Properties

Label 414.2.m.a.25.2
Level $414$
Weight $2$
Character 414.25
Analytic conductor $3.306$
Analytic rank $0$
Dimension $240$
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] = [414,2,Mod(13,414)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(414, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([22, 42]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("414.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 414.m (of order \(33\), degree \(20\), 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: \(3.30580664368\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(12\) over \(\Q(\zeta_{33})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 25.2
Character \(\chi\) \(=\) 414.25
Dual form 414.2.m.a.265.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.888835 - 0.458227i) q^{2} +(-1.33859 - 1.09917i) q^{3} +(0.580057 - 0.814576i) q^{4} +(0.448804 + 1.84999i) q^{5} +(-1.69346 - 0.363606i) q^{6} +(1.59879 + 4.61941i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.583642 + 2.94268i) q^{9} +O(q^{10})\) \(q+(0.888835 - 0.458227i) q^{2} +(-1.33859 - 1.09917i) q^{3} +(0.580057 - 0.814576i) q^{4} +(0.448804 + 1.84999i) q^{5} +(-1.69346 - 0.363606i) q^{6} +(1.59879 + 4.61941i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.583642 + 2.94268i) q^{9} +(1.24663 + 1.43869i) q^{10} +(-0.0108972 - 0.228760i) q^{11} +(-1.67182 + 0.452800i) q^{12} +(-1.76863 + 5.11011i) q^{13} +(3.53780 + 3.37328i) q^{14} +(1.43270 - 2.96969i) q^{15} +(-0.327068 - 0.945001i) q^{16} +(0.938641 - 2.05534i) q^{17} +(1.86718 + 2.34812i) q^{18} +(-1.96310 - 4.29858i) q^{19} +(1.76729 + 0.707517i) q^{20} +(2.93740 - 7.94084i) q^{21} +(-0.114510 - 0.198336i) q^{22} +(4.79107 + 0.213736i) q^{23} +(-1.27849 + 1.16854i) q^{24} +(1.22313 - 0.630565i) q^{25} +(0.769571 + 5.35248i) q^{26} +(2.45325 - 4.58056i) q^{27} +(4.69025 + 1.37718i) q^{28} +(2.11897 + 2.97568i) q^{29} +(-0.0873601 - 3.29607i) q^{30} +(-4.65707 + 1.86441i) q^{31} +(-0.723734 - 0.690079i) q^{32} +(-0.236859 + 0.318193i) q^{33} +(-0.107513 - 2.25697i) q^{34} +(-7.82833 + 5.03096i) q^{35} +(2.73558 + 1.23150i) q^{36} +(3.86467 - 1.13477i) q^{37} +(-3.71459 - 2.92119i) q^{38} +(7.98436 - 4.89632i) q^{39} +(1.89503 - 0.180954i) q^{40} +(0.295248 + 1.21703i) q^{41} +(-1.02784 - 8.40409i) q^{42} +(-4.70773 - 1.88469i) q^{43} +(-0.192663 - 0.123817i) q^{44} +(-5.18200 + 2.40042i) q^{45} +(4.35641 - 2.00542i) q^{46} +(5.55942 - 9.62920i) q^{47} +(-0.600909 + 1.62447i) q^{48} +(-13.2804 + 10.4438i) q^{49} +(0.798216 - 1.12094i) q^{50} +(-3.51562 + 1.71952i) q^{51} +(3.13667 + 4.40484i) q^{52} +(-3.90795 + 4.51002i) q^{53} +(0.0816043 - 5.19551i) q^{54} +(0.418313 - 0.122828i) q^{55} +(4.79992 - 0.925109i) q^{56} +(-2.09710 + 7.91181i) q^{57} +(3.24695 + 1.67392i) q^{58} +(3.64188 - 10.5225i) q^{59} +(-1.58799 - 2.88963i) q^{60} +(-7.88094 - 6.19764i) q^{61} +(-3.28505 + 3.79115i) q^{62} +(-12.6603 + 7.40081i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-10.2474 - 0.978512i) q^{65} +(-0.0647245 + 0.391357i) q^{66} +(-0.316723 + 6.64883i) q^{67} +(-1.12976 - 1.95681i) q^{68} +(-6.17834 - 5.55231i) q^{69} +(-4.65278 + 8.05885i) q^{70} +(7.34237 + 4.71865i) q^{71} +(2.99579 - 0.158914i) q^{72} +(5.97584 + 13.0853i) q^{73} +(2.91508 - 2.77952i) q^{74} +(-2.33036 - 0.500358i) q^{75} +(-4.64023 - 0.894330i) q^{76} +(1.03931 - 0.416078i) q^{77} +(4.85316 - 8.01067i) q^{78} +(10.8392 - 2.08908i) q^{79} +(1.60146 - 1.02919i) q^{80} +(-8.31872 + 3.43494i) q^{81} +(0.820102 + 0.946448i) q^{82} +(0.586047 - 2.41572i) q^{83} +(-4.76456 - 6.99887i) q^{84} +(4.22362 + 0.814037i) q^{85} +(-5.04801 + 0.482027i) q^{86} +(0.434351 - 6.31233i) q^{87} +(-0.227982 - 0.0217697i) q^{88} +(-1.73267 - 12.0510i) q^{89} +(-3.50601 + 4.50811i) q^{90} -26.4334 q^{91} +(2.95320 - 3.77871i) q^{92} +(8.28321 + 2.62324i) q^{93} +(0.529056 - 11.1062i) q^{94} +(7.07130 - 5.56093i) q^{95} +(0.210267 + 1.71924i) q^{96} +(-2.39513 + 2.28375i) q^{97} +(-7.01846 + 15.3683i) q^{98} +(0.666807 - 0.165581i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/414\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(235\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.888835 0.458227i 0.628502 0.324015i
\(3\) −1.33859 1.09917i −0.772835 0.634607i
\(4\) 0.580057 0.814576i 0.290028 0.407288i
\(5\) 0.448804 + 1.84999i 0.200711 + 0.827342i 0.979727 + 0.200338i \(0.0642040\pi\)
−0.779016 + 0.627004i \(0.784281\pi\)
\(6\) −1.69346 0.363606i −0.691350 0.148442i
\(7\) 1.59879 + 4.61941i 0.604287 + 1.74597i 0.663975 + 0.747755i \(0.268868\pi\)
−0.0596880 + 0.998217i \(0.519011\pi\)
\(8\) 0.142315 0.989821i 0.0503159 0.349955i
\(9\) 0.583642 + 2.94268i 0.194547 + 0.980893i
\(10\) 1.24663 + 1.43869i 0.394219 + 0.454952i
\(11\) −0.0108972 0.228760i −0.00328562 0.0689737i 0.996629 0.0820404i \(-0.0261436\pi\)
−0.999915 + 0.0130667i \(0.995841\pi\)
\(12\) −1.67182 + 0.452800i −0.482612 + 0.130712i
\(13\) −1.76863 + 5.11011i −0.490529 + 1.41729i 0.379914 + 0.925022i \(0.375954\pi\)
−0.870443 + 0.492269i \(0.836168\pi\)
\(14\) 3.53780 + 3.37328i 0.945516 + 0.901548i
\(15\) 1.43270 2.96969i 0.369921 0.766772i
\(16\) −0.327068 0.945001i −0.0817670 0.236250i
\(17\) 0.938641 2.05534i 0.227654 0.498492i −0.760991 0.648762i \(-0.775287\pi\)
0.988645 + 0.150270i \(0.0480143\pi\)
\(18\) 1.86718 + 2.34812i 0.440097 + 0.553457i
\(19\) −1.96310 4.29858i −0.450365 0.986162i −0.989579 0.143993i \(-0.954006\pi\)
0.539214 0.842169i \(-0.318721\pi\)
\(20\) 1.76729 + 0.707517i 0.395178 + 0.158206i
\(21\) 2.93740 7.94084i 0.640993 1.73283i
\(22\) −0.114510 0.198336i −0.0244135 0.0422855i
\(23\) 4.79107 + 0.213736i 0.999006 + 0.0445670i
\(24\) −1.27849 + 1.16854i −0.260970 + 0.238526i
\(25\) 1.22313 0.630565i 0.244625 0.126113i
\(26\) 0.769571 + 5.35248i 0.150925 + 1.04971i
\(27\) 2.45325 4.58056i 0.472129 0.881529i
\(28\) 4.69025 + 1.37718i 0.886374 + 0.260263i
\(29\) 2.11897 + 2.97568i 0.393483 + 0.552570i 0.963032 0.269388i \(-0.0868213\pi\)
−0.569549 + 0.821958i \(0.692882\pi\)
\(30\) −0.0873601 3.29607i −0.0159497 0.601777i
\(31\) −4.65707 + 1.86441i −0.836435 + 0.334858i −0.750031 0.661402i \(-0.769962\pi\)
−0.0864034 + 0.996260i \(0.527537\pi\)
\(32\) −0.723734 0.690079i −0.127939 0.121990i
\(33\) −0.236859 + 0.318193i −0.0412319 + 0.0553903i
\(34\) −0.107513 2.25697i −0.0184382 0.387066i
\(35\) −7.82833 + 5.03096i −1.32323 + 0.850388i
\(36\) 2.73558 + 1.23150i 0.455930 + 0.205250i
\(37\) 3.86467 1.13477i 0.635348 0.186555i 0.0518311 0.998656i \(-0.483494\pi\)
0.583517 + 0.812101i \(0.301676\pi\)
\(38\) −3.71459 2.92119i −0.602586 0.473879i
\(39\) 7.98436 4.89632i 1.27852 0.784038i
\(40\) 1.89503 0.180954i 0.299631 0.0286113i
\(41\) 0.295248 + 1.21703i 0.0461100 + 0.190068i 0.990209 0.139595i \(-0.0445800\pi\)
−0.944099 + 0.329663i \(0.893065\pi\)
\(42\) −1.02784 8.40409i −0.158599 1.29678i
\(43\) −4.70773 1.88469i −0.717922 0.287413i −0.0162052 0.999869i \(-0.505158\pi\)
−0.701717 + 0.712456i \(0.747583\pi\)
\(44\) −0.192663 0.123817i −0.0290451 0.0186661i
\(45\) −5.18200 + 2.40042i −0.772486 + 0.357833i
\(46\) 4.35641 2.00542i 0.642317 0.295683i
\(47\) 5.55942 9.62920i 0.810925 1.40456i −0.101292 0.994857i \(-0.532298\pi\)
0.912217 0.409707i \(-0.134369\pi\)
\(48\) −0.600909 + 1.62447i −0.0867337 + 0.234472i
\(49\) −13.2804 + 10.4438i −1.89720 + 1.49198i
\(50\) 0.798216 1.12094i 0.112885 0.158525i
\(51\) −3.51562 + 1.71952i −0.492286 + 0.240781i
\(52\) 3.13667 + 4.40484i 0.434978 + 0.610841i
\(53\) −3.90795 + 4.51002i −0.536799 + 0.619499i −0.957756 0.287582i \(-0.907149\pi\)
0.420957 + 0.907080i \(0.361694\pi\)
\(54\) 0.0816043 5.19551i 0.0111049 0.707020i
\(55\) 0.418313 0.122828i 0.0564054 0.0165621i
\(56\) 4.79992 0.925109i 0.641416 0.123623i
\(57\) −2.09710 + 7.91181i −0.277768 + 1.04794i
\(58\) 3.24695 + 1.67392i 0.426346 + 0.219797i
\(59\) 3.64188 10.5225i 0.474132 1.36991i −0.413980 0.910286i \(-0.635862\pi\)
0.888112 0.459628i \(-0.152017\pi\)
\(60\) −1.58799 2.88963i −0.205009 0.373050i
\(61\) −7.88094 6.19764i −1.00905 0.793526i −0.0305002 0.999535i \(-0.509710\pi\)
−0.978550 + 0.206009i \(0.933952\pi\)
\(62\) −3.28505 + 3.79115i −0.417201 + 0.481476i
\(63\) −12.6603 + 7.40081i −1.59505 + 0.932415i
\(64\) −0.959493 0.281733i −0.119937 0.0352166i
\(65\) −10.2474 0.978512i −1.27104 0.121369i
\(66\) −0.0647245 + 0.391357i −0.00796704 + 0.0481727i
\(67\) −0.316723 + 6.64883i −0.0386938 + 0.812284i 0.893223 + 0.449613i \(0.148438\pi\)
−0.931917 + 0.362671i \(0.881865\pi\)
\(68\) −1.12976 1.95681i −0.137004 0.237298i
\(69\) −6.17834 5.55231i −0.743784 0.668420i
\(70\) −4.65278 + 8.05885i −0.556113 + 0.963216i
\(71\) 7.34237 + 4.71865i 0.871379 + 0.560001i 0.898174 0.439640i \(-0.144894\pi\)
−0.0267952 + 0.999641i \(0.508530\pi\)
\(72\) 2.99579 0.158914i 0.353057 0.0187282i
\(73\) 5.97584 + 13.0853i 0.699419 + 1.53151i 0.840674 + 0.541541i \(0.182159\pi\)
−0.141255 + 0.989973i \(0.545114\pi\)
\(74\) 2.91508 2.77952i 0.338871 0.323113i
\(75\) −2.33036 0.500358i −0.269087 0.0577764i
\(76\) −4.64023 0.894330i −0.532270 0.102587i
\(77\) 1.03931 0.416078i 0.118441 0.0474165i
\(78\) 4.85316 8.01067i 0.549512 0.907029i
\(79\) 10.8392 2.08908i 1.21950 0.235040i 0.461411 0.887187i \(-0.347343\pi\)
0.758093 + 0.652146i \(0.226131\pi\)
\(80\) 1.60146 1.02919i 0.179048 0.115067i
\(81\) −8.31872 + 3.43494i −0.924303 + 0.381660i
\(82\) 0.820102 + 0.946448i 0.0905651 + 0.104518i
\(83\) 0.586047 2.41572i 0.0643270 0.265160i −0.930562 0.366134i \(-0.880681\pi\)
0.994889 + 0.100975i \(0.0321962\pi\)
\(84\) −4.76456 6.99887i −0.519856 0.763639i
\(85\) 4.22362 + 0.814037i 0.458116 + 0.0882947i
\(86\) −5.04801 + 0.482027i −0.544341 + 0.0519783i
\(87\) 0.434351 6.31233i 0.0465673 0.676753i
\(88\) −0.227982 0.0217697i −0.0243030 0.00232065i
\(89\) −1.73267 12.0510i −0.183663 1.27740i −0.848010 0.529980i \(-0.822199\pi\)
0.664347 0.747424i \(-0.268710\pi\)
\(90\) −3.50601 + 4.50811i −0.369566 + 0.475196i
\(91\) −26.4334 −2.77097
\(92\) 2.95320 3.77871i 0.307892 0.393958i
\(93\) 8.28321 + 2.62324i 0.858929 + 0.272018i
\(94\) 0.529056 11.1062i 0.0545679 1.14552i
\(95\) 7.07130 5.56093i 0.725500 0.570539i
\(96\) 0.210267 + 1.71924i 0.0214603 + 0.175469i
\(97\) −2.39513 + 2.28375i −0.243188 + 0.231880i −0.801864 0.597507i \(-0.796158\pi\)
0.558676 + 0.829386i \(0.311310\pi\)
\(98\) −7.01846 + 15.3683i −0.708972 + 1.55243i
\(99\) 0.666807 0.165581i 0.0670166 0.0166415i
\(100\) 0.195839 1.36209i 0.0195839 0.136209i
\(101\) −2.21338 + 9.12367i −0.220239 + 0.907839i 0.749168 + 0.662380i \(0.230454\pi\)
−0.969407 + 0.245458i \(0.921062\pi\)
\(102\) −2.33688 + 3.13932i −0.231385 + 0.310839i
\(103\) −12.0905 6.23310i −1.19132 0.614166i −0.255552 0.966795i \(-0.582257\pi\)
−0.935763 + 0.352630i \(0.885288\pi\)
\(104\) 4.80640 + 2.47787i 0.471306 + 0.242975i
\(105\) 16.0088 + 1.87029i 1.56230 + 0.182522i
\(106\) −1.40692 + 5.79939i −0.136652 + 0.563287i
\(107\) 2.29139 15.9370i 0.221517 1.54069i −0.510786 0.859708i \(-0.670645\pi\)
0.732303 0.680979i \(-0.238445\pi\)
\(108\) −2.30819 4.65535i −0.222106 0.447961i
\(109\) 0.118735 0.259994i 0.0113728 0.0249029i −0.903860 0.427828i \(-0.859279\pi\)
0.915233 + 0.402925i \(0.132006\pi\)
\(110\) 0.315529 0.300856i 0.0300845 0.0286855i
\(111\) −6.42052 2.72895i −0.609409 0.259020i
\(112\) 3.84243 3.02172i 0.363076 0.285526i
\(113\) 0.121549 2.55164i 0.0114344 0.240038i −0.985913 0.167256i \(-0.946509\pi\)
0.997348 0.0727817i \(-0.0231876\pi\)
\(114\) 1.76142 + 7.99324i 0.164973 + 0.748636i
\(115\) 1.75484 + 8.95937i 0.163639 + 0.835465i
\(116\) 3.65304 0.339176
\(117\) −16.0697 2.22203i −1.48564 0.205427i
\(118\) −1.58466 11.0216i −0.145880 1.01462i
\(119\) 10.9951 + 1.04991i 1.00792 + 0.0962449i
\(120\) −2.73557 1.84075i −0.249722 0.168036i
\(121\) 10.8980 1.04063i 0.990725 0.0946028i
\(122\) −9.84478 1.89743i −0.891304 0.171785i
\(123\) 0.942508 1.95363i 0.0849831 0.176153i
\(124\) −1.18266 + 4.87500i −0.106206 + 0.437788i
\(125\) 7.94863 + 9.17321i 0.710947 + 0.820476i
\(126\) −7.86169 + 12.3794i −0.700375 + 1.10284i
\(127\) 13.4744 8.65948i 1.19566 0.768405i 0.217461 0.976069i \(-0.430222\pi\)
0.978200 + 0.207664i \(0.0665861\pi\)
\(128\) −0.981929 + 0.189251i −0.0867911 + 0.0167276i
\(129\) 4.23012 + 7.69743i 0.372441 + 0.677721i
\(130\) −9.55667 + 3.82591i −0.838175 + 0.335555i
\(131\) −1.40564 0.270914i −0.122811 0.0236699i 0.127475 0.991842i \(-0.459313\pi\)
−0.250286 + 0.968172i \(0.580525\pi\)
\(132\) 0.121801 + 0.377510i 0.0106014 + 0.0328580i
\(133\) 16.7183 15.9409i 1.44966 1.38225i
\(134\) 2.76516 + 6.05485i 0.238873 + 0.523059i
\(135\) 9.57504 + 2.48273i 0.824088 + 0.213680i
\(136\) −1.90083 1.22159i −0.162995 0.104751i
\(137\) 4.27720 7.40833i 0.365426 0.632936i −0.623419 0.781888i \(-0.714257\pi\)
0.988844 + 0.148952i \(0.0475900\pi\)
\(138\) −8.03574 2.10401i −0.684048 0.179105i
\(139\) −1.22776 2.12654i −0.104137 0.180371i 0.809248 0.587467i \(-0.199875\pi\)
−0.913385 + 0.407096i \(0.866541\pi\)
\(140\) −0.442776 + 9.29501i −0.0374214 + 0.785572i
\(141\) −18.0259 + 6.77878i −1.51806 + 0.570877i
\(142\) 8.68837 + 0.829639i 0.729112 + 0.0696217i
\(143\) 1.18826 + 0.348905i 0.0993674 + 0.0291769i
\(144\) 2.58994 1.51400i 0.215829 0.126167i
\(145\) −4.55399 + 5.25558i −0.378188 + 0.436452i
\(146\) 11.3076 + 8.89236i 0.935820 + 0.735937i
\(147\) 29.2566 + 0.617457i 2.41304 + 0.0509270i
\(148\) 1.31737 3.80630i 0.108287 0.312876i
\(149\) 2.36180 + 1.21759i 0.193486 + 0.0997491i 0.552247 0.833680i \(-0.313770\pi\)
−0.358761 + 0.933429i \(0.616801\pi\)
\(150\) −2.30059 + 0.623098i −0.187842 + 0.0508758i
\(151\) −15.3629 + 2.96095i −1.25021 + 0.240959i −0.771054 0.636770i \(-0.780270\pi\)
−0.479158 + 0.877728i \(0.659058\pi\)
\(152\) −4.53420 + 1.33136i −0.367772 + 0.107988i
\(153\) 6.59603 + 1.56254i 0.533257 + 0.126324i
\(154\) 0.733120 0.846065i 0.0590765 0.0681779i
\(155\) −5.53926 7.77880i −0.444924 0.624808i
\(156\) 0.642961 9.34401i 0.0514781 0.748120i
\(157\) 5.05525 7.09910i 0.403453 0.566570i −0.562004 0.827135i \(-0.689969\pi\)
0.965456 + 0.260565i \(0.0839088\pi\)
\(158\) 8.67698 6.82365i 0.690304 0.542861i
\(159\) 10.1884 1.74155i 0.807995 0.138114i
\(160\) 0.951827 1.64861i 0.0752485 0.130334i
\(161\) 6.67259 + 22.4736i 0.525874 + 1.77117i
\(162\) −5.82000 + 6.86496i −0.457262 + 0.539362i
\(163\) −4.64904 2.98775i −0.364141 0.234019i 0.345757 0.938324i \(-0.387622\pi\)
−0.709897 + 0.704305i \(0.751259\pi\)
\(164\) 1.16262 + 0.465444i 0.0907856 + 0.0363451i
\(165\) −0.694959 0.295382i −0.0541025 0.0229955i
\(166\) −0.586047 2.41572i −0.0454861 0.187496i
\(167\) 3.52075 0.336191i 0.272444 0.0260152i 0.0420601 0.999115i \(-0.486608\pi\)
0.230384 + 0.973100i \(0.426002\pi\)
\(168\) −7.44198 4.03760i −0.574161 0.311507i
\(169\) −12.7665 10.0397i −0.982041 0.772285i
\(170\) 4.12712 1.21183i 0.316536 0.0929433i
\(171\) 11.5036 8.28559i 0.879702 0.633615i
\(172\) −4.26597 + 2.74157i −0.325277 + 0.209043i
\(173\) −0.608200 12.7677i −0.0462406 0.970709i −0.896142 0.443767i \(-0.853642\pi\)
0.849902 0.526942i \(-0.176661\pi\)
\(174\) −2.50641 5.80965i −0.190010 0.440429i
\(175\) 4.86836 + 4.64198i 0.368014 + 0.350900i
\(176\) −0.212614 + 0.0851178i −0.0160264 + 0.00641600i
\(177\) −16.4410 + 10.0823i −1.23578 + 0.757830i
\(178\) −7.06216 9.91741i −0.529331 0.743341i
\(179\) −16.7149 4.90794i −1.24933 0.366837i −0.410818 0.911717i \(-0.634757\pi\)
−0.838514 + 0.544880i \(0.816575\pi\)
\(180\) −1.05053 + 5.61351i −0.0783019 + 0.418406i
\(181\) 0.276939 + 1.92615i 0.0205847 + 0.143170i 0.997522 0.0703573i \(-0.0224139\pi\)
−0.976937 + 0.213527i \(0.931505\pi\)
\(182\) −23.4949 + 12.1125i −1.74156 + 0.897836i
\(183\) 3.73707 + 16.9586i 0.276252 + 1.25362i
\(184\) 0.893400 4.71188i 0.0658623 0.347365i
\(185\) 3.83380 + 6.64033i 0.281866 + 0.488207i
\(186\) 8.56445 1.46396i 0.627976 0.107342i
\(187\) −0.480407 0.192326i −0.0351308 0.0140643i
\(188\) −4.61893 10.1141i −0.336870 0.737643i
\(189\) 25.0817 + 4.00921i 1.82443 + 0.291627i
\(190\) 3.73705 8.18301i 0.271114 0.593658i
\(191\) −2.59934 7.51030i −0.188082 0.543426i 0.811055 0.584970i \(-0.198894\pi\)
−0.999137 + 0.0415436i \(0.986772\pi\)
\(192\) 0.974694 + 1.43177i 0.0703425 + 0.103329i
\(193\) −3.31413 3.16002i −0.238557 0.227463i 0.561364 0.827569i \(-0.310277\pi\)
−0.799921 + 0.600106i \(0.795125\pi\)
\(194\) −1.08240 + 3.12739i −0.0777117 + 0.224533i
\(195\) 12.6416 + 12.5735i 0.905281 + 0.900409i
\(196\) 0.803900 + 16.8759i 0.0574214 + 1.20542i
\(197\) 0.127865 + 0.147564i 0.00910998 + 0.0105135i 0.760286 0.649588i \(-0.225059\pi\)
−0.751176 + 0.660102i \(0.770513\pi\)
\(198\) 0.516808 0.452722i 0.0367279 0.0321736i
\(199\) −2.07777 + 14.4512i −0.147290 + 1.02442i 0.773342 + 0.633989i \(0.218584\pi\)
−0.920632 + 0.390432i \(0.872326\pi\)
\(200\) −0.450078 1.30042i −0.0318253 0.0919533i
\(201\) 7.73217 8.55192i 0.545385 0.603206i
\(202\) 2.21338 + 9.12367i 0.155733 + 0.641939i
\(203\) −10.3581 + 14.5459i −0.726995 + 1.02092i
\(204\) −0.638579 + 3.86116i −0.0447094 + 0.270335i
\(205\) −2.11899 + 1.09241i −0.147996 + 0.0762975i
\(206\) −13.6027 −0.947742
\(207\) 2.16731 + 14.2233i 0.150639 + 0.988589i
\(208\) 5.40752 0.374944
\(209\) −0.961950 + 0.495919i −0.0665394 + 0.0343035i
\(210\) 15.0862 5.67328i 1.04105 0.391494i
\(211\) −2.02456 + 2.84310i −0.139377 + 0.195727i −0.878364 0.477992i \(-0.841365\pi\)
0.738988 + 0.673719i \(0.235304\pi\)
\(212\) 1.40692 + 5.79939i 0.0966275 + 0.398304i
\(213\) −4.64180 14.3869i −0.318051 0.985772i
\(214\) −5.26608 15.2153i −0.359982 1.04010i
\(215\) 1.37382 9.55512i 0.0936937 0.651654i
\(216\) −4.18480 3.08017i −0.284740 0.209579i
\(217\) −16.0582 18.5321i −1.09010 1.25804i
\(218\) −0.0136000 0.285499i −0.000921108 0.0193364i
\(219\) 6.38376 24.0843i 0.431375 1.62746i
\(220\) 0.142593 0.411995i 0.00961361 0.0277767i
\(221\) 8.84290 + 8.43169i 0.594838 + 0.567177i
\(222\) −6.95726 + 0.516465i −0.466941 + 0.0346628i
\(223\) 1.61658 + 4.67079i 0.108254 + 0.312779i 0.986097 0.166168i \(-0.0531395\pi\)
−0.877843 + 0.478948i \(0.841018\pi\)
\(224\) 2.03066 4.44652i 0.135679 0.297095i
\(225\) 2.56942 + 3.23124i 0.171295 + 0.215416i
\(226\) −1.06119 2.32368i −0.0705893 0.154569i
\(227\) −10.1604 4.06763i −0.674372 0.269978i 0.00909543 0.999959i \(-0.497105\pi\)
−0.683468 + 0.729981i \(0.739529\pi\)
\(228\) 5.22833 + 6.29755i 0.346255 + 0.417065i
\(229\) 7.25794 + 12.5711i 0.479618 + 0.830723i 0.999727 0.0233769i \(-0.00744177\pi\)
−0.520108 + 0.854100i \(0.674108\pi\)
\(230\) 5.66518 + 7.15929i 0.373551 + 0.472070i
\(231\) −1.84855 0.585426i −0.121626 0.0385182i
\(232\) 3.24695 1.67392i 0.213173 0.109898i
\(233\) −2.14093 14.8905i −0.140257 0.975508i −0.931431 0.363918i \(-0.881439\pi\)
0.791174 0.611591i \(-0.209470\pi\)
\(234\) −15.3015 + 5.38853i −1.00029 + 0.352259i
\(235\) 20.3090 + 5.96327i 1.32482 + 0.389001i
\(236\) −6.45889 9.07024i −0.420438 0.590422i
\(237\) −16.8055 9.11771i −1.09163 0.592259i
\(238\) 10.2540 4.10506i 0.664665 0.266092i
\(239\) 17.4635 + 16.6515i 1.12962 + 1.07709i 0.996293 + 0.0860217i \(0.0274154\pi\)
0.133330 + 0.991072i \(0.457433\pi\)
\(240\) −3.27495 0.382609i −0.211397 0.0246973i
\(241\) −0.237004 4.97533i −0.0152668 0.320489i −0.993563 0.113279i \(-0.963865\pi\)
0.978296 0.207210i \(-0.0664384\pi\)
\(242\) 9.20967 5.91869i 0.592020 0.380468i
\(243\) 14.9109 + 4.54573i 0.956538 + 0.291609i
\(244\) −9.61984 + 2.82464i −0.615847 + 0.180829i
\(245\) −25.2813 19.8815i −1.61516 1.27018i
\(246\) −0.0574703 2.16834i −0.00366418 0.138248i
\(247\) 25.4382 2.42905i 1.61859 0.154557i
\(248\) 1.18266 + 4.87500i 0.0750992 + 0.309563i
\(249\) −3.43977 + 2.58949i −0.217986 + 0.164102i
\(250\) 11.2684 + 4.51120i 0.712678 + 0.285313i
\(251\) −17.1761 11.0384i −1.08415 0.696739i −0.128636 0.991692i \(-0.541060\pi\)
−0.955512 + 0.294953i \(0.904696\pi\)
\(252\) −1.31518 + 14.6057i −0.0828484 + 0.920071i
\(253\) −0.00331493 1.09833i −0.000208408 0.0690516i
\(254\) 8.00854 13.8712i 0.502500 0.870356i
\(255\) −4.75893 5.73215i −0.298016 0.358961i
\(256\) −0.786053 + 0.618159i −0.0491283 + 0.0386349i
\(257\) −0.707692 + 0.993814i −0.0441446 + 0.0619924i −0.836058 0.548641i \(-0.815146\pi\)
0.791914 + 0.610633i \(0.209085\pi\)
\(258\) 7.28704 + 4.90340i 0.453671 + 0.305272i
\(259\) 11.4208 + 16.0382i 0.709653 + 0.996568i
\(260\) −6.74117 + 7.77973i −0.418070 + 0.482478i
\(261\) −7.51975 + 7.97219i −0.465461 + 0.493466i
\(262\) −1.37352 + 0.403302i −0.0848563 + 0.0249161i
\(263\) 18.6603 3.59647i 1.15064 0.221768i 0.421956 0.906616i \(-0.361344\pi\)
0.728686 + 0.684848i \(0.240132\pi\)
\(264\) 0.281246 + 0.279732i 0.0173095 + 0.0172163i
\(265\) −10.0974 5.20558i −0.620279 0.319776i
\(266\) 7.55529 21.8296i 0.463245 1.33846i
\(267\) −10.9268 + 18.0359i −0.668709 + 1.10378i
\(268\) 5.23226 + 4.11469i 0.319611 + 0.251345i
\(269\) −18.5317 + 21.3867i −1.12990 + 1.30397i −0.182754 + 0.983159i \(0.558501\pi\)
−0.947143 + 0.320812i \(0.896044\pi\)
\(270\) 9.64829 2.18080i 0.587176 0.132719i
\(271\) 9.28768 + 2.72711i 0.564186 + 0.165660i 0.551374 0.834258i \(-0.314104\pi\)
0.0128118 + 0.999918i \(0.495922\pi\)
\(272\) −2.24929 0.214782i −0.136383 0.0130230i
\(273\) 35.3834 + 29.0548i 2.14150 + 1.75848i
\(274\) 0.407035 8.54471i 0.0245899 0.516205i
\(275\) −0.157577 0.272931i −0.00950223 0.0164583i
\(276\) −8.10657 + 1.81207i −0.487958 + 0.109074i
\(277\) 7.68047 13.3030i 0.461475 0.799298i −0.537560 0.843226i \(-0.680654\pi\)
0.999035 + 0.0439278i \(0.0139871\pi\)
\(278\) −2.06571 1.32755i −0.123893 0.0796212i
\(279\) −8.20442 12.6161i −0.491186 0.755307i
\(280\) 3.86567 + 8.46463i 0.231018 + 0.505858i
\(281\) −15.6363 + 14.9091i −0.932781 + 0.889405i −0.994073 0.108715i \(-0.965326\pi\)
0.0612918 + 0.998120i \(0.480478\pi\)
\(282\) −12.9159 + 14.2852i −0.769129 + 0.850670i
\(283\) 29.9000 + 5.76276i 1.77737 + 0.342560i 0.969179 0.246357i \(-0.0792335\pi\)
0.808193 + 0.588917i \(0.200446\pi\)
\(284\) 8.10270 3.24383i 0.480807 0.192486i
\(285\) −15.5780 0.328772i −0.922760 0.0194748i
\(286\) 1.21605 0.234374i 0.0719063 0.0138588i
\(287\) −5.14991 + 3.30965i −0.303990 + 0.195362i
\(288\) 1.60828 2.53248i 0.0947688 0.149228i
\(289\) 7.78927 + 8.98930i 0.458192 + 0.528782i
\(290\) −1.63950 + 6.75810i −0.0962746 + 0.396849i
\(291\) 5.71632 0.424345i 0.335097 0.0248755i
\(292\) 14.1253 + 2.72242i 0.826619 + 0.159318i
\(293\) 2.73896 0.261539i 0.160012 0.0152793i −0.0147425 0.999891i \(-0.504693\pi\)
0.174755 + 0.984612i \(0.444087\pi\)
\(294\) 26.2872 12.8573i 1.53310 0.749855i
\(295\) 21.1011 + 2.01491i 1.22855 + 0.117312i
\(296\) −0.573220 3.98683i −0.0333177 0.231730i
\(297\) −1.07458 0.511291i −0.0623536 0.0296681i
\(298\) 2.65719 0.153927
\(299\) −9.56583 + 24.1049i −0.553206 + 1.39402i
\(300\) −1.75932 + 1.60802i −0.101575 + 0.0928392i
\(301\) 1.17947 24.7601i 0.0679836 1.42715i
\(302\) −12.2983 + 9.67147i −0.707686 + 0.556531i
\(303\) 12.9913 9.77996i 0.746330 0.561844i
\(304\) −3.42009 + 3.26105i −0.196156 + 0.187034i
\(305\) 7.92859 17.3612i 0.453990 0.994099i
\(306\) 6.57878 1.63363i 0.376084 0.0933887i
\(307\) −0.866325 + 6.02542i −0.0494438 + 0.343889i 0.950051 + 0.312096i \(0.101031\pi\)
−0.999494 + 0.0317933i \(0.989878\pi\)
\(308\) 0.263933 1.08795i 0.0150390 0.0619916i
\(309\) 9.33300 + 21.6331i 0.530936 + 1.23067i
\(310\) −8.48794 4.37584i −0.482083 0.248531i
\(311\) −27.5408 14.1982i −1.56169 0.805109i −0.561937 0.827180i \(-0.689944\pi\)
−0.999756 + 0.0220716i \(0.992974\pi\)
\(312\) −3.71019 8.59991i −0.210048 0.486874i
\(313\) 3.92837 16.1930i 0.222044 0.915280i −0.746290 0.665621i \(-0.768167\pi\)
0.968334 0.249658i \(-0.0803183\pi\)
\(314\) 1.24029 8.62638i 0.0699934 0.486815i
\(315\) −19.3735 20.1000i −1.09157 1.13251i
\(316\) 4.58563 10.0411i 0.257962 0.564858i
\(317\) 21.8267 20.8117i 1.22591 1.16890i 0.246043 0.969259i \(-0.420869\pi\)
0.979868 0.199645i \(-0.0639790\pi\)
\(318\) 8.25781 6.21656i 0.463075 0.348607i
\(319\) 0.657625 0.517162i 0.0368199 0.0289555i
\(320\) 0.0905795 1.90150i 0.00506355 0.106297i
\(321\) −20.5847 + 18.8144i −1.14893 + 1.05012i
\(322\) 16.2288 + 16.9178i 0.904398 + 0.942791i
\(323\) −10.6777 −0.594121
\(324\) −2.02731 + 8.76869i −0.112628 + 0.487150i
\(325\) 1.05901 + 7.36555i 0.0587431 + 0.408567i
\(326\) −5.50130 0.525310i −0.304689 0.0290942i
\(327\) −0.444715 + 0.217514i −0.0245928 + 0.0120286i
\(328\) 1.24666 0.119042i 0.0688353 0.00657297i
\(329\) 53.3696 + 10.2861i 2.94236 + 0.567093i
\(330\) −0.753056 + 0.0559023i −0.0414544 + 0.00307732i
\(331\) 4.08120 16.8229i 0.224323 0.924672i −0.742627 0.669706i \(-0.766420\pi\)
0.966950 0.254967i \(-0.0820645\pi\)
\(332\) −1.62785 1.87863i −0.0893396 0.103103i
\(333\) 5.59485 + 10.7102i 0.306596 + 0.586915i
\(334\) 2.97532 1.91212i 0.162802 0.104627i
\(335\) −12.4424 + 2.39808i −0.679803 + 0.131021i
\(336\) −8.46483 0.178649i −0.461794 0.00974612i
\(337\) −23.0357 + 9.22212i −1.25484 + 0.502361i −0.901355 0.433081i \(-0.857427\pi\)
−0.353482 + 0.935442i \(0.615002\pi\)
\(338\) −15.9478 3.07369i −0.867446 0.167187i
\(339\) −2.96739 + 3.28199i −0.161167 + 0.178253i
\(340\) 3.11304 2.96827i 0.168828 0.160977i
\(341\) 0.477251 + 1.04503i 0.0258446 + 0.0565917i
\(342\) 6.42812 12.6358i 0.347593 0.683265i
\(343\) −40.6911 26.1506i −2.19711 1.41200i
\(344\) −2.53549 + 4.39159i −0.136704 + 0.236779i
\(345\) 7.49888 13.9218i 0.403726 0.749523i
\(346\) −6.39108 11.0697i −0.343587 0.595109i
\(347\) −1.32905 + 27.9001i −0.0713469 + 1.49776i 0.625324 + 0.780365i \(0.284967\pi\)
−0.696671 + 0.717391i \(0.745336\pi\)
\(348\) −4.88992 4.01532i −0.262127 0.215244i
\(349\) −14.1951 1.35547i −0.759848 0.0725567i −0.292063 0.956399i \(-0.594342\pi\)
−0.467785 + 0.883842i \(0.654948\pi\)
\(350\) 6.45425 + 1.89514i 0.344994 + 0.101299i
\(351\) 19.0683 + 20.6377i 1.01779 + 1.10156i
\(352\) −0.149976 + 0.173081i −0.00799373 + 0.00922525i
\(353\) 20.3369 + 15.9931i 1.08242 + 0.851228i 0.989513 0.144446i \(-0.0461401\pi\)
0.0929120 + 0.995674i \(0.470382\pi\)
\(354\) −9.99340 + 16.4952i −0.531143 + 0.876709i
\(355\) −5.43420 + 15.7011i −0.288417 + 0.833327i
\(356\) −10.8215 5.57888i −0.573539 0.295680i
\(357\) −13.5639 13.4909i −0.717879 0.714016i
\(358\) −17.1058 + 3.29687i −0.904068 + 0.174245i
\(359\) −27.8856 + 8.18794i −1.47174 + 0.432143i −0.916666 0.399655i \(-0.869130\pi\)
−0.555079 + 0.831798i \(0.687312\pi\)
\(360\) 1.63851 + 5.47087i 0.0863571 + 0.288340i
\(361\) −2.18168 + 2.51779i −0.114825 + 0.132515i
\(362\) 1.12877 + 1.58513i 0.0593267 + 0.0833127i
\(363\) −15.7317 10.5858i −0.825703 0.555609i
\(364\) −15.3329 + 21.5320i −0.803660 + 1.12858i
\(365\) −21.5257 + 16.9280i −1.12671 + 0.886051i
\(366\) 11.0925 + 13.3610i 0.579815 + 0.698389i
\(367\) −5.77589 + 10.0041i −0.301499 + 0.522212i −0.976476 0.215627i \(-0.930820\pi\)
0.674977 + 0.737839i \(0.264154\pi\)
\(368\) −1.36502 4.59747i −0.0711568 0.239660i
\(369\) −3.40901 + 1.57913i −0.177466 + 0.0822062i
\(370\) 6.45039 + 4.14541i 0.335340 + 0.215510i
\(371\) −27.0816 10.8418i −1.40601 0.562881i
\(372\) 6.94157 5.22568i 0.359903 0.270939i
\(373\) −5.99459 24.7100i −0.310388 1.27944i −0.886753 0.462244i \(-0.847044\pi\)
0.576365 0.817192i \(-0.304471\pi\)
\(374\) −0.515131 + 0.0491891i −0.0266368 + 0.00254351i
\(375\) −0.557017 21.0161i −0.0287642 1.08526i
\(376\) −8.74000 6.87321i −0.450731 0.354459i
\(377\) −18.9537 + 5.56532i −0.976167 + 0.286628i
\(378\) 24.1307 7.92958i 1.24115 0.407854i
\(379\) 5.02736 3.23089i 0.258238 0.165960i −0.405116 0.914265i \(-0.632769\pi\)
0.663354 + 0.748306i \(0.269132\pi\)
\(380\) −0.428045 8.98577i −0.0219582 0.460960i
\(381\) −27.5550 3.21921i −1.41168 0.164925i
\(382\) −5.75180 5.48433i −0.294288 0.280603i
\(383\) −28.6714 + 11.4783i −1.46504 + 0.586514i −0.960848 0.277077i \(-0.910634\pi\)
−0.504193 + 0.863591i \(0.668210\pi\)
\(384\) 1.52242 + 0.825979i 0.0776906 + 0.0421506i
\(385\) 1.23619 + 1.73598i 0.0630020 + 0.0884739i
\(386\) −4.39373 1.29011i −0.223635 0.0656651i
\(387\) 2.79841 14.9533i 0.142251 0.760120i
\(388\) 0.470977 + 3.27572i 0.0239102 + 0.166299i
\(389\) 9.99307 5.15178i 0.506669 0.261206i −0.185886 0.982571i \(-0.559516\pi\)
0.692555 + 0.721366i \(0.256485\pi\)
\(390\) 16.9978 + 5.38310i 0.860717 + 0.272584i
\(391\) 4.93639 9.64663i 0.249644 0.487851i
\(392\) 8.44753 + 14.6316i 0.426665 + 0.739005i
\(393\) 1.58379 + 1.90768i 0.0798915 + 0.0962297i
\(394\) 0.181268 + 0.0725689i 0.00913217 + 0.00365597i
\(395\) 8.72945 + 19.1148i 0.439227 + 0.961772i
\(396\) 0.251908 0.639211i 0.0126588 0.0321216i
\(397\) 7.46929 16.3555i 0.374873 0.820858i −0.624338 0.781154i \(-0.714631\pi\)
0.999212 0.0397035i \(-0.0126414\pi\)
\(398\) 4.77514 + 13.7969i 0.239356 + 0.691574i
\(399\) −39.9007 + 2.96199i −1.99753 + 0.148285i
\(400\) −0.995930 0.949618i −0.0497965 0.0474809i
\(401\) 1.60947 4.65027i 0.0803733 0.232223i −0.897654 0.440701i \(-0.854730\pi\)
0.978027 + 0.208478i \(0.0668510\pi\)
\(402\) 2.95391 11.1443i 0.147328 0.555829i
\(403\) −1.29072 27.0956i −0.0642955 1.34973i
\(404\) 6.14803 + 7.09521i 0.305876 + 0.353000i
\(405\) −10.0881 13.8480i −0.501281 0.688111i
\(406\) −2.54132 + 17.6753i −0.126123 + 0.877208i
\(407\) −0.301704 0.871716i −0.0149549 0.0432094i
\(408\) 1.20170 + 3.72455i 0.0594928 + 0.184393i
\(409\) 2.33421 + 9.62173i 0.115419 + 0.475764i 0.999957 + 0.00929538i \(0.00295885\pi\)
−0.884538 + 0.466469i \(0.845526\pi\)
\(410\) −1.38286 + 1.94195i −0.0682945 + 0.0959062i
\(411\) −13.8684 + 5.21533i −0.684080 + 0.257253i
\(412\) −12.0905 + 6.23310i −0.595658 + 0.307083i
\(413\) 54.4304 2.67834
\(414\) 8.44388 + 11.6491i 0.414994 + 0.572521i
\(415\) 4.73208 0.232289
\(416\) 4.80640 2.47787i 0.235653 0.121488i
\(417\) −0.693968 + 4.19608i −0.0339838 + 0.205483i
\(418\) −0.627771 + 0.881582i −0.0307053 + 0.0431196i
\(419\) −5.59583 23.0663i −0.273374 1.12686i −0.928497 0.371341i \(-0.878898\pi\)
0.655122 0.755523i \(-0.272617\pi\)
\(420\) 10.8095 11.9555i 0.527450 0.583370i
\(421\) −0.0721045 0.208332i −0.00351416 0.0101535i 0.943230 0.332140i \(-0.107771\pi\)
−0.946744 + 0.321986i \(0.895649\pi\)
\(422\) −0.496719 + 3.45476i −0.0241799 + 0.168175i
\(423\) 31.5804 + 10.7396i 1.53549 + 0.522177i
\(424\) 3.90795 + 4.51002i 0.189787 + 0.219026i
\(425\) −0.147948 3.10581i −0.00717653 0.150654i
\(426\) −10.7182 10.6606i −0.519301 0.516506i
\(427\) 16.0294 46.3140i 0.775718 2.24129i
\(428\) −11.6527 11.1109i −0.563257 0.537064i
\(429\) −1.20709 1.77314i −0.0582787 0.0856082i
\(430\) −3.15731 9.12245i −0.152259 0.439924i
\(431\) −5.43861 + 11.9089i −0.261968 + 0.573631i −0.994215 0.107409i \(-0.965745\pi\)
0.732246 + 0.681040i \(0.238472\pi\)
\(432\) −5.13102 0.820172i −0.246866 0.0394605i
\(433\) −9.53419 20.8770i −0.458184 1.00328i −0.987898 0.155106i \(-0.950428\pi\)
0.529714 0.848176i \(-0.322299\pi\)
\(434\) −22.7650 9.11372i −1.09275 0.437472i
\(435\) 11.8727 2.02945i 0.569253 0.0973046i
\(436\) −0.142911 0.247530i −0.00684421 0.0118545i
\(437\) −8.48656 21.0144i −0.405967 1.00525i
\(438\) −5.36194 24.3322i −0.256203 1.16264i
\(439\) −22.2407 + 11.4659i −1.06149 + 0.547237i −0.898311 0.439359i \(-0.855206\pi\)
−0.163180 + 0.986596i \(0.552175\pi\)
\(440\) −0.0620455 0.431536i −0.00295790 0.0205727i
\(441\) −38.4839 32.9846i −1.83257 1.57069i
\(442\) 11.7235 + 3.44233i 0.557630 + 0.163735i
\(443\) 2.03509 + 2.85789i 0.0966901 + 0.135782i 0.860087 0.510148i \(-0.170409\pi\)
−0.763397 + 0.645930i \(0.776470\pi\)
\(444\) −5.94720 + 3.64705i −0.282242 + 0.173082i
\(445\) 21.5167 8.61397i 1.01999 0.408341i
\(446\) 3.57715 + 3.41081i 0.169383 + 0.161506i
\(447\) −1.82314 4.22588i −0.0862314 0.199877i
\(448\) −0.232593 4.88272i −0.0109890 0.230687i
\(449\) −3.91025 + 2.51297i −0.184536 + 0.118594i −0.629647 0.776881i \(-0.716801\pi\)
0.445111 + 0.895475i \(0.353164\pi\)
\(450\) 3.76443 + 1.69467i 0.177457 + 0.0798874i
\(451\) 0.275190 0.0808030i 0.0129582 0.00380487i
\(452\) −2.00800 1.57911i −0.0944482 0.0742749i
\(453\) 23.8192 + 12.9229i 1.11912 + 0.607173i
\(454\) −10.8949 + 1.04033i −0.511321 + 0.0488252i
\(455\) −11.8634 48.9016i −0.556164 2.29254i
\(456\) 7.53283 + 3.20172i 0.352757 + 0.149934i
\(457\) 37.3572 + 14.9556i 1.74750 + 0.699592i 0.999350 + 0.0360586i \(0.0114803\pi\)
0.748147 + 0.663533i \(0.230944\pi\)
\(458\) 12.2115 + 7.84788i 0.570608 + 0.366707i
\(459\) −7.11187 9.34176i −0.331954 0.436036i
\(460\) 8.31599 + 3.76749i 0.387735 + 0.175660i
\(461\) −16.3445 + 28.3094i −0.761237 + 1.31850i 0.180976 + 0.983487i \(0.442074\pi\)
−0.942213 + 0.335014i \(0.891259\pi\)
\(462\) −1.91132 + 0.326709i −0.0889225 + 0.0151999i
\(463\) −23.9964 + 18.8710i −1.11521 + 0.877009i −0.993304 0.115533i \(-0.963142\pi\)
−0.121904 + 0.992542i \(0.538900\pi\)
\(464\) 2.11897 2.97568i 0.0983708 0.138142i
\(465\) −1.13545 + 16.5012i −0.0526551 + 0.765225i
\(466\) −8.72615 12.2542i −0.404231 0.567663i
\(467\) 8.48521 9.79246i 0.392649 0.453141i −0.524663 0.851310i \(-0.675809\pi\)
0.917312 + 0.398169i \(0.130354\pi\)
\(468\) −11.1313 + 11.8011i −0.514546 + 0.545504i
\(469\) −31.2200 + 9.16703i −1.44161 + 0.423294i
\(470\) 20.7839 4.00577i 0.958691 0.184773i
\(471\) −14.5700 + 3.94619i −0.671351 + 0.181831i
\(472\) −9.89711 5.10232i −0.455551 0.234853i
\(473\) −0.379840 + 1.09748i −0.0174651 + 0.0504620i
\(474\) −19.1153 0.403426i −0.877994 0.0185300i
\(475\) −5.11165 4.01984i −0.234538 0.184443i
\(476\) 7.23303 8.34736i 0.331525 0.382601i
\(477\) −15.5524 8.86762i −0.712095 0.406020i
\(478\) 23.1524 + 6.79815i 1.05896 + 0.310940i
\(479\) 9.56463 + 0.913312i 0.437019 + 0.0417303i 0.311247 0.950329i \(-0.399253\pi\)
0.125772 + 0.992059i \(0.459859\pi\)
\(480\) −3.08621 + 1.16059i −0.140866 + 0.0529736i
\(481\) −1.03636 + 21.7559i −0.0472540 + 0.991984i
\(482\) −2.49048 4.31365i −0.113438 0.196481i
\(483\) 15.7705 37.4173i 0.717583 1.70254i
\(484\) 5.47378 9.48086i 0.248808 0.430948i
\(485\) −5.29986 3.40601i −0.240654 0.154659i
\(486\) 15.3364 2.79218i 0.695671 0.126656i
\(487\) 15.4725 + 33.8801i 0.701127 + 1.53525i 0.838600 + 0.544748i \(0.183375\pi\)
−0.137473 + 0.990506i \(0.543898\pi\)
\(488\) −7.25613 + 6.91870i −0.328469 + 0.313195i
\(489\) 2.93909 + 9.10946i 0.132910 + 0.411944i
\(490\) −31.5812 6.08677i −1.42669 0.274972i
\(491\) 13.9019 5.56546i 0.627382 0.251166i −0.0361116 0.999348i \(-0.511497\pi\)
0.663494 + 0.748182i \(0.269073\pi\)
\(492\) −1.04467 1.90096i −0.0470974 0.0857019i
\(493\) 8.10498 1.56211i 0.365030 0.0703537i
\(494\) 21.4973 13.8155i 0.967210 0.621588i
\(495\) 0.605588 + 1.15927i 0.0272192 + 0.0521055i
\(496\) 3.28505 + 3.79115i 0.147503 + 0.170228i
\(497\) −10.0585 + 41.4616i −0.451184 + 1.85980i
\(498\) −1.87081 + 3.87782i −0.0838332 + 0.173769i
\(499\) 11.3738 + 2.19212i 0.509161 + 0.0981327i 0.437360 0.899286i \(-0.355913\pi\)
0.0718005 + 0.997419i \(0.477126\pi\)
\(500\) 12.0829 1.15378i 0.540365 0.0515986i
\(501\) −5.08237 3.41989i −0.227064 0.152789i
\(502\) −20.3249 1.94079i −0.907142 0.0866216i
\(503\) 1.51919 + 10.5662i 0.0677374 + 0.471124i 0.995252 + 0.0973362i \(0.0310322\pi\)
−0.927514 + 0.373788i \(0.878059\pi\)
\(504\) 5.52373 + 13.5847i 0.246047 + 0.605110i
\(505\) −17.8721 −0.795298
\(506\) −0.506231 0.974718i −0.0225047 0.0433315i
\(507\) 6.05377 + 27.4717i 0.268857 + 1.22006i
\(508\) 0.762123 15.9989i 0.0338137 0.709838i
\(509\) 8.05995 6.33841i 0.357251 0.280945i −0.423361 0.905961i \(-0.639150\pi\)
0.780612 + 0.625016i \(0.214907\pi\)
\(510\) −6.85653 2.91427i −0.303612 0.129046i
\(511\) −50.8921 + 48.5255i −2.25133 + 2.14664i
\(512\) −0.415415 + 0.909632i −0.0183589 + 0.0402004i
\(513\) −24.5059 1.55343i −1.08196 0.0685855i
\(514\) −0.173630 + 1.20762i −0.00765847 + 0.0532659i
\(515\) 6.10492 25.1648i 0.269015 1.10890i
\(516\) 8.72385 + 1.01920i 0.384046 + 0.0448676i
\(517\) −2.26336 1.16684i −0.0995423 0.0513176i
\(518\) 17.5003 + 9.02205i 0.768921 + 0.396406i
\(519\) −13.2197 + 17.7592i −0.580283 + 0.779542i
\(520\) −2.42692 + 10.0039i −0.106427 + 0.438699i
\(521\) 2.93437 20.4090i 0.128557 0.894133i −0.818829 0.574038i \(-0.805376\pi\)
0.947386 0.320095i \(-0.103715\pi\)
\(522\) −3.03075 + 10.5317i −0.132652 + 0.460960i
\(523\) −14.4524 + 31.6463i −0.631959 + 1.38380i 0.274534 + 0.961577i \(0.411476\pi\)
−0.906493 + 0.422220i \(0.861251\pi\)
\(524\) −1.03603 + 0.987852i −0.0452591 + 0.0431545i
\(525\) −1.41441 11.5649i −0.0617299 0.504732i
\(526\) 14.9379 11.7473i 0.651324 0.512207i
\(527\) −0.539327 + 11.3219i −0.0234934 + 0.493188i
\(528\) 0.378162 + 0.119762i 0.0164574 + 0.00521195i
\(529\) 22.9086 + 2.04804i 0.996028 + 0.0890454i
\(530\) −11.3603 −0.493458
\(531\) 33.0899 + 4.57550i 1.43598 + 0.198560i
\(532\) −3.28748 22.8649i −0.142530 0.991321i
\(533\) −6.74134 0.643720i −0.292000 0.0278826i
\(534\) −1.44761 + 21.0379i −0.0626444 + 0.910397i
\(535\) 30.5117 2.91351i 1.31914 0.125962i
\(536\) 6.53608 + 1.25973i 0.282316 + 0.0544119i
\(537\) 16.9797 + 24.9423i 0.732730 + 1.07634i
\(538\) −6.67166 + 27.5010i −0.287636 + 1.18565i
\(539\) 2.53385 + 2.92422i 0.109141 + 0.125955i
\(540\) 7.57644 6.35947i 0.326038 0.273668i
\(541\) −18.9830 + 12.1997i −0.816145 + 0.524504i −0.880847 0.473400i \(-0.843026\pi\)
0.0647027 + 0.997905i \(0.479390\pi\)
\(542\) 9.50485 1.83191i 0.408268 0.0786873i
\(543\) 1.74647 2.88273i 0.0749480 0.123710i
\(544\) −2.09767 + 0.839781i −0.0899369 + 0.0360053i
\(545\) 0.534275 + 0.102973i 0.0228858 + 0.00441088i
\(546\) 44.7637 + 9.61133i 1.91571 + 0.411327i
\(547\) 14.6114 13.9320i 0.624740 0.595689i −0.310123 0.950696i \(-0.600370\pi\)
0.934863 + 0.355008i \(0.115522\pi\)
\(548\) −3.55363 7.78136i −0.151803 0.332403i
\(549\) 13.6380 26.8083i 0.582056 1.14415i
\(550\) −0.265124 0.170385i −0.0113049 0.00726523i
\(551\) 8.63145 14.9501i 0.367712 0.636896i
\(552\) −6.37506 + 5.32527i −0.271341 + 0.226659i
\(553\) 26.9799 + 46.7306i 1.14730 + 1.98719i
\(554\) 0.730903 15.3435i 0.0310531 0.651885i
\(555\) 2.16699 13.1027i 0.0919835 0.556178i
\(556\) −2.44440 0.233411i −0.103665 0.00989885i
\(557\) −9.14477 2.68515i −0.387477 0.113773i 0.0821913 0.996617i \(-0.473808\pi\)
−0.469668 + 0.882843i \(0.655626\pi\)
\(558\) −13.0734 7.45417i −0.553442 0.315560i
\(559\) 17.9572 20.7237i 0.759509 0.876520i
\(560\) 7.31466 + 5.75231i 0.309101 + 0.243080i
\(561\) 0.431668 + 0.785495i 0.0182250 + 0.0331636i
\(562\) −7.06630 + 20.4167i −0.298074 + 0.861228i
\(563\) −25.7660 13.2833i −1.08591 0.559825i −0.180159 0.983637i \(-0.557661\pi\)
−0.905750 + 0.423812i \(0.860692\pi\)
\(564\) −4.93423 + 18.6156i −0.207769 + 0.783857i
\(565\) 4.77506 0.920318i 0.200888 0.0387181i
\(566\) 29.2169 8.57884i 1.22808 0.360596i
\(567\) −29.1673 32.9358i −1.22491 1.38317i
\(568\) 5.71555 6.59610i 0.239819 0.276766i
\(569\) 7.49049 + 10.5189i 0.314018 + 0.440976i 0.941177 0.337915i \(-0.109722\pi\)
−0.627159 + 0.778891i \(0.715782\pi\)
\(570\) −13.9969 + 6.84602i −0.586266 + 0.286748i
\(571\) −13.6554 + 19.1764i −0.571462 + 0.802506i −0.994624 0.103548i \(-0.966981\pi\)
0.423162 + 0.906054i \(0.360920\pi\)
\(572\) 0.973469 0.765544i 0.0407028 0.0320090i
\(573\) −4.77566 + 12.9103i −0.199506 + 0.539337i
\(574\) −3.06086 + 5.30156i −0.127758 + 0.221283i
\(575\) 5.99485 2.75965i 0.250003 0.115086i
\(576\) 0.269048 2.98791i 0.0112103 0.124496i
\(577\) −8.91791 5.73119i −0.371257 0.238593i 0.341686 0.939814i \(-0.389002\pi\)
−0.712943 + 0.701222i \(0.752638\pi\)
\(578\) 11.0425 + 4.42076i 0.459308 + 0.183879i
\(579\) 0.962858 + 7.87277i 0.0400150 + 0.327181i
\(580\) 1.63950 + 6.75810i 0.0680764 + 0.280615i
\(581\) 12.0962 1.15504i 0.501833 0.0479193i
\(582\) 4.88642 2.99654i 0.202549 0.124211i
\(583\) 1.07430 + 0.844836i 0.0444928 + 0.0349895i
\(584\) 13.8025 4.05279i 0.571153 0.167706i
\(585\) −3.10139 30.7260i −0.128227 1.27037i
\(586\) 2.31464 1.48753i 0.0956171 0.0614494i
\(587\) 0.219921 + 4.61671i 0.00907710 + 0.190552i 0.998852 + 0.0479110i \(0.0152564\pi\)
−0.989775 + 0.142641i \(0.954441\pi\)
\(588\) 17.4735 23.4736i 0.720593 0.968033i
\(589\) 17.1566 + 16.3588i 0.706925 + 0.674051i
\(590\) 19.6787 7.87814i 0.810157 0.324338i
\(591\) −0.00896039 0.338073i −0.000368581 0.0139064i
\(592\) −2.33637 3.28097i −0.0960242 0.134847i
\(593\) 27.7643 + 8.15233i 1.14014 + 0.334776i 0.796686 0.604393i \(-0.206584\pi\)
0.343456 + 0.939169i \(0.388402\pi\)
\(594\) −1.18941 + 0.0379486i −0.0488022 + 0.00155705i
\(595\) 2.99233 + 20.8121i 0.122674 + 0.853214i
\(596\) 2.36180 1.21759i 0.0967431 0.0498745i
\(597\) 18.6657 17.0604i 0.763936 0.698237i
\(598\) 2.54305 + 25.8086i 0.103993 + 1.05539i
\(599\) −12.4076 21.4906i −0.506961 0.878081i −0.999968 0.00805605i \(-0.997436\pi\)
0.493007 0.870025i \(-0.335898\pi\)
\(600\) −0.826910 + 2.23544i −0.0337585 + 0.0912613i
\(601\) 35.2331 + 14.1052i 1.43719 + 0.575364i 0.953908 0.300101i \(-0.0970202\pi\)
0.483282 + 0.875465i \(0.339444\pi\)
\(602\) −10.2974 22.5482i −0.419691 0.918994i
\(603\) −19.7502 + 2.94852i −0.804291 + 0.120073i
\(604\) −6.49942 + 14.2317i −0.264458 + 0.579081i
\(605\) 6.81621 + 19.6942i 0.277118 + 0.800681i
\(606\) 7.06568 14.6457i 0.287023 0.594942i
\(607\) −12.6881 12.0981i −0.514994 0.491046i 0.387428 0.921900i \(-0.373364\pi\)
−0.902421 + 0.430854i \(0.858212\pi\)
\(608\) −1.54560 + 4.46572i −0.0626824 + 0.181109i
\(609\) 29.8537 8.08566i 1.20973 0.327647i
\(610\) −0.908147 19.0643i −0.0367698 0.771893i
\(611\) 39.3738 + 45.4397i 1.59289 + 1.83830i
\(612\) 5.09888 4.46660i 0.206110 0.180552i
\(613\) 3.37697 23.4873i 0.136395 0.948645i −0.800575 0.599233i \(-0.795472\pi\)
0.936969 0.349412i \(-0.113619\pi\)
\(614\) 1.99099 + 5.75258i 0.0803497 + 0.232155i
\(615\) 4.03720 + 0.866838i 0.162796 + 0.0349543i
\(616\) −0.263933 1.08795i −0.0106342 0.0438347i
\(617\) 0.841796 1.18214i 0.0338894 0.0475911i −0.797284 0.603605i \(-0.793730\pi\)
0.831173 + 0.556014i \(0.187670\pi\)
\(618\) 18.2084 + 14.9517i 0.732448 + 0.601444i
\(619\) −10.7190 + 5.52601i −0.430831 + 0.222109i −0.659981 0.751282i \(-0.729436\pi\)
0.229150 + 0.973391i \(0.426405\pi\)
\(620\) −9.54951 −0.383517
\(621\) 12.7327 21.4214i 0.510947 0.859612i
\(622\) −30.9852 −1.24239
\(623\) 52.8984 27.2710i 2.11933 1.09259i
\(624\) −7.23845 5.94380i −0.289770 0.237942i
\(625\) −9.41192 + 13.2172i −0.376477 + 0.528688i
\(626\) −3.92837 16.1930i −0.157009 0.647201i
\(627\) 1.83276 + 0.393516i 0.0731932 + 0.0157155i
\(628\) −2.85043 8.23576i −0.113744 0.328643i
\(629\) 1.29520 9.00835i 0.0516432 0.359186i
\(630\) −26.4302 8.98815i −1.05300 0.358096i
\(631\) −16.7408 19.3200i −0.666442 0.769116i 0.317373 0.948301i \(-0.397199\pi\)
−0.983815 + 0.179185i \(0.942654\pi\)
\(632\) −0.525241 11.0262i −0.0208930 0.438597i
\(633\) 5.83511 1.58040i 0.231925 0.0628153i
\(634\) 9.86388 28.4998i 0.391745 1.13187i
\(635\) 22.0674 + 21.0412i 0.875716 + 0.834994i
\(636\) 4.49125 9.30945i 0.178089 0.369144i
\(637\) −29.8811 86.3357i −1.18393 3.42075i
\(638\) 0.347543 0.761013i 0.0137594 0.0301288i
\(639\) −9.60017 + 24.3602i −0.379777 + 0.963676i
\(640\) −0.790807 1.73162i −0.0312594 0.0684485i
\(641\) 13.6377 + 5.45970i 0.538656 + 0.215645i 0.625006 0.780620i \(-0.285096\pi\)
−0.0863508 + 0.996265i \(0.527521\pi\)
\(642\) −9.67516 + 26.1554i −0.381848 + 1.03227i
\(643\) 21.8770 + 37.8921i 0.862746 + 1.49432i 0.869268 + 0.494340i \(0.164590\pi\)
−0.00652287 + 0.999979i \(0.502076\pi\)
\(644\) 22.1769 + 7.60064i 0.873894 + 0.299507i
\(645\) −12.3417 + 11.2803i −0.485954 + 0.444162i
\(646\) −9.49069 + 4.89279i −0.373406 + 0.192504i
\(647\) 4.90609 + 34.1226i 0.192878 + 1.34150i 0.824342 + 0.566092i \(0.191545\pi\)
−0.631464 + 0.775405i \(0.717546\pi\)
\(648\) 2.21610 + 8.72289i 0.0870567 + 0.342668i
\(649\) −2.44681 0.718449i −0.0960458 0.0282016i
\(650\) 4.31637 + 6.06150i 0.169302 + 0.237751i
\(651\) 1.12531 + 42.4576i 0.0441043 + 1.66404i
\(652\) −5.13046 + 2.05393i −0.200924 + 0.0804379i
\(653\) 14.1963 + 13.5362i 0.555546 + 0.529712i 0.915001 0.403450i \(-0.132189\pi\)
−0.359456 + 0.933162i \(0.617038\pi\)
\(654\) −0.295608 + 0.397115i −0.0115592 + 0.0155284i
\(655\) −0.129665 2.72200i −0.00506643 0.106358i
\(656\) 1.05353 0.677061i 0.0411333 0.0264348i
\(657\) −35.0180 + 25.2221i −1.36618 + 0.984008i
\(658\) 52.1501 15.3127i 2.03302 0.596950i
\(659\) 23.4488 + 18.4404i 0.913437 + 0.718335i 0.959828 0.280588i \(-0.0905295\pi\)
−0.0463908 + 0.998923i \(0.514772\pi\)
\(660\) −0.643727 + 0.394758i −0.0250570 + 0.0153659i
\(661\) 6.83353 0.652523i 0.265794 0.0253802i 0.0386917 0.999251i \(-0.487681\pi\)
0.227102 + 0.973871i \(0.427075\pi\)
\(662\) −4.08120 16.8229i −0.158620 0.653842i
\(663\) −2.56913 21.0064i −0.0997769 0.815822i
\(664\) −2.30773 0.923874i −0.0895572 0.0358533i
\(665\) 36.9937 + 23.7744i 1.43456 + 0.921933i
\(666\) 9.88060 + 6.95589i 0.382865 + 0.269535i
\(667\) 9.51613 + 14.7096i 0.368466 + 0.569557i
\(668\) 1.76838 3.06293i 0.0684208 0.118508i
\(669\) 2.97007 8.02917i 0.114830 0.310426i
\(670\) −9.96041 + 7.83296i −0.384804 + 0.302613i
\(671\) −1.33189 + 1.87038i −0.0514170 + 0.0722051i
\(672\) −7.60570 + 3.72002i −0.293396 + 0.143503i
\(673\) −9.95305 13.9771i −0.383662 0.538778i 0.576911 0.816807i \(-0.304258\pi\)
−0.960573 + 0.278029i \(0.910319\pi\)
\(674\) −16.2492 + 18.7525i −0.625894 + 0.722321i
\(675\) 0.112296 7.14954i 0.00432226 0.275186i
\(676\) −15.5834 + 4.57570i −0.599362 + 0.175989i
\(677\) −19.0433 + 3.67029i −0.731893 + 0.141061i −0.541564 0.840659i \(-0.682168\pi\)
−0.190329 + 0.981720i \(0.560956\pi\)
\(678\) −1.13363 + 4.27689i −0.0435368 + 0.164253i
\(679\) −14.3789 7.41283i −0.551811 0.284478i
\(680\) 1.40684 4.06478i 0.0539497 0.155877i
\(681\) 9.12964 + 16.6130i 0.349848 + 0.636610i
\(682\) 0.903060 + 0.710174i 0.0345799 + 0.0271940i
\(683\) 3.28984 3.79668i 0.125882 0.145276i −0.689310 0.724467i \(-0.742086\pi\)
0.815192 + 0.579191i \(0.196631\pi\)
\(684\) −0.0765031 14.1767i −0.00292517 0.542058i
\(685\) 15.6250 + 4.58791i 0.597000 + 0.175295i
\(686\) −48.1506 4.59783i −1.83840 0.175546i
\(687\) 4.10243 24.8053i 0.156517 0.946381i
\(688\) −0.241287 + 5.06523i −0.00919897 + 0.193110i
\(689\) −16.1350 27.9466i −0.614694 1.06468i
\(690\) 0.285940 15.8104i 0.0108855 0.601890i
\(691\) 4.58560 7.94249i 0.174445 0.302147i −0.765524 0.643407i \(-0.777520\pi\)
0.939969 + 0.341260i \(0.110854\pi\)
\(692\) −10.7530 6.91056i −0.408769 0.262700i
\(693\) 1.83097 + 2.81552i 0.0695528 + 0.106953i
\(694\) 11.6033 + 25.4076i 0.440454 + 0.964459i
\(695\) 3.38306 3.22574i 0.128327 0.122359i
\(696\) −6.18626 1.32827i −0.234490 0.0503479i
\(697\) 2.77854 + 0.535519i 0.105245 + 0.0202842i
\(698\) −13.2382 + 5.29979i −0.501075 + 0.200600i
\(699\) −13.5014 + 22.2855i −0.510669 + 0.842915i
\(700\) 6.60517 1.27304i 0.249652 0.0481165i
\(701\) −32.9775 + 21.1933i −1.24554 + 0.800461i −0.986237 0.165335i \(-0.947130\pi\)
−0.259304 + 0.965796i \(0.583493\pi\)
\(702\) 26.4053 + 9.60593i 0.996605 + 0.362553i
\(703\) −12.4646 14.3849i −0.470112 0.542538i
\(704\) −0.0539933 + 0.222563i −0.00203495 + 0.00838818i
\(705\) −20.6308 30.3055i −0.777001 1.14137i
\(706\) 25.4046 + 4.89634i 0.956116 + 0.184276i
\(707\) −45.6847 + 4.36236i −1.71815 + 0.164063i
\(708\) −1.32395 + 19.2407i −0.0497573 + 0.723112i
\(709\) −4.76953 0.455435i −0.179123 0.0171042i 0.00510888 0.999987i \(-0.498374\pi\)
−0.184232 + 0.982883i \(0.558980\pi\)
\(710\) 2.36455 + 16.4458i 0.0887398 + 0.617199i
\(711\) 12.4737 + 30.6770i 0.467800 + 1.15048i
\(712\) −12.1749 −0.456275
\(713\) −22.7108 + 7.93713i −0.850527 + 0.297248i
\(714\) −18.2380 5.77587i −0.682540 0.216156i
\(715\) −0.112176 + 2.35487i −0.00419515 + 0.0880670i
\(716\) −13.6935 + 10.7687i −0.511750 + 0.402445i
\(717\) −5.07370 41.4849i −0.189481 1.54928i
\(718\) −21.0338 + 20.0556i −0.784973 + 0.748470i
\(719\) 10.6347 23.2867i 0.396607 0.868449i −0.600996 0.799252i \(-0.705229\pi\)
0.997603 0.0691965i \(-0.0220435\pi\)
\(720\) 3.96326 + 4.11189i 0.147702 + 0.153241i
\(721\) 9.46299 65.8165i 0.352420 2.45114i
\(722\) −0.785435 + 3.23761i −0.0292309 + 0.120491i
\(723\) −5.15149 + 6.92043i −0.191586 + 0.257373i
\(724\) 1.72964 + 0.891691i 0.0642815 + 0.0331394i
\(725\) 4.46813 + 2.30348i 0.165942 + 0.0855492i
\(726\) −18.8336 2.20031i −0.698981 0.0816611i
\(727\) −7.53140 + 31.0448i −0.279324 + 1.15139i 0.643277 + 0.765634i \(0.277574\pi\)
−0.922601 + 0.385756i \(0.873941\pi\)
\(728\) −3.76186 + 26.1643i −0.139424 + 0.969714i
\(729\) −14.9631 22.4746i −0.554188 0.832391i
\(730\) −11.3759 + 24.9098i −0.421042 + 0.921954i
\(731\) −8.29254 + 7.90692i −0.306711 + 0.292448i
\(732\) 15.9818 + 6.79282i 0.590703 + 0.251070i
\(733\) −21.6727 + 17.0436i −0.800500 + 0.629520i −0.932271 0.361760i \(-0.882176\pi\)
0.131771 + 0.991280i \(0.457934\pi\)
\(734\) −0.549656 + 11.5387i −0.0202882 + 0.425901i
\(735\) 11.9882 + 54.4016i 0.442190 + 2.00663i
\(736\) −3.31996 3.46090i −0.122375 0.127571i
\(737\) 1.52444 0.0561533
\(738\) −2.30645 + 2.96568i −0.0849015 + 0.109168i
\(739\) 4.00237 + 27.8371i 0.147230 + 1.02400i 0.920728 + 0.390206i \(0.127596\pi\)
−0.773498 + 0.633798i \(0.781495\pi\)
\(740\) 7.63287 + 0.728851i 0.280590 + 0.0267931i
\(741\) −36.7213 24.7095i −1.34899 0.907725i
\(742\) −29.0391 + 2.77290i −1.06606 + 0.101796i
\(743\) −17.9480 3.45920i −0.658449 0.126906i −0.150928 0.988545i \(-0.548226\pi\)
−0.507521 + 0.861639i \(0.669438\pi\)
\(744\) 3.77537 7.82557i 0.138412 0.286899i
\(745\) −1.19255 + 4.91578i −0.0436918 + 0.180100i
\(746\) −16.6510 19.2163i −0.609636 0.703557i
\(747\) 7.45073 + 0.314634i 0.272608 + 0.0115118i
\(748\) −0.435327 + 0.279768i −0.0159171 + 0.0102293i
\(749\) 77.2829 14.8951i 2.82386 0.544254i
\(750\) −10.1252 18.4246i −0.369721 0.672771i
\(751\) −11.7344 + 4.69773i −0.428193 + 0.171422i −0.575741 0.817632i \(-0.695286\pi\)
0.147548 + 0.989055i \(0.452862\pi\)
\(752\) −10.9179 2.10426i −0.398135 0.0767343i
\(753\) 10.8586 + 33.6554i 0.395711 + 1.22647i
\(754\) −14.2966 + 13.6318i −0.520651 + 0.496439i
\(755\) −12.3726 27.0923i −0.450287 0.985990i
\(756\) 17.8146 18.1054i 0.647912 0.658487i
\(757\) 18.0412 + 11.5943i 0.655717 + 0.421404i 0.825751 0.564034i \(-0.190751\pi\)
−0.170034 + 0.985438i \(0.554388\pi\)
\(758\) 2.98802 5.17540i 0.108530 0.187979i
\(759\) −1.20282 + 1.47386i −0.0436596 + 0.0534977i
\(760\) −4.49798 7.79073i −0.163159 0.282599i
\(761\) −0.960656 + 20.1666i −0.0348237 + 0.731040i 0.912175 + 0.409802i \(0.134402\pi\)
−0.946998 + 0.321239i \(0.895901\pi\)
\(762\) −25.9670 + 9.76507i −0.940684 + 0.353751i
\(763\) 1.39085 + 0.132810i 0.0503521 + 0.00480804i
\(764\) −7.62547 2.23904i −0.275880 0.0810057i
\(765\) 0.0696347 + 12.9039i 0.00251765 + 0.466541i
\(766\) −20.2245 + 23.3403i −0.730741 + 0.843320i
\(767\) 47.3301 + 37.2208i 1.70899 + 1.34397i
\(768\) 1.73167 + 0.0365466i 0.0624861 + 0.00131876i
\(769\) 9.50089 27.4510i 0.342611 0.989909i −0.633708 0.773572i \(-0.718468\pi\)
0.976319 0.216337i \(-0.0694109\pi\)
\(770\) 1.89424 + 0.976549i 0.0682637 + 0.0351924i
\(771\) 2.03968 0.552434i 0.0734573 0.0198954i
\(772\) −4.49646 + 0.866622i −0.161831 + 0.0311904i
\(773\) 11.8780 3.48770i 0.427222 0.125444i −0.0610510 0.998135i \(-0.519445\pi\)
0.488273 + 0.872691i \(0.337627\pi\)
\(774\) −4.36468 14.5733i −0.156885 0.523828i
\(775\) −4.52055 + 5.21700i −0.162383 + 0.187400i
\(776\) 1.91964 + 2.69576i 0.0689111 + 0.0967721i
\(777\) 2.34105 34.0220i 0.0839848 1.22053i
\(778\) 6.52151 9.15818i 0.233807 0.328336i
\(779\) 4.65189 3.65829i 0.166671 0.131072i
\(780\) 17.5749 3.00415i 0.629283 0.107566i
\(781\) 0.999427 1.73106i 0.0357623 0.0619422i
\(782\) −0.0327054 10.8363i −0.00116954 0.387504i
\(783\) 18.8287 2.40598i 0.672881 0.0859828i
\(784\) 14.2130 + 9.13416i 0.507608 + 0.326220i
\(785\) 15.4021 + 6.16607i 0.549725 + 0.220076i
\(786\) 2.28188 + 0.969879i 0.0813918 + 0.0345944i
\(787\) −10.1252 41.7367i −0.360925 1.48775i −0.805814 0.592168i \(-0.798272\pi\)
0.444889 0.895586i \(-0.353243\pi\)
\(788\) 0.194371 0.0185601i 0.00692417 0.000661178i
\(789\) −28.9316 15.6966i −1.02999 0.558815i
\(790\) 16.5180 + 12.9899i 0.587683 + 0.462159i
\(791\) 11.9814 3.51805i 0.426009 0.125088i
\(792\) −0.0689988 0.683584i −0.00245177 0.0242901i
\(793\) 45.6091 29.3112i 1.61963 1.04087i
\(794\) −0.855538 17.9599i −0.0303619 0.637375i
\(795\) 7.79446 + 18.0669i 0.276441 + 0.640767i
\(796\) 10.5664 + 10.0750i 0.374516 + 0.357101i
\(797\) −32.2033 + 12.8922i −1.14070 + 0.456667i −0.863601 0.504175i \(-0.831797\pi\)
−0.277097 + 0.960842i \(0.589372\pi\)
\(798\) −34.1079 + 20.9163i −1.20741 + 0.740428i
\(799\) −14.5729 20.4648i −0.515554 0.723994i
\(800\) −1.32036 0.387692i −0.0466817 0.0137070i
\(801\) 34.4510 12.1322i 1.21727 0.428670i
\(802\) −0.700319 4.87083i −0.0247291 0.171995i
\(803\) 2.92826 1.50962i 0.103336 0.0532735i
\(804\) −2.48109 11.2590i −0.0875013 0.397076i
\(805\) −38.5813 + 22.4305i −1.35981 + 0.790571i
\(806\) −13.5632 23.4921i −0.477742 0.827474i
\(807\) 48.3140 8.25850i 1.70073 0.290713i
\(808\) 8.71580 + 3.48928i 0.306621 + 0.122752i
\(809\) −17.7988 38.9738i −0.625771 1.37025i −0.911246 0.411861i \(-0.864879\pi\)
0.285475 0.958386i \(-0.407849\pi\)
\(810\) −15.3122 7.68594i −0.538015 0.270056i
\(811\) 0.301638 0.660495i 0.0105919 0.0231931i −0.904262 0.426978i \(-0.859578\pi\)
0.914854 + 0.403785i \(0.132306\pi\)
\(812\) 5.84046 + 16.8749i 0.204960 + 0.592192i
\(813\) −9.43482 13.8592i −0.330894 0.486065i
\(814\) −0.667608 0.636563i −0.0233997 0.0223115i
\(815\) 3.44082 9.94160i 0.120527 0.348239i
\(816\) 2.77480 + 2.75987i 0.0971374 + 0.0966146i
\(817\) 1.14023 + 23.9364i 0.0398916 + 0.837427i
\(818\) 6.48366 + 7.48254i 0.226696 + 0.261621i
\(819\) −15.4276 77.7849i −0.539085 2.71803i
\(820\) −0.339279 + 2.35974i −0.0118481 + 0.0824056i
\(821\) −7.10818 20.5377i −0.248077 0.716772i −0.998445 0.0557512i \(-0.982245\pi\)
0.750367 0.661021i \(-0.229877\pi\)
\(822\) −9.93696 + 10.9905i −0.346591 + 0.383336i
\(823\) −7.78054 32.0718i −0.271213 1.11795i −0.930567 0.366121i \(-0.880686\pi\)
0.659355 0.751832i \(-0.270830\pi\)
\(824\) −7.89032 + 11.0804i −0.274872 + 0.386004i
\(825\) −0.0890674 + 0.538546i −0.00310093 + 0.0187498i
\(826\) 48.3796 24.9414i 1.68334 0.867823i
\(827\) −2.81837 −0.0980045 −0.0490022 0.998799i \(-0.515604\pi\)
−0.0490022 + 0.998799i \(0.515604\pi\)
\(828\) 12.8431 + 6.48489i 0.446330 + 0.225366i
\(829\) 9.01001 0.312931 0.156465 0.987683i \(-0.449990\pi\)
0.156465 + 0.987683i \(0.449990\pi\)
\(830\) 4.20604 2.16837i 0.145994 0.0752651i
\(831\) −24.9032 + 9.36505i −0.863884 + 0.324870i
\(832\) 3.13667 4.40484i 0.108745 0.152710i
\(833\) 9.00006 + 37.0987i 0.311833 + 1.28540i
\(834\) 1.30593 + 4.04762i 0.0452207 + 0.140157i
\(835\) 2.20208 + 6.36248i 0.0762060 + 0.220183i
\(836\) −0.154021 + 1.07124i −0.00532694 + 0.0370497i
\(837\) −2.88493 + 25.9059i −0.0997179 + 0.895438i
\(838\) −15.5434 17.9380i −0.536937 0.619658i
\(839\) −2.64014 55.4235i −0.0911479 1.91343i −0.332684 0.943038i \(-0.607954\pi\)
0.241536 0.970392i \(-0.422349\pi\)
\(840\) 4.12954 15.5797i 0.142483 0.537551i
\(841\) 5.12034 14.7943i 0.176564 0.510147i
\(842\) −0.159552 0.152133i −0.00549854 0.00524285i
\(843\) 37.3182 2.77028i 1.28531 0.0954135i
\(844\) 1.14156 + 3.29832i 0.0392941 + 0.113533i
\(845\) 12.8437 28.1239i 0.441838 0.967490i
\(846\) 32.9909 4.92523i 1.13425 0.169333i
\(847\) 22.2307 + 48.6785i 0.763856 + 1.67261i
\(848\) 5.54014 + 2.21794i 0.190249 + 0.0761643i
\(849\) −33.6896 40.5792i −1.15622 1.39268i
\(850\) −1.55467 2.69276i −0.0533246 0.0923609i
\(851\) 18.7584 4.61074i 0.643031 0.158054i
\(852\) −14.4117 4.56410i −0.493737 0.156363i
\(853\) 11.3346 5.84337i 0.388088 0.200073i −0.253130 0.967432i \(-0.581460\pi\)
0.641218 + 0.767359i \(0.278430\pi\)
\(854\) −6.97477 48.5106i −0.238672 1.66000i
\(855\) 20.4911 + 17.5630i 0.700782 + 0.600641i
\(856\) −15.4487 4.53614i −0.528025 0.155042i
\(857\) 25.2931 + 35.5192i 0.863996 + 1.21331i 0.975599 + 0.219560i \(0.0704620\pi\)
−0.111603 + 0.993753i \(0.535599\pi\)
\(858\) −1.88540 1.02291i −0.0643666 0.0349217i
\(859\) −19.9825 + 7.99977i −0.681793 + 0.272949i −0.686595 0.727040i \(-0.740896\pi\)
0.00480236 + 0.999988i \(0.498471\pi\)
\(860\) −6.98648 6.66159i −0.238237 0.227158i
\(861\) 10.5315 + 1.23038i 0.358912 + 0.0419313i
\(862\) 0.622942 + 13.0772i 0.0212175 + 0.445410i
\(863\) 29.1406 18.7275i 0.991957 0.637492i 0.0592938 0.998241i \(-0.481115\pi\)
0.932663 + 0.360749i \(0.117479\pi\)
\(864\) −4.93645 + 1.62217i −0.167942 + 0.0551873i
\(865\) 23.3472 6.85535i 0.793827 0.233089i
\(866\) −18.0407 14.1874i −0.613048 0.482106i
\(867\) −0.545849 20.5947i −0.0185380 0.699434i
\(868\) −24.4105 + 2.33092i −0.828545 + 0.0791164i
\(869\) −0.596014 2.45680i −0.0202184 0.0833414i
\(870\) 9.62293 7.24423i 0.326248 0.245602i
\(871\) −33.4161 13.3778i −1.13226 0.453289i
\(872\) −0.240449 0.154527i −0.00814264 0.00523296i
\(873\) −8.11824 5.71520i −0.274761 0.193430i
\(874\) −17.1725 14.7895i −0.580868 0.500264i
\(875\) −29.6666 + 51.3840i −1.00291 + 1.73710i
\(876\) −15.9155 19.1703i −0.537736 0.647705i
\(877\) 1.03992 0.817799i 0.0351154 0.0276151i −0.600447 0.799665i \(-0.705011\pi\)
0.635562 + 0.772049i \(0.280768\pi\)
\(878\) −14.5144 + 20.3826i −0.489836 + 0.687879i
\(879\) −3.95382 2.66050i −0.133359 0.0897364i
\(880\) −0.252889 0.355133i −0.00852490 0.0119715i
\(881\) 7.54574 8.70824i 0.254222 0.293388i −0.614265 0.789100i \(-0.710547\pi\)
0.868487 + 0.495712i \(0.165093\pi\)
\(882\) −49.3202 11.6835i −1.66070 0.393404i
\(883\) −18.7069 + 5.49285i −0.629538 + 0.184849i −0.580910 0.813968i \(-0.697303\pi\)
−0.0486284 + 0.998817i \(0.515485\pi\)
\(884\) 11.9976 2.31235i 0.403524 0.0777729i
\(885\) −26.0309 25.8908i −0.875020 0.870310i
\(886\) 3.11842 + 1.60766i 0.104765 + 0.0540103i
\(887\) −4.90579 + 14.1743i −0.164720 + 0.475928i −0.996909 0.0785645i \(-0.974966\pi\)
0.832189 + 0.554492i \(0.187088\pi\)
\(888\) −3.61491 + 5.96680i −0.121308 + 0.200233i
\(889\) 61.5445 + 48.3991i 2.06414 + 1.62325i
\(890\) 15.1776 17.5159i 0.508755 0.587135i
\(891\) 0.876427 + 1.86556i 0.0293614 + 0.0624985i
\(892\) 4.74242 + 1.39250i 0.158788 + 0.0466244i
\(893\) −52.3056 4.99457i −1.75034 0.167137i
\(894\) −3.55688 2.92070i −0.118960 0.0976829i
\(895\) 1.57795 33.1252i 0.0527450 1.10725i
\(896\) −2.44413 4.23336i −0.0816526 0.141426i
\(897\) 39.3001 21.7520i 1.31219 0.726279i
\(898\) −2.32406 + 4.02540i −0.0775550 + 0.134329i
\(899\) −15.4161 9.90732i −0.514155 0.330428i
\(900\) 4.12250 0.218682i 0.137417 0.00728940i
\(901\) 5.60144 + 12.2654i 0.186611 + 0.408621i
\(902\) 0.207572 0.197920i 0.00691140 0.00659001i
\(903\) −28.7945 + 31.8472i −0.958220 + 1.05981i
\(904\) −2.50837 0.483448i −0.0834270 0.0160792i
\(905\) −3.43908 + 1.37680i −0.114319 + 0.0457664i
\(906\) 27.0929 + 0.571794i 0.900103 + 0.0189966i
\(907\) −2.78471 + 0.536709i −0.0924648 + 0.0178211i −0.235274 0.971929i \(-0.575599\pi\)
0.142809 + 0.989750i \(0.454387\pi\)
\(908\) −9.20703 + 5.91700i −0.305546 + 0.196362i
\(909\) −28.1398 1.18831i −0.933340 0.0394136i
\(910\) −32.9526 38.0293i −1.09237 1.26066i
\(911\) −13.9827 + 57.6375i −0.463267 + 1.90961i −0.0506333 + 0.998717i \(0.516124\pi\)
−0.412634 + 0.910897i \(0.635391\pi\)
\(912\) 8.16256 0.605939i 0.270289 0.0200646i
\(913\) −0.559005 0.107739i −0.0185004 0.00356566i
\(914\) 40.0574 3.82502i 1.32498 0.126520i
\(915\) −29.6961 + 14.5246i −0.981722 + 0.480169i
\(916\) 14.4502 + 1.37982i 0.477447 + 0.0455906i
\(917\) −0.995858 6.92634i −0.0328861 0.228728i
\(918\) −10.6019 5.04444i −0.349916 0.166491i
\(919\) −35.5764 −1.17356 −0.586779 0.809747i \(-0.699604\pi\)
−0.586779 + 0.809747i \(0.699604\pi\)
\(920\) 9.11791 0.461925i 0.300609 0.0152292i
\(921\) 7.78263 7.11332i 0.256446 0.234392i
\(922\) −1.55540 + 32.6519i −0.0512244 + 1.07533i
\(923\) −37.0988 + 29.1748i −1.22112 + 0.960300i
\(924\) −1.54914 + 1.16621i −0.0509630 + 0.0383654i
\(925\) 4.01144 3.82490i 0.131895 0.125762i
\(926\) −12.6817 + 27.7690i −0.416746 + 0.912545i
\(927\) 11.2855 39.2164i 0.370664 1.28804i
\(928\) 0.519882 3.61586i 0.0170660 0.118696i
\(929\) 2.21414 9.12681i 0.0726436 0.299441i −0.923887 0.382665i \(-0.875006\pi\)
0.996531 + 0.0832238i \(0.0265216\pi\)
\(930\) 6.55207 + 15.1872i 0.214851 + 0.498006i
\(931\) 70.9644 + 36.5847i 2.32576 + 1.19901i
\(932\) −13.3713 6.89338i −0.437991 0.225800i
\(933\) 21.2594 + 49.2776i 0.696003 + 1.61328i
\(934\) 3.05479 12.5920i 0.0999559 0.412024i
\(935\) 0.140193 0.975066i 0.00458481 0.0318881i
\(936\) −4.48636 + 15.5899i −0.146641 + 0.509571i
\(937\) −3.53457 + 7.73963i −0.115469 + 0.252843i −0.958539 0.284962i \(-0.908019\pi\)
0.843069 + 0.537805i \(0.180746\pi\)
\(938\) −23.5489 + 22.4538i −0.768899 + 0.733143i
\(939\) −23.0573 + 17.3578i −0.752447 + 0.566449i
\(940\) 16.6379 13.0842i 0.542670 0.426760i
\(941\) 1.59635 33.5115i 0.0520395 1.09244i −0.810268 0.586059i \(-0.800679\pi\)
0.862308 0.506384i \(-0.169018\pi\)
\(942\) −11.1421 + 10.1839i −0.363029 + 0.331809i
\(943\) 1.15443 + 5.89397i 0.0375934 + 0.191934i
\(944\) −11.1349 −0.362411
\(945\) 3.83975 + 48.2004i 0.124907 + 1.56796i
\(946\) 0.165277 + 1.14953i 0.00537363 + 0.0373744i
\(947\) −27.3756 2.61406i −0.889589 0.0849455i −0.359755 0.933047i \(-0.617140\pi\)
−0.529834 + 0.848101i \(0.677746\pi\)
\(948\) −17.1752 + 8.40055i −0.557825 + 0.272837i
\(949\) −77.4362 + 7.39427i −2.51369 + 0.240028i
\(950\) −6.38541 1.23069i −0.207170 0.0399288i
\(951\) −52.0927 + 3.86705i −1.68922 + 0.125398i
\(952\) 2.60399 10.7338i 0.0843958 0.347884i
\(953\) −19.3807 22.3665i −0.627803 0.724523i 0.349366 0.936986i \(-0.386397\pi\)
−0.977169 + 0.212463i \(0.931851\pi\)
\(954\) −17.8869 0.755338i −0.579109 0.0244550i
\(955\) 12.7274 8.17941i 0.411849 0.264680i
\(956\) 23.6937 4.56659i 0.766310 0.147694i
\(957\) −1.44874 0.0305755i −0.0468311 0.000988366i
\(958\) 8.91989 3.57099i 0.288189 0.115373i
\(959\) 41.0604 + 7.91375i 1.32591 + 0.255548i
\(960\) −2.21132 + 2.44576i −0.0713701 + 0.0789366i
\(961\) −4.22347 + 4.02707i −0.136241 + 0.129905i
\(962\) 9.04798 + 19.8123i 0.291719 + 0.638775i
\(963\) 48.2348 2.55866i 1.55434 0.0824516i
\(964\) −4.19026 2.69292i −0.134959 0.0867330i
\(965\) 4.35862 7.54936i 0.140309 0.243022i
\(966\) −3.12819 40.4842i −0.100648 1.30256i
\(967\) 21.7889 + 37.7395i 0.700684 + 1.21362i 0.968227 + 0.250074i \(0.0804551\pi\)
−0.267543 + 0.963546i \(0.586212\pi\)
\(968\) 0.520905 10.9352i 0.0167425 0.351469i
\(969\) 14.2930 + 11.7366i 0.459158 + 0.377034i
\(970\) −6.27143 0.598849i −0.201363 0.0192279i
\(971\) −32.3796 9.50751i −1.03911 0.305111i −0.282701 0.959208i \(-0.591230\pi\)
−0.756410 + 0.654097i \(0.773049\pi\)
\(972\) 12.3520 9.50931i 0.396192 0.305011i
\(973\) 7.86042 9.07140i 0.251993 0.290816i
\(974\) 29.2773 + 23.0239i 0.938105 + 0.737734i
\(975\) 6.67843 11.0235i 0.213881 0.353034i
\(976\) −3.27917 + 9.47454i −0.104964 + 0.303273i
\(977\) −26.8254 13.8295i −0.858222 0.442444i −0.0278227 0.999613i \(-0.508857\pi\)
−0.830399 + 0.557169i \(0.811888\pi\)
\(978\) 6.78657 + 6.75004i 0.217011 + 0.215843i
\(979\) −2.73791 + 0.527688i −0.0875038 + 0.0168650i
\(980\) −30.8596 + 9.06119i −0.985773 + 0.289449i
\(981\) 0.834376 + 0.197656i 0.0266396 + 0.00631067i
\(982\) 9.80622 11.3170i 0.312929 0.361139i
\(983\) −24.4763 34.3722i −0.780673 1.09630i −0.992885 0.119078i \(-0.962006\pi\)
0.212212 0.977224i \(-0.431933\pi\)
\(984\) −1.79961 1.21095i −0.0573695 0.0386035i
\(985\) −0.215606 + 0.302776i −0.00686977 + 0.00964725i
\(986\) 6.48819 5.10237i 0.206626 0.162493i
\(987\) −60.1337 72.4313i −1.91408 2.30551i
\(988\) 12.7770 22.1303i 0.406489 0.704060i
\(989\) −22.1522 10.0359i −0.704399 0.319123i
\(990\) 1.06948 + 0.752908i 0.0339903 + 0.0239290i
\(991\) −22.8613 14.6920i −0.726212 0.466708i 0.124581 0.992209i \(-0.460241\pi\)
−0.850793 + 0.525501i \(0.823878\pi\)
\(992\) 4.65707 + 1.86441i 0.147862 + 0.0591951i
\(993\) −23.9544 + 18.0331i −0.760168 + 0.572262i
\(994\) 10.0585 + 41.4616i 0.319035 + 1.31508i
\(995\) −27.6672 + 2.64190i −0.877110 + 0.0837538i
\(996\) 0.114075 + 4.30400i 0.00361459 + 0.136378i
\(997\) 36.8424 + 28.9732i 1.16681 + 0.917590i 0.997685 0.0680039i \(-0.0216630\pi\)
0.169126 + 0.985594i \(0.445905\pi\)
\(998\) 11.1139 3.26334i 0.351805 0.103299i
\(999\) 4.28314 20.4863i 0.135513 0.648156i
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 414.2.m.a.25.2 240
9.4 even 3 inner 414.2.m.a.301.10 yes 240
23.12 even 11 inner 414.2.m.a.403.10 yes 240
207.58 even 33 inner 414.2.m.a.265.2 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
414.2.m.a.25.2 240 1.1 even 1 trivial
414.2.m.a.265.2 yes 240 207.58 even 33 inner
414.2.m.a.301.10 yes 240 9.4 even 3 inner
414.2.m.a.403.10 yes 240 23.12 even 11 inner