Properties

Label 162.2.g.a.7.1
Level $162$
Weight $2$
Character 162.7
Analytic conductor $1.294$
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] = [162,2,Mod(7,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 162.g (of order \(27\), degree \(18\), 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: \(1.29357651274\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(4\) over \(\Q(\zeta_{27})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 7.1
Character \(\chi\) \(=\) 162.7
Dual form 162.2.g.a.139.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.597159 - 0.802123i) q^{2} +(-1.65406 + 0.513880i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(2.13228 - 1.40243i) q^{5} +(1.39993 + 1.01990i) q^{6} +(-0.606844 + 0.643217i) q^{7} +(0.939693 - 0.342020i) q^{8} +(2.47185 - 1.69998i) q^{9} +O(q^{10})\) \(q+(-0.597159 - 0.802123i) q^{2} +(-1.65406 + 0.513880i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(2.13228 - 1.40243i) q^{5} +(1.39993 + 1.01990i) q^{6} +(-0.606844 + 0.643217i) q^{7} +(0.939693 - 0.342020i) q^{8} +(2.47185 - 1.69998i) q^{9} +(-2.39823 - 0.872884i) q^{10} +(4.06416 - 2.04110i) q^{11} +(-0.0179009 - 1.73196i) q^{12} +(-2.69275 - 6.24250i) q^{13} +(0.878322 + 0.102661i) q^{14} +(-2.80626 + 3.41544i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(1.89618 - 1.59109i) q^{17} +(-2.83968 - 0.967574i) q^{18} +(4.81115 + 4.03704i) q^{19} +(0.731963 + 2.44493i) q^{20} +(0.673223 - 1.37577i) q^{21} +(-4.06416 - 2.04110i) q^{22} +(0.808531 + 0.856993i) q^{23} +(-1.37855 + 1.04861i) q^{24} +(0.599441 - 1.38966i) q^{25} +(-3.39926 + 5.88769i) q^{26} +(-3.21502 + 4.08211i) q^{27} +(-0.442151 - 0.765827i) q^{28} +(-0.855129 + 0.0999503i) q^{29} +(4.41538 + 0.211404i) q^{30} +(-7.52782 + 1.78413i) q^{31} +(0.0581448 + 0.998308i) q^{32} +(-5.67350 + 5.46460i) q^{33} +(-2.40857 - 0.570841i) q^{34} +(-0.391900 + 2.22258i) q^{35} +(0.919628 + 2.85557i) q^{36} +(1.51717 + 8.60431i) q^{37} +(0.365179 - 6.26989i) q^{38} +(7.66188 + 8.94175i) q^{39} +(1.52403 - 2.04713i) q^{40} +(4.25521 - 5.71574i) q^{41} +(-1.50556 + 0.281544i) q^{42} +(0.375968 - 6.45512i) q^{43} +(0.789737 + 4.47882i) q^{44} +(2.88660 - 7.09144i) q^{45} +(0.204593 - 1.16030i) q^{46} +(-4.65668 - 1.10365i) q^{47} +(1.66433 + 0.479582i) q^{48} +(0.361545 + 6.20749i) q^{49} +(-1.47264 + 0.349022i) q^{50} +(-2.31878 + 3.60617i) q^{51} +(6.75254 - 0.789259i) q^{52} +(2.47156 + 4.28086i) q^{53} +(5.19423 + 0.141172i) q^{54} +(5.80346 - 10.0519i) q^{55} +(-0.350254 + 0.811980i) q^{56} +(-10.0325 - 4.20516i) q^{57} +(0.590820 + 0.626233i) q^{58} +(-4.45417 - 2.23697i) q^{59} +(-2.46711 - 3.66792i) q^{60} +(0.694103 + 2.31847i) q^{61} +(5.92639 + 4.97283i) q^{62} +(-0.406574 + 2.62156i) q^{63} +(0.766044 - 0.642788i) q^{64} +(-14.4964 - 9.53441i) q^{65} +(7.77127 + 1.28762i) q^{66} +(2.81724 + 0.329288i) q^{67} +(0.980412 + 2.27285i) q^{68} +(-1.77775 - 1.00203i) q^{69} +(2.01681 - 1.01288i) q^{70} +(-10.2786 - 3.74111i) q^{71} +(1.74136 - 2.44288i) q^{72} +(-5.92032 + 2.15482i) q^{73} +(5.99572 - 6.35510i) q^{74} +(-0.277395 + 2.60663i) q^{75} +(-5.24729 + 3.45120i) q^{76} +(-1.15344 + 3.85277i) q^{77} +(2.59702 - 11.4854i) q^{78} +(1.95423 + 2.62498i) q^{79} -2.55214 q^{80} +(3.22013 - 8.40421i) q^{81} -7.12577 q^{82} +(-1.88641 - 2.53389i) q^{83} +(1.12489 + 1.03952i) q^{84} +(1.81182 - 6.05190i) q^{85} +(-5.40232 + 3.55316i) q^{86} +(1.36308 - 0.604758i) q^{87} +(3.12097 - 3.30803i) q^{88} +(5.44891 - 1.98324i) q^{89} +(-7.41196 + 1.91930i) q^{90} +(5.64937 + 2.05620i) q^{91} +(-1.05288 + 0.528776i) q^{92} +(11.5347 - 6.81946i) q^{93} +(1.89551 + 4.39429i) q^{94} +(15.9204 + 1.86083i) q^{95} +(-0.609186 - 1.62139i) q^{96} +(0.222871 + 0.146585i) q^{97} +(4.76327 - 3.99686i) q^{98} +(6.57619 - 11.9543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 9 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{8}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.597159 0.802123i −0.422255 0.567187i
\(3\) −1.65406 + 0.513880i −0.954974 + 0.296689i
\(4\) −0.286803 + 0.957990i −0.143402 + 0.478995i
\(5\) 2.13228 1.40243i 0.953587 0.627184i 0.0255503 0.999674i \(-0.491866\pi\)
0.928036 + 0.372490i \(0.121496\pi\)
\(6\) 1.39993 + 1.01990i 0.571520 + 0.416370i
\(7\) −0.606844 + 0.643217i −0.229366 + 0.243113i −0.831827 0.555034i \(-0.812705\pi\)
0.602462 + 0.798148i \(0.294187\pi\)
\(8\) 0.939693 0.342020i 0.332232 0.120922i
\(9\) 2.47185 1.69998i 0.823952 0.566660i
\(10\) −2.39823 0.872884i −0.758387 0.276030i
\(11\) 4.06416 2.04110i 1.22539 0.615415i 0.285989 0.958233i \(-0.407678\pi\)
0.939402 + 0.342818i \(0.111381\pi\)
\(12\) −0.0179009 1.73196i −0.00516754 0.499973i
\(13\) −2.69275 6.24250i −0.746835 1.73136i −0.679554 0.733625i \(-0.737827\pi\)
−0.0672811 0.997734i \(-0.521432\pi\)
\(14\) 0.878322 + 0.102661i 0.234741 + 0.0274373i
\(15\) −2.80626 + 3.41544i −0.724572 + 0.881863i
\(16\) −0.835488 0.549509i −0.208872 0.137377i
\(17\) 1.89618 1.59109i 0.459892 0.385895i −0.383199 0.923666i \(-0.625178\pi\)
0.843091 + 0.537771i \(0.180733\pi\)
\(18\) −2.83968 0.967574i −0.669320 0.228059i
\(19\) 4.81115 + 4.03704i 1.10375 + 0.926160i 0.997672 0.0681975i \(-0.0217248\pi\)
0.106083 + 0.994357i \(0.466169\pi\)
\(20\) 0.731963 + 2.44493i 0.163672 + 0.546702i
\(21\) 0.673223 1.37577i 0.146909 0.300217i
\(22\) −4.06416 2.04110i −0.866482 0.435164i
\(23\) 0.808531 + 0.856993i 0.168590 + 0.178695i 0.806160 0.591697i \(-0.201542\pi\)
−0.637570 + 0.770392i \(0.720060\pi\)
\(24\) −1.37855 + 1.04861i −0.281396 + 0.214047i
\(25\) 0.599441 1.38966i 0.119888 0.277932i
\(26\) −3.39926 + 5.88769i −0.666649 + 1.15467i
\(27\) −3.21502 + 4.08211i −0.618731 + 0.785603i
\(28\) −0.442151 0.765827i −0.0835586 0.144728i
\(29\) −0.855129 + 0.0999503i −0.158794 + 0.0185603i −0.195118 0.980780i \(-0.562509\pi\)
0.0363247 + 0.999340i \(0.488435\pi\)
\(30\) 4.41538 + 0.211404i 0.806135 + 0.0385969i
\(31\) −7.52782 + 1.78413i −1.35204 + 0.320439i −0.841890 0.539649i \(-0.818557\pi\)
−0.510146 + 0.860088i \(0.670409\pi\)
\(32\) 0.0581448 + 0.998308i 0.0102787 + 0.176478i
\(33\) −5.67350 + 5.46460i −0.987630 + 0.951265i
\(34\) −2.40857 0.570841i −0.413066 0.0978985i
\(35\) −0.391900 + 2.22258i −0.0662432 + 0.375684i
\(36\) 0.919628 + 2.85557i 0.153271 + 0.475928i
\(37\) 1.51717 + 8.60431i 0.249421 + 1.41454i 0.809996 + 0.586435i \(0.199469\pi\)
−0.560574 + 0.828104i \(0.689420\pi\)
\(38\) 0.365179 6.26989i 0.0592399 1.01711i
\(39\) 7.66188 + 8.94175i 1.22688 + 1.43183i
\(40\) 1.52403 2.04713i 0.240971 0.323680i
\(41\) 4.25521 5.71574i 0.664552 0.892649i −0.334204 0.942501i \(-0.608467\pi\)
0.998757 + 0.0498518i \(0.0158749\pi\)
\(42\) −1.50556 + 0.281544i −0.232312 + 0.0434432i
\(43\) 0.375968 6.45512i 0.0573346 0.984397i −0.839871 0.542785i \(-0.817370\pi\)
0.897206 0.441612i \(-0.145593\pi\)
\(44\) 0.789737 + 4.47882i 0.119057 + 0.675207i
\(45\) 2.88660 7.09144i 0.430309 1.05713i
\(46\) 0.204593 1.16030i 0.0301655 0.171077i
\(47\) −4.65668 1.10365i −0.679247 0.160985i −0.123511 0.992343i \(-0.539415\pi\)
−0.555736 + 0.831359i \(0.687564\pi\)
\(48\) 1.66433 + 0.479582i 0.240226 + 0.0692218i
\(49\) 0.361545 + 6.20749i 0.0516493 + 0.886784i
\(50\) −1.47264 + 0.349022i −0.208263 + 0.0493592i
\(51\) −2.31878 + 3.60617i −0.324694 + 0.504964i
\(52\) 6.75254 0.789259i 0.936409 0.109451i
\(53\) 2.47156 + 4.28086i 0.339494 + 0.588021i 0.984338 0.176293i \(-0.0564108\pi\)
−0.644843 + 0.764315i \(0.723077\pi\)
\(54\) 5.19423 + 0.141172i 0.706846 + 0.0192110i
\(55\) 5.80346 10.0519i 0.782539 1.35540i
\(56\) −0.350254 + 0.811980i −0.0468046 + 0.108505i
\(57\) −10.0325 4.20516i −1.32884 0.556987i
\(58\) 0.590820 + 0.626233i 0.0775785 + 0.0822284i
\(59\) −4.45417 2.23697i −0.579884 0.291229i 0.134578 0.990903i \(-0.457032\pi\)
−0.714462 + 0.699674i \(0.753328\pi\)
\(60\) −2.46711 3.66792i −0.318503 0.473527i
\(61\) 0.694103 + 2.31847i 0.0888708 + 0.296849i 0.990857 0.134916i \(-0.0430763\pi\)
−0.901986 + 0.431765i \(0.857891\pi\)
\(62\) 5.92639 + 4.97283i 0.752653 + 0.631550i
\(63\) −0.406574 + 2.62156i −0.0512235 + 0.330286i
\(64\) 0.766044 0.642788i 0.0957556 0.0803485i
\(65\) −14.4964 9.53441i −1.79805 1.18260i
\(66\) 7.77127 + 1.28762i 0.956577 + 0.158495i
\(67\) 2.81724 + 0.329288i 0.344181 + 0.0402289i 0.286427 0.958102i \(-0.407532\pi\)
0.0577532 + 0.998331i \(0.481606\pi\)
\(68\) 0.980412 + 2.27285i 0.118892 + 0.275624i
\(69\) −1.77775 1.00203i −0.214016 0.120631i
\(70\) 2.01681 1.01288i 0.241055 0.121062i
\(71\) −10.2786 3.74111i −1.21985 0.443988i −0.349738 0.936848i \(-0.613729\pi\)
−0.870109 + 0.492860i \(0.835952\pi\)
\(72\) 1.74136 2.44288i 0.205221 0.287897i
\(73\) −5.92032 + 2.15482i −0.692921 + 0.252202i −0.664385 0.747390i \(-0.731307\pi\)
−0.0285354 + 0.999593i \(0.509084\pi\)
\(74\) 5.99572 6.35510i 0.696989 0.738765i
\(75\) −0.277395 + 2.60663i −0.0320308 + 0.300987i
\(76\) −5.24729 + 3.45120i −0.601906 + 0.395880i
\(77\) −1.15344 + 3.85277i −0.131447 + 0.439064i
\(78\) 2.59702 11.4854i 0.294055 1.30047i
\(79\) 1.95423 + 2.62498i 0.219868 + 0.295334i 0.898348 0.439285i \(-0.144768\pi\)
−0.678480 + 0.734619i \(0.737361\pi\)
\(80\) −2.55214 −0.285338
\(81\) 3.22013 8.40421i 0.357792 0.933801i
\(82\) −7.12577 −0.786909
\(83\) −1.88641 2.53389i −0.207061 0.278131i 0.686446 0.727181i \(-0.259170\pi\)
−0.893507 + 0.449050i \(0.851762\pi\)
\(84\) 1.12489 + 1.03952i 0.122735 + 0.113420i
\(85\) 1.81182 6.05190i 0.196520 0.656421i
\(86\) −5.40232 + 3.55316i −0.582547 + 0.383147i
\(87\) 1.36308 0.604758i 0.146137 0.0648369i
\(88\) 3.12097 3.30803i 0.332696 0.352637i
\(89\) 5.44891 1.98324i 0.577583 0.210223i −0.0366764 0.999327i \(-0.511677\pi\)
0.614259 + 0.789104i \(0.289455\pi\)
\(90\) −7.41196 + 1.91930i −0.781289 + 0.202312i
\(91\) 5.64937 + 2.05620i 0.592215 + 0.215549i
\(92\) −1.05288 + 0.528776i −0.109770 + 0.0551287i
\(93\) 11.5347 6.81946i 1.19609 0.707145i
\(94\) 1.89551 + 4.39429i 0.195507 + 0.453236i
\(95\) 15.9204 + 1.86083i 1.63340 + 0.190917i
\(96\) −0.609186 1.62139i −0.0621748 0.165482i
\(97\) 0.222871 + 0.146585i 0.0226292 + 0.0148834i 0.560773 0.827969i \(-0.310504\pi\)
−0.538144 + 0.842853i \(0.680874\pi\)
\(98\) 4.76327 3.99686i 0.481163 0.403744i
\(99\) 6.57619 11.9543i 0.660932 1.20145i
\(100\) 1.15936 + 0.972817i 0.115936 + 0.0972817i
\(101\) 4.91049 + 16.4022i 0.488612 + 1.63208i 0.746128 + 0.665803i \(0.231911\pi\)
−0.257516 + 0.966274i \(0.582904\pi\)
\(102\) 4.27727 0.293508i 0.423513 0.0290616i
\(103\) −1.71448 0.861043i −0.168933 0.0848411i 0.362324 0.932052i \(-0.381984\pi\)
−0.531256 + 0.847211i \(0.678280\pi\)
\(104\) −4.66542 4.94506i −0.457482 0.484903i
\(105\) −0.493910 3.87767i −0.0482007 0.378422i
\(106\) 1.95787 4.53884i 0.190165 0.440851i
\(107\) −9.11205 + 15.7825i −0.880895 + 1.52575i −0.0305470 + 0.999533i \(0.509725\pi\)
−0.850348 + 0.526221i \(0.823608\pi\)
\(108\) −2.98854 4.25072i −0.287573 0.409026i
\(109\) 5.96993 + 10.3402i 0.571816 + 0.990414i 0.996380 + 0.0850161i \(0.0270942\pi\)
−0.424564 + 0.905398i \(0.639572\pi\)
\(110\) −11.5284 + 1.34748i −1.09919 + 0.128477i
\(111\) −6.93108 13.4524i −0.657869 1.27685i
\(112\) 0.860465 0.203934i 0.0813063 0.0192699i
\(113\) −0.522123 8.96451i −0.0491172 0.843310i −0.929449 0.368951i \(-0.879717\pi\)
0.880332 0.474359i \(-0.157320\pi\)
\(114\) 2.61794 + 10.5585i 0.245193 + 0.988890i
\(115\) 2.92589 + 0.693448i 0.272840 + 0.0646643i
\(116\) 0.149503 0.847871i 0.0138810 0.0787228i
\(117\) −17.2682 10.8529i −1.59645 1.00335i
\(118\) 0.865522 + 4.90862i 0.0796778 + 0.451875i
\(119\) −0.127273 + 2.18520i −0.0116671 + 0.200317i
\(120\) −1.46887 + 4.16926i −0.134089 + 0.380600i
\(121\) 5.78259 7.76737i 0.525690 0.706124i
\(122\) 1.44521 1.94125i 0.130843 0.175752i
\(123\) −4.10119 + 11.6409i −0.369792 + 1.04962i
\(124\) 0.449829 7.72327i 0.0403958 0.693570i
\(125\) 1.54516 + 8.76303i 0.138203 + 0.783789i
\(126\) 2.34561 1.23937i 0.208963 0.110412i
\(127\) −3.15631 + 17.9003i −0.280077 + 1.58840i 0.442281 + 0.896876i \(0.354169\pi\)
−0.722358 + 0.691519i \(0.756942\pi\)
\(128\) −0.973045 0.230616i −0.0860058 0.0203838i
\(129\) 2.69528 + 10.8704i 0.237307 + 0.957085i
\(130\) 1.00886 + 17.3214i 0.0884827 + 1.51919i
\(131\) 12.9101 3.05976i 1.12796 0.267332i 0.376054 0.926598i \(-0.377281\pi\)
0.751910 + 0.659265i \(0.229133\pi\)
\(132\) −3.60785 7.00242i −0.314023 0.609483i
\(133\) −5.51631 + 0.644765i −0.478325 + 0.0559082i
\(134\) −1.41821 2.45641i −0.122515 0.212202i
\(135\) −1.13047 + 13.2131i −0.0972957 + 1.13720i
\(136\) 1.23765 2.14366i 0.106127 0.183818i
\(137\) 3.45487 8.00929i 0.295170 0.684280i −0.704507 0.709697i \(-0.748832\pi\)
0.999677 + 0.0254168i \(0.00809128\pi\)
\(138\) 0.257847 + 2.02435i 0.0219494 + 0.172324i
\(139\) −0.0882163 0.0935038i −0.00748241 0.00793089i 0.723622 0.690197i \(-0.242476\pi\)
−0.731104 + 0.682266i \(0.760995\pi\)
\(140\) −2.01681 1.01288i −0.170451 0.0856039i
\(141\) 8.26960 0.567462i 0.696426 0.0477890i
\(142\) 3.13713 + 10.4787i 0.263262 + 0.879357i
\(143\) −23.6854 19.8744i −1.98067 1.66198i
\(144\) −2.99936 + 0.0620071i −0.249947 + 0.00516726i
\(145\) −1.68321 + 1.41238i −0.139783 + 0.117292i
\(146\) 5.26380 + 3.46205i 0.435635 + 0.286522i
\(147\) −3.78793 10.0818i −0.312423 0.831533i
\(148\) −8.67797 1.01431i −0.713324 0.0833757i
\(149\) 4.30950 + 9.99055i 0.353048 + 0.818458i 0.998505 + 0.0546609i \(0.0174078\pi\)
−0.645457 + 0.763797i \(0.723333\pi\)
\(150\) 2.25649 1.33407i 0.184241 0.108926i
\(151\) 7.03070 3.53095i 0.572150 0.287344i −0.139106 0.990277i \(-0.544423\pi\)
0.711256 + 0.702933i \(0.248127\pi\)
\(152\) 5.90175 + 2.14806i 0.478695 + 0.174231i
\(153\) 1.98227 7.15641i 0.160257 0.578561i
\(154\) 3.77919 1.37551i 0.304535 0.110842i
\(155\) −13.5494 + 14.3615i −1.08831 + 1.15354i
\(156\) −10.7636 + 4.77548i −0.861774 + 0.382345i
\(157\) 8.24535 5.42305i 0.658051 0.432807i −0.176078 0.984376i \(-0.556341\pi\)
0.834129 + 0.551569i \(0.185971\pi\)
\(158\) 0.938576 3.13506i 0.0746691 0.249412i
\(159\) −6.28796 5.81073i −0.498668 0.460821i
\(160\) 1.52403 + 2.04713i 0.120485 + 0.161840i
\(161\) −1.04189 −0.0821121
\(162\) −8.66414 + 2.43571i −0.680719 + 0.191367i
\(163\) 10.5493 0.826288 0.413144 0.910666i \(-0.364431\pi\)
0.413144 + 0.910666i \(0.364431\pi\)
\(164\) 4.25521 + 5.71574i 0.332276 + 0.446324i
\(165\) −4.43383 + 19.6088i −0.345173 + 1.52654i
\(166\) −0.906005 + 3.02627i −0.0703197 + 0.234884i
\(167\) −3.55094 + 2.33549i −0.274780 + 0.180726i −0.679418 0.733751i \(-0.737768\pi\)
0.404638 + 0.914477i \(0.367397\pi\)
\(168\) 0.162082 1.52305i 0.0125049 0.117506i
\(169\) −22.7968 + 24.1632i −1.75360 + 1.85871i
\(170\) −5.93632 + 2.16064i −0.455295 + 0.165714i
\(171\) 18.7554 + 1.80010i 1.43426 + 0.137657i
\(172\) 6.07611 + 2.21152i 0.463299 + 0.168627i
\(173\) 0.254068 0.127598i 0.0193165 0.00970110i −0.439115 0.898431i \(-0.644708\pi\)
0.458431 + 0.888730i \(0.348412\pi\)
\(174\) −1.29906 0.732218i −0.0984817 0.0555093i
\(175\) 0.530086 + 1.22888i 0.0400708 + 0.0928945i
\(176\) −4.51716 0.527980i −0.340494 0.0397980i
\(177\) 8.51702 + 1.41118i 0.640178 + 0.106071i
\(178\) −4.84466 3.18639i −0.363123 0.238830i
\(179\) 11.8953 9.98138i 0.889100 0.746043i −0.0789297 0.996880i \(-0.525150\pi\)
0.968029 + 0.250837i \(0.0807058\pi\)
\(180\) 5.96563 + 4.79918i 0.444652 + 0.357710i
\(181\) −18.1872 15.2608i −1.35184 1.13433i −0.978410 0.206671i \(-0.933737\pi\)
−0.373431 0.927658i \(-0.621819\pi\)
\(182\) −1.72424 5.75937i −0.127809 0.426913i
\(183\) −2.33950 3.47820i −0.172941 0.257116i
\(184\) 1.05288 + 0.528776i 0.0776193 + 0.0389819i
\(185\) 15.3019 + 16.2191i 1.12502 + 1.19245i
\(186\) −12.3581 5.17993i −0.906138 0.379811i
\(187\) 4.45883 10.3367i 0.326062 0.755896i
\(188\) 2.39284 4.14452i 0.174516 0.302270i
\(189\) −0.674671 4.54516i −0.0490751 0.330612i
\(190\) −8.01439 13.8813i −0.581425 1.00706i
\(191\) −19.2480 + 2.24976i −1.39273 + 0.162787i −0.779147 0.626841i \(-0.784348\pi\)
−0.613586 + 0.789628i \(0.710273\pi\)
\(192\) −0.936771 + 1.45687i −0.0676056 + 0.105140i
\(193\) −19.7857 + 4.68929i −1.42420 + 0.337543i −0.869264 0.494348i \(-0.835407\pi\)
−0.554940 + 0.831891i \(0.687259\pi\)
\(194\) −0.0155105 0.266305i −0.00111359 0.0191196i
\(195\) 28.8775 + 8.32113i 2.06796 + 0.595888i
\(196\) −6.05040 1.43397i −0.432172 0.102427i
\(197\) 2.52128 14.2989i 0.179634 1.01875i −0.753024 0.657993i \(-0.771406\pi\)
0.932658 0.360761i \(-0.117483\pi\)
\(198\) −13.5158 + 1.86370i −0.960530 + 0.132447i
\(199\) −2.76820 15.6993i −0.196233 1.11289i −0.910652 0.413173i \(-0.864420\pi\)
0.714420 0.699717i \(-0.246691\pi\)
\(200\) 0.0879984 1.51087i 0.00622243 0.106835i
\(201\) −4.82911 + 0.903060i −0.340619 + 0.0636969i
\(202\) 10.2242 13.7335i 0.719374 0.966287i
\(203\) 0.454641 0.610688i 0.0319095 0.0428619i
\(204\) −2.78964 3.25563i −0.195314 0.227939i
\(205\) 1.05742 18.1552i 0.0738534 1.26801i
\(206\) 0.333152 + 1.88940i 0.0232118 + 0.131641i
\(207\) 3.45544 + 0.743874i 0.240170 + 0.0517028i
\(208\) −1.18055 + 6.69523i −0.0818564 + 0.464231i
\(209\) 27.7933 + 6.58713i 1.92250 + 0.455642i
\(210\) −2.81543 + 2.71176i −0.194283 + 0.187129i
\(211\) 0.804379 + 13.8107i 0.0553757 + 0.950765i 0.905544 + 0.424253i \(0.139463\pi\)
−0.850168 + 0.526512i \(0.823500\pi\)
\(212\) −4.80987 + 1.13996i −0.330343 + 0.0782928i
\(213\) 18.9240 + 0.906059i 1.29665 + 0.0620821i
\(214\) 18.1009 2.11569i 1.23735 0.144625i
\(215\) −8.25116 14.2914i −0.562725 0.974667i
\(216\) −1.62496 + 4.93553i −0.110565 + 0.335821i
\(217\) 3.42063 5.92471i 0.232208 0.402196i
\(218\) 4.72914 10.9634i 0.320298 0.742534i
\(219\) 8.68526 6.60654i 0.586896 0.446429i
\(220\) 7.96515 + 8.44257i 0.537011 + 0.569198i
\(221\) −15.0383 7.55252i −1.01159 0.508038i
\(222\) −6.65155 + 13.5928i −0.446423 + 0.912290i
\(223\) 2.07404 + 6.92777i 0.138888 + 0.463918i 0.998927 0.0463101i \(-0.0147462\pi\)
−0.860039 + 0.510228i \(0.829561\pi\)
\(224\) −0.677414 0.568418i −0.0452616 0.0379790i
\(225\) −0.880665 4.45408i −0.0587110 0.296938i
\(226\) −6.87885 + 5.77204i −0.457574 + 0.383950i
\(227\) 4.75675 + 3.12856i 0.315716 + 0.207650i 0.697470 0.716614i \(-0.254309\pi\)
−0.381753 + 0.924264i \(0.624680\pi\)
\(228\) 6.90586 8.40498i 0.457352 0.556634i
\(229\) −3.67805 0.429902i −0.243052 0.0284087i −0.00630543 0.999980i \(-0.502007\pi\)
−0.236747 + 0.971571i \(0.576081\pi\)
\(230\) −1.19099 2.76102i −0.0785314 0.182056i
\(231\) −0.0719924 6.96546i −0.00473675 0.458294i
\(232\) −0.769374 + 0.386394i −0.0505119 + 0.0253680i
\(233\) 22.6677 + 8.25035i 1.48501 + 0.540499i 0.952130 0.305694i \(-0.0988883\pi\)
0.532878 + 0.846192i \(0.321111\pi\)
\(234\) 1.60648 + 20.3322i 0.105019 + 1.32916i
\(235\) −11.4772 + 4.17735i −0.748688 + 0.272500i
\(236\) 3.42046 3.62548i 0.222653 0.235999i
\(237\) −4.58135 3.33765i −0.297590 0.216804i
\(238\) 1.82880 1.20282i 0.118544 0.0779673i
\(239\) −3.68585 + 12.3116i −0.238418 + 0.796371i 0.752107 + 0.659040i \(0.229037\pi\)
−0.990525 + 0.137330i \(0.956148\pi\)
\(240\) 4.22141 1.31150i 0.272491 0.0846567i
\(241\) −10.1786 13.6722i −0.655660 0.880704i 0.342611 0.939477i \(-0.388689\pi\)
−0.998271 + 0.0587730i \(0.981281\pi\)
\(242\) −9.68351 −0.622479
\(243\) −1.00754 + 15.5559i −0.0646339 + 0.997909i
\(244\) −2.42014 −0.154933
\(245\) 9.47646 + 12.7291i 0.605429 + 0.813232i
\(246\) 11.7865 3.66179i 0.751478 0.233467i
\(247\) 12.2460 40.9044i 0.779193 2.60268i
\(248\) −6.46363 + 4.25120i −0.410441 + 0.269951i
\(249\) 4.42236 + 3.22183i 0.280256 + 0.204175i
\(250\) 6.10632 6.47233i 0.386198 0.409346i
\(251\) 10.1177 3.68253i 0.638622 0.232439i −0.00235792 0.999997i \(-0.500751\pi\)
0.640980 + 0.767558i \(0.278528\pi\)
\(252\) −2.39482 1.14137i −0.150860 0.0718993i
\(253\) 5.03521 + 1.83267i 0.316561 + 0.115219i
\(254\) 16.2431 8.15757i 1.01918 0.511852i
\(255\) 0.113085 + 10.9413i 0.00708166 + 0.685170i
\(256\) 0.396080 + 0.918216i 0.0247550 + 0.0573885i
\(257\) −10.7548 1.25705i −0.670865 0.0784129i −0.226160 0.974090i \(-0.572617\pi\)
−0.444705 + 0.895677i \(0.646691\pi\)
\(258\) 7.10988 8.65330i 0.442642 0.538731i
\(259\) −6.45513 4.24560i −0.401102 0.263809i
\(260\) 13.2915 11.1529i 0.824302 0.691671i
\(261\) −1.94384 + 1.70077i −0.120321 + 0.105275i
\(262\) −10.1637 8.52836i −0.627916 0.526884i
\(263\) 4.10800 + 13.7217i 0.253310 + 0.846114i 0.986170 + 0.165735i \(0.0529996\pi\)
−0.732860 + 0.680379i \(0.761815\pi\)
\(264\) −3.46235 + 7.07550i −0.213093 + 0.435467i
\(265\) 11.2736 + 5.66184i 0.692535 + 0.347804i
\(266\) 3.81130 + 4.03974i 0.233686 + 0.247692i
\(267\) −7.99369 + 6.08049i −0.489206 + 0.372120i
\(268\) −1.12345 + 2.60445i −0.0686255 + 0.159092i
\(269\) 0.700424 1.21317i 0.0427056 0.0739682i −0.843883 0.536528i \(-0.819736\pi\)
0.886588 + 0.462560i \(0.153069\pi\)
\(270\) 11.2736 6.98351i 0.686088 0.425003i
\(271\) −13.5650 23.4952i −0.824013 1.42723i −0.902671 0.430330i \(-0.858397\pi\)
0.0786586 0.996902i \(-0.474936\pi\)
\(272\) −2.45855 + 0.287364i −0.149072 + 0.0174240i
\(273\) −10.4011 0.497992i −0.629501 0.0301398i
\(274\) −8.48754 + 2.01158i −0.512751 + 0.121524i
\(275\) −0.400209 6.87132i −0.0241335 0.414356i
\(276\) 1.46980 1.41568i 0.0884717 0.0852141i
\(277\) 5.89811 + 1.39788i 0.354383 + 0.0839903i 0.403951 0.914780i \(-0.367636\pi\)
−0.0495685 + 0.998771i \(0.515785\pi\)
\(278\) −0.0223225 + 0.126597i −0.00133881 + 0.00759278i
\(279\) −15.5747 + 17.2073i −0.932433 + 1.03017i
\(280\) 0.391900 + 2.22258i 0.0234205 + 0.132824i
\(281\) 0.366850 6.29857i 0.0218844 0.375741i −0.969529 0.244977i \(-0.921220\pi\)
0.991413 0.130765i \(-0.0417432\pi\)
\(282\) −5.39344 6.29437i −0.321174 0.374824i
\(283\) 1.91231 2.56868i 0.113675 0.152692i −0.741644 0.670794i \(-0.765954\pi\)
0.855319 + 0.518101i \(0.173361\pi\)
\(284\) 6.53188 8.77384i 0.387596 0.520632i
\(285\) −27.2896 + 5.10325i −1.61650 + 0.302290i
\(286\) −1.79778 + 30.8667i −0.106305 + 1.82519i
\(287\) 1.09421 + 6.20559i 0.0645894 + 0.366305i
\(288\) 1.84083 + 2.36883i 0.108472 + 0.139584i
\(289\) −1.88807 + 10.7078i −0.111063 + 0.629868i
\(290\) 2.13804 + 0.506725i 0.125550 + 0.0297559i
\(291\) −0.443971 0.127931i −0.0260260 0.00749948i
\(292\) −0.366328 6.28961i −0.0214377 0.368072i
\(293\) −22.2902 + 5.28286i −1.30221 + 0.308628i −0.822482 0.568792i \(-0.807411\pi\)
−0.479723 + 0.877420i \(0.659263\pi\)
\(294\) −5.82485 + 9.05881i −0.339712 + 0.528321i
\(295\) −12.6347 + 1.47679i −0.735623 + 0.0859820i
\(296\) 4.36852 + 7.56650i 0.253915 + 0.439794i
\(297\) −4.73436 + 23.1525i −0.274715 + 1.34345i
\(298\) 5.44020 9.42269i 0.315142 0.545842i
\(299\) 3.17261 7.35493i 0.183477 0.425346i
\(300\) −2.41756 1.01333i −0.139578 0.0585047i
\(301\) 3.92389 + 4.15909i 0.226170 + 0.239726i
\(302\) −7.03070 3.53095i −0.404571 0.203183i
\(303\) −16.5510 24.6068i −0.950831 1.41363i
\(304\) −1.80127 6.01667i −0.103310 0.345080i
\(305\) 4.73150 + 3.97020i 0.270925 + 0.227333i
\(306\) −6.92405 + 2.68348i −0.395822 + 0.153405i
\(307\) 20.9420 17.5724i 1.19522 1.00291i 0.195468 0.980710i \(-0.437377\pi\)
0.999754 0.0222000i \(-0.00706707\pi\)
\(308\) −3.36010 2.20997i −0.191460 0.125925i
\(309\) 3.27833 + 0.543184i 0.186498 + 0.0309007i
\(310\) 19.6108 + 2.29217i 1.11382 + 0.130187i
\(311\) −9.40973 21.8142i −0.533577 1.23697i −0.945461 0.325734i \(-0.894389\pi\)
0.411884 0.911236i \(-0.364871\pi\)
\(312\) 10.2581 + 5.78198i 0.580749 + 0.327340i
\(313\) −19.0791 + 9.58190i −1.07842 + 0.541601i −0.897102 0.441824i \(-0.854332\pi\)
−0.181315 + 0.983425i \(0.558035\pi\)
\(314\) −9.27374 3.37537i −0.523348 0.190483i
\(315\) 2.80962 + 6.16011i 0.158304 + 0.347083i
\(316\) −3.07519 + 1.11928i −0.172993 + 0.0629642i
\(317\) 10.0762 10.6802i 0.565938 0.599859i −0.379688 0.925115i \(-0.623969\pi\)
0.945626 + 0.325255i \(0.105450\pi\)
\(318\) −0.906014 + 8.51365i −0.0508067 + 0.477422i
\(319\) −3.27138 + 2.15162i −0.183162 + 0.120467i
\(320\) 0.731963 2.44493i 0.0409180 0.136676i
\(321\) 6.96158 30.7878i 0.388557 1.71841i
\(322\) 0.622171 + 0.835720i 0.0346722 + 0.0465729i
\(323\) 15.5461 0.865008
\(324\) 7.12760 + 5.49521i 0.395978 + 0.305289i
\(325\) −10.2891 −0.570737
\(326\) −6.29963 8.46187i −0.348904 0.468659i
\(327\) −15.1883 14.0356i −0.839914 0.776169i
\(328\) 2.04369 6.82641i 0.112844 0.376925i
\(329\) 3.53577 2.32551i 0.194933 0.128210i
\(330\) 18.3763 8.15306i 1.01158 0.448811i
\(331\) −0.958085 + 1.01551i −0.0526611 + 0.0558175i −0.753169 0.657828i \(-0.771476\pi\)
0.700507 + 0.713645i \(0.252957\pi\)
\(332\) 2.96847 1.08043i 0.162916 0.0592965i
\(333\) 18.3774 + 18.6894i 1.00707 + 1.02417i
\(334\) 3.99382 + 1.45363i 0.218532 + 0.0795392i
\(335\) 6.46896 3.24883i 0.353437 0.177503i
\(336\) −1.31847 + 0.779495i −0.0719282 + 0.0425250i
\(337\) 13.5371 + 31.3824i 0.737410 + 1.70951i 0.704138 + 0.710063i \(0.251333\pi\)
0.0332717 + 0.999446i \(0.489407\pi\)
\(338\) 32.9952 + 3.85658i 1.79470 + 0.209770i
\(339\) 5.47031 + 14.5596i 0.297106 + 0.790767i
\(340\) 5.27802 + 3.47141i 0.286241 + 0.188264i
\(341\) −26.9527 + 22.6160i −1.45957 + 1.22473i
\(342\) −9.75602 16.1191i −0.527545 0.871619i
\(343\) −8.95407 7.51335i −0.483474 0.405683i
\(344\) −1.85449 6.19442i −0.0999873 0.333981i
\(345\) −5.19595 + 0.356548i −0.279741 + 0.0191959i
\(346\) −0.254068 0.127598i −0.0136588 0.00685971i
\(347\) −1.49937 1.58924i −0.0804902 0.0853146i 0.685877 0.727718i \(-0.259419\pi\)
−0.766367 + 0.642403i \(0.777937\pi\)
\(348\) 0.188417 + 1.47926i 0.0101002 + 0.0792966i
\(349\) −8.22188 + 19.0605i −0.440107 + 1.02028i 0.543410 + 0.839467i \(0.317133\pi\)
−0.983517 + 0.180815i \(0.942126\pi\)
\(350\) 0.669166 1.15903i 0.0357684 0.0619528i
\(351\) 34.1399 + 9.07764i 1.82225 + 0.484529i
\(352\) 2.27396 + 3.93861i 0.121202 + 0.209928i
\(353\) −8.52487 + 0.996414i −0.453733 + 0.0530338i −0.339890 0.940465i \(-0.610390\pi\)
−0.113842 + 0.993499i \(0.536316\pi\)
\(354\) −3.95407 7.67440i −0.210157 0.407890i
\(355\) −27.1636 + 6.43788i −1.44169 + 0.341687i
\(356\) 0.337159 + 5.78879i 0.0178694 + 0.306806i
\(357\) −0.912412 3.67986i −0.0482900 0.194759i
\(358\) −15.1097 3.58106i −0.798573 0.189265i
\(359\) 3.02344 17.1468i 0.159571 0.904974i −0.794915 0.606720i \(-0.792485\pi\)
0.954487 0.298254i \(-0.0964041\pi\)
\(360\) 0.287103 7.65104i 0.0151317 0.403245i
\(361\) 3.55021 + 20.1343i 0.186853 + 1.05970i
\(362\) −1.38045 + 23.7015i −0.0725551 + 1.24572i
\(363\) −5.57328 + 15.8193i −0.292521 + 0.830297i
\(364\) −3.59008 + 4.82231i −0.188171 + 0.252758i
\(365\) −9.60182 + 12.8975i −0.502582 + 0.675085i
\(366\) −1.39289 + 3.95361i −0.0728077 + 0.206658i
\(367\) −0.654713 + 11.2410i −0.0341757 + 0.586775i 0.937136 + 0.348965i \(0.113467\pi\)
−0.971312 + 0.237810i \(0.923570\pi\)
\(368\) −0.204593 1.16030i −0.0106651 0.0604849i
\(369\) 0.801613 21.3623i 0.0417303 1.11207i
\(370\) 3.87204 21.9594i 0.201298 1.14162i
\(371\) −4.25337 1.00807i −0.220824 0.0523363i
\(372\) 3.22479 + 13.0059i 0.167197 + 0.674326i
\(373\) −0.429192 7.36894i −0.0222227 0.381549i −0.991022 0.133701i \(-0.957314\pi\)
0.968799 0.247848i \(-0.0797234\pi\)
\(374\) −10.9540 + 2.59614i −0.566416 + 0.134243i
\(375\) −7.05894 13.7006i −0.364522 0.707495i
\(376\) −4.75332 + 0.555584i −0.245134 + 0.0286520i
\(377\) 2.92659 + 5.06901i 0.150727 + 0.261067i
\(378\) −3.24290 + 3.25535i −0.166797 + 0.167437i
\(379\) −1.15880 + 2.00709i −0.0595233 + 0.103097i −0.894252 0.447565i \(-0.852291\pi\)
0.834728 + 0.550662i \(0.185625\pi\)
\(380\) −6.34867 + 14.7179i −0.325680 + 0.755011i
\(381\) −3.97788 31.2302i −0.203793 1.59997i
\(382\) 13.2987 + 14.0958i 0.680419 + 0.721202i
\(383\) 5.28873 + 2.65610i 0.270241 + 0.135720i 0.578760 0.815498i \(-0.303537\pi\)
−0.308518 + 0.951218i \(0.599833\pi\)
\(384\) 1.72799 0.118575i 0.0881810 0.00605101i
\(385\) 2.94375 + 9.83282i 0.150028 + 0.501127i
\(386\) 15.5766 + 13.0703i 0.792827 + 0.665261i
\(387\) −10.0443 16.5953i −0.510578 0.843585i
\(388\) −0.204347 + 0.171467i −0.0103741 + 0.00870494i
\(389\) −3.04831 2.00490i −0.154555 0.101653i 0.469876 0.882733i \(-0.344299\pi\)
−0.624431 + 0.781080i \(0.714669\pi\)
\(390\) −10.5699 28.1323i −0.535225 1.42453i
\(391\) 2.89667 + 0.338572i 0.146491 + 0.0171223i
\(392\) 2.46283 + 5.70948i 0.124392 + 0.288372i
\(393\) −19.7819 + 11.6953i −0.997862 + 0.589950i
\(394\) −12.9751 + 6.51633i −0.653675 + 0.328288i
\(395\) 7.84832 + 2.85655i 0.394892 + 0.143729i
\(396\) 9.56602 + 9.72845i 0.480711 + 0.488873i
\(397\) 11.1881 4.07213i 0.561514 0.204375i −0.0456407 0.998958i \(-0.514533\pi\)
0.607155 + 0.794583i \(0.292311\pi\)
\(398\) −10.9397 + 11.5954i −0.548357 + 0.581224i
\(399\) 8.79300 3.90121i 0.440201 0.195305i
\(400\) −1.26446 + 0.831646i −0.0632228 + 0.0415823i
\(401\) −5.36480 + 17.9197i −0.267905 + 0.894866i 0.713129 + 0.701033i \(0.247277\pi\)
−0.981034 + 0.193833i \(0.937908\pi\)
\(402\) 3.60811 + 3.33427i 0.179956 + 0.166298i
\(403\) 31.4080 + 42.1882i 1.56454 + 2.10155i
\(404\) −17.1214 −0.851824
\(405\) −4.92005 22.4362i −0.244479 1.11486i
\(406\) −0.761340 −0.0377847
\(407\) 23.7283 + 31.8726i 1.17617 + 1.57987i
\(408\) −0.945558 + 4.18176i −0.0468121 + 0.207028i
\(409\) 2.77586 9.27201i 0.137257 0.458471i −0.861530 0.507707i \(-0.830493\pi\)
0.998787 + 0.0492356i \(0.0156785\pi\)
\(410\) −15.1942 + 9.99336i −0.750386 + 0.493537i
\(411\) −1.59876 + 15.0233i −0.0788611 + 0.741043i
\(412\) 1.31659 1.39550i 0.0648636 0.0687514i
\(413\) 4.14185 1.50751i 0.203807 0.0741797i
\(414\) −1.46677 3.21590i −0.0720877 0.158053i
\(415\) −7.57596 2.75742i −0.371889 0.135357i
\(416\) 6.07537 3.05117i 0.297870 0.149596i
\(417\) 0.193965 + 0.109329i 0.00949851 + 0.00535385i
\(418\) −11.3133 26.2272i −0.553353 1.28282i
\(419\) −33.6890 3.93767i −1.64581 0.192368i −0.757897 0.652374i \(-0.773773\pi\)
−0.887916 + 0.460006i \(0.847847\pi\)
\(420\) 3.85643 + 0.638969i 0.188174 + 0.0311785i
\(421\) −20.1800 13.2726i −0.983515 0.646868i −0.0475156 0.998870i \(-0.515130\pi\)
−0.935999 + 0.352003i \(0.885501\pi\)
\(422\) 10.5975 8.89236i 0.515879 0.432874i
\(423\) −13.3868 + 5.18820i −0.650890 + 0.252259i
\(424\) 3.78664 + 3.17737i 0.183896 + 0.154307i
\(425\) −1.07442 3.58881i −0.0521170 0.174083i
\(426\) −10.5738 15.7204i −0.512304 0.761656i
\(427\) −1.91249 0.960488i −0.0925519 0.0464813i
\(428\) −12.5061 13.2557i −0.604507 0.640740i
\(429\) 49.3901 + 20.7021i 2.38458 + 0.999505i
\(430\) −6.53624 + 15.1527i −0.315205 + 0.730728i
\(431\) 4.49405 7.78392i 0.216471 0.374938i −0.737256 0.675614i \(-0.763879\pi\)
0.953726 + 0.300676i \(0.0972121\pi\)
\(432\) 4.92927 1.64387i 0.237159 0.0790910i
\(433\) 10.4614 + 18.1197i 0.502742 + 0.870775i 0.999995 + 0.00316933i \(0.00100883\pi\)
−0.497253 + 0.867606i \(0.665658\pi\)
\(434\) −6.79501 + 0.794223i −0.326171 + 0.0381239i
\(435\) 2.05834 3.20113i 0.0986897 0.153482i
\(436\) −11.6180 + 2.75352i −0.556403 + 0.131870i
\(437\) 0.430255 + 7.38719i 0.0205819 + 0.353377i
\(438\) −10.4857 3.02150i −0.501028 0.144373i
\(439\) 19.5922 + 4.64343i 0.935084 + 0.221619i 0.669792 0.742549i \(-0.266383\pi\)
0.265292 + 0.964168i \(0.414531\pi\)
\(440\) 2.01552 11.4306i 0.0960862 0.544932i
\(441\) 11.4463 + 14.7294i 0.545062 + 0.701400i
\(442\) 2.92220 + 16.5726i 0.138995 + 0.788280i
\(443\) 0.627345 10.7711i 0.0298061 0.511750i −0.950057 0.312078i \(-0.898975\pi\)
0.979863 0.199673i \(-0.0639879\pi\)
\(444\) 14.8751 2.78170i 0.705943 0.132014i
\(445\) 8.83727 11.8705i 0.418927 0.562717i
\(446\) 4.31840 5.80061i 0.204482 0.274667i
\(447\) −12.2621 14.3104i −0.579979 0.676861i
\(448\) −0.0514175 + 0.882805i −0.00242925 + 0.0417086i
\(449\) −7.05769 40.0261i −0.333073 1.88895i −0.445487 0.895289i \(-0.646969\pi\)
0.112414 0.993661i \(-0.464142\pi\)
\(450\) −3.04682 + 3.36619i −0.143629 + 0.158684i
\(451\) 5.62748 31.9150i 0.264988 1.50282i
\(452\) 8.73765 + 2.07086i 0.410985 + 0.0974051i
\(453\) −9.81474 + 9.45335i −0.461137 + 0.444157i
\(454\) −0.331040 5.68375i −0.0155365 0.266751i
\(455\) 14.9297 3.53841i 0.699917 0.165883i
\(456\) −10.8657 0.520239i −0.508834 0.0243624i
\(457\) 31.1797 3.64439i 1.45853 0.170477i 0.650447 0.759552i \(-0.274582\pi\)
0.808079 + 0.589074i \(0.200508\pi\)
\(458\) 1.85154 + 3.20697i 0.0865169 + 0.149852i
\(459\) 0.398732 + 12.8558i 0.0186112 + 0.600057i
\(460\) −1.50347 + 2.60409i −0.0700996 + 0.121416i
\(461\) 5.57032 12.9135i 0.259436 0.601440i −0.737858 0.674956i \(-0.764163\pi\)
0.997294 + 0.0735160i \(0.0234220\pi\)
\(462\) −5.54417 + 4.21723i −0.257938 + 0.196203i
\(463\) 12.4631 + 13.2101i 0.579209 + 0.613926i 0.949033 0.315176i \(-0.102064\pi\)
−0.369824 + 0.929102i \(0.620582\pi\)
\(464\) 0.769374 + 0.386394i 0.0357173 + 0.0179379i
\(465\) 15.0314 30.7175i 0.697065 1.42449i
\(466\) −6.91839 23.1090i −0.320488 1.07050i
\(467\) −29.1271 24.4405i −1.34784 1.13097i −0.979536 0.201268i \(-0.935494\pi\)
−0.368305 0.929705i \(-0.620062\pi\)
\(468\) 15.3496 13.4301i 0.709535 0.620808i
\(469\) −1.92143 + 1.61227i −0.0887234 + 0.0744478i
\(470\) 10.2044 + 6.71156i 0.470696 + 0.309581i
\(471\) −10.8515 + 13.2072i −0.500013 + 0.608556i
\(472\) −4.95064 0.578647i −0.227872 0.0266344i
\(473\) −11.6476 27.0021i −0.535555 1.24156i
\(474\) 0.0585814 + 5.66791i 0.00269073 + 0.260336i
\(475\) 8.49411 4.26590i 0.389737 0.195733i
\(476\) −2.05690 0.748649i −0.0942776 0.0343143i
\(477\) 13.3867 + 6.38006i 0.612935 + 0.292123i
\(478\) 12.0765 4.39547i 0.552364 0.201044i
\(479\) 8.05347 8.53618i 0.367973 0.390028i −0.516758 0.856132i \(-0.672861\pi\)
0.884730 + 0.466104i \(0.154343\pi\)
\(480\) −3.57283 2.60292i −0.163077 0.118806i
\(481\) 49.6271 32.6402i 2.26280 1.48827i
\(482\) −4.88857 + 16.3290i −0.222668 + 0.743763i
\(483\) 1.72334 0.535404i 0.0784149 0.0243617i
\(484\) 5.78259 + 7.76737i 0.262845 + 0.353062i
\(485\) 0.680800 0.0309135
\(486\) 13.0794 8.48114i 0.593293 0.384712i
\(487\) 13.6206 0.617210 0.308605 0.951190i \(-0.400138\pi\)
0.308605 + 0.951190i \(0.400138\pi\)
\(488\) 1.44521 + 1.94125i 0.0654214 + 0.0878761i
\(489\) −17.4493 + 5.42109i −0.789084 + 0.245150i
\(490\) 4.55135 15.2026i 0.205609 0.686783i
\(491\) 17.4899 11.5033i 0.789309 0.519137i −0.0896845 0.995970i \(-0.528586\pi\)
0.878994 + 0.476833i \(0.158215\pi\)
\(492\) −9.97560 7.26753i −0.449735 0.327646i
\(493\) −1.46245 + 1.55011i −0.0658655 + 0.0698133i
\(494\) −40.1232 + 14.6036i −1.80523 + 0.657048i
\(495\) −2.74271 34.7126i −0.123276 1.56021i
\(496\) 7.26980 + 2.64599i 0.326423 + 0.118808i
\(497\) 8.64386 4.34111i 0.387730 0.194725i
\(498\) −0.0565485 5.47122i −0.00253400 0.245171i
\(499\) 7.15992 + 16.5986i 0.320522 + 0.743054i 0.999957 + 0.00931768i \(0.00296595\pi\)
−0.679434 + 0.733736i \(0.737775\pi\)
\(500\) −8.83805 1.03302i −0.395249 0.0461980i
\(501\) 4.67332 5.68780i 0.208788 0.254112i
\(502\) −8.99570 5.91656i −0.401498 0.264069i
\(503\) −21.1388 + 17.7376i −0.942534 + 0.790880i −0.978024 0.208490i \(-0.933145\pi\)
0.0354905 + 0.999370i \(0.488701\pi\)
\(504\) 0.514573 + 2.60252i 0.0229209 + 0.115925i
\(505\) 33.4734 + 28.0875i 1.48955 + 1.24988i
\(506\) −1.53679 5.13325i −0.0683188 0.228201i
\(507\) 25.2904 51.6823i 1.12318 2.29529i
\(508\) −16.2431 8.15757i −0.720670 0.361934i
\(509\) −7.85731 8.32827i −0.348269 0.369144i 0.529432 0.848353i \(-0.322405\pi\)
−0.877701 + 0.479209i \(0.840924\pi\)
\(510\) 8.70873 6.62439i 0.385629 0.293333i
\(511\) 2.20669 5.11569i 0.0976184 0.226305i
\(512\) 0.500000 0.866025i 0.0220971 0.0382733i
\(513\) −31.9476 + 6.66053i −1.41052 + 0.294069i
\(514\) 5.41400 + 9.37732i 0.238801 + 0.413616i
\(515\) −4.86330 + 0.568439i −0.214303 + 0.0250484i
\(516\) −11.1867 0.535609i −0.492469 0.0235789i
\(517\) −21.1782 + 5.01932i −0.931416 + 0.220750i
\(518\) 0.449237 + 7.71311i 0.0197384 + 0.338894i
\(519\) −0.354675 + 0.341616i −0.0155685 + 0.0149953i
\(520\) −16.8831 4.00137i −0.740372 0.175471i
\(521\) −6.83079 + 38.7393i −0.299262 + 1.69720i 0.350092 + 0.936715i \(0.386150\pi\)
−0.649355 + 0.760486i \(0.724961\pi\)
\(522\) 2.52501 + 0.543573i 0.110516 + 0.0237916i
\(523\) −5.54442 31.4440i −0.242441 1.37495i −0.826362 0.563139i \(-0.809593\pi\)
0.583921 0.811810i \(-0.301518\pi\)
\(524\) −0.771453 + 13.2453i −0.0337011 + 0.578625i
\(525\) −1.50829 1.76024i −0.0658273 0.0768233i
\(526\) 8.55334 11.4891i 0.372943 0.500950i
\(527\) −11.4354 + 15.3604i −0.498135 + 0.669111i
\(528\) 7.74299 1.44797i 0.336970 0.0630146i
\(529\) 1.25662 21.5753i 0.0546355 0.938056i
\(530\) −2.19066 12.4239i −0.0951563 0.539658i
\(531\) −14.8129 + 2.04255i −0.642824 + 0.0886389i
\(532\) 0.964419 5.46949i 0.0418129 0.237133i
\(533\) −47.1388 11.1721i −2.04181 0.483917i
\(534\) 9.65080 + 2.78091i 0.417631 + 0.120342i
\(535\) 2.70434 + 46.4318i 0.116919 + 2.00742i
\(536\) 2.75996 0.654123i 0.119212 0.0282538i
\(537\) −14.5464 + 22.6226i −0.627725 + 0.976238i
\(538\) −1.39138 + 0.162628i −0.0599865 + 0.00701141i
\(539\) 14.1395 + 24.4903i 0.609031 + 1.05487i
\(540\) −12.3337 4.87253i −0.530760 0.209680i
\(541\) −2.43494 + 4.21744i −0.104686 + 0.181322i −0.913610 0.406592i \(-0.866717\pi\)
0.808924 + 0.587914i \(0.200051\pi\)
\(542\) −10.7456 + 24.9111i −0.461564 + 1.07002i
\(543\) 37.9250 + 15.8964i 1.62752 + 0.682179i
\(544\) 1.69865 + 1.80046i 0.0728289 + 0.0771941i
\(545\) 27.2310 + 13.6759i 1.16645 + 0.585812i
\(546\) 5.81163 + 8.64031i 0.248715 + 0.369771i
\(547\) −2.70344 9.03013i −0.115591 0.386101i 0.880541 0.473970i \(-0.157179\pi\)
−0.996132 + 0.0878692i \(0.971994\pi\)
\(548\) 6.68195 + 5.60682i 0.285439 + 0.239511i
\(549\) 5.65707 + 4.55095i 0.241438 + 0.194230i
\(550\) −5.27266 + 4.42429i −0.224827 + 0.188652i
\(551\) −4.51766 2.97131i −0.192459 0.126582i
\(552\) −2.01326 0.333575i −0.0856899 0.0141979i
\(553\) −2.87435 0.335963i −0.122230 0.0142866i
\(554\) −2.40084 5.56576i −0.102002 0.236467i
\(555\) −33.6451 18.9641i −1.42815 0.804981i
\(556\) 0.114876 0.0576931i 0.00487184 0.00244673i
\(557\) 22.5380 + 8.20316i 0.954965 + 0.347579i 0.772059 0.635551i \(-0.219227\pi\)
0.182907 + 0.983130i \(0.441449\pi\)
\(558\) 23.1029 + 2.21737i 0.978024 + 0.0938686i
\(559\) −41.3085 + 15.0351i −1.74716 + 0.635916i
\(560\) 1.54875 1.64158i 0.0654468 0.0693695i
\(561\) −2.06335 + 19.3889i −0.0871147 + 0.818601i
\(562\) −5.27130 + 3.46699i −0.222356 + 0.146246i
\(563\) 5.83501 19.4903i 0.245916 0.821418i −0.742526 0.669818i \(-0.766372\pi\)
0.988442 0.151600i \(-0.0484425\pi\)
\(564\) −1.82812 + 8.08494i −0.0769779 + 0.340437i
\(565\) −13.6854 18.3826i −0.575748 0.773364i
\(566\) −3.20236 −0.134605
\(567\) 3.45162 + 7.17129i 0.144954 + 0.301166i
\(568\) −10.9383 −0.458960
\(569\) −18.5307 24.8910i −0.776847 1.04349i −0.997674 0.0681730i \(-0.978283\pi\)
0.220827 0.975313i \(-0.429124\pi\)
\(570\) 20.3896 + 18.8422i 0.854028 + 0.789211i
\(571\) −3.45648 + 11.5454i −0.144649 + 0.483161i −0.999353 0.0359536i \(-0.988553\pi\)
0.854704 + 0.519115i \(0.173738\pi\)
\(572\) 25.8325 16.9903i 1.08011 0.710400i
\(573\) 30.6812 13.6124i 1.28173 0.568666i
\(574\) 4.32423 4.58342i 0.180490 0.191308i
\(575\) 1.67560 0.609867i 0.0698772 0.0254332i
\(576\) 0.800824 2.89114i 0.0333677 0.120464i
\(577\) −6.57434 2.39287i −0.273694 0.0996163i 0.201527 0.979483i \(-0.435410\pi\)
−0.475221 + 0.879867i \(0.657632\pi\)
\(578\) 9.71641 4.87977i 0.404150 0.202972i
\(579\) 30.3170 17.9238i 1.25993 0.744890i
\(580\) −0.870294 2.01757i −0.0361370 0.0837750i
\(581\) 2.77460 + 0.324304i 0.115110 + 0.0134544i
\(582\) 0.162504 + 0.432515i 0.00673601 + 0.0179283i
\(583\) 18.7825 + 12.3534i 0.777890 + 0.511626i
\(584\) −4.82629 + 4.04973i −0.199713 + 0.167579i
\(585\) −52.0412 + 1.07587i −2.15164 + 0.0444818i
\(586\) 17.5483 + 14.7247i 0.724912 + 0.608274i
\(587\) 4.21156 + 14.0676i 0.173830 + 0.580631i 0.999856 + 0.0169992i \(0.00541129\pi\)
−0.826026 + 0.563632i \(0.809404\pi\)
\(588\) 10.7446 0.737301i 0.443102 0.0304058i
\(589\) −43.4201 21.8064i −1.78909 0.898517i
\(590\) 8.72952 + 9.25275i 0.359388 + 0.380929i
\(591\) 3.17756 + 24.9469i 0.130707 + 1.02618i
\(592\) 3.46057 8.02249i 0.142228 0.329722i
\(593\) 6.72451 11.6472i 0.276142 0.478293i −0.694280 0.719705i \(-0.744277\pi\)
0.970423 + 0.241412i \(0.0776105\pi\)
\(594\) 21.3984 10.0282i 0.877985 0.411462i
\(595\) 2.79320 + 4.83796i 0.114510 + 0.198337i
\(596\) −10.8068 + 1.26314i −0.442665 + 0.0517401i
\(597\) 12.6463 + 24.5450i 0.517579 + 1.00456i
\(598\) −7.79411 + 1.84724i −0.318725 + 0.0755392i
\(599\) −0.630836 10.8310i −0.0257753 0.442544i −0.986365 0.164573i \(-0.947375\pi\)
0.960590 0.277971i \(-0.0896618\pi\)
\(600\) 0.630853 + 2.54430i 0.0257545 + 0.103871i
\(601\) −5.29117 1.25403i −0.215831 0.0511530i 0.121278 0.992619i \(-0.461301\pi\)
−0.337109 + 0.941466i \(0.609449\pi\)
\(602\) 0.992911 5.63108i 0.0404681 0.229506i
\(603\) 7.52359 3.97530i 0.306384 0.161887i
\(604\) 1.36619 + 7.74802i 0.0555893 + 0.315262i
\(605\) 1.43697 24.6719i 0.0584213 1.00305i
\(606\) −9.85414 + 27.9701i −0.400297 + 1.13621i
\(607\) −8.92745 + 11.9916i −0.362354 + 0.486726i −0.945491 0.325648i \(-0.894418\pi\)
0.583137 + 0.812374i \(0.301825\pi\)
\(608\) −3.75046 + 5.03775i −0.152101 + 0.204308i
\(609\) −0.438184 + 1.24375i −0.0177561 + 0.0503992i
\(610\) 0.359134 6.16608i 0.0145409 0.249657i
\(611\) 5.64973 + 32.0412i 0.228564 + 1.29625i
\(612\) 6.28724 + 3.95148i 0.254147 + 0.159729i
\(613\) 1.49965 8.50493i 0.0605702 0.343511i −0.939429 0.342742i \(-0.888644\pi\)
1.00000 0.000768585i \(-0.000244648\pi\)
\(614\) −26.6009 6.30453i −1.07353 0.254430i
\(615\) 7.58056 + 30.5733i 0.305678 + 1.23283i
\(616\) 0.233843 + 4.01492i 0.00942178 + 0.161766i
\(617\) −33.0572 + 7.83469i −1.33083 + 0.315413i −0.833679 0.552250i \(-0.813769\pi\)
−0.497153 + 0.867663i \(0.665621\pi\)
\(618\) −1.52198 2.95399i −0.0612231 0.118827i
\(619\) −0.273547 + 0.0319731i −0.0109948 + 0.00128511i −0.121589 0.992581i \(-0.538799\pi\)
0.110594 + 0.993866i \(0.464725\pi\)
\(620\) −9.87214 17.0991i −0.396475 0.686715i
\(621\) −6.09778 + 0.545268i −0.244696 + 0.0218808i
\(622\) −11.8786 + 20.5743i −0.476288 + 0.824955i
\(623\) −2.03098 + 4.70835i −0.0813696 + 0.188636i
\(624\) −1.48784 11.6810i −0.0595613 0.467614i
\(625\) 20.7771 + 22.0225i 0.831085 + 0.880899i
\(626\) 19.0791 + 9.58190i 0.762556 + 0.382970i
\(627\) −49.3569 + 3.38689i −1.97112 + 0.135259i
\(628\) 2.83044 + 9.45431i 0.112947 + 0.377268i
\(629\) 16.5670 + 13.9014i 0.660571 + 0.554285i
\(630\) 3.26338 5.93222i 0.130016 0.236345i
\(631\) −11.3712 + 9.54158i −0.452681 + 0.379844i −0.840430 0.541921i \(-0.817697\pi\)
0.387749 + 0.921765i \(0.373253\pi\)
\(632\) 2.73417 + 1.79829i 0.108759 + 0.0715322i
\(633\) −8.42752 22.4304i −0.334964 0.891527i
\(634\) −14.5839 1.70462i −0.579202 0.0676990i
\(635\) 18.3737 + 42.5950i 0.729138 + 1.69033i
\(636\) 7.37003 4.35726i 0.292241 0.172777i
\(637\) 37.7767 18.9722i 1.49677 0.751706i
\(638\) 3.67939 + 1.33919i 0.145669 + 0.0530190i
\(639\) −31.7670 + 8.22597i −1.25669 + 0.325414i
\(640\) −2.39823 + 0.872884i −0.0947984 + 0.0345038i
\(641\) 25.3341 26.8526i 1.00064 1.06061i 0.00247661 0.999997i \(-0.499212\pi\)
0.998161 0.0606171i \(-0.0193068\pi\)
\(642\) −28.8528 + 12.8012i −1.13873 + 0.505221i
\(643\) 4.81729 3.16838i 0.189975 0.124949i −0.450958 0.892545i \(-0.648918\pi\)
0.640934 + 0.767596i \(0.278547\pi\)
\(644\) 0.298816 0.998115i 0.0117750 0.0393312i
\(645\) 20.9920 + 19.3988i 0.826560 + 0.763828i
\(646\) −9.28349 12.4699i −0.365254 0.490621i
\(647\) 8.03991 0.316082 0.158041 0.987433i \(-0.449482\pi\)
0.158041 + 0.987433i \(0.449482\pi\)
\(648\) 0.151522 8.99872i 0.00595236 0.353503i
\(649\) −22.6684 −0.889811
\(650\) 6.14423 + 8.25313i 0.240996 + 0.323714i
\(651\) −2.61336 + 11.5576i −0.102425 + 0.452980i
\(652\) −3.02558 + 10.1062i −0.118491 + 0.395788i
\(653\) −7.40917 + 4.87309i −0.289943 + 0.190699i −0.686145 0.727465i \(-0.740698\pi\)
0.396202 + 0.918163i \(0.370328\pi\)
\(654\) −2.18844 + 20.5643i −0.0855747 + 0.804129i
\(655\) 23.2370 24.6298i 0.907945 0.962366i
\(656\) −6.69603 + 2.43716i −0.261436 + 0.0951549i
\(657\) −10.9710 + 15.3908i −0.428020 + 0.600453i
\(658\) −3.97677 1.44742i −0.155030 0.0564265i
\(659\) −11.4692 + 5.76003i −0.446775 + 0.224379i −0.657938 0.753072i \(-0.728571\pi\)
0.211163 + 0.977451i \(0.432275\pi\)
\(660\) −17.5133 9.87142i −0.681706 0.384244i
\(661\) 10.6938 + 24.7909i 0.415939 + 0.964255i 0.989426 + 0.145040i \(0.0463312\pi\)
−0.573487 + 0.819215i \(0.694410\pi\)
\(662\) 1.38669 + 0.162081i 0.0538954 + 0.00629947i
\(663\) 28.7554 + 4.76447i 1.11677 + 0.185037i
\(664\) −2.63929 1.73589i −0.102424 0.0673655i
\(665\) −10.8581 + 9.11104i −0.421060 + 0.353311i
\(666\) 4.01701 25.9015i 0.155656 1.00366i
\(667\) −0.777055 0.652027i −0.0300877 0.0252466i
\(668\) −1.21895 4.07159i −0.0471627 0.157534i
\(669\) −6.99063 10.3932i −0.270274 0.401823i
\(670\) −6.46896 3.24883i −0.249918 0.125513i
\(671\) 7.55317 + 8.00589i 0.291587 + 0.309064i
\(672\) 1.41258 + 0.592090i 0.0544916 + 0.0228404i
\(673\) 9.47018 21.9544i 0.365049 0.846278i −0.632383 0.774656i \(-0.717923\pi\)
0.997432 0.0716223i \(-0.0228176\pi\)
\(674\) 17.0888 29.5987i 0.658236 1.14010i
\(675\) 3.74554 + 6.91477i 0.144166 + 0.266150i
\(676\) −16.6099 28.7692i −0.638842 1.10651i
\(677\) 27.6660 3.23370i 1.06329 0.124281i 0.433584 0.901113i \(-0.357249\pi\)
0.629708 + 0.776832i \(0.283175\pi\)
\(678\) 8.41192 13.0822i 0.323058 0.502420i
\(679\) −0.229534 + 0.0544006i −0.00880871 + 0.00208770i
\(680\) −0.367318 6.30661i −0.0140860 0.241847i
\(681\) −9.47567 2.73044i −0.363108 0.104631i
\(682\) 34.2359 + 8.11405i 1.31096 + 0.310703i
\(683\) 1.17701 6.67515i 0.0450370 0.255418i −0.953974 0.299891i \(-0.903050\pi\)
0.999011 + 0.0444731i \(0.0141609\pi\)
\(684\) −7.10357 + 17.4512i −0.271612 + 0.667262i
\(685\) −3.86567 21.9233i −0.147700 0.837646i
\(686\) −0.679638 + 11.6689i −0.0259487 + 0.445522i
\(687\) 6.30464 1.17899i 0.240537 0.0449813i
\(688\) −3.86127 + 5.18658i −0.147209 + 0.197737i
\(689\) 20.0680 26.9560i 0.764530 1.02694i
\(690\) 3.38880 + 3.95488i 0.129010 + 0.150560i
\(691\) −2.37423 + 40.7639i −0.0903199 + 1.55073i 0.583669 + 0.811992i \(0.301617\pi\)
−0.673989 + 0.738741i \(0.735421\pi\)
\(692\) 0.0493699 + 0.279990i 0.00187676 + 0.0106436i
\(693\) 3.69849 + 11.4843i 0.140494 + 0.436253i
\(694\) −0.379403 + 2.15170i −0.0144019 + 0.0816775i
\(695\) −0.319234 0.0756599i −0.0121093 0.00286995i
\(696\) 1.07403 1.03449i 0.0407111 0.0392121i
\(697\) −1.02558 17.6085i −0.0388465 0.666969i
\(698\) 20.1986 4.78715i 0.764528 0.181196i
\(699\) −41.7335 1.99815i −1.57850 0.0755771i
\(700\) −1.32928 + 0.155371i −0.0502422 + 0.00587247i
\(701\) −2.50398 4.33703i −0.0945742 0.163807i 0.814857 0.579663i \(-0.196816\pi\)
−0.909431 + 0.415855i \(0.863482\pi\)
\(702\) −13.1055 32.8052i −0.494636 1.23815i
\(703\) −27.4366 + 47.5215i −1.03479 + 1.79231i
\(704\) 1.80134 4.17597i 0.0678904 0.157388i
\(705\) 16.8373 12.8075i 0.634130 0.482358i
\(706\) 5.88994 + 6.24298i 0.221671 + 0.234958i
\(707\) −13.5301 6.79505i −0.508850 0.255554i
\(708\) −3.79460 + 7.75448i −0.142610 + 0.291431i
\(709\) −5.91270 19.7498i −0.222056 0.741719i −0.994321 0.106419i \(-0.966062\pi\)
0.772265 0.635300i \(-0.219124\pi\)
\(710\) 21.3849 + 17.9441i 0.802562 + 0.673429i
\(711\) 9.29299 + 3.16643i 0.348514 + 0.118750i
\(712\) 4.44199 3.72727i 0.166471 0.139685i
\(713\) −7.61546 5.00877i −0.285201 0.187580i
\(714\) −2.40685 + 2.92933i −0.0900740 + 0.109627i
\(715\) −78.3763 9.16087i −2.93111 0.342597i
\(716\) 6.15043 + 14.2583i 0.229852 + 0.532858i
\(717\) −0.230053 22.2583i −0.00859149 0.831250i
\(718\) −15.5593 + 7.81419i −0.580669 + 0.291623i
\(719\) −13.9245 5.06812i −0.519298 0.189009i 0.0690555 0.997613i \(-0.478001\pi\)
−0.588354 + 0.808604i \(0.700224\pi\)
\(720\) −6.30853 + 4.33859i −0.235105 + 0.161690i
\(721\) 1.59426 0.580263i 0.0593733 0.0216101i
\(722\) 14.0301 14.8711i 0.522147 0.553444i
\(723\) 23.8619 + 17.3841i 0.887433 + 0.646523i
\(724\) 19.8359 13.0463i 0.737194 0.484860i
\(725\) −0.373703 + 1.24825i −0.0138790 + 0.0463590i
\(726\) 16.0171 4.97616i 0.594452 0.184683i
\(727\) −23.5747 31.6664i −0.874339 1.17444i −0.983588 0.180427i \(-0.942252\pi\)
0.109249 0.994014i \(-0.465155\pi\)
\(728\) 6.01193 0.222817
\(729\) −6.32731 26.2481i −0.234345 0.972154i
\(730\) 16.0792 0.595117
\(731\) −9.55775 12.8383i −0.353506 0.474841i
\(732\) 4.00306 1.24366i 0.147957 0.0459670i
\(733\) 6.27529 20.9609i 0.231783 0.774209i −0.760404 0.649450i \(-0.774999\pi\)
0.992187 0.124759i \(-0.0398158\pi\)
\(734\) 9.40762 6.18749i 0.347242 0.228384i
\(735\) −22.2159 16.1850i −0.819446 0.596992i
\(736\) −0.808531 + 0.856993i −0.0298028 + 0.0315892i
\(737\) 12.1218 4.41199i 0.446513 0.162518i
\(738\) −17.6139 + 12.1137i −0.648375 + 0.445910i
\(739\) −19.9756 7.27052i −0.734814 0.267450i −0.0526126 0.998615i \(-0.516755\pi\)
−0.682201 + 0.731165i \(0.738977\pi\)
\(740\) −19.9264 + 10.0074i −0.732509 + 0.367880i
\(741\) 0.764335 + 73.9514i 0.0280785 + 2.71667i
\(742\) 1.73134 + 4.01371i 0.0635596 + 0.147348i
\(743\) 29.2201 + 3.41534i 1.07198 + 0.125297i 0.633729 0.773555i \(-0.281523\pi\)
0.438253 + 0.898852i \(0.355597\pi\)
\(744\) 8.50665 10.3533i 0.311869 0.379570i
\(745\) 23.2001 + 15.2589i 0.849985 + 0.559044i
\(746\) −5.65450 + 4.74469i −0.207026 + 0.173716i
\(747\) −8.97050 3.05654i −0.328213 0.111833i
\(748\) 8.62367 + 7.23612i 0.315313 + 0.264579i
\(749\) −4.62200 15.4386i −0.168884 0.564113i
\(750\) −6.77425 + 13.8436i −0.247361 + 0.505495i
\(751\) 0.669138 + 0.336054i 0.0244172 + 0.0122628i 0.460966 0.887418i \(-0.347503\pi\)
−0.436549 + 0.899681i \(0.643799\pi\)
\(752\) 3.28413 + 3.48098i 0.119760 + 0.126938i
\(753\) −14.8429 + 11.2904i −0.540905 + 0.411445i
\(754\) 2.31833 5.37449i 0.0844285 0.195727i
\(755\) 10.0396 17.3890i 0.365377 0.632851i
\(756\) 4.54772 + 0.657240i 0.165399 + 0.0239036i
\(757\) 7.72635 + 13.3824i 0.280819 + 0.486393i 0.971587 0.236684i \(-0.0760606\pi\)
−0.690768 + 0.723077i \(0.742727\pi\)
\(758\) 2.30192 0.269056i 0.0836095 0.00977255i
\(759\) −9.27033 0.443853i −0.336492 0.0161109i
\(760\) 15.5967 3.69649i 0.565752 0.134086i
\(761\) −2.23822 38.4287i −0.0811354 1.39304i −0.755745 0.654866i \(-0.772725\pi\)
0.674610 0.738175i \(-0.264312\pi\)
\(762\) −22.6751 + 21.8401i −0.821431 + 0.791185i
\(763\) −10.2738 2.43494i −0.371938 0.0881509i
\(764\) 3.36513 19.0846i 0.121746 0.690456i
\(765\) −5.80956 18.0395i −0.210045 0.652219i
\(766\) −1.02769 5.82832i −0.0371320 0.210586i
\(767\) −1.97030 + 33.8288i −0.0711435 + 1.22149i
\(768\) −1.12699 1.31525i −0.0406669 0.0474600i
\(769\) −10.8162 + 14.5287i −0.390042 + 0.523918i −0.953163 0.302457i \(-0.902193\pi\)
0.563121 + 0.826375i \(0.309601\pi\)
\(770\) 6.12925 8.23301i 0.220883 0.296697i
\(771\) 18.4351 3.44742i 0.663923 0.124156i
\(772\) 1.18230 20.2994i 0.0425520 0.730590i
\(773\) −3.74608 21.2451i −0.134737 0.764133i −0.975042 0.222019i \(-0.928735\pi\)
0.840305 0.542114i \(-0.182376\pi\)
\(774\) −7.31344 + 17.9667i −0.262876 + 0.645801i
\(775\) −2.03315 + 11.5306i −0.0730331 + 0.414191i
\(776\) 0.259566 + 0.0615182i 0.00931786 + 0.00220837i
\(777\) 12.8589 + 3.70534i 0.461311 + 0.132928i
\(778\) 0.212144 + 3.64237i 0.00760572 + 0.130585i
\(779\) 43.5471 10.3209i 1.56024 0.369783i
\(780\) −16.2537 + 25.2778i −0.581976 + 0.905089i
\(781\) −49.4099 + 5.77519i −1.76803 + 0.206653i
\(782\) −1.45820 2.52567i −0.0521450 0.0903177i
\(783\) 2.34125 3.81208i 0.0836694 0.136233i
\(784\) 3.10901 5.38496i 0.111036 0.192320i
\(785\) 9.97601 23.1270i 0.356059 0.825438i
\(786\) 21.1940 + 8.88353i 0.755964 + 0.316865i
\(787\) −11.9253 12.6401i −0.425092 0.450571i 0.479060 0.877782i \(-0.340978\pi\)
−0.904152 + 0.427211i \(0.859496\pi\)
\(788\) 12.9751 + 6.51633i 0.462218 + 0.232135i
\(789\) −13.8462 20.5855i −0.492937 0.732863i
\(790\) −2.39538 8.00113i −0.0852239 0.284667i
\(791\) 6.08298 + 5.10422i 0.216286 + 0.181485i
\(792\) 2.09099 13.4826i 0.0742999 0.479082i
\(793\) 12.6040 10.5760i 0.447581 0.375565i
\(794\) −9.94742 6.54252i −0.353021 0.232185i
\(795\) −21.5568 3.57174i −0.764542 0.126677i
\(796\) 15.8337 + 1.85069i 0.561209 + 0.0655959i
\(797\) 2.66897 + 6.18736i 0.0945397 + 0.219168i 0.958923 0.283665i \(-0.0915504\pi\)
−0.864384 + 0.502833i \(0.832291\pi\)
\(798\) −8.38007 4.72343i −0.296651 0.167208i
\(799\) −10.5859 + 5.31645i −0.374503 + 0.188083i
\(800\) 1.42216 + 0.517625i 0.0502811 + 0.0183008i
\(801\) 10.0974 14.1653i 0.356775 0.500507i
\(802\) 17.5774 6.39766i 0.620681 0.225909i
\(803\) −19.6629 + 20.8415i −0.693890 + 0.735480i
\(804\) 0.519882 4.88524i 0.0183348 0.172289i
\(805\) −2.22160 + 1.46117i −0.0783010 + 0.0514993i
\(806\) 15.0846 50.3861i 0.531333 1.77478i
\(807\) −0.535122 + 2.36659i −0.0188372 + 0.0833080i
\(808\) 10.2242 + 13.7335i 0.359687 + 0.483143i
\(809\) 2.66088 0.0935517 0.0467758 0.998905i \(-0.485105\pi\)
0.0467758 + 0.998905i \(0.485105\pi\)
\(810\) −15.0585 + 17.3444i −0.529102 + 0.609421i
\(811\) 47.1734 1.65648 0.828241 0.560373i \(-0.189342\pi\)
0.828241 + 0.560373i \(0.189342\pi\)
\(812\) 0.454641 + 0.610688i 0.0159548 + 0.0214310i
\(813\) 34.5110 + 31.8918i 1.21035 + 1.11849i
\(814\) 11.3962 38.0660i 0.399437 1.33421i
\(815\) 22.4942 14.7947i 0.787937 0.518234i
\(816\) 3.91893 1.73872i 0.137190 0.0608673i
\(817\) 27.8684 29.5388i 0.974993 1.03343i
\(818\) −9.09492 + 3.31028i −0.317996 + 0.115741i
\(819\) 17.4599 4.52119i 0.610099 0.157983i
\(820\) 17.0892 + 6.21997i 0.596782 + 0.217211i
\(821\) −32.3307 + 16.2371i −1.12835 + 0.566679i −0.912226 0.409687i \(-0.865638\pi\)
−0.216124 + 0.976366i \(0.569342\pi\)
\(822\) 13.0052 7.68887i 0.453609 0.268180i
\(823\) 4.32113 + 10.0175i 0.150625 + 0.349188i 0.976777 0.214260i \(-0.0687339\pi\)
−0.826152 + 0.563448i \(0.809475\pi\)
\(824\) −1.90558 0.222730i −0.0663839 0.00775916i
\(825\) 4.19301 + 11.1600i 0.145982 + 0.388540i
\(826\) −3.68255 2.42205i −0.128132 0.0842739i
\(827\) −23.9099 + 20.0628i −0.831430 + 0.697653i −0.955619 0.294606i \(-0.904812\pi\)
0.124189 + 0.992259i \(0.460367\pi\)
\(828\) −1.70366 + 3.09693i −0.0592061 + 0.107626i
\(829\) −37.2041 31.2179i −1.29215 1.08424i −0.991445 0.130527i \(-0.958333\pi\)
−0.300706 0.953717i \(-0.597222\pi\)
\(830\) 2.31226 + 7.72347i 0.0802596 + 0.268086i
\(831\) −10.4742 + 0.718742i −0.363346 + 0.0249329i
\(832\) −6.07537 3.05117i −0.210626 0.105780i
\(833\) 10.5622 + 11.1953i 0.365959 + 0.387894i
\(834\) −0.0281329 0.220871i −0.000974162 0.00764812i
\(835\) −4.29626 + 9.95985i −0.148678 + 0.344675i
\(836\) −14.2816 + 24.7365i −0.493940 + 0.855529i
\(837\) 16.9191 36.4654i 0.584809 1.26043i
\(838\) 16.9592 + 29.3741i 0.585844 + 1.01471i
\(839\) 31.8107 3.71813i 1.09823 0.128364i 0.452375 0.891828i \(-0.350577\pi\)
0.645851 + 0.763464i \(0.276503\pi\)
\(840\) −1.79037 3.47489i −0.0617735 0.119895i
\(841\) −27.4970 + 6.51692i −0.948174 + 0.224721i
\(842\) 1.40441 + 24.1127i 0.0483990 + 0.830979i
\(843\) 2.62992 + 10.6068i 0.0905792 + 0.365316i
\(844\) −13.4612 3.19035i −0.463352 0.109817i
\(845\) −14.7222 + 83.4936i −0.506458 + 2.87227i
\(846\) 12.1556 + 7.63971i 0.417920 + 0.262659i
\(847\) 1.48697 + 8.43305i 0.0510930 + 0.289763i
\(848\) 0.287416 4.93475i 0.00986992 0.169460i
\(849\) −1.84309 + 5.23147i −0.0632548 + 0.179543i
\(850\) −2.23707 + 3.00491i −0.0767309 + 0.103067i
\(851\) −6.14715 + 8.25705i −0.210722 + 0.283048i
\(852\) −6.29545 + 17.8691i −0.215679 + 0.612185i
\(853\) 2.14862 36.8904i 0.0735674 1.26310i −0.736367 0.676583i \(-0.763460\pi\)
0.809934 0.586521i \(-0.199503\pi\)
\(854\) 0.371630 + 2.10762i 0.0127169 + 0.0721211i
\(855\) 42.5163 22.4647i 1.45403 0.768276i
\(856\) −3.16458 + 17.9472i −0.108163 + 0.613424i
\(857\) 23.2408 + 5.50818i 0.793892 + 0.188156i 0.607500 0.794320i \(-0.292172\pi\)
0.186392 + 0.982475i \(0.440321\pi\)
\(858\) −12.8882 51.9794i −0.439994 1.77455i
\(859\) 0.719697 + 12.3567i 0.0245558 + 0.421606i 0.988076 + 0.153969i \(0.0492057\pi\)
−0.963520 + 0.267637i \(0.913757\pi\)
\(860\) 16.0575 3.80570i 0.547556 0.129773i
\(861\) −4.99883 9.70215i −0.170360 0.330648i
\(862\) −8.92732 + 1.04345i −0.304066 + 0.0355402i
\(863\) 3.49949 + 6.06129i 0.119124 + 0.206329i 0.919421 0.393275i \(-0.128658\pi\)
−0.800297 + 0.599604i \(0.795325\pi\)
\(864\) −4.26214 2.97223i −0.145001 0.101117i
\(865\) 0.362800 0.628387i 0.0123356 0.0213658i
\(866\) 8.28709 19.2116i 0.281607 0.652838i
\(867\) −2.37952 18.6815i −0.0808127 0.634459i
\(868\) 4.69476 + 4.97616i 0.159351 + 0.168902i
\(869\) 13.3002 + 6.67959i 0.451177 + 0.226590i
\(870\) −3.79685 + 0.260541i −0.128725 + 0.00883318i
\(871\) −5.53055 18.4733i −0.187396 0.625945i
\(872\) 9.14647 + 7.67480i 0.309739 + 0.259901i
\(873\) 0.800097 0.0165408i 0.0270792 0.000559821i
\(874\) 5.66851 4.75644i 0.191740 0.160889i
\(875\) −6.57420 4.32392i −0.222249 0.146175i
\(876\) 3.83804 + 10.2152i 0.129675 + 0.345139i
\(877\) 10.2378 + 1.19663i 0.345706 + 0.0404073i 0.287174 0.957878i \(-0.407284\pi\)
0.0585317 + 0.998286i \(0.481358\pi\)
\(878\) −7.97504 18.4882i −0.269145 0.623947i
\(879\) 34.1546 20.1927i 1.15201 0.681082i
\(880\) −10.3723 + 5.20918i −0.349651 + 0.175601i
\(881\) 10.9041 + 3.96877i 0.367369 + 0.133711i 0.519107 0.854709i \(-0.326265\pi\)
−0.151738 + 0.988421i \(0.548487\pi\)
\(882\) 4.97953 17.9771i 0.167670 0.605321i
\(883\) 33.5241 12.2018i 1.12818 0.410623i 0.290547 0.956861i \(-0.406163\pi\)
0.837630 + 0.546238i \(0.183941\pi\)
\(884\) 11.5483 12.2405i 0.388411 0.411691i
\(885\) 20.1398 8.93545i 0.676991 0.300362i
\(886\) −9.01437 + 5.92885i −0.302844 + 0.199183i
\(887\) 12.7553 42.6057i 0.428282 1.43056i −0.423133 0.906068i \(-0.639070\pi\)
0.851415 0.524493i \(-0.175745\pi\)
\(888\) −11.1141 10.2706i −0.372964 0.344658i
\(889\) −9.59840 12.8929i −0.321920 0.432414i
\(890\) −14.7989 −0.496059
\(891\) −4.06670 40.7287i −0.136240 1.36446i
\(892\) −7.23157 −0.242131
\(893\) −17.9485 24.1091i −0.600625 0.806779i
\(894\) −4.15630 + 18.3813i −0.139007 + 0.614764i
\(895\) 11.3661 37.9655i 0.379927 1.26905i
\(896\) 0.738823 0.485932i 0.0246823 0.0162338i
\(897\) −1.46814 + 13.7959i −0.0490198 + 0.460630i
\(898\) −27.8913 + 29.5631i −0.930746 + 0.986533i
\(899\) 6.25894 2.27807i 0.208747 0.0759778i
\(900\) 4.51954 + 0.433775i 0.150651 + 0.0144592i
\(901\) 11.4977 + 4.18483i 0.383045 + 0.139417i
\(902\) −28.9603 + 14.5444i −0.964272 + 0.484275i
\(903\) −8.62764 4.86298i −0.287110 0.161830i
\(904\) −3.55668 8.24530i −0.118293 0.274235i
\(905\) −60.1824 7.03431i −2.00053 0.233828i
\(906\) 13.4437 + 2.22748i 0.446637 + 0.0740030i
\(907\) 16.5981 + 10.9167i 0.551130 + 0.362484i 0.794324 0.607494i \(-0.207825\pi\)
−0.243195 + 0.969977i \(0.578195\pi\)
\(908\) −4.36138 + 3.65963i −0.144737 + 0.121449i
\(909\) 40.0214 + 32.1960i 1.32743 + 1.06788i
\(910\) −11.7537 9.86249i −0.389630 0.326938i
\(911\) −11.9543 39.9301i −0.396063 1.32294i −0.890996 0.454011i \(-0.849993\pi\)
0.494933 0.868931i \(-0.335192\pi\)
\(912\) 6.07126 + 9.02631i 0.201040 + 0.298891i
\(913\) −12.8386 6.44779i −0.424896 0.213391i
\(914\) −21.5425 22.8337i −0.712562 0.755272i
\(915\) −9.86641 4.13554i −0.326173 0.136717i
\(916\) 1.46672 3.40023i 0.0484617 0.112347i
\(917\) −5.86636 + 10.1608i −0.193724 + 0.335540i
\(918\) 10.0738 7.99678i 0.332486 0.263933i
\(919\) −0.0817467 0.141589i −0.00269657 0.00467060i 0.864674 0.502333i \(-0.167525\pi\)
−0.867371 + 0.497663i \(0.834192\pi\)
\(920\) 2.98661 0.349084i 0.0984655 0.0115090i
\(921\) −25.6093 + 39.8275i −0.843854 + 1.31236i
\(922\) −13.6845 + 3.24330i −0.450677 + 0.106812i
\(923\) 4.32388 + 74.2382i 0.142322 + 2.44358i
\(924\) 6.69349 + 1.92875i 0.220199 + 0.0634512i
\(925\) 12.8665 + 3.04942i 0.423049 + 0.100264i
\(926\) 3.15369 17.8855i 0.103637 0.587753i
\(927\) −5.70170 + 0.786206i −0.187268 + 0.0258224i
\(928\) −0.149503 0.847871i −0.00490766 0.0278327i
\(929\) −3.17203 + 54.4617i −0.104071 + 1.78683i 0.393417 + 0.919360i \(0.371293\pi\)
−0.497488 + 0.867471i \(0.665744\pi\)
\(930\) −33.6154 + 6.28619i −1.10229 + 0.206132i
\(931\) −23.3204 + 31.3248i −0.764296 + 1.02663i
\(932\) −14.4049 + 19.3492i −0.471849 + 0.633803i
\(933\) 26.7742 + 31.2466i 0.876547 + 1.02297i
\(934\) −2.21082 + 37.9584i −0.0723404 + 1.24204i
\(935\) −4.98900 28.2940i −0.163158 0.925313i
\(936\) −19.9388 4.29234i −0.651719 0.140299i
\(937\) −1.44253 + 8.18100i −0.0471254 + 0.267262i −0.999262 0.0384113i \(-0.987770\pi\)
0.952137 + 0.305673i \(0.0988814\pi\)
\(938\) 2.44064 + 0.578442i 0.0796897 + 0.0188868i
\(939\) 26.6342 25.6535i 0.869173 0.837169i
\(940\) −0.710166 12.1931i −0.0231631 0.397695i
\(941\) 16.6814 3.95357i 0.543799 0.128883i 0.0504698 0.998726i \(-0.483928\pi\)
0.493329 + 0.869843i \(0.335780\pi\)
\(942\) 17.0739 + 0.817480i 0.556298 + 0.0266349i
\(943\) 8.33882 0.974668i 0.271549 0.0317396i
\(944\) 2.49217 + 4.31657i 0.0811133 + 0.140492i
\(945\) −7.81284 8.74541i −0.254152 0.284488i
\(946\) −14.7035 + 25.4673i −0.478054 + 0.828013i
\(947\) −6.99249 + 16.2104i −0.227226 + 0.526768i −0.993243 0.116052i \(-0.962976\pi\)
0.766018 + 0.642820i \(0.222235\pi\)
\(948\) 4.51138 3.43163i 0.146523 0.111454i
\(949\) 29.3934 + 31.1552i 0.954151 + 1.01134i
\(950\) −8.49411 4.26590i −0.275585 0.138404i
\(951\) −11.1784 + 22.8437i −0.362485 + 0.740758i
\(952\) 0.627784 + 2.09695i 0.0203466 + 0.0679624i
\(953\) −30.9439 25.9650i −1.00237 0.841089i −0.0150592 0.999887i \(-0.504794\pi\)
−0.987311 + 0.158798i \(0.949238\pi\)
\(954\) −2.87639 14.5477i −0.0931265 0.470999i
\(955\) −37.8870 + 31.7910i −1.22599 + 1.02873i
\(956\) −10.7373 7.06201i −0.347268 0.228402i
\(957\) 4.30539 5.24001i 0.139174 0.169385i
\(958\) −11.6563 1.36242i −0.376597 0.0440179i
\(959\) 3.05515 + 7.08263i 0.0986558 + 0.228710i
\(960\) 0.0456856 + 4.42021i 0.00147450 + 0.142662i
\(961\) 25.7824 12.9484i 0.831689 0.417690i
\(962\) −55.8167 20.3156i −1.79960 0.655002i
\(963\) 4.30634 + 54.5024i 0.138770 + 1.75632i
\(964\) 16.0171 5.82974i 0.515875 0.187763i
\(965\) −35.6123 + 37.7468i −1.14640 + 1.21511i
\(966\) −1.45857 1.06261i −0.0469287 0.0341890i
\(967\) 23.9147 15.7290i 0.769046 0.505810i −0.103329 0.994647i \(-0.532949\pi\)
0.872375 + 0.488838i \(0.162579\pi\)
\(968\) 2.77726 9.27670i 0.0892646 0.298164i
\(969\) −25.7142 + 7.98883i −0.826060 + 0.256638i
\(970\) −0.406545 0.546085i −0.0130534 0.0175337i
\(971\) 49.5340 1.58962 0.794811 0.606857i \(-0.207570\pi\)
0.794811 + 0.606857i \(0.207570\pi\)
\(972\) −14.6134 5.42669i −0.468725 0.174061i
\(973\) 0.113677 0.00364431
\(974\) −8.13369 10.9254i −0.260620 0.350074i
\(975\) 17.0188 5.28737i 0.545039 0.169331i
\(976\) 0.694103 2.31847i 0.0222177 0.0742123i
\(977\) −41.2145 + 27.1072i −1.31857 + 0.867237i −0.996828 0.0795901i \(-0.974639\pi\)
−0.321742 + 0.946827i \(0.604268\pi\)
\(978\) 14.7684 + 10.7592i 0.472240 + 0.344042i
\(979\) 18.0973 19.1820i 0.578391 0.613058i
\(980\) −14.9122 + 5.42760i −0.476353 + 0.173378i
\(981\) 32.3350 + 15.4108i 1.03238 + 0.492028i
\(982\) −19.6713 7.15978i −0.627737 0.228478i
\(983\) 7.40493 3.71890i 0.236181 0.118614i −0.326773 0.945103i \(-0.605961\pi\)
0.562954 + 0.826488i \(0.309665\pi\)
\(984\) 0.127557 + 12.3415i 0.00406638 + 0.393434i
\(985\) −14.6770 34.0252i −0.467650 1.08413i
\(986\) 2.11669 + 0.247406i 0.0674092 + 0.00787901i
\(987\) −4.65336 + 5.66351i −0.148118 + 0.180272i
\(988\) 35.6738 + 23.4630i 1.13493 + 0.746458i
\(989\) 5.83598 4.89697i 0.185573 0.155714i
\(990\) −26.2059 + 22.9289i −0.832879 + 0.728729i
\(991\) 18.6820 + 15.6761i 0.593454 + 0.497967i 0.889334 0.457258i \(-0.151168\pi\)
−0.295880 + 0.955225i \(0.595613\pi\)
\(992\) −2.21881 7.41135i −0.0704473 0.235311i
\(993\) 1.06288 2.17206i 0.0337296 0.0689283i
\(994\) −8.64386 4.34111i −0.274167 0.137692i
\(995\) −27.9196 29.5931i −0.885112 0.938164i
\(996\) −4.35482 + 3.31254i −0.137988 + 0.104962i
\(997\) −12.8119 + 29.7013i −0.405757 + 0.940650i 0.585738 + 0.810501i \(0.300805\pi\)
−0.991494 + 0.130149i \(0.958454\pi\)
\(998\) 9.03849 15.6551i 0.286108 0.495554i
\(999\) −40.0015 21.4697i −1.26559 0.679273i
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 162.2.g.a.7.1 72
3.2 odd 2 486.2.g.a.343.1 72
81.23 odd 54 486.2.g.a.469.1 72
81.58 even 27 inner 162.2.g.a.139.1 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
162.2.g.a.7.1 72 1.1 even 1 trivial
162.2.g.a.139.1 yes 72 81.58 even 27 inner
486.2.g.a.343.1 72 3.2 odd 2
486.2.g.a.469.1 72 81.23 odd 54