Properties

Label 680.2.co.a.419.94
Level $680$
Weight $2$
Character 680.419
Analytic conductor $5.430$
Analytic rank $0$
Dimension $832$
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [680,2,Mod(99,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 8, 8, 9])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.99"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 680.co (of order \(16\), degree \(8\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.42982733745\)
Analytic rank: \(0\)
Dimension: \(832\)
Relative dimension: \(104\) over \(\Q(\zeta_{16})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 419.94
Character \(\chi\) \(=\) 680.419
Dual form 680.2.co.a.99.94

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.35478 + 0.405659i) q^{2} +(3.02940 - 0.602586i) q^{3} +(1.67088 + 1.09916i) q^{4} +(0.0803191 - 2.23462i) q^{5} +(4.34863 + 0.412531i) q^{6} +(-3.84724 + 2.57064i) q^{7} +(1.81780 + 2.16693i) q^{8} +(6.04253 - 2.50290i) q^{9} +(1.01531 - 2.99485i) q^{10} +(2.30746 + 0.458983i) q^{11} +(5.72411 + 2.32295i) q^{12} +(-0.474407 + 0.474407i) q^{13} +(-6.25499 + 1.92200i) q^{14} +(-1.10323 - 6.81798i) q^{15} +(1.58369 + 3.67314i) q^{16} +(-3.71414 + 1.79030i) q^{17} +(9.20166 - 0.939681i) q^{18} +(-6.53598 - 2.70729i) q^{19} +(2.59042 - 3.64551i) q^{20} +(-10.1058 + 10.1058i) q^{21} +(2.93992 + 1.55787i) q^{22} +(1.31540 - 6.61299i) q^{23} +(6.81261 + 5.46914i) q^{24} +(-4.98710 - 0.358966i) q^{25} +(-0.835166 + 0.450272i) q^{26} +(9.09245 - 6.07538i) q^{27} +(-9.25383 + 0.0665044i) q^{28} +(4.89597 + 3.27138i) q^{29} +(1.27113 - 9.68443i) q^{30} +(-0.996655 - 5.01052i) q^{31} +(0.655518 + 5.61875i) q^{32} +7.26681 q^{33} +(-5.75811 + 0.918803i) q^{34} +(5.43542 + 8.80361i) q^{35} +(12.8474 + 2.45967i) q^{36} +(1.03900 + 5.22343i) q^{37} +(-7.75660 - 6.31917i) q^{38} +(-1.15130 + 1.72304i) q^{39} +(4.98829 - 3.88805i) q^{40} +(-3.57941 + 2.39169i) q^{41} +(-17.7907 + 9.59168i) q^{42} +(-0.819076 - 1.97742i) q^{43} +(3.35100 + 3.30318i) q^{44} +(-5.10771 - 13.7038i) q^{45} +(4.46471 - 8.42556i) q^{46} +(-1.24163 + 1.24163i) q^{47} +(7.01101 + 10.1731i) q^{48} +(5.51427 - 13.3126i) q^{49} +(-6.61082 - 2.50938i) q^{50} +(-10.1728 + 7.66164i) q^{51} +(-1.31413 + 0.271228i) q^{52} +(-2.20958 - 0.915237i) q^{53} +(14.7828 - 4.54240i) q^{54} +(1.21099 - 5.11945i) q^{55} +(-12.5639 - 3.66380i) q^{56} +(-21.4315 - 4.26299i) q^{57} +(5.30591 + 6.41811i) q^{58} +(0.257860 + 0.622529i) q^{59} +(5.65068 - 12.6047i) q^{60} +(-3.33081 + 2.22558i) q^{61} +(0.682311 - 7.19248i) q^{62} +(-16.8130 + 25.1625i) q^{63} +(-1.39121 + 7.87810i) q^{64} +(1.02202 + 1.09823i) q^{65} +(9.84496 + 2.94785i) q^{66} -0.662256 q^{67} +(-8.17371 - 1.09105i) q^{68} -20.8260i q^{69} +(3.79255 + 14.1319i) q^{70} +(2.50239 - 0.497757i) q^{71} +(16.4077 + 8.54401i) q^{72} +(-0.683178 + 1.02245i) q^{73} +(-0.711304 + 7.49810i) q^{74} +(-15.3242 + 1.91770i) q^{75} +(-7.94509 - 11.7077i) q^{76} +(-10.0572 + 4.16585i) q^{77} +(-2.25873 + 1.86731i) q^{78} +(0.742184 - 3.73121i) q^{79} +(8.33528 - 3.24393i) q^{80} +(10.0095 - 10.0095i) q^{81} +(-5.81954 + 1.78820i) q^{82} +(5.07078 + 2.10039i) q^{83} +(-27.9935 + 5.77770i) q^{84} +(3.70234 + 8.44350i) q^{85} +(-0.307511 - 3.01125i) q^{86} +(16.8031 + 6.96009i) q^{87} +(3.19992 + 5.83446i) q^{88} +(5.59049 + 5.59049i) q^{89} +(-1.36077 - 20.6377i) q^{90} +(0.605626 - 3.04469i) q^{91} +(9.46662 - 9.60367i) q^{92} +(-6.03854 - 14.5783i) q^{93} +(-2.18582 + 1.17846i) q^{94} +(-6.57474 + 14.3880i) q^{95} +(5.37160 + 16.6264i) q^{96} +(11.5356 + 7.70783i) q^{97} +(12.8710 - 15.7988i) q^{98} +(15.0917 - 3.00193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 832 q - 16 q^{4} - 16 q^{6} - 32 q^{9} - 8 q^{10} - 32 q^{11} - 16 q^{14} - 32 q^{19} - 8 q^{20} - 32 q^{24} - 16 q^{25} - 48 q^{26} + 56 q^{30} + 48 q^{34} - 32 q^{35} + 48 q^{36} - 72 q^{40} - 32 q^{41}+ \cdots - 128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/680\mathbb{Z}\right)^\times\).

\(n\) \(137\) \(241\) \(341\) \(511\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{16}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.35478 + 0.405659i 0.957977 + 0.286844i
\(3\) 3.02940 0.602586i 1.74903 0.347903i 0.786189 0.617986i \(-0.212051\pi\)
0.962837 + 0.270083i \(0.0870510\pi\)
\(4\) 1.67088 + 1.09916i 0.835441 + 0.549581i
\(5\) 0.0803191 2.23462i 0.0359198 0.999355i
\(6\) 4.34863 + 0.412531i 1.77532 + 0.168415i
\(7\) −3.84724 + 2.57064i −1.45412 + 0.971612i −0.457522 + 0.889198i \(0.651263\pi\)
−0.996598 + 0.0824138i \(0.973737\pi\)
\(8\) 1.81780 + 2.16693i 0.642689 + 0.766127i
\(9\) 6.04253 2.50290i 2.01418 0.834300i
\(10\) 1.01531 2.99485i 0.321070 0.947056i
\(11\) 2.30746 + 0.458983i 0.695726 + 0.138389i 0.530270 0.847829i \(-0.322090\pi\)
0.165456 + 0.986217i \(0.447090\pi\)
\(12\) 5.72411 + 2.32295i 1.65241 + 0.670579i
\(13\) −0.474407 + 0.474407i −0.131577 + 0.131577i −0.769828 0.638251i \(-0.779658\pi\)
0.638251 + 0.769828i \(0.279658\pi\)
\(14\) −6.25499 + 1.92200i −1.67172 + 0.513676i
\(15\) −1.10323 6.81798i −0.284854 1.76039i
\(16\) 1.58369 + 3.67314i 0.395922 + 0.918284i
\(17\) −3.71414 + 1.79030i −0.900810 + 0.434213i
\(18\) 9.20166 0.939681i 2.16885 0.221485i
\(19\) −6.53598 2.70729i −1.49946 0.621095i −0.526106 0.850419i \(-0.676348\pi\)
−0.973350 + 0.229324i \(0.926348\pi\)
\(20\) 2.59042 3.64551i 0.579235 0.815161i
\(21\) −10.1058 + 10.1058i −2.20527 + 2.20527i
\(22\) 2.93992 + 1.55787i 0.626794 + 0.332138i
\(23\) 1.31540 6.61299i 0.274281 1.37890i −0.560424 0.828206i \(-0.689362\pi\)
0.834705 0.550697i \(-0.185638\pi\)
\(24\) 6.81261 + 5.46914i 1.39062 + 1.11638i
\(25\) −4.98710 0.358966i −0.997420 0.0717933i
\(26\) −0.835166 + 0.450272i −0.163790 + 0.0883055i
\(27\) 9.09245 6.07538i 1.74984 1.16921i
\(28\) −9.25383 + 0.0665044i −1.74881 + 0.0125681i
\(29\) 4.89597 + 3.27138i 0.909158 + 0.607480i 0.919768 0.392464i \(-0.128377\pi\)
−0.0106093 + 0.999944i \(0.503377\pi\)
\(30\) 1.27113 9.68443i 0.232076 1.76813i
\(31\) −0.996655 5.01052i −0.179005 0.899917i −0.960982 0.276610i \(-0.910789\pi\)
0.781978 0.623306i \(-0.214211\pi\)
\(32\) 0.655518 + 5.61875i 0.115880 + 0.993263i
\(33\) 7.26681 1.26499
\(34\) −5.75811 + 0.918803i −0.987507 + 0.157573i
\(35\) 5.43542 + 8.80361i 0.918753 + 1.48808i
\(36\) 12.8474 + 2.45967i 2.14124 + 0.409945i
\(37\) 1.03900 + 5.22343i 0.170811 + 0.858727i 0.967215 + 0.253961i \(0.0817334\pi\)
−0.796403 + 0.604766i \(0.793267\pi\)
\(38\) −7.75660 6.31917i −1.25829 1.02511i
\(39\) −1.15130 + 1.72304i −0.184355 + 0.275907i
\(40\) 4.98829 3.88805i 0.788718 0.614755i
\(41\) −3.57941 + 2.39169i −0.559010 + 0.373519i −0.802744 0.596323i \(-0.796628\pi\)
0.243734 + 0.969842i \(0.421628\pi\)
\(42\) −17.7907 + 9.59168i −2.74517 + 1.48003i
\(43\) −0.819076 1.97742i −0.124908 0.301554i 0.849039 0.528330i \(-0.177182\pi\)
−0.973947 + 0.226776i \(0.927182\pi\)
\(44\) 3.35100 + 3.30318i 0.505182 + 0.497973i
\(45\) −5.10771 13.7038i −0.761413 2.04285i
\(46\) 4.46471 8.42556i 0.658285 1.24228i
\(47\) −1.24163 + 1.24163i −0.181110 + 0.181110i −0.791840 0.610729i \(-0.790876\pi\)
0.610729 + 0.791840i \(0.290876\pi\)
\(48\) 7.01101 + 10.1731i 1.01195 + 1.46836i
\(49\) 5.51427 13.3126i 0.787752 1.90180i
\(50\) −6.61082 2.50938i −0.934912 0.354880i
\(51\) −10.1728 + 7.66164i −1.42448 + 1.07284i
\(52\) −1.31413 + 0.271228i −0.182237 + 0.0376126i
\(53\) −2.20958 0.915237i −0.303509 0.125717i 0.225731 0.974190i \(-0.427523\pi\)
−0.529240 + 0.848472i \(0.677523\pi\)
\(54\) 14.7828 4.54240i 2.01169 0.618142i
\(55\) 1.21099 5.11945i 0.163290 0.690306i
\(56\) −12.5639 3.66380i −1.67893 0.489596i
\(57\) −21.4315 4.26299i −2.83867 0.564646i
\(58\) 5.30591 + 6.41811i 0.696701 + 0.842739i
\(59\) 0.257860 + 0.622529i 0.0335705 + 0.0810463i 0.939776 0.341792i \(-0.111034\pi\)
−0.906205 + 0.422838i \(0.861034\pi\)
\(60\) 5.65068 12.6047i 0.729500 1.62726i
\(61\) −3.33081 + 2.22558i −0.426467 + 0.284956i −0.750224 0.661184i \(-0.770054\pi\)
0.323756 + 0.946140i \(0.395054\pi\)
\(62\) 0.682311 7.19248i 0.0866536 0.913446i
\(63\) −16.8130 + 25.1625i −2.11824 + 3.17017i
\(64\) −1.39121 + 7.87810i −0.173901 + 0.984763i
\(65\) 1.02202 + 1.09823i 0.126766 + 0.136218i
\(66\) 9.84496 + 2.94785i 1.21183 + 0.362855i
\(67\) −0.662256 −0.0809074 −0.0404537 0.999181i \(-0.512880\pi\)
−0.0404537 + 0.999181i \(0.512880\pi\)
\(68\) −8.17371 1.09105i −0.991209 0.132309i
\(69\) 20.8260i 2.50716i
\(70\) 3.79255 + 14.1319i 0.453297 + 1.68909i
\(71\) 2.50239 0.497757i 0.296979 0.0590729i −0.0443517 0.999016i \(-0.514122\pi\)
0.341331 + 0.939943i \(0.389122\pi\)
\(72\) 16.4077 + 8.54401i 1.93367 + 1.00692i
\(73\) −0.683178 + 1.02245i −0.0799600 + 0.119669i −0.869294 0.494296i \(-0.835426\pi\)
0.789334 + 0.613964i \(0.210426\pi\)
\(74\) −0.711304 + 7.49810i −0.0826874 + 0.871637i
\(75\) −15.3242 + 1.91770i −1.76949 + 0.221437i
\(76\) −7.94509 11.7077i −0.911365 1.34296i
\(77\) −10.0572 + 4.16585i −1.14613 + 0.474742i
\(78\) −2.25873 + 1.86731i −0.255751 + 0.211432i
\(79\) 0.742184 3.73121i 0.0835022 0.419794i −0.916311 0.400467i \(-0.868848\pi\)
0.999813 0.0193266i \(-0.00615225\pi\)
\(80\) 8.33528 3.24393i 0.931913 0.362682i
\(81\) 10.0095 10.0095i 1.11217 1.11217i
\(82\) −5.81954 + 1.78820i −0.642661 + 0.197474i
\(83\) 5.07078 + 2.10039i 0.556590 + 0.230547i 0.643204 0.765695i \(-0.277605\pi\)
−0.0866138 + 0.996242i \(0.527605\pi\)
\(84\) −27.9935 + 5.77770i −3.05434 + 0.630398i
\(85\) 3.70234 + 8.44350i 0.401575 + 0.915826i
\(86\) −0.307511 3.01125i −0.0331598 0.324711i
\(87\) 16.8031 + 6.96009i 1.80149 + 0.746200i
\(88\) 3.19992 + 5.83446i 0.341112 + 0.621955i
\(89\) 5.59049 + 5.59049i 0.592591 + 0.592591i 0.938330 0.345740i \(-0.112372\pi\)
−0.345740 + 0.938330i \(0.612372\pi\)
\(90\) −1.36077 20.6377i −0.143437 2.17541i
\(91\) 0.605626 3.04469i 0.0634869 0.319170i
\(92\) 9.46662 9.60367i 0.986964 1.00125i
\(93\) −6.03854 14.5783i −0.626167 1.51170i
\(94\) −2.18582 + 1.17846i −0.225450 + 0.121549i
\(95\) −6.57474 + 14.3880i −0.674554 + 1.47618i
\(96\) 5.37160 + 16.6264i 0.548237 + 1.69693i
\(97\) 11.5356 + 7.70783i 1.17126 + 0.782612i 0.980014 0.198930i \(-0.0637467\pi\)
0.191247 + 0.981542i \(0.438747\pi\)
\(98\) 12.8710 15.7988i 1.30017 1.59592i
\(99\) 15.0917 3.00193i 1.51677 0.301705i
\(100\) −7.93829 6.08141i −0.793829 0.608141i
\(101\) 9.64388 0.959602 0.479801 0.877377i \(-0.340709\pi\)
0.479801 + 0.877377i \(0.340709\pi\)
\(102\) −16.8900 + 6.25318i −1.67236 + 0.619157i
\(103\) −8.39042 −0.826733 −0.413367 0.910565i \(-0.635647\pi\)
−0.413367 + 0.910565i \(0.635647\pi\)
\(104\) −1.89038 0.165632i −0.185367 0.0162416i
\(105\) 21.7710 + 23.3944i 2.12463 + 2.28306i
\(106\) −2.62223 2.13628i −0.254693 0.207494i
\(107\) 2.87140 4.29736i 0.277589 0.415441i −0.666310 0.745675i \(-0.732127\pi\)
0.943899 + 0.330233i \(0.107127\pi\)
\(108\) 21.8702 0.157174i 2.10446 0.0151241i
\(109\) 8.15843 + 12.2099i 0.781436 + 1.16950i 0.981826 + 0.189785i \(0.0607790\pi\)
−0.200390 + 0.979716i \(0.564221\pi\)
\(110\) 3.71738 6.44450i 0.354438 0.614459i
\(111\) 6.29513 + 15.1978i 0.597507 + 1.44251i
\(112\) −15.5352 10.0603i −1.46793 0.950612i
\(113\) −2.15817 + 10.8499i −0.203024 + 1.02067i 0.736043 + 0.676935i \(0.236692\pi\)
−0.939067 + 0.343735i \(0.888308\pi\)
\(114\) −27.3057 14.4693i −2.55741 1.35517i
\(115\) −14.6719 3.47059i −1.36816 0.323634i
\(116\) 4.58481 + 10.8475i 0.425689 + 1.00717i
\(117\) −1.67923 + 4.05401i −0.155245 + 0.374794i
\(118\) 0.0968101 + 0.947995i 0.00891209 + 0.0872701i
\(119\) 9.68694 16.4355i 0.888000 1.50664i
\(120\) 12.7687 14.7844i 1.16561 1.34962i
\(121\) −5.04896 2.09135i −0.458996 0.190122i
\(122\) −5.41536 + 1.66400i −0.490284 + 0.150652i
\(123\) −9.40229 + 9.40229i −0.847776 + 0.847776i
\(124\) 3.84208 9.46747i 0.345029 0.850204i
\(125\) −1.20271 + 11.1155i −0.107574 + 0.994197i
\(126\) −32.9854 + 27.2694i −2.93857 + 2.42935i
\(127\) −1.16418 2.81058i −0.103304 0.249399i 0.863773 0.503881i \(-0.168095\pi\)
−0.967078 + 0.254482i \(0.918095\pi\)
\(128\) −5.08061 + 10.1088i −0.449067 + 0.893498i
\(129\) −3.67288 5.49685i −0.323379 0.483971i
\(130\) 0.939108 + 1.90245i 0.0823652 + 0.166856i
\(131\) −2.06466 + 3.08997i −0.180390 + 0.269972i −0.910634 0.413214i \(-0.864406\pi\)
0.730244 + 0.683186i \(0.239406\pi\)
\(132\) 12.1420 + 7.98739i 1.05682 + 0.695213i
\(133\) 32.1050 6.38607i 2.78385 0.553743i
\(134\) −0.897213 0.268650i −0.0775074 0.0232078i
\(135\) −12.8459 20.8062i −1.10560 1.79071i
\(136\) −10.6310 4.79388i −0.911603 0.411071i
\(137\) 18.1100i 1.54724i −0.633647 0.773622i \(-0.718443\pi\)
0.633647 0.773622i \(-0.281557\pi\)
\(138\) 8.44827 28.2148i 0.719165 2.40180i
\(139\) −3.76434 18.9246i −0.319287 1.60516i −0.723383 0.690447i \(-0.757414\pi\)
0.404096 0.914717i \(-0.367586\pi\)
\(140\) −0.594648 + 20.6842i −0.0502569 + 1.74813i
\(141\) −3.01321 + 4.50959i −0.253758 + 0.379776i
\(142\) 3.59212 + 0.340765i 0.301444 + 0.0285964i
\(143\) −1.31242 + 0.876931i −0.109750 + 0.0733327i
\(144\) 18.7630 + 18.2312i 1.56358 + 1.51927i
\(145\) 7.70355 10.6779i 0.639745 0.886751i
\(146\) −1.34032 + 1.10806i −0.110926 + 0.0917037i
\(147\) 8.68294 43.6521i 0.716157 3.60036i
\(148\) −4.00534 + 9.86977i −0.329237 + 0.811290i
\(149\) −12.0584 12.0584i −0.987865 0.987865i 0.0120627 0.999927i \(-0.496160\pi\)
−0.999927 + 0.0120627i \(0.996160\pi\)
\(150\) −21.5390 3.61834i −1.75865 0.295437i
\(151\) 12.5641 + 5.20422i 1.02245 + 0.423514i 0.829983 0.557789i \(-0.188350\pi\)
0.192470 + 0.981303i \(0.438350\pi\)
\(152\) −6.01458 19.0843i −0.487846 1.54794i
\(153\) −17.9618 + 20.1141i −1.45213 + 1.62613i
\(154\) −15.3153 + 1.56401i −1.23414 + 0.126032i
\(155\) −11.2767 + 1.82471i −0.905766 + 0.146564i
\(156\) −3.81758 + 1.61353i −0.305651 + 0.129186i
\(157\) −3.51971 3.51971i −0.280903 0.280903i 0.552566 0.833469i \(-0.313649\pi\)
−0.833469 + 0.552566i \(0.813649\pi\)
\(158\) 2.51910 4.75391i 0.200409 0.378201i
\(159\) −7.24521 1.44116i −0.574582 0.114292i
\(160\) 12.6084 1.01354i 0.996785 0.0801276i
\(161\) 11.9390 + 28.8232i 0.940921 + 2.27159i
\(162\) 17.6211 9.50026i 1.38445 0.746411i
\(163\) −6.27516 + 4.19293i −0.491509 + 0.328416i −0.776503 0.630114i \(-0.783008\pi\)
0.284994 + 0.958529i \(0.408008\pi\)
\(164\) −8.60962 + 0.0618746i −0.672299 + 0.00483160i
\(165\) 0.583664 16.2386i 0.0454382 1.26417i
\(166\) 6.01777 + 4.90258i 0.467070 + 0.380514i
\(167\) 6.97603 1.38762i 0.539822 0.107377i 0.0823535 0.996603i \(-0.473756\pi\)
0.457468 + 0.889226i \(0.348756\pi\)
\(168\) −40.2690 3.52829i −3.10682 0.272214i
\(169\) 12.5499i 0.965375i
\(170\) 1.59069 + 12.9410i 0.122001 + 0.992530i
\(171\) −46.2699 −3.53835
\(172\) 0.804929 4.20434i 0.0613753 0.320578i
\(173\) 0.767815 + 3.86007i 0.0583759 + 0.293475i 0.998934 0.0461568i \(-0.0146974\pi\)
−0.940558 + 0.339632i \(0.889697\pi\)
\(174\) 19.9412 + 16.2458i 1.51174 + 1.23159i
\(175\) 20.1093 11.4390i 1.52012 0.864709i
\(176\) 1.96840 + 9.20251i 0.148374 + 0.693665i
\(177\) 1.15629 + 1.73051i 0.0869120 + 0.130073i
\(178\) 5.30608 + 9.84174i 0.397707 + 0.737670i
\(179\) −0.0746106 + 0.0309047i −0.00557666 + 0.00230993i −0.385470 0.922720i \(-0.625961\pi\)
0.379893 + 0.925030i \(0.375961\pi\)
\(180\) 6.52834 28.5117i 0.486593 2.12513i
\(181\) 3.90988 19.6563i 0.290619 1.46104i −0.509121 0.860695i \(-0.670030\pi\)
0.799741 0.600346i \(-0.204970\pi\)
\(182\) 2.05560 3.87922i 0.152371 0.287547i
\(183\) −8.74928 + 8.74928i −0.646765 + 0.646765i
\(184\) 16.7210 9.17069i 1.23269 0.676072i
\(185\) 11.7559 1.90224i 0.864308 0.139856i
\(186\) −2.26709 22.2001i −0.166231 1.62779i
\(187\) −9.39195 + 2.42634i −0.686807 + 0.177431i
\(188\) −3.43937 + 0.709866i −0.250842 + 0.0517723i
\(189\) −19.3632 + 46.7469i −1.40847 + 3.40034i
\(190\) −14.7440 + 16.8255i −1.06964 + 1.22065i
\(191\) 7.64238 7.64238i 0.552983 0.552983i −0.374317 0.927301i \(-0.622123\pi\)
0.927301 + 0.374317i \(0.122123\pi\)
\(192\) 0.532699 + 24.7043i 0.0384442 + 1.78288i
\(193\) 26.3626 + 5.24384i 1.89762 + 0.377460i 0.998218 0.0596648i \(-0.0190032\pi\)
0.899401 + 0.437125i \(0.144003\pi\)
\(194\) 12.5015 + 15.1220i 0.897554 + 1.08569i
\(195\) 3.75788 + 2.71111i 0.269107 + 0.194147i
\(196\) 23.8464 16.1827i 1.70331 1.15591i
\(197\) 2.39931 + 3.59083i 0.170944 + 0.255836i 0.907043 0.421038i \(-0.138334\pi\)
−0.736099 + 0.676874i \(0.763334\pi\)
\(198\) 21.6638 + 2.05512i 1.53958 + 0.146051i
\(199\) 13.0589 + 8.72570i 0.925723 + 0.618548i 0.924389 0.381451i \(-0.124575\pi\)
0.00133382 + 0.999999i \(0.499575\pi\)
\(200\) −8.28769 11.4592i −0.586028 0.810291i
\(201\) −2.00624 + 0.399066i −0.141509 + 0.0281479i
\(202\) 13.0654 + 3.91213i 0.919277 + 0.275256i
\(203\) −27.2455 −1.91226
\(204\) −25.4189 + 1.62014i −1.77968 + 0.113432i
\(205\) 5.05703 + 8.19074i 0.353198 + 0.572066i
\(206\) −11.3672 3.40365i −0.791991 0.237144i
\(207\) −8.60326 43.2515i −0.597968 3.00619i
\(208\) −2.49387 0.991247i −0.172919 0.0687306i
\(209\) −13.8389 9.24687i −0.957258 0.639620i
\(210\) 20.0049 + 40.5259i 1.38047 + 2.79656i
\(211\) 10.8875 7.27478i 0.749525 0.500817i −0.121175 0.992631i \(-0.538666\pi\)
0.870700 + 0.491815i \(0.163666\pi\)
\(212\) −2.68595 3.95793i −0.184472 0.271832i
\(213\) 7.28082 3.01581i 0.498873 0.206640i
\(214\) 5.63339 4.65718i 0.385091 0.318359i
\(215\) −4.48459 + 1.67150i −0.305846 + 0.113996i
\(216\) 29.6932 + 8.65892i 2.02037 + 0.589165i
\(217\) 16.7146 + 16.7146i 1.13466 + 1.13466i
\(218\) 6.09983 + 19.8514i 0.413133 + 1.34451i
\(219\) −1.45351 + 3.50908i −0.0982191 + 0.237122i
\(220\) 7.65052 7.22292i 0.515798 0.486969i
\(221\) 0.912679 2.61134i 0.0613934 0.175658i
\(222\) 2.36342 + 23.1434i 0.158623 + 1.55328i
\(223\) −8.19765 3.39558i −0.548955 0.227385i 0.0909273 0.995858i \(-0.471017\pi\)
−0.639882 + 0.768473i \(0.721017\pi\)
\(224\) −16.9657 19.9316i −1.13357 1.33173i
\(225\) −31.0332 + 10.3131i −2.06888 + 0.687543i
\(226\) −7.32520 + 13.8237i −0.487265 + 0.919542i
\(227\) −15.6337 3.10973i −1.03764 0.206400i −0.353262 0.935525i \(-0.614927\pi\)
−0.684381 + 0.729125i \(0.739927\pi\)
\(228\) −31.1238 30.6796i −2.06122 2.03181i
\(229\) −11.5640 + 4.78996i −0.764170 + 0.316530i −0.730509 0.682904i \(-0.760717\pi\)
−0.0336619 + 0.999433i \(0.510717\pi\)
\(230\) −18.4694 10.6537i −1.21783 0.702483i
\(231\) −27.9572 + 18.6804i −1.83945 + 1.22908i
\(232\) 1.81102 + 16.5560i 0.118899 + 1.08695i
\(233\) 8.30073 + 5.54637i 0.543799 + 0.363355i 0.796925 0.604078i \(-0.206459\pi\)
−0.253126 + 0.967433i \(0.581459\pi\)
\(234\) −3.91954 + 4.81112i −0.256228 + 0.314513i
\(235\) 2.67485 + 2.87431i 0.174488 + 0.187499i
\(236\) −0.253406 + 1.32360i −0.0164953 + 0.0861591i
\(237\) 11.7506i 0.763282i
\(238\) 19.7909 18.3369i 1.28285 1.18860i
\(239\) 14.8681i 0.961737i −0.876793 0.480868i \(-0.840322\pi\)
0.876793 0.480868i \(-0.159678\pi\)
\(240\) 23.2962 14.8499i 1.50376 0.958556i
\(241\) 0.111847 + 0.562292i 0.00720469 + 0.0362204i 0.984220 0.176947i \(-0.0566221\pi\)
−0.977016 + 0.213167i \(0.931622\pi\)
\(242\) −5.99187 4.88148i −0.385172 0.313793i
\(243\) 6.06506 9.07700i 0.389074 0.582290i
\(244\) −8.01167 + 0.0575773i −0.512894 + 0.00368601i
\(245\) −29.3058 13.3916i −1.87228 0.855556i
\(246\) −16.5522 + 8.92395i −1.05533 + 0.568970i
\(247\) 4.38507 1.81635i 0.279015 0.115572i
\(248\) 9.04576 11.2678i 0.574406 0.715507i
\(249\) 16.6271 + 3.30734i 1.05370 + 0.209594i
\(250\) −6.13851 + 14.5712i −0.388233 + 0.921561i
\(251\) 6.76542 6.76542i 0.427029 0.427029i −0.460586 0.887615i \(-0.652361\pi\)
0.887615 + 0.460586i \(0.152361\pi\)
\(252\) −55.7502 + 23.5633i −3.51193 + 1.48435i
\(253\) 6.07049 14.6555i 0.381649 0.921381i
\(254\) −0.437077 4.28000i −0.0274246 0.268551i
\(255\) 16.3038 + 23.3478i 1.02098 + 1.46209i
\(256\) −10.9839 + 11.6342i −0.686491 + 0.727139i
\(257\) 11.5256 27.8252i 0.718946 1.73569i 0.0426152 0.999092i \(-0.486431\pi\)
0.676331 0.736598i \(-0.263569\pi\)
\(258\) −2.74611 8.93699i −0.170965 0.556392i
\(259\) −17.4249 17.4249i −1.08273 1.08273i
\(260\) 0.500543 + 2.95837i 0.0310424 + 0.183470i
\(261\) 37.7720 + 7.51332i 2.33803 + 0.465063i
\(262\) −4.05064 + 3.34870i −0.250249 + 0.206884i
\(263\) −1.74904 4.22255i −0.107850 0.260374i 0.860736 0.509052i \(-0.170004\pi\)
−0.968586 + 0.248678i \(0.920004\pi\)
\(264\) 13.2096 + 15.7467i 0.812995 + 0.969142i
\(265\) −2.22268 + 4.86406i −0.136538 + 0.298797i
\(266\) 46.0859 + 4.37191i 2.82571 + 0.268059i
\(267\) 20.3046 + 13.5671i 1.24262 + 0.830293i
\(268\) −1.10655 0.727926i −0.0675933 0.0444651i
\(269\) 2.06052 + 10.3590i 0.125632 + 0.631596i 0.991369 + 0.131097i \(0.0418501\pi\)
−0.865737 + 0.500499i \(0.833150\pi\)
\(270\) −8.96321 33.3989i −0.545483 2.03260i
\(271\) −21.4104 −1.30059 −0.650296 0.759681i \(-0.725355\pi\)
−0.650296 + 0.759681i \(0.725355\pi\)
\(272\) −12.4581 10.8072i −0.755382 0.655285i
\(273\) 9.58853i 0.580324i
\(274\) 7.34650 24.5352i 0.443818 1.48222i
\(275\) −11.3428 3.11729i −0.683995 0.187980i
\(276\) 22.8912 34.7979i 1.37789 2.09458i
\(277\) 8.62180 + 5.76090i 0.518034 + 0.346139i 0.786942 0.617027i \(-0.211663\pi\)
−0.268908 + 0.963166i \(0.586663\pi\)
\(278\) 2.57707 27.1658i 0.154562 1.62930i
\(279\) −18.5632 27.7817i −1.11135 1.66325i
\(280\) −9.19635 + 27.7814i −0.549587 + 1.66026i
\(281\) −26.5442 + 10.9950i −1.58349 + 0.655905i −0.988962 0.148168i \(-0.952662\pi\)
−0.594531 + 0.804072i \(0.702662\pi\)
\(282\) −5.91161 + 4.88719i −0.352031 + 0.291028i
\(283\) 2.50060 12.5713i 0.148645 0.747289i −0.832501 0.554023i \(-0.813092\pi\)
0.981146 0.193266i \(-0.0619080\pi\)
\(284\) 4.72832 + 1.91884i 0.280574 + 0.113862i
\(285\) −11.2475 + 47.5489i −0.666246 + 2.81656i
\(286\) −2.13378 + 0.655658i −0.126173 + 0.0387698i
\(287\) 7.62269 18.4028i 0.449953 1.08628i
\(288\) 18.0241 + 32.3108i 1.06208 + 1.90393i
\(289\) 10.5896 13.2989i 0.622919 0.782286i
\(290\) 14.7682 11.3412i 0.867220 0.665980i
\(291\) 39.5906 + 16.3989i 2.32084 + 0.961323i
\(292\) −2.26535 + 0.957467i −0.132569 + 0.0560315i
\(293\) −15.0394 15.0394i −0.878613 0.878613i 0.114778 0.993391i \(-0.463384\pi\)
−0.993391 + 0.114778i \(0.963384\pi\)
\(294\) 29.4714 55.6169i 1.71881 3.24364i
\(295\) 1.41183 0.526219i 0.0821999 0.0306377i
\(296\) −9.43013 + 11.7466i −0.548115 + 0.682758i
\(297\) 23.7690 9.84543i 1.37922 0.571290i
\(298\) −11.4450 21.2282i −0.662989 1.22972i
\(299\) 2.51321 + 3.76128i 0.145343 + 0.217521i
\(300\) −27.7128 13.6396i −1.60000 0.787480i
\(301\) 8.23444 + 5.50207i 0.474625 + 0.317134i
\(302\) 14.9105 + 12.1473i 0.858004 + 0.699001i
\(303\) 29.2152 5.81126i 1.67837 0.333848i
\(304\) −0.406716 28.2950i −0.0233268 1.62283i
\(305\) 4.70581 + 7.62188i 0.269454 + 0.436427i
\(306\) −32.4939 + 19.9639i −1.85755 + 1.14126i
\(307\) 26.9859i 1.54017i 0.637943 + 0.770083i \(0.279785\pi\)
−0.637943 + 0.770083i \(0.720215\pi\)
\(308\) −21.3834 4.09389i −1.21843 0.233271i
\(309\) −25.4180 + 5.05595i −1.44598 + 0.287623i
\(310\) −16.0177 2.10240i −0.909744 0.119409i
\(311\) −8.78046 + 13.1409i −0.497894 + 0.745151i −0.992270 0.124097i \(-0.960397\pi\)
0.494376 + 0.869248i \(0.335397\pi\)
\(312\) −5.82655 + 0.637353i −0.329863 + 0.0360830i
\(313\) −16.3030 24.3992i −0.921501 1.37912i −0.925343 0.379131i \(-0.876223\pi\)
0.00384177 0.999993i \(-0.498777\pi\)
\(314\) −3.34065 6.19625i −0.188524 0.349675i
\(315\) 54.8783 + 39.5918i 3.09204 + 2.23075i
\(316\) 5.34130 5.41863i 0.300472 0.304822i
\(317\) 12.7689 + 2.53989i 0.717171 + 0.142654i 0.540169 0.841556i \(-0.318360\pi\)
0.177002 + 0.984211i \(0.443360\pi\)
\(318\) −9.23107 4.89155i −0.517653 0.274304i
\(319\) 9.79575 + 9.79575i 0.548457 + 0.548457i
\(320\) 17.4929 + 3.74159i 0.977881 + 0.209161i
\(321\) 6.10911 14.7487i 0.340977 0.823192i
\(322\) 4.48232 + 43.8923i 0.249790 + 2.44602i
\(323\) 29.1224 1.64614i 1.62041 0.0915938i
\(324\) 27.7267 5.72263i 1.54037 0.317924i
\(325\) 2.53621 2.19562i 0.140684 0.121791i
\(326\) −10.2024 + 3.13494i −0.565058 + 0.173628i
\(327\) 32.0727 + 32.0727i 1.77362 + 1.77362i
\(328\) −11.6893 3.40875i −0.645433 0.188216i
\(329\) 1.58506 7.96864i 0.0873873 0.439326i
\(330\) 7.37807 21.7630i 0.406149 1.19802i
\(331\) 3.67576 + 8.87408i 0.202038 + 0.487763i 0.992128 0.125228i \(-0.0399661\pi\)
−0.790090 + 0.612991i \(0.789966\pi\)
\(332\) 6.16401 + 9.08310i 0.338294 + 0.498500i
\(333\) 19.3519 + 28.9622i 1.06048 + 1.58712i
\(334\) 10.0139 + 0.949966i 0.547937 + 0.0519798i
\(335\) −0.0531918 + 1.47989i −0.00290618 + 0.0808552i
\(336\) −53.1245 21.1155i −2.89818 1.15195i
\(337\) 1.51971 + 7.64009i 0.0827838 + 0.416182i 0.999848 + 0.0174423i \(0.00555234\pi\)
−0.917064 + 0.398740i \(0.869448\pi\)
\(338\) −5.09097 + 17.0024i −0.276912 + 0.924807i
\(339\) 34.1691i 1.85581i
\(340\) −3.09459 + 18.1776i −0.167828 + 0.985816i
\(341\) 12.0190i 0.650868i
\(342\) −62.6858 18.7698i −3.38966 1.01496i
\(343\) 6.68845 + 33.6251i 0.361143 + 1.81559i
\(344\) 2.79603 5.36945i 0.150752 0.289501i
\(345\) −46.5384 1.67273i −2.50554 0.0900568i
\(346\) −0.525647 + 5.54103i −0.0282590 + 0.297888i
\(347\) −7.66148 11.4662i −0.411290 0.615538i 0.566767 0.823878i \(-0.308194\pi\)
−0.978057 + 0.208340i \(0.933194\pi\)
\(348\) 20.4258 + 30.0988i 1.09494 + 1.61347i
\(349\) −1.56644 3.78172i −0.0838496 0.202431i 0.876394 0.481595i \(-0.159943\pi\)
−0.960243 + 0.279165i \(0.909943\pi\)
\(350\) 31.8842 7.33987i 1.70428 0.392333i
\(351\) −1.43132 + 7.19572i −0.0763981 + 0.384079i
\(352\) −1.06633 + 13.2659i −0.0568353 + 0.707076i
\(353\) −5.12718 5.12718i −0.272892 0.272892i 0.557371 0.830263i \(-0.311810\pi\)
−0.830263 + 0.557371i \(0.811810\pi\)
\(354\) 0.864525 + 2.81352i 0.0459490 + 0.149537i
\(355\) −0.911310 5.63189i −0.0483673 0.298910i
\(356\) 3.19620 + 15.4859i 0.169398 + 0.820751i
\(357\) 19.4419 55.6268i 1.02897 2.94408i
\(358\) −0.113618 + 0.0116028i −0.00600490 + 0.000613226i
\(359\) −0.508478 + 1.22757i −0.0268364 + 0.0647889i −0.936730 0.350054i \(-0.886163\pi\)
0.909893 + 0.414843i \(0.136163\pi\)
\(360\) 20.4105 35.9789i 1.07573 1.89625i
\(361\) 21.9545 + 21.9545i 1.15550 + 1.15550i
\(362\) 13.2708 25.0440i 0.697497 1.31628i
\(363\) −16.5555 3.29310i −0.868941 0.172843i
\(364\) 4.35853 4.42163i 0.228449 0.231757i
\(365\) 2.22992 + 1.60877i 0.116719 + 0.0842068i
\(366\) −15.4026 + 8.30416i −0.805107 + 0.434065i
\(367\) 4.29723 + 6.43125i 0.224313 + 0.335709i 0.926507 0.376277i \(-0.122796\pi\)
−0.702194 + 0.711986i \(0.747796\pi\)
\(368\) 26.3736 5.64126i 1.37482 0.294071i
\(369\) −15.6426 + 23.4108i −0.814320 + 1.21872i
\(370\) 16.6983 + 2.19174i 0.868104 + 0.113943i
\(371\) 10.8535 2.15890i 0.563487 0.112084i
\(372\) 5.93424 30.9960i 0.307676 1.60707i
\(373\) 24.3172i 1.25910i −0.776960 0.629549i \(-0.783240\pi\)
0.776960 0.629549i \(-0.216760\pi\)
\(374\) −13.7083 0.522768i −0.708841 0.0270317i
\(375\) 3.05451 + 34.3980i 0.157734 + 1.77630i
\(376\) −4.94757 0.433497i −0.255151 0.0223559i
\(377\) −3.87465 + 0.770715i −0.199554 + 0.0396938i
\(378\) −45.1963 + 55.4771i −2.32464 + 2.85343i
\(379\) 21.8652 + 14.6099i 1.12314 + 0.750459i 0.971279 0.237943i \(-0.0764732\pi\)
0.151862 + 0.988402i \(0.451473\pi\)
\(380\) −26.8004 + 16.8140i −1.37483 + 0.862538i
\(381\) −5.22040 7.81287i −0.267449 0.400266i
\(382\) 13.4540 7.25358i 0.688365 0.371125i
\(383\) −12.7732 + 5.29085i −0.652682 + 0.270350i −0.684355 0.729149i \(-0.739916\pi\)
0.0316735 + 0.999498i \(0.489916\pi\)
\(384\) −9.29982 + 33.6851i −0.474580 + 1.71898i
\(385\) 8.50132 + 22.8088i 0.433267 + 1.16244i
\(386\) 33.5884 + 17.7985i 1.70960 + 0.905919i
\(387\) −9.89859 9.89859i −0.503174 0.503174i
\(388\) 10.8024 + 25.5583i 0.548411 + 1.29753i
\(389\) 28.1359 + 11.6543i 1.42655 + 0.590895i 0.956496 0.291745i \(-0.0942360\pi\)
0.470050 + 0.882640i \(0.344236\pi\)
\(390\) 3.99133 + 5.19739i 0.202109 + 0.263180i
\(391\) 6.95366 + 26.9165i 0.351662 + 1.36123i
\(392\) 38.8714 12.2506i 1.96330 0.618749i
\(393\) −4.39270 + 10.6049i −0.221582 + 0.534947i
\(394\) 1.79390 + 5.83810i 0.0903755 + 0.294119i
\(395\) −8.27825 1.95819i −0.416524 0.0985273i
\(396\) 28.5161 + 11.5724i 1.43299 + 0.581533i
\(397\) −5.81201 + 29.2189i −0.291696 + 1.46646i 0.505547 + 0.862799i \(0.331291\pi\)
−0.797244 + 0.603658i \(0.793709\pi\)
\(398\) 14.1524 + 17.1189i 0.709394 + 0.858094i
\(399\) 93.4107 38.6920i 4.67638 1.93702i
\(400\) −6.57948 18.8868i −0.328974 0.944339i
\(401\) −0.979570 1.46603i −0.0489174 0.0732100i 0.806205 0.591637i \(-0.201518\pi\)
−0.855122 + 0.518427i \(0.826518\pi\)
\(402\) −2.87991 0.273201i −0.143637 0.0136260i
\(403\) 2.84985 + 1.90421i 0.141961 + 0.0948553i
\(404\) 16.1138 + 10.6002i 0.801691 + 0.527379i
\(405\) −21.5635 23.1714i −1.07150 1.15140i
\(406\) −36.9118 11.0524i −1.83190 0.548521i
\(407\) 12.5298i 0.621077i
\(408\) −35.0944 8.11648i −1.73743 0.401825i
\(409\) 20.4889 1.01311 0.506554 0.862208i \(-0.330919\pi\)
0.506554 + 0.862208i \(0.330919\pi\)
\(410\) 3.52853 + 13.1481i 0.174262 + 0.649339i
\(411\) −10.9128 54.8626i −0.538291 2.70617i
\(412\) −14.0194 9.22243i −0.690686 0.454356i
\(413\) −2.59235 1.73215i −0.127561 0.0852336i
\(414\) 5.88980 62.0865i 0.289468 3.05138i
\(415\) 5.10086 11.1626i 0.250391 0.547950i
\(416\) −2.97655 2.35459i −0.145938 0.115443i
\(417\) −22.8074 55.0619i −1.11688 2.69639i
\(418\) −14.9977 18.1414i −0.733560 0.887325i
\(419\) −21.0452 4.18615i −1.02812 0.204507i −0.347916 0.937526i \(-0.613111\pi\)
−0.680208 + 0.733019i \(0.738111\pi\)
\(420\) 10.6626 + 63.0191i 0.520280 + 3.07502i
\(421\) 6.24485 + 6.24485i 0.304355 + 0.304355i 0.842715 0.538360i \(-0.180956\pi\)
−0.538360 + 0.842715i \(0.680956\pi\)
\(422\) 17.7013 5.43915i 0.861684 0.264774i
\(423\) −4.39492 + 10.6103i −0.213688 + 0.515889i
\(424\) −2.03331 6.45172i −0.0987462 0.313323i
\(425\) 19.1654 7.59517i 0.929659 0.368420i
\(426\) 11.0873 1.13225i 0.537183 0.0548576i
\(427\) 7.09327 17.1247i 0.343267 0.828721i
\(428\) 9.52126 4.02424i 0.460228 0.194519i
\(429\) −3.44742 + 3.44742i −0.166443 + 0.166443i
\(430\) −6.75371 + 0.445312i −0.325693 + 0.0214748i
\(431\) 7.66662 + 1.52499i 0.369288 + 0.0734560i 0.376246 0.926520i \(-0.377215\pi\)
−0.00695775 + 0.999976i \(0.502215\pi\)
\(432\) 36.7153 + 23.7763i 1.76647 + 1.14394i
\(433\) 15.6913 6.49954i 0.754075 0.312348i 0.0276718 0.999617i \(-0.491191\pi\)
0.726403 + 0.687269i \(0.241191\pi\)
\(434\) 15.8643 + 29.4252i 0.761510 + 1.41245i
\(435\) 16.9028 36.9897i 0.810428 1.77352i
\(436\) 0.211064 + 29.3688i 0.0101081 + 1.40651i
\(437\) −26.5007 + 39.6611i −1.26770 + 1.89725i
\(438\) −3.39268 + 4.16442i −0.162109 + 0.198984i
\(439\) −0.593019 2.98131i −0.0283033 0.142290i 0.964050 0.265721i \(-0.0856101\pi\)
−0.992353 + 0.123431i \(0.960610\pi\)
\(440\) 13.2948 6.68200i 0.633807 0.318552i
\(441\) 94.2436i 4.48779i
\(442\) 2.29580 3.16757i 0.109200 0.150666i
\(443\) 36.5984i 1.73884i −0.494071 0.869422i \(-0.664492\pi\)
0.494071 0.869422i \(-0.335508\pi\)
\(444\) −6.18640 + 32.3131i −0.293594 + 1.53351i
\(445\) 12.9417 12.0436i 0.613494 0.570923i
\(446\) −9.72860 7.92572i −0.460662 0.375294i
\(447\) −43.7961 29.2636i −2.07148 1.38412i
\(448\) −14.8995 33.8853i −0.703934 1.60093i
\(449\) −26.0335 + 17.3951i −1.22860 + 0.820923i −0.988705 0.149876i \(-0.952113\pi\)
−0.239894 + 0.970799i \(0.577113\pi\)
\(450\) −46.2269 + 1.38320i −2.17916 + 0.0652045i
\(451\) −9.35710 + 3.87584i −0.440609 + 0.182506i
\(452\) −15.5318 + 15.7567i −0.730554 + 0.741131i
\(453\) 41.1977 + 8.19474i 1.93564 + 0.385022i
\(454\) −19.9188 10.5549i −0.934833 0.495368i
\(455\) −6.75509 1.59789i −0.316684 0.0749104i
\(456\) −29.7205 54.1899i −1.39179 2.53767i
\(457\) −1.92714 0.798247i −0.0901477 0.0373404i 0.337154 0.941450i \(-0.390536\pi\)
−0.427302 + 0.904109i \(0.640536\pi\)
\(458\) −17.6098 + 1.79833i −0.822853 + 0.0840304i
\(459\) −22.8938 + 38.8430i −1.06859 + 1.81304i
\(460\) −20.7003 21.9257i −0.965155 1.02229i
\(461\) −2.11083 + 5.09600i −0.0983113 + 0.237344i −0.965382 0.260841i \(-0.916000\pi\)
0.867070 + 0.498185i \(0.166000\pi\)
\(462\) −45.4538 + 13.9668i −2.11470 + 0.649795i
\(463\) −12.5310 12.5310i −0.582367 0.582367i 0.353186 0.935553i \(-0.385098\pi\)
−0.935553 + 0.353186i \(0.885098\pi\)
\(464\) −4.26253 + 23.1644i −0.197883 + 1.07538i
\(465\) −33.0621 + 12.3230i −1.53322 + 0.571463i
\(466\) 8.99577 + 10.8814i 0.416721 + 0.504072i
\(467\) −10.0201 + 4.15047i −0.463676 + 0.192061i −0.602277 0.798287i \(-0.705740\pi\)
0.138601 + 0.990348i \(0.455740\pi\)
\(468\) −7.26180 + 4.92803i −0.335677 + 0.227798i
\(469\) 2.54786 1.70242i 0.117649 0.0786106i
\(470\) 2.45786 + 4.97914i 0.113373 + 0.229671i
\(471\) −12.7835 8.54169i −0.589035 0.393580i
\(472\) −0.880241 + 1.69040i −0.0405164 + 0.0778069i
\(473\) −0.982383 4.93877i −0.0451700 0.227085i
\(474\) 4.76673 15.9195i 0.218943 0.731207i
\(475\) 31.6237 + 15.8477i 1.45100 + 0.727143i
\(476\) 34.2509 16.8142i 1.56989 0.770677i
\(477\) −15.6422 −0.716207
\(478\) 6.03137 20.1431i 0.275869 0.921322i
\(479\) −33.4364 + 6.65092i −1.52775 + 0.303888i −0.886240 0.463227i \(-0.846692\pi\)
−0.641509 + 0.767115i \(0.721692\pi\)
\(480\) 37.5853 10.6681i 1.71553 0.486930i
\(481\) −2.97094 1.98512i −0.135463 0.0905137i
\(482\) −0.0765705 + 0.807156i −0.00348769 + 0.0367649i
\(483\) 53.5363 + 80.1228i 2.43599 + 3.64571i
\(484\) −6.13748 9.04401i −0.278976 0.411091i
\(485\) 18.1506 25.1586i 0.824178 1.14239i
\(486\) 11.8990 9.83703i 0.539750 0.446217i
\(487\) −1.81761 0.361545i −0.0823638 0.0163832i 0.153736 0.988112i \(-0.450869\pi\)
−0.236100 + 0.971729i \(0.575869\pi\)
\(488\) −10.8774 3.17200i −0.492398 0.143590i
\(489\) −16.4834 + 16.4834i −0.745405 + 0.745405i
\(490\) −34.2706 30.0309i −1.54819 1.35666i
\(491\) −4.80286 + 11.5951i −0.216750 + 0.523281i −0.994432 0.105376i \(-0.966395\pi\)
0.777682 + 0.628658i \(0.216395\pi\)
\(492\) −26.0447 + 5.37548i −1.17419 + 0.242345i
\(493\) −24.0411 3.38508i −1.08275 0.152456i
\(494\) 6.67764 0.681927i 0.300441 0.0306813i
\(495\) −5.49603 33.9654i −0.247028 1.52663i
\(496\) 16.8259 11.5960i 0.755507 0.520674i
\(497\) −8.34775 + 8.34775i −0.374448 + 0.374448i
\(498\) 21.1845 + 11.2257i 0.949299 + 0.503034i
\(499\) −6.39294 + 32.1395i −0.286187 + 1.43876i 0.523564 + 0.851987i \(0.324602\pi\)
−0.809751 + 0.586774i \(0.800398\pi\)
\(500\) −14.2273 + 17.2506i −0.636263 + 0.771472i
\(501\) 20.2971 8.40732i 0.906806 0.375611i
\(502\) 11.9101 6.42123i 0.531575 0.286594i
\(503\) 16.8664 + 25.2424i 0.752036 + 1.12550i 0.988107 + 0.153766i \(0.0491400\pi\)
−0.236072 + 0.971736i \(0.575860\pi\)
\(504\) −85.0881 + 9.30760i −3.79013 + 0.414593i
\(505\) 0.774588 21.5505i 0.0344687 0.958983i
\(506\) 14.1693 17.3924i 0.629904 0.773189i
\(507\) 7.56238 + 38.0186i 0.335857 + 1.68847i
\(508\) 1.14407 5.97578i 0.0507601 0.265132i
\(509\) 5.68733 0.252087 0.126043 0.992025i \(-0.459772\pi\)
0.126043 + 0.992025i \(0.459772\pi\)
\(510\) 12.6169 + 38.2450i 0.558687 + 1.69352i
\(511\) 5.68981i 0.251703i
\(512\) −19.6003 + 11.3062i −0.866218 + 0.499666i
\(513\) −75.8759 + 15.0926i −3.35000 + 0.666357i
\(514\) 26.9022 33.0217i 1.18661 1.45653i
\(515\) −0.673912 + 18.7495i −0.0296961 + 0.826199i
\(516\) −0.0950200 13.2217i −0.00418302 0.582052i
\(517\) −3.43490 + 2.29513i −0.151067 + 0.100940i
\(518\) −16.5384 30.6755i −0.726655 1.34780i
\(519\) 4.65204 + 11.2310i 0.204202 + 0.492987i
\(520\) −0.521959 + 4.21100i −0.0228894 + 0.184664i
\(521\) 5.48013 + 1.09007i 0.240089 + 0.0477567i 0.313668 0.949533i \(-0.398442\pi\)
−0.0735790 + 0.997289i \(0.523442\pi\)
\(522\) 48.1251 + 25.5015i 2.10638 + 1.11617i
\(523\) −14.3521 14.3521i −0.627573 0.627573i 0.319884 0.947457i \(-0.396356\pi\)
−0.947457 + 0.319884i \(0.896356\pi\)
\(524\) −6.84617 + 2.89359i −0.299076 + 0.126407i
\(525\) 54.0263 46.7710i 2.35790 2.04125i
\(526\) −0.656654 6.43016i −0.0286315 0.280368i
\(527\) 12.6721 + 16.8255i 0.552004 + 0.732928i
\(528\) 11.5084 + 26.6920i 0.500838 + 1.16162i
\(529\) −20.7521 8.59579i −0.902264 0.373730i
\(530\) −4.98441 + 5.68811i −0.216509 + 0.247076i
\(531\) 3.11625 + 3.11625i 0.135234 + 0.135234i
\(532\) 60.6629 + 24.6181i 2.63007 + 1.06733i
\(533\) 0.563465 2.83273i 0.0244064 0.122699i
\(534\) 22.0047 + 26.6172i 0.952238 + 1.15184i
\(535\) −9.37236 6.76167i −0.405202 0.292332i
\(536\) −1.20385 1.43506i −0.0519983 0.0619853i
\(537\) −0.207403 + 0.138582i −0.00895010 + 0.00598026i
\(538\) −1.41064 + 14.8700i −0.0608169 + 0.641092i
\(539\) 18.8342 28.1874i 0.811247 1.21412i
\(540\) 1.40537 48.8844i 0.0604776 2.10365i
\(541\) −1.32194 6.64586i −0.0568348 0.285728i 0.941907 0.335873i \(-0.109031\pi\)
−0.998742 + 0.0501457i \(0.984031\pi\)
\(542\) −29.0065 8.68534i −1.24594 0.373067i
\(543\) 61.9029i 2.65651i
\(544\) −12.4939 19.6952i −0.535674 0.844425i
\(545\) 27.9399 17.2503i 1.19682 0.738923i
\(546\) 3.88967 12.9904i 0.166463 0.555937i
\(547\) 0.517804 0.102998i 0.0221397 0.00440386i −0.184008 0.982925i \(-0.558907\pi\)
0.206148 + 0.978521i \(0.433907\pi\)
\(548\) 19.9058 30.2597i 0.850335 1.29263i
\(549\) −14.5562 + 21.7848i −0.621242 + 0.929754i
\(550\) −14.1025 8.82456i −0.601331 0.376281i
\(551\) −23.1434 34.6365i −0.985940 1.47556i
\(552\) 45.1287 37.8576i 1.92080 1.61133i
\(553\) 6.73626 + 16.2628i 0.286455 + 0.691563i
\(554\) 9.34372 + 11.3023i 0.396977 + 0.480189i
\(555\) 34.4670 12.8466i 1.46304 0.545307i
\(556\) 14.5114 35.7584i 0.615422 1.51649i
\(557\) −7.07083 + 7.07083i −0.299601 + 0.299601i −0.840857 0.541257i \(-0.817949\pi\)
0.541257 + 0.840857i \(0.317949\pi\)
\(558\) −13.8792 45.1686i −0.587552 1.91214i
\(559\) 1.32668 + 0.549528i 0.0561125 + 0.0232426i
\(560\) −23.7288 + 33.9072i −1.00273 + 1.43284i
\(561\) −26.9899 + 13.0098i −1.13952 + 0.549274i
\(562\) −40.4219 + 4.12791i −1.70509 + 0.174126i
\(563\) −5.01599 + 12.1097i −0.211399 + 0.510362i −0.993639 0.112615i \(-0.964077\pi\)
0.782240 + 0.622978i \(0.214077\pi\)
\(564\) −9.99149 + 4.22299i −0.420717 + 0.177820i
\(565\) 24.0720 + 5.69416i 1.01272 + 0.239555i
\(566\) 8.48745 16.0171i 0.356754 0.673248i
\(567\) −12.7781 + 64.2397i −0.536629 + 2.69782i
\(568\) 5.62746 + 4.51770i 0.236123 + 0.189558i
\(569\) 5.02147 + 12.1229i 0.210511 + 0.508219i 0.993502 0.113814i \(-0.0363069\pi\)
−0.782991 + 0.622033i \(0.786307\pi\)
\(570\) −34.5266 + 59.8559i −1.44616 + 2.50709i
\(571\) 6.28432 + 9.40515i 0.262991 + 0.393593i 0.939340 0.342988i \(-0.111439\pi\)
−0.676349 + 0.736581i \(0.736439\pi\)
\(572\) −3.15679 + 0.0226868i −0.131992 + 0.000948584i
\(573\) 18.5467 27.7570i 0.774798 1.15957i
\(574\) 17.7924 21.8396i 0.742639 0.911567i
\(575\) −8.93389 + 32.5074i −0.372569 + 1.35565i
\(576\) 11.3117 + 51.0858i 0.471320 + 2.12857i
\(577\) 35.4243 1.47473 0.737366 0.675493i \(-0.236069\pi\)
0.737366 + 0.675493i \(0.236069\pi\)
\(578\) 19.7415 13.7213i 0.821136 0.570732i
\(579\) 83.0227 3.45031
\(580\) 24.6084 9.37406i 1.02181 0.389237i
\(581\) −24.9079 + 4.95448i −1.03335 + 0.205546i
\(582\) 46.9843 + 38.2773i 1.94756 + 1.58665i
\(583\) −4.67844 3.12603i −0.193761 0.129467i
\(584\) −3.45746 + 0.378204i −0.143071 + 0.0156502i
\(585\) 8.92432 + 4.07806i 0.368975 + 0.168607i
\(586\) −14.2743 26.4761i −0.589666 1.09372i
\(587\) 3.42440 + 8.26724i 0.141340 + 0.341226i 0.978659 0.205489i \(-0.0658784\pi\)
−0.837319 + 0.546714i \(0.815878\pi\)
\(588\) 62.4888 63.3935i 2.57700 2.61430i
\(589\) −7.05083 + 35.4469i −0.290524 + 1.46056i
\(590\) 2.12619 0.140192i 0.0875339 0.00577162i
\(591\) 9.43227 + 9.43227i 0.387992 + 0.387992i
\(592\) −17.5409 + 12.0887i −0.720927 + 0.496843i
\(593\) −20.4753 8.48116i −0.840821 0.348280i −0.0796440 0.996823i \(-0.525378\pi\)
−0.761177 + 0.648544i \(0.775378\pi\)
\(594\) 36.1957 3.69634i 1.48513 0.151663i
\(595\) −35.9490 22.9668i −1.47377 0.941546i
\(596\) −6.89405 33.4023i −0.282391 1.36821i
\(597\) 44.8187 + 18.5645i 1.83431 + 0.759796i
\(598\) 1.87906 + 6.11523i 0.0768404 + 0.250070i
\(599\) −9.05146 + 9.05146i −0.369832 + 0.369832i −0.867416 0.497584i \(-0.834221\pi\)
0.497584 + 0.867416i \(0.334221\pi\)
\(600\) −32.0119 29.7206i −1.30688 1.21334i
\(601\) −4.90373 + 24.6527i −0.200027 + 1.00561i 0.742084 + 0.670306i \(0.233837\pi\)
−0.942112 + 0.335299i \(0.891163\pi\)
\(602\) 8.92392 + 10.7945i 0.363712 + 0.439951i
\(603\) −4.00170 + 1.65756i −0.162962 + 0.0675010i
\(604\) 15.2729 + 22.5056i 0.621443 + 0.915740i
\(605\) −5.07890 + 11.1146i −0.206487 + 0.451871i
\(606\) 41.9377 + 3.97840i 1.70360 + 0.161611i
\(607\) 20.8307 31.1753i 0.845492 1.26537i −0.116747 0.993162i \(-0.537247\pi\)
0.962239 0.272207i \(-0.0877534\pi\)
\(608\) 10.9271 38.4987i 0.443153 1.56133i
\(609\) −82.5377 + 16.4178i −3.34459 + 0.665281i
\(610\) 3.28347 + 12.2350i 0.132944 + 0.495379i
\(611\) 1.17808i 0.0476599i
\(612\) −52.1207 + 13.8653i −2.10686 + 0.560471i
\(613\) −18.2924 −0.738821 −0.369411 0.929266i \(-0.620440\pi\)
−0.369411 + 0.929266i \(0.620440\pi\)
\(614\) −10.9471 + 36.5601i −0.441788 + 1.47544i
\(615\) 20.2554 + 21.7658i 0.816777 + 0.877681i
\(616\) −27.3092 14.2207i −1.10032 0.572969i
\(617\) 10.0381 15.0231i 0.404119 0.604806i −0.572469 0.819926i \(-0.694014\pi\)
0.976588 + 0.215120i \(0.0690143\pi\)
\(618\) −36.4869 3.46131i −1.46772 0.139234i
\(619\) −17.1673 + 11.4709i −0.690014 + 0.461053i −0.850493 0.525987i \(-0.823696\pi\)
0.160479 + 0.987039i \(0.448696\pi\)
\(620\) −20.8477 9.34603i −0.837262 0.375345i
\(621\) −28.2162 68.1198i −1.13228 2.73355i
\(622\) −17.2264 + 14.2412i −0.690714 + 0.571020i
\(623\) −35.8791 7.13680i −1.43747 0.285930i
\(624\) −8.15226 1.50011i −0.326352 0.0600527i
\(625\) 24.7423 + 3.58040i 0.989691 + 0.143216i
\(626\) −12.1893 39.6691i −0.487183 1.58550i
\(627\) −47.4957 19.6734i −1.89680 0.785679i
\(628\) −2.01229 9.74975i −0.0802991 0.389057i
\(629\) −13.2105 17.5404i −0.526739 0.699381i
\(630\) 58.2874 + 75.9002i 2.32223 + 3.02394i
\(631\) −3.60818 + 8.71092i −0.143639 + 0.346776i −0.979283 0.202496i \(-0.935095\pi\)
0.835644 + 0.549272i \(0.185095\pi\)
\(632\) 9.43443 5.17433i 0.375282 0.205824i
\(633\) 28.5989 28.5989i 1.13670 1.13670i
\(634\) 16.2687 + 8.62081i 0.646114 + 0.342376i
\(635\) −6.37411 + 2.37577i −0.252949 + 0.0942794i
\(636\) −10.5218 10.3717i −0.417217 0.411263i
\(637\) 3.69959 + 8.93160i 0.146583 + 0.353883i
\(638\) 9.29740 + 17.2449i 0.368087 + 0.682731i
\(639\) 13.8750 9.27095i 0.548885 0.366753i
\(640\) 22.1813 + 12.1652i 0.876791 + 0.480872i
\(641\) −13.4708 + 20.1605i −0.532064 + 0.796290i −0.995979 0.0895896i \(-0.971444\pi\)
0.463915 + 0.885880i \(0.346444\pi\)
\(642\) 14.2595 17.5031i 0.562776 0.690792i
\(643\) 3.81347 + 19.1716i 0.150388 + 0.756054i 0.980200 + 0.198010i \(0.0634479\pi\)
−0.829812 + 0.558044i \(0.811552\pi\)
\(644\) −11.7327 + 61.2830i −0.462335 + 2.41489i
\(645\) −12.5784 + 7.76600i −0.495274 + 0.305786i
\(646\) 40.1223 + 9.58359i 1.57859 + 0.377061i
\(647\) −31.9601 −1.25648 −0.628241 0.778018i \(-0.716225\pi\)
−0.628241 + 0.778018i \(0.716225\pi\)
\(648\) 39.8851 + 3.49466i 1.56684 + 0.137283i
\(649\) 0.309272 + 1.55482i 0.0121400 + 0.0610318i
\(650\) 4.32669 1.94575i 0.169707 0.0763187i
\(651\) 60.7074 + 40.5634i 2.37931 + 1.58980i
\(652\) −15.0938 + 0.108474i −0.591117 + 0.00424817i
\(653\) −32.2102 + 21.5222i −1.26048 + 0.842228i −0.992624 0.121230i \(-0.961316\pi\)
−0.267859 + 0.963458i \(0.586316\pi\)
\(654\) 30.4410 + 56.4622i 1.19034 + 2.20785i
\(655\) 6.73910 + 4.86191i 0.263319 + 0.189971i
\(656\) −14.4537 9.35998i −0.564321 0.365446i
\(657\) −1.56904 + 7.88811i −0.0612142 + 0.307744i
\(658\) 5.37997 10.1528i 0.209733 0.395797i
\(659\) −13.6422 + 13.6422i −0.531424 + 0.531424i −0.920996 0.389572i \(-0.872623\pi\)
0.389572 + 0.920996i \(0.372623\pi\)
\(660\) 18.8241 26.4912i 0.732726 1.03117i
\(661\) −19.3537 8.01657i −0.752772 0.311808i −0.0269000 0.999638i \(-0.508564\pi\)
−0.725872 + 0.687830i \(0.758564\pi\)
\(662\) 1.38002 + 13.5136i 0.0536359 + 0.525220i
\(663\) 1.19131 8.46078i 0.0462668 0.328590i
\(664\) 4.66626 + 14.8061i 0.181086 + 0.574589i
\(665\) −11.6918 72.2555i −0.453390 2.80195i
\(666\) 14.4689 + 47.0879i 0.560659 + 1.82462i
\(667\) 28.0738 28.0738i 1.08702 1.08702i
\(668\) 13.1813 + 5.34924i 0.510001 + 0.206968i
\(669\) −26.8801 5.34679i −1.03924 0.206719i
\(670\) −0.672395 + 1.98336i −0.0259769 + 0.0766238i
\(671\) −8.70723 + 3.60665i −0.336139 + 0.139233i
\(672\) −63.4065 50.1574i −2.44596 1.93486i
\(673\) 33.9787 22.7038i 1.30978 0.875169i 0.312578 0.949892i \(-0.398807\pi\)
0.997204 + 0.0747236i \(0.0238074\pi\)
\(674\) −1.04039 + 10.9672i −0.0400745 + 0.422439i
\(675\) −47.5258 + 27.0346i −1.82927 + 1.04056i
\(676\) −13.7943 + 20.9694i −0.530551 + 0.806514i
\(677\) 32.5951 6.48358i 1.25273 0.249184i 0.476243 0.879314i \(-0.341998\pi\)
0.776490 + 0.630130i \(0.216998\pi\)
\(678\) −13.8610 + 46.2918i −0.532329 + 1.77782i
\(679\) −64.1942 −2.46355
\(680\) −11.5664 + 23.3713i −0.443551 + 0.896249i
\(681\) −49.2345 −1.88667
\(682\) 4.87563 16.2832i 0.186698 0.623516i
\(683\) 40.1356 7.98347i 1.53575 0.305479i 0.646503 0.762912i \(-0.276231\pi\)
0.889244 + 0.457433i \(0.151231\pi\)
\(684\) −77.3116 50.8581i −2.95608 1.94461i
\(685\) −40.4691 1.45458i −1.54625 0.0555767i
\(686\) −4.57892 + 48.2680i −0.174824 + 1.84288i
\(687\) −32.1456 + 21.4790i −1.22643 + 0.819476i
\(688\) 5.96619 6.14020i 0.227459 0.234093i
\(689\) 1.48243 0.614044i 0.0564762 0.0233932i
\(690\) −62.3709 21.1449i −2.37442 0.804973i
\(691\) −43.5640 8.66542i −1.65725 0.329648i −0.724255 0.689532i \(-0.757816\pi\)
−0.932997 + 0.359884i \(0.882816\pi\)
\(692\) −2.95991 + 7.29366i −0.112519 + 0.277264i
\(693\) −50.3445 + 50.3445i −1.91243 + 1.91243i
\(694\) −5.72828 18.6422i −0.217442 0.707648i
\(695\) −42.5917 + 6.89188i −1.61560 + 0.261424i
\(696\) 15.4627 + 49.0634i 0.586112 + 1.85974i
\(697\) 9.01258 15.2913i 0.341376 0.579199i
\(698\) −0.588099 5.75886i −0.0222599 0.217976i
\(699\) 28.4884 + 11.8003i 1.07753 + 0.446328i
\(700\) 46.1737 + 2.99015i 1.74520 + 0.113017i
\(701\) −24.9507 + 24.9507i −0.942374 + 0.942374i −0.998428 0.0560536i \(-0.982148\pi\)
0.0560536 + 0.998428i \(0.482148\pi\)
\(702\) −4.85814 + 9.16802i −0.183359 + 0.346025i
\(703\) 7.35043 36.9531i 0.277227 1.39371i
\(704\) −6.82608 + 17.5399i −0.257268 + 0.661059i
\(705\) 9.83522 + 7.09560i 0.370416 + 0.267236i
\(706\) −4.86633 9.02610i −0.183147 0.339702i
\(707\) −37.1023 + 24.7910i −1.39538 + 0.932361i
\(708\) 0.0299140 + 4.16242i 0.00112424 + 0.156433i
\(709\) −40.1803 26.8476i −1.50900 1.00828i −0.987952 0.154758i \(-0.950540\pi\)
−0.521051 0.853525i \(-0.674460\pi\)
\(710\) 1.05000 7.99968i 0.0394057 0.300223i
\(711\) −4.85418 24.4036i −0.182046 0.915206i
\(712\) −1.95183 + 22.2766i −0.0731481 + 0.834851i
\(713\) −34.4455 −1.29000
\(714\) 48.9051 67.4756i 1.83023 2.52521i
\(715\) 1.85420 + 3.00320i 0.0693432 + 0.112313i
\(716\) −0.158635 0.0303709i −0.00592846 0.00113502i
\(717\) −8.95930 45.0414i −0.334591 1.68210i
\(718\) −1.18685 + 1.45683i −0.0442930 + 0.0543684i
\(719\) 11.4596 17.1506i 0.427373 0.639609i −0.553821 0.832636i \(-0.686831\pi\)
0.981193 + 0.193027i \(0.0618307\pi\)
\(720\) 42.2470 40.4639i 1.57445 1.50800i
\(721\) 32.2800 21.5688i 1.20217 0.803264i
\(722\) 20.8376 + 38.6497i 0.775496 + 1.43839i
\(723\) 0.677658 + 1.63601i 0.0252024 + 0.0608439i
\(724\) 28.1384 28.5457i 1.04575 1.06089i
\(725\) −23.2424 18.0722i −0.863199 0.671184i
\(726\) −21.0933 11.1773i −0.782846 0.414830i
\(727\) 11.6539 11.6539i 0.432220 0.432220i −0.457163 0.889383i \(-0.651134\pi\)
0.889383 + 0.457163i \(0.151134\pi\)
\(728\) 7.69855 4.22228i 0.285327 0.156488i
\(729\) −3.34745 + 8.08147i −0.123980 + 0.299314i
\(730\) 2.36844 + 3.08412i 0.0876601 + 0.114148i
\(731\) 6.58235 + 5.87803i 0.243457 + 0.217407i
\(732\) −24.2359 + 5.00214i −0.895783 + 0.184884i
\(733\) −18.1974 7.53760i −0.672136 0.278408i 0.0203994 0.999792i \(-0.493506\pi\)
−0.692535 + 0.721384i \(0.743506\pi\)
\(734\) 3.21292 + 10.4562i 0.118591 + 0.385944i
\(735\) −96.8486 22.9092i −3.57232 0.845019i
\(736\) 38.0190 + 3.05599i 1.40140 + 0.112645i
\(737\) −1.52813 0.303964i −0.0562894 0.0111967i
\(738\) −30.6891 + 25.3710i −1.12968 + 0.933919i
\(739\) −14.7461 35.6002i −0.542443 1.30957i −0.922994 0.384814i \(-0.874266\pi\)
0.380551 0.924760i \(-0.375734\pi\)
\(740\) 21.7335 + 9.74316i 0.798940 + 0.358166i
\(741\) 12.1896 8.14485i 0.447797 0.299209i
\(742\) 15.5800 + 1.47799i 0.571958 + 0.0542585i
\(743\) −9.70475 + 14.5242i −0.356033 + 0.532841i −0.965647 0.259858i \(-0.916324\pi\)
0.609614 + 0.792698i \(0.291324\pi\)
\(744\) 20.6134 39.5856i 0.755725 1.45128i
\(745\) −27.9146 + 25.9775i −1.02271 + 0.951743i
\(746\) 9.86451 32.9446i 0.361165 1.20619i
\(747\) 35.8974 1.31342
\(748\) −18.3598 6.26915i −0.671300 0.229223i
\(749\) 23.9143i 0.873811i
\(750\) −9.81564 + 47.8409i −0.358416 + 1.74690i
\(751\) 39.1835 7.79408i 1.42983 0.284410i 0.581354 0.813650i \(-0.302523\pi\)
0.848472 + 0.529240i \(0.177523\pi\)
\(752\) −6.52704 2.59432i −0.238017 0.0946051i
\(753\) 16.4184 24.5719i 0.598321 0.895451i
\(754\) −5.56196 0.527632i −0.202555 0.0192152i
\(755\) 12.6386 27.6581i 0.459967 1.00658i
\(756\) −83.7360 + 56.8253i −3.04545 + 2.06671i
\(757\) −11.2462 + 4.65834i −0.408751 + 0.169310i −0.577578 0.816335i \(-0.696002\pi\)
0.168827 + 0.985646i \(0.446002\pi\)
\(758\) 23.6960 + 28.6630i 0.860679 + 1.04109i
\(759\) 9.55880 48.0553i 0.346962 1.74430i
\(760\) −43.1294 + 11.9075i −1.56447 + 0.431930i
\(761\) 24.8892 24.8892i 0.902231 0.902231i −0.0933975 0.995629i \(-0.529773\pi\)
0.995629 + 0.0933975i \(0.0297727\pi\)
\(762\) −3.90315 12.7025i −0.141396 0.460162i
\(763\) −62.7749 26.0022i −2.27260 0.941343i
\(764\) 21.1697 4.36930i 0.765893 0.158076i
\(765\) 43.5048 + 41.7535i 1.57292 + 1.50960i
\(766\) −19.4513 + 1.98638i −0.702803 + 0.0717708i
\(767\) −0.417662 0.173001i −0.0150809 0.00624672i
\(768\) −26.2639 + 41.8634i −0.947717 + 1.51062i
\(769\) 5.65391 + 5.65391i 0.203885 + 0.203885i 0.801662 0.597777i \(-0.203949\pi\)
−0.597777 + 0.801662i \(0.703949\pi\)
\(770\) 2.26487 + 34.3496i 0.0816202 + 1.23787i
\(771\) 18.1486 91.2390i 0.653604 3.28589i
\(772\) 38.2849 + 37.7385i 1.37790 + 1.35824i
\(773\) 15.4563 + 37.3149i 0.555925 + 1.34212i 0.912967 + 0.408034i \(0.133785\pi\)
−0.357042 + 0.934089i \(0.616215\pi\)
\(774\) −9.39500 17.4259i −0.337696 0.626361i
\(775\) 3.17181 + 25.3457i 0.113935 + 0.910446i
\(776\) 4.26701 + 39.0081i 0.153177 + 1.40031i
\(777\) −63.2870 42.2870i −2.27041 1.51704i
\(778\) 33.3904 + 27.2026i 1.19710 + 0.975260i
\(779\) 29.8700 5.94150i 1.07020 0.212876i
\(780\) 3.29902 + 8.66046i 0.118124 + 0.310094i
\(781\) 6.00264 0.214791
\(782\) −1.49821 + 39.2869i −0.0535758 + 1.40490i
\(783\) 64.3912 2.30115
\(784\) 57.6319 0.828408i 2.05828 0.0295860i
\(785\) −8.14793 + 7.58253i −0.290812 + 0.270632i
\(786\) −10.2531 + 12.5854i −0.365717 + 0.448907i
\(787\) 9.12912 13.6627i 0.325418 0.487022i −0.632303 0.774721i \(-0.717890\pi\)
0.957721 + 0.287699i \(0.0928902\pi\)
\(788\) 0.0620720 + 8.63708i 0.00221122 + 0.307683i
\(789\) −7.84300 11.7379i −0.279218 0.417879i
\(790\) −10.4209 6.01107i −0.370758 0.213864i
\(791\) −19.5881 47.2899i −0.696474 1.68144i
\(792\) 33.9387 + 27.2458i 1.20596 + 0.968139i
\(793\) 0.524331 2.63599i 0.0186195 0.0936068i
\(794\) −19.7269 + 37.2277i −0.700083 + 1.32116i
\(795\) −3.80238 + 16.0746i −0.134857 + 0.570106i
\(796\) 12.2290 + 28.9335i 0.433445 + 1.02552i
\(797\) −16.2731 + 39.2868i −0.576424 + 1.39161i 0.319578 + 0.947560i \(0.396459\pi\)
−0.896002 + 0.444050i \(0.853541\pi\)
\(798\) 142.247 14.5264i 5.03549 0.514229i
\(799\) 2.38869 6.83448i 0.0845058 0.241787i
\(800\) −1.25219 28.2565i −0.0442716 0.999020i
\(801\) 47.7732 + 19.7883i 1.68798 + 0.699185i
\(802\) −0.732397 2.38352i −0.0258619 0.0841652i
\(803\) −2.04569 + 2.04569i −0.0721910 + 0.0721910i
\(804\) −3.79083 1.53839i −0.133692 0.0542548i
\(805\) 65.3679 24.3640i 2.30392 0.858719i
\(806\) 3.08847 + 3.73585i 0.108787 + 0.131590i
\(807\) 12.4843 + 30.1398i 0.439469 + 1.06097i
\(808\) 17.5306 + 20.8977i 0.616726 + 0.735177i
\(809\) −7.20992 10.7904i −0.253487 0.379371i 0.682800 0.730605i \(-0.260762\pi\)
−0.936287 + 0.351235i \(0.885762\pi\)
\(810\) −19.8142 40.1397i −0.696200 1.41036i
\(811\) 0.282462 0.422734i 0.00991857 0.0148442i −0.826477 0.562970i \(-0.809659\pi\)
0.836396 + 0.548126i \(0.184659\pi\)
\(812\) −45.5240 29.9472i −1.59758 1.05094i
\(813\) −64.8608 + 12.9016i −2.27477 + 0.452480i
\(814\) −5.08281 + 16.9751i −0.178152 + 0.594978i
\(815\) 8.86561 + 14.3594i 0.310549 + 0.502988i
\(816\) −44.2528 25.2324i −1.54916 0.883312i
\(817\) 15.1419i 0.529747i
\(818\) 27.7580 + 8.31149i 0.970535 + 0.290604i
\(819\) −3.96103 19.9135i −0.138410 0.695832i
\(820\) −0.553251 + 19.2443i −0.0193204 + 0.672038i
\(821\) −11.8178 + 17.6866i −0.412444 + 0.617267i −0.978289 0.207245i \(-0.933550\pi\)
0.565845 + 0.824512i \(0.308550\pi\)
\(822\) 7.47095 78.7539i 0.260579 2.74686i
\(823\) 30.9347 20.6699i 1.07832 0.720507i 0.116221 0.993223i \(-0.462922\pi\)
0.962095 + 0.272716i \(0.0879220\pi\)
\(824\) −15.2521 18.1815i −0.531332 0.633382i
\(825\) −36.2403 2.60854i −1.26173 0.0908177i
\(826\) −2.80941 3.39830i −0.0977519 0.118242i
\(827\) −8.42546 + 42.3576i −0.292982 + 1.47292i 0.501249 + 0.865303i \(0.332874\pi\)
−0.794231 + 0.607616i \(0.792126\pi\)
\(828\) 33.1654 81.7245i 1.15258 2.84012i
\(829\) 25.1539 + 25.1539i 0.873632 + 0.873632i 0.992866 0.119234i \(-0.0380439\pi\)
−0.119234 + 0.992866i \(0.538044\pi\)
\(830\) 11.4388 13.0537i 0.397045 0.453100i
\(831\) 29.5904 + 12.2567i 1.02648 + 0.425181i
\(832\) −3.07743 4.39743i −0.106691 0.152453i
\(833\) 3.35290 + 59.3171i 0.116171 + 2.05521i
\(834\) −8.56274 83.8491i −0.296503 2.90346i
\(835\) −2.54050 15.7003i −0.0879176 0.543330i
\(836\) −12.9594 30.6616i −0.448210 1.06045i
\(837\) −39.5029 39.5029i −1.36542 1.36542i
\(838\) −26.8135 14.2085i −0.926259 0.490824i
\(839\) 32.7696 + 6.51827i 1.13133 + 0.225036i 0.725039 0.688707i \(-0.241822\pi\)
0.406292 + 0.913743i \(0.366822\pi\)
\(840\) −11.1188 + 89.7026i −0.383634 + 3.09503i
\(841\) 2.17074 + 5.24064i 0.0748532 + 0.180712i
\(842\) 5.92715 + 10.9937i 0.204263 + 0.378868i
\(843\) −73.7876 + 49.3033i −2.54138 + 1.69810i
\(844\) 26.1878 0.188204i 0.901423 0.00647824i
\(845\) 28.0443 + 1.00800i 0.964752 + 0.0346761i
\(846\) −10.2583 + 12.5918i −0.352688 + 0.432915i
\(847\) 24.8007 4.93316i 0.852161 0.169505i
\(848\) −0.137496 9.56553i −0.00472163 0.328481i
\(849\) 39.5905i 1.35874i
\(850\) 29.0461 2.51520i 0.996272 0.0862705i
\(851\) 35.9092 1.23095
\(852\) 15.4802 + 2.96372i 0.530345 + 0.101536i
\(853\) −4.54863 22.8675i −0.155742 0.782969i −0.977137 0.212609i \(-0.931804\pi\)
0.821395 0.570360i \(-0.193196\pi\)
\(854\) 16.5566 20.3228i 0.566556 0.695432i
\(855\) −3.71636 + 103.396i −0.127097 + 3.53607i
\(856\) 14.5317 1.58959i 0.496684 0.0543312i
\(857\) 14.7329 + 22.0493i 0.503265 + 0.753189i 0.992927 0.118723i \(-0.0378800\pi\)
−0.489663 + 0.871912i \(0.662880\pi\)
\(858\) −6.06900 + 3.27204i −0.207192 + 0.111706i
\(859\) −25.9168 + 10.7351i −0.884270 + 0.366277i −0.778151 0.628077i \(-0.783842\pi\)
−0.106119 + 0.994353i \(0.533842\pi\)
\(860\) −9.33047 2.13640i −0.318166 0.0728507i
\(861\) 12.0029 60.3428i 0.409059 2.05648i
\(862\) 9.76800 + 5.17606i 0.332699 + 0.176297i
\(863\) −18.4466 + 18.4466i −0.627928 + 0.627928i −0.947546 0.319618i \(-0.896445\pi\)
0.319618 + 0.947546i \(0.396445\pi\)
\(864\) 40.0963 + 47.1056i 1.36410 + 1.60257i
\(865\) 8.68747 1.40574i 0.295383 0.0477966i
\(866\) 23.8949 2.44017i 0.811982 0.0829202i
\(867\) 24.0665 46.6688i 0.817342 1.58496i
\(868\) 9.55610 + 46.3003i 0.324355 + 1.57153i
\(869\) 3.42512 8.26898i 0.116189 0.280506i
\(870\) 37.9049 43.2563i 1.28510 1.46653i
\(871\) 0.314179 0.314179i 0.0106455 0.0106455i
\(872\) −11.6278 + 39.8740i −0.393766 + 1.35030i
\(873\) 88.9961 + 17.7024i 3.01206 + 0.599136i
\(874\) −51.9917 + 42.9820i −1.75864 + 1.45389i
\(875\) −23.9468 45.8556i −0.809548 1.55020i
\(876\) −6.28569 + 4.26562i −0.212374 + 0.144122i
\(877\) −13.3258 19.9435i −0.449980 0.673443i 0.535247 0.844696i \(-0.320219\pi\)
−0.985227 + 0.171253i \(0.945219\pi\)
\(878\) 0.405982 4.27959i 0.0137012 0.144429i
\(879\) −54.6231 36.4980i −1.84239 1.23105i
\(880\) 20.7223 3.65950i 0.698547 0.123362i
\(881\) −44.7081 + 8.89300i −1.50625 + 0.299613i −0.878101 0.478476i \(-0.841189\pi\)
−0.628154 + 0.778089i \(0.716189\pi\)
\(882\) 38.2308 127.680i 1.28730 4.29920i
\(883\) −27.6490 −0.930462 −0.465231 0.885189i \(-0.654029\pi\)
−0.465231 + 0.885189i \(0.654029\pi\)
\(884\) 4.39527 3.36007i 0.147829 0.113011i
\(885\) 3.95991 2.44488i 0.133111 0.0821837i
\(886\) 14.8465 49.5830i 0.498777 1.66577i
\(887\) −5.71744 28.7435i −0.191973 0.965113i −0.949848 0.312713i \(-0.898762\pi\)
0.757875 0.652400i \(-0.226238\pi\)
\(888\) −21.4893 + 41.2677i −0.721134 + 1.38485i
\(889\) 11.7039 + 7.82030i 0.392536 + 0.262284i
\(890\) 22.4188 11.0666i 0.751479 0.370954i
\(891\) 27.6907 18.5023i 0.927673 0.619852i
\(892\) −9.96501 14.6841i −0.333653 0.491661i
\(893\) 11.4767 4.75382i 0.384054 0.159080i
\(894\) −47.4632 57.4121i −1.58741 1.92015i
\(895\) 0.0630678 + 0.169209i 0.00210813 + 0.00565603i
\(896\) −6.43972 51.9513i −0.215136 1.73557i
\(897\) 9.88002 + 9.88002i 0.329884 + 0.329884i
\(898\) −42.3263 + 13.0058i −1.41245 + 0.434009i
\(899\) 11.5117 27.7918i 0.383938 0.926908i
\(900\) −63.1885 16.8784i −2.10628 0.562614i
\(901\) 9.84522 0.556501i 0.327992 0.0185397i
\(902\) −14.2491 + 1.45513i −0.474444 + 0.0484506i
\(903\) 28.2609 + 11.7060i 0.940464 + 0.389553i
\(904\) −27.4341 + 15.0463i −0.912444 + 0.500431i
\(905\) −43.6104 10.3159i −1.44966 0.342912i
\(906\) 52.4898 + 27.8143i 1.74386 + 0.924069i
\(907\) −17.4275 3.46654i −0.578669 0.115104i −0.102927 0.994689i \(-0.532821\pi\)
−0.475743 + 0.879584i \(0.657821\pi\)
\(908\) −22.7039 22.3799i −0.753456 0.742703i
\(909\) 58.2735 24.1377i 1.93281 0.800596i
\(910\) −8.50349 4.90507i −0.281888 0.162601i
\(911\) 18.7799 12.5483i 0.622205 0.415744i −0.204114 0.978947i \(-0.565431\pi\)
0.826318 + 0.563203i \(0.190431\pi\)
\(912\) −18.2823 85.4720i −0.605387 2.83026i
\(913\) 10.7366 + 7.17396i 0.355329 + 0.237424i
\(914\) −2.28704 1.86321i −0.0756486 0.0616296i
\(915\) 18.8486 + 20.2541i 0.623116 + 0.669579i
\(916\) −24.5870 4.70723i −0.812378 0.155531i
\(917\) 17.1954i 0.567841i
\(918\) −46.7732 + 43.3369i −1.54375 + 1.43033i
\(919\) 7.45779i 0.246010i −0.992406 0.123005i \(-0.960747\pi\)
0.992406 0.123005i \(-0.0392531\pi\)
\(920\) −19.1500 38.1019i −0.631358 1.25618i
\(921\) 16.2613 + 81.7512i 0.535829 + 2.69379i
\(922\) −4.92696 + 6.04770i −0.162261 + 0.199171i
\(923\) −0.951013 + 1.42329i −0.0313030 + 0.0468482i
\(924\) −67.2459 + 0.483275i −2.21223 + 0.0158986i
\(925\) −3.30658 26.4227i −0.108720 0.868774i
\(926\) −11.8935 22.0602i −0.390846 0.724943i
\(927\) −50.6994 + 21.0004i −1.66519 + 0.689743i
\(928\) −15.1717 + 29.6536i −0.498034 + 0.973428i
\(929\) 43.8254 + 8.71741i 1.43786 + 0.286009i 0.851635 0.524136i \(-0.175612\pi\)
0.586230 + 0.810145i \(0.300612\pi\)
\(930\) −49.7909 + 3.28301i −1.63271 + 0.107654i
\(931\) −72.0822 + 72.0822i −2.36240 + 2.36240i
\(932\) 7.77319 + 18.3912i 0.254619 + 0.602423i
\(933\) −18.6810 + 45.1000i −0.611590 + 1.47651i
\(934\) −15.2588 + 1.55824i −0.499283 + 0.0509872i
\(935\) 4.66760 + 21.1824i 0.152647 + 0.692737i
\(936\) −11.8373 + 3.73061i −0.386913 + 0.121939i
\(937\) −12.2093 + 29.4759i −0.398862 + 0.962937i 0.589075 + 0.808078i \(0.299492\pi\)
−0.987937 + 0.154859i \(0.950508\pi\)
\(938\) 4.14240 1.27286i 0.135254 0.0415602i
\(939\) −64.0910 64.0910i −2.09153 2.09153i
\(940\) 1.31004 + 7.74272i 0.0427287 + 0.252540i
\(941\) −53.0362 10.5495i −1.72893 0.343905i −0.772310 0.635246i \(-0.780899\pi\)
−0.956619 + 0.291341i \(0.905899\pi\)
\(942\) −13.8539 16.7579i −0.451386 0.546002i
\(943\) 11.1078 + 26.8166i 0.361720 + 0.873270i
\(944\) −1.87826 + 1.93305i −0.0611322 + 0.0629153i
\(945\) 102.907 + 47.0242i 3.34755 + 1.52970i
\(946\) 0.672541 7.08949i 0.0218662 0.230499i
\(947\) 3.39667 + 2.26958i 0.110377 + 0.0737515i 0.609534 0.792760i \(-0.291357\pi\)
−0.499157 + 0.866512i \(0.666357\pi\)
\(948\) 12.9158 19.6338i 0.419485 0.637677i
\(949\) −0.160952 0.809161i −0.00522473 0.0262665i
\(950\) 36.4146 + 34.2987i 1.18144 + 1.11280i
\(951\) 40.2126 1.30398
\(952\) 53.2235 8.88539i 1.72498 0.287977i
\(953\) 12.3069i 0.398660i 0.979932 + 0.199330i \(0.0638766\pi\)
−0.979932 + 0.199330i \(0.936123\pi\)
\(954\) −21.1918 6.34539i −0.686110 0.205440i
\(955\) −16.4640 17.6917i −0.532763 0.572489i
\(956\) 16.3424 24.8428i 0.528552 0.803474i
\(957\) 35.5781 + 23.7725i 1.15008 + 0.768456i
\(958\) −47.9972 4.55323i −1.55072 0.147108i
\(959\) 46.5544 + 69.6736i 1.50332 + 2.24988i
\(960\) 55.2476 + 0.793844i 1.78311 + 0.0256212i
\(961\) 4.52824 1.87566i 0.146072 0.0605052i
\(962\) −3.21970 3.89460i −0.103807 0.125567i
\(963\) 6.59470 33.1538i 0.212511 1.06837i
\(964\) −0.431167 + 1.06246i −0.0138869 + 0.0342196i
\(965\) 13.8354 58.4893i 0.445378 1.88284i
\(966\) 40.0277 + 130.267i 1.28787 + 4.19126i
\(967\) 22.2182 53.6396i 0.714491 1.72493i 0.0260278 0.999661i \(-0.491714\pi\)
0.688463 0.725272i \(-0.258286\pi\)
\(968\) −4.64618 14.7424i −0.149334 0.473839i
\(969\) 87.2315 22.5356i 2.80228 0.723947i
\(970\) 34.7960 26.7215i 1.11723 0.857977i
\(971\) 18.4211 + 7.63026i 0.591160 + 0.244867i 0.658150 0.752887i \(-0.271339\pi\)
−0.0669895 + 0.997754i \(0.521339\pi\)
\(972\) 20.1111 8.50012i 0.645063 0.272641i
\(973\) 63.1307 + 63.1307i 2.02388 + 2.02388i
\(974\) −2.31581 1.22715i −0.0742032 0.0393203i
\(975\) 6.36015 8.17969i 0.203688 0.261960i
\(976\) −13.4498 8.70991i −0.430519 0.278797i
\(977\) −18.1960 + 7.53703i −0.582141 + 0.241131i −0.654266 0.756265i \(-0.727022\pi\)
0.0721243 + 0.997396i \(0.477022\pi\)
\(978\) −29.0181 + 15.6448i −0.927896 + 0.500266i
\(979\) 10.3339 + 15.4658i 0.330273 + 0.494289i
\(980\) −34.2470 54.5875i −1.09398 1.74373i
\(981\) 79.8579 + 53.3593i 2.54967 + 1.70363i
\(982\) −11.2105 + 13.7606i −0.357742 + 0.439118i
\(983\) −22.6886 + 4.51305i −0.723655 + 0.143944i −0.543157 0.839631i \(-0.682771\pi\)
−0.180498 + 0.983575i \(0.557771\pi\)
\(984\) −37.4656 3.28267i −1.19436 0.104648i
\(985\) 8.21686 5.07316i 0.261811 0.161644i
\(986\) −31.1973 14.3385i −0.993523 0.456632i
\(987\) 25.0954i 0.798794i
\(988\) 9.32340 + 1.78498i 0.296617 + 0.0567879i
\(989\) −14.1541 + 2.81542i −0.450074 + 0.0895253i
\(990\) 6.33245 48.2453i 0.201258 1.53334i
\(991\) −20.1923 + 30.2199i −0.641429 + 0.959967i 0.358224 + 0.933636i \(0.383382\pi\)
−0.999653 + 0.0263313i \(0.991618\pi\)
\(992\) 27.4995 8.88444i 0.873111 0.282081i
\(993\) 16.4828 + 24.6682i 0.523065 + 0.782821i
\(994\) −14.6957 + 7.92307i −0.466121 + 0.251304i
\(995\) 20.5475 28.4810i 0.651401 0.902907i
\(996\) 24.1466 + 23.8020i 0.765115 + 0.754196i
\(997\) −28.0244 5.57440i −0.887542 0.176543i −0.269793 0.962918i \(-0.586955\pi\)
−0.617749 + 0.786375i \(0.711955\pi\)
\(998\) −21.6987 + 40.9487i −0.686861 + 1.29621i
\(999\) 41.1814 + 41.1814i 1.30292 + 1.30292i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 680.2.co.a.419.94 yes 832
5.4 even 2 inner 680.2.co.a.419.11 yes 832
8.3 odd 2 inner 680.2.co.a.419.16 yes 832
17.14 odd 16 inner 680.2.co.a.99.89 yes 832
40.19 odd 2 inner 680.2.co.a.419.89 yes 832
85.14 odd 16 inner 680.2.co.a.99.16 yes 832
136.99 even 16 inner 680.2.co.a.99.11 832
680.99 even 16 inner 680.2.co.a.99.94 yes 832
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
680.2.co.a.99.11 832 136.99 even 16 inner
680.2.co.a.99.16 yes 832 85.14 odd 16 inner
680.2.co.a.99.89 yes 832 17.14 odd 16 inner
680.2.co.a.99.94 yes 832 680.99 even 16 inner
680.2.co.a.419.11 yes 832 5.4 even 2 inner
680.2.co.a.419.16 yes 832 8.3 odd 2 inner
680.2.co.a.419.89 yes 832 40.19 odd 2 inner
680.2.co.a.419.94 yes 832 1.1 even 1 trivial