Properties

Label 378.2.w.a.25.3
Level $378$
Weight $2$
Character 378.25
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(25,378)]
 
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([10, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.w (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 25.3
Character \(\chi\) \(=\) 378.25
Dual form 378.2.w.a.121.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.939693 + 0.342020i) q^{2} +(-1.25749 + 1.19110i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.98579 + 0.722770i) q^{5} +(0.774279 - 1.54935i) q^{6} +(2.63247 + 0.264792i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.162584 - 2.99559i) q^{9} +O(q^{10})\) \(q+(-0.939693 + 0.342020i) q^{2} +(-1.25749 + 1.19110i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.98579 + 0.722770i) q^{5} +(0.774279 - 1.54935i) q^{6} +(2.63247 + 0.264792i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.162584 - 2.99559i) q^{9} -2.11324 q^{10} +(2.13695 - 0.777787i) q^{11} +(-0.197675 + 1.72073i) q^{12} +(-0.774677 - 4.39341i) q^{13} +(-2.56427 + 0.651534i) q^{14} +(-3.35801 + 1.45639i) q^{15} +(0.173648 - 0.984808i) q^{16} -1.10097 q^{17} +(0.871774 + 2.87054i) q^{18} +6.55502 q^{19} +(1.98579 - 0.722770i) q^{20} +(-3.62570 + 2.80255i) q^{21} +(-1.74206 + 1.46176i) q^{22} +(0.981032 + 5.56371i) q^{23} +(-0.402772 - 1.68457i) q^{24} +(-0.409243 - 0.343396i) q^{25} +(2.23059 + 3.86350i) q^{26} +(3.36359 + 3.96059i) q^{27} +(2.18679 - 1.48928i) q^{28} +(-0.886000 + 5.02476i) q^{29} +(2.65738 - 2.51707i) q^{30} +(5.42690 - 4.55371i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-1.76079 + 3.52338i) q^{33} +(1.03458 - 0.376555i) q^{34} +(5.03615 + 2.42849i) q^{35} +(-1.80098 - 2.39926i) q^{36} +(-5.50275 + 9.53104i) q^{37} +(-6.15971 + 2.24195i) q^{38} +(6.20712 + 4.60197i) q^{39} +(-1.61883 + 1.35836i) q^{40} +(1.28738 + 7.30109i) q^{41} +(2.44852 - 3.87360i) q^{42} +(-4.90452 - 4.11538i) q^{43} +(1.13705 - 1.96943i) q^{44} +(2.48798 - 5.83111i) q^{45} +(-2.82477 - 4.89264i) q^{46} +(-5.53120 - 4.64123i) q^{47} +(0.954638 + 1.44522i) q^{48} +(6.85977 + 1.39411i) q^{49} +(0.502011 + 0.182717i) q^{50} +(1.38447 - 1.31137i) q^{51} +(-3.41747 - 2.86759i) q^{52} +(2.35202 - 4.07382i) q^{53} +(-4.51534 - 2.57132i) q^{54} +4.80571 q^{55} +(-1.54555 + 2.14739i) q^{56} +(-8.24290 + 7.80766i) q^{57} +(-0.886000 - 5.02476i) q^{58} +(0.595915 + 3.37960i) q^{59} +(-1.63624 + 3.27415i) q^{60} +(-1.09424 - 0.918179i) q^{61} +(-3.54216 + 6.13519i) q^{62} +(1.22120 - 7.84275i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.63708 - 9.28432i) q^{65} +(0.449533 - 3.91312i) q^{66} +(6.70999 + 2.44224i) q^{67} +(-0.843395 + 0.707693i) q^{68} +(-7.86055 - 5.82783i) q^{69} +(-5.56303 - 0.559568i) q^{70} +(-2.73928 - 4.74457i) q^{71} +(2.51297 + 1.63860i) q^{72} +(-6.53126 - 11.3125i) q^{73} +(1.91108 - 10.8383i) q^{74} +(0.923637 - 0.0556294i) q^{75} +(5.02144 - 4.21349i) q^{76} +(5.83141 - 1.48165i) q^{77} +(-7.40675 - 2.20148i) q^{78} +(-5.38398 + 1.95961i) q^{79} +(1.05662 - 1.83012i) q^{80} +(-8.94713 - 0.974069i) q^{81} +(-3.70686 - 6.42047i) q^{82} +(-0.173835 + 0.985869i) q^{83} +(-0.976009 + 4.47743i) q^{84} +(-2.18631 - 0.795751i) q^{85} +(6.01628 + 2.18975i) q^{86} +(-4.87082 - 7.37391i) q^{87} +(-0.394893 + 2.23955i) q^{88} -8.11989 q^{89} +(-0.343578 + 6.33039i) q^{90} +(-0.875973 - 11.7706i) q^{91} +(4.32780 + 3.63145i) q^{92} +(-1.40039 + 12.1902i) q^{93} +(6.78502 + 2.46955i) q^{94} +(13.0169 + 4.73777i) q^{95} +(-1.39136 - 1.03156i) q^{96} +(0.607697 + 0.509919i) q^{97} +(-6.92289 + 1.03614i) q^{98} +(-1.98250 - 6.52789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9} + 12 q^{10} - 6 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} + 36 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} + 9 q^{35} + 9 q^{36} + 3 q^{39} - 6 q^{41} + 3 q^{42} + 24 q^{43} - 30 q^{45} - 9 q^{47} - 6 q^{48} + 51 q^{49} + 6 q^{50} + 12 q^{51} + 6 q^{52} - 15 q^{53} - 27 q^{54} + 72 q^{55} + 6 q^{56} - 63 q^{57} + 3 q^{58} + 15 q^{59} - 3 q^{60} - 18 q^{61} - 24 q^{62} - 48 q^{63} - 36 q^{64} - 18 q^{65} - 36 q^{66} + 66 q^{67} - 18 q^{68} - 21 q^{69} - 6 q^{70} + 12 q^{71} - 12 q^{72} - 66 q^{73} + 9 q^{74} + 15 q^{75} - 15 q^{77} + 30 q^{78} + 9 q^{79} - 6 q^{80} - 33 q^{82} - 18 q^{83} - 12 q^{84} + 21 q^{85} - 12 q^{86} - 48 q^{87} + 12 q^{88} + 72 q^{89} + 69 q^{90} + 12 q^{91} + 30 q^{92} + 60 q^{93} - 36 q^{94} + 93 q^{95} - 48 q^{97} + 6 q^{98} - 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.939693 + 0.342020i −0.664463 + 0.241845i
\(3\) −1.25749 + 1.19110i −0.726015 + 0.687679i
\(4\) 0.766044 0.642788i 0.383022 0.321394i
\(5\) 1.98579 + 0.722770i 0.888074 + 0.323232i 0.745463 0.666546i \(-0.232228\pi\)
0.142610 + 0.989779i \(0.454450\pi\)
\(6\) 0.774279 1.54935i 0.316098 0.632520i
\(7\) 2.63247 + 0.264792i 0.994979 + 0.100082i
\(8\) −0.500000 + 0.866025i −0.176777 + 0.306186i
\(9\) 0.162584 2.99559i 0.0541946 0.998530i
\(10\) −2.11324 −0.668264
\(11\) 2.13695 0.777787i 0.644315 0.234512i 0.000865256 1.00000i \(-0.499725\pi\)
0.643450 + 0.765488i \(0.277502\pi\)
\(12\) −0.197675 + 1.72073i −0.0570639 + 0.496733i
\(13\) −0.774677 4.39341i −0.214857 1.21851i −0.881155 0.472827i \(-0.843233\pi\)
0.666298 0.745685i \(-0.267878\pi\)
\(14\) −2.56427 + 0.651534i −0.685331 + 0.174130i
\(15\) −3.35801 + 1.45639i −0.867035 + 0.376038i
\(16\) 0.173648 0.984808i 0.0434120 0.246202i
\(17\) −1.10097 −0.267025 −0.133513 0.991047i \(-0.542626\pi\)
−0.133513 + 0.991047i \(0.542626\pi\)
\(18\) 0.871774 + 2.87054i 0.205479 + 0.676593i
\(19\) 6.55502 1.50383 0.751913 0.659263i \(-0.229132\pi\)
0.751913 + 0.659263i \(0.229132\pi\)
\(20\) 1.98579 0.722770i 0.444037 0.161616i
\(21\) −3.62570 + 2.80255i −0.791194 + 0.611566i
\(22\) −1.74206 + 1.46176i −0.371408 + 0.311649i
\(23\) 0.981032 + 5.56371i 0.204559 + 1.16011i 0.898132 + 0.439727i \(0.144925\pi\)
−0.693572 + 0.720387i \(0.743964\pi\)
\(24\) −0.402772 1.68457i −0.0822154 0.343861i
\(25\) −0.409243 0.343396i −0.0818486 0.0686791i
\(26\) 2.23059 + 3.86350i 0.437455 + 0.757695i
\(27\) 3.36359 + 3.96059i 0.647323 + 0.762216i
\(28\) 2.18679 1.48928i 0.413265 0.281447i
\(29\) −0.886000 + 5.02476i −0.164526 + 0.933074i 0.785026 + 0.619463i \(0.212650\pi\)
−0.949552 + 0.313610i \(0.898461\pi\)
\(30\) 2.65738 2.51707i 0.485170 0.459551i
\(31\) 5.42690 4.55371i 0.974700 0.817870i −0.00858156 0.999963i \(-0.502732\pi\)
0.983281 + 0.182093i \(0.0582872\pi\)
\(32\) 0.173648 + 0.984808i 0.0306970 + 0.174091i
\(33\) −1.76079 + 3.52338i −0.306514 + 0.613341i
\(34\) 1.03458 0.376555i 0.177429 0.0645787i
\(35\) 5.03615 + 2.42849i 0.851265 + 0.410490i
\(36\) −1.80098 2.39926i −0.300164 0.399877i
\(37\) −5.50275 + 9.53104i −0.904646 + 1.56689i −0.0832543 + 0.996528i \(0.526531\pi\)
−0.821392 + 0.570365i \(0.806802\pi\)
\(38\) −6.15971 + 2.24195i −0.999236 + 0.363692i
\(39\) 6.20712 + 4.60197i 0.993935 + 0.736906i
\(40\) −1.61883 + 1.35836i −0.255960 + 0.214776i
\(41\) 1.28738 + 7.30109i 0.201055 + 1.14024i 0.903528 + 0.428528i \(0.140968\pi\)
−0.702474 + 0.711710i \(0.747921\pi\)
\(42\) 2.44852 3.87360i 0.377815 0.597709i
\(43\) −4.90452 4.11538i −0.747932 0.627589i 0.187023 0.982356i \(-0.440116\pi\)
−0.934955 + 0.354766i \(0.884560\pi\)
\(44\) 1.13705 1.96943i 0.171417 0.296902i
\(45\) 2.48798 5.83111i 0.370886 0.869251i
\(46\) −2.82477 4.89264i −0.416489 0.721381i
\(47\) −5.53120 4.64123i −0.806808 0.676993i 0.143035 0.989718i \(-0.454314\pi\)
−0.949844 + 0.312725i \(0.898758\pi\)
\(48\) 0.954638 + 1.44522i 0.137790 + 0.208600i
\(49\) 6.85977 + 1.39411i 0.979967 + 0.199159i
\(50\) 0.502011 + 0.182717i 0.0709950 + 0.0258401i
\(51\) 1.38447 1.31137i 0.193864 0.183628i
\(52\) −3.41747 2.86759i −0.473917 0.397664i
\(53\) 2.35202 4.07382i 0.323075 0.559582i −0.658046 0.752978i \(-0.728617\pi\)
0.981121 + 0.193396i \(0.0619501\pi\)
\(54\) −4.51534 2.57132i −0.614460 0.349913i
\(55\) 4.80571 0.648001
\(56\) −1.54555 + 2.14739i −0.206533 + 0.286957i
\(57\) −8.24290 + 7.80766i −1.09180 + 1.03415i
\(58\) −0.886000 5.02476i −0.116337 0.659783i
\(59\) 0.595915 + 3.37960i 0.0775816 + 0.439987i 0.998712 + 0.0507335i \(0.0161559\pi\)
−0.921131 + 0.389254i \(0.872733\pi\)
\(60\) −1.63624 + 3.27415i −0.211237 + 0.422691i
\(61\) −1.09424 0.918179i −0.140103 0.117561i 0.570043 0.821615i \(-0.306927\pi\)
−0.710146 + 0.704054i \(0.751371\pi\)
\(62\) −3.54216 + 6.13519i −0.449854 + 0.779171i
\(63\) 1.22120 7.84275i 0.153857 0.988093i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) 1.63708 9.28432i 0.203054 1.15158i
\(66\) 0.449533 3.91312i 0.0553336 0.481671i
\(67\) 6.70999 + 2.44224i 0.819755 + 0.298367i 0.717647 0.696407i \(-0.245219\pi\)
0.102108 + 0.994773i \(0.467441\pi\)
\(68\) −0.843395 + 0.707693i −0.102277 + 0.0858203i
\(69\) −7.86055 5.82783i −0.946299 0.701588i
\(70\) −5.56303 0.559568i −0.664909 0.0668811i
\(71\) −2.73928 4.74457i −0.325093 0.563077i 0.656438 0.754380i \(-0.272062\pi\)
−0.981531 + 0.191302i \(0.938729\pi\)
\(72\) 2.51297 + 1.63860i 0.296156 + 0.193111i
\(73\) −6.53126 11.3125i −0.764427 1.32403i −0.940549 0.339657i \(-0.889689\pi\)
0.176123 0.984368i \(-0.443644\pi\)
\(74\) 1.91108 10.8383i 0.222159 1.25993i
\(75\) 0.923637 0.0556294i 0.106652 0.00642352i
\(76\) 5.02144 4.21349i 0.575998 0.483320i
\(77\) 5.83141 1.48165i 0.664551 0.168850i
\(78\) −7.40675 2.20148i −0.838650 0.249269i
\(79\) −5.38398 + 1.95961i −0.605745 + 0.220473i −0.626641 0.779308i \(-0.715571\pi\)
0.0208953 + 0.999782i \(0.493348\pi\)
\(80\) 1.05662 1.83012i 0.118134 0.204613i
\(81\) −8.94713 0.974069i −0.994126 0.108230i
\(82\) −3.70686 6.42047i −0.409354 0.709022i
\(83\) −0.173835 + 0.985869i −0.0190809 + 0.108213i −0.992861 0.119279i \(-0.961942\pi\)
0.973780 + 0.227492i \(0.0730527\pi\)
\(84\) −0.976009 + 4.47743i −0.106491 + 0.488528i
\(85\) −2.18631 0.795751i −0.237138 0.0863113i
\(86\) 6.01628 + 2.18975i 0.648752 + 0.236127i
\(87\) −4.87082 7.37391i −0.522207 0.790566i
\(88\) −0.394893 + 2.23955i −0.0420957 + 0.238737i
\(89\) −8.11989 −0.860707 −0.430353 0.902661i \(-0.641611\pi\)
−0.430353 + 0.902661i \(0.641611\pi\)
\(90\) −0.343578 + 6.33039i −0.0362163 + 0.667282i
\(91\) −0.875973 11.7706i −0.0918269 1.23390i
\(92\) 4.32780 + 3.63145i 0.451204 + 0.378605i
\(93\) −1.40039 + 12.1902i −0.145214 + 1.26407i
\(94\) 6.78502 + 2.46955i 0.699821 + 0.254714i
\(95\) 13.0169 + 4.73777i 1.33551 + 0.486085i
\(96\) −1.39136 1.03156i −0.142005 0.105283i
\(97\) 0.607697 + 0.509919i 0.0617023 + 0.0517744i 0.673117 0.739536i \(-0.264955\pi\)
−0.611415 + 0.791310i \(0.709399\pi\)
\(98\) −6.92289 + 1.03614i −0.699317 + 0.104666i
\(99\) −1.98250 6.52789i −0.199249 0.656078i
\(100\) −0.534229 −0.0534229
\(101\) 1.91252 10.8464i 0.190302 1.07926i −0.728649 0.684887i \(-0.759851\pi\)
0.918951 0.394371i \(-0.129037\pi\)
\(102\) −0.852462 + 1.70580i −0.0844063 + 0.168899i
\(103\) 14.6920 + 5.34744i 1.44764 + 0.526899i 0.941932 0.335803i \(-0.109008\pi\)
0.505712 + 0.862703i \(0.331230\pi\)
\(104\) 4.19214 + 1.52582i 0.411073 + 0.149618i
\(105\) −9.22550 + 2.94473i −0.900316 + 0.287376i
\(106\) −0.816848 + 4.63258i −0.0793393 + 0.449956i
\(107\) 5.60715 + 9.71187i 0.542063 + 0.938881i 0.998785 + 0.0492719i \(0.0156901\pi\)
−0.456722 + 0.889610i \(0.650977\pi\)
\(108\) 5.12248 + 0.871917i 0.492910 + 0.0839003i
\(109\) 3.22127 5.57940i 0.308542 0.534410i −0.669502 0.742810i \(-0.733492\pi\)
0.978044 + 0.208400i \(0.0668257\pi\)
\(110\) −4.51589 + 1.64365i −0.430573 + 0.156716i
\(111\) −4.43270 18.5395i −0.420733 1.75969i
\(112\) 0.717892 2.54649i 0.0678344 0.240621i
\(113\) −9.57952 + 8.03817i −0.901165 + 0.756167i −0.970418 0.241432i \(-0.922383\pi\)
0.0692526 + 0.997599i \(0.477939\pi\)
\(114\) 5.07542 10.1560i 0.475357 0.951200i
\(115\) −2.07315 + 11.7574i −0.193323 + 1.09639i
\(116\) 2.55114 + 4.41870i 0.236867 + 0.410266i
\(117\) −13.2868 + 1.60632i −1.22837 + 0.148504i
\(118\) −1.71587 2.97197i −0.157959 0.273592i
\(119\) −2.89828 0.291529i −0.265685 0.0267244i
\(120\) 0.417735 3.63632i 0.0381338 0.331949i
\(121\) −4.46488 + 3.74648i −0.405898 + 0.340589i
\(122\) 1.34229 + 0.488553i 0.121525 + 0.0442315i
\(123\) −10.3152 7.64768i −0.930087 0.689568i
\(124\) 1.23018 6.97669i 0.110473 0.626525i
\(125\) −5.84757 10.1283i −0.523022 0.905901i
\(126\) 1.53482 + 7.78745i 0.136733 + 0.693761i
\(127\) −9.45707 + 16.3801i −0.839179 + 1.45350i 0.0514030 + 0.998678i \(0.483631\pi\)
−0.890582 + 0.454823i \(0.849703\pi\)
\(128\) 0.766044 + 0.642788i 0.0677094 + 0.0568149i
\(129\) 11.0692 0.666683i 0.974590 0.0586981i
\(130\) 1.63708 + 9.28432i 0.143581 + 0.814288i
\(131\) −2.47821 14.0546i −0.216522 1.22796i −0.878246 0.478209i \(-0.841286\pi\)
0.661724 0.749747i \(-0.269825\pi\)
\(132\) 0.915942 + 3.83088i 0.0797225 + 0.333435i
\(133\) 17.2559 + 1.73572i 1.49627 + 0.150506i
\(134\) −7.14062 −0.616856
\(135\) 3.81679 + 10.2960i 0.328497 + 0.886140i
\(136\) 0.550487 0.953472i 0.0472039 0.0817595i
\(137\) −14.1821 11.9002i −1.21166 1.01670i −0.999218 0.0395314i \(-0.987413\pi\)
−0.212443 0.977173i \(-0.568142\pi\)
\(138\) 9.37974 + 2.78790i 0.798456 + 0.237322i
\(139\) −0.894249 0.325480i −0.0758492 0.0276069i 0.303817 0.952730i \(-0.401739\pi\)
−0.379666 + 0.925124i \(0.623961\pi\)
\(140\) 5.41892 1.37685i 0.457982 0.116365i
\(141\) 12.4836 0.751869i 1.05131 0.0633188i
\(142\) 4.19682 + 3.52155i 0.352190 + 0.295522i
\(143\) −5.07258 8.78597i −0.424191 0.734720i
\(144\) −2.92185 0.680293i −0.243487 0.0566911i
\(145\) −5.39115 + 9.33775i −0.447711 + 0.775458i
\(146\) 10.0065 + 8.39643i 0.828142 + 0.694894i
\(147\) −10.2866 + 6.41755i −0.848428 + 0.529311i
\(148\) 1.91108 + 10.8383i 0.157090 + 0.890902i
\(149\) 13.6840 11.4822i 1.12103 0.940659i 0.122377 0.992484i \(-0.460948\pi\)
0.998656 + 0.0518251i \(0.0165038\pi\)
\(150\) −0.848909 + 0.368177i −0.0693131 + 0.0300615i
\(151\) −5.88949 + 2.14360i −0.479280 + 0.174444i −0.570351 0.821401i \(-0.693193\pi\)
0.0910717 + 0.995844i \(0.470971\pi\)
\(152\) −3.27751 + 5.67682i −0.265841 + 0.460451i
\(153\) −0.179000 + 3.29807i −0.0144713 + 0.266633i
\(154\) −4.97298 + 3.38676i −0.400734 + 0.272913i
\(155\) 14.0680 5.12033i 1.12997 0.411275i
\(156\) 7.71302 0.464544i 0.617536 0.0371933i
\(157\) 1.19882 + 6.79885i 0.0956764 + 0.542608i 0.994538 + 0.104375i \(0.0332842\pi\)
−0.898862 + 0.438233i \(0.855605\pi\)
\(158\) 4.38906 3.68286i 0.349175 0.292993i
\(159\) 1.89466 + 7.92429i 0.150256 + 0.628437i
\(160\) −0.366960 + 2.08113i −0.0290107 + 0.164528i
\(161\) 1.10931 + 14.9061i 0.0874260 + 1.17476i
\(162\) 8.74071 2.14477i 0.686735 0.168509i
\(163\) 7.72077 + 13.3728i 0.604737 + 1.04744i 0.992093 + 0.125505i \(0.0400551\pi\)
−0.387356 + 0.921930i \(0.626612\pi\)
\(164\) 5.67924 + 4.76545i 0.443474 + 0.372119i
\(165\) −6.04315 + 5.72406i −0.470459 + 0.445617i
\(166\) −0.173835 0.985869i −0.0134922 0.0765183i
\(167\) −0.125142 + 0.105007i −0.00968378 + 0.00812566i −0.647617 0.761966i \(-0.724234\pi\)
0.637933 + 0.770092i \(0.279790\pi\)
\(168\) −0.614223 4.54123i −0.0473884 0.350363i
\(169\) −6.48592 + 2.36068i −0.498917 + 0.181591i
\(170\) 2.32662 0.178444
\(171\) 1.06574 19.6362i 0.0814992 1.50162i
\(172\) −6.40239 −0.488178
\(173\) 2.78951 15.8201i 0.212083 1.20278i −0.673815 0.738900i \(-0.735346\pi\)
0.885898 0.463880i \(-0.153543\pi\)
\(174\) 7.09910 + 5.26329i 0.538182 + 0.399009i
\(175\) −0.986390 1.01234i −0.0745641 0.0765258i
\(176\) −0.394893 2.23955i −0.0297662 0.168812i
\(177\) −4.77479 3.54004i −0.358895 0.266086i
\(178\) 7.63020 2.77717i 0.571908 0.208157i
\(179\) 5.25131 0.392502 0.196251 0.980554i \(-0.437123\pi\)
0.196251 + 0.980554i \(0.437123\pi\)
\(180\) −1.84226 6.06614i −0.137314 0.452143i
\(181\) 8.10196 14.0330i 0.602214 1.04307i −0.390271 0.920700i \(-0.627619\pi\)
0.992485 0.122365i \(-0.0390480\pi\)
\(182\) 4.84894 + 10.7612i 0.359427 + 0.797672i
\(183\) 2.46964 0.148743i 0.182561 0.0109954i
\(184\) −5.30883 1.93226i −0.391372 0.142448i
\(185\) −17.8161 + 14.9495i −1.30986 + 1.09911i
\(186\) −2.85336 11.9340i −0.209219 0.875045i
\(187\) −2.35273 + 0.856324i −0.172049 + 0.0626206i
\(188\) −7.22047 −0.526607
\(189\) 7.80580 + 11.3168i 0.567788 + 0.823174i
\(190\) −13.8523 −1.00495
\(191\) −4.42665 + 1.61117i −0.320301 + 0.116580i −0.497167 0.867655i \(-0.665626\pi\)
0.176866 + 0.984235i \(0.443404\pi\)
\(192\) 1.66027 + 0.493474i 0.119819 + 0.0356134i
\(193\) 5.17801 4.34486i 0.372721 0.312750i −0.437116 0.899405i \(-0.644000\pi\)
0.809837 + 0.586655i \(0.199556\pi\)
\(194\) −0.745451 0.271322i −0.0535203 0.0194798i
\(195\) 8.99989 + 13.6249i 0.644496 + 0.975699i
\(196\) 6.15101 3.34142i 0.439358 0.238673i
\(197\) 5.01390 8.68433i 0.357226 0.618733i −0.630271 0.776376i \(-0.717056\pi\)
0.987496 + 0.157643i \(0.0503894\pi\)
\(198\) 4.09561 + 5.45616i 0.291062 + 0.387752i
\(199\) −4.14019 −0.293491 −0.146745 0.989174i \(-0.546880\pi\)
−0.146745 + 0.989174i \(0.546880\pi\)
\(200\) 0.502011 0.182717i 0.0354975 0.0129200i
\(201\) −11.3467 + 4.92114i −0.800335 + 0.347110i
\(202\) 1.91252 + 10.8464i 0.134564 + 0.763151i
\(203\) −3.66288 + 12.9929i −0.257084 + 0.911923i
\(204\) 0.217635 1.89448i 0.0152375 0.132640i
\(205\) −2.72054 + 15.4289i −0.190011 + 1.07760i
\(206\) −15.6349 −1.08933
\(207\) 16.8261 2.03420i 1.16949 0.141387i
\(208\) −4.46119 −0.309328
\(209\) 14.0078 5.09841i 0.968938 0.352665i
\(210\) 7.66197 5.92244i 0.528726 0.408687i
\(211\) 6.04115 5.06913i 0.415890 0.348973i −0.410707 0.911767i \(-0.634718\pi\)
0.826597 + 0.562794i \(0.190274\pi\)
\(212\) −0.816848 4.63258i −0.0561014 0.318167i
\(213\) 9.09587 + 2.70353i 0.623239 + 0.185243i
\(214\) −8.59065 7.20841i −0.587245 0.492757i
\(215\) −6.76489 11.7171i −0.461361 0.799102i
\(216\) −5.11177 + 0.932656i −0.347812 + 0.0634592i
\(217\) 15.4919 10.5505i 1.05166 0.716214i
\(218\) −1.11874 + 6.34466i −0.0757703 + 0.429715i
\(219\) 21.6873 + 6.44602i 1.46549 + 0.435582i
\(220\) 3.68139 3.08905i 0.248199 0.208264i
\(221\) 0.852899 + 4.83703i 0.0573722 + 0.325374i
\(222\) 10.5063 + 15.9054i 0.705134 + 1.06750i
\(223\) −26.9328 + 9.80273i −1.80355 + 0.656440i −0.805602 + 0.592457i \(0.798158\pi\)
−0.997951 + 0.0639823i \(0.979620\pi\)
\(224\) 0.196354 + 2.63846i 0.0131195 + 0.176289i
\(225\) −1.09521 + 1.17009i −0.0730139 + 0.0780063i
\(226\) 6.25259 10.8298i 0.415916 0.720387i
\(227\) −14.8777 + 5.41502i −0.987465 + 0.359408i −0.784738 0.619828i \(-0.787203\pi\)
−0.202727 + 0.979235i \(0.564980\pi\)
\(228\) −1.29576 + 11.2794i −0.0858141 + 0.747000i
\(229\) −8.90461 + 7.47186i −0.588433 + 0.493754i −0.887704 0.460414i \(-0.847701\pi\)
0.299271 + 0.954168i \(0.403257\pi\)
\(230\) −2.07315 11.7574i −0.136700 0.775262i
\(231\) −5.56818 + 8.80893i −0.366359 + 0.579585i
\(232\) −3.90857 3.27968i −0.256610 0.215321i
\(233\) −0.855748 + 1.48220i −0.0560619 + 0.0971021i −0.892694 0.450663i \(-0.851188\pi\)
0.836632 + 0.547765i \(0.184521\pi\)
\(234\) 11.9361 6.05380i 0.780289 0.395749i
\(235\) −7.62928 13.2143i −0.497679 0.862006i
\(236\) 2.62887 + 2.20588i 0.171125 + 0.143591i
\(237\) 4.43625 8.87703i 0.288165 0.576625i
\(238\) 2.82320 0.717322i 0.183001 0.0464971i
\(239\) 1.80505 + 0.656984i 0.116759 + 0.0424968i 0.399739 0.916629i \(-0.369101\pi\)
−0.282980 + 0.959126i \(0.591323\pi\)
\(240\) 0.851152 + 3.55990i 0.0549416 + 0.229790i
\(241\) 11.7853 + 9.88901i 0.759155 + 0.637007i 0.937907 0.346887i \(-0.112761\pi\)
−0.178751 + 0.983894i \(0.557206\pi\)
\(242\) 2.91424 5.04761i 0.187334 0.324473i
\(243\) 12.4112 9.43200i 0.796177 0.605063i
\(244\) −1.42843 −0.0914460
\(245\) 12.6145 + 7.72645i 0.805909 + 0.493625i
\(246\) 12.3087 + 3.65848i 0.784777 + 0.233256i
\(247\) −5.07802 28.7989i −0.323107 1.83243i
\(248\) 1.23018 + 6.97669i 0.0781164 + 0.443020i
\(249\) −0.955667 1.44678i −0.0605629 0.0916859i
\(250\) 8.95900 + 7.51749i 0.566617 + 0.475448i
\(251\) 8.80203 15.2456i 0.555579 0.962292i −0.442279 0.896878i \(-0.645830\pi\)
0.997858 0.0654140i \(-0.0208368\pi\)
\(252\) −4.10572 6.79287i −0.258636 0.427910i
\(253\) 6.42380 + 11.1263i 0.403861 + 0.699507i
\(254\) 3.28440 18.6268i 0.206082 1.16875i
\(255\) 3.69708 1.60345i 0.231520 0.100412i
\(256\) −0.939693 0.342020i −0.0587308 0.0213763i
\(257\) −3.50764 + 2.94326i −0.218801 + 0.183596i −0.745599 0.666395i \(-0.767837\pi\)
0.526799 + 0.849990i \(0.323392\pi\)
\(258\) −10.1736 + 4.41237i −0.633383 + 0.274702i
\(259\) −17.0095 + 23.6331i −1.05692 + 1.46849i
\(260\) −4.71377 8.16449i −0.292336 0.506340i
\(261\) 14.9081 + 3.47104i 0.922786 + 0.214852i
\(262\) 7.13571 + 12.3594i 0.440846 + 0.763567i
\(263\) −3.70247 + 20.9977i −0.228304 + 1.29478i 0.627964 + 0.778243i \(0.283889\pi\)
−0.856267 + 0.516533i \(0.827222\pi\)
\(264\) −2.17094 3.28657i −0.133612 0.202275i
\(265\) 7.61506 6.38980i 0.467790 0.392522i
\(266\) −16.8089 + 4.27082i −1.03062 + 0.261861i
\(267\) 10.2107 9.67156i 0.624886 0.591890i
\(268\) 6.70999 2.44224i 0.409878 0.149183i
\(269\) −11.0845 + 19.1990i −0.675836 + 1.17058i 0.300387 + 0.953817i \(0.402884\pi\)
−0.976224 + 0.216766i \(0.930449\pi\)
\(270\) −7.10806 8.36967i −0.432583 0.509362i
\(271\) −10.0283 17.3695i −0.609175 1.05512i −0.991377 0.131044i \(-0.958167\pi\)
0.382201 0.924079i \(-0.375166\pi\)
\(272\) −0.191182 + 1.08425i −0.0115921 + 0.0657422i
\(273\) 15.1215 + 13.7581i 0.915194 + 0.832681i
\(274\) 17.3970 + 6.33198i 1.05099 + 0.382529i
\(275\) −1.14162 0.415516i −0.0688423 0.0250566i
\(276\) −9.76759 + 0.588288i −0.587940 + 0.0354108i
\(277\) −1.02156 + 5.79353i −0.0613794 + 0.348100i 0.938616 + 0.344965i \(0.112109\pi\)
−0.999995 + 0.00313519i \(0.999002\pi\)
\(278\) 0.951640 0.0570756
\(279\) −12.7587 16.9971i −0.763845 1.01759i
\(280\) −4.62121 + 3.14719i −0.276170 + 0.188081i
\(281\) −23.2653 19.5219i −1.38789 1.16458i −0.966186 0.257847i \(-0.916987\pi\)
−0.421706 0.906733i \(-0.638569\pi\)
\(282\) −11.4736 + 4.97617i −0.683242 + 0.296326i
\(283\) −0.146520 0.0533290i −0.00870972 0.00317008i 0.337662 0.941268i \(-0.390364\pi\)
−0.346371 + 0.938097i \(0.612586\pi\)
\(284\) −5.14816 1.87378i −0.305487 0.111188i
\(285\) −22.0118 + 9.54667i −1.30387 + 0.565496i
\(286\) 7.77165 + 6.52119i 0.459547 + 0.385606i
\(287\) 1.45572 + 19.5608i 0.0859282 + 1.15464i
\(288\) 2.97831 0.360065i 0.175499 0.0212170i
\(289\) −15.7879 −0.928697
\(290\) 1.87233 10.6185i 0.109947 0.623540i
\(291\) −1.37154 + 0.0826058i −0.0804010 + 0.00484244i
\(292\) −12.2748 4.46765i −0.718326 0.261449i
\(293\) 5.17996 + 1.88535i 0.302617 + 0.110143i 0.488866 0.872359i \(-0.337411\pi\)
−0.186249 + 0.982503i \(0.559633\pi\)
\(294\) 7.47135 9.54877i 0.435738 0.556895i
\(295\) −1.25931 + 7.14191i −0.0733199 + 0.415818i
\(296\) −5.50275 9.53104i −0.319841 0.553980i
\(297\) 10.2683 + 5.84744i 0.595828 + 0.339303i
\(298\) −8.93157 + 15.4699i −0.517392 + 0.896149i
\(299\) 23.6837 8.62015i 1.36966 0.498516i
\(300\) 0.671789 0.636317i 0.0387858 0.0367378i
\(301\) −11.8213 12.1323i −0.681366 0.699293i
\(302\) 4.80116 4.02865i 0.276275 0.231823i
\(303\) 10.5141 + 15.9173i 0.604021 + 0.914424i
\(304\) 1.13827 6.45544i 0.0652841 0.370245i
\(305\) −1.50931 2.61420i −0.0864227 0.149689i
\(306\) −0.959801 3.16039i −0.0548681 0.180668i
\(307\) −6.56559 11.3719i −0.374718 0.649031i 0.615567 0.788085i \(-0.288927\pi\)
−0.990285 + 0.139054i \(0.955594\pi\)
\(308\) 3.51473 4.88337i 0.200270 0.278256i
\(309\) −24.8444 + 10.7752i −1.41335 + 0.612978i
\(310\) −11.4683 + 9.62307i −0.651357 + 0.546553i
\(311\) 6.56014 + 2.38770i 0.371992 + 0.135394i 0.521249 0.853404i \(-0.325466\pi\)
−0.149258 + 0.988798i \(0.547688\pi\)
\(312\) −7.08899 + 3.07454i −0.401335 + 0.174061i
\(313\) 1.71402 9.72070i 0.0968822 0.549446i −0.897272 0.441478i \(-0.854454\pi\)
0.994154 0.107968i \(-0.0344346\pi\)
\(314\) −3.45187 5.97881i −0.194800 0.337404i
\(315\) 8.09356 14.6914i 0.456020 0.827768i
\(316\) −2.86476 + 4.96190i −0.161155 + 0.279129i
\(317\) −18.5409 15.5576i −1.04136 0.873803i −0.0491995 0.998789i \(-0.515667\pi\)
−0.992159 + 0.124986i \(0.960111\pi\)
\(318\) −4.49066 6.79838i −0.251824 0.381234i
\(319\) 2.01485 + 11.4268i 0.112810 + 0.639777i
\(320\) −0.366960 2.08113i −0.0205137 0.116339i
\(321\) −18.6187 5.53397i −1.03920 0.308876i
\(322\) −6.14058 13.6277i −0.342201 0.759442i
\(323\) −7.21691 −0.401560
\(324\) −7.48002 + 5.00493i −0.415557 + 0.278051i
\(325\) −1.19165 + 2.06399i −0.0661006 + 0.114490i
\(326\) −11.8289 9.92563i −0.655142 0.549730i
\(327\) 2.59487 + 10.8529i 0.143497 + 0.600167i
\(328\) −6.96662 2.53564i −0.384667 0.140007i
\(329\) −13.3317 13.6825i −0.735003 0.754340i
\(330\) 3.72096 7.44573i 0.204832 0.409874i
\(331\) −19.4046 16.2824i −1.06658 0.894963i −0.0718373 0.997416i \(-0.522886\pi\)
−0.994738 + 0.102454i \(0.967331\pi\)
\(332\) 0.500539 + 0.866958i 0.0274706 + 0.0475805i
\(333\) 27.6564 + 18.0336i 1.51556 + 0.988234i
\(334\) 0.0816807 0.141475i 0.00446937 0.00774117i
\(335\) 11.5595 + 9.69955i 0.631562 + 0.529943i
\(336\) 2.13037 + 4.05728i 0.116221 + 0.221343i
\(337\) 3.37701 + 19.1520i 0.183958 + 1.04328i 0.927287 + 0.374350i \(0.122134\pi\)
−0.743330 + 0.668925i \(0.766755\pi\)
\(338\) 5.28737 4.43663i 0.287595 0.241321i
\(339\) 2.47196 21.5181i 0.134259 1.16870i
\(340\) −2.18631 + 0.795751i −0.118569 + 0.0431556i
\(341\) 8.05521 13.9520i 0.436214 0.755545i
\(342\) 5.71450 + 18.8165i 0.309005 + 1.01748i
\(343\) 17.6890 + 5.48636i 0.955115 + 0.296236i
\(344\) 6.01628 2.18975i 0.324376 0.118063i
\(345\) −11.3972 17.2542i −0.613607 0.928937i
\(346\) 2.78951 + 15.8201i 0.149965 + 0.850494i
\(347\) 13.0223 10.9270i 0.699073 0.586592i −0.222437 0.974947i \(-0.571401\pi\)
0.921510 + 0.388355i \(0.126957\pi\)
\(348\) −8.47113 2.51784i −0.454100 0.134970i
\(349\) −3.12520 + 17.7239i −0.167288 + 0.948737i 0.779386 + 0.626544i \(0.215531\pi\)
−0.946674 + 0.322193i \(0.895580\pi\)
\(350\) 1.27314 + 0.613925i 0.0680525 + 0.0328157i
\(351\) 14.7948 17.8458i 0.789688 0.952538i
\(352\) 1.13705 + 1.96943i 0.0606049 + 0.104971i
\(353\) −25.6495 21.5225i −1.36518 1.14552i −0.974344 0.225066i \(-0.927740\pi\)
−0.390840 0.920459i \(-0.627815\pi\)
\(354\) 5.69760 + 1.69348i 0.302824 + 0.0900072i
\(355\) −2.01041 11.4016i −0.106702 0.605135i
\(356\) −6.22020 + 5.21936i −0.329670 + 0.276626i
\(357\) 3.99181 3.08553i 0.211269 0.163304i
\(358\) −4.93462 + 1.79606i −0.260803 + 0.0949245i
\(359\) −19.2161 −1.01418 −0.507092 0.861892i \(-0.669280\pi\)
−0.507092 + 0.861892i \(0.669280\pi\)
\(360\) 3.80590 + 5.07021i 0.200589 + 0.267224i
\(361\) 23.9683 1.26149
\(362\) −2.81378 + 15.9577i −0.147889 + 0.838721i
\(363\) 1.15215 10.0293i 0.0604720 0.526400i
\(364\) −8.23705 8.45377i −0.431739 0.443098i
\(365\) −4.79342 27.1848i −0.250899 1.42292i
\(366\) −2.26983 + 0.984440i −0.118646 + 0.0514575i
\(367\) 17.4733 6.35975i 0.912097 0.331976i 0.157007 0.987597i \(-0.449815\pi\)
0.755090 + 0.655621i \(0.227593\pi\)
\(368\) 5.64954 0.294503
\(369\) 22.0804 2.66942i 1.14946 0.138965i
\(370\) 11.6286 20.1413i 0.604543 1.04710i
\(371\) 7.27033 10.1014i 0.377457 0.524439i
\(372\) 6.76296 + 10.2384i 0.350643 + 0.530836i
\(373\) −22.2873 8.11191i −1.15399 0.420019i −0.307045 0.951695i \(-0.599340\pi\)
−0.846948 + 0.531676i \(0.821562\pi\)
\(374\) 1.91796 1.60936i 0.0991755 0.0832181i
\(375\) 19.4170 + 5.77125i 1.00269 + 0.298026i
\(376\) 6.78502 2.46955i 0.349911 0.127357i
\(377\) 22.7622 1.17231
\(378\) −11.2056 7.96455i −0.576355 0.409652i
\(379\) −2.81922 −0.144814 −0.0724069 0.997375i \(-0.523068\pi\)
−0.0724069 + 0.997375i \(0.523068\pi\)
\(380\) 13.0169 4.73777i 0.667754 0.243043i
\(381\) −7.61808 31.8622i −0.390286 1.63235i
\(382\) 3.60864 3.02801i 0.184634 0.154926i
\(383\) −5.85628 2.13151i −0.299242 0.108915i 0.188036 0.982162i \(-0.439788\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(384\) −1.72892 + 0.104130i −0.0882285 + 0.00531387i
\(385\) 12.6509 + 1.27251i 0.644748 + 0.0648532i
\(386\) −3.37970 + 5.85382i −0.172022 + 0.297951i
\(387\) −13.1254 + 14.0228i −0.667201 + 0.712821i
\(388\) 0.793293 0.0402733
\(389\) −22.4562 + 8.17339i −1.13858 + 0.414407i −0.841399 0.540415i \(-0.818267\pi\)
−0.297177 + 0.954823i \(0.596045\pi\)
\(390\) −13.1171 9.72506i −0.664211 0.492448i
\(391\) −1.08009 6.12550i −0.0546225 0.309780i
\(392\) −4.63722 + 5.24368i −0.234215 + 0.264846i
\(393\) 19.8567 + 14.7218i 1.00164 + 0.742617i
\(394\) −1.74131 + 9.87546i −0.0877259 + 0.497518i
\(395\) −12.1078 −0.609211
\(396\) −5.71473 3.72633i −0.287176 0.187255i
\(397\) 8.63907 0.433583 0.216791 0.976218i \(-0.430441\pi\)
0.216791 + 0.976218i \(0.430441\pi\)
\(398\) 3.89051 1.41603i 0.195014 0.0709792i
\(399\) −23.7666 + 18.3707i −1.18982 + 0.919688i
\(400\) −0.409243 + 0.343396i −0.0204621 + 0.0171698i
\(401\) 0.979422 + 5.55458i 0.0489100 + 0.277382i 0.999448 0.0332264i \(-0.0105782\pi\)
−0.950538 + 0.310609i \(0.899467\pi\)
\(402\) 8.97929 8.50516i 0.447846 0.424199i
\(403\) −24.2104 20.3149i −1.20601 1.01196i
\(404\) −5.50687 9.53817i −0.273977 0.474542i
\(405\) −17.0631 8.40102i −0.847874 0.417450i
\(406\) −1.00185 13.4621i −0.0497211 0.668113i
\(407\) −4.34599 + 24.6473i −0.215423 + 1.22172i
\(408\) 0.443441 + 1.85467i 0.0219536 + 0.0918197i
\(409\) 8.57056 7.19155i 0.423787 0.355599i −0.405815 0.913955i \(-0.633012\pi\)
0.829601 + 0.558356i \(0.188568\pi\)
\(410\) −2.72054 15.4289i −0.134358 0.761980i
\(411\) 32.0083 1.92781i 1.57885 0.0950919i
\(412\) 14.6920 5.34744i 0.723822 0.263450i
\(413\) 0.673837 + 9.05449i 0.0331573 + 0.445542i
\(414\) −15.1156 + 7.66639i −0.742892 + 0.376782i
\(415\) −1.05776 + 1.83209i −0.0519232 + 0.0899337i
\(416\) 4.19214 1.52582i 0.205537 0.0748092i
\(417\) 1.51219 0.655847i 0.0740523 0.0321169i
\(418\) −11.4192 + 9.58188i −0.558533 + 0.468665i
\(419\) 6.33507 + 35.9280i 0.309488 + 1.75520i 0.601587 + 0.798808i \(0.294535\pi\)
−0.292098 + 0.956388i \(0.594353\pi\)
\(420\) −5.17431 + 8.18583i −0.252480 + 0.399427i
\(421\) 7.37289 + 6.18659i 0.359333 + 0.301516i 0.804525 0.593919i \(-0.202420\pi\)
−0.445192 + 0.895435i \(0.646865\pi\)
\(422\) −3.94308 + 6.82962i −0.191946 + 0.332461i
\(423\) −14.8025 + 15.8146i −0.719722 + 0.768933i
\(424\) 2.35202 + 4.07382i 0.114224 + 0.197842i
\(425\) 0.450566 + 0.378070i 0.0218557 + 0.0183391i
\(426\) −9.47198 + 0.570484i −0.458919 + 0.0276400i
\(427\) −2.63743 2.70682i −0.127634 0.130992i
\(428\) 10.5380 + 3.83552i 0.509373 + 0.185397i
\(429\) 16.8437 + 5.00638i 0.813221 + 0.241710i
\(430\) 10.3644 + 8.69677i 0.499816 + 0.419396i
\(431\) −10.4177 + 18.0440i −0.501802 + 0.869147i 0.498195 + 0.867065i \(0.333996\pi\)
−0.999998 + 0.00208252i \(0.999337\pi\)
\(432\) 4.48450 2.62474i 0.215761 0.126283i
\(433\) −5.88744 −0.282932 −0.141466 0.989943i \(-0.545182\pi\)
−0.141466 + 0.989943i \(0.545182\pi\)
\(434\) −10.9492 + 15.2128i −0.525577 + 0.730236i
\(435\) −4.34281 18.1635i −0.208222 0.870875i
\(436\) −1.11874 6.34466i −0.0535777 0.303854i
\(437\) 6.43069 + 36.4702i 0.307621 + 1.74461i
\(438\) −22.5840 + 1.36020i −1.07911 + 0.0649931i
\(439\) 8.38562 + 7.03637i 0.400224 + 0.335828i 0.820580 0.571531i \(-0.193650\pi\)
−0.420356 + 0.907359i \(0.638095\pi\)
\(440\) −2.40285 + 4.16186i −0.114552 + 0.198409i
\(441\) 5.29147 20.3224i 0.251975 0.967734i
\(442\) −2.45583 4.25361i −0.116812 0.202324i
\(443\) 1.65875 9.40723i 0.0788095 0.446951i −0.919712 0.392594i \(-0.871578\pi\)
0.998522 0.0543573i \(-0.0173110\pi\)
\(444\) −15.3126 11.3528i −0.726705 0.538781i
\(445\) −16.1244 5.86881i −0.764371 0.278208i
\(446\) 21.9558 18.4231i 1.03964 0.872360i
\(447\) −3.53110 + 30.7377i −0.167015 + 1.45384i
\(448\) −1.08692 2.41218i −0.0513520 0.113965i
\(449\) 11.1673 + 19.3423i 0.527016 + 0.912818i 0.999504 + 0.0314814i \(0.0100225\pi\)
−0.472488 + 0.881337i \(0.656644\pi\)
\(450\) 0.628964 1.47411i 0.0296496 0.0694903i
\(451\) 8.42976 + 14.6008i 0.396942 + 0.687523i
\(452\) −2.17150 + 12.3152i −0.102139 + 0.579258i
\(453\) 4.85277 9.71051i 0.228003 0.456239i
\(454\) 12.1284 10.1769i 0.569213 0.477626i
\(455\) 6.76796 24.0072i 0.317287 1.12547i
\(456\) −2.64018 11.0424i −0.123638 0.517107i
\(457\) 22.6895 8.25832i 1.06137 0.386308i 0.248429 0.968650i \(-0.420086\pi\)
0.812944 + 0.582342i \(0.197864\pi\)
\(458\) 5.81207 10.0668i 0.271580 0.470391i
\(459\) −3.70322 4.36051i −0.172852 0.203531i
\(460\) 5.96941 + 10.3393i 0.278325 + 0.482073i
\(461\) −2.93414 + 16.6404i −0.136657 + 0.775019i 0.837035 + 0.547149i \(0.184287\pi\)
−0.973692 + 0.227869i \(0.926824\pi\)
\(462\) 2.21954 10.1821i 0.103262 0.473715i
\(463\) −19.7896 7.20282i −0.919701 0.334744i −0.161581 0.986859i \(-0.551659\pi\)
−0.758119 + 0.652116i \(0.773882\pi\)
\(464\) 4.79457 + 1.74508i 0.222582 + 0.0810133i
\(465\) −11.5916 + 23.1951i −0.537548 + 1.07565i
\(466\) 0.297198 1.68550i 0.0137674 0.0780791i
\(467\) 26.1988 1.21233 0.606167 0.795337i \(-0.292706\pi\)
0.606167 + 0.795337i \(0.292706\pi\)
\(468\) −9.14577 + 9.77111i −0.422763 + 0.451670i
\(469\) 17.0171 + 8.20586i 0.785779 + 0.378911i
\(470\) 11.6887 + 9.80801i 0.539161 + 0.452410i
\(471\) −9.60559 7.12161i −0.442602 0.328146i
\(472\) −3.22478 1.17372i −0.148433 0.0540250i
\(473\) −13.6816 4.97970i −0.629081 0.228967i
\(474\) −1.13258 + 9.85897i −0.0520212 + 0.452837i
\(475\) −2.68260 2.25097i −0.123086 0.103281i
\(476\) −2.40760 + 1.63965i −0.110352 + 0.0751534i
\(477\) −11.8211 7.70803i −0.541251 0.352927i
\(478\) −1.92089 −0.0878596
\(479\) −4.52515 + 25.6634i −0.206760 + 1.17259i 0.687887 + 0.725818i \(0.258538\pi\)
−0.894647 + 0.446774i \(0.852573\pi\)
\(480\) −2.01738 3.05410i −0.0920803 0.139400i
\(481\) 46.1366 + 16.7923i 2.10365 + 0.765665i
\(482\) −14.4568 5.26183i −0.658487 0.239670i
\(483\) −19.1495 17.4230i −0.871332 0.792773i
\(484\) −1.01211 + 5.73993i −0.0460048 + 0.260906i
\(485\) 0.838208 + 1.45182i 0.0380611 + 0.0659237i
\(486\) −8.43676 + 13.1081i −0.382699 + 0.594594i
\(487\) 5.52175 9.56395i 0.250214 0.433384i −0.713370 0.700787i \(-0.752832\pi\)
0.963585 + 0.267403i \(0.0861655\pi\)
\(488\) 1.34229 0.488553i 0.0607625 0.0221157i
\(489\) −25.6371 7.62000i −1.15935 0.344588i
\(490\) −14.4963 2.94609i −0.654877 0.133091i
\(491\) 5.21300 4.37422i 0.235259 0.197406i −0.517535 0.855662i \(-0.673150\pi\)
0.752794 + 0.658256i \(0.228706\pi\)
\(492\) −12.8177 + 0.771992i −0.577867 + 0.0348041i
\(493\) 0.975463 5.53213i 0.0439326 0.249154i
\(494\) 14.6216 + 25.3253i 0.657856 + 1.13944i
\(495\) 0.781330 14.3959i 0.0351182 0.647049i
\(496\) −3.54216 6.13519i −0.159048 0.275478i
\(497\) −5.95475 13.2153i −0.267107 0.592786i
\(498\) 1.39286 + 1.03267i 0.0624156 + 0.0462750i
\(499\) −26.5263 + 22.2582i −1.18748 + 0.996413i −0.187579 + 0.982250i \(0.560064\pi\)
−0.999900 + 0.0141634i \(0.995492\pi\)
\(500\) −10.9898 3.99997i −0.491480 0.178884i
\(501\) 0.0322925 0.281101i 0.00144272 0.0125587i
\(502\) −3.05691 + 17.3366i −0.136437 + 0.773771i
\(503\) 17.7568 + 30.7556i 0.791735 + 1.37133i 0.924892 + 0.380231i \(0.124155\pi\)
−0.133157 + 0.991095i \(0.542511\pi\)
\(504\) 6.18142 + 4.97897i 0.275342 + 0.221781i
\(505\) 11.6373 20.1564i 0.517854 0.896949i
\(506\) −9.84183 8.25828i −0.437523 0.367125i
\(507\) 5.34421 10.6939i 0.237345 0.474933i
\(508\) 3.28440 + 18.6268i 0.145722 + 0.826430i
\(509\) 5.03795 + 28.5716i 0.223303 + 1.26641i 0.865903 + 0.500212i \(0.166745\pi\)
−0.642600 + 0.766202i \(0.722144\pi\)
\(510\) −2.92571 + 2.77123i −0.129553 + 0.122712i
\(511\) −14.1979 31.5092i −0.628078 1.39388i
\(512\) 1.00000 0.0441942
\(513\) 22.0484 + 25.9618i 0.973460 + 1.14624i
\(514\) 2.28945 3.96545i 0.100983 0.174908i
\(515\) 25.3103 + 21.2378i 1.11530 + 0.935851i
\(516\) 8.05097 7.62586i 0.354424 0.335710i
\(517\) −15.4298 5.61599i −0.678602 0.246991i
\(518\) 7.90076 28.0254i 0.347139 1.23137i
\(519\) 15.3355 + 23.2163i 0.673152 + 1.01908i
\(520\) 7.22192 + 6.05991i 0.316702 + 0.265745i
\(521\) −17.9808 31.1437i −0.787754 1.36443i −0.927340 0.374221i \(-0.877910\pi\)
0.139585 0.990210i \(-0.455423\pi\)
\(522\) −15.1962 + 1.83715i −0.665118 + 0.0804099i
\(523\) 1.08651 1.88190i 0.0475100 0.0822897i −0.841292 0.540580i \(-0.818205\pi\)
0.888802 + 0.458291i \(0.151538\pi\)
\(524\) −10.9325 9.17349i −0.477590 0.400746i
\(525\) 2.44618 + 0.0981290i 0.106760 + 0.00428270i
\(526\) −3.70247 20.9977i −0.161435 0.915544i
\(527\) −5.97488 + 5.01352i −0.260270 + 0.218392i
\(528\) 3.16409 + 2.34586i 0.137699 + 0.102091i
\(529\) −8.37950 + 3.04989i −0.364326 + 0.132604i
\(530\) −4.97038 + 8.60895i −0.215899 + 0.373949i
\(531\) 10.2208 1.23565i 0.443545 0.0536227i
\(532\) 14.3345 9.76223i 0.621478 0.423246i
\(533\) 31.0794 11.3120i 1.34620 0.489976i
\(534\) −6.28706 + 12.5806i −0.272068 + 0.544414i
\(535\) 4.11520 + 23.3384i 0.177915 + 1.00901i
\(536\) −5.47003 + 4.58990i −0.236269 + 0.198254i
\(537\) −6.60350 + 6.25482i −0.284962 + 0.269915i
\(538\) 3.84962 21.8323i 0.165969 0.941256i
\(539\) 15.7433 2.35629i 0.678113 0.101493i
\(540\) 9.54198 + 5.43382i 0.410622 + 0.233834i
\(541\) 9.39992 + 16.2811i 0.404134 + 0.699981i 0.994220 0.107359i \(-0.0342395\pi\)
−0.590086 + 0.807340i \(0.700906\pi\)
\(542\) 15.3642 + 12.8921i 0.659950 + 0.553764i
\(543\) 6.52648 + 27.2966i 0.280078 + 1.17141i
\(544\) −0.191182 1.08425i −0.00819687 0.0464867i
\(545\) 10.4294 8.75130i 0.446746 0.374865i
\(546\) −18.9151 7.75657i −0.809492 0.331951i
\(547\) 8.86581 3.22689i 0.379075 0.137972i −0.145453 0.989365i \(-0.546464\pi\)
0.524528 + 0.851393i \(0.324242\pi\)
\(548\) −18.5135 −0.790856
\(549\) −2.92839 + 3.12862i −0.124981 + 0.133526i
\(550\) 1.21489 0.0518030
\(551\) −5.80775 + 32.9374i −0.247418 + 1.40318i
\(552\) 8.97732 3.89352i 0.382100 0.165719i
\(553\) −14.6920 + 3.73297i −0.624769 + 0.158742i
\(554\) −1.02156 5.79353i −0.0434018 0.246144i
\(555\) 4.59737 40.0195i 0.195148 1.69873i
\(556\) −0.894249 + 0.325480i −0.0379246 + 0.0138034i
\(557\) 45.4188 1.92446 0.962229 0.272241i \(-0.0877648\pi\)
0.962229 + 0.272241i \(0.0877648\pi\)
\(558\) 17.8026 + 11.6083i 0.753646 + 0.491420i
\(559\) −14.2811 + 24.7356i −0.604027 + 1.04621i
\(560\) 3.26611 4.53794i 0.138019 0.191763i
\(561\) 1.93858 3.87915i 0.0818470 0.163778i
\(562\) 28.5391 + 10.3874i 1.20385 + 0.438166i
\(563\) 15.3230 12.8576i 0.645789 0.541881i −0.260001 0.965608i \(-0.583723\pi\)
0.905790 + 0.423727i \(0.139278\pi\)
\(564\) 9.07970 8.60027i 0.382324 0.362137i
\(565\) −24.8327 + 9.03836i −1.04472 + 0.380247i
\(566\) 0.155924 0.00655396
\(567\) −23.2951 4.93333i −0.978303 0.207180i
\(568\) 5.47856 0.229875
\(569\) 33.5534 12.2124i 1.40663 0.511972i 0.476493 0.879178i \(-0.341908\pi\)
0.930140 + 0.367206i \(0.119686\pi\)
\(570\) 17.4192 16.4994i 0.729610 0.691085i
\(571\) 3.28157 2.75357i 0.137330 0.115233i −0.571535 0.820577i \(-0.693652\pi\)
0.708865 + 0.705344i \(0.249208\pi\)
\(572\) −9.53334 3.46985i −0.398609 0.145082i
\(573\) 3.64743 7.29860i 0.152374 0.304903i
\(574\) −8.05810 17.8832i −0.336339 0.746431i
\(575\) 1.50907 2.61379i 0.0629327 0.109003i
\(576\) −2.67555 + 1.35699i −0.111481 + 0.0565414i
\(577\) 8.30212 0.345622 0.172811 0.984955i \(-0.444715\pi\)
0.172811 + 0.984955i \(0.444715\pi\)
\(578\) 14.8357 5.39976i 0.617085 0.224601i
\(579\) −1.33617 + 11.6311i −0.0555292 + 0.483374i
\(580\) 1.87233 + 10.6185i 0.0777442 + 0.440909i
\(581\) −0.718666 + 2.54924i −0.0298153 + 0.105760i
\(582\) 1.26057 0.546718i 0.0522524 0.0226622i
\(583\) 1.85759 10.5349i 0.0769336 0.436312i
\(584\) 13.0625 0.540531
\(585\) −27.5459 6.41349i −1.13888 0.265165i
\(586\) −5.51240 −0.227715
\(587\) −17.7914 + 6.47553i −0.734328 + 0.267274i −0.681996 0.731356i \(-0.738888\pi\)
−0.0523324 + 0.998630i \(0.516666\pi\)
\(588\) −3.75490 + 11.5283i −0.154849 + 0.475417i
\(589\) 35.5734 29.8497i 1.46578 1.22993i
\(590\) −1.25931 7.14191i −0.0518450 0.294028i
\(591\) 4.03892 + 16.8925i 0.166139 + 0.694866i
\(592\) 8.43070 + 7.07419i 0.346500 + 0.290748i
\(593\) −6.46570 11.1989i −0.265515 0.459885i 0.702184 0.711996i \(-0.252209\pi\)
−0.967698 + 0.252111i \(0.918875\pi\)
\(594\) −11.6490 1.98282i −0.477965 0.0813563i
\(595\) −5.54468 2.67370i −0.227310 0.109611i
\(596\) 3.10190 17.5918i 0.127059 0.720586i
\(597\) 5.20627 4.93137i 0.213078 0.201827i
\(598\) −19.3071 + 16.2006i −0.789526 + 0.662491i
\(599\) −3.73640 21.1902i −0.152665 0.865807i −0.960889 0.276933i \(-0.910682\pi\)
0.808224 0.588875i \(-0.200429\pi\)
\(600\) −0.413642 + 0.827708i −0.0168869 + 0.0337910i
\(601\) 12.1343 4.41654i 0.494970 0.180154i −0.0824604 0.996594i \(-0.526278\pi\)
0.577430 + 0.816440i \(0.304056\pi\)
\(602\) 15.2578 + 7.35750i 0.621863 + 0.299869i
\(603\) 8.40687 19.7033i 0.342354 0.802381i
\(604\) −3.13373 + 5.42778i −0.127510 + 0.220853i
\(605\) −11.5742 + 4.21265i −0.470556 + 0.171269i
\(606\) −15.3241 11.3613i −0.622499 0.461522i
\(607\) −15.8153 + 13.2706i −0.641924 + 0.538638i −0.904608 0.426244i \(-0.859837\pi\)
0.262684 + 0.964882i \(0.415392\pi\)
\(608\) 1.13827 + 6.45544i 0.0461628 + 0.261803i
\(609\) −10.8697 20.7013i −0.440464 0.838860i
\(610\) 2.31239 + 1.94033i 0.0936261 + 0.0785616i
\(611\) −16.1059 + 27.8963i −0.651576 + 1.12856i
\(612\) 1.98284 + 2.64153i 0.0801514 + 0.106777i
\(613\) −2.96631 5.13780i −0.119808 0.207514i 0.799883 0.600155i \(-0.204895\pi\)
−0.919692 + 0.392642i \(0.871561\pi\)
\(614\) 10.0591 + 8.44057i 0.405951 + 0.340633i
\(615\) −14.9563 22.6422i −0.603095 0.913022i
\(616\) −1.63256 + 5.79098i −0.0657776 + 0.233325i
\(617\) −26.7010 9.71835i −1.07494 0.391246i −0.256918 0.966433i \(-0.582707\pi\)
−0.818022 + 0.575187i \(0.804929\pi\)
\(618\) 19.6608 18.6226i 0.790872 0.749112i
\(619\) 26.7041 + 22.4074i 1.07333 + 0.900629i 0.995350 0.0963256i \(-0.0307090\pi\)
0.0779784 + 0.996955i \(0.475153\pi\)
\(620\) 7.48542 12.9651i 0.300622 0.520692i
\(621\) −18.7358 + 22.5995i −0.751841 + 0.906886i
\(622\) −6.98116 −0.279919
\(623\) −21.3753 2.15008i −0.856385 0.0861411i
\(624\) 5.60991 5.31370i 0.224576 0.212718i
\(625\) −3.82781 21.7086i −0.153112 0.868343i
\(626\) 1.71402 + 9.72070i 0.0685061 + 0.388517i
\(627\) −11.5420 + 23.0958i −0.460943 + 0.922358i
\(628\) 5.28857 + 4.43764i 0.211037 + 0.177081i
\(629\) 6.05838 10.4934i 0.241564 0.418400i
\(630\) −2.58069 + 16.5736i −0.102817 + 0.660307i
\(631\) 6.04573 + 10.4715i 0.240677 + 0.416865i 0.960907 0.276870i \(-0.0892972\pi\)
−0.720230 + 0.693735i \(0.755964\pi\)
\(632\) 0.994920 5.64247i 0.0395758 0.224445i
\(633\) −1.55890 + 13.5700i −0.0619607 + 0.539359i
\(634\) 22.7437 + 8.27804i 0.903269 + 0.328763i
\(635\) −30.6188 + 25.6923i −1.21507 + 1.01957i
\(636\) 6.54502 + 4.85250i 0.259527 + 0.192414i
\(637\) 0.810796 31.2178i 0.0321249 1.23689i
\(638\) −5.80153 10.0485i −0.229685 0.397826i
\(639\) −14.6582 + 7.43438i −0.579868 + 0.294099i
\(640\) 1.05662 + 1.83012i 0.0417665 + 0.0723417i
\(641\) −7.57696 + 42.9711i −0.299272 + 1.69726i 0.350041 + 0.936734i \(0.386168\pi\)
−0.649313 + 0.760521i \(0.724944\pi\)
\(642\) 19.3886 1.16775i 0.765207 0.0460873i
\(643\) 18.1099 15.1960i 0.714183 0.599271i −0.211587 0.977359i \(-0.567863\pi\)
0.925769 + 0.378089i \(0.123419\pi\)
\(644\) 10.4312 + 10.7056i 0.411047 + 0.421862i
\(645\) 22.4630 + 6.67660i 0.884481 + 0.262891i
\(646\) 6.78168 2.46833i 0.266822 0.0971151i
\(647\) 5.83538 10.1072i 0.229412 0.397354i −0.728222 0.685342i \(-0.759653\pi\)
0.957634 + 0.287988i \(0.0929862\pi\)
\(648\) 5.31713 7.26141i 0.208877 0.285255i
\(649\) 3.90206 + 6.75856i 0.153169 + 0.265297i
\(650\) 0.413854 2.34709i 0.0162327 0.0920603i
\(651\) −6.91436 + 31.7195i −0.270995 + 1.24319i
\(652\) 14.5103 + 5.28132i 0.568267 + 0.206832i
\(653\) −17.2836 6.29072i −0.676360 0.246175i −0.0190763 0.999818i \(-0.506073\pi\)
−0.657284 + 0.753643i \(0.728295\pi\)
\(654\) −6.15029 9.31090i −0.240496 0.364085i
\(655\) 5.23704 29.7007i 0.204628 1.16050i
\(656\) 7.41372 0.289457
\(657\) −34.9494 + 17.7258i −1.36351 + 0.691548i
\(658\) 17.2074 + 8.29762i 0.670816 + 0.323475i
\(659\) 20.4084 + 17.1247i 0.795000 + 0.667084i 0.946978 0.321300i \(-0.104120\pi\)
−0.151977 + 0.988384i \(0.548564\pi\)
\(660\) −0.949969 + 8.26934i −0.0369775 + 0.321884i
\(661\) −33.4499 12.1748i −1.30105 0.473543i −0.403711 0.914887i \(-0.632280\pi\)
−0.897338 + 0.441344i \(0.854502\pi\)
\(662\) 23.8033 + 8.66370i 0.925142 + 0.336724i
\(663\) −6.83388 5.06665i −0.265406 0.196773i
\(664\) −0.766870 0.643480i −0.0297603 0.0249719i
\(665\) 33.0121 + 15.9188i 1.28015 + 0.617305i
\(666\) −32.1564 7.48696i −1.24603 0.290114i
\(667\) −28.8255 −1.11613
\(668\) −0.0283674 + 0.160879i −0.00109757 + 0.00622461i
\(669\) 22.1918 44.4064i 0.857986 1.71685i
\(670\) −14.1798 5.16102i −0.547813 0.199388i
\(671\) −3.05249 1.11102i −0.117840 0.0428903i
\(672\) −3.38957 3.08397i −0.130755 0.118967i
\(673\) 2.95225 16.7430i 0.113801 0.645397i −0.873536 0.486759i \(-0.838179\pi\)
0.987337 0.158637i \(-0.0507101\pi\)
\(674\) −9.72372 16.8420i −0.374544 0.648729i
\(675\) −0.0164744 2.77588i −0.000634101 0.106844i
\(676\) −3.45109 + 5.97746i −0.132734 + 0.229902i
\(677\) −15.4539 + 5.62476i −0.593942 + 0.216177i −0.621462 0.783444i \(-0.713461\pi\)
0.0275205 + 0.999621i \(0.491239\pi\)
\(678\) 5.03673 + 21.0658i 0.193434 + 0.809028i
\(679\) 1.46472 + 1.50326i 0.0562109 + 0.0576897i
\(680\) 1.78229 1.49552i 0.0683479 0.0573507i
\(681\) 12.2588 24.5301i 0.469757 0.939994i
\(682\) −2.79754 + 15.8657i −0.107124 + 0.607528i
\(683\) −22.4479 38.8809i −0.858946 1.48774i −0.872935 0.487836i \(-0.837786\pi\)
0.0139894 0.999902i \(-0.495547\pi\)
\(684\) −11.8055 15.7272i −0.451394 0.601345i
\(685\) −19.5617 33.8818i −0.747413 1.29456i
\(686\) −18.4986 + 0.894492i −0.706282 + 0.0341519i
\(687\) 2.29780 20.0021i 0.0876667 0.763126i
\(688\) −4.90452 + 4.11538i −0.186983 + 0.156897i
\(689\) −19.7200 7.17750i −0.751273 0.273441i
\(690\) 16.6112 + 12.3156i 0.632378 + 0.468846i
\(691\) 7.87985 44.6889i 0.299764 1.70004i −0.347419 0.937710i \(-0.612942\pi\)
0.647183 0.762335i \(-0.275947\pi\)
\(692\) −8.03208 13.9120i −0.305334 0.528854i
\(693\) −3.49033 17.7094i −0.132587 0.672725i
\(694\) −8.49969 + 14.7219i −0.322644 + 0.558836i
\(695\) −1.54055 1.29267i −0.0584363 0.0490339i
\(696\) 8.82141 0.531301i 0.334375 0.0201389i
\(697\) −1.41737 8.03831i −0.0536867 0.304473i
\(698\) −3.12520 17.7239i −0.118290 0.670858i
\(699\) −0.689342 2.88314i −0.0260733 0.109050i
\(700\) −1.40634 0.141459i −0.0531546 0.00534666i
\(701\) −24.0239 −0.907369 −0.453684 0.891162i \(-0.649891\pi\)
−0.453684 + 0.891162i \(0.649891\pi\)
\(702\) −7.79895 + 21.8297i −0.294352 + 0.823908i
\(703\) −36.0706 + 62.4762i −1.36043 + 2.35633i
\(704\) −1.74206 1.46176i −0.0656563 0.0550922i
\(705\) 25.3333 + 7.52971i 0.954106 + 0.283585i
\(706\) 31.4637 + 11.4519i 1.18415 + 0.430996i
\(707\) 7.90667 28.0464i 0.297361 1.05479i
\(708\) −5.93320 + 0.357348i −0.222983 + 0.0134300i
\(709\) 16.4977 + 13.8432i 0.619586 + 0.519894i 0.897673 0.440662i \(-0.145256\pi\)
−0.278088 + 0.960556i \(0.589701\pi\)
\(710\) 5.78875 + 10.0264i 0.217248 + 0.376284i
\(711\) 4.99484 + 16.4468i 0.187321 + 0.616804i
\(712\) 4.05995 7.03203i 0.152153 0.263537i
\(713\) 30.6595 + 25.7263i 1.14821 + 0.963459i
\(714\) −2.69576 + 4.26473i −0.100886 + 0.159603i
\(715\) −3.72287 21.1134i −0.139227 0.789598i
\(716\) 4.02274 3.37548i 0.150337 0.126148i
\(717\) −3.05237 + 1.32383i −0.113993 + 0.0494394i
\(718\) 18.0572 6.57228i 0.673888 0.245275i
\(719\) 14.4754 25.0722i 0.539842 0.935034i −0.459070 0.888400i \(-0.651817\pi\)
0.998912 0.0466336i \(-0.0148493\pi\)
\(720\) −5.31049 3.46274i −0.197910 0.129049i
\(721\) 37.2602 + 17.9673i 1.38764 + 0.669137i
\(722\) −22.5228 + 8.19764i −0.838213 + 0.305085i
\(723\) −26.5986 + 1.60200i −0.989214 + 0.0595790i
\(724\) −2.81378 15.9577i −0.104573 0.593065i
\(725\) 2.08807 1.75210i 0.0775489 0.0650712i
\(726\) 2.34755 + 9.81848i 0.0871256 + 0.364398i
\(727\) −3.65752 + 20.7428i −0.135650 + 0.769309i 0.838755 + 0.544509i \(0.183284\pi\)
−0.974405 + 0.224800i \(0.927827\pi\)
\(728\) 10.6317 + 5.12670i 0.394035 + 0.190008i
\(729\) −4.37257 + 26.6436i −0.161947 + 0.986799i
\(730\) 13.8021 + 23.9060i 0.510839 + 0.884799i
\(731\) 5.39975 + 4.53093i 0.199717 + 0.167582i
\(732\) 1.79625 1.70140i 0.0663911 0.0628855i
\(733\) 5.20888 + 29.5410i 0.192394 + 1.09112i 0.916081 + 0.400993i \(0.131335\pi\)
−0.723687 + 0.690129i \(0.757554\pi\)
\(734\) −14.2443 + 11.9524i −0.525768 + 0.441172i
\(735\) −25.0656 + 5.30906i −0.924557 + 0.195828i
\(736\) −5.30883 + 1.93226i −0.195686 + 0.0712239i
\(737\) 16.2385 0.598152
\(738\) −19.8358 + 10.0604i −0.730165 + 0.370327i
\(739\) 23.7338 0.873063 0.436531 0.899689i \(-0.356207\pi\)
0.436531 + 0.899689i \(0.356207\pi\)
\(740\) −4.03857 + 22.9039i −0.148461 + 0.841964i
\(741\) 40.6878 + 30.1660i 1.49470 + 1.10818i
\(742\) −3.37700 + 11.9788i −0.123973 + 0.439756i
\(743\) −3.02135 17.1349i −0.110843 0.628619i −0.988725 0.149743i \(-0.952155\pi\)
0.877882 0.478876i \(-0.158956\pi\)
\(744\) −9.85684 7.30788i −0.361369 0.267920i
\(745\) 35.4725 12.9109i 1.29961 0.473020i
\(746\) 23.7176 0.868365
\(747\) 2.92500 + 0.681026i 0.107020 + 0.0249174i
\(748\) −1.25186 + 2.16829i −0.0457726 + 0.0792804i
\(749\) 12.1890 + 27.0509i 0.445377 + 0.988418i
\(750\) −20.2199 + 1.21782i −0.738328 + 0.0444684i
\(751\) −37.8942 13.7924i −1.38278 0.503290i −0.459760 0.888043i \(-0.652064\pi\)
−0.923020 + 0.384753i \(0.874287\pi\)
\(752\) −5.53120 + 4.64123i −0.201702 + 0.169248i
\(753\) 7.09042 + 29.6553i 0.258389 + 1.08070i
\(754\) −21.3894 + 7.78512i −0.778958 + 0.283517i
\(755\) −13.2446 −0.482022
\(756\) 13.2539 + 3.65168i 0.482039 + 0.132810i
\(757\) −22.4182 −0.814804 −0.407402 0.913249i \(-0.633565\pi\)
−0.407402 + 0.913249i \(0.633565\pi\)
\(758\) 2.64920 0.964231i 0.0962234 0.0350224i
\(759\) −21.3304 6.33996i −0.774246 0.230126i
\(760\) −10.6115 + 8.90410i −0.384919 + 0.322986i
\(761\) 21.8188 + 7.94138i 0.790930 + 0.287875i 0.705723 0.708488i \(-0.250623\pi\)
0.0852073 + 0.996363i \(0.472845\pi\)
\(762\) 18.0562 + 27.3351i 0.654106 + 0.990247i
\(763\) 9.95727 13.8346i 0.360477 0.500847i
\(764\) −2.35537 + 4.07962i −0.0852144 + 0.147596i
\(765\) −2.73920 + 6.41991i −0.0990361 + 0.232112i
\(766\) 6.23212 0.225176
\(767\) 14.3863 5.23620i 0.519461 0.189068i
\(768\) 1.58904 0.689175i 0.0573394 0.0248685i
\(769\) −5.33742 30.2700i −0.192472 1.09157i −0.915972 0.401241i \(-0.868579\pi\)
0.723500 0.690324i \(-0.242532\pi\)
\(770\) −12.3232 + 3.13108i −0.444096 + 0.112836i
\(771\) 0.905136 7.87907i 0.0325977 0.283758i
\(772\) 1.17376 6.65672i 0.0422445 0.239580i
\(773\) 19.2530 0.692484 0.346242 0.938145i \(-0.387458\pi\)
0.346242 + 0.938145i \(0.387458\pi\)
\(774\) 7.53774 17.6663i 0.270938 0.635002i
\(775\) −3.78464 −0.135948
\(776\) −0.745451 + 0.271322i −0.0267601 + 0.00973990i
\(777\) −6.75983 49.9784i −0.242508 1.79297i
\(778\) 18.3065 15.3610i 0.656319 0.550717i
\(779\) 8.43880 + 47.8588i 0.302351 + 1.71472i
\(780\) 15.6522 + 4.65225i 0.560440 + 0.166577i
\(781\) −9.54398 8.00835i −0.341511 0.286561i
\(782\) 3.11000 + 5.38667i 0.111213 + 0.192627i
\(783\) −22.8811 + 13.3921i −0.817705 + 0.478595i
\(784\) 2.56412 6.51347i 0.0915756 0.232624i
\(785\) −2.53339 + 14.3676i −0.0904207 + 0.512801i
\(786\) −23.6944 7.04258i −0.845150 0.251200i
\(787\) 3.41137 2.86248i 0.121602 0.102036i −0.579959 0.814646i \(-0.696931\pi\)
0.701561 + 0.712609i \(0.252487\pi\)
\(788\) −1.74131 9.87546i −0.0620316 0.351799i
\(789\) −20.3545 30.8145i −0.724638 1.09703i
\(790\) 11.3776 4.14112i 0.404798 0.147334i
\(791\) −27.3462 + 18.6236i −0.972319 + 0.662181i
\(792\) 6.64457 + 1.54705i 0.236104 + 0.0549721i
\(793\) −3.18625 + 5.51875i −0.113147 + 0.195976i
\(794\) −8.11807 + 2.95474i −0.288100 + 0.104860i
\(795\) −1.96504 + 17.1054i −0.0696928 + 0.606666i
\(796\) −3.17157 + 2.66127i −0.112413 + 0.0943261i
\(797\) 4.49255 + 25.4785i 0.159134 + 0.902495i 0.954908 + 0.296901i \(0.0959532\pi\)
−0.795774 + 0.605594i \(0.792936\pi\)
\(798\) 16.0501 25.3915i 0.568168 0.898850i
\(799\) 6.08971 + 5.10987i 0.215438 + 0.180774i
\(800\) 0.267114 0.462656i 0.00944392 0.0163573i
\(801\) −1.32016 + 24.3239i −0.0466456 + 0.859442i
\(802\) −2.82013 4.88461i −0.0995824 0.172482i
\(803\) −22.7557 19.0943i −0.803031 0.673823i
\(804\) −5.52884 + 11.0633i −0.194987 + 0.390174i
\(805\) −8.57078 + 30.4021i −0.302080 + 1.07153i
\(806\) 29.6985 + 10.8094i 1.04608 + 0.380743i
\(807\) −8.92908 37.3454i −0.314318 1.31462i
\(808\) 8.43701 + 7.07949i 0.296813 + 0.249056i
\(809\) 0.236349 0.409369i 0.00830960 0.0143926i −0.861841 0.507179i \(-0.830688\pi\)
0.870150 + 0.492786i \(0.164022\pi\)
\(810\) 18.9074 + 2.05844i 0.664339 + 0.0723261i
\(811\) 23.2467 0.816302 0.408151 0.912914i \(-0.366174\pi\)
0.408151 + 0.912914i \(0.366174\pi\)
\(812\) 5.54575 + 12.3076i 0.194618 + 0.431912i
\(813\) 33.2993 + 9.89741i 1.16786 + 0.347117i
\(814\) −4.34599 24.6473i −0.152327 0.863889i
\(815\) 5.66642 + 32.1359i 0.198486 + 1.12567i
\(816\) −1.05103 1.59115i −0.0367935 0.0557015i
\(817\) −32.1492 26.9764i −1.12476 0.943785i
\(818\) −5.59404 + 9.68915i −0.195591 + 0.338773i
\(819\) −35.4024 + 0.710343i −1.23706 + 0.0248214i
\(820\) 7.83347 + 13.5680i 0.273557 + 0.473814i
\(821\) 6.13769 34.8085i 0.214207 1.21483i −0.668071 0.744097i \(-0.732880\pi\)
0.882278 0.470729i \(-0.156009\pi\)
\(822\) −29.4186 + 12.7590i −1.02609 + 0.445022i
\(823\) −50.6792 18.4457i −1.76657 0.642977i −1.00000 0.000811243i \(-0.999742\pi\)
−0.766566 0.642166i \(-0.778036\pi\)
\(824\) −11.9770 + 10.0499i −0.417239 + 0.350105i
\(825\) 1.93050 0.837271i 0.0672114 0.0291500i
\(826\) −3.73002 8.27797i −0.129784 0.288028i
\(827\) −24.2384 41.9822i −0.842853 1.45986i −0.887472 0.460861i \(-0.847541\pi\)
0.0446191 0.999004i \(-0.485793\pi\)
\(828\) 11.5820 12.3739i 0.402502 0.430023i
\(829\) −20.2250 35.0307i −0.702444 1.21667i −0.967606 0.252464i \(-0.918759\pi\)
0.265163 0.964204i \(-0.414574\pi\)
\(830\) 0.367355 2.08337i 0.0127511 0.0723150i
\(831\) −5.61605 8.50211i −0.194819 0.294935i
\(832\) −3.41747 + 2.86759i −0.118479 + 0.0994160i
\(833\) −7.55243 1.53488i −0.261676 0.0531804i
\(834\) −1.19668 + 1.13349i −0.0414377 + 0.0392497i
\(835\) −0.324402 + 0.118073i −0.0112264 + 0.00408607i
\(836\) 7.45338 12.9096i 0.257781 0.446489i
\(837\) 36.2892 + 6.17693i 1.25434 + 0.213506i
\(838\) −18.2411 31.5945i −0.630128 1.09141i
\(839\) 5.09185 28.8773i 0.175790 0.996955i −0.761438 0.648238i \(-0.775506\pi\)
0.937228 0.348717i \(-0.113383\pi\)
\(840\) 2.06254 9.46188i 0.0711644 0.326466i
\(841\) 2.78792 + 1.01472i 0.0961351 + 0.0349903i
\(842\) −9.04419 3.29182i −0.311684 0.113444i
\(843\) 52.5084 3.16251i 1.80849 0.108923i
\(844\) 1.36942 7.76635i 0.0471373 0.267329i
\(845\) −14.5859 −0.501771
\(846\) 8.50088 19.9236i 0.292266 0.684989i
\(847\) −12.7457 + 8.68021i −0.437947 + 0.298256i
\(848\) −3.60351 3.02370i −0.123745 0.103834i
\(849\) 0.247768 0.107459i 0.00850339 0.00368797i
\(850\) −0.552701 0.201167i −0.0189575 0.00689996i
\(851\) −58.4263 21.2654i −2.00283 0.728969i
\(852\) 8.70564 3.77569i 0.298250 0.129353i
\(853\) 16.0202 + 13.4426i 0.548522 + 0.460265i 0.874440 0.485133i \(-0.161229\pi\)
−0.325918 + 0.945398i \(0.605673\pi\)
\(854\) 3.40416 + 1.64153i 0.116488 + 0.0561718i
\(855\) 16.3088 38.2231i 0.557748 1.30720i
\(856\) −11.2143 −0.383297
\(857\) −2.07277 + 11.7553i −0.0708044 + 0.401552i 0.928722 + 0.370777i \(0.120909\pi\)
−0.999526 + 0.0307748i \(0.990203\pi\)
\(858\) −17.5402 + 1.05642i −0.598811 + 0.0360655i
\(859\) 25.8701 + 9.41596i 0.882678 + 0.321268i 0.743290 0.668970i \(-0.233264\pi\)
0.139388 + 0.990238i \(0.455487\pi\)
\(860\) −12.7138 4.62746i −0.433538 0.157795i
\(861\) −25.1293 22.8637i −0.856404 0.779191i
\(862\) 3.61803 20.5188i 0.123230 0.698875i
\(863\) 11.0269 + 19.0992i 0.375360 + 0.650143i 0.990381 0.138368i \(-0.0441857\pi\)
−0.615021 + 0.788511i \(0.710852\pi\)
\(864\) −3.31634 + 4.00024i −0.112824 + 0.136091i
\(865\) 16.9737 29.3993i 0.577122 0.999605i
\(866\) 5.53238 2.01362i 0.187998 0.0684257i
\(867\) 19.8531 18.8048i 0.674248 0.638646i
\(868\) 5.08577 18.0402i 0.172622 0.612323i
\(869\) −9.98116 + 8.37518i −0.338588 + 0.284109i
\(870\) 10.2932 + 15.5828i 0.348972 + 0.528307i
\(871\) 5.53167 31.3717i 0.187434 1.06299i
\(872\) 3.22127 + 5.57940i 0.109086 + 0.188942i
\(873\) 1.62631 1.73751i 0.0550422 0.0588058i
\(874\) −18.5164 32.0714i −0.626327 1.08483i
\(875\) −12.7116 28.2108i −0.429732 0.953698i
\(876\) 20.7568 9.00237i 0.701308 0.304162i
\(877\) 2.94708 2.47289i 0.0995157 0.0835036i −0.591672 0.806179i \(-0.701532\pi\)
0.691188 + 0.722675i \(0.257088\pi\)
\(878\) −10.2865 3.74397i −0.347152 0.126353i
\(879\) −8.75940 + 3.79901i −0.295447 + 0.128137i
\(880\) 0.834502 4.73270i 0.0281311 0.159539i
\(881\) −13.5058 23.3928i −0.455024 0.788124i 0.543666 0.839302i \(-0.317036\pi\)
−0.998690 + 0.0511778i \(0.983702\pi\)
\(882\) 1.97831 + 20.9066i 0.0666133 + 0.703962i
\(883\) 11.0352 19.1135i 0.371363 0.643220i −0.618412 0.785854i \(-0.712224\pi\)
0.989776 + 0.142634i \(0.0455571\pi\)
\(884\) 3.76254 + 3.15715i 0.126548 + 0.106186i
\(885\) −6.92311 10.4809i −0.232718 0.352310i
\(886\) 1.65875 + 9.40723i 0.0557267 + 0.316042i
\(887\) −0.772574 4.38148i −0.0259405 0.147116i 0.969087 0.246721i \(-0.0793531\pi\)
−0.995027 + 0.0996052i \(0.968242\pi\)
\(888\) 18.2720 + 5.43093i 0.613170 + 0.182250i
\(889\) −29.2327 + 40.6160i −0.980435 + 1.36222i
\(890\) 17.1593 0.575179
\(891\) −19.8772 + 4.87743i −0.665912 + 0.163400i
\(892\) −14.3306 + 24.8214i −0.479825 + 0.831082i
\(893\) −36.2571 30.4233i −1.21330 1.01808i
\(894\) −7.19476 30.0917i −0.240629 1.00642i
\(895\) 10.4280 + 3.79549i 0.348570 + 0.126869i
\(896\) 1.84638 + 1.89496i 0.0616833 + 0.0633062i
\(897\) −19.5147 + 39.0493i −0.651575 + 1.30382i
\(898\) −17.1092 14.3564i −0.570943 0.479078i
\(899\) 18.0730 + 31.3034i 0.602770 + 1.04403i
\(900\) −0.0868569 + 1.60033i −0.00289523 + 0.0533444i
\(901\) −2.58952 + 4.48517i −0.0862693 + 0.149423i
\(902\) −12.9151 10.8371i −0.430027 0.360836i
\(903\) 29.3159 + 1.17601i 0.975571 + 0.0391353i
\(904\) −2.17150 12.3152i −0.0722230 0.409597i
\(905\) 26.2315 22.0108i 0.871963 0.731664i
\(906\) −1.23892 + 10.7846i −0.0411604 + 0.358296i
\(907\) 5.63998 2.05278i 0.187272 0.0681616i −0.246682 0.969097i \(-0.579340\pi\)
0.433954 + 0.900935i \(0.357118\pi\)
\(908\) −7.91624 + 13.7113i −0.262710 + 0.455026i
\(909\) −32.1805 7.49256i −1.06736 0.248513i
\(910\) 1.85114 + 24.8741i 0.0613646 + 0.824570i
\(911\) −51.4444 + 18.7242i −1.70443 + 0.620361i −0.996317 0.0857407i \(-0.972674\pi\)
−0.708110 + 0.706102i \(0.750452\pi\)
\(912\) 6.25768 + 9.47346i 0.207212 + 0.313698i
\(913\) 0.395318 + 2.24196i 0.0130831 + 0.0741981i
\(914\) −18.4967 + 15.5206i −0.611816 + 0.513375i
\(915\) 5.01171 + 1.48961i 0.165682 + 0.0492450i
\(916\) −2.01851 + 11.4475i −0.0666935 + 0.378238i
\(917\) −2.80225 37.6545i −0.0925386 1.24346i
\(918\) 4.97127 + 2.83096i 0.164076 + 0.0934357i
\(919\) 1.77414 + 3.07290i 0.0585234 + 0.101366i 0.893803 0.448460i \(-0.148027\pi\)
−0.835279 + 0.549826i \(0.814694\pi\)
\(920\) −9.14566 7.67412i −0.301524 0.253008i
\(921\) 21.8013 + 6.47990i 0.718376 + 0.213520i
\(922\) −2.93414 16.6404i −0.0966309 0.548021i
\(923\) −18.7228 + 15.7103i −0.616269 + 0.517111i
\(924\) 1.39680 + 10.3272i 0.0459515 + 0.339740i
\(925\) 5.52488 2.01089i 0.181657 0.0661177i
\(926\) 21.0596 0.692063
\(927\) 18.4074 43.1418i 0.604579 1.41696i
\(928\) −5.10227 −0.167490
\(929\) −6.92440 + 39.2702i −0.227182 + 1.28841i 0.631287 + 0.775549i \(0.282527\pi\)
−0.858469 + 0.512865i \(0.828584\pi\)
\(930\) 2.95936 25.7608i 0.0970413 0.844731i
\(931\) 44.9659 + 9.13843i 1.47370 + 0.299500i
\(932\) 0.297198 + 1.68550i 0.00973505 + 0.0552102i
\(933\) −11.0933 + 4.81124i −0.363179 + 0.157513i
\(934\) −24.6188 + 8.96051i −0.805552 + 0.293197i
\(935\) −5.29096 −0.173033
\(936\) 5.25229 12.3099i 0.171677 0.402361i
\(937\) −28.3974 + 49.1857i −0.927702 + 1.60683i −0.140545 + 0.990074i \(0.544885\pi\)
−0.787157 + 0.616753i \(0.788448\pi\)
\(938\) −18.7974 1.89078i −0.613758 0.0617360i
\(939\) 9.42291 + 14.2653i 0.307505 + 0.465530i
\(940\) −14.3384 5.21874i −0.467666 0.170216i
\(941\) 0.144954 0.121631i 0.00472538 0.00396506i −0.640422 0.768023i \(-0.721240\pi\)
0.645147 + 0.764058i \(0.276796\pi\)
\(942\) 11.4620 + 3.40682i 0.373453 + 0.111000i
\(943\) −39.3582 + 14.3252i −1.28168 + 0.466493i
\(944\) 3.43174 0.111694
\(945\) 7.32128 + 28.1146i 0.238161 + 0.914567i
\(946\) 14.5597 0.473376
\(947\) 5.27557 1.92015i 0.171433 0.0623966i −0.254878 0.966973i \(-0.582035\pi\)
0.426311 + 0.904577i \(0.359813\pi\)
\(948\) −2.30769 9.65177i −0.0749502 0.313475i
\(949\) −44.6407 + 37.4580i −1.44910 + 1.21594i
\(950\) 3.29069 + 1.19771i 0.106764 + 0.0388590i
\(951\) 41.8456 2.52030i 1.35694 0.0817264i
\(952\) 1.70161 2.36422i 0.0551495 0.0766248i
\(953\) 3.13594 5.43160i 0.101583 0.175947i −0.810754 0.585387i \(-0.800943\pi\)
0.912337 + 0.409440i \(0.134276\pi\)
\(954\) 13.7445 + 3.20013i 0.444995 + 0.103608i
\(955\) −9.95492 −0.322134
\(956\) 1.80505 0.656984i 0.0583795 0.0212484i
\(957\) −16.1441 11.9692i −0.521863 0.386910i
\(958\) −4.52515 25.6634i −0.146201 0.829148i
\(959\) −34.1829 35.0823i −1.10382 1.13287i
\(960\) 2.94028 + 2.17993i 0.0948970 + 0.0703569i
\(961\) 3.33187 18.8960i 0.107480 0.609548i
\(962\) −49.0975 −1.58297
\(963\) 30.0044 15.2177i 0.966879 0.490385i
\(964\) 15.3846 0.495503
\(965\) 13.4228 4.88549i 0.432095 0.157270i
\(966\) 23.9536 + 9.82274i 0.770696 + 0.316041i
\(967\) 0.593779 0.498240i 0.0190946 0.0160223i −0.633190 0.773996i \(-0.718255\pi\)
0.652285 + 0.757974i \(0.273811\pi\)
\(968\) −1.01211 5.73993i −0.0325303 0.184488i
\(969\) 9.07522 8.59603i 0.291538 0.276144i
\(970\) −1.28421 1.07758i −0.0412335 0.0345990i
\(971\) 16.7134 + 28.9484i 0.536358 + 0.928999i 0.999096 + 0.0425041i \(0.0135335\pi\)
−0.462739 + 0.886495i \(0.653133\pi\)
\(972\) 3.44474 15.2031i 0.110490 0.487639i
\(973\) −2.26790 1.09361i −0.0727055 0.0350594i
\(974\) −1.91768 + 10.8757i −0.0614466 + 0.348481i
\(975\) −0.959923 4.01482i −0.0307421 0.128577i
\(976\) −1.09424 + 0.918179i −0.0350259 + 0.0293902i
\(977\) −4.27560 24.2481i −0.136789 0.775767i −0.973597 0.228272i \(-0.926693\pi\)
0.836809 0.547495i \(-0.184419\pi\)
\(978\) 26.6971 1.60793i 0.853680 0.0514159i
\(979\) −17.3518 + 6.31555i −0.554567 + 0.201846i
\(980\) 14.6297 2.18962i 0.467329 0.0699448i
\(981\) −16.1899 10.5567i −0.516903 0.337050i
\(982\) −3.40254 + 5.89337i −0.108579 + 0.188065i
\(983\) 32.5862 11.8604i 1.03934 0.378288i 0.234708 0.972066i \(-0.424586\pi\)
0.804629 + 0.593778i \(0.202364\pi\)
\(984\) 11.7807 5.10935i 0.375554 0.162880i
\(985\) 16.2333 13.6214i 0.517237 0.434014i
\(986\) 0.975463 + 5.53213i 0.0310651 + 0.176179i
\(987\) 33.0617 + 1.32628i 1.05237 + 0.0422160i
\(988\) −22.4016 18.7971i −0.712689 0.598017i
\(989\) 18.0853 31.3246i 0.575078 0.996065i
\(990\) 4.18949 + 13.7950i 0.133151 + 0.438433i
\(991\) 26.1419 + 45.2791i 0.830425 + 1.43834i 0.897701 + 0.440604i \(0.145236\pi\)
−0.0672761 + 0.997734i \(0.521431\pi\)
\(992\) 5.42690 + 4.55371i 0.172304 + 0.144580i
\(993\) 43.7951 2.63772i 1.38980 0.0837054i
\(994\) 10.1155 + 10.3817i 0.320845 + 0.329286i
\(995\) −8.22157 2.99241i −0.260641 0.0948657i
\(996\) −1.66205 0.494006i −0.0526642 0.0156532i
\(997\) 11.9761 + 10.0491i 0.379287 + 0.318259i 0.812422 0.583069i \(-0.198148\pi\)
−0.433136 + 0.901329i \(0.642593\pi\)
\(998\) 17.3138 29.9884i 0.548058 0.949265i
\(999\) −56.2575 + 10.2643i −1.77991 + 0.324749i
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.w.a.25.3 yes 72
7.2 even 3 378.2.v.b.79.5 yes 72
27.13 even 9 378.2.v.b.67.5 72
189.121 even 9 inner 378.2.w.a.121.3 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.v.b.67.5 72 27.13 even 9
378.2.v.b.79.5 yes 72 7.2 even 3
378.2.w.a.25.3 yes 72 1.1 even 1 trivial
378.2.w.a.121.3 yes 72 189.121 even 9 inner