 0.667920i \(0.767185\pi\)
\(62\) −4.36285 + 2.57093i −0.554083 + 0.326509i
\(63\) 11.7685i 1.48269i
\(64\) −5.57651 −0.697064
\(65\) 5.71852 + 12.3297i 0.709296 + 1.52932i
\(66\) −0.126385 −0.0155569
\(67\) −7.25205 4.18697i −0.885978 0.511520i −0.0133535 0.999911i \(-0.504251\pi\)
−0.872625 + 0.488391i \(0.837584\pi\)
\(68\) −0.421485 0.730033i −0.0511125 0.0885295i
\(69\) 1.04496 + 1.80992i 0.125798 + 0.217889i
\(70\) 14.1598i 1.69242i
\(71\) −8.34100 4.81568i −0.989894 0.571516i −0.0846515 0.996411i \(-0.526978\pi\)
−0.905243 + 0.424895i \(0.860311\pi\)
\(72\) −7.12114 4.11139i −0.839234 0.484532i
\(73\) 1.72044 + 0.993294i 0.201362 + 0.116256i 0.597290 0.802025i \(-0.296244\pi\)
−0.395929 + 0.918281i \(0.629577\pi\)
\(74\) −3.03362 5.25439i −0.352651 0.610810i
\(75\) −1.78646 + 3.09424i −0.206283 + 0.357293i
\(76\) −6.18140 + 3.56883i −0.709055 + 0.409373i
\(77\) 1.47928 0.168580
\(78\) 1.26717 + 0.113497i 0.143479 + 0.0128510i
\(79\) −3.43571 5.95083i −0.386548 0.669521i 0.605435 0.795895i \(-0.292999\pi\)
−0.991983 + 0.126374i \(0.959666\pi\)
\(80\) −0.911045 0.525992i −0.101858 0.0588077i
\(81\) −3.83402 6.64072i −0.426003 0.737858i
\(82\) −0.119377 + 0.206767i −0.0131830 + 0.0228336i
\(83\) 11.1050 + 6.41147i 1.21893 + 0.703751i 0.964690 0.263390i \(-0.0848405\pi\)
0.254243 + 0.967140i \(0.418174\pi\)
\(84\) −1.62736 0.939555i −0.177559 0.102514i
\(85\) 2.70950i 0.293887i
\(86\) −2.15542 + 1.24443i −0.232425 + 0.134191i
\(87\) −1.12441 1.94754i −0.120549 0.208798i
\(88\) −0.516795 + 0.895115i −0.0550905 + 0.0954196i
\(89\) 10.6987i 1.13406i 0.823697 + 0.567030i \(0.191908\pi\)
−0.823697 + 0.567030i \(0.808092\pi\)
\(90\) −4.88473 8.46060i −0.514896 0.891825i
\(91\) −14.8317 1.32844i −1.55478 0.139258i
\(92\) 6.31766 0.658662
\(93\) 1.06334 1.88021i 0.110263 0.194968i
\(94\) −3.20804 −0.330884
\(95\) −22.9421 −2.35381
\(96\) 1.85381 1.07030i 0.189204 0.109237i
\(97\) 2.44420i 0.248171i 0.992272 + 0.124086i \(0.0395997\pi\)
−0.992272 + 0.124086i \(0.960400\pi\)
\(98\) −7.92177 4.57364i −0.800220 0.462007i
\(99\) −0.883881 + 0.510309i −0.0888334 + 0.0512880i
\(100\) 5.40034 + 9.35366i 0.540034 + 0.935366i
\(101\) 4.60510 0.458224 0.229112 0.973400i \(-0.426418\pi\)
0.229112 + 0.973400i \(0.426418\pi\)
\(102\) −0.219649 0.126814i −0.0217485 0.0125565i
\(103\) −5.42061 + 9.38876i −0.534108 + 0.925102i 0.465098 + 0.885259i \(0.346019\pi\)
−0.999206 + 0.0398431i \(0.987314\pi\)
\(104\) 5.98537 8.51058i 0.586914 0.834531i
\(105\) −3.01995 5.23071i −0.294717 0.510465i
\(106\) 1.80869 + 1.04425i 0.175676 + 0.101427i
\(107\) 1.13520 + 1.96622i 0.109744 + 0.190082i 0.915666 0.401939i \(-0.131664\pi\)
−0.805923 + 0.592021i \(0.798330\pi\)
\(108\) 2.66144 0.256097
\(109\) 19.6376i 1.88094i −0.339871 0.940472i \(-0.610383\pi\)
0.339871 0.940472i \(-0.389617\pi\)
\(110\) −1.06348 + 0.614002i −0.101399 + 0.0585428i
\(111\) 2.24127 + 1.29400i 0.212732 + 0.122821i
\(112\) 0.998169 0.576293i 0.0943181 0.0544546i
\(113\) −8.81868 + 15.2744i −0.829592 + 1.43690i 0.0687667 + 0.997633i \(0.478094\pi\)
−0.898359 + 0.439263i \(0.855240\pi\)
\(114\) −1.07377 + 1.85983i −0.100568 + 0.174189i
\(115\) 17.5859 + 10.1532i 1.63989 + 0.946793i
\(116\) −6.79801 −0.631180
\(117\) 9.32032 4.32275i 0.861664 0.399639i
\(118\) 1.81134 + 3.13733i 0.166747 + 0.288815i
\(119\) 2.57089 + 1.48431i 0.235673 + 0.136066i
\(120\) 4.22015 0.385245
\(121\) −5.43585 9.41518i −0.494169 0.855925i
\(122\) 10.5735i 0.957277i
\(123\) 0.101841i 0.00918271i
\(124\) −3.31505 5.62561i −0.297700 0.505195i
\(125\) 15.8681i 1.41929i
\(126\) 10.7037 0.953563
\(127\) 6.45201 + 11.1752i 0.572523 + 0.991639i 0.996306 + 0.0858754i \(0.0273687\pi\)
−0.423783 + 0.905764i \(0.639298\pi\)
\(128\) 5.96321i 0.527078i
\(129\) 0.530816 0.919400i 0.0467357 0.0809486i
\(130\) 11.2142 5.20112i 0.983549 0.456169i
\(131\) 2.03888 + 3.53144i 0.178137 + 0.308543i 0.941243 0.337731i \(-0.109660\pi\)
−0.763105 + 0.646274i \(0.776326\pi\)
\(132\) 0.162965i 0.0141843i
\(133\) 12.5681 21.7685i 1.08979 1.88757i
\(134\) −3.80814 + 6.59590i −0.328973 + 0.569799i
\(135\) 7.40840 + 4.27724i 0.637613 + 0.368126i
\(136\) −1.79631 + 1.03710i −0.154032 + 0.0889307i
\(137\) 8.78186 + 5.07021i 0.750285 + 0.433177i 0.825797 0.563968i \(-0.190726\pi\)
−0.0755119 + 0.997145i \(0.524059\pi\)
\(138\) 1.64616 0.950414i 0.140131 0.0809046i
\(139\) 22.1029 1.87475 0.937373 0.348327i \(-0.113250\pi\)
0.937373 + 0.348327i \(0.113250\pi\)
\(140\) −18.2582 −1.54310
\(141\) 1.18507 0.684198i 0.0998005 0.0576199i
\(142\) −4.37996 + 7.58632i −0.367558 + 0.636630i
\(143\) −0.543363 1.17155i −0.0454383 0.0979699i
\(144\) −0.397609 + 0.688679i −0.0331341 + 0.0573899i
\(145\) −18.9230 10.9252i −1.57147 0.907289i
\(146\) 0.903423 1.56477i 0.0747678 0.129502i
\(147\) 3.90179 0.321814
\(148\) 6.77519 3.91166i 0.556917 0.321536i
\(149\) −7.99387 + 4.61526i −0.654883 + 0.378097i −0.790325 0.612688i \(-0.790088\pi\)
0.135441 + 0.990785i \(0.456755\pi\)
\(150\) 2.81428 + 1.62483i 0.229785 + 0.132667i
\(151\) 11.8009i 0.960345i −0.877174 0.480173i \(-0.840574\pi\)
0.877174 0.480173i \(-0.159426\pi\)
\(152\) 8.78144 + 15.2099i 0.712269 + 1.23369i
\(153\) −2.04817 −0.165585
\(154\) 1.34544i 0.108419i
\(155\) −0.186784 20.9872i −0.0150028 1.68573i
\(156\) −0.146347 + 1.63393i −0.0117172 + 0.130819i
\(157\) −14.3208 −1.14292 −0.571461 0.820629i \(-0.693623\pi\)
−0.571461 + 0.820629i \(0.693623\pi\)
\(158\) −5.41241 + 3.12486i −0.430588 + 0.248600i
\(159\) −0.890855 −0.0706494
\(160\) 10.3994 18.0123i 0.822147 1.42400i
\(161\) −19.2677 + 11.1242i −1.51850 + 0.876708i
\(162\) −6.03989 + 3.48713i −0.474538 + 0.273975i
\(163\) 11.7697i 0.921873i −0.887433 0.460936i \(-0.847514\pi\)
0.887433 0.460936i \(-0.152486\pi\)
\(164\) −0.266613 0.153929i −0.0208190 0.0120198i
\(165\) 0.261904 0.453631i 0.0203892 0.0353151i
\(166\) 5.83138 10.1002i 0.452603 0.783931i
\(167\) −0.00504232 + 0.00291118i −0.000390186 + 0.000225274i −0.500195 0.865913i \(-0.666738\pi\)
0.499805 + 0.866138i \(0.333405\pi\)
\(168\) −2.31186 + 4.00426i −0.178364 + 0.308935i
\(169\) 4.39583 + 12.2342i 0.338141 + 0.941096i
\(170\) −2.46435 −0.189007
\(171\) 17.3425i 1.32621i
\(172\) −1.60461 2.77927i −0.122351 0.211918i
\(173\) 1.23700 2.14255i 0.0940476 0.162895i −0.815163 0.579231i \(-0.803353\pi\)
0.909211 + 0.416336i \(0.136686\pi\)
\(174\) −1.77133 + 1.02268i −0.134284 + 0.0775289i
\(175\) −32.9400 19.0179i −2.49003 1.43762i
\(176\) 0.0865658 + 0.0499788i 0.00652514 + 0.00376729i
\(177\) −1.33824 0.772630i −0.100588 0.0580745i
\(178\) 9.73071 0.729348
\(179\) 8.40949 + 14.5657i 0.628555 + 1.08869i 0.987842 + 0.155462i \(0.0496867\pi\)
−0.359287 + 0.933227i \(0.616980\pi\)
\(180\) 10.9094 6.29854i 0.813137 0.469465i
\(181\) 0.575818 0.997346i 0.0428002 0.0741321i −0.843832 0.536608i \(-0.819705\pi\)
0.886632 + 0.462476i \(0.153039\pi\)
\(182\) −1.20824 + 13.4898i −0.0895610 + 0.999928i
\(183\) −2.25507 3.90589i −0.166699 0.288732i
\(184\) 15.5452i 1.14601i
\(185\) 25.1460 1.84877
\(186\) −1.71009 0.967132i −0.125390 0.0709135i
\(187\) 0.257452i 0.0188267i
\(188\) 4.13656i 0.301689i
\(189\) −8.11686 + 4.68627i −0.590415 + 0.340876i
\(190\) 20.8664i 1.51381i
\(191\) −2.91734 + 5.05298i −0.211091 + 0.365621i −0.952056 0.305923i \(-0.901035\pi\)
0.740965 + 0.671544i \(0.234368\pi\)
\(192\) −1.08173 1.87361i −0.0780670 0.135216i
\(193\) 1.84632 1.06597i 0.132901 0.0767303i −0.432076 0.901837i \(-0.642219\pi\)
0.564976 + 0.825107i \(0.308885\pi\)
\(194\) 2.22306 0.159606
\(195\) −3.03330 + 4.31304i −0.217219 + 0.308863i
\(196\) 5.89741 10.2146i 0.421243 0.729615i
\(197\) −22.5595 13.0247i −1.60730 0.927975i −0.989971 0.141269i \(-0.954882\pi\)
−0.617328 0.786706i \(-0.711785\pi\)
\(198\) 0.464138 + 0.803910i 0.0329848 + 0.0571314i
\(199\) −10.1525 + 17.5847i −0.719694 + 1.24655i 0.241426 + 0.970419i \(0.422385\pi\)
−0.961121 + 0.276128i \(0.910949\pi\)
\(200\) 23.0155 13.2880i 1.62744 0.939605i
\(201\) 3.24874i 0.229149i
\(202\) 4.18844i 0.294697i
\(203\) 20.7326 11.9700i 1.45515 0.840129i
\(204\) 0.163519 0.283223i 0.0114486 0.0198295i
\(205\) −0.494764 0.856956i −0.0345558 0.0598524i
\(206\) 8.53929 + 4.93016i 0.594961 + 0.343501i
\(207\) 7.67504 13.2936i 0.533452 0.923966i
\(208\) −0.823051 0.578840i −0.0570683 0.0401353i
\(209\) 2.17992 0.150788
\(210\) −4.75745 + 2.74671i −0.328295 + 0.189541i
\(211\) −6.70147 11.6073i −0.461348 0.799079i 0.537680 0.843149i \(-0.319301\pi\)
−0.999028 + 0.0440701i \(0.985968\pi\)
\(212\) −1.34649 + 2.33219i −0.0924775 + 0.160176i
\(213\) 3.73657i 0.256025i
\(214\) 1.78832 1.03249i 0.122247 0.0705795i
\(215\) 10.3152i 0.703492i
\(216\) 6.54870i 0.445583i
\(217\) 20.0159 + 11.3199i 1.35877 + 0.768442i
\(218\) −17.8609 −1.20969
\(219\) 0.770714i 0.0520800i
\(220\) −0.791716 1.37129i −0.0533775 0.0924525i
\(221\) 0.231199 2.58128i 0.0155521 0.173636i
\(222\) 1.17692 2.03848i 0.0789897 0.136814i
\(223\) 6.61419 3.81870i 0.442919 0.255719i −0.261916 0.965091i \(-0.584354\pi\)
0.704835 + 0.709371i \(0.251021\pi\)
\(224\) 11.3939 + 19.7349i 0.761289 + 1.31859i
\(225\) 26.2425 1.74950
\(226\) 13.8924 + 8.02079i 0.924110 + 0.533535i
\(227\) 9.57173 + 5.52624i 0.635298 + 0.366789i 0.782801 0.622272i \(-0.213790\pi\)
−0.147503 + 0.989062i \(0.547124\pi\)
\(228\) −2.39813 1.38456i −0.158820 0.0916947i
\(229\) 13.1055 7.56649i 0.866038 0.500007i 8.59468e−6 1.00000i \(-0.499997\pi\)
0.866030 + 0.499993i \(0.166664\pi\)
\(230\) 9.23459 15.9948i 0.608911 1.05466i
\(231\) 0.286950 + 0.497012i 0.0188799 + 0.0327010i
\(232\) 16.7271i 1.09819i
\(233\) 10.6864 0.700088 0.350044 0.936733i \(-0.386167\pi\)
0.350044 + 0.936733i \(0.386167\pi\)
\(234\) −3.93164 8.47704i −0.257019 0.554161i
\(235\) 6.64793 11.5146i 0.433663 0.751127i
\(236\) −4.04538 + 2.33560i −0.263332 + 0.152035i
\(237\) 1.33291 2.30868i 0.0865821 0.149965i
\(238\) 1.35001 2.33828i 0.0875081 0.151568i
\(239\) 16.0487 + 9.26574i 1.03811 + 0.599351i 0.919296 0.393566i \(-0.128759\pi\)
0.118810 + 0.992917i \(0.462092\pi\)
\(240\) 0.408126i 0.0263445i
\(241\) −17.3984 + 10.0450i −1.12073 + 0.647052i −0.941587 0.336771i \(-0.890665\pi\)
−0.179141 + 0.983823i \(0.557332\pi\)
\(242\) −8.56331 + 4.94403i −0.550471 + 0.317814i
\(243\) 4.89148 8.47230i 0.313789 0.543498i
\(244\) −13.6338 −0.872814
\(245\) 32.8321 18.9556i 2.09757 1.21103i
\(246\) −0.0926268 −0.00590567
\(247\) −21.8565 1.95763i −1.39070 0.124561i
\(248\) −13.8423 + 8.15697i −0.878988 + 0.517968i
\(249\) 4.97477i 0.315264i
\(250\) 14.4324 0.912787
\(251\) −9.87326 17.1010i −0.623195 1.07941i −0.988887 0.148669i \(-0.952501\pi\)
0.365692 0.930736i \(-0.380832\pi\)
\(252\) 13.8017i 0.869428i
\(253\) −1.67098 0.964740i −0.105054 0.0606527i
\(254\) 10.1641 5.86825i 0.637752 0.368206i
\(255\) 0.910344 0.525587i 0.0570079 0.0329136i
\(256\) −16.5767 −1.03604
\(257\) −8.11638 + 14.0580i −0.506286 + 0.876913i 0.493687 + 0.869639i \(0.335649\pi\)
−0.999974 + 0.00727389i \(0.997685\pi\)
\(258\) −0.836215 0.482789i −0.0520604 0.0300571i
\(259\) −13.7753 + 23.8596i −0.855958 + 1.48256i
\(260\) 6.70651 + 14.4599i 0.415920 + 0.896768i
\(261\) −8.25860 + 14.3043i −0.511194 + 0.885415i
\(262\) 3.21192 1.85440i 0.198433 0.114565i
\(263\) 8.12284 0.500876 0.250438 0.968133i \(-0.419425\pi\)
0.250438 + 0.968133i \(0.419425\pi\)
\(264\) −0.400990 −0.0246792
\(265\) −7.49622 + 4.32794i −0.460489 + 0.265863i
\(266\) −19.7989 11.4309i −1.21395 0.700875i
\(267\) −3.59457 + 2.07533i −0.219984 + 0.127008i
\(268\) −8.50498 4.91035i −0.519524 0.299947i
\(269\) 10.6539 18.4531i 0.649581 1.12511i −0.333642 0.942700i \(-0.608278\pi\)
0.983223 0.182407i \(-0.0583889\pi\)
\(270\) 3.89024 6.73810i 0.236753 0.410068i
\(271\) 4.57329i 0.277808i −0.990306 0.138904i \(-0.955642\pi\)
0.990306 0.138904i \(-0.0443579\pi\)
\(272\) 0.100297 + 0.173720i 0.00608140 + 0.0105333i
\(273\) −2.43071 5.24087i −0.147113 0.317192i
\(274\) 4.61147 7.98730i 0.278589 0.482530i
\(275\) 3.29864i 0.198916i
\(276\) 1.22550 + 2.12262i 0.0737662 + 0.127767i
\(277\) 33.1115 1.98948 0.994739 0.102446i \(-0.0326668\pi\)
0.994739 + 0.102446i \(0.0326668\pi\)
\(278\) 20.1031i 1.20570i
\(279\) −15.8646 + 0.141194i −0.949792 + 0.00845305i
\(280\) 44.9258i 2.68483i
\(281\) 19.4695i 1.16145i 0.814099 + 0.580726i \(0.197231\pi\)
−0.814099 + 0.580726i \(0.802769\pi\)
\(282\) −0.622293 1.07784i −0.0370570 0.0641846i
\(283\) 17.7417 1.05463 0.527317 0.849669i \(-0.323198\pi\)
0.527317 + 0.849669i \(0.323198\pi\)
\(284\) −9.78206 5.64768i −0.580459 0.335128i
\(285\) −4.45030 7.70815i −0.263613 0.456591i
\(286\) −1.06555 + 0.494201i −0.0630073 + 0.0292227i
\(287\) 1.08416 0.0639958
\(288\) −13.6159 7.86115i −0.802325 0.463222i
\(289\) 8.24167 14.2750i 0.484804 0.839706i
\(290\) −9.93672 + 17.2109i −0.583504 + 1.01066i
\(291\) −0.821208 + 0.474125i −0.0481401 + 0.0277937i
\(292\) 2.01767 + 1.16490i 0.118075 + 0.0681709i
\(293\) −0.385170 + 0.222378i −0.0225019 + 0.0129915i −0.511209 0.859457i \(-0.670802\pi\)
0.488707 + 0.872448i \(0.337469\pi\)
\(294\) 3.54876i 0.206968i
\(295\) −15.0143 −0.874169
\(296\) −9.62498 16.6710i −0.559441 0.968979i
\(297\) −0.703932 0.406415i −0.0408463 0.0235826i
\(298\) 4.19768 + 7.27060i 0.243165 + 0.421175i
\(299\) 15.8873 + 11.1733i 0.918789 + 0.646171i
\(300\) −2.09511 + 3.62883i −0.120961 + 0.209511i
\(301\) 9.78753 + 5.65083i 0.564144 + 0.325709i
\(302\) −10.7332 −0.617626
\(303\) 0.893294 + 1.54723i 0.0513184 + 0.0888860i
\(304\) 1.47094 0.849245i 0.0843639 0.0487075i
\(305\) −37.9512 21.9111i −2.17308 1.25463i
\(306\) 1.86286i 0.106492i
\(307\) 0.0971280 0.0560769i 0.00554339 0.00320048i −0.497226 0.867621i \(-0.665648\pi\)
0.502769 + 0.864421i \(0.332315\pi\)
\(308\) 1.73486 0.0988526
\(309\) −4.20594 −0.239268
\(310\) −19.0883 + 0.169884i −1.08414 + 0.00964876i
\(311\) 20.5808 1.16703 0.583515 0.812102i \(-0.301677\pi\)
0.583515 + 0.812102i \(0.301677\pi\)
\(312\) 4.02044 + 0.360101i 0.227613 + 0.0203867i
\(313\) 2.77025 + 4.79821i 0.156584 + 0.271211i 0.933635 0.358227i \(-0.116619\pi\)
−0.777051 + 0.629438i \(0.783285\pi\)
\(314\) 13.0251i 0.735047i
\(315\) −22.1810 + 38.4186i −1.24976 + 2.16464i
\(316\) −4.02930 6.97895i −0.226666 0.392597i
\(317\) 2.08553 1.20408i 0.117135 0.0676280i −0.440288 0.897857i \(-0.645124\pi\)
0.557423 + 0.830229i \(0.311790\pi\)
\(318\) 0.810252i 0.0454367i
\(319\) 1.79803 + 1.03809i 0.100670 + 0.0581220i
\(320\) −18.2047 10.5105i −1.01767 0.587554i
\(321\) −0.440410 + 0.762813i −0.0245813 + 0.0425761i
\(322\) 10.1177 + 17.5244i 0.563837 + 0.976594i
\(323\) 3.78856 + 2.18732i 0.210801 + 0.121706i
\(324\) −4.49642 7.78804i −0.249801 0.432669i
\(325\) −2.96228 + 33.0731i −0.164317 + 1.83457i
\(326\) −10.7048 −0.592883
\(327\) 6.59789 3.80930i 0.364864 0.210655i
\(328\) −0.378756 + 0.656025i −0.0209133 + 0.0362229i
\(329\) 7.28368 + 12.6157i 0.401562 + 0.695526i
\(330\) −0.412588 0.238208i −0.0227122 0.0131129i
\(331\) 21.4478 + 12.3829i 1.17888 + 0.680626i 0.955755 0.294164i \(-0.0950413\pi\)
0.223124 + 0.974790i \(0.428375\pi\)
\(332\) 13.0236 + 7.51918i 0.714763 + 0.412669i
\(333\) 19.0084i 1.04165i
\(334\) 0.00264779 + 0.00458610i 0.000144880 + 0.000250940i
\(335\) −15.7830 27.3370i −0.862318 1.49358i
\(336\) 0.387248 + 0.223578i 0.0211261 + 0.0121972i
\(337\) −0.784988 −0.0427610 −0.0213805 0.999771i \(-0.506806\pi\)
−0.0213805 + 0.999771i \(0.506806\pi\)
\(338\) 11.1273 3.99811i 0.605246 0.217468i
\(339\) −6.84257 −0.371637
\(340\) 3.17762i 0.172331i
\(341\) 0.0177478 + 1.99416i 0.000961099 + 0.107990i
\(342\) 15.7734 0.852925
\(343\) 12.6265i 0.681766i
\(344\) −6.83866 + 3.94830i −0.368716 + 0.212878i
\(345\) 7.87806i 0.424141i
\(346\) −1.94870 1.12508i −0.104763 0.0604848i
\(347\) 4.16488 + 7.21378i 0.223582 + 0.387256i 0.955893 0.293715i \(-0.0948915\pi\)
−0.732311 + 0.680970i \(0.761558\pi\)
\(348\) −1.31867 2.28401i −0.0706884 0.122436i
\(349\) 24.9286i 1.33440i 0.744880 + 0.667199i \(0.232507\pi\)
−0.744880 + 0.667199i \(0.767493\pi\)
\(350\) −17.2972 + 29.9597i −0.924575 + 1.60141i
\(351\) 6.69285 + 4.70698i 0.357238 + 0.251240i
\(352\) −0.988133 + 1.71150i −0.0526677 + 0.0912231i
\(353\) 23.1970 13.3928i 1.23465 0.712825i 0.266654 0.963792i \(-0.414082\pi\)
0.967996 + 0.250967i \(0.0807486\pi\)
\(354\) −0.702725 + 1.21715i −0.0373494 + 0.0646910i
\(355\) −18.1530 31.4419i −0.963459 1.66876i
\(356\) 12.5471i 0.664996i
\(357\) 1.15170i 0.0609544i
\(358\) 13.2478 7.64862i 0.700168 0.404242i
\(359\) 25.9688 + 14.9931i 1.37058 + 0.791305i 0.991001 0.133855i \(-0.0427356\pi\)
0.379579 + 0.925159i \(0.376069\pi\)
\(360\) −15.4981 26.8435i −0.816822 1.41478i
\(361\) 9.02071 15.6243i 0.474774 0.822333i
\(362\) −0.907108 0.523719i −0.0476766 0.0275261i
\(363\) 2.10889 3.65270i 0.110688 0.191717i
\(364\) −17.3942 1.55795i −0.911702 0.0816588i
\(365\) 3.74428 + 6.48528i 0.195984 + 0.339455i
\(366\) −3.55250 + 2.05103i −0.185692 + 0.107209i
\(367\) −0.537599 + 0.931148i −0.0280624 + 0.0486055i −0.879716 0.475500i \(-0.842267\pi\)
0.851653 + 0.524106i \(0.175600\pi\)
\(368\) −1.50336 −0.0783681
\(369\) −0.647792 + 0.374003i −0.0337227 + 0.0194698i
\(370\) 22.8708i 1.18900i
\(371\) 9.48365i 0.492367i
\(372\) 1.24705 2.20505i 0.0646567 0.114326i
\(373\) −25.1653 −1.30301 −0.651506 0.758643i \(-0.725863\pi\)
−0.651506 + 0.758643i \(0.725863\pi\)
\(374\) 0.234158 0.0121080
\(375\) −5.33141 + 3.07809i −0.275313 + 0.158952i
\(376\) −10.1784 −0.524909
\(377\) −17.0953 12.0229i −0.880453 0.619211i
\(378\) 4.26227 + 7.38247i 0.219227 + 0.379713i
\(379\) −7.17721 + 4.14376i −0.368668 + 0.212851i −0.672877 0.739755i \(-0.734941\pi\)
0.304208 + 0.952606i \(0.401608\pi\)
\(380\) −26.9058 −1.38024
\(381\) −2.50311 + 4.33552i −0.128238 + 0.222115i
\(382\) 4.59580 + 2.65339i 0.235142 + 0.135759i
\(383\) −14.8393 8.56747i −0.758253 0.437777i 0.0704154 0.997518i \(-0.477568\pi\)
−0.828668 + 0.559740i \(0.810901\pi\)
\(384\) 2.00353 1.15674i 0.102242 0.0590296i
\(385\) 4.82916 + 2.78812i 0.246117 + 0.142096i
\(386\) −0.969525 1.67927i −0.0493475 0.0854724i
\(387\) −7.79750 −0.396369
\(388\) 2.86648i 0.145524i
\(389\) −0.00591396 0.0102433i −0.000299849 0.000519354i 0.865875 0.500260i \(-0.166762\pi\)
−0.866175 + 0.499740i \(0.833429\pi\)
\(390\) 3.92280 + 2.75885i 0.198639 + 0.139700i
\(391\) −1.93603 3.35331i −0.0979095 0.169584i
\(392\) −25.1340 14.5111i −1.26946 0.732921i
\(393\) −0.790999 + 1.37005i −0.0399006 + 0.0691099i
\(394\) −11.8463 + 20.5184i −0.596808 + 1.03370i
\(395\) 25.9022i 1.30328i
\(396\) −1.03659 + 0.598475i −0.0520906 + 0.0300745i
\(397\) −0.778571 + 0.449508i −0.0390754 + 0.0225602i −0.519410 0.854525i \(-0.673848\pi\)
0.480335 + 0.877085i \(0.340515\pi\)
\(398\) 15.9937 + 9.23396i 0.801691 + 0.462857i
\(399\) 9.75177 0.488199
\(400\) −1.28507 2.22581i −0.0642536 0.111291i
\(401\) 26.1075i 1.30375i 0.758328 + 0.651873i \(0.226017\pi\)
−0.758328 + 0.651873i \(0.773983\pi\)
\(402\) −2.95480 −0.147372
\(403\) 1.61287 20.0100i 0.0803427 0.996767i
\(404\) 5.40072 0.268696
\(405\) 28.9051i 1.43631i
\(406\) −10.8870 18.8568i −0.540311 0.935847i
\(407\) −2.38932 −0.118434
\(408\) −0.696895 0.402352i −0.0345014 0.0199194i
\(409\) 20.3475 11.7476i 1.00612 0.580882i 0.0960643 0.995375i \(-0.469375\pi\)
0.910052 + 0.414493i \(0.136041\pi\)
\(410\) −0.779421 + 0.449999i −0.0384929 + 0.0222239i
\(411\) 3.93406i 0.194053i
\(412\) −6.35712 + 11.0109i −0.313193 + 0.542466i
\(413\) 8.22509 14.2463i 0.404730 0.701013i
\(414\) −12.0908 6.98062i −0.594230 0.343079i
\(415\) 24.1684 + 41.8609i 1.18638 + 2.05487i
\(416\) 11.4443 16.2726i 0.561102 0.797829i
\(417\) 4.28751 + 7.42619i 0.209960 + 0.363662i
\(418\) 1.98268i 0.0969763i
\(419\) −7.93033 −0.387422 −0.193711 0.981059i \(-0.562052\pi\)
−0.193711 + 0.981059i \(0.562052\pi\)
\(420\) −3.54171 6.13441i −0.172818 0.299329i
\(421\) 10.1889 + 5.88256i 0.496577 + 0.286699i 0.727299 0.686321i \(-0.240776\pi\)
−0.230722 + 0.973020i \(0.574109\pi\)
\(422\) −10.5571 + 6.09514i −0.513911 + 0.296707i
\(423\) −8.70410 5.02531i −0.423208 0.244339i
\(424\) 5.73857 + 3.31317i 0.278690 + 0.160902i
\(425\) 3.30985 5.73282i 0.160551 0.278083i
\(426\) −3.39849 −0.164657
\(427\) 41.5804 24.0065i 2.01222 1.16175i
\(428\) 1.33133 + 2.30593i 0.0643521 + 0.111461i
\(429\) 0.288218 0.409817i 0.0139153 0.0197861i
\(430\) −9.38192 −0.452436
\(431\) −21.9290 + 12.6607i −1.05628 + 0.609844i −0.924401 0.381422i \(-0.875435\pi\)
−0.131880 + 0.991266i \(0.542101\pi\)
\(432\) −0.633319 −0.0304706
\(433\) 4.52861 0.217631 0.108816 0.994062i \(-0.465294\pi\)
0.108816 + 0.994062i \(0.465294\pi\)
\(434\) 10.2957 18.2049i 0.494208 0.873862i
\(435\) 8.47706i 0.406444i
\(436\) 23.0304i 1.10296i
\(437\) −28.3935 + 16.3930i −1.35824 + 0.784182i
\(438\) 0.700981 0.0334942
\(439\) −8.50172 + 14.7254i −0.405765 + 0.702805i −0.994410 0.105586i \(-0.966328\pi\)
0.588645 + 0.808391i \(0.299662\pi\)
\(440\) −3.37419 + 1.94809i −0.160858 + 0.0928714i
\(441\) −14.3290 24.8185i −0.682332 1.18183i
\(442\) −2.34774 0.210281i −0.111670 0.0100020i
\(443\) −9.59205 + 16.6139i −0.455732 + 0.789351i −0.998730 0.0503831i \(-0.983956\pi\)
0.542998 + 0.839734i \(0.317289\pi\)
\(444\) 2.62849 + 1.51756i 0.124743 + 0.0720202i
\(445\) −20.1647 + 34.9263i −0.955898 + 1.65566i
\(446\) −3.47319 6.01575i −0.164461 0.284854i
\(447\) −3.10129 1.79053i −0.146686 0.0846892i
\(448\) 19.9456 11.5156i 0.942342 0.544062i
\(449\) 37.8768i 1.78752i −0.448550 0.893758i \(-0.648060\pi\)
0.448550 0.893758i \(-0.351940\pi\)
\(450\) 23.8681i 1.12516i
\(451\) 0.0470115 + 0.0814264i 0.00221369 + 0.00383422i
\(452\) −10.3423 + 17.9134i −0.486460 + 0.842573i
\(453\) 3.96490 2.28913i 0.186287 0.107553i
\(454\) 5.02624 8.70570i 0.235893 0.408579i
\(455\) −45.9147 32.2912i −2.15252 1.51383i
\(456\) −3.40683 + 5.90081i −0.159540 + 0.276331i
\(457\) 24.7668i 1.15854i 0.815134 + 0.579272i \(0.196663\pi\)
−0.815134 + 0.579272i \(0.803337\pi\)
\(458\) −6.88189 11.9198i −0.321569 0.556975i
\(459\) −0.815591 1.41265i −0.0380685 0.0659366i
\(460\) 20.6242 + 11.9074i 0.961609 + 0.555185i
\(461\) 35.5704i 1.65668i 0.560228 + 0.828338i \(0.310713\pi\)
−0.560228 + 0.828338i \(0.689287\pi\)
\(462\) 0.452043 0.260987i 0.0210310 0.0121422i
\(463\) 26.4008i 1.22695i 0.789715 + 0.613474i \(0.210229\pi\)
−0.789715 + 0.613474i \(0.789771\pi\)
\(464\) 1.61767 0.0750982
\(465\) 7.01508 4.13383i 0.325317 0.191702i
\(466\) 9.71950i 0.450247i
\(467\) 7.08448 0.327831 0.163915 0.986474i \(-0.447588\pi\)
0.163915 + 0.986474i \(0.447588\pi\)
\(468\) 10.9306 5.06959i 0.505266 0.234342i
\(469\) 34.5847 1.59697
\(470\) −10.4727 6.04644i −0.483072 0.278902i
\(471\) −2.77794 4.81153i −0.128001 0.221703i
\(472\) 5.74696 + 9.95403i 0.264525 + 0.458171i
\(473\) 0.980132i 0.0450665i
\(474\) −2.09979 1.21232i −0.0964466 0.0556835i
\(475\) −48.5415 28.0254i −2.22724 1.28590i
\(476\) 3.01506 + 1.74075i 0.138195 + 0.0797871i
\(477\) 3.27159 + 5.66655i 0.149796 + 0.259454i
\(478\) 8.42739 14.5967i 0.385460 0.667636i
\(479\) 4.07687 2.35378i 0.186277 0.107547i −0.403962 0.914776i \(-0.632367\pi\)
0.590238 + 0.807229i \(0.299034\pi\)
\(480\) 8.06909 0.368302
\(481\) 23.9560 + 2.14568i 1.09230 + 0.0978346i
\(482\) 9.13611 + 15.8242i 0.416138 + 0.720773i
\(483\) −7.47505 4.31572i −0.340127 0.196372i
\(484\) −6.37500 11.0418i −0.289773 0.501901i
\(485\) −4.60678 + 7.97917i −0.209183 + 0.362316i
\(486\) −7.70574 4.44891i −0.349540 0.201807i
\(487\) 17.1608 + 9.90781i 0.777632 + 0.448966i 0.835590 0.549353i \(-0.185126\pi\)
−0.0579586 + 0.998319i \(0.518459\pi\)
\(488\) 33.5472i 1.51861i
\(489\) 3.95440 2.28308i 0.178824 0.103244i
\(490\) −17.2406 29.8616i −0.778850 1.34901i
\(491\) −7.72222 + 13.3753i −0.348499 + 0.603618i −0.985983 0.166846i \(-0.946642\pi\)
0.637484 + 0.770464i \(0.279975\pi\)
\(492\) 0.119436i 0.00538460i
\(493\) 2.08324 + 3.60827i 0.0938243 + 0.162508i
\(494\) −1.78051 + 19.8790i −0.0801089 + 0.894397i
\(495\) −3.84728 −0.172922
\(496\) 0.788854 + 1.33868i 0.0354206 + 0.0601084i
\(497\) 39.7779 1.78428
\(498\) 4.52467 0.202755
\(499\) −36.1001 + 20.8424i −1.61606 + 0.933034i −0.628137 + 0.778103i \(0.716182\pi\)
−0.987925 + 0.154931i \(0.950484\pi\)
\(500\) 18.6097i 0.832250i
\(501\) −0.00195621 0.00112942i −8.73970e−5 5.04587e-5i
\(502\) −15.5537 + 8.97995i −0.694197 + 0.400795i
\(503\) −12.5797 21.7887i −0.560902 0.971511i −0.997418 0.0718144i \(-0.977121\pi\)
0.436516 0.899697i \(-0.356212\pi\)
\(504\) 33.9604 1.51272
\(505\) 15.0335 + 8.67959i 0.668981 + 0.386236i
\(506\) −0.877453 + 1.51979i −0.0390075 + 0.0675630i
\(507\) −3.25779 + 3.85011i −0.144683 + 0.170989i
\(508\) 7.56672 + 13.1059i 0.335719 + 0.581482i
\(509\) 25.4518 + 14.6946i 1.12813 + 0.651328i 0.943465 0.331473i \(-0.107546\pi\)
0.184668 + 0.982801i \(0.440879\pi\)
\(510\) −0.478033 0.827978i −0.0211677 0.0366635i
\(511\) −8.20469 −0.362954
\(512\) 3.15046i 0.139232i
\(513\) −11.9613 + 6.90585i −0.528104 + 0.304901i
\(514\) 12.7861 + 7.38203i 0.563969 + 0.325607i
\(515\) −35.3915 + 20.4333i −1.55953 + 0.900398i
\(516\) 0.622524 1.07824i 0.0274051 0.0474670i
\(517\) −0.631674 + 1.09409i −0.0277810 + 0.0481181i
\(518\) 21.7008 + 12.5290i 0.953479 + 0.550492i
\(519\) 0.959812 0.0421311
\(520\) 35.5800 16.5020i 1.56029 0.723659i
\(521\) −11.8267 20.4845i −0.518137 0.897440i −0.999778 0.0210715i \(-0.993292\pi\)
0.481641 0.876369i \(-0.340041\pi\)
\(522\) 13.0101 + 7.51138i 0.569436 + 0.328764i
\(523\) −19.8878 −0.869634 −0.434817 0.900519i \(-0.643187\pi\)
−0.434817 + 0.900519i \(0.643187\pi\)
\(524\) 2.39113 + 4.14156i 0.104457 + 0.180925i
\(525\) 14.7563i 0.644019i
\(526\) 7.38790i 0.322128i
\(527\) −1.97009 + 3.48353i −0.0858185 + 0.151745i
\(528\) 0.0387794i 0.00168766i
\(529\) 6.01935 0.261711
\(530\) 3.93636 + 6.81798i 0.170985 + 0.296154i
\(531\) 11.3497i 0.492534i
\(532\) 14.7394 25.5294i 0.639035 1.10684i
\(533\) −0.398228 0.858622i −0.0172492 0.0371910i
\(534\) 1.88756 + 3.26935i 0.0816826 + 0.141478i
\(535\) 8.55839i 0.370012i
\(536\) −12.0824 + 20.9273i −0.521878 + 0.903920i
\(537\) −3.26254 + 5.65088i −0.140789 + 0.243853i
\(538\) −16.7835 9.68998i −0.723589 0.417765i
\(539\) −3.11965 + 1.80113i −0.134373 + 0.0775801i
\(540\) 8.68834 + 5.01621i 0.373887 + 0.215863i
\(541\) 24.5522 14.1752i 1.05558 0.609441i 0.131376 0.991333i \(-0.458061\pi\)
0.924207 + 0.381892i \(0.124727\pi\)
\(542\) −4.15951 −0.178666
\(543\) 0.446787 0.0191735
\(544\) −3.43462 + 1.98298i −0.147258 + 0.0850195i
\(545\) 37.0126 64.1077i 1.58544 2.74607i
\(546\) −4.76669 + 2.21079i −0.203996 + 0.0946129i
\(547\) 12.3886 21.4576i 0.529696 0.917461i −0.469704 0.882824i \(-0.655639\pi\)
0.999400 0.0346367i \(-0.0110274\pi\)
\(548\) 10.2991 + 5.94619i 0.439956 + 0.254008i
\(549\) −16.5631 + 28.6881i −0.706895 + 1.22438i
\(550\) −3.00019 −0.127928
\(551\) 30.5523 17.6394i 1.30157 0.751463i
\(552\) 5.22290 3.01544i 0.222301 0.128346i
\(553\) 24.5772 + 14.1896i 1.04513 + 0.603404i
\(554\) 30.1156i 1.27949i
\(555\) 4.87780 + 8.44859i 0.207051 + 0.358623i
\(556\) 25.9216 1.09932
\(557\) 27.4248i 1.16202i −0.813895 0.581012i \(-0.802657\pi\)
0.813895 0.581012i \(-0.197343\pi\)
\(558\) 0.128419 + 14.4293i 0.00543641 + 0.610839i
\(559\) 0.880187 9.82709i 0.0372280 0.415642i
\(560\) 4.34474 0.183599
\(561\) −0.0864991 + 0.0499403i −0.00365200 + 0.00210848i
\(562\) 17.7079 0.746964
\(563\) 1.39229 2.41152i 0.0586782 0.101634i −0.835194 0.549955i \(-0.814645\pi\)
0.893872 + 0.448322i \(0.147978\pi\)
\(564\) 1.38981 0.802406i 0.0585215 0.0337874i
\(565\) −57.5777 + 33.2425i −2.42231 + 1.39852i
\(566\) 16.1365i 0.678266i
\(567\) 27.4265 + 15.8347i 1.15180 + 0.664994i
\(568\) −13.8966 + 24.0696i −0.583089 + 1.00994i
\(569\) −6.86922 + 11.8978i −0.287973 + 0.498783i −0.973326 0.229428i \(-0.926315\pi\)
0.685353 + 0.728211i \(0.259648\pi\)
\(570\) −7.01073 + 4.04765i −0.293647 + 0.169537i
\(571\) 13.1347 22.7501i 0.549672 0.952060i −0.448625 0.893720i \(-0.648086\pi\)
0.998297 0.0583397i \(-0.0185807\pi\)
\(572\) −0.637240 1.37396i −0.0266443 0.0574480i
\(573\) −2.26362 −0.0945639
\(574\) 0.986065i 0.0411576i
\(575\) 24.8058 + 42.9648i 1.03447 + 1.79176i
\(576\) −7.94510 + 13.7613i −0.331046 + 0.573389i
\(577\) 10.5431 6.08703i 0.438913 0.253407i −0.264223 0.964462i \(-0.585116\pi\)
0.703136 + 0.711055i \(0.251782\pi\)
\(578\) −12.9834 7.49599i −0.540039 0.311792i
\(579\) 0.716295 + 0.413553i 0.0297682 + 0.0171867i
\(580\) −22.1923 12.8127i −0.921486 0.532020i
\(581\) −52.9593 −2.19712
\(582\) 0.431227 + 0.746907i 0.0178749 + 0.0309603i
\(583\) 0.712276 0.411233i 0.0294995 0.0170315i
\(584\) 2.86635 4.96467i 0.118610 0.205439i
\(585\) 38.5739 + 3.45497i 1.59483 + 0.142845i
\(586\) 0.202258 + 0.350321i 0.00835520 + 0.0144716i
\(587\) 29.9359i 1.23559i −0.786340 0.617793i \(-0.788027\pi\)
0.786340 0.617793i \(-0.211973\pi\)
\(588\) 4.57590 0.188707
\(589\) 29.4961 + 16.6813i 1.21536 + 0.687342i
\(590\) 13.6559i 0.562204i
\(591\) 10.1061i 0.415710i
\(592\) −1.61223 + 0.930823i −0.0662624 + 0.0382566i
\(593\) 13.7440i 0.564397i 0.959356 + 0.282199i \(0.0910637\pi\)
−0.959356 + 0.282199i \(0.908936\pi\)
\(594\) −0.369644 + 0.640241i −0.0151667 + 0.0262694i
\(595\) 5.59517 + 9.69113i 0.229380 + 0.397297i
\(596\) −9.37496 + 5.41264i −0.384013 + 0.221710i
\(597\) −7.87753 −0.322406
\(598\) 10.1624 14.4499i 0.415572 0.590900i
\(599\) 20.5094 35.5233i 0.837991 1.45144i −0.0535801 0.998564i \(-0.517063\pi\)
0.891571 0.452880i \(-0.149603\pi\)
\(600\) 8.92907 + 5.15520i 0.364528 + 0.210460i
\(601\) −14.5900 25.2707i −0.595139 1.03081i −0.993527 0.113594i \(-0.963764\pi\)
0.398388 0.917217i \(-0.369570\pi\)
\(602\) 5.13956 8.90198i 0.209473 0.362818i
\(603\) −20.6646 + 11.9307i −0.841528 + 0.485857i
\(604\) 13.8398i 0.563132i
\(605\) 40.9815i 1.66614i
\(606\) 1.40724 0.812470i 0.0571652 0.0330044i
\(607\) −12.6001 + 21.8240i −0.511421 + 0.885808i 0.488491 + 0.872569i \(0.337547\pi\)
−0.999912 + 0.0132387i \(0.995786\pi\)
\(608\) 16.7905 + 29.0819i 0.680943 + 1.17943i
\(609\) 8.04340 + 4.64386i 0.325935 + 0.188179i
\(610\) −19.9286 + 34.5174i −0.806887 + 1.39757i
\(611\) 7.31587 10.4024i 0.295968 0.420836i
\(612\) −2.40203 −0.0970963
\(613\) −24.7990 + 14.3177i −1.00162 + 0.578287i −0.908728 0.417389i \(-0.862945\pi\)
−0.0928949 + 0.995676i \(0.529612\pi\)
\(614\) −0.0510032 0.0883401i −0.00205832 0.00356512i
\(615\) 0.191948 0.332464i 0.00774009 0.0134062i
\(616\) 4.26877i 0.171994i
\(617\) 19.4862 11.2504i 0.784486 0.452923i −0.0535315 0.998566i \(-0.517048\pi\)
0.838018 + 0.545643i \(0.183714\pi\)
\(618\) 3.82540i 0.153880i
\(619\) 29.1973i 1.17354i −0.809754 0.586770i \(-0.800399\pi\)
0.809754 0.586770i \(-0.199601\pi\)
\(620\) −0.219054 24.6131i −0.00879743 0.988486i
\(621\) 12.2250 0.490570
\(622\) 18.7187i 0.750551i
\(623\) −22.0930 38.2663i −0.885139 1.53311i
\(624\) 0.0348250 0.388813i 0.00139412 0.0155650i
\(625\) −6.88404 + 11.9235i −0.275362 + 0.476941i
\(626\) 4.36408 2.51960i 0.174424 0.100704i
\(627\) 0.422859 + 0.732414i 0.0168874 + 0.0292498i
\(628\) −16.7950 −0.670192
\(629\) −4.15248 2.39744i −0.165570 0.0955921i
\(630\) 34.9426 + 20.1741i 1.39215 + 0.803756i
\(631\) −11.7942 6.80937i −0.469519 0.271077i 0.246519 0.969138i \(-0.420713\pi\)
−0.716038 + 0.698061i \(0.754046\pi\)
\(632\) −17.1723 + 9.91445i −0.683079 + 0.394376i
\(633\) 2.59989 4.50315i 0.103337 0.178984i
\(634\) −1.09514 1.89684i −0.0434935 0.0753330i
\(635\) 48.6424i 1.93032i
\(636\) −1.04477 −0.0414277
\(637\) 32.8959 15.2571i 1.30338 0.604509i
\(638\) 0.944168 1.63535i 0.0373800 0.0647440i
\(639\) −23.7676 + 13.7222i −0.940230 + 0.542842i
\(640\) 11.2393 19.4671i 0.444273 0.769504i
\(641\) 14.0757 24.3799i 0.555958 0.962948i −0.441870 0.897079i \(-0.645685\pi\)
0.997828 0.0658686i \(-0.0209818\pi\)
\(642\) 0.693796 + 0.400563i 0.0273819 + 0.0158090i
\(643\) 10.7145i 0.422540i 0.977428 + 0.211270i \(0.0677600\pi\)
−0.977428 + 0.211270i \(0.932240\pi\)
\(644\) −22.5965 + 13.0461i −0.890427 + 0.514088i
\(645\) 3.46573 2.00094i 0.136463 0.0787869i
\(646\) 1.98942 3.44578i 0.0782727 0.135572i
\(647\) 22.4955 0.884388 0.442194 0.896919i \(-0.354200\pi\)
0.442194 + 0.896919i \(0.354200\pi\)
\(648\) −19.1632 + 11.0639i −0.752800 + 0.434629i
\(649\) 1.42663 0.0560003
\(650\) 30.0807 + 2.69426i 1.17986 + 0.105677i
\(651\) 0.0793941 + 8.92079i 0.00311170 + 0.349633i
\(652\) 13.8031i 0.540572i
\(653\) −19.7254 −0.771915 −0.385957 0.922517i \(-0.626129\pi\)
−0.385957 + 0.922517i \(0.626129\pi\)
\(654\) −3.46464 6.00093i −0.135478 0.234655i
\(655\) 15.3713i 0.600607i
\(656\) 0.0634436 + 0.0366292i 0.00247706 + 0.00143013i
\(657\) 4.90236 2.83038i 0.191259 0.110424i
\(658\) 11.4743 6.62466i 0.447313 0.258256i
\(659\) 31.4173 1.22384 0.611922 0.790918i \(-0.290397\pi\)
0.611922 + 0.790918i \(0.290397\pi\)
\(660\) 0.307153 0.532005i 0.0119559 0.0207082i
\(661\) 3.40515 + 1.96596i 0.132445 + 0.0764671i 0.564759 0.825256i \(-0.308969\pi\)
−0.432314 + 0.901723i \(0.642303\pi\)
\(662\) 11.2625 19.5073i 0.437730 0.758171i
\(663\) 0.912113 0.423037i 0.0354235 0.0164294i
\(664\) 18.5016 32.0457i 0.718002 1.24362i
\(665\) 82.0576 47.3760i 3.18206 1.83716i
\(666\) −17.2885 −0.669917
\(667\) −31.2258 −1.20907
\(668\) −0.00591347 + 0.00341415i −0.000228799 + 0.000132097i
\(669\) 2.56603 + 1.48150i 0.0992085 + 0.0572780i
\(670\) −24.8636 + 14.3550i −0.960565 + 0.554582i
\(671\) 3.60605 + 2.08195i 0.139210 + 0.0803729i
\(672\) −4.42037 + 7.65631i −0.170520 + 0.295348i
\(673\) −9.55937 + 16.5573i −0.368487 + 0.638238i −0.989329 0.145698i \(-0.953457\pi\)
0.620842 + 0.783935i \(0.286791\pi\)
\(674\) 0.713964i 0.0275009i
\(675\) 10.4499 + 18.0997i 0.402217 + 0.696659i
\(676\) 5.15529 + 14.3479i 0.198281 + 0.551844i
\(677\) −18.7512 + 32.4780i −0.720667 + 1.24823i 0.240066 + 0.970757i \(0.422831\pi\)
−0.960733 + 0.277475i \(0.910502\pi\)
\(678\) 6.22347i 0.239011i
\(679\) −5.04732 8.74222i −0.193699 0.335496i
\(680\) −7.81882 −0.299838
\(681\) 4.28791i 0.164313i
\(682\) 1.81373 0.0161420i 0.0694514 0.000618111i
\(683\) 38.4580i 1.47156i 0.677223 + 0.735778i \(0.263183\pi\)
−0.677223 + 0.735778i \(0.736817\pi\)
\(684\) 20.3387i 0.777670i
\(685\) 19.1124 + 33.1037i 0.730249 + 1.26483i
\(686\) 11.4841 0.438464
\(687\) 5.08441 + 2.93548i 0.193982 + 0.111996i
\(688\) 0.381836 + 0.661360i 0.0145574 + 0.0252141i
\(689\) −7.51079 + 3.48349i −0.286138 + 0.132711i
\(690\) 7.16527 0.272777
\(691\) −25.3906 14.6593i −0.965904 0.557665i −0.0679188 0.997691i \(-0.521636\pi\)
−0.897985 + 0.440026i \(0.854969\pi\)
\(692\) 1.45072 2.51272i 0.0551481 0.0955193i
\(693\) 2.10760 3.65047i 0.0800610 0.138670i
\(694\) 6.56109 3.78805i 0.249056 0.143792i
\(695\) 72.1557 + 41.6591i 2.73702 + 1.58022i
\(696\) −5.62001 + 3.24472i −0.213026 + 0.122991i
\(697\) 0.188685i 0.00714695i
\(698\) 22.6731 0.858191
\(699\) 2.07294 + 3.59043i 0.0784057 + 0.135803i
\(700\) −38.6310 22.3036i −1.46011 0.842998i
\(701\) −21.2663 36.8343i −0.803217 1.39121i −0.917488 0.397763i \(-0.869787\pi\)
0.114271 0.993450i \(-0.463547\pi\)
\(702\) 4.28111 6.08729i 0.161580 0.229750i
\(703\) −20.2998 + 35.1603i −0.765622 + 1.32610i
\(704\) 1.72978 + 0.998687i 0.0651934 + 0.0376394i
\(705\) 5.15824 0.194271
\(706\) −12.1810 21.0982i −0.458439 0.794039i
\(707\) −16.4711 + 9.50962i −0.619461 + 0.357646i
\(708\) −1.56944 0.906117i −0.0589832 0.0340540i
\(709\) 12.5966i 0.473075i 0.971622 + 0.236537i \(0.0760126\pi\)
−0.971622 + 0.236537i \(0.923987\pi\)
\(710\) −28.5971 + 16.5105i −1.07323 + 0.619629i
\(711\) −19.5800 −0.734309
\(712\) 30.8733 1.15703
\(713\) −15.2272 25.8405i −0.570265 0.967734i
\(714\) 1.04750 0.0392015
\(715\) 0.434284 4.84868i 0.0162413 0.181330i
\(716\) 9.86240 + 17.0822i 0.368575 + 0.638391i
\(717\) 7.18945i 0.268495i
\(718\) 13.6365 23.6192i 0.508911 0.881460i
\(719\) 19.4311 + 33.6557i 0.724658 + 1.25515i 0.959114 + 0.283018i \(0.0913358\pi\)
−0.234456 + 0.972127i \(0.575331\pi\)
\(720\) −2.59601 + 1.49881i −0.0967477 + 0.0558573i
\(721\) 44.7746i 1.66749i
\(722\) −14.2107 8.20454i −0.528867 0.305341i
\(723\) −6.74985 3.89703i −0.251030 0.144932i
\(724\) 0.675302 1.16966i 0.0250974 0.0434699i
\(725\) −26.6918 46.2316i −0.991309 1.71700i
\(726\) −3.32221 1.91808i −0.123299 0.0711866i
\(727\) −3.60003 6.23544i −0.133518 0.231260i 0.791512 0.611153i \(-0.209294\pi\)
−0.925030 + 0.379893i \(0.875961\pi\)
\(728\) −3.83348 + 42.7999i −0.142078 + 1.58627i
\(729\) −19.2088 −0.711435
\(730\) 5.89850 3.40550i 0.218313 0.126043i
\(731\) −0.983462 + 1.70341i −0.0363746 + 0.0630027i
\(732\) −2.64467 4.58071i −0.0977500 0.169308i
\(733\) 13.1856 + 7.61271i 0.487022 + 0.281182i 0.723338 0.690494i \(-0.242607\pi\)
−0.236316 + 0.971676i \(0.575940\pi\)
\(734\) 0.846900 + 0.488958i 0.0312596 + 0.0180478i
\(735\) 12.7375 + 7.35401i 0.469830 + 0.271257i
\(736\) 29.7230i 1.09560i
\(737\) 1.49967 + 2.59751i 0.0552411 + 0.0956805i
\(738\) 0.340164 + 0.589181i 0.0125216 + 0.0216881i
\(739\) −40.5581 23.4162i −1.49195 0.861380i −0.491997 0.870597i \(-0.663733\pi\)
−0.999958 + 0.00921712i \(0.997066\pi\)
\(740\) 29.4904 1.08409
\(741\) −3.58198 7.72313i −0.131587 0.283716i
\(742\) −8.62559 −0.316655
\(743\) 28.0698i 1.02978i 0.857256 + 0.514891i \(0.172168\pi\)
−0.857256 + 0.514891i \(0.827832\pi\)
\(744\) −5.42572 3.06849i −0.198917 0.112496i
\(745\) −34.7950 −1.27479
\(746\) 22.8884i 0.838006i
\(747\) 31.6436 18.2694i 1.15778 0.668443i
\(748\) 0.301931i 0.0110397i
\(749\) −8.12058 4.68842i −0.296719 0.171311i
\(750\) 2.79959 + 4.84904i 0.102227 + 0.177062i
\(751\) 3.14791 + 5.45234i 0.114869 + 0.198959i 0.917727 0.397211i \(-0.130022\pi\)
−0.802858 + 0.596170i \(0.796689\pi\)
\(752\) 0.984341i 0.0358952i
\(753\) 3.83042 6.63448i 0.139588 0.241774i
\(754\) −10.9351 + 15.5486i −0.398232 + 0.566245i
\(755\) 22.2421 38.5245i 0.809473 1.40205i
\(756\) −9.51921 + 5.49592i −0.346210 + 0.199885i
\(757\) −0.383099 + 0.663547i −0.0139240 + 0.0241170i −0.872903 0.487893i \(-0.837766\pi\)
0.858979 + 0.512010i \(0.171099\pi\)
\(758\) 3.76884 + 6.52783i 0.136891 + 0.237101i
\(759\) 0.748559i 0.0271710i
\(760\) 66.2042i 2.40148i
\(761\) 10.5386 6.08448i 0.382025 0.220562i −0.296674 0.954979i \(-0.595877\pi\)
0.678699 + 0.734416i \(0.262544\pi\)
\(762\) 3.94325 + 2.27664i 0.142849 + 0.0824738i
\(763\) 40.5521 + 70.2383i 1.46809 + 2.54280i
\(764\) −3.42137 + 5.92598i −0.123781 + 0.214395i