Properties

Label 756.2.cf.a.659.48
Level $756$
Weight $2$
Character 756.659
Analytic conductor $6.037$
Analytic rank $0$
Dimension $648$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [756,2,Mod(155,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 7, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.155");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.cf (of order \(18\), 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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(108\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 659.48
Character \(\chi\) \(=\) 756.659
Dual form 756.2.cf.a.491.48

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.224874 - 1.39622i) q^{2} +(0.283220 + 1.70874i) q^{3} +(-1.89886 + 0.627946i) q^{4} +(0.747603 - 2.05402i) q^{5} +(2.32209 - 0.779687i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(1.30376 + 2.51002i) q^{8} +(-2.83957 + 0.967897i) q^{9} +O(q^{10})\) \(q+(-0.224874 - 1.39622i) q^{2} +(0.283220 + 1.70874i) q^{3} +(-1.89886 + 0.627946i) q^{4} +(0.747603 - 2.05402i) q^{5} +(2.32209 - 0.779687i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(1.30376 + 2.51002i) q^{8} +(-2.83957 + 0.967897i) q^{9} +(-3.03598 - 0.581923i) q^{10} +(-3.57896 + 1.30263i) q^{11} +(-1.61079 - 3.06681i) q^{12} +(0.135281 - 0.113514i) q^{13} +(-0.0209939 + 1.41406i) q^{14} +(3.72152 + 0.695718i) q^{15} +(3.21137 - 2.38477i) q^{16} +(-5.31680 + 3.06966i) q^{17} +(1.98994 + 3.74702i) q^{18} +(1.99685 + 1.15288i) q^{19} +(-0.129781 + 4.36976i) q^{20} +(0.0178022 - 1.73196i) q^{21} +(2.62358 + 4.70408i) q^{22} +(-0.0492249 - 0.279169i) q^{23} +(-3.91972 + 2.93867i) q^{24} +(0.170124 + 0.142751i) q^{25} +(-0.188912 - 0.163356i) q^{26} +(-2.45811 - 4.57796i) q^{27} +(1.97906 - 0.288672i) q^{28} +(-4.88155 + 5.81761i) q^{29} +(0.134504 - 5.35252i) q^{30} +(-4.41115 + 0.777805i) q^{31} +(-4.05181 - 3.94751i) q^{32} +(-3.23949 - 5.74657i) q^{33} +(5.48153 + 6.73314i) q^{34} +(-1.09292 + 1.89300i) q^{35} +(4.78418 - 3.62100i) q^{36} +(0.564446 + 0.977649i) q^{37} +(1.16064 - 3.04730i) q^{38} +(0.232281 + 0.199011i) q^{39} +(6.13034 - 0.801442i) q^{40} +(-7.24325 - 8.63216i) q^{41} +(-2.42220 + 0.364616i) q^{42} +(-0.101877 - 0.279904i) q^{43} +(5.97797 - 4.72092i) q^{44} +(-0.134791 + 6.55615i) q^{45} +(-0.378711 + 0.131507i) q^{46} +(-1.47637 + 8.37293i) q^{47} +(4.98447 + 4.81197i) q^{48} +(0.939693 + 0.342020i) q^{49} +(0.161055 - 0.269631i) q^{50} +(-6.75107 - 8.21564i) q^{51} +(-0.185600 + 0.300498i) q^{52} +1.17351i q^{53} +(-5.83908 + 4.46152i) q^{54} +8.32511i q^{55} +(-0.848088 - 2.69829i) q^{56} +(-1.40443 + 3.73862i) q^{57} +(9.22040 + 5.50750i) q^{58} +(3.05479 + 1.11185i) q^{59} +(-7.50354 + 1.01584i) q^{60} +(-2.13712 + 12.1202i) q^{61} +(2.07794 + 5.98403i) q^{62} +(2.96451 - 0.460106i) q^{63} +(-4.60044 + 6.54492i) q^{64} +(-0.132025 - 0.362734i) q^{65} +(-7.29500 + 5.81530i) q^{66} +(-4.21151 - 5.01908i) q^{67} +(8.16830 - 9.16753i) q^{68} +(0.463084 - 0.163179i) q^{69} +(2.88881 + 1.10028i) q^{70} +(-0.0796712 - 0.137995i) q^{71} +(-6.13155 - 5.86550i) q^{72} +(-4.16572 + 7.21524i) q^{73} +(1.23808 - 1.00794i) q^{74} +(-0.195741 + 0.331126i) q^{75} +(-4.51571 - 0.935254i) q^{76} +(3.75078 - 0.661364i) q^{77} +(0.225629 - 0.369067i) q^{78} +(1.06892 - 1.27389i) q^{79} +(-2.49754 - 8.37908i) q^{80} +(7.12635 - 5.49683i) q^{81} +(-10.4236 + 12.0543i) q^{82} +(-6.85632 - 5.75314i) q^{83} +(1.05377 + 3.29993i) q^{84} +(2.33029 + 13.2157i) q^{85} +(-0.367898 + 0.205185i) q^{86} +(-11.3233 - 6.69363i) q^{87} +(-7.93573 - 7.28495i) q^{88} +(1.26098 + 0.728026i) q^{89} +(9.18414 - 1.28611i) q^{90} +(-0.152938 + 0.0882985i) q^{91} +(0.268774 + 0.499192i) q^{92} +(-2.57839 - 7.31721i) q^{93} +(12.0225 + 0.178492i) q^{94} +(3.86091 - 3.23969i) q^{95} +(5.59770 - 8.04150i) q^{96} +(12.1677 - 4.42868i) q^{97} +(0.266224 - 1.38893i) q^{98} +(8.90189 - 7.16298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q+O(q^{10}) \) Copy content Toggle raw display \( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66} - 78 q^{68} - 42 q^{72} - 24 q^{81} - 30 q^{86} - 36 q^{89} + 198 q^{90} + 114 q^{92} - 144 q^{93} - 54 q^{94} + 156 q^{96} + 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.224874 1.39622i −0.159010 0.987277i
\(3\) 0.283220 + 1.70874i 0.163517 + 0.986541i
\(4\) −1.89886 + 0.627946i −0.949432 + 0.313973i
\(5\) 0.747603 2.05402i 0.334338 0.918587i −0.652631 0.757676i \(-0.726335\pi\)
0.986969 0.160911i \(-0.0514431\pi\)
\(6\) 2.32209 0.779687i 0.947988 0.318306i
\(7\) −0.984808 0.173648i −0.372222 0.0656328i
\(8\) 1.30376 + 2.51002i 0.460947 + 0.887428i
\(9\) −2.83957 + 0.967897i −0.946524 + 0.322632i
\(10\) −3.03598 0.581923i −0.960063 0.184020i
\(11\) −3.57896 + 1.30263i −1.07910 + 0.392759i −0.819571 0.572978i \(-0.805788\pi\)
−0.259525 + 0.965736i \(0.583566\pi\)
\(12\) −1.61079 3.06681i −0.464995 0.885313i
\(13\) 0.135281 0.113514i 0.0375203 0.0314832i −0.623835 0.781556i \(-0.714426\pi\)
0.661355 + 0.750073i \(0.269982\pi\)
\(14\) −0.0209939 + 1.41406i −0.00561086 + 0.377923i
\(15\) 3.72152 + 0.695718i 0.960893 + 0.179634i
\(16\) 3.21137 2.38477i 0.802842 0.596192i
\(17\) −5.31680 + 3.06966i −1.28951 + 0.744501i −0.978568 0.205926i \(-0.933979\pi\)
−0.310947 + 0.950427i \(0.600646\pi\)
\(18\) 1.98994 + 3.74702i 0.469034 + 0.883180i
\(19\) 1.99685 + 1.15288i 0.458110 + 0.264490i 0.711249 0.702940i \(-0.248130\pi\)
−0.253139 + 0.967430i \(0.581463\pi\)
\(20\) −0.129781 + 4.36976i −0.0290198 + 0.977109i
\(21\) 0.0178022 1.73196i 0.00388476 0.377945i
\(22\) 2.62358 + 4.70408i 0.559348 + 1.00291i
\(23\) −0.0492249 0.279169i −0.0102641 0.0582107i 0.979246 0.202678i \(-0.0649644\pi\)
−0.989510 + 0.144467i \(0.953853\pi\)
\(24\) −3.91972 + 2.93867i −0.800110 + 0.599853i
\(25\) 0.170124 + 0.142751i 0.0340247 + 0.0285501i
\(26\) −0.188912 0.163356i −0.0370488 0.0320367i
\(27\) −2.45811 4.57796i −0.473063 0.881029i
\(28\) 1.97906 0.288672i 0.374007 0.0545539i
\(29\) −4.88155 + 5.81761i −0.906482 + 1.08030i 0.0899540 + 0.995946i \(0.471328\pi\)
−0.996436 + 0.0843568i \(0.973116\pi\)
\(30\) 0.134504 5.35252i 0.0245569 0.977231i
\(31\) −4.41115 + 0.777805i −0.792266 + 0.139698i −0.555114 0.831775i \(-0.687325\pi\)
−0.237152 + 0.971472i \(0.576214\pi\)
\(32\) −4.05181 3.94751i −0.716266 0.697827i
\(33\) −3.23949 5.74657i −0.563923 1.00035i
\(34\) 5.48153 + 6.73314i 0.940074 + 1.15472i
\(35\) −1.09292 + 1.89300i −0.184738 + 0.319975i
\(36\) 4.78418 3.62100i 0.797363 0.603501i
\(37\) 0.564446 + 0.977649i 0.0927943 + 0.160724i 0.908686 0.417480i \(-0.137087\pi\)
−0.815892 + 0.578205i \(0.803753\pi\)
\(38\) 1.16064 3.04730i 0.188281 0.494338i
\(39\) 0.232281 + 0.199011i 0.0371947 + 0.0318672i
\(40\) 6.13034 0.801442i 0.969292 0.126719i
\(41\) −7.24325 8.63216i −1.13120 1.34812i −0.929565 0.368658i \(-0.879817\pi\)
−0.201640 0.979460i \(-0.564627\pi\)
\(42\) −2.42220 + 0.364616i −0.373754 + 0.0562615i
\(43\) −0.101877 0.279904i −0.0155361 0.0426850i 0.931682 0.363274i \(-0.118341\pi\)
−0.947218 + 0.320589i \(0.896119\pi\)
\(44\) 5.97797 4.72092i 0.901212 0.711705i
\(45\) −0.134791 + 6.55615i −0.0200935 + 0.977333i
\(46\) −0.378711 + 0.131507i −0.0558380 + 0.0193896i
\(47\) −1.47637 + 8.37293i −0.215351 + 1.22132i 0.664945 + 0.746893i \(0.268455\pi\)
−0.880296 + 0.474425i \(0.842656\pi\)
\(48\) 4.98447 + 4.81197i 0.719446 + 0.694548i
\(49\) 0.939693 + 0.342020i 0.134242 + 0.0488600i
\(50\) 0.161055 0.269631i 0.0227766 0.0381316i
\(51\) −6.75107 8.21564i −0.945338 1.15042i
\(52\) −0.185600 + 0.300498i −0.0257380 + 0.0416715i
\(53\) 1.17351i 0.161195i 0.996747 + 0.0805973i \(0.0256828\pi\)
−0.996747 + 0.0805973i \(0.974317\pi\)
\(54\) −5.83908 + 4.46152i −0.794598 + 0.607136i
\(55\) 8.32511i 1.12256i
\(56\) −0.848088 2.69829i −0.113330 0.360574i
\(57\) −1.40443 + 3.73862i −0.186021 + 0.495193i
\(58\) 9.22040 + 5.50750i 1.21070 + 0.723170i
\(59\) 3.05479 + 1.11185i 0.397700 + 0.144751i 0.533124 0.846037i \(-0.321018\pi\)
−0.135425 + 0.990788i \(0.543240\pi\)
\(60\) −7.50354 + 1.01584i −0.968703 + 0.131145i
\(61\) −2.13712 + 12.1202i −0.273630 + 1.55183i 0.469649 + 0.882853i \(0.344381\pi\)
−0.743279 + 0.668982i \(0.766731\pi\)
\(62\) 2.07794 + 5.98403i 0.263898 + 0.759973i
\(63\) 2.96451 0.460106i 0.373493 0.0579679i
\(64\) −4.60044 + 6.54492i −0.575055 + 0.818115i
\(65\) −0.132025 0.362734i −0.0163756 0.0449917i
\(66\) −7.29500 + 5.81530i −0.897952 + 0.715813i
\(67\) −4.21151 5.01908i −0.514518 0.613179i 0.444757 0.895651i \(-0.353290\pi\)
−0.959275 + 0.282472i \(0.908845\pi\)
\(68\) 8.16830 9.16753i 0.990552 1.11173i
\(69\) 0.463084 0.163179i 0.0557488 0.0196444i
\(70\) 2.88881 + 1.10028i 0.345279 + 0.131508i
\(71\) −0.0796712 0.137995i −0.00945523 0.0163769i 0.861259 0.508166i \(-0.169676\pi\)
−0.870714 + 0.491789i \(0.836343\pi\)
\(72\) −6.13155 5.86550i −0.722611 0.691255i
\(73\) −4.16572 + 7.21524i −0.487560 + 0.844480i −0.999898 0.0143048i \(-0.995446\pi\)
0.512337 + 0.858784i \(0.328780\pi\)
\(74\) 1.23808 1.00794i 0.143924 0.117170i
\(75\) −0.195741 + 0.331126i −0.0226022 + 0.0382352i
\(76\) −4.51571 0.935254i −0.517987 0.107281i
\(77\) 3.75078 0.661364i 0.427441 0.0753695i
\(78\) 0.225629 0.369067i 0.0255474 0.0417887i
\(79\) 1.06892 1.27389i 0.120263 0.143324i −0.702554 0.711631i \(-0.747957\pi\)
0.822817 + 0.568307i \(0.192401\pi\)
\(80\) −2.49754 8.37908i −0.279234 0.936810i
\(81\) 7.12635 5.49683i 0.791817 0.610759i
\(82\) −10.4236 + 12.0543i −1.15109 + 1.33118i
\(83\) −6.85632 5.75314i −0.752579 0.631489i 0.183605 0.983000i \(-0.441223\pi\)
−0.936184 + 0.351511i \(0.885668\pi\)
\(84\) 1.05377 + 3.29993i 0.114976 + 0.360052i
\(85\) 2.33029 + 13.2157i 0.252755 + 1.43345i
\(86\) −0.367898 + 0.205185i −0.0396715 + 0.0221257i
\(87\) −11.3233 6.69363i −1.21399 0.717633i
\(88\) −7.93573 7.28495i −0.845951 0.776578i
\(89\) 1.26098 + 0.728026i 0.133663 + 0.0771706i 0.565341 0.824858i \(-0.308745\pi\)
−0.431677 + 0.902028i \(0.642078\pi\)
\(90\) 9.18414 1.28611i 0.968094 0.135568i
\(91\) −0.152938 + 0.0882985i −0.0160322 + 0.00925620i
\(92\) 0.268774 + 0.499192i 0.0280217 + 0.0520444i
\(93\) −2.57839 7.31721i −0.267367 0.758760i
\(94\) 12.0225 + 0.178492i 1.24002 + 0.0184101i
\(95\) 3.86091 3.23969i 0.396121 0.332385i
\(96\) 5.59770 8.04150i 0.571313 0.820732i
\(97\) 12.1677 4.42868i 1.23544 0.449665i 0.359985 0.932958i \(-0.382782\pi\)
0.875458 + 0.483293i \(0.160560\pi\)
\(98\) 0.266224 1.38893i 0.0268926 0.140303i
\(99\) 8.90189 7.16298i 0.894674 0.719907i
\(100\) −0.412681 0.164236i −0.0412681 0.0164236i
\(101\) 12.8452 + 2.26495i 1.27814 + 0.225371i 0.771192 0.636603i \(-0.219661\pi\)
0.506953 + 0.861974i \(0.330772\pi\)
\(102\) −9.95271 + 11.2735i −0.985465 + 1.11624i
\(103\) 3.09264 8.49696i 0.304727 0.837231i −0.688935 0.724823i \(-0.741922\pi\)
0.993662 0.112408i \(-0.0358562\pi\)
\(104\) 0.461298 + 0.191564i 0.0452339 + 0.0187844i
\(105\) −3.54417 1.33138i −0.345876 0.129930i
\(106\) 1.63849 0.263892i 0.159144 0.0256315i
\(107\) −9.29019 −0.898117 −0.449058 0.893502i \(-0.648241\pi\)
−0.449058 + 0.893502i \(0.648241\pi\)
\(108\) 7.54232 + 7.14936i 0.725760 + 0.687948i
\(109\) −7.22711 −0.692231 −0.346116 0.938192i \(-0.612500\pi\)
−0.346116 + 0.938192i \(0.612500\pi\)
\(110\) 11.6237 1.87210i 1.10828 0.178497i
\(111\) −1.51068 + 1.24138i −0.143388 + 0.117827i
\(112\) −3.57669 + 1.79089i −0.337965 + 0.169223i
\(113\) 4.92062 13.5193i 0.462893 1.27179i −0.460406 0.887708i \(-0.652296\pi\)
0.923299 0.384081i \(-0.125482\pi\)
\(114\) 5.53576 + 1.12018i 0.518471 + 0.104914i
\(115\) −0.610219 0.107598i −0.0569032 0.0100336i
\(116\) 5.61626 14.1122i 0.521457 1.31028i
\(117\) −0.274271 + 0.453271i −0.0253563 + 0.0419049i
\(118\) 0.865450 4.51518i 0.0796711 0.415656i
\(119\) 5.76907 2.09977i 0.528850 0.192486i
\(120\) 3.10569 + 10.2482i 0.283509 + 0.935525i
\(121\) 2.68559 2.25347i 0.244144 0.204861i
\(122\) 17.4031 + 0.258376i 1.57560 + 0.0233923i
\(123\) 12.6987 14.8216i 1.14500 1.33642i
\(124\) 7.88775 4.24691i 0.708341 0.381384i
\(125\) 9.88539 5.70733i 0.884176 0.510479i
\(126\) −1.30905 4.03564i −0.116619 0.359523i
\(127\) 9.51426 + 5.49306i 0.844254 + 0.487430i 0.858708 0.512465i \(-0.171268\pi\)
−0.0144542 + 0.999896i \(0.504601\pi\)
\(128\) 10.1727 + 4.95145i 0.899145 + 0.437651i
\(129\) 0.449429 0.253355i 0.0395700 0.0223067i
\(130\) −0.476768 + 0.265905i −0.0418154 + 0.0233214i
\(131\) −1.05923 6.00720i −0.0925455 0.524852i −0.995472 0.0950565i \(-0.969697\pi\)
0.902926 0.429795i \(-0.141414\pi\)
\(132\) 9.75989 + 8.87772i 0.849489 + 0.772707i
\(133\) −1.76632 1.48212i −0.153160 0.128516i
\(134\) −6.06069 + 7.00886i −0.523564 + 0.605473i
\(135\) −11.2409 + 1.62651i −0.967464 + 0.139988i
\(136\) −14.6367 9.34322i −1.25509 0.801175i
\(137\) −12.8919 + 15.3640i −1.10143 + 1.31264i −0.155660 + 0.987811i \(0.549750\pi\)
−0.945774 + 0.324826i \(0.894694\pi\)
\(138\) −0.331969 0.609873i −0.0282591 0.0519159i
\(139\) 16.6832 2.94169i 1.41505 0.249511i 0.586735 0.809779i \(-0.300413\pi\)
0.828312 + 0.560268i \(0.189302\pi\)
\(140\) 0.886611 4.28084i 0.0749323 0.361797i
\(141\) −14.7253 0.151356i −1.24009 0.0127465i
\(142\) −0.174755 + 0.142270i −0.0146651 + 0.0119390i
\(143\) −0.336298 + 0.582485i −0.0281226 + 0.0487098i
\(144\) −6.81070 + 9.88000i −0.567558 + 0.823333i
\(145\) 8.30003 + 14.3761i 0.689280 + 1.19387i
\(146\) 11.0108 + 4.19375i 0.911262 + 0.347077i
\(147\) −0.318283 + 1.70256i −0.0262516 + 0.140424i
\(148\) −1.68572 1.50198i −0.138565 0.123462i
\(149\) −6.24398 7.44128i −0.511527 0.609614i 0.447029 0.894520i \(-0.352482\pi\)
−0.958556 + 0.284906i \(0.908038\pi\)
\(150\) 0.506343 + 0.198836i 0.0413427 + 0.0162349i
\(151\) −7.50767 20.6272i −0.610966 1.67861i −0.728077 0.685496i \(-0.759585\pi\)
0.117111 0.993119i \(-0.462637\pi\)
\(152\) −0.290357 + 6.51523i −0.0235511 + 0.528455i
\(153\) 12.1263 13.8626i 0.980356 1.12073i
\(154\) −1.76686 5.08820i −0.142378 0.410019i
\(155\) −1.70016 + 9.64209i −0.136560 + 0.774471i
\(156\) −0.566037 0.232034i −0.0453193 0.0185776i
\(157\) 8.95421 + 3.25907i 0.714624 + 0.260102i 0.673642 0.739058i \(-0.264729\pi\)
0.0409823 + 0.999160i \(0.486951\pi\)
\(158\) −2.01900 1.20598i −0.160623 0.0959429i
\(159\) −2.00523 + 0.332363i −0.159025 + 0.0263581i
\(160\) −11.1374 + 5.37135i −0.880490 + 0.424643i
\(161\) 0.283475i 0.0223410i
\(162\) −9.27731 8.71387i −0.728895 0.684626i
\(163\) 12.7508i 0.998718i 0.866395 + 0.499359i \(0.166431\pi\)
−0.866395 + 0.499359i \(0.833569\pi\)
\(164\) 19.1745 + 11.8429i 1.49727 + 0.924778i
\(165\) −14.2254 + 2.35784i −1.10745 + 0.183557i
\(166\) −6.49084 + 10.8667i −0.503787 + 0.843417i
\(167\) 0.976334 + 0.355357i 0.0755510 + 0.0274983i 0.379519 0.925184i \(-0.376089\pi\)
−0.303968 + 0.952682i \(0.598312\pi\)
\(168\) 4.37047 2.21337i 0.337189 0.170765i
\(169\) −2.25201 + 12.7718i −0.173232 + 0.982445i
\(170\) 17.9280 6.22546i 1.37502 0.477471i
\(171\) −6.78609 1.34095i −0.518945 0.102545i
\(172\) 0.369215 + 0.467527i 0.0281524 + 0.0356486i
\(173\) −4.99923 13.7353i −0.380084 1.04427i −0.971320 0.237774i \(-0.923582\pi\)
0.591236 0.806498i \(-0.298640\pi\)
\(174\) −6.79947 + 17.3151i −0.515467 + 1.31265i
\(175\) −0.142751 0.170124i −0.0107909 0.0128601i
\(176\) −8.38686 + 12.7182i −0.632184 + 0.958672i
\(177\) −1.03469 + 5.53473i −0.0777719 + 0.416016i
\(178\) 0.732924 1.92432i 0.0549350 0.144234i
\(179\) −10.7107 18.5515i −0.800555 1.38660i −0.919251 0.393672i \(-0.871205\pi\)
0.118696 0.992931i \(-0.462129\pi\)
\(180\) −3.86096 12.5339i −0.287779 0.934220i
\(181\) 5.65404 9.79309i 0.420262 0.727914i −0.575703 0.817659i \(-0.695272\pi\)
0.995965 + 0.0897443i \(0.0286050\pi\)
\(182\) 0.157676 + 0.193679i 0.0116877 + 0.0143564i
\(183\) −21.3156 0.219095i −1.57569 0.0161960i
\(184\) 0.636542 0.487523i 0.0469265 0.0359407i
\(185\) 2.43009 0.428491i 0.178664 0.0315033i
\(186\) −9.63663 + 5.24545i −0.706592 + 0.384615i
\(187\) 15.0300 17.9120i 1.09910 1.30986i
\(188\) −2.45432 16.8261i −0.179000 1.22717i
\(189\) 1.62581 + 4.93526i 0.118260 + 0.358987i
\(190\) −5.39153 4.66216i −0.391143 0.338228i
\(191\) 13.0242 + 10.9286i 0.942398 + 0.790765i 0.978001 0.208601i \(-0.0668909\pi\)
−0.0356034 + 0.999366i \(0.511335\pi\)
\(192\) −12.4865 6.00730i −0.901134 0.433540i
\(193\) 0.219069 + 1.24240i 0.0157689 + 0.0894301i 0.991677 0.128754i \(-0.0410978\pi\)
−0.975908 + 0.218184i \(0.929987\pi\)
\(194\) −8.91962 15.9929i −0.640391 1.14822i
\(195\) 0.582426 0.328329i 0.0417084 0.0235121i
\(196\) −1.99912 0.0593732i −0.142794 0.00424094i
\(197\) −18.4993 10.6806i −1.31802 0.760959i −0.334609 0.942357i \(-0.608604\pi\)
−0.983410 + 0.181398i \(0.941938\pi\)
\(198\) −12.0029 10.8182i −0.853009 0.768819i
\(199\) −8.97138 + 5.17963i −0.635964 + 0.367174i −0.783058 0.621948i \(-0.786341\pi\)
0.147094 + 0.989122i \(0.453008\pi\)
\(200\) −0.136508 + 0.613126i −0.00965257 + 0.0433546i
\(201\) 7.38352 8.61788i 0.520793 0.607858i
\(202\) 0.273831 18.4441i 0.0192667 1.29772i
\(203\) 5.81761 4.88155i 0.408316 0.342618i
\(204\) 17.9783 + 11.3611i 1.25874 + 0.795434i
\(205\) −23.1457 + 8.42436i −1.61657 + 0.588383i
\(206\) −12.5591 2.40727i −0.875033 0.167722i
\(207\) 0.409984 + 0.745075i 0.0284959 + 0.0517863i
\(208\) 0.163732 0.687151i 0.0113528 0.0476453i
\(209\) −8.64844 1.52495i −0.598225 0.105483i
\(210\) −1.06191 + 5.24784i −0.0732791 + 0.362136i
\(211\) 2.82100 7.75062i 0.194205 0.533575i −0.803923 0.594734i \(-0.797257\pi\)
0.998128 + 0.0611589i \(0.0194797\pi\)
\(212\) −0.736904 2.22834i −0.0506108 0.153043i
\(213\) 0.213232 0.175220i 0.0146104 0.0120059i
\(214\) 2.08912 + 12.9712i 0.142809 + 0.886690i
\(215\) −0.651093 −0.0444042
\(216\) 8.28602 12.1384i 0.563792 0.825917i
\(217\) 4.47920 0.304068
\(218\) 1.62519 + 10.0906i 0.110071 + 0.683424i
\(219\) −13.5088 5.07462i −0.912838 0.342911i
\(220\) −5.22772 15.8083i −0.352453 1.06579i
\(221\) −0.370813 + 1.01880i −0.0249436 + 0.0685320i
\(222\) 2.07295 + 1.83009i 0.139127 + 0.122828i
\(223\) 7.15724 + 1.26201i 0.479284 + 0.0845107i 0.408071 0.912950i \(-0.366202\pi\)
0.0712135 + 0.997461i \(0.477313\pi\)
\(224\) 3.30478 + 4.59112i 0.220810 + 0.306757i
\(225\) −0.621246 0.240689i −0.0414164 0.0160459i
\(226\) −19.9825 3.83014i −1.32921 0.254777i
\(227\) 14.2760 5.19605i 0.947534 0.344874i 0.178397 0.983959i \(-0.442909\pi\)
0.769137 + 0.639085i \(0.220687\pi\)
\(228\) 0.319166 7.98104i 0.0211373 0.528557i
\(229\) −9.56396 + 8.02512i −0.632004 + 0.530315i −0.901551 0.432673i \(-0.857571\pi\)
0.269547 + 0.962987i \(0.413126\pi\)
\(230\) −0.0130085 + 0.876197i −0.000857756 + 0.0577747i
\(231\) 2.19240 + 6.22180i 0.144249 + 0.409364i
\(232\) −20.9667 4.66808i −1.37653 0.306474i
\(233\) 17.8354 10.2973i 1.16844 0.674598i 0.215126 0.976586i \(-0.430984\pi\)
0.953311 + 0.301989i \(0.0976505\pi\)
\(234\) 0.694542 + 0.281014i 0.0454036 + 0.0183704i
\(235\) 16.0945 + 9.29214i 1.04989 + 0.606152i
\(236\) −6.49881 0.193013i −0.423037 0.0125641i
\(237\) 2.47948 + 1.46571i 0.161060 + 0.0952083i
\(238\) −4.22905 7.58271i −0.274129 0.491514i
\(239\) 3.86304 + 21.9084i 0.249879 + 1.41713i 0.808883 + 0.587970i \(0.200073\pi\)
−0.559004 + 0.829165i \(0.688816\pi\)
\(240\) 13.6103 6.64077i 0.878541 0.428660i
\(241\) 12.3156 + 10.3340i 0.793317 + 0.665672i 0.946564 0.322516i \(-0.104529\pi\)
−0.153247 + 0.988188i \(0.548973\pi\)
\(242\) −3.75026 3.24292i −0.241076 0.208463i
\(243\) 11.4110 + 10.6203i 0.732014 + 0.681290i
\(244\) −3.55274 24.3566i −0.227441 1.55927i
\(245\) 1.40503 1.67445i 0.0897643 0.106977i
\(246\) −23.5498 14.3972i −1.50148 0.917930i
\(247\) 0.401006 0.0707082i 0.0255154 0.00449905i
\(248\) −7.70337 10.0580i −0.489165 0.638685i
\(249\) 7.88876 13.3451i 0.499930 0.845709i
\(250\) −10.1917 12.5188i −0.644577 0.791755i
\(251\) −11.4578 + 19.8455i −0.723210 + 1.25264i 0.236496 + 0.971632i \(0.424001\pi\)
−0.959706 + 0.281004i \(0.909332\pi\)
\(252\) −5.34027 + 2.73523i −0.336406 + 0.172303i
\(253\) 0.539828 + 0.935010i 0.0339387 + 0.0587836i
\(254\) 5.53002 14.5192i 0.346984 0.911018i
\(255\) −21.9222 + 7.72481i −1.37282 + 0.483746i
\(256\) 4.62576 15.3167i 0.289110 0.957296i
\(257\) −4.21238 5.02012i −0.262761 0.313147i 0.618492 0.785791i \(-0.287744\pi\)
−0.881253 + 0.472645i \(0.843299\pi\)
\(258\) −0.454804 0.570530i −0.0283149 0.0355196i
\(259\) −0.386104 1.06081i −0.0239913 0.0659156i
\(260\) 0.478474 + 0.605879i 0.0296737 + 0.0375750i
\(261\) 8.23068 21.2444i 0.509466 1.31499i
\(262\) −8.14919 + 2.82978i −0.503458 + 0.174825i
\(263\) −3.84540 + 21.8083i −0.237117 + 1.34476i 0.600991 + 0.799256i \(0.294773\pi\)
−0.838108 + 0.545504i \(0.816338\pi\)
\(264\) 10.2005 15.6233i 0.627799 0.961549i
\(265\) 2.41043 + 0.877323i 0.148071 + 0.0538935i
\(266\) −1.67217 + 2.79946i −0.102527 + 0.171646i
\(267\) −0.886872 + 2.36087i −0.0542757 + 0.144483i
\(268\) 11.1488 + 6.88595i 0.681022 + 0.420627i
\(269\) 17.6558i 1.07649i 0.842788 + 0.538246i \(0.180913\pi\)
−0.842788 + 0.538246i \(0.819087\pi\)
\(270\) 4.79875 + 15.3290i 0.292043 + 0.932896i
\(271\) 8.29896i 0.504126i 0.967711 + 0.252063i \(0.0811090\pi\)
−0.967711 + 0.252063i \(0.918891\pi\)
\(272\) −9.75378 + 22.5371i −0.591410 + 1.36651i
\(273\) −0.194194 0.236322i −0.0117532 0.0143029i
\(274\) 24.3506 + 14.5450i 1.47107 + 0.878698i
\(275\) −0.794817 0.289290i −0.0479292 0.0174448i
\(276\) −0.776867 + 0.600646i −0.0467619 + 0.0361546i
\(277\) 1.00431 5.69571i 0.0603429 0.342222i −0.939657 0.342118i \(-0.888856\pi\)
1.00000 0.000103968i \(-3.30941e-5\pi\)
\(278\) −7.85885 22.6319i −0.471343 1.35737i
\(279\) 11.7729 6.47817i 0.704828 0.387838i
\(280\) −6.17637 0.275256i −0.369109 0.0164497i
\(281\) −5.68165 15.6102i −0.338939 0.931227i −0.985696 0.168531i \(-0.946098\pi\)
0.646757 0.762696i \(-0.276125\pi\)
\(282\) 3.10000 + 20.5938i 0.184602 + 1.22634i
\(283\) 17.3005 + 20.6180i 1.02841 + 1.22561i 0.973872 + 0.227099i \(0.0729241\pi\)
0.0545378 + 0.998512i \(0.482631\pi\)
\(284\) 0.237938 + 0.212004i 0.0141190 + 0.0125801i
\(285\) 6.62926 + 5.67974i 0.392683 + 0.336438i
\(286\) 0.888902 + 0.338560i 0.0525619 + 0.0200195i
\(287\) 5.63424 + 9.75880i 0.332579 + 0.576044i
\(288\) 15.3262 + 7.28749i 0.903105 + 0.429419i
\(289\) 10.3456 17.9191i 0.608565 1.05406i
\(290\) 18.2057 14.8215i 1.06908 0.870347i
\(291\) 11.0136 + 19.5371i 0.645629 + 1.14529i
\(292\) 3.37935 16.3166i 0.197762 0.954857i
\(293\) −32.2588 + 5.68811i −1.88458 + 0.332303i −0.992763 0.120090i \(-0.961682\pi\)
−0.891819 + 0.452392i \(0.850571\pi\)
\(294\) 2.44872 + 0.0615340i 0.142812 + 0.00358873i
\(295\) 4.56754 5.44338i 0.265932 0.316926i
\(296\) −1.71802 + 2.69139i −0.0998580 + 0.156434i
\(297\) 14.7609 + 13.1823i 0.856512 + 0.764915i
\(298\) −8.98557 + 10.3913i −0.520520 + 0.601953i
\(299\) −0.0383489 0.0321785i −0.00221777 0.00186093i
\(300\) 0.163756 0.751679i 0.00945446 0.0433982i
\(301\) 0.0517242 + 0.293342i 0.00298133 + 0.0169080i
\(302\) −27.1118 + 15.1209i −1.56011 + 0.870108i
\(303\) −0.232200 + 22.5906i −0.0133396 + 1.29779i
\(304\) 9.16200 1.05970i 0.525477 0.0607780i
\(305\) 23.2975 + 13.4508i 1.33401 + 0.770191i
\(306\) −22.0822 13.8137i −1.26235 0.789677i
\(307\) −22.8520 + 13.1936i −1.30423 + 0.752999i −0.981127 0.193364i \(-0.938060\pi\)
−0.323105 + 0.946363i \(0.604727\pi\)
\(308\) −6.70693 + 3.61113i −0.382163 + 0.205763i
\(309\) 15.3950 + 2.87801i 0.875790 + 0.163724i
\(310\) 13.8448 + 0.205548i 0.786332 + 0.0116743i
\(311\) 24.3635 20.4434i 1.38153 1.15924i 0.412883 0.910784i \(-0.364522\pi\)
0.968644 0.248454i \(-0.0799226\pi\)
\(312\) −0.196684 + 0.842492i −0.0111350 + 0.0476967i
\(313\) 10.2095 3.71596i 0.577076 0.210039i −0.0369595 0.999317i \(-0.511767\pi\)
0.614036 + 0.789278i \(0.289545\pi\)
\(314\) 2.53681 13.2349i 0.143161 0.746891i
\(315\) 1.27121 6.43314i 0.0716244 0.362466i
\(316\) −1.22980 + 3.09016i −0.0691816 + 0.173835i
\(317\) −20.1104 3.54601i −1.12951 0.199164i −0.422500 0.906363i \(-0.638847\pi\)
−0.707014 + 0.707199i \(0.749958\pi\)
\(318\) 0.914975 + 2.72500i 0.0513092 + 0.152811i
\(319\) 9.89265 27.1798i 0.553882 1.52178i
\(320\) 10.0041 + 14.3424i 0.559246 + 0.801765i
\(321\) −2.63117 15.8745i −0.146857 0.886029i
\(322\) 0.395794 0.0637461i 0.0220567 0.00355243i
\(323\) −14.1558 −0.787652
\(324\) −10.0803 + 14.9127i −0.560014 + 0.828483i
\(325\) 0.0392188 0.00217547
\(326\) 17.8029 2.86731i 0.986011 0.158806i
\(327\) −2.04686 12.3492i −0.113192 0.682914i
\(328\) 12.2235 29.4350i 0.674931 1.62527i
\(329\) 2.90789 7.98936i 0.160317 0.440468i
\(330\) 6.49098 + 19.3316i 0.357317 + 1.06417i
\(331\) −11.3917 2.00866i −0.626144 0.110406i −0.148432 0.988923i \(-0.547423\pi\)
−0.477712 + 0.878516i \(0.658534\pi\)
\(332\) 16.6319 + 6.61902i 0.912793 + 0.363266i
\(333\) −2.54905 2.22978i −0.139687 0.122191i
\(334\) 0.276604 1.44309i 0.0151351 0.0789623i
\(335\) −13.4579 + 4.89826i −0.735281 + 0.267620i
\(336\) −4.07315 5.60441i −0.222209 0.305746i
\(337\) −13.5389 + 11.3605i −0.737510 + 0.618845i −0.932168 0.362027i \(-0.882085\pi\)
0.194657 + 0.980871i \(0.437641\pi\)
\(338\) 18.3387 + 0.272266i 0.997491 + 0.0148093i
\(339\) 24.4946 + 4.57912i 1.33036 + 0.248704i
\(340\) −12.7237 23.6316i −0.690037 1.28160i
\(341\) 14.7741 8.52984i 0.800063 0.461917i
\(342\) −0.346250 + 9.77642i −0.0187231 + 0.528648i
\(343\) −0.866025 0.500000i −0.0467610 0.0269975i
\(344\) 0.569744 0.620640i 0.0307185 0.0334627i
\(345\) 0.0110308 1.07318i 0.000593880 0.0577780i
\(346\) −18.0533 + 10.0687i −0.970550 + 0.541298i
\(347\) 3.57866 + 20.2956i 0.192112 + 1.08952i 0.916471 + 0.400100i \(0.131025\pi\)
−0.724359 + 0.689423i \(0.757864\pi\)
\(348\) 25.7047 + 5.59986i 1.37792 + 0.300184i
\(349\) 1.31685 + 1.10497i 0.0704894 + 0.0591476i 0.677352 0.735659i \(-0.263128\pi\)
−0.606862 + 0.794807i \(0.707572\pi\)
\(350\) −0.205429 + 0.237568i −0.0109807 + 0.0126985i
\(351\) −0.852200 0.340281i −0.0454871 0.0181629i
\(352\) 19.6434 + 8.84992i 1.04700 + 0.471702i
\(353\) −18.0497 + 21.5107i −0.960686 + 1.14490i 0.0286993 + 0.999588i \(0.490863\pi\)
−0.989386 + 0.145313i \(0.953581\pi\)
\(354\) 7.96038 + 0.200037i 0.423089 + 0.0106318i
\(355\) −0.343006 + 0.0604813i −0.0182049 + 0.00321001i
\(356\) −2.85159 0.590596i −0.151134 0.0313015i
\(357\) 5.22187 + 9.26313i 0.276371 + 0.490257i
\(358\) −23.4934 + 19.1262i −1.24166 + 1.01085i
\(359\) −12.4623 + 21.5853i −0.657734 + 1.13923i 0.323467 + 0.946239i \(0.395152\pi\)
−0.981201 + 0.192989i \(0.938182\pi\)
\(360\) −16.6318 + 8.20929i −0.876574 + 0.432668i
\(361\) −6.84171 11.8502i −0.360090 0.623695i
\(362\) −14.9448 5.69208i −0.785479 0.299169i
\(363\) 4.61121 + 3.95073i 0.242026 + 0.207360i
\(364\) 0.234961 0.263703i 0.0123153 0.0138218i
\(365\) 11.7060 + 13.9506i 0.612718 + 0.730208i
\(366\) 4.48740 + 29.8105i 0.234560 + 1.55822i
\(367\) 5.00710 + 13.7569i 0.261368 + 0.718104i 0.999076 + 0.0429832i \(0.0136862\pi\)
−0.737707 + 0.675121i \(0.764092\pi\)
\(368\) −0.823832 0.779123i −0.0429452 0.0406146i
\(369\) 28.9228 + 17.5009i 1.50566 + 0.911063i
\(370\) −1.14473 3.29659i −0.0595118 0.171382i
\(371\) 0.203779 1.15569i 0.0105797 0.0600003i
\(372\) 9.49083 + 12.2753i 0.492076 + 0.636445i
\(373\) −4.89188 1.78050i −0.253292 0.0921908i 0.212254 0.977215i \(-0.431920\pi\)
−0.465546 + 0.885024i \(0.654142\pi\)
\(374\) −28.3890 16.9572i −1.46796 0.876836i
\(375\) 12.5521 + 15.2751i 0.648186 + 0.788803i
\(376\) −22.9411 + 7.21053i −1.18310 + 0.371854i
\(377\) 1.34114i 0.0690722i
\(378\) 6.52510 3.37979i 0.335615 0.173838i
\(379\) 37.0304i 1.90213i −0.308997 0.951063i \(-0.599993\pi\)
0.308997 0.951063i \(-0.400007\pi\)
\(380\) −5.29699 + 8.57616i −0.271730 + 0.439948i
\(381\) −6.69157 + 17.8131i −0.342820 + 0.912594i
\(382\) 12.3299 20.6422i 0.630854 1.05615i
\(383\) 23.5859 + 8.58457i 1.20518 + 0.438651i 0.865031 0.501719i \(-0.167299\pi\)
0.340154 + 0.940370i \(0.389521\pi\)
\(384\) −5.57964 + 18.7848i −0.284735 + 0.958606i
\(385\) 1.44564 8.19863i 0.0736766 0.417841i
\(386\) 1.68541 0.585252i 0.0857849 0.0297886i
\(387\) 0.560205 + 0.696202i 0.0284768 + 0.0353899i
\(388\) −20.3238 + 16.0501i −1.03179 + 0.814822i
\(389\) 3.70320 + 10.1745i 0.187760 + 0.515866i 0.997480 0.0709505i \(-0.0226032\pi\)
−0.809720 + 0.586816i \(0.800381\pi\)
\(390\) −0.589392 0.739363i −0.0298450 0.0374391i
\(391\) 1.11867 + 1.33318i 0.0565736 + 0.0674218i
\(392\) 0.366651 + 2.80456i 0.0185187 + 0.141652i
\(393\) 9.96474 3.51131i 0.502655 0.177122i
\(394\) −10.7524 + 28.2308i −0.541699 + 1.42225i
\(395\) −1.81747 3.14795i −0.0914468 0.158390i
\(396\) −12.4055 + 19.1914i −0.623400 + 0.964406i
\(397\) 0.983315 1.70315i 0.0493512 0.0854788i −0.840295 0.542130i \(-0.817618\pi\)
0.889646 + 0.456651i \(0.150951\pi\)
\(398\) 9.24933 + 11.3613i 0.463627 + 0.569488i
\(399\) 2.03230 3.43795i 0.101742 0.172113i
\(400\) 0.886757 + 0.0527193i 0.0443378 + 0.00263597i
\(401\) 36.8083 6.49030i 1.83812 0.324110i 0.856676 0.515854i \(-0.172525\pi\)
0.981445 + 0.191744i \(0.0614144\pi\)
\(402\) −13.6928 8.37109i −0.682936 0.417512i
\(403\) −0.508454 + 0.605952i −0.0253279 + 0.0301846i
\(404\) −25.8135 + 3.76525i −1.28427 + 0.187328i
\(405\) −5.96293 18.7471i −0.296300 0.931552i
\(406\) −8.12395 7.02493i −0.403185 0.348642i
\(407\) −3.29365 2.76370i −0.163260 0.136991i
\(408\) 11.8197 27.6565i 0.585163 1.36920i
\(409\) 3.93598 + 22.3220i 0.194622 + 1.10375i 0.912957 + 0.408057i \(0.133793\pi\)
−0.718335 + 0.695697i \(0.755095\pi\)
\(410\) 16.9671 + 30.4221i 0.837947 + 1.50244i
\(411\) −29.9043 17.6776i −1.47507 0.871970i
\(412\) −0.536869 + 18.0766i −0.0264497 + 0.890570i
\(413\) −2.81531 1.62542i −0.138532 0.0799816i
\(414\) 0.948094 0.739976i 0.0465963 0.0363678i
\(415\) −16.9429 + 9.78198i −0.831693 + 0.480178i
\(416\) −0.996233 0.0740839i −0.0488443 0.00363226i
\(417\) 9.75158 + 27.6740i 0.477537 + 1.35520i
\(418\) −0.184366 + 12.4181i −0.00901762 + 0.607387i
\(419\) −8.17538 + 6.85996i −0.399393 + 0.335131i −0.820259 0.571992i \(-0.806171\pi\)
0.420866 + 0.907123i \(0.361726\pi\)
\(420\) 7.56594 + 0.302566i 0.369180 + 0.0147637i
\(421\) −18.5983 + 6.76921i −0.906424 + 0.329911i −0.752824 0.658222i \(-0.771309\pi\)
−0.153600 + 0.988133i \(0.549087\pi\)
\(422\) −11.4559 2.19582i −0.557667 0.106891i
\(423\) −3.91187 25.2045i −0.190201 1.22549i
\(424\) −2.94555 + 1.52998i −0.143049 + 0.0743022i
\(425\) −1.34271 0.236756i −0.0651310 0.0114843i
\(426\) −0.292596 0.258317i −0.0141763 0.0125155i
\(427\) 4.20931 11.5650i 0.203703 0.559669i
\(428\) 17.6408 5.83374i 0.852701 0.281985i
\(429\) −1.09056 0.409674i −0.0526528 0.0197792i
\(430\) 0.146414 + 0.909069i 0.00706069 + 0.0438392i
\(431\) 8.83068 0.425359 0.212680 0.977122i \(-0.431781\pi\)
0.212680 + 0.977122i \(0.431781\pi\)
\(432\) −18.8113 8.83949i −0.905057 0.425290i
\(433\) 12.8952 0.619706 0.309853 0.950785i \(-0.399720\pi\)
0.309853 + 0.950785i \(0.399720\pi\)
\(434\) −1.00725 6.25395i −0.0483497 0.300199i
\(435\) −22.2142 + 18.2542i −1.06509 + 0.875221i
\(436\) 13.7233 4.53823i 0.657226 0.217342i
\(437\) 0.223554 0.614210i 0.0106940 0.0293816i
\(438\) −4.04753 + 20.0024i −0.193399 + 0.955750i
\(439\) 19.6785 + 3.46985i 0.939204 + 0.165607i 0.622237 0.782829i \(-0.286224\pi\)
0.316968 + 0.948436i \(0.397335\pi\)
\(440\) −20.8962 + 10.8539i −0.996189 + 0.517440i
\(441\) −2.99937 0.0616654i −0.142827 0.00293645i
\(442\) 1.50586 + 0.288636i 0.0716263 + 0.0137290i
\(443\) −4.66514 + 1.69797i −0.221648 + 0.0806731i −0.450457 0.892798i \(-0.648739\pi\)
0.228809 + 0.973471i \(0.426517\pi\)
\(444\) 2.08906 3.30584i 0.0991425 0.156888i
\(445\) 2.43809 2.04580i 0.115577 0.0969804i
\(446\) 0.152576 10.2769i 0.00722470 0.486624i
\(447\) 10.9468 12.7768i 0.517765 0.604324i
\(448\) 5.66706 5.64663i 0.267744 0.266778i
\(449\) 1.65970 0.958226i 0.0783259 0.0452215i −0.460326 0.887750i \(-0.652267\pi\)
0.538651 + 0.842529i \(0.318934\pi\)
\(450\) −0.196353 + 0.921521i −0.00925615 + 0.0434409i
\(451\) 37.1678 + 21.4588i 1.75016 + 1.01046i
\(452\) −0.854199 + 28.7612i −0.0401782 + 1.35281i
\(453\) 33.1201 18.6707i 1.55612 0.877225i
\(454\) −10.4651 18.7640i −0.491153 0.880640i
\(455\) 0.0670306 + 0.380149i 0.00314244 + 0.0178217i
\(456\) −11.2151 + 1.34910i −0.525194 + 0.0631773i
\(457\) −29.7730 24.9826i −1.39272 1.16863i −0.964223 0.265094i \(-0.914597\pi\)
−0.428502 0.903541i \(-0.640958\pi\)
\(458\) 13.3555 + 11.5488i 0.624062 + 0.539638i
\(459\) 27.1220 + 16.7946i 1.26595 + 0.783903i
\(460\) 1.22629 0.178871i 0.0571760 0.00833989i
\(461\) −7.39837 + 8.81703i −0.344576 + 0.410650i −0.910303 0.413943i \(-0.864151\pi\)
0.565727 + 0.824593i \(0.308596\pi\)
\(462\) 8.19399 4.46018i 0.381219 0.207507i
\(463\) −37.1225 + 6.54569i −1.72523 + 0.304204i −0.946391 0.323023i \(-0.895301\pi\)
−0.778837 + 0.627227i \(0.784190\pi\)
\(464\) −1.80281 + 30.3238i −0.0836933 + 1.40775i
\(465\) −16.9573 0.174299i −0.786377 0.00808290i
\(466\) −18.3880 22.5866i −0.851808 1.04630i
\(467\) −6.44932 + 11.1706i −0.298439 + 0.516911i −0.975779 0.218759i \(-0.929799\pi\)
0.677340 + 0.735670i \(0.263133\pi\)
\(468\) 0.236173 1.03293i 0.0109171 0.0477470i
\(469\) 3.27597 + 5.67415i 0.151270 + 0.262008i
\(470\) 9.35466 24.5610i 0.431498 1.13291i
\(471\) −3.03288 + 16.2234i −0.139748 + 0.747537i
\(472\) 1.19192 + 9.11718i 0.0548627 + 0.419652i
\(473\) 0.729225 + 0.869056i 0.0335298 + 0.0399593i
\(474\) 1.48889 3.79150i 0.0683869 0.174150i
\(475\) 0.175137 + 0.481185i 0.00803584 + 0.0220783i
\(476\) −9.63613 + 7.60984i −0.441671 + 0.348797i
\(477\) −1.13584 3.33228i −0.0520066 0.152575i
\(478\) 29.7202 10.3203i 1.35937 0.472038i
\(479\) 4.47199 25.3619i 0.204330 1.15882i −0.694160 0.719821i \(-0.744224\pi\)
0.898490 0.438994i \(-0.144665\pi\)
\(480\) −12.3326 17.5097i −0.562902 0.799203i
\(481\) 0.187336 + 0.0681848i 0.00854179 + 0.00310896i
\(482\) 11.6591 19.5191i 0.531058 0.889072i
\(483\) −0.484385 + 0.0802858i −0.0220403 + 0.00365313i
\(484\) −3.68450 + 5.96544i −0.167477 + 0.271156i
\(485\) 28.3036i 1.28520i
\(486\) 12.2622 18.3204i 0.556225 0.831032i
\(487\) 40.0991i 1.81706i 0.417817 + 0.908531i \(0.362795\pi\)
−0.417817 + 0.908531i \(0.637205\pi\)
\(488\) −33.2083 + 10.4376i −1.50327 + 0.472487i
\(489\) −21.7877 + 3.61127i −0.985276 + 0.163307i
\(490\) −2.65386 1.58520i −0.119889 0.0716119i
\(491\) 0.150560 + 0.0547994i 0.00679468 + 0.00247306i 0.345415 0.938450i \(-0.387738\pi\)
−0.338621 + 0.940923i \(0.609960\pi\)
\(492\) −14.8059 + 36.1183i −0.667501 + 1.62834i
\(493\) 8.09619 45.9158i 0.364634 2.06794i
\(494\) −0.188900 0.543992i −0.00849901 0.0244754i
\(495\) −8.05785 23.6398i −0.362173 1.06253i
\(496\) −12.3109 + 13.0174i −0.552777 + 0.584498i
\(497\) 0.0544983 + 0.149733i 0.00244458 + 0.00671644i
\(498\) −20.4066 8.01350i −0.914443 0.359093i
\(499\) −16.6077 19.7923i −0.743463 0.886025i 0.253220 0.967409i \(-0.418510\pi\)
−0.996683 + 0.0813840i \(0.974066\pi\)
\(500\) −15.1871 + 17.0449i −0.679188 + 0.762273i
\(501\) −0.330694 + 1.76894i −0.0147743 + 0.0790306i
\(502\) 30.2852 + 11.5349i 1.35170 + 0.514827i
\(503\) 9.95792 + 17.2476i 0.444002 + 0.769034i 0.997982 0.0634960i \(-0.0202250\pi\)
−0.553980 + 0.832530i \(0.686892\pi\)
\(504\) 5.01987 + 6.84112i 0.223603 + 0.304728i
\(505\) 14.2554 24.6910i 0.634356 1.09874i
\(506\) 1.18409 0.963978i 0.0526391 0.0428541i
\(507\) −22.4615 0.230874i −0.997548 0.0102535i
\(508\) −21.5156 4.45613i −0.954601 0.197709i
\(509\) −30.5016 + 5.37826i −1.35196 + 0.238387i −0.802260 0.596975i \(-0.796369\pi\)
−0.549700 + 0.835362i \(0.685258\pi\)
\(510\) 15.7153 + 28.8712i 0.695883 + 1.27844i
\(511\) 5.35534 6.38225i 0.236906 0.282334i
\(512\) −22.4258 3.01425i −0.991088 0.133212i
\(513\) 0.369378 11.9754i 0.0163084 0.528728i
\(514\) −6.06194 + 7.01031i −0.267381 + 0.309211i
\(515\) −15.1409 12.7047i −0.667187 0.559836i
\(516\) −0.694312 + 0.763304i −0.0305654 + 0.0336026i
\(517\) −5.62299 31.8895i −0.247299 1.40250i
\(518\) −1.39430 + 0.777634i −0.0612621 + 0.0341673i
\(519\) 22.0541 12.4325i 0.968067 0.545725i
\(520\) 0.738344 0.804302i 0.0323785 0.0352710i
\(521\) −10.5056 6.06544i −0.460261 0.265732i 0.251893 0.967755i \(-0.418947\pi\)
−0.712154 + 0.702023i \(0.752280\pi\)
\(522\) −31.5127 6.71455i −1.37927 0.293888i
\(523\) −18.0467 + 10.4193i −0.789128 + 0.455604i −0.839656 0.543119i \(-0.817243\pi\)
0.0505272 + 0.998723i \(0.483910\pi\)
\(524\) 5.78354 + 10.7417i 0.252655 + 0.469254i
\(525\) 0.250267 0.292106i 0.0109225 0.0127485i
\(526\) 31.3140 + 0.464905i 1.36535 + 0.0202708i
\(527\) 21.0656 17.6762i 0.917633 0.769986i
\(528\) −24.1074 10.7289i −1.04914 0.466916i
\(529\) 21.5374 7.83898i 0.936409 0.340825i
\(530\) 0.682896 3.56277i 0.0296631 0.154757i
\(531\) −9.75045 0.200464i −0.423134 0.00869941i
\(532\) 4.28470 + 1.70519i 0.185765 + 0.0739293i
\(533\) −1.95975 0.345557i −0.0848862 0.0149677i
\(534\) 3.49573 + 0.707371i 0.151275 + 0.0306109i
\(535\) −6.94538 + 19.0823i −0.300275 + 0.824998i
\(536\) 7.10724 17.1147i 0.306986 0.739241i
\(537\) 28.6661 23.5559i 1.23704 1.01651i
\(538\) 24.6514 3.97032i 1.06280 0.171173i
\(539\) −3.80865 −0.164050
\(540\) 20.3236 10.1472i 0.874589 0.436667i
\(541\) 11.3240 0.486856 0.243428 0.969919i \(-0.421728\pi\)
0.243428 + 0.969919i \(0.421728\pi\)
\(542\) 11.5872 1.86622i 0.497712 0.0801608i
\(543\) 18.3352 + 6.88768i 0.786837 + 0.295579i
\(544\) 33.6602 + 8.55042i 1.44317 + 0.366596i
\(545\) −5.40301 + 14.8446i −0.231439 + 0.635875i
\(546\) −0.286289 + 0.324280i −0.0122520 + 0.0138779i
\(547\) −9.15710 1.61464i −0.391529 0.0690372i −0.0255819 0.999673i \(-0.508144\pi\)
−0.365947 + 0.930636i \(0.619255\pi\)
\(548\) 14.8323 37.2696i 0.633603 1.59208i
\(549\) −5.66261 36.4848i −0.241674 1.55713i
\(550\) −0.225179 + 1.17479i −0.00960166 + 0.0500933i
\(551\) −16.4548 + 5.98905i −0.700997 + 0.255142i
\(552\) 1.01333 + 0.949608i 0.0431302 + 0.0404180i
\(553\) −1.27389 + 1.06892i −0.0541713 + 0.0454551i
\(554\) −8.17830 0.121420i −0.347463 0.00515863i
\(555\) 1.42043 + 4.03104i 0.0602939 + 0.171108i
\(556\) −29.8318 + 16.0620i −1.26515 + 0.681180i
\(557\) −24.7086 + 14.2655i −1.04694 + 0.604448i −0.921790 0.387690i \(-0.873273\pi\)
−0.125146 + 0.992138i \(0.539940\pi\)
\(558\) −11.6924 14.9809i −0.494978 0.634191i
\(559\) −0.0455552 0.0263013i −0.00192678 0.00111243i
\(560\) 1.00459 + 8.68548i 0.0424515 + 0.367028i
\(561\) 34.8637 + 20.6092i 1.47195 + 0.870123i
\(562\) −20.5176 + 11.4432i −0.865484 + 0.482701i
\(563\) −5.22300 29.6211i −0.220123 1.24838i −0.871792 0.489877i \(-0.837042\pi\)
0.651668 0.758504i \(-0.274069\pi\)
\(564\) 28.0564 8.95929i 1.18139 0.377254i
\(565\) −24.0903 20.2142i −1.01349 0.850416i
\(566\) 24.8968 28.7918i 1.04649 1.21021i
\(567\) −7.97260 + 4.17584i −0.334818 + 0.175369i
\(568\) 0.242498 0.379888i 0.0101750 0.0159397i
\(569\) −15.2708 + 18.1990i −0.640184 + 0.762942i −0.984399 0.175949i \(-0.943701\pi\)
0.344215 + 0.938891i \(0.388145\pi\)
\(570\) 6.43942 10.5331i 0.269718 0.441184i
\(571\) −1.38001 + 0.243333i −0.0577515 + 0.0101831i −0.202449 0.979293i \(-0.564890\pi\)
0.144698 + 0.989476i \(0.453779\pi\)
\(572\) 0.272815 1.31724i 0.0114070 0.0550764i
\(573\) −14.9854 + 25.3501i −0.626024 + 1.05902i
\(574\) 12.3584 10.0611i 0.515831 0.419944i
\(575\) 0.0314772 0.0545200i 0.00131269 0.00227364i
\(576\) 6.72849 23.0375i 0.280354 0.959897i
\(577\) −0.778077 1.34767i −0.0323918 0.0561042i 0.849375 0.527790i \(-0.176979\pi\)
−0.881767 + 0.471686i \(0.843646\pi\)
\(578\) −27.3455 10.4152i −1.13742 0.433215i
\(579\) −2.06090 + 0.726205i −0.0856479 + 0.0301800i
\(580\) −24.7880 22.0862i −1.02927 0.917081i
\(581\) 5.75314 + 6.85632i 0.238680 + 0.284448i
\(582\) 24.8015 19.7708i 1.02805 0.819526i
\(583\) −1.52866 4.19996i −0.0633106 0.173944i
\(584\) −23.5415 1.04915i −0.974154 0.0434141i
\(585\) 0.725983 + 0.902225i 0.0300157 + 0.0373024i
\(586\) 15.1960 + 43.7614i 0.627741 + 1.80777i
\(587\) 4.45061 25.2406i 0.183696 1.04179i −0.743923 0.668265i \(-0.767037\pi\)
0.927619 0.373527i \(-0.121852\pi\)
\(588\) −0.464737 3.43279i −0.0191654 0.141566i
\(589\) −9.70515 3.53238i −0.399894 0.145549i
\(590\) −8.62728 5.15322i −0.355179 0.212155i
\(591\) 13.0109 34.6354i 0.535198 1.42471i
\(592\) 4.14411 + 1.79352i 0.170322 + 0.0737131i
\(593\) 44.3021i 1.81927i 0.415410 + 0.909634i \(0.363638\pi\)
−0.415410 + 0.909634i \(0.636362\pi\)
\(594\) 15.0861 23.5738i 0.618989 0.967243i
\(595\) 13.4196i 0.550150i
\(596\) 16.5292 + 10.2091i 0.677062 + 0.418181i
\(597\) −11.3915 13.8628i −0.466223 0.567365i
\(598\) −0.0363047 + 0.0607796i −0.00148461 + 0.00248546i
\(599\) −21.2864 7.74763i −0.869740 0.316559i −0.131678 0.991293i \(-0.542037\pi\)
−0.738062 + 0.674733i \(0.764259\pi\)
\(600\) −1.08633 0.0596068i −0.0443494 0.00243344i
\(601\) −0.527176 + 2.98977i −0.0215040 + 0.121955i −0.993670 0.112337i \(-0.964166\pi\)
0.972166 + 0.234293i \(0.0752774\pi\)
\(602\) 0.397939 0.138183i 0.0162188 0.00563193i
\(603\) 16.8169 + 10.1757i 0.684835 + 0.414388i
\(604\) 27.2088 + 34.4538i 1.10711 + 1.40190i
\(605\) −2.62093 7.20096i −0.106556 0.292761i
\(606\) 31.5936 4.75582i 1.28340 0.193192i
\(607\) 18.2084 + 21.7000i 0.739058 + 0.880775i 0.996333 0.0855633i \(-0.0272690\pi\)
−0.257275 + 0.966338i \(0.582825\pi\)
\(608\) −3.53987 12.5539i −0.143561 0.509127i
\(609\) 9.98896 + 8.55822i 0.404773 + 0.346796i
\(610\) 13.5413 35.5532i 0.548272 1.43951i
\(611\) 0.750723 + 1.30029i 0.0303710 + 0.0526041i
\(612\) −14.3213 + 33.9379i −0.578903 + 1.37186i
\(613\) −9.79418 + 16.9640i −0.395583 + 0.685170i −0.993175 0.116630i \(-0.962791\pi\)
0.597592 + 0.801800i \(0.296124\pi\)
\(614\) 23.5600 + 28.9395i 0.950804 + 1.16790i
\(615\) −20.9504 37.1641i −0.844800 1.49860i
\(616\) 6.55015 + 8.55230i 0.263913 + 0.344582i
\(617\) −10.1893 + 1.79665i −0.410207 + 0.0723305i −0.374944 0.927048i \(-0.622338\pi\)
−0.0352630 + 0.999378i \(0.511227\pi\)
\(618\) 0.556407 22.1420i 0.0223820 0.890681i
\(619\) 6.67445 7.95429i 0.268269 0.319710i −0.615046 0.788492i \(-0.710862\pi\)
0.883314 + 0.468781i \(0.155307\pi\)
\(620\) −2.82634 19.3766i −0.113509 0.778184i
\(621\) −1.15702 + 0.911576i −0.0464297 + 0.0365803i
\(622\) −34.0222 29.4196i −1.36417 1.17962i
\(623\) −1.11540 0.935932i −0.0446876 0.0374973i
\(624\) 1.22053 + 0.0851604i 0.0488604 + 0.00340915i
\(625\) −4.13982 23.4781i −0.165593 0.939124i
\(626\) −7.48416 13.4191i −0.299127 0.536336i
\(627\) 0.156336 15.2098i 0.00624348 0.607422i
\(628\) −19.0494 0.565760i −0.760152 0.0225763i
\(629\) −6.00209 3.46531i −0.239319 0.138171i
\(630\) −9.26795 0.328242i −0.369244 0.0130775i
\(631\) 13.6242 7.86596i 0.542372 0.313139i −0.203668 0.979040i \(-0.565286\pi\)
0.746040 + 0.665901i \(0.231953\pi\)
\(632\) 4.59110 + 1.02217i 0.182624 + 0.0406599i
\(633\) 14.0427 + 2.62521i 0.558149 + 0.104343i
\(634\) −0.428710 + 28.8760i −0.0170262 + 1.14681i
\(635\) 18.3958 15.4359i 0.730013 0.612554i
\(636\) 3.59895 1.89029i 0.142708 0.0749548i
\(637\) 0.165947 0.0603998i 0.00657506 0.00239313i
\(638\) −40.1736 7.70030i −1.59049 0.304858i
\(639\) 0.359797 + 0.314732i 0.0142333 + 0.0124506i
\(640\) 17.7755 17.1932i 0.702639 0.679619i
\(641\) 30.4646 + 5.37173i 1.20328 + 0.212171i 0.739115 0.673579i \(-0.235244\pi\)
0.464164 + 0.885750i \(0.346355\pi\)
\(642\) −21.5726 + 7.24345i −0.851404 + 0.285876i
\(643\) −16.3309 + 44.8688i −0.644028 + 1.76945i −0.00534211 + 0.999986i \(0.501700\pi\)
−0.638686 + 0.769467i \(0.720522\pi\)
\(644\) −0.178007 0.538281i −0.00701446 0.0212112i
\(645\) −0.184402 1.11255i −0.00726084 0.0438065i
\(646\) 3.18328 + 19.7647i 0.125244 + 0.777631i
\(647\) −1.37617 −0.0541026 −0.0270513 0.999634i \(-0.508612\pi\)
−0.0270513 + 0.999634i \(0.508612\pi\)
\(648\) 23.0882 + 10.7208i 0.906990 + 0.421152i
\(649\) −12.3813 −0.486008
\(650\) −0.00881927 0.0547581i −0.000345920 0.00214779i
\(651\) 1.26860 + 7.65378i 0.0497203 + 0.299975i
\(652\) −8.00680 24.2120i −0.313571 0.948215i
\(653\) −5.32442 + 14.6287i −0.208361 + 0.572467i −0.999218 0.0395339i \(-0.987413\pi\)
0.790857 + 0.612000i \(0.209635\pi\)
\(654\) −16.7820 + 5.63488i −0.656227 + 0.220341i
\(655\) −13.1308 2.31532i −0.513063 0.0904669i
\(656\) −43.8464 10.4476i −1.71192 0.407910i
\(657\) 4.84526 24.5202i 0.189031 0.956623i
\(658\) −11.8088 2.26346i −0.460356 0.0882388i
\(659\) 13.4743 4.90425i 0.524885 0.191043i −0.0659679 0.997822i \(-0.521013\pi\)
0.590853 + 0.806779i \(0.298791\pi\)
\(660\) 25.5316 13.4100i 0.993815 0.521984i
\(661\) −25.7146 + 21.5771i −1.00018 + 0.839252i −0.987010 0.160661i \(-0.948637\pi\)
−0.0131721 + 0.999913i \(0.504193\pi\)
\(662\) −0.242846 + 16.3570i −0.00943847 + 0.635734i
\(663\) −1.84589 0.345078i −0.0716883 0.0134017i
\(664\) 5.50154 24.7102i 0.213501 0.958942i
\(665\) −4.36482 + 2.52003i −0.169260 + 0.0977225i
\(666\) −2.54005 + 4.06045i −0.0984250 + 0.157339i
\(667\) 1.86439 + 1.07640i 0.0721894 + 0.0416785i
\(668\) −2.07707 0.0616884i −0.0803643 0.00238680i
\(669\) −0.129380 + 12.5873i −0.00500213 + 0.486652i
\(670\) 9.86536 + 17.6886i 0.381132 + 0.683372i
\(671\) −8.13954 46.1616i −0.314223 1.78205i
\(672\) −6.90905 + 6.94730i −0.266522 + 0.267998i
\(673\) −9.43320 7.91539i −0.363623 0.305116i 0.442610 0.896714i \(-0.354053\pi\)
−0.806233 + 0.591598i \(0.798497\pi\)
\(674\) 18.9063 + 16.3486i 0.728242 + 0.629725i
\(675\) 0.235325 1.12972i 0.00905766 0.0434828i
\(676\) −3.74373 25.6660i −0.143990 0.987155i
\(677\) −5.46389 + 6.51161i −0.209994 + 0.250262i −0.860753 0.509023i \(-0.830007\pi\)
0.650758 + 0.759285i \(0.274451\pi\)
\(678\) 0.885286 35.2296i 0.0339992 1.35298i
\(679\) −12.7519 + 2.24850i −0.489373 + 0.0862896i
\(680\) −30.1336 + 23.0791i −1.15557 + 0.885045i
\(681\) 12.9219 + 22.9224i 0.495170 + 0.878388i
\(682\) −15.2319 18.7098i −0.583258 0.716435i
\(683\) −23.3781 + 40.4920i −0.894536 + 1.54938i −0.0601592 + 0.998189i \(0.519161\pi\)
−0.834377 + 0.551194i \(0.814172\pi\)
\(684\) 13.7279 1.71502i 0.524900 0.0655753i
\(685\) 21.9200 + 37.9665i 0.837520 + 1.45063i
\(686\) −0.503364 + 1.32160i −0.0192185 + 0.0504589i
\(687\) −16.4215 14.0694i −0.626520 0.536783i
\(688\) −0.994670 0.655922i −0.0379214 0.0250068i
\(689\) 0.133211 + 0.158754i 0.00507493 + 0.00604806i
\(690\) −1.50087 + 0.225928i −0.0571373 + 0.00860093i
\(691\) −0.243635 0.669382i −0.00926832 0.0254645i 0.934972 0.354721i \(-0.115424\pi\)
−0.944241 + 0.329257i \(0.893202\pi\)
\(692\) 18.1179 + 22.9422i 0.688738 + 0.872130i
\(693\) −10.0105 + 5.50837i −0.380267 + 0.209246i
\(694\) 27.5323 9.56053i 1.04511 0.362913i
\(695\) 6.43008 36.4668i 0.243907 1.38326i
\(696\) 2.03834 37.1487i 0.0772630 1.40812i
\(697\) 65.0087 + 23.6612i 2.46238 + 0.896233i
\(698\) 1.24666 2.08709i 0.0471866 0.0789976i
\(699\) 22.6467 + 27.5597i 0.856577 + 1.04240i
\(700\) 0.377892 + 0.233402i 0.0142830 + 0.00882176i
\(701\) 28.6244i 1.08113i 0.841302 + 0.540565i \(0.181789\pi\)
−0.841302 + 0.540565i \(0.818211\pi\)
\(702\) −0.283471 + 1.26638i −0.0106989 + 0.0477964i
\(703\) 2.60296i 0.0981726i
\(704\) 7.93915 29.4167i 0.299218 1.10868i
\(705\) −11.3196 + 30.1329i −0.426319 + 1.13487i
\(706\) 34.0926 + 20.3641i 1.28309 + 0.766413i
\(707\) −12.2567 4.46109i −0.460962 0.167777i
\(708\) −1.51078 11.1594i −0.0567787 0.419397i
\(709\) 5.55408 31.4987i 0.208588 1.18296i −0.683106 0.730320i \(-0.739371\pi\)
0.891693 0.452640i \(-0.149518\pi\)
\(710\) 0.161578 + 0.465312i 0.00606392 + 0.0174628i
\(711\) −1.80228 + 4.65190i −0.0675908 + 0.174460i
\(712\) −0.183356 + 4.11425i −0.00687154 + 0.154188i
\(713\) 0.434277 + 1.19317i 0.0162638 + 0.0446845i
\(714\) 11.7591 9.37392i 0.440074 0.350810i
\(715\) 0.945020 + 1.12623i 0.0353417 + 0.0421186i
\(716\) 31.9875 + 28.5010i 1.19543 + 1.06513i
\(717\) −36.3416 + 12.8058i −1.35720 + 0.478241i
\(718\) 32.9403 + 12.5461i 1.22932 + 0.468217i
\(719\) 1.01481 + 1.75770i 0.0378459 + 0.0655511i 0.884328 0.466866i \(-0.154617\pi\)
−0.846482 + 0.532417i \(0.821284\pi\)
\(720\) 15.2020 + 21.3757i 0.566547 + 0.796623i
\(721\) −4.52114 + 7.83084i −0.168376 + 0.291636i
\(722\) −15.0070 + 12.2173i −0.558501 + 0.454682i
\(723\) −14.1701 + 23.9709i −0.526991 + 0.891488i
\(724\) −4.58672 + 22.1462i −0.170464 + 0.823056i
\(725\) −1.66093 + 0.292868i −0.0616856 + 0.0108768i
\(726\) 4.47916 7.32668i 0.166237 0.271919i
\(727\) 5.01434 5.97585i 0.185971 0.221632i −0.665001 0.746842i \(-0.731569\pi\)
0.850972 + 0.525210i \(0.176013\pi\)
\(728\) −0.421025 0.268757i −0.0156042 0.00996081i
\(729\) −14.9154 + 22.5062i −0.552423 + 0.833564i
\(730\) 16.8458 19.4812i 0.623490 0.721032i
\(731\) 1.40087 + 1.17547i 0.0518130 + 0.0434763i
\(732\) 40.6129 12.9690i 1.50110 0.479348i
\(733\) 3.16145 + 17.9294i 0.116771 + 0.662239i 0.985858 + 0.167581i \(0.0535956\pi\)
−0.869088 + 0.494658i \(0.835293\pi\)
\(734\) 18.0817 10.0846i 0.667407 0.372228i
\(735\) 3.25914 + 1.92660i 0.120215 + 0.0710636i
\(736\) −0.902569 + 1.32545i −0.0332691 + 0.0488569i
\(737\) 21.6108 + 12.4770i 0.796046 + 0.459597i
\(738\) 17.9312 44.3181i 0.660057 1.63137i
\(739\) 16.3268 9.42626i 0.600590 0.346751i −0.168684 0.985670i \(-0.553952\pi\)
0.769274 + 0.638920i \(0.220618\pi\)
\(740\) −4.34535 + 2.33961i −0.159738 + 0.0860060i
\(741\) 0.234395 + 0.665188i 0.00861070 + 0.0244363i
\(742\) −1.65942 0.0246367i −0.0609191 0.000904441i
\(743\) −7.18364 + 6.02779i −0.263542 + 0.221138i −0.764978 0.644057i \(-0.777250\pi\)
0.501435 + 0.865195i \(0.332806\pi\)
\(744\) 15.0048 16.0117i 0.550102 0.587017i
\(745\) −19.9526 + 7.26215i −0.731006 + 0.266064i
\(746\) −1.38592 + 7.23053i −0.0507420 + 0.264729i
\(747\) 25.0375 + 9.70024i 0.916073 + 0.354913i
\(748\) −17.2921 + 43.4505i −0.632261 + 1.58871i
\(749\) 9.14906 + 1.61323i 0.334299 + 0.0589460i
\(750\) 18.5048 20.9604i 0.675699 0.765367i
\(751\) 10.8232 29.7365i 0.394944 1.08510i −0.569771 0.821804i \(-0.692968\pi\)
0.964715 0.263297i \(-0.0848099\pi\)
\(752\) 15.2263 + 30.4094i 0.555247 + 1.10892i
\(753\) −37.1558 13.9577i −1.35403 0.508649i
\(754\) 1.87253 0.301587i 0.0681934 0.0109831i
\(755\) −47.9814 −1.74622
\(756\) −6.18626 8.35046i −0.224992 0.303703i
\(757\) 20.0872 0.730083 0.365041 0.930991i \(-0.381055\pi\)
0.365041 + 0.930991i \(0.381055\pi\)
\(758\) −51.7027 + 8.32717i −1.87793 + 0.302456i
\(759\) −1.44480 + 1.18724i −0.0524428 + 0.0430940i
\(760\) 13.1654 + 5.46721i 0.477558 + 0.198317i
\(761\) 9.48243 26.0528i 0.343738 0.944412i −0.640562 0.767907i \(-0.721298\pi\)
0.984300 0.176505i \(-0.0564793\pi\)
\(762\) 26.3758 + 5.33721i 0.955494 + 0.193347i
\(763\) 7.11731 + 1.25497i 0.257664 + 0.0454331i
\(764\) −31.5937 12.5734i −1.14302 0.454890i
\(765\) −19.4085 35.2715i −0.701715 1.27524i
\(766\) 6.68211 34.8616i 0.241434 1.25960i
\(767\) 0.539467 0.196350i 0.0194790 0.00708978i
\(768\) 27.4824 + 3.56621i 0.991686 + 0.128684i
\(769\) −20.8017 + 17.4547i −0.750130 + 0.629434i −0.935537 0.353228i \(-0.885084\pi\)
0.185407 + 0.982662i \(0.440640\pi\)
\(770\) −11.7722 0.174777i −0.424240 0.00629851i
\(771\) 7.38504 8.61965i 0.265966 0.310429i
\(772\) −1.19614 2.22159i −0.0430502 0.0799568i
\(773\) −6.38872 + 3.68853i −0.229786 + 0.132667i −0.610473 0.792037i \(-0.709021\pi\)
0.380687 + 0.924704i \(0.375687\pi\)
\(774\) 0.846076 0.938727i 0.0304116 0.0337418i
\(775\) −0.861473 0.497372i −0.0309450 0.0178661i
\(776\) 26.9798 + 24.7673i 0.968519 + 0.889095i
\(777\) 1.70330 0.960193i 0.0611054 0.0344467i
\(778\) 13.3730 7.45846i 0.479447 0.267399i
\(779\) −4.51182 25.5878i −0.161653 0.916778i
\(780\) −0.899775 + 0.989184i −0.0322171 + 0.0354185i
\(781\) 0.464896 + 0.390094i 0.0166353 + 0.0139587i
\(782\) 1.60985 1.86171i 0.0575683 0.0665746i
\(783\) 38.6322 + 8.04725i 1.38060 + 0.287585i
\(784\) 3.83334 1.14260i 0.136905 0.0408070i
\(785\) 13.3884 15.9557i 0.477852 0.569482i
\(786\) −7.14337 13.1234i −0.254796 0.468095i
\(787\) −18.6334 + 3.28558i −0.664210 + 0.117118i −0.495582 0.868561i \(-0.665045\pi\)
−0.168629 + 0.985680i \(0.553934\pi\)
\(788\) 41.8344 + 8.66438i 1.49029 + 0.308656i
\(789\) −38.3538 0.394226i −1.36543 0.0140348i
\(790\) −3.98653 + 3.24548i −0.141834 + 0.115469i
\(791\) −7.19347 + 12.4595i −0.255770 + 0.443007i
\(792\) 29.5852 + 13.0052i 1.05126 + 0.462119i
\(793\) 1.08671 + 1.88223i 0.0385901 + 0.0668400i
\(794\) −2.59910 0.989931i −0.0922385 0.0351313i
\(795\) −0.816435 + 4.36726i −0.0289560 + 0.154891i
\(796\) 13.7829 15.4689i 0.488522 0.548282i
\(797\) 14.5117 + 17.2943i 0.514030 + 0.612597i 0.959158 0.282870i \(-0.0912865\pi\)
−0.445129 + 0.895467i \(0.646842\pi\)
\(798\) −5.25714 2.06443i −0.186101 0.0730801i
\(799\) −17.8525 49.0492i −0.631574 1.73524i
\(800\) −0.125800 1.24996i −0.00444771 0.0441929i
\(801\) −4.28529 0.846786i −0.151413 0.0299197i
\(802\) −17.3391 49.9331i −0.612266 1.76320i
\(803\) 5.51012 31.2494i 0.194448 1.10277i
\(804\) −8.60873 + 21.0006i −0.303607 + 0.740635i
\(805\) 0.582264 + 0.211927i 0.0205221 + 0.00746944i
\(806\) 0.960380 + 0.573651i 0.0338279 + 0.0202060i
\(807\) −30.1691 + 5.00047i −1.06200 + 0.176025i
\(808\) 11.0619 + 35.1947i 0.389156 + 1.23814i
\(809\) 21.5151i 0.756431i −0.925718 0.378215i \(-0.876538\pi\)
0.925718 0.378215i \(-0.123462\pi\)
\(810\) −24.8342 + 12.5413i −0.872586 + 0.440656i
\(811\) 31.6085i 1.10992i −0.831876 0.554962i \(-0.812733\pi\)
0.831876 0.554962i \(-0.187267\pi\)
\(812\) −7.98149 + 12.9225i −0.280095 + 0.453493i
\(813\) −14.1807 + 2.35043i −0.497340 + 0.0824331i
\(814\) −3.11808 + 5.22014i −0.109289 + 0.182966i
\(815\) 26.1904 + 9.53252i 0.917409 + 0.333910i
\(816\) −41.2725 10.2837i −1.44483 0.360001i
\(817\) 0.119264 0.676380i 0.00417252 0.0236635i
\(818\) 30.2814 10.5151i 1.05876 0.367653i
\(819\) 0.348813 0.398758i 0.0121885 0.0139337i
\(820\) 38.6606 30.5310i 1.35008 1.06619i
\(821\) −12.7115 34.9245i −0.443633 1.21887i −0.937086 0.349100i \(-0.886487\pi\)
0.493452 0.869773i \(-0.335735\pi\)
\(822\) −17.9571 + 45.7283i −0.626325 + 1.59496i
\(823\) −11.1923 13.3385i −0.390141 0.464952i 0.534847 0.844949i \(-0.320369\pi\)
−0.924988 + 0.379997i \(0.875925\pi\)
\(824\) 25.3596 3.31536i 0.883445 0.115496i
\(825\) 0.269212 1.44007i 0.00937277 0.0501367i
\(826\) −1.63635 + 4.29630i −0.0569361 + 0.149488i
\(827\) 4.33266 + 7.50438i 0.150661 + 0.260953i 0.931471 0.363816i \(-0.118526\pi\)
−0.780809 + 0.624769i \(0.785193\pi\)
\(828\) −1.24637 1.15735i −0.0433144 0.0402206i
\(829\) 9.71584 16.8283i 0.337445 0.584472i −0.646506 0.762909i \(-0.723771\pi\)
0.983951 + 0.178437i \(0.0571040\pi\)
\(830\) 17.4678 + 21.4563i 0.606316 + 0.744759i
\(831\) 10.0169 + 0.102960i 0.347483 + 0.00357165i
\(832\) 0.120589 + 1.40762i 0.00418067 + 0.0488005i
\(833\) −6.04605 + 1.06608i −0.209483 + 0.0369375i
\(834\) 36.4461 19.8385i 1.26203 0.686951i
\(835\) 1.45982 1.73975i 0.0505192 0.0602064i
\(836\) 17.3798 2.53508i 0.601093 0.0876775i
\(837\) 14.4038 + 18.2821i 0.497869 + 0.631923i
\(838\) 11.4164 + 9.87201i 0.394374 + 0.341023i
\(839\) −21.3896 17.9480i −0.738450 0.619633i 0.193971 0.981007i \(-0.437863\pi\)
−0.932421 + 0.361374i \(0.882308\pi\)
\(840\) −1.27893 10.6318i −0.0441273 0.366831i
\(841\) −4.97921 28.2385i −0.171697 0.973741i
\(842\) 13.6336 + 24.4451i 0.469844 + 0.842432i
\(843\) 25.0646 14.1296i 0.863271 0.486648i
\(844\) −0.489713 + 16.4888i −0.0168566 + 0.567568i
\(845\) 24.5499 + 14.1739i 0.844543 + 0.487597i
\(846\) −34.3114 + 11.1297i −1.17965 + 0.382646i
\(847\) −3.03610 + 1.75289i −0.104322 + 0.0602301i
\(848\) 2.79856 + 3.76859i 0.0961030 + 0.129414i
\(849\) −30.3309 + 35.4015i −1.04095 + 1.21498i
\(850\) −0.0286236 + 1.92796i −0.000981781 + 0.0661284i
\(851\) 0.245144 0.205700i 0.00840343 0.00705131i
\(852\) −0.294870 + 0.466617i −0.0101021 + 0.0159860i
\(853\) 2.49711 0.908875i 0.0854995 0.0311193i −0.298916 0.954279i \(-0.596625\pi\)
0.384416 + 0.923160i \(0.374403\pi\)
\(854\) −17.0938 3.27646i −0.584939 0.112118i
\(855\) −7.82764 + 12.9363i −0.267700 + 0.442412i
\(856\) −12.1121 23.3186i −0.413985 0.797014i
\(857\) 43.4043 + 7.65335i 1.48266 + 0.261434i 0.855642 0.517569i \(-0.173163\pi\)
0.627021 + 0.779002i \(0.284274\pi\)
\(858\) −0.326757 + 1.61479i −0.0111553 + 0.0551279i
\(859\) 13.5716 37.2876i 0.463056 1.27224i −0.460119 0.887857i \(-0.652193\pi\)
0.923175 0.384379i \(-0.125584\pi\)
\(860\) 1.23634 0.408851i 0.0421587 0.0139417i
\(861\) −15.0795 + 12.3913i −0.513908 + 0.422296i
\(862\) −1.98579 12.3296i −0.0676362 0.419947i
\(863\) 49.8265 1.69611 0.848057 0.529904i \(-0.177772\pi\)
0.848057 + 0.529904i \(0.177772\pi\)
\(864\) −8.11173 + 28.2524i −0.275967 + 0.961167i
\(865\) −31.9500 −1.08633
\(866\) −2.89980 18.0046i −0.0985391 0.611821i
\(867\) 33.5491 + 12.6029i 1.13939 + 0.428016i
\(868\) −8.50539 + 2.81270i −0.288692 + 0.0954691i
\(869\) −2.16621 + 5.95160i −0.0734835 + 0.201894i
\(870\) 30.4823 + 26.9111i 1.03345 + 0.912371i
\(871\) −1.13948 0.200921i −0.0386097 0.00680793i
\(872\) −9.42238 18.1402i −0.319082 0.614305i
\(873\) −30.2646 + 24.3527i −1.02430 + 0.824213i
\(874\) −0.907844 0.174011i −0.0307083 0.00588602i
\(875\) −10.7263 + 3.90404i −0.362614 + 0.131981i
\(876\) 28.8379 + 1.15324i 0.974342 + 0.0389645i
\(877\) −23.3679 + 19.6080i −0.789078 + 0.662115i −0.945517 0.325572i \(-0.894443\pi\)
0.156439 + 0.987688i \(0.449999\pi\)
\(878\) 0.419502 28.2558i 0.0141575 0.953588i
\(879\) −18.8558 53.5109i −0.635991 1.80488i
\(880\) 19.8535 + 26.7350i 0.669260 + 0.901236i
\(881\) 24.4412 14.1111i 0.823446 0.475417i −0.0281576 0.999603i \(-0.508964\pi\)
0.851603 + 0.524187i \(0.175631\pi\)
\(882\) 0.588380 + 4.20164i 0.0198118 + 0.141477i
\(883\) −0.679809 0.392488i −0.0228774 0.0132083i 0.488518 0.872554i \(-0.337538\pi\)
−0.511395 + 0.859346i \(0.670871\pi\)
\(884\) 0.0643716 2.16741i 0.00216505 0.0728980i
\(885\) 10.5949 + 6.26305i 0.356145 + 0.210530i
\(886\) 3.41981 + 6.13174i 0.114891 + 0.206000i
\(887\) 5.70903 + 32.3775i 0.191690 + 1.08713i 0.917054 + 0.398764i \(0.130561\pi\)
−0.725363 + 0.688366i \(0.758328\pi\)
\(888\) −5.08546 2.17340i −0.170657 0.0729344i
\(889\) −8.41585 7.06174i −0.282259 0.236843i
\(890\) −3.40466 2.94407i −0.114124 0.0986854i
\(891\) −18.3445 + 28.9559i −0.614565 + 0.970060i
\(892\) −14.3831 + 2.09797i −0.481582 + 0.0702451i
\(893\) −12.6011 + 15.0174i −0.421681 + 0.502540i
\(894\) −20.3009 12.4110i −0.678965 0.415085i
\(895\) −46.1125 + 8.13088i −1.54137 + 0.271785i
\(896\) −9.15831 6.64269i −0.305958 0.221917i
\(897\) 0.0441235 0.0746418i 0.00147324 0.00249222i
\(898\) −1.71112 2.10182i −0.0571007 0.0701387i
\(899\) 17.0083 29.4592i 0.567259 0.982521i
\(900\) 1.33080 + 0.0669259i 0.0443601 + 0.00223086i
\(901\) −3.60229 6.23935i −0.120010 0.207863i
\(902\) 21.6032 56.7200i 0.719309 1.88857i
\(903\) −0.486596 + 0.171463i −0.0161929 + 0.00570595i
\(904\) 40.3491 5.27498i 1.34199 0.175443i
\(905\) −15.8882 18.9349i −0.528143 0.629416i
\(906\) −33.5162 42.0444i −1.11350 1.39683i
\(907\) 2.67176 + 7.34061i 0.0887145 + 0.243741i 0.976114 0.217261i \(-0.0697123\pi\)
−0.887399 + 0.461002i \(0.847490\pi\)
\(908\) −23.8454 + 18.8312i −0.791337 + 0.624935i
\(909\) −38.6671 + 6.00132i −1.28251 + 0.199051i
\(910\) 0.515699 0.179075i 0.0170953 0.00593628i
\(911\) −5.16034 + 29.2657i −0.170970 + 0.969617i 0.771724 + 0.635958i \(0.219395\pi\)
−0.942694 + 0.333660i \(0.891716\pi\)
\(912\) 4.40561 + 15.3553i 0.145884 + 0.508466i
\(913\) 32.0327 + 11.6590i 1.06013 + 0.385855i
\(914\) −28.1860 + 47.1877i −0.932309 + 1.56083i
\(915\) −16.3856 + 43.6188i −0.541691 + 1.44199i
\(916\) 13.1213 21.2443i 0.433541 0.701930i
\(917\) 6.09987i 0.201436i
\(918\) 17.3499 41.6450i 0.572632 1.37449i
\(919\) 32.7521i 1.08039i 0.841539 + 0.540196i \(0.181650\pi\)
−0.841539 + 0.540196i \(0.818350\pi\)
\(920\) −0.525503 1.67195i −0.0173253 0.0551224i
\(921\) −29.0166 35.3114i −0.956128 1.16355i
\(922\) 13.9742 + 8.34704i 0.460216 + 0.274895i
\(923\) −0.0264424 0.00962424i −0.000870362 0.000316786i
\(924\) −8.07001 10.4376i −0.265484 0.343373i
\(925\) −0.0435344 + 0.246896i −0.00143140 + 0.00811789i
\(926\) 17.4871 + 50.3592i 0.574662 + 1.65491i
\(927\) −0.557596 + 27.1211i −0.0183138 + 0.890774i
\(928\) 42.7442 4.30191i 1.40315 0.141217i
\(929\) 3.94064 + 10.8268i 0.129288 + 0.355216i 0.987399 0.158247i \(-0.0505844\pi\)
−0.858111 + 0.513464i \(0.828362\pi\)
\(930\) 3.56990 + 23.7154i 0.117062 + 0.777658i
\(931\) 1.48212 + 1.76632i 0.0485745 + 0.0578889i
\(932\) −27.4009 + 30.7528i −0.897546 + 1.00734i
\(933\) 41.8326 + 35.8408i 1.36954 + 1.17338i
\(934\) 17.0468 + 6.49271i 0.557790 + 0.212448i
\(935\) −25.5552 44.2630i −0.835746 1.44755i
\(936\) −1.49530 0.0974715i −0.0488755 0.00318596i
\(937\) 2.11278 3.65945i 0.0690217 0.119549i −0.829449 0.558582i \(-0.811346\pi\)
0.898471 + 0.439033i \(0.144679\pi\)
\(938\) 7.18569 5.84995i 0.234621 0.191008i
\(939\) 9.24115 + 16.3930i 0.301573 + 0.534964i
\(940\) −36.3961 7.53805i −1.18711 0.245864i
\(941\) 51.3277 9.05046i 1.67323 0.295036i 0.745009 0.667054i \(-0.232445\pi\)
0.928226 + 0.372018i \(0.121334\pi\)
\(942\) 23.3335 + 0.586349i 0.760247 + 0.0191043i
\(943\) −2.05328 + 2.44700i −0.0668640 + 0.0796854i
\(944\) 12.4616 3.71440i 0.405589 0.120893i
\(945\) 11.3526 + 0.350167i 0.369300 + 0.0113909i
\(946\) 1.04941 1.21359i 0.0341193 0.0394571i
\(947\) −15.4993 13.0054i −0.503659 0.422620i 0.355232 0.934778i \(-0.384402\pi\)
−0.858891 + 0.512158i \(0.828846\pi\)
\(948\) −5.62859 1.22621i −0.182808 0.0398254i
\(949\) 0.255490 + 1.44895i 0.00829355 + 0.0470351i
\(950\) 0.632457 0.352736i 0.0205196 0.0114443i
\(951\) 0.363533 35.3677i 0.0117884 1.14688i
\(952\) 12.7919 + 11.7429i 0.414589 + 0.380590i
\(953\) −6.76936 3.90829i −0.219281 0.126602i 0.386336 0.922358i \(-0.373740\pi\)
−0.605617 + 0.795756i \(0.707074\pi\)
\(954\) −4.39718 + 2.33523i −0.142364 + 0.0756058i
\(955\) 32.1845 18.5817i 1.04147 0.601291i
\(956\) −21.0927 39.1752i −0.682185 1.26702i
\(957\) 49.2450 + 9.20608i 1.59187 + 0.297590i
\(958\) −36.4165 0.540660i −1.17656 0.0174679i
\(959\) 15.3640 12.8919i 0.496130 0.416303i
\(960\) −21.6741 + 21.1564i −0.699528 + 0.682821i
\(961\) −10.2772 + 3.74060i −0.331523 + 0.120664i
\(962\) 0.0530740 0.276896i 0.00171118 0.00892747i
\(963\) 26.3802 8.99195i 0.850090 0.289762i
\(964\) −29.8748 11.8893i −0.962203 0.382930i
\(965\) 2.71570 + 0.478851i 0.0874215 + 0.0154148i
\(966\) 0.221022 + 0.658254i 0.00711127 + 0.0211790i
\(967\) −12.7589 + 35.0547i −0.410297 + 1.12728i 0.546736 + 0.837305i \(0.315870\pi\)
−0.957034 + 0.289977i \(0.906352\pi\)
\(968\) 9.15762 + 3.80290i 0.294337 + 0.122230i
\(969\) −4.00922 24.1886i −0.128795 0.777051i
\(970\) −39.5181 + 6.36474i −1.26885 + 0.204360i
\(971\) 50.9231 1.63420 0.817100 0.576496i \(-0.195580\pi\)
0.817100 + 0.576496i \(0.195580\pi\)
\(972\) −28.3368 13.0009i −0.908904 0.417006i
\(973\) −16.9405 −0.543088
\(974\) 55.9871 9.01722i 1.79394 0.288930i
\(975\) 0.0111075 + 0.0670146i 0.000355726 + 0.00214619i
\(976\) 22.0408 + 44.0190i 0.705510 + 1.40901i
\(977\) 16.2384 44.6146i 0.519512 1.42735i −0.351548 0.936170i \(-0.614345\pi\)
0.871060 0.491177i \(-0.163433\pi\)
\(978\) 9.94162 + 29.6084i 0.317898 + 0.946773i
\(979\) −5.46134 0.962981i −0.174545 0.0307770i
\(980\) −1.61650 + 4.06185i −0.0516372 + 0.129751i
\(981\) 20.5219 6.99510i 0.655214 0.223336i
\(982\) 0.0426551 0.222538i 0.00136118 0.00710148i
\(983\) 27.9118 10.1591i 0.890247 0.324024i 0.143910 0.989591i \(-0.454033\pi\)
0.746338 + 0.665567i \(0.231810\pi\)
\(984\) 53.7586 + 12.5502i 1.71376 + 0.400087i
\(985\) −35.7682 + 30.0131i −1.13967 + 0.956297i
\(986\) −65.9292 0.978823i −2.09961 0.0311721i
\(987\) 14.4753 + 2.70608i 0.460754 + 0.0861354i
\(988\) −0.717055 + 0.386075i −0.0228126 + 0.0122827i
\(989\) −0.0731255 + 0.0422190i −0.00232526 + 0.00134249i
\(990\) −31.1943 + 16.5665i −0.991421 + 0.526518i
\(991\) −47.8654 27.6351i −1.52050 0.877858i −0.999708 0.0241722i \(-0.992305\pi\)
−0.520788 0.853686i \(-0.674362\pi\)
\(992\) 20.9436 + 14.2615i 0.664958 + 0.452804i
\(993\) 0.205926 20.0343i 0.00653486 0.635770i
\(994\) 0.196805 0.109763i 0.00624227 0.00348146i
\(995\) 3.93204 + 22.2997i 0.124654 + 0.706949i
\(996\) −6.59970 + 30.2942i −0.209119 + 0.959907i
\(997\) −11.8448 9.93898i −0.375129 0.314771i 0.435658 0.900112i \(-0.356516\pi\)
−0.810787 + 0.585342i \(0.800960\pi\)
\(998\) −23.8998 + 27.6388i −0.756534 + 0.874890i
\(999\) 3.08817 4.98717i 0.0977053 0.157787i
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 756.2.cf.a.659.48 yes 648
4.3 odd 2 inner 756.2.cf.a.659.108 yes 648
27.5 odd 18 inner 756.2.cf.a.491.108 yes 648
108.59 even 18 inner 756.2.cf.a.491.48 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.cf.a.491.48 648 108.59 even 18 inner
756.2.cf.a.491.108 yes 648 27.5 odd 18 inner
756.2.cf.a.659.48 yes 648 1.1 even 1 trivial
756.2.cf.a.659.108 yes 648 4.3 odd 2 inner