Properties

Label 69.2.e.c.31.1
Level $69$
Weight $2$
Character 69.31
Analytic conductor $0.551$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [69,2,Mod(4,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 69.e (of order \(11\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.550967773947\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + 4165 x^{12} - 7040 x^{11} + 10649 x^{10} - 13519 x^{9} + 15111 x^{8} - 12101 x^{7} + \cdots + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 31.1
Root \(-0.932269 + 2.04138i\) of defining polynomial
Character \(\chi\) \(=\) 69.31
Dual form 69.2.e.c.49.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.164520 + 1.14426i) q^{2} +(0.415415 + 0.909632i) q^{3} +(0.636711 + 0.186955i) q^{4} +(-1.13298 - 1.30753i) q^{5} +(-1.10920 + 0.325692i) q^{6} +(-0.589836 - 0.379064i) q^{7} +(-1.27914 + 2.80093i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\) \(q+(-0.164520 + 1.14426i) q^{2} +(0.415415 + 0.909632i) q^{3} +(0.636711 + 0.186955i) q^{4} +(-1.13298 - 1.30753i) q^{5} +(-1.10920 + 0.325692i) q^{6} +(-0.589836 - 0.379064i) q^{7} +(-1.27914 + 2.80093i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(1.68256 - 1.08131i) q^{10} +(-0.485534 - 3.37697i) q^{11} +(0.0944389 + 0.656837i) q^{12} +(3.32423 - 2.13635i) q^{13} +(0.530790 - 0.612564i) q^{14} +(0.718713 - 1.57376i) q^{15} +(-1.87807 - 1.20696i) q^{16} +(0.920848 - 0.270385i) q^{17} +(-0.757040 - 0.873670i) q^{18} +(-5.70077 - 1.67390i) q^{19} +(-0.476932 - 1.04433i) q^{20} +(0.0997825 - 0.694002i) q^{21} +3.94402 q^{22} +(2.27813 + 4.22021i) q^{23} -3.07920 q^{24} +(0.285587 - 1.98630i) q^{25} +(1.89765 + 4.15528i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(-0.304687 - 0.351627i) q^{28} +(2.25187 - 0.661210i) q^{29} +(1.68256 + 1.08131i) q^{30} +(-3.58618 + 7.85263i) q^{31} +(-2.34282 + 2.70376i) q^{32} +(2.87010 - 1.84450i) q^{33} +(0.157894 + 1.09818i) q^{34} +(0.172634 + 1.20070i) q^{35} +(-0.558249 + 0.358765i) q^{36} +(-6.17667 + 7.12826i) q^{37} +(2.85328 - 6.24780i) q^{38} +(3.32423 + 2.13635i) q^{39} +(5.11155 - 1.50089i) q^{40} +(-4.08680 - 4.71641i) q^{41} +(0.777706 + 0.228355i) q^{42} +(3.32229 + 7.27480i) q^{43} +(0.322196 - 2.24093i) q^{44} +1.73011 q^{45} +(-5.20383 + 1.91247i) q^{46} -2.99078 q^{47} +(0.317713 - 2.20974i) q^{48} +(-2.70369 - 5.92025i) q^{49} +(2.22587 + 0.653574i) q^{50} +(0.628485 + 0.725311i) q^{51} +(2.51598 - 0.738758i) q^{52} +(3.96305 + 2.54690i) q^{53} +(0.480233 - 1.05156i) q^{54} +(-3.86538 + 4.46088i) q^{55} +(1.81622 - 1.16721i) q^{56} +(-0.845555 - 5.88097i) q^{57} +(0.386120 + 2.68552i) q^{58} +(7.51851 - 4.83185i) q^{59} +(0.751836 - 0.867665i) q^{60} +(3.64086 - 7.97236i) q^{61} +(-8.39549 - 5.39545i) q^{62} +(0.672738 - 0.197534i) q^{63} +(-5.63228 - 6.50000i) q^{64} +(-6.55963 - 1.92608i) q^{65} +(1.63841 + 3.58761i) q^{66} +(0.241257 - 1.67798i) q^{67} +0.636864 q^{68} +(-2.89247 + 3.82539i) q^{69} -1.40232 q^{70} +(-1.65698 + 11.5246i) q^{71} +(-1.27914 - 2.80093i) q^{72} +(8.34684 + 2.45085i) q^{73} +(-7.14042 - 8.24049i) q^{74} +(1.92544 - 0.565360i) q^{75} +(-3.31680 - 2.13158i) q^{76} +(-0.993702 + 2.17590i) q^{77} +(-2.99146 + 3.45233i) q^{78} +(-6.43376 + 4.13473i) q^{79} +(0.549677 + 3.82309i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(6.06919 - 3.90043i) q^{82} +(9.33402 - 10.7720i) q^{83} +(0.193280 - 0.423224i) q^{84} +(-1.39684 - 0.897694i) q^{85} +(-8.87088 + 2.60472i) q^{86} +(1.53692 + 1.77370i) q^{87} +(10.0797 + 2.95968i) q^{88} +(4.45010 + 9.74435i) q^{89} +(-0.284638 + 1.97970i) q^{90} -2.77057 q^{91} +(0.661520 + 3.11296i) q^{92} -8.63276 q^{93} +(0.492045 - 3.42225i) q^{94} +(4.27019 + 9.35041i) q^{95} +(-3.43267 - 1.00792i) q^{96} +(-1.30891 - 1.51056i) q^{97} +(7.21915 - 2.11973i) q^{98} +(2.87010 + 1.84450i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{3}{11}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.164520 + 1.14426i −0.116334 + 0.809117i 0.845204 + 0.534444i \(0.179479\pi\)
−0.961538 + 0.274674i \(0.911430\pi\)
\(3\) 0.415415 + 0.909632i 0.239840 + 0.525176i
\(4\) 0.636711 + 0.186955i 0.318356 + 0.0934776i
\(5\) −1.13298 1.30753i −0.506684 0.584745i 0.443562 0.896243i \(-0.353714\pi\)
−0.950247 + 0.311499i \(0.899169\pi\)
\(6\) −1.10920 + 0.325692i −0.452831 + 0.132963i
\(7\) −0.589836 0.379064i −0.222937 0.143273i 0.424405 0.905472i \(-0.360483\pi\)
−0.647342 + 0.762199i \(0.724120\pi\)
\(8\) −1.27914 + 2.80093i −0.452246 + 0.990280i
\(9\) −0.654861 + 0.755750i −0.218287 + 0.251917i
\(10\) 1.68256 1.08131i 0.532071 0.341941i
\(11\) −0.485534 3.37697i −0.146394 1.01819i −0.922059 0.387049i \(-0.873494\pi\)
0.775665 0.631145i \(-0.217415\pi\)
\(12\) 0.0944389 + 0.656837i 0.0272622 + 0.189612i
\(13\) 3.32423 2.13635i 0.921976 0.592518i 0.00874595 0.999962i \(-0.497216\pi\)
0.913230 + 0.407444i \(0.133580\pi\)
\(14\) 0.530790 0.612564i 0.141860 0.163715i
\(15\) 0.718713 1.57376i 0.185571 0.406344i
\(16\) −1.87807 1.20696i −0.469517 0.301740i
\(17\) 0.920848 0.270385i 0.223338 0.0655781i −0.168149 0.985762i \(-0.553779\pi\)
0.391487 + 0.920184i \(0.371961\pi\)
\(18\) −0.757040 0.873670i −0.178436 0.205926i
\(19\) −5.70077 1.67390i −1.30785 0.384018i −0.447754 0.894157i \(-0.647776\pi\)
−0.860092 + 0.510138i \(0.829594\pi\)
\(20\) −0.476932 1.04433i −0.106645 0.233520i
\(21\) 0.0997825 0.694002i 0.0217743 0.151444i
\(22\) 3.94402 0.840869
\(23\) 2.27813 + 4.22021i 0.475022 + 0.879974i
\(24\) −3.07920 −0.628538
\(25\) 0.285587 1.98630i 0.0571174 0.397260i
\(26\) 1.89765 + 4.15528i 0.372160 + 0.814917i
\(27\) −0.959493 0.281733i −0.184655 0.0542195i
\(28\) −0.304687 0.351627i −0.0575804 0.0664513i
\(29\) 2.25187 0.661210i 0.418163 0.122784i −0.0658810 0.997827i \(-0.520986\pi\)
0.484044 + 0.875044i \(0.339168\pi\)
\(30\) 1.68256 + 1.08131i 0.307191 + 0.197420i
\(31\) −3.58618 + 7.85263i −0.644096 + 1.41037i 0.252531 + 0.967589i \(0.418737\pi\)
−0.896628 + 0.442785i \(0.853990\pi\)
\(32\) −2.34282 + 2.70376i −0.414157 + 0.477962i
\(33\) 2.87010 1.84450i 0.499620 0.321086i
\(34\) 0.157894 + 1.09818i 0.0270786 + 0.188336i
\(35\) 0.172634 + 1.20070i 0.0291806 + 0.202955i
\(36\) −0.558249 + 0.358765i −0.0930414 + 0.0597941i
\(37\) −6.17667 + 7.12826i −1.01544 + 1.17188i −0.0304007 + 0.999538i \(0.509678\pi\)
−0.985037 + 0.172340i \(0.944867\pi\)
\(38\) 2.85328 6.24780i 0.462862 1.01353i
\(39\) 3.32423 + 2.13635i 0.532303 + 0.342091i
\(40\) 5.11155 1.50089i 0.808206 0.237311i
\(41\) −4.08680 4.71641i −0.638250 0.736580i 0.340814 0.940131i \(-0.389297\pi\)
−0.979064 + 0.203551i \(0.934752\pi\)
\(42\) 0.777706 + 0.228355i 0.120003 + 0.0352360i
\(43\) 3.32229 + 7.27480i 0.506644 + 1.10940i 0.974252 + 0.225460i \(0.0723885\pi\)
−0.467608 + 0.883936i \(0.654884\pi\)
\(44\) 0.322196 2.24093i 0.0485729 0.337832i
\(45\) 1.73011 0.257909
\(46\) −5.20383 + 1.91247i −0.767263 + 0.281978i
\(47\) −2.99078 −0.436251 −0.218125 0.975921i \(-0.569994\pi\)
−0.218125 + 0.975921i \(0.569994\pi\)
\(48\) 0.317713 2.20974i 0.0458579 0.318949i
\(49\) −2.70369 5.92025i −0.386241 0.845750i
\(50\) 2.22587 + 0.653574i 0.314785 + 0.0924293i
\(51\) 0.628485 + 0.725311i 0.0880055 + 0.101564i
\(52\) 2.51598 0.738758i 0.348904 0.102447i
\(53\) 3.96305 + 2.54690i 0.544367 + 0.349843i 0.783745 0.621083i \(-0.213307\pi\)
−0.239378 + 0.970927i \(0.576943\pi\)
\(54\) 0.480233 1.05156i 0.0653514 0.143100i
\(55\) −3.86538 + 4.46088i −0.521208 + 0.601506i
\(56\) 1.81622 1.16721i 0.242702 0.155975i
\(57\) −0.845555 5.88097i −0.111997 0.778953i
\(58\) 0.386120 + 2.68552i 0.0507000 + 0.352626i
\(59\) 7.51851 4.83185i 0.978826 0.629053i 0.0496797 0.998765i \(-0.484180\pi\)
0.929146 + 0.369712i \(0.120544\pi\)
\(60\) 0.751836 0.867665i 0.0970616 0.112015i
\(61\) 3.64086 7.97236i 0.466164 1.02076i −0.519875 0.854242i \(-0.674022\pi\)
0.986039 0.166514i \(-0.0532511\pi\)
\(62\) −8.39549 5.39545i −1.06623 0.685223i
\(63\) 0.672738 0.197534i 0.0847570 0.0248869i
\(64\) −5.63228 6.50000i −0.704036 0.812500i
\(65\) −6.55963 1.92608i −0.813622 0.238901i
\(66\) 1.63841 + 3.58761i 0.201674 + 0.441604i
\(67\) 0.241257 1.67798i 0.0294742 0.204997i −0.969763 0.244048i \(-0.921524\pi\)
0.999237 + 0.0390510i \(0.0124335\pi\)
\(68\) 0.636864 0.0772311
\(69\) −2.89247 + 3.82539i −0.348212 + 0.460523i
\(70\) −1.40232 −0.167609
\(71\) −1.65698 + 11.5246i −0.196648 + 1.36772i 0.617277 + 0.786746i \(0.288236\pi\)
−0.813925 + 0.580970i \(0.802673\pi\)
\(72\) −1.27914 2.80093i −0.150749 0.330093i
\(73\) 8.34684 + 2.45085i 0.976924 + 0.286851i 0.730954 0.682427i \(-0.239075\pi\)
0.245970 + 0.969277i \(0.420894\pi\)
\(74\) −7.14042 8.24049i −0.830057 0.957937i
\(75\) 1.92544 0.565360i 0.222331 0.0652821i
\(76\) −3.31680 2.13158i −0.380463 0.244509i
\(77\) −0.993702 + 2.17590i −0.113243 + 0.247967i
\(78\) −2.99146 + 3.45233i −0.338716 + 0.390899i
\(79\) −6.43376 + 4.13473i −0.723854 + 0.465193i −0.849976 0.526822i \(-0.823383\pi\)
0.126121 + 0.992015i \(0.459747\pi\)
\(80\) 0.549677 + 3.82309i 0.0614558 + 0.427435i
\(81\) −0.142315 0.989821i −0.0158128 0.109980i
\(82\) 6.06919 3.90043i 0.670230 0.430730i
\(83\) 9.33402 10.7720i 1.02454 1.18238i 0.0414747 0.999140i \(-0.486794\pi\)
0.983067 0.183245i \(-0.0586602\pi\)
\(84\) 0.193280 0.423224i 0.0210886 0.0461775i
\(85\) −1.39684 0.897694i −0.151508 0.0973686i
\(86\) −8.87088 + 2.60472i −0.956571 + 0.280875i
\(87\) 1.53692 + 1.77370i 0.164775 + 0.190161i
\(88\) 10.0797 + 2.95968i 1.07450 + 0.315502i
\(89\) 4.45010 + 9.74435i 0.471709 + 1.03290i 0.984660 + 0.174481i \(0.0558249\pi\)
−0.512951 + 0.858418i \(0.671448\pi\)
\(90\) −0.284638 + 1.97970i −0.0300035 + 0.208679i
\(91\) −2.77057 −0.290434
\(92\) 0.661520 + 3.11296i 0.0689682 + 0.324549i
\(93\) −8.63276 −0.895175
\(94\) 0.492045 3.42225i 0.0507506 0.352978i
\(95\) 4.27019 + 9.35041i 0.438112 + 0.959332i
\(96\) −3.43267 1.00792i −0.350346 0.102871i
\(97\) −1.30891 1.51056i −0.132899 0.153374i 0.685399 0.728168i \(-0.259628\pi\)
−0.818298 + 0.574794i \(0.805082\pi\)
\(98\) 7.21915 2.11973i 0.729244 0.214125i
\(99\) 2.87010 + 1.84450i 0.288456 + 0.185379i
\(100\) 0.553186 1.21131i 0.0553186 0.121131i
\(101\) 6.28290 7.25085i 0.625172 0.721487i −0.351509 0.936185i \(-0.614331\pi\)
0.976681 + 0.214698i \(0.0688766\pi\)
\(102\) −0.933346 + 0.599825i −0.0924150 + 0.0593915i
\(103\) −0.244984 1.70390i −0.0241389 0.167890i 0.974186 0.225747i \(-0.0724823\pi\)
−0.998325 + 0.0578571i \(0.981573\pi\)
\(104\) 1.73162 + 12.0437i 0.169799 + 1.18098i
\(105\) −1.02048 + 0.655822i −0.0995886 + 0.0640017i
\(106\) −3.56633 + 4.11576i −0.346393 + 0.399758i
\(107\) −5.63063 + 12.3294i −0.544333 + 1.19192i 0.415045 + 0.909801i \(0.363766\pi\)
−0.959378 + 0.282123i \(0.908962\pi\)
\(108\) −0.558249 0.358765i −0.0537175 0.0345221i
\(109\) 18.9174 5.55464i 1.81195 0.532038i 0.813202 0.581981i \(-0.197722\pi\)
0.998752 + 0.0499435i \(0.0159041\pi\)
\(110\) −4.46850 5.15692i −0.426055 0.491693i
\(111\) −9.04997 2.65731i −0.858985 0.252221i
\(112\) 0.650236 + 1.42382i 0.0614415 + 0.134538i
\(113\) 0.642387 4.46790i 0.0604307 0.420305i −0.937040 0.349223i \(-0.886446\pi\)
0.997470 0.0710821i \(-0.0226452\pi\)
\(114\) 6.86849 0.643293
\(115\) 2.93697 7.76012i 0.273873 0.723635i
\(116\) 1.55741 0.144602
\(117\) −0.562360 + 3.91130i −0.0519902 + 0.361600i
\(118\) 4.29197 + 9.39810i 0.395108 + 0.865165i
\(119\) −0.645642 0.189578i −0.0591859 0.0173786i
\(120\) 3.48867 + 4.02614i 0.318470 + 0.367534i
\(121\) −0.613732 + 0.180208i −0.0557938 + 0.0163825i
\(122\) 8.52350 + 5.47772i 0.771681 + 0.495929i
\(123\) 2.59248 5.67675i 0.233756 0.511855i
\(124\) −3.75145 + 4.32940i −0.336890 + 0.388792i
\(125\) −10.1980 + 6.55386i −0.912137 + 0.586195i
\(126\) 0.115352 + 0.802289i 0.0102763 + 0.0714735i
\(127\) −1.54704 10.7599i −0.137278 0.954788i −0.935727 0.352726i \(-0.885255\pi\)
0.798449 0.602063i \(-0.205654\pi\)
\(128\) 2.34503 1.50706i 0.207273 0.133206i
\(129\) −5.23726 + 6.04412i −0.461115 + 0.532155i
\(130\) 3.28314 7.18908i 0.287951 0.630524i
\(131\) −12.5648 8.07490i −1.09779 0.705507i −0.139192 0.990265i \(-0.544450\pi\)
−0.958599 + 0.284758i \(0.908087\pi\)
\(132\) 2.17226 0.637834i 0.189071 0.0555163i
\(133\) 2.72800 + 3.14828i 0.236548 + 0.272991i
\(134\) 1.88036 + 0.552123i 0.162438 + 0.0476962i
\(135\) 0.718713 + 1.57376i 0.0618570 + 0.135448i
\(136\) −0.420565 + 2.92510i −0.0360632 + 0.250825i
\(137\) −13.0209 −1.11245 −0.556226 0.831031i \(-0.687751\pi\)
−0.556226 + 0.831031i \(0.687751\pi\)
\(138\) −3.90139 3.93910i −0.332109 0.335319i
\(139\) −7.77065 −0.659098 −0.329549 0.944139i \(-0.606897\pi\)
−0.329549 + 0.944139i \(0.606897\pi\)
\(140\) −0.114559 + 0.796774i −0.00968198 + 0.0673397i
\(141\) −1.24242 2.72051i −0.104630 0.229109i
\(142\) −12.9146 3.79206i −1.08377 0.318223i
\(143\) −8.82843 10.1885i −0.738270 0.852009i
\(144\) 2.14203 0.628958i 0.178503 0.0524131i
\(145\) −3.41588 2.19525i −0.283673 0.182306i
\(146\) −4.17765 + 9.14778i −0.345745 + 0.757076i
\(147\) 4.26210 4.91872i 0.351532 0.405689i
\(148\) −5.26542 + 3.38388i −0.432815 + 0.278153i
\(149\) −1.10872 7.71135i −0.0908302 0.631738i −0.983484 0.180995i \(-0.942068\pi\)
0.892654 0.450743i \(-0.148841\pi\)
\(150\) 0.330147 + 2.29623i 0.0269564 + 0.187486i
\(151\) 2.56615 1.64917i 0.208830 0.134207i −0.432045 0.901852i \(-0.642208\pi\)
0.640875 + 0.767645i \(0.278571\pi\)
\(152\) 11.9806 13.8263i 0.971754 1.12146i
\(153\) −0.398684 + 0.872995i −0.0322317 + 0.0705775i
\(154\) −2.32633 1.49504i −0.187461 0.120474i
\(155\) 14.3306 4.20785i 1.15106 0.337982i
\(156\) 1.71717 + 1.98172i 0.137484 + 0.158665i
\(157\) 9.12488 + 2.67931i 0.728245 + 0.213832i 0.624780 0.780801i \(-0.285189\pi\)
0.103465 + 0.994633i \(0.467007\pi\)
\(158\) −3.67274 8.04217i −0.292187 0.639801i
\(159\) −0.670429 + 4.66294i −0.0531685 + 0.369795i
\(160\) 6.18962 0.489333
\(161\) 0.256008 3.35278i 0.0201763 0.264236i
\(162\) 1.15603 0.0908264
\(163\) 2.09196 14.5499i 0.163855 1.13964i −0.727426 0.686186i \(-0.759284\pi\)
0.891281 0.453451i \(-0.149807\pi\)
\(164\) −1.72035 3.76704i −0.134337 0.294156i
\(165\) −5.66350 1.66295i −0.440903 0.129461i
\(166\) 10.7904 + 12.4528i 0.837499 + 0.966526i
\(167\) −6.52044 + 1.91457i −0.504567 + 0.148154i −0.524103 0.851655i \(-0.675599\pi\)
0.0195361 + 0.999809i \(0.493781\pi\)
\(168\) 1.81622 + 1.16721i 0.140124 + 0.0900524i
\(169\) 1.08612 2.37827i 0.0835475 0.182944i
\(170\) 1.25701 1.45066i 0.0964081 0.111261i
\(171\) 4.99826 3.21219i 0.382226 0.245642i
\(172\) 0.755276 + 5.25306i 0.0575893 + 0.400542i
\(173\) −1.95943 13.6281i −0.148972 1.03613i −0.917906 0.396798i \(-0.870121\pi\)
0.768934 0.639329i \(-0.220788\pi\)
\(174\) −2.28244 + 1.46683i −0.173031 + 0.111200i
\(175\) −0.921385 + 1.06333i −0.0696501 + 0.0803806i
\(176\) −3.16400 + 6.92819i −0.238495 + 0.522232i
\(177\) 7.51851 + 4.83185i 0.565126 + 0.363184i
\(178\) −11.8822 + 3.48894i −0.890612 + 0.261507i
\(179\) 13.7642 + 15.8848i 1.02879 + 1.18728i 0.982097 + 0.188376i \(0.0603222\pi\)
0.0466911 + 0.998909i \(0.485132\pi\)
\(180\) 1.10158 + 0.323453i 0.0821069 + 0.0241088i
\(181\) 7.68650 + 16.8311i 0.571333 + 1.25105i 0.946085 + 0.323920i \(0.105001\pi\)
−0.374751 + 0.927125i \(0.622272\pi\)
\(182\) 0.455815 3.17026i 0.0337872 0.234995i
\(183\) 8.76438 0.647882
\(184\) −14.7346 + 0.982636i −1.08625 + 0.0724409i
\(185\) 16.3184 1.19976
\(186\) 1.42026 9.87816i 0.104139 0.724302i
\(187\) −1.36019 2.97839i −0.0994666 0.217802i
\(188\) −1.90427 0.559143i −0.138883 0.0407797i
\(189\) 0.459148 + 0.529885i 0.0333981 + 0.0385435i
\(190\) −11.4019 + 3.34789i −0.827179 + 0.242882i
\(191\) 0.347803 + 0.223520i 0.0251662 + 0.0161733i 0.553163 0.833073i \(-0.313421\pi\)
−0.527997 + 0.849246i \(0.677057\pi\)
\(192\) 3.57288 7.82351i 0.257850 0.564613i
\(193\) −5.88092 + 6.78694i −0.423318 + 0.488535i −0.926845 0.375445i \(-0.877490\pi\)
0.503527 + 0.863979i \(0.332035\pi\)
\(194\) 1.94382 1.24922i 0.139558 0.0896887i
\(195\) −0.972944 6.76698i −0.0696740 0.484593i
\(196\) −0.614646 4.27496i −0.0439033 0.305354i
\(197\) −14.0999 + 9.06148i −1.00458 + 0.645604i −0.935985 0.352041i \(-0.885488\pi\)
−0.0685945 + 0.997645i \(0.521851\pi\)
\(198\) −2.58279 + 2.98069i −0.183551 + 0.211829i
\(199\) −2.39487 + 5.24404i −0.169768 + 0.371740i −0.975324 0.220780i \(-0.929140\pi\)
0.805555 + 0.592520i \(0.201867\pi\)
\(200\) 5.19819 + 3.34067i 0.367568 + 0.236221i
\(201\) 1.62656 0.477602i 0.114729 0.0336874i
\(202\) 7.26323 + 8.38222i 0.511039 + 0.589771i
\(203\) −1.57888 0.463600i −0.110815 0.0325384i
\(204\) 0.264563 + 0.579312i 0.0185231 + 0.0405600i
\(205\) −1.53659 + 10.6872i −0.107320 + 0.746427i
\(206\) 1.99002 0.138651
\(207\) −4.68127 1.04195i −0.325371 0.0724207i
\(208\) −8.82163 −0.611670
\(209\) −2.88477 + 20.0640i −0.199544 + 1.38786i
\(210\) −0.582545 1.27559i −0.0401994 0.0880244i
\(211\) −4.78535 1.40511i −0.329437 0.0967315i 0.112831 0.993614i \(-0.464008\pi\)
−0.442269 + 0.896883i \(0.645826\pi\)
\(212\) 2.04716 + 2.36255i 0.140600 + 0.162261i
\(213\) −11.1715 + 3.28024i −0.765456 + 0.224758i
\(214\) −13.1817 8.47136i −0.901082 0.579090i
\(215\) 5.74792 12.5862i 0.392005 0.858371i
\(216\) 2.01644 2.32710i 0.137202 0.158339i
\(217\) 5.09191 3.27237i 0.345661 0.222143i
\(218\) 3.24368 + 22.5603i 0.219690 + 1.52798i
\(219\) 1.23803 + 8.61067i 0.0836582 + 0.581855i
\(220\) −3.29512 + 2.11764i −0.222157 + 0.142771i
\(221\) 2.48347 2.86608i 0.167057 0.192794i
\(222\) 4.52957 9.91838i 0.304005 0.665678i
\(223\) 13.5387 + 8.70081i 0.906620 + 0.582649i 0.908746 0.417349i \(-0.137041\pi\)
−0.00212667 + 0.999998i \(0.500677\pi\)
\(224\) 2.40678 0.706695i 0.160810 0.0472180i
\(225\) 1.31413 + 1.51658i 0.0876084 + 0.101105i
\(226\) 5.00678 + 1.47012i 0.333046 + 0.0977911i
\(227\) −5.51919 12.0853i −0.366322 0.802133i −0.999602 0.0282101i \(-0.991019\pi\)
0.633280 0.773922i \(-0.281708\pi\)
\(228\) 0.561103 3.90256i 0.0371600 0.258453i
\(229\) −2.11353 −0.139666 −0.0698330 0.997559i \(-0.522247\pi\)
−0.0698330 + 0.997559i \(0.522247\pi\)
\(230\) 8.39645 + 4.63737i 0.553645 + 0.305779i
\(231\) −2.39207 −0.157387
\(232\) −1.02847 + 7.15314i −0.0675221 + 0.469626i
\(233\) 6.18779 + 13.5494i 0.405376 + 0.887649i 0.996697 + 0.0812126i \(0.0258793\pi\)
−0.591321 + 0.806436i \(0.701393\pi\)
\(234\) −4.38305 1.28698i −0.286529 0.0841324i
\(235\) 3.38850 + 3.91054i 0.221041 + 0.255095i
\(236\) 5.69046 1.67087i 0.370417 0.108764i
\(237\) −6.43376 4.13473i −0.417918 0.268579i
\(238\) 0.323148 0.707596i 0.0209466 0.0458667i
\(239\) 12.1799 14.0564i 0.787854 0.909232i −0.209796 0.977745i \(-0.567280\pi\)
0.997650 + 0.0685134i \(0.0218256\pi\)
\(240\) −3.24926 + 2.08817i −0.209739 + 0.134791i
\(241\) −0.952069 6.62178i −0.0613281 0.426547i −0.997236 0.0743012i \(-0.976327\pi\)
0.935908 0.352245i \(-0.114582\pi\)
\(242\) −0.105234 0.731919i −0.00676471 0.0470496i
\(243\) 0.841254 0.540641i 0.0539664 0.0346821i
\(244\) 3.80865 4.39541i 0.243824 0.281388i
\(245\) −4.67767 + 10.2427i −0.298846 + 0.654381i
\(246\) 6.06919 + 3.90043i 0.386957 + 0.248682i
\(247\) −22.5267 + 6.61445i −1.43334 + 0.420867i
\(248\) −17.4075 20.0893i −1.10538 1.27567i
\(249\) 13.6761 + 4.01566i 0.866686 + 0.254482i
\(250\) −5.82157 12.7475i −0.368188 0.806220i
\(251\) 2.56489 17.8392i 0.161895 1.12600i −0.733163 0.680053i \(-0.761957\pi\)
0.895058 0.445950i \(-0.147134\pi\)
\(252\) 0.465270 0.0293092
\(253\) 13.1454 9.74221i 0.826443 0.612488i
\(254\) 12.5667 0.788506
\(255\) 0.236303 1.64352i 0.0147979 0.102922i
\(256\) −5.80708 12.7157i −0.362943 0.794734i
\(257\) 13.0326 + 3.82671i 0.812949 + 0.238703i 0.661677 0.749789i \(-0.269845\pi\)
0.151272 + 0.988492i \(0.451663\pi\)
\(258\) −6.05444 6.98719i −0.376933 0.435004i
\(259\) 6.34529 1.86314i 0.394277 0.115770i
\(260\) −3.81650 2.45272i −0.236689 0.152111i
\(261\) −0.974955 + 2.13485i −0.0603482 + 0.132144i
\(262\) 11.3070 13.0490i 0.698548 0.806168i
\(263\) −15.6675 + 10.0689i −0.966100 + 0.620875i −0.925680 0.378308i \(-0.876506\pi\)
−0.0404201 + 0.999183i \(0.512870\pi\)
\(264\) 1.49506 + 10.3983i 0.0920143 + 0.639973i
\(265\) −1.15992 8.06739i −0.0712530 0.495576i
\(266\) −4.05128 + 2.60360i −0.248400 + 0.159637i
\(267\) −7.01514 + 8.09590i −0.429319 + 0.495461i
\(268\) 0.467317 1.02328i 0.0285460 0.0625069i
\(269\) −15.2705 9.81376i −0.931059 0.598356i −0.0152130 0.999884i \(-0.504843\pi\)
−0.915846 + 0.401529i \(0.868479\pi\)
\(270\) −1.91904 + 0.563482i −0.116789 + 0.0342924i
\(271\) 8.86191 + 10.2272i 0.538323 + 0.621257i 0.958122 0.286359i \(-0.0924451\pi\)
−0.419800 + 0.907617i \(0.637900\pi\)
\(272\) −2.05576 0.603626i −0.124649 0.0366002i
\(273\) −1.15094 2.52020i −0.0696578 0.152529i
\(274\) 2.14221 14.8994i 0.129415 0.900104i
\(275\) −6.84633 −0.412849
\(276\) −2.55684 + 1.89491i −0.153904 + 0.114060i
\(277\) 16.1449 0.970051 0.485026 0.874500i \(-0.338810\pi\)
0.485026 + 0.874500i \(0.338810\pi\)
\(278\) 1.27843 8.89168i 0.0766752 0.533287i
\(279\) −3.58618 7.85263i −0.214699 0.470125i
\(280\) −3.58390 1.05233i −0.214179 0.0628887i
\(281\) −3.62572 4.18430i −0.216292 0.249615i 0.637227 0.770676i \(-0.280082\pi\)
−0.853519 + 0.521062i \(0.825536\pi\)
\(282\) 3.31739 0.974074i 0.197548 0.0580052i
\(283\) 2.89150 + 1.85826i 0.171882 + 0.110462i 0.623753 0.781621i \(-0.285607\pi\)
−0.451871 + 0.892083i \(0.649243\pi\)
\(284\) −3.20960 + 7.02805i −0.190455 + 0.417038i
\(285\) −6.73153 + 7.76860i −0.398742 + 0.460172i
\(286\) 13.1109 8.42583i 0.775261 0.498230i
\(287\) 0.622713 + 4.33107i 0.0367576 + 0.255655i
\(288\) −0.509144 3.54118i −0.0300016 0.208666i
\(289\) −13.5265 + 8.69293i −0.795674 + 0.511349i
\(290\) 3.07393 3.54751i 0.180508 0.208317i
\(291\) 0.830314 1.81813i 0.0486739 0.106581i
\(292\) 4.85633 + 3.12097i 0.284195 + 0.182641i
\(293\) −27.4240 + 8.05241i −1.60213 + 0.470427i −0.956137 0.292919i \(-0.905373\pi\)
−0.645990 + 0.763346i \(0.723555\pi\)
\(294\) 4.92712 + 5.68620i 0.287355 + 0.331626i
\(295\) −14.8361 4.35627i −0.863791 0.253632i
\(296\) −12.0649 26.4185i −0.701260 1.53554i
\(297\) −0.485534 + 3.37697i −0.0281736 + 0.195951i
\(298\) 9.00623 0.521717
\(299\) 16.5889 + 9.16206i 0.959360 + 0.529855i
\(300\) 1.33165 0.0768826
\(301\) 0.798012 5.55029i 0.0459966 0.319914i
\(302\) 1.46490 + 3.20768i 0.0842954 + 0.184581i
\(303\) 9.20562 + 2.70301i 0.528849 + 0.155284i
\(304\) 8.68611 + 10.0243i 0.498182 + 0.574933i
\(305\) −14.5491 + 4.27200i −0.833079 + 0.244614i
\(306\) −0.933346 0.599825i −0.0533558 0.0342897i
\(307\) 7.04603 15.4286i 0.402138 0.880559i −0.594911 0.803792i \(-0.702813\pi\)
0.997049 0.0767678i \(-0.0244600\pi\)
\(308\) −1.03950 + 1.19964i −0.0592309 + 0.0683561i
\(309\) 1.44815 0.930670i 0.0823824 0.0529439i
\(310\) 2.45721 + 17.0903i 0.139560 + 0.970663i
\(311\) 0.0675021 + 0.469487i 0.00382769 + 0.0266222i 0.991646 0.128991i \(-0.0411738\pi\)
−0.987818 + 0.155613i \(0.950265\pi\)
\(312\) −10.2360 + 6.57825i −0.579497 + 0.372420i
\(313\) −11.3589 + 13.1089i −0.642043 + 0.740957i −0.979735 0.200300i \(-0.935808\pi\)
0.337692 + 0.941257i \(0.390354\pi\)
\(314\) −4.56707 + 10.0005i −0.257734 + 0.564360i
\(315\) −1.02048 0.655822i −0.0574975 0.0369514i
\(316\) −4.86945 + 1.42980i −0.273928 + 0.0804326i
\(317\) 11.1679 + 12.8884i 0.627251 + 0.723886i 0.977067 0.212932i \(-0.0683014\pi\)
−0.349816 + 0.936818i \(0.613756\pi\)
\(318\) −5.22534 1.53430i −0.293022 0.0860391i
\(319\) −3.32625 7.28346i −0.186234 0.407796i
\(320\) −2.11767 + 14.7287i −0.118382 + 0.823362i
\(321\) −13.5542 −0.756523
\(322\) 3.79435 + 0.844543i 0.211451 + 0.0470645i
\(323\) −5.70214 −0.317276
\(324\) 0.0944389 0.656837i 0.00524661 0.0364909i
\(325\) −3.29408 7.21304i −0.182723 0.400107i
\(326\) 16.3048 + 4.78751i 0.903038 + 0.265156i
\(327\) 12.9112 + 14.9004i 0.713993 + 0.823991i
\(328\) 18.4380 5.41387i 1.01807 0.298931i
\(329\) 1.76407 + 1.13370i 0.0972564 + 0.0625029i
\(330\) 2.83462 6.20695i 0.156041 0.341682i
\(331\) 2.87641 3.31955i 0.158102 0.182459i −0.671172 0.741301i \(-0.734209\pi\)
0.829274 + 0.558842i \(0.188754\pi\)
\(332\) 7.95697 5.11363i 0.436695 0.280647i
\(333\) −1.34232 9.33603i −0.0735586 0.511611i
\(334\) −1.11803 7.77609i −0.0611761 0.425489i
\(335\) −2.46734 + 1.58566i −0.134805 + 0.0866341i
\(336\) −1.02503 + 1.18295i −0.0559201 + 0.0645352i
\(337\) −4.79510 + 10.4998i −0.261206 + 0.571961i −0.994111 0.108370i \(-0.965437\pi\)
0.732905 + 0.680331i \(0.238164\pi\)
\(338\) 2.54268 + 1.63408i 0.138303 + 0.0888822i
\(339\) 4.33100 1.27170i 0.235228 0.0690691i
\(340\) −0.721554 0.832718i −0.0391318 0.0451605i
\(341\) 28.2593 + 8.29767i 1.53033 + 0.449344i
\(342\) 2.85328 + 6.24780i 0.154287 + 0.337842i
\(343\) −1.34790 + 9.37486i −0.0727799 + 0.506195i
\(344\) −24.6259 −1.32774
\(345\) 8.27892 0.552114i 0.445722 0.0297248i
\(346\) 15.9165 0.855678
\(347\) 2.64630 18.4054i 0.142061 0.988055i −0.786689 0.617349i \(-0.788207\pi\)
0.928750 0.370706i \(-0.120884\pi\)
\(348\) 0.646972 + 1.41667i 0.0346813 + 0.0759415i
\(349\) 14.3921 + 4.22589i 0.770390 + 0.226207i 0.643228 0.765675i \(-0.277595\pi\)
0.127162 + 0.991882i \(0.459413\pi\)
\(350\) −1.06515 1.22925i −0.0569347 0.0657061i
\(351\) −3.79146 + 1.11327i −0.202373 + 0.0594221i
\(352\) 10.2680 + 6.59887i 0.547288 + 0.351721i
\(353\) −5.64873 + 12.3690i −0.300651 + 0.658335i −0.998311 0.0580947i \(-0.981497\pi\)
0.697660 + 0.716429i \(0.254225\pi\)
\(354\) −6.76586 + 7.80822i −0.359602 + 0.415002i
\(355\) 16.9461 10.8906i 0.899403 0.578011i
\(356\) 1.01167 + 7.03631i 0.0536183 + 0.372924i
\(357\) −0.0957636 0.666050i −0.00506835 0.0352511i
\(358\) −20.4409 + 13.1366i −1.08034 + 0.694289i
\(359\) 2.82547 3.26077i 0.149123 0.172097i −0.676274 0.736651i \(-0.736406\pi\)
0.825396 + 0.564554i \(0.190952\pi\)
\(360\) −2.21306 + 4.84592i −0.116638 + 0.255402i
\(361\) 13.7130 + 8.81284i 0.721739 + 0.463834i
\(362\) −20.5238 + 6.02633i −1.07871 + 0.316737i
\(363\) −0.418876 0.483409i −0.0219853 0.0253724i
\(364\) −1.76405 0.517972i −0.0924614 0.0271491i
\(365\) −6.25224 13.6905i −0.327257 0.716593i
\(366\) −1.44192 + 10.0288i −0.0753703 + 0.524212i
\(367\) −10.8916 −0.568535 −0.284267 0.958745i \(-0.591750\pi\)
−0.284267 + 0.958745i \(0.591750\pi\)
\(368\) 0.815145 10.6754i 0.0424924 0.556496i
\(369\) 6.24071 0.324878
\(370\) −2.68472 + 18.6726i −0.139572 + 0.970743i
\(371\) −1.37211 3.00450i −0.0712364 0.155986i
\(372\) −5.49657 1.61394i −0.284984 0.0836788i
\(373\) −7.48393 8.63692i −0.387503 0.447203i 0.528162 0.849143i \(-0.322881\pi\)
−0.915666 + 0.401941i \(0.868336\pi\)
\(374\) 3.63185 1.06641i 0.187798 0.0551425i
\(375\) −10.1980 6.55386i −0.526623 0.338440i
\(376\) 3.82564 8.37699i 0.197293 0.432010i
\(377\) 6.07318 7.00882i 0.312785 0.360973i
\(378\) −0.681869 + 0.438210i −0.0350715 + 0.0225391i
\(379\) −4.90875 34.1411i −0.252146 1.75371i −0.585279 0.810832i \(-0.699015\pi\)
0.333133 0.942880i \(-0.391894\pi\)
\(380\) 0.970769 + 6.75185i 0.0497994 + 0.346362i
\(381\) 9.14490 5.87707i 0.468508 0.301092i
\(382\) −0.312986 + 0.361206i −0.0160138 + 0.0184809i
\(383\) −2.05523 + 4.50033i −0.105017 + 0.229956i −0.954845 0.297105i \(-0.903979\pi\)
0.849827 + 0.527061i \(0.176706\pi\)
\(384\) 2.34503 + 1.50706i 0.119669 + 0.0769067i
\(385\) 3.97090 1.16596i 0.202376 0.0594229i
\(386\) −6.79853 7.84592i −0.346036 0.399347i
\(387\) −7.67356 2.25316i −0.390069 0.114535i
\(388\) −0.550989 1.20650i −0.0279722 0.0612506i
\(389\) −1.66969 + 11.6130i −0.0846568 + 0.588801i 0.902698 + 0.430275i \(0.141583\pi\)
−0.987355 + 0.158526i \(0.949326\pi\)
\(390\) 7.90328 0.400198
\(391\) 3.23889 + 3.27020i 0.163798 + 0.165381i
\(392\) 20.0406 1.01221
\(393\) 2.12559 14.7838i 0.107222 0.745743i
\(394\) −8.04901 17.6249i −0.405503 0.887928i
\(395\) 12.6956 + 3.72776i 0.638784 + 0.187564i
\(396\) 1.48258 + 1.71099i 0.0745027 + 0.0859807i
\(397\) −27.1680 + 7.97725i −1.36352 + 0.400367i −0.880004 0.474966i \(-0.842460\pi\)
−0.483520 + 0.875333i \(0.660642\pi\)
\(398\) −5.60657 3.60312i −0.281032 0.180608i
\(399\) −1.73053 + 3.78932i −0.0866347 + 0.189703i
\(400\) −2.93374 + 3.38571i −0.146687 + 0.169286i
\(401\) 23.7395 15.2565i 1.18550 0.761872i 0.209107 0.977893i \(-0.432944\pi\)
0.976389 + 0.216021i \(0.0693079\pi\)
\(402\) 0.278900 + 1.93979i 0.0139103 + 0.0967481i
\(403\) 4.85472 + 33.7653i 0.241831 + 1.68197i
\(404\) 5.35598 3.44208i 0.266470 0.171250i
\(405\) −1.13298 + 1.30753i −0.0562982 + 0.0649716i
\(406\) 0.790239 1.73038i 0.0392189 0.0858774i
\(407\) 27.0709 + 17.3974i 1.34185 + 0.862357i
\(408\) −2.83547 + 0.832569i −0.140377 + 0.0412183i
\(409\) −15.6532 18.0648i −0.774002 0.893246i 0.222659 0.974896i \(-0.428526\pi\)
−0.996661 + 0.0816507i \(0.973981\pi\)
\(410\) −11.9762 3.51653i −0.591462 0.173669i
\(411\) −5.40908 11.8442i −0.266810 0.584233i
\(412\) 0.162569 1.13069i 0.00800920 0.0557052i
\(413\) −6.26627 −0.308343
\(414\) 1.96244 5.18520i 0.0964484 0.254838i
\(415\) −24.6600 −1.21051
\(416\) −2.01190 + 13.9930i −0.0986413 + 0.686065i
\(417\) −3.22804 7.06843i −0.158078 0.346143i
\(418\) −22.4840 6.60189i −1.09973 0.322909i
\(419\) 4.13517 + 4.77224i 0.202016 + 0.233139i 0.847714 0.530454i \(-0.177979\pi\)
−0.645697 + 0.763594i \(0.723433\pi\)
\(420\) −0.772360 + 0.226785i −0.0376873 + 0.0110660i
\(421\) 13.2789 + 8.53385i 0.647176 + 0.415915i 0.822633 0.568572i \(-0.192504\pi\)
−0.175457 + 0.984487i \(0.556140\pi\)
\(422\) 2.39510 5.24454i 0.116592 0.255300i
\(423\) 1.95855 2.26028i 0.0952278 0.109899i
\(424\) −12.2030 + 7.84240i −0.592631 + 0.380861i
\(425\) −0.274084 1.90630i −0.0132950 0.0924691i
\(426\) −1.91553 13.3228i −0.0928076 0.645491i
\(427\) −5.16954 + 3.32226i −0.250172 + 0.160776i
\(428\) −5.89012 + 6.79756i −0.284710 + 0.328572i
\(429\) 5.60037 12.2631i 0.270388 0.592068i
\(430\) 13.4563 + 8.64782i 0.648919 + 0.417035i
\(431\) 4.11677 1.20879i 0.198298 0.0582255i −0.181075 0.983469i \(-0.557958\pi\)
0.379373 + 0.925244i \(0.376140\pi\)
\(432\) 1.46195 + 1.68718i 0.0703382 + 0.0811747i
\(433\) −25.5847 7.51236i −1.22952 0.361021i −0.398454 0.917188i \(-0.630453\pi\)
−0.831070 + 0.556168i \(0.812271\pi\)
\(434\) 2.90673 + 6.36486i 0.139528 + 0.305523i
\(435\) 0.577864 4.01913i 0.0277065 0.192703i
\(436\) 13.0834 0.626579
\(437\) −5.92289 27.8718i −0.283330 1.33329i
\(438\) −10.0566 −0.480522
\(439\) 1.79597 12.4913i 0.0857171 0.596176i −0.901011 0.433796i \(-0.857174\pi\)
0.986728 0.162380i \(-0.0519170\pi\)
\(440\) −7.55027 16.5328i −0.359945 0.788170i
\(441\) 6.24477 + 1.83363i 0.297370 + 0.0873157i
\(442\) 2.87097 + 3.31328i 0.136558 + 0.157597i
\(443\) −5.37110 + 1.57710i −0.255189 + 0.0749302i −0.406825 0.913506i \(-0.633364\pi\)
0.151636 + 0.988436i \(0.451546\pi\)
\(444\) −5.26542 3.38388i −0.249886 0.160592i
\(445\) 7.69915 16.8588i 0.364975 0.799183i
\(446\) −12.1834 + 14.0604i −0.576902 + 0.665780i
\(447\) 6.55391 4.21194i 0.309989 0.199218i
\(448\) 0.858203 + 5.96893i 0.0405463 + 0.282006i
\(449\) −2.35429 16.3745i −0.111106 0.772759i −0.966847 0.255355i \(-0.917808\pi\)
0.855741 0.517404i \(-0.173102\pi\)
\(450\) −1.95157 + 1.25420i −0.0919980 + 0.0591235i
\(451\) −13.9429 + 16.0909i −0.656545 + 0.757693i
\(452\) 1.24431 2.72466i 0.0585275 0.128157i
\(453\) 2.56615 + 1.64917i 0.120568 + 0.0774846i
\(454\) 14.7369 4.32713i 0.691635 0.203082i
\(455\) 3.13900 + 3.62260i 0.147158 + 0.169830i
\(456\) 17.5538 + 5.15426i 0.822031 + 0.241370i
\(457\) −16.2613 35.6074i −0.760674 1.66564i −0.746177 0.665748i \(-0.768113\pi\)
−0.0144970 0.999895i \(-0.504615\pi\)
\(458\) 0.347719 2.41844i 0.0162478 0.113006i
\(459\) −0.959724 −0.0447961
\(460\) 3.32080 4.39188i 0.154833 0.204772i
\(461\) 15.1721 0.706635 0.353318 0.935503i \(-0.385053\pi\)
0.353318 + 0.935503i \(0.385053\pi\)
\(462\) 0.393544 2.73716i 0.0183093 0.127344i
\(463\) 8.12864 + 17.7992i 0.377770 + 0.827201i 0.999049 + 0.0436112i \(0.0138863\pi\)
−0.621279 + 0.783590i \(0.713386\pi\)
\(464\) −5.02723 1.47613i −0.233383 0.0685275i
\(465\) 9.78074 + 11.2876i 0.453571 + 0.523449i
\(466\) −16.5221 + 4.85132i −0.765371 + 0.224733i
\(467\) −22.1453 14.2319i −1.02476 0.658575i −0.0835896 0.996500i \(-0.526638\pi\)
−0.941173 + 0.337925i \(0.890275\pi\)
\(468\) −1.08930 + 2.38523i −0.0503529 + 0.110257i
\(469\) −0.778363 + 0.898279i −0.0359415 + 0.0414787i
\(470\) −5.03217 + 3.23398i −0.232117 + 0.149172i
\(471\) 1.35343 + 9.41331i 0.0623627 + 0.433742i
\(472\) 3.91645 + 27.2395i 0.180269 + 1.25380i
\(473\) 22.9537 14.7514i 1.05541 0.678271i
\(474\) 5.78971 6.68168i 0.265930 0.306900i
\(475\) −4.95293 + 10.8454i −0.227256 + 0.497621i
\(476\) −0.375645 0.241413i −0.0172177 0.0110651i
\(477\) −4.52006 + 1.32721i −0.206960 + 0.0607688i
\(478\) 14.0804 + 16.2496i 0.644021 + 0.743240i
\(479\) −12.4125 3.64463i −0.567141 0.166528i −0.0144229 0.999896i \(-0.504591\pi\)
−0.552718 + 0.833368i \(0.686409\pi\)
\(480\) 2.57126 + 5.63028i 0.117361 + 0.256986i
\(481\) −5.30420 + 36.8915i −0.241851 + 1.68211i
\(482\) 7.73371 0.352261
\(483\) 3.15615 1.15992i 0.143610 0.0527783i
\(484\) −0.424461 −0.0192937
\(485\) −0.492134 + 3.42287i −0.0223467 + 0.155424i
\(486\) 0.480233 + 1.05156i 0.0217838 + 0.0476999i
\(487\) 7.65688 + 2.24826i 0.346966 + 0.101878i 0.450572 0.892740i \(-0.351220\pi\)
−0.103606 + 0.994618i \(0.533038\pi\)
\(488\) 17.6729 + 20.3956i 0.800014 + 0.923265i
\(489\) 14.1041 4.14134i 0.637809 0.187278i
\(490\) −10.9508 7.03763i −0.494705 0.317928i
\(491\) 0.273712 0.599345i 0.0123524 0.0270481i −0.903355 0.428893i \(-0.858904\pi\)
0.915708 + 0.401845i \(0.131631\pi\)
\(492\) 2.71196 3.12977i 0.122265 0.141101i
\(493\) 1.89485 1.21775i 0.0853399 0.0548446i
\(494\) −3.86257 26.8648i −0.173785 1.20870i
\(495\) −0.840027 5.84252i −0.0377564 0.262602i
\(496\) 16.2129 10.4194i 0.727981 0.467845i
\(497\) 5.34591 6.16951i 0.239797 0.276740i
\(498\) −6.84497 + 14.9884i −0.306731 + 0.671646i
\(499\) 17.0771 + 10.9748i 0.764476 + 0.491299i 0.863849 0.503751i \(-0.168047\pi\)
−0.0993725 + 0.995050i \(0.531684\pi\)
\(500\) −7.71846 + 2.26635i −0.345180 + 0.101354i
\(501\) −4.45024 5.13586i −0.198822 0.229453i
\(502\) 19.9908 + 5.86984i 0.892234 + 0.261984i
\(503\) 5.09665 + 11.1601i 0.227249 + 0.497605i 0.988569 0.150771i \(-0.0481757\pi\)
−0.761320 + 0.648376i \(0.775448\pi\)
\(504\) −0.307250 + 2.13697i −0.0136860 + 0.0951882i
\(505\) −16.5991 −0.738650
\(506\) 8.98499 + 16.6446i 0.399431 + 0.739942i
\(507\) 2.61454 0.116116
\(508\) 1.02660 7.14019i 0.0455482 0.316795i
\(509\) 3.50514 + 7.67519i 0.155363 + 0.340197i 0.971268 0.237989i \(-0.0764882\pi\)
−0.815905 + 0.578186i \(0.803761\pi\)
\(510\) 1.84175 + 0.540787i 0.0815541 + 0.0239464i
\(511\) −3.99423 4.60959i −0.176694 0.203916i
\(512\) 20.8548 6.12352i 0.921661 0.270624i
\(513\) 4.99826 + 3.21219i 0.220679 + 0.141821i
\(514\) −6.52289 + 14.2831i −0.287712 + 0.630002i
\(515\) −1.95033 + 2.25081i −0.0859420 + 0.0991823i
\(516\) −4.46460 + 2.86922i −0.196543 + 0.126311i
\(517\) 1.45213 + 10.0998i 0.0638646 + 0.444188i
\(518\) 1.08800 + 7.56721i 0.0478040 + 0.332484i
\(519\) 11.5826 7.44368i 0.508419 0.326741i
\(520\) 13.7855 15.9094i 0.604536 0.697672i
\(521\) 0.313228 0.685873i 0.0137228 0.0300487i −0.902647 0.430383i \(-0.858379\pi\)
0.916369 + 0.400334i \(0.131106\pi\)
\(522\) −2.28244 1.46683i −0.0998996 0.0642016i
\(523\) −21.1241 + 6.20259i −0.923692 + 0.271220i −0.708794 0.705416i \(-0.750760\pi\)
−0.214898 + 0.976636i \(0.568942\pi\)
\(524\) −6.49050 7.49043i −0.283539 0.327221i
\(525\) −1.35000 0.396396i −0.0589189 0.0173001i
\(526\) −8.94386 19.5843i −0.389971 0.853917i
\(527\) −1.17909 + 8.20073i −0.0513618 + 0.357229i
\(528\) −7.61648 −0.331465
\(529\) −12.6203 + 19.2283i −0.548707 + 0.836015i
\(530\) 9.42206 0.409268
\(531\) −1.27191 + 8.84630i −0.0551960 + 0.383897i
\(532\) 1.14836 + 2.51456i 0.0497878 + 0.109020i
\(533\) −23.6614 6.94761i −1.02489 0.300934i
\(534\) −8.10972 9.35912i −0.350942 0.405009i
\(535\) 22.5004 6.60670i 0.972776 0.285633i
\(536\) 4.39130 + 2.82212i 0.189675 + 0.121897i
\(537\) −8.73144 + 19.1192i −0.376789 + 0.825054i
\(538\) 13.7419 15.8589i 0.592453 0.683728i
\(539\) −18.6798 + 12.0048i −0.804594 + 0.517081i
\(540\) 0.163389 + 1.13640i 0.00703116 + 0.0489028i
\(541\) 2.17878 + 15.1537i 0.0936730 + 0.651510i 0.981518 + 0.191368i \(0.0612924\pi\)
−0.887845 + 0.460142i \(0.847798\pi\)
\(542\) −13.1606 + 8.45779i −0.565295 + 0.363293i
\(543\) −12.1170 + 13.9838i −0.519991 + 0.600101i
\(544\) −1.42633 + 3.12322i −0.0611533 + 0.133907i
\(545\) −28.6958 18.4417i −1.22919 0.789955i
\(546\) 3.07312 0.902351i 0.131518 0.0386170i
\(547\) −2.84283 3.28081i −0.121551 0.140277i 0.691712 0.722173i \(-0.256857\pi\)
−0.813263 + 0.581896i \(0.802311\pi\)
\(548\) −8.29056 2.43433i −0.354155 0.103989i
\(549\) 3.64086 + 7.97236i 0.155388 + 0.340252i
\(550\) 1.12636 7.83401i 0.0480282 0.334043i
\(551\) −13.9442 −0.594044
\(552\) −7.01480 12.9948i −0.298570 0.553097i
\(553\) 5.36219 0.228023
\(554\) −2.65616 + 18.4740i −0.112849 + 0.784885i
\(555\) 6.77893 + 14.8438i 0.287749 + 0.630083i
\(556\) −4.94766 1.45276i −0.209827 0.0616109i
\(557\) 1.51952 + 1.75362i 0.0643841 + 0.0743032i 0.787028 0.616917i \(-0.211619\pi\)
−0.722644 + 0.691221i \(0.757073\pi\)
\(558\) 9.57549 2.81162i 0.405363 0.119025i
\(559\) 26.5856 + 17.0855i 1.12445 + 0.722641i
\(560\) 1.12498 2.46336i 0.0475390 0.104096i
\(561\) 2.14420 2.47454i 0.0905281 0.104475i
\(562\) 5.38445 3.46038i 0.227129 0.145967i
\(563\) 5.34799 + 37.1961i 0.225391 + 1.56763i 0.717163 + 0.696905i \(0.245440\pi\)
−0.491772 + 0.870724i \(0.663651\pi\)
\(564\) −0.282446 1.96446i −0.0118931 0.0827186i
\(565\) −6.56972 + 4.22210i −0.276390 + 0.177625i
\(566\) −2.60205 + 3.00292i −0.109372 + 0.126222i
\(567\) −0.291264 + 0.637778i −0.0122319 + 0.0267842i
\(568\) −30.1601 19.3827i −1.26549 0.813280i
\(569\) 38.5871 11.3302i 1.61765 0.474986i 0.657268 0.753657i \(-0.271712\pi\)
0.960387 + 0.278671i \(0.0898938\pi\)
\(570\) −7.78186 8.98075i −0.325946 0.376162i
\(571\) 3.62322 + 1.06387i 0.151627 + 0.0445217i 0.356665 0.934232i \(-0.383914\pi\)
−0.205038 + 0.978754i \(0.565732\pi\)
\(572\) −3.71636 8.13768i −0.155389 0.340254i
\(573\) −0.0588379 + 0.409226i −0.00245799 + 0.0170957i
\(574\) −5.05834 −0.211131
\(575\) 9.03320 3.31981i 0.376710 0.138446i
\(576\) 8.60074 0.358364
\(577\) −0.523644 + 3.64203i −0.0217996 + 0.151620i −0.997814 0.0660871i \(-0.978948\pi\)
0.976014 + 0.217707i \(0.0698576\pi\)
\(578\) −7.72163 16.9080i −0.321177 0.703281i
\(579\) −8.61664 2.53007i −0.358095 0.105146i
\(580\) −1.76451 2.03636i −0.0732675 0.0845552i
\(581\) −9.58883 + 2.81554i −0.397812 + 0.116808i
\(582\) 1.94382 + 1.24922i 0.0805740 + 0.0517818i
\(583\) 6.67659 14.6197i 0.276516 0.605486i
\(584\) −17.5415 + 20.2440i −0.725872 + 0.837701i
\(585\) 5.75128 3.69612i 0.237786 0.152816i
\(586\) −4.70228 32.7051i −0.194250 1.35104i
\(587\) −1.46701 10.2033i −0.0605499 0.421134i −0.997440 0.0715096i \(-0.977218\pi\)
0.936890 0.349624i \(-0.113691\pi\)
\(588\) 3.63331 2.33498i 0.149835 0.0962931i
\(589\) 33.5885 38.7632i 1.38399 1.59721i
\(590\) 7.42557 16.2597i 0.305706 0.669402i
\(591\) −14.0999 9.06148i −0.579994 0.372740i
\(592\) 20.2037 5.93235i 0.830368 0.243818i
\(593\) 1.00032 + 1.15443i 0.0410781 + 0.0474067i 0.775917 0.630835i \(-0.217288\pi\)
−0.734839 + 0.678242i \(0.762742\pi\)
\(594\) −3.78426 1.11116i −0.155270 0.0455914i
\(595\) 0.483622 + 1.05898i 0.0198266 + 0.0434141i
\(596\) 0.735740 5.11718i 0.0301371 0.209608i
\(597\) −5.76502 −0.235946
\(598\) −13.2130 + 17.4747i −0.540321 + 0.714595i
\(599\) −41.8601 −1.71036 −0.855178 0.518335i \(-0.826552\pi\)
−0.855178 + 0.518335i \(0.826552\pi\)
\(600\) −0.879378 + 6.11621i −0.0359004 + 0.249693i
\(601\) 2.34216 + 5.12861i 0.0955386 + 0.209200i 0.951367 0.308059i \(-0.0996795\pi\)
−0.855829 + 0.517259i \(0.826952\pi\)
\(602\) 6.21972 + 1.82627i 0.253497 + 0.0744334i
\(603\) 1.11014 + 1.28117i 0.0452084 + 0.0521733i
\(604\) 1.94222 0.570287i 0.0790277 0.0232046i
\(605\) 0.930973 + 0.598300i 0.0378494 + 0.0243243i
\(606\) −4.60748 + 10.0890i −0.187166 + 0.409836i
\(607\) 0.682821 0.788018i 0.0277149 0.0319846i −0.741723 0.670706i \(-0.765991\pi\)
0.769438 + 0.638722i \(0.220537\pi\)
\(608\) 17.8817 11.4919i 0.725200 0.466058i
\(609\) −0.234184 1.62878i −0.00948960 0.0660016i
\(610\) −2.49468 17.3509i −0.101007 0.702516i
\(611\) −9.94207 + 6.38938i −0.402213 + 0.258487i
\(612\) −0.417057 + 0.481310i −0.0168585 + 0.0194558i
\(613\) 11.9534 26.1743i 0.482794 1.05717i −0.498891 0.866664i \(-0.666259\pi\)
0.981686 0.190508i \(-0.0610134\pi\)
\(614\) 16.4952 + 10.6008i 0.665694 + 0.427815i
\(615\) −10.3597 + 3.04190i −0.417745 + 0.122661i
\(616\) −4.82348 5.56659i −0.194343 0.224284i
\(617\) 38.4153 + 11.2797i 1.54654 + 0.454106i 0.940065 0.340996i \(-0.110764\pi\)
0.606477 + 0.795101i \(0.292582\pi\)
\(618\) 0.826682 + 1.81018i 0.0332540 + 0.0728162i
\(619\) 4.65013 32.3424i 0.186905 1.29995i −0.653059 0.757307i \(-0.726515\pi\)
0.839964 0.542643i \(-0.182576\pi\)
\(620\) 9.91114 0.398041
\(621\) −0.996878 4.69108i −0.0400033 0.188247i
\(622\) −0.548323 −0.0219858
\(623\) 1.06891 7.43444i 0.0428250 0.297855i
\(624\) −3.66464 8.02444i −0.146703 0.321235i
\(625\) 10.4963 + 3.08199i 0.419852 + 0.123280i
\(626\) −13.1312 15.1543i −0.524830 0.605686i
\(627\) −19.4493 + 5.71082i −0.776729 + 0.228068i
\(628\) 5.30900 + 3.41189i 0.211852 + 0.136149i
\(629\) −3.76040 + 8.23412i −0.149937 + 0.328316i
\(630\) 0.918324 1.05980i 0.0365869 0.0422235i
\(631\) −4.94602 + 3.17862i −0.196898 + 0.126539i −0.635375 0.772204i \(-0.719154\pi\)
0.438477 + 0.898742i \(0.355518\pi\)
\(632\) −3.35139 23.3094i −0.133311 0.927200i
\(633\) −0.709778 4.93661i −0.0282111 0.196213i
\(634\) −16.5851 + 10.6586i −0.658679 + 0.423307i
\(635\) −12.3161 + 14.2136i −0.488751 + 0.564049i
\(636\) −1.29863 + 2.84360i −0.0514941 + 0.112756i
\(637\) −21.6355 13.9043i −0.857228 0.550907i
\(638\) 8.88145 2.60783i 0.351620 0.103245i
\(639\) −7.62460 8.79926i −0.301625 0.348093i
\(640\) −4.62739 1.35872i −0.182914 0.0537083i
\(641\) 18.7747 + 41.1108i 0.741555 + 1.62378i 0.780980 + 0.624556i \(0.214720\pi\)
−0.0394258 + 0.999222i \(0.512553\pi\)
\(642\) 2.22995 15.5096i 0.0880089 0.612116i
\(643\) 33.5453 1.32290 0.661449 0.749990i \(-0.269942\pi\)
0.661449 + 0.749990i \(0.269942\pi\)
\(644\) 0.789824 2.08689i 0.0311234 0.0822351i
\(645\) 13.8366 0.544814
\(646\) 0.938119 6.52476i 0.0369098 0.256713i
\(647\) 2.40384 + 5.26368i 0.0945048 + 0.206937i 0.950981 0.309251i \(-0.100078\pi\)
−0.856476 + 0.516187i \(0.827351\pi\)
\(648\) 2.95447 + 0.867510i 0.116062 + 0.0340790i
\(649\) −19.9675 23.0437i −0.783792 0.904545i
\(650\) 8.79557 2.58261i 0.344991 0.101298i
\(651\) 5.09191 + 3.27237i 0.199568 + 0.128254i
\(652\) 4.05216 8.87299i 0.158695 0.347493i
\(653\) 25.6574 29.6103i 1.00405 1.15874i 0.0167555 0.999860i \(-0.494666\pi\)
0.987298 0.158880i \(-0.0507882\pi\)
\(654\) −19.1741 + 12.3225i −0.749767 + 0.481846i
\(655\) 3.67749 + 25.5775i 0.143692 + 0.999397i
\(656\) 1.98275 + 13.7903i 0.0774135 + 0.538423i
\(657\) −7.31825 + 4.70315i −0.285512 + 0.183487i
\(658\) −1.58748 + 1.83205i −0.0618864 + 0.0714207i
\(659\) 2.40123 5.25796i 0.0935387 0.204821i −0.857079 0.515184i \(-0.827723\pi\)
0.950618 + 0.310363i \(0.100451\pi\)
\(660\) −3.29512 2.11764i −0.128262 0.0824291i
\(661\) −9.17712 + 2.69465i −0.356949 + 0.104810i −0.455290 0.890343i \(-0.650464\pi\)
0.0983415 + 0.995153i \(0.468646\pi\)
\(662\) 3.32522 + 3.83750i 0.129238 + 0.149149i
\(663\) 3.63875 + 1.06843i 0.141317 + 0.0414945i
\(664\) 18.2322 + 39.9230i 0.707547 + 1.54931i
\(665\) 1.02570 7.13388i 0.0397748 0.276640i
\(666\) 10.9037 0.422511
\(667\) 7.92050 + 7.99705i 0.306683 + 0.309647i
\(668\) −4.50958 −0.174481
\(669\) −2.29035 + 15.9297i −0.0885499 + 0.615878i
\(670\) −1.40849 3.08417i −0.0544148 0.119152i
\(671\) −28.6902 8.42419i −1.10757 0.325212i
\(672\) 1.64265 + 1.89571i 0.0633664 + 0.0731288i
\(673\) −10.2614 + 3.01303i −0.395549 + 0.116144i −0.473457 0.880817i \(-0.656994\pi\)
0.0779079 + 0.996961i \(0.475176\pi\)
\(674\) −11.2257 7.21430i −0.432397 0.277884i
\(675\) −0.833624 + 1.82538i −0.0320862 + 0.0702590i
\(676\) 1.13617 1.31121i 0.0436990 0.0504313i
\(677\) −26.7147 + 17.1685i −1.02673 + 0.659838i −0.941670 0.336538i \(-0.890744\pi\)
−0.0850577 + 0.996376i \(0.527107\pi\)
\(678\) 0.742620 + 5.16503i 0.0285201 + 0.198362i
\(679\) 0.199441 + 1.38714i 0.00765384 + 0.0532336i
\(680\) 4.30114 2.76417i 0.164941 0.106001i
\(681\) 8.70046 10.0409i 0.333402 0.384767i
\(682\) −14.1440 + 30.9710i −0.541600 + 1.18594i
\(683\) −7.74023 4.97434i −0.296172 0.190338i 0.384113 0.923286i \(-0.374507\pi\)
−0.680284 + 0.732948i \(0.738144\pi\)
\(684\) 3.78298 1.11078i 0.144646 0.0424719i
\(685\) 14.7524 + 17.0252i 0.563661 + 0.650500i
\(686\) −10.5056 3.08471i −0.401105 0.117775i
\(687\) −0.877992 1.92254i −0.0334975 0.0733493i
\(688\) 2.54091 17.6724i 0.0968714 0.673755i
\(689\) 18.6152 0.709182
\(690\) −0.730286 + 9.56411i −0.0278015 + 0.364099i
\(691\) −28.7634 −1.09421 −0.547105 0.837064i \(-0.684270\pi\)
−0.547105 + 0.837064i \(0.684270\pi\)
\(692\) 1.30026 9.04350i 0.0494284 0.343782i
\(693\) −0.993702 2.17590i −0.0377476 0.0826557i
\(694\) 20.6253 + 6.05614i 0.782926 + 0.229888i
\(695\) 8.80399 + 10.1603i 0.333954 + 0.385404i
\(696\) −6.93396 + 2.03600i −0.262831 + 0.0771742i
\(697\) −5.03857 3.23809i −0.190849 0.122651i
\(698\) −7.20333 + 15.7731i −0.272650 + 0.597020i
\(699\) −9.75444 + 11.2572i −0.368947 + 0.425787i
\(700\) −0.785452 + 0.504779i −0.0296873 + 0.0190789i
\(701\) 0.839552 + 5.83921i 0.0317094 + 0.220544i 0.999515 0.0311569i \(-0.00991916\pi\)
−0.967805 + 0.251701i \(0.919010\pi\)
\(702\) −0.650106 4.52159i −0.0245367 0.170656i
\(703\) 47.1438 30.2974i 1.77806 1.14269i
\(704\) −19.2156 + 22.1760i −0.724216 + 0.835790i
\(705\) −2.14952 + 4.70678i −0.0809554 + 0.177268i
\(706\) −13.2241 8.49859i −0.497694 0.319849i
\(707\) −6.45442 + 1.89519i −0.242743 + 0.0712759i
\(708\) 3.88378 + 4.48212i 0.145961 + 0.168448i
\(709\) −10.1644 2.98454i −0.381733 0.112087i 0.0852358 0.996361i \(-0.472836\pi\)
−0.466968 + 0.884274i \(0.654654\pi\)
\(710\) 9.67372 + 21.1825i 0.363048 + 0.794965i
\(711\) 1.08840 7.56998i 0.0408181 0.283896i
\(712\) −32.9856 −1.23619
\(713\) −41.3095 + 2.75490i −1.54705 + 0.103172i
\(714\) 0.777893 0.0291119
\(715\) −3.31939 + 23.0868i −0.124138 + 0.863399i
\(716\) 5.79411 + 12.6873i 0.216536 + 0.474147i
\(717\) 17.8459 + 5.24002i 0.666466 + 0.195692i
\(718\) 3.26634 + 3.76955i 0.121899 + 0.140678i
\(719\) 11.9533 3.50982i 0.445784 0.130894i −0.0511331 0.998692i \(-0.516283\pi\)
0.496918 + 0.867798i \(0.334465\pi\)
\(720\) −3.24926 2.08817i −0.121093 0.0778216i
\(721\) −0.501387 + 1.09788i −0.0186726 + 0.0408873i
\(722\) −12.3403 + 14.2415i −0.459258 + 0.530012i
\(723\) 5.62788 3.61682i 0.209303 0.134511i
\(724\) 1.74742 + 12.1536i 0.0649424 + 0.451684i
\(725\) −0.670256 4.66173i −0.0248927 0.173132i
\(726\) 0.622062 0.399775i 0.0230869 0.0148370i
\(727\) 13.6473 15.7498i 0.506151 0.584130i −0.443958 0.896048i \(-0.646426\pi\)
0.950109 + 0.311918i \(0.100971\pi\)
\(728\) 3.54395 7.76018i 0.131348 0.287611i
\(729\) 0.841254 + 0.540641i 0.0311575 + 0.0200237i
\(730\) 16.6942 4.90185i 0.617879 0.181426i
\(731\) 5.02632 + 5.80068i 0.185905 + 0.214546i
\(732\) 5.58038 + 1.63855i 0.206257 + 0.0605624i
\(733\) 11.1825 + 24.4863i 0.413035 + 0.904420i 0.995781 + 0.0917658i \(0.0292511\pi\)
−0.582746 + 0.812655i \(0.698022\pi\)
\(734\) 1.79188 12.4628i 0.0661397 0.460011i
\(735\) −11.2602 −0.415340
\(736\) −16.7477 3.72768i −0.617328 0.137404i
\(737\) −5.78361 −0.213042
\(738\) −1.02672 + 7.14102i −0.0377942 + 0.262865i
\(739\) 13.9697 + 30.5895i 0.513886 + 1.12525i 0.971703 + 0.236206i \(0.0759040\pi\)
−0.457817 + 0.889046i \(0.651369\pi\)
\(740\) 10.3901 + 3.05082i 0.381949 + 0.112150i
\(741\) −15.3747 17.7433i −0.564802 0.651816i
\(742\) 3.66369 1.07576i 0.134498 0.0394922i
\(743\) 14.7677 + 9.49063i 0.541775 + 0.348177i 0.782733 0.622358i \(-0.213825\pi\)
−0.240958 + 0.970536i \(0.577462\pi\)
\(744\) 11.0425 24.1798i 0.404839 0.886474i
\(745\) −8.82665 + 10.1865i −0.323383 + 0.373204i
\(746\) 11.1142 7.14265i 0.406919 0.261511i
\(747\) 2.02848 + 14.1084i 0.0742181 + 0.516198i
\(748\) −0.309219 2.15067i −0.0113062 0.0786362i
\(749\) 7.99476 5.13792i 0.292122 0.187736i
\(750\) 9.17713 10.5910i 0.335101 0.386728i
\(751\) 10.8737 23.8101i 0.396788 0.868844i −0.600798 0.799401i \(-0.705150\pi\)
0.997586 0.0694434i \(-0.0221223\pi\)
\(752\) 5.61690 + 3.60976i 0.204827 + 0.131634i
\(753\) 17.2926 5.07758i 0.630179 0.185037i
\(754\) 7.02078 + 8.10242i 0.255682 + 0.295073i
\(755\) −5.06373 1.48685i −0.184288 0.0541118i
\(756\) 0.193280 + 0.423224i 0.00702953 + 0.0153925i
\(757\) −2.30452 + 16.0283i −0.0837592 + 0.582558i 0.904114 + 0.427292i \(0.140532\pi\)
−0.987873 + 0.155266i \(0.950377\pi\)
\(758\) 39.8741 1.44829
\(759\) 14.3226 + 7.91040i 0.519878 + 0.287129i
\(760\) −31.6521 −1.14814
\(761\) 7.12949 49.5867i 0.258444 1.79752i −0.285484 0.958383i \(-0.592154\pi\)
0.543928 0.839132i \(-0.316936\pi\)
\(762\) 5.22040 + 11.4311i 0.189115 + 0.414105i
\(763\) −13.2637 3.89457i −0.480178 0.140993i
\(764\) 0.179662 + 0.207341i 0.00649995 + 0.00750134i
\(765\) 1.59317 0.467796i 0.0576011 0.0169132i
\(766\) −4.81144 3.09213i −0.173845 0.111723i
\(767\) 14.6707 32.1244i 0.529729 1.15994i
\(768\) 9.15429 10.5646i 0.330327 0.381218i
\(769\) −15.4147 + 9.90642i −0.555868 + 0.357235i −0.788217 0.615398i \(-0.788995\pi\)
0.232349 + 0.972633i \(0.425359\pi\)
\(770\) 0.680874 + 4.73559i 0.0245370 + 0.170659i
\(771\) 1.93303 + 13.4445i 0.0696163 + 0.484192i
\(772\) −5.01330 + 3.22185i −0.180433 + 0.115957i
\(773\) −22.4455 + 25.9035i −0.807308 + 0.931683i −0.998758 0.0498196i \(-0.984135\pi\)
0.191451 + 0.981502i \(0.438681\pi\)
\(774\) 3.84067 8.40989i 0.138050 0.302287i
\(775\) 14.5735 + 9.36583i 0.523496 + 0.336431i
\(776\) 5.90526 1.73394i 0.211987 0.0622449i
\(777\) 4.33070 + 4.99790i 0.155363 + 0.179299i
\(778\) −13.0136 3.82114i −0.466560 0.136995i
\(779\) 15.4031 + 33.7281i 0.551873 + 1.20843i
\(780\) 0.645637 4.49051i 0.0231175 0.160786i
\(781\) 39.7226 1.42139
\(782\) −4.27483 + 3.16813i −0.152868 + 0.113292i
\(783\) −2.34694 −0.0838729
\(784\) −2.06780 + 14.3819i −0.0738501 + 0.513639i
\(785\) −6.83504 14.9666i −0.243953 0.534182i
\(786\) 16.5668 + 4.86447i 0.590920 + 0.173510i
\(787\) −6.11416 7.05611i −0.217946 0.251523i 0.636239 0.771492i \(-0.280489\pi\)
−0.854185 + 0.519969i \(0.825944\pi\)
\(788\) −10.6717 + 3.13349i −0.380163 + 0.111626i
\(789\) −15.6675 10.0689i −0.557778 0.358462i
\(790\) −6.35423 + 13.9138i −0.226073 + 0.495032i
\(791\) −2.07252 + 2.39182i −0.0736905 + 0.0850434i
\(792\) −8.83759 + 5.67958i −0.314030 + 0.201815i
\(793\) −4.92874 34.2801i −0.175025 1.21732i
\(794\) −4.65839 32.3998i −0.165320 1.14983i
\(795\) 6.85651 4.40641i 0.243175 0.156279i
\(796\) −2.50525 + 2.89121i −0.0887961 + 0.102476i
\(797\) 17.7241 38.8104i 0.627821 1.37474i −0.281871 0.959452i \(-0.590955\pi\)
0.909692 0.415283i \(-0.136318\pi\)
\(798\) −4.05128 2.60360i −0.143414 0.0921665i
\(799\) −2.75406 + 0.808664i −0.0974316 + 0.0286085i
\(800\) 4.70141 + 5.42571i 0.166220 + 0.191828i
\(801\) −10.2785 3.01803i −0.363172 0.106637i
\(802\) 13.5518 + 29.6743i 0.478531 + 1.04784i
\(803\) 4.22377 29.3770i 0.149054 1.03669i
\(804\) 1.12494 0.0396736
\(805\) −4.67391 + 3.46390i −0.164734 + 0.122086i
\(806\) −39.4352 −1.38904
\(807\) 2.58331 17.9673i 0.0909369 0.632480i
\(808\) 12.2724 + 26.8729i 0.431743 + 0.945385i
\(809\) −23.3411 6.85357i −0.820631 0.240959i −0.155643 0.987813i \(-0.549745\pi\)
−0.664987 + 0.746855i \(0.731563\pi\)
\(810\) −1.30976 1.51154i −0.0460203 0.0531102i
\(811\) 2.69179 0.790382i 0.0945216 0.0277541i −0.234130 0.972205i \(-0.575224\pi\)
0.328651 + 0.944451i \(0.393406\pi\)
\(812\) −0.918616 0.590359i −0.0322371 0.0207175i
\(813\) −5.62161 + 12.3096i −0.197158 + 0.431717i
\(814\) −24.3609 + 28.1140i −0.853850 + 0.985395i
\(815\) −21.3946 + 13.7495i −0.749419 + 0.481622i
\(816\) −0.304916 2.12074i −0.0106742 0.0742408i
\(817\) −6.76234 47.0331i −0.236584 1.64548i
\(818\) 23.2462 14.9394i 0.812783 0.522344i
\(819\) 1.81434 2.09385i 0.0633980 0.0731652i
\(820\) −2.97639 + 6.51739i −0.103940 + 0.227597i
\(821\) −17.1180 11.0011i −0.597423 0.383941i 0.206699 0.978405i \(-0.433728\pi\)
−0.804122 + 0.594464i \(0.797364\pi\)
\(822\) 14.4428 4.24080i 0.503752 0.147915i
\(823\) −31.8028 36.7024i −1.10858 1.27937i −0.956735 0.290960i \(-0.906025\pi\)
−0.151841 0.988405i \(-0.548520\pi\)
\(824\) 5.08588 + 1.49335i 0.177175 + 0.0520232i
\(825\) −2.84407 6.22764i −0.0990177 0.216819i
\(826\) 1.03093 7.17027i 0.0358706 0.249485i
\(827\) 34.2876 1.19230 0.596148 0.802875i \(-0.296697\pi\)
0.596148 + 0.802875i \(0.296697\pi\)
\(828\) −2.78582 1.53861i −0.0968140 0.0534705i
\(829\) 11.8024 0.409916 0.204958 0.978771i \(-0.434294\pi\)
0.204958 + 0.978771i \(0.434294\pi\)
\(830\) 4.05707 28.2176i 0.140823 0.979446i
\(831\) 6.70682 + 14.6859i 0.232657 + 0.509448i
\(832\) −32.6093 9.57497i −1.13053 0.331952i
\(833\) −4.09044 4.72061i −0.141725 0.163560i
\(834\) 8.61923 2.53084i 0.298460 0.0876357i
\(835\) 9.89088 + 6.35649i 0.342288 + 0.219975i
\(836\) −5.58785 + 12.2357i −0.193260 + 0.423180i
\(837\) 5.65325 6.52420i 0.195405 0.225509i
\(838\) −6.14103 + 3.94660i −0.212138 + 0.136333i
\(839\) −6.15046 42.7774i −0.212338 1.47684i −0.765322 0.643648i \(-0.777420\pi\)
0.552984 0.833192i \(-0.313489\pi\)
\(840\) −0.531575 3.69719i −0.0183411 0.127565i
\(841\) −19.7626 + 12.7007i −0.681469 + 0.437954i
\(842\) −11.9496 + 13.7906i −0.411812 + 0.475256i
\(843\) 2.30000 5.03629i 0.0792161 0.173459i
\(844\) −2.78420 1.78929i −0.0958360 0.0615900i
\(845\) −4.34020 + 1.27440i −0.149307 + 0.0438406i
\(846\) 2.26414 + 2.61296i 0.0778428 + 0.0898354i
\(847\) 0.430311 + 0.126351i 0.0147857 + 0.00434146i
\(848\) −4.36887 9.56650i −0.150028 0.328515i
\(849\) −0.489155 + 3.40215i −0.0167878 + 0.116761i
\(850\) 2.22640 0.0763650
\(851\) −44.1539 9.82774i −1.51358 0.336890i
\(852\) −7.72626 −0.264697
\(853\) −4.54279 + 31.5958i −0.155542 + 1.08182i 0.751182 + 0.660095i \(0.229484\pi\)
−0.906724 + 0.421725i \(0.861425\pi\)
\(854\) −2.95105 6.46191i −0.100983 0.221122i
\(855\) −9.86295 2.89602i −0.337306 0.0990419i
\(856\) −27.3313 31.5420i −0.934165 1.07808i
\(857\) −8.00629 + 2.35086i −0.273490 + 0.0803038i −0.415602 0.909547i \(-0.636429\pi\)
0.142112 + 0.989851i \(0.454611\pi\)
\(858\) 13.1109 + 8.42583i 0.447597 + 0.287653i
\(859\) −22.7113 + 49.7307i −0.774899 + 1.69679i −0.0593407 + 0.998238i \(0.518900\pi\)
−0.715558 + 0.698553i \(0.753827\pi\)
\(860\) 6.01282 6.93916i 0.205035 0.236623i
\(861\) −3.68099 + 2.36563i −0.125448 + 0.0806205i
\(862\) 0.705886 + 4.90955i 0.0240426 + 0.167220i
\(863\) 2.93394 + 20.4060i 0.0998724 + 0.694628i 0.976823 + 0.214048i \(0.0686648\pi\)
−0.876951 + 0.480580i \(0.840426\pi\)
\(864\) 3.00966 1.93419i 0.102391 0.0658026i
\(865\) −15.5992 + 18.0024i −0.530387 + 0.612099i
\(866\) 12.8053 28.0398i 0.435143 0.952830i
\(867\) −13.5265 8.69293i −0.459383 0.295227i
\(868\) 3.85386 1.13160i 0.130809 0.0384089i
\(869\) 17.0866 + 19.7190i 0.579624 + 0.668922i
\(870\) 4.50388 + 1.32246i 0.152696 + 0.0448356i
\(871\) −2.78276 6.09340i −0.0942902 0.206467i
\(872\) −8.63985 + 60.0915i −0.292582 + 2.03495i
\(873\) 1.99876 0.0676477
\(874\) 32.8671 2.19188i 1.11175 0.0741415i
\(875\) 8.49948 0.287335
\(876\) −0.821545 + 5.71397i −0.0277574 + 0.193057i
\(877\) −14.8242 32.4605i −0.500578 1.09611i −0.976281 0.216507i \(-0.930533\pi\)
0.475703 0.879606i \(-0.342194\pi\)
\(878\) 13.9978 + 4.11014i 0.472404 + 0.138710i
\(879\) −18.7171 21.6007i −0.631311 0.728572i
\(880\) 12.6436 3.71248i 0.426214 0.125148i
\(881\) 38.0771 + 24.4707i 1.28285 + 0.824438i 0.991237 0.132098i \(-0.0421713\pi\)
0.291614 + 0.956536i \(0.405808\pi\)
\(882\) −3.12555 + 6.84400i −0.105243 + 0.230449i
\(883\) 31.3719 36.2052i 1.05575 1.21840i 0.0806253 0.996744i \(-0.474308\pi\)
0.975125 0.221656i \(-0.0711463\pi\)
\(884\) 2.11708 1.36057i 0.0712053 0.0457609i
\(885\) −2.20053 15.3051i −0.0739701 0.514474i
\(886\) −0.920962 6.40543i −0.0309403 0.215195i
\(887\) −14.1225 + 9.07599i −0.474188 + 0.304742i −0.755819 0.654781i \(-0.772761\pi\)
0.281631 + 0.959523i \(0.409125\pi\)
\(888\) 19.0192 21.9493i 0.638242 0.736570i
\(889\) −3.16620 + 6.93301i −0.106191 + 0.232526i
\(890\) 18.0242 + 11.5835i 0.604174 + 0.388279i
\(891\) −3.27349 + 0.961185i −0.109666 + 0.0322009i
\(892\) 6.99359 + 8.07104i 0.234163 + 0.270238i
\(893\) 17.0498 + 5.00627i 0.570549 + 0.167528i
\(894\) 3.74132 + 8.19236i 0.125129 + 0.273993i
\(895\) 5.17520 35.9943i 0.172988 1.20316i
\(896\) −1.95445 −0.0652936
\(897\) −1.44283 + 18.8958i −0.0481747 + 0.630914i
\(898\) 19.1241 0.638178
\(899\) −2.88338 + 20.0544i −0.0961661 + 0.668850i
\(900\) 0.553186 + 1.21131i 0.0184395 + 0.0403769i
\(901\) 4.33801 + 1.27376i 0.144520 + 0.0424349i
\(902\) −16.1184 18.6016i −0.536685 0.619367i
\(903\) 5.38023 1.57978i 0.179043 0.0525717i
\(904\) 11.6926 + 7.51437i 0.388890 + 0.249924i
\(905\) 13.2985 29.1196i 0.442056 0.967969i
\(906\) −2.30927 + 2.66504i −0.0767202 + 0.0885399i
\(907\) −8.42322 + 5.41328i −0.279689 + 0.179745i −0.672963 0.739676i \(-0.734979\pi\)
0.393274 + 0.919421i \(0.371342\pi\)
\(908\) −1.25471 8.72672i −0.0416391 0.289606i
\(909\) 1.36540 + 9.49660i 0.0452876 + 0.314982i
\(910\) −4.66164 + 2.99585i −0.154532 + 0.0993115i
\(911\) 22.6336 26.1205i 0.749884 0.865412i −0.244673 0.969606i \(-0.578681\pi\)
0.994557 + 0.104194i \(0.0332262\pi\)
\(912\) −5.51009 + 12.0654i −0.182457 + 0.399526i
\(913\) −40.9088 26.2905i −1.35388 0.870088i
\(914\) 43.4196 12.7491i 1.43619 0.421704i
\(915\) −9.92987 11.4597i −0.328271 0.378845i
\(916\) −1.34571 0.395136i −0.0444635 0.0130557i
\(917\) 4.35025 + 9.52573i 0.143658 + 0.314567i
\(918\) 0.157894 1.09818i 0.00521128 0.0362453i
\(919\) −5.18631 −0.171080 −0.0855402 0.996335i \(-0.527262\pi\)
−0.0855402 + 0.996335i \(0.527262\pi\)
\(920\) 17.9788 + 18.1526i 0.592743 + 0.598472i
\(921\) 16.9614 0.558898
\(922\) −2.49612 + 17.3609i −0.0822054 + 0.571751i
\(923\) 19.1124 + 41.8503i 0.629092 + 1.37752i
\(924\) −1.52306 0.447210i −0.0501049 0.0147121i
\(925\) 12.3949 + 14.3045i 0.407541 + 0.470328i
\(926\) −21.7044 + 6.37298i −0.713250 + 0.209429i
\(927\) 1.44815 + 0.930670i 0.0475635 + 0.0305672i
\(928\) −3.48799 + 7.63764i −0.114499 + 0.250718i
\(929\) −36.6945 + 42.3477i −1.20391 + 1.38938i −0.304363 + 0.952556i \(0.598443\pi\)
−0.899545 + 0.436827i \(0.856102\pi\)
\(930\) −14.5251 + 9.33472i −0.476297 + 0.306097i
\(931\) 5.50322 + 38.2757i 0.180361 + 1.25444i
\(932\) 1.40671 + 9.78387i 0.0460783 + 0.320481i
\(933\) −0.399019 + 0.256434i −0.0130633 + 0.00839528i
\(934\) 19.9284 22.9986i 0.652079 0.752539i
\(935\) −2.35327 + 5.15294i −0.0769601 + 0.168519i
\(936\) −10.2360 6.57825i −0.334573 0.215017i
\(937\) −6.67339 + 1.95949i −0.218010 + 0.0640136i −0.388914 0.921274i \(-0.627150\pi\)
0.170903 + 0.985288i \(0.445331\pi\)
\(938\) −0.899812 1.03844i −0.0293799 0.0339062i
\(939\) −16.6429 4.88679i −0.543120 0.159475i
\(940\) 1.42640 + 3.12338i 0.0465240 + 0.101873i
\(941\) −7.16070 + 49.8038i −0.233432 + 1.62356i 0.449643 + 0.893208i \(0.351551\pi\)
−0.683075 + 0.730348i \(0.739358\pi\)
\(942\) −10.9940 −0.358203
\(943\) 10.5940 27.9917i 0.344988 0.911535i
\(944\) −19.9521 −0.649386
\(945\) 0.172634 1.20070i 0.00561580 0.0390587i
\(946\) 13.1032 + 28.6920i 0.426021 + 0.932856i
\(947\) −29.9542 8.79533i −0.973379 0.285810i −0.243890 0.969803i \(-0.578424\pi\)
−0.729489 + 0.683993i \(0.760242\pi\)
\(948\) −3.32344 3.83545i −0.107940 0.124570i
\(949\) 32.9827 9.68460i 1.07066 0.314376i
\(950\) −11.5952 7.45175i −0.376196 0.241767i
\(951\) −7.08442 + 15.5127i −0.229728 + 0.503034i
\(952\) 1.35686 1.56590i 0.0439762 0.0507513i
\(953\) 38.4314 24.6984i 1.24492 0.800059i 0.258770 0.965939i \(-0.416683\pi\)
0.986146 + 0.165880i \(0.0530464\pi\)
\(954\) −0.775037 5.39050i −0.0250928 0.174524i
\(955\) −0.101796 0.708006i −0.00329404 0.0229105i
\(956\) 10.3830 6.67275i 0.335810 0.215812i
\(957\) 5.24350 6.05132i 0.169498 0.195611i
\(958\) 6.21253 13.6035i 0.200718 0.439511i
\(959\) 7.68020 + 4.93576i 0.248006 + 0.159384i
\(960\) −14.2775 + 4.19224i −0.460803 + 0.135304i
\(961\) −28.5025 32.8936i −0.919434 1.06108i
\(962\) −41.3410 12.1388i −1.33289 0.391371i
\(963\) −5.63063 12.3294i −0.181444 0.397308i
\(964\) 0.631784 4.39416i 0.0203484 0.141526i
\(965\) 15.5371 0.500156
\(966\) 0.808008 + 3.80230i 0.0259972 + 0.122337i
\(967\) 46.4073 1.49236 0.746180 0.665745i \(-0.231886\pi\)
0.746180 + 0.665745i \(0.231886\pi\)
\(968\) 0.280301 1.94953i 0.00900921 0.0626604i
\(969\) −2.36876 5.18685i −0.0760954 0.166626i
\(970\) −3.83570 1.12626i −0.123157 0.0361621i
\(971\) 15.1815 + 17.5204i 0.487199 + 0.562257i 0.945115 0.326738i \(-0.105949\pi\)
−0.457916 + 0.888995i \(0.651404\pi\)
\(972\) 0.636711 0.186955i 0.0204225 0.00599659i
\(973\) 4.58341 + 2.94558i 0.146937 + 0.0944308i
\(974\) −3.83232 + 8.39161i −0.122795 + 0.268885i
\(975\) 5.19280 5.99281i 0.166303 0.191924i
\(976\) −16.4601 + 10.5783i −0.526875 + 0.338602i
\(977\) 6.28322 + 43.7007i 0.201018 + 1.39811i 0.801272 + 0.598301i \(0.204157\pi\)
−0.600254 + 0.799810i \(0.704934\pi\)
\(978\) 2.41837 + 16.8202i 0.0773310 + 0.537849i
\(979\) 30.7457 19.7590i 0.982636 0.631502i
\(980\) −4.89325 + 5.64711i −0.156309 + 0.180390i
\(981\) −8.19032 + 17.9343i −0.261497 + 0.572598i
\(982\) 0.640778 + 0.411803i 0.0204481 + 0.0131412i
\(983\) 51.4331 15.1021i 1.64046 0.481683i 0.674051 0.738685i \(-0.264553\pi\)
0.966411 + 0.257002i \(0.0827348\pi\)
\(984\) 12.5840 + 14.5228i 0.401165 + 0.462969i
\(985\) 27.8231 + 8.16960i 0.886518 + 0.260305i
\(986\) 1.08168 + 2.36856i 0.0344478 + 0.0754302i
\(987\) −0.298428 + 2.07561i −0.00949907 + 0.0660675i
\(988\) −15.5796 −0.495654
\(989\) −23.1325 + 30.5936i −0.735572 + 0.972821i
\(990\) 6.82359 0.216868
\(991\) 4.59139 31.9338i 0.145850 1.01441i −0.777069 0.629416i \(-0.783294\pi\)
0.922919 0.384995i \(-0.125797\pi\)
\(992\) −12.8299 28.0935i −0.407349 0.891970i
\(993\) 4.21447 + 1.23748i 0.133742 + 0.0392703i
\(994\) 6.18004 + 7.13214i 0.196019 + 0.226218i
\(995\) 9.57008 2.81003i 0.303392 0.0890839i
\(996\) 7.95697 + 5.11363i 0.252126 + 0.162032i
\(997\) −20.8174 + 45.5838i −0.659294 + 1.44365i 0.223884 + 0.974616i \(0.428126\pi\)
−0.883178 + 0.469037i \(0.844601\pi\)
\(998\) −15.3676 + 17.7352i −0.486453 + 0.561396i
\(999\) 7.93473 5.09934i 0.251044 0.161336i
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 69.2.e.c.31.1 20
3.2 odd 2 207.2.i.d.100.2 20
23.3 even 11 inner 69.2.e.c.49.1 yes 20
23.7 odd 22 1587.2.a.t.1.7 10
23.16 even 11 1587.2.a.u.1.7 10
69.26 odd 22 207.2.i.d.118.2 20
69.53 even 22 4761.2.a.bu.1.4 10
69.62 odd 22 4761.2.a.bt.1.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.2.e.c.31.1 20 1.1 even 1 trivial
69.2.e.c.49.1 yes 20 23.3 even 11 inner
207.2.i.d.100.2 20 3.2 odd 2
207.2.i.d.118.2 20 69.26 odd 22
1587.2.a.t.1.7 10 23.7 odd 22
1587.2.a.u.1.7 10 23.16 even 11
4761.2.a.bt.1.4 10 69.62 odd 22
4761.2.a.bu.1.4 10 69.53 even 22