Properties

Label 490.2.w.a.243.13
Level $490$
Weight $2$
Character 490.243
Analytic conductor $3.913$
Analytic rank $0$
Dimension $672$
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] = [490,2,Mod(3,490)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(490, base_ring=CyclotomicField(84))
 
chi = DirichletCharacter(H, H._module([63, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("490.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.w (of order \(84\), degree \(24\), 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: \(3.91266969904\)
Analytic rank: \(0\)
Dimension: \(672\)
Relative dimension: \(28\) over \(\Q(\zeta_{84})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label 243.13
Character \(\chi\) \(=\) 490.243
Dual form 490.2.w.a.367.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.884115 + 0.467269i) q^{2} +(1.04098 + 2.38595i) q^{3} +(0.563320 - 0.826239i) q^{4} +(-1.44716 + 1.70462i) q^{5} +(-2.03522 - 1.62304i) q^{6} +(-2.46540 - 0.960107i) q^{7} +(-0.111964 + 0.993712i) q^{8} +(-2.56858 + 2.76828i) q^{9} +O(q^{10})\) \(q+(-0.884115 + 0.467269i) q^{2} +(1.04098 + 2.38595i) q^{3} +(0.563320 - 0.826239i) q^{4} +(-1.44716 + 1.70462i) q^{5} +(-2.03522 - 1.62304i) q^{6} +(-2.46540 - 0.960107i) q^{7} +(-0.111964 + 0.993712i) q^{8} +(-2.56858 + 2.76828i) q^{9} +(0.482937 - 2.18329i) q^{10} +(0.342886 - 0.318152i) q^{11} +(2.55776 + 0.483955i) q^{12} +(-3.39432 - 2.13279i) q^{13} +(2.62833 - 0.303159i) q^{14} +(-5.57359 - 1.67836i) q^{15} +(-0.365341 - 0.930874i) q^{16} +(-1.97706 + 2.29739i) q^{17} +(0.977397 - 3.64769i) q^{18} +(-0.173183 + 0.299963i) q^{19} +(0.593213 + 2.15594i) q^{20} +(-0.275663 - 6.88176i) q^{21} +(-0.154489 + 0.441503i) q^{22} +(-2.25228 + 1.93825i) q^{23} +(-2.48750 + 0.767291i) q^{24} +(-0.811476 - 4.93371i) q^{25} +(3.99755 + 0.299575i) q^{26} +(-1.90759 - 0.667496i) q^{27} +(-2.18209 + 1.49616i) q^{28} +(-1.26558 + 2.62800i) q^{29} +(5.71195 - 1.12050i) q^{30} +(2.53765 - 1.46512i) q^{31} +(0.757972 + 0.652287i) q^{32} +(1.11603 + 0.486919i) q^{33} +(0.674454 - 2.95498i) q^{34} +(5.20444 - 2.81315i) q^{35} +(0.840322 + 3.68169i) q^{36} +(-1.63066 + 8.61826i) q^{37} +(0.0129511 - 0.346125i) q^{38} +(1.55531 - 10.3188i) q^{39} +(-1.53187 - 1.62891i) q^{40} +(3.84792 - 3.06861i) q^{41} +(3.45935 + 5.95546i) q^{42} +(-4.68323 + 0.527673i) q^{43} +(-0.0697147 - 0.462527i) q^{44} +(-1.00172 - 8.38460i) q^{45} +(1.08560 - 2.76606i) q^{46} +(4.10248 + 7.76226i) q^{47} +(1.84070 - 1.84070i) q^{48} +(5.15639 + 4.73409i) q^{49} +(3.02281 + 3.98279i) q^{50} +(-7.53952 - 2.32563i) q^{51} +(-3.67428 + 1.60307i) q^{52} +(-1.72713 - 9.12811i) q^{53} +(1.99843 - 0.301215i) q^{54} +(0.0461189 + 1.04491i) q^{55} +(1.23011 - 2.34240i) q^{56} +(-0.895974 - 0.100952i) q^{57} +(-0.109065 - 2.91482i) q^{58} +(-0.345750 - 0.0521134i) q^{59} +(-4.52645 + 3.65966i) q^{60} +(-2.93584 - 4.30609i) q^{61} +(-1.55898 + 2.48110i) q^{62} +(8.99043 - 4.35879i) q^{63} +(-0.974928 - 0.222521i) q^{64} +(8.54771 - 2.69955i) q^{65} +(-1.21422 + 0.0909933i) q^{66} +(-9.08721 - 2.43491i) q^{67} +(0.784472 + 2.92769i) q^{68} +(-6.96913 - 3.35615i) q^{69} +(-3.28683 + 4.91902i) q^{70} +(-11.8321 + 5.69802i) q^{71} +(-2.46328 - 2.86238i) q^{72} +(-6.40025 + 12.1099i) q^{73} +(-2.58535 - 8.38150i) q^{74} +(10.9268 - 7.07202i) q^{75} +(0.150283 + 0.312066i) q^{76} +(-1.15081 + 0.455164i) q^{77} +(3.44659 + 9.84979i) q^{78} +(-13.7173 - 7.91968i) q^{79} +(2.11549 + 0.724351i) q^{80} +(0.453472 + 6.05117i) q^{81} +(-1.96814 + 4.51102i) q^{82} +(3.39830 + 5.40836i) q^{83} +(-5.84126 - 3.64887i) q^{84} +(-1.05506 - 6.69483i) q^{85} +(3.89395 - 2.65485i) q^{86} +(-7.58770 - 0.283912i) q^{87} +(0.277760 + 0.376352i) q^{88} +(12.7478 + 11.8283i) q^{89} +(4.80350 + 6.94488i) q^{90} +(6.32064 + 8.51708i) q^{91} +(0.332698 + 2.95278i) q^{92} +(6.13733 + 4.52955i) q^{93} +(-7.25412 - 4.94578i) q^{94} +(-0.260699 - 0.729305i) q^{95} +(-0.767291 + 2.48750i) q^{96} +(10.4936 + 10.4936i) q^{97} +(-6.77094 - 1.77607i) q^{98} +1.76640i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 672 q + 12 q^{5} - 28 q^{6} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 672 q + 12 q^{5} - 28 q^{6} - 8 q^{7} + 12 q^{10} + 4 q^{11} - 44 q^{15} - 56 q^{16} + 8 q^{17} + 28 q^{21} + 20 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 4 q^{28} - 12 q^{30} - 24 q^{31} - 48 q^{33} - 8 q^{35} + 92 q^{36} - 12 q^{37} - 24 q^{38} - 112 q^{41} + 76 q^{42} + 24 q^{43} - 100 q^{45} - 160 q^{46} + 72 q^{47} + 32 q^{50} - 208 q^{51} + 160 q^{53} - 84 q^{55} - 52 q^{56} - 92 q^{57} + 128 q^{58} - 212 q^{61} + 36 q^{63} - 16 q^{67} + 36 q^{68} - 16 q^{70} - 16 q^{71} + 12 q^{73} + 132 q^{75} - 16 q^{77} + 80 q^{78} + 12 q^{80} - 36 q^{81} + 48 q^{82} - 308 q^{83} - 40 q^{85} - 4 q^{86} + 52 q^{87} - 4 q^{88} + 84 q^{90} - 124 q^{91} - 8 q^{92} - 536 q^{93} - 28 q^{95} - 12 q^{96} - 40 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.884115 + 0.467269i −0.625164 + 0.330409i
\(3\) 1.04098 + 2.38595i 0.601009 + 1.37753i 0.905229 + 0.424925i \(0.139699\pi\)
−0.304220 + 0.952602i \(0.598396\pi\)
\(4\) 0.563320 0.826239i 0.281660 0.413119i
\(5\) −1.44716 + 1.70462i −0.647188 + 0.762330i
\(6\) −2.03522 1.62304i −0.830876 0.662601i
\(7\) −2.46540 0.960107i −0.931833 0.362886i
\(8\) −0.111964 + 0.993712i −0.0395854 + 0.351330i
\(9\) −2.56858 + 2.76828i −0.856195 + 0.922759i
\(10\) 0.482937 2.18329i 0.152718 0.690418i
\(11\) 0.342886 0.318152i 0.103384 0.0959264i −0.626788 0.779190i \(-0.715631\pi\)
0.730172 + 0.683264i \(0.239440\pi\)
\(12\) 2.55776 + 0.483955i 0.738363 + 0.139706i
\(13\) −3.39432 2.13279i −0.941414 0.591529i −0.0284611 0.999595i \(-0.509061\pi\)
−0.912953 + 0.408065i \(0.866204\pi\)
\(14\) 2.62833 0.303159i 0.702450 0.0810226i
\(15\) −5.57359 1.67836i −1.43910 0.433352i
\(16\) −0.365341 0.930874i −0.0913353 0.232718i
\(17\) −1.97706 + 2.29739i −0.479508 + 0.557198i −0.944668 0.328028i \(-0.893616\pi\)
0.465160 + 0.885227i \(0.345997\pi\)
\(18\) 0.977397 3.64769i 0.230375 0.859770i
\(19\) −0.173183 + 0.299963i −0.0397310 + 0.0688161i −0.885207 0.465197i \(-0.845983\pi\)
0.845476 + 0.534013i \(0.179317\pi\)
\(20\) 0.593213 + 2.15594i 0.132646 + 0.482084i
\(21\) −0.275663 6.88176i −0.0601545 1.50172i
\(22\) −0.154489 + 0.441503i −0.0329371 + 0.0941287i
\(23\) −2.25228 + 1.93825i −0.469634 + 0.404152i −0.855014 0.518606i \(-0.826451\pi\)
0.385380 + 0.922758i \(0.374070\pi\)
\(24\) −2.48750 + 0.767291i −0.507758 + 0.156623i
\(25\) −0.811476 4.93371i −0.162295 0.986742i
\(26\) 3.99755 + 0.299575i 0.783985 + 0.0587515i
\(27\) −1.90759 0.667496i −0.367117 0.128460i
\(28\) −2.18209 + 1.49616i −0.412376 + 0.282748i
\(29\) −1.26558 + 2.62800i −0.235012 + 0.488007i −0.984805 0.173665i \(-0.944439\pi\)
0.749793 + 0.661673i \(0.230153\pi\)
\(30\) 5.71195 1.12050i 1.04285 0.204574i
\(31\) 2.53765 1.46512i 0.455776 0.263143i −0.254490 0.967075i \(-0.581908\pi\)
0.710267 + 0.703933i \(0.248574\pi\)
\(32\) 0.757972 + 0.652287i 0.133992 + 0.115309i
\(33\) 1.11603 + 0.486919i 0.194276 + 0.0847617i
\(34\) 0.674454 2.95498i 0.115668 0.506774i
\(35\) 5.20444 2.81315i 0.879711 0.475509i
\(36\) 0.840322 + 3.68169i 0.140054 + 0.613615i
\(37\) −1.63066 + 8.61826i −0.268079 + 1.41683i 0.546829 + 0.837244i \(0.315835\pi\)
−0.814909 + 0.579590i \(0.803213\pi\)
\(38\) 0.0129511 0.346125i 0.00210094 0.0561488i
\(39\) 1.55531 10.3188i 0.249050 1.65234i
\(40\) −1.53187 1.62891i −0.242211 0.257554i
\(41\) 3.84792 3.06861i 0.600944 0.479237i −0.275135 0.961406i \(-0.588722\pi\)
0.876078 + 0.482169i \(0.160151\pi\)
\(42\) 3.45935 + 5.95546i 0.533789 + 0.918947i
\(43\) −4.68323 + 0.527673i −0.714185 + 0.0804693i −0.461578 0.887100i \(-0.652717\pi\)
−0.252607 + 0.967569i \(0.581288\pi\)
\(44\) −0.0697147 0.462527i −0.0105099 0.0697286i
\(45\) −1.00172 8.38460i −0.149328 1.24990i
\(46\) 1.08560 2.76606i 0.160062 0.407833i
\(47\) 4.10248 + 7.76226i 0.598408 + 1.13224i 0.978296 + 0.207210i \(0.0664384\pi\)
−0.379889 + 0.925032i \(0.624038\pi\)
\(48\) 1.84070 1.84070i 0.265683 0.265683i
\(49\) 5.15639 + 4.73409i 0.736627 + 0.676299i
\(50\) 3.02281 + 3.98279i 0.427489 + 0.563252i
\(51\) −7.53952 2.32563i −1.05574 0.325654i
\(52\) −3.67428 + 1.60307i −0.509531 + 0.222306i
\(53\) −1.72713 9.12811i −0.237240 1.25384i −0.875195 0.483770i \(-0.839267\pi\)
0.637956 0.770073i \(-0.279780\pi\)
\(54\) 1.99843 0.301215i 0.271952 0.0409902i
\(55\) 0.0461189 + 1.04491i 0.00621867 + 0.140895i
\(56\) 1.23011 2.34240i 0.164380 0.313016i
\(57\) −0.895974 0.100952i −0.118675 0.0133714i
\(58\) −0.109065 2.91482i −0.0143209 0.382735i
\(59\) −0.345750 0.0521134i −0.0450128 0.00678459i 0.126497 0.991967i \(-0.459627\pi\)
−0.171510 + 0.985182i \(0.554865\pi\)
\(60\) −4.52645 + 3.65966i −0.584362 + 0.472461i
\(61\) −2.93584 4.30609i −0.375896 0.551339i 0.590947 0.806711i \(-0.298754\pi\)
−0.966843 + 0.255372i \(0.917802\pi\)
\(62\) −1.55898 + 2.48110i −0.197990 + 0.315100i
\(63\) 8.99043 4.35879i 1.13269 0.549156i
\(64\) −0.974928 0.222521i −0.121866 0.0278151i
\(65\) 8.54771 2.69955i 1.06021 0.334837i
\(66\) −1.21422 + 0.0909933i −0.149460 + 0.0112005i
\(67\) −9.08721 2.43491i −1.11018 0.297472i −0.343276 0.939235i \(-0.611537\pi\)
−0.766903 + 0.641763i \(0.778203\pi\)
\(68\) 0.784472 + 2.92769i 0.0951312 + 0.355035i
\(69\) −6.96913 3.35615i −0.838984 0.404034i
\(70\) −3.28683 + 4.91902i −0.392851 + 0.587935i
\(71\) −11.8321 + 5.69802i −1.40421 + 0.676230i −0.974010 0.226505i \(-0.927270\pi\)
−0.430197 + 0.902735i \(0.641556\pi\)
\(72\) −2.46328 2.86238i −0.290300 0.337335i
\(73\) −6.40025 + 12.1099i −0.749093 + 1.41735i 0.154072 + 0.988060i \(0.450761\pi\)
−0.903165 + 0.429294i \(0.858763\pi\)
\(74\) −2.58535 8.38150i −0.300541 0.974329i
\(75\) 10.9268 7.07202i 1.26172 0.816607i
\(76\) 0.150283 + 0.312066i 0.0172386 + 0.0357964i
\(77\) −1.15081 + 0.455164i −0.131147 + 0.0518708i
\(78\) 3.44659 + 9.84979i 0.390250 + 1.11527i
\(79\) −13.7173 7.91968i −1.54332 0.891034i −0.998626 0.0523959i \(-0.983314\pi\)
−0.544689 0.838638i \(-0.683352\pi\)
\(80\) 2.11549 + 0.724351i 0.236519 + 0.0809850i
\(81\) 0.453472 + 6.05117i 0.0503858 + 0.672352i
\(82\) −1.96814 + 4.51102i −0.217344 + 0.498158i
\(83\) 3.39830 + 5.40836i 0.373012 + 0.593644i 0.979499 0.201449i \(-0.0645649\pi\)
−0.606488 + 0.795093i \(0.707422\pi\)
\(84\) −5.84126 3.64887i −0.637334 0.398124i
\(85\) −1.05506 6.69483i −0.114437 0.726156i
\(86\) 3.89395 2.65485i 0.419895 0.286280i
\(87\) −7.58770 0.283912i −0.813487 0.0304385i
\(88\) 0.277760 + 0.376352i 0.0296093 + 0.0401192i
\(89\) 12.7478 + 11.8283i 1.35127 + 1.25379i 0.939519 + 0.342496i \(0.111272\pi\)
0.411749 + 0.911297i \(0.364918\pi\)
\(90\) 4.80350 + 6.94488i 0.506333 + 0.732054i
\(91\) 6.32064 + 8.51708i 0.662583 + 0.892833i
\(92\) 0.332698 + 2.95278i 0.0346862 + 0.307848i
\(93\) 6.13733 + 4.52955i 0.636411 + 0.469693i
\(94\) −7.25412 4.94578i −0.748206 0.510118i
\(95\) −0.260699 0.729305i −0.0267472 0.0748251i
\(96\) −0.767291 + 2.48750i −0.0783113 + 0.253879i
\(97\) 10.4936 + 10.4936i 1.06547 + 1.06547i 0.997701 + 0.0677663i \(0.0215872\pi\)
0.0677663 + 0.997701i \(0.478413\pi\)
\(98\) −6.77094 1.77607i −0.683968 0.179410i
\(99\) 1.76640i 0.177530i
\(100\) −4.53354 2.10879i −0.453354 0.210879i
\(101\) 13.0075 + 5.10508i 1.29430 + 0.507974i 0.909760 0.415135i \(-0.136266\pi\)
0.384538 + 0.923109i \(0.374361\pi\)
\(102\) 7.75250 1.46685i 0.767612 0.145240i
\(103\) −0.678668 + 0.919563i −0.0668712 + 0.0906072i −0.836757 0.547575i \(-0.815551\pi\)
0.769886 + 0.638182i \(0.220313\pi\)
\(104\) 2.49942 3.13418i 0.245088 0.307331i
\(105\) 12.1297 + 9.48908i 1.18374 + 0.926040i
\(106\) 5.79226 + 7.26327i 0.562594 + 0.705471i
\(107\) −3.36408 + 0.125875i −0.325218 + 0.0121688i −0.199502 0.979897i \(-0.563932\pi\)
−0.125716 + 0.992066i \(0.540123\pi\)
\(108\) −1.62610 + 1.20011i −0.156471 + 0.115481i
\(109\) −9.38078 10.1101i −0.898516 0.968370i 0.101133 0.994873i \(-0.467753\pi\)
−0.999649 + 0.0265031i \(0.991563\pi\)
\(110\) −0.529027 0.902268i −0.0504407 0.0860279i
\(111\) −22.2602 + 5.08074i −2.11284 + 0.482243i
\(112\) 0.00697341 + 2.64574i 0.000658926 + 0.249999i
\(113\) 14.2703 8.96659i 1.34243 0.843506i 0.346898 0.937903i \(-0.387235\pi\)
0.995535 + 0.0943967i \(0.0300922\pi\)
\(114\) 0.839317 0.329407i 0.0786092 0.0308518i
\(115\) −0.0445722 6.64424i −0.00415638 0.619579i
\(116\) 1.45843 + 2.52607i 0.135412 + 0.234540i
\(117\) 14.6227 3.91815i 1.35187 0.362233i
\(118\) 0.330034 0.115484i 0.0303821 0.0106311i
\(119\) 7.07999 3.76579i 0.649021 0.345209i
\(120\) 2.29185 5.35063i 0.209217 0.488444i
\(121\) −0.805681 + 10.7511i −0.0732437 + 0.977369i
\(122\) 4.60773 + 2.43525i 0.417164 + 0.220478i
\(123\) 11.3271 + 5.98656i 1.02133 + 0.539790i
\(124\) 0.218976 2.92204i 0.0196647 0.262407i
\(125\) 9.58445 + 5.75659i 0.857259 + 0.514885i
\(126\) −5.91185 + 8.05462i −0.526669 + 0.717562i
\(127\) 1.88808 0.660669i 0.167540 0.0586249i −0.245206 0.969471i \(-0.578855\pi\)
0.412746 + 0.910846i \(0.364570\pi\)
\(128\) 0.965926 0.258819i 0.0853766 0.0228766i
\(129\) −6.13413 10.6246i −0.540080 0.935446i
\(130\) −6.29575 + 6.38079i −0.552174 + 0.559632i
\(131\) −13.1512 + 5.16148i −1.14903 + 0.450960i −0.861973 0.506954i \(-0.830772\pi\)
−0.287055 + 0.957914i \(0.592676\pi\)
\(132\) 1.03099 0.647816i 0.0897364 0.0563851i
\(133\) 0.714962 0.573253i 0.0619951 0.0497073i
\(134\) 9.17190 2.09343i 0.792331 0.180844i
\(135\) 3.89842 2.28576i 0.335522 0.196727i
\(136\) −2.06158 2.22186i −0.176779 0.190523i
\(137\) 7.11634 5.25210i 0.607990 0.448717i −0.245810 0.969318i \(-0.579054\pi\)
0.853800 + 0.520601i \(0.174292\pi\)
\(138\) 7.72974 0.289226i 0.657999 0.0246206i
\(139\) 4.83143 + 6.05843i 0.409797 + 0.513869i 0.943306 0.331926i \(-0.107698\pi\)
−0.533509 + 0.845795i \(0.679127\pi\)
\(140\) 0.607430 5.88481i 0.0513372 0.497358i
\(141\) −14.2498 + 17.8686i −1.20005 + 1.50481i
\(142\) 7.79840 10.5665i 0.654427 0.886717i
\(143\) −1.84241 + 0.348604i −0.154070 + 0.0291517i
\(144\) 3.51532 + 1.37966i 0.292944 + 0.114972i
\(145\) −2.64826 5.96046i −0.219926 0.494989i
\(146\) 13.6972i 1.13359i
\(147\) −5.92760 + 17.2310i −0.488901 + 1.42118i
\(148\) 6.20216 + 6.20216i 0.509814 + 0.509814i
\(149\) −4.10899 + 13.3210i −0.336621 + 1.09130i 0.616155 + 0.787625i \(0.288690\pi\)
−0.952776 + 0.303674i \(0.901787\pi\)
\(150\) −6.35605 + 11.3583i −0.518970 + 0.927397i
\(151\) 18.1311 + 12.3616i 1.47549 + 1.00597i 0.991388 + 0.130957i \(0.0418050\pi\)
0.484099 + 0.875013i \(0.339147\pi\)
\(152\) −0.278686 0.205680i −0.0226044 0.0166828i
\(153\) −1.28155 11.3741i −0.103607 0.919541i
\(154\) 0.804766 0.940155i 0.0648499 0.0757599i
\(155\) −1.17491 + 6.44600i −0.0943714 + 0.517755i
\(156\) −7.64968 7.09787i −0.612465 0.568284i
\(157\) −4.15527 5.63020i −0.331627 0.449339i 0.606780 0.794870i \(-0.292461\pi\)
−0.938407 + 0.345531i \(0.887699\pi\)
\(158\) 15.8283 + 0.592253i 1.25923 + 0.0471171i
\(159\) 19.9813 13.6230i 1.58462 1.08037i
\(160\) −2.20881 + 0.348094i −0.174622 + 0.0275192i
\(161\) 7.41370 2.61612i 0.584282 0.206179i
\(162\) −3.22844 5.13804i −0.253650 0.403682i
\(163\) −4.52082 + 10.3618i −0.354098 + 0.811601i 0.644786 + 0.764363i \(0.276947\pi\)
−0.998884 + 0.0472377i \(0.984958\pi\)
\(164\) −0.367797 4.90791i −0.0287201 0.383243i
\(165\) −2.44508 + 1.19776i −0.190349 + 0.0932456i
\(166\) −5.53164 3.19370i −0.429339 0.247879i
\(167\) 1.48618 + 4.24726i 0.115004 + 0.328663i 0.986970 0.160904i \(-0.0514408\pi\)
−0.871966 + 0.489566i \(0.837155\pi\)
\(168\) 6.86935 + 0.496583i 0.529982 + 0.0383122i
\(169\) 1.33210 + 2.76613i 0.102469 + 0.212779i
\(170\) 4.06108 + 5.42600i 0.311470 + 0.416155i
\(171\) −0.385543 1.24990i −0.0294832 0.0955821i
\(172\) −2.20217 + 4.16671i −0.167914 + 0.317709i
\(173\) −7.50969 8.72642i −0.570952 0.663458i 0.396050 0.918229i \(-0.370381\pi\)
−0.967001 + 0.254771i \(0.918000\pi\)
\(174\) 6.84107 3.29449i 0.518620 0.249754i
\(175\) −2.73628 + 12.9427i −0.206843 + 0.978374i
\(176\) −0.421429 0.202950i −0.0317664 0.0152979i
\(177\) −0.235578 0.879189i −0.0177071 0.0660839i
\(178\) −16.7975 4.50089i −1.25903 0.337356i
\(179\) −11.0204 + 0.825868i −0.823706 + 0.0617283i −0.479912 0.877317i \(-0.659331\pi\)
−0.343794 + 0.939045i \(0.611712\pi\)
\(180\) −7.49197 3.89555i −0.558418 0.290357i
\(181\) 6.85434 + 1.56446i 0.509479 + 0.116285i 0.469530 0.882917i \(-0.344423\pi\)
0.0399488 + 0.999202i \(0.487281\pi\)
\(182\) −9.56794 4.57665i −0.709223 0.339244i
\(183\) 7.21795 11.4873i 0.533567 0.849166i
\(184\) −1.67388 2.45514i −0.123400 0.180995i
\(185\) −12.3311 15.2516i −0.906598 1.12132i
\(186\) −7.54262 1.13687i −0.553052 0.0833592i
\(187\) 0.0530110 + 1.41675i 0.00387655 + 0.103603i
\(188\) 8.72449 + 0.983014i 0.636299 + 0.0716937i
\(189\) 4.06212 + 3.47714i 0.295475 + 0.252925i
\(190\) 0.571270 + 0.522973i 0.0414443 + 0.0379405i
\(191\) −16.4143 + 2.47406i −1.18770 + 0.179016i −0.713020 0.701144i \(-0.752673\pi\)
−0.474676 + 0.880160i \(0.657435\pi\)
\(192\) −0.483955 2.55776i −0.0349265 0.184591i
\(193\) 10.2666 4.47925i 0.739003 0.322424i 0.00354485 0.999994i \(-0.498872\pi\)
0.735458 + 0.677570i \(0.236967\pi\)
\(194\) −14.1809 4.37424i −1.01813 0.314052i
\(195\) 15.3389 + 17.5842i 1.09844 + 1.25923i
\(196\) 6.81619 1.59360i 0.486871 0.113829i
\(197\) −0.0556935 + 0.0556935i −0.00396800 + 0.00396800i −0.709088 0.705120i \(-0.750893\pi\)
0.705120 + 0.709088i \(0.250893\pi\)
\(198\) −0.825385 1.56170i −0.0586575 0.110985i
\(199\) 5.04025 12.8424i 0.357294 0.910371i −0.633346 0.773869i \(-0.718319\pi\)
0.990640 0.136502i \(-0.0435859\pi\)
\(200\) 4.99355 0.253973i 0.353097 0.0179586i
\(201\) −3.65002 24.2163i −0.257452 1.70808i
\(202\) −13.8856 + 1.56453i −0.976987 + 0.110080i
\(203\) 5.64332 5.26398i 0.396083 0.369459i
\(204\) −6.16869 + 4.91937i −0.431895 + 0.344425i
\(205\) −0.337714 + 11.0000i −0.0235870 + 0.768274i
\(206\) 0.170338 1.13012i 0.0118680 0.0787392i
\(207\) 0.419579 11.2135i 0.0291628 0.779392i
\(208\) −0.745275 + 3.93887i −0.0516755 + 0.273112i
\(209\) 0.0360514 + 0.157952i 0.00249373 + 0.0109257i
\(210\) −15.1580 2.72160i −1.04600 0.187808i
\(211\) 4.32026 18.9283i 0.297419 1.30308i −0.576536 0.817072i \(-0.695596\pi\)
0.873955 0.486007i \(-0.161547\pi\)
\(212\) −8.51493 3.71503i −0.584808 0.255149i
\(213\) −25.9121 22.2991i −1.77547 1.52791i
\(214\) 2.91542 1.68322i 0.199294 0.115062i
\(215\) 5.87788 8.74676i 0.400868 0.596524i
\(216\) 0.876882 1.82086i 0.0596643 0.123894i
\(217\) −7.66300 + 1.17568i −0.520198 + 0.0798101i
\(218\) 13.0178 + 4.55513i 0.881678 + 0.308512i
\(219\) −35.5560 2.66456i −2.40265 0.180054i
\(220\) 0.889322 + 0.550512i 0.0599581 + 0.0371155i
\(221\) 11.6106 3.58140i 0.781015 0.240911i
\(222\) 17.3065 14.8935i 1.16154 0.999583i
\(223\) −0.639995 + 1.82900i −0.0428572 + 0.122479i −0.963323 0.268344i \(-0.913524\pi\)
0.920466 + 0.390823i \(0.127809\pi\)
\(224\) −1.24244 2.33588i −0.0830139 0.156073i
\(225\) 15.7422 + 10.4263i 1.04948 + 0.695084i
\(226\) −8.42674 + 14.5955i −0.560539 + 0.970881i
\(227\) −4.87220 + 18.1833i −0.323379 + 1.20687i 0.592552 + 0.805532i \(0.298120\pi\)
−0.915931 + 0.401335i \(0.868546\pi\)
\(228\) −0.588131 + 0.683420i −0.0389499 + 0.0452606i
\(229\) 4.17738 + 10.6438i 0.276049 + 0.703361i 0.999910 + 0.0134152i \(0.00427032\pi\)
−0.723861 + 0.689946i \(0.757634\pi\)
\(230\) 3.14405 + 5.85345i 0.207313 + 0.385965i
\(231\) −2.28396 2.27196i −0.150274 0.149484i
\(232\) −2.46978 1.55186i −0.162149 0.101885i
\(233\) 22.3397 + 4.22690i 1.46352 + 0.276913i 0.855829 0.517259i \(-0.173048\pi\)
0.607693 + 0.794172i \(0.292095\pi\)
\(234\) −11.0974 + 10.2968i −0.725457 + 0.673126i
\(235\) −19.1687 4.24004i −1.25043 0.276590i
\(236\) −0.237826 + 0.256315i −0.0154811 + 0.0166847i
\(237\) 4.61654 40.9729i 0.299876 2.66148i
\(238\) −4.49989 + 6.63765i −0.291685 + 0.430255i
\(239\) 2.34618 + 1.87102i 0.151762 + 0.121026i 0.696427 0.717627i \(-0.254772\pi\)
−0.544665 + 0.838653i \(0.683343\pi\)
\(240\) 0.473918 + 5.80149i 0.0305913 + 0.374484i
\(241\) 14.6494 21.4867i 0.943651 1.38408i 0.0204389 0.999791i \(-0.493494\pi\)
0.923212 0.384291i \(-0.125554\pi\)
\(242\) −4.31132 9.88165i −0.277142 0.635216i
\(243\) −19.3261 + 10.2141i −1.23977 + 0.655238i
\(244\) −5.21168 −0.333644
\(245\) −15.5319 + 1.93872i −0.992300 + 0.123861i
\(246\) −12.8118 −0.816852
\(247\) 1.22760 0.648804i 0.0781101 0.0412824i
\(248\) 1.17178 + 2.68574i 0.0744079 + 0.170545i
\(249\) −9.36650 + 13.7381i −0.593578 + 0.870619i
\(250\) −11.1636 0.610980i −0.706050 0.0386418i
\(251\) 4.61798 + 3.68272i 0.291484 + 0.232451i 0.758303 0.651902i \(-0.226029\pi\)
−0.466819 + 0.884353i \(0.654600\pi\)
\(252\) 1.46309 9.88363i 0.0921658 0.622610i
\(253\) −0.155620 + 1.38117i −0.00978375 + 0.0868331i
\(254\) −1.36057 + 1.46635i −0.0853701 + 0.0920070i
\(255\) 14.8752 9.48648i 0.931521 0.594066i
\(256\) −0.733052 + 0.680173i −0.0458157 + 0.0425108i
\(257\) −6.00897 1.13696i −0.374829 0.0709215i −0.00491619 0.999988i \(-0.501565\pi\)
−0.369913 + 0.929066i \(0.620612\pi\)
\(258\) 10.3878 + 6.52711i 0.646718 + 0.406360i
\(259\) 12.2947 19.6819i 0.763955 1.22297i
\(260\) 2.58463 8.58316i 0.160292 0.532305i
\(261\) −4.02428 10.2537i −0.249097 0.634689i
\(262\) 9.21541 10.7085i 0.569330 0.661573i
\(263\) −0.402229 + 1.50114i −0.0248025 + 0.0925641i −0.977218 0.212240i \(-0.931924\pi\)
0.952415 + 0.304804i \(0.0985909\pi\)
\(264\) −0.608813 + 1.05449i −0.0374698 + 0.0648997i
\(265\) 18.0594 + 10.2657i 1.10938 + 0.630617i
\(266\) −0.364246 + 0.840901i −0.0223334 + 0.0515590i
\(267\) −14.9514 + 42.7286i −0.915010 + 2.61495i
\(268\) −7.13082 + 6.13657i −0.435584 + 0.374851i
\(269\) −6.80303 + 2.09846i −0.414788 + 0.127945i −0.495123 0.868823i \(-0.664877\pi\)
0.0803352 + 0.996768i \(0.474401\pi\)
\(270\) −2.37859 + 3.84248i −0.144756 + 0.233846i
\(271\) −15.5400 1.16456i −0.943990 0.0707423i −0.406166 0.913799i \(-0.633135\pi\)
−0.537824 + 0.843057i \(0.680754\pi\)
\(272\) 2.86088 + 1.00107i 0.173466 + 0.0606985i
\(273\) −13.7417 + 23.9468i −0.831683 + 1.44933i
\(274\) −3.83752 + 7.96870i −0.231833 + 0.481407i
\(275\) −1.84791 1.43353i −0.111433 0.0864450i
\(276\) −6.69883 + 3.86757i −0.403222 + 0.232801i
\(277\) −15.5398 13.3731i −0.933695 0.803509i 0.0470319 0.998893i \(-0.485024\pi\)
−0.980727 + 0.195384i \(0.937405\pi\)
\(278\) −7.10246 3.09877i −0.425977 0.185852i
\(279\) −2.46234 + 10.7882i −0.147416 + 0.645873i
\(280\) 2.21275 + 5.48669i 0.132237 + 0.327892i
\(281\) −6.87623 30.1267i −0.410201 1.79721i −0.583246 0.812296i \(-0.698218\pi\)
0.173044 0.984914i \(-0.444640\pi\)
\(282\) 4.24898 22.4564i 0.253023 1.33726i
\(283\) 0.879341 23.5009i 0.0522714 1.39698i −0.688505 0.725231i \(-0.741733\pi\)
0.740777 0.671751i \(-0.234458\pi\)
\(284\) −1.95731 + 12.9859i −0.116145 + 0.770572i
\(285\) 1.46870 1.38120i 0.0869983 0.0818155i
\(286\) 1.46602 1.16911i 0.0866873 0.0691308i
\(287\) −12.4328 + 3.87094i −0.733888 + 0.228494i
\(288\) −3.75263 + 0.422819i −0.221126 + 0.0249149i
\(289\) 1.16450 + 7.72596i 0.0685001 + 0.454468i
\(290\) 5.12650 + 4.03229i 0.301039 + 0.236784i
\(291\) −14.1136 + 35.9609i −0.827354 + 2.10806i
\(292\) 6.40025 + 12.1099i 0.374547 + 0.708677i
\(293\) −0.203174 + 0.203174i −0.0118696 + 0.0118696i −0.713017 0.701147i \(-0.752672\pi\)
0.701147 + 0.713017i \(0.252672\pi\)
\(294\) −2.81080 18.0039i −0.163929 1.05001i
\(295\) 0.589188 0.513957i 0.0343038 0.0299237i
\(296\) −8.38150 2.58535i −0.487165 0.150270i
\(297\) −0.866453 + 0.378029i −0.0502767 + 0.0219355i
\(298\) −2.59167 13.6973i −0.150131 0.793464i
\(299\) 11.7788 1.77537i 0.681188 0.102672i
\(300\) 0.312130 13.0120i 0.0180209 0.751248i
\(301\) 12.0526 + 3.19547i 0.694703 + 0.184184i
\(302\) −21.8061 2.45696i −1.25480 0.141382i
\(303\) 1.36010 + 36.3495i 0.0781359 + 2.08823i
\(304\) 0.342498 + 0.0516233i 0.0196436 + 0.00296080i
\(305\) 11.5889 + 1.22708i 0.663578 + 0.0702626i
\(306\) 6.44780 + 9.45718i 0.368596 + 0.540631i
\(307\) −7.77527 + 12.3743i −0.443758 + 0.706237i −0.991456 0.130439i \(-0.958361\pi\)
0.547698 + 0.836676i \(0.315504\pi\)
\(308\) −0.272201 + 1.20725i −0.0155101 + 0.0687893i
\(309\) −2.90051 0.662022i −0.165004 0.0376611i
\(310\) −1.97325 6.24800i −0.112073 0.354863i
\(311\) 27.1886 2.03750i 1.54172 0.115536i 0.723455 0.690371i \(-0.242553\pi\)
0.818269 + 0.574835i \(0.194934\pi\)
\(312\) 10.0798 + 2.70088i 0.570657 + 0.152907i
\(313\) −4.68181 17.4728i −0.264632 0.987619i −0.962475 0.271369i \(-0.912524\pi\)
0.697844 0.716250i \(-0.254143\pi\)
\(314\) 6.30456 + 3.03611i 0.355787 + 0.171338i
\(315\) −5.58046 + 21.6331i −0.314423 + 1.21889i
\(316\) −14.2708 + 6.87244i −0.802794 + 0.386605i
\(317\) 2.61068 + 3.03366i 0.146630 + 0.170388i 0.826484 0.562960i \(-0.190338\pi\)
−0.679854 + 0.733348i \(0.737957\pi\)
\(318\) −11.3002 + 21.3809i −0.633681 + 1.19898i
\(319\) 0.402154 + 1.30375i 0.0225163 + 0.0729960i
\(320\) 1.79019 1.33986i 0.100075 0.0749005i
\(321\) −3.80226 7.89548i −0.212222 0.440683i
\(322\) −5.33214 + 5.77714i −0.297148 + 0.321948i
\(323\) −0.346736 0.990914i −0.0192929 0.0551359i
\(324\) 5.25516 + 3.03407i 0.291953 + 0.168559i
\(325\) −7.76816 + 18.4773i −0.430900 + 1.02494i
\(326\) −0.844831 11.2735i −0.0467909 0.624381i
\(327\) 14.3569 32.9064i 0.793939 1.81973i
\(328\) 2.61849 + 4.16730i 0.144582 + 0.230100i
\(329\) −2.66164 23.0759i −0.146741 1.27222i
\(330\) 1.60206 2.20147i 0.0881904 0.121187i
\(331\) 22.4105 15.2792i 1.23179 0.839820i 0.240389 0.970677i \(-0.422725\pi\)
0.991401 + 0.130856i \(0.0417726\pi\)
\(332\) 6.38292 + 0.238832i 0.350308 + 0.0131076i
\(333\) −19.6692 26.6509i −1.07787 1.46046i
\(334\) −3.29857 3.06062i −0.180490 0.167470i
\(335\) 17.3012 11.9666i 0.945266 0.653803i
\(336\) −6.30534 + 2.77080i −0.343984 + 0.151159i
\(337\) −1.82612 16.2072i −0.0994748 0.882864i −0.940019 0.341121i \(-0.889193\pi\)
0.840545 0.541742i \(-0.182235\pi\)
\(338\) −2.47025 1.82313i −0.134364 0.0991652i
\(339\) 36.2488 + 24.7140i 1.96877 + 1.34228i
\(340\) −6.12586 2.89960i −0.332221 0.157253i
\(341\) 0.403997 1.30973i 0.0218777 0.0709257i
\(342\) 0.924903 + 0.924903i 0.0500130 + 0.0500130i
\(343\) −8.16733 16.6221i −0.440994 0.897510i
\(344\) 4.71286i 0.254100i
\(345\) 15.8064 7.02285i 0.850988 0.378098i
\(346\) 10.7170 + 4.20612i 0.576151 + 0.226122i
\(347\) 2.06332 0.390401i 0.110765 0.0209578i −0.130234 0.991483i \(-0.541573\pi\)
0.240998 + 0.970526i \(0.422525\pi\)
\(348\) −4.50888 + 6.10932i −0.241702 + 0.327494i
\(349\) 7.80508 9.78726i 0.417796 0.523900i −0.527745 0.849403i \(-0.676962\pi\)
0.945541 + 0.325503i \(0.105534\pi\)
\(350\) −3.62852 12.7214i −0.193953 0.679987i
\(351\) 5.05135 + 6.33419i 0.269621 + 0.338094i
\(352\) 0.467424 0.0174898i 0.0249138 0.000932209i
\(353\) 1.41578 1.04489i 0.0753542 0.0556139i −0.555492 0.831522i \(-0.687470\pi\)
0.630846 + 0.775908i \(0.282708\pi\)
\(354\) 0.619096 + 0.667226i 0.0329046 + 0.0354627i
\(355\) 7.40987 28.4151i 0.393275 1.50812i
\(356\) 16.9541 3.86966i 0.898565 0.205092i
\(357\) 16.3551 + 12.9724i 0.865602 + 0.686570i
\(358\) 9.35744 5.87967i 0.494556 0.310750i
\(359\) 3.87783 1.52194i 0.204664 0.0803248i −0.260795 0.965394i \(-0.583985\pi\)
0.465459 + 0.885069i \(0.345889\pi\)
\(360\) 8.44403 0.0566459i 0.445040 0.00298550i
\(361\) 9.44001 + 16.3506i 0.496843 + 0.860557i
\(362\) −6.79105 + 1.81966i −0.356929 + 0.0956390i
\(363\) −26.4901 + 9.26930i −1.39037 + 0.486512i
\(364\) 10.5977 0.424512i 0.555470 0.0222505i
\(365\) −11.3806 28.4349i −0.595687 1.48835i
\(366\) −1.01385 + 13.5288i −0.0529946 + 0.707163i
\(367\) 17.9742 + 9.49964i 0.938246 + 0.495877i 0.865186 0.501450i \(-0.167200\pi\)
0.0730591 + 0.997328i \(0.476724\pi\)
\(368\) 2.62711 + 1.38847i 0.136948 + 0.0723790i
\(369\) −1.38894 + 18.5341i −0.0723052 + 0.964846i
\(370\) 18.0287 + 7.72229i 0.937267 + 0.401463i
\(371\) −4.50589 + 24.1627i −0.233934 + 1.25446i
\(372\) 7.19977 2.51931i 0.373291 0.130620i
\(373\) 12.0478 3.22819i 0.623809 0.167149i 0.0669503 0.997756i \(-0.478673\pi\)
0.556859 + 0.830607i \(0.312006\pi\)
\(374\) −0.708870 1.22780i −0.0366548 0.0634880i
\(375\) −3.75772 + 28.8605i −0.194048 + 1.49035i
\(376\) −8.17279 + 3.20758i −0.421479 + 0.165418i
\(377\) 9.90074 6.22105i 0.509914 0.320400i
\(378\) −5.21614 1.17609i −0.268289 0.0604917i
\(379\) −9.59293 + 2.18952i −0.492756 + 0.112468i −0.461676 0.887049i \(-0.652752\pi\)
−0.0310797 + 0.999517i \(0.509895\pi\)
\(380\) −0.749437 0.195432i −0.0384453 0.0100255i
\(381\) 3.54178 + 3.81713i 0.181451 + 0.195557i
\(382\) 13.3561 9.85723i 0.683356 0.504340i
\(383\) −0.526886 + 0.0197147i −0.0269226 + 0.00100737i −0.0508491 0.998706i \(-0.516193\pi\)
0.0239265 + 0.999714i \(0.492383\pi\)
\(384\) 1.62304 + 2.03522i 0.0828252 + 0.103859i
\(385\) 0.889521 2.62039i 0.0453342 0.133548i
\(386\) −6.98381 + 8.75742i −0.355467 + 0.445741i
\(387\) 10.5685 14.3198i 0.537228 0.727918i
\(388\) 14.5815 2.75897i 0.740265 0.140066i
\(389\) 34.5380 + 13.5552i 1.75115 + 0.687274i 0.999620 + 0.0275710i \(0.00877724\pi\)
0.751526 + 0.659703i \(0.229318\pi\)
\(390\) −21.7779 8.37906i −1.10277 0.424290i
\(391\) 9.00640i 0.455473i
\(392\) −5.28166 + 4.59392i −0.266764 + 0.232028i
\(393\) −26.0051 26.0051i −1.31179 1.31179i
\(394\) 0.0232156 0.0752633i 0.00116959 0.00379171i
\(395\) 33.3511 11.9218i 1.67808 0.599850i
\(396\) 1.45947 + 0.995050i 0.0733412 + 0.0500032i
\(397\) −6.73057 4.96739i −0.337798 0.249306i 0.411691 0.911324i \(-0.364938\pi\)
−0.749488 + 0.662018i \(0.769700\pi\)
\(398\) 1.54466 + 13.7093i 0.0774270 + 0.687184i
\(399\) 2.11201 + 1.10912i 0.105733 + 0.0555254i
\(400\) −4.29620 + 2.55787i −0.214810 + 0.127893i
\(401\) −8.30518 7.70608i −0.414741 0.384823i 0.445020 0.895521i \(-0.353197\pi\)
−0.859760 + 0.510698i \(0.829387\pi\)
\(402\) 14.5425 + 19.7044i 0.725316 + 0.982768i
\(403\) −11.7384 0.439219i −0.584731 0.0218791i
\(404\) 11.5454 7.87153i 0.574406 0.391623i
\(405\) −10.9712 7.98399i −0.545163 0.396728i
\(406\) −2.52965 + 7.29091i −0.125544 + 0.361842i
\(407\) 2.18278 + 3.47388i 0.108197 + 0.172194i
\(408\) 3.15517 7.23173i 0.156204 0.358024i
\(409\) 0.257426 + 3.43511i 0.0127289 + 0.169855i 0.999945 + 0.0104690i \(0.00333244\pi\)
−0.987216 + 0.159386i \(0.949049\pi\)
\(410\) −4.84138 9.88308i −0.239099 0.488090i
\(411\) 19.9392 + 11.5119i 0.983526 + 0.567839i
\(412\) 0.377471 + 1.07875i 0.0185967 + 0.0531462i
\(413\) 0.802377 + 0.460437i 0.0394824 + 0.0226566i
\(414\) 4.86876 + 10.1101i 0.239286 + 0.496883i
\(415\) −14.1371 2.03393i −0.693962 0.0998416i
\(416\) −1.18160 3.83066i −0.0579329 0.187814i
\(417\) −9.42566 + 17.8342i −0.461577 + 0.873346i
\(418\) −0.105679 0.122802i −0.00516895 0.00600643i
\(419\) −11.9066 + 5.73391i −0.581675 + 0.280120i −0.701493 0.712676i \(-0.747483\pi\)
0.119819 + 0.992796i \(0.461769\pi\)
\(420\) 14.6732 4.67666i 0.715977 0.228198i
\(421\) 26.6209 + 12.8200i 1.29743 + 0.624807i 0.949809 0.312830i \(-0.101277\pi\)
0.347616 + 0.937637i \(0.386991\pi\)
\(422\) 5.02499 + 18.7535i 0.244613 + 0.912908i
\(423\) −32.0256 8.58124i −1.55714 0.417234i
\(424\) 9.26409 0.694248i 0.449904 0.0337157i
\(425\) 12.9390 + 7.88998i 0.627633 + 0.382720i
\(426\) 33.3289 + 7.60711i 1.61479 + 0.368566i
\(427\) 3.10372 + 13.4350i 0.150200 + 0.650163i
\(428\) −1.79105 + 2.85044i −0.0865737 + 0.137781i
\(429\) −2.74966 4.03301i −0.132755 0.194716i
\(430\) −1.10964 + 10.4797i −0.0535114 + 0.505376i
\(431\) −4.73300 0.713385i −0.227981 0.0343625i 0.0340583 0.999420i \(-0.489157\pi\)
−0.262039 + 0.965057i \(0.584395\pi\)
\(432\) 0.0755679 + 2.01959i 0.00363576 + 0.0971677i
\(433\) 7.35336 + 0.828524i 0.353380 + 0.0398163i 0.286870 0.957969i \(-0.407385\pi\)
0.0665095 + 0.997786i \(0.478814\pi\)
\(434\) 6.22562 4.62011i 0.298839 0.221773i
\(435\) 11.4646 12.5233i 0.549683 0.600447i
\(436\) −13.6377 + 2.05556i −0.653128 + 0.0984433i
\(437\) −0.191343 1.01127i −0.00915318 0.0483757i
\(438\) 32.6807 14.2584i 1.56154 0.681294i
\(439\) −0.637507 0.196645i −0.0304266 0.00938535i 0.279505 0.960144i \(-0.409830\pi\)
−0.309931 + 0.950759i \(0.600306\pi\)
\(440\) −1.04350 0.0711635i −0.0497469 0.00339259i
\(441\) −26.3499 + 2.11439i −1.25476 + 0.100685i
\(442\) −8.59165 + 8.59165i −0.408663 + 0.408663i
\(443\) 2.48424 + 4.70042i 0.118030 + 0.223324i 0.936051 0.351865i \(-0.114452\pi\)
−0.818021 + 0.575189i \(0.804929\pi\)
\(444\) −8.34171 + 21.2543i −0.395880 + 1.00869i
\(445\) −38.6108 + 4.61290i −1.83033 + 0.218672i
\(446\) −0.288805 1.91610i −0.0136753 0.0907298i
\(447\) −36.0606 + 4.06305i −1.70561 + 0.192176i
\(448\) 2.18994 + 1.48464i 0.103465 + 0.0701425i
\(449\) −23.2205 + 18.5178i −1.09584 + 0.873907i −0.992682 0.120757i \(-0.961468\pi\)
−0.103163 + 0.994664i \(0.532896\pi\)
\(450\) −18.7898 1.86218i −0.885760 0.0877839i
\(451\) 0.343113 2.27641i 0.0161566 0.107192i
\(452\) 0.630172 16.8417i 0.0296408 0.792167i
\(453\) −10.6200 + 56.1279i −0.498970 + 2.63712i
\(454\) −4.18889 18.3527i −0.196595 0.861337i
\(455\) −23.6654 1.55125i −1.10945 0.0727238i
\(456\) 0.200635 0.879038i 0.00939558 0.0411647i
\(457\) 32.1781 + 14.0392i 1.50523 + 0.656724i 0.980851 0.194762i \(-0.0623934\pi\)
0.524377 + 0.851486i \(0.324298\pi\)
\(458\) −8.66679 7.45837i −0.404972 0.348507i
\(459\) 5.30493 3.06280i 0.247613 0.142959i
\(460\) −5.51484 3.70601i −0.257131 0.172793i
\(461\) 2.66546 5.53489i 0.124143 0.257786i −0.829630 0.558314i \(-0.811449\pi\)
0.953773 + 0.300528i \(0.0971629\pi\)
\(462\) 3.08090 + 0.941447i 0.143337 + 0.0438001i
\(463\) −15.4583 5.40909i −0.718407 0.251382i −0.0537759 0.998553i \(-0.517126\pi\)
−0.664631 + 0.747171i \(0.731411\pi\)
\(464\) 2.90870 + 0.217977i 0.135033 + 0.0101193i
\(465\) −16.6029 + 3.90685i −0.769939 + 0.181176i
\(466\) −21.7260 + 6.70157i −1.00644 + 0.310444i
\(467\) −16.8261 + 14.4801i −0.778621 + 0.670057i −0.948984 0.315324i \(-0.897887\pi\)
0.170363 + 0.985381i \(0.445506\pi\)
\(468\) 4.99995 14.2890i 0.231123 0.660511i
\(469\) 20.0658 + 14.7277i 0.926554 + 0.680063i
\(470\) 18.9285 5.20823i 0.873108 0.240238i
\(471\) 9.10780 15.7752i 0.419665 0.726881i
\(472\) 0.0904974 0.337741i 0.00416548 0.0155458i
\(473\) −1.43793 + 1.67091i −0.0661162 + 0.0768284i
\(474\) 15.0638 + 38.3820i 0.691904 + 1.76294i
\(475\) 1.62046 + 0.611025i 0.0743519 + 0.0280357i
\(476\) 0.876858 7.97110i 0.0401907 0.365355i
\(477\) 29.7054 + 18.6652i 1.36012 + 0.854619i
\(478\) −2.94856 0.557898i −0.134864 0.0255176i
\(479\) −21.9525 + 20.3690i −1.00304 + 0.930683i −0.997596 0.0693023i \(-0.977923\pi\)
−0.00544186 + 0.999985i \(0.501732\pi\)
\(480\) −3.12985 4.90774i −0.142858 0.224007i
\(481\) 23.9159 25.7752i 1.09047 1.17525i
\(482\) −2.91169 + 25.8420i −0.132624 + 1.17707i
\(483\) 13.9594 + 14.9654i 0.635175 + 0.680948i
\(484\) 8.42909 + 6.72197i 0.383140 + 0.305544i
\(485\) −33.0736 + 2.70176i −1.50180 + 0.122680i
\(486\) 12.3138 18.0610i 0.558564 0.819262i
\(487\) −10.9191 25.0268i −0.494791 1.13407i −0.967504 0.252856i \(-0.918630\pi\)
0.472713 0.881216i \(-0.343275\pi\)
\(488\) 4.60773 2.43525i 0.208582 0.110239i
\(489\) −29.4288 −1.33082
\(490\) 12.8261 8.97165i 0.579425 0.405298i
\(491\) 33.9469 1.53200 0.766001 0.642839i \(-0.222244\pi\)
0.766001 + 0.642839i \(0.222244\pi\)
\(492\) 11.3271 5.98656i 0.510667 0.269895i
\(493\) −3.53541 8.10324i −0.159227 0.364952i
\(494\) −0.782171 + 1.14723i −0.0351915 + 0.0516165i
\(495\) −3.01105 2.55626i −0.135337 0.114895i
\(496\) −2.29095 1.82697i −0.102867 0.0820333i
\(497\) 34.6415 2.68785i 1.55388 0.120567i
\(498\) 1.86167 16.5228i 0.0834233 0.740403i
\(499\) −2.59909 + 2.80115i −0.116351 + 0.125397i −0.788541 0.614982i \(-0.789163\pi\)
0.672190 + 0.740379i \(0.265354\pi\)
\(500\) 10.1554 4.67624i 0.454165 0.209128i
\(501\) −8.58665 + 7.96725i −0.383623 + 0.355950i
\(502\) −5.80364 1.09811i −0.259029 0.0490110i
\(503\) −27.2226 17.1051i −1.21380 0.762679i −0.235901 0.971777i \(-0.575804\pi\)
−0.977895 + 0.209098i \(0.932947\pi\)
\(504\) 3.32477 + 9.42193i 0.148097 + 0.419686i
\(505\) −27.5262 + 14.7851i −1.22490 + 0.657927i
\(506\) −0.507789 1.29383i −0.0225740 0.0575176i
\(507\) −5.21315 + 6.05779i −0.231524 + 0.269036i
\(508\) 0.517725 1.93218i 0.0229703 0.0857265i
\(509\) −12.4305 + 21.5302i −0.550971 + 0.954310i 0.447234 + 0.894417i \(0.352409\pi\)
−0.998205 + 0.0598927i \(0.980924\pi\)
\(510\) −8.71865 + 15.3379i −0.386069 + 0.679172i
\(511\) 27.4060 23.7107i 1.21237 1.04890i
\(512\) 0.330279 0.943883i 0.0145964 0.0417141i
\(513\) 0.530588 0.456608i 0.0234260 0.0201597i
\(514\) 5.84389 1.80260i 0.257763 0.0795093i
\(515\) −0.585369 2.48763i −0.0257944 0.109618i
\(516\) −12.2340 0.916808i −0.538570 0.0403602i
\(517\) 3.87626 + 1.35636i 0.170478 + 0.0596527i
\(518\) −1.67321 + 23.1460i −0.0735167 + 1.01697i
\(519\) 13.0033 27.0017i 0.570784 1.18524i
\(520\) 1.72553 + 8.79621i 0.0756696 + 0.385740i
\(521\) −26.0936 + 15.0651i −1.14318 + 0.660015i −0.947216 0.320596i \(-0.896117\pi\)
−0.195964 + 0.980611i \(0.562784\pi\)
\(522\) 8.34917 + 7.18504i 0.365433 + 0.314481i
\(523\) 17.5217 + 7.64462i 0.766168 + 0.334276i 0.746373 0.665528i \(-0.231794\pi\)
0.0197957 + 0.999804i \(0.493698\pi\)
\(524\) −3.14374 + 13.7736i −0.137335 + 0.601703i
\(525\) −33.7289 + 6.94442i −1.47205 + 0.303079i
\(526\) −0.345818 1.51513i −0.0150784 0.0660627i
\(527\) −1.65116 + 8.72660i −0.0719258 + 0.380137i
\(528\) 0.0455285 1.21677i 0.00198137 0.0529533i
\(529\) −2.11199 + 14.0121i −0.0918257 + 0.609224i
\(530\) −20.7634 0.637464i −0.901907 0.0276897i
\(531\) 1.03235 0.823273i 0.0448002 0.0357270i
\(532\) −0.0708911 0.913655i −0.00307352 0.0396120i
\(533\) −19.6057 + 2.20904i −0.849219 + 0.0956840i
\(534\) −6.74699 44.7633i −0.291971 1.93710i
\(535\) 4.65378 5.91665i 0.201201 0.255799i
\(536\) 3.43704 8.75744i 0.148458 0.378264i
\(537\) −13.4425 25.4345i −0.580087 1.09758i
\(538\) 5.03412 5.03412i 0.217036 0.217036i
\(539\) 3.27421 0.0172599i 0.141030 0.000743436i
\(540\) 0.307475 4.50864i 0.0132316 0.194021i
\(541\) 7.83901 + 2.41801i 0.337025 + 0.103959i 0.458648 0.888618i \(-0.348334\pi\)
−0.121623 + 0.992576i \(0.538810\pi\)
\(542\) 14.2834 6.23176i 0.613522 0.267677i
\(543\) 3.40250 + 17.9826i 0.146015 + 0.771709i
\(544\) −2.99711 + 0.451742i −0.128500 + 0.0193683i
\(545\) 30.8093 1.35983i 1.31973 0.0582486i
\(546\) 0.959628 27.5928i 0.0410683 1.18086i
\(547\) −38.1334 4.29660i −1.63047 0.183709i −0.751211 0.660062i \(-0.770530\pi\)
−0.879255 + 0.476352i \(0.841959\pi\)
\(548\) −0.330710 8.83840i −0.0141272 0.377558i
\(549\) 19.4614 + 2.93334i 0.830593 + 0.125192i
\(550\) 2.30361 + 0.403933i 0.0982263 + 0.0172238i
\(551\) −0.569124 0.834752i −0.0242455 0.0355616i
\(552\) 4.11535 6.54954i 0.175161 0.278767i
\(553\) 26.2149 + 32.6952i 1.11477 + 1.39034i
\(554\) 19.9878 + 4.56208i 0.849199 + 0.193824i
\(555\) 23.5532 45.2979i 0.999779 1.92279i
\(556\) 7.72735 0.579085i 0.327713 0.0245587i
\(557\) −12.1791 3.26338i −0.516045 0.138274i −0.00860843 0.999963i \(-0.502740\pi\)
−0.507437 + 0.861689i \(0.669407\pi\)
\(558\) −2.86400 10.6886i −0.121243 0.452484i
\(559\) 17.0218 + 8.19725i 0.719944 + 0.346707i
\(560\) −4.52008 3.81692i −0.191008 0.161294i
\(561\) −3.32510 + 1.60128i −0.140386 + 0.0676063i
\(562\) 20.1567 + 23.4225i 0.850257 + 0.988017i
\(563\) −9.59419 + 18.1531i −0.404347 + 0.765062i −0.999249 0.0387361i \(-0.987667\pi\)
0.594903 + 0.803798i \(0.297191\pi\)
\(564\) 6.73658 + 21.8395i 0.283661 + 0.919607i
\(565\) −5.36663 + 37.3015i −0.225776 + 1.56928i
\(566\) 10.2038 + 21.1884i 0.428897 + 0.890614i
\(567\) 4.69178 15.3539i 0.197036 0.644804i
\(568\) −4.33742 12.3956i −0.181994 0.520109i
\(569\) 17.9212 + 10.3468i 0.751297 + 0.433761i 0.826162 0.563432i \(-0.190519\pi\)
−0.0748656 + 0.997194i \(0.523853\pi\)
\(570\) −0.653107 + 1.90742i −0.0273556 + 0.0798931i
\(571\) −0.618145 8.24857i −0.0258686 0.345192i −0.995088 0.0989937i \(-0.968438\pi\)
0.969220 0.246198i \(-0.0791814\pi\)
\(572\) −0.749839 + 1.71865i −0.0313523 + 0.0718603i
\(573\) −22.9899 36.5882i −0.960415 1.52849i
\(574\) 9.18330 9.23184i 0.383304 0.385329i
\(575\) 11.3904 + 9.53928i 0.475013 + 0.397815i
\(576\) 3.12018 2.12731i 0.130008 0.0886377i
\(577\) −11.4831 0.429667i −0.478047 0.0178873i −0.202718 0.979237i \(-0.564977\pi\)
−0.275329 + 0.961350i \(0.588787\pi\)
\(578\) −4.63965 6.28651i −0.192984 0.261484i
\(579\) 21.3745 + 19.8327i 0.888295 + 0.824217i
\(580\) −6.41658 1.16955i −0.266434 0.0485630i
\(581\) −3.18556 16.5965i −0.132159 0.688538i
\(582\) −4.32534 38.3884i −0.179291 1.59125i
\(583\) −3.49633 2.58041i −0.144803 0.106870i
\(584\) −11.3171 7.71589i −0.468306 0.319286i
\(585\) −14.4824 + 30.5964i −0.598774 + 1.26501i
\(586\) 0.0846925 0.274566i 0.00349861 0.0113422i
\(587\) −12.8087 12.8087i −0.528673 0.528673i 0.391504 0.920177i \(-0.371955\pi\)
−0.920177 + 0.391504i \(0.871955\pi\)
\(588\) 10.8977 + 14.6042i 0.449415 + 0.602265i
\(589\) 1.01494i 0.0418197i
\(590\) −0.280754 + 0.729706i −0.0115585 + 0.0300415i
\(591\) −0.190857 0.0749060i −0.00785082 0.00308122i
\(592\) 8.61826 1.63066i 0.354208 0.0670199i
\(593\) −20.3940 + 27.6329i −0.837480 + 1.13475i 0.151756 + 0.988418i \(0.451507\pi\)
−0.989236 + 0.146328i \(0.953255\pi\)
\(594\) 0.589403 0.739088i 0.0241835 0.0303251i
\(595\) −3.82660 + 17.5184i −0.156875 + 0.718184i
\(596\) 8.69166 + 10.8990i 0.356024 + 0.446440i
\(597\) 35.8880 1.34283i 1.46880 0.0549585i
\(598\) −9.58427 + 7.07351i −0.391930 + 0.289258i
\(599\) −22.2372 23.9660i −0.908585 0.979222i 0.0912767 0.995826i \(-0.470905\pi\)
−0.999862 + 0.0166033i \(0.994715\pi\)
\(600\) 5.80413 + 11.6499i 0.236953 + 0.475607i
\(601\) −37.2395 + 8.49967i −1.51903 + 0.346709i −0.899028 0.437891i \(-0.855725\pi\)
−0.620002 + 0.784600i \(0.712868\pi\)
\(602\) −12.1491 + 2.80666i −0.495159 + 0.114391i
\(603\) 30.0818 18.9016i 1.22502 0.769734i
\(604\) 20.4272 8.01709i 0.831172 0.326211i
\(605\) −17.1606 16.9319i −0.697676 0.688378i
\(606\) −18.1875 31.5016i −0.738816 1.27967i
\(607\) 33.5035 8.97724i 1.35987 0.364375i 0.496099 0.868266i \(-0.334765\pi\)
0.863767 + 0.503891i \(0.168099\pi\)
\(608\) −0.326930 + 0.114398i −0.0132588 + 0.00463944i
\(609\) 18.4341 + 7.98496i 0.746989 + 0.323567i
\(610\) −10.8193 + 4.33024i −0.438060 + 0.175326i
\(611\) 2.63018 35.0973i 0.106406 1.41988i
\(612\) −10.1196 5.34838i −0.409062 0.216196i
\(613\) −2.79673 1.47811i −0.112959 0.0597005i 0.409835 0.912160i \(-0.365586\pi\)
−0.522794 + 0.852459i \(0.675110\pi\)
\(614\) 1.09213 14.5734i 0.0440747 0.588136i
\(615\) −26.5970 + 10.6450i −1.07249 + 0.429247i
\(616\) −0.323452 1.19454i −0.0130323 0.0481293i
\(617\) 29.3618 10.2742i 1.18206 0.413622i 0.333517 0.942744i \(-0.391764\pi\)
0.848546 + 0.529122i \(0.177479\pi\)
\(618\) 2.87372 0.770012i 0.115598 0.0309744i
\(619\) −16.6532 28.8442i −0.669350 1.15935i −0.978086 0.208200i \(-0.933240\pi\)
0.308737 0.951148i \(-0.400094\pi\)
\(620\) 4.66408 + 4.60192i 0.187314 + 0.184817i
\(621\) 5.59022 2.19400i 0.224328 0.0880421i
\(622\) −23.0858 + 14.5058i −0.925656 + 0.581628i
\(623\) −20.0721 41.4007i −0.804172 1.65868i
\(624\) −10.1738 + 2.32209i −0.407276 + 0.0929581i
\(625\) −23.6830 + 8.00718i −0.947321 + 0.320287i
\(626\) 12.3037 + 13.2603i 0.491756 + 0.529987i
\(627\) −0.339335 + 0.250441i −0.0135517 + 0.0100016i
\(628\) −6.99264 + 0.261646i −0.279037 + 0.0104408i
\(629\) −16.5756 20.7851i −0.660911 0.828757i
\(630\) −5.17471 21.7338i −0.206165 0.865894i
\(631\) 0.399612 0.501098i 0.0159083 0.0199484i −0.773814 0.633413i \(-0.781653\pi\)
0.789722 + 0.613465i \(0.210225\pi\)
\(632\) 9.40573 12.7443i 0.374140 0.506942i
\(633\) 49.6592 9.39603i 1.97378 0.373459i
\(634\) −3.72568 1.46222i −0.147966 0.0580722i
\(635\) −1.60616 + 4.17456i −0.0637386 + 0.165663i
\(636\) 24.1834i 0.958935i
\(637\) −7.40559 27.0665i −0.293420 1.07241i
\(638\) −0.964752 0.964752i −0.0381949 0.0381949i
\(639\) 14.6180 47.3902i 0.578277 1.87473i
\(640\) −0.956657 + 2.02109i −0.0378152 + 0.0798906i
\(641\) 31.4033 + 21.4104i 1.24036 + 0.845661i 0.992393 0.123108i \(-0.0392862\pi\)
0.247964 + 0.968769i \(0.420239\pi\)
\(642\) 7.05095 + 5.20384i 0.278279 + 0.205379i
\(643\) −0.942320 8.36332i −0.0371615 0.329817i −0.998514 0.0544966i \(-0.982645\pi\)
0.961352 0.275320i \(-0.0887840\pi\)
\(644\) 2.01475 7.59920i 0.0793922 0.299450i
\(645\) 26.9880 + 4.91912i 1.06265 + 0.193690i
\(646\) 0.769578 + 0.714064i 0.0302786 + 0.0280945i
\(647\) 11.5346 + 15.6288i 0.453471 + 0.614432i 0.970373 0.241613i \(-0.0776766\pi\)
−0.516902 + 0.856045i \(0.672915\pi\)
\(648\) −6.06389 0.226895i −0.238212 0.00891327i
\(649\) −0.135133 + 0.0921319i −0.00530442 + 0.00361649i
\(650\) −1.76590 19.9659i −0.0692643 0.783126i
\(651\) −10.7821 17.0597i −0.422584 0.668620i
\(652\) 6.01468 + 9.57230i 0.235553 + 0.374880i
\(653\) 15.6208 35.8033i 0.611290 1.40109i −0.285390 0.958412i \(-0.592123\pi\)
0.896680 0.442680i \(-0.145972\pi\)
\(654\) 2.68296 + 35.8016i 0.104912 + 1.39995i
\(655\) 10.2335 29.8874i 0.399857 1.16780i
\(656\) −4.26229 2.46083i −0.166415 0.0960795i
\(657\) −17.0839 48.8229i −0.666505 1.90476i
\(658\) 13.1358 + 19.1581i 0.512088 + 0.746859i
\(659\) 3.79622 + 7.88294i 0.147880 + 0.307076i 0.961730 0.273999i \(-0.0883466\pi\)
−0.813850 + 0.581075i \(0.802632\pi\)
\(660\) −0.387727 + 2.69494i −0.0150922 + 0.104901i
\(661\) 9.77230 + 31.6810i 0.380098 + 1.23225i 0.920467 + 0.390820i \(0.127809\pi\)
−0.540369 + 0.841428i \(0.681715\pi\)
\(662\) −12.6739 + 23.9803i −0.492587 + 0.932020i
\(663\) 20.6314 + 23.9741i 0.801258 + 0.931079i
\(664\) −5.75484 + 2.77138i −0.223331 + 0.107551i
\(665\) −0.0574828 + 2.04833i −0.00222909 + 0.0794307i
\(666\) 29.8430 + 14.3716i 1.15639 + 0.556889i
\(667\) −2.24327 8.37200i −0.0868598 0.324165i
\(668\) 4.34645 + 1.16463i 0.168169 + 0.0450608i
\(669\) −5.03012 + 0.376955i −0.194476 + 0.0145739i
\(670\) −9.70467 + 18.6641i −0.374924 + 0.721058i
\(671\) −2.37665 0.542455i −0.0917496 0.0209412i
\(672\) 4.27994 5.39599i 0.165102 0.208155i
\(673\) 14.7453 23.4670i 0.568390 0.904588i −0.431607 0.902062i \(-0.642053\pi\)
0.999997 0.00252593i \(-0.000804029\pi\)
\(674\) 9.18762 + 13.4758i 0.353894 + 0.519067i
\(675\) −1.74527 + 9.95318i −0.0671753 + 0.383098i
\(676\) 3.03588 + 0.457585i 0.116765 + 0.0175994i
\(677\) 0.352692 + 9.42590i 0.0135551 + 0.362267i 0.989525 + 0.144362i \(0.0461129\pi\)
−0.975970 + 0.217905i \(0.930078\pi\)
\(678\) −43.5962 4.91211i −1.67430 0.188649i
\(679\) −15.7960 35.9460i −0.606195 1.37948i
\(680\) 6.77086 0.298844i 0.259651 0.0114602i
\(681\) −48.4562 + 7.30359i −1.85684 + 0.279874i
\(682\) 0.254814 + 1.34673i 0.00975734 + 0.0515688i
\(683\) 23.6343 10.3115i 0.904342 0.394560i 0.104329 0.994543i \(-0.466731\pi\)
0.800013 + 0.599983i \(0.204826\pi\)
\(684\) −1.24990 0.385543i −0.0477911 0.0147416i
\(685\) −1.34561 + 19.7313i −0.0514132 + 0.753893i
\(686\) 14.9879 + 10.8795i 0.572239 + 0.415383i
\(687\) −21.0469 + 21.0469i −0.802990 + 0.802990i
\(688\) 2.20217 + 4.16671i 0.0839570 + 0.158854i
\(689\) −13.6059 + 34.6673i −0.518344 + 1.32072i
\(690\) −10.6931 + 13.5948i −0.407080 + 0.517547i
\(691\) 1.25334 + 8.31539i 0.0476794 + 0.316332i 0.999939 + 0.0110428i \(0.00351511\pi\)
−0.952260 + 0.305289i \(0.901247\pi\)
\(692\) −11.4405 + 1.28903i −0.434901 + 0.0490016i
\(693\) 1.69594 4.35489i 0.0644233 0.165429i
\(694\) −1.64179 + 1.30928i −0.0623215 + 0.0496997i
\(695\) −17.3192 0.531720i −0.656954 0.0201693i
\(696\) 1.13168 7.50821i 0.0428962 0.284598i
\(697\) −0.557780 + 14.9070i −0.0211274 + 0.564643i
\(698\) −2.32731 + 12.3001i −0.0880901 + 0.465567i
\(699\) 13.1700 + 57.7014i 0.498134 + 2.18247i
\(700\) 9.15234 + 9.55169i 0.345926 + 0.361020i
\(701\) −5.05618 + 22.1526i −0.190969 + 0.836692i 0.785124 + 0.619339i \(0.212599\pi\)
−0.976093 + 0.217353i \(0.930258\pi\)
\(702\) −7.42574 3.23982i −0.280267 0.122279i
\(703\) −2.30275 1.98168i −0.0868500 0.0747404i
\(704\) −0.405085 + 0.233876i −0.0152672 + 0.00881452i
\(705\) −9.83764 50.1492i −0.370507 1.88873i
\(706\) −0.763465 + 1.58535i −0.0287334 + 0.0596655i
\(707\) −27.1673 25.0747i −1.02173 0.943030i
\(708\) −0.859126 0.300621i −0.0322879 0.0112980i
\(709\) −30.3892 2.27736i −1.14129 0.0855280i −0.509361 0.860553i \(-0.670118\pi\)
−0.631931 + 0.775025i \(0.717737\pi\)
\(710\) 6.72631 + 28.5846i 0.252434 + 1.07276i
\(711\) 57.1579 17.6309i 2.14359 0.661209i
\(712\) −13.1812 + 11.3433i −0.493986 + 0.425109i
\(713\) −2.87576 + 8.21846i −0.107698 + 0.307784i
\(714\) −20.5214 3.82685i −0.767992 0.143216i
\(715\) 2.07202 3.64511i 0.0774893 0.136319i
\(716\) −5.52567 + 9.57074i −0.206504 + 0.357676i
\(717\) −2.02182 + 7.54554i −0.0755063 + 0.281793i
\(718\) −2.71730 + 3.15756i −0.101409 + 0.117839i
\(719\) 12.1653 + 30.9968i 0.453691 + 1.15599i 0.956537 + 0.291610i \(0.0941908\pi\)
−0.502847 + 0.864376i \(0.667714\pi\)
\(720\) −7.43903 + 3.99571i −0.277236 + 0.148911i
\(721\) 2.55607 1.61550i 0.0951929 0.0601642i
\(722\) −15.9862 10.0448i −0.594944 0.373828i
\(723\) 66.5159 + 12.5855i 2.47375 + 0.468059i
\(724\) 5.15380 4.78203i 0.191540 0.177723i
\(725\) 13.9928 + 4.11144i 0.519679 + 0.152695i
\(726\) 19.0891 20.5731i 0.708463 0.763541i
\(727\) 2.61607 23.2183i 0.0970246 0.861117i −0.847079 0.531468i \(-0.821641\pi\)
0.944103 0.329650i \(-0.106931\pi\)
\(728\) −9.17122 + 5.32728i −0.339908 + 0.197442i
\(729\) −30.2557 24.1281i −1.12058 0.893633i
\(730\) 23.3485 + 19.8219i 0.864166 + 0.733643i
\(731\) 8.04676 11.8024i 0.297620 0.436529i
\(732\) −5.42524 12.4348i −0.200523 0.459603i
\(733\) 43.2891 22.8790i 1.59892 0.845054i 0.599932 0.800051i \(-0.295194\pi\)
0.998987 0.0450028i \(-0.0143297\pi\)
\(734\) −20.3302 −0.750400
\(735\) −20.7941 35.0402i −0.767002 1.29248i
\(736\) −2.97146 −0.109530
\(737\) −3.89055 + 2.05621i −0.143310 + 0.0757416i
\(738\) −7.43241 17.0353i −0.273591 0.627077i
\(739\) −3.29260 + 4.82936i −0.121120 + 0.177651i −0.882010 0.471230i \(-0.843810\pi\)
0.760890 + 0.648881i \(0.224763\pi\)
\(740\) −19.5478 + 1.59684i −0.718593 + 0.0587012i
\(741\) 2.82591 + 2.25359i 0.103812 + 0.0827876i
\(742\) −7.30673 23.4681i −0.268239 0.861539i
\(743\) −3.39153 + 30.1006i −0.124423 + 1.10429i 0.763986 + 0.645233i \(0.223240\pi\)
−0.888409 + 0.459053i \(0.848189\pi\)
\(744\) −5.18824 + 5.59159i −0.190210 + 0.204998i
\(745\) −16.7609 26.2818i −0.614073 0.962892i
\(746\) −9.14318 + 8.48363i −0.334755 + 0.310608i
\(747\) −23.7006 4.48440i −0.867161 0.164076i
\(748\) 1.20043 + 0.754283i 0.0438922 + 0.0275793i
\(749\) 8.41466 + 2.91954i 0.307465 + 0.106678i
\(750\) −10.1633 27.2718i −0.371112 0.995827i
\(751\) 10.7455 + 27.3791i 0.392109 + 0.999078i 0.981540 + 0.191259i \(0.0612571\pi\)
−0.589430 + 0.807819i \(0.700648\pi\)
\(752\) 5.72688 6.65476i 0.208838 0.242674i
\(753\) −3.97955 + 14.8519i −0.145023 + 0.541232i
\(754\) −5.84650 + 10.1264i −0.212917 + 0.368783i
\(755\) −47.3103 + 13.0175i −1.72180 + 0.473757i
\(756\) 5.16122 1.39753i 0.187712 0.0508279i
\(757\) −9.26757 + 26.4852i −0.336836 + 0.962621i 0.643528 + 0.765423i \(0.277470\pi\)
−0.980364 + 0.197198i \(0.936816\pi\)
\(758\) 7.45816 6.41827i 0.270893 0.233122i
\(759\) −3.45738 + 1.06646i −0.125495 + 0.0387101i
\(760\) 0.753909 0.177404i 0.0273471 0.00643511i
\(761\) −37.2511 2.79158i −1.35035 0.101195i −0.620180 0.784459i \(-0.712940\pi\)
−0.730171 + 0.683265i \(0.760560\pi\)
\(762\) −4.91496 1.71982i −0.178050 0.0623025i
\(763\) 13.4206 + 33.9319i 0.485859 + 1.22842i
\(764\) −7.20234 + 14.9558i −0.260571 + 0.541082i
\(765\) 21.2431 + 14.2755i 0.768047 + 0.516133i
\(766\) 0.456616 0.263627i 0.0164982 0.00952524i
\(767\) 1.06244 + 0.914301i 0.0383624 + 0.0330135i
\(768\) −2.38595 1.04098i −0.0860954 0.0375630i
\(769\) 5.60002 24.5353i 0.201942 0.884765i −0.767811 0.640676i \(-0.778654\pi\)
0.969753 0.244089i \(-0.0784888\pi\)
\(770\) 0.437988 + 2.73237i 0.0157840 + 0.0984679i
\(771\) −3.54248 15.5206i −0.127579 0.558961i
\(772\) 2.08243 11.0059i 0.0749481 0.396110i
\(773\) −1.16881 + 31.2371i −0.0420392 + 1.12352i 0.805435 + 0.592684i \(0.201932\pi\)
−0.847474 + 0.530837i \(0.821878\pi\)
\(774\) −2.65258 + 17.5987i −0.0953450 + 0.632573i
\(775\) −9.28770 11.3311i −0.333624 0.407027i
\(776\) −11.6026 + 9.25274i −0.416508 + 0.332154i
\(777\) 59.7583 + 8.84610i 2.14382 + 0.317352i
\(778\) −36.8695 + 4.15419i −1.32183 + 0.148935i
\(779\) 0.254073 + 1.68566i 0.00910311 + 0.0603952i
\(780\) 23.1695 2.76810i 0.829600 0.0991137i
\(781\) −2.24421 + 5.71816i −0.0803042 + 0.204612i
\(782\) 4.20841 + 7.96270i 0.150492 + 0.284746i
\(783\) 4.16839 4.16839i 0.148966 0.148966i
\(784\) 2.52300 6.52951i 0.0901072 0.233197i
\(785\) 15.6107 + 1.06460i 0.557169 + 0.0379973i
\(786\) 35.1429 + 10.8402i 1.25351 + 0.386656i
\(787\) −43.5558 + 19.0032i −1.55260 + 0.677392i −0.988899 0.148589i \(-0.952527\pi\)
−0.563699 + 0.825980i \(0.690622\pi\)
\(788\) 0.0146429 + 0.0773894i 0.000521630 + 0.00275688i
\(789\) −4.00034 + 0.602955i −0.142416 + 0.0214658i
\(790\) −23.9156 + 26.1242i −0.850878 + 0.929456i
\(791\) −43.7908 + 8.40527i −1.55702 + 0.298857i
\(792\) −1.75530 0.197774i −0.0623717 0.00702761i
\(793\) 0.781191 + 20.8778i 0.0277409 + 0.741392i
\(794\) 8.27170 + 1.24676i 0.293552 + 0.0442458i
\(795\) −5.69396 + 53.7751i −0.201944 + 1.90721i
\(796\) −7.77158 11.3988i −0.275456 0.404020i
\(797\) 6.45092 10.2666i 0.228503 0.363661i −0.712719 0.701450i \(-0.752536\pi\)
0.941222 + 0.337789i \(0.109679\pi\)
\(798\) −2.38552 + 0.00628754i −0.0844464 + 0.000222576i
\(799\) −25.9438 5.92150i −0.917825 0.209488i
\(800\) 2.60312 4.26893i 0.0920343 0.150929i
\(801\) −65.4878 + 4.90763i −2.31390 + 0.173403i
\(802\) 10.9435 + 2.93231i 0.386430 + 0.103544i
\(803\) 1.65822 + 6.18856i 0.0585173 + 0.218389i
\(804\) −22.0645 10.6257i −0.778157 0.374740i
\(805\) −6.26929 + 16.4235i −0.220963 + 0.578852i
\(806\) 10.5833 5.09666i 0.372782 0.179522i
\(807\) −12.0886 14.0472i −0.425539 0.494485i
\(808\) −6.52936 + 12.3542i −0.229702 + 0.434618i
\(809\) −2.56748 8.32356i −0.0902678 0.292641i 0.899170 0.437600i \(-0.144171\pi\)
−0.989438 + 0.144959i \(0.953695\pi\)
\(810\) 13.4305 + 1.93227i 0.471899 + 0.0678930i
\(811\) 13.5874 + 28.2144i 0.477117 + 0.990743i 0.991122 + 0.132956i \(0.0424469\pi\)
−0.514005 + 0.857787i \(0.671839\pi\)
\(812\) −1.17031 7.62803i −0.0410699 0.267691i
\(813\) −13.3982 38.2900i −0.469897 1.34289i
\(814\) −3.55307 2.05137i −0.124535 0.0719003i
\(815\) −11.1207 22.7015i −0.389540 0.795198i
\(816\) 0.589624 + 7.86799i 0.0206410 + 0.275435i
\(817\) 0.652775 1.49618i 0.0228377 0.0523446i
\(818\) −1.83271 2.91674i −0.0640793 0.101982i
\(819\) −39.8127 4.37958i −1.39117 0.153035i
\(820\) 8.89839 + 6.47556i 0.310745 + 0.226136i
\(821\) −19.3481 + 13.1913i −0.675252 + 0.460379i −0.851768 0.523919i \(-0.824470\pi\)
0.176516 + 0.984298i \(0.443517\pi\)
\(822\) −23.0077 0.860886i −0.802484 0.0300268i
\(823\) 25.6113 + 34.7020i 0.892753 + 1.20964i 0.977010 + 0.213193i \(0.0683864\pi\)
−0.0842572 + 0.996444i \(0.526852\pi\)
\(824\) −0.837794 0.777360i −0.0291859 0.0270806i
\(825\) 1.49669 5.90129i 0.0521079 0.205457i
\(826\) −0.924541 0.0321539i −0.0321689 0.00111878i
\(827\) −4.87827 43.2958i −0.169634 1.50554i −0.733507 0.679682i \(-0.762118\pi\)
0.563873 0.825862i \(-0.309311\pi\)
\(828\) −9.02866 6.66346i −0.313768 0.231571i
\(829\) 45.3796 + 30.9393i 1.57610 + 1.07457i 0.957331 + 0.288992i \(0.0933202\pi\)
0.618768 + 0.785574i \(0.287632\pi\)
\(830\) 13.4492 4.80759i 0.466828 0.166874i
\(831\) 15.7308 50.9981i 0.545697 1.76911i
\(832\) 2.83462 + 2.83462i 0.0982729 + 0.0982729i
\(833\) −21.0706 + 2.48663i −0.730051 + 0.0861567i
\(834\) 20.1718i 0.698493i
\(835\) −9.39071 3.61307i −0.324979 0.125036i
\(836\) 0.150814 + 0.0591902i 0.00521602 + 0.00204714i
\(837\) −5.81878 + 1.10097i −0.201126 + 0.0380552i
\(838\) 7.84752 10.6330i 0.271088 0.367311i
\(839\) 1.25847 1.57807i 0.0434471 0.0544809i −0.759633 0.650352i \(-0.774622\pi\)
0.803080 + 0.595871i \(0.203193\pi\)
\(840\) −10.7875 + 10.9910i −0.372205 + 0.379226i
\(841\) 12.7765 + 16.0212i 0.440569 + 0.552456i
\(842\) −29.5264 + 1.10480i −1.01755 + 0.0380739i
\(843\) 64.7227 47.7675i 2.22917 1.64520i
\(844\) −13.2056 14.2323i −0.454556 0.489895i
\(845\) −6.64296 1.73230i −0.228525 0.0595929i
\(846\) 32.3241 7.37777i 1.11133 0.253653i
\(847\) 12.3085 25.7321i 0.422925 0.884166i
\(848\) −7.86613 + 4.94262i −0.270124 + 0.169730i
\(849\) 56.9872 22.3658i 1.95580 0.767593i
\(850\) −15.1263 0.929669i −0.518828 0.0318874i
\(851\) −13.0316 22.5714i −0.446718 0.773738i
\(852\) −33.0212 + 8.84800i −1.13129 + 0.303128i
\(853\) 43.1773 15.1084i 1.47836 0.517302i 0.533794 0.845614i \(-0.320766\pi\)
0.944569 + 0.328313i \(0.106480\pi\)
\(854\) −9.02178 10.4278i −0.308719 0.356831i
\(855\) 2.68855 + 1.15159i 0.0919463 + 0.0393837i
\(856\) 0.251574 3.35702i 0.00859862 0.114741i
\(857\) 41.4134 + 21.8876i 1.41466 + 0.747667i 0.987664 0.156588i \(-0.0500495\pi\)
0.426992 + 0.904256i \(0.359573\pi\)
\(858\) 4.31552 + 2.28082i 0.147329 + 0.0778658i
\(859\) 2.89545 38.6371i 0.0987914 1.31828i −0.698903 0.715217i \(-0.746328\pi\)
0.797694 0.603062i \(-0.206053\pi\)
\(860\) −3.91578 9.78375i −0.133527 0.333623i
\(861\) −22.1782 25.6345i −0.755830 0.873622i
\(862\) 4.51786 1.58087i 0.153879 0.0538446i
\(863\) −26.5709 + 7.11964i −0.904482 + 0.242355i −0.680940 0.732339i \(-0.738429\pi\)
−0.223542 + 0.974694i \(0.571762\pi\)
\(864\) −1.01050 1.75024i −0.0343780 0.0595445i
\(865\) 25.7430 0.172694i 0.875287 0.00587178i
\(866\) −6.88836 + 2.70348i −0.234076 + 0.0918680i
\(867\) −17.2215 + 10.8210i −0.584873 + 0.367500i
\(868\) −3.34533 + 6.99375i −0.113548 + 0.237383i
\(869\) −7.22313 + 1.64863i −0.245028 + 0.0559260i
\(870\) −4.28424 + 16.4291i −0.145249 + 0.556998i
\(871\) 25.6517 + 27.6460i 0.869175 + 0.936747i
\(872\) 11.0968 8.18983i 0.375786 0.277343i
\(873\) −56.0031 + 2.09549i −1.89542 + 0.0709215i
\(874\) 0.641706 + 0.804673i 0.0217060 + 0.0272185i
\(875\) −18.1026 23.3944i −0.611978 0.790875i
\(876\) −22.2310 + 27.8768i −0.751115 + 0.941869i
\(877\) −2.84263 + 3.85162i −0.0959887 + 0.130060i −0.849960 0.526847i \(-0.823374\pi\)
0.753971 + 0.656908i \(0.228136\pi\)
\(878\) 0.655516 0.124030i 0.0221226 0.00418582i
\(879\) −0.696262 0.273263i −0.0234843 0.00921693i
\(880\) 0.955827 0.424678i 0.0322209 0.0143159i
\(881\) 25.9001i 0.872597i −0.899802 0.436299i \(-0.856289\pi\)
0.899802 0.436299i \(-0.143711\pi\)
\(882\) 22.3084 14.1818i 0.751162 0.477528i
\(883\) −17.3951 17.3951i −0.585393 0.585393i 0.350987 0.936380i \(-0.385846\pi\)
−0.936380 + 0.350987i \(0.885846\pi\)
\(884\) 3.58140 11.6106i 0.120456 0.390507i
\(885\) 1.83960 + 0.870753i 0.0618376 + 0.0292700i
\(886\) −4.39271 2.99490i −0.147576 0.100616i
\(887\) 13.2634 + 9.78886i 0.445343 + 0.328678i 0.793298 0.608833i \(-0.208362\pi\)
−0.347956 + 0.937511i \(0.613124\pi\)
\(888\) −2.55645 22.6891i −0.0857887 0.761396i
\(889\) −5.28920 0.183949i −0.177394 0.00616945i
\(890\) 31.9810 22.1200i 1.07200 0.741463i
\(891\) 2.08068 + 1.93059i 0.0697054 + 0.0646771i
\(892\) 1.15067 + 1.55910i 0.0385273 + 0.0522026i
\(893\) −3.03887 0.113706i −0.101692 0.00380504i
\(894\) 29.9832 20.4422i 1.00279 0.683688i
\(895\) 14.5405 19.9809i 0.486036 0.667886i
\(896\) −2.62989 0.289300i −0.0878584 0.00966482i
\(897\) 16.4974 + 26.2555i 0.550834 + 0.876647i
\(898\) 11.8769 27.2221i 0.396336 0.908412i
\(899\) 0.638724 + 8.52318i 0.0213026 + 0.284264i
\(900\) 17.4825 7.13351i 0.582750 0.237784i
\(901\) 24.3855 + 14.0790i 0.812398 + 0.469038i
\(902\) 0.760341 + 2.17293i 0.0253166 + 0.0723507i
\(903\) 4.92231 + 32.0834i 0.163804 + 1.06767i
\(904\) 7.31245 + 15.1845i 0.243209 + 0.505028i
\(905\) −12.5861 + 9.42004i −0.418376 + 0.313133i
\(906\) −16.8375 54.5859i −0.559389 1.81350i
\(907\) 10.4158 19.7076i 0.345850 0.654379i −0.648420 0.761283i \(-0.724570\pi\)
0.994269 + 0.106904i \(0.0340936\pi\)
\(908\) 12.2791 + 14.2686i 0.407497 + 0.473520i
\(909\) −47.5432 + 22.8956i −1.57691 + 0.759399i
\(910\) 21.6478 9.68660i 0.717616 0.321108i
\(911\) −48.3275 23.2733i −1.60116 0.771079i −0.601547 0.798837i \(-0.705449\pi\)
−0.999615 + 0.0277584i \(0.991163\pi\)
\(912\) 0.233363 + 0.870921i 0.00772741 + 0.0288391i
\(913\) 2.88591 + 0.773277i 0.0955096 + 0.0255917i
\(914\) −35.0092 + 2.62358i −1.15800 + 0.0867802i
\(915\) 9.13602 + 28.9278i 0.302027 + 0.956324i
\(916\) 11.1475 + 2.54434i 0.368324 + 0.0840675i
\(917\) 37.3786 0.0985193i 1.23435 0.00325339i
\(918\) −3.25902 + 5.18670i −0.107564 + 0.171187i
\(919\) −0.442611 0.649191i −0.0146004 0.0214148i 0.818869 0.573980i \(-0.194601\pi\)
−0.833470 + 0.552565i \(0.813649\pi\)
\(920\) 6.60745 + 0.699627i 0.217841 + 0.0230660i
\(921\) −37.6182 5.67004i −1.23956 0.186834i
\(922\) 0.229704 + 6.13897i 0.00756490 + 0.202176i
\(923\) 52.3144 + 5.89442i 1.72195 + 0.194017i
\(924\) −3.16378 + 0.607261i −0.104081 + 0.0199774i
\(925\) 43.8433 + 1.05171i 1.44156 + 0.0345800i
\(926\) 16.1944 2.44091i 0.532181 0.0802134i
\(927\) −0.802387 4.24072i −0.0263538 0.139283i
\(928\) −2.67348 + 1.16643i −0.0877614 + 0.0382899i
\(929\) −39.7451 12.2598i −1.30400 0.402229i −0.436514 0.899698i \(-0.643787\pi\)
−0.867482 + 0.497468i \(0.834263\pi\)
\(930\) 12.8533 11.2121i 0.421476 0.367659i
\(931\) −2.31305 + 0.726857i −0.0758072 + 0.0238218i
\(932\) 16.0768 16.0768i 0.526614 0.526614i
\(933\) 33.1641 + 62.7495i 1.08574 + 2.05433i
\(934\) 8.11017 20.6644i 0.265373 0.676159i
\(935\) −2.49174 1.95989i −0.0814885 0.0640953i
\(936\) 2.25629 + 14.9695i 0.0737490 + 0.489293i
\(937\) −13.6820 + 1.54159i −0.446973 + 0.0503617i −0.332582 0.943074i \(-0.607920\pi\)
−0.114390 + 0.993436i \(0.536491\pi\)
\(938\) −24.6223 3.64487i −0.803947 0.119009i
\(939\) 36.8154 29.3593i 1.20143 0.958105i
\(940\) −14.3014 + 13.4494i −0.466459 + 0.438671i
\(941\) −3.32510 + 22.0606i −0.108395 + 0.719154i 0.866938 + 0.498416i \(0.166085\pi\)
−0.975333 + 0.220738i \(0.929153\pi\)
\(942\) −0.681103 + 18.2029i −0.0221915 + 0.593081i
\(943\) −2.71887 + 14.3696i −0.0885387 + 0.467938i
\(944\) 0.0778056 + 0.340889i 0.00253236 + 0.0110950i
\(945\) −11.8057 + 1.89241i −0.384040 + 0.0615601i
\(946\) 0.490536 2.14918i 0.0159487 0.0698758i
\(947\) −0.304273 0.132753i −0.00988755 0.00431389i 0.394942 0.918706i \(-0.370765\pi\)
−0.404830 + 0.914392i \(0.632669\pi\)
\(948\) −31.2528 26.8952i −1.01504 0.873517i
\(949\) 47.5523 27.4543i 1.54361 0.891205i
\(950\) −1.71819 + 0.216975i −0.0557454 + 0.00703960i
\(951\) −4.52050 + 9.38692i −0.146587 + 0.304392i
\(952\) 2.94940 + 7.45710i 0.0955907 + 0.241686i
\(953\) −26.4412 9.25219i −0.856515 0.299708i −0.133931 0.990991i \(-0.542760\pi\)
−0.722584 + 0.691283i \(0.757046\pi\)
\(954\) −34.9847 2.62174i −1.13267 0.0848819i
\(955\) 19.5367 31.5605i 0.632193 1.02127i
\(956\) 2.86755 0.884524i 0.0927434 0.0286075i
\(957\) −2.69204 + 2.31669i −0.0870215 + 0.0748880i
\(958\) 9.89080 28.2663i 0.319557 0.913242i
\(959\) −22.5872 + 6.11607i −0.729378 + 0.197498i
\(960\) 5.06038 + 2.87652i 0.163323 + 0.0928394i
\(961\) −11.2069 + 19.4109i −0.361512 + 0.626157i
\(962\) −9.10048 + 33.9635i −0.293411 + 1.09503i
\(963\) 8.29247 9.63602i 0.267221 0.310517i
\(964\) −9.50087 24.2078i −0.306002 0.779681i
\(965\) −7.22188 + 23.9828i −0.232481 + 0.772033i
\(966\) −19.3346 6.70832i −0.622080 0.215837i
\(967\) 1.69880 + 1.06743i 0.0546297 + 0.0343261i 0.559070 0.829120i \(-0.311158\pi\)
−0.504440 + 0.863447i \(0.668301\pi\)
\(968\) −10.5933 2.00435i −0.340480 0.0644223i
\(969\) 2.00332 1.85881i 0.0643560 0.0597137i
\(970\) 27.9785 17.8429i 0.898334 0.572902i
\(971\) −32.7016 + 35.2439i −1.04944 + 1.13103i −0.0582908 + 0.998300i \(0.518565\pi\)
−0.991152 + 0.132731i \(0.957625\pi\)
\(972\) −2.44746 + 21.7218i −0.0785024 + 0.696728i
\(973\) −6.09468 19.5751i −0.195386 0.627550i
\(974\) 21.3480 + 17.0244i 0.684033 + 0.545498i
\(975\) −52.1723 + 0.700016i −1.67085 + 0.0224185i
\(976\) −2.93584 + 4.30609i −0.0939741 + 0.137835i
\(977\) −2.89700 6.64000i −0.0926833 0.212432i 0.864045 0.503414i \(-0.167923\pi\)
−0.956729 + 0.290982i \(0.906018\pi\)
\(978\) 26.0185 13.7512i 0.831979 0.439714i
\(979\) 8.13424 0.259971
\(980\) −7.14761 + 13.9252i −0.228322 + 0.444825i
\(981\) 52.0828 1.66288
\(982\) −30.0130 + 15.8623i −0.957753 + 0.506187i
\(983\) −0.574249 1.31619i −0.0183157 0.0419801i 0.907164 0.420777i \(-0.138243\pi\)
−0.925480 + 0.378797i \(0.876338\pi\)
\(984\) −7.21716 + 10.5856i −0.230075 + 0.337457i
\(985\) −0.0143392 0.175534i −0.000456884 0.00559296i
\(986\) 6.91210 + 5.51222i 0.220126 + 0.175545i
\(987\) 52.2871 30.3720i 1.66432 0.966752i
\(988\) 0.155463 1.37977i 0.00494594 0.0438964i
\(989\) 9.52519 10.2657i 0.302883 0.326431i
\(990\) 3.85658 + 0.853061i 0.122570 + 0.0271121i
\(991\) −22.7820 + 21.1386i −0.723694 + 0.671490i −0.953379 0.301775i \(-0.902421\pi\)
0.229685 + 0.973265i \(0.426230\pi\)
\(992\) 2.87915 + 0.544764i 0.0914130 + 0.0172963i
\(993\) 59.7841 + 37.5648i 1.89719 + 1.19208i
\(994\) −29.3711 + 18.5632i −0.931594 + 0.588790i
\(995\) 14.5973 + 27.1766i 0.462767 + 0.861557i
\(996\) 6.07464 + 15.4779i 0.192482 + 0.490437i
\(997\) −3.70842 + 4.30926i −0.117447 + 0.136476i −0.813617 0.581401i \(-0.802505\pi\)
0.696170 + 0.717877i \(0.254886\pi\)
\(998\) 0.989003 3.69101i 0.0313063 0.116837i
\(999\) 8.86330 15.3517i 0.280423 0.485706i
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 490.2.w.a.243.13 yes 672
5.2 odd 4 inner 490.2.w.a.47.13 672
49.24 odd 42 inner 490.2.w.a.73.13 yes 672
245.122 even 84 inner 490.2.w.a.367.13 yes 672
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
490.2.w.a.47.13 672 5.2 odd 4 inner
490.2.w.a.73.13 yes 672 49.24 odd 42 inner
490.2.w.a.243.13 yes 672 1.1 even 1 trivial
490.2.w.a.367.13 yes 672 245.122 even 84 inner