Properties

Label 1050.2.bc.g.607.3
Level $1050$
Weight $2$
Character 1050.607
Analytic conductor $8.384$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 607.3
Root \(-0.424637 + 3.22544i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.g.493.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-1.42843 - 2.22701i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(-1.42843 - 2.22701i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.230557 - 0.399337i) q^{11} +(0.258819 + 0.965926i) q^{12} +(-4.00275 - 4.00275i) q^{13} +(-1.95615 - 1.78142i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.58394 - 0.424416i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(2.91323 - 5.04586i) q^{19} +(2.52083 - 0.803365i) q^{21} +(-0.326057 - 0.326057i) q^{22} +(-1.14199 - 4.26196i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.90235 - 2.83037i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.35056 - 1.21443i) q^{28} +5.53773i q^{29} +(0.0280956 - 0.0162210i) q^{31} +(0.258819 - 0.965926i) q^{32} +(0.445403 - 0.119345i) q^{33} -1.63982 q^{34} -1.00000 q^{36} +(7.78966 - 2.08723i) q^{37} +(1.50800 - 5.62793i) q^{38} +(4.90235 - 2.83037i) q^{39} -10.9453i q^{41} +(2.22701 - 1.42843i) q^{42} +(-4.75146 + 4.75146i) q^{43} +(-0.399337 - 0.230557i) q^{44} +(-2.20615 - 3.82117i) q^{46} +(2.33979 + 8.73220i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-2.91917 + 6.36227i) q^{49} +(0.819909 - 1.42012i) q^{51} +(-5.46786 - 1.46511i) q^{52} +(2.65301 + 0.710873i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.58479 - 0.564683i) q^{56} +(4.11993 + 4.11993i) q^{57} +(1.43327 + 5.34903i) q^{58} +(-0.958791 - 1.66067i) q^{59} +(-11.7393 - 6.77768i) q^{61} +(0.0229400 - 0.0229400i) q^{62} +(0.123551 + 2.64286i) q^{63} -1.00000i q^{64} +(0.399337 - 0.230557i) q^{66} +(0.986161 - 3.68040i) q^{67} +(-1.58394 + 0.424416i) q^{68} +4.41231 q^{69} +8.85877 q^{71} +(-0.965926 + 0.258819i) q^{72} +(1.05010 - 3.91904i) q^{73} +(6.98401 - 4.03222i) q^{74} -5.82646i q^{76} +(-0.559993 + 1.08388i) q^{77} +(4.00275 - 4.00275i) q^{78} +(4.38319 + 2.53064i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-2.83285 - 10.5723i) q^{82} +(1.08813 + 1.08813i) q^{83} +(1.78142 - 1.95615i) q^{84} +(-3.35979 + 5.81932i) q^{86} +(-5.34903 - 1.43327i) q^{87} +(-0.445403 - 0.119345i) q^{88} +(5.71423 - 9.89734i) q^{89} +(-3.19652 + 14.6318i) q^{91} +(-3.11997 - 3.11997i) q^{92} +(0.00839662 + 0.0313366i) q^{93} +(4.52012 + 7.82908i) q^{94} +(0.866025 + 0.500000i) q^{96} +(2.51799 - 2.51799i) q^{97} +(-1.17303 + 6.90101i) q^{98} +0.461115i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{7} + O(q^{10}) \) \( 16q + 4q^{7} + 4q^{11} - 16q^{13} - 16q^{14} + 8q^{16} - 12q^{17} + 8q^{19} + 8q^{21} - 4q^{22} + 40q^{23} + 8q^{24} - 12q^{26} + 4q^{28} - 24q^{31} - 4q^{33} - 16q^{34} - 16q^{36} + 8q^{37} + 20q^{38} + 12q^{39} - 8q^{42} + 24q^{43} - 4q^{46} - 52q^{49} + 8q^{51} - 8q^{52} + 28q^{53} + 8q^{54} + 8q^{56} + 8q^{57} + 12q^{58} - 8q^{59} + 24q^{61} + 8q^{62} + 4q^{63} + 84q^{67} - 12q^{68} + 8q^{69} - 32q^{71} - 16q^{73} + 24q^{74} - 44q^{77} + 16q^{78} - 12q^{79} + 8q^{81} - 36q^{82} - 16q^{83} - 4q^{84} - 8q^{86} - 48q^{87} + 4q^{88} + 16q^{89} + 8q^{91} - 8q^{92} + 32q^{93} - 8q^{94} + 44q^{97} - 24q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 0.258819i 0.683013 0.183013i
\(3\) −0.258819 + 0.965926i −0.149429 + 0.557678i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) −1.42843 2.22701i −0.539896 0.841732i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) 0 0
\(11\) −0.230557 0.399337i −0.0695156 0.120405i 0.829173 0.558993i \(-0.188812\pi\)
−0.898688 + 0.438588i \(0.855479\pi\)
\(12\) 0.258819 + 0.965926i 0.0747146 + 0.278839i
\(13\) −4.00275 4.00275i −1.11016 1.11016i −0.993128 0.117035i \(-0.962661\pi\)
−0.117035 0.993128i \(-0.537339\pi\)
\(14\) −1.95615 1.78142i −0.522803 0.476106i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −1.58394 0.424416i −0.384162 0.102936i 0.0615689 0.998103i \(-0.480390\pi\)
−0.445731 + 0.895167i \(0.647056\pi\)
\(18\) −0.965926 0.258819i −0.227671 0.0610042i
\(19\) 2.91323 5.04586i 0.668341 1.15760i −0.310027 0.950728i \(-0.600338\pi\)
0.978368 0.206872i \(-0.0663285\pi\)
\(20\) 0 0
\(21\) 2.52083 0.803365i 0.550091 0.175309i
\(22\) −0.326057 0.326057i −0.0695156 0.0695156i
\(23\) −1.14199 4.26196i −0.238121 0.888680i −0.976717 0.214532i \(-0.931177\pi\)
0.738596 0.674149i \(-0.235489\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0 0
\(26\) −4.90235 2.83037i −0.961429 0.555081i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −2.35056 1.21443i −0.444215 0.229507i
\(29\) 5.53773i 1.02833i 0.857691 + 0.514165i \(0.171898\pi\)
−0.857691 + 0.514165i \(0.828102\pi\)
\(30\) 0 0
\(31\) 0.0280956 0.0162210i 0.00504612 0.00291338i −0.497475 0.867478i \(-0.665739\pi\)
0.502521 + 0.864565i \(0.332406\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) 0.445403 0.119345i 0.0775346 0.0207753i
\(34\) −1.63982 −0.281226
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 7.78966 2.08723i 1.28061 0.343139i 0.446524 0.894772i \(-0.352662\pi\)
0.834087 + 0.551633i \(0.185995\pi\)
\(38\) 1.50800 5.62793i 0.244630 0.912970i
\(39\) 4.90235 2.83037i 0.785003 0.453222i
\(40\) 0 0
\(41\) 10.9453i 1.70937i −0.519149 0.854684i \(-0.673751\pi\)
0.519149 0.854684i \(-0.326249\pi\)
\(42\) 2.22701 1.42843i 0.343636 0.220412i
\(43\) −4.75146 + 4.75146i −0.724591 + 0.724591i −0.969537 0.244946i \(-0.921230\pi\)
0.244946 + 0.969537i \(0.421230\pi\)
\(44\) −0.399337 0.230557i −0.0602023 0.0347578i
\(45\) 0 0
\(46\) −2.20615 3.82117i −0.325280 0.563401i
\(47\) 2.33979 + 8.73220i 0.341293 + 1.27372i 0.896884 + 0.442266i \(0.145825\pi\)
−0.555591 + 0.831456i \(0.687508\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) −2.91917 + 6.36227i −0.417025 + 0.908895i
\(50\) 0 0
\(51\) 0.819909 1.42012i 0.114810 0.198857i
\(52\) −5.46786 1.46511i −0.758255 0.203174i
\(53\) 2.65301 + 0.710873i 0.364419 + 0.0976459i 0.436382 0.899761i \(-0.356260\pi\)
−0.0719627 + 0.997407i \(0.522926\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) −2.58479 0.564683i −0.345407 0.0754589i
\(57\) 4.11993 + 4.11993i 0.545698 + 0.545698i
\(58\) 1.43327 + 5.34903i 0.188197 + 0.702362i
\(59\) −0.958791 1.66067i −0.124824 0.216201i 0.796840 0.604190i \(-0.206503\pi\)
−0.921664 + 0.387989i \(0.873170\pi\)
\(60\) 0 0
\(61\) −11.7393 6.77768i −1.50306 0.867793i −0.999994 0.00354661i \(-0.998871\pi\)
−0.503068 0.864247i \(-0.667796\pi\)
\(62\) 0.0229400 0.0229400i 0.00291338 0.00291338i
\(63\) 0.123551 + 2.64286i 0.0155659 + 0.332970i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0.399337 0.230557i 0.0491550 0.0283796i
\(67\) 0.986161 3.68040i 0.120479 0.449633i −0.879160 0.476528i \(-0.841895\pi\)
0.999638 + 0.0268948i \(0.00856192\pi\)
\(68\) −1.58394 + 0.424416i −0.192081 + 0.0514680i
\(69\) 4.41231 0.531179
\(70\) 0 0
\(71\) 8.85877 1.05134 0.525671 0.850688i \(-0.323814\pi\)
0.525671 + 0.850688i \(0.323814\pi\)
\(72\) −0.965926 + 0.258819i −0.113835 + 0.0305021i
\(73\) 1.05010 3.91904i 0.122905 0.458689i −0.876851 0.480762i \(-0.840360\pi\)
0.999756 + 0.0220733i \(0.00702672\pi\)
\(74\) 6.98401 4.03222i 0.811875 0.468736i
\(75\) 0 0
\(76\) 5.82646i 0.668341i
\(77\) −0.559993 + 1.08388i −0.0638172 + 0.123519i
\(78\) 4.00275 4.00275i 0.453222 0.453222i
\(79\) 4.38319 + 2.53064i 0.493148 + 0.284719i 0.725879 0.687822i \(-0.241433\pi\)
−0.232732 + 0.972541i \(0.574766\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −2.83285 10.5723i −0.312836 1.16752i
\(83\) 1.08813 + 1.08813i 0.119438 + 0.119438i 0.764299 0.644861i \(-0.223085\pi\)
−0.644861 + 0.764299i \(0.723085\pi\)
\(84\) 1.78142 1.95615i 0.194369 0.213434i
\(85\) 0 0
\(86\) −3.35979 + 5.81932i −0.362295 + 0.627514i
\(87\) −5.34903 1.43327i −0.573476 0.153663i
\(88\) −0.445403 0.119345i −0.0474801 0.0127222i
\(89\) 5.71423 9.89734i 0.605708 1.04912i −0.386232 0.922402i \(-0.626223\pi\)
0.991939 0.126714i \(-0.0404432\pi\)
\(90\) 0 0
\(91\) −3.19652 + 14.6318i −0.335087 + 1.53383i
\(92\) −3.11997 3.11997i −0.325280 0.325280i
\(93\) 0.00839662 + 0.0313366i 0.000870688 + 0.00324945i
\(94\) 4.52012 + 7.82908i 0.466215 + 0.807508i
\(95\) 0 0
\(96\) 0.866025 + 0.500000i 0.0883883 + 0.0510310i
\(97\) 2.51799 2.51799i 0.255663 0.255663i −0.567624 0.823288i \(-0.692137\pi\)
0.823288 + 0.567624i \(0.192137\pi\)
\(98\) −1.17303 + 6.90101i −0.118494 + 0.697108i
\(99\) 0.461115i 0.0463438i
\(100\) 0 0
\(101\) 3.90734 2.25590i 0.388795 0.224471i −0.292843 0.956161i \(-0.594601\pi\)
0.681638 + 0.731690i \(0.261268\pi\)
\(102\) 0.424416 1.58394i 0.0420234 0.156834i
\(103\) −14.2719 + 3.82414i −1.40625 + 0.376804i −0.880585 0.473888i \(-0.842850\pi\)
−0.525665 + 0.850692i \(0.676183\pi\)
\(104\) −5.66074 −0.555081
\(105\) 0 0
\(106\) 2.74660 0.266773
\(107\) 5.69821 1.52683i 0.550867 0.147604i 0.0273597 0.999626i \(-0.491290\pi\)
0.523507 + 0.852021i \(0.324623\pi\)
\(108\) 0.258819 0.965926i 0.0249049 0.0929463i
\(109\) −14.3923 + 8.30937i −1.37853 + 0.795893i −0.991982 0.126377i \(-0.959665\pi\)
−0.386546 + 0.922270i \(0.626332\pi\)
\(110\) 0 0
\(111\) 8.06444i 0.765443i
\(112\) −2.64286 + 0.123551i −0.249727 + 0.0116744i
\(113\) −6.35390 + 6.35390i −0.597724 + 0.597724i −0.939706 0.341982i \(-0.888902\pi\)
0.341982 + 0.939706i \(0.388902\pi\)
\(114\) 5.04586 + 2.91323i 0.472588 + 0.272849i
\(115\) 0 0
\(116\) 2.76886 + 4.79581i 0.257082 + 0.445280i
\(117\) 1.46511 + 5.46786i 0.135449 + 0.505503i
\(118\) −1.35593 1.35593i −0.124824 0.124824i
\(119\) 1.31737 + 4.13371i 0.120763 + 0.378936i
\(120\) 0 0
\(121\) 5.39369 9.34214i 0.490335 0.849285i
\(122\) −13.0935 3.50839i −1.18543 0.317634i
\(123\) 10.5723 + 2.83285i 0.953276 + 0.255430i
\(124\) 0.0162210 0.0280956i 0.00145669 0.00252306i
\(125\) 0 0
\(126\) 0.803365 + 2.52083i 0.0715694 + 0.224574i
\(127\) 11.7757 + 11.7757i 1.04493 + 1.04493i 0.998942 + 0.0459856i \(0.0146428\pi\)
0.0459856 + 0.998942i \(0.485357\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) −3.35979 5.81932i −0.295813 0.512363i
\(130\) 0 0
\(131\) 16.4341 + 9.48825i 1.43586 + 0.828992i 0.997558 0.0698379i \(-0.0222482\pi\)
0.438298 + 0.898830i \(0.355582\pi\)
\(132\) 0.326057 0.326057i 0.0283796 0.0283796i
\(133\) −15.3985 + 0.719863i −1.33522 + 0.0624200i
\(134\) 3.81023i 0.329154i
\(135\) 0 0
\(136\) −1.42012 + 0.819909i −0.121775 + 0.0703066i
\(137\) 1.14632 4.27811i 0.0979364 0.365503i −0.899512 0.436896i \(-0.856078\pi\)
0.997448 + 0.0713928i \(0.0227444\pi\)
\(138\) 4.26196 1.14199i 0.362802 0.0972126i
\(139\) 4.35020 0.368979 0.184489 0.982835i \(-0.440937\pi\)
0.184489 + 0.982835i \(0.440937\pi\)
\(140\) 0 0
\(141\) −9.04024 −0.761325
\(142\) 8.55692 2.29282i 0.718080 0.192409i
\(143\) −0.675582 + 2.52131i −0.0564950 + 0.210842i
\(144\) −0.866025 + 0.500000i −0.0721688 + 0.0416667i
\(145\) 0 0
\(146\) 4.05729i 0.335784i
\(147\) −5.38994 4.46638i −0.444555 0.368381i
\(148\) 5.70242 5.70242i 0.468736 0.468736i
\(149\) −3.75900 2.17026i −0.307949 0.177794i 0.338059 0.941125i \(-0.390230\pi\)
−0.646008 + 0.763330i \(0.723563\pi\)
\(150\) 0 0
\(151\) −4.09257 7.08854i −0.333049 0.576857i 0.650059 0.759884i \(-0.274744\pi\)
−0.983108 + 0.183026i \(0.941411\pi\)
\(152\) −1.50800 5.62793i −0.122315 0.456485i
\(153\) 1.15953 + 1.15953i 0.0937421 + 0.0937421i
\(154\) −0.260384 + 1.19188i −0.0209823 + 0.0960447i
\(155\) 0 0
\(156\) 2.83037 4.90235i 0.226611 0.392502i
\(157\) −21.0333 5.63586i −1.67864 0.449790i −0.711221 0.702969i \(-0.751857\pi\)
−0.967420 + 0.253178i \(0.918524\pi\)
\(158\) 4.88882 + 1.30995i 0.388933 + 0.104214i
\(159\) −1.37330 + 2.37863i −0.108910 + 0.188637i
\(160\) 0 0
\(161\) −7.86019 + 8.63114i −0.619470 + 0.680229i
\(162\) 0.707107 + 0.707107i 0.0555556 + 0.0555556i
\(163\) 3.02164 + 11.2769i 0.236673 + 0.883275i 0.977388 + 0.211456i \(0.0678204\pi\)
−0.740715 + 0.671820i \(0.765513\pi\)
\(164\) −5.47265 9.47890i −0.427342 0.740178i
\(165\) 0 0
\(166\) 1.33268 + 0.769426i 0.103436 + 0.0597190i
\(167\) −15.5061 + 15.5061i −1.19990 + 1.19990i −0.225703 + 0.974196i \(0.572468\pi\)
−0.974196 + 0.225703i \(0.927532\pi\)
\(168\) 1.21443 2.35056i 0.0936957 0.181350i
\(169\) 19.0440i 1.46492i
\(170\) 0 0
\(171\) −5.04586 + 2.91323i −0.385867 + 0.222780i
\(172\) −1.73915 + 6.49061i −0.132609 + 0.494905i
\(173\) 9.41238 2.52204i 0.715610 0.191747i 0.117398 0.993085i \(-0.462545\pi\)
0.598212 + 0.801338i \(0.295878\pi\)
\(174\) −5.53773 −0.419814
\(175\) 0 0
\(176\) −0.461115 −0.0347578
\(177\) 1.85224 0.496307i 0.139223 0.0373047i
\(178\) 2.95790 11.0391i 0.221704 0.827412i
\(179\) −1.39876 + 0.807576i −0.104548 + 0.0603611i −0.551363 0.834266i \(-0.685892\pi\)
0.446814 + 0.894627i \(0.352559\pi\)
\(180\) 0 0
\(181\) 12.8519i 0.955277i 0.878556 + 0.477639i \(0.158507\pi\)
−0.878556 + 0.477639i \(0.841493\pi\)
\(182\) 0.699388 + 14.9606i 0.0518421 + 1.10895i
\(183\) 9.58509 9.58509i 0.708550 0.708550i
\(184\) −3.82117 2.20615i −0.281700 0.162640i
\(185\) 0 0
\(186\) 0.0162210 + 0.0280956i 0.00118938 + 0.00206007i
\(187\) 0.195704 + 0.730379i 0.0143113 + 0.0534106i
\(188\) 6.39241 + 6.39241i 0.466215 + 0.466215i
\(189\) −2.58479 0.564683i −0.188016 0.0410746i
\(190\) 0 0
\(191\) 5.30033 9.18043i 0.383518 0.664273i −0.608044 0.793903i \(-0.708046\pi\)
0.991562 + 0.129630i \(0.0413790\pi\)
\(192\) 0.965926 + 0.258819i 0.0697097 + 0.0186787i
\(193\) 6.97019 + 1.86766i 0.501726 + 0.134437i 0.500801 0.865563i \(-0.333039\pi\)
0.000924826 1.00000i \(0.499706\pi\)
\(194\) 1.78049 3.08389i 0.127832 0.221411i
\(195\) 0 0
\(196\) 0.653056 + 6.96947i 0.0466468 + 0.497819i
\(197\) 9.72803 + 9.72803i 0.693093 + 0.693093i 0.962911 0.269818i \(-0.0869635\pi\)
−0.269818 + 0.962911i \(0.586964\pi\)
\(198\) 0.119345 + 0.445403i 0.00848150 + 0.0316534i
\(199\) −4.82648 8.35971i −0.342140 0.592604i 0.642690 0.766127i \(-0.277818\pi\)
−0.984830 + 0.173522i \(0.944485\pi\)
\(200\) 0 0
\(201\) 3.29976 + 1.90512i 0.232747 + 0.134377i
\(202\) 3.19033 3.19033i 0.224471 0.224471i
\(203\) 12.3326 7.91026i 0.865578 0.555191i
\(204\) 1.63982i 0.114810i
\(205\) 0 0
\(206\) −12.7958 + 7.38767i −0.891527 + 0.514723i
\(207\) −1.14199 + 4.26196i −0.0793737 + 0.296227i
\(208\) −5.46786 + 1.46511i −0.379128 + 0.101587i
\(209\) −2.68667 −0.185841
\(210\) 0 0
\(211\) 1.33273 0.0917487 0.0458744 0.998947i \(-0.485393\pi\)
0.0458744 + 0.998947i \(0.485393\pi\)
\(212\) 2.65301 0.710873i 0.182210 0.0488229i
\(213\) −2.29282 + 8.55692i −0.157101 + 0.586310i
\(214\) 5.10888 2.94961i 0.349236 0.201631i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −0.0762571 0.0393987i −0.00517667 0.00267456i
\(218\) −11.7512 + 11.7512i −0.795893 + 0.795893i
\(219\) 3.51371 + 2.02864i 0.237435 + 0.137083i
\(220\) 0 0
\(221\) 4.64129 + 8.03895i 0.312207 + 0.540758i
\(222\) 2.08723 + 7.78966i 0.140086 + 0.522807i
\(223\) 8.25284 + 8.25284i 0.552651 + 0.552651i 0.927205 0.374554i \(-0.122204\pi\)
−0.374554 + 0.927205i \(0.622204\pi\)
\(224\) −2.52083 + 0.803365i −0.168430 + 0.0536771i
\(225\) 0 0
\(226\) −4.49288 + 7.78190i −0.298862 + 0.517645i
\(227\) 21.6006 + 5.78787i 1.43368 + 0.384154i 0.890317 0.455341i \(-0.150483\pi\)
0.543367 + 0.839496i \(0.317149\pi\)
\(228\) 5.62793 + 1.50800i 0.372719 + 0.0998696i
\(229\) −2.48311 + 4.30087i −0.164088 + 0.284209i −0.936331 0.351118i \(-0.885802\pi\)
0.772243 + 0.635328i \(0.219135\pi\)
\(230\) 0 0
\(231\) −0.902010 0.821441i −0.0593479 0.0540468i
\(232\) 3.91576 + 3.91576i 0.257082 + 0.257082i
\(233\) −7.41098 27.6582i −0.485509 1.81195i −0.577756 0.816210i \(-0.696071\pi\)
0.0922466 0.995736i \(-0.470595\pi\)
\(234\) 2.83037 + 4.90235i 0.185027 + 0.320476i
\(235\) 0 0
\(236\) −1.66067 0.958791i −0.108101 0.0624120i
\(237\) −3.57886 + 3.57886i −0.232472 + 0.232472i
\(238\) 2.34237 + 3.65189i 0.151833 + 0.236717i
\(239\) 13.9230i 0.900603i 0.892877 + 0.450302i \(0.148684\pi\)
−0.892877 + 0.450302i \(0.851316\pi\)
\(240\) 0 0
\(241\) 0.915881 0.528784i 0.0589971 0.0340620i −0.470211 0.882554i \(-0.655822\pi\)
0.529208 + 0.848492i \(0.322489\pi\)
\(242\) 2.79198 10.4198i 0.179475 0.669810i
\(243\) −0.965926 + 0.258819i −0.0619642 + 0.0166032i
\(244\) −13.5554 −0.867793
\(245\) 0 0
\(246\) 10.9453 0.697847
\(247\) −31.8582 + 8.53639i −2.02709 + 0.543157i
\(248\) 0.00839662 0.0313366i 0.000533186 0.00198988i
\(249\) −1.33268 + 0.769426i −0.0844554 + 0.0487604i
\(250\) 0 0
\(251\) 6.36260i 0.401604i 0.979632 + 0.200802i \(0.0643548\pi\)
−0.979632 + 0.200802i \(0.935645\pi\)
\(252\) 1.42843 + 2.22701i 0.0899827 + 0.140289i
\(253\) −1.43866 + 1.43866i −0.0904481 + 0.0904481i
\(254\) 14.4223 + 8.32670i 0.904934 + 0.522464i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −2.68681 10.0273i −0.167599 0.625488i −0.997694 0.0678664i \(-0.978381\pi\)
0.830096 0.557621i \(-0.188286\pi\)
\(258\) −4.75146 4.75146i −0.295813 0.295813i
\(259\) −15.7753 14.3662i −0.980228 0.892672i
\(260\) 0 0
\(261\) 2.76886 4.79581i 0.171388 0.296853i
\(262\) 18.3299 + 4.91148i 1.13242 + 0.303432i
\(263\) 22.9523 + 6.15005i 1.41530 + 0.379228i 0.883814 0.467839i \(-0.154967\pi\)
0.531486 + 0.847067i \(0.321634\pi\)
\(264\) 0.230557 0.399337i 0.0141898 0.0245775i
\(265\) 0 0
\(266\) −14.6875 + 4.68077i −0.900551 + 0.286996i
\(267\) 8.08115 + 8.08115i 0.494558 + 0.494558i
\(268\) −0.986161 3.68040i −0.0602394 0.224816i
\(269\) 0.710036 + 1.22982i 0.0432917 + 0.0749834i 0.886859 0.462040i \(-0.152882\pi\)
−0.843568 + 0.537023i \(0.819549\pi\)
\(270\) 0 0
\(271\) −0.306228 0.176801i −0.0186020 0.0107399i 0.490670 0.871345i \(-0.336752\pi\)
−0.509272 + 0.860606i \(0.670085\pi\)
\(272\) −1.15953 + 1.15953i −0.0703066 + 0.0703066i
\(273\) −13.3059 6.87460i −0.805312 0.416070i
\(274\) 4.42902i 0.267567i
\(275\) 0 0
\(276\) 3.82117 2.20615i 0.230007 0.132795i
\(277\) 6.08269 22.7009i 0.365474 1.36397i −0.501304 0.865271i \(-0.667146\pi\)
0.866778 0.498695i \(-0.166187\pi\)
\(278\) 4.20197 1.12591i 0.252017 0.0675278i
\(279\) −0.0324420 −0.00194225
\(280\) 0 0
\(281\) 28.4747 1.69866 0.849330 0.527862i \(-0.177006\pi\)
0.849330 + 0.527862i \(0.177006\pi\)
\(282\) −8.73220 + 2.33979i −0.519995 + 0.139332i
\(283\) 0.972612 3.62984i 0.0578158 0.215771i −0.930974 0.365085i \(-0.881040\pi\)
0.988790 + 0.149314i \(0.0477065\pi\)
\(284\) 7.67192 4.42939i 0.455245 0.262836i
\(285\) 0 0
\(286\) 2.61025i 0.154347i
\(287\) −24.3753 + 15.6346i −1.43883 + 0.922881i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) −12.3937 7.15550i −0.729041 0.420912i
\(290\) 0 0
\(291\) 1.78049 + 3.08389i 0.104374 + 0.180781i
\(292\) −1.05010 3.91904i −0.0614527 0.229344i
\(293\) 4.18500 + 4.18500i 0.244490 + 0.244490i 0.818705 0.574215i \(-0.194692\pi\)
−0.574215 + 0.818705i \(0.694692\pi\)
\(294\) −6.36227 2.91917i −0.371055 0.170250i
\(295\) 0 0
\(296\) 4.03222 6.98401i 0.234368 0.405938i
\(297\) −0.445403 0.119345i −0.0258449 0.00692511i
\(298\) −4.19262 1.12341i −0.242872 0.0650773i
\(299\) −12.4885 + 21.6307i −0.722226 + 1.25093i
\(300\) 0 0
\(301\) 17.3687 + 3.79443i 1.00111 + 0.218707i
\(302\) −5.78777 5.78777i −0.333049 0.333049i
\(303\) 1.16774 + 4.35807i 0.0670850 + 0.250365i
\(304\) −2.91323 5.04586i −0.167085 0.289400i
\(305\) 0 0
\(306\) 1.42012 + 0.819909i 0.0811831 + 0.0468711i
\(307\) 18.0884 18.0884i 1.03236 1.03236i 0.0329031 0.999459i \(-0.489525\pi\)
0.999459 0.0329031i \(-0.0104753\pi\)
\(308\) 0.0569710 + 1.21866i 0.00324623 + 0.0694398i
\(309\) 14.7753i 0.840540i
\(310\) 0 0
\(311\) −29.1137 + 16.8088i −1.65089 + 0.953139i −0.674177 + 0.738569i \(0.735502\pi\)
−0.976709 + 0.214570i \(0.931165\pi\)
\(312\) 1.46511 5.46786i 0.0829454 0.309556i
\(313\) −22.1819 + 5.94363i −1.25380 + 0.335954i −0.823802 0.566877i \(-0.808151\pi\)
−0.429995 + 0.902831i \(0.641485\pi\)
\(314\) −21.7753 −1.22885
\(315\) 0 0
\(316\) 5.06128 0.284719
\(317\) 24.7683 6.63663i 1.39112 0.372751i 0.515975 0.856604i \(-0.327430\pi\)
0.875149 + 0.483853i \(0.160763\pi\)
\(318\) −0.710873 + 2.65301i −0.0398638 + 0.148774i
\(319\) 2.21142 1.27676i 0.123816 0.0714850i
\(320\) 0 0
\(321\) 5.89922i 0.329262i
\(322\) −5.35846 + 10.3714i −0.298615 + 0.577976i
\(323\) −6.75593 + 6.75593i −0.375910 + 0.375910i
\(324\) 0.866025 + 0.500000i 0.0481125 + 0.0277778i
\(325\) 0 0
\(326\) 5.83736 + 10.1106i 0.323301 + 0.559974i
\(327\) −4.30125 16.0525i −0.237860 0.887704i
\(328\) −7.73949 7.73949i −0.427342 0.427342i
\(329\) 16.1045 17.6841i 0.887870 0.974955i
\(330\) 0 0
\(331\) 5.93242 10.2753i 0.326076 0.564779i −0.655654 0.755062i \(-0.727607\pi\)
0.981729 + 0.190282i \(0.0609403\pi\)
\(332\) 1.48642 + 0.398284i 0.0815777 + 0.0218587i
\(333\) −7.78966 2.08723i −0.426870 0.114380i
\(334\) −10.9645 + 18.9910i −0.599950 + 1.03914i
\(335\) 0 0
\(336\) 0.564683 2.58479i 0.0308060 0.141012i
\(337\) 3.18746 + 3.18746i 0.173632 + 0.173632i 0.788573 0.614941i \(-0.210820\pi\)
−0.614941 + 0.788573i \(0.710820\pi\)
\(338\) 4.92895 + 18.3951i 0.268099 + 1.00056i
\(339\) −4.49288 7.78190i −0.244020 0.422655i
\(340\) 0 0
\(341\) −0.0129553 0.00747975i −0.000701569 0.000405051i
\(342\) −4.11993 + 4.11993i −0.222780 + 0.222780i
\(343\) 18.3387 2.58702i 0.990196 0.139686i
\(344\) 6.71958i 0.362295i
\(345\) 0 0
\(346\) 8.43891 4.87221i 0.453679 0.261931i
\(347\) 5.54445 20.6922i 0.297642 1.11081i −0.641455 0.767161i \(-0.721669\pi\)
0.939097 0.343653i \(-0.111664\pi\)
\(348\) −5.34903 + 1.43327i −0.286738 + 0.0768313i
\(349\) 16.0682 0.860113 0.430056 0.902802i \(-0.358494\pi\)
0.430056 + 0.902802i \(0.358494\pi\)
\(350\) 0 0
\(351\) −5.66074 −0.302148
\(352\) −0.445403 + 0.119345i −0.0237400 + 0.00636112i
\(353\) 7.60823 28.3943i 0.404945 1.51128i −0.399211 0.916859i \(-0.630716\pi\)
0.804156 0.594418i \(-0.202617\pi\)
\(354\) 1.66067 0.958791i 0.0882638 0.0509592i
\(355\) 0 0
\(356\) 11.4285i 0.605708i
\(357\) −4.33382 + 0.202601i −0.229370 + 0.0107228i
\(358\) −1.14209 + 1.14209i −0.0603611 + 0.0603611i
\(359\) 11.8017 + 6.81369i 0.622868 + 0.359613i 0.777985 0.628283i \(-0.216242\pi\)
−0.155117 + 0.987896i \(0.549575\pi\)
\(360\) 0 0
\(361\) −7.47381 12.9450i −0.393359 0.681317i
\(362\) 3.32633 + 12.4140i 0.174828 + 0.652466i
\(363\) 7.62782 + 7.62782i 0.400357 + 0.400357i
\(364\) 4.54764 + 14.2698i 0.238361 + 0.747940i
\(365\) 0 0
\(366\) 6.77768 11.7393i 0.354275 0.613622i
\(367\) −12.3244 3.30230i −0.643326 0.172379i −0.0776164 0.996983i \(-0.524731\pi\)
−0.565709 + 0.824605i \(0.691398\pi\)
\(368\) −4.26196 1.14199i −0.222170 0.0595303i
\(369\) −5.47265 + 9.47890i −0.284895 + 0.493452i
\(370\) 0 0
\(371\) −2.20652 6.92373i −0.114557 0.359462i
\(372\) 0.0229400 + 0.0229400i 0.00118938 + 0.00118938i
\(373\) −1.03563 3.86501i −0.0536227 0.200123i 0.933918 0.357488i \(-0.116367\pi\)
−0.987540 + 0.157365i \(0.949700\pi\)
\(374\) 0.378072 + 0.654840i 0.0195496 + 0.0338610i
\(375\) 0 0
\(376\) 7.82908 + 4.52012i 0.403754 + 0.233107i
\(377\) 22.1661 22.1661i 1.14161 1.14161i
\(378\) −2.64286 + 0.123551i −0.135934 + 0.00635476i
\(379\) 1.00281i 0.0515109i 0.999668 + 0.0257555i \(0.00819912\pi\)
−0.999668 + 0.0257555i \(0.991801\pi\)
\(380\) 0 0
\(381\) −14.4223 + 8.32670i −0.738875 + 0.426590i
\(382\) 2.74365 10.2394i 0.140377 0.523895i
\(383\) 17.1965 4.60780i 0.878702 0.235447i 0.208855 0.977947i \(-0.433026\pi\)
0.669847 + 0.742499i \(0.266360\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 7.21608 0.367289
\(387\) 6.49061 1.73915i 0.329936 0.0884062i
\(388\) 0.921648 3.43964i 0.0467896 0.174621i
\(389\) 9.75032 5.62935i 0.494361 0.285419i −0.232021 0.972711i \(-0.574534\pi\)
0.726382 + 0.687291i \(0.241200\pi\)
\(390\) 0 0
\(391\) 7.23538i 0.365909i
\(392\) 2.43463 + 6.56297i 0.122968 + 0.331480i
\(393\) −13.4184 + 13.4184i −0.676869 + 0.676869i
\(394\) 11.9144 + 6.87875i 0.600236 + 0.346547i
\(395\) 0 0
\(396\) 0.230557 + 0.399337i 0.0115859 + 0.0200674i
\(397\) 0.992011 + 3.70224i 0.0497876 + 0.185810i 0.986341 0.164714i \(-0.0526702\pi\)
−0.936554 + 0.350524i \(0.886003\pi\)
\(398\) −6.82567 6.82567i −0.342140 0.342140i
\(399\) 3.29010 15.0602i 0.164711 0.753951i
\(400\) 0 0
\(401\) −0.450022 + 0.779461i −0.0224730 + 0.0389244i −0.877043 0.480412i \(-0.840487\pi\)
0.854570 + 0.519336i \(0.173821\pi\)
\(402\) 3.68040 + 0.986161i 0.183562 + 0.0491852i
\(403\) −0.177388 0.0475311i −0.00883634 0.00236769i
\(404\) 2.25590 3.90734i 0.112235 0.194397i
\(405\) 0 0
\(406\) 9.86504 10.8326i 0.489594 0.537614i
\(407\) −2.62947 2.62947i −0.130338 0.130338i
\(408\) −0.424416 1.58394i −0.0210117 0.0784168i
\(409\) −6.44633 11.1654i −0.318751 0.552092i 0.661477 0.749965i \(-0.269930\pi\)
−0.980228 + 0.197873i \(0.936597\pi\)
\(410\) 0 0
\(411\) 3.83565 + 2.21451i 0.189199 + 0.109234i
\(412\) −10.4477 + 10.4477i −0.514723 + 0.514723i
\(413\) −2.32878 + 4.50740i −0.114592 + 0.221795i
\(414\) 4.41231i 0.216853i
\(415\) 0 0
\(416\) −4.90235 + 2.83037i −0.240357 + 0.138770i
\(417\) −1.12591 + 4.20197i −0.0551362 + 0.205771i
\(418\) −2.59512 + 0.695360i −0.126931 + 0.0340112i
\(419\) 19.8918 0.971777 0.485888 0.874021i \(-0.338496\pi\)
0.485888 + 0.874021i \(0.338496\pi\)
\(420\) 0 0
\(421\) −12.6339 −0.615740 −0.307870 0.951428i \(-0.599616\pi\)
−0.307870 + 0.951428i \(0.599616\pi\)
\(422\) 1.28732 0.344935i 0.0626655 0.0167912i
\(423\) 2.33979 8.73220i 0.113764 0.424574i
\(424\) 2.37863 1.37330i 0.115516 0.0666934i
\(425\) 0 0
\(426\) 8.85877i 0.429209i
\(427\) 1.67477 + 35.8250i 0.0810480 + 1.73369i
\(428\) 4.17138 4.17138i 0.201631 0.201631i
\(429\) −2.26054 1.30513i −0.109140 0.0630120i
\(430\) 0 0
\(431\) −15.3851 26.6477i −0.741073 1.28358i −0.952007 0.306075i \(-0.900984\pi\)
0.210935 0.977500i \(-0.432349\pi\)
\(432\) −0.258819 0.965926i −0.0124524 0.0464731i
\(433\) 3.04743 + 3.04743i 0.146450 + 0.146450i 0.776530 0.630080i \(-0.216978\pi\)
−0.630080 + 0.776530i \(0.716978\pi\)
\(434\) −0.0838558 0.0183195i −0.00402521 0.000879362i
\(435\) 0 0
\(436\) −8.30937 + 14.3923i −0.397947 + 0.689264i
\(437\) −24.8321 6.65375i −1.18788 0.318292i
\(438\) 3.91904 + 1.05010i 0.187259 + 0.0501759i
\(439\) 18.4993 32.0418i 0.882926 1.52927i 0.0348530 0.999392i \(-0.488904\pi\)
0.848073 0.529880i \(-0.177763\pi\)
\(440\) 0 0
\(441\) 5.70921 4.05030i 0.271867 0.192871i
\(442\) 6.56378 + 6.56378i 0.312207 + 0.312207i
\(443\) 4.60633 + 17.1911i 0.218854 + 0.816773i 0.984774 + 0.173838i \(0.0556168\pi\)
−0.765921 + 0.642935i \(0.777717\pi\)
\(444\) 4.03222 + 6.98401i 0.191361 + 0.331447i
\(445\) 0 0
\(446\) 10.1076 + 5.83564i 0.478610 + 0.276326i
\(447\) 3.06921 3.06921i 0.145169 0.145169i
\(448\) −2.22701 + 1.42843i −0.105216 + 0.0674870i
\(449\) 2.41945i 0.114181i 0.998369 + 0.0570904i \(0.0181823\pi\)
−0.998369 + 0.0570904i \(0.981818\pi\)
\(450\) 0 0
\(451\) −4.37086 + 2.52352i −0.205816 + 0.118828i
\(452\) −2.32569 + 8.67959i −0.109391 + 0.408253i
\(453\) 7.90624 2.11847i 0.371468 0.0995345i
\(454\) 22.3626 1.04953
\(455\) 0 0
\(456\) 5.82646 0.272849
\(457\) −26.6198 + 7.13275i −1.24522 + 0.333656i −0.820488 0.571663i \(-0.806298\pi\)
−0.424732 + 0.905319i \(0.639632\pi\)
\(458\) −1.28535 + 4.79700i −0.0600605 + 0.224149i
\(459\) −1.42012 + 0.819909i −0.0662857 + 0.0382701i
\(460\) 0 0
\(461\) 1.02712i 0.0478378i −0.999714 0.0239189i \(-0.992386\pi\)
0.999714 0.0239189i \(-0.00761434\pi\)
\(462\) −1.08388 0.559993i −0.0504266 0.0260533i
\(463\) 8.26507 8.26507i 0.384111 0.384111i −0.488470 0.872581i \(-0.662445\pi\)
0.872581 + 0.488470i \(0.162445\pi\)
\(464\) 4.79581 + 2.76886i 0.222640 + 0.128541i
\(465\) 0 0
\(466\) −14.3169 24.7976i −0.663218 1.14873i
\(467\) 4.79974 + 17.9129i 0.222106 + 0.828910i 0.983543 + 0.180672i \(0.0578271\pi\)
−0.761438 + 0.648238i \(0.775506\pi\)
\(468\) 4.00275 + 4.00275i 0.185027 + 0.185027i
\(469\) −9.60497 + 3.06101i −0.443516 + 0.141344i
\(470\) 0 0
\(471\) 10.8876 18.8579i 0.501676 0.868928i
\(472\) −1.85224 0.496307i −0.0852563 0.0228444i
\(473\) 2.99292 + 0.801949i 0.137614 + 0.0368737i
\(474\) −2.53064 + 4.38319i −0.116236 + 0.201327i
\(475\) 0 0
\(476\) 3.20773 + 2.92121i 0.147026 + 0.133893i
\(477\) −1.94214 1.94214i −0.0889245 0.0889245i
\(478\) 3.60353 + 13.4486i 0.164822 + 0.615123i
\(479\) −4.23872 7.34168i −0.193672 0.335450i 0.752792 0.658258i \(-0.228706\pi\)
−0.946464 + 0.322808i \(0.895373\pi\)
\(480\) 0 0
\(481\) −39.5347 22.8254i −1.80263 1.04075i
\(482\) 0.747813 0.747813i 0.0340620 0.0340620i
\(483\) −6.30267 9.82626i −0.286782 0.447110i
\(484\) 10.7874i 0.490335i
\(485\) 0 0
\(486\) −0.866025 + 0.500000i −0.0392837 + 0.0226805i
\(487\) 1.25691 4.69084i 0.0569558 0.212562i −0.931583 0.363529i \(-0.881572\pi\)
0.988539 + 0.150967i \(0.0482386\pi\)
\(488\) −13.0935 + 3.50839i −0.592714 + 0.158817i
\(489\) −11.6747 −0.527949
\(490\) 0 0
\(491\) −37.8594 −1.70857 −0.854286 0.519803i \(-0.826005\pi\)
−0.854286 + 0.519803i \(0.826005\pi\)
\(492\) 10.5723 2.83285i 0.476638 0.127715i
\(493\) 2.35030 8.77144i 0.105852 0.395046i
\(494\) −28.5633 + 16.4910i −1.28512 + 0.741967i
\(495\) 0 0
\(496\) 0.0324420i 0.00145669i
\(497\) −12.6541 19.7286i −0.567616 0.884949i
\(498\) −1.08813 + 1.08813i −0.0487604 + 0.0487604i
\(499\) 0.443575 + 0.256098i 0.0198571 + 0.0114645i 0.509896 0.860236i \(-0.329684\pi\)
−0.490039 + 0.871701i \(0.663017\pi\)
\(500\) 0 0
\(501\) −10.9645 18.9910i −0.489857 0.848457i
\(502\) 1.64676 + 6.14580i 0.0734986 + 0.274301i
\(503\) −8.58209 8.58209i −0.382657 0.382657i 0.489402 0.872058i \(-0.337215\pi\)
−0.872058 + 0.489402i \(0.837215\pi\)
\(504\) 1.95615 + 1.78142i 0.0871339 + 0.0793509i
\(505\) 0 0
\(506\) −1.01729 + 1.76200i −0.0452240 + 0.0783303i
\(507\) −18.3951 4.92895i −0.816954 0.218902i
\(508\) 16.0860 + 4.31022i 0.713699 + 0.191235i
\(509\) −5.69382 + 9.86199i −0.252374 + 0.437125i −0.964179 0.265252i \(-0.914545\pi\)
0.711805 + 0.702377i \(0.247878\pi\)
\(510\) 0 0
\(511\) −10.2278 + 3.25948i −0.452449 + 0.144191i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −1.50800 5.62793i −0.0665798 0.248479i
\(514\) −5.19053 8.99026i −0.228944 0.396543i
\(515\) 0 0
\(516\) −5.81932 3.35979i −0.256181 0.147906i
\(517\) 2.94764 2.94764i 0.129637 0.129637i
\(518\) −18.9560 9.79374i −0.832878 0.430312i
\(519\) 9.74441i 0.427732i
\(520\) 0 0
\(521\) 16.8886 9.75063i 0.739902 0.427183i −0.0821316 0.996621i \(-0.526173\pi\)
0.822034 + 0.569439i \(0.192839\pi\)
\(522\) 1.43327 5.34903i 0.0627325 0.234121i
\(523\) 14.3848 3.85439i 0.629003 0.168541i 0.0697859 0.997562i \(-0.477768\pi\)
0.559217 + 0.829021i \(0.311102\pi\)
\(524\) 18.9765 0.828992
\(525\) 0 0
\(526\) 23.7620 1.03607
\(527\) −0.0513863 + 0.0137689i −0.00223842 + 0.000599783i
\(528\) 0.119345 0.445403i 0.00519383 0.0193837i
\(529\) 3.05841 1.76577i 0.132974 0.0767728i
\(530\) 0 0
\(531\) 1.91758i 0.0832159i
\(532\) −12.9756 + 8.32269i −0.562564 + 0.360834i
\(533\) −43.8113 + 43.8113i −1.89768 + 1.89768i
\(534\) 9.89734 + 5.71423i 0.428300 + 0.247279i
\(535\) 0 0
\(536\) −1.90512 3.29976i −0.0822885 0.142528i
\(537\) −0.418032 1.56012i −0.0180394 0.0673241i
\(538\) 1.00414 + 1.00414i 0.0432917 + 0.0432917i
\(539\) 3.21372 0.301133i 0.138425 0.0129707i
\(540\) 0 0
\(541\) −21.9060 + 37.9422i −0.941810 + 1.63126i −0.179796 + 0.983704i \(0.557544\pi\)
−0.762015 + 0.647559i \(0.775790\pi\)
\(542\) −0.341553 0.0915187i −0.0146709 0.00393107i
\(543\) −12.4140 3.32633i −0.532737 0.142746i
\(544\) −0.819909 + 1.42012i −0.0351533 + 0.0608873i
\(545\) 0 0
\(546\) −14.6318 3.19652i −0.626184 0.136799i
\(547\) −8.59346 8.59346i −0.367430 0.367430i 0.499109 0.866539i \(-0.333661\pi\)
−0.866539 + 0.499109i \(0.833661\pi\)
\(548\) −1.14632 4.27811i −0.0489682 0.182752i
\(549\) 6.77768 + 11.7393i 0.289264 + 0.501021i
\(550\) 0 0
\(551\) 27.9426 + 16.1327i 1.19039 + 0.687275i
\(552\) 3.11997 3.11997i 0.132795 0.132795i
\(553\) −0.625324 13.3763i −0.0265915 0.568817i
\(554\) 23.5017i 0.998492i
\(555\) 0 0
\(556\) 3.76738 2.17510i 0.159772 0.0922447i
\(557\) −2.20835 + 8.24166i −0.0935706 + 0.349210i −0.996799 0.0799502i \(-0.974524\pi\)
0.903228 + 0.429160i \(0.141191\pi\)
\(558\) −0.0313366 + 0.00839662i −0.00132658 + 0.000355457i
\(559\) 38.0378 1.60883
\(560\) 0 0
\(561\) −0.756144 −0.0319244
\(562\) 27.5045 7.36980i 1.16021 0.310876i
\(563\) 0.0365566 0.136431i 0.00154068 0.00574988i −0.965151 0.261693i \(-0.915719\pi\)
0.966692 + 0.255943i \(0.0823859\pi\)
\(564\) −7.82908 + 4.52012i −0.329664 + 0.190331i
\(565\) 0 0
\(566\) 3.75788i 0.157956i
\(567\) 1.21443 2.35056i 0.0510015 0.0987144i
\(568\) 6.26410 6.26410i 0.262836 0.262836i
\(569\) −3.62902 2.09521i −0.152136 0.0878359i 0.421999 0.906596i \(-0.361328\pi\)
−0.574136 + 0.818760i \(0.694662\pi\)
\(570\) 0 0
\(571\) 4.89756 + 8.48282i 0.204957 + 0.354995i 0.950119 0.311888i \(-0.100961\pi\)
−0.745162 + 0.666883i \(0.767628\pi\)
\(572\) 0.675582 + 2.52131i 0.0282475 + 0.105421i
\(573\) 7.49579 + 7.49579i 0.313141 + 0.313141i
\(574\) −19.4982 + 21.4107i −0.813840 + 0.893663i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −7.85753 2.10542i −0.327113 0.0876498i 0.0915250 0.995803i \(-0.470826\pi\)
−0.418638 + 0.908153i \(0.637493\pi\)
\(578\) −13.8234 3.70396i −0.574976 0.154064i
\(579\) −3.60804 + 6.24930i −0.149945 + 0.259712i
\(580\) 0 0
\(581\) 0.868963 3.97761i 0.0360507 0.165019i
\(582\) 2.51799 + 2.51799i 0.104374 + 0.104374i
\(583\) −0.327794 1.22334i −0.0135758 0.0506657i
\(584\) −2.02864 3.51371i −0.0839459 0.145399i
\(585\) 0 0
\(586\) 5.12556 + 2.95924i 0.211735 + 0.122245i
\(587\) 20.3618 20.3618i 0.840423 0.840423i −0.148491 0.988914i \(-0.547442\pi\)
0.988914 + 0.148491i \(0.0474416\pi\)
\(588\) −6.90101 1.17303i −0.284593 0.0483749i
\(589\) 0.189022i 0.00778852i
\(590\) 0 0
\(591\) −11.9144 + 6.87875i −0.490091 + 0.282954i
\(592\) 2.08723 7.78966i 0.0857847 0.320153i
\(593\) −18.1374 + 4.85990i −0.744814 + 0.199572i −0.611217 0.791463i \(-0.709320\pi\)
−0.133597 + 0.991036i \(0.542653\pi\)
\(594\) −0.461115 −0.0189198
\(595\) 0 0
\(596\) −4.34052 −0.177794
\(597\) 9.32405 2.49837i 0.381608 0.102251i
\(598\) −6.46450 + 24.1259i −0.264353 + 0.986580i
\(599\) 21.0442 12.1499i 0.859844 0.496431i −0.00411624 0.999992i \(-0.501310\pi\)
0.863960 + 0.503561i \(0.167977\pi\)
\(600\) 0 0
\(601\) 21.1930i 0.864481i −0.901758 0.432241i \(-0.857723\pi\)
0.901758 0.432241i \(-0.142277\pi\)
\(602\) 17.7589 0.830208i 0.723800 0.0338368i
\(603\) −2.69424 + 2.69424i −0.109718 + 0.109718i
\(604\) −7.08854 4.09257i −0.288429 0.166524i
\(605\) 0 0
\(606\) 2.25590 + 3.90734i 0.0916398 + 0.158725i
\(607\) −2.46768 9.20949i −0.100160 0.373802i 0.897591 0.440829i \(-0.145315\pi\)
−0.997751 + 0.0670268i \(0.978649\pi\)
\(608\) −4.11993 4.11993i −0.167085 0.167085i
\(609\) 4.44881 + 13.9597i 0.180275 + 0.565675i
\(610\) 0 0
\(611\) 25.5872 44.3184i 1.03515 1.79293i
\(612\) 1.58394 + 0.424416i 0.0640271 + 0.0171560i
\(613\) −21.5587 5.77664i −0.870748 0.233316i −0.204337 0.978901i \(-0.565504\pi\)
−0.666411 + 0.745585i \(0.732170\pi\)
\(614\) 12.7905 22.1537i 0.516181 0.894051i
\(615\) 0 0
\(616\) 0.370443 + 1.16239i 0.0149256 + 0.0468342i
\(617\) −15.4571 15.4571i −0.622278 0.622278i 0.323836 0.946113i \(-0.395027\pi\)
−0.946113 + 0.323836i \(0.895027\pi\)
\(618\) −3.82414 14.2719i −0.153829 0.574099i
\(619\) 12.3595 + 21.4073i 0.496772 + 0.860434i 0.999993 0.00372371i \(-0.00118530\pi\)
−0.503221 + 0.864158i \(0.667852\pi\)
\(620\) 0 0
\(621\) −3.82117 2.20615i −0.153338 0.0885299i
\(622\) −23.7712 + 23.7712i −0.953139 + 0.953139i
\(623\) −30.2039 + 1.41200i −1.21009 + 0.0565704i
\(624\) 5.66074i 0.226611i
\(625\) 0 0
\(626\) −19.8878 + 11.4822i −0.794876 + 0.458922i
\(627\) 0.695360 2.59512i 0.0277700 0.103639i
\(628\) −21.0333 + 5.63586i −0.839320 + 0.224895i
\(629\) −13.2242 −0.527284
\(630\) 0 0
\(631\) 34.7305 1.38260 0.691299 0.722569i \(-0.257039\pi\)
0.691299 + 0.722569i \(0.257039\pi\)
\(632\) 4.88882 1.30995i 0.194467 0.0521072i
\(633\) −0.344935 + 1.28732i −0.0137099 + 0.0511662i
\(634\) 22.2066 12.8210i 0.881937 0.509187i
\(635\) 0 0
\(636\) 2.74660i 0.108910i
\(637\) 37.1513 13.7818i 1.47199 0.546056i
\(638\) 1.80562 1.80562i 0.0714850 0.0714850i
\(639\) −7.67192 4.42939i −0.303497 0.175224i
\(640\) 0 0
\(641\) −5.82603 10.0910i −0.230115 0.398570i 0.727727 0.685867i \(-0.240577\pi\)
−0.957842 + 0.287297i \(0.907243\pi\)
\(642\) 1.52683 + 5.69821i 0.0602592 + 0.224890i
\(643\) 21.8198 + 21.8198i 0.860489 + 0.860489i 0.991395 0.130906i \(-0.0417886\pi\)
−0.130906 + 0.991395i \(0.541789\pi\)
\(644\) −2.49155 + 11.4049i −0.0981810 + 0.449415i
\(645\) 0 0
\(646\) −4.77716 + 8.27429i −0.187955 + 0.325548i
\(647\) −35.8827 9.61474i −1.41069 0.377994i −0.528521 0.848920i \(-0.677253\pi\)
−0.882173 + 0.470926i \(0.843920\pi\)
\(648\) 0.965926 + 0.258819i 0.0379452 + 0.0101674i
\(649\) −0.442112 + 0.765761i −0.0173544 + 0.0300588i
\(650\) 0 0
\(651\) 0.0577930 0.0634615i 0.00226509 0.00248725i
\(652\) 8.25527 + 8.25527i 0.323301 + 0.323301i
\(653\) −8.18328 30.5404i −0.320237 1.19514i −0.919014 0.394224i \(-0.871013\pi\)
0.598778 0.800915i \(-0.295653\pi\)
\(654\) −8.30937 14.3923i −0.324922 0.562782i
\(655\) 0 0
\(656\) −9.47890 5.47265i −0.370089 0.213671i
\(657\) −2.86894 + 2.86894i −0.111928 + 0.111928i
\(658\) 10.9788 21.2497i 0.427997 0.828398i
\(659\) 38.7284i 1.50864i 0.656504 + 0.754322i \(0.272034\pi\)
−0.656504 + 0.754322i \(0.727966\pi\)
\(660\) 0 0
\(661\) 29.3286 16.9329i 1.14075 0.658613i 0.194135 0.980975i \(-0.437810\pi\)
0.946617 + 0.322361i \(0.104477\pi\)
\(662\) 3.07085 11.4606i 0.119352 0.445427i
\(663\) −8.96628 + 2.40251i −0.348222 + 0.0933057i
\(664\) 1.53885 0.0597190
\(665\) 0 0
\(666\) −8.06444 −0.312491
\(667\) 23.6016 6.32402i 0.913856 0.244867i
\(668\) −5.67563 + 21.1817i −0.219597 + 0.819546i
\(669\) −10.1076 + 5.83564i −0.390784 + 0.225619i
\(670\) 0 0
\(671\) 6.25058i 0.241301i
\(672\) −0.123551 2.64286i −0.00476607 0.101951i
\(673\) 24.7046 24.7046i 0.952294 0.952294i −0.0466190 0.998913i \(-0.514845\pi\)
0.998913 + 0.0466190i \(0.0148447\pi\)
\(674\) 3.90382 + 2.25387i 0.150370 + 0.0868159i
\(675\) 0 0
\(676\) 9.52199 + 16.4926i 0.366230 + 0.634330i
\(677\) 4.55637 + 17.0046i 0.175116 + 0.653540i 0.996532 + 0.0832112i \(0.0265176\pi\)
−0.821416 + 0.570329i \(0.806816\pi\)
\(678\) −6.35390 6.35390i −0.244020 0.244020i
\(679\) −9.20437 2.01082i −0.353231 0.0771683i
\(680\) 0 0
\(681\) −11.1813 + 19.3666i −0.428469 + 0.742129i
\(682\) −0.0144498 0.00387180i −0.000553310 0.000148259i
\(683\) −23.3499 6.25658i −0.893458 0.239401i −0.217254 0.976115i \(-0.569710\pi\)
−0.676205 + 0.736714i \(0.736377\pi\)
\(684\) −2.91323 + 5.04586i −0.111390 + 0.192933i
\(685\) 0 0
\(686\) 17.0442 7.24527i 0.650752 0.276626i
\(687\) −3.51165 3.51165i −0.133978 0.133978i
\(688\) 1.73915 + 6.49061i 0.0663046 + 0.247452i
\(689\) −7.77390 13.4648i −0.296162 0.512968i
\(690\) 0 0
\(691\) −2.56844 1.48289i −0.0977081 0.0564118i 0.450350 0.892852i \(-0.351299\pi\)
−0.548058 + 0.836440i \(0.684633\pi\)
\(692\) 6.89034 6.89034i 0.261931 0.261931i
\(693\) 1.02691 0.658670i 0.0390090 0.0250208i
\(694\) 21.4221i 0.813172i
\(695\) 0 0
\(696\) −4.79581 + 2.76886i −0.181785 + 0.104953i
\(697\) −4.64536 + 17.3367i −0.175955 + 0.656675i
\(698\) 15.5207 4.15876i 0.587468 0.157412i
\(699\) 28.6338 1.08303
\(700\) 0 0
\(701\) −18.6815 −0.705591 −0.352795 0.935701i \(-0.614769\pi\)
−0.352795 + 0.935701i \(0.614769\pi\)
\(702\) −5.46786 + 1.46511i −0.206371 + 0.0552969i
\(703\) 12.1612 45.3861i 0.458667 1.71177i
\(704\) −0.399337 + 0.230557i −0.0150506 + 0.00868946i
\(705\) 0 0
\(706\) 29.3960i 1.10633i
\(707\) −10.6053 5.47930i −0.398853 0.206070i
\(708\) 1.35593 1.35593i 0.0509592 0.0509592i
\(709\) −18.3186 10.5763i −0.687971 0.397200i 0.114880 0.993379i \(-0.463351\pi\)
−0.802851 + 0.596179i \(0.796685\pi\)
\(710\) 0 0
\(711\) −2.53064 4.38319i −0.0949063 0.164383i
\(712\) −2.95790 11.0391i −0.110852 0.413706i
\(713\) −0.101218 0.101218i −0.00379065 0.00379065i
\(714\) −4.13371 + 1.31737i −0.154700 + 0.0493014i
\(715\) 0 0
\(716\) −0.807576 + 1.39876i −0.0301805 + 0.0522742i
\(717\) −13.4486 3.60353i −0.502246 0.134576i
\(718\) 13.1630 + 3.52703i 0.491241 + 0.131628i
\(719\) −4.30625 + 7.45864i −0.160596 + 0.278160i −0.935083 0.354430i \(-0.884675\pi\)
0.774487 + 0.632590i \(0.218008\pi\)
\(720\) 0 0
\(721\) 28.9028 + 26.3211i 1.07640 + 0.980251i
\(722\) −10.5696 10.5696i −0.393359 0.393359i
\(723\) 0.273719 + 1.02153i 0.0101797 + 0.0379912i
\(724\) 6.42597 + 11.1301i 0.238819 + 0.413647i
\(725\) 0 0
\(726\) 9.34214 + 5.39369i 0.346719 + 0.200178i
\(727\) 12.8013 12.8013i 0.474774 0.474774i −0.428682 0.903455i \(-0.641022\pi\)
0.903455 + 0.428682i \(0.141022\pi\)
\(728\) 8.08597 + 12.6065i 0.299686 + 0.467230i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 9.54263 5.50944i 0.352947 0.203774i
\(732\) 3.50839 13.0935i 0.129674 0.483949i
\(733\) 31.9503 8.56107i 1.18011 0.316210i 0.385142 0.922857i \(-0.374153\pi\)
0.794971 + 0.606647i \(0.207486\pi\)
\(734\) −12.7591 −0.470947
\(735\) 0 0
\(736\) −4.41231 −0.162640
\(737\) −1.69709 + 0.454733i −0.0625130 + 0.0167503i
\(738\) −2.83285 + 10.5723i −0.104279 + 0.389173i
\(739\) 40.9779 23.6586i 1.50740 0.870296i 0.507434 0.861690i \(-0.330594\pi\)
0.999963 0.00860599i \(-0.00273940\pi\)
\(740\) 0 0
\(741\) 32.9821i 1.21163i
\(742\) −3.92333 6.11672i −0.144030 0.224552i
\(743\) 21.5587 21.5587i 0.790914 0.790914i −0.190729 0.981643i \(-0.561085\pi\)
0.981643 + 0.190729i \(0.0610852\pi\)
\(744\) 0.0280956 + 0.0162210i 0.00103004 + 0.000594691i
\(745\) 0 0
\(746\) −2.00068 3.46527i −0.0732500 0.126873i
\(747\) −0.398284 1.48642i −0.0145724 0.0543851i
\(748\) 0.534674 + 0.534674i 0.0195496 + 0.0195496i
\(749\) −11.5398 10.5090i −0.421654 0.383991i
\(750\) 0 0
\(751\) −15.5069 + 26.8587i −0.565854 + 0.980088i 0.431116 + 0.902297i \(0.358120\pi\)
−0.996970 + 0.0777911i \(0.975213\pi\)
\(752\) 8.73220 + 2.33979i 0.318431 + 0.0853232i
\(753\) −6.14580 1.64676i −0.223965 0.0600114i
\(754\) 15.6738 27.1478i 0.570807 0.988666i
\(755\) 0 0
\(756\) −2.52083 + 0.803365i −0.0916819 + 0.0292181i
\(757\) 16.7486 + 16.7486i 0.608738 + 0.608738i 0.942616 0.333879i \(-0.108358\pi\)
−0.333879 + 0.942616i \(0.608358\pi\)
\(758\) 0.259546 + 0.968641i 0.00942715 + 0.0351826i
\(759\) −1.01729 1.76200i −0.0369253 0.0639564i
\(760\) 0 0
\(761\) −14.7359 8.50777i −0.534175 0.308406i 0.208540 0.978014i \(-0.433129\pi\)
−0.742715 + 0.669608i \(0.766462\pi\)
\(762\) −11.7757 + 11.7757i −0.426590 + 0.426590i
\(763\) 39.0634 + 20.1824i 1.41419 + 0.730651i
\(764\) 10.6007i 0.383518i
\(765\) 0 0
\(766\) 15.4180 8.90158i 0.557075 0.321627i
\(767\) −2.80946 + 10.4851i −0.101444 + 0.378593i
\(768\) 0.965926 0.258819i 0.0348548 0.00933933i
\(769\) −7.70275 −0.277768 −0.138884 0.990309i \(-0.544352\pi\)
−0.138884 + 0.990309i \(0.544352\pi\)
\(770\) 0 0
\(771\) 10.3811 0.373865
\(772\) 6.97019 1.86766i 0.250863 0.0672185i
\(773\) −0.783229 + 2.92305i −0.0281708 + 0.105135i −0.978580 0.205868i \(-0.933998\pi\)
0.950409 + 0.311003i \(0.100665\pi\)
\(774\) 5.81932 3.35979i 0.209171 0.120765i
\(775\) 0 0
\(776\) 3.56097i 0.127832i
\(777\) 17.9596 11.5195i 0.644298 0.413260i
\(778\) 7.96110 7.96110i 0.285419 0.285419i
\(779\) −55.2284 31.8862i −1.97876 1.14244i
\(780\) 0 0
\(781\) −2.04245 3.53763i −0.0730848