Properties

Label 672.2.ch.a.11.9
Level $672$
Weight $2$
Character 672.11
Analytic conductor $5.366$
Analytic rank $0$
Dimension $992$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [672,2,Mod(11,672)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(672, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([12, 15, 12, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("672.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 672.ch (of order \(24\), degree \(8\), 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: \(5.36594701583\)
Analytic rank: \(0\)
Dimension: \(992\)
Relative dimension: \(124\) over \(\Q(\zeta_{24})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label 11.9
Character \(\chi\) \(=\) 672.11
Dual form 672.2.ch.a.611.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36685 + 0.362941i) q^{2} +(-0.0108601 + 1.73202i) q^{3} +(1.73655 - 0.992170i) q^{4} +(0.167832 + 1.27481i) q^{5} +(-0.613775 - 2.37135i) q^{6} +(-2.51370 + 0.825424i) q^{7} +(-2.01350 + 1.98641i) q^{8} +(-2.99976 - 0.0376198i) q^{9} +O(q^{10})\) \(q+(-1.36685 + 0.362941i) q^{2} +(-0.0108601 + 1.73202i) q^{3} +(1.73655 - 0.992170i) q^{4} +(0.167832 + 1.27481i) q^{5} +(-0.613775 - 2.37135i) q^{6} +(-2.51370 + 0.825424i) q^{7} +(-2.01350 + 1.98641i) q^{8} +(-2.99976 - 0.0376198i) q^{9} +(-0.692080 - 1.68156i) q^{10} +(0.390523 - 0.299659i) q^{11} +(1.69960 + 3.01851i) q^{12} +(-0.622434 - 1.50269i) q^{13} +(3.13626 - 2.04055i) q^{14} +(-2.20981 + 0.276843i) q^{15} +(2.03120 - 3.44590i) q^{16} +(-0.869726 + 1.50641i) q^{17} +(4.11388 - 1.03732i) q^{18} +(-3.25942 - 2.50104i) q^{19} +(1.55627 + 2.04725i) q^{20} +(-1.40235 - 4.36273i) q^{21} +(-0.425028 + 0.551326i) q^{22} +(-8.05174 - 2.15746i) q^{23} +(-3.41863 - 3.50899i) q^{24} +(3.23266 - 0.866189i) q^{25} +(1.39616 + 1.82804i) q^{26} +(0.0977360 - 5.19523i) q^{27} +(-3.54620 + 3.92740i) q^{28} +(-0.425504 - 1.02726i) q^{29} +(2.92000 - 1.18043i) q^{30} +(5.23676 + 3.02345i) q^{31} +(-1.52568 + 5.44723i) q^{32} +(0.514774 + 0.679648i) q^{33} +(0.642046 - 2.37469i) q^{34} +(-1.47413 - 3.06595i) q^{35} +(-5.24656 + 2.91095i) q^{36} +(-2.03281 + 0.267625i) q^{37} +(5.36287 + 2.23557i) q^{38} +(2.60944 - 1.06175i) q^{39} +(-2.87022 - 2.23344i) q^{40} +(1.42879 + 1.42879i) q^{41} +(3.50021 + 5.45422i) q^{42} +(-2.43170 + 5.87063i) q^{43} +(0.380850 - 0.907838i) q^{44} +(-0.455497 - 3.83044i) q^{45} +(11.7885 + 0.0266121i) q^{46} +(-3.55011 + 2.04966i) q^{47} +(5.94630 + 3.55549i) q^{48} +(5.63735 - 4.14973i) q^{49} +(-4.10418 + 2.35721i) q^{50} +(-2.59968 - 1.52274i) q^{51} +(-2.57181 - 1.99193i) q^{52} +(-1.99280 - 2.59707i) q^{53} +(1.75197 + 7.13657i) q^{54} +(0.447550 + 0.447550i) q^{55} +(3.42170 - 6.65522i) q^{56} +(4.36725 - 5.61821i) q^{57} +(0.954432 + 1.24967i) q^{58} +(-4.10131 - 5.34494i) q^{59} +(-3.56277 + 2.67326i) q^{60} +(0.387972 + 0.297701i) q^{61} +(-8.25519 - 2.23196i) q^{62} +(7.57155 - 2.38151i) q^{63} +(0.108354 - 7.99927i) q^{64} +(1.81118 - 1.04568i) q^{65} +(-0.950289 - 0.742143i) q^{66} +(-5.89723 - 0.776385i) q^{67} +(-0.0157068 + 3.47887i) q^{68} +(3.82420 - 13.9223i) q^{69} +(3.12768 + 3.65566i) q^{70} +(-10.8313 - 10.8313i) q^{71} +(6.11475 - 5.88301i) q^{72} +(-3.68012 - 13.7344i) q^{73} +(2.68142 - 1.10359i) q^{74} +(1.46515 + 5.60843i) q^{75} +(-8.14160 - 1.10928i) q^{76} +(-0.734312 + 1.07560i) q^{77} +(-3.18136 + 2.39832i) q^{78} +(2.90372 + 5.02939i) q^{79} +(4.73376 + 2.01106i) q^{80} +(8.99717 + 0.225701i) q^{81} +(-2.47151 - 1.43437i) q^{82} +(-1.11853 - 2.70038i) q^{83} +(-6.76382 - 6.18472i) q^{84} +(-2.06635 - 0.855910i) q^{85} +(1.19307 - 8.90682i) q^{86} +(1.78385 - 0.725823i) q^{87} +(-0.191073 + 1.37910i) q^{88} +(12.2514 + 3.28275i) q^{89} +(2.01282 + 5.07031i) q^{90} +(2.80497 + 3.26353i) q^{91} +(-16.1228 + 4.24217i) q^{92} +(-5.29353 + 9.03732i) q^{93} +(4.10856 - 4.09005i) q^{94} +(2.64131 - 4.57489i) q^{95} +(-9.41812 - 2.70166i) q^{96} +10.0790 q^{97} +(-6.19929 + 7.71808i) q^{98} +(-1.18275 + 0.884216i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9} - 8 q^{10} - 4 q^{12} - 32 q^{13} - 32 q^{15} + 24 q^{16} - 4 q^{18} - 8 q^{19} - 8 q^{21} - 32 q^{22} - 44 q^{24} - 8 q^{25} - 16 q^{27} - 16 q^{28} - 36 q^{30} - 8 q^{33} + 64 q^{36} - 8 q^{37} - 4 q^{39} - 72 q^{40} - 68 q^{42} - 32 q^{43} - 4 q^{45} - 8 q^{46} - 16 q^{48} + 20 q^{51} + 16 q^{52} - 92 q^{54} - 32 q^{55} - 16 q^{57} + 24 q^{58} - 20 q^{60} - 8 q^{61} - 128 q^{64} - 20 q^{66} - 72 q^{67} - 16 q^{69} - 16 q^{70} - 4 q^{72} - 8 q^{73} + 16 q^{75} - 32 q^{76} + 136 q^{78} - 16 q^{79} - 48 q^{82} + 124 q^{84} + 48 q^{85} - 4 q^{87} - 8 q^{88} + 128 q^{90} - 64 q^{91} - 28 q^{93} - 64 q^{94} - 72 q^{96} - 64 q^{97} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(421\) \(449\) \(577\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36685 + 0.362941i −0.966508 + 0.256638i
\(3\) −0.0108601 + 1.73202i −0.00627010 + 0.999980i
\(4\) 1.73655 0.992170i 0.868274 0.496085i
\(5\) 0.167832 + 1.27481i 0.0750566 + 0.570111i 0.987110 + 0.160041i \(0.0511626\pi\)
−0.912054 + 0.410071i \(0.865504\pi\)
\(6\) −0.613775 2.37135i −0.250573 0.968098i
\(7\) −2.51370 + 0.825424i −0.950088 + 0.311981i
\(8\) −2.01350 + 1.98641i −0.711879 + 0.702302i
\(9\) −2.99976 0.0376198i −0.999921 0.0125399i
\(10\) −0.692080 1.68156i −0.218855 0.531755i
\(11\) 0.390523 0.299659i 0.117747 0.0903507i −0.548209 0.836341i \(-0.684690\pi\)
0.665957 + 0.745991i \(0.268024\pi\)
\(12\) 1.69960 + 3.01851i 0.490631 + 0.871367i
\(13\) −0.622434 1.50269i −0.172632 0.416771i 0.813756 0.581207i \(-0.197419\pi\)
−0.986388 + 0.164436i \(0.947419\pi\)
\(14\) 3.13626 2.04055i 0.838202 0.545361i
\(15\) −2.20981 + 0.276843i −0.570571 + 0.0714804i
\(16\) 2.03120 3.44590i 0.507800 0.861475i
\(17\) −0.869726 + 1.50641i −0.210940 + 0.365358i −0.952009 0.306071i \(-0.900986\pi\)
0.741069 + 0.671429i \(0.234319\pi\)
\(18\) 4.11388 1.03732i 0.969650 0.244498i
\(19\) −3.25942 2.50104i −0.747763 0.573779i 0.163040 0.986619i \(-0.447870\pi\)
−0.910803 + 0.412841i \(0.864537\pi\)
\(20\) 1.55627 + 2.04725i 0.347993 + 0.457778i
\(21\) −1.40235 4.36273i −0.306018 0.952026i
\(22\) −0.425028 + 0.551326i −0.0906162 + 0.117543i
\(23\) −8.05174 2.15746i −1.67890 0.449861i −0.711415 0.702772i \(-0.751945\pi\)
−0.967490 + 0.252911i \(0.918612\pi\)
\(24\) −3.41863 3.50899i −0.697824 0.716269i
\(25\) 3.23266 0.866189i 0.646532 0.173238i
\(26\) 1.39616 + 1.82804i 0.273809 + 0.358508i
\(27\) 0.0977360 5.19523i 0.0188093 0.999823i
\(28\) −3.54620 + 3.92740i −0.670168 + 0.742209i
\(29\) −0.425504 1.02726i −0.0790140 0.190757i 0.879436 0.476017i \(-0.157920\pi\)
−0.958450 + 0.285260i \(0.907920\pi\)
\(30\) 2.92000 1.18043i 0.533116 0.215516i
\(31\) 5.23676 + 3.02345i 0.940550 + 0.543027i 0.890133 0.455701i \(-0.150611\pi\)
0.0504174 + 0.998728i \(0.483945\pi\)
\(32\) −1.52568 + 5.44723i −0.269705 + 0.962943i
\(33\) 0.514774 + 0.679648i 0.0896106 + 0.118311i
\(34\) 0.642046 2.37469i 0.110110 0.407256i
\(35\) −1.47413 3.06595i −0.249174 0.518240i
\(36\) −5.24656 + 2.91095i −0.874427 + 0.485158i
\(37\) −2.03281 + 0.267625i −0.334192 + 0.0439973i −0.295755 0.955264i \(-0.595571\pi\)
−0.0384372 + 0.999261i \(0.512238\pi\)
\(38\) 5.36287 + 2.23557i 0.869972 + 0.362657i
\(39\) 2.60944 1.06175i 0.417845 0.170016i
\(40\) −2.87022 2.23344i −0.453821 0.353138i
\(41\) 1.42879 + 1.42879i 0.223140 + 0.223140i 0.809819 0.586680i \(-0.199565\pi\)
−0.586680 + 0.809819i \(0.699565\pi\)
\(42\) 3.50021 + 5.45422i 0.540094 + 0.841604i
\(43\) −2.43170 + 5.87063i −0.370830 + 0.895263i 0.622780 + 0.782397i \(0.286003\pi\)
−0.993610 + 0.112866i \(0.963997\pi\)
\(44\) 0.380850 0.907838i 0.0574153 0.136862i
\(45\) −0.455497 3.83044i −0.0679015 0.571008i
\(46\) 11.7885 + 0.0266121i 1.73813 + 0.00392373i
\(47\) −3.55011 + 2.04966i −0.517837 + 0.298973i −0.736049 0.676928i \(-0.763311\pi\)
0.218212 + 0.975901i \(0.429978\pi\)
\(48\) 5.94630 + 3.55549i 0.858274 + 0.513191i
\(49\) 5.63735 4.14973i 0.805336 0.592819i
\(50\) −4.10418 + 2.35721i −0.580419 + 0.333360i
\(51\) −2.59968 1.52274i −0.364028 0.213226i
\(52\) −2.57181 1.99193i −0.356646 0.276231i
\(53\) −1.99280 2.59707i −0.273733 0.356735i 0.636176 0.771544i \(-0.280515\pi\)
−0.909909 + 0.414809i \(0.863849\pi\)
\(54\) 1.75197 + 7.13657i 0.238413 + 0.971164i
\(55\) 0.447550 + 0.447550i 0.0603476 + 0.0603476i
\(56\) 3.42170 6.65522i 0.457243 0.889342i
\(57\) 4.36725 5.61821i 0.578456 0.744151i
\(58\) 0.954432 + 1.24967i 0.125323 + 0.164090i
\(59\) −4.10131 5.34494i −0.533945 0.695851i 0.446019 0.895023i \(-0.352841\pi\)
−0.979965 + 0.199172i \(0.936175\pi\)
\(60\) −3.56277 + 2.67326i −0.459951 + 0.345116i
\(61\) 0.387972 + 0.297701i 0.0496747 + 0.0381168i 0.633300 0.773906i \(-0.281700\pi\)
−0.583626 + 0.812023i \(0.698366\pi\)
\(62\) −8.25519 2.23196i −1.04841 0.283459i
\(63\) 7.57155 2.38151i 0.953926 0.300042i
\(64\) 0.108354 7.99927i 0.0135443 0.999908i
\(65\) 1.81118 1.04568i 0.224649 0.129701i
\(66\) −0.950289 0.742143i −0.116973 0.0913515i
\(67\) −5.89723 0.776385i −0.720461 0.0948505i −0.238625 0.971112i \(-0.576697\pi\)
−0.481836 + 0.876261i \(0.660030\pi\)
\(68\) −0.0157068 + 3.47887i −0.00190473 + 0.421875i
\(69\) 3.82420 13.9223i 0.460379 1.67605i
\(70\) 3.12768 + 3.65566i 0.373829 + 0.436935i
\(71\) −10.8313 10.8313i −1.28544 1.28544i −0.937528 0.347910i \(-0.886892\pi\)
−0.347910 0.937528i \(-0.613108\pi\)
\(72\) 6.11475 5.88301i 0.720630 0.693320i
\(73\) −3.68012 13.7344i −0.430725 1.60749i −0.751094 0.660195i \(-0.770473\pi\)
0.320369 0.947293i \(-0.396193\pi\)
\(74\) 2.68142 1.10359i 0.311708 0.128290i
\(75\) 1.46515 + 5.60843i 0.169181 + 0.647606i
\(76\) −8.14160 1.10928i −0.933906 0.127243i
\(77\) −0.734312 + 1.07560i −0.0836826 + 0.122576i
\(78\) −3.18136 + 2.39832i −0.360218 + 0.271556i
\(79\) 2.90372 + 5.02939i 0.326694 + 0.565850i 0.981854 0.189640i \(-0.0607321\pi\)
−0.655160 + 0.755490i \(0.727399\pi\)
\(80\) 4.73376 + 2.01106i 0.529250 + 0.224843i
\(81\) 8.99717 + 0.225701i 0.999685 + 0.0250779i
\(82\) −2.47151 1.43437i −0.272932 0.158400i
\(83\) −1.11853 2.70038i −0.122775 0.296405i 0.850528 0.525930i \(-0.176283\pi\)
−0.973303 + 0.229525i \(0.926283\pi\)
\(84\) −6.76382 6.18472i −0.737993 0.674809i
\(85\) −2.06635 0.855910i −0.224127 0.0928365i
\(86\) 1.19307 8.90682i 0.128652 0.960448i
\(87\) 1.78385 0.725823i 0.191248 0.0778164i
\(88\) −0.191073 + 1.37910i −0.0203684 + 0.147013i
\(89\) 12.2514 + 3.28275i 1.29864 + 0.347970i 0.840937 0.541133i \(-0.182004\pi\)
0.457706 + 0.889103i \(0.348671\pi\)
\(90\) 2.01282 + 5.07031i 0.212170 + 0.534457i
\(91\) 2.80497 + 3.26353i 0.294040 + 0.342111i
\(92\) −16.1228 + 4.24217i −1.68092 + 0.442277i
\(93\) −5.29353 + 9.03732i −0.548914 + 0.937127i
\(94\) 4.10856 4.09005i 0.423766 0.421857i
\(95\) 2.64131 4.57489i 0.270993 0.469374i
\(96\) −9.41812 2.70166i −0.961233 0.275737i
\(97\) 10.0790 1.02337 0.511684 0.859174i \(-0.329022\pi\)
0.511684 + 0.859174i \(0.329022\pi\)
\(98\) −6.19929 + 7.71808i −0.626223 + 0.779644i
\(99\) −1.18275 + 0.884216i −0.118871 + 0.0888670i
\(100\) 4.75427 4.71153i 0.475427 0.471153i
\(101\) −3.72093 + 2.85517i −0.370247 + 0.284100i −0.777080 0.629402i \(-0.783300\pi\)
0.406833 + 0.913503i \(0.366633\pi\)
\(102\) 4.10603 + 1.13782i 0.406558 + 0.112661i
\(103\) −8.25094 2.21083i −0.812989 0.217840i −0.171710 0.985147i \(-0.554929\pi\)
−0.641279 + 0.767308i \(0.721596\pi\)
\(104\) 4.23823 + 1.78925i 0.415592 + 0.175451i
\(105\) 5.32628 2.51993i 0.519792 0.245920i
\(106\) 3.66644 + 2.82653i 0.356116 + 0.274537i
\(107\) 1.90657 + 14.4818i 0.184315 + 1.40001i 0.794265 + 0.607572i \(0.207856\pi\)
−0.609950 + 0.792440i \(0.708810\pi\)
\(108\) −4.98483 9.11874i −0.479666 0.877451i
\(109\) −12.1522 1.59986i −1.16397 0.153239i −0.476312 0.879277i \(-0.658027\pi\)
−0.687655 + 0.726037i \(0.741360\pi\)
\(110\) −0.774167 0.449299i −0.0738139 0.0428390i
\(111\) −0.441454 3.52377i −0.0419010 0.334462i
\(112\) −2.26149 + 10.3386i −0.213691 + 0.976901i
\(113\) −16.1961 −1.52360 −0.761802 0.647810i \(-0.775685\pi\)
−0.761802 + 0.647810i \(0.775685\pi\)
\(114\) −3.93028 + 9.26430i −0.368105 + 0.867681i
\(115\) 1.39901 10.6265i 0.130458 0.990928i
\(116\) −1.75812 1.36171i −0.163237 0.126431i
\(117\) 1.81062 + 4.53113i 0.167392 + 0.418903i
\(118\) 7.54577 + 5.81718i 0.694644 + 0.535515i
\(119\) 0.942801 4.50455i 0.0864264 0.412931i
\(120\) 3.89953 4.94701i 0.355977 0.451598i
\(121\) −2.78430 + 10.3911i −0.253118 + 0.944649i
\(122\) −0.638347 0.266102i −0.0577932 0.0240917i
\(123\) −2.49021 + 2.45917i −0.224534 + 0.221736i
\(124\) 12.0937 + 0.0546020i 1.08604 + 0.00490340i
\(125\) 4.10705 + 9.91531i 0.367346 + 0.886852i
\(126\) −9.48481 + 6.00319i −0.844974 + 0.534807i
\(127\) 18.9104i 1.67802i 0.544114 + 0.839011i \(0.316866\pi\)
−0.544114 + 0.839011i \(0.683134\pi\)
\(128\) 2.75516 + 10.9731i 0.243524 + 0.969895i
\(129\) −10.1416 4.27549i −0.892920 0.376436i
\(130\) −2.09608 + 2.08664i −0.183838 + 0.183010i
\(131\) 3.41292 + 2.61883i 0.298188 + 0.228808i 0.747009 0.664814i \(-0.231489\pi\)
−0.448821 + 0.893622i \(0.648156\pi\)
\(132\) 1.56825 + 0.669498i 0.136499 + 0.0582723i
\(133\) 10.2576 + 3.59646i 0.889449 + 0.311853i
\(134\) 8.34240 1.07914i 0.720673 0.0932239i
\(135\) 6.63933 0.747330i 0.571422 0.0643199i
\(136\) −1.24115 4.76079i −0.106428 0.408234i
\(137\) 11.5760 3.10179i 0.989007 0.265004i 0.272174 0.962248i \(-0.412258\pi\)
0.716833 + 0.697245i \(0.245591\pi\)
\(138\) −0.174118 + 20.4177i −0.0148219 + 1.73807i
\(139\) −0.803954 + 1.94092i −0.0681905 + 0.164626i −0.954301 0.298848i \(-0.903398\pi\)
0.886110 + 0.463475i \(0.153398\pi\)
\(140\) −5.60185 3.86157i −0.473443 0.326363i
\(141\) −3.51149 6.17111i −0.295721 0.519701i
\(142\) 18.7358 + 10.8736i 1.57228 + 0.912493i
\(143\) −0.693370 0.400317i −0.0579825 0.0334762i
\(144\) −6.22275 + 10.2605i −0.518562 + 0.855040i
\(145\) 1.23814 0.714841i 0.102822 0.0593643i
\(146\) 10.0149 + 17.4372i 0.828842 + 1.44311i
\(147\) 7.12618 + 9.80905i 0.587758 + 0.809037i
\(148\) −3.26455 + 2.48164i −0.268344 + 0.203990i
\(149\) −23.5824 + 3.10469i −1.93195 + 0.254346i −0.995370 0.0961126i \(-0.969359\pi\)
−0.936578 + 0.350458i \(0.886026\pi\)
\(150\) −4.03816 7.13411i −0.329715 0.582498i
\(151\) −13.4149 + 3.59450i −1.09169 + 0.292516i −0.759375 0.650653i \(-0.774495\pi\)
−0.332311 + 0.943170i \(0.607828\pi\)
\(152\) 11.5309 1.43870i 0.935283 0.116694i
\(153\) 2.66564 4.48615i 0.215505 0.362684i
\(154\) 0.613314 1.73669i 0.0494222 0.139947i
\(155\) −2.97542 + 7.18329i −0.238991 + 0.576976i
\(156\) 3.47799 4.43278i 0.278462 0.354907i
\(157\) −1.36575 + 10.3739i −0.108999 + 0.827928i 0.846387 + 0.532568i \(0.178773\pi\)
−0.955386 + 0.295360i \(0.904560\pi\)
\(158\) −5.79431 5.82053i −0.460971 0.463057i
\(159\) 4.51981 3.42336i 0.358445 0.271490i
\(160\) −7.20023 1.03073i −0.569228 0.0814866i
\(161\) 22.0205 1.22291i 1.73546 0.0963785i
\(162\) −12.3797 + 2.95694i −0.972640 + 0.232319i
\(163\) −7.16422 + 9.33659i −0.561145 + 0.731298i −0.984639 0.174601i \(-0.944137\pi\)
0.423495 + 0.905899i \(0.360803\pi\)
\(164\) 3.89877 + 1.06356i 0.304443 + 0.0830502i
\(165\) −0.780025 + 0.770304i −0.0607248 + 0.0599681i
\(166\) 2.50894 + 3.28504i 0.194732 + 0.254969i
\(167\) −8.09595 8.09595i −0.626483 0.626483i 0.320698 0.947181i \(-0.396082\pi\)
−0.947181 + 0.320698i \(0.896082\pi\)
\(168\) 11.4898 + 5.99871i 0.886457 + 0.462811i
\(169\) 7.32174 7.32174i 0.563211 0.563211i
\(170\) 3.13503 + 0.419937i 0.240446 + 0.0322077i
\(171\) 9.68341 + 7.62516i 0.740509 + 0.583111i
\(172\) 1.60191 + 12.6073i 0.122144 + 0.961297i
\(173\) −10.2282 7.84835i −0.777633 0.596699i 0.141823 0.989892i \(-0.454704\pi\)
−0.919456 + 0.393193i \(0.871370\pi\)
\(174\) −2.17482 + 1.63952i −0.164872 + 0.124292i
\(175\) −7.41096 + 4.84565i −0.560216 + 0.366297i
\(176\) −0.239365 1.95437i −0.0180428 0.147316i
\(177\) 9.30206 7.04550i 0.699186 0.529572i
\(178\) −17.9372 0.0404924i −1.34445 0.00303503i
\(179\) 1.78942 + 0.235581i 0.133747 + 0.0176082i 0.197103 0.980383i \(-0.436847\pi\)
−0.0633553 + 0.997991i \(0.520180\pi\)
\(180\) −4.59144 6.19981i −0.342225 0.462106i
\(181\) 6.74634 + 2.79443i 0.501452 + 0.207708i 0.619048 0.785353i \(-0.287519\pi\)
−0.117596 + 0.993062i \(0.537519\pi\)
\(182\) −5.01843 3.44272i −0.371991 0.255191i
\(183\) −0.519837 + 0.668741i −0.0384275 + 0.0494348i
\(184\) 20.4978 11.6500i 1.51112 0.858851i
\(185\) −0.682341 2.54653i −0.0501667 0.187225i
\(186\) 3.95544 14.2739i 0.290027 1.04661i
\(187\) 0.111761 + 0.848910i 0.00817278 + 0.0620784i
\(188\) −4.13133 + 7.08164i −0.301308 + 0.516482i
\(189\) 4.04259 + 13.1399i 0.294055 + 0.955788i
\(190\) −1.94986 + 7.21182i −0.141458 + 0.523201i
\(191\) 1.79947 + 3.11678i 0.130205 + 0.225522i 0.923756 0.382982i \(-0.125103\pi\)
−0.793550 + 0.608505i \(0.791770\pi\)
\(192\) 13.8537 + 0.274544i 0.999804 + 0.0198135i
\(193\) 0.0758085 0.131304i 0.00545681 0.00945148i −0.863284 0.504718i \(-0.831596\pi\)
0.868741 + 0.495267i \(0.164930\pi\)
\(194\) −13.7765 + 3.65808i −0.989092 + 0.262635i
\(195\) 1.79147 + 3.14834i 0.128290 + 0.225457i
\(196\) 5.67229 12.7994i 0.405164 0.914244i
\(197\) 10.7385 + 4.44804i 0.765089 + 0.316910i 0.730881 0.682505i \(-0.239109\pi\)
0.0342073 + 0.999415i \(0.489109\pi\)
\(198\) 1.29572 1.63786i 0.0920831 0.116397i
\(199\) 2.75306 + 10.2746i 0.195159 + 0.728344i 0.992226 + 0.124452i \(0.0397174\pi\)
−0.797066 + 0.603892i \(0.793616\pi\)
\(200\) −4.78835 + 8.16546i −0.338588 + 0.577385i
\(201\) 1.40876 10.2057i 0.0993660 0.719852i
\(202\) 4.04969 5.25307i 0.284935 0.369605i
\(203\) 1.91751 + 2.23099i 0.134583 + 0.156585i
\(204\) −6.02529 0.0649854i −0.421855 0.00454989i
\(205\) −1.58164 + 2.06123i −0.110466 + 0.143963i
\(206\) 12.0802 + 0.0272704i 0.841666 + 0.00190002i
\(207\) 24.0722 + 6.77477i 1.67313 + 0.470879i
\(208\) −6.44240 0.907412i −0.446700 0.0629177i
\(209\) −2.02234 −0.139888
\(210\) −6.36564 + 5.37749i −0.439271 + 0.371082i
\(211\) −18.8965 + 7.82719i −1.30089 + 0.538846i −0.922213 0.386683i \(-0.873621\pi\)
−0.378677 + 0.925529i \(0.623621\pi\)
\(212\) −6.03734 2.53274i −0.414646 0.173949i
\(213\) 18.8776 18.6424i 1.29347 1.27735i
\(214\) −7.86204 19.1025i −0.537438 1.30582i
\(215\) −7.89204 2.11467i −0.538233 0.144219i
\(216\) 10.1231 + 10.6547i 0.688788 + 0.724963i
\(217\) −15.6593 3.27748i −1.06302 0.222490i
\(218\) 17.1908 2.22375i 1.16431 0.150611i
\(219\) 23.8282 6.22487i 1.61016 0.420638i
\(220\) 1.22124 + 0.333147i 0.0823358 + 0.0224607i
\(221\) 2.80501 + 0.369287i 0.188686 + 0.0248409i
\(222\) 1.88232 + 4.65624i 0.126333 + 0.312506i
\(223\) 9.59662i 0.642637i 0.946971 + 0.321319i \(0.104126\pi\)
−0.946971 + 0.321319i \(0.895874\pi\)
\(224\) −0.661172 14.9520i −0.0441764 0.999024i
\(225\) −9.72981 + 2.47675i −0.648654 + 0.165117i
\(226\) 22.1377 5.87824i 1.47258 0.391015i
\(227\) −2.92671 + 22.2306i −0.194253 + 1.47550i 0.565211 + 0.824946i \(0.308795\pi\)
−0.759464 + 0.650549i \(0.774539\pi\)
\(228\) 2.00971 14.0893i 0.133096 0.933090i
\(229\) −24.3904 + 3.21106i −1.61176 + 0.212193i −0.881913 0.471413i \(-0.843744\pi\)
−0.729852 + 0.683605i \(0.760411\pi\)
\(230\) 1.94456 + 15.0326i 0.128221 + 0.991220i
\(231\) −1.85498 1.28352i −0.122049 0.0844495i
\(232\) 2.89730 + 1.22316i 0.190217 + 0.0803041i
\(233\) −2.06900 + 7.72163i −0.135545 + 0.505861i 0.864450 + 0.502719i \(0.167667\pi\)
−0.999995 + 0.00314212i \(0.999000\pi\)
\(234\) −4.11938 5.53621i −0.269292 0.361914i
\(235\) −3.20874 4.18171i −0.209315 0.272785i
\(236\) −12.4252 5.21254i −0.808812 0.339307i
\(237\) −8.74252 + 4.97467i −0.567888 + 0.323139i
\(238\) 0.346219 + 6.49922i 0.0224420 + 0.421282i
\(239\) 0.653926i 0.0422990i 0.999776 + 0.0211495i \(0.00673259\pi\)
−0.999776 + 0.0211495i \(0.993267\pi\)
\(240\) −3.53459 + 8.17711i −0.228157 + 0.527830i
\(241\) −5.05410 2.91799i −0.325563 0.187964i 0.328306 0.944571i \(-0.393522\pi\)
−0.653870 + 0.756607i \(0.726856\pi\)
\(242\) 0.0343441 15.2136i 0.00220772 0.977970i
\(243\) −0.488629 + 15.5808i −0.0313456 + 0.999509i
\(244\) 0.969103 + 0.132039i 0.0620404 + 0.00845291i
\(245\) 6.23624 + 6.49008i 0.398419 + 0.414636i
\(246\) 2.51120 4.26511i 0.160108 0.271934i
\(247\) −1.72951 + 6.45463i −0.110046 + 0.410699i
\(248\) −16.5500 + 4.31465i −1.05093 + 0.273981i
\(249\) 4.68924 1.90799i 0.297169 0.120914i
\(250\) −9.21239 12.0621i −0.582643 0.762874i
\(251\) 9.47322 22.8704i 0.597945 1.44357i −0.277727 0.960660i \(-0.589581\pi\)
0.875672 0.482906i \(-0.160419\pi\)
\(252\) 10.7855 11.6479i 0.679423 0.733747i
\(253\) −3.79090 + 1.57024i −0.238332 + 0.0987202i
\(254\) −6.86334 25.8476i −0.430644 1.62182i
\(255\) 1.50489 3.56966i 0.0942400 0.223541i
\(256\) −7.74847 13.9986i −0.484279 0.874913i
\(257\) 16.5630 9.56264i 1.03317 0.596501i 0.115279 0.993333i \(-0.463224\pi\)
0.917891 + 0.396832i \(0.129890\pi\)
\(258\) 15.4138 + 2.16314i 0.959622 + 0.134671i
\(259\) 4.88897 2.35066i 0.303786 0.146063i
\(260\) 2.10770 3.61287i 0.130714 0.224061i
\(261\) 1.23777 + 3.09754i 0.0766157 + 0.191733i
\(262\) −5.61542 2.34085i −0.346922 0.144618i
\(263\) 16.9694 4.54694i 1.04638 0.280376i 0.305624 0.952152i \(-0.401135\pi\)
0.740754 + 0.671776i \(0.234468\pi\)
\(264\) −2.38655 0.345918i −0.146882 0.0212898i
\(265\) 2.97631 2.97631i 0.182833 0.182833i
\(266\) −15.3259 1.19290i −0.939692 0.0731417i
\(267\) −5.81882 + 21.1839i −0.356106 + 1.29644i
\(268\) −11.0111 + 4.50282i −0.672612 + 0.275054i
\(269\) −1.08268 + 8.22377i −0.0660122 + 0.501412i 0.926217 + 0.376990i \(0.123041\pi\)
−0.992229 + 0.124422i \(0.960292\pi\)
\(270\) −8.80371 + 3.43117i −0.535777 + 0.208814i
\(271\) −10.9175 18.9097i −0.663191 1.14868i −0.979772 0.200115i \(-0.935869\pi\)
0.316582 0.948565i \(-0.397465\pi\)
\(272\) 3.42435 + 6.05681i 0.207632 + 0.367248i
\(273\) −5.68296 + 4.82281i −0.343948 + 0.291890i
\(274\) −14.6969 + 8.44109i −0.887873 + 0.509945i
\(275\) 1.00287 1.30696i 0.0604753 0.0788129i
\(276\) −7.17241 27.9710i −0.431728 1.68366i
\(277\) 17.9962 13.8090i 1.08129 0.829701i 0.0951220 0.995466i \(-0.469676\pi\)
0.986165 + 0.165765i \(0.0530092\pi\)
\(278\) 0.394445 2.94472i 0.0236573 0.176613i
\(279\) −15.5953 9.26663i −0.933667 0.554779i
\(280\) 9.05840 + 3.24505i 0.541343 + 0.193929i
\(281\) −4.83866 + 4.83866i −0.288650 + 0.288650i −0.836546 0.547896i \(-0.815429\pi\)
0.547896 + 0.836546i \(0.315429\pi\)
\(282\) 7.03942 + 7.16051i 0.419191 + 0.426402i
\(283\) −17.5315 + 13.4524i −1.04214 + 0.799661i −0.980118 0.198414i \(-0.936421\pi\)
−0.0620198 + 0.998075i \(0.519754\pi\)
\(284\) −29.5555 8.06258i −1.75380 0.478426i
\(285\) 7.89510 + 4.62449i 0.467666 + 0.273931i
\(286\) 1.09302 + 0.295521i 0.0646318 + 0.0174745i
\(287\) −4.77091 2.41219i −0.281618 0.142387i
\(288\) 4.78161 16.2830i 0.281759 0.959485i
\(289\) 6.98715 + 12.1021i 0.411009 + 0.711889i
\(290\) −1.43291 + 1.42645i −0.0841432 + 0.0837641i
\(291\) −0.109459 + 17.4570i −0.00641661 + 1.02335i
\(292\) −20.0175 20.1991i −1.17144 1.18206i
\(293\) −12.8559 5.32508i −0.751049 0.311095i −0.0258793 0.999665i \(-0.508239\pi\)
−0.725169 + 0.688571i \(0.758239\pi\)
\(294\) −13.3005 10.8211i −0.775702 0.631099i
\(295\) 6.12543 6.12543i 0.356637 0.356637i
\(296\) 3.56145 4.57686i 0.207005 0.266025i
\(297\) −1.51863 2.05815i −0.0881199 0.119426i
\(298\) 31.1068 12.8027i 1.80197 0.741638i
\(299\) 1.76969 + 13.4421i 0.102344 + 0.777379i
\(300\) 8.10882 + 8.28564i 0.468163 + 0.478371i
\(301\) 1.26679 16.7642i 0.0730163 0.966271i
\(302\) 17.0315 9.78194i 0.980052 0.562887i
\(303\) −4.90480 6.47573i −0.281773 0.372021i
\(304\) −15.2389 + 6.15154i −0.874010 + 0.352815i
\(305\) −0.314398 + 0.544553i −0.0180024 + 0.0311810i
\(306\) −2.01532 + 7.09936i −0.115208 + 0.405844i
\(307\) 26.4076 10.9384i 1.50716 0.624286i 0.532191 0.846624i \(-0.321369\pi\)
0.974970 + 0.222338i \(0.0713688\pi\)
\(308\) −0.207990 + 2.59639i −0.0118513 + 0.147943i
\(309\) 3.91881 14.2668i 0.222933 0.811608i
\(310\) 1.45983 10.8984i 0.0829130 0.618986i
\(311\) 2.37031 + 8.84611i 0.134408 + 0.501617i 1.00000 0.000866600i \(0.000275847\pi\)
−0.865592 + 0.500750i \(0.833057\pi\)
\(312\) −3.14504 + 7.32125i −0.178053 + 0.414484i
\(313\) 0.613684 2.29030i 0.0346875 0.129455i −0.946411 0.322965i \(-0.895320\pi\)
0.981098 + 0.193510i \(0.0619871\pi\)
\(314\) −1.89834 14.6752i −0.107130 0.828172i
\(315\) 4.30672 + 9.25258i 0.242656 + 0.521324i
\(316\) 10.0325 + 5.85279i 0.564370 + 0.329245i
\(317\) −2.70787 + 3.52896i −0.152089 + 0.198206i −0.863184 0.504890i \(-0.831533\pi\)
0.711095 + 0.703096i \(0.248200\pi\)
\(318\) −4.93542 + 6.31965i −0.276765 + 0.354388i
\(319\) −0.473996 0.273662i −0.0265387 0.0153221i
\(320\) 10.2157 1.20440i 0.571076 0.0673280i
\(321\) −25.1035 + 3.14494i −1.40114 + 0.175533i
\(322\) −29.6548 + 9.66365i −1.65260 + 0.538534i
\(323\) 6.60240 2.73480i 0.367367 0.152169i
\(324\) 15.8480 8.53478i 0.880442 0.474154i
\(325\) −3.31373 4.31854i −0.183813 0.239549i
\(326\) 6.40377 15.3619i 0.354672 0.850816i
\(327\) 2.90296 21.0304i 0.160534 1.16298i
\(328\) −5.71503 0.0387048i −0.315560 0.00213711i
\(329\) 7.23207 8.08257i 0.398717 0.445606i
\(330\) 0.786601 1.33599i 0.0433009 0.0735439i
\(331\) 17.9655 2.36521i 0.987475 0.130004i 0.380548 0.924761i \(-0.375735\pi\)
0.606927 + 0.794758i \(0.292402\pi\)
\(332\) −4.62162 3.57956i −0.253644 0.196454i
\(333\) 6.10803 0.726338i 0.334718 0.0398031i
\(334\) 14.0043 + 8.12758i 0.766280 + 0.444722i
\(335\) 7.64813i 0.417862i
\(336\) −17.8820 4.02921i −0.975542 0.219812i
\(337\) 20.5265i 1.11815i 0.829117 + 0.559075i \(0.188843\pi\)
−0.829117 + 0.559075i \(0.811157\pi\)
\(338\) −7.35035 + 12.6651i −0.399806 + 0.688889i
\(339\) 0.175892 28.0520i 0.00955315 1.52357i
\(340\) −4.43752 + 0.563841i −0.240659 + 0.0305786i
\(341\) 2.95108 0.388517i 0.159810 0.0210394i
\(342\) −16.0032 6.90793i −0.865356 0.373538i
\(343\) −10.7453 + 15.0844i −0.580192 + 0.814480i
\(344\) −6.76526 16.6509i −0.364759 0.897754i
\(345\) 18.3901 + 2.53851i 0.990090 + 0.136669i
\(346\) 16.8288 + 7.01528i 0.904724 + 0.377144i
\(347\) 1.66965 + 2.17594i 0.0896317 + 0.116810i 0.836016 0.548704i \(-0.184879\pi\)
−0.746385 + 0.665515i \(0.768212\pi\)
\(348\) 2.37760 3.03031i 0.127453 0.162441i
\(349\) −22.7564 + 9.42600i −1.21812 + 0.504562i −0.896812 0.442412i \(-0.854123\pi\)
−0.321309 + 0.946974i \(0.604123\pi\)
\(350\) 8.37097 9.31301i 0.447447 0.497802i
\(351\) −7.86765 + 3.08682i −0.419944 + 0.164762i
\(352\) 1.03650 + 2.58446i 0.0552455 + 0.137752i
\(353\) 6.42867 + 3.71159i 0.342164 + 0.197548i 0.661228 0.750185i \(-0.270035\pi\)
−0.319065 + 0.947733i \(0.603369\pi\)
\(354\) −10.1574 + 13.0062i −0.539860 + 0.691273i
\(355\) 11.9900 15.6256i 0.636362 0.829323i
\(356\) 24.5321 6.45480i 1.30020 0.342104i
\(357\) 7.79172 + 1.68187i 0.412381 + 0.0890139i
\(358\) −2.53136 + 0.327448i −0.133787 + 0.0173062i
\(359\) −4.34886 + 16.2302i −0.229524 + 0.856596i 0.751017 + 0.660283i \(0.229564\pi\)
−0.980541 + 0.196313i \(0.937103\pi\)
\(360\) 8.52596 + 6.80777i 0.449357 + 0.358801i
\(361\) −0.548940 2.04867i −0.0288916 0.107825i
\(362\) −10.2354 1.37103i −0.537963 0.0720600i
\(363\) −17.9674 4.93530i −0.943043 0.259036i
\(364\) 8.10894 + 2.88428i 0.425024 + 0.151177i
\(365\) 16.8911 6.99651i 0.884118 0.366214i
\(366\) 0.467825 1.10274i 0.0244536 0.0576410i
\(367\) 14.9785 25.9436i 0.781874 1.35424i −0.148975 0.988841i \(-0.547598\pi\)
0.930849 0.365404i \(-0.119069\pi\)
\(368\) −23.7891 + 23.3633i −1.24009 + 1.21790i
\(369\) −4.23229 4.33979i −0.220324 0.225920i
\(370\) 1.85690 + 3.23307i 0.0965354 + 0.168079i
\(371\) 7.15299 + 4.88335i 0.371365 + 0.253531i
\(372\) −0.225910 + 20.9458i −0.0117129 + 1.08599i
\(373\) −2.73227 20.7537i −0.141472 1.07458i −0.903970 0.427595i \(-0.859361\pi\)
0.762499 0.646990i \(-0.223972\pi\)
\(374\) −0.460864 1.11977i −0.0238307 0.0579018i
\(375\) −17.2181 + 7.00581i −0.889138 + 0.361778i
\(376\) 3.07669 11.1790i 0.158668 0.576511i
\(377\) −1.27880 + 1.27880i −0.0658615 + 0.0658615i
\(378\) −10.2946 16.4931i −0.529498 0.848311i
\(379\) −9.92118 4.10949i −0.509617 0.211090i 0.113032 0.993591i \(-0.463944\pi\)
−0.622649 + 0.782501i \(0.713944\pi\)
\(380\) 0.0477009 10.5652i 0.00244700 0.541981i
\(381\) −32.7530 0.205369i −1.67799 0.0105214i
\(382\) −3.59082 3.60706i −0.183722 0.184553i
\(383\) −13.6571 23.6548i −0.697846 1.20871i −0.969212 0.246229i \(-0.920808\pi\)
0.271365 0.962476i \(-0.412525\pi\)
\(384\) −19.0355 + 4.65281i −0.971403 + 0.237438i
\(385\) −1.49442 0.755587i −0.0761629 0.0385083i
\(386\) −0.0559630 + 0.206987i −0.00284844 + 0.0105353i
\(387\) 7.51536 17.5190i 0.382027 0.890542i
\(388\) 17.5027 10.0001i 0.888563 0.507677i
\(389\) 1.64205 1.25999i 0.0832550 0.0638838i −0.566295 0.824202i \(-0.691624\pi\)
0.649550 + 0.760319i \(0.274957\pi\)
\(390\) −3.59133 3.65311i −0.181854 0.184982i
\(391\) 10.2528 10.2528i 0.518508 0.518508i
\(392\) −3.10773 + 19.5536i −0.156964 + 0.987604i
\(393\) −4.57292 + 5.88280i −0.230673 + 0.296748i
\(394\) −16.2923 2.18235i −0.820795 0.109945i
\(395\) −5.92417 + 4.54577i −0.298077 + 0.228723i
\(396\) −1.17661 + 2.70897i −0.0591270 + 0.136131i
\(397\) −18.8737 + 24.5967i −0.947246 + 1.23447i 0.0248021 + 0.999692i \(0.492104\pi\)
−0.972048 + 0.234782i \(0.924562\pi\)
\(398\) −7.49207 13.0446i −0.375544 0.653865i
\(399\) −6.34053 + 17.7273i −0.317423 + 0.887476i
\(400\) 3.58137 12.8988i 0.179069 0.644942i
\(401\) 8.65420 + 14.9895i 0.432170 + 0.748540i 0.997060 0.0766259i \(-0.0244147\pi\)
−0.564890 + 0.825166i \(0.691081\pi\)
\(402\) 1.77850 + 14.4609i 0.0887033 + 0.721244i
\(403\) 1.28376 9.75112i 0.0639486 0.485738i
\(404\) −3.62876 + 8.64994i −0.180538 + 0.430351i
\(405\) 1.22228 + 11.5075i 0.0607358 + 0.571814i
\(406\) −3.43066 2.35348i −0.170261 0.116801i
\(407\) −0.713665 + 0.713665i −0.0353751 + 0.0353751i
\(408\) 8.25924 2.09800i 0.408893 0.103866i
\(409\) −13.2423 + 3.54826i −0.654789 + 0.175450i −0.570893 0.821024i \(-0.693403\pi\)
−0.0838959 + 0.996475i \(0.526736\pi\)
\(410\) 1.41375 3.39143i 0.0698203 0.167491i
\(411\) 5.24663 + 20.0836i 0.258797 + 0.990649i
\(412\) −16.5217 + 4.34712i −0.813965 + 0.214167i
\(413\) 14.7213 + 10.0502i 0.724388 + 0.494539i
\(414\) −35.3618 0.523313i −1.73794 0.0257194i
\(415\) 3.25473 1.87912i 0.159769 0.0922425i
\(416\) 9.13513 1.09792i 0.447886 0.0538298i
\(417\) −3.35297 1.41354i −0.164196 0.0692213i
\(418\) 2.76423 0.733990i 0.135203 0.0359006i
\(419\) 21.4772 8.89614i 1.04923 0.434605i 0.209612 0.977785i \(-0.432780\pi\)
0.839616 + 0.543180i \(0.182780\pi\)
\(420\) 6.74915 9.66056i 0.329325 0.471387i
\(421\) −0.898205 + 2.16846i −0.0437759 + 0.105684i −0.944255 0.329215i \(-0.893216\pi\)
0.900479 + 0.434899i \(0.143216\pi\)
\(422\) 22.9879 17.5569i 1.11903 0.854656i
\(423\) 10.7266 6.01494i 0.521545 0.292456i
\(424\) 9.17136 + 1.27068i 0.445400 + 0.0617096i
\(425\) −1.50669 + 5.62306i −0.0730854 + 0.272758i
\(426\) −19.0368 + 32.3327i −0.922334 + 1.56653i
\(427\) −1.22097 0.428090i −0.0590871 0.0207167i
\(428\) 17.6793 + 23.2568i 0.854561 + 1.12416i
\(429\) 0.700886 1.19658i 0.0338391 0.0577714i
\(430\) 11.5547 + 0.0260842i 0.557218 + 0.00125789i
\(431\) −0.281144 0.162318i −0.0135422 0.00781860i 0.493214 0.869908i \(-0.335822\pi\)
−0.506756 + 0.862090i \(0.669155\pi\)
\(432\) −17.7037 10.8893i −0.851772 0.523913i
\(433\) 9.68527i 0.465444i 0.972543 + 0.232722i \(0.0747633\pi\)
−0.972543 + 0.232722i \(0.925237\pi\)
\(434\) 22.5934 1.20357i 1.08452 0.0577731i
\(435\) 1.22467 + 2.15225i 0.0587185 + 0.103192i
\(436\) −22.6902 + 9.27878i −1.08666 + 0.444373i
\(437\) 20.8481 + 27.1698i 0.997302 + 1.29971i
\(438\) −30.3102 + 17.1567i −1.44828 + 0.819777i
\(439\) 3.24814 12.1222i 0.155025 0.578561i −0.844078 0.536220i \(-0.819852\pi\)
0.999103 0.0423412i \(-0.0134817\pi\)
\(440\) −1.79016 0.0121238i −0.0853425 0.000577977i
\(441\) −17.0668 + 12.2361i −0.812706 + 0.582674i
\(442\) −3.96805 + 0.513294i −0.188741 + 0.0244149i
\(443\) −37.0417 + 4.87663i −1.75990 + 0.231696i −0.940088 0.340932i \(-0.889258\pi\)
−0.819816 + 0.572627i \(0.805924\pi\)
\(444\) −4.26279 5.68120i −0.202303 0.269618i
\(445\) −2.12870 + 16.1691i −0.100910 + 0.766489i
\(446\) −3.48300 13.1171i −0.164925 0.621114i
\(447\) −5.12126 40.8789i −0.242227 1.93351i
\(448\) 6.33042 + 20.1972i 0.299084 + 0.954227i
\(449\) 4.87830i 0.230221i −0.993353 0.115111i \(-0.963278\pi\)
0.993353 0.115111i \(-0.0367223\pi\)
\(450\) 12.4003 6.91669i 0.584554 0.326056i
\(451\) 0.986127 + 0.129826i 0.0464349 + 0.00611327i
\(452\) −28.1254 + 16.0693i −1.32291 + 0.755837i
\(453\) −6.08005 23.2738i −0.285666 1.09350i
\(454\) −4.06801 31.4481i −0.190921 1.47593i
\(455\) −3.68961 + 4.12352i −0.172972 + 0.193313i
\(456\) 2.36663 + 19.9874i 0.110828 + 0.935996i
\(457\) −5.18444 1.38917i −0.242518 0.0649825i 0.135513 0.990776i \(-0.456732\pi\)
−0.378031 + 0.925793i \(0.623399\pi\)
\(458\) 32.1726 13.2413i 1.50333 0.618726i
\(459\) 7.74114 + 4.66566i 0.361326 + 0.217774i
\(460\) −8.11386 19.8415i −0.378311 0.925115i
\(461\) 0.0979730 0.0405817i 0.00456306 0.00189008i −0.380401 0.924822i \(-0.624214\pi\)
0.384964 + 0.922932i \(0.374214\pi\)
\(462\) 3.00132 + 1.08113i 0.139634 + 0.0502988i
\(463\) 39.0331 1.81402 0.907012 0.421106i \(-0.138358\pi\)
0.907012 + 0.421106i \(0.138358\pi\)
\(464\) −4.40411 0.620318i −0.204456 0.0287976i
\(465\) −12.4093 5.23148i −0.575466 0.242604i
\(466\) 0.0255210 11.3052i 0.00118224 0.523704i
\(467\) 10.9603 14.2838i 0.507184 0.660975i −0.467648 0.883915i \(-0.654899\pi\)
0.974832 + 0.222940i \(0.0715653\pi\)
\(468\) 7.63988 + 6.07207i 0.353154 + 0.280682i
\(469\) 15.4647 2.91612i 0.714093 0.134654i
\(470\) 5.90358 + 4.55118i 0.272312 + 0.209930i
\(471\) −17.9530 2.47817i −0.827228 0.114188i
\(472\) 18.8752 + 2.61513i 0.868802 + 0.120371i
\(473\) 0.809555 + 3.02130i 0.0372234 + 0.138920i
\(474\) 10.1442 9.97263i 0.465938 0.458058i
\(475\) −12.7030 5.26175i −0.582853 0.241426i
\(476\) −2.83206 8.75779i −0.129807 0.401413i
\(477\) 5.88024 + 7.86557i 0.269238 + 0.360140i
\(478\) −0.237336 0.893818i −0.0108555 0.0408823i
\(479\) 16.0872 27.8639i 0.735044 1.27313i −0.219661 0.975576i \(-0.570495\pi\)
0.954704 0.297556i \(-0.0961716\pi\)
\(480\) 1.86344 12.4597i 0.0850542 0.568706i
\(481\) 1.66745 + 2.88811i 0.0760291 + 0.131686i
\(482\) 7.96725 + 2.15411i 0.362898 + 0.0981169i
\(483\) 1.87895 + 38.1531i 0.0854951 + 1.73603i
\(484\) 5.47471 + 20.8072i 0.248850 + 0.945782i
\(485\) 1.69157 + 12.8488i 0.0768104 + 0.583433i
\(486\) −4.98702 21.4739i −0.226216 0.974077i
\(487\) −6.95980 25.9743i −0.315379 1.17701i −0.923636 0.383270i \(-0.874798\pi\)
0.608258 0.793740i \(-0.291869\pi\)
\(488\) −1.37254 + 0.171250i −0.0621319 + 0.00775212i
\(489\) −16.0933 12.5099i −0.727765 0.565719i
\(490\) −10.8795 6.60757i −0.491486 0.298500i
\(491\) 30.8066 + 12.7605i 1.39028 + 0.575874i 0.947210 0.320613i \(-0.103889\pi\)
0.443072 + 0.896486i \(0.353889\pi\)
\(492\) −1.88445 + 6.74118i −0.0849574 + 0.303916i
\(493\) 1.91754 + 0.252449i 0.0863617 + 0.0113697i
\(494\) 0.0213334 9.45022i 0.000959835 0.425185i
\(495\) −1.32571 1.35938i −0.0595861 0.0610996i
\(496\) 21.0554 11.9041i 0.945415 0.534512i
\(497\) 36.1670 + 18.2862i 1.62231 + 0.820247i
\(498\) −5.71700 + 4.30985i −0.256185 + 0.193129i
\(499\) −26.8177 20.5780i −1.20053 0.921196i −0.202218 0.979340i \(-0.564815\pi\)
−0.998308 + 0.0581440i \(0.981482\pi\)
\(500\) 16.9698 + 13.1435i 0.758911 + 0.587796i
\(501\) 14.1102 13.9344i 0.630399 0.622543i
\(502\) −4.64786 + 34.6986i −0.207444 + 1.54867i
\(503\) 16.3056 16.3056i 0.727030 0.727030i −0.242997 0.970027i \(-0.578130\pi\)
0.970027 + 0.242997i \(0.0781305\pi\)
\(504\) −10.5147 + 19.8354i −0.468360 + 0.883538i
\(505\) −4.26429 4.26429i −0.189758 0.189758i
\(506\) 4.61168 3.52215i 0.205014 0.156579i
\(507\) 12.6019 + 12.7609i 0.559668 + 0.566731i
\(508\) 18.7623 + 32.8387i 0.832442 + 1.45698i
\(509\) 9.96036 12.9806i 0.441485 0.575355i −0.518616 0.855007i \(-0.673553\pi\)
0.960101 + 0.279653i \(0.0902193\pi\)
\(510\) −0.761384 + 5.42537i −0.0337147 + 0.240239i
\(511\) 20.5874 + 31.4864i 0.910733 + 1.39288i
\(512\) 15.6716 + 16.3217i 0.692596 + 0.721326i
\(513\) −13.3121 + 16.6890i −0.587742 + 0.736838i
\(514\) −19.1684 + 19.0821i −0.845482 + 0.841674i
\(515\) 1.43362 10.8894i 0.0631728 0.479845i
\(516\) −21.8534 + 2.63761i −0.962044 + 0.116115i
\(517\) −0.772203 + 1.86426i −0.0339615 + 0.0819902i
\(518\) −5.82933 + 4.98740i −0.256126 + 0.219134i
\(519\) 13.7045 17.6301i 0.601563 0.773876i
\(520\) −1.56965 + 5.70322i −0.0688335 + 0.250103i
\(521\) 26.2088 7.02263i 1.14823 0.307667i 0.365974 0.930625i \(-0.380736\pi\)
0.782255 + 0.622958i \(0.214069\pi\)
\(522\) −2.81606 3.78462i −0.123256 0.165649i
\(523\) 34.3552 4.52295i 1.50225 0.197775i 0.665929 0.746015i \(-0.268035\pi\)
0.836321 + 0.548240i \(0.184702\pi\)
\(524\) 8.52502 + 1.16152i 0.372417 + 0.0507413i
\(525\) −8.31227 12.8885i −0.362777 0.562502i
\(526\) −21.5443 + 12.3739i −0.939377 + 0.539526i
\(527\) −9.10909 + 5.25914i −0.396798 + 0.229092i
\(528\) 3.38761 0.393360i 0.147427 0.0171188i
\(529\) 40.2574 + 23.2426i 1.75032 + 1.01055i
\(530\) −2.98794 + 5.14839i −0.129788 + 0.223632i
\(531\) 12.1019 + 16.1878i 0.525178 + 0.702492i
\(532\) 21.3812 3.93188i 0.926991 0.170469i
\(533\) 1.25770 3.03636i 0.0544770 0.131519i
\(534\) 0.264934 31.0671i 0.0114648 1.34441i
\(535\) −18.1416 + 4.86102i −0.784329 + 0.210160i
\(536\) 13.4163 10.1511i 0.579495 0.438459i
\(537\) −0.427464 + 3.09674i −0.0184464 + 0.133634i
\(538\) −1.50488 11.6336i −0.0648801 0.501560i
\(539\) 0.958012 3.30985i 0.0412645 0.142565i
\(540\) 10.7880 7.88511i 0.464243 0.339321i
\(541\) 7.30838 + 5.60792i 0.314212 + 0.241103i 0.753812 0.657090i \(-0.228213\pi\)
−0.439600 + 0.898194i \(0.644880\pi\)
\(542\) 21.7856 + 21.8842i 0.935774 + 0.940008i
\(543\) −4.91326 + 11.6544i −0.210848 + 0.500140i
\(544\) −6.87883 7.03590i −0.294927 0.301662i
\(545\) 15.7602i 0.675092i
\(546\) 6.01735 8.65462i 0.257519 0.370384i
\(547\) −8.20867 19.8175i −0.350977 0.847334i −0.996500 0.0835931i \(-0.973360\pi\)
0.645523 0.763741i \(-0.276640\pi\)
\(548\) 17.0248 16.8718i 0.727265 0.720727i
\(549\) −1.15263 0.907630i −0.0491928 0.0387367i
\(550\) −0.896419 + 2.15040i −0.0382234 + 0.0916935i
\(551\) −1.18232 + 4.41247i −0.0503684 + 0.187977i
\(552\) 19.9554 + 35.6290i 0.849359 + 1.51647i
\(553\) −11.4504 10.2456i −0.486923 0.435686i
\(554\) −19.5862 + 25.4063i −0.832140 + 1.07941i
\(555\) 4.41804 1.15417i 0.187535 0.0489918i
\(556\) 0.529614 + 4.16815i 0.0224606 + 0.176769i
\(557\) −2.59852 + 19.7377i −0.110103 + 0.836313i 0.843897 + 0.536505i \(0.180256\pi\)
−0.954000 + 0.299808i \(0.903077\pi\)
\(558\) 24.6797 + 7.00590i 1.04477 + 0.296584i
\(559\) 10.3353 0.437137
\(560\) −13.5592 1.14783i −0.572981 0.0485045i
\(561\) −1.47154 + 0.184353i −0.0621284 + 0.00778338i
\(562\) 4.85757 8.36986i 0.204904 0.353061i
\(563\) −42.9040 5.64842i −1.80819 0.238053i −0.850524 0.525936i \(-0.823715\pi\)
−0.957665 + 0.287884i \(0.907048\pi\)
\(564\) −12.2207 7.23244i −0.514583 0.304541i
\(565\) −2.71822 20.6470i −0.114357 0.868624i
\(566\) 19.0805 24.7502i 0.802011 1.04033i
\(567\) −22.8025 + 6.85914i −0.957613 + 0.288057i
\(568\) 43.3242 + 0.293411i 1.81784 + 0.0123112i
\(569\) −2.75246 0.737519i −0.115389 0.0309184i 0.200662 0.979660i \(-0.435691\pi\)
−0.316052 + 0.948742i \(0.602357\pi\)
\(570\) −12.4698 3.45552i −0.522303 0.144736i
\(571\) −28.0033 + 21.4876i −1.17190 + 0.899230i −0.996360 0.0852423i \(-0.972834\pi\)
−0.175539 + 0.984472i \(0.556167\pi\)
\(572\) −1.60125 0.00722954i −0.0669517 0.000302282i
\(573\) −5.41786 + 3.08287i −0.226334 + 0.128789i
\(574\) 7.39659 + 1.56554i 0.308728 + 0.0653444i
\(575\) −27.8973 −1.16340
\(576\) −0.625968 + 23.9918i −0.0260820 + 0.999660i
\(577\) −9.94471 + 17.2248i −0.414004 + 0.717076i −0.995323 0.0965997i \(-0.969203\pi\)
0.581319 + 0.813675i \(0.302537\pi\)
\(578\) −13.9427 14.0058i −0.579941 0.582565i
\(579\) 0.226598 + 0.132727i 0.00941707 + 0.00551597i
\(580\) 1.44085 2.46980i 0.0598280 0.102553i
\(581\) 5.04061 + 5.86466i 0.209120 + 0.243307i
\(582\) −6.18624 23.9008i −0.256428 0.990720i
\(583\) −1.55647 0.417056i −0.0644625 0.0172727i
\(584\) 34.6920 + 20.3439i 1.43557 + 0.841839i
\(585\) −5.47244 + 3.06866i −0.226257 + 0.126874i
\(586\) 19.5047 + 2.61265i 0.805733 + 0.107928i
\(587\) −38.8683 16.0998i −1.60427 0.664509i −0.612255 0.790660i \(-0.709738\pi\)
−0.992011 + 0.126151i \(0.959738\pi\)
\(588\) 22.1072 + 9.96350i 0.911686 + 0.410888i
\(589\) −9.50705 22.9521i −0.391731 0.945723i
\(590\) −6.14937 + 10.5957i −0.253166 + 0.436218i
\(591\) −7.82071 + 18.5510i −0.321701 + 0.763086i
\(592\) −3.20684 + 7.54847i −0.131800 + 0.310240i
\(593\) −5.30449 9.18765i −0.217829 0.377292i 0.736315 0.676639i \(-0.236564\pi\)
−0.954144 + 0.299348i \(0.903231\pi\)
\(594\) 2.82272 + 2.26200i 0.115818 + 0.0928111i
\(595\) 5.90067 + 0.445884i 0.241904 + 0.0182795i
\(596\) −37.8717 + 28.7892i −1.55128 + 1.17925i
\(597\) −17.8256 + 4.65676i −0.729553 + 0.190589i
\(598\) −7.29760 17.7311i −0.298421 0.725078i
\(599\) −5.53711 20.6648i −0.226240 0.844339i −0.981904 0.189380i \(-0.939352\pi\)
0.755664 0.654960i \(-0.227314\pi\)
\(600\) −14.0907 8.38219i −0.575251 0.342201i
\(601\) 29.6762 + 29.6762i 1.21052 + 1.21052i 0.970856 + 0.239662i \(0.0770367\pi\)
0.239662 + 0.970856i \(0.422963\pi\)
\(602\) 4.35290 + 23.3738i 0.177411 + 0.952647i
\(603\) 17.6611 + 2.55082i 0.719215 + 0.103878i
\(604\) −19.7292 + 19.5519i −0.802770 + 0.795554i
\(605\) −13.7140 1.80548i −0.557553 0.0734033i
\(606\) 9.05442 + 7.07119i 0.367811 + 0.287247i
\(607\) 30.0293 17.3374i 1.21885 0.703704i 0.254179 0.967157i \(-0.418195\pi\)
0.964672 + 0.263453i \(0.0848614\pi\)
\(608\) 18.5966 13.9390i 0.754192 0.565302i
\(609\) −3.88494 + 3.29693i −0.157426 + 0.133598i
\(610\) 0.232094 0.858430i 0.00939720 0.0347568i
\(611\) 5.28971 + 4.05894i 0.213999 + 0.164207i
\(612\) 0.177991 10.4352i 0.00719487 0.421818i
\(613\) 23.1868 + 30.2177i 0.936507 + 1.22048i 0.975222 + 0.221230i \(0.0710071\pi\)
−0.0387143 + 0.999250i \(0.512326\pi\)
\(614\) −32.1252 + 24.5355i −1.29647 + 0.990172i
\(615\) −3.55291 2.76181i −0.143267 0.111367i
\(616\) −0.658046 3.62436i −0.0265134 0.146030i
\(617\) −3.17065 3.17065i −0.127645 0.127645i 0.640398 0.768043i \(-0.278769\pi\)
−0.768043 + 0.640398i \(0.778769\pi\)
\(618\) −0.178425 + 20.9228i −0.00717731 + 0.841638i
\(619\) 9.68775 + 12.6253i 0.389383 + 0.507454i 0.946378 0.323062i \(-0.104712\pi\)
−0.556994 + 0.830516i \(0.688046\pi\)
\(620\) 1.96009 + 15.4263i 0.0787192 + 0.619533i
\(621\) −11.9954 + 41.6198i −0.481361 + 1.67015i
\(622\) −6.45047 11.2310i −0.258640 0.450322i
\(623\) −33.5059 + 1.86075i −1.34239 + 0.0745494i
\(624\) 1.64162 11.1485i 0.0657174 0.446297i
\(625\) 2.54081 1.46694i 0.101633 0.0586776i
\(626\) −0.00756973 + 3.35322i −0.000302547 + 0.134022i
\(627\) 0.0219629 3.50273i 0.000877113 0.139886i
\(628\) 7.92099 + 19.3698i 0.316082 + 0.772941i
\(629\) 1.36484 3.29501i 0.0544196 0.131381i
\(630\) −9.24477 11.0838i −0.368320 0.441589i
\(631\) 0.708057 + 0.708057i 0.0281873 + 0.0281873i 0.721060 0.692873i \(-0.243655\pi\)
−0.692873 + 0.721060i \(0.743655\pi\)
\(632\) −15.8371 4.35869i −0.629964 0.173379i
\(633\) −13.3516 32.8141i −0.530679 1.30424i
\(634\) 2.42044 5.80635i 0.0961279 0.230600i
\(635\) −24.1071 + 3.17375i −0.956660 + 0.125947i
\(636\) 4.45232 10.4293i 0.176546 0.413547i
\(637\) −9.74464 5.88825i −0.386097 0.233301i
\(638\) 0.747204 + 0.202022i 0.0295821 + 0.00799811i
\(639\) 32.0838 + 32.8988i 1.26922 + 1.30146i
\(640\) −13.5262 + 5.35393i −0.534670 + 0.211633i
\(641\) −2.28337 1.31831i −0.0901878 0.0520700i 0.454228 0.890886i \(-0.349915\pi\)
−0.544416 + 0.838816i \(0.683249\pi\)
\(642\) 33.1712 13.4097i 1.30916 0.529240i
\(643\) −8.13184 19.6320i −0.320688 0.774210i −0.999214 0.0396336i \(-0.987381\pi\)
0.678526 0.734576i \(-0.262619\pi\)
\(644\) 37.0263 23.9717i 1.45904 0.944616i
\(645\) 3.74835 13.6462i 0.147591 0.537318i
\(646\) −8.03191 + 6.13434i −0.316011 + 0.241352i
\(647\) −8.35547 + 2.23884i −0.328487 + 0.0880180i −0.419294 0.907851i \(-0.637722\pi\)
0.0908063 + 0.995869i \(0.471056\pi\)
\(648\) −18.5641 + 17.4176i −0.729268 + 0.684229i
\(649\) −3.20332 0.858327i −0.125741 0.0336923i
\(650\) 6.09674 + 4.70010i 0.239134 + 0.184353i
\(651\) 5.84671 27.0865i 0.229151 1.06160i
\(652\) −3.17752 + 23.3216i −0.124441 + 0.913343i
\(653\) −18.5047 14.1992i −0.724145 0.555656i 0.179593 0.983741i \(-0.442522\pi\)
−0.903739 + 0.428085i \(0.859189\pi\)
\(654\) 3.66487 + 29.7989i 0.143308 + 1.16523i
\(655\) −2.76570 + 4.79034i −0.108065 + 0.187174i
\(656\) 7.82563 2.02132i 0.305540 0.0789191i
\(657\) 10.5228 + 41.3384i 0.410534 + 1.61276i
\(658\) −6.95165 + 13.6725i −0.271003 + 0.533008i
\(659\) 1.91215 + 4.61634i 0.0744868 + 0.179827i 0.956737 0.290953i \(-0.0939724\pi\)
−0.882250 + 0.470780i \(0.843972\pi\)
\(660\) −0.590278 + 2.11159i −0.0229765 + 0.0821934i
\(661\) −11.0387 + 8.47026i −0.429354 + 0.329455i −0.800728 0.599029i \(-0.795554\pi\)
0.371374 + 0.928483i \(0.378887\pi\)
\(662\) −23.6977 + 9.75331i −0.921038 + 0.379073i
\(663\) −0.670074 + 4.85432i −0.0260235 + 0.188526i
\(664\) 7.61622 + 3.21534i 0.295567 + 0.124779i
\(665\) −2.86324 + 13.6801i −0.111032 + 0.530491i
\(666\) −8.08513 + 3.20965i −0.313292 + 0.124371i
\(667\) 1.20978 + 9.18921i 0.0468430 + 0.355808i
\(668\) −22.0916 6.02645i −0.854748 0.233170i
\(669\) −16.6215 0.104221i −0.642625 0.00402940i
\(670\) 2.77582 + 10.4538i 0.107239 + 0.403867i
\(671\) 0.240721 0.00929294
\(672\) 25.9043 0.982779i 0.999281 0.0379115i
\(673\) 29.9251 1.15353 0.576765 0.816910i \(-0.304315\pi\)
0.576765 + 0.816910i \(0.304315\pi\)
\(674\) −7.44990 28.0566i −0.286959 1.08070i
\(675\) −4.18411 16.8791i −0.161046 0.649677i
\(676\) 5.45014 19.9790i 0.209621 0.768421i
\(677\) 5.68180 + 43.1575i 0.218369 + 1.65868i 0.652470 + 0.757815i \(0.273733\pi\)
−0.434100 + 0.900865i \(0.642934\pi\)
\(678\) 9.94079 + 38.4066i 0.381774 + 1.47500i
\(679\) −25.3356 + 8.31945i −0.972289 + 0.319271i
\(680\) 5.86078 2.38124i 0.224751 0.0913165i
\(681\) −38.4720 5.31054i −1.47425 0.203500i
\(682\) −3.89267 + 1.60211i −0.149058 + 0.0613480i
\(683\) −2.77583 + 2.12997i −0.106214 + 0.0815011i −0.660503 0.750823i \(-0.729657\pi\)
0.554289 + 0.832324i \(0.312990\pi\)
\(684\) 24.3812 + 3.63387i 0.932237 + 0.138944i
\(685\) 5.89701 + 14.2366i 0.225313 + 0.543954i
\(686\) 9.21246 24.5180i 0.351733 0.936100i
\(687\) −5.29673 42.2795i −0.202083 1.61306i
\(688\) 15.2904 + 20.3038i 0.582940 + 0.774075i
\(689\) −2.66220 + 4.61107i −0.101422 + 0.175668i
\(690\) −26.0578 + 3.20476i −0.992004 + 0.122003i
\(691\) 20.5646 + 15.7798i 0.782314 + 0.600291i 0.920783 0.390076i \(-0.127551\pi\)
−0.138468 + 0.990367i \(0.544218\pi\)
\(692\) −25.5486 3.48096i −0.971212 0.132326i
\(693\) 2.24323 3.19892i 0.0852131 0.121517i
\(694\) −3.07190 2.36819i −0.116608 0.0898952i
\(695\) −2.60922 0.699139i −0.0989735 0.0265199i
\(696\) −2.14999 + 5.00489i −0.0814952 + 0.189710i
\(697\) −3.39500 + 0.909688i −0.128595 + 0.0344569i
\(698\) 27.6834 21.1431i 1.04783 0.800279i
\(699\) −13.3515 3.66741i −0.505001 0.138714i
\(700\) −8.06178 + 15.7676i −0.304707 + 0.595961i
\(701\) −15.9689 38.5523i −0.603136 1.45610i −0.870336 0.492458i \(-0.836098\pi\)
0.267200 0.963641i \(-0.413902\pi\)
\(702\) 9.63355 7.07471i 0.363595 0.267018i
\(703\) 7.29514 + 4.21185i 0.275141 + 0.158853i
\(704\) −2.35474 3.15637i −0.0887476 0.118960i
\(705\) 7.27764 5.51218i 0.274092 0.207601i
\(706\) −10.1341 2.73996i −0.381402 0.103120i
\(707\) 6.99657 10.2484i 0.263133 0.385430i
\(708\) 9.16314 21.4641i 0.344372 0.806669i
\(709\) −24.7195 + 3.25438i −0.928360 + 0.122221i −0.579517 0.814960i \(-0.696759\pi\)
−0.348843 + 0.937181i \(0.613425\pi\)
\(710\) −10.7173 + 25.7095i −0.402213 + 0.964862i
\(711\) −8.52127 15.1962i −0.319572 0.569903i
\(712\) −31.1890 + 17.7264i −1.16886 + 0.664327i
\(713\) −35.6421 35.6421i −1.33481 1.33481i
\(714\) −11.2605 + 0.529075i −0.421414 + 0.0198001i
\(715\) 0.393958 0.951099i 0.0147332 0.0355691i
\(716\) 3.34114 1.36631i 0.124864 0.0510613i
\(717\) −1.13261 0.00710172i −0.0422981 0.000265219i
\(718\) 0.0536428 23.7626i 0.00200193 0.886811i
\(719\) 40.0065 23.0978i 1.49199 0.861401i 0.492032 0.870577i \(-0.336254\pi\)
0.999958 + 0.00917582i \(0.00292080\pi\)
\(720\) −14.1245 6.21078i −0.526389 0.231462i
\(721\) 22.5652 1.25316i 0.840374 0.0466701i
\(722\) 1.49386 + 2.60099i 0.0555959 + 0.0967989i
\(723\) 5.10889 8.72210i 0.190002 0.324379i
\(724\) 14.4879 1.84086i 0.538438 0.0684151i
\(725\) −2.26531 2.95221i −0.0841314 0.109642i
\(726\) 26.3499 + 0.224707i 0.977937 + 0.00833964i
\(727\) 29.2754 + 29.2754i 1.08577 + 1.08577i 0.995959 + 0.0898062i \(0.0286248\pi\)
0.0898062 + 0.995959i \(0.471375\pi\)
\(728\) −12.1305 0.999307i −0.449587 0.0370368i
\(729\) −26.9809 1.01552i −0.999292 0.0376120i
\(730\) −20.5482 + 15.6936i −0.760523 + 0.580847i
\(731\) −6.72867 8.76897i −0.248869 0.324332i
\(732\) −0.239218 + 1.67707i −0.00884174 + 0.0619862i
\(733\) −5.47458 4.20079i −0.202208 0.155160i 0.502694 0.864465i \(-0.332342\pi\)
−0.704902 + 0.709305i \(0.749009\pi\)
\(734\) −11.0574 + 40.8973i −0.408136 + 1.50955i
\(735\) −11.3087 + 10.7308i −0.417126 + 0.395811i
\(736\) 24.0366 40.5681i 0.886000 1.49536i
\(737\) −2.53566 + 1.46396i −0.0934021 + 0.0539258i
\(738\) 7.35998 + 4.39576i 0.270925 + 0.161810i
\(739\) −31.2131 4.10928i −1.14819 0.151162i −0.467679 0.883898i \(-0.654910\pi\)
−0.680513 + 0.732736i \(0.738243\pi\)
\(740\) −3.71151 3.74517i −0.136438 0.137675i
\(741\) −11.1608 3.06565i −0.410000 0.112619i
\(742\) −11.5494 4.07868i −0.423993 0.149733i
\(743\) 25.5939 + 25.5939i 0.938951 + 0.938951i 0.998241 0.0592902i \(-0.0188837\pi\)
−0.0592902 + 0.998241i \(0.518884\pi\)
\(744\) −7.29331 28.7118i −0.267386 1.05262i
\(745\) −7.91576 29.5420i −0.290011 1.08234i
\(746\) 11.2670 + 27.3755i 0.412513 + 1.00229i
\(747\) 3.25375 + 8.14257i 0.119048 + 0.297921i
\(748\) 1.03634 + 1.36329i 0.0378924 + 0.0498467i
\(749\) −16.7462 34.8292i −0.611893 1.27263i
\(750\) 20.9918 15.8250i 0.766512 0.577848i
\(751\) 23.0828 + 39.9805i 0.842303 + 1.45891i 0.887943 + 0.459953i \(0.152134\pi\)
−0.0456409 + 0.998958i \(0.514533\pi\)
\(752\) −0.148062 + 16.3966i −0.00539926 + 0.597922i
\(753\) 39.5090 + 16.6562i 1.43979 + 0.606984i
\(754\) 1.28380 2.21205i 0.0467531 0.0805582i
\(755\) −6.83374 16.4981i −0.248705 0.600427i
\(756\) 20.0572 + 18.8072i 0.729473 + 0.684010i
\(757\) −37.8087 15.6609i −1.37418 0.569204i −0.431261 0.902227i \(-0.641931\pi\)
−0.942919 + 0.333023i \(0.891931\pi\)
\(758\) 15.0522 + 2.01624i 0.546722 + 0.0732333i
\(759\) −2.67851 6.58295i −0.0972239 0.238946i
\(760\) 3.76932 + 14.4583i 0.136728 + 0.524457i
\(761\) −47.0669 12.6115i −1.70617 0.457168i −0.731692 0.681635i \(-0.761269\pi\)
−0.974482 + 0.224467i \(0.927936\pi\)
\(762\) 44.8430 11.6067i 1.62449 0.420467i
\(763\) 31.8674 6.00912i 1.15368 0.217545i
\(764\) 6.21725 + 3.62706i 0.224932 + 0.131222i
\(765\) 6.16636 + 2.64526i 0.222945 + 0.0956397i
\(766\) 27.2525 + 27.3758i 0.984673 + 0.989129i
\(767\) −5.47898 + 9.48987i −0.197834 + 0.342659i
\(768\) 24.3300 13.2684i 0.877933 0.478784i
\(769\) −26.7035 −0.962953 −0.481477 0.876459i \(-0.659899\pi\)
−0.481477 + 0.876459i \(0.659899\pi\)
\(770\) 2.31688 + 0.490385i 0.0834947 + 0.0176723i
\(771\) 16.3828 + 28.7912i 0.590011 + 1.03689i
\(772\) 0.00136906 0.303231i 4.92737e−5 0.0109135i
\(773\) 19.4118 14.8952i 0.698194 0.535743i −0.197561 0.980291i \(-0.563302\pi\)
0.895755 + 0.444547i \(0.146635\pi\)
\(774\) −3.91399 + 26.6735i −0.140686 + 0.958759i
\(775\) 19.5476 + 5.23775i 0.702169 + 0.188146i
\(776\) −20.2941 + 20.0210i −0.728514 + 0.718713i
\(777\) 4.01829 + 8.49331i 0.144155 + 0.304696i
\(778\) −1.78713 + 2.31817i −0.0640716 + 0.0831106i
\(779\) −1.08357 8.23050i −0.0388228 0.294888i
\(780\) 6.23466 + 3.68980i 0.223237 + 0.132116i
\(781\) −7.47557 0.984178i −0.267497 0.0352166i
\(782\) −10.2929 + 17.7352i −0.368073 + 0.634210i
\(783\) −5.37842 + 2.11019i −0.192209 + 0.0754121i
\(784\) −2.84899 27.8547i −0.101750 0.994810i
\(785\) −13.4540 −0.480192
\(786\) 4.11538 9.70059i 0.146791 0.346009i
\(787\) 6.08245 46.2008i 0.216816 1.64688i −0.443777 0.896137i \(-0.646362\pi\)
0.660593 0.750744i \(-0.270305\pi\)
\(788\) 23.0612 2.93020i 0.821521 0.104384i
\(789\) 7.69108 + 29.4407i 0.273810 + 1.04812i
\(790\) 6.44759 8.36350i 0.229395 0.297560i
\(791\) 40.7122 13.3687i 1.44756 0.475336i
\(792\) 0.625054 4.12980i 0.0222103 0.146746i
\(793\) 0.205866 0.768301i 0.00731050 0.0272832i
\(794\) 16.8704 40.4701i 0.598707 1.43623i
\(795\) 5.12270 + 5.18735i 0.181683 + 0.183976i
\(796\) 14.9749 + 15.1108i 0.530772 + 0.535587i
\(797\) −5.96087 14.3908i −0.211145 0.509749i 0.782455 0.622707i \(-0.213967\pi\)
−0.993600 + 0.112959i \(0.963967\pi\)
\(798\) 2.23257 26.5318i 0.0790322 0.939215i
\(799\) 7.13056i 0.252261i
\(800\) −0.213683 + 18.9306i −0.00755483 + 0.669297i
\(801\) −36.6277 10.3084i −1.29418 0.364228i
\(802\) −17.2693 17.3474i −0.609799 0.612559i
\(803\) −5.55281 4.26082i −0.195954 0.150361i
\(804\) −7.67938 19.1204i −0.270831 0.674323i
\(805\) 5.25470 + 27.8666i 0.185204 + 0.982169i
\(806\) 1.78437 + 13.7942i 0.0628519 + 0.485881i
\(807\) −14.2320 1.96453i −0.500988 0.0691548i
\(808\) 1.82055 13.1402i 0.0640468 0.462270i
\(809\) −13.4872 + 3.61390i −0.474186 + 0.127058i −0.487994 0.872847i \(-0.662271\pi\)
0.0138080 + 0.999905i \(0.495605\pi\)
\(810\) −5.84723 15.2854i −0.205451 0.537076i
\(811\) 3.17409 7.66292i 0.111457 0.269082i −0.858302 0.513145i \(-0.828480\pi\)
0.969759 + 0.244063i \(0.0784804\pi\)
\(812\) 5.54337 + 1.97173i 0.194534 + 0.0691941i
\(813\) 32.8704 18.7039i 1.15282 0.655975i
\(814\) 0.716454 1.23449i 0.0251117 0.0432689i
\(815\) −13.1047 7.56602i −0.459039 0.265026i
\(816\) −10.5277 + 5.86526i −0.368542 + 0.205325i
\(817\) 22.6086 13.0531i 0.790976 0.456670i
\(818\) 16.8124 9.65610i 0.587832 0.337618i
\(819\) −8.29146 9.89535i −0.289727 0.345772i
\(820\) −0.701499 + 5.14868i −0.0244974 + 0.179800i
\(821\) −18.5308 + 2.43962i −0.646728 + 0.0851434i −0.446753 0.894658i \(-0.647420\pi\)
−0.199975 + 0.979801i \(0.564086\pi\)
\(822\) −14.4605 25.5470i −0.504368 0.891053i
\(823\) −28.6075 + 7.66535i −0.997194 + 0.267197i −0.720270 0.693694i \(-0.755982\pi\)
−0.276925 + 0.960892i \(0.589315\pi\)
\(824\) 21.0049 11.9382i 0.731740 0.415888i
\(825\) 2.25279 + 1.75118i 0.0784322 + 0.0609682i
\(826\) −23.7694 8.39418i −0.827044 0.292071i
\(827\) −6.89521 + 16.6465i −0.239770 + 0.578856i −0.997259 0.0739924i \(-0.976426\pi\)
0.757489 + 0.652848i \(0.226426\pi\)
\(828\) 48.5242 12.1190i 1.68633 0.421163i
\(829\) −4.92778 + 37.4302i −0.171149 + 1.30001i 0.663064 + 0.748563i \(0.269256\pi\)
−0.834213 + 0.551443i \(0.814078\pi\)
\(830\) −3.76672 + 3.74975i −0.130745 + 0.130156i
\(831\) 23.7219 + 31.3197i 0.822905 + 1.08647i
\(832\) −12.0879 + 4.81619i −0.419071 + 0.166971i
\(833\) 1.34825 + 12.1013i 0.0467140 + 0.419285i
\(834\) 5.09603 + 0.715166i 0.176461 + 0.0247642i
\(835\) 8.96202 11.6795i 0.310144 0.404187i
\(836\) −3.51189 + 2.00651i −0.121461 + 0.0693965i
\(837\) 16.2193 26.9107i 0.560622 0.930170i
\(838\) −26.1273 + 19.9546i −0.902552 + 0.689321i
\(839\) 22.3934 + 22.3934i 0.773106 + 0.773106i 0.978648 0.205542i \(-0.0658957\pi\)
−0.205542 + 0.978648i \(0.565896\pi\)
\(840\) −5.71885 + 15.6541i −0.197319 + 0.540116i
\(841\) 19.6319 19.6319i 0.676962 0.676962i
\(842\) 0.440688 3.28995i 0.0151871 0.113379i
\(843\) −8.32809 8.43319i −0.286835 0.290455i
\(844\) −25.0488 + 32.3408i −0.862215 + 1.11322i
\(845\) 10.5626 + 8.10499i 0.363365 + 0.278820i
\(846\) −12.4786 + 12.1146i −0.429022 + 0.416509i
\(847\) −1.57822 28.4184i −0.0542281 0.976468i
\(848\) −12.9970 + 1.59184i −0.446320 + 0.0546639i
\(849\) −23.1093 30.5109i −0.793111 1.04713i
\(850\) 0.0185849 8.23271i 0.000637458 0.282380i
\(851\) 16.9451 + 2.23086i 0.580870 + 0.0764730i
\(852\) 14.2855 51.1031i 0.489413 1.75076i
\(853\) 25.0932 + 10.3940i 0.859176 + 0.355882i 0.768385 0.639988i \(-0.221061\pi\)
0.0907909 + 0.995870i \(0.471061\pi\)
\(854\) 1.82426 + 0.141993i 0.0624248 + 0.00485888i
\(855\) −8.09543 + 13.6242i −0.276858 + 0.465939i
\(856\) −32.6057 25.3719i −1.11444 0.867195i
\(857\) −13.2810 49.5653i −0.453670 1.69312i −0.691968 0.721928i \(-0.743256\pi\)
0.238298 0.971192i \(-0.423410\pi\)
\(858\) −0.523717 + 1.88992i −0.0178794 + 0.0645209i
\(859\) −5.64194 42.8548i −0.192500 1.46219i −0.765927 0.642928i \(-0.777719\pi\)
0.573426 0.819257i \(-0.305614\pi\)
\(860\) −15.8030 + 4.15803i −0.538878 + 0.141788i
\(861\) 4.22977 8.23710i 0.144150 0.280719i
\(862\) 0.443193 + 0.119826i 0.0150952 + 0.00408129i
\(863\) 2.06186 + 3.57125i 0.0701866 + 0.121567i 0.898983 0.437984i \(-0.144307\pi\)
−0.828796 + 0.559550i \(0.810974\pi\)
\(864\) 28.1505 + 8.45866i 0.957700 + 0.287770i
\(865\) 8.28852 14.3561i 0.281818 0.488124i
\(866\) −3.51518 13.2383i −0.119451 0.449856i
\(867\) −21.0369 + 11.9704i −0.714452 + 0.406537i
\(868\) −30.4449 + 9.84515i −1.03337 + 0.334166i
\(869\) 2.64107 + 1.09397i 0.0895923 + 0.0371103i
\(870\) −2.45508 2.49731i −0.0832349 0.0846667i
\(871\) 2.50397 + 9.34495i 0.0848438 + 0.316642i
\(872\) 27.6464 20.9179i 0.936224 0.708368i
\(873\) −30.2346 0.379170i −1.02329 0.0128330i
\(874\) −38.3573 29.5704i −1.29745 1.00023i
\(875\) −18.5082 21.5340i −0.625692 0.727983i
\(876\) 35.2026 34.4514i 1.18939 1.16400i
\(877\) 15.0184 19.5723i 0.507135 0.660911i −0.467688 0.883894i \(-0.654913\pi\)
0.974822 + 0.222983i \(0.0715794\pi\)
\(878\) −0.0400655 + 17.7481i −0.00135214 + 0.598969i
\(879\) 9.36275 22.2088i 0.315798 0.749083i
\(880\) 2.45128 0.633150i 0.0826325 0.0213435i
\(881\) 39.0449 1.31546 0.657728 0.753256i \(-0.271518\pi\)
0.657728 + 0.753256i \(0.271518\pi\)
\(882\) 18.8868 22.9192i 0.635951 0.771730i
\(883\) 27.8727 11.5453i 0.937992 0.388529i 0.139287 0.990252i \(-0.455519\pi\)
0.798705 + 0.601723i \(0.205519\pi\)
\(884\) 5.23743 2.14176i 0.176154 0.0720353i
\(885\) 10.5428 + 10.6759i 0.354393 + 0.358866i
\(886\) 48.8604 20.1096i 1.64150 0.675594i
\(887\) 32.7122 + 8.76522i 1.09837 + 0.294307i 0.762100 0.647459i \(-0.224168\pi\)
0.336269 + 0.941766i \(0.390835\pi\)
\(888\) 7.88852 + 6.21820i 0.264722 + 0.208669i
\(889\) −15.6091 47.5349i −0.523511 1.59427i
\(890\) −2.95881 22.8733i −0.0991796 0.766715i
\(891\) 3.58124 2.60794i 0.119976 0.0873694i
\(892\) 9.52148 + 16.6650i 0.318803 + 0.557985i
\(893\) 16.6976 + 2.19828i 0.558764 + 0.0735627i
\(894\) 21.8366 + 54.0165i 0.730325 + 1.80658i
\(895\) 2.32070i 0.0775724i
\(896\) −15.9831 25.3089i −0.533958 0.845511i
\(897\) −23.3012 + 2.91915i −0.778006 + 0.0974677i
\(898\) 1.77053 + 6.66790i 0.0590835 + 0.222511i
\(899\) 0.877594 6.66599i 0.0292694 0.222323i
\(900\) −14.4389 + 13.9546i −0.481297 + 0.465154i
\(901\) 5.64545 0.743237i 0.188077 0.0247608i
\(902\) −1.39501 + 0.180453i −0.0464486 + 0.00600843i
\(903\) 29.0221 + 2.37615i 0.965794 + 0.0790735i
\(904\) 32.6109 32.1722i 1.08462 1.07003i
\(905\) −2.43011 + 9.06928i −0.0807795 + 0.301473i
\(906\) 16.7575 + 29.6051i 0.556731 + 0.983563i
\(907\) −14.5354 18.9429i −0.482641 0.628990i 0.487036 0.873382i \(-0.338078\pi\)
−0.969676 + 0.244393i \(0.921411\pi\)
\(908\) 16.9741 + 41.5083i 0.563307 + 1.37750i
\(909\) 11.2693 8.42487i 0.373780 0.279435i
\(910\) 3.54655 6.97533i 0.117567 0.231230i
\(911\) 0.0225461i 0.000746986i −1.00000 0.000373493i \(-0.999881\pi\)
1.00000 0.000373493i \(-0.000118886\pi\)
\(912\) −10.4891 26.4608i −0.347328 0.876205i
\(913\) −1.24601 0.719382i −0.0412368 0.0238081i
\(914\) 7.59053 + 0.0171353i 0.251072 + 0.000566784i
\(915\) −0.939761 0.550457i −0.0310676 0.0181975i
\(916\) −39.1692 + 29.7756i −1.29419 + 0.983814i
\(917\) −10.7407 3.76583i −0.354689 0.124359i
\(918\) −12.2743 3.56767i −0.405113 0.117751i
\(919\) 9.02282 33.6736i 0.297635 1.11079i −0.641467 0.767151i \(-0.721674\pi\)
0.939102 0.343639i \(-0.111660\pi\)
\(920\) 18.2917 + 24.1755i 0.603060 + 0.797042i
\(921\) 18.6587 + 45.8572i 0.614824 + 1.51105i
\(922\) −0.119185 + 0.0910275i −0.00392516 + 0.00299783i
\(923\) −9.53430 + 23.0178i −0.313825 + 0.757641i
\(924\) −4.49474 0.388439i −0.147866 0.0127787i
\(925\) −6.33958 + 2.62594i −0.208444 + 0.0863404i
\(926\) −53.3524 + 14.1667i −1.75327 + 0.465547i
\(927\) 24.6677 + 6.94238i 0.810194 + 0.228018i
\(928\) 6.24488 0.750549i 0.204998 0.0246380i
\(929\) −35.4146 + 20.4466i −1.16192 + 0.670833i −0.951763 0.306836i \(-0.900730\pi\)
−0.210154 + 0.977668i \(0.567397\pi\)
\(930\) 18.8603 + 2.64682i 0.618454 + 0.0867925i
\(931\) −28.7532 0.573521i −0.942347 0.0187964i
\(932\) 4.06824 + 15.4618i 0.133260 + 0.506468i
\(933\) −15.3474 + 4.00934i −0.502450 + 0.131260i
\(934\) −9.79695 + 23.5017i −0.320566 + 0.769000i
\(935\) −1.06344 + 0.284948i −0.0347782 + 0.00931879i
\(936\) −12.6464 5.52678i −0.413359 0.180648i
\(937\) 16.2502 16.2502i 0.530871 0.530871i −0.389960 0.920832i \(-0.627511\pi\)
0.920832 + 0.389960i \(0.127511\pi\)
\(938\) −20.0795 + 9.59866i −0.655619 + 0.313407i
\(939\) 3.96017 + 1.08778i 0.129235 + 0.0354985i
\(940\) −9.72110 4.07813i −0.317067 0.133014i
\(941\) −3.38265 + 25.6938i −0.110271 + 0.837593i 0.843515 + 0.537106i \(0.180483\pi\)
−0.953786 + 0.300487i \(0.902851\pi\)
\(942\) 25.4384 3.12858i 0.828827 0.101935i
\(943\) −8.42170 14.5868i −0.274248 0.475012i
\(944\) −26.7487 + 3.27610i −0.870596 + 0.106628i
\(945\) −16.0724 + 7.35882i −0.522835 + 0.239382i
\(946\) −2.20309 3.83584i −0.0716287 0.124714i
\(947\) 21.6727 28.2444i 0.704268 0.917820i −0.295022 0.955491i \(-0.595327\pi\)
0.999290 + 0.0376701i \(0.0119936\pi\)
\(948\) −10.2461 + 17.3128i −0.332777 + 0.562294i
\(949\) −18.3479 + 14.0788i −0.595597 + 0.457018i
\(950\) 19.2728 + 2.58158i 0.625291 + 0.0837576i
\(951\) −6.08281 4.72839i −0.197249 0.153329i
\(952\) 7.04955 + 10.9427i 0.228477 + 0.354655i
\(953\) −32.7852 + 32.7852i −1.06202 + 1.06202i −0.0640728 + 0.997945i \(0.520409\pi\)
−0.997945 + 0.0640728i \(0.979591\pi\)
\(954\) −10.8921 8.61687i −0.352646 0.278981i
\(955\) −3.67129 + 2.81708i −0.118800 + 0.0911585i
\(956\) 0.648806 + 1.13557i 0.0209839 + 0.0367271i
\(957\) 0.479134 0.817997i 0.0154882 0.0264421i
\(958\) −11.8758 + 43.9244i −0.383691 + 1.41913i
\(959\) −26.5383 + 17.3521i −0.856968 + 0.560328i
\(960\) 1.97510 + 17.7069i 0.0637459 + 0.571487i
\(961\) 2.78245 + 4.81934i 0.0897564 + 0.155463i
\(962\) −3.32736 3.34242i −0.107278 0.107764i
\(963\) −5.17446 43.5138i −0.166745 1.40221i
\(964\) −11.6718 0.0526975i −0.375925 0.00169727i
\(965\) 0.180111 + 0.0746042i 0.00579796 + 0.00240159i
\(966\) −16.4156 51.4675i −0.528162 1.65594i
\(967\) −8.48274 + 8.48274i −0.272787 + 0.272787i −0.830221 0.557434i \(-0.811786\pi\)
0.557434 + 0.830221i \(0.311786\pi\)
\(968\) −15.0349 26.4533i −0.483239 0.850241i
\(969\) 4.66502 + 11.4652i 0.149862 + 0.368314i
\(970\) −6.97547 16.9484i −0.223969 0.544180i
\(971\) 1.64039 + 12.4600i 0.0526426 + 0.399861i 0.997398 + 0.0720856i \(0.0229655\pi\)
−0.944756 + 0.327775i \(0.893701\pi\)
\(972\) 14.6103 + 27.5416i 0.468625 + 0.883397i
\(973\) 0.418818 5.54248i 0.0134267 0.177684i
\(974\) 18.9401 + 32.9770i 0.606881 + 1.05665i
\(975\) 7.51577 5.69254i 0.240697 0.182307i
\(976\) 1.81390 0.732223i 0.0580615 0.0234379i
\(977\) −1.14608 + 1.98506i −0.0366662 + 0.0635077i −0.883776 0.467910i \(-0.845007\pi\)
0.847110 + 0.531418i \(0.178340\pi\)
\(978\) 26.5375 + 11.2583i 0.848576 + 0.360000i
\(979\) 5.76816 2.38925i 0.184351 0.0763607i
\(980\) 17.2688 + 5.08293i 0.551631 + 0.162368i
\(981\) 36.3935 + 5.25638i 1.16195 + 0.167823i
\(982\) −46.7392 6.26071i −1.49151 0.199787i
\(983\) 14.2233 + 53.0820i 0.453652 + 1.69305i 0.692022 + 0.721877i \(0.256720\pi\)
−0.238370 + 0.971174i \(0.576613\pi\)
\(984\) 0.129103 9.89811i 0.00411566 0.315540i
\(985\) −3.86814 + 14.4361i −0.123249 + 0.459972i
\(986\) −2.71261 + 0.350894i −0.0863871 + 0.0111747i
\(987\) 13.9206 + 12.6138i 0.443098 + 0.401503i
\(988\) 3.40071 + 12.9248i 0.108191 + 0.411191i
\(989\) 32.2450 42.0225i 1.02533 1.33624i
\(990\) 2.30542 + 1.37691i 0.0732709 + 0.0437612i
\(991\) 18.3136 + 10.5734i 0.581751 + 0.335874i 0.761829 0.647778i \(-0.224302\pi\)
−0.180078 + 0.983652i \(0.557635\pi\)
\(992\) −24.4590 + 23.9130i −0.776575 + 0.759239i
\(993\) 3.90147 + 31.1423i 0.123809 + 0.988271i
\(994\) −56.0716 11.8680i −1.77848 0.376429i
\(995\) −12.6360 + 5.23402i −0.400589 + 0.165929i
\(996\) 6.25005 7.96584i 0.198040 0.252407i
\(997\) −6.44310 8.39681i −0.204055 0.265930i 0.680104 0.733116i \(-0.261935\pi\)
−0.884159 + 0.467186i \(0.845268\pi\)
\(998\) 44.1244 + 18.3937i 1.39673 + 0.582243i
\(999\) 1.19169 + 10.5871i 0.0377036 + 0.334961i
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 672.2.ch.a.11.9 992
3.2 odd 2 inner 672.2.ch.a.11.116 yes 992
7.2 even 3 inner 672.2.ch.a.107.93 yes 992
21.2 odd 6 inner 672.2.ch.a.107.32 yes 992
32.3 odd 8 inner 672.2.ch.a.515.32 yes 992
96.35 even 8 inner 672.2.ch.a.515.93 yes 992
224.163 odd 24 inner 672.2.ch.a.611.116 yes 992
672.611 even 24 inner 672.2.ch.a.611.9 yes 992
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
672.2.ch.a.11.9 992 1.1 even 1 trivial
672.2.ch.a.11.116 yes 992 3.2 odd 2 inner
672.2.ch.a.107.32 yes 992 21.2 odd 6 inner
672.2.ch.a.107.93 yes 992 7.2 even 3 inner
672.2.ch.a.515.32 yes 992 32.3 odd 8 inner
672.2.ch.a.515.93 yes 992 96.35 even 8 inner
672.2.ch.a.611.9 yes 992 672.611 even 24 inner
672.2.ch.a.611.116 yes 992 224.163 odd 24 inner