Properties

Label 378.2.v.a.67.8
Level $378$
Weight $2$
Character 378.67
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 67.8
Character \(\chi\) \(=\) 378.67
Dual form 378.2.v.a.79.8

$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 0.636471 + 0.771301i \(0.280394\pi\)
−0.861887 + 0.507100i \(0.830718\pi\)
\(6\) −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 0.991581 0.129491i \(-0.0413344\pi\)
−0.976070 + 0.217459i \(0.930223\pi\)
\(12\) 1.73203 0.00936395i 0.499993 0.00270314i
\(13\) 0.719192 4.07874i 0.199468 1.13124i −0.706442 0.707771i \(-0.749701\pi\)
0.905910 0.423469i \(-0.139188\pi\)
\(14\) 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 0.757371 0.652984i \(-0.226483\pi\)
−0.944187 + 0.329411i \(0.893150\pi\)
\(18\) 1.47182 2.61414i 0.346912 0.616159i
\(19\) −1.64227 + 2.84449i −0.376762 + 0.652572i −0.990589 0.136869i \(-0.956296\pi\)
0.613827 + 0.789441i \(0.289629\pi\)
\(20\) 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 0.948158 0.317799i \(-0.102944\pi\)
−0.148325 + 0.988939i \(0.547388\pi\)
\(24\) −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 0.959985 + 0.280051i \(0.0903513\pi\)
−0.806308 + 0.591496i \(0.798538\pi\)
\(30\) 3.83384 3.25246i 0.699960 0.593814i
\(31\) 0.531893 3.01651i 0.0955307 0.541782i −0.899053 0.437840i \(-0.855743\pi\)
0.994583 0.103941i \(-0.0331454\pi\)
\(32\) 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 −0.892557 0.450935i \(-0.851091\pi\)
0.992958 0.118468i \(-0.0377984\pi\)
\(42\) 4.06117 + 2.12294i 0.626652 + 0.327577i
\(43\) −9.42283 + 7.90669i −1.43697 + 1.20576i −0.495522 + 0.868596i \(0.665023\pi\)
−0.941446 + 0.337163i \(0.890532\pi\)
\(44\) 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 0.996080 0.0884609i \(-0.0281948\pi\)
−0.966264 + 0.257553i \(0.917084\pi\)
\(48\) 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 0.166243 + 0.986085i \(0.446836\pi\)
−0.937096 + 0.349072i \(0.886497\pi\)
\(54\) 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 −0.339101 0.940750i \(-0.610123\pi\)
0.344936 + 0.938626i \(0.387901\pi\)
\(60\) −0.846254 + 4.95587i −0.109251 + 0.639800i
\(61\) −0.333064 1.88890i −0.0426445 0.241849i 0.956033 0.293259i \(-0.0947397\pi\)
−0.998678 + 0.0514096i \(0.983629\pi\)
\(62\) 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 0.982353 0.187034i \(-0.0598875\pi\)
−0.0136089 + 0.999907i \(0.504332\pi\)
\(68\) −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 0.308051 + 0.951370i \(0.400323\pi\)
−0.977936 + 0.208905i \(0.933010\pi\)
\(72\) −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 −0.815320 0.579011i \(-0.803439\pi\)
0.428636 + 0.903477i \(0.358994\pi\)
\(80\) 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 0.945010 + 0.327042i \(0.106052\pi\)
−0.776164 + 0.630531i \(0.782837\pi\)
\(84\) −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 −0.473000 0.881062i \(-0.656829\pi\)
0.999522 0.0309012i \(-0.00983773\pi\)
\(90\) 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 −0.711018 0.703174i \(-0.751765\pi\)
0.569025 + 0.822321i \(0.307321\pi\)
\(98\) −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 −0.910450 0.413620i \(-0.864264\pi\)
0.249238 + 0.968442i \(0.419820\pi\)
\(102\) −0.449125 + 2.63018i −0.0444700 + 0.260427i
\(103\) −1.97563 + 11.2044i −0.194665 + 1.10400i 0.718230 + 0.695806i \(0.244953\pi\)
−0.912895 + 0.408195i \(0.866158\pi\)
\(104\) 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 0.912016 + 0.410154i \(0.134525\pi\)
−0.100804 + 0.994906i \(0.532142\pi\)
\(108\) −4.85332 + 1.85615i −0.467011 + 0.178608i
\(109\) 9.34891 16.1928i 0.895463 1.55099i 0.0622322 0.998062i \(-0.480178\pi\)
0.833231 0.552926i \(-0.186489\pi\)
\(110\) 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 0.953008 0.302944i \(-0.0979695\pi\)
−0.132853 + 0.991136i \(0.542414\pi\)
\(114\) 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 0.998376 0.0569675i \(-0.0181431\pi\)
−0.548523 + 0.836135i \(0.684810\pi\)
\(128\) −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 0.328041 0.944664i \(-0.393612\pi\)
−0.873348 + 0.487096i \(0.838056\pi\)
\(132\) 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 −0.548634 0.836062i \(-0.684852\pi\)
−0.957689 + 0.287806i \(0.907074\pi\)
\(138\) −1.55221 8.53299i −0.132133 0.726376i
\(139\) 20.4185 7.43173i 1.73188 0.630351i 0.733115 0.680105i \(-0.238066\pi\)
0.998762 + 0.0497539i \(0.0158437\pi\)
\(140\) −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 0.188565 0.982061i \(-0.439616\pi\)
0.775706 + 0.631095i \(0.217394\pi\)
\(150\) 2.99439 + 5.12229i 0.244491 + 0.418233i
\(151\) −3.24832 18.4221i −0.264344 1.49917i −0.770896 0.636961i \(-0.780191\pi\)
0.506552 0.862209i \(-0.330920\pi\)
\(152\) −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 −0.767060 0.641575i \(-0.778281\pi\)
−0.175206 + 0.984532i \(0.556059\pi\)
\(158\) 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 0.622494 0.782625i \(-0.286120\pi\)
−0.989020 + 0.147783i \(0.952786\pi\)
\(164\) −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 −0.00865161 0.999963i \(-0.502754\pi\)
−0.986273 + 0.165122i \(0.947198\pi\)
\(168\) 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 0.589768 0.807573i \(-0.299219\pi\)
−0.0673089 + 0.997732i \(0.521441\pi\)
\(174\) 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 0.987083 + 0.160212i \(0.0512179\pi\)
−0.354793 + 0.934945i \(0.615449\pi\)
\(180\) −8.70756 + 0.0941551i −0.649023 + 0.00701790i
\(181\) −5.09029 8.81664i −0.378358 0.655335i 0.612465 0.790497i \(-0.290178\pi\)
−0.990824 + 0.135162i \(0.956845\pi\)
\(182\) −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 −0.976034 0.217620i \(-0.930171\pi\)
0.0448277 + 0.998995i \(0.485726\pi\)
\(192\) −1.63077 0.583588i −0.117691 0.0421169i
\(193\) 1.35345 7.67582i 0.0974238 0.552518i −0.896554 0.442935i \(-0.853937\pi\)
0.993978 0.109583i \(-0.0349516\pi\)
\(194\) 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 0.583665 0.811995i \(-0.301618\pi\)
−0.995040 + 0.0994711i \(0.968285\pi\)
\(198\) 0.838404 + 0.294928i 0.0595828 + 0.0209596i
\(199\) 11.5359 + 19.9808i 0.817760 + 1.41640i 0.907329 + 0.420422i \(0.138118\pi\)
−0.0895686 + 0.995981i \(0.528549\pi\)
\(200\) −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 0.568362 0.822778i \(-0.307577\pi\)
−0.711583 + 0.702602i \(0.752022\pi\)
\(212\) 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 0.180564 0.983563i \(-0.442208\pi\)
−0.493902 + 0.869517i \(0.664430\pi\)
\(224\) −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 0.974638 0.223787i \(-0.0718422\pi\)
−0.992400 + 0.123054i \(0.960731\pi\)
\(228\) −2.81782 + 4.94211i −0.186614 + 0.327299i
\(229\) 3.84784 1.40050i 0.254273 0.0925476i −0.211739 0.977326i \(-0.567913\pi\)
0.466012 + 0.884779i \(0.345690\pi\)
\(230\) 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 −0.476993 0.878907i \(-0.658273\pi\)
0.199553 + 0.979887i \(0.436051\pi\)
\(240\) 4.73363 + 1.69398i 0.305554 + 0.109346i
\(241\) 26.2672 + 9.56048i 1.69202 + 0.615845i 0.994877 0.101089i \(-0.0322326\pi\)
0.697142 + 0.716933i \(0.254455\pi\)
\(242\) −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 0.628011 0.778204i \(-0.283869\pi\)
−0.987950 + 0.154772i \(0.950536\pi\)
\(252\) −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 −0.451816 0.892111i \(-0.649224\pi\)
0.227327 + 0.973818i \(0.427001\pi\)
\(258\) 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 0.343756 0.939059i \(-0.388301\pi\)
0.984485 0.175468i \(-0.0561437\pi\)
\(264\) −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 −0.599889 0.800083i \(-0.704789\pi\)
0.992837 + 0.119477i \(0.0381219\pi\)
\(270\) −7.32857 + 13.1827i −0.446003 + 0.802273i
\(271\) 3.15205 + 5.45951i 0.191473 + 0.331642i 0.945739 0.324928i \(-0.105340\pi\)
−0.754265 + 0.656570i \(0.772007\pi\)
\(272\) 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 −0.834822 0.550520i \(-0.814429\pi\)
0.397191 + 0.917736i \(0.369985\pi\)
\(278\) −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 0.547369 0.836892i \(-0.315630\pi\)
0.919227 0.393728i \(-0.128815\pi\)
\(282\) 1.00986 1.77117i 0.0601361 0.105471i
\(283\) 16.2025 + 13.5955i 0.963137 + 0.808168i 0.981461 0.191665i \(-0.0613886\pi\)
−0.0183239 + 0.999832i \(0.505833\pi\)
\(284\) 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 −0.551657 0.834071i \(-0.686004\pi\)
0.113537 + 0.993534i \(0.463782\pi\)
\(294\) −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 0.293572 0.955937i \(-0.405156\pi\)
0.681080 0.732209i \(-0.261511\pi\)
\(308\) −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 0.427930 0.903812i \(-0.359243\pi\)
−0.815772 + 0.578374i \(0.803687\pi\)
\(312\) 3.62032 + 6.19301i 0.204960 + 0.350610i
\(313\) −13.1423 4.78339i −0.742845 0.270373i −0.0572531 0.998360i \(-0.518234\pi\)
−0.685592 + 0.727986i \(0.740456\pi\)
\(314\) 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 0.895786 + 0.444486i \(0.146614\pi\)
−0.689740 + 0.724057i \(0.742275\pi\)
\(318\) 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 0.987371 + 0.158423i \(0.0506409\pi\)
−0.873642 + 0.486570i \(0.838248\pi\)
\(332\) 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 −0.935066 0.354473i \(-0.884660\pi\)
0.999912 0.0132843i \(-0.00422865\pi\)
\(338\) 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 0.699261 + 0.714866i \(0.253512\pi\)
−0.901589 + 0.432593i \(0.857599\pi\)
\(348\) 1.47733 + 8.12138i 0.0791934 + 0.435352i
\(349\) 3.07425 + 17.4349i 0.164561 + 0.933271i 0.949516 + 0.313718i \(0.101575\pi\)
−0.784955 + 0.619553i \(0.787314\pi\)
\(350\) −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 0.898946 0.438060i \(-0.144334\pi\)
0.407053 + 0.913404i \(0.366556\pi\)
\(354\) −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 0.425889 + 0.904775i \(0.359961\pi\)
−0.996503 + 0.0835567i \(0.973372\pi\)
\(360\) 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 −0.978329 0.207057i \(-0.933612\pi\)
0.848511 0.529178i \(-0.177500\pi\)
\(368\) −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 0.822295 + 0.569062i \(0.192694\pi\)
−0.967335 + 0.253502i \(0.918418\pi\)
\(374\) −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 0.930444 + 0.366434i \(0.119421\pi\)
−0.999659 + 0.0261043i \(0.991690\pi\)
\(384\) 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 0.970168 + 0.242435i \(0.0779461\pi\)
−0.828742 + 0.559631i \(0.810943\pi\)
\(390\) −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 −0.487599 0.873068i \(-0.662127\pi\)
0.999898 0.0142611i \(-0.00453959\pi\)
\(398\) −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 0.689520 0.724267i \(-0.257821\pi\)
−0.593529 + 0.804812i \(0.702266\pi\)
\(402\) −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 −0.999486 0.0320553i \(-0.989795\pi\)
0.950173 + 0.311722i \(0.100906\pi\)
\(410\) −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 0.895829 + 0.444399i \(0.146583\pi\)
−0.993797 + 0.111207i \(0.964528\pi\)
\(420\) −0.557494 13.2901i −0.0272029 0.648491i
\(421\) −21.2715 + 17.8489i −1.03671 + 0.869901i −0.991634 0.129083i \(-0.958797\pi\)
−0.0450738 + 0.998984i \(0.514352\pi\)
\(422\) 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 −0.649663 0.760223i \(-0.725090\pi\)
0.983203 + 0.182513i \(0.0584232\pi\)
\(432\) 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 0.967084 0.254457i \(-0.0818967\pi\)
−0.995791 + 0.0916509i \(0.970786\pi\)
\(440\) −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 0.720285 0.693678i \(-0.244011\pi\)
0.105882 + 0.994379i \(0.466233\pi\)
\(444\) −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 −0.509333 0.860570i \(-0.670108\pi\)
0.999942 + 0.0108104i \(0.00344112\pi\)
\(450\) −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 −0.622665 0.782489i \(-0.713950\pi\)
0.662477 + 0.749083i \(0.269505\pi\)
\(458\) −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 −0.864225 0.503106i \(-0.832190\pi\)
0.640033 0.768347i \(-0.278921\pi\)
\(462\) −0.410455 + 1.29408i −0.0190961 + 0.0602059i
\(463\) −16.8063 + 6.11699i −0.781054 + 0.284281i −0.701612 0.712559i \(-0.747536\pi\)
−0.0794421 + 0.996839i \(0.525314\pi\)
\(464\) 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 −0.579208 0.815180i \(-0.696638\pi\)
0.995570 + 0.0940186i \(0.0299713\pi\)
\(468\) 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 −0.555076 0.831800i \(-0.687311\pi\)
0.722775 + 0.691084i \(0.242866\pi\)
\(480\) −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 −0.817533 0.575882i \(-0.804659\pi\)
0.907495 + 0.420064i \(0.137992\pi\)
\(488\) 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 0.271806 0.962352i \(-0.412379\pi\)
−0.900533 + 0.434787i \(0.856824\pi\)
\(492\) 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 −0.714225 0.699916i \(-0.753221\pi\)
−0.0972306 + 0.995262i \(0.530998\pi\)
\(500\) 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 −0.543509 0.839403i \(-0.682905\pi\)
0.998699 + 0.0509915i \(0.0162381\pi\)
\(504\) 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 0.904620 + 0.426219i \(0.140155\pi\)
0.576829 + 0.816865i \(0.304290\pi\)
\(510\) −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 0.518459 0.855102i \(-0.326506\pi\)
−0.999770 + 0.0214478i \(0.993172\pi\)
\(542\) −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 0.862272 0.506445i \(-0.169041\pi\)
0.335002 + 0.942217i \(0.391263\pi\)
\(548\) −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 0.995346 + 0.0963671i \(0.0307223\pi\)
−0.414217 + 0.910178i \(0.635944\pi\)
\(558\) −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 −0.708247 0.705965i \(-0.750513\pi\)
0.906988 0.421156i \(-0.138375\pi\)
\(564\) 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 −0.445533 0.895265i \(-0.646986\pi\)
0.804298 + 0.594226i \(0.202542\pi\)
\(570\) 2.95539 + 16.2467i 0.123788 + 0.680501i
\(571\) −0.986364 + 5.59395i −0.0412780 + 0.234099i −0.998466 0.0553676i \(-0.982367\pi\)
0.957188 + 0.289467i \(0.0934780\pi\)
\(572\) 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 0.969427 0.245380i \(-0.0789126\pi\)
−0.697219 + 0.716859i \(0.745579\pi\)
\(578\) 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 −0.401738 0.915755i \(-0.631594\pi\)
−0.896385 + 0.443276i \(0.853816\pi\)
\(588\) 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 0.996189 + 0.0872245i \(0.0277997\pi\)
−0.422556 + 0.906337i \(0.638867\pi\)
\(594\) −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 −0.293371 0.955999i \(-0.594777\pi\)
0.389769 + 0.920913i \(0.372555\pi\)
\(600\) 5.56444 2.05943i 0.227167 0.0840757i
\(601\) 13.4389 + 4.89138i 0.548186 + 0.199523i 0.601240 0.799068i \(-0.294673\pi\)
−0.0530544 + 0.998592i \(0.516896\pi\)
\(602\) 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 −0.675520 0.737342i \(-0.736081\pi\)
−0.0435238 + 0.999052i \(0.513858\pi\)
\(608\) −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 0.0763383 0.997082i \(-0.475677\pi\)
0.699390 + 0.714740i \(0.253455\pi\)
\(618\) 15.0269 12.7482i 0.604472 0.512806i
\(619\) −24.2966 8.84324i −0.976563 0.355440i −0.196060 0.980592i \(-0.562815\pi\)
−0.780503 + 0.625152i \(0.785037\pi\)
\(620\) 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 −0.620310 0.784357i \(-0.712993\pi\)
0.989428 + 0.145026i \(0.0463265\pi\)
\(632\) −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 −0.809678 0.586875i \(-0.800358\pi\)
0.437360 + 0.899286i \(0.355914\pi\)
\(642\) 4.89279 28.6534i 0.193103 1.13086i
\(643\) −29.8571 25.0531i −1.17745 0.987998i −0.999993 0.00386972i \(-0.998768\pi\)
−0.177458 0.984128i \(-0.556787\pi\)
\(644\) −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 0.136106 0.990694i \(-0.456541\pi\)
0.789914 0.613218i \(-0.210125\pi\)
\(648\) 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 −0.755004 0.655720i \(-0.772365\pi\)
0.933741 0.357949i \(-0.116524\pi\)
\(654\) −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 −0.717453 0.696607i \(-0.754692\pi\)
0.561440 + 0.827518i \(0.310248\pi\)
\(660\) −1.48943 + 0.00805240i −0.0579760 + 0.000313439i
\(661\) 31.0713 + 26.0719i 1.20853 + 1.01408i 0.999344 + 0.0362050i \(0.0115269\pi\)
0.209189 + 0.977875i \(0.432918\pi\)
\(662\) −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 0.994626 + 0.103535i \(0.0330154\pi\)
−0.899231 + 0.437473i \(0.855874\pi\)
\(674\) 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 −0.566645 0.823962i \(-0.691759\pi\)
0.713047 + 0.701116i \(0.247315\pi\)
\(678\) −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 0.545611 0.838038i \(-0.316297\pi\)
−0.120718 + 0.992687i \(0.538520\pi\)
\(692\) 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 0.994776 0.102078i \(-0.0325492\pi\)
−0.969697 + 0.244311i \(0.921438\pi\)
\(710\) 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 −0.998937 0.0460921i \(-0.985323\pi\)
0.922929 0.384969i \(-0.125788\pi\)
\(728\) −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 0.957143 0.289616i \(-0.0935276\pi\)
−0.119010 + 0.992893i \(0.537972\pi\)
\(734\) 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 0.999110 0.0421730i \(-0.0134281\pi\)
−0.536078 + 0.844168i \(0.680095\pi\)
\(740\) −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 0.907348 + 0.420381i \(0.138104\pi\)
−0.996407 + 0.0846981i \(0.973007\pi\)
\(744\) 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 −0.998318 0.0579795i \(-0.981534\pi\)
0.957942 + 0.286962i \(0.0926453\pi\)
\(752\) 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 0.871568 + 0.490276i \(0.163104\pi\)
−0.986690 + 0.162615i \(0.948007\pi\)
\(762\) 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 −0.943721 0.330744i \(-0.892700\pi\)
0.999928 + 0.0119740i \(0.00381155\pi\)
\(770\) −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 0.953862 0.300244i \(-0.0970682\pi\)
−0.736950 + 0.675947i \(0.763735\pi\)
\(774\) 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 −0.832686 0.553745i \(-0.813198\pi\)
0.971861 0.235554i \(-0.0756906\pi\)
\(788\) −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 0.617027 + 0.786942i \(0.288337\pi\)
−0.848966 + 0.528448i \(0.822774\pi\)
\(798\) −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 −0.991286 0.131730i \(-0.957947\pi\)
0.609724 + 0.792614i \(0.291280\pi\)
\(810\) −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 −0.0380861 0.999274i \(-0.512126\pi\)
−0.671497 + 0.741007i \(0.734348\pi\)
\(822\) 16.4008 + 28.0556i 0.572043 + 0.978552i
\(823\) 37.2136 + 31.2259i 1.29719 + 1.08847i 0.990624 + 0.136617i \(0.0436231\pi\)
0.306562 + 0.951851i \(0.400821\pi\)
\(824\) −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 −0.357143 0.934050i \(-0.616249\pi\)
0.987482 0.157730i \(-0.0504175\pi\)
\(828\) −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 0.949879 0.312619i \(-0.101206\pi\)
−0.999516 + 0.0311119i \(0.990095\pi\)
\(840\) 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 −0.906633 0.421920i \(-0.861356\pi\)
0.258075 + 0.966125i \(0.416912\pi\)
\(854\) −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 −0.990179 0.139807i \(-0.955352\pi\)
−0.0342596 + 0.999413i \(0.510907\pi\)
\(858\) −1.63536 1.35724i −0.0558304 0.0463353i
\(859\) 0.749420 4.25017i 0.0255699 0.145014i −0.969350 0.245684i \(-0.920987\pi\)
0.994920 + 0.100670i \(0.0320986\pi\)
\(860\) −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 0.892465 0.451117i \(-0.148974\pi\)
−0.836911 + 0.547339i \(0.815641\pi\)
\(864\) −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 −0.983840 0.179050i \(-0.942698\pi\)
−0.638574 + 0.769560i \(0.720476\pi\)
\(878\) 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 −0.0533863 + 0.998574i \(0.517001\pi\)
−0.838097 + 0.545521i \(0.816332\pi\)
\(882\) 1.90179 20.9137i 0.0640368 0.704201i
\(883\) −11.5763 20.0507i −0.389573 0.674761i 0.602819 0.797878i \(-0.294044\pi\)
−0.992392 + 0.123117i \(0.960711\pi\)
\(884\) 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 0.553958 0.832545i \(-0.313117\pi\)
−0.723703 + 0.690112i \(0.757561\pi\)
\(888\) 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 0.535952 + 0.844249i \(0.319953\pi\)
−0.214880 + 0.976641i \(0.568936\pi\)
\(908\) −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 0.271665 0.962392i \(-0.412426\pi\)
−0.410506 + 0.911858i \(0.634648\pi\)
\(912\) 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 −0.932098 0.362206i \(-0.882024\pi\)
0.152370 0.988324i \(-0.451310\pi\)
\(920\) −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 −0.515786 0.856718i \(-0.672500\pi\)
−0.945802 + 0.324743i \(0.894722\pi\)
\(930\) −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 −0.997760 0.0668936i \(-0.978691\pi\)
0.440949 0.897532i \(-0.354642\pi\)
\(938\) 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 −0.999928 0.0120072i \(-0.996178\pi\)
0.943732 + 0.330712i \(0.107289\pi\)
\(942\) 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 −0.410316 0.911944i \(-0.634581\pi\)
0.826839 + 0.562439i \(0.190137\pi\)
\(948\) −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 0.563653 0.826011i \(-0.309395\pi\)
−0.997174 + 0.0751323i \(0.976062\pi\)
\(954\) 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 0.576286 0.817248i \(-0.304501\pi\)
−0.704761 + 0.709445i \(0.748946\pi\)
\(968\) 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 0.888927 + 0.458049i \(0.151452\pi\)
−0.0477809 + 0.998858i \(0.515215\pi\)
\(972\) 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 −0.697421 0.716661i \(-0.745669\pi\)
−0.0735945 + 0.997288i \(0.523447\pi\)
\(978\) −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 −0.946602 0.322403i \(-0.895509\pi\)
0.779247 0.626717i \(-0.215602\pi\)
\(984\) 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 0.710032 0.704170i \(-0.248681\pi\)
0.0912840 + 0.995825i \(0.470903\pi\)
\(998\) 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.67.8 72
7.2 even 3 378.2.w.b.121.1 yes 72
27.25 even 9 378.2.w.b.25.1 yes 72
189.79 even 9 inner 378.2.v.a.79.8 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.v.a.67.8 72 1.1 even 1 trivial
378.2.v.a.79.8 yes 72 189.79 even 9 inner
378.2.w.b.25.1 yes 72 27.25 even 9
378.2.w.b.121.1 yes 72 7.2 even 3