Properties

Label 95.2.p.a.54.7
Level $95$
Weight $2$
Character 95.54
Analytic conductor $0.759$
Analytic rank $0$
Dimension $48$
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] = [95,2,Mod(4,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.p (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: \(0.758578819202\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 54.7
Character \(\chi\) \(=\) 95.54
Dual form 95.2.p.a.44.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.14717 - 1.36714i) q^{2} +(-0.815296 - 2.24001i) q^{3} +(-0.205786 - 1.16707i) q^{4} +(1.67705 + 1.47903i) q^{5} +(-3.99769 - 1.45504i) q^{6} +(-3.67118 + 2.11955i) q^{7} +(1.25953 + 0.727188i) q^{8} +(-2.05480 + 1.72418i) q^{9} +O(q^{10})\) \(q+(1.14717 - 1.36714i) q^{2} +(-0.815296 - 2.24001i) q^{3} +(-0.205786 - 1.16707i) q^{4} +(1.67705 + 1.47903i) q^{5} +(-3.99769 - 1.45504i) q^{6} +(-3.67118 + 2.11955i) q^{7} +(1.25953 + 0.727188i) q^{8} +(-2.05480 + 1.72418i) q^{9} +(3.94589 - 0.596068i) q^{10} +(0.245445 - 0.425123i) q^{11} +(-2.44648 + 1.41247i) q^{12} +(1.42349 - 3.91099i) q^{13} +(-1.31373 + 7.45051i) q^{14} +(1.94574 - 4.96244i) q^{15} +(4.66628 - 1.69839i) q^{16} +(-1.30884 + 1.55982i) q^{17} +4.78713i q^{18} +(-1.86816 + 3.93827i) q^{19} +(1.38102 - 2.26160i) q^{20} +(7.74092 + 6.49540i) q^{21} +(-0.299637 - 0.823245i) q^{22} +(-4.32847 + 0.763227i) q^{23} +(0.602020 - 3.41422i) q^{24} +(0.624964 + 4.96079i) q^{25} +(-3.71391 - 6.43268i) q^{26} +(-0.655764 - 0.378606i) q^{27} +(3.22915 + 3.84835i) q^{28} +(2.49937 - 2.09722i) q^{29} +(-4.55227 - 8.35287i) q^{30} +(-2.04416 - 3.54059i) q^{31} +(2.03622 - 5.59447i) q^{32} +(-1.15239 - 0.203197i) q^{33} +(0.631029 + 3.57874i) q^{34} +(-9.29160 - 1.87517i) q^{35} +(2.43509 + 2.04328i) q^{36} +2.14440i q^{37} +(3.24108 + 7.07191i) q^{38} -9.92123 q^{39} +(1.03675 + 3.08240i) q^{40} +(-4.10271 + 1.49327i) q^{41} +(17.7603 - 3.13162i) q^{42} +(10.4627 + 1.84485i) q^{43} +(-0.546658 - 0.198967i) q^{44} +(-5.99609 - 0.147571i) q^{45} +(-3.92205 + 6.79319i) q^{46} +(-1.68502 - 2.00812i) q^{47} +(-7.60880 - 9.06781i) q^{48} +(5.48502 - 9.50033i) q^{49} +(7.49905 + 4.83645i) q^{50} +(4.56109 + 1.66010i) q^{51} +(-4.85735 - 0.856482i) q^{52} +(-11.2604 + 1.98551i) q^{53} +(-1.26988 + 0.462199i) q^{54} +(1.04039 - 0.349931i) q^{55} -6.16526 q^{56} +(10.3449 + 0.973843i) q^{57} -5.82287i q^{58} +(0.415431 + 0.348588i) q^{59} +(-6.19194 - 1.24962i) q^{60} +(-2.36895 - 13.4350i) q^{61} +(-7.18550 - 1.26700i) q^{62} +(3.88903 - 10.6850i) q^{63} +(-0.346803 - 0.600680i) q^{64} +(8.17171 - 4.45354i) q^{65} +(-1.59978 + 1.34238i) q^{66} +(4.60042 + 5.48257i) q^{67} +(2.08976 + 1.20652i) q^{68} +(5.23862 + 9.07356i) q^{69} +(-13.2227 + 10.5518i) q^{70} +(1.04859 - 5.94684i) q^{71} +(-3.84187 + 0.677426i) q^{72} +(-0.702575 - 1.93031i) q^{73} +(2.93170 + 2.45999i) q^{74} +(10.6027 - 5.44444i) q^{75} +(4.98069 + 1.36984i) q^{76} +2.08093i q^{77} +(-11.3813 + 13.5637i) q^{78} +(5.01823 - 1.82649i) q^{79} +(10.3375 + 4.05327i) q^{80} +(-1.71079 + 9.70238i) q^{81} +(-2.66500 + 7.32202i) q^{82} +(7.02847 - 4.05789i) q^{83} +(5.98763 - 10.3709i) q^{84} +(-4.50199 + 0.680073i) q^{85} +(14.5246 - 12.1876i) q^{86} +(-6.73553 - 3.88876i) q^{87} +(0.618288 - 0.356969i) q^{88} +(-4.07920 - 1.48471i) q^{89} +(-7.08028 + 8.02823i) q^{90} +(3.06370 + 17.3751i) q^{91} +(1.78148 + 4.89458i) q^{92} +(-6.26436 + 7.46558i) q^{93} -4.67839 q^{94} +(-8.95780 + 3.84160i) q^{95} -14.1918 q^{96} +(3.62962 - 4.32562i) q^{97} +(-6.69607 - 18.3973i) q^{98} +(0.228649 + 1.29673i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9} - 15 q^{10} - 12 q^{11} + 6 q^{14} + 3 q^{15} - 42 q^{16} + 12 q^{19} + 42 q^{20} - 54 q^{21} + 24 q^{24} + 12 q^{25} + 12 q^{26} + 18 q^{30} - 42 q^{31} - 36 q^{34} + 6 q^{35} + 18 q^{36} - 48 q^{39} + 66 q^{40} + 6 q^{41} - 6 q^{44} - 9 q^{45} - 6 q^{46} + 12 q^{49} - 18 q^{50} + 108 q^{51} + 24 q^{54} + 36 q^{56} - 36 q^{59} - 114 q^{60} + 48 q^{61} - 18 q^{65} + 180 q^{66} + 66 q^{69} - 123 q^{70} - 24 q^{71} + 84 q^{74} + 72 q^{75} + 66 q^{76} + 48 q^{79} - 39 q^{80} - 78 q^{81} - 54 q^{84} - 84 q^{85} - 42 q^{86} - 12 q^{89} + 18 q^{90} - 30 q^{91} - 72 q^{94} - 63 q^{95} - 240 q^{96} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.14717 1.36714i 0.811171 0.966716i −0.188712 0.982033i \(-0.560431\pi\)
0.999883 + 0.0153165i \(0.00487559\pi\)
\(3\) −0.815296 2.24001i −0.470712 1.29327i −0.917181 0.398471i \(-0.869541\pi\)
0.446469 0.894799i \(-0.352681\pi\)
\(4\) −0.205786 1.16707i −0.102893 0.583536i
\(5\) 1.67705 + 1.47903i 0.749998 + 0.661441i
\(6\) −3.99769 1.45504i −1.63205 0.594018i
\(7\) −3.67118 + 2.11955i −1.38757 + 0.801116i −0.993041 0.117766i \(-0.962427\pi\)
−0.394532 + 0.918882i \(0.629093\pi\)
\(8\) 1.25953 + 0.727188i 0.445310 + 0.257100i
\(9\) −2.05480 + 1.72418i −0.684932 + 0.574726i
\(10\) 3.94589 0.596068i 1.24780 0.188493i
\(11\) 0.245445 0.425123i 0.0740043 0.128179i −0.826649 0.562719i \(-0.809755\pi\)
0.900653 + 0.434539i \(0.143089\pi\)
\(12\) −2.44648 + 1.41247i −0.706237 + 0.407746i
\(13\) 1.42349 3.91099i 0.394804 1.08471i −0.569977 0.821661i \(-0.693048\pi\)
0.964781 0.263054i \(-0.0847298\pi\)
\(14\) −1.31373 + 7.45051i −0.351108 + 1.99123i
\(15\) 1.94574 4.96244i 0.502388 1.28130i
\(16\) 4.66628 1.69839i 1.16657 0.424596i
\(17\) −1.30884 + 1.55982i −0.317440 + 0.378311i −0.901044 0.433728i \(-0.857198\pi\)
0.583603 + 0.812039i \(0.301642\pi\)
\(18\) 4.78713i 1.12834i
\(19\) −1.86816 + 3.93827i −0.428586 + 0.903501i
\(20\) 1.38102 2.26160i 0.308805 0.505709i
\(21\) 7.74092 + 6.49540i 1.68921 + 1.41741i
\(22\) −0.299637 0.823245i −0.0638828 0.175517i
\(23\) −4.32847 + 0.763227i −0.902549 + 0.159144i −0.605618 0.795755i \(-0.707074\pi\)
−0.296931 + 0.954899i \(0.595963\pi\)
\(24\) 0.602020 3.41422i 0.122887 0.696925i
\(25\) 0.624964 + 4.96079i 0.124993 + 0.992158i
\(26\) −3.71391 6.43268i −0.728358 1.26155i
\(27\) −0.655764 0.378606i −0.126202 0.0728627i
\(28\) 3.22915 + 3.84835i 0.610252 + 0.727270i
\(29\) 2.49937 2.09722i 0.464122 0.389445i −0.380523 0.924772i \(-0.624256\pi\)
0.844645 + 0.535327i \(0.179812\pi\)
\(30\) −4.55227 8.35287i −0.831127 1.52502i
\(31\) −2.04416 3.54059i −0.367143 0.635909i 0.621975 0.783037i \(-0.286331\pi\)
−0.989118 + 0.147128i \(0.952997\pi\)
\(32\) 2.03622 5.59447i 0.359956 0.988972i
\(33\) −1.15239 0.203197i −0.200605 0.0353721i
\(34\) 0.631029 + 3.57874i 0.108221 + 0.613750i
\(35\) −9.29160 1.87517i −1.57057 0.316962i
\(36\) 2.43509 + 2.04328i 0.405849 + 0.340547i
\(37\) 2.14440i 0.352538i 0.984342 + 0.176269i \(0.0564028\pi\)
−0.984342 + 0.176269i \(0.943597\pi\)
\(38\) 3.24108 + 7.07191i 0.525772 + 1.14721i
\(39\) −9.92123 −1.58867
\(40\) 1.03675 + 3.08240i 0.163925 + 0.487370i
\(41\) −4.10271 + 1.49327i −0.640736 + 0.233209i −0.641897 0.766790i \(-0.721853\pi\)
0.00116142 + 0.999999i \(0.499630\pi\)
\(42\) 17.7603 3.13162i 2.74047 0.483219i
\(43\) 10.4627 + 1.84485i 1.59554 + 0.281337i 0.899584 0.436748i \(-0.143870\pi\)
0.695956 + 0.718085i \(0.254981\pi\)
\(44\) −0.546658 0.198967i −0.0824118 0.0299955i
\(45\) −5.99609 0.147571i −0.893845 0.0219985i
\(46\) −3.92205 + 6.79319i −0.578275 + 1.00160i
\(47\) −1.68502 2.00812i −0.245785 0.292915i 0.629021 0.777388i \(-0.283456\pi\)
−0.874806 + 0.484473i \(0.839011\pi\)
\(48\) −7.60880 9.06781i −1.09824 1.30883i
\(49\) 5.48502 9.50033i 0.783574 1.35719i
\(50\) 7.49905 + 4.83645i 1.06053 + 0.683977i
\(51\) 4.56109 + 1.66010i 0.638681 + 0.232461i
\(52\) −4.85735 0.856482i −0.673593 0.118773i
\(53\) −11.2604 + 1.98551i −1.54673 + 0.272730i −0.880874 0.473350i \(-0.843045\pi\)
−0.665856 + 0.746080i \(0.731934\pi\)
\(54\) −1.26988 + 0.462199i −0.172809 + 0.0628973i
\(55\) 1.04039 0.349931i 0.140286 0.0471847i
\(56\) −6.16526 −0.823867
\(57\) 10.3449 + 0.973843i 1.37021 + 0.128989i
\(58\) 5.82287i 0.764581i
\(59\) 0.415431 + 0.348588i 0.0540845 + 0.0453823i 0.669429 0.742876i \(-0.266539\pi\)
−0.615345 + 0.788258i \(0.710983\pi\)
\(60\) −6.19194 1.24962i −0.799376 0.161325i
\(61\) −2.36895 13.4350i −0.303313 1.72018i −0.631339 0.775507i \(-0.717494\pi\)
0.328026 0.944669i \(-0.393617\pi\)
\(62\) −7.18550 1.26700i −0.912559 0.160909i
\(63\) 3.88903 10.6850i 0.489972 1.34619i
\(64\) −0.346803 0.600680i −0.0433503 0.0750850i
\(65\) 8.17171 4.45354i 1.01358 0.552394i
\(66\) −1.59978 + 1.34238i −0.196920 + 0.165235i
\(67\) 4.60042 + 5.48257i 0.562031 + 0.669802i 0.969975 0.243205i \(-0.0781986\pi\)
−0.407944 + 0.913007i \(0.633754\pi\)
\(68\) 2.08976 + 1.20652i 0.253421 + 0.146312i
\(69\) 5.23862 + 9.07356i 0.630656 + 1.09233i
\(70\) −13.2227 + 10.5518i −1.58041 + 1.26118i
\(71\) 1.04859 5.94684i 0.124444 0.705760i −0.857192 0.514997i \(-0.827793\pi\)
0.981636 0.190762i \(-0.0610960\pi\)
\(72\) −3.84187 + 0.677426i −0.452769 + 0.0798354i
\(73\) −0.702575 1.93031i −0.0822302 0.225925i 0.891763 0.452503i \(-0.149469\pi\)
−0.973993 + 0.226577i \(0.927246\pi\)
\(74\) 2.93170 + 2.45999i 0.340804 + 0.285968i
\(75\) 10.6027 5.44444i 1.22429 0.628670i
\(76\) 4.98069 + 1.36984i 0.571324 + 0.157131i
\(77\) 2.08093i 0.237144i
\(78\) −11.3813 + 13.5637i −1.28868 + 1.53579i
\(79\) 5.01823 1.82649i 0.564595 0.205496i −0.0439240 0.999035i \(-0.513986\pi\)
0.608519 + 0.793539i \(0.291764\pi\)
\(80\) 10.3375 + 4.05327i 1.15577 + 0.453170i
\(81\) −1.71079 + 9.70238i −0.190088 + 1.07804i
\(82\) −2.66500 + 7.32202i −0.294300 + 0.808582i
\(83\) 7.02847 4.05789i 0.771475 0.445411i −0.0619255 0.998081i \(-0.519724\pi\)
0.833401 + 0.552669i \(0.186391\pi\)
\(84\) 5.98763 10.3709i 0.653304 1.13156i
\(85\) −4.50199 + 0.680073i −0.488310 + 0.0737642i
\(86\) 14.5246 12.1876i 1.56623 1.31422i
\(87\) −6.73553 3.88876i −0.722125 0.416919i
\(88\) 0.618288 0.356969i 0.0659097 0.0380530i
\(89\) −4.07920 1.48471i −0.432394 0.157379i 0.116648 0.993173i \(-0.462785\pi\)
−0.549042 + 0.835795i \(0.685007\pi\)
\(90\) −7.08028 + 8.02823i −0.746327 + 0.846250i
\(91\) 3.06370 + 17.3751i 0.321163 + 1.82141i
\(92\) 1.78148 + 4.89458i 0.185732 + 0.510296i
\(93\) −6.26436 + 7.46558i −0.649584 + 0.774144i
\(94\) −4.67839 −0.482539
\(95\) −8.95780 + 3.84160i −0.919051 + 0.394140i
\(96\) −14.1918 −1.44844
\(97\) 3.62962 4.32562i 0.368533 0.439200i −0.549627 0.835410i \(-0.685230\pi\)
0.918160 + 0.396210i \(0.129675\pi\)
\(98\) −6.69607 18.3973i −0.676405 1.85841i
\(99\) 0.228649 + 1.29673i 0.0229801 + 0.130326i
\(100\) 5.66099 1.75024i 0.566099 0.175024i
\(101\) 3.10176 + 1.12895i 0.308637 + 0.112335i 0.491695 0.870767i \(-0.336378\pi\)
−0.183058 + 0.983102i \(0.558600\pi\)
\(102\) 7.50194 4.33125i 0.742803 0.428858i
\(103\) 2.95805 + 1.70783i 0.291466 + 0.168278i 0.638603 0.769537i \(-0.279513\pi\)
−0.347137 + 0.937814i \(0.612846\pi\)
\(104\) 4.63695 3.89086i 0.454690 0.381530i
\(105\) 3.37500 + 22.3421i 0.329367 + 2.18037i
\(106\) −10.2031 + 17.6722i −0.991010 + 1.71648i
\(107\) 1.51772 0.876258i 0.146724 0.0847110i −0.424841 0.905268i \(-0.639670\pi\)
0.571565 + 0.820557i \(0.306337\pi\)
\(108\) −0.306913 + 0.843237i −0.0295327 + 0.0811405i
\(109\) 0.611108 3.46576i 0.0585335 0.331960i −0.941453 0.337144i \(-0.890539\pi\)
0.999987 + 0.00518405i \(0.00165014\pi\)
\(110\) 0.715097 1.82379i 0.0681818 0.173892i
\(111\) 4.80348 1.74832i 0.455926 0.165944i
\(112\) −13.5309 + 16.1255i −1.27855 + 1.52372i
\(113\) 13.2583i 1.24723i 0.781731 + 0.623616i \(0.214337\pi\)
−0.781731 + 0.623616i \(0.785663\pi\)
\(114\) 13.1987 13.0257i 1.23617 1.21997i
\(115\) −8.38788 5.12196i −0.782174 0.477625i
\(116\) −2.96195 2.48537i −0.275010 0.230761i
\(117\) 3.81828 + 10.4906i 0.353000 + 0.969860i
\(118\) 0.953138 0.168064i 0.0877435 0.0154715i
\(119\) 1.49887 8.50051i 0.137401 0.779241i
\(120\) 6.05934 4.83541i 0.553140 0.441410i
\(121\) 5.37951 + 9.31759i 0.489047 + 0.847054i
\(122\) −21.0852 12.1735i −1.90896 1.10214i
\(123\) 6.68985 + 7.97266i 0.603204 + 0.718870i
\(124\) −3.71147 + 3.11429i −0.333300 + 0.279672i
\(125\) −6.28904 + 9.24381i −0.562509 + 0.826791i
\(126\) −10.1466 17.5744i −0.903929 1.56565i
\(127\) 6.77480 18.6136i 0.601166 1.65169i −0.147749 0.989025i \(-0.547203\pi\)
0.748915 0.662666i \(-0.230575\pi\)
\(128\) 10.5071 + 1.85268i 0.928702 + 0.163755i
\(129\) −4.39769 24.9405i −0.387195 2.19589i
\(130\) 3.28571 16.2809i 0.288175 1.42793i
\(131\) −2.62756 2.20479i −0.229571 0.192633i 0.520745 0.853712i \(-0.325654\pi\)
−0.750316 + 0.661079i \(0.770099\pi\)
\(132\) 1.38674i 0.120700i
\(133\) −1.48902 18.4178i −0.129115 1.59702i
\(134\) 12.7729 1.10341
\(135\) −0.539779 1.60483i −0.0464568 0.138122i
\(136\) −2.78280 + 1.01286i −0.238623 + 0.0868517i
\(137\) 0.599055 0.105629i 0.0511807 0.00902454i −0.147999 0.988987i \(-0.547283\pi\)
0.199180 + 0.979963i \(0.436172\pi\)
\(138\) 18.4144 + 3.24696i 1.56754 + 0.276400i
\(139\) −7.94791 2.89280i −0.674133 0.245364i −0.0178066 0.999841i \(-0.505668\pi\)
−0.656326 + 0.754477i \(0.727891\pi\)
\(140\) −0.276379 + 11.2299i −0.0233583 + 0.949097i
\(141\) −3.12443 + 5.41167i −0.263124 + 0.455744i
\(142\) −6.92727 8.25560i −0.581324 0.692794i
\(143\) −1.31327 1.56509i −0.109821 0.130879i
\(144\) −6.65993 + 11.5353i −0.554994 + 0.961278i
\(145\) 7.29341 + 0.179499i 0.605685 + 0.0149066i
\(146\) −3.44498 1.25387i −0.285109 0.103771i
\(147\) −25.7527 4.54090i −2.12405 0.374527i
\(148\) 2.50267 0.441289i 0.205719 0.0362737i
\(149\) −4.35768 + 1.58607i −0.356995 + 0.129936i −0.514291 0.857616i \(-0.671945\pi\)
0.157295 + 0.987552i \(0.449723\pi\)
\(150\) 4.71974 20.7411i 0.385365 1.69350i
\(151\) 14.2109 1.15646 0.578232 0.815872i \(-0.303743\pi\)
0.578232 + 0.815872i \(0.303743\pi\)
\(152\) −5.21686 + 3.60185i −0.423143 + 0.292149i
\(153\) 5.46178i 0.441559i
\(154\) 2.84493 + 2.38718i 0.229251 + 0.192365i
\(155\) 1.80848 8.96111i 0.145260 0.719774i
\(156\) 2.04165 + 11.5788i 0.163463 + 0.927045i
\(157\) −10.5651 1.86291i −0.843186 0.148676i −0.264662 0.964341i \(-0.585260\pi\)
−0.578525 + 0.815665i \(0.696371\pi\)
\(158\) 3.25969 8.95593i 0.259327 0.712496i
\(159\) 13.6281 + 23.6045i 1.08078 + 1.87196i
\(160\) 11.6892 6.37056i 0.924112 0.503637i
\(161\) 14.2729 11.9764i 1.12486 0.943870i
\(162\) 11.3020 + 13.4692i 0.887967 + 1.05824i
\(163\) 14.6675 + 8.46831i 1.14885 + 0.663289i 0.948607 0.316457i \(-0.102493\pi\)
0.200244 + 0.979746i \(0.435827\pi\)
\(164\) 2.58703 + 4.48087i 0.202013 + 0.349897i
\(165\) −1.63207 2.04518i −0.127057 0.159217i
\(166\) 2.51513 14.2640i 0.195212 1.10710i
\(167\) 16.0097 2.82295i 1.23887 0.218446i 0.484439 0.874825i \(-0.339024\pi\)
0.754432 + 0.656379i \(0.227913\pi\)
\(168\) 5.02651 + 13.8102i 0.387804 + 1.06548i
\(169\) −3.31099 2.77825i −0.254692 0.213712i
\(170\) −4.23479 + 6.93503i −0.324794 + 0.531892i
\(171\) −2.95159 11.3134i −0.225714 0.865157i
\(172\) 12.5903i 0.960003i
\(173\) −5.52227 + 6.58118i −0.419850 + 0.500358i −0.933966 0.357363i \(-0.883676\pi\)
0.514115 + 0.857721i \(0.328120\pi\)
\(174\) −13.0433 + 4.74737i −0.988809 + 0.359897i
\(175\) −12.8090 16.8873i −0.968270 1.27656i
\(176\) 0.423290 2.40060i 0.0319067 0.180952i
\(177\) 0.442140 1.21477i 0.0332333 0.0913077i
\(178\) −6.70934 + 3.87364i −0.502886 + 0.290342i
\(179\) −11.7638 + 20.3755i −0.879267 + 1.52293i −0.0271196 + 0.999632i \(0.508633\pi\)
−0.852147 + 0.523302i \(0.824700\pi\)
\(180\) 1.06169 + 7.02825i 0.0791336 + 0.523855i
\(181\) −12.7266 + 10.6789i −0.945964 + 0.793758i −0.978613 0.205709i \(-0.934050\pi\)
0.0326493 + 0.999467i \(0.489606\pi\)
\(182\) 27.2688 + 15.7437i 2.02130 + 1.16700i
\(183\) −28.1631 + 16.2600i −2.08188 + 1.20197i
\(184\) −6.00684 2.18631i −0.442830 0.161177i
\(185\) −3.17163 + 3.59626i −0.233183 + 0.264402i
\(186\) 3.02023 + 17.1286i 0.221454 + 1.25593i
\(187\) 0.341865 + 0.939266i 0.0249996 + 0.0686859i
\(188\) −1.99687 + 2.37978i −0.145637 + 0.173563i
\(189\) 3.20990 0.233486
\(190\) −5.02410 + 16.6536i −0.364486 + 1.20818i
\(191\) −12.8109 −0.926965 −0.463482 0.886106i \(-0.653400\pi\)
−0.463482 + 0.886106i \(0.653400\pi\)
\(192\) −1.06278 + 1.26657i −0.0766996 + 0.0914071i
\(193\) −3.29702 9.05848i −0.237324 0.652043i −0.999986 0.00524597i \(-0.998330\pi\)
0.762662 0.646797i \(-0.223892\pi\)
\(194\) −1.74994 9.92443i −0.125639 0.712533i
\(195\) −16.6383 14.6737i −1.19150 1.05081i
\(196\) −12.2163 4.44638i −0.872594 0.317598i
\(197\) −2.68677 + 1.55121i −0.191424 + 0.110519i −0.592649 0.805461i \(-0.701918\pi\)
0.401225 + 0.915980i \(0.368585\pi\)
\(198\) 2.03512 + 1.17497i 0.144629 + 0.0835018i
\(199\) −0.401629 + 0.337007i −0.0284708 + 0.0238898i −0.656912 0.753967i \(-0.728138\pi\)
0.628441 + 0.777857i \(0.283693\pi\)
\(200\) −2.82027 + 6.70271i −0.199423 + 0.473953i
\(201\) 8.53029 14.7749i 0.601681 1.04214i
\(202\) 5.10168 2.94545i 0.358953 0.207241i
\(203\) −4.73046 + 12.9968i −0.332013 + 0.912199i
\(204\) 0.998849 5.66475i 0.0699334 0.396612i
\(205\) −9.08901 3.56374i −0.634804 0.248903i
\(206\) 5.72824 2.08491i 0.399105 0.145262i
\(207\) 7.57819 9.03134i 0.526721 0.627722i
\(208\) 20.6674i 1.43303i
\(209\) 1.21572 + 1.76083i 0.0840929 + 0.121799i
\(210\) 34.4165 + 21.0160i 2.37497 + 1.45025i
\(211\) −14.6037 12.2539i −1.00536 0.843596i −0.0176404 0.999844i \(-0.505615\pi\)
−0.987718 + 0.156249i \(0.950060\pi\)
\(212\) 4.63446 + 12.7331i 0.318296 + 0.874512i
\(213\) −14.1759 + 2.49959i −0.971315 + 0.171269i
\(214\) 0.543115 3.08016i 0.0371266 0.210555i
\(215\) 14.8178 + 18.5684i 1.01056 + 1.26636i
\(216\) −0.550635 0.953728i −0.0374660 0.0648929i
\(217\) 15.0090 + 8.66543i 1.01887 + 0.588248i
\(218\) −4.03715 4.81129i −0.273430 0.325862i
\(219\) −3.75110 + 3.14755i −0.253476 + 0.212692i
\(220\) −0.622493 1.14220i −0.0419685 0.0770070i
\(221\) 4.23731 + 7.33924i 0.285033 + 0.493691i
\(222\) 3.12020 8.57267i 0.209414 0.575360i
\(223\) −3.11478 0.549220i −0.208581 0.0367785i 0.0683812 0.997659i \(-0.478217\pi\)
−0.276962 + 0.960881i \(0.589328\pi\)
\(224\) 4.38246 + 24.8542i 0.292815 + 1.66064i
\(225\) −9.83746 9.11586i −0.655831 0.607724i
\(226\) 18.1259 + 15.2095i 1.20572 + 1.01172i
\(227\) 9.04654i 0.600440i 0.953870 + 0.300220i \(0.0970600\pi\)
−0.953870 + 0.300220i \(0.902940\pi\)
\(228\) −0.992287 12.2736i −0.0657158 0.812840i
\(229\) 17.8920 1.18234 0.591168 0.806549i \(-0.298667\pi\)
0.591168 + 0.806549i \(0.298667\pi\)
\(230\) −16.6248 + 5.59168i −1.09620 + 0.368704i
\(231\) 4.66131 1.69658i 0.306692 0.111627i
\(232\) 4.67310 0.823994i 0.306804 0.0540979i
\(233\) 6.34541 + 1.11887i 0.415701 + 0.0732994i 0.377587 0.925974i \(-0.376754\pi\)
0.0381142 + 0.999273i \(0.487865\pi\)
\(234\) 18.7224 + 6.81441i 1.22392 + 0.445472i
\(235\) 0.144219 5.85990i 0.00940778 0.382257i
\(236\) 0.321337 0.556572i 0.0209173 0.0362298i
\(237\) −8.18270 9.75176i −0.531523 0.633445i
\(238\) −9.90196 11.8007i −0.641849 0.764926i
\(239\) −6.73708 + 11.6690i −0.435785 + 0.754802i −0.997359 0.0726241i \(-0.976863\pi\)
0.561574 + 0.827426i \(0.310196\pi\)
\(240\) 0.651228 26.4607i 0.0420366 1.70803i
\(241\) 16.5716 + 6.03157i 1.06747 + 0.388528i 0.815231 0.579137i \(-0.196610\pi\)
0.252241 + 0.967664i \(0.418832\pi\)
\(242\) 18.9097 + 3.33429i 1.21556 + 0.214336i
\(243\) 20.8911 3.68366i 1.34016 0.236307i
\(244\) −15.1921 + 5.52948i −0.972576 + 0.353989i
\(245\) 23.2499 7.82000i 1.48538 0.499602i
\(246\) 18.5742 1.18424
\(247\) 12.7433 + 12.9124i 0.810834 + 0.821599i
\(248\) 5.94596i 0.377569i
\(249\) −14.8200 12.4355i −0.939179 0.788065i
\(250\) 5.42301 + 19.2022i 0.342981 + 1.21446i
\(251\) 3.07923 + 17.4632i 0.194360 + 1.10227i 0.913328 + 0.407225i \(0.133504\pi\)
−0.718968 + 0.695043i \(0.755385\pi\)
\(252\) −13.2705 2.33995i −0.835963 0.147403i
\(253\) −0.737936 + 2.02746i −0.0463936 + 0.127465i
\(254\) −17.6756 30.6151i −1.10907 1.92096i
\(255\) 5.19383 + 9.53004i 0.325250 + 0.596794i
\(256\) 15.6489 13.1310i 0.978058 0.820688i
\(257\) −17.8358 21.2558i −1.11256 1.32590i −0.940105 0.340885i \(-0.889273\pi\)
−0.172459 0.985017i \(-0.555171\pi\)
\(258\) −39.1422 22.5987i −2.43688 1.40694i
\(259\) −4.54518 7.87248i −0.282424 0.489172i
\(260\) −6.87924 8.62051i −0.426632 0.534621i
\(261\) −1.51972 + 8.61874i −0.0940681 + 0.533487i
\(262\) −6.02852 + 1.06299i −0.372443 + 0.0656718i
\(263\) 1.90174 + 5.22499i 0.117266 + 0.322187i 0.984415 0.175864i \(-0.0562718\pi\)
−0.867148 + 0.498050i \(0.834050\pi\)
\(264\) −1.30370 1.09394i −0.0802373 0.0673271i
\(265\) −21.8208 13.3246i −1.34044 0.818523i
\(266\) −26.8879 19.0926i −1.64860 1.17064i
\(267\) 10.3479i 0.633282i
\(268\) 5.45185 6.49727i 0.333025 0.396884i
\(269\) −4.34856 + 1.58275i −0.265137 + 0.0965019i −0.471168 0.882044i \(-0.656167\pi\)
0.206031 + 0.978545i \(0.433945\pi\)
\(270\) −2.81325 1.10306i −0.171209 0.0671300i
\(271\) −1.32118 + 7.49279i −0.0802561 + 0.455155i 0.918024 + 0.396525i \(0.129784\pi\)
−0.998280 + 0.0586294i \(0.981327\pi\)
\(272\) −3.45824 + 9.50144i −0.209687 + 0.576110i
\(273\) 36.4226 21.0286i 2.20439 1.27271i
\(274\) 0.542806 0.940168i 0.0327921 0.0567976i
\(275\) 2.26234 + 0.951912i 0.136424 + 0.0574025i
\(276\) 9.51147 7.98107i 0.572523 0.480404i
\(277\) −6.52588 3.76772i −0.392102 0.226380i 0.290968 0.956733i \(-0.406023\pi\)
−0.683071 + 0.730352i \(0.739356\pi\)
\(278\) −13.0725 + 7.54740i −0.784035 + 0.452663i
\(279\) 10.3050 + 3.75070i 0.616942 + 0.224548i
\(280\) −10.3394 9.11857i −0.617898 0.544939i
\(281\) −3.16993 17.9776i −0.189102 1.07245i −0.920570 0.390577i \(-0.872276\pi\)
0.731468 0.681876i \(-0.238836\pi\)
\(282\) 3.81427 + 10.4796i 0.227137 + 0.624053i
\(283\) −19.8836 + 23.6963i −1.18196 + 1.40860i −0.289671 + 0.957126i \(0.593546\pi\)
−0.892284 + 0.451474i \(0.850898\pi\)
\(284\) −7.15618 −0.424641
\(285\) 15.9085 + 16.9335i 0.942337 + 1.00305i
\(286\) −3.64624 −0.215607
\(287\) 11.8967 14.1780i 0.702241 0.836898i
\(288\) 5.46185 + 15.0063i 0.321842 + 0.884255i
\(289\) 2.23206 + 12.6586i 0.131298 + 0.744625i
\(290\) 8.61218 9.76522i 0.505725 0.573434i
\(291\) −12.6486 4.60373i −0.741476 0.269875i
\(292\) −2.10823 + 1.21719i −0.123375 + 0.0712305i
\(293\) 18.9653 + 10.9496i 1.10796 + 0.639683i 0.938301 0.345820i \(-0.112399\pi\)
0.169662 + 0.985502i \(0.445732\pi\)
\(294\) −35.7508 + 29.9985i −2.08503 + 1.74955i
\(295\) 0.181126 + 1.19903i 0.0105456 + 0.0698102i
\(296\) −1.55938 + 2.70093i −0.0906373 + 0.156988i
\(297\) −0.321908 + 0.185853i −0.0186790 + 0.0107843i
\(298\) −2.83062 + 7.77706i −0.163973 + 0.450513i
\(299\) −3.17654 + 18.0151i −0.183704 + 1.04184i
\(300\) −8.53594 11.2537i −0.492823 0.649733i
\(301\) −42.3205 + 15.4034i −2.43931 + 0.887837i
\(302\) 16.3023 19.4283i 0.938090 1.11797i
\(303\) 7.86840i 0.452028i
\(304\) −2.02866 + 21.5499i −0.116352 + 1.23597i
\(305\) 15.8979 26.0349i 0.910309 1.49075i
\(306\) −7.46703 6.26559i −0.426862 0.358180i
\(307\) 1.86587 + 5.12643i 0.106491 + 0.292581i 0.981481 0.191560i \(-0.0613546\pi\)
−0.874990 + 0.484141i \(0.839132\pi\)
\(308\) 2.42860 0.428228i 0.138382 0.0244005i
\(309\) 1.41387 8.01845i 0.0804322 0.456154i
\(310\) −10.1765 12.7524i −0.577986 0.724285i
\(311\) −3.34861 5.79996i −0.189882 0.328885i 0.755329 0.655346i \(-0.227477\pi\)
−0.945211 + 0.326461i \(0.894144\pi\)
\(312\) −12.4960 7.21459i −0.707449 0.408446i
\(313\) −2.94576 3.51062i −0.166504 0.198432i 0.676340 0.736590i \(-0.263565\pi\)
−0.842844 + 0.538157i \(0.819121\pi\)
\(314\) −14.6668 + 12.3069i −0.827696 + 0.694520i
\(315\) 22.3255 12.1673i 1.25790 0.685549i
\(316\) −3.16433 5.48078i −0.178007 0.308318i
\(317\) −9.46690 + 26.0101i −0.531714 + 1.46087i 0.325316 + 0.945605i \(0.394529\pi\)
−0.857030 + 0.515267i \(0.827693\pi\)
\(318\) 47.9045 + 8.44686i 2.68635 + 0.473676i
\(319\) −0.278119 1.57729i −0.0155717 0.0883115i
\(320\) 0.306817 1.52030i 0.0171516 0.0849872i
\(321\) −3.20022 2.68530i −0.178619 0.149879i
\(322\) 33.2520i 1.85306i
\(323\) −3.69785 8.06856i −0.205754 0.448946i
\(324\) 11.6754 0.648636
\(325\) 20.2912 + 4.61738i 1.12556 + 0.256126i
\(326\) 28.4035 10.3380i 1.57313 0.572571i
\(327\) −8.26158 + 1.45674i −0.456866 + 0.0805579i
\(328\) −6.25336 1.10264i −0.345284 0.0608829i
\(329\) 10.4423 + 3.80069i 0.575703 + 0.209539i
\(330\) −4.66832 0.114893i −0.256983 0.00632463i
\(331\) 7.06509 12.2371i 0.388332 0.672611i −0.603893 0.797065i \(-0.706385\pi\)
0.992225 + 0.124454i \(0.0397179\pi\)
\(332\) −6.18222 7.36768i −0.339293 0.404354i
\(333\) −3.69733 4.40631i −0.202613 0.241464i
\(334\) 14.5065 25.1260i 0.793761 1.37483i
\(335\) −0.393745 + 15.9987i −0.0215126 + 0.874100i
\(336\) 47.1529 + 17.1623i 2.57240 + 0.936278i
\(337\) 14.7696 + 2.60428i 0.804550 + 0.141864i 0.560775 0.827968i \(-0.310503\pi\)
0.243775 + 0.969832i \(0.421614\pi\)
\(338\) −7.59654 + 1.33947i −0.413197 + 0.0728578i
\(339\) 29.6986 10.8094i 1.61301 0.587087i
\(340\) 1.72014 + 5.11420i 0.0932879 + 0.277357i
\(341\) −2.00692 −0.108681
\(342\) −18.8530 8.94313i −1.01945 0.483589i
\(343\) 16.8294i 0.908703i
\(344\) 11.8364 + 9.93195i 0.638178 + 0.535495i
\(345\) −4.63462 + 22.9648i −0.249520 + 1.23639i
\(346\) 2.66244 + 15.0995i 0.143134 + 0.811752i
\(347\) −20.5956 3.63155i −1.10563 0.194952i −0.409106 0.912487i \(-0.634159\pi\)
−0.696522 + 0.717535i \(0.745270\pi\)
\(348\) −3.15239 + 8.66111i −0.168986 + 0.464284i
\(349\) −1.56527 2.71113i −0.0837872 0.145124i 0.821087 0.570804i \(-0.193368\pi\)
−0.904874 + 0.425680i \(0.860035\pi\)
\(350\) −37.7814 1.86081i −2.01950 0.0994646i
\(351\) −2.41420 + 2.02575i −0.128860 + 0.108127i
\(352\) −1.87856 2.23878i −0.100127 0.119327i
\(353\) 6.96750 + 4.02269i 0.370843 + 0.214106i 0.673827 0.738890i \(-0.264650\pi\)
−0.302984 + 0.952996i \(0.597983\pi\)
\(354\) −1.15356 1.99802i −0.0613108 0.106193i
\(355\) 10.5541 8.42223i 0.560151 0.447006i
\(356\) −0.893318 + 5.06626i −0.0473457 + 0.268511i
\(357\) −20.2632 + 3.57296i −1.07244 + 0.189101i
\(358\) 14.3611 + 39.4569i 0.759010 + 2.08536i
\(359\) −23.4289 19.6592i −1.23653 1.03757i −0.997787 0.0664886i \(-0.978820\pi\)
−0.238742 0.971083i \(-0.576735\pi\)
\(360\) −7.44493 4.54616i −0.392382 0.239603i
\(361\) −12.0199 14.7147i −0.632628 0.774456i
\(362\) 29.6497i 1.55835i
\(363\) 16.4856 19.6468i 0.865269 1.03119i
\(364\) 19.6475 7.15112i 1.02981 0.374821i
\(365\) 1.67673 4.27634i 0.0877639 0.223834i
\(366\) −10.0781 + 57.1560i −0.526793 + 2.98759i
\(367\) −3.40370 + 9.35159i −0.177672 + 0.488149i −0.996277 0.0862072i \(-0.972525\pi\)
0.818606 + 0.574356i \(0.194748\pi\)
\(368\) −18.9016 + 10.9128i −0.985314 + 0.568871i
\(369\) 5.85558 10.1422i 0.304830 0.527980i
\(370\) 1.27821 + 8.46159i 0.0664510 + 0.439897i
\(371\) 37.1304 31.1561i 1.92771 1.61754i
\(372\) 10.0020 + 5.77465i 0.518579 + 0.299402i
\(373\) 8.03335 4.63806i 0.415951 0.240149i −0.277392 0.960757i \(-0.589470\pi\)
0.693343 + 0.720607i \(0.256137\pi\)
\(374\) 1.67629 + 0.610119i 0.0866788 + 0.0315485i
\(375\) 25.8336 + 6.55106i 1.33404 + 0.338295i
\(376\) −0.662039 3.75461i −0.0341420 0.193629i
\(377\) −4.64441 12.7604i −0.239199 0.657195i
\(378\) 3.68230 4.38839i 0.189397 0.225715i
\(379\) 21.1472 1.08626 0.543129 0.839649i \(-0.317239\pi\)
0.543129 + 0.839649i \(0.317239\pi\)
\(380\) 6.32682 + 9.66385i 0.324559 + 0.495745i
\(381\) −47.2181 −2.41906
\(382\) −14.6963 + 17.5143i −0.751927 + 0.896112i
\(383\) −5.18165 14.2365i −0.264770 0.727450i −0.998830 0.0483649i \(-0.984599\pi\)
0.734060 0.679085i \(-0.237623\pi\)
\(384\) −4.41636 25.0464i −0.225371 1.27814i
\(385\) −3.07775 + 3.48982i −0.156857 + 0.177858i
\(386\) −16.1665 5.88411i −0.822851 0.299493i
\(387\) −24.6795 + 14.2487i −1.25453 + 0.724302i
\(388\) −5.79524 3.34588i −0.294209 0.169861i
\(389\) 24.0908 20.2146i 1.22145 1.02492i 0.222706 0.974886i \(-0.428511\pi\)
0.998747 0.0500353i \(-0.0159334\pi\)
\(390\) −39.1481 + 5.91373i −1.98234 + 0.299453i
\(391\) 4.47479 7.75056i 0.226300 0.391963i
\(392\) 13.8171 7.97728i 0.697866 0.402913i
\(393\) −2.79650 + 7.68332i −0.141065 + 0.387572i
\(394\) −0.961457 + 5.45269i −0.0484375 + 0.274703i
\(395\) 11.1172 + 4.35900i 0.559369 + 0.219325i
\(396\) 1.46633 0.533699i 0.0736857 0.0268194i
\(397\) 6.03294 7.18978i 0.302784 0.360844i −0.593102 0.805127i \(-0.702097\pi\)
0.895887 + 0.444283i \(0.146541\pi\)
\(398\) 0.935689i 0.0469019i
\(399\) −40.0419 + 18.3514i −2.00460 + 0.918717i
\(400\) 11.3416 + 22.0870i 0.567079 + 1.10435i
\(401\) 4.71921 + 3.95989i 0.235666 + 0.197747i 0.752971 0.658054i \(-0.228620\pi\)
−0.517305 + 0.855801i \(0.673065\pi\)
\(402\) −10.4137 28.6114i −0.519389 1.42701i
\(403\) −16.7571 + 2.95473i −0.834730 + 0.147185i
\(404\) 0.679265 3.85230i 0.0337947 0.191659i
\(405\) −17.2191 + 13.7410i −0.855626 + 0.682797i
\(406\) 12.3419 + 21.3768i 0.612518 + 1.06091i
\(407\) 0.911634 + 0.526332i 0.0451880 + 0.0260893i
\(408\) 4.53761 + 5.40771i 0.224645 + 0.267722i
\(409\) −1.75027 + 1.46865i −0.0865454 + 0.0726202i −0.685034 0.728511i \(-0.740213\pi\)
0.598489 + 0.801131i \(0.295768\pi\)
\(410\) −15.2988 + 8.33776i −0.755553 + 0.411773i
\(411\) −0.725018 1.25577i −0.0357625 0.0619425i
\(412\) 1.38444 3.80371i 0.0682064 0.187395i
\(413\) −2.26397 0.399199i −0.111403 0.0196433i
\(414\) −3.65366 20.7210i −0.179568 1.01838i
\(415\) 17.7888 + 3.59003i 0.873218 + 0.176227i
\(416\) −18.9814 15.9273i −0.930640 0.780900i
\(417\) 20.1619i 0.987332i
\(418\) 3.80193 + 0.357906i 0.185959 + 0.0175057i
\(419\) 22.6494 1.10649 0.553247 0.833017i \(-0.313389\pi\)
0.553247 + 0.833017i \(0.313389\pi\)
\(420\) 25.3803 8.53658i 1.23843 0.416542i
\(421\) 21.6100 7.86540i 1.05321 0.383336i 0.243335 0.969942i \(-0.421759\pi\)
0.809872 + 0.586606i \(0.199536\pi\)
\(422\) −33.5058 + 5.90797i −1.63103 + 0.287595i
\(423\) 6.92473 + 1.22102i 0.336692 + 0.0593679i
\(424\) −15.6266 5.68761i −0.758893 0.276215i
\(425\) −8.55589 5.51805i −0.415022 0.267665i
\(426\) −12.8448 + 22.2479i −0.622334 + 1.07791i
\(427\) 37.1730 + 44.3011i 1.79893 + 2.14388i
\(428\) −1.33498 1.59097i −0.0645289 0.0769025i
\(429\) −2.43511 + 4.21774i −0.117568 + 0.203634i
\(430\) 42.3842 + 1.04312i 2.04395 + 0.0503038i
\(431\) −24.0861 8.76663i −1.16019 0.422274i −0.311023 0.950402i \(-0.600672\pi\)
−0.849164 + 0.528129i \(0.822894\pi\)
\(432\) −3.70299 0.652938i −0.178160 0.0314145i
\(433\) −2.32740 + 0.410383i −0.111847 + 0.0197217i −0.229292 0.973358i \(-0.573641\pi\)
0.117444 + 0.993079i \(0.462530\pi\)
\(434\) 29.0647 10.5787i 1.39515 0.507793i
\(435\) −5.54422 16.4837i −0.265825 0.790331i
\(436\) −4.17056 −0.199734
\(437\) 5.08050 18.4725i 0.243033 0.883661i
\(438\) 8.73906i 0.417568i
\(439\) 4.83879 + 4.06022i 0.230943 + 0.193784i 0.750914 0.660400i \(-0.229613\pi\)
−0.519972 + 0.854183i \(0.674058\pi\)
\(440\) 1.56486 + 0.315811i 0.0746019 + 0.0150557i
\(441\) 5.10967 + 28.9784i 0.243318 + 1.37992i
\(442\) 14.8947 + 2.62634i 0.708469 + 0.124922i
\(443\) 10.7821 29.6234i 0.512271 1.40745i −0.366594 0.930381i \(-0.619476\pi\)
0.878865 0.477071i \(-0.158302\pi\)
\(444\) −3.02891 5.24623i −0.143746 0.248975i
\(445\) −4.64508 8.52317i −0.220198 0.404037i
\(446\) −4.32404 + 3.62830i −0.204749 + 0.171805i
\(447\) 7.10561 + 8.46813i 0.336084 + 0.400529i
\(448\) 2.54635 + 1.47013i 0.120304 + 0.0694573i
\(449\) −7.54142 13.0621i −0.355902 0.616440i 0.631370 0.775482i \(-0.282493\pi\)
−0.987272 + 0.159042i \(0.949159\pi\)
\(450\) −23.7479 + 2.99178i −1.11949 + 0.141034i
\(451\) −0.372168 + 2.11067i −0.0175247 + 0.0993876i
\(452\) 15.4734 2.72837i 0.727805 0.128332i
\(453\) −11.5861 31.8325i −0.544361 1.49562i
\(454\) 12.3679 + 10.3779i 0.580455 + 0.487059i
\(455\) −20.5603 + 33.6701i −0.963880 + 1.57848i
\(456\) 12.3215 + 8.74924i 0.577005 + 0.409721i
\(457\) 20.1347i 0.941861i −0.882170 0.470930i \(-0.843918\pi\)
0.882170 0.470930i \(-0.156082\pi\)
\(458\) 20.5251 24.4609i 0.959076 1.14298i
\(459\) 1.44885 0.527337i 0.0676263 0.0246140i
\(460\) −4.25159 + 10.8433i −0.198231 + 0.505571i
\(461\) −1.29974 + 7.37118i −0.0605348 + 0.343310i 0.939465 + 0.342645i \(0.111323\pi\)
−1.00000 0.000665051i \(0.999788\pi\)
\(462\) 3.02784 8.31893i 0.140868 0.387032i
\(463\) −18.7038 + 10.7986i −0.869239 + 0.501855i −0.867095 0.498142i \(-0.834016\pi\)
−0.00214362 + 0.999998i \(0.500682\pi\)
\(464\) 8.10087 14.0311i 0.376074 0.651379i
\(465\) −21.5474 + 3.25496i −0.999237 + 0.150945i
\(466\) 8.80891 7.39155i 0.408065 0.342407i
\(467\) −23.4263 13.5252i −1.08404 0.625870i −0.152056 0.988372i \(-0.548589\pi\)
−0.931983 + 0.362501i \(0.881923\pi\)
\(468\) 11.4576 6.61505i 0.529628 0.305781i
\(469\) −28.5096 10.3766i −1.31645 0.479148i
\(470\) −7.84587 6.91946i −0.361903 0.319171i
\(471\) 4.44075 + 25.1847i 0.204619 + 1.16045i
\(472\) 0.269757 + 0.741151i 0.0124166 + 0.0341143i
\(473\) 3.35229 3.99510i 0.154138 0.183695i
\(474\) −22.7190 −1.04352
\(475\) −20.7045 6.80628i −0.949986 0.312294i
\(476\) −10.2292 −0.468853
\(477\) 19.7144 23.4947i 0.902660 1.07575i
\(478\) 8.22457 + 22.5968i 0.376183 + 1.03355i
\(479\) 6.60791 + 37.4753i 0.301923 + 1.71229i 0.637646 + 0.770329i \(0.279908\pi\)
−0.335723 + 0.941961i \(0.608981\pi\)
\(480\) −23.8003 20.9900i −1.08633 0.958059i
\(481\) 8.38675 + 3.05253i 0.382403 + 0.139183i
\(482\) 27.2565 15.7365i 1.24150 0.716779i
\(483\) −38.4638 22.2071i −1.75016 1.01046i
\(484\) 9.76728 8.19572i 0.443967 0.372533i
\(485\) 12.4847 1.88595i 0.566903 0.0856366i
\(486\) 18.9295 32.7869i 0.858661 1.48724i
\(487\) 15.8788 9.16764i 0.719538 0.415426i −0.0950445 0.995473i \(-0.530299\pi\)
0.814583 + 0.580047i \(0.196966\pi\)
\(488\) 6.78601 18.6444i 0.307188 0.843993i
\(489\) 7.01069 39.7596i 0.317034 1.79799i
\(490\) 15.9805 40.7568i 0.721924 1.84120i
\(491\) 14.1588 5.15338i 0.638978 0.232569i −0.00215650 0.999998i \(-0.500686\pi\)
0.641134 + 0.767429i \(0.278464\pi\)
\(492\) 7.92799 9.44821i 0.357421 0.425958i
\(493\) 6.64350i 0.299208i
\(494\) 32.2718 2.60909i 1.45198 0.117388i
\(495\) −1.53444 + 2.51285i −0.0689682 + 0.112944i
\(496\) −15.5519 13.0496i −0.698302 0.585945i
\(497\) 8.75509 + 24.0544i 0.392720 + 1.07899i
\(498\) −34.0021 + 5.99549i −1.52367 + 0.268664i
\(499\) −5.99606 + 34.0053i −0.268420 + 1.52229i 0.490695 + 0.871332i \(0.336743\pi\)
−0.759115 + 0.650956i \(0.774368\pi\)
\(500\) 12.0824 + 5.43752i 0.540341 + 0.243173i
\(501\) −19.3761 33.5604i −0.865661 1.49937i
\(502\) 27.4071 + 15.8235i 1.22324 + 0.706237i
\(503\) −19.8431 23.6481i −0.884760 1.05442i −0.998146 0.0608649i \(-0.980614\pi\)
0.113386 0.993551i \(-0.463830\pi\)
\(504\) 12.6683 10.6300i 0.564293 0.473498i
\(505\) 3.53205 + 6.48088i 0.157174 + 0.288395i
\(506\) 1.92529 + 3.33471i 0.0855897 + 0.148246i
\(507\) −3.52387 + 9.68175i −0.156501 + 0.429982i
\(508\) −23.1176 4.07626i −1.02568 0.180855i
\(509\) −1.76734 10.0231i −0.0783358 0.444264i −0.998597 0.0529589i \(-0.983135\pi\)
0.920261 0.391305i \(-0.127976\pi\)
\(510\) 18.9871 + 3.83187i 0.840764 + 0.169678i
\(511\) 6.67067 + 5.59735i 0.295093 + 0.247612i
\(512\) 15.1195i 0.668194i
\(513\) 2.71613 1.87528i 0.119920 0.0827956i
\(514\) −49.5204 −2.18425
\(515\) 2.43486 + 7.23915i 0.107293 + 0.318995i
\(516\) −28.2024 + 10.2648i −1.24154 + 0.451885i
\(517\) −1.26728 + 0.223455i −0.0557348 + 0.00982754i
\(518\) −15.9769 2.81716i −0.701984 0.123779i
\(519\) 19.2442 + 7.00431i 0.844726 + 0.307455i
\(520\) 13.5311 + 0.333014i 0.593376 + 0.0146036i
\(521\) −8.27116 + 14.3261i −0.362366 + 0.627636i −0.988350 0.152200i \(-0.951364\pi\)
0.625984 + 0.779836i \(0.284698\pi\)
\(522\) 10.0397 + 11.9648i 0.439425 + 0.523686i
\(523\) −5.14102 6.12683i −0.224801 0.267908i 0.641841 0.766838i \(-0.278171\pi\)
−0.866642 + 0.498930i \(0.833726\pi\)
\(524\) −2.03243 + 3.52027i −0.0887871 + 0.153784i
\(525\) −27.3845 + 42.4604i −1.19516 + 1.85313i
\(526\) 9.32492 + 3.39399i 0.406586 + 0.147985i
\(527\) 8.19816 + 1.44556i 0.357117 + 0.0629694i
\(528\) −5.72247 + 1.00903i −0.249039 + 0.0439122i
\(529\) −3.45976 + 1.25925i −0.150424 + 0.0547500i
\(530\) −43.2487 + 14.5465i −1.87860 + 0.631862i
\(531\) −1.45465 −0.0631266
\(532\) −21.1884 + 5.52792i −0.918635 + 0.239666i
\(533\) 18.1713i 0.787088i
\(534\) 14.1471 + 11.8708i 0.612204 + 0.513700i
\(535\) 3.84130 + 0.775227i 0.166074 + 0.0335160i
\(536\) 1.80749 + 10.2508i 0.0780719 + 0.442768i
\(537\) 55.2322 + 9.73893i 2.38345 + 0.420266i
\(538\) −2.82470 + 7.76079i −0.121781 + 0.334591i
\(539\) −2.69254 4.66361i −0.115976 0.200876i
\(540\) −1.76188 + 0.960214i −0.0758191 + 0.0413210i
\(541\) 3.98380 3.34280i 0.171277 0.143718i −0.553120 0.833102i \(-0.686563\pi\)
0.724397 + 0.689383i \(0.242118\pi\)
\(542\) 8.72810 + 10.4017i 0.374904 + 0.446793i
\(543\) 34.2969 + 19.8013i 1.47182 + 0.849755i
\(544\) 6.06125 + 10.4984i 0.259874 + 0.450115i
\(545\) 6.15081 4.90840i 0.263472 0.210253i
\(546\) 13.0338 73.9182i 0.557794 3.16341i
\(547\) 10.8663 1.91602i 0.464610 0.0819233i 0.0635572 0.997978i \(-0.479755\pi\)
0.401053 + 0.916055i \(0.368644\pi\)
\(548\) −0.246555 0.677403i −0.0105323 0.0289372i
\(549\) 28.0321 + 23.5217i 1.19638 + 1.00388i
\(550\) 3.89668 2.00093i 0.166155 0.0853201i
\(551\) 3.59020 + 13.7612i 0.152948 + 0.586245i
\(552\) 15.2379i 0.648566i
\(553\) −14.5515 + 17.3418i −0.618792 + 0.737447i
\(554\) −12.6373 + 4.59960i −0.536907 + 0.195418i
\(555\) 10.6415 + 4.17245i 0.451705 + 0.177111i
\(556\) −1.74054 + 9.87109i −0.0738153 + 0.418628i
\(557\) 7.27877 19.9983i 0.308411 0.847353i −0.684555 0.728961i \(-0.740004\pi\)
0.992967 0.118393i \(-0.0377741\pi\)
\(558\) 16.9493 9.78567i 0.717520 0.414260i
\(559\) 22.1086 38.2933i 0.935095 1.61963i
\(560\) −46.5420 + 7.03064i −1.96676 + 0.297099i
\(561\) 1.82524 1.53156i 0.0770618 0.0646625i
\(562\) −28.2144 16.2896i −1.19015 0.687134i
\(563\) 12.7368 7.35358i 0.536791 0.309917i −0.206986 0.978344i \(-0.566366\pi\)
0.743778 + 0.668427i \(0.233032\pi\)
\(564\) 6.95877 + 2.53279i 0.293017 + 0.106650i
\(565\) −19.6093 + 22.2347i −0.824970 + 0.935421i
\(566\) 9.58644 + 54.3674i 0.402948 + 2.28523i
\(567\) −14.2841 39.2453i −0.599876 1.64815i
\(568\) 5.64519 6.72768i 0.236867 0.282287i
\(569\) −40.6551 −1.70435 −0.852174 0.523258i \(-0.824716\pi\)
−0.852174 + 0.523258i \(0.824716\pi\)
\(570\) 41.4002 2.32356i 1.73406 0.0973233i
\(571\) −24.3240 −1.01793 −0.508964 0.860788i \(-0.669972\pi\)
−0.508964 + 0.860788i \(0.669972\pi\)
\(572\) −1.55632 + 1.85475i −0.0650730 + 0.0775510i
\(573\) 10.4447 + 28.6966i 0.436333 + 1.19882i
\(574\) −5.73575 32.5290i −0.239405 1.35774i
\(575\) −6.49135 20.9957i −0.270708 0.875579i
\(576\) 1.74829 + 0.636325i 0.0728454 + 0.0265136i
\(577\) −29.1743 + 16.8438i −1.21454 + 0.701216i −0.963745 0.266824i \(-0.914026\pi\)
−0.250796 + 0.968040i \(0.580692\pi\)
\(578\) 19.8667 + 11.4700i 0.826346 + 0.477091i
\(579\) −17.6030 + 14.7707i −0.731557 + 0.613849i
\(580\) −1.29140 8.54888i −0.0536224 0.354973i
\(581\) −17.2018 + 29.7945i −0.713652 + 1.23608i
\(582\) −20.8041 + 12.0112i −0.862357 + 0.497882i
\(583\) −1.91971 + 5.27437i −0.0795064 + 0.218442i
\(584\) 0.518785 2.94218i 0.0214675 0.121748i
\(585\) −9.11250 + 23.2406i −0.376756 + 0.960882i
\(586\) 36.7261 13.3672i 1.51714 0.552194i
\(587\) −1.44613 + 1.72343i −0.0596880 + 0.0711334i −0.795062 0.606528i \(-0.792562\pi\)
0.735374 + 0.677661i \(0.237006\pi\)
\(588\) 30.9898i 1.27800i
\(589\) 17.7626 1.43606i 0.731897 0.0591718i
\(590\) 1.84703 + 1.12787i 0.0760409 + 0.0464335i
\(591\) 5.66523 + 4.75369i 0.233036 + 0.195541i
\(592\) 3.64202 + 10.0064i 0.149686 + 0.411259i
\(593\) 30.9103 5.45032i 1.26933 0.223818i 0.501888 0.864932i \(-0.332639\pi\)
0.767445 + 0.641115i \(0.221528\pi\)
\(594\) −0.115194 + 0.653299i −0.00472648 + 0.0268052i
\(595\) 15.0862 12.0389i 0.618472 0.493546i
\(596\) 2.74781 + 4.75934i 0.112555 + 0.194950i
\(597\) 1.08235 + 0.624893i 0.0442975 + 0.0255752i
\(598\) 20.9852 + 25.0091i 0.858147 + 1.02270i
\(599\) −7.97210 + 6.68939i −0.325731 + 0.273321i −0.790958 0.611871i \(-0.790417\pi\)
0.465227 + 0.885192i \(0.345973\pi\)
\(600\) 17.3135 + 0.852724i 0.706820 + 0.0348123i
\(601\) 0.647959 + 1.12230i 0.0264308 + 0.0457795i 0.878938 0.476936i \(-0.158253\pi\)
−0.852507 + 0.522715i \(0.824919\pi\)
\(602\) −27.4901 + 75.5285i −1.12041 + 3.07831i
\(603\) −18.9059 3.33361i −0.769906 0.135755i
\(604\) −2.92440 16.5851i −0.118992 0.674839i
\(605\) −4.75927 + 23.5825i −0.193492 + 0.958764i
\(606\) −10.7572 9.02638i −0.436982 0.366672i
\(607\) 5.50902i 0.223604i −0.993730 0.111802i \(-0.964338\pi\)
0.993730 0.111802i \(-0.0356623\pi\)
\(608\) 18.2285 + 18.4706i 0.739265 + 0.749080i
\(609\) 32.9698 1.33600
\(610\) −17.3558 51.6010i −0.702716 2.08927i
\(611\) −10.2524 + 3.73155i −0.414766 + 0.150962i
\(612\) −6.37430 + 1.12396i −0.257666 + 0.0454334i
\(613\) −40.0547 7.06273i −1.61780 0.285261i −0.709851 0.704351i \(-0.751238\pi\)
−0.907945 + 0.419090i \(0.862349\pi\)
\(614\) 9.14903 + 3.32997i 0.369225 + 0.134387i
\(615\) −0.572577 + 23.2650i −0.0230885 + 0.938134i
\(616\) −1.51323 + 2.62099i −0.0609697 + 0.105603i
\(617\) −19.6085 23.3684i −0.789407 0.940778i 0.209911 0.977721i \(-0.432683\pi\)
−0.999317 + 0.0369423i \(0.988238\pi\)
\(618\) −9.34043 11.1315i −0.375727 0.447774i
\(619\) 2.90205 5.02651i 0.116643 0.202032i −0.801792 0.597603i \(-0.796120\pi\)
0.918436 + 0.395571i \(0.129453\pi\)
\(620\) −10.8304 0.266549i −0.434960 0.0107049i
\(621\) 3.12742 + 1.13829i 0.125499 + 0.0456779i
\(622\) −11.7708 2.07551i −0.471966 0.0832203i
\(623\) 18.1224 3.19546i 0.726058 0.128024i
\(624\) −46.2952 + 16.8501i −1.85329 + 0.674542i
\(625\) −24.2188 + 6.20063i −0.968754 + 0.248025i
\(626\) −8.17881 −0.326891
\(627\) 2.95309 4.15881i 0.117935 0.166087i
\(628\) 12.7136i 0.507328i
\(629\) −3.34487 2.80668i −0.133369 0.111910i
\(630\) 8.97670 44.4801i 0.357640 1.77213i
\(631\) −4.05716 23.0093i −0.161513 0.915985i −0.952587 0.304265i \(-0.901589\pi\)
0.791074 0.611720i \(-0.209522\pi\)
\(632\) 7.64880 + 1.34869i 0.304253 + 0.0536480i
\(633\) −15.5426 + 42.7029i −0.617763 + 1.69729i
\(634\) 24.6994 + 42.7806i 0.980937 + 1.69903i
\(635\) 38.8917 21.1958i 1.54337 0.841129i
\(636\) 24.7437 20.7625i 0.981153 0.823285i
\(637\) −29.3479 34.9755i −1.16281 1.38578i
\(638\) −2.47544 1.42919i −0.0980034 0.0565823i
\(639\) 8.09878 + 14.0275i 0.320383 + 0.554919i
\(640\) 14.8807 + 18.6473i 0.588210 + 0.737097i
\(641\) 3.18574 18.0672i 0.125829 0.713612i −0.854983 0.518656i \(-0.826432\pi\)
0.980812 0.194956i \(-0.0624564\pi\)
\(642\) −7.34238 + 1.29466i −0.289781 + 0.0510962i
\(643\) −5.39128 14.8124i −0.212611 0.584144i 0.786844 0.617152i \(-0.211714\pi\)
−0.999455 + 0.0330077i \(0.989491\pi\)
\(644\) −16.9145 14.1929i −0.666523 0.559279i
\(645\) 29.5126 48.3307i 1.16206 1.90302i
\(646\) −15.2729 4.20051i −0.600905 0.165267i
\(647\) 25.0443i 0.984592i 0.870428 + 0.492296i \(0.163842\pi\)
−0.870428 + 0.492296i \(0.836158\pi\)
\(648\) −9.21024 + 10.9763i −0.361812 + 0.431191i
\(649\) 0.250158 0.0910500i 0.00981955 0.00357402i
\(650\) 29.5901 22.4441i 1.16062 0.880331i
\(651\) 7.17388 40.6851i 0.281167 1.59457i
\(652\) 6.86475 18.8608i 0.268844 0.738644i
\(653\) 2.58813 1.49426i 0.101282 0.0584749i −0.448504 0.893781i \(-0.648043\pi\)
0.549785 + 0.835306i \(0.314710\pi\)
\(654\) −7.48586 + 12.9659i −0.292720 + 0.507006i
\(655\) −1.14561 7.58376i −0.0447625 0.296322i
\(656\) −16.6082 + 13.9360i −0.648443 + 0.544108i
\(657\) 4.77185 + 2.75503i 0.186167 + 0.107484i
\(658\) 17.1752 9.91610i 0.669559 0.386570i
\(659\) −33.6123 12.2339i −1.30935 0.476564i −0.409320 0.912391i \(-0.634234\pi\)
−0.900031 + 0.435827i \(0.856456\pi\)
\(660\) −2.05102 + 2.32562i −0.0798358 + 0.0905247i
\(661\) 0.559402 + 3.17253i 0.0217582 + 0.123397i 0.993752 0.111609i \(-0.0356003\pi\)
−0.971994 + 0.235006i \(0.924489\pi\)
\(662\) −8.62500 23.6970i −0.335220 0.921010i
\(663\) 12.9853 15.4753i 0.504307 0.601010i
\(664\) 11.8034 0.458061
\(665\) 24.7432 33.0897i 0.959499 1.28316i
\(666\) −10.2655 −0.397781
\(667\) −9.21782 + 10.9854i −0.356915 + 0.425355i
\(668\) −6.58918 18.1036i −0.254943 0.700450i
\(669\) 1.30921 + 7.42491i 0.0506170 + 0.287064i
\(670\) 21.4208 + 18.8915i 0.827556 + 0.729841i
\(671\) −6.29297 2.29045i −0.242937 0.0884220i
\(672\) 52.1005 30.0802i 2.00982 1.16037i
\(673\) 0.554001 + 0.319853i 0.0213552 + 0.0123294i 0.510640 0.859795i \(-0.329409\pi\)
−0.489284 + 0.872124i \(0.662742\pi\)
\(674\) 20.5036 17.2046i 0.789770 0.662696i
\(675\) 1.46835 3.48972i 0.0565169 0.134319i
\(676\) −2.56107 + 4.43590i −0.0985025 + 0.170611i
\(677\) −22.3439 + 12.9002i −0.858744 + 0.495796i −0.863592 0.504192i \(-0.831790\pi\)
0.00484733 + 0.999988i \(0.498457\pi\)
\(678\) 19.2913 53.0025i 0.740879 2.03555i
\(679\) −4.15661 + 23.5733i −0.159516 + 0.904660i
\(680\) −6.16492 2.41723i −0.236414 0.0926964i
\(681\) 20.2643 7.37561i 0.776530 0.282634i
\(682\) −2.30227 + 2.74374i −0.0881585 + 0.105063i
\(683\) 5.33696i 0.204213i 0.994773 + 0.102107i \(0.0325583\pi\)
−0.994773 + 0.102107i \(0.967442\pi\)
\(684\) −12.5962 + 5.77286i −0.481626 + 0.220731i
\(685\) 1.16087 + 0.708872i 0.0443546 + 0.0270846i
\(686\) 23.0082 + 19.3062i 0.878458 + 0.737114i
\(687\) −14.5873 40.0782i −0.556539 1.52908i
\(688\) 51.9549 9.16105i 1.98076 0.349262i
\(689\) −8.26367 + 46.8656i −0.314821 + 1.78544i
\(690\) 26.0795 + 32.6807i 0.992830 + 1.24413i
\(691\) −6.62534 11.4754i −0.252040 0.436545i 0.712048 0.702131i \(-0.247768\pi\)
−0.964087 + 0.265586i \(0.914435\pi\)
\(692\) 8.81712 + 5.09057i 0.335177 + 0.193514i
\(693\) −3.58790 4.27589i −0.136293 0.162428i
\(694\) −28.5915 + 23.9911i −1.08532 + 0.910689i
\(695\) −9.05048 16.6065i −0.343304 0.629922i
\(696\) −5.65572 9.79599i −0.214379 0.371316i
\(697\) 3.04058 8.35392i 0.115170 0.316427i
\(698\) −5.50214 0.970176i −0.208259 0.0367217i
\(699\) −2.66712 15.1260i −0.100880 0.572117i
\(700\) −17.0728 + 18.4242i −0.645290 + 0.696370i
\(701\) 31.3081 + 26.2706i 1.18249 + 0.992228i 0.999959 + 0.00902862i \(0.00287394\pi\)
0.182533 + 0.983200i \(0.441571\pi\)
\(702\) 5.62443i 0.212280i
\(703\) −8.44523 4.00609i −0.318518 0.151093i
\(704\) −0.340484 −0.0128325
\(705\) −13.2438 + 4.45450i −0.498790 + 0.167766i
\(706\) 13.4925 4.91087i 0.507797 0.184823i
\(707\) −13.7800 + 2.42978i −0.518249 + 0.0913813i
\(708\) −1.50871 0.266027i −0.0567009 0.00999789i
\(709\) 6.91375 + 2.51640i 0.259651 + 0.0945053i 0.468566 0.883429i \(-0.344771\pi\)
−0.208915 + 0.977934i \(0.566993\pi\)
\(710\) 0.592897 24.0906i 0.0222510 0.904105i
\(711\) −7.16226 + 12.4054i −0.268606 + 0.465239i
\(712\) −4.05820 4.83637i −0.152087 0.181251i
\(713\) 11.5504 + 13.7652i 0.432565 + 0.515511i
\(714\) −18.3606 + 31.8015i −0.687129 + 1.19014i
\(715\) 0.112401 4.56708i 0.00420355 0.170799i
\(716\) 26.2005 + 9.53620i 0.979158 + 0.356384i
\(717\) 31.6313 + 5.57745i 1.18129 + 0.208294i
\(718\) −53.7538 + 9.47825i −2.00607 + 0.353725i
\(719\) −30.0323 + 10.9309i −1.12002 + 0.407653i −0.834658 0.550768i \(-0.814335\pi\)
−0.285358 + 0.958421i \(0.592113\pi\)
\(720\) −28.2301 + 9.49507i −1.05207 + 0.353861i
\(721\) −14.4794 −0.539240
\(722\) −33.9059 0.447227i −1.26185 0.0166441i
\(723\) 42.0381i 1.56341i
\(724\) 15.0820 + 12.6553i 0.560520 + 0.470332i
\(725\) 11.9659 + 11.0882i 0.444403 + 0.411805i
\(726\) −7.94817 45.0763i −0.294984 1.67294i
\(727\) 28.9418 + 5.10323i 1.07339 + 0.189268i 0.682292 0.731079i \(-0.260983\pi\)
0.391101 + 0.920348i \(0.372094\pi\)
\(728\) −8.77615 + 24.1123i −0.325266 + 0.893661i
\(729\) −10.5058 18.1966i −0.389103 0.673947i
\(730\) −3.92288 7.19801i −0.145192 0.266410i
\(731\) −16.5716 + 13.9052i −0.612922 + 0.514302i
\(732\) 24.7722 + 29.5223i 0.915606 + 1.09118i
\(733\) 44.0187 + 25.4142i 1.62587 + 0.938696i 0.985307 + 0.170790i \(0.0546319\pi\)
0.640562 + 0.767906i \(0.278701\pi\)
\(734\) 8.88034 + 15.3812i 0.327779 + 0.567730i
\(735\) −36.4724 45.7043i −1.34531 1.68583i
\(736\) −4.54388 + 25.7696i −0.167490 + 0.949880i
\(737\) 3.45991 0.610076i 0.127448 0.0224724i
\(738\) −7.14845 19.6402i −0.263138 0.722966i
\(739\) −11.2796 9.46473i −0.414928 0.348166i 0.411302 0.911499i \(-0.365074\pi\)
−0.826230 + 0.563334i \(0.809519\pi\)
\(740\) 4.84978 + 2.96146i 0.178281 + 0.108865i
\(741\) 18.5345 39.0725i 0.680880 1.43536i
\(742\) 86.5039i 3.17566i
\(743\) −22.2770 + 26.5487i −0.817263 + 0.973976i −0.999958 0.00919385i \(-0.997073\pi\)
0.182695 + 0.983170i \(0.441518\pi\)
\(744\) −13.3190 + 4.84772i −0.488298 + 0.177726i
\(745\) −9.65387 3.78522i −0.353690 0.138680i
\(746\) 2.87472 16.3034i 0.105251 0.596909i
\(747\) −7.44555 + 20.4565i −0.272418 + 0.748464i
\(748\) 1.02584 0.592270i 0.0375085 0.0216555i
\(749\) −3.71455 + 6.43379i −0.135727 + 0.235086i
\(750\) 38.5918 27.8031i 1.40917 1.01523i
\(751\) −6.40060 + 5.37074i −0.233561 + 0.195981i −0.752055 0.659100i \(-0.770937\pi\)
0.518494 + 0.855081i \(0.326493\pi\)
\(752\) −11.2733 6.50865i −0.411095 0.237346i
\(753\) 36.6072 21.1352i 1.33404 0.770210i
\(754\) −22.7732 8.28878i −0.829352 0.301859i
\(755\) 23.8323 + 21.0182i 0.867345 + 0.764932i
\(756\) −0.660554 3.74619i −0.0240241 0.136248i
\(757\) 4.74412 + 13.0344i 0.172428 + 0.473742i 0.995562 0.0941046i \(-0.0299988\pi\)
−0.823134 + 0.567847i \(0.807777\pi\)
\(758\) 24.2594 28.9112i 0.881142 1.05010i
\(759\) 5.14317 0.186685
\(760\) −14.0761 1.67541i −0.510595 0.0607735i
\(761\) 44.3970 1.60939 0.804696 0.593687i \(-0.202328\pi\)
0.804696 + 0.593687i \(0.202328\pi\)
\(762\) −54.1672 + 64.5539i −1.96227 + 2.33854i
\(763\) 5.10239 + 14.0187i 0.184719 + 0.507511i
\(764\) 2.63631 + 14.9513i 0.0953784 + 0.540918i
\(765\) 8.07811 9.15965i 0.292065 0.331168i
\(766\) −25.4075 9.24758i −0.918011 0.334129i
\(767\) 1.95468 1.12854i 0.0705796 0.0407491i
\(768\) −42.1721 24.3481i −1.52175 0.878585i
\(769\) −14.5549 + 12.2130i −0.524863 + 0.440412i −0.866323 0.499484i \(-0.833523\pi\)
0.341460 + 0.939896i \(0.389079\pi\)
\(770\) 1.24038 + 8.21114i 0.0447001 + 0.295909i
\(771\) −33.0718 + 57.2820i −1.19105 + 2.06296i
\(772\) −9.89342 + 5.71197i −0.356072 + 0.205578i
\(773\) −0.638682 + 1.75476i −0.0229718 + 0.0631144i −0.950648 0.310270i \(-0.899581\pi\)
0.927677 + 0.373384i \(0.121803\pi\)
\(774\) −8.83152 + 50.0860i −0.317442 + 1.80031i
\(775\) 16.2866 12.3534i 0.585032 0.443747i
\(776\) 7.71714 2.80881i 0.277029 0.100830i
\(777\) −13.9287 + 16.5996i −0.499691 + 0.595509i
\(778\) 56.1252i 2.01218i
\(779\) 1.78365 18.9473i 0.0639060 0.678856i
\(780\) −13.7014 + 22.4378i −0.490588 + 0.803403i
\(781\) −2.27077 1.90540i −0.0812544 0.0681805i
\(782\) −5.46279 15.0089i −0.195349 0.536717i
\(783\) −2.43302 + 0.429007i −0.0869491 + 0.0153315i
\(784\) 9.45938 53.6468i 0.337835 1.91596i
\(785\) −14.9629 18.7502i −0.534047 0.669225i
\(786\) 7.29614 + 12.6373i 0.260245 + 0.450757i
\(787\) 11.2314 + 6.48445i 0.400356 + 0.231146i 0.686638 0.727000i \(-0.259086\pi\)
−0.286282 + 0.958146i \(0.592419\pi\)
\(788\) 2.36327 + 2.81644i 0.0841881 + 0.100331i
\(789\) 10.1535 8.51983i 0.361475 0.303314i
\(790\) 18.7127 10.1983i 0.665769 0.362841i
\(791\) −28.1016 48.6734i −0.999178 1.73063i
\(792\) −0.654978 + 1.79954i −0.0232736 + 0.0639438i
\(793\) −55.9164 9.85957i −1.98565 0.350124i
\(794\) −2.90865 16.4958i −0.103224 0.585413i
\(795\) −12.0568 + 59.7422i −0.427611 + 2.11884i
\(796\) 0.475962 + 0.399379i 0.0168700 + 0.0141556i
\(797\) 29.9226i 1.05991i 0.848025 + 0.529956i \(0.177791\pi\)
−0.848025 + 0.529956i \(0.822209\pi\)
\(798\) −20.8459 + 75.7951i −0.737938 + 2.68312i
\(799\) 5.33772 0.188835
\(800\) 29.0255 + 6.60491i 1.02621 + 0.233519i
\(801\) 10.9418 3.98250i 0.386611 0.140715i
\(802\) 10.8275 1.90918i 0.382331 0.0674153i
\(803\) −0.993061 0.175103i −0.0350444 0.00617927i
\(804\) −18.9988 6.91500i −0.670036 0.243873i
\(805\) 41.6496 + 1.02504i 1.46796 + 0.0361281i
\(806\) −15.1837 + 26.2989i −0.534822 + 0.926339i
\(807\) 7.09074 + 8.45041i 0.249606 + 0.297469i
\(808\) 3.08579 + 3.67750i 0.108558 + 0.129374i
\(809\) 21.2289 36.7696i 0.746369 1.29275i −0.203183 0.979141i \(-0.565129\pi\)
0.949552 0.313608i \(-0.101538\pi\)
\(810\) −0.967323 + 39.3043i −0.0339883 + 1.38101i
\(811\) 29.2727 + 10.6544i 1.02790 + 0.374126i 0.800282 0.599623i \(-0.204683\pi\)
0.227621 + 0.973750i \(0.426905\pi\)
\(812\) 16.1417 + 2.84622i 0.566463 + 0.0998828i
\(813\) 17.8611 3.14939i 0.626415 0.110454i
\(814\) 1.76537 0.642542i 0.0618762 0.0225211i
\(815\) 12.0733 + 35.8954i 0.422909 + 1.25736i
\(816\) 24.1028 0.843767
\(817\) −26.8114 + 37.7583i −0.938014 + 1.32099i
\(818\) 4.07767i 0.142572i
\(819\) −36.2531 30.4199i −1.26678 1.06296i
\(820\) −2.28875 + 11.3409i −0.0799267 + 0.396042i
\(821\) −1.07790 6.11310i −0.0376191 0.213349i 0.960204 0.279301i \(-0.0901026\pi\)
−0.997823 + 0.0659521i \(0.978992\pi\)
\(822\) −2.54853 0.449375i −0.0888903 0.0156738i
\(823\) 12.3025 33.8009i 0.428839 1.17823i −0.517679 0.855575i \(-0.673204\pi\)
0.946518 0.322651i \(-0.104574\pi\)
\(824\) 2.48383 + 4.30212i 0.0865283 + 0.149871i
\(825\) 0.287816 5.84375i 0.0100205 0.203453i
\(826\) −3.14292 + 2.63722i −0.109356 + 0.0917606i
\(827\) 9.88848 + 11.7846i 0.343856 + 0.409792i 0.910062 0.414472i \(-0.136034\pi\)
−0.566206 + 0.824264i \(0.691589\pi\)
\(828\) −12.0997 6.98578i −0.420494 0.242773i
\(829\) −12.0970 20.9527i −0.420148 0.727717i 0.575806 0.817586i \(-0.304688\pi\)
−0.995954 + 0.0898693i \(0.971355\pi\)
\(830\) 25.3148 20.2015i 0.878691 0.701203i
\(831\) −3.11920 + 17.6898i −0.108204 + 0.613654i
\(832\) −2.84293 + 0.501284i −0.0985607 + 0.0173789i
\(833\) 7.63975 + 20.9900i 0.264702 + 0.727262i
\(834\) 27.5642 + 23.1291i 0.954469 + 0.800895i
\(835\) 31.0243 + 18.9446i 1.07364 + 0.655605i
\(836\) 1.80483 1.78118i 0.0624215 0.0616035i
\(837\) 3.09573i 0.107004i
\(838\) 25.9827 30.9649i 0.897556 1.06967i
\(839\) 11.6771 4.25013i 0.403139 0.146731i −0.132489 0.991184i \(-0.542297\pi\)
0.535628 + 0.844454i \(0.320075\pi\)
\(840\) −11.9960 + 30.5947i −0.413901 + 1.05562i
\(841\) −3.18727 + 18.0759i −0.109906 + 0.623308i
\(842\) 14.0372 38.5669i 0.483754 1.32910i
\(843\) −37.6855 + 21.7577i −1.29796 + 0.749376i
\(844\) −11.2960 + 19.5652i −0.388824 + 0.673463i
\(845\) −1.44358 9.55630i −0.0496606 0.328747i
\(846\) 9.61314 8.06638i 0.330507 0.277328i
\(847\) −39.4983 22.8043i −1.35718 0.783566i
\(848\) −49.1718 + 28.3894i −1.68857 + 0.974895i
\(849\) 69.2910 + 25.2199i 2.37806 + 0.865543i
\(850\) −17.3590 + 5.36699i −0.595410 + 0.184086i
\(851\) −1.63667 9.28199i −0.0561042 0.318182i
\(852\) 5.83441 + 16.0299i 0.199883 + 0.549175i
\(853\) 14.8823 17.7360i 0.509560 0.607270i −0.448519 0.893773i \(-0.648049\pi\)
0.958079 + 0.286503i \(0.0924930\pi\)
\(854\) 103.210 3.53176
\(855\) 11.7829 23.3386i 0.402965 0.798162i
\(856\) 2.54882 0.0871167
\(857\) 1.82726 2.17765i 0.0624181 0.0743870i −0.733932 0.679223i \(-0.762317\pi\)
0.796350 + 0.604836i \(0.206761\pi\)
\(858\) 2.97276 + 8.16760i 0.101489 + 0.278837i
\(859\) 4.49254 + 25.4785i 0.153284 + 0.869314i 0.960338 + 0.278838i \(0.0899492\pi\)
−0.807055 + 0.590477i \(0.798940\pi\)
\(860\) 18.6214 21.1145i 0.634985 0.720000i
\(861\) −41.4581 15.0895i −1.41289 0.514249i
\(862\) −39.6161 + 22.8724i −1.34933 + 0.779036i
\(863\) −32.9118 19.0016i −1.12033 0.646823i −0.178844 0.983877i \(-0.557236\pi\)
−0.941485 + 0.337055i \(0.890569\pi\)
\(864\) −3.45338 + 2.89773i −0.117486 + 0.0985827i
\(865\) −18.9948 + 2.86936i −0.645843 + 0.0975613i
\(866\) −2.10886 + 3.65266i −0.0716621 + 0.124122i
\(867\) 26.5357 15.3204i 0.901198 0.520307i
\(868\) 7.02455 19.2998i 0.238429 0.655077i
\(869\) 0.455217 2.58167i 0.0154422 0.0875770i
\(870\) −28.8957 11.3298i −0.979655 0.384116i
\(871\) 27.9909 10.1879i 0.948437 0.345203i
\(872\) 3.28997 3.92083i 0.111412 0.132776i
\(873\) 15.1464i 0.512628i
\(874\) −19.4264 28.1369i −0.657108 0.951744i
\(875\) 3.49542 47.2656i 0.118167 1.59787i
\(876\) 4.44534 + 3.73008i 0.150194 + 0.126028i
\(877\) −16.7912 46.1335i −0.567000 1.55782i −0.809164 0.587583i \(-0.800079\pi\)
0.242164 0.970235i \(-0.422143\pi\)
\(878\) 11.1018 1.95755i 0.374668 0.0660641i
\(879\) 9.06489 51.4095i 0.305751 1.73400i
\(880\) 4.26043 3.39986i 0.143619 0.114609i
\(881\) 27.8747 + 48.2804i 0.939123 + 1.62661i 0.767112 + 0.641514i \(0.221693\pi\)
0.172011 + 0.985095i \(0.444973\pi\)
\(882\) 45.4793 + 26.2575i 1.53137 + 0.884135i
\(883\) 10.6931 + 12.7435i 0.359851 + 0.428853i 0.915347 0.402666i \(-0.131916\pi\)
−0.555496 + 0.831519i \(0.687472\pi\)
\(884\) 7.69345 6.45557i 0.258759 0.217124i
\(885\) 2.53817 1.38329i 0.0853195 0.0464987i
\(886\) −28.1307 48.7237i −0.945068 1.63691i
\(887\) 14.8397 40.7717i 0.498267 1.36898i −0.394680 0.918818i \(-0.629145\pi\)
0.892948 0.450160i \(-0.148633\pi\)
\(888\) 7.32147 + 1.29097i 0.245692 + 0.0433222i
\(889\) 14.5811 + 82.6934i 0.489034 + 2.77345i
\(890\) −16.9811 3.42702i −0.569207 0.114874i
\(891\) 3.70480 + 3.10869i 0.124115 + 0.104145i
\(892\) 3.74820i 0.125499i
\(893\) 11.0564 2.88455i 0.369989 0.0965276i
\(894\) 19.7285 0.659819
\(895\) −49.8643 + 16.7717i −1.66678 + 0.560615i
\(896\) −42.5001 + 15.4688i −1.41983 + 0.516776i
\(897\) 42.9438 7.57214i 1.43385 0.252827i
\(898\) −26.5091 4.67426i −0.884619 0.155982i
\(899\) −12.5345 4.56220i −0.418051 0.152158i
\(900\) −8.61446 + 13.3570i −0.287149 + 0.445232i
\(901\) 11.6410 20.1628i 0.387818 0.671721i
\(902\) 2.45865 + 2.93010i 0.0818640 + 0.0975617i
\(903\) 69.0075 + 82.2399i 2.29643 + 2.73677i
\(904\) −9.64125 + 16.6991i −0.320663 + 0.555405i
\(905\) −37.1376 0.913997i −1.23449 0.0303823i
\(906\) −56.8107 20.6774i −1.88741 0.686961i
\(907\) 19.5350 + 3.44455i 0.648649 + 0.114374i 0.488286 0.872684i \(-0.337622\pi\)
0.160363 + 0.987058i \(0.448733\pi\)
\(908\) 10.5580 1.86165i 0.350378 0.0617812i
\(909\) −8.32000 + 3.02823i −0.275957 + 0.100440i
\(910\) 22.4458 + 66.7342i 0.744070 + 2.21222i
\(911\) 15.4076 0.510478 0.255239 0.966878i \(-0.417846\pi\)
0.255239 + 0.966878i \(0.417846\pi\)
\(912\) 49.9259 13.0253i 1.65321 0.431312i
\(913\) 3.98395i 0.131849i
\(914\) −27.5270 23.0979i −0.910512 0.764010i
\(915\) −71.2798 14.3852i −2.35644 0.475562i
\(916\) −3.68193 20.8812i −0.121654 0.689936i
\(917\) 14.3194 + 2.52490i 0.472869 + 0.0833795i
\(918\) 0.941127 2.58572i 0.0310618 0.0853416i
\(919\) −6.62805 11.4801i −0.218639 0.378694i 0.735753 0.677250i \(-0.236828\pi\)
−0.954392 + 0.298556i \(0.903495\pi\)
\(920\) −6.84013 12.5508i −0.225512 0.413788i
\(921\) 9.96201 8.35912i 0.328259 0.275442i
\(922\) 8.58644 + 10.2329i 0.282779 + 0.337003i
\(923\) −21.7654 12.5663i −0.716417 0.413624i
\(924\) −2.93926 5.09095i −0.0966947 0.167480i
\(925\) −10.6379 + 1.34017i −0.349773 + 0.0440647i
\(926\) −6.69313 + 37.9586i −0.219950 + 1.24740i
\(927\) −9.02281 + 1.59096i −0.296348 + 0.0522541i
\(928\) −6.64358 18.2531i −0.218086 0.599187i
\(929\) −23.9018 20.0560i −0.784193 0.658016i 0.160108 0.987100i \(-0.448816\pi\)
−0.944301 + 0.329083i \(0.893260\pi\)
\(930\) −20.2685 + 33.1924i −0.664631 + 1.08842i
\(931\) 27.1680 + 39.3496i 0.890394 + 1.28963i
\(932\) 7.63580i 0.250119i
\(933\) −10.2618 + 12.2296i −0.335958 + 0.400379i
\(934\) −45.3648 + 16.5114i −1.48438 + 0.540270i
\(935\) −0.815876 + 2.08082i −0.0266820 + 0.0680501i
\(936\) −2.81944 + 15.9899i −0.0921564 + 0.522645i
\(937\) −5.54711 + 15.2405i −0.181216 + 0.497887i −0.996726 0.0808564i \(-0.974234\pi\)
0.815510 + 0.578743i \(0.196457\pi\)
\(938\) −46.8916 + 27.0729i −1.53107 + 0.883961i
\(939\) −5.46216 + 9.46074i −0.178251 + 0.308739i
\(940\) −6.86860 + 1.03757i −0.224029 + 0.0338419i
\(941\) 26.9454 22.6099i 0.878396 0.737062i −0.0874525 0.996169i \(-0.527873\pi\)
0.965849 + 0.259107i \(0.0834281\pi\)
\(942\) 39.5254 + 22.8200i 1.28781 + 0.743516i
\(943\) 16.6188 9.59486i 0.541182 0.312452i
\(944\) 2.53055 + 0.921045i 0.0823624 + 0.0299775i
\(945\) 5.38315 + 4.74753i 0.175114 + 0.154437i
\(946\) −1.61623 9.16612i −0.0525483 0.298016i
\(947\) 7.61965 + 20.9348i 0.247605 + 0.680290i 0.999773 + 0.0213182i \(0.00678632\pi\)
−0.752167 + 0.658972i \(0.770991\pi\)
\(948\) −9.69713 + 11.5566i −0.314948 + 0.375340i
\(949\) −8.54953 −0.277530
\(950\) −33.0567 + 20.4980i −1.07250 + 0.665043i
\(951\) 65.9811 2.13958
\(952\) 8.06934 9.61666i 0.261529 0.311678i
\(953\) −1.45699 4.00305i −0.0471966 0.129672i 0.913855 0.406041i \(-0.133091\pi\)
−0.961052 + 0.276369i \(0.910869\pi\)
\(954\) −9.50487 53.9048i −0.307732 1.74523i
\(955\) −21.4845 18.9477i −0.695222 0.613132i
\(956\) 15.0049 + 5.46135i 0.485294 + 0.176633i
\(957\) −3.30640 + 1.90895i −0.106881 + 0.0617076i
\(958\) 58.8145 + 33.9566i 1.90021 + 1.09709i
\(959\) −1.97535 + 1.65751i −0.0637873 + 0.0535239i
\(960\) −3.65563 + 0.552220i −0.117985 + 0.0178228i
\(961\) 7.14280 12.3717i 0.230413 0.399087i
\(962\) 13.7943 7.96412i 0.444745 0.256773i
\(963\) −1.60779 + 4.41736i −0.0518102 + 0.142347i
\(964\) 3.62907 20.5815i 0.116885 0.662885i
\(965\) 7.86848 20.0678i 0.253295 0.646007i
\(966\) −74.4848 + 27.1102i −2.39651 + 0.872258i
\(967\) 0.783596 0.933854i 0.0251988 0.0300307i −0.753298 0.657679i \(-0.771538\pi\)
0.778497 + 0.627649i \(0.215983\pi\)
\(968\) 15.6477i 0.502935i
\(969\) −15.0588 + 14.8615i −0.483758 + 0.477419i
\(970\) 11.7438 19.2319i 0.377069 0.617500i
\(971\) −3.32466 2.78972i −0.106693 0.0895264i 0.587880 0.808948i \(-0.299963\pi\)
−0.694574 + 0.719421i \(0.744407\pi\)
\(972\) −8.59821 23.6234i −0.275788 0.757720i
\(973\) 35.3096 6.22604i 1.13197 0.199598i
\(974\) 5.68222 32.2255i 0.182070 1.03257i
\(975\) −6.20041 49.2171i −0.198572 1.57621i
\(976\) −33.8720 58.6680i −1.08422 1.87792i
\(977\) −18.6429 10.7635i −0.596440 0.344355i 0.171200 0.985236i \(-0.445236\pi\)
−0.767640 + 0.640882i \(0.778569\pi\)
\(978\) −46.3146 55.1956i −1.48098 1.76496i
\(979\) −1.63240 + 1.36975i −0.0521718 + 0.0437773i
\(980\) −13.9110 25.5250i −0.444371 0.815367i
\(981\) 4.71990 + 8.17510i 0.150695 + 0.261011i
\(982\) 9.19713 25.2689i 0.293492 0.806363i
\(983\) −14.3780 2.53522i −0.458586 0.0808611i −0.0604172 0.998173i \(-0.519243\pi\)
−0.398169 + 0.917312i \(0.630354\pi\)
\(984\) 2.62843 + 14.9066i 0.0837912 + 0.475204i
\(985\) −6.80011 1.37236i −0.216669 0.0437269i
\(986\) 9.08261 + 7.62121i 0.289249 + 0.242709i
\(987\) 26.4896i 0.843172i
\(988\) 12.4474 17.5295i 0.396004 0.557688i
\(989\) −46.6954 −1.48483
\(990\) 1.67516 + 4.98047i 0.0532402 + 0.158290i
\(991\) −30.0031 + 10.9202i −0.953080 + 0.346893i −0.771318 0.636450i \(-0.780402\pi\)
−0.181762 + 0.983343i \(0.558180\pi\)
\(992\) −23.9701 + 4.22658i −0.761052 + 0.134194i
\(993\) −33.1713 5.84900i −1.05266 0.185612i
\(994\) 42.9294 + 15.6250i 1.36164 + 0.495596i
\(995\) −1.17199 0.0288441i −0.0371547 0.000914418i
\(996\) −11.4633 + 19.8551i −0.363229 + 0.629132i
\(997\) 35.4698 + 42.2712i 1.12334 + 1.33874i 0.934182 + 0.356797i \(0.116131\pi\)
0.189157 + 0.981947i \(0.439424\pi\)
\(998\) 39.6117 + 47.2073i 1.25389 + 1.49432i
\(999\) 0.811883 1.40622i 0.0256868 0.0444909i
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 95.2.p.a.54.7 yes 48
3.2 odd 2 855.2.da.b.244.2 48
5.2 odd 4 475.2.l.f.301.7 48
5.3 odd 4 475.2.l.f.301.2 48
5.4 even 2 inner 95.2.p.a.54.2 yes 48
15.14 odd 2 855.2.da.b.244.7 48
19.5 even 9 1805.2.b.k.1084.5 24
19.6 even 9 inner 95.2.p.a.44.2 48
19.14 odd 18 1805.2.b.l.1084.20 24
57.44 odd 18 855.2.da.b.424.7 48
95.14 odd 18 1805.2.b.l.1084.5 24
95.24 even 18 1805.2.b.k.1084.20 24
95.33 even 36 9025.2.a.ct.1.20 24
95.43 odd 36 9025.2.a.cu.1.5 24
95.44 even 18 inner 95.2.p.a.44.7 yes 48
95.52 even 36 9025.2.a.ct.1.5 24
95.62 odd 36 9025.2.a.cu.1.20 24
95.63 odd 36 475.2.l.f.101.2 48
95.82 odd 36 475.2.l.f.101.7 48
285.44 odd 18 855.2.da.b.424.2 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.p.a.44.2 48 19.6 even 9 inner
95.2.p.a.44.7 yes 48 95.44 even 18 inner
95.2.p.a.54.2 yes 48 5.4 even 2 inner
95.2.p.a.54.7 yes 48 1.1 even 1 trivial
475.2.l.f.101.2 48 95.63 odd 36
475.2.l.f.101.7 48 95.82 odd 36
475.2.l.f.301.2 48 5.3 odd 4
475.2.l.f.301.7 48 5.2 odd 4
855.2.da.b.244.2 48 3.2 odd 2
855.2.da.b.244.7 48 15.14 odd 2
855.2.da.b.424.2 48 285.44 odd 18
855.2.da.b.424.7 48 57.44 odd 18
1805.2.b.k.1084.5 24 19.5 even 9
1805.2.b.k.1084.20 24 95.24 even 18
1805.2.b.l.1084.5 24 95.14 odd 18
1805.2.b.l.1084.20 24 19.14 odd 18
9025.2.a.ct.1.5 24 95.52 even 36
9025.2.a.ct.1.20 24 95.33 even 36
9025.2.a.cu.1.5 24 95.43 odd 36
9025.2.a.cu.1.20 24 95.62 odd 36