Properties

Label 13.3.d.a.5.2
Level 13
Weight 3
Character 13.5
Analytic conductor 0.354
Analytic rank 0
Dimension 4
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 13.d (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.354224343668\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{10})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.2
Root \(1.58114 - 1.58114i\)
Character \(\chi\) = 13.5
Dual form 13.3.d.a.8.2

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(0.581139 - 0.581139i) q^{2}\) \(-4.16228 q^{3}\) \(+3.32456i q^{4}\) \(+(3.58114 - 3.58114i) q^{5}\) \(+(-2.41886 + 2.41886i) q^{6}\) \(+(-4.58114 - 4.58114i) q^{7}\) \(+(4.25658 + 4.25658i) q^{8}\) \(+8.32456 q^{9}\) \(+O(q^{10})\) \(q\)\(+(0.581139 - 0.581139i) q^{2}\) \(-4.16228 q^{3}\) \(+3.32456i q^{4}\) \(+(3.58114 - 3.58114i) q^{5}\) \(+(-2.41886 + 2.41886i) q^{6}\) \(+(-4.58114 - 4.58114i) q^{7}\) \(+(4.25658 + 4.25658i) q^{8}\) \(+8.32456 q^{9}\) \(-4.16228i q^{10}\) \(+(5.32456 + 5.32456i) q^{11}\) \(-13.8377i q^{12}\) \(+(-5.90569 + 11.5811i) q^{13}\) \(-5.32456 q^{14}\) \(+(-14.9057 + 14.9057i) q^{15}\) \(-8.35089 q^{16}\) \(-21.9737i q^{17}\) \(+(4.83772 - 4.83772i) q^{18}\) \(+(3.16228 - 3.16228i) q^{19}\) \(+(11.9057 + 11.9057i) q^{20}\) \(+(19.0680 + 19.0680i) q^{21}\) \(+6.18861 q^{22}\) \(-8.51317i q^{23}\) \(+(-17.7171 - 17.7171i) q^{24}\) \(-0.649111i q^{25}\) \(+(3.29822 + 10.1623i) q^{26}\) \(+2.81139 q^{27}\) \(+(15.2302 - 15.2302i) q^{28}\) \(-5.81139 q^{29}\) \(+17.3246i q^{30}\) \(+(0.513167 - 0.513167i) q^{31}\) \(+(-21.8794 + 21.8794i) q^{32}\) \(+(-22.1623 - 22.1623i) q^{33}\) \(+(-12.7698 - 12.7698i) q^{34}\) \(-32.8114 q^{35}\) \(+27.6754i q^{36}\) \(+(24.2302 + 24.2302i) q^{37}\) \(-3.67544i q^{38}\) \(+(24.5811 - 48.2039i) q^{39}\) \(+30.4868 q^{40}\) \(+(4.83772 - 4.83772i) q^{41}\) \(+22.1623 q^{42}\) \(+30.4868i q^{43}\) \(+(-17.7018 + 17.7018i) q^{44}\) \(+(29.8114 - 29.8114i) q^{45}\) \(+(-4.94733 - 4.94733i) q^{46}\) \(+(-37.3662 - 37.3662i) q^{47}\) \(+34.7587 q^{48}\) \(-7.02633i q^{49}\) \(+(-0.377223 - 0.377223i) q^{50}\) \(+91.4605i q^{51}\) \(+(-38.5021 - 19.6338i) q^{52}\) \(-35.8114 q^{53}\) \(+(1.63381 - 1.63381i) q^{54}\) \(+38.1359 q^{55}\) \(-39.0000i q^{56}\) \(+(-13.1623 + 13.1623i) q^{57}\) \(+(-3.37722 + 3.37722i) q^{58}\) \(+(58.2719 + 58.2719i) q^{59}\) \(+(-49.5548 - 49.5548i) q^{60}\) \(-80.3246 q^{61}\) \(-0.596443i q^{62}\) \(+(-38.1359 - 38.1359i) q^{63}\) \(-7.97367i q^{64}\) \(+(20.3246 + 62.6228i) q^{65}\) \(-25.7587 q^{66}\) \(+(39.0833 - 39.0833i) q^{67}\) \(+73.0527 q^{68}\) \(+35.4342i q^{69}\) \(+(-19.0680 + 19.0680i) q^{70}\) \(+(91.5548 - 91.5548i) q^{71}\) \(+(35.4342 + 35.4342i) q^{72}\) \(+(31.6228 + 31.6228i) q^{73}\) \(+28.1623 q^{74}\) \(+2.70178i q^{75}\) \(+(10.5132 + 10.5132i) q^{76}\) \(-48.7851i q^{77}\) \(+(-13.7281 - 42.2982i) q^{78}\) \(-18.7851 q^{79}\) \(+(-29.9057 + 29.9057i) q^{80}\) \(-86.6228 q^{81}\) \(-5.62278i q^{82}\) \(+(-44.6228 + 44.6228i) q^{83}\) \(+(-63.3925 + 63.3925i) q^{84}\) \(+(-78.6907 - 78.6907i) q^{85}\) \(+(17.7171 + 17.7171i) q^{86}\) \(+24.1886 q^{87}\) \(+45.3288i q^{88}\) \(+(8.89039 + 8.89039i) q^{89}\) \(-34.6491i q^{90}\) \(+(80.1096 - 26.0000i) q^{91}\) \(+28.3025 q^{92}\) \(+(-2.13594 + 2.13594i) q^{93}\) \(-43.4299 q^{94}\) \(-22.6491i q^{95}\) \(+(91.0680 - 91.0680i) q^{96}\) \(+(-121.355 + 121.355i) q^{97}\) \(+(-4.08328 - 4.08328i) q^{98}\) \(+(44.3246 + 44.3246i) q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(4q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 36q^{8} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 36q^{8} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 28q^{15} \) \(\mathstrut -\mathstrut 84q^{16} \) \(\mathstrut +\mathstrut 32q^{18} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut +\mathstrut 32q^{21} \) \(\mathstrut +\mathstrut 88q^{22} \) \(\mathstrut +\mathstrut 24q^{24} \) \(\mathstrut -\mathstrut 88q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 40q^{29} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 20q^{32} \) \(\mathstrut -\mathstrut 76q^{33} \) \(\mathstrut -\mathstrut 108q^{34} \) \(\mathstrut -\mathstrut 68q^{35} \) \(\mathstrut +\mathstrut 40q^{37} \) \(\mathstrut +\mathstrut 92q^{39} \) \(\mathstrut +\mathstrut 84q^{40} \) \(\mathstrut +\mathstrut 32q^{41} \) \(\mathstrut +\mathstrut 76q^{42} \) \(\mathstrut -\mathstrut 172q^{44} \) \(\mathstrut +\mathstrut 56q^{45} \) \(\mathstrut +\mathstrut 132q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 76q^{48} \) \(\mathstrut -\mathstrut 128q^{50} \) \(\mathstrut +\mathstrut 80q^{52} \) \(\mathstrut -\mathstrut 80q^{53} \) \(\mathstrut +\mathstrut 152q^{54} \) \(\mathstrut +\mathstrut 64q^{55} \) \(\mathstrut -\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 140q^{58} \) \(\mathstrut +\mathstrut 56q^{59} \) \(\mathstrut -\mathstrut 116q^{60} \) \(\mathstrut -\mathstrut 296q^{61} \) \(\mathstrut -\mathstrut 64q^{63} \) \(\mathstrut +\mathstrut 56q^{65} \) \(\mathstrut +\mathstrut 112q^{66} \) \(\mathstrut -\mathstrut 84q^{67} \) \(\mathstrut +\mathstrut 444q^{68} \) \(\mathstrut -\mathstrut 32q^{70} \) \(\mathstrut +\mathstrut 284q^{71} \) \(\mathstrut -\mathstrut 48q^{72} \) \(\mathstrut +\mathstrut 100q^{74} \) \(\mathstrut +\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 232q^{78} \) \(\mathstrut +\mathstrut 64q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut -\mathstrut 220q^{81} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 184q^{84} \) \(\mathstrut -\mathstrut 144q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 160q^{87} \) \(\mathstrut +\mathstrut 200q^{89} \) \(\mathstrut +\mathstrut 156q^{91} \) \(\mathstrut -\mathstrut 456q^{92} \) \(\mathstrut +\mathstrut 80q^{93} \) \(\mathstrut -\mathstrut 452q^{94} \) \(\mathstrut +\mathstrut 320q^{96} \) \(\mathstrut -\mathstrut 68q^{97} \) \(\mathstrut +\mathstrut 224q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.581139 0.581139i 0.290569 0.290569i −0.546736 0.837305i \(-0.684130\pi\)
0.837305 + 0.546736i \(0.184130\pi\)
\(3\) −4.16228 −1.38743 −0.693713 0.720252i \(-0.744026\pi\)
−0.693713 + 0.720252i \(0.744026\pi\)
\(4\) 3.32456i 0.831139i
\(5\) 3.58114 3.58114i 0.716228 0.716228i −0.251603 0.967831i \(-0.580958\pi\)
0.967831 + 0.251603i \(0.0809577\pi\)
\(6\) −2.41886 + 2.41886i −0.403144 + 0.403144i
\(7\) −4.58114 4.58114i −0.654448 0.654448i 0.299613 0.954061i \(-0.403143\pi\)
−0.954061 + 0.299613i \(0.903143\pi\)
\(8\) 4.25658 + 4.25658i 0.532073 + 0.532073i
\(9\) 8.32456 0.924951
\(10\) 4.16228i 0.416228i
\(11\) 5.32456 + 5.32456i 0.484050 + 0.484050i 0.906423 0.422372i \(-0.138802\pi\)
−0.422372 + 0.906423i \(0.638802\pi\)
\(12\) 13.8377i 1.15314i
\(13\) −5.90569 + 11.5811i −0.454284 + 0.890857i
\(14\) −5.32456 −0.380325
\(15\) −14.9057 + 14.9057i −0.993713 + 0.993713i
\(16\) −8.35089 −0.521931
\(17\) 21.9737i 1.29257i −0.763097 0.646284i \(-0.776322\pi\)
0.763097 0.646284i \(-0.223678\pi\)
\(18\) 4.83772 4.83772i 0.268762 0.268762i
\(19\) 3.16228 3.16228i 0.166436 0.166436i −0.618975 0.785411i \(-0.712452\pi\)
0.785411 + 0.618975i \(0.212452\pi\)
\(20\) 11.9057 + 11.9057i 0.595285 + 0.595285i
\(21\) 19.0680 + 19.0680i 0.907999 + 0.907999i
\(22\) 6.18861 0.281301
\(23\) 8.51317i 0.370138i −0.982726 0.185069i \(-0.940749\pi\)
0.982726 0.185069i \(-0.0592508\pi\)
\(24\) −17.7171 17.7171i −0.738212 0.738212i
\(25\) 0.649111i 0.0259644i
\(26\) 3.29822 + 10.1623i 0.126855 + 0.390857i
\(27\) 2.81139 0.104125
\(28\) 15.2302 15.2302i 0.543937 0.543937i
\(29\) −5.81139 −0.200393 −0.100196 0.994968i \(-0.531947\pi\)
−0.100196 + 0.994968i \(0.531947\pi\)
\(30\) 17.3246i 0.577485i
\(31\) 0.513167 0.513167i 0.0165538 0.0165538i −0.698781 0.715335i \(-0.746274\pi\)
0.715335 + 0.698781i \(0.246274\pi\)
\(32\) −21.8794 + 21.8794i −0.683730 + 0.683730i
\(33\) −22.1623 22.1623i −0.671584 0.671584i
\(34\) −12.7698 12.7698i −0.375581 0.375581i
\(35\) −32.8114 −0.937468
\(36\) 27.6754i 0.768762i
\(37\) 24.2302 + 24.2302i 0.654872 + 0.654872i 0.954162 0.299290i \(-0.0967499\pi\)
−0.299290 + 0.954162i \(0.596750\pi\)
\(38\) 3.67544i 0.0967222i
\(39\) 24.5811 48.2039i 0.630286 1.23600i
\(40\) 30.4868 0.762171
\(41\) 4.83772 4.83772i 0.117993 0.117993i −0.645645 0.763638i \(-0.723411\pi\)
0.763638 + 0.645645i \(0.223411\pi\)
\(42\) 22.1623 0.527673
\(43\) 30.4868i 0.708996i 0.935057 + 0.354498i \(0.115348\pi\)
−0.935057 + 0.354498i \(0.884652\pi\)
\(44\) −17.7018 + 17.7018i −0.402313 + 0.402313i
\(45\) 29.8114 29.8114i 0.662475 0.662475i
\(46\) −4.94733 4.94733i −0.107551 0.107551i
\(47\) −37.3662 37.3662i −0.795025 0.795025i 0.187281 0.982306i \(-0.440033\pi\)
−0.982306 + 0.187281i \(0.940033\pi\)
\(48\) 34.7587 0.724140
\(49\) 7.02633i 0.143395i
\(50\) −0.377223 0.377223i −0.00754447 0.00754447i
\(51\) 91.4605i 1.79334i
\(52\) −38.5021 19.6338i −0.740426 0.377573i
\(53\) −35.8114 −0.675687 −0.337843 0.941202i \(-0.609697\pi\)
−0.337843 + 0.941202i \(0.609697\pi\)
\(54\) 1.63381 1.63381i 0.0302557 0.0302557i
\(55\) 38.1359 0.693381
\(56\) 39.0000i 0.696429i
\(57\) −13.1623 + 13.1623i −0.230917 + 0.230917i
\(58\) −3.37722 + 3.37722i −0.0582280 + 0.0582280i
\(59\) 58.2719 + 58.2719i 0.987659 + 0.987659i 0.999925 0.0122657i \(-0.00390438\pi\)
−0.0122657 + 0.999925i \(0.503904\pi\)
\(60\) −49.5548 49.5548i −0.825913 0.825913i
\(61\) −80.3246 −1.31680 −0.658398 0.752670i \(-0.728766\pi\)
−0.658398 + 0.752670i \(0.728766\pi\)
\(62\) 0.596443i 0.00962004i
\(63\) −38.1359 38.1359i −0.605332 0.605332i
\(64\) 7.97367i 0.124589i
\(65\) 20.3246 + 62.6228i 0.312685 + 0.963427i
\(66\) −25.7587 −0.390284
\(67\) 39.0833 39.0833i 0.583332 0.583332i −0.352485 0.935817i \(-0.614663\pi\)
0.935817 + 0.352485i \(0.114663\pi\)
\(68\) 73.0527 1.07430
\(69\) 35.4342i 0.513539i
\(70\) −19.0680 + 19.0680i −0.272400 + 0.272400i
\(71\) 91.5548 91.5548i 1.28950 1.28950i 0.354417 0.935088i \(-0.384679\pi\)
0.935088 0.354417i \(-0.115321\pi\)
\(72\) 35.4342 + 35.4342i 0.492141 + 0.492141i
\(73\) 31.6228 + 31.6228i 0.433189 + 0.433189i 0.889712 0.456523i \(-0.150905\pi\)
−0.456523 + 0.889712i \(0.650905\pi\)
\(74\) 28.1623 0.380571
\(75\) 2.70178i 0.0360237i
\(76\) 10.5132 + 10.5132i 0.138331 + 0.138331i
\(77\) 48.7851i 0.633572i
\(78\) −13.7281 42.2982i −0.176001 0.542285i
\(79\) −18.7851 −0.237785 −0.118893 0.992907i \(-0.537934\pi\)
−0.118893 + 0.992907i \(0.537934\pi\)
\(80\) −29.9057 + 29.9057i −0.373821 + 0.373821i
\(81\) −86.6228 −1.06942
\(82\) 5.62278i 0.0685704i
\(83\) −44.6228 + 44.6228i −0.537624 + 0.537624i −0.922830 0.385207i \(-0.874130\pi\)
0.385207 + 0.922830i \(0.374130\pi\)
\(84\) −63.3925 + 63.3925i −0.754673 + 0.754673i
\(85\) −78.6907 78.6907i −0.925774 0.925774i
\(86\) 17.7171 + 17.7171i 0.206013 + 0.206013i
\(87\) 24.1886 0.278030
\(88\) 45.3288i 0.515100i
\(89\) 8.89039 + 8.89039i 0.0998920 + 0.0998920i 0.755287 0.655395i \(-0.227498\pi\)
−0.655395 + 0.755287i \(0.727498\pi\)
\(90\) 34.6491i 0.384990i
\(91\) 80.1096 26.0000i 0.880325 0.285714i
\(92\) 28.3025 0.307636
\(93\) −2.13594 + 2.13594i −0.0229671 + 0.0229671i
\(94\) −43.4299 −0.462020
\(95\) 22.6491i 0.238412i
\(96\) 91.0680 91.0680i 0.948625 0.948625i
\(97\) −121.355 + 121.355i −1.25108 + 1.25108i −0.295850 + 0.955235i \(0.595603\pi\)
−0.955235 + 0.295850i \(0.904397\pi\)
\(98\) −4.08328 4.08328i −0.0416661 0.0416661i
\(99\) 44.3246 + 44.3246i 0.447723 + 0.447723i
\(100\) 2.15800 0.0215800
\(101\) 104.921i 1.03882i −0.854525 0.519411i \(-0.826151\pi\)
0.854525 0.519411i \(-0.173849\pi\)
\(102\) 53.1512 + 53.1512i 0.521091 + 0.521091i
\(103\) 35.4342i 0.344021i 0.985095 + 0.172011i \(0.0550263\pi\)
−0.985095 + 0.172011i \(0.944974\pi\)
\(104\) −74.4342 + 24.1580i −0.715713 + 0.232289i
\(105\) 136.570 1.30067
\(106\) −20.8114 + 20.8114i −0.196334 + 0.196334i
\(107\) −4.42989 −0.0414009 −0.0207004 0.999786i \(-0.506590\pi\)
−0.0207004 + 0.999786i \(0.506590\pi\)
\(108\) 9.34662i 0.0865427i
\(109\) 120.774 120.774i 1.10802 1.10802i 0.114608 0.993411i \(-0.463439\pi\)
0.993411 0.114608i \(-0.0365611\pi\)
\(110\) 22.1623 22.1623i 0.201475 0.201475i
\(111\) −100.853 100.853i −0.908586 0.908586i
\(112\) 38.2566 + 38.2566i 0.341577 + 0.341577i
\(113\) 68.5438 0.606582 0.303291 0.952898i \(-0.401915\pi\)
0.303291 + 0.952898i \(0.401915\pi\)
\(114\) 15.2982i 0.134195i
\(115\) −30.4868 30.4868i −0.265103 0.265103i
\(116\) 19.3203i 0.166554i
\(117\) −49.1623 + 96.4078i −0.420190 + 0.823999i
\(118\) 67.7281 0.573967
\(119\) −100.664 + 100.664i −0.845919 + 0.845919i
\(120\) −126.895 −1.05746
\(121\) 64.2982i 0.531390i
\(122\) −46.6797 + 46.6797i −0.382621 + 0.382621i
\(123\) −20.1359 + 20.1359i −0.163707 + 0.163707i
\(124\) 1.70605 + 1.70605i 0.0137585 + 0.0137585i
\(125\) 87.2039 + 87.2039i 0.697631 + 0.697631i
\(126\) −44.3246 −0.351782
\(127\) 101.162i 0.796553i 0.917265 + 0.398277i \(0.130392\pi\)
−0.917265 + 0.398277i \(0.869608\pi\)
\(128\) −92.1512 92.1512i −0.719932 0.719932i
\(129\) 126.895i 0.983680i
\(130\) 48.2039 + 24.5811i 0.370799 + 0.189086i
\(131\) −257.732 −1.96742 −0.983711 0.179755i \(-0.942469\pi\)
−0.983711 + 0.179755i \(0.942469\pi\)
\(132\) 73.6797 73.6797i 0.558180 0.558180i
\(133\) −28.9737 −0.217847
\(134\) 45.4256i 0.338997i
\(135\) 10.0680 10.0680i 0.0745776 0.0745776i
\(136\) 93.5327 93.5327i 0.687741 0.687741i
\(137\) 175.272 + 175.272i 1.27936 + 1.27936i 0.941028 + 0.338329i \(0.109862\pi\)
0.338329 + 0.941028i \(0.390138\pi\)
\(138\) 20.5922 + 20.5922i 0.149219 + 0.149219i
\(139\) 135.460 0.974536 0.487268 0.873252i \(-0.337993\pi\)
0.487268 + 0.873252i \(0.337993\pi\)
\(140\) 109.083i 0.779166i
\(141\) 155.528 + 155.528i 1.10304 + 1.10304i
\(142\) 106.412i 0.749381i
\(143\) −93.1096 + 30.2192i −0.651116 + 0.211323i
\(144\) −69.5174 −0.482760
\(145\) −20.8114 + 20.8114i −0.143527 + 0.143527i
\(146\) 36.7544 0.251743
\(147\) 29.2456i 0.198949i
\(148\) −80.5548 + 80.5548i −0.544289 + 0.544289i
\(149\) 36.2192 36.2192i 0.243082 0.243082i −0.575042 0.818124i \(-0.695014\pi\)
0.818124 + 0.575042i \(0.195014\pi\)
\(150\) 1.57011 + 1.57011i 0.0104674 + 0.0104674i
\(151\) −75.1776 75.1776i −0.497865 0.497865i 0.412908 0.910773i \(-0.364513\pi\)
−0.910773 + 0.412908i \(0.864513\pi\)
\(152\) 26.9210 0.177112
\(153\) 182.921i 1.19556i
\(154\) −28.3509 28.3509i −0.184097 0.184097i
\(155\) 3.67544i 0.0237125i
\(156\) 160.257 + 81.7214i 1.02729 + 0.523855i
\(157\) 55.4562 0.353224 0.176612 0.984281i \(-0.443486\pi\)
0.176612 + 0.984281i \(0.443486\pi\)
\(158\) −10.9167 + 10.9167i −0.0690932 + 0.0690932i
\(159\) 149.057 0.937465
\(160\) 156.706i 0.979413i
\(161\) −39.0000 + 39.0000i −0.242236 + 0.242236i
\(162\) −50.3399 + 50.3399i −0.310740 + 0.310740i
\(163\) −45.4605 45.4605i −0.278899 0.278899i 0.553771 0.832669i \(-0.313188\pi\)
−0.832669 + 0.553771i \(0.813188\pi\)
\(164\) 16.0833 + 16.0833i 0.0980688 + 0.0980688i
\(165\) −158.732 −0.962014
\(166\) 51.8641i 0.312434i
\(167\) −137.215 137.215i −0.821646 0.821646i 0.164698 0.986344i \(-0.447335\pi\)
−0.986344 + 0.164698i \(0.947335\pi\)
\(168\) 162.329i 0.966243i
\(169\) −99.2456 136.789i −0.587252 0.809404i
\(170\) −91.4605 −0.538003
\(171\) 26.3246 26.3246i 0.153945 0.153945i
\(172\) −101.355 −0.589274
\(173\) 79.3815i 0.458853i −0.973326 0.229426i \(-0.926315\pi\)
0.973326 0.229426i \(-0.0736850\pi\)
\(174\) 14.0569 14.0569i 0.0807870 0.0807870i
\(175\) −2.97367 + 2.97367i −0.0169924 + 0.0169924i
\(176\) −44.4648 44.4648i −0.252641 0.252641i
\(177\) −242.544 242.544i −1.37030 1.37030i
\(178\) 10.3331 0.0580511
\(179\) 318.329i 1.77837i 0.457545 + 0.889187i \(0.348729\pi\)
−0.457545 + 0.889187i \(0.651271\pi\)
\(180\) 99.1096 + 99.1096i 0.550609 + 0.550609i
\(181\) 238.144i 1.31572i 0.753142 + 0.657858i \(0.228537\pi\)
−0.753142 + 0.657858i \(0.771463\pi\)
\(182\) 31.4452 61.6644i 0.172776 0.338815i
\(183\) 334.333 1.82696
\(184\) 36.2370 36.2370i 0.196940 0.196940i
\(185\) 173.544 0.938074
\(186\) 2.48256i 0.0133471i
\(187\) 117.000 117.000i 0.625668 0.625668i
\(188\) 124.226 124.226i 0.660776 0.660776i
\(189\) −12.8794 12.8794i −0.0681448 0.0681448i
\(190\) −13.1623 13.1623i −0.0692751 0.0692751i
\(191\) −3.70605 −0.0194034 −0.00970171 0.999953i \(-0.503088\pi\)
−0.00970171 + 0.999953i \(0.503088\pi\)
\(192\) 33.1886i 0.172857i
\(193\) 43.1359 + 43.1359i 0.223502 + 0.223502i 0.809972 0.586469i \(-0.199483\pi\)
−0.586469 + 0.809972i \(0.699483\pi\)
\(194\) 141.048i 0.727054i
\(195\) −84.5964 260.653i −0.433828 1.33668i
\(196\) 23.3594 0.119181
\(197\) 126.094 126.094i 0.640073 0.640073i −0.310501 0.950573i \(-0.600497\pi\)
0.950573 + 0.310501i \(0.100497\pi\)
\(198\) 51.5174 0.260189
\(199\) 152.241i 0.765032i 0.923949 + 0.382516i \(0.124942\pi\)
−0.923949 + 0.382516i \(0.875058\pi\)
\(200\) 2.76299 2.76299i 0.0138150 0.0138150i
\(201\) −162.675 + 162.675i −0.809331 + 0.809331i
\(202\) −60.9737 60.9737i −0.301850 0.301850i
\(203\) 26.6228 + 26.6228i 0.131147 + 0.131147i
\(204\) −304.065 −1.49052
\(205\) 34.6491i 0.169020i
\(206\) 20.5922 + 20.5922i 0.0999620 + 0.0999620i
\(207\) 70.8683i 0.342359i
\(208\) 49.3178 96.7128i 0.237105 0.464965i
\(209\) 33.6754 0.161127
\(210\) 79.3662 79.3662i 0.377934 0.377934i
\(211\) −47.5744 −0.225471 −0.112736 0.993625i \(-0.535961\pi\)
−0.112736 + 0.993625i \(0.535961\pi\)
\(212\) 119.057i 0.561589i
\(213\) −381.077 + 381.077i −1.78909 + 1.78909i
\(214\) −2.57438 + 2.57438i −0.0120298 + 0.0120298i
\(215\) 109.178 + 109.178i 0.507803 + 0.507803i
\(216\) 11.9669 + 11.9669i 0.0554024 + 0.0554024i
\(217\) −4.70178 −0.0216672
\(218\) 140.373i 0.643913i
\(219\) −131.623 131.623i −0.601017 0.601017i
\(220\) 126.785i 0.576296i
\(221\) 254.480 + 129.770i 1.15149 + 0.587193i
\(222\) −117.219 −0.528015
\(223\) −38.2260 + 38.2260i −0.171417 + 0.171417i −0.787602 0.616185i \(-0.788677\pi\)
0.616185 + 0.787602i \(0.288677\pi\)
\(224\) 200.465 0.894932
\(225\) 5.40356i 0.0240158i
\(226\) 39.8334 39.8334i 0.176254 0.176254i
\(227\) 44.7324 44.7324i 0.197059 0.197059i −0.601679 0.798738i \(-0.705501\pi\)
0.798738 + 0.601679i \(0.205501\pi\)
\(228\) −43.7587 43.7587i −0.191924 0.191924i
\(229\) −167.634 167.634i −0.732025 0.732025i 0.238995 0.971021i \(-0.423182\pi\)
−0.971021 + 0.238995i \(0.923182\pi\)
\(230\) −35.4342 −0.154062
\(231\) 203.057i 0.879034i
\(232\) −24.7367 24.7367i −0.106624 0.106624i
\(233\) 292.789i 1.25661i −0.777969 0.628303i \(-0.783750\pi\)
0.777969 0.628303i \(-0.216250\pi\)
\(234\) 27.4562 + 84.5964i 0.117334 + 0.361523i
\(235\) −267.627 −1.13884
\(236\) −193.728 + 193.728i −0.820882 + 0.820882i
\(237\) 78.1886 0.329910
\(238\) 117.000i 0.491597i
\(239\) 0.0153037 0.0153037i 6.40324e−5 6.40324e-5i −0.707075 0.707139i \(-0.749986\pi\)
0.707139 + 0.707075i \(0.249986\pi\)
\(240\) 124.476 124.476i 0.518649 0.518649i
\(241\) 240.197 + 240.197i 0.996669 + 0.996669i 0.999994 0.00332576i \(-0.00105862\pi\)
−0.00332576 + 0.999994i \(0.501059\pi\)
\(242\) −37.3662 37.3662i −0.154406 0.154406i
\(243\) 335.246 1.37961
\(244\) 267.043i 1.09444i
\(245\) −25.1623 25.1623i −0.102703 0.102703i
\(246\) 23.4036i 0.0951364i
\(247\) 17.9473 + 55.2982i 0.0726613 + 0.223879i
\(248\) 4.36868 0.0176156
\(249\) 185.732 185.732i 0.745913 0.745913i
\(250\) 101.355 0.405421
\(251\) 131.842i 0.525267i −0.964896 0.262633i \(-0.915409\pi\)
0.964896 0.262633i \(-0.0845910\pi\)
\(252\) 126.785 126.785i 0.503115 0.503115i
\(253\) 45.3288 45.3288i 0.179165 0.179165i
\(254\) 58.7893 + 58.7893i 0.231454 + 0.231454i
\(255\) 327.533 + 327.533i 1.28444 + 1.28444i
\(256\) −75.2107 −0.293792
\(257\) 156.579i 0.609255i 0.952471 + 0.304628i \(0.0985320\pi\)
−0.952471 + 0.304628i \(0.901468\pi\)
\(258\) −73.7434 73.7434i −0.285827 0.285827i
\(259\) 222.004i 0.857159i
\(260\) −208.193 + 67.5701i −0.800742 + 0.259885i
\(261\) −48.3772 −0.185353
\(262\) −149.778 + 149.778i −0.571673 + 0.571673i
\(263\) −338.982 −1.28891 −0.644453 0.764644i \(-0.722915\pi\)
−0.644453 + 0.764644i \(0.722915\pi\)
\(264\) 188.671i 0.714664i
\(265\) −128.246 + 128.246i −0.483945 + 0.483945i
\(266\) −16.8377 + 16.8377i −0.0632997 + 0.0632997i
\(267\) −37.0043 37.0043i −0.138593 0.138593i
\(268\) 129.935 + 129.935i 0.484830 + 0.484830i
\(269\) −222.061 −0.825506 −0.412753 0.910843i \(-0.635433\pi\)
−0.412753 + 0.910843i \(0.635433\pi\)
\(270\) 11.7018i 0.0433399i
\(271\) 39.0722 + 39.0722i 0.144178 + 0.144178i 0.775511 0.631333i \(-0.217492\pi\)
−0.631333 + 0.775511i \(0.717492\pi\)
\(272\) 183.500i 0.674631i
\(273\) −333.438 + 108.219i −1.22139 + 0.396407i
\(274\) 203.715 0.743484
\(275\) 3.45623 3.45623i 0.0125681 0.0125681i
\(276\) −117.803 −0.426822
\(277\) 112.053i 0.404522i −0.979332 0.202261i \(-0.935171\pi\)
0.979332 0.202261i \(-0.0648290\pi\)
\(278\) 78.7214 78.7214i 0.283170 0.283170i
\(279\) 4.27189 4.27189i 0.0153114 0.0153114i
\(280\) −139.664 139.664i −0.498801 0.498801i
\(281\) −174.846 174.846i −0.622229 0.622229i 0.323872 0.946101i \(-0.395015\pi\)
−0.946101 + 0.323872i \(0.895015\pi\)
\(282\) 180.767 0.641019
\(283\) 271.201i 0.958309i −0.877731 0.479154i \(-0.840943\pi\)
0.877731 0.479154i \(-0.159057\pi\)
\(284\) 304.379 + 304.379i 1.07176 + 1.07176i
\(285\) 94.2719i 0.330779i
\(286\) −36.5480 + 71.6712i −0.127790 + 0.250599i
\(287\) −44.3246 −0.154441
\(288\) −182.136 + 182.136i −0.632416 + 0.632416i
\(289\) −193.842 −0.670734
\(290\) 24.1886i 0.0834090i
\(291\) 505.114 505.114i 1.73579 1.73579i
\(292\) −105.132 + 105.132i −0.360040 + 0.360040i
\(293\) −240.156 240.156i −0.819643 0.819643i 0.166413 0.986056i \(-0.446782\pi\)
−0.986056 + 0.166413i \(0.946782\pi\)
\(294\) 16.9957 + 16.9957i 0.0578086 + 0.0578086i
\(295\) 417.359 1.41478
\(296\) 206.276i 0.696879i
\(297\) 14.9694 + 14.9694i 0.0504020 + 0.0504020i
\(298\) 42.0968i 0.141264i
\(299\) 98.5922 + 50.2762i 0.329740 + 0.168148i
\(300\) −8.98221 −0.0299407
\(301\) 139.664 139.664i 0.464001 0.464001i
\(302\) −87.3772 −0.289329
\(303\) 436.710i 1.44129i
\(304\) −26.4078 + 26.4078i −0.0868679 + 0.0868679i
\(305\) −287.653 + 287.653i −0.943126 + 0.943126i
\(306\) −106.302 106.302i −0.347394 0.347394i
\(307\) 219.684 + 219.684i 0.715583 + 0.715583i 0.967697 0.252114i \(-0.0811259\pi\)
−0.252114 + 0.967697i \(0.581126\pi\)
\(308\) 162.189 0.526586
\(309\) 147.487i 0.477304i
\(310\) −2.13594 2.13594i −0.00689014 0.00689014i
\(311\) 341.684i 1.09866i −0.835605 0.549331i \(-0.814883\pi\)
0.835605 0.549331i \(-0.185117\pi\)
\(312\) 309.816 100.552i 0.992999 0.322283i
\(313\) 438.517 1.40101 0.700507 0.713645i \(-0.252957\pi\)
0.700507 + 0.713645i \(0.252957\pi\)
\(314\) 32.2278 32.2278i 0.102636 0.102636i
\(315\) −273.140 −0.867112
\(316\) 62.4520i 0.197633i
\(317\) 153.140 153.140i 0.483092 0.483092i −0.423026 0.906118i \(-0.639032\pi\)
0.906118 + 0.423026i \(0.139032\pi\)
\(318\) 86.6228 86.6228i 0.272399 0.272399i
\(319\) −30.9431 30.9431i −0.0970002 0.0970002i
\(320\) −28.5548 28.5548i −0.0892338 0.0892338i
\(321\) 18.4384 0.0574406
\(322\) 45.3288i 0.140773i
\(323\) −69.4868 69.4868i −0.215130 0.215130i
\(324\) 287.982i 0.888834i
\(325\) 7.51744 + 3.83345i 0.0231306 + 0.0117952i
\(326\) −52.8377 −0.162079
\(327\) −502.695 + 502.695i −1.53729 + 1.53729i
\(328\) 41.1843 0.125562
\(329\) 342.359i 1.04061i
\(330\) −92.2456 + 92.2456i −0.279532 + 0.279532i
\(331\) −195.982 + 195.982i −0.592091 + 0.592091i −0.938196 0.346105i \(-0.887504\pi\)
0.346105 + 0.938196i \(0.387504\pi\)
\(332\) −148.351 148.351i −0.446840 0.446840i
\(333\) 201.706 + 201.706i 0.605724 + 0.605724i
\(334\) −159.482 −0.477491
\(335\) 279.925i 0.835598i
\(336\) −159.235 159.235i −0.473912 0.473912i
\(337\) 7.32456i 0.0217346i 0.999941 + 0.0108673i \(0.00345923\pi\)
−0.999941 + 0.0108673i \(0.996541\pi\)
\(338\) −137.169 21.8181i −0.405826 0.0645507i
\(339\) −285.298 −0.841588
\(340\) 261.612 261.612i 0.769446 0.769446i
\(341\) 5.46477 0.0160257
\(342\) 30.5964i 0.0894633i
\(343\) −256.664 + 256.664i −0.748293 + 0.748293i
\(344\) −129.770 + 129.770i −0.377238 + 0.377238i
\(345\) 126.895 + 126.895i 0.367811 + 0.367811i
\(346\) −46.1317 46.1317i −0.133329 0.133329i
\(347\) −154.759 −0.445991 −0.222995 0.974820i \(-0.571583\pi\)
−0.222995 + 0.974820i \(0.571583\pi\)
\(348\) 80.4164i 0.231082i
\(349\) 220.419 + 220.419i 0.631573 + 0.631573i 0.948462 0.316890i \(-0.102639\pi\)
−0.316890 + 0.948462i \(0.602639\pi\)
\(350\) 3.45623i 0.00987493i
\(351\) −16.6032 + 32.5591i −0.0473026 + 0.0927609i
\(352\) −232.996 −0.661920
\(353\) 331.680 331.680i 0.939603 0.939603i −0.0586746 0.998277i \(-0.518687\pi\)
0.998277 + 0.0586746i \(0.0186874\pi\)
\(354\) −281.903 −0.796337
\(355\) 655.741i 1.84716i
\(356\) −29.5566 + 29.5566i −0.0830241 + 0.0830241i
\(357\) 418.993 418.993i 1.17365 1.17365i
\(358\) 184.993 + 184.993i 0.516741 + 0.516741i
\(359\) 132.785 + 132.785i 0.369875 + 0.369875i 0.867431 0.497557i \(-0.165769\pi\)
−0.497557 + 0.867431i \(0.665769\pi\)
\(360\) 253.789 0.704970
\(361\) 341.000i 0.944598i
\(362\) 138.395 + 138.395i 0.382307 + 0.382307i
\(363\) 267.627i 0.737265i
\(364\) 86.4384 + 266.329i 0.237468 + 0.731673i
\(365\) 226.491 0.620524
\(366\) 194.294 194.294i 0.530858 0.530858i
\(367\) 282.416 0.769527 0.384763 0.923015i \(-0.374283\pi\)
0.384763 + 0.923015i \(0.374283\pi\)
\(368\) 71.0925i 0.193186i
\(369\) 40.2719 40.2719i 0.109138 0.109138i
\(370\) 100.853 100.853i 0.272576 0.272576i
\(371\) 164.057 + 164.057i 0.442202 + 0.442202i
\(372\) −7.10106 7.10106i −0.0190889 0.0190889i
\(373\) −648.877 −1.73962 −0.869808 0.493390i \(-0.835758\pi\)
−0.869808 + 0.493390i \(0.835758\pi\)
\(374\) 135.986i 0.363600i
\(375\) −362.967 362.967i −0.967912 0.967912i
\(376\) 318.105i 0.846023i
\(377\) 34.3203 67.3025i 0.0910352 0.178521i
\(378\) −14.9694 −0.0396016
\(379\) −429.302 + 429.302i −1.13272 + 1.13272i −0.143002 + 0.989722i \(0.545675\pi\)
−0.989722 + 0.143002i \(0.954325\pi\)
\(380\) 75.2982 0.198153
\(381\) 421.065i 1.10516i
\(382\) −2.15373 + 2.15373i −0.00563804 + 0.00563804i
\(383\) 132.739 132.739i 0.346577 0.346577i −0.512256 0.858833i \(-0.671190\pi\)
0.858833 + 0.512256i \(0.171190\pi\)
\(384\) 383.559 + 383.559i 0.998852 + 0.998852i
\(385\) −174.706 174.706i −0.453782 0.453782i
\(386\) 50.1359 0.129886
\(387\) 253.789i 0.655786i
\(388\) −403.452 403.452i −1.03982 1.03982i
\(389\) 510.342i 1.31193i 0.754790 + 0.655966i \(0.227739\pi\)
−0.754790 + 0.655966i \(0.772261\pi\)
\(390\) −200.638 102.314i −0.514457 0.262342i
\(391\) −187.065 −0.478428
\(392\) 29.9082 29.9082i 0.0762964 0.0762964i
\(393\) 1072.75 2.72965
\(394\) 146.557i 0.371971i
\(395\) −67.2719 + 67.2719i −0.170309 + 0.170309i
\(396\) −147.359 + 147.359i −0.372120 + 0.372120i
\(397\) −142.061 142.061i −0.357837 0.357837i 0.505178 0.863015i \(-0.331427\pi\)
−0.863015 + 0.505178i \(0.831427\pi\)
\(398\) 88.4733 + 88.4733i 0.222295 + 0.222295i
\(399\) 120.596 0.302247
\(400\) 5.42065i 0.0135516i
\(401\) 144.298 + 144.298i 0.359846 + 0.359846i 0.863756 0.503910i \(-0.168106\pi\)
−0.503910 + 0.863756i \(0.668106\pi\)
\(402\) 189.074i 0.470333i
\(403\) 2.91245 + 8.97367i 0.00722693 + 0.0222672i
\(404\) 348.816 0.863405
\(405\) −310.208 + 310.208i −0.765946 + 0.765946i
\(406\) 30.9431 0.0762144
\(407\) 258.031i 0.633982i
\(408\) −389.309 + 389.309i −0.954189 + 0.954189i
\(409\) 91.8598 91.8598i 0.224596 0.224596i −0.585835 0.810431i \(-0.699233\pi\)
0.810431 + 0.585835i \(0.199233\pi\)
\(410\) −20.1359 20.1359i −0.0491121 0.0491121i
\(411\) −729.530 729.530i −1.77501 1.77501i
\(412\) −117.803 −0.285929
\(413\) 533.903i 1.29274i
\(414\) −41.1843 41.1843i −0.0994791 0.0994791i
\(415\) 319.601i 0.770122i
\(416\) −124.175 382.601i −0.298498 0.919713i
\(417\) −563.824 −1.35210
\(418\) 19.5701 19.5701i 0.0468184 0.0468184i
\(419\) −83.2327 −0.198646 −0.0993231 0.995055i \(-0.531668\pi\)
−0.0993231 + 0.995055i \(0.531668\pi\)
\(420\) 454.035i 1.08104i
\(421\) 68.3135 68.3135i 0.162265 0.162265i −0.621304 0.783569i \(-0.713397\pi\)
0.783569 + 0.621304i \(0.213397\pi\)
\(422\) −27.6473 + 27.6473i −0.0655150 + 0.0655150i
\(423\) −311.057 311.057i −0.735359 0.735359i
\(424\) −152.434 152.434i −0.359515 0.359515i
\(425\) −14.2633 −0.0335608
\(426\) 442.917i 1.03971i
\(427\) 367.978 + 367.978i 0.861775 + 0.861775i
\(428\) 14.7274i 0.0344099i
\(429\) 387.548 125.781i 0.903375 0.293195i
\(430\) 126.895 0.295104
\(431\) 469.963 469.963i 1.09040 1.09040i 0.0949152 0.995485i \(-0.469742\pi\)
0.995485 0.0949152i \(-0.0302580\pi\)
\(432\) −23.4776 −0.0543463
\(433\) 122.140i 0.282079i 0.990004 + 0.141040i \(0.0450445\pi\)
−0.990004 + 0.141040i \(0.954956\pi\)
\(434\) −2.73239 + 2.73239i −0.00629582 + 0.00629582i
\(435\) 86.6228 86.6228i 0.199133 0.199133i
\(436\) 401.520 + 401.520i 0.920917 + 0.920917i
\(437\) −26.9210 26.9210i −0.0616041 0.0616041i
\(438\) −152.982 −0.349274
\(439\) 31.2897i 0.0712749i −0.999365 0.0356374i \(-0.988654\pi\)
0.999365 0.0356374i \(-0.0113462\pi\)
\(440\) 162.329 + 162.329i 0.368929 + 0.368929i
\(441\) 58.4911i 0.132633i
\(442\) 223.302 72.4740i 0.505209 0.163968i
\(443\) 567.372 1.28075 0.640375 0.768062i \(-0.278779\pi\)
0.640375 + 0.768062i \(0.278779\pi\)
\(444\) 335.291 335.291i 0.755161 0.755161i
\(445\) 63.6754 0.143091
\(446\) 44.4292i 0.0996170i
\(447\) −150.754 + 150.754i −0.337258 + 0.337258i
\(448\) −36.5285 + 36.5285i −0.0815368 + 0.0815368i
\(449\) −530.873 530.873i −1.18234 1.18234i −0.979135 0.203209i \(-0.934863\pi\)
−0.203209 0.979135i \(-0.565137\pi\)
\(450\) −3.14022 3.14022i −0.00697826 0.00697826i
\(451\) 51.5174 0.114229
\(452\) 227.878i 0.504154i
\(453\) 312.910 + 312.910i 0.690750 + 0.690750i
\(454\) 51.9915i 0.114519i
\(455\) 193.774 379.993i 0.425877 0.835150i
\(456\) −112.053 −0.245730
\(457\) 232.092 232.092i 0.507860 0.507860i −0.406009 0.913869i \(-0.633080\pi\)
0.913869 + 0.406009i \(0.133080\pi\)
\(458\) −194.837 −0.425408
\(459\) 61.7765i 0.134589i
\(460\) 101.355 101.355i 0.220337 0.220337i
\(461\) −209.748 + 209.748i −0.454984 + 0.454984i −0.897005 0.442021i \(-0.854262\pi\)
0.442021 + 0.897005i \(0.354262\pi\)
\(462\) 118.004 + 118.004i 0.255421 + 0.255421i
\(463\) 127.645 + 127.645i 0.275691 + 0.275691i 0.831386 0.555695i \(-0.187548\pi\)
−0.555695 + 0.831386i \(0.687548\pi\)
\(464\) 48.5303 0.104591
\(465\) 15.2982i 0.0328994i
\(466\) −170.151 170.151i −0.365131 0.365131i
\(467\) 687.737i 1.47267i 0.676617 + 0.736335i \(0.263445\pi\)
−0.676617 + 0.736335i \(0.736555\pi\)
\(468\) −320.513 163.443i −0.684857 0.349237i
\(469\) −358.092 −0.763522
\(470\) −155.528 + 155.528i −0.330912 + 0.330912i
\(471\) −230.824 −0.490073
\(472\) 496.078i 1.05101i
\(473\) −162.329 + 162.329i −0.343190 + 0.343190i
\(474\) 45.4384 45.4384i 0.0958617 0.0958617i
\(475\) −2.05267 2.05267i −0.00432141 0.00432141i
\(476\) −334.664 334.664i −0.703077 0.703077i
\(477\) −298.114 −0.624977
\(478\) 0.0177872i 3.72117e-5i
\(479\) −318.642 318.642i −0.665224 0.665224i 0.291383 0.956607i \(-0.405885\pi\)
−0.956607 + 0.291383i \(0.905885\pi\)
\(480\) 652.254i 1.35886i
\(481\) −423.710 + 137.517i −0.880895 + 0.285899i
\(482\) 279.176 0.579203
\(483\) 162.329 162.329i 0.336085 0.336085i
\(484\) 213.763 0.441659
\(485\) 869.179i 1.79212i
\(486\) 194.824 194.824i 0.400873 0.400873i
\(487\) 557.065 557.065i 1.14387 1.14387i 0.156136 0.987736i \(-0.450096\pi\)
0.987736 0.156136i \(-0.0499038\pi\)
\(488\) −341.908 341.908i −0.700632 0.700632i
\(489\) 189.219 + 189.219i 0.386951 + 0.386951i
\(490\) −29.2456 −0.0596848
\(491\) 400.698i 0.816085i 0.912963 + 0.408042i \(0.133788\pi\)
−0.912963 + 0.408042i \(0.866212\pi\)
\(492\) −66.9431 66.9431i −0.136063 0.136063i
\(493\) 127.698i 0.259021i
\(494\) 42.5658 + 21.7061i 0.0861657 + 0.0439394i
\(495\) 317.465 0.641343
\(496\) −4.28540 + 4.28540i −0.00863992 + 0.00863992i
\(497\) −838.851 −1.68783
\(498\) 215.873i 0.433479i
\(499\) 102.671 102.671i 0.205754 0.205754i −0.596706 0.802460i \(-0.703524\pi\)
0.802460 + 0.596706i \(0.203524\pi\)
\(500\) −289.914 + 289.914i −0.579828 + 0.579828i
\(501\) 571.127 + 571.127i 1.13997 + 1.13997i
\(502\) −76.6185 76.6185i −0.152627 0.152627i
\(503\) −46.2719 −0.0919918 −0.0459959 0.998942i \(-0.514646\pi\)
−0.0459959 + 0.998942i \(0.514646\pi\)
\(504\) 324.658i 0.644162i
\(505\) −375.737 375.737i −0.744033 0.744033i
\(506\) 52.6847i 0.104120i
\(507\) 413.088 + 569.355i 0.814768 + 1.12299i
\(508\) −336.320 −0.662046
\(509\) −372.280 + 372.280i −0.731396 + 0.731396i −0.970896 0.239500i \(-0.923016\pi\)
0.239500 + 0.970896i \(0.423016\pi\)
\(510\) 380.684 0.746439
\(511\) 289.737i 0.566999i
\(512\) 324.897 324.897i 0.634565 0.634565i
\(513\) 8.89039 8.89039i 0.0173302 0.0173302i
\(514\) 90.9939 + 90.9939i 0.177031 + 0.177031i
\(515\) 126.895 + 126.895i 0.246397 + 0.246397i
\(516\) 421.868 0.817574
\(517\) 397.917i 0.769665i
\(518\) −129.015 129.015i −0.249064 0.249064i
\(519\) 330.408i 0.636624i
\(520\) −180.046 + 353.072i −0.346242 + 0.678985i
\(521\) 27.1224 0.0520584 0.0260292 0.999661i \(-0.491714\pi\)
0.0260292 + 0.999661i \(0.491714\pi\)
\(522\) −28.1139 + 28.1139i −0.0538580 + 0.0538580i
\(523\) 473.851 0.906024 0.453012 0.891504i \(-0.350349\pi\)
0.453012 + 0.891504i \(0.350349\pi\)
\(524\) 856.846i 1.63520i
\(525\) 12.3772 12.3772i 0.0235757 0.0235757i
\(526\) −196.996 + 196.996i −0.374517 + 0.374517i
\(527\) −11.2762 11.2762i −0.0213969 0.0213969i
\(528\) 185.075 + 185.075i 0.350520 + 0.350520i
\(529\) 456.526 0.862998
\(530\) 149.057i 0.281240i
\(531\) 485.088 + 485.088i 0.913536 + 0.913536i
\(532\) 96.3246i 0.181061i
\(533\) 27.4562 + 84.5964i 0.0515126 + 0.158718i
\(534\) −43.0092 −0.0805416
\(535\) −15.8641 + 15.8641i −0.0296524 + 0.0296524i
\(536\) 332.722 0.620751
\(537\) 1324.97i 2.46736i
\(538\) −129.048 + 129.048i −0.239867 + 0.239867i
\(539\) 37.4121 37.4121i 0.0694102 0.0694102i
\(540\) 33.4715 + 33.4715i 0.0619843 + 0.0619843i
\(541\) 531.379 + 531.379i 0.982216 + 0.982216i 0.999845 0.0176283i \(-0.00561156\pi\)
−0.0176283 + 0.999845i \(0.505612\pi\)
\(542\) 45.4128 0.0837874
\(543\) 991.223i 1.82546i
\(544\) 480.770 + 480.770i 0.883768 + 0.883768i
\(545\) 865.017i 1.58719i
\(546\) −130.884 + 256.664i −0.239714 + 0.470081i
\(547\) −716.223 −1.30937 −0.654683 0.755903i \(-0.727198\pi\)
−0.654683 + 0.755903i \(0.727198\pi\)
\(548\) −582.701 + 582.701i −1.06332 + 1.06332i
\(549\) −668.666 −1.21797
\(550\) 4.01709i 0.00730381i
\(551\) −18.3772 + 18.3772i −0.0333525 + 0.0333525i
\(552\) −150.828 + 150.828i −0.273240 + 0.273240i
\(553\) 86.0569 + 86.0569i 0.155618 + 0.155618i
\(554\) −65.1182 65.1182i −0.117542 0.117542i
\(555\) −722.337 −1.30151
\(556\) 450.346i 0.809975i
\(557\) −248.577 248.577i −0.446278 0.446278i 0.447837 0.894115i \(-0.352194\pi\)
−0.894115 + 0.447837i \(0.852194\pi\)
\(558\) 4.96512i 0.00889806i
\(559\) −353.072 180.046i −0.631614 0.322086i
\(560\) 274.004 0.489293
\(561\) −486.986 + 486.986i −0.868069 + 0.868069i
\(562\) −203.220 −0.361601
\(563\) 708.329i 1.25813i 0.777352 + 0.629066i \(0.216563\pi\)
−0.777352 + 0.629066i \(0.783437\pi\)
\(564\) −517.063 + 517.063i −0.916778 + 0.916778i
\(565\) 245.465 245.465i 0.434451 0.434451i
\(566\) −157.606 157.606i −0.278455 0.278455i
\(567\) 396.831 + 396.831i 0.699878 + 0.699878i
\(568\) 779.421 1.37222
\(569\) 349.394i 0.614050i 0.951701 + 0.307025i \(0.0993335\pi\)
−0.951701 + 0.307025i \(0.900667\pi\)
\(570\) 54.7851 + 54.7851i 0.0961141 + 0.0961141i
\(571\) 906.285i 1.58719i −0.608447 0.793594i \(-0.708207\pi\)
0.608447 0.793594i \(-0.291793\pi\)
\(572\) −100.465 309.548i −0.175639 0.541168i
\(573\) 15.4256 0.0269208
\(574\) −25.7587 + 25.7587i −0.0448758 + 0.0448758i
\(575\) −5.52599 −0.00961041
\(576\) 66.3772i 0.115238i
\(577\) 357.842 357.842i 0.620177 0.620177i −0.325400 0.945577i \(-0.605499\pi\)
0.945577 + 0.325400i \(0.105499\pi\)
\(578\) −112.649 + 112.649i −0.194895 + 0.194895i
\(579\) −179.544 179.544i −0.310093 0.310093i
\(580\) −69.1886 69.1886i −0.119291 0.119291i
\(581\) 408.846 0.703694
\(582\) 587.083i 1.00873i
\(583\) −190.680 190.680i −0.327066 0.327066i
\(584\) 269.210i 0.460976i
\(585\) 169.193 + 521.307i 0.289219 + 0.891123i
\(586\) −279.127 −0.476327
\(587\) 405.311 405.311i 0.690479 0.690479i −0.271858 0.962337i \(-0.587638\pi\)
0.962337 + 0.271858i \(0.0876383\pi\)
\(588\) −97.2285 −0.165355
\(589\) 3.24555i 0.00551028i
\(590\) 242.544 242.544i 0.411091 0.411091i
\(591\) −524.840 + 524.840i −0.888053 + 0.888053i
\(592\) −202.344 202.344i −0.341798 0.341798i
\(593\) 550.285 + 550.285i 0.927967 + 0.927967i 0.997574 0.0696070i \(-0.0221745\pi\)
−0.0696070 + 0.997574i \(0.522175\pi\)
\(594\) 17.3986 0.0292906
\(595\) 720.986i 1.21174i
\(596\) 120.413 + 120.413i 0.202035 + 0.202035i
\(597\) 633.670i 1.06142i
\(598\) 86.5132 28.0783i 0.144671 0.0469537i
\(599\) 235.228 0.392702 0.196351 0.980534i \(-0.437091\pi\)
0.196351 + 0.980534i \(0.437091\pi\)
\(600\) −11.5003 + 11.5003i −0.0191672 + 0.0191672i
\(601\) −559.298 −0.930612 −0.465306 0.885150i \(-0.654056\pi\)
−0.465306 + 0.885150i \(0.654056\pi\)
\(602\) 162.329i 0.269649i
\(603\) 325.351 325.351i 0.539554 0.539554i
\(604\) 249.932 249.932i 0.413795 0.413795i
\(605\) −230.261 230.261i −0.380596 0.380596i
\(606\) 253.789 + 253.789i 0.418794 + 0.418794i
\(607\) −507.912 −0.836757 −0.418379 0.908273i \(-0.637402\pi\)
−0.418379 + 0.908273i \(0.637402\pi\)
\(608\) 138.377i 0.227594i
\(609\) −110.811 110.811i −0.181956 0.181956i
\(610\) 334.333i 0.548087i
\(611\) 653.416 212.070i 1.06942 0.347086i
\(612\) 608.131 0.993678
\(613\) −231.540 + 231.540i −0.377715 + 0.377715i −0.870277 0.492562i \(-0.836060\pi\)
0.492562 + 0.870277i \(0.336060\pi\)
\(614\) 255.334 0.415853
\(615\) 144.219i 0.234503i
\(616\) 207.658 207.658i 0.337107 0.337107i
\(617\) −271.412 + 271.412i −0.439890 + 0.439890i −0.891975 0.452085i \(-0.850680\pi\)
0.452085 + 0.891975i \(0.350680\pi\)
\(618\) −85.7103 85.7103i −0.138690 0.138690i
\(619\) −235.048 235.048i −0.379723 0.379723i 0.491279 0.871002i \(-0.336529\pi\)
−0.871002 + 0.491279i \(0.836529\pi\)
\(620\) 12.2192 0.0197084
\(621\) 23.9338i 0.0385408i
\(622\) −198.566 198.566i −0.319238 0.319238i
\(623\) 81.4562i 0.130748i
\(624\) −205.274 + 402.546i −0.328965 + 0.645105i
\(625\) 640.806 1.02529
\(626\) 254.840 254.840i 0.407092 0.407092i
\(627\) −140.167 −0.223551
\(628\) 184.367i 0.293578i
\(629\) 532.427 532.427i 0.846466 0.846466i
\(630\) −158.732 + 158.732i −0.251956 + 0.251956i
\(631\) −95.4630 95.4630i −0.151288 0.151288i 0.627405 0.778693i \(-0.284117\pi\)
−0.778693 + 0.627405i \(0.784117\pi\)
\(632\) −79.9602 79.9602i −0.126519 0.126519i
\(633\) 198.018 0.312824
\(634\) 177.991i 0.280744i
\(635\) 362.276 + 362.276i 0.570514 + 0.570514i
\(636\) 495.548i 0.779164i
\(637\) 81.3729 + 41.4954i 0.127744 + 0.0651419i
\(638\) −35.9644 −0.0563706
\(639\) 762.153 762.153i 1.19273 1.19273i
\(640\) −660.013 −1.03127
\(641\) 904.710i 1.41140i 0.708508 + 0.705702i \(0.249368\pi\)
−0.708508 + 0.705702i \(0.750632\pi\)
\(642\) 10.7153 10.7153i 0.0166905 0.0166905i
\(643\) −108.312 + 108.312i −0.168447 + 0.168447i −0.786297 0.617849i \(-0.788004\pi\)
0.617849 + 0.786297i \(0.288004\pi\)
\(644\) −129.658 129.658i −0.201332 0.201332i
\(645\) −454.427 454.427i −0.704539 0.704539i
\(646\) −80.7630 −0.125020
\(647\) 306.474i 0.473685i −0.971548 0.236842i \(-0.923888\pi\)
0.971548 0.236842i \(-0.0761125\pi\)
\(648\) −368.717 368.717i −0.569008 0.569008i
\(649\) 620.544i 0.956154i
\(650\) 6.59644 2.14091i 0.0101484 0.00329371i
\(651\) 19.5701 0.0300616
\(652\) 151.136 151.136i 0.231804 0.231804i
\(653\) −1009.69 −1.54624 −0.773118 0.634262i \(-0.781304\pi\)
−0.773118 + 0.634262i \(0.781304\pi\)
\(654\) 584.271i 0.893381i
\(655\) −922.975 + 922.975i −1.40912 + 1.40912i
\(656\) −40.3993 + 40.3993i −0.0615843 + 0.0615843i
\(657\) 263.246 + 263.246i 0.400678 + 0.400678i
\(658\) 198.958 + 198.958i 0.302368 + 0.302368i
\(659\) −211.009 −0.320196 −0.160098 0.987101i \(-0.551181\pi\)
−0.160098 + 0.987101i \(0.551181\pi\)
\(660\) 527.715i 0.799568i
\(661\) −61.5922 61.5922i −0.0931803 0.0931803i 0.658980 0.752160i \(-0.270988\pi\)
−0.752160 + 0.658980i \(0.770988\pi\)
\(662\) 227.786i 0.344087i
\(663\) −1059.22 540.138i −1.59761 0.814687i
\(664\) −379.881 −0.572110
\(665\) −103.759 + 103.759i −0.156028 + 0.156028i
\(666\) 234.438 0.352010
\(667\) 49.4733i 0.0741729i
\(668\) 456.179 456.179i 0.682902 0.682902i
\(669\) 159.107 159.107i 0.237828 0.237828i
\(670\) −162.675 162.675i −0.242799 0.242799i
\(671\) −427.693 427.693i −0.637396 0.637396i
\(672\) −834.390 −1.24165
\(673\) 105.500i 0.156760i −0.996924 0.0783801i \(-0.975025\pi\)
0.996924 0.0783801i \(-0.0249748\pi\)
\(674\) 4.25658 + 4.25658i 0.00631541 + 0.00631541i
\(675\) 1.82490i 0.00270356i
\(676\) 454.764 329.947i 0.672727 0.488088i
\(677\) −215.969 −0.319009 −0.159505 0.987197i \(-0.550990\pi\)
−0.159505 + 0.987197i \(0.550990\pi\)
\(678\) −165.798 + 165.798i −0.244540 + 0.244540i
\(679\) 1111.89 1.63754
\(680\) 669.907i 0.985158i
\(681\) −186.189 + 186.189i −0.273405 + 0.273405i
\(682\) 3.17579 3.17579i 0.00465659 0.00465659i
\(683\) 672.956 + 672.956i 0.985294 + 0.985294i 0.999893 0.0145993i \(-0.00464727\pi\)
−0.0145993 + 0.999893i \(0.504647\pi\)
\(684\) 87.5174 + 87.5174i 0.127949 + 0.127949i
\(685\) 1255.35 1.83262
\(686\) 298.315i 0.434862i
\(687\) 697.738 + 697.738i 1.01563 + 1.01563i
\(688\) 254.592i 0.370047i
\(689\) 211.491 414.737i 0.306954 0.601940i
\(690\) 147.487 0.213749
\(691\) −563.105 + 563.105i −0.814913 + 0.814913i −0.985366 0.170453i \(-0.945477\pi\)
0.170453 + 0.985366i \(0.445477\pi\)
\(692\) 263.908 0.381370
\(693\) 406.114i 0.586023i
\(694\) −89.9363 + 89.9363i −0.129591 + 0.129591i
\(695\) 485.103 485.103i 0.697990 0.697990i
\(696\) 102.961 + 102.961i 0.147932 + 0.147932i
\(697\) −106.302 106.302i −0.152514 0.152514i
\(698\) 256.188 0.367031
\(699\) 1218.67i 1.74345i
\(700\) −9.88612 9.88612i −0.0141230 0.0141230i
\(701\) 179.934i 0.256682i 0.991730 + 0.128341i \(0.0409651\pi\)
−0.991730 + 0.128341i \(0.959035\pi\)
\(702\) 9.27258 + 28.5701i 0.0132088 + 0.0406982i
\(703\) 153.246 0.217988
\(704\) 42.4562 42.4562i 0.0603071 0.0603071i
\(705\) 1113.94 1.58005
\(706\) 385.504i 0.546040i
\(707\) −480.658 + 480.658i −0.679855 + 0.679855i
\(708\) 806.350 806.350i 1.13891 1.13891i
\(709\) −291.315 291.315i −0.410882 0.410882i 0.471164 0.882046i \(-0.343834\pi\)
−0.882046 + 0.471164i \(0.843834\pi\)
\(710\) −381.077 381.077i −0.536727 0.536727i
\(711\) −156.377 −0.219940
\(712\) 75.6854i 0.106300i
\(713\) −4.36868 4.36868i −0.00612718 0.00612718i
\(714\) 486.986i 0.682054i
\(715\) −225.219 + 441.658i −0.314992 + 0.617703i
\(716\) −1058.30 −1.47808
\(717\) −0.0636984 + 0.0636984i −8.88401e−5 + 8.88401e-5i
\(718\) 154.333 0.214949
\(719\) 487.565i 0.678116i −0.940766 0.339058i \(-0.889892\pi\)
0.940766 0.339058i \(-0.110108\pi\)
\(720\) −248.952 + 248.952i −0.345766 + 0.345766i
\(721\) 162.329 162.329i 0.225144 0.225144i
\(722\) 198.168 + 198.168i 0.274471 + 0.274471i
\(723\) −999.767 999.767i −1.38280 1.38280i
\(724\) −791.725 −1.09354
\(725\) 3.77223i 0.00520308i
\(726\) 155.528 + 155.528i 0.214227 + 0.214227i
\(727\) 277.337i 0.381482i 0.981640 + 0.190741i \(0.0610891\pi\)
−0.981640 + 0.190741i \(0.938911\pi\)
\(728\) 451.664 + 230.322i 0.620418 + 0.316376i
\(729\) −615.780 −0.844691
\(730\) 131.623 131.623i 0.180305 0.180305i
\(731\) 669.907 0.916426
\(732\) 1111.51i 1.51845i
\(733\) −235.559 + 235.559i −0.321363 + 0.321363i −0.849290 0.527927i \(-0.822970\pi\)
0.527927 + 0.849290i \(0.322970\pi\)
\(734\) 164.123 164.123i 0.223601 0.223601i
\(735\) 104.732 + 104.732i 0.142493 + 0.142493i
\(736\) 186.263 + 186.263i 0.253074 + 0.253074i
\(737\) 416.202 0.564725
\(738\) 46.8071i 0.0634243i
\(739\) −667.732 667.732i −0.903561 0.903561i 0.0921811 0.995742i \(-0.470616\pi\)
−0.995742 + 0.0921811i \(0.970616\pi\)
\(740\) 576.956i 0.779670i
\(741\) −74.7018 230.167i −0.100812 0.310616i
\(742\) 190.680 0.256981
\(743\) 335.358 335.358i 0.451356 0.451356i −0.444448 0.895804i \(-0.646600\pi\)
0.895804 + 0.444448i \(0.146600\pi\)
\(744\) −18.1836 −0.0244404
\(745\) 259.412i 0.348204i
\(746\) −377.088 + 377.088i −0.505479 + 0.505479i
\(747\) −371.465 + 371.465i −0.497275 + 0.497275i
\(748\) 388.973 + 388.973i 0.520017 + 0.520017i
\(749\) 20.2939 + 20.2939i 0.0270947 + 0.0270947i
\(750\) −421.868 −0.562491
\(751\) 1300.24i 1.73134i −0.500615 0.865670i \(-0.666893\pi\)
0.500615 0.865670i \(-0.333107\pi\)
\(752\) 312.041 + 312.041i 0.414948 + 0.414948i
\(753\) 548.763i 0.728769i
\(754\) −19.1672 59.0569i −0.0254207 0.0783249i
\(755\) −538.443 −0.713169
\(756\) 42.8181 42.8181i 0.0566378 0.0566378i
\(757\) 1155.45 1.52636 0.763178 0.646188i \(-0.223638\pi\)
0.763178 + 0.646188i \(0.223638\pi\)
\(758\) 498.969i 0.658270i
\(759\) −188.671 + 188.671i −0.248579 + 0.248579i
\(760\) 96.4078 96.4078i 0.126852 0.126852i
\(761\) −205.412 205.412i −0.269924 0.269924i 0.559146 0.829069i \(-0.311129\pi\)
−0.829069 + 0.559146i \(0.811129\pi\)
\(762\) −244.698 244.698i −0.321125 0.321125i
\(763\) −1106.57 −1.45028
\(764\) 12.3210i 0.0161269i
\(765\) −655.065 655.065i −0.856295 0.856295i
\(766\) 154.280i 0.201410i
\(767\) −1018.99 + 330.719i −1.32854 + 0.431185i
\(768\) 313.048 0.407614
\(769\) 62.0527 62.0527i 0.0806927 0.0806927i −0.665608 0.746301i \(-0.731828\pi\)
0.746301 + 0.665608i \(0.231828\pi\)
\(770\) −203.057 −0.263710
\(771\) 651.724i 0.845297i
\(772\) −143.408 + 143.408i −0.185761 + 0.185761i
\(773\) −318.813 + 318.813i −0.412436 + 0.412436i −0.882586 0.470150i \(-0.844200\pi\)
0.470150 + 0.882586i \(0.344200\pi\)
\(774\) 147.487 + 147.487i 0.190551 + 0.190551i
\(775\) −0.333102 0.333102i −0.000429809 0.000429809i
\(776\) −1033.12 −1.33134
\(777\) 924.043i 1.18925i
\(778\) 296.579 + 296.579i 0.381207 + 0.381207i
\(779\) 30.5964i 0.0392766i
\(780\) 866.557 281.246i 1.11097 0.360571i
\(781\) 974.977 1.24837
\(782\) −108.711