Properties

Label 378.2.v.a.79.8
Level $378$
Weight $2$
Character 378.79
Analytic conductor $3.018$
Analytic rank $0$
Dimension $72$
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] = [378,2,Mod(67,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.v (of order \(9\), degree \(6\), 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: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(12\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 79.8
Character \(\chi\) \(=\) 378.79
Dual form 378.2.v.a.67.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.766044 - 0.642788i) q^{2} +(0.309985 - 1.70409i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.504047 - 2.85859i) q^{5} +(-1.33283 + 1.10615i) q^{6} +(-2.58705 - 0.554250i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.80782 - 1.05648i) q^{9} +O(q^{10})\) \(q+(-0.766044 - 0.642788i) q^{2} +(0.309985 - 1.70409i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.504047 - 2.85859i) q^{5} +(-1.33283 + 1.10615i) q^{6} +(-2.58705 - 0.554250i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.80782 - 1.05648i) q^{9} +(-1.45134 + 2.51380i) q^{10} +(0.0514442 - 0.291754i) q^{11} +(1.73203 + 0.00936395i) q^{12} +(0.719192 + 4.07874i) q^{13} +(1.62553 + 2.08750i) q^{14} +(-5.02753 - 0.0271806i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.770259 + 1.33413i) q^{17} +(1.47182 + 2.61414i) q^{18} +(-1.64227 - 2.84449i) q^{19} +(2.72763 - 0.992778i) q^{20} +(-1.74643 + 4.23674i) q^{21} +(-0.226945 + 0.190429i) q^{22} +(3.83587 - 3.21867i) q^{23} +(-1.32079 - 1.12050i) q^{24} +(-3.21901 + 1.17162i) q^{25} +(2.07083 - 3.58679i) q^{26} +(-2.67072 + 4.45727i) q^{27} +(0.0965940 - 2.64399i) q^{28} +(0.827577 - 4.69342i) q^{29} +(3.83384 + 3.25246i) q^{30} +(0.531893 + 3.01651i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.481228 - 0.178105i) q^{33} +(1.44761 - 0.526888i) q^{34} +(-0.280382 + 7.67467i) q^{35} +(0.552858 - 2.94862i) q^{36} -7.47027 q^{37} +(-0.570354 + 3.23464i) q^{38} +(7.17347 + 0.0387823i) q^{39} +(-2.72763 - 0.992778i) q^{40} +(0.642881 + 3.64596i) q^{41} +(4.06117 - 2.12294i) q^{42} +(-9.42283 - 7.90669i) q^{43} +0.296255 q^{44} +(-1.60478 + 8.55892i) q^{45} -5.00737 q^{46} +(0.204405 - 1.15924i) q^{47} +(0.291541 + 1.70734i) q^{48} +(6.38561 + 2.86774i) q^{49} +(3.21901 + 1.17162i) q^{50} +(2.03470 + 1.72615i) q^{51} +(-3.89189 + 1.41653i) q^{52} +(-5.61189 - 9.72008i) q^{53} +(4.91097 - 1.69777i) q^{54} -0.859936 q^{55} +(-1.77352 + 1.96332i) q^{56} +(-5.35634 + 1.91682i) q^{57} +(-3.65083 + 3.06341i) q^{58} +(0.0448198 + 0.0163131i) q^{59} +(-0.846254 - 4.95587i) q^{60} +(-0.333064 + 1.88890i) q^{61} +(1.53152 - 2.65268i) q^{62} +(6.67840 + 4.28940i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(11.2969 - 4.11175i) q^{65} +(0.254158 + 0.445763i) q^{66} +(7.92952 - 6.65365i) q^{67} +(-1.44761 - 0.526888i) q^{68} +(-4.29584 - 7.53439i) q^{69} +(5.14797 - 5.69891i) q^{70} +(-5.64455 - 9.77665i) q^{71} +(-2.31885 + 1.90340i) q^{72} +12.2003 q^{73} +(5.72256 + 4.80180i) q^{74} +(0.998704 + 5.84866i) q^{75} +(2.51610 - 2.11126i) q^{76} +(-0.294793 + 0.726269i) q^{77} +(-5.47027 - 4.64073i) q^{78} +(-3.43692 - 2.88392i) q^{79} +(1.45134 + 2.51380i) q^{80} +(6.76769 + 5.93282i) q^{81} +(1.85110 - 3.20621i) q^{82} +(1.53826 - 8.72391i) q^{83} +(-4.47564 - 0.984200i) q^{84} +(4.20197 + 1.52939i) q^{85} +(2.13598 + 12.1138i) q^{86} +(-7.74146 - 2.86515i) q^{87} +(-0.226945 - 0.190429i) q^{88} +(4.96720 + 8.60345i) q^{89} +(6.73090 - 5.52498i) q^{90} +(0.400060 - 10.9505i) q^{91} +(3.83587 + 3.21867i) q^{92} +(5.30528 + 0.0286822i) q^{93} +(-0.901727 + 0.756639i) q^{94} +(-7.30346 + 6.12833i) q^{95} +(0.874122 - 1.49530i) q^{96} +(-1.39847 - 1.17345i) q^{97} +(-3.04832 - 6.30141i) q^{98} +(-0.452679 + 0.764843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.766044 0.642788i −0.541675 0.454519i
\(3\) 0.309985 1.70409i 0.178970 0.983855i
\(4\) 0.173648 + 0.984808i 0.0868241 + 0.492404i
\(5\) −0.504047 2.85859i −0.225416 1.27840i −0.861887 0.507100i \(-0.830718\pi\)
0.636471 0.771301i \(-0.280394\pi\)
\(6\) −1.33283 + 1.10615i −0.544125 + 0.451584i
\(7\) −2.58705 0.554250i −0.977811 0.209487i
\(8\) 0.500000 0.866025i 0.176777 0.306186i
\(9\) −2.80782 1.05648i −0.935940 0.352160i
\(10\) −1.45134 + 2.51380i −0.458955 + 0.794934i
\(11\) 0.0514442 0.291754i 0.0155110 0.0879672i −0.976070 0.217459i \(-0.930223\pi\)
0.991581 + 0.129491i \(0.0413344\pi\)
\(12\) 1.73203 + 0.00936395i 0.499993 + 0.00270314i
\(13\) 0.719192 + 4.07874i 0.199468 + 1.13124i 0.905910 + 0.423469i \(0.139188\pi\)
−0.706442 + 0.707771i \(0.749701\pi\)
\(14\) 1.62553 + 2.08750i 0.434440 + 0.557908i
\(15\) −5.02753 0.0271806i −1.29810 0.00701801i
\(16\) −0.939693 + 0.342020i −0.234923 + 0.0855050i
\(17\) −0.770259 + 1.33413i −0.186815 + 0.323573i −0.944187 0.329411i \(-0.893150\pi\)
0.757371 + 0.652984i \(0.226483\pi\)
\(18\) 1.47182 + 2.61414i 0.346912 + 0.616159i
\(19\) −1.64227 2.84449i −0.376762 0.652572i 0.613827 0.789441i \(-0.289629\pi\)
−0.990589 + 0.136869i \(0.956296\pi\)
\(20\) 2.72763 0.992778i 0.609918 0.221992i
\(21\) −1.74643 + 4.23674i −0.381103 + 0.924532i
\(22\) −0.226945 + 0.190429i −0.0483847 + 0.0405996i
\(23\) 3.83587 3.21867i 0.799833 0.671140i −0.148325 0.988939i \(-0.547388\pi\)
0.948158 + 0.317799i \(0.102944\pi\)
\(24\) −1.32079 1.12050i −0.269605 0.228721i
\(25\) −3.21901 + 1.17162i −0.643802 + 0.234325i
\(26\) 2.07083 3.58679i 0.406124 0.703427i
\(27\) −2.67072 + 4.45727i −0.513980 + 0.857802i
\(28\) 0.0965940 2.64399i 0.0182545 0.499667i
\(29\) 0.827577 4.69342i 0.153677 0.871547i −0.806308 0.591496i \(-0.798538\pi\)
0.959985 0.280051i \(-0.0903513\pi\)
\(30\) 3.83384 + 3.25246i 0.699960 + 0.593814i
\(31\) 0.531893 + 3.01651i 0.0955307 + 0.541782i 0.994583 + 0.103941i \(0.0331454\pi\)
−0.899053 + 0.437840i \(0.855743\pi\)
\(32\) 0.939693 + 0.342020i 0.166116 + 0.0604612i
\(33\) −0.481228 0.178105i −0.0837710 0.0310040i
\(34\) 1.44761 0.526888i 0.248264 0.0903606i
\(35\) −0.280382 + 7.67467i −0.0473932 + 1.29726i
\(36\) 0.552858 2.94862i 0.0921431 0.491436i
\(37\) −7.47027 −1.22810 −0.614052 0.789265i \(-0.710462\pi\)
−0.614052 + 0.789265i \(0.710462\pi\)
\(38\) −0.570354 + 3.23464i −0.0925237 + 0.524728i
\(39\) 7.17347 + 0.0387823i 1.14867 + 0.00621014i
\(40\) −2.72763 0.992778i −0.431277 0.156972i
\(41\) 0.642881 + 3.64596i 0.100401 + 0.569404i 0.992958 + 0.118468i \(0.0377984\pi\)
−0.892557 + 0.450935i \(0.851091\pi\)
\(42\) 4.06117 2.12294i 0.626652 0.327577i
\(43\) −9.42283 7.90669i −1.43697 1.20576i −0.941446 0.337163i \(-0.890532\pi\)
−0.495522 0.868596i \(-0.665023\pi\)
\(44\) 0.296255 0.0446621
\(45\) −1.60478 + 8.55892i −0.239226 + 1.27589i
\(46\) −5.00737 −0.738296
\(47\) 0.204405 1.15924i 0.0298155 0.169092i −0.966264 0.257553i \(-0.917084\pi\)
0.996080 + 0.0884609i \(0.0281948\pi\)
\(48\) 0.291541 + 1.70734i 0.0420804 + 0.246433i
\(49\) 6.38561 + 2.86774i 0.912231 + 0.409677i
\(50\) 3.21901 + 1.17162i 0.455237 + 0.165693i
\(51\) 2.03470 + 1.72615i 0.284915 + 0.241709i
\(52\) −3.89189 + 1.41653i −0.539708 + 0.196438i
\(53\) −5.61189 9.72008i −0.770853 1.33516i −0.937096 0.349072i \(-0.886497\pi\)
0.166243 0.986085i \(-0.446836\pi\)
\(54\) 4.91097 1.69777i 0.668298 0.231037i
\(55\) −0.859936 −0.115954
\(56\) −1.77352 + 1.96332i −0.236996 + 0.262360i
\(57\) −5.35634 + 1.91682i −0.709465 + 0.253889i
\(58\) −3.65083 + 3.06341i −0.479378 + 0.402246i
\(59\) 0.0448198 + 0.0163131i 0.00583504 + 0.00212378i 0.344936 0.938626i \(-0.387901\pi\)
−0.339101 + 0.940750i \(0.610123\pi\)
\(60\) −0.846254 4.95587i −0.109251 0.639800i
\(61\) −0.333064 + 1.88890i −0.0426445 + 0.241849i −0.998678 0.0514096i \(-0.983629\pi\)
0.956033 + 0.293259i \(0.0947397\pi\)
\(62\) 1.53152 2.65268i 0.194504 0.336890i
\(63\) 6.67840 + 4.28940i 0.841400 + 0.540414i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) 11.2969 4.11175i 1.40121 0.510000i
\(66\) 0.254158 + 0.445763i 0.0312847 + 0.0548697i
\(67\) 7.92952 6.65365i 0.968745 0.812873i −0.0136089 0.999907i \(-0.504332\pi\)
0.982353 + 0.187034i \(0.0598875\pi\)
\(68\) −1.44761 0.526888i −0.175549 0.0638946i
\(69\) −4.29584 7.53439i −0.517158 0.907034i
\(70\) 5.14797 5.69891i 0.615300 0.681150i
\(71\) −5.64455 9.77665i −0.669885 1.16028i −0.977936 0.208905i \(-0.933010\pi\)
0.308051 0.951370i \(-0.400323\pi\)
\(72\) −2.31885 + 1.90340i −0.273279 + 0.224318i
\(73\) 12.2003 1.42793 0.713966 0.700180i \(-0.246897\pi\)
0.713966 + 0.700180i \(0.246897\pi\)
\(74\) 5.72256 + 4.80180i 0.665234 + 0.558197i
\(75\) 0.998704 + 5.84866i 0.115320 + 0.675345i
\(76\) 2.51610 2.11126i 0.288617 0.242178i
\(77\) −0.294793 + 0.726269i −0.0335948 + 0.0827660i
\(78\) −5.47027 4.64073i −0.619386 0.525459i
\(79\) −3.43692 2.88392i −0.386684 0.324466i 0.428636 0.903477i \(-0.358994\pi\)
−0.815320 + 0.579011i \(0.803439\pi\)
\(80\) 1.45134 + 2.51380i 0.162265 + 0.281052i
\(81\) 6.76769 + 5.93282i 0.751966 + 0.659202i
\(82\) 1.85110 3.20621i 0.204420 0.354066i
\(83\) 1.53826 8.72391i 0.168846 0.957574i −0.776164 0.630531i \(-0.782837\pi\)
0.945010 0.327042i \(-0.106052\pi\)
\(84\) −4.47564 0.984200i −0.488332 0.107385i
\(85\) 4.20197 + 1.52939i 0.455768 + 0.165886i
\(86\) 2.13598 + 12.1138i 0.230329 + 1.30626i
\(87\) −7.74146 2.86515i −0.829972 0.307177i
\(88\) −0.226945 0.190429i −0.0241924 0.0202998i
\(89\) 4.96720 + 8.60345i 0.526522 + 0.911964i 0.999522 + 0.0309012i \(0.00983773\pi\)
−0.473000 + 0.881062i \(0.656829\pi\)
\(90\) 6.73090 5.52498i 0.709499 0.582384i
\(91\) 0.400060 10.9505i 0.0419377 1.14793i
\(92\) 3.83587 + 3.21867i 0.399917 + 0.335570i
\(93\) 5.30528 + 0.0286822i 0.550131 + 0.00297421i
\(94\) −0.901727 + 0.756639i −0.0930061 + 0.0780413i
\(95\) −7.30346 + 6.12833i −0.749319 + 0.628754i
\(96\) 0.874122 1.49530i 0.0892147 0.152613i
\(97\) −1.39847 1.17345i −0.141993 0.119146i 0.569025 0.822321i \(-0.307321\pi\)
−0.711018 + 0.703174i \(0.751765\pi\)
\(98\) −3.04832 6.30141i −0.307926 0.636539i
\(99\) −0.452679 + 0.764843i −0.0454959 + 0.0768697i
\(100\) −1.71280 2.96666i −0.171280 0.296666i
\(101\) −6.64509 5.57589i −0.661211 0.554822i 0.249238 0.968442i \(-0.419820\pi\)
−0.910450 + 0.413620i \(0.864264\pi\)
\(102\) −0.449125 2.63018i −0.0444700 0.260427i
\(103\) −1.97563 11.2044i −0.194665 1.10400i −0.912895 0.408195i \(-0.866158\pi\)
0.718230 0.695806i \(-0.244953\pi\)
\(104\) 3.89189 + 1.41653i 0.381631 + 0.138902i
\(105\) 12.9914 + 2.85683i 1.26783 + 0.278798i
\(106\) −1.94899 + 11.0533i −0.189303 + 1.07359i
\(107\) 8.39124 14.5341i 0.811212 1.40506i −0.100804 0.994906i \(-0.532142\pi\)
0.912016 0.410154i \(-0.134525\pi\)
\(108\) −4.85332 1.85615i −0.467011 0.178608i
\(109\) 9.34891 + 16.1928i 0.895463 + 1.55099i 0.833231 + 0.552926i \(0.186489\pi\)
0.0622322 + 0.998062i \(0.480178\pi\)
\(110\) 0.658749 + 0.552756i 0.0628093 + 0.0527032i
\(111\) −2.31567 + 12.7300i −0.219794 + 1.20828i
\(112\) 2.62059 0.363997i 0.247623 0.0343945i
\(113\) 8.71837 7.31558i 0.820155 0.688192i −0.132853 0.991136i \(-0.542414\pi\)
0.953008 + 0.302944i \(0.0979695\pi\)
\(114\) 5.33530 + 1.97462i 0.499697 + 0.184940i
\(115\) −11.1343 9.34281i −1.03828 0.871221i
\(116\) 4.76583 0.442496
\(117\) 2.28975 12.2122i 0.211688 1.12902i
\(118\) −0.0238481 0.0413061i −0.00219540 0.00380254i
\(119\) 2.73214 3.02453i 0.250454 0.277258i
\(120\) −2.53730 + 4.34038i −0.231623 + 0.396221i
\(121\) 10.2541 + 3.73220i 0.932195 + 0.339291i
\(122\) 1.46930 1.23289i 0.133025 0.111621i
\(123\) 6.41232 + 0.0346673i 0.578179 + 0.00312584i
\(124\) −2.87832 + 1.04762i −0.258481 + 0.0940794i
\(125\) −2.28500 3.95773i −0.204376 0.353990i
\(126\) −2.35878 7.57866i −0.210137 0.675161i
\(127\) 5.06958 8.78078i 0.449853 0.779168i −0.548523 0.836135i \(-0.684810\pi\)
0.998376 + 0.0569675i \(0.0181431\pi\)
\(128\) −0.173648 + 0.984808i −0.0153485 + 0.0870455i
\(129\) −16.3946 + 13.6064i −1.44347 + 1.19797i
\(130\) −11.2969 4.11175i −0.990808 0.360625i
\(131\) −6.24133 + 5.23710i −0.545308 + 0.457568i −0.873348 0.487096i \(-0.838056\pi\)
0.328041 + 0.944664i \(0.393612\pi\)
\(132\) 0.0918346 0.504844i 0.00799317 0.0439410i
\(133\) 2.67207 + 8.26906i 0.231697 + 0.717019i
\(134\) −10.3512 −0.894212
\(135\) 14.0877 + 5.38781i 1.21247 + 0.463709i
\(136\) 0.770259 + 1.33413i 0.0660491 + 0.114400i
\(137\) −17.6311 + 6.41718i −1.50632 + 0.548257i −0.957689 0.287806i \(-0.907074\pi\)
−0.548634 + 0.836062i \(0.684852\pi\)
\(138\) −1.55221 + 8.53299i −0.132133 + 0.726376i
\(139\) 20.4185 + 7.43173i 1.73188 + 0.630351i 0.998762 0.0497539i \(-0.0158437\pi\)
0.733115 + 0.680105i \(0.238066\pi\)
\(140\) −7.60676 + 1.05657i −0.642889 + 0.0892965i
\(141\) −1.91208 0.707670i −0.161026 0.0595965i
\(142\) −1.96033 + 11.1176i −0.164507 + 0.932968i
\(143\) 1.22699 0.102606
\(144\) 2.99982 + 0.0324372i 0.249985 + 0.00270310i
\(145\) −13.8337 −1.14883
\(146\) −9.34594 7.84217i −0.773475 0.649023i
\(147\) 6.86632 9.99268i 0.566325 0.824182i
\(148\) −1.29720 7.35678i −0.106629 0.604723i
\(149\) 11.7704 + 4.28409i 0.964271 + 0.350966i 0.775706 0.631095i \(-0.217394\pi\)
0.188565 + 0.982061i \(0.439616\pi\)
\(150\) 2.99439 5.12229i 0.244491 0.418233i
\(151\) −3.24832 + 18.4221i −0.264344 + 1.49917i 0.506552 + 0.862209i \(0.330920\pi\)
−0.770896 + 0.636961i \(0.780191\pi\)
\(152\) −3.28454 −0.266411
\(153\) 3.57223 2.93222i 0.288798 0.237056i
\(154\) 0.692661 0.366865i 0.0558162 0.0295628i
\(155\) 8.35487 3.04093i 0.671080 0.244253i
\(156\) 1.20747 + 7.07122i 0.0966747 + 0.566151i
\(157\) −11.8066 4.29724i −0.942266 0.342957i −0.175206 0.984532i \(-0.556059\pi\)
−0.767060 + 0.641575i \(0.778281\pi\)
\(158\) 0.779086 + 4.41842i 0.0619808 + 0.351511i
\(159\) −18.3035 + 6.55007i −1.45156 + 0.519454i
\(160\) 0.504047 2.85859i 0.0398484 0.225991i
\(161\) −11.7075 + 6.20083i −0.922681 + 0.488694i
\(162\) −1.37081 8.89499i −0.107701 0.698857i
\(163\) −4.67949 + 8.10512i −0.366526 + 0.634842i −0.989020 0.147783i \(-0.952786\pi\)
0.622494 + 0.782625i \(0.286120\pi\)
\(164\) −3.47894 + 1.26623i −0.271659 + 0.0988759i
\(165\) −0.266567 + 1.46541i −0.0207522 + 0.114082i
\(166\) −6.78600 + 5.69413i −0.526696 + 0.441950i
\(167\) −12.8573 + 10.7885i −0.994925 + 0.834841i −0.986273 0.165122i \(-0.947198\pi\)
−0.00865161 + 0.999963i \(0.502754\pi\)
\(168\) 2.79591 + 3.63083i 0.215709 + 0.280124i
\(169\) −3.90290 + 1.42054i −0.300223 + 0.109272i
\(170\) −2.23582 3.87256i −0.171480 0.297012i
\(171\) 1.60604 + 9.72185i 0.122817 + 0.743448i
\(172\) 6.15031 10.6527i 0.468957 0.812257i
\(173\) 6.87188 2.50116i 0.522459 0.190160i −0.0673089 0.997732i \(-0.521441\pi\)
0.589768 + 0.807573i \(0.299219\pi\)
\(174\) 4.08862 + 7.17095i 0.309957 + 0.543628i
\(175\) 8.97710 1.24691i 0.678605 0.0942574i
\(176\) 0.0514442 + 0.291754i 0.00387775 + 0.0219918i
\(177\) 0.0416923 0.0713200i 0.00313379 0.00536074i
\(178\) 1.72509 9.78348i 0.129301 0.733303i
\(179\) 8.45945 14.6522i 0.632289 1.09516i −0.354793 0.934945i \(-0.615449\pi\)
0.987083 0.160212i \(-0.0512179\pi\)
\(180\) −8.70756 0.0941551i −0.649023 0.00701790i
\(181\) −5.09029 + 8.81664i −0.378358 + 0.655335i −0.990824 0.135162i \(-0.956845\pi\)
0.612465 + 0.790497i \(0.290178\pi\)
\(182\) −7.34531 + 8.13142i −0.544471 + 0.602741i
\(183\) 3.11561 + 1.15310i 0.230312 + 0.0852397i
\(184\) −0.869520 4.93129i −0.0641019 0.363540i
\(185\) 3.76536 + 21.3544i 0.276835 + 1.57001i
\(186\) −4.04564 3.43214i −0.296641 0.251657i
\(187\) 0.349612 + 0.293359i 0.0255662 + 0.0214526i
\(188\) 1.17712 0.0858504
\(189\) 9.37971 10.0509i 0.682273 0.731097i
\(190\) 9.53399 0.691668
\(191\) −12.8695 10.7988i −0.931206 0.781374i 0.0448277 0.998995i \(-0.485726\pi\)
−0.976034 + 0.217620i \(0.930171\pi\)
\(192\) −1.63077 + 0.583588i −0.117691 + 0.0421169i
\(193\) 1.35345 + 7.67582i 0.0974238 + 0.552518i 0.993978 + 0.109583i \(0.0349516\pi\)
−0.896554 + 0.442935i \(0.853937\pi\)
\(194\) 0.317007 + 1.79784i 0.0227598 + 0.129077i
\(195\) −3.50490 20.5256i −0.250991 1.46987i
\(196\) −1.71532 + 6.78658i −0.122523 + 0.484756i
\(197\) −5.77393 + 10.0007i −0.411376 + 0.712524i −0.995040 0.0994711i \(-0.968285\pi\)
0.583665 + 0.811995i \(0.301618\pi\)
\(198\) 0.838404 0.294928i 0.0595828 0.0209596i
\(199\) 11.5359 19.9808i 0.817760 1.41640i −0.0895686 0.995981i \(-0.528549\pi\)
0.907329 0.420422i \(-0.138118\pi\)
\(200\) −0.594849 + 3.37356i −0.0420622 + 0.238547i
\(201\) −8.88037 15.5751i −0.626373 1.09858i
\(202\) 1.50632 + 8.54277i 0.105984 + 0.601067i
\(203\) −4.74231 + 11.6834i −0.332845 + 0.820015i
\(204\) −1.34660 + 2.30353i −0.0942809 + 0.161279i
\(205\) 10.0983 3.67547i 0.705294 0.256706i
\(206\) −5.68861 + 9.85297i −0.396345 + 0.686489i
\(207\) −14.1709 + 4.98493i −0.984945 + 0.346477i
\(208\) −2.07083 3.58679i −0.143586 0.248699i
\(209\) −0.914378 + 0.332807i −0.0632489 + 0.0230207i
\(210\) −8.11565 10.5392i −0.560033 0.727271i
\(211\) −2.08041 + 1.74567i −0.143221 + 0.120177i −0.711583 0.702602i \(-0.752022\pi\)
0.568362 + 0.822778i \(0.307577\pi\)
\(212\) 8.59792 7.21451i 0.590508 0.495495i
\(213\) −18.4100 + 6.58819i −1.26143 + 0.451415i
\(214\) −15.7704 + 5.73995i −1.07804 + 0.392375i
\(215\) −17.8524 + 30.9213i −1.21753 + 2.10882i
\(216\) 2.52475 + 4.54154i 0.171788 + 0.309013i
\(217\) 0.295872 8.09866i 0.0200851 0.549773i
\(218\) 3.24684 18.4138i 0.219904 1.24714i
\(219\) 3.78189 20.7903i 0.255557 1.40488i
\(220\) −0.149326 0.846872i −0.0100676 0.0570961i
\(221\) −5.99553 2.18219i −0.403303 0.146790i
\(222\) 9.95658 8.26325i 0.668242 0.554593i
\(223\) −4.67914 + 1.70307i −0.313339 + 0.114046i −0.493902 0.869517i \(-0.664430\pi\)
0.180564 + 0.983563i \(0.442208\pi\)
\(224\) −2.24146 1.40565i −0.149764 0.0939187i
\(225\) 10.2762 + 0.111117i 0.685080 + 0.00740779i
\(226\) −11.3810 −0.757054
\(227\) −0.267611 + 1.51770i −0.0177620 + 0.100733i −0.992400 0.123054i \(-0.960731\pi\)
0.974638 + 0.223787i \(0.0718422\pi\)
\(228\) −2.81782 4.94211i −0.186614 0.327299i
\(229\) 3.84784 + 1.40050i 0.254273 + 0.0925476i 0.466012 0.884779i \(-0.345690\pi\)
−0.211739 + 0.977326i \(0.567913\pi\)
\(230\) 2.52395 + 14.3140i 0.166424 + 0.943838i
\(231\) 1.14624 + 0.727485i 0.0754173 + 0.0478650i
\(232\) −3.65083 3.06341i −0.239689 0.201123i
\(233\) −19.5071 −1.27795 −0.638975 0.769227i \(-0.720641\pi\)
−0.638975 + 0.769227i \(0.720641\pi\)
\(234\) −9.60389 + 7.88325i −0.627826 + 0.515344i
\(235\) −3.41682 −0.222889
\(236\) −0.00828236 + 0.0469716i −0.000539136 + 0.00305759i
\(237\) −5.97984 + 4.96284i −0.388432 + 0.322371i
\(238\) −4.03707 + 0.560744i −0.261684 + 0.0363476i
\(239\) −4.28912 1.56111i −0.277440 0.100980i 0.199553 0.979887i \(-0.436051\pi\)
−0.476993 + 0.878907i \(0.658273\pi\)
\(240\) 4.73363 1.69398i 0.305554 0.109346i
\(241\) 26.2672 9.56048i 1.69202 0.615845i 0.697142 0.716933i \(-0.254455\pi\)
0.994877 + 0.101089i \(0.0322326\pi\)
\(242\) −5.45612 9.45027i −0.350732 0.607486i
\(243\) 12.2079 9.69365i 0.783138 0.621848i
\(244\) −1.91804 −0.122790
\(245\) 4.97905 19.6993i 0.318100 1.25854i
\(246\) −4.88984 4.14831i −0.311765 0.264487i
\(247\) 10.4209 8.74413i 0.663063 0.556376i
\(248\) 2.87832 + 1.04762i 0.182774 + 0.0665242i
\(249\) −14.3895 5.32561i −0.911895 0.337497i
\(250\) −0.793571 + 4.50056i −0.0501898 + 0.284641i
\(251\) −5.70251 + 9.87703i −0.359939 + 0.623433i −0.987950 0.154772i \(-0.950536\pi\)
0.628011 + 0.778204i \(0.283869\pi\)
\(252\) −3.06454 + 7.32179i −0.193048 + 0.461229i
\(253\) −0.741729 1.28471i −0.0466321 0.0807692i
\(254\) −9.52770 + 3.46780i −0.597821 + 0.217589i
\(255\) 3.90876 6.68643i 0.244776 0.418720i
\(256\) 0.766044 0.642788i 0.0478778 0.0401742i
\(257\) −3.59882 1.30986i −0.224488 0.0817071i 0.227327 0.973818i \(-0.427001\pi\)
−0.451816 + 0.892111i \(0.649224\pi\)
\(258\) 21.3050 + 0.115182i 1.32639 + 0.00717095i
\(259\) 19.3259 + 4.14040i 1.20085 + 0.257272i
\(260\) 6.01098 + 10.4113i 0.372785 + 0.645683i
\(261\) −7.28220 + 12.3040i −0.450757 + 0.761596i
\(262\) 8.14748 0.503353
\(263\) 21.5405 + 18.0746i 1.32824 + 1.11453i 0.984485 + 0.175468i \(0.0561437\pi\)
0.343756 + 0.939059i \(0.388301\pi\)
\(264\) −0.394857 + 0.327703i −0.0243018 + 0.0201687i
\(265\) −24.9571 + 20.9415i −1.53310 + 1.28642i
\(266\) 3.26833 8.05204i 0.200394 0.493702i
\(267\) 16.2008 5.79760i 0.991471 0.354808i
\(268\) 7.92952 + 6.65365i 0.484372 + 0.406437i
\(269\) 6.44483 + 11.1628i 0.392948 + 0.680606i 0.992837 0.119477i \(-0.0381219\pi\)
−0.599889 + 0.800083i \(0.704789\pi\)
\(270\) −7.32857 13.1827i −0.446003 0.802273i
\(271\) 3.15205 5.45951i 0.191473 0.331642i −0.754265 0.656570i \(-0.772007\pi\)
0.945739 + 0.324928i \(0.105340\pi\)
\(272\) 0.267508 1.51711i 0.0162201 0.0919885i
\(273\) −18.5366 4.07623i −1.12189 0.246704i
\(274\) 17.6311 + 6.41718i 1.06513 + 0.387676i
\(275\) 0.176227 + 0.999434i 0.0106269 + 0.0602681i
\(276\) 6.67396 5.53891i 0.401725 0.333403i
\(277\) −7.28363 6.11169i −0.437631 0.367216i 0.397191 0.917736i \(-0.369985\pi\)
−0.834822 + 0.550520i \(0.814429\pi\)
\(278\) −10.8645 18.8178i −0.651607 1.12862i
\(279\) 1.69343 9.03176i 0.101383 0.540717i
\(280\) 6.50627 + 4.08015i 0.388824 + 0.243836i
\(281\) 24.5846 + 20.6289i 1.46660 + 1.23062i 0.919227 + 0.393728i \(0.128815\pi\)
0.547369 + 0.836892i \(0.315630\pi\)
\(282\) 1.00986 + 1.77117i 0.0601361 + 0.105471i
\(283\) 16.2025 13.5955i 0.963137 0.808168i −0.0183239 0.999832i \(-0.505833\pi\)
0.981461 + 0.191665i \(0.0613886\pi\)
\(284\) 8.64796 7.25650i 0.513162 0.430594i
\(285\) 8.17924 + 14.3454i 0.484497 + 0.849749i
\(286\) −0.939928 0.788693i −0.0555791 0.0466364i
\(287\) 0.357611 9.78859i 0.0211091 0.577802i
\(288\) −2.27715 1.95310i −0.134182 0.115087i
\(289\) 7.31340 + 12.6672i 0.430200 + 0.745129i
\(290\) 10.5972 + 8.89214i 0.622291 + 0.522164i
\(291\) −2.43317 + 2.01936i −0.142635 + 0.118377i
\(292\) 2.11855 + 12.0149i 0.123979 + 0.703119i
\(293\) −7.49941 2.72956i −0.438120 0.159463i 0.113537 0.993534i \(-0.463782\pi\)
−0.551657 + 0.834071i \(0.686004\pi\)
\(294\) −11.6831 + 3.24125i −0.681371 + 0.189034i
\(295\) 0.0240411 0.136344i 0.00139973 0.00793825i
\(296\) −3.73513 + 6.46944i −0.217100 + 0.376029i
\(297\) 1.16304 + 1.00849i 0.0674862 + 0.0585187i
\(298\) −6.26291 10.8477i −0.362801 0.628390i
\(299\) 15.8869 + 13.3307i 0.918761 + 0.770932i
\(300\) −5.58638 + 1.99914i −0.322530 + 0.115420i
\(301\) 19.9950 + 25.6776i 1.15249 + 1.48003i
\(302\) 14.3299 12.0242i 0.824591 0.691914i
\(303\) −11.5617 + 9.59537i −0.664201 + 0.551239i
\(304\) 2.51610 + 2.11126i 0.144308 + 0.121089i
\(305\) 5.56748 0.318793
\(306\) −4.62128 0.0499701i −0.264181 0.00285660i
\(307\) 17.0773 + 29.5787i 0.974652 + 1.68815i 0.681080 + 0.732209i \(0.261511\pi\)
0.293572 + 0.955937i \(0.405156\pi\)
\(308\) −0.766425 0.164199i −0.0436711 0.00935613i
\(309\) −19.7056 0.106536i −1.12102 0.00606061i
\(310\) −8.35487 3.04093i −0.474525 0.172713i
\(311\) −6.83967 + 5.73916i −0.387842 + 0.325438i −0.815772 0.578374i \(-0.803687\pi\)
0.427930 + 0.903812i \(0.359243\pi\)
\(312\) 3.62032 6.19301i 0.204960 0.350610i
\(313\) −13.1423 + 4.78339i −0.742845 + 0.270373i −0.685592 0.727986i \(-0.740456\pi\)
−0.0572531 + 0.998360i \(0.518234\pi\)
\(314\) 6.28214 + 10.8810i 0.354522 + 0.614049i
\(315\) 8.89541 21.2529i 0.501200 1.19746i
\(316\) 2.24329 3.88549i 0.126195 0.218576i
\(317\) 3.66854 20.8053i 0.206046 1.16854i −0.689740 0.724057i \(-0.742275\pi\)
0.895786 0.444486i \(-0.146614\pi\)
\(318\) 18.2316 + 6.74759i 1.02238 + 0.378386i
\(319\) −1.32675 0.482898i −0.0742839 0.0270371i
\(320\) −2.22359 + 1.86581i −0.124302 + 0.104302i
\(321\) −22.1661 18.8047i −1.23719 1.04958i
\(322\) 12.9543 + 2.77533i 0.721914 + 0.154663i
\(323\) 5.05989 0.281540
\(324\) −4.66749 + 7.69510i −0.259305 + 0.427506i
\(325\) −7.09384 12.2869i −0.393496 0.681554i
\(326\) 8.79457 3.20096i 0.487086 0.177285i
\(327\) 30.4919 10.9118i 1.68621 0.603425i
\(328\) 3.47894 + 1.26623i 0.192092 + 0.0699158i
\(329\) −1.17131 + 2.88571i −0.0645766 + 0.159094i
\(330\) 1.14615 0.951220i 0.0630933 0.0523629i
\(331\) 2.06913 11.7346i 0.113730 0.644992i −0.873642 0.486570i \(-0.838248\pi\)
0.987371 0.158423i \(-0.0506409\pi\)
\(332\) 8.85849 0.486173
\(333\) 20.9752 + 7.89220i 1.14943 + 0.432490i
\(334\) 16.7840 0.918378
\(335\) −23.0169 19.3135i −1.25755 1.05521i
\(336\) 0.192061 4.57855i 0.0104778 0.249780i
\(337\) 1.19041 + 6.75113i 0.0648456 + 0.367757i 0.999912 + 0.0132843i \(0.00422865\pi\)
−0.935066 + 0.354473i \(0.884660\pi\)
\(338\) 3.90290 + 1.42054i 0.212290 + 0.0772672i
\(339\) −9.76381 17.1246i −0.530298 0.930079i
\(340\) −0.776493 + 4.40371i −0.0421112 + 0.238825i
\(341\) 0.907443 0.0491408
\(342\) 5.01879 8.47971i 0.271385 0.458530i
\(343\) −14.9304 10.9582i −0.806167 0.591687i
\(344\) −11.5588 + 4.20706i −0.623209 + 0.226830i
\(345\) −19.3724 + 16.0777i −1.04298 + 0.865595i
\(346\) −6.87188 2.50116i −0.369435 0.134463i
\(347\) −3.76895 21.3748i −0.202328 1.14746i −0.901589 0.432593i \(-0.857599\pi\)
0.699261 0.714866i \(-0.253512\pi\)
\(348\) 1.47733 8.12138i 0.0791934 0.435352i
\(349\) 3.07425 17.4349i 0.164561 0.933271i −0.784955 0.619553i \(-0.787314\pi\)
0.949516 0.313718i \(-0.101575\pi\)
\(350\) −7.67836 4.81518i −0.410425 0.257382i
\(351\) −20.1008 7.68753i −1.07290 0.410330i
\(352\) 0.148128 0.256564i 0.00789522 0.0136749i
\(353\) 24.5375 8.93092i 1.30600 0.475345i 0.407053 0.913404i \(-0.366556\pi\)
0.898946 + 0.438060i \(0.144334\pi\)
\(354\) −0.0777818 + 0.0278350i −0.00413405 + 0.00147941i
\(355\) −25.1023 + 21.0633i −1.33229 + 1.11793i
\(356\) −7.61020 + 6.38571i −0.403340 + 0.338442i
\(357\) −4.30714 5.59335i −0.227958 0.296032i
\(358\) −15.8986 + 5.78661i −0.840266 + 0.305832i
\(359\) −10.8116 18.7262i −0.570614 0.988332i −0.996503 0.0835567i \(-0.973372\pi\)
0.425889 0.904775i \(-0.359961\pi\)
\(360\) 6.60985 + 5.66924i 0.348370 + 0.298795i
\(361\) 4.10590 7.11163i 0.216100 0.374297i
\(362\) 9.56661 3.48196i 0.502810 0.183008i
\(363\) 9.53862 16.3170i 0.500648 0.856421i
\(364\) 10.8536 1.50755i 0.568884 0.0790173i
\(365\) −6.14950 34.8755i −0.321879 1.82547i
\(366\) −1.64549 2.88600i −0.0860113 0.150854i
\(367\) −2.48696 + 14.1042i −0.129818 + 0.736235i 0.848511 + 0.529178i \(0.177500\pi\)
−0.978329 + 0.207057i \(0.933612\pi\)
\(368\) −2.50368 + 4.33651i −0.130514 + 0.226056i
\(369\) 2.04680 10.9164i 0.106552 0.568285i
\(370\) 10.8419 18.7788i 0.563645 0.976262i
\(371\) 9.13087 + 28.2567i 0.474051 + 1.46701i
\(372\) 0.893005 + 5.22966i 0.0463002 + 0.271145i
\(373\) −2.80119 15.8863i −0.145040 0.822564i −0.967335 0.253502i \(-0.918418\pi\)
0.822295 0.569062i \(-0.192694\pi\)
\(374\) −0.0792506 0.449453i −0.00409795 0.0232406i
\(375\) −7.45262 + 2.66699i −0.384852 + 0.137723i
\(376\) −0.901727 0.756639i −0.0465030 0.0390207i
\(377\) 19.7385 1.01658
\(378\) −13.6459 + 1.67029i −0.701868 + 0.0859106i
\(379\) −7.89841 −0.405714 −0.202857 0.979208i \(-0.565023\pi\)
−0.202857 + 0.979208i \(0.565023\pi\)
\(380\) −7.30346 6.12833i −0.374660 0.314377i
\(381\) −13.3917 11.3609i −0.686078 0.582037i
\(382\) 2.91728 + 16.5447i 0.149261 + 0.846502i
\(383\) −1.35456 7.68212i −0.0692150 0.392538i −0.999659 0.0261043i \(-0.991690\pi\)
0.930444 0.366434i \(-0.119421\pi\)
\(384\) 1.62437 + 0.601187i 0.0828932 + 0.0306792i
\(385\) 2.22469 + 0.476620i 0.113381 + 0.0242908i
\(386\) 3.89712 6.75000i 0.198358 0.343566i
\(387\) 18.1043 + 32.1556i 0.920294 + 1.63456i
\(388\) 0.912785 1.58099i 0.0463397 0.0802626i
\(389\) 2.78935 15.8192i 0.141426 0.802066i −0.828742 0.559631i \(-0.810943\pi\)
0.970168 0.242435i \(-0.0779461\pi\)
\(390\) −10.5087 + 17.9764i −0.532127 + 0.910270i
\(391\) 1.33951 + 7.59675i 0.0677420 + 0.384184i
\(392\) 5.67634 4.09623i 0.286699 0.206891i
\(393\) 6.98975 + 12.2592i 0.352586 + 0.618394i
\(394\) 10.8514 3.94960i 0.546688 0.198978i
\(395\) −6.51157 + 11.2784i −0.327633 + 0.567477i
\(396\) −0.831831 0.312988i −0.0418011 0.0157282i
\(397\) 10.2075 + 17.6799i 0.512300 + 0.887329i 0.999898 + 0.0142611i \(0.00453959\pi\)
−0.487599 + 0.873068i \(0.662127\pi\)
\(398\) −21.6805 + 7.89104i −1.08674 + 0.395542i
\(399\) 14.9195 1.99015i 0.746909 0.0996319i
\(400\) 2.62416 2.20193i 0.131208 0.110097i
\(401\) 1.92221 1.61293i 0.0959907 0.0805458i −0.593529 0.804812i \(-0.702266\pi\)
0.689520 + 0.724267i \(0.257821\pi\)
\(402\) −3.20873 + 17.6394i −0.160037 + 0.879774i
\(403\) −11.9210 + 4.33891i −0.593830 + 0.216136i
\(404\) 4.33728 7.51238i 0.215788 0.373755i
\(405\) 13.5483 22.3365i 0.673218 1.10991i
\(406\) 11.1428 5.90172i 0.553007 0.292897i
\(407\) −0.384302 + 2.17948i −0.0190491 + 0.108033i
\(408\) 2.51224 0.899028i 0.124374 0.0445085i
\(409\) −0.997291 5.65592i −0.0493128 0.279667i 0.950173 0.311722i \(-0.100906\pi\)
−0.999486 + 0.0320553i \(0.989795\pi\)
\(410\) −10.0983 3.67547i −0.498718 0.181518i
\(411\) 5.47007 + 32.0341i 0.269819 + 1.58012i
\(412\) 10.6911 3.89124i 0.526713 0.191708i
\(413\) −0.106909 0.0670440i −0.00526066 0.00329902i
\(414\) 14.0598 + 5.29019i 0.691001 + 0.259999i
\(415\) −25.7134 −1.26222
\(416\) −0.719192 + 4.07874i −0.0352613 + 0.199977i
\(417\) 18.9937 32.4912i 0.930128 1.59110i
\(418\) 0.914378 + 0.332807i 0.0447237 + 0.0162781i
\(419\) −2.00536 11.3730i −0.0979683 0.555606i −0.993797 0.111207i \(-0.964528\pi\)
0.895829 0.444399i \(-0.146583\pi\)
\(420\) −0.557494 + 13.2901i −0.0272029 + 0.648491i
\(421\) −21.2715 17.8489i −1.03671 0.869901i −0.0450738 0.998984i \(-0.514352\pi\)
−0.991634 + 0.129083i \(0.958797\pi\)
\(422\) 2.71578 0.132202
\(423\) −1.79865 + 3.03898i −0.0874531 + 0.147760i
\(424\) −11.2238 −0.545075
\(425\) 0.916376 5.19703i 0.0444508 0.252093i
\(426\) 18.3377 + 6.78686i 0.888463 + 0.328824i
\(427\) 1.90858 4.70207i 0.0923625 0.227549i
\(428\) 15.7704 + 5.73995i 0.762290 + 0.277451i
\(429\) 0.380348 2.09089i 0.0183634 0.100949i
\(430\) 33.5516 12.2118i 1.61800 0.588905i
\(431\) 6.92449 + 11.9936i 0.333541 + 0.577710i 0.983203 0.182513i \(-0.0584232\pi\)
−0.649663 + 0.760223i \(0.725090\pi\)
\(432\) 0.985176 5.10190i 0.0473993 0.245465i
\(433\) −30.2784 −1.45509 −0.727543 0.686062i \(-0.759338\pi\)
−0.727543 + 0.686062i \(0.759338\pi\)
\(434\) −5.43237 + 6.01375i −0.260762 + 0.288669i
\(435\) −4.28824 + 23.5738i −0.205605 + 1.13028i
\(436\) −14.3234 + 12.0187i −0.685964 + 0.575592i
\(437\) −15.4550 5.62517i −0.739314 0.269088i
\(438\) −16.2608 + 13.4953i −0.776973 + 0.644832i
\(439\) −0.601480 + 3.41116i −0.0287071 + 0.162806i −0.995791 0.0916509i \(-0.970786\pi\)
0.967084 + 0.254457i \(0.0818967\pi\)
\(440\) −0.429968 + 0.744727i −0.0204979 + 0.0355034i
\(441\) −14.8999 14.7984i −0.709521 0.704685i
\(442\) 3.19015 + 5.52551i 0.151740 + 0.262822i
\(443\) 17.3888 6.32901i 0.826167 0.300700i 0.105882 0.994379i \(-0.466233\pi\)
0.720285 + 0.693678i \(0.244011\pi\)
\(444\) −12.9387 0.0699512i −0.614043 0.00331974i
\(445\) 22.0900 18.5357i 1.04717 0.878678i
\(446\) 4.67914 + 1.70307i 0.221564 + 0.0806426i
\(447\) 10.9491 18.7298i 0.517875 0.885890i
\(448\) 0.813528 + 2.51757i 0.0384356 + 0.118944i
\(449\) 10.3958 + 18.0061i 0.490609 + 0.849759i 0.999942 0.0108104i \(-0.00344112\pi\)
−0.509333 + 0.860570i \(0.670108\pi\)
\(450\) −7.80060 6.69053i −0.367724 0.315395i
\(451\) 1.09680 0.0516462
\(452\) 8.71837 + 7.31558i 0.410077 + 0.344096i
\(453\) 30.3859 + 11.2460i 1.42766 + 0.528382i
\(454\) 1.18056 0.990607i 0.0554064 0.0464915i
\(455\) −31.5047 + 4.37596i −1.47696 + 0.205148i
\(456\) −1.01816 + 5.59714i −0.0476796 + 0.262110i
\(457\) 0.851085 + 0.714145i 0.0398121 + 0.0334063i 0.662477 0.749083i \(-0.269505\pi\)
−0.622665 + 0.782489i \(0.713950\pi\)
\(458\) −2.04739 3.54619i −0.0956684 0.165703i
\(459\) −3.88943 6.99633i −0.181543 0.326561i
\(460\) 7.26741 12.5875i 0.338845 0.586897i
\(461\) −4.81360 + 27.2993i −0.224192 + 1.27145i 0.640033 + 0.768347i \(0.278921\pi\)
−0.864225 + 0.503106i \(0.832190\pi\)
\(462\) −0.410455 1.29408i −0.0190961 0.0602059i
\(463\) −16.8063 6.11699i −0.781054 0.284281i −0.0794421 0.996839i \(-0.525314\pi\)
−0.701612 + 0.712559i \(0.747536\pi\)
\(464\) 0.827577 + 4.69342i 0.0384193 + 0.217887i
\(465\) −2.59212 15.1801i −0.120206 0.703959i
\(466\) 14.9433 + 12.5389i 0.692234 + 0.580853i
\(467\) 8.99768 + 15.5844i 0.416363 + 0.721161i 0.995570 0.0940186i \(-0.0299713\pi\)
−0.579208 + 0.815180i \(0.696638\pi\)
\(468\) 12.4243 + 0.134344i 0.574312 + 0.00621005i
\(469\) −24.2018 + 12.8184i −1.11754 + 0.591897i
\(470\) 2.61743 + 2.19629i 0.120733 + 0.101307i
\(471\) −10.9827 + 18.7873i −0.506057 + 0.865674i
\(472\) 0.0365374 0.0306585i 0.00168177 0.00141117i
\(473\) −2.79156 + 2.34240i −0.128356 + 0.107704i
\(474\) 7.77087 + 0.0420121i 0.356928 + 0.00192968i
\(475\) 8.61916 + 7.23234i 0.395474 + 0.331842i
\(476\) 3.45301 + 2.16542i 0.158269 + 0.0992520i
\(477\) 5.48809 + 33.2211i 0.251282 + 1.52109i
\(478\) 2.28219 + 3.95287i 0.104385 + 0.180800i
\(479\) 3.67027 + 3.07972i 0.167699 + 0.140716i 0.722775 0.691084i \(-0.242866\pi\)
−0.555076 + 0.831800i \(0.687311\pi\)
\(480\) −4.71504 1.74506i −0.215211 0.0796506i
\(481\) −5.37256 30.4693i −0.244968 1.38928i
\(482\) −26.2672 9.56048i −1.19644 0.435468i
\(483\) 6.93759 + 21.8728i 0.315671 + 0.995246i
\(484\) −1.89489 + 10.7465i −0.0861313 + 0.488475i
\(485\) −2.64953 + 4.58912i −0.120309 + 0.208381i
\(486\) −15.5828 0.421328i −0.706848 0.0191118i
\(487\) 1.98528 + 3.43861i 0.0899616 + 0.155818i 0.907495 0.420064i \(-0.137992\pi\)
−0.817533 + 0.575882i \(0.804659\pi\)
\(488\) 1.46930 + 1.23289i 0.0665123 + 0.0558104i
\(489\) 12.3612 + 10.4867i 0.558995 + 0.474226i
\(490\) −16.4767 + 11.8901i −0.744339 + 0.537139i
\(491\) −13.9317 + 11.6901i −0.628728 + 0.527565i −0.900533 0.434787i \(-0.856824\pi\)
0.271806 + 0.962352i \(0.412379\pi\)
\(492\) 1.07935 + 6.32092i 0.0486607 + 0.284969i
\(493\) 5.62418 + 4.71924i 0.253300 + 0.212544i
\(494\) −13.6035 −0.612048
\(495\) 2.41455 + 0.908507i 0.108526 + 0.0408343i
\(496\) −1.53152 2.65268i −0.0687674 0.119109i
\(497\) 9.18401 + 28.4211i 0.411959 + 1.27486i
\(498\) 7.59973 + 13.3290i 0.340552 + 0.597288i
\(499\) −18.1265 6.59752i −0.811456 0.295346i −0.0972306 0.995262i \(-0.530998\pi\)
−0.714225 + 0.699916i \(0.753221\pi\)
\(500\) 3.50082 2.93753i 0.156561 0.131371i
\(501\) 14.3990 + 25.2542i 0.643301 + 1.12827i
\(502\) 10.7172 3.90074i 0.478332 0.174099i
\(503\) 10.2088 + 17.6822i 0.455190 + 0.788412i 0.998699 0.0509915i \(-0.0162381\pi\)
−0.543509 + 0.839403i \(0.682905\pi\)
\(504\) 7.05393 3.63897i 0.314207 0.162092i
\(505\) −12.5898 + 21.8061i −0.560237 + 0.970359i
\(506\) −0.257600 + 1.46092i −0.0114517 + 0.0649459i
\(507\) 1.21088 + 7.09123i 0.0537772 + 0.314933i
\(508\) 9.52770 + 3.46780i 0.422723 + 0.153859i
\(509\) 33.4230 28.0452i 1.48145 1.24308i 0.576829 0.816865i \(-0.304290\pi\)
0.904620 0.426219i \(-0.140155\pi\)
\(510\) −7.29224 + 2.60960i −0.322906 + 0.115555i
\(511\) −31.5626 6.76199i −1.39625 0.299133i
\(512\) −1.00000 −0.0441942
\(513\) 17.0647 + 0.276795i 0.753426 + 0.0122208i
\(514\) 1.91489 + 3.31669i 0.0844623 + 0.146293i
\(515\) −31.0329 + 11.2951i −1.36747 + 0.497720i
\(516\) −16.2465 13.7828i −0.715214 0.606755i
\(517\) −0.327697 0.119272i −0.0144121 0.00524558i
\(518\) −12.1431 15.5942i −0.533538 0.685170i
\(519\) −2.13201 12.4856i −0.0935850 0.548057i
\(520\) 2.08759 11.8393i 0.0915469 0.519189i
\(521\) −15.2210 −0.666844 −0.333422 0.942778i \(-0.608203\pi\)
−0.333422 + 0.942778i \(0.608203\pi\)
\(522\) 13.4873 4.74447i 0.590324 0.207660i
\(523\) 10.6619 0.466211 0.233106 0.972451i \(-0.425111\pi\)
0.233106 + 0.972451i \(0.425111\pi\)
\(524\) −6.24133 5.23710i −0.272654 0.228784i
\(525\) 0.657925 15.6843i 0.0287142 0.684518i
\(526\) −4.88282 27.6919i −0.212901 1.20742i
\(527\) −4.43411 1.61388i −0.193153 0.0703018i
\(528\) 0.513121 + 0.00277412i 0.0223307 + 0.000120728i
\(529\) 0.360100 2.04223i 0.0156565 0.0887925i
\(530\) 32.5792 1.41515
\(531\) −0.108611 0.0931554i −0.00471333 0.00404260i
\(532\) −7.67944 + 4.06738i −0.332946 + 0.176343i
\(533\) −14.4086 + 5.24430i −0.624105 + 0.227156i
\(534\) −16.1371 5.97243i −0.698322 0.258453i
\(535\) −45.7765 16.6613i −1.97909 0.720330i
\(536\) −1.79748 10.1940i −0.0776391 0.440313i
\(537\) −22.3463 18.9576i −0.964315 0.818081i
\(538\) 2.23826 12.6938i 0.0964984 0.547270i
\(539\) 1.16518 1.71550i 0.0501878 0.0738919i
\(540\) −2.85966 + 14.8092i −0.123060 + 0.637288i
\(541\) −11.1950 + 19.3903i −0.481311 + 0.833654i −0.999770 0.0214478i \(-0.993172\pi\)
0.518459 + 0.855102i \(0.326506\pi\)
\(542\) −5.92392 + 2.15613i −0.254454 + 0.0926137i
\(543\) 13.4464 + 11.4073i 0.577040 + 0.489535i
\(544\) −1.18010 + 0.990226i −0.0505966 + 0.0424556i
\(545\) 41.5762 34.8866i 1.78093 1.49438i
\(546\) 11.5797 + 15.0377i 0.495566 + 0.643553i
\(547\) 28.0019 10.1918i 1.19727 0.435772i 0.335002 0.942217i \(-0.391263\pi\)
0.862272 + 0.506445i \(0.169041\pi\)
\(548\) −9.38129 16.2489i −0.400749 0.694118i
\(549\) 2.93077 4.95182i 0.125082 0.211338i
\(550\) 0.507426 0.878887i 0.0216367 0.0374759i
\(551\) −14.7095 + 5.35383i −0.626646 + 0.228081i
\(552\) −8.67289 0.0468887i −0.369143 0.00199572i
\(553\) 7.29306 + 9.36574i 0.310132 + 0.398272i
\(554\) 1.65106 + 9.36365i 0.0701470 + 0.397823i
\(555\) 37.5570 + 0.203047i 1.59421 + 0.00861885i
\(556\) −3.77319 + 21.3988i −0.160019 + 0.907512i
\(557\) 13.7151 23.7553i 0.581129 1.00655i −0.414217 0.910178i \(-0.635944\pi\)
0.995346 0.0963671i \(-0.0307223\pi\)
\(558\) −7.10274 + 5.83021i −0.300683 + 0.246812i
\(559\) 25.4725 44.1197i 1.07737 1.86607i
\(560\) −2.36142 7.30773i −0.0997882 0.308808i
\(561\) 0.608284 0.504832i 0.0256818 0.0213140i
\(562\) −5.57288 31.6054i −0.235078 1.33319i
\(563\) 4.71567 + 26.7439i 0.198742 + 1.12712i 0.906988 + 0.421156i \(0.138375\pi\)
−0.708247 + 0.705965i \(0.750513\pi\)
\(564\) 0.364890 2.00592i 0.0153646 0.0844643i
\(565\) −25.3067 21.2348i −1.06466 0.893357i
\(566\) −21.1508 −0.889035
\(567\) −14.2201 19.0995i −0.597187 0.802102i
\(568\) −11.2891 −0.473680
\(569\) 8.55787 + 7.18091i 0.358765 + 0.301039i 0.804298 0.594226i \(-0.202542\pi\)
−0.445533 + 0.895265i \(0.646986\pi\)
\(570\) 2.95539 16.2467i 0.123788 0.680501i
\(571\) −0.986364 5.59395i −0.0412780 0.234099i 0.957188 0.289467i \(-0.0934780\pi\)
−0.998466 + 0.0553676i \(0.982367\pi\)
\(572\) 0.213064 + 1.20835i 0.00890867 + 0.0505236i
\(573\) −22.3915 + 18.5833i −0.935416 + 0.776329i
\(574\) −6.56593 + 7.26863i −0.274057 + 0.303387i
\(575\) −8.57662 + 14.8551i −0.357670 + 0.619502i
\(576\) 0.488970 + 2.95988i 0.0203737 + 0.123328i
\(577\) 6.53867 11.3253i 0.272209 0.471479i −0.697219 0.716859i \(-0.745579\pi\)
0.969427 + 0.245380i \(0.0789126\pi\)
\(578\) 2.53992 14.4046i 0.105647 0.599152i
\(579\) 13.4998 + 0.0729848i 0.561033 + 0.00303315i
\(580\) −2.40220 13.6235i −0.0997459 0.565687i
\(581\) −8.81478 + 21.7166i −0.365699 + 0.900955i
\(582\) 3.16194 + 0.0170946i 0.131066 + 0.000708592i
\(583\) −3.12458 + 1.13725i −0.129407 + 0.0471002i
\(584\) 6.10013 10.5657i 0.252425 0.437213i
\(585\) −36.0638 0.389959i −1.49105 0.0161228i
\(586\) 3.99035 + 6.91149i 0.164840 + 0.285511i
\(587\) −31.4510 + 11.4472i −1.29812 + 0.472478i −0.896385 0.443276i \(-0.853816\pi\)
−0.401738 + 0.915755i \(0.631594\pi\)
\(588\) 11.0332 + 5.02679i 0.455001 + 0.207302i
\(589\) 7.70694 6.46689i 0.317559 0.266464i
\(590\) −0.106057 + 0.0889922i −0.00436629 + 0.00366375i
\(591\) 15.2523 + 12.9394i 0.627396 + 0.532254i
\(592\) 7.01976 2.55498i 0.288510 0.105009i
\(593\) 13.9689 24.1948i 0.573633 0.993561i −0.422556 0.906337i \(-0.638867\pi\)
0.996189 0.0872245i \(-0.0277997\pi\)
\(594\) −0.242690 1.52014i −0.00995768 0.0623719i
\(595\) −10.0230 6.28555i −0.410904 0.257682i
\(596\) −2.17509 + 12.3355i −0.0890950 + 0.505283i
\(597\) −30.4731 25.8520i −1.24718 1.05805i
\(598\) −3.60126 20.4238i −0.147267 0.835190i
\(599\) 2.35927 + 0.858704i 0.0963972 + 0.0350857i 0.389769 0.920913i \(-0.372555\pi\)
−0.293371 + 0.955999i \(0.594777\pi\)
\(600\) 5.56444 + 2.05943i 0.227167 + 0.0840757i
\(601\) 13.4389 4.89138i 0.548186 0.199523i −0.0530544 0.998592i \(-0.516896\pi\)
0.601240 + 0.799068i \(0.294673\pi\)
\(602\) 1.18817 32.5227i 0.0484260 1.32553i
\(603\) −29.2941 + 10.3049i −1.19295 + 0.419647i
\(604\) −18.7063 −0.761149
\(605\) 5.50027 31.1936i 0.223618 1.26820i
\(606\) 15.0245 + 0.0812281i 0.610330 + 0.00329966i
\(607\) −17.7153 6.44786i −0.719044 0.261710i −0.0435238 0.999052i \(-0.513858\pi\)
−0.675520 + 0.737342i \(0.736081\pi\)
\(608\) −0.570354 3.23464i −0.0231309 0.131182i
\(609\) 18.4395 + 11.7030i 0.747206 + 0.474229i
\(610\) −4.26493 3.57870i −0.172682 0.144897i
\(611\) 4.87524 0.197231
\(612\) 3.50799 + 3.00878i 0.141802 + 0.121623i
\(613\) −13.0544 −0.527264 −0.263632 0.964623i \(-0.584920\pi\)
−0.263632 + 0.964623i \(0.584920\pi\)
\(614\) 5.93088 33.6357i 0.239351 1.35743i
\(615\) −3.13301 18.3477i −0.126335 0.739849i
\(616\) 0.481571 + 0.618433i 0.0194030 + 0.0249174i
\(617\) 19.2687 + 7.01323i 0.775729 + 0.282342i 0.699390 0.714740i \(-0.253455\pi\)
0.0763383 + 0.997082i \(0.475677\pi\)
\(618\) 15.0269 + 12.7482i 0.604472 + 0.512806i
\(619\) −24.2966 + 8.84324i −0.976563 + 0.355440i −0.780503 0.625152i \(-0.785037\pi\)
−0.196060 + 0.980592i \(0.562815\pi\)
\(620\) 4.44554 + 7.69989i 0.178537 + 0.309235i
\(621\) 4.10199 + 25.6937i 0.164607 + 1.03105i
\(622\) 8.92855 0.358002
\(623\) −8.08192 25.0106i −0.323795 1.00203i
\(624\) −6.75412 + 2.41703i −0.270381 + 0.0967585i
\(625\) −23.2826 + 19.5364i −0.931304 + 0.781457i
\(626\) 13.1423 + 4.78339i 0.525271 + 0.191183i
\(627\) 0.283688 + 1.66134i 0.0113294 + 0.0663477i
\(628\) 2.18176 12.3734i 0.0870619 0.493752i
\(629\) 5.75404 9.96629i 0.229429 0.397382i
\(630\) −20.4754 + 10.5628i −0.815758 + 0.420831i
\(631\) 9.27214 + 16.0598i 0.369118 + 0.639331i 0.989428 0.145026i \(-0.0463265\pi\)
−0.620310 + 0.784357i \(0.712993\pi\)
\(632\) −4.21601 + 1.53450i −0.167704 + 0.0610392i
\(633\) 2.32988 + 4.08632i 0.0926043 + 0.162417i
\(634\) −16.1837 + 13.5797i −0.642735 + 0.539319i
\(635\) −27.6559 10.0659i −1.09749 0.399455i
\(636\) −9.62892 16.8880i −0.381812 0.669652i
\(637\) −7.10429 + 28.1077i −0.281482 + 1.11367i
\(638\) 0.705950 + 1.22274i 0.0279488 + 0.0484088i
\(639\) 5.52003 + 33.4144i 0.218369 + 1.32185i
\(640\) 2.90269 0.114739
\(641\) −9.42633 7.90963i −0.372318 0.312411i 0.437360 0.899286i \(-0.355914\pi\)
−0.809678 + 0.586875i \(0.800358\pi\)
\(642\) 4.89279 + 28.6534i 0.193103 + 1.13086i
\(643\) −29.8571 + 25.0531i −1.17745 + 0.987998i −0.177458 + 0.984128i \(0.556787\pi\)
−0.999993 + 0.00386972i \(0.998768\pi\)
\(644\) −8.13961 10.4529i −0.320746 0.411901i
\(645\) 47.1586 + 40.0072i 1.85687 + 1.57528i
\(646\) −3.87610 3.25243i −0.152503 0.127965i
\(647\) 23.5544 + 40.7974i 0.926019 + 1.60391i 0.789914 + 0.613218i \(0.210125\pi\)
0.136106 + 0.990694i \(0.456541\pi\)
\(648\) 8.52182 2.89459i 0.334769 0.113710i
\(649\) 0.00706512 0.0122372i 0.000277330 0.000480350i
\(650\) −2.46367 + 13.9721i −0.0966329 + 0.548033i
\(651\) −13.7091 3.01465i −0.537302 0.118154i
\(652\) −8.79457 3.20096i −0.344422 0.125359i
\(653\) 4.56742 + 25.9032i 0.178737 + 1.01367i 0.933741 + 0.357949i \(0.116524\pi\)
−0.755004 + 0.655720i \(0.772365\pi\)
\(654\) −30.3721 11.2409i −1.18764 0.439553i
\(655\) 18.1166 + 15.2017i 0.707876 + 0.593978i
\(656\) −1.85110 3.20621i −0.0722734 0.125181i
\(657\) −34.2561 12.8893i −1.33646 0.502861i
\(658\) 2.75218 1.45768i 0.107291 0.0568262i
\(659\) −4.00501 3.36060i −0.156013 0.130910i 0.561440 0.827518i \(-0.310248\pi\)
−0.717453 + 0.696607i \(0.754692\pi\)
\(660\) −1.48943 0.00805240i −0.0579760 0.000313439i
\(661\) 31.0713 26.0719i 1.20853 1.01408i 0.209189 0.977875i \(-0.432918\pi\)
0.999344 0.0362050i \(-0.0115269\pi\)
\(662\) −9.12790 + 7.65922i −0.354766 + 0.297684i
\(663\) −5.57717 + 9.54045i −0.216599 + 0.370520i
\(664\) −6.78600 5.69413i −0.263348 0.220975i
\(665\) 22.2910 11.8063i 0.864409 0.457830i
\(666\) −10.9949 19.5284i −0.426044 0.756708i
\(667\) −11.9321 20.6670i −0.462014 0.800231i
\(668\) −12.8573 10.7885i −0.497462 0.417421i
\(669\) 1.45171 + 8.50159i 0.0561265 + 0.328690i
\(670\) 5.21751 + 29.5900i 0.201570 + 1.14316i
\(671\) 0.533961 + 0.194346i 0.0206133 + 0.00750264i
\(672\) −3.09016 + 3.38392i −0.119206 + 0.130537i
\(673\) 2.47474 14.0350i 0.0953943 0.541008i −0.899231 0.437473i \(-0.855874\pi\)
0.994626 0.103535i \(-0.0330154\pi\)
\(674\) 3.42764 5.93684i 0.132028 0.228679i
\(675\) 3.37482 17.4771i 0.129897 0.672693i
\(676\) −2.07669 3.59693i −0.0798727 0.138344i
\(677\) 3.80927 + 3.19636i 0.146402 + 0.122846i 0.713047 0.701116i \(-0.247315\pi\)
−0.566645 + 0.823962i \(0.691759\pi\)
\(678\) −3.52794 + 19.3942i −0.135490 + 0.744831i
\(679\) 2.96751 + 3.81088i 0.113883 + 0.146248i
\(680\) 3.42548 2.87432i 0.131361 0.110225i
\(681\) 2.50333 + 0.926495i 0.0959279 + 0.0355034i
\(682\) −0.695142 0.583293i −0.0266184 0.0223355i
\(683\) 19.3156 0.739091 0.369545 0.929213i \(-0.379513\pi\)
0.369545 + 0.929213i \(0.379513\pi\)
\(684\) −9.29527 + 3.26982i −0.355413 + 0.125025i
\(685\) 27.2310 + 47.1654i 1.04044 + 1.80210i
\(686\) 4.39358 + 17.9916i 0.167747 + 0.686921i
\(687\) 3.57934 6.12292i 0.136560 0.233604i
\(688\) 11.5588 + 4.20706i 0.440675 + 0.160393i
\(689\) 35.6097 29.8801i 1.35662 1.13834i
\(690\) 25.1747 + 0.136103i 0.958384 + 0.00518137i
\(691\) 11.1691 4.06523i 0.424893 0.154649i −0.120718 0.992687i \(-0.538520\pi\)
0.545611 + 0.838038i \(0.316297\pi\)
\(692\) 3.65645 + 6.33316i 0.138997 + 0.240751i
\(693\) 1.59502 1.72779i 0.0605896 0.0656332i
\(694\) −10.8523 + 18.7967i −0.411946 + 0.713512i
\(695\) 10.9524 62.1141i 0.415448 2.35612i
\(696\) −6.35202 + 5.27173i −0.240773 + 0.199824i
\(697\) −5.35936 1.95065i −0.203000 0.0738861i
\(698\) −13.5620 + 11.3799i −0.513328 + 0.430734i
\(699\) −6.04689 + 33.2417i −0.228714 + 1.25732i
\(700\) 2.78682 + 8.62420i 0.105332 + 0.325964i
\(701\) 1.66339 0.0628253 0.0314126 0.999507i \(-0.489999\pi\)
0.0314126 + 0.999507i \(0.489999\pi\)
\(702\) 10.4567 + 18.8096i 0.394662 + 0.709921i
\(703\) 12.2682 + 21.2491i 0.462704 + 0.801426i
\(704\) −0.278389 + 0.101325i −0.0104922 + 0.00381884i
\(705\) −1.05916 + 5.82255i −0.0398903 + 0.219290i
\(706\) −24.5375 8.93092i −0.923481 0.336120i
\(707\) 14.1007 + 18.1081i 0.530312 + 0.681027i
\(708\) 0.0774762 + 0.0286743i 0.00291174 + 0.00107765i
\(709\) 0.667793 3.78724i 0.0250795 0.142233i −0.969697 0.244311i \(-0.921438\pi\)
0.994776 + 0.102078i \(0.0325492\pi\)
\(710\) 32.7688 1.22979
\(711\) 6.60344 + 11.7286i 0.247648 + 0.439855i
\(712\) 9.93441 0.372308
\(713\) 11.7494 + 9.85895i 0.440020 + 0.369221i
\(714\) −0.295874 + 7.05334i −0.0110728 + 0.263964i
\(715\) −0.618460 3.50746i −0.0231291 0.131172i
\(716\) 15.8986 + 5.78661i 0.594157 + 0.216256i
\(717\) −3.98983 + 6.82511i −0.149003 + 0.254888i
\(718\) −3.75483 + 21.2947i −0.140129 + 0.794710i
\(719\) −15.7621 −0.587827 −0.293914 0.955832i \(-0.594958\pi\)
−0.293914 + 0.955832i \(0.594958\pi\)
\(720\) −1.41933 8.59162i −0.0528952 0.320191i
\(721\) −1.09897 + 30.0812i −0.0409278 + 1.12028i
\(722\) −7.71657 + 2.80860i −0.287181 + 0.104525i
\(723\) −8.14945 47.7252i −0.303081 1.77492i
\(724\) −9.56661 3.48196i −0.355540 0.129406i
\(725\) 2.83495 + 16.0778i 0.105287 + 0.597114i
\(726\) −17.7954 + 6.36825i −0.660449 + 0.236348i
\(727\) −2.04939 + 11.6227i −0.0760077 + 0.431061i 0.922929 + 0.384969i \(0.125788\pi\)
−0.998937 + 0.0460921i \(0.985323\pi\)
\(728\) −9.28339 5.82172i −0.344065 0.215767i
\(729\) −12.7345 23.8082i −0.471650 0.881786i
\(730\) −17.7068 + 30.6690i −0.655357 + 1.13511i
\(731\) 17.8065 6.48105i 0.658599 0.239710i
\(732\) −0.594563 + 3.26851i −0.0219757 + 0.120807i
\(733\) 22.6916 19.0405i 0.838133 0.703277i −0.119010 0.992893i \(-0.537972\pi\)
0.957143 + 0.289616i \(0.0935276\pi\)
\(734\) 10.9711 9.20588i 0.404952 0.339795i
\(735\) −32.0259 14.5912i −1.18129 0.538205i
\(736\) 4.70539 1.71262i 0.173443 0.0631280i
\(737\) −1.53330 2.65576i −0.0564800 0.0978262i
\(738\) −8.58486 + 7.04679i −0.316013 + 0.259396i
\(739\) 12.5873 21.8019i 0.463032 0.801995i −0.536078 0.844168i \(-0.680095\pi\)
0.999110 + 0.0421730i \(0.0134281\pi\)
\(740\) −20.3762 + 7.41632i −0.749043 + 0.272629i
\(741\) −11.6704 20.4686i −0.428725 0.751932i
\(742\) 11.1684 27.5151i 0.410005 1.01011i
\(743\) −2.42758 13.7675i −0.0890591 0.505079i −0.996407 0.0846981i \(-0.973007\pi\)
0.907348 0.420381i \(-0.138104\pi\)
\(744\) 2.67748 4.58016i 0.0981611 0.167917i
\(745\) 6.31360 35.8062i 0.231312 1.31184i
\(746\) −8.06571 + 13.9702i −0.295307 + 0.511486i
\(747\) −13.5358 + 22.8700i −0.495249 + 0.836770i
\(748\) −0.228193 + 0.395242i −0.00834357 + 0.0144515i
\(749\) −29.7640 + 32.9494i −1.08755 + 1.20395i
\(750\) 7.42335 + 2.74742i 0.271062 + 0.100322i
\(751\) −1.10647 6.27512i −0.0403758 0.228982i 0.957942 0.286962i \(-0.0926453\pi\)
−0.998318 + 0.0579795i \(0.981534\pi\)
\(752\) 0.204405 + 1.15924i 0.00745388 + 0.0422731i
\(753\) 15.0636 + 12.7793i 0.548949 + 0.465703i
\(754\) −15.1205 12.6876i −0.550657 0.462056i
\(755\) 54.2986 1.97613
\(756\) 11.5270 + 7.49189i 0.419233 + 0.272477i
\(757\) 40.1257 1.45839 0.729196 0.684305i \(-0.239894\pi\)
0.729196 + 0.684305i \(0.239894\pi\)
\(758\) 6.05053 + 5.07700i 0.219765 + 0.184405i
\(759\) −2.41919 + 0.865729i −0.0878109 + 0.0314240i
\(760\) 1.65556 + 9.38915i 0.0600535 + 0.340580i
\(761\) −3.17579 18.0108i −0.115122 0.652890i −0.986690 0.162615i \(-0.948007\pi\)
0.871568 0.490276i \(-0.163104\pi\)
\(762\) 2.95599 + 17.3110i 0.107084 + 0.627111i
\(763\) −15.2112 47.0731i −0.550682 1.70416i
\(764\) 8.39998 14.5492i 0.303901 0.526371i
\(765\) −10.1826 8.73356i −0.368153 0.315762i
\(766\) −3.90031 + 6.75554i −0.140924 + 0.244088i
\(767\) −0.0343028 + 0.194541i −0.00123860 + 0.00702445i
\(768\) −0.857903 1.50466i −0.0309569 0.0542947i
\(769\) 1.55869 + 8.83975i 0.0562077 + 0.318770i 0.999928 0.0119740i \(-0.00381155\pi\)
−0.943721 + 0.330744i \(0.892700\pi\)
\(770\) −1.39785 1.79512i −0.0503750 0.0646916i
\(771\) −3.34770 + 5.72666i −0.120565 + 0.206241i
\(772\) −7.32418 + 2.66579i −0.263603 + 0.0959437i
\(773\) 6.03078 10.4456i 0.216912 0.375703i −0.736950 0.675947i \(-0.763735\pi\)
0.953862 + 0.300244i \(0.0970682\pi\)
\(774\) 6.80051 36.2699i 0.244439 1.30369i
\(775\) −5.24639 9.08701i −0.188456 0.326415i
\(776\) −1.71548 + 0.624382i −0.0615820 + 0.0224140i
\(777\) 13.0463 31.6496i 0.468035 1.13542i
\(778\) −12.3052 + 10.3253i −0.441162 + 0.370178i
\(779\) 9.31513 7.81632i 0.333749 0.280049i
\(780\) 19.6051 7.01588i 0.701975 0.251209i
\(781\) −3.14276 + 1.14387i −0.112457 + 0.0409309i
\(782\) 3.85697 6.68047i 0.137925 0.238893i
\(783\) 18.7096 + 16.2235i 0.668628 + 0.579782i
\(784\) −6.98134 0.510786i −0.249334 0.0182424i
\(785\) −6.33298 + 35.9161i −0.226034 + 1.28190i
\(786\) 2.52560 13.8840i 0.0900850 0.495226i
\(787\) 3.90434 + 22.1426i 0.139175 + 0.789299i 0.971861 + 0.235554i \(0.0756906\pi\)
−0.832686 + 0.553745i \(0.813198\pi\)
\(788\) −10.8514 3.94960i −0.386567 0.140699i
\(789\) 37.4779 31.1039i 1.33425 1.10733i
\(790\) 12.2378 4.45418i 0.435400 0.158473i
\(791\) −26.6095 + 14.0936i −0.946124 + 0.501110i
\(792\) 0.436034 + 0.774453i 0.0154938 + 0.0275190i
\(793\) −7.94388 −0.282096
\(794\) 3.54503 20.1048i 0.125808 0.713494i
\(795\) 27.9498 + 49.0206i 0.991276 + 1.73858i
\(796\) 21.6805 + 7.89104i 0.768443 + 0.279690i
\(797\) −6.54790 37.1350i −0.231939 1.31539i −0.848966 0.528448i \(-0.822774\pi\)
0.617027 0.786942i \(-0.288337\pi\)
\(798\) −12.7082 8.06553i −0.449867 0.285517i
\(799\) 1.38913 + 1.16562i 0.0491438 + 0.0412365i
\(800\) −3.42560 −0.121113
\(801\) −4.85762 29.4047i −0.171636 1.03896i
\(802\) −2.50927 −0.0886054
\(803\) 0.627632 3.55948i 0.0221486 0.125611i
\(804\) 13.7964 11.4500i 0.486562 0.403812i
\(805\) 23.6268 + 30.3415i 0.832734 + 1.06940i
\(806\) 11.9210 + 4.33891i 0.419901 + 0.152831i
\(807\) 21.0201 7.52225i 0.739943 0.264796i
\(808\) −8.15141 + 2.96687i −0.286766 + 0.104374i
\(809\) −10.8527 18.7975i −0.381562 0.660884i 0.609724 0.792614i \(-0.291280\pi\)
−0.991286 + 0.131730i \(0.957947\pi\)
\(810\) −24.7362 + 8.40208i −0.869141 + 0.295219i
\(811\) 49.8708 1.75120 0.875600 0.483037i \(-0.160466\pi\)
0.875600 + 0.483037i \(0.160466\pi\)
\(812\) −12.3294 2.64146i −0.432678 0.0926971i
\(813\) −8.32639 7.06373i −0.292019 0.247736i
\(814\) 1.69534 1.42256i 0.0594215 0.0498606i
\(815\) 25.5279 + 9.29139i 0.894203 + 0.325463i
\(816\) −2.50237 0.926139i −0.0876004 0.0324213i
\(817\) −7.01571 + 39.7881i −0.245449 + 1.39201i
\(818\) −2.87158 + 4.97373i −0.100403 + 0.173902i
\(819\) −12.6923 + 30.3244i −0.443505 + 1.05962i
\(820\) 5.37318 + 9.30661i 0.187639 + 0.325001i
\(821\) −20.3318 + 7.40015i −0.709583 + 0.258267i −0.671497 0.741007i \(-0.734348\pi\)
−0.0380861 + 0.999274i \(0.512126\pi\)
\(822\) 16.4008 28.0556i 0.572043 0.978552i
\(823\) 37.2136 31.2259i 1.29719 1.08847i 0.306562 0.951851i \(-0.400821\pi\)
0.990624 0.136617i \(-0.0436231\pi\)
\(824\) −10.6911 3.89124i −0.372442 0.135558i
\(825\) 1.75775 + 0.00950302i 0.0611970 + 0.000330853i
\(826\) 0.0388022 + 0.120079i 0.00135010 + 0.00417807i
\(827\) 18.1270 + 31.3970i 0.630339 + 1.09178i 0.987482 + 0.157730i \(0.0504175\pi\)
−0.357143 + 0.934050i \(0.616249\pi\)
\(828\) −7.36995 13.0900i −0.256123 0.454908i
\(829\) 2.93822 0.102049 0.0510243 0.998697i \(-0.483751\pi\)
0.0510243 + 0.998697i \(0.483751\pi\)
\(830\) 19.6976 + 16.5283i 0.683715 + 0.573705i
\(831\) −12.6727 + 10.5174i −0.439610 + 0.364845i
\(832\) 3.17270 2.66221i 0.109994 0.0922955i
\(833\) −8.74451 + 6.31032i −0.302979 + 0.218640i
\(834\) −35.4350 + 12.6808i −1.22701 + 0.439099i
\(835\) 37.3206 + 31.3157i 1.29153 + 1.08373i
\(836\) −0.486531 0.842696i −0.0168270 0.0291452i
\(837\) −14.8660 5.68546i −0.513842 0.196518i
\(838\) −5.77420 + 10.0012i −0.199467 + 0.345486i
\(839\) −1.43777 + 8.15399i −0.0496373 + 0.281507i −0.999516 0.0311119i \(-0.990095\pi\)
0.949879 + 0.312619i \(0.101206\pi\)
\(840\) 8.96978 9.82246i 0.309487 0.338907i
\(841\) 5.90775 + 2.15025i 0.203716 + 0.0741464i
\(842\) 4.82185 + 27.3461i 0.166172 + 0.942408i
\(843\) 42.7744 35.4997i 1.47323 1.22267i
\(844\) −2.08041 1.74567i −0.0716106 0.0600884i
\(845\) 6.02799 + 10.4408i 0.207369 + 0.359174i
\(846\) 3.33126 1.17185i 0.114531 0.0402889i
\(847\) −24.4594 15.3387i −0.840434 0.527045i
\(848\) 8.59792 + 7.21451i 0.295254 + 0.247747i
\(849\) −18.1454 31.8248i −0.622747 1.09222i
\(850\) −4.04257 + 3.39212i −0.138659 + 0.116349i
\(851\) −28.6550 + 24.0444i −0.982279 + 0.824230i
\(852\) −9.68496 16.9863i −0.331801 0.581940i
\(853\) −18.9419 15.8941i −0.648559 0.544205i 0.258075 0.966125i \(-0.416912\pi\)
−0.906633 + 0.421920i \(0.861356\pi\)
\(854\) −4.48449 + 2.37519i −0.153456 + 0.0812773i
\(855\) 26.9813 9.49127i 0.922740 0.324595i
\(856\) −8.39124 14.5341i −0.286807 0.496764i
\(857\) −29.9900 25.1646i −1.02444 0.859606i −0.0342596 0.999413i \(-0.510907\pi\)
−0.990179 + 0.139807i \(0.955352\pi\)
\(858\) −1.63536 + 1.35724i −0.0558304 + 0.0463353i
\(859\) 0.749420 + 4.25017i 0.0255699 + 0.145014i 0.994920 0.100670i \(-0.0320986\pi\)
−0.969350 + 0.245684i \(0.920987\pi\)
\(860\) −33.5516 12.2118i −1.14410 0.416419i
\(861\) −16.5697 3.64371i −0.564695 0.124177i
\(862\) 2.40485 13.6386i 0.0819095 0.464532i
\(863\) 1.63200 2.82670i 0.0555538 0.0962220i −0.836911 0.547339i \(-0.815641\pi\)
0.892465 + 0.451117i \(0.148974\pi\)
\(864\) −4.03413 + 3.27503i −0.137244 + 0.111419i
\(865\) −10.6135 18.3832i −0.360871 0.625047i
\(866\) 23.1946 + 19.4626i 0.788184 + 0.661365i
\(867\) 23.8530 8.53603i 0.810091 0.289899i
\(868\) 8.02700 1.11494i 0.272454 0.0378435i
\(869\) −1.01820 + 0.854375i −0.0345402 + 0.0289827i
\(870\) 18.4379 15.3022i 0.625105 0.518792i
\(871\) 32.8414 + 27.5572i 1.11279 + 0.933740i
\(872\) 18.6978 0.633188
\(873\) 2.68691 + 4.77230i 0.0909382 + 0.161518i
\(874\) 8.22345 + 14.2434i 0.278162 + 0.481791i
\(875\) 3.71782 + 11.5053i 0.125685 + 0.388950i
\(876\) 21.1312 + 0.114243i 0.713956 + 0.00385990i
\(877\) −48.0465 17.4875i −1.62241 0.590511i −0.638574 0.769560i \(-0.720476\pi\)
−0.983840 + 0.179050i \(0.942698\pi\)
\(878\) 2.65341 2.22648i 0.0895484 0.0751400i
\(879\) −6.97611 + 11.9335i −0.235298 + 0.402507i
\(880\) 0.808076 0.294115i 0.0272402 0.00991463i
\(881\) −26.4607 45.8313i −0.891484 1.54409i −0.838097 0.545521i \(-0.816332\pi\)
−0.0533863 0.998574i \(-0.517001\pi\)
\(882\) 1.90179 + 20.9137i 0.0640368 + 0.704201i
\(883\) −11.5763 + 20.0507i −0.389573 + 0.674761i −0.992392 0.123117i \(-0.960711\pi\)
0.602819 + 0.797878i \(0.294044\pi\)
\(884\) 1.10793 6.28338i 0.0372637 0.211333i
\(885\) −0.224889 0.0832327i −0.00755957 0.00279784i
\(886\) −17.3888 6.32901i −0.584188 0.212627i
\(887\) −5.05544 + 4.24202i −0.169745 + 0.142433i −0.723703 0.690112i \(-0.757561\pi\)
0.553958 + 0.832545i \(0.313117\pi\)
\(888\) 9.86665 + 8.37042i 0.331103 + 0.280893i
\(889\) −17.9820 + 19.9065i −0.603097 + 0.667641i
\(890\) −28.8365 −0.966601
\(891\) 2.07908 1.66929i 0.0696519 0.0559235i
\(892\) −2.48972 4.31232i −0.0833620 0.144387i
\(893\) −3.63313 + 1.32235i −0.121578 + 0.0442508i
\(894\) −20.4268 + 7.30993i −0.683174 + 0.244481i
\(895\) −46.1486 16.7967i −1.54258 0.561452i
\(896\) 0.995066 2.45150i 0.0332428 0.0818988i
\(897\) 27.6413 22.9403i 0.922916 0.765954i
\(898\) 3.61043 20.4758i 0.120482 0.683285i
\(899\) 14.5980 0.486869
\(900\) 1.67501 + 10.1394i 0.0558338 + 0.337979i
\(901\) 17.2904 0.576028
\(902\) −0.840196 0.705008i −0.0279755 0.0234742i
\(903\) 49.9549 26.1136i 1.66240 0.869005i
\(904\) −1.97629 11.2081i −0.0657305 0.372776i
\(905\) 27.7689 + 10.1071i 0.923069 + 0.335970i
\(906\) −16.0482 28.1466i −0.533166 0.935109i
\(907\) 9.66954 54.8387i 0.321072 1.82089i −0.214880 0.976641i \(-0.568936\pi\)
0.535952 0.844249i \(-0.319953\pi\)
\(908\) −1.54111 −0.0511435
\(909\) 12.7674 + 22.6765i 0.423467 + 0.752133i
\(910\) 26.9468 + 16.8986i 0.893277 + 0.560184i
\(911\) −4.19059 + 1.52525i −0.138840 + 0.0505338i −0.410506 0.911858i \(-0.634648\pi\)
0.271665 + 0.962392i \(0.412426\pi\)
\(912\) 4.37772 3.63320i 0.144961 0.120307i
\(913\) −2.46610 0.897588i −0.0816161 0.0297058i
\(914\) −0.192925 1.09413i −0.00638140 0.0361907i
\(915\) 1.72583 9.48746i 0.0570543 0.313646i
\(916\) −0.711052 + 4.03258i −0.0234938 + 0.133240i
\(917\) 19.0493 10.0894i 0.629063 0.333180i
\(918\) −1.51768 + 7.85957i −0.0500909 + 0.259405i
\(919\) −23.6375 + 40.9413i −0.779728 + 1.35053i 0.152370 + 0.988324i \(0.451310\pi\)
−0.932098 + 0.362206i \(0.882024\pi\)
\(920\) −13.6583 + 4.97120i −0.450300 + 0.163896i
\(921\) 55.6984 19.9322i 1.83532 0.656788i
\(922\) 21.2351 17.8183i 0.699340 0.586816i
\(923\) 35.8169 30.0540i 1.17893 0.989239i
\(924\) −0.517390 + 1.25516i −0.0170209 + 0.0412916i
\(925\) 24.0469 8.75235i 0.790657 0.287775i
\(926\) 8.94244 + 15.4888i 0.293867 + 0.508992i
\(927\) −6.29000 + 33.5471i −0.206591 + 1.10183i
\(928\) 2.38291 4.12733i 0.0782230 0.135486i
\(929\) −44.5485 + 16.2143i −1.46159 + 0.531974i −0.945802 0.324743i \(-0.894722\pi\)
−0.515786 + 0.856718i \(0.672500\pi\)
\(930\) −7.77188 + 13.2948i −0.254850 + 0.435953i
\(931\) −2.32963 22.8734i −0.0763504 0.749647i
\(932\) −3.38737 19.2107i −0.110957 0.629268i
\(933\) 7.65983 + 13.4344i 0.250772 + 0.439824i
\(934\) 3.12486 17.7220i 0.102249 0.579880i
\(935\) 0.662373 1.14726i 0.0216619 0.0375196i
\(936\) −9.43119 8.08908i −0.308268 0.264400i
\(937\) −17.0443 + 29.5215i −0.556812 + 0.964426i 0.440949 + 0.897532i \(0.354642\pi\)
−0.997760 + 0.0668936i \(0.978691\pi\)
\(938\) 26.7792 + 5.73718i 0.874370 + 0.187326i
\(939\) 4.07741 + 23.8783i 0.133061 + 0.779240i
\(940\) −0.593324 3.36491i −0.0193521 0.109751i
\(941\) −1.72386 9.77652i −0.0561963 0.318705i 0.943732 0.330712i \(-0.107289\pi\)
−0.999928 + 0.0120072i \(0.996178\pi\)
\(942\) 20.4895 7.33237i 0.667584 0.238901i
\(943\) 14.2012 + 11.9162i 0.462454 + 0.388045i
\(944\) −0.0476962 −0.00155238
\(945\) −33.4593 21.7466i −1.08843 0.707417i
\(946\) 3.64412 0.118481
\(947\) 12.8178 + 10.7554i 0.416523 + 0.349504i 0.826839 0.562439i \(-0.190137\pi\)
−0.410316 + 0.911944i \(0.634581\pi\)
\(948\) −5.92583 5.02720i −0.192462 0.163276i
\(949\) 8.77433 + 49.7617i 0.284827 + 1.61533i
\(950\) −1.95381 11.0806i −0.0633898 0.359501i
\(951\) −34.3169 12.7008i −1.11280 0.411853i
\(952\) −1.25325 3.87836i −0.0406182 0.125699i
\(953\) −13.3831 + 23.1802i −0.433520 + 0.750879i −0.997174 0.0751323i \(-0.976062\pi\)
0.563653 + 0.826011i \(0.309395\pi\)
\(954\) 17.1500 28.9765i 0.555251 0.938149i
\(955\) −24.3825 + 42.2318i −0.789000 + 1.36659i
\(956\) 0.792597 4.49504i 0.0256344 0.145380i
\(957\) −1.23417 + 2.11121i −0.0398952 + 0.0682457i
\(958\) −0.831982 4.71840i −0.0268801 0.152445i
\(959\) 49.1691 6.82953i 1.58775 0.220537i
\(960\) 2.49023 + 4.36756i 0.0803717 + 0.140962i
\(961\) 20.3140 7.39370i 0.655291 0.238507i
\(962\) −15.4697 + 26.7943i −0.498762 + 0.863882i
\(963\) −38.9160 + 31.9438i −1.25405 + 1.02937i
\(964\) 13.9765 + 24.2080i 0.450152 + 0.779687i
\(965\) 21.2598 7.73794i 0.684378 0.249093i
\(966\) 8.74504 21.2149i 0.281367 0.682579i
\(967\) −3.99514 + 3.35232i −0.128475 + 0.107803i −0.704761 0.709445i \(-0.748946\pi\)
0.576286 + 0.817248i \(0.304501\pi\)
\(968\) 8.35926 7.01425i 0.268677 0.225446i
\(969\) 1.56849 8.62249i 0.0503871 0.276994i
\(970\) 4.97949 1.81239i 0.159882 0.0581922i
\(971\) 26.2108 45.3985i 0.841146 1.45691i −0.0477809 0.998858i \(-0.515215\pi\)
0.888927 0.458049i \(-0.151452\pi\)
\(972\) 11.6663 + 10.3392i 0.374196 + 0.331629i
\(973\) −48.7046 30.5432i −1.56140 0.979170i
\(974\) 0.689481 3.91024i 0.0220924 0.125292i
\(975\) −23.1369 + 8.27977i −0.740974 + 0.265165i
\(976\) −0.333064 1.88890i −0.0106611 0.0604623i
\(977\) −24.0996 8.77155i −0.771016 0.280627i −0.0735945 0.997288i \(-0.523447\pi\)
−0.697421 + 0.716661i \(0.745669\pi\)
\(978\) −2.72853 15.9789i −0.0872488 0.510950i
\(979\) 2.76563 1.00661i 0.0883898 0.0321713i
\(980\) 20.2647 + 1.48265i 0.647331 + 0.0473616i
\(981\) −9.14266 55.3433i −0.291903 1.76698i
\(982\) 18.1865 0.580355
\(983\) −5.24707 + 29.7576i −0.167356 + 0.949120i 0.779247 + 0.626717i \(0.215602\pi\)
−0.946602 + 0.322403i \(0.895509\pi\)
\(984\) 3.23618 5.53590i 0.103166 0.176478i
\(985\) 31.4984 + 11.4645i 1.00362 + 0.365288i
\(986\) −1.27490 7.23030i −0.0406010 0.230260i
\(987\) 4.55441 + 2.89054i 0.144968 + 0.0920070i
\(988\) 10.4209 + 8.74413i 0.331531 + 0.278188i
\(989\) −61.5938 −1.95857
\(990\) −1.26567 2.24800i −0.0402257 0.0714460i
\(991\) −37.1393 −1.17977 −0.589884 0.807488i \(-0.700827\pi\)
−0.589884 + 0.807488i \(0.700827\pi\)
\(992\) −0.531893 + 3.01651i −0.0168876 + 0.0957744i
\(993\) −19.3554 7.16352i −0.614224 0.227327i
\(994\) 11.2334 27.6752i 0.356302 0.877805i
\(995\) −62.9316 22.9052i −1.99507 0.726145i
\(996\) 2.74600 15.0956i 0.0870102 0.478323i
\(997\) 25.3018 9.20910i 0.801316 0.291655i 0.0912840 0.995825i \(-0.470903\pi\)
0.710032 + 0.704170i \(0.248681\pi\)
\(998\) 9.64493 + 16.7055i 0.305305 + 0.528804i
\(999\) 19.9510 33.2970i 0.631221 1.05347i
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 378.2.v.a.79.8 yes 72
7.4 even 3 378.2.w.b.25.1 yes 72
27.13 even 9 378.2.w.b.121.1 yes 72
189.67 even 9 inner 378.2.v.a.67.8 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.v.a.67.8 72 189.67 even 9 inner
378.2.v.a.79.8 yes 72 1.1 even 1 trivial
378.2.w.b.25.1 yes 72 7.4 even 3
378.2.w.b.121.1 yes 72 27.13 even 9