Properties

Label 441.2.bh.a.20.2
Level $441$
Weight $2$
Character 441.20
Analytic conductor $3.521$
Analytic rank $0$
Dimension $648$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(20,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([7, 39]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.20");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bh (of order \(42\), degree \(12\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 20.2
Character \(\chi\) \(=\) 441.20
Dual form 441.2.bh.a.419.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.53439 - 2.25054i) q^{2} +(1.47003 + 0.915972i) q^{3} +(-1.97989 + 5.04466i) q^{4} +(-0.202216 + 0.187629i) q^{5} +(-0.194174 - 4.71382i) q^{6} +(-1.68008 - 2.04385i) q^{7} +(9.08004 - 2.07246i) q^{8} +(1.32199 + 2.69302i) q^{9} +O(q^{10})\) \(q+(-1.53439 - 2.25054i) q^{2} +(1.47003 + 0.915972i) q^{3} +(-1.97989 + 5.04466i) q^{4} +(-0.202216 + 0.187629i) q^{5} +(-0.194174 - 4.71382i) q^{6} +(-1.68008 - 2.04385i) q^{7} +(9.08004 - 2.07246i) q^{8} +(1.32199 + 2.69302i) q^{9} +(0.732545 + 0.167199i) q^{10} +(2.99294 + 4.38983i) q^{11} +(-7.53127 + 5.60230i) q^{12} +(-3.60651 + 0.270270i) q^{13} +(-2.02186 + 6.91715i) q^{14} +(-0.469127 + 0.0905965i) q^{15} +(-10.6513 - 9.88293i) q^{16} +(-1.30876 + 1.64113i) q^{17} +(4.03229 - 7.10733i) q^{18} +2.97408i q^{19} +(-0.546161 - 1.39160i) q^{20} +(-0.597663 - 4.54343i) q^{21} +(5.28715 - 13.4714i) q^{22} +(6.71819 + 2.63670i) q^{23} +(15.2463 + 5.27048i) q^{24} +(-0.367964 + 4.91014i) q^{25} +(6.14204 + 7.70188i) q^{26} +(-0.523362 + 5.16973i) q^{27} +(13.6369 - 4.42886i) q^{28} +(1.00644 - 0.394997i) q^{29} +(0.923716 + 0.916778i) q^{30} +(1.04205 - 0.601630i) q^{31} +(-3.12248 + 20.7163i) q^{32} +(0.378749 + 9.19464i) q^{33} +(5.70157 + 0.427274i) q^{34} +(0.723225 + 0.0980674i) q^{35} +(-16.2028 + 1.33713i) q^{36} +(1.31792 - 1.65261i) q^{37} +(6.69329 - 4.56341i) q^{38} +(-5.54924 - 2.90615i) q^{39} +(-1.44728 + 2.12277i) q^{40} +(6.90047 - 6.40270i) q^{41} +(-9.30813 + 8.31647i) q^{42} +(3.53924 + 3.28394i) q^{43} +(-28.0709 + 6.40700i) q^{44} +(-0.772616 - 0.296528i) q^{45} +(-4.37435 - 19.1653i) q^{46} +(4.29581 - 2.92883i) q^{47} +(-6.60521 - 24.2845i) q^{48} +(-1.35465 + 6.86767i) q^{49} +(11.6150 - 6.70595i) q^{50} +(-3.42715 + 1.21373i) q^{51} +(5.77704 - 18.7287i) q^{52} +(3.11854 - 2.48695i) q^{53} +(12.4377 - 6.75454i) q^{54} +(-1.42888 - 0.326133i) q^{55} +(-19.4910 - 15.0764i) q^{56} +(-2.72418 + 4.37200i) q^{57} +(-2.43322 - 1.65894i) q^{58} +(-8.91122 + 2.74875i) q^{59} +(0.471789 - 2.54596i) q^{60} +(-9.05325 + 3.55314i) q^{61} +(-2.95291 - 1.42205i) q^{62} +(3.28308 - 7.22644i) q^{63} +(25.2317 - 12.1510i) q^{64} +(0.678583 - 0.731339i) q^{65} +(20.1117 - 14.9606i) q^{66} +(0.798141 + 1.38242i) q^{67} +(-5.68776 - 9.85150i) q^{68} +(7.46082 + 10.0297i) q^{69} +(-0.889006 - 1.77812i) q^{70} +(-11.0720 + 8.82960i) q^{71} +(17.5849 + 21.7129i) q^{72} +(-2.53899 - 5.27227i) q^{73} +(-5.74147 - 0.430263i) q^{74} +(-5.03847 + 6.88101i) q^{75} +(-15.0033 - 5.88835i) q^{76} +(3.94379 - 13.4924i) q^{77} +(1.97429 + 16.9480i) q^{78} +(0.141308 - 0.244752i) q^{79} +4.00818 q^{80} +(-5.50469 + 7.12028i) q^{81} +(-24.9975 - 5.70553i) q^{82} +(0.618725 - 8.25632i) q^{83} +(24.1034 + 5.98047i) q^{84} +(-0.0432720 - 0.577424i) q^{85} +(1.96004 - 13.0040i) q^{86} +(1.84130 + 0.341209i) q^{87} +(36.2737 + 33.6571i) q^{88} +(10.9955 - 5.29513i) q^{89} +(0.518148 + 2.19379i) q^{90} +(6.61161 + 6.91708i) q^{91} +(-26.6025 + 28.6707i) q^{92} +(2.08293 + 0.0700768i) q^{93} +(-13.1829 - 5.17390i) q^{94} +(-0.558025 - 0.601408i) q^{95} +(-23.5657 + 27.5935i) q^{96} +(11.1993 + 6.46591i) q^{97} +(17.5345 - 7.48899i) q^{98} +(-7.86526 + 13.8633i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 15 q^{2} - 14 q^{3} - 57 q^{4} - 21 q^{5} + 14 q^{6} - 5 q^{7} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 15 q^{2} - 14 q^{3} - 57 q^{4} - 21 q^{5} + 14 q^{6} - 5 q^{7} - 20 q^{9} - 28 q^{10} - 15 q^{11} + 21 q^{12} - 7 q^{13} - 114 q^{14} - 10 q^{15} + 39 q^{16} - 18 q^{18} - 21 q^{20} + 10 q^{21} + 3 q^{22} + 30 q^{23} - 14 q^{24} + 41 q^{25} + 7 q^{27} - 20 q^{28} + 75 q^{29} - 70 q^{30} - 39 q^{32} - 14 q^{33} - 7 q^{34} - 128 q^{36} - 10 q^{37} + 21 q^{38} - 36 q^{39} - 7 q^{40} - 21 q^{41} + 104 q^{42} + 3 q^{43} - 35 q^{45} - 72 q^{46} - 147 q^{47} - 13 q^{49} - 18 q^{50} + 22 q^{51} - 35 q^{52} - 14 q^{54} - 112 q^{55} - 63 q^{56} - 16 q^{57} + 33 q^{58} - 21 q^{59} - 90 q^{60} - 56 q^{61} - 38 q^{63} + 52 q^{64} + 27 q^{65} - 42 q^{66} - 26 q^{67} - 182 q^{69} - 25 q^{70} + 24 q^{72} - 28 q^{73} + 33 q^{74} - 14 q^{75} + 21 q^{76} + 3 q^{77} + 90 q^{78} - 2 q^{79} + 56 q^{81} - 28 q^{82} - 21 q^{83} + 116 q^{84} + 5 q^{85} - 123 q^{86} - 70 q^{87} - 41 q^{88} - 224 q^{90} - 4 q^{91} - 225 q^{92} + 112 q^{93} - 7 q^{94} - 12 q^{95} - 371 q^{96} + 224 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.53439 2.25054i −1.08498 1.59137i −0.765099 0.643913i \(-0.777310\pi\)
−0.319879 0.947458i \(-0.603642\pi\)
\(3\) 1.47003 + 0.915972i 0.848724 + 0.528837i
\(4\) −1.97989 + 5.04466i −0.989943 + 2.52233i
\(5\) −0.202216 + 0.187629i −0.0904338 + 0.0839103i −0.724094 0.689701i \(-0.757742\pi\)
0.633661 + 0.773611i \(0.281552\pi\)
\(6\) −0.194174 4.71382i −0.0792710 1.92441i
\(7\) −1.68008 2.04385i −0.635011 0.772503i
\(8\) 9.08004 2.07246i 3.21028 0.732726i
\(9\) 1.32199 + 2.69302i 0.440663 + 0.897673i
\(10\) 0.732545 + 0.167199i 0.231651 + 0.0528729i
\(11\) 2.99294 + 4.38983i 0.902404 + 1.32358i 0.945876 + 0.324529i \(0.105206\pi\)
−0.0434713 + 0.999055i \(0.513842\pi\)
\(12\) −7.53127 + 5.60230i −2.17409 + 1.61724i
\(13\) −3.60651 + 0.270270i −1.00026 + 0.0749595i −0.564784 0.825239i \(-0.691041\pi\)
−0.435481 + 0.900198i \(0.643422\pi\)
\(14\) −2.02186 + 6.91715i −0.540366 + 1.84869i
\(15\) −0.469127 + 0.0905965i −0.121128 + 0.0233919i
\(16\) −10.6513 9.88293i −2.66282 2.47073i
\(17\) −1.30876 + 1.64113i −0.317420 + 0.398033i −0.914788 0.403935i \(-0.867642\pi\)
0.597367 + 0.801968i \(0.296214\pi\)
\(18\) 4.03229 7.10733i 0.950420 1.67521i
\(19\) 2.97408i 0.682302i 0.940009 + 0.341151i \(0.110817\pi\)
−0.940009 + 0.341151i \(0.889183\pi\)
\(20\) −0.546161 1.39160i −0.122125 0.311170i
\(21\) −0.597663 4.54343i −0.130421 0.991459i
\(22\) 5.28715 13.4714i 1.12722 2.87212i
\(23\) 6.71819 + 2.63670i 1.40084 + 0.549789i 0.941059 0.338243i \(-0.109832\pi\)
0.459781 + 0.888032i \(0.347928\pi\)
\(24\) 15.2463 + 5.27048i 3.11213 + 1.07583i
\(25\) −0.367964 + 4.91014i −0.0735928 + 0.982027i
\(26\) 6.14204 + 7.70188i 1.20455 + 1.51046i
\(27\) −0.523362 + 5.16973i −0.100721 + 0.994915i
\(28\) 13.6369 4.42886i 2.57713 0.836975i
\(29\) 1.00644 0.394997i 0.186890 0.0733491i −0.270050 0.962846i \(-0.587040\pi\)
0.456941 + 0.889497i \(0.348945\pi\)
\(30\) 0.923716 + 0.916778i 0.168647 + 0.167380i
\(31\) 1.04205 0.601630i 0.187158 0.108056i −0.403493 0.914983i \(-0.632204\pi\)
0.590652 + 0.806927i \(0.298871\pi\)
\(32\) −3.12248 + 20.7163i −0.551982 + 3.66216i
\(33\) 0.378749 + 9.19464i 0.0659318 + 1.60058i
\(34\) 5.70157 + 0.427274i 0.977812 + 0.0732769i
\(35\) 0.723225 + 0.0980674i 0.122247 + 0.0165764i
\(36\) −16.2028 + 1.33713i −2.70046 + 0.222855i
\(37\) 1.31792 1.65261i 0.216664 0.271688i −0.661608 0.749850i \(-0.730126\pi\)
0.878271 + 0.478162i \(0.158697\pi\)
\(38\) 6.69329 4.56341i 1.08580 0.740283i
\(39\) −5.54924 2.90615i −0.888590 0.465357i
\(40\) −1.44728 + 2.12277i −0.228835 + 0.335639i
\(41\) 6.90047 6.40270i 1.07767 0.999934i 0.0776769 0.996979i \(-0.475250\pi\)
0.999996 0.00295535i \(-0.000940718\pi\)
\(42\) −9.30813 + 8.31647i −1.43628 + 1.28326i
\(43\) 3.53924 + 3.28394i 0.539729 + 0.500795i 0.902269 0.431173i \(-0.141900\pi\)
−0.362540 + 0.931968i \(0.618090\pi\)
\(44\) −28.0709 + 6.40700i −4.23185 + 0.965892i
\(45\) −0.772616 0.296528i −0.115175 0.0442038i
\(46\) −4.37435 19.1653i −0.644963 2.82577i
\(47\) 4.29581 2.92883i 0.626608 0.427214i −0.207946 0.978140i \(-0.566678\pi\)
0.834554 + 0.550926i \(0.185725\pi\)
\(48\) −6.60521 24.2845i −0.953380 3.50516i
\(49\) −1.35465 + 6.86767i −0.193522 + 0.981096i
\(50\) 11.6150 6.70595i 1.64262 0.948365i
\(51\) −3.42715 + 1.21373i −0.479897 + 0.169956i
\(52\) 5.77704 18.7287i 0.801132 2.59721i
\(53\) 3.11854 2.48695i 0.428365 0.341609i −0.385455 0.922726i \(-0.625956\pi\)
0.813820 + 0.581117i \(0.197384\pi\)
\(54\) 12.4377 6.75454i 1.69256 0.919176i
\(55\) −1.42888 0.326133i −0.192670 0.0439757i
\(56\) −19.4910 15.0764i −2.60460 2.01466i
\(57\) −2.72418 + 4.37200i −0.360826 + 0.579086i
\(58\) −2.43322 1.65894i −0.319498 0.217830i
\(59\) −8.91122 + 2.74875i −1.16014 + 0.357857i −0.814305 0.580438i \(-0.802881\pi\)
−0.345838 + 0.938294i \(0.612405\pi\)
\(60\) 0.471789 2.54596i 0.0609077 0.328682i
\(61\) −9.05325 + 3.55314i −1.15915 + 0.454933i −0.865465 0.500970i \(-0.832977\pi\)
−0.293685 + 0.955902i \(0.594882\pi\)
\(62\) −2.95291 1.42205i −0.375020 0.180600i
\(63\) 3.28308 7.22644i 0.413629 0.910446i
\(64\) 25.2317 12.1510i 3.15397 1.51887i
\(65\) 0.678583 0.731339i 0.0841679 0.0907114i
\(66\) 20.1117 14.9606i 2.47558 1.84152i
\(67\) 0.798141 + 1.38242i 0.0975085 + 0.168890i 0.910653 0.413173i \(-0.135579\pi\)
−0.813144 + 0.582062i \(0.802246\pi\)
\(68\) −5.68776 9.85150i −0.689743 1.19467i
\(69\) 7.46082 + 10.0297i 0.898177 + 1.20744i
\(70\) −0.889006 1.77812i −0.106257 0.212526i
\(71\) −11.0720 + 8.82960i −1.31400 + 1.04788i −0.319027 + 0.947746i \(0.603356\pi\)
−0.994974 + 0.100135i \(0.968073\pi\)
\(72\) 17.5849 + 21.7129i 2.07240 + 2.55890i
\(73\) −2.53899 5.27227i −0.297167 0.617073i 0.697910 0.716186i \(-0.254114\pi\)
−0.995076 + 0.0991132i \(0.968399\pi\)
\(74\) −5.74147 0.430263i −0.667432 0.0500171i
\(75\) −5.03847 + 6.88101i −0.581792 + 0.794551i
\(76\) −15.0033 5.88835i −1.72099 0.675440i
\(77\) 3.94379 13.4924i 0.449436 1.53760i
\(78\) 1.97429 + 16.9480i 0.223545 + 1.91898i
\(79\) 0.141308 0.244752i 0.0158984 0.0275368i −0.857967 0.513705i \(-0.828273\pi\)
0.873865 + 0.486168i \(0.161606\pi\)
\(80\) 4.00818 0.448128
\(81\) −5.50469 + 7.12028i −0.611632 + 0.791142i
\(82\) −24.9975 5.70553i −2.76052 0.630070i
\(83\) 0.618725 8.25632i 0.0679139 0.906248i −0.854353 0.519694i \(-0.826046\pi\)
0.922267 0.386555i \(-0.126335\pi\)
\(84\) 24.1034 + 5.98047i 2.62990 + 0.652523i
\(85\) −0.0432720 0.577424i −0.00469350 0.0626304i
\(86\) 1.96004 13.0040i 0.211357 1.40226i
\(87\) 1.84130 + 0.341209i 0.197408 + 0.0365815i
\(88\) 36.2737 + 33.6571i 3.86679 + 3.58786i
\(89\) 10.9955 5.29513i 1.16552 0.561283i 0.251857 0.967764i \(-0.418959\pi\)
0.913659 + 0.406481i \(0.133244\pi\)
\(90\) 0.518148 + 2.19379i 0.0546176 + 0.231246i
\(91\) 6.61161 + 6.91708i 0.693086 + 0.725108i
\(92\) −26.6025 + 28.6707i −2.77350 + 2.98913i
\(93\) 2.08293 + 0.0700768i 0.215990 + 0.00726663i
\(94\) −13.1829 5.17390i −1.35971 0.533648i
\(95\) −0.558025 0.601408i −0.0572521 0.0617031i
\(96\) −23.5657 + 27.5935i −2.40516 + 2.81625i
\(97\) 11.1993 + 6.46591i 1.13711 + 0.656513i 0.945714 0.324999i \(-0.105364\pi\)
0.191400 + 0.981512i \(0.438697\pi\)
\(98\) 17.5345 7.48899i 1.77125 0.756503i
\(99\) −7.86526 + 13.8633i −0.790489 + 1.39332i
\(100\) −24.0415 11.5778i −2.40415 1.15778i
\(101\) 5.06940 + 1.56370i 0.504424 + 0.155594i 0.536515 0.843891i \(-0.319740\pi\)
−0.0320909 + 0.999485i \(0.510217\pi\)
\(102\) 7.99013 + 5.85059i 0.791140 + 0.579295i
\(103\) −10.0595 10.8415i −0.991188 1.06825i −0.997667 0.0682675i \(-0.978253\pi\)
0.00647909 0.999979i \(-0.497938\pi\)
\(104\) −32.1871 + 9.92841i −3.15621 + 0.973560i
\(105\) 0.973338 + 0.806617i 0.0949880 + 0.0787177i
\(106\) −10.3820 3.20244i −1.00839 0.311048i
\(107\) −3.94800 8.19811i −0.381668 0.792542i −0.999978 0.00660747i \(-0.997897\pi\)
0.618310 0.785934i \(-0.287818\pi\)
\(108\) −25.0434 12.8757i −2.40980 1.23896i
\(109\) 0.0383532 + 0.0184699i 0.00367357 + 0.00176910i 0.435720 0.900082i \(-0.356494\pi\)
−0.432046 + 0.901852i \(0.642208\pi\)
\(110\) 1.45849 + 3.71617i 0.139061 + 0.354322i
\(111\) 3.45113 1.22222i 0.327566 0.116008i
\(112\) −2.30425 + 38.3737i −0.217731 + 3.62598i
\(113\) −8.30235 + 12.1773i −0.781020 + 1.14555i 0.204975 + 0.978767i \(0.434289\pi\)
−0.985994 + 0.166778i \(0.946664\pi\)
\(114\) 14.0193 0.577489i 1.31303 0.0540868i
\(115\) −1.85325 + 0.727346i −0.172816 + 0.0678254i
\(116\) 5.85918i 0.544011i
\(117\) −5.49561 9.35509i −0.508069 0.864878i
\(118\) 19.8595 + 15.8374i 1.82821 + 1.45795i
\(119\) 5.55305 0.0823264i 0.509047 0.00754685i
\(120\) −4.07194 + 1.79487i −0.371715 + 0.163848i
\(121\) −6.29420 + 16.0374i −0.572200 + 1.45794i
\(122\) 21.8877 + 14.9228i 1.98162 + 1.35105i
\(123\) 16.0086 3.09154i 1.44345 0.278755i
\(124\) 0.971875 + 6.44797i 0.0872770 + 0.579045i
\(125\) −1.70684 2.14031i −0.152664 0.191435i
\(126\) −21.3009 + 3.69949i −1.89764 + 0.329577i
\(127\) 5.38458 6.75205i 0.477804 0.599147i −0.483259 0.875478i \(-0.660547\pi\)
0.961063 + 0.276330i \(0.0891184\pi\)
\(128\) −29.7746 17.1904i −2.63173 1.51943i
\(129\) 2.19480 + 8.06934i 0.193242 + 0.710466i
\(130\) −2.68712 0.405018i −0.235676 0.0355224i
\(131\) −1.20328 + 0.371162i −0.105131 + 0.0324286i −0.346874 0.937912i \(-0.612757\pi\)
0.241743 + 0.970340i \(0.422281\pi\)
\(132\) −47.1338 16.2937i −4.10247 1.41818i
\(133\) 6.07859 4.99670i 0.527080 0.433269i
\(134\) 1.88653 3.91742i 0.162972 0.338414i
\(135\) −0.864159 1.14360i −0.0743750 0.0984254i
\(136\) −8.48240 + 17.6139i −0.727360 + 1.51038i
\(137\) −2.22645 + 2.39955i −0.190219 + 0.205007i −0.820959 0.570987i \(-0.806561\pi\)
0.630740 + 0.775994i \(0.282751\pi\)
\(138\) 11.1244 32.1804i 0.946974 2.73937i
\(139\) −5.27836 5.68872i −0.447705 0.482511i 0.468362 0.883537i \(-0.344844\pi\)
−0.916067 + 0.401026i \(0.868654\pi\)
\(140\) −1.92662 + 3.45427i −0.162829 + 0.291939i
\(141\) 8.99770 0.370637i 0.757743 0.0312132i
\(142\) 36.8601 + 11.3698i 3.09323 + 0.954135i
\(143\) −11.9805 15.0231i −1.00186 1.25629i
\(144\) 12.5340 41.7492i 1.04450 3.47910i
\(145\) −0.129405 + 0.268711i −0.0107465 + 0.0223153i
\(146\) −7.96964 + 13.8038i −0.659572 + 1.14241i
\(147\) −8.28198 + 8.85487i −0.683086 + 0.730338i
\(148\) 5.72756 + 9.92042i 0.470803 + 0.815454i
\(149\) 0.332842 0.0249430i 0.0272674 0.00204341i −0.0610894 0.998132i \(-0.519457\pi\)
0.0883568 + 0.996089i \(0.471838\pi\)
\(150\) 23.2170 + 0.781098i 1.89566 + 0.0637764i
\(151\) 9.34030 1.40782i 0.760103 0.114567i 0.242457 0.970162i \(-0.422047\pi\)
0.517646 + 0.855595i \(0.326808\pi\)
\(152\) 6.16367 + 27.0048i 0.499940 + 2.19038i
\(153\) −6.14976 1.35495i −0.497178 0.109541i
\(154\) −36.4165 + 11.8270i −2.93452 + 0.953044i
\(155\) −0.0978367 + 0.317179i −0.00785844 + 0.0254764i
\(156\) 25.6474 22.2402i 2.05344 1.78064i
\(157\) −6.25057 20.2638i −0.498850 1.61723i −0.758601 0.651555i \(-0.774117\pi\)
0.259752 0.965675i \(-0.416359\pi\)
\(158\) −0.767646 + 0.0575271i −0.0610706 + 0.00457661i
\(159\) 6.86234 0.799405i 0.544219 0.0633969i
\(160\) −3.25557 4.77504i −0.257375 0.377500i
\(161\) −5.89810 18.1609i −0.464835 1.43128i
\(162\) 24.4708 + 1.46321i 1.92261 + 0.114961i
\(163\) 4.58699 20.0969i 0.359281 1.57411i −0.395709 0.918376i \(-0.629501\pi\)
0.754990 0.655737i \(-0.227642\pi\)
\(164\) 18.6373 + 47.4872i 1.45533 + 3.70813i
\(165\) −1.80177 1.78824i −0.140268 0.139214i
\(166\) −19.5305 + 11.2760i −1.51586 + 0.875184i
\(167\) 16.9733 + 2.55831i 1.31343 + 0.197968i 0.768142 0.640279i \(-0.221181\pi\)
0.545290 + 0.838247i \(0.316419\pi\)
\(168\) −14.8429 40.0160i −1.14515 3.08730i
\(169\) 0.0790376 0.0119130i 0.00607982 0.000916385i
\(170\) −1.23312 + 0.983380i −0.0945759 + 0.0754218i
\(171\) −8.00926 + 3.93171i −0.612484 + 0.300665i
\(172\) −23.5736 + 11.3525i −1.79747 + 0.865618i
\(173\) −4.94743 + 0.745704i −0.376146 + 0.0566949i −0.334395 0.942433i \(-0.608532\pi\)
−0.0417512 + 0.999128i \(0.513294\pi\)
\(174\) −2.05737 4.66746i −0.155969 0.353839i
\(175\) 10.6538 7.49736i 0.805351 0.566747i
\(176\) 11.5058 76.3362i 0.867285 5.75406i
\(177\) −15.6176 4.12169i −1.17389 0.309805i
\(178\) −28.7882 16.6209i −2.15777 1.24579i
\(179\) −0.191219 0.152492i −0.0142924 0.0113978i 0.616318 0.787498i \(-0.288624\pi\)
−0.630610 + 0.776100i \(0.717195\pi\)
\(180\) 3.02557 3.31050i 0.225513 0.246750i
\(181\) 3.40660 + 7.07388i 0.253211 + 0.525798i 0.988365 0.152103i \(-0.0486044\pi\)
−0.735154 + 0.677900i \(0.762890\pi\)
\(182\) 5.42236 25.4932i 0.401932 1.88968i
\(183\) −16.5631 3.06930i −1.22438 0.226889i
\(184\) 66.4660 + 10.0181i 4.89993 + 0.738546i
\(185\) 0.0435747 + 0.581464i 0.00320368 + 0.0427501i
\(186\) −3.03832 4.79524i −0.222780 0.351604i
\(187\) −11.1213 0.833427i −0.813271 0.0609463i
\(188\) 6.26977 + 27.4697i 0.457270 + 2.00343i
\(189\) 11.4454 7.61589i 0.832534 0.553974i
\(190\) −0.497263 + 2.17865i −0.0360752 + 0.158056i
\(191\) 0.924680 2.99774i 0.0669075 0.216909i −0.915945 0.401305i \(-0.868557\pi\)
0.982852 + 0.184396i \(0.0590330\pi\)
\(192\) 48.2214 + 5.24926i 3.48008 + 0.378833i
\(193\) −7.57273 + 7.02646i −0.545097 + 0.505776i −0.903962 0.427614i \(-0.859354\pi\)
0.358865 + 0.933390i \(0.383164\pi\)
\(194\) −2.63230 35.1256i −0.188988 2.52187i
\(195\) 1.66742 0.453528i 0.119407 0.0324778i
\(196\) −31.9630 20.4310i −2.28307 1.45936i
\(197\) 1.98483i 0.141414i −0.997497 0.0707068i \(-0.977475\pi\)
0.997497 0.0707068i \(-0.0225255\pi\)
\(198\) 43.2684 3.57071i 3.07495 0.253760i
\(199\) −7.37074 + 1.68232i −0.522498 + 0.119257i −0.475632 0.879644i \(-0.657781\pi\)
−0.0468662 + 0.998901i \(0.514923\pi\)
\(200\) 6.83494 + 45.3468i 0.483303 + 3.20651i
\(201\) −0.0929661 + 2.76328i −0.00655733 + 0.194907i
\(202\) −4.25927 13.8082i −0.299681 0.971542i
\(203\) −2.49821 1.39338i −0.175340 0.0977960i
\(204\) 0.662501 19.6918i 0.0463843 1.37871i
\(205\) −0.194053 + 2.58946i −0.0135533 + 0.180856i
\(206\) −8.96411 + 39.2743i −0.624559 + 2.73637i
\(207\) 1.78071 + 21.5779i 0.123768 + 1.49977i
\(208\) 41.0849 + 32.7641i 2.84873 + 2.27178i
\(209\) −13.0557 + 8.90125i −0.903084 + 0.615712i
\(210\) 0.321841 3.42820i 0.0222092 0.236568i
\(211\) −18.9325 12.9079i −1.30336 0.888619i −0.305389 0.952228i \(-0.598787\pi\)
−0.997975 + 0.0636090i \(0.979739\pi\)
\(212\) 6.37149 + 20.6559i 0.437596 + 1.41865i
\(213\) −24.3638 + 2.83818i −1.66938 + 0.194469i
\(214\) −12.3924 + 21.4642i −0.847126 + 1.46727i
\(215\) −1.33185 −0.0908317
\(216\) 5.96191 + 48.0260i 0.405656 + 3.26776i
\(217\) −2.98038 1.11902i −0.202321 0.0759637i
\(218\) −0.0172815 0.114655i −0.00117045 0.00776544i
\(219\) 1.09685 10.0761i 0.0741185 0.680877i
\(220\) 4.47425 6.56252i 0.301654 0.442445i
\(221\) 4.27649 6.27247i 0.287668 0.421932i
\(222\) −8.04603 5.89153i −0.540014 0.395413i
\(223\) 3.74997 + 24.8794i 0.251116 + 1.66605i 0.658341 + 0.752720i \(0.271259\pi\)
−0.407224 + 0.913328i \(0.633503\pi\)
\(224\) 47.5871 28.4232i 3.17954 1.89910i
\(225\) −13.7095 + 5.50022i −0.913968 + 0.366681i
\(226\) 40.1446 2.67038
\(227\) 10.9691 18.9990i 0.728042 1.26101i −0.229667 0.973269i \(-0.573764\pi\)
0.957710 0.287737i \(-0.0929028\pi\)
\(228\) −16.6617 22.3986i −1.10345 1.48339i
\(229\) −0.424460 1.37606i −0.0280491 0.0909329i 0.940466 0.339888i \(-0.110389\pi\)
−0.968515 + 0.248955i \(0.919913\pi\)
\(230\) 4.48053 + 3.05477i 0.295437 + 0.201426i
\(231\) 18.1561 16.2219i 1.19459 1.06732i
\(232\) 8.31987 5.67239i 0.546226 0.372411i
\(233\) 11.0160 + 8.78495i 0.721681 + 0.575522i 0.913953 0.405820i \(-0.133014\pi\)
−0.192272 + 0.981342i \(0.561586\pi\)
\(234\) −12.6216 + 26.7224i −0.825098 + 1.74690i
\(235\) −0.319147 + 1.39828i −0.0208189 + 0.0912134i
\(236\) 3.77668 50.3963i 0.245841 3.28052i
\(237\) 0.431913 0.230360i 0.0280558 0.0149635i
\(238\) −8.70582 12.3710i −0.564315 0.801894i
\(239\) −1.30403 4.22756i −0.0843506 0.273458i 0.903565 0.428451i \(-0.140941\pi\)
−0.987916 + 0.154993i \(0.950464\pi\)
\(240\) 5.89216 + 3.67138i 0.380337 + 0.236987i
\(241\) 0.846583 + 5.61671i 0.0545332 + 0.361804i 0.999409 + 0.0343751i \(0.0109441\pi\)
−0.944876 + 0.327429i \(0.893818\pi\)
\(242\) 45.7505 10.4422i 2.94095 0.671253i
\(243\) −14.6140 + 5.42490i −0.937492 + 0.348008i
\(244\) 52.7054i 3.37412i
\(245\) −1.01464 1.64293i −0.0648231 0.104963i
\(246\) −31.5211 31.2844i −2.00971 1.99462i
\(247\) −0.803807 10.7261i −0.0511450 0.682482i
\(248\) 8.21504 7.62244i 0.521655 0.484026i
\(249\) 8.47210 11.5703i 0.536898 0.733239i
\(250\) −2.19789 + 7.12538i −0.139007 + 0.450649i
\(251\) 4.13377 18.1112i 0.260921 1.14317i −0.659334 0.751850i \(-0.729162\pi\)
0.920255 0.391320i \(-0.127981\pi\)
\(252\) 29.9548 + 30.8695i 1.88698 + 1.94460i
\(253\) 8.53247 + 37.3832i 0.536432 + 2.35026i
\(254\) −23.4578 1.75792i −1.47187 0.110302i
\(255\) 0.465293 0.888468i 0.0291378 0.0556380i
\(256\) 2.81263 + 37.5319i 0.175789 + 2.34575i
\(257\) 16.4438 + 2.47851i 1.02574 + 0.154605i 0.640297 0.768128i \(-0.278811\pi\)
0.385440 + 0.922733i \(0.374050\pi\)
\(258\) 14.7927 17.3210i 0.920951 1.07836i
\(259\) −5.59190 + 0.0829024i −0.347464 + 0.00515130i
\(260\) 2.34584 + 4.87119i 0.145483 + 0.302098i
\(261\) 2.39423 + 2.18817i 0.148199 + 0.135444i
\(262\) 2.68162 + 2.13852i 0.165671 + 0.132118i
\(263\) 13.9341 + 8.04487i 0.859215 + 0.496068i 0.863749 0.503922i \(-0.168110\pi\)
−0.00453424 + 0.999990i \(0.501443\pi\)
\(264\) 22.4946 + 82.7028i 1.38445 + 5.09001i
\(265\) −0.163994 + 1.08803i −0.0100741 + 0.0668372i
\(266\) −20.5722 6.01319i −1.26136 0.368693i
\(267\) 21.0139 + 2.28752i 1.28603 + 0.139994i
\(268\) −8.55408 + 1.28932i −0.522524 + 0.0787578i
\(269\) 22.6960 10.9298i 1.38380 0.666402i 0.413993 0.910280i \(-0.364134\pi\)
0.969806 + 0.243878i \(0.0784196\pi\)
\(270\) −1.24776 + 3.69955i −0.0759361 + 0.225148i
\(271\) 8.81854 7.03255i 0.535688 0.427197i −0.317916 0.948119i \(-0.602983\pi\)
0.853604 + 0.520922i \(0.174412\pi\)
\(272\) 30.1591 4.54575i 1.82866 0.275627i
\(273\) 3.38343 + 16.2244i 0.204774 + 0.981945i
\(274\) 8.81653 + 1.32888i 0.532626 + 0.0802804i
\(275\) −22.6560 + 13.0804i −1.36621 + 0.788779i
\(276\) −65.3681 + 17.7797i −3.93470 + 1.07021i
\(277\) −10.2251 26.0531i −0.614365 1.56538i −0.811092 0.584919i \(-0.801126\pi\)
0.196727 0.980458i \(-0.436969\pi\)
\(278\) −4.70361 + 20.6079i −0.282104 + 1.23598i
\(279\) 2.99778 + 2.01092i 0.179473 + 0.120391i
\(280\) 6.77016 0.608400i 0.404594 0.0363588i
\(281\) 0.0100297 + 0.0147108i 0.000598321 + 0.000877575i 0.826538 0.562881i \(-0.190307\pi\)
−0.825939 + 0.563759i \(0.809355\pi\)
\(282\) −14.6401 19.6810i −0.871807 1.17198i
\(283\) 13.7148 1.02778i 0.815258 0.0610952i 0.339428 0.940632i \(-0.389767\pi\)
0.475831 + 0.879537i \(0.342148\pi\)
\(284\) −22.6211 73.3359i −1.34232 4.35169i
\(285\) −0.269442 1.39522i −0.0159604 0.0826460i
\(286\) −15.4272 + 50.0138i −0.912230 + 2.95738i
\(287\) −24.6795 3.34648i −1.45679 0.197536i
\(288\) −59.9173 + 18.9778i −3.53066 + 1.11828i
\(289\) 2.80239 + 12.2781i 0.164847 + 0.722241i
\(290\) 0.803303 0.121078i 0.0471716 0.00710997i
\(291\) 10.5407 + 19.7633i 0.617907 + 1.15855i
\(292\) 31.6238 2.36987i 1.85064 0.138686i
\(293\) 7.32103 + 12.6804i 0.427699 + 0.740797i 0.996668 0.0815621i \(-0.0259909\pi\)
−0.568969 + 0.822359i \(0.692658\pi\)
\(294\) 32.6360 + 5.05208i 1.90337 + 0.294643i
\(295\) 1.28625 2.22785i 0.0748882 0.129710i
\(296\) 8.54175 17.7371i 0.496479 1.03095i
\(297\) −24.2606 + 13.1752i −1.40774 + 0.764503i
\(298\) −0.566844 0.710800i −0.0328364 0.0411756i
\(299\) −24.9418 7.69354i −1.44242 0.444929i
\(300\) −24.7368 39.0410i −1.42818 2.25403i
\(301\) 0.765663 12.7510i 0.0441321 0.734953i
\(302\) −17.5000 18.8606i −1.00701 1.08530i
\(303\) 6.01987 + 6.94212i 0.345833 + 0.398815i
\(304\) 29.3927 31.6778i 1.68579 1.81684i
\(305\) 1.16404 2.41716i 0.0666528 0.138406i
\(306\) 6.38677 + 15.9193i 0.365107 + 0.910045i
\(307\) 0.734650 1.52552i 0.0419287 0.0870658i −0.878952 0.476910i \(-0.841757\pi\)
0.920881 + 0.389844i \(0.127471\pi\)
\(308\) 60.2563 + 46.6085i 3.43342 + 2.65576i
\(309\) −4.85720 25.1516i −0.276316 1.43082i
\(310\) 0.863943 0.266491i 0.0490687 0.0151357i
\(311\) −28.7867 4.33890i −1.63235 0.246037i −0.732030 0.681273i \(-0.761427\pi\)
−0.900316 + 0.435236i \(0.856665\pi\)
\(312\) −56.4102 14.8874i −3.19360 0.842834i
\(313\) 9.84851 + 5.68604i 0.556671 + 0.321394i 0.751808 0.659382i \(-0.229182\pi\)
−0.195137 + 0.980776i \(0.562515\pi\)
\(314\) −36.0137 + 45.1598i −2.03237 + 2.54851i
\(315\) 0.691999 + 2.07730i 0.0389897 + 0.117043i
\(316\) 0.954920 + 1.19743i 0.0537185 + 0.0673608i
\(317\) 1.51172 + 10.0296i 0.0849067 + 0.563319i 0.990322 + 0.138791i \(0.0443218\pi\)
−0.905415 + 0.424528i \(0.860440\pi\)
\(318\) −12.3286 14.2174i −0.691353 0.797269i
\(319\) 4.74617 + 3.23588i 0.265734 + 0.181175i
\(320\) −2.82239 + 7.19133i −0.157776 + 0.402007i
\(321\) 1.70555 15.6678i 0.0951947 0.874489i
\(322\) −31.8217 + 41.1397i −1.77335 + 2.29263i
\(323\) −4.88086 3.89236i −0.271578 0.216577i
\(324\) −25.0208 41.8666i −1.39004 2.32592i
\(325\) 17.8079i 0.987804i
\(326\) −52.2672 + 20.5133i −2.89481 + 1.13613i
\(327\) 0.0394625 + 0.0622818i 0.00218228 + 0.00344419i
\(328\) 49.3872 72.4378i 2.72695 3.99971i
\(329\) −13.2034 3.85931i −0.727927 0.212771i
\(330\) −1.25988 + 6.79882i −0.0693542 + 0.374263i
\(331\) −12.6697 32.2819i −0.696390 1.77437i −0.630021 0.776578i \(-0.716954\pi\)
−0.0663694 0.997795i \(-0.521142\pi\)
\(332\) 40.4253 + 19.4678i 2.21863 + 1.06844i
\(333\) 6.19279 + 1.36443i 0.339363 + 0.0747704i
\(334\) −20.2861 42.1245i −1.11001 2.30495i
\(335\) −0.420780 0.129793i −0.0229896 0.00709137i
\(336\) −38.5366 + 54.3000i −2.10234 + 2.96231i
\(337\) 7.38430 2.27776i 0.402249 0.124077i −0.0870281 0.996206i \(-0.527737\pi\)
0.489277 + 0.872129i \(0.337261\pi\)
\(338\) −0.148085 0.159598i −0.00805478 0.00868098i
\(339\) −23.3588 + 10.2963i −1.26868 + 0.559219i
\(340\) 2.99858 + 0.924941i 0.162621 + 0.0501620i
\(341\) 5.75986 + 2.77380i 0.311914 + 0.150210i
\(342\) 21.1378 + 11.9924i 1.14300 + 0.648473i
\(343\) 16.3124 8.76953i 0.880788 0.473510i
\(344\) 38.9423 + 22.4833i 2.09963 + 1.21222i
\(345\) −3.39056 0.628301i −0.182542 0.0338266i
\(346\) 9.26952 + 9.99017i 0.498333 + 0.537075i
\(347\) 19.2427 + 7.55222i 1.03300 + 0.405424i 0.820446 0.571724i \(-0.193725\pi\)
0.212558 + 0.977148i \(0.431821\pi\)
\(348\) −5.36685 + 8.61318i −0.287693 + 0.461715i
\(349\) 1.97491 2.12845i 0.105714 0.113933i −0.677978 0.735082i \(-0.737143\pi\)
0.783692 + 0.621149i \(0.213334\pi\)
\(350\) −33.2202 12.4729i −1.77569 0.666704i
\(351\) 0.490285 18.7861i 0.0261695 1.00273i
\(352\) −100.286 + 48.2954i −5.34529 + 2.57415i
\(353\) 3.76327 + 3.49181i 0.200299 + 0.185850i 0.773945 0.633253i \(-0.218281\pi\)
−0.573646 + 0.819104i \(0.694471\pi\)
\(354\) 14.6874 + 41.4722i 0.780629 + 2.20422i
\(355\) 0.582240 3.86291i 0.0309021 0.205022i
\(356\) 4.94243 + 65.9522i 0.261948 + 3.49546i
\(357\) 8.23857 + 4.96541i 0.436031 + 0.262798i
\(358\) −0.0497846 + 0.664329i −0.00263120 + 0.0351109i
\(359\) 4.34856 + 0.992531i 0.229508 + 0.0523838i 0.335728 0.941959i \(-0.391018\pi\)
−0.106220 + 0.994343i \(0.533875\pi\)
\(360\) −7.62993 1.09127i −0.402133 0.0575149i
\(361\) 10.1548 0.534464
\(362\) 10.6930 18.5208i 0.562011 0.973431i
\(363\) −23.9425 + 17.8101i −1.25665 + 0.934789i
\(364\) −47.9846 + 19.6583i −2.51508 + 1.03038i
\(365\) 1.50266 + 0.589749i 0.0786526 + 0.0308689i
\(366\) 18.5068 + 41.9855i 0.967364 + 2.19462i
\(367\) −9.93723 0.744692i −0.518719 0.0388726i −0.187201 0.982322i \(-0.559942\pi\)
−0.331518 + 0.943449i \(0.607561\pi\)
\(368\) −45.4990 94.4796i −2.37180 4.92509i
\(369\) 26.3649 + 10.1188i 1.37250 + 0.526763i
\(370\) 1.24175 0.990260i 0.0645554 0.0514812i
\(371\) −10.3224 2.19555i −0.535910 0.113987i
\(372\) −4.47747 + 10.3689i −0.232146 + 0.537604i
\(373\) 2.97336 + 5.15001i 0.153955 + 0.266658i 0.932678 0.360710i \(-0.117466\pi\)
−0.778723 + 0.627368i \(0.784132\pi\)
\(374\) 15.1888 + 26.3078i 0.785394 + 1.36034i
\(375\) −0.548646 4.70974i −0.0283319 0.243210i
\(376\) 32.9362 35.4968i 1.69856 1.83061i
\(377\) −3.52296 + 1.69657i −0.181442 + 0.0873777i
\(378\) −34.7016 14.0727i −1.78486 0.723820i
\(379\) 10.6024 + 5.10587i 0.544611 + 0.262271i 0.685898 0.727698i \(-0.259410\pi\)
−0.141287 + 0.989969i \(0.545124\pi\)
\(380\) 4.13873 1.62433i 0.212312 0.0833264i
\(381\) 14.1002 4.99360i 0.722375 0.255830i
\(382\) −8.16535 + 2.51868i −0.417775 + 0.128867i
\(383\) −21.8282 14.8822i −1.11537 0.760446i −0.142040 0.989861i \(-0.545366\pi\)
−0.973329 + 0.229415i \(0.926319\pi\)
\(384\) −28.0237 52.5431i −1.43008 2.68133i
\(385\) 1.73407 + 3.46835i 0.0883763 + 0.176763i
\(386\) 27.4328 + 6.26137i 1.39630 + 0.318695i
\(387\) −4.16486 + 13.8726i −0.211712 + 0.705182i
\(388\) −54.7916 + 43.6948i −2.78162 + 2.21827i
\(389\) −3.13547 + 10.1649i −0.158975 + 0.515383i −0.999658 0.0261435i \(-0.991677\pi\)
0.840683 + 0.541527i \(0.182154\pi\)
\(390\) −3.57916 3.05671i −0.181238 0.154783i
\(391\) −13.1197 + 7.57464i −0.663489 + 0.383066i
\(392\) 1.93266 + 65.1662i 0.0976141 + 3.29139i
\(393\) −2.10883 0.556549i −0.106377 0.0280742i
\(394\) −4.46695 + 3.04551i −0.225041 + 0.153431i
\(395\) 0.0173480 + 0.0760063i 0.000872870 + 0.00382429i
\(396\) −54.3636 67.1254i −2.73187 3.37318i
\(397\) 24.2097 5.52571i 1.21505 0.277328i 0.433492 0.901158i \(-0.357281\pi\)
0.781560 + 0.623830i \(0.214424\pi\)
\(398\) 15.0957 + 14.0068i 0.756681 + 0.702097i
\(399\) 13.5126 1.77750i 0.676474 0.0889863i
\(400\) 52.4458 48.6626i 2.62229 2.43313i
\(401\) 10.9635 16.0806i 0.547493 0.803025i −0.448374 0.893846i \(-0.647997\pi\)
0.995867 + 0.0908212i \(0.0289492\pi\)
\(402\) 6.36151 4.03073i 0.317283 0.201034i
\(403\) −3.59557 + 2.45142i −0.179108 + 0.122114i
\(404\) −17.9252 + 22.4775i −0.891811 + 1.11830i
\(405\) −0.222836 2.47268i −0.0110728 0.122868i
\(406\) 0.697379 + 7.76030i 0.0346103 + 0.385137i
\(407\) 11.1991 + 0.839259i 0.555120 + 0.0416005i
\(408\) −28.6032 + 18.1233i −1.41607 + 0.897239i
\(409\) −3.65576 + 24.2544i −0.180766 + 1.19930i 0.695877 + 0.718161i \(0.255016\pi\)
−0.876643 + 0.481142i \(0.840222\pi\)
\(410\) 6.12543 3.53652i 0.302513 0.174656i
\(411\) −5.47088 + 1.48804i −0.269859 + 0.0733997i
\(412\) 74.6084 29.2816i 3.67569 1.44260i
\(413\) 20.5896 + 13.5951i 1.01315 + 0.668971i
\(414\) 45.8296 37.1165i 2.25240 1.82418i
\(415\) 1.42401 + 1.78565i 0.0699019 + 0.0876542i
\(416\) 5.66224 75.5574i 0.277614 3.70451i
\(417\) −2.54865 13.1974i −0.124808 0.646281i
\(418\) 40.0652 + 15.7244i 1.95965 + 0.769107i
\(419\) −2.23929 + 5.70562i −0.109396 + 0.278738i −0.975080 0.221854i \(-0.928789\pi\)
0.865683 + 0.500592i \(0.166884\pi\)
\(420\) −5.99621 + 3.31315i −0.292585 + 0.161665i
\(421\) 6.33556 + 16.1427i 0.308776 + 0.786749i 0.998060 + 0.0622576i \(0.0198300\pi\)
−0.689284 + 0.724491i \(0.742075\pi\)
\(422\) 62.4140i 3.03827i
\(423\) 13.5664 + 7.69680i 0.659621 + 0.374231i
\(424\) 23.1624 29.0447i 1.12486 1.41054i
\(425\) −7.57660 7.03006i −0.367519 0.341008i
\(426\) 43.7711 + 50.4768i 2.12071 + 2.44561i
\(427\) 22.4723 + 12.5339i 1.08751 + 0.606559i
\(428\) 49.1733 3.68503i 2.37688 0.178123i
\(429\) −3.85100 33.0582i −0.185928 1.59606i
\(430\) 2.04358 + 2.99739i 0.0985504 + 0.144547i
\(431\) 26.3995 + 6.02552i 1.27162 + 0.290239i 0.804499 0.593954i \(-0.202434\pi\)
0.467121 + 0.884193i \(0.345291\pi\)
\(432\) 56.6665 49.8918i 2.72637 2.40042i
\(433\) −9.05254 + 2.06618i −0.435037 + 0.0992944i −0.434430 0.900705i \(-0.643050\pi\)
−0.000606833 1.00000i \(0.500193\pi\)
\(434\) 2.05468 + 8.42446i 0.0986277 + 0.404387i
\(435\) −0.436361 + 0.276483i −0.0209219 + 0.0132564i
\(436\) −0.169109 + 0.156911i −0.00809887 + 0.00751465i
\(437\) −7.84176 + 19.9805i −0.375122 + 0.955796i
\(438\) −24.3596 + 12.9921i −1.16394 + 0.620786i
\(439\) 1.76275 + 2.58548i 0.0841315 + 0.123398i 0.865998 0.500048i \(-0.166684\pi\)
−0.781866 + 0.623446i \(0.785732\pi\)
\(440\) −13.6502 −0.650747
\(441\) −20.2856 + 5.43088i −0.965981 + 0.258613i
\(442\) −20.6782 −0.983564
\(443\) −6.98743 10.2487i −0.331983 0.486930i 0.623562 0.781774i \(-0.285685\pi\)
−0.955545 + 0.294844i \(0.904732\pi\)
\(444\) −0.667136 + 19.8296i −0.0316609 + 0.941073i
\(445\) −1.22994 + 3.13383i −0.0583046 + 0.148558i
\(446\) 50.2381 46.6142i 2.37885 2.20725i
\(447\) 0.512135 + 0.268207i 0.0242231 + 0.0126857i
\(448\) −67.2261 31.1553i −3.17614 1.47195i
\(449\) 27.1279 6.19177i 1.28025 0.292208i 0.472286 0.881445i \(-0.343429\pi\)
0.807960 + 0.589238i \(0.200572\pi\)
\(450\) 33.4142 + 22.4143i 1.57516 + 1.05662i
\(451\) 48.7595 + 11.1290i 2.29599 + 0.524045i
\(452\) −44.9928 65.9923i −2.11628 3.10402i
\(453\) 15.0201 + 6.48591i 0.705705 + 0.304735i
\(454\) −59.5887 + 4.46556i −2.79664 + 0.209579i
\(455\) −2.63482 0.158214i −0.123522 0.00741721i
\(456\) −15.6749 + 45.3437i −0.734043 + 2.12341i
\(457\) 3.21654 + 2.98452i 0.150464 + 0.139610i 0.751813 0.659376i \(-0.229180\pi\)
−0.601349 + 0.798986i \(0.705370\pi\)
\(458\) −2.44560 + 3.06668i −0.114275 + 0.143297i
\(459\) −7.79925 7.62483i −0.364038 0.355897i
\(460\) 10.7891i 0.503043i
\(461\) −7.49813 19.1049i −0.349223 0.889805i −0.992283 0.123990i \(-0.960431\pi\)
0.643061 0.765815i \(-0.277664\pi\)
\(462\) −64.3665 15.9704i −2.99460 0.743012i
\(463\) −8.59620 + 21.9028i −0.399499 + 1.01791i 0.579668 + 0.814853i \(0.303182\pi\)
−0.979167 + 0.203055i \(0.934913\pi\)
\(464\) −14.6235 5.73932i −0.678881 0.266441i
\(465\) −0.434350 + 0.376647i −0.0201425 + 0.0174666i
\(466\) 2.86805 38.2715i 0.132860 1.77289i
\(467\) −8.21483 10.3011i −0.380137 0.476677i 0.554549 0.832151i \(-0.312891\pi\)
−0.934686 + 0.355474i \(0.884319\pi\)
\(468\) 58.0740 9.20149i 2.68447 0.425339i
\(469\) 1.48452 3.95386i 0.0685488 0.182572i
\(470\) 3.63657 1.42725i 0.167742 0.0658340i
\(471\) 9.37258 35.5138i 0.431866 1.63639i
\(472\) −75.2176 + 43.4269i −3.46217 + 1.99889i
\(473\) −3.82320 + 25.3653i −0.175791 + 1.16630i
\(474\) −1.18116 0.618576i −0.0542524 0.0284121i
\(475\) −14.6032 1.09436i −0.670039 0.0502125i
\(476\) −10.5791 + 28.1763i −0.484892 + 1.29146i
\(477\) 10.8201 + 5.11056i 0.495418 + 0.233996i
\(478\) −7.51339 + 9.42149i −0.343654 + 0.430929i
\(479\) 4.38426 2.98914i 0.200322 0.136577i −0.459005 0.888434i \(-0.651794\pi\)
0.659327 + 0.751857i \(0.270841\pi\)
\(480\) −0.411984 10.0015i −0.0188044 0.456503i
\(481\) −4.30642 + 6.31635i −0.196356 + 0.288001i
\(482\) 11.3416 10.5235i 0.516597 0.479332i
\(483\) 7.96445 32.0995i 0.362395 1.46058i
\(484\) −68.4413 63.5043i −3.11097 2.88656i
\(485\) −3.47787 + 0.793800i −0.157922 + 0.0360446i
\(486\) 34.6326 + 24.5656i 1.57097 + 1.11432i
\(487\) −4.12247 18.0617i −0.186807 0.818455i −0.978286 0.207259i \(-0.933546\pi\)
0.791479 0.611196i \(-0.209311\pi\)
\(488\) −74.8402 + 51.0252i −3.38785 + 2.30980i
\(489\) 25.1513 25.3416i 1.13738 1.14599i
\(490\) −2.14061 + 4.80438i −0.0967029 + 0.217040i
\(491\) 0.142377 0.0822012i 0.00642537 0.00370969i −0.496784 0.867874i \(-0.665486\pi\)
0.503209 + 0.864165i \(0.332152\pi\)
\(492\) −16.0994 + 86.8790i −0.725819 + 3.91681i
\(493\) −0.668939 + 2.16865i −0.0301275 + 0.0976710i
\(494\) −22.9060 + 18.2670i −1.03059 + 0.821869i
\(495\) −1.01068 4.27914i −0.0454269 0.192333i
\(496\) −17.0451 3.89042i −0.765346 0.174685i
\(497\) 36.6482 + 7.79501i 1.64390 + 0.349654i
\(498\) −39.0390 1.31340i −1.74938 0.0588550i
\(499\) −3.01490 2.05553i −0.134966 0.0920180i 0.493955 0.869487i \(-0.335551\pi\)
−0.628921 + 0.777469i \(0.716503\pi\)
\(500\) 14.1765 4.37287i 0.633992 0.195561i
\(501\) 22.6079 + 19.3079i 1.01005 + 0.862612i
\(502\) −47.1028 + 18.4865i −2.10230 + 0.825093i
\(503\) −32.6586 15.7276i −1.45617 0.701257i −0.472520 0.881320i \(-0.656656\pi\)
−0.983655 + 0.180063i \(0.942370\pi\)
\(504\) 14.8340 72.4204i 0.660758 3.22586i
\(505\) −1.31851 + 0.634961i −0.0586730 + 0.0282554i
\(506\) 71.0402 76.5631i 3.15812 3.40365i
\(507\) 0.127100 + 0.0548838i 0.00564470 + 0.00243747i
\(508\) 23.4010 + 40.5317i 1.03825 + 1.79830i
\(509\) 10.3897 + 17.9955i 0.460516 + 0.797637i 0.998987 0.0450075i \(-0.0143312\pi\)
−0.538471 + 0.842644i \(0.680998\pi\)
\(510\) −2.71347 + 0.316097i −0.120155 + 0.0139970i
\(511\) −6.51002 + 14.0472i −0.287987 + 0.621410i
\(512\) 26.3915 21.0466i 1.16635 0.930135i
\(513\) −15.3752 1.55652i −0.678832 0.0687222i
\(514\) −19.6533 40.8104i −0.866869 1.80007i
\(515\) 4.06837 + 0.304882i 0.179274 + 0.0134347i
\(516\) −45.0526 4.90431i −1.98333 0.215900i
\(517\) 25.7142 + 10.0921i 1.13091 + 0.443848i
\(518\) 8.76674 + 12.4576i 0.385188 + 0.547355i
\(519\) −7.95592 3.43549i −0.349226 0.150801i
\(520\) 4.64589 8.04692i 0.203736 0.352881i
\(521\) 42.0022 1.84015 0.920076 0.391740i \(-0.128127\pi\)
0.920076 + 0.391740i \(0.128127\pi\)
\(522\) 1.25087 8.74581i 0.0547490 0.382794i
\(523\) −31.6246 7.21811i −1.38285 0.315626i −0.534546 0.845139i \(-0.679518\pi\)
−0.848302 + 0.529513i \(0.822375\pi\)
\(524\) 0.509964 6.80500i 0.0222779 0.297278i
\(525\) 22.5288 1.26279i 0.983237 0.0551125i
\(526\) −3.27511 43.7033i −0.142801 1.90555i
\(527\) −0.376443 + 2.49753i −0.0163981 + 0.108794i
\(528\) 86.8358 101.678i 3.77904 4.42495i
\(529\) 21.3218 + 19.7837i 0.927034 + 0.860161i
\(530\) 2.70029 1.30039i 0.117293 0.0564853i
\(531\) −19.1830 20.3643i −0.832470 0.883734i
\(532\) 13.1718 + 40.5573i 0.571070 + 1.75838i
\(533\) −23.1561 + 24.9564i −1.00300 + 1.08098i
\(534\) −27.0954 50.8025i −1.17253 2.19844i
\(535\) 2.33655 + 0.917030i 0.101018 + 0.0396467i
\(536\) 10.1122 + 10.8983i 0.436779 + 0.470736i
\(537\) −0.141420 0.399320i −0.00610271 0.0172319i
\(538\) −59.4225 34.3076i −2.56189 1.47911i
\(539\) −34.2023 + 14.6078i −1.47320 + 0.629203i
\(540\) 7.48002 2.09520i 0.321889 0.0901629i
\(541\) 23.3825 + 11.2604i 1.00529 + 0.484122i 0.862731 0.505664i \(-0.168752\pi\)
0.142560 + 0.989786i \(0.454467\pi\)
\(542\) −29.3581 9.05578i −1.26104 0.388979i
\(543\) −1.47167 + 13.5192i −0.0631552 + 0.580164i
\(544\) −29.9116 32.2370i −1.28245 1.38215i
\(545\) −0.0112211 + 0.00346126i −0.000480660 + 0.000148264i
\(546\) 31.3221 32.5091i 1.34046 1.39126i
\(547\) 29.1142 + 8.98053i 1.24483 + 0.383980i 0.846068 0.533074i \(-0.178963\pi\)
0.398763 + 0.917054i \(0.369440\pi\)
\(548\) −7.69679 15.9825i −0.328790 0.682740i
\(549\) −21.5370 19.6833i −0.919175 0.840065i
\(550\) 64.2011 + 30.9176i 2.73754 + 1.31833i
\(551\) 1.17475 + 2.99323i 0.0500462 + 0.127516i
\(552\) 88.5308 + 75.6079i 3.76812 + 3.21809i
\(553\) −0.737646 + 0.122392i −0.0313679 + 0.00520462i
\(554\) −42.9442 + 62.9875i −1.82452 + 2.67608i
\(555\) −0.468549 + 0.894685i −0.0198888 + 0.0379772i
\(556\) 39.1482 15.3645i 1.66025 0.651602i
\(557\) 17.3412i 0.734772i −0.930069 0.367386i \(-0.880253\pi\)
0.930069 0.367386i \(-0.119747\pi\)
\(558\) −0.0741201 9.83217i −0.00313775 0.416229i
\(559\) −13.6518 10.8870i −0.577411 0.460470i
\(560\) −6.73407 8.19213i −0.284567 0.346181i
\(561\) −15.5853 11.4120i −0.658012 0.481814i
\(562\) 0.0177179 0.0451444i 0.000747383 0.00190430i
\(563\) −8.63055 5.88421i −0.363734 0.247990i 0.367637 0.929969i \(-0.380167\pi\)
−0.731371 + 0.681979i \(0.761119\pi\)
\(564\) −15.9447 + 46.1242i −0.671392 + 1.94218i
\(565\) −0.605950 4.02021i −0.0254925 0.169132i
\(566\) −23.3569 29.2886i −0.981763 1.23109i
\(567\) 23.8011 0.711892i 0.999553 0.0298967i
\(568\) −82.2349 + 103.119i −3.45050 + 4.32679i
\(569\) 20.7003 + 11.9513i 0.867801 + 0.501025i 0.866617 0.498974i \(-0.166290\pi\)
0.00118441 + 0.999999i \(0.499623\pi\)
\(570\) −2.72658 + 2.74721i −0.114204 + 0.115068i
\(571\) 18.5534 + 2.79648i 0.776437 + 0.117029i 0.525294 0.850921i \(-0.323955\pi\)
0.251143 + 0.967950i \(0.419193\pi\)
\(572\) 99.5062 30.6936i 4.16057 1.28336i
\(573\) 4.10515 3.55979i 0.171495 0.148712i
\(574\) 30.3367 + 60.6770i 1.26623 + 2.53261i
\(575\) −15.4186 + 32.0170i −0.643000 + 1.33520i
\(576\) 66.0788 + 51.8861i 2.75329 + 2.16192i
\(577\) 9.88102 20.5182i 0.411352 0.854182i −0.587632 0.809128i \(-0.699940\pi\)
0.998985 0.0450537i \(-0.0143459\pi\)
\(578\) 23.3323 25.1463i 0.970498 1.04595i
\(579\) −17.5682 + 3.39272i −0.730109 + 0.140997i
\(580\) −1.09935 1.18482i −0.0456481 0.0491970i
\(581\) −17.9142 + 12.6067i −0.743206 + 0.523014i
\(582\) 28.3045 54.0469i 1.17326 2.24032i
\(583\) 20.2509 + 6.24658i 0.838707 + 0.258707i
\(584\) −33.9807 42.6105i −1.40613 1.76323i
\(585\) 2.86659 + 0.860614i 0.118519 + 0.0355820i
\(586\) 17.3044 35.9330i 0.714838 1.48438i
\(587\) 2.64388 4.57934i 0.109125 0.189009i −0.806291 0.591519i \(-0.798529\pi\)
0.915416 + 0.402509i \(0.131862\pi\)
\(588\) −28.2725 59.3115i −1.16594 2.44596i
\(589\) 1.78930 + 3.09916i 0.0737268 + 0.127698i
\(590\) −6.98746 + 0.523638i −0.287669 + 0.0215578i
\(591\) 1.81805 2.91777i 0.0747847 0.120021i
\(592\) −30.3701 + 4.57756i −1.24820 + 0.188137i
\(593\) −8.16709 35.7824i −0.335382 1.46941i −0.808547 0.588432i \(-0.799745\pi\)
0.473164 0.880974i \(-0.343112\pi\)
\(594\) 66.8766 + 34.3836i 2.74398 + 1.41077i
\(595\) −1.10747 + 1.05856i −0.0454018 + 0.0433968i
\(596\) −0.533159 + 1.72846i −0.0218390 + 0.0708004i
\(597\) −12.3762 4.27833i −0.506524 0.175100i
\(598\) 20.9559 + 67.9374i 0.856951 + 2.77817i
\(599\) −5.61489 + 0.420778i −0.229418 + 0.0171925i −0.188943 0.981988i \(-0.560506\pi\)
−0.0404751 + 0.999181i \(0.512887\pi\)
\(600\) −31.4889 + 72.9219i −1.28553 + 2.97703i
\(601\) 7.46542 + 10.9498i 0.304521 + 0.446650i 0.947745 0.319027i \(-0.103356\pi\)
−0.643225 + 0.765678i \(0.722404\pi\)
\(602\) −29.8713 + 17.8418i −1.21747 + 0.727178i
\(603\) −2.66775 + 3.97696i −0.108639 + 0.161954i
\(604\) −11.3907 + 49.9060i −0.463482 + 2.03065i
\(605\) −1.73629 4.42399i −0.0705901 0.179861i
\(606\) 6.38668 24.1999i 0.259441 0.983053i
\(607\) −13.2755 + 7.66462i −0.538836 + 0.311097i −0.744607 0.667503i \(-0.767363\pi\)
0.205771 + 0.978600i \(0.434030\pi\)
\(608\) −61.6120 9.28652i −2.49870 0.376618i
\(609\) −2.39615 4.33660i −0.0970970 0.175728i
\(610\) −7.22599 + 1.08914i −0.292572 + 0.0440981i
\(611\) −14.7013 + 11.7239i −0.594750 + 0.474297i
\(612\) 19.0111 28.3408i 0.768478 1.14561i
\(613\) −1.92727 + 0.928124i −0.0778417 + 0.0374866i −0.472400 0.881385i \(-0.656612\pi\)
0.394558 + 0.918871i \(0.370898\pi\)
\(614\) −4.56047 + 0.687381i −0.184046 + 0.0277404i
\(615\) −2.65714 + 3.62884i −0.107146 + 0.146329i
\(616\) 7.84730 130.685i 0.316177 5.26544i
\(617\) −0.460719 + 3.05667i −0.0185479 + 0.123057i −0.996189 0.0872250i \(-0.972200\pi\)
0.977641 + 0.210282i \(0.0674382\pi\)
\(618\) −49.1517 + 49.5237i −1.97717 + 1.99213i
\(619\) −4.19274 2.42068i −0.168521 0.0972954i 0.413368 0.910564i \(-0.364352\pi\)
−0.581888 + 0.813269i \(0.697686\pi\)
\(620\) −1.40636 1.12153i −0.0564806 0.0450418i
\(621\) −17.1471 + 33.3513i −0.688088 + 1.33834i
\(622\) 34.4052 + 71.4432i 1.37952 + 2.86461i
\(623\) −29.2957 13.5768i −1.17371 0.543944i
\(624\) 30.3851 + 85.7970i 1.21638 + 3.43463i
\(625\) −23.5978 3.55680i −0.943912 0.142272i
\(626\) −2.31482 30.8891i −0.0925186 1.23458i
\(627\) −27.3456 + 1.12643i −1.09208 + 0.0449854i
\(628\) 114.600 + 8.58806i 4.57303 + 0.342701i
\(629\) 0.987322 + 4.32574i 0.0393671 + 0.172479i
\(630\) 3.61325 4.74477i 0.143955 0.189036i
\(631\) 1.01169 4.43252i 0.0402749 0.176456i −0.950790 0.309836i \(-0.899726\pi\)
0.991065 + 0.133380i \(0.0425831\pi\)
\(632\) 0.775842 2.51522i 0.0308613 0.100050i
\(633\) −16.0080 36.3167i −0.636262 1.44346i
\(634\) 20.2525 18.7915i 0.804328 0.746307i
\(635\) 0.178032 + 2.37568i 0.00706500 + 0.0942758i
\(636\) −9.55391 + 36.2009i −0.378837 + 1.43546i
\(637\) 3.02944 25.1344i 0.120031 0.995862i
\(638\) 15.6465i 0.619453i
\(639\) −38.4153 18.1444i −1.51969 0.717780i
\(640\) 9.24631 2.11041i 0.365492 0.0834213i
\(641\) −1.12856 7.48750i −0.0445754 0.295739i −1.00000 0.000502869i \(-0.999840\pi\)
0.955424 0.295236i \(-0.0953982\pi\)
\(642\) −37.8779 + 20.2021i −1.49492 + 0.797311i
\(643\) −2.74653 8.90402i −0.108312 0.351140i 0.885149 0.465308i \(-0.154056\pi\)
−0.993462 + 0.114167i \(0.963580\pi\)
\(644\) 103.293 + 6.20248i 4.07031 + 0.244412i
\(645\) −1.95787 1.21994i −0.0770910 0.0480351i
\(646\) −1.27075 + 16.9570i −0.0499969 + 0.667163i
\(647\) −7.06998 + 30.9756i −0.277950 + 1.21778i 0.622431 + 0.782675i \(0.286145\pi\)
−0.900381 + 0.435103i \(0.856712\pi\)
\(648\) −35.2263 + 76.0607i −1.38382 + 2.98795i
\(649\) −38.7373 30.8919i −1.52057 1.21261i
\(650\) −40.0773 + 27.3243i −1.57196 + 1.07175i
\(651\) −3.35626 4.37493i −0.131542 0.171467i
\(652\) 92.3006 + 62.9295i 3.61477 + 2.46451i
\(653\) 2.10713 + 6.83116i 0.0824585 + 0.267324i 0.987408 0.158196i \(-0.0505676\pi\)
−0.904949 + 0.425519i \(0.860091\pi\)
\(654\) 0.0796167 0.184376i 0.00311326 0.00720969i
\(655\) 0.173682 0.300825i 0.00678630 0.0117542i
\(656\) −136.776 −5.34021
\(657\) 10.8418 13.8074i 0.422979 0.538679i
\(658\) 11.5736 + 35.6365i 0.451188 + 1.38925i
\(659\) 2.57192 + 17.0636i 0.100188 + 0.664703i 0.981399 + 0.191980i \(0.0614908\pi\)
−0.881211 + 0.472723i \(0.843271\pi\)
\(660\) 12.5884 5.54882i 0.490002 0.215988i
\(661\) 8.20350 12.0323i 0.319079 0.468003i −0.632870 0.774258i \(-0.718123\pi\)
0.951950 + 0.306254i \(0.0990758\pi\)
\(662\) −53.2114 + 78.0467i −2.06812 + 3.03337i
\(663\) 12.0320 5.30358i 0.467284 0.205974i
\(664\) −11.4928 76.2500i −0.446009 2.95907i
\(665\) −0.291661 + 2.15093i −0.0113101 + 0.0834096i
\(666\) −6.43145 16.0307i −0.249214 0.621176i
\(667\) 7.80292 0.302130
\(668\) −46.5110 + 80.5594i −1.79956 + 3.11694i
\(669\) −17.2763 + 40.0084i −0.667939 + 1.54681i
\(670\) 0.353536 + 1.14613i 0.0136583 + 0.0442790i
\(671\) −42.6935 29.1079i −1.64816 1.12370i
\(672\) 95.9894 + 1.80542i 3.70287 + 0.0696457i
\(673\) 33.9138 23.1220i 1.30728 0.891288i 0.309067 0.951040i \(-0.399983\pi\)
0.998213 + 0.0597522i \(0.0190310\pi\)
\(674\) −16.4566 13.1237i −0.633884 0.505506i
\(675\) −25.1915 4.47205i −0.969621 0.172129i
\(676\) −0.0963883 + 0.422305i −0.00370724 + 0.0162425i
\(677\) −1.28278 + 17.1175i −0.0493012 + 0.657879i 0.916739 + 0.399487i \(0.130812\pi\)
−0.966040 + 0.258392i \(0.916807\pi\)
\(678\) 59.0138 + 36.7713i 2.26641 + 1.41219i
\(679\) −5.60035 33.7529i −0.214922 1.29532i
\(680\) −1.58960 5.15336i −0.0609584 0.197622i
\(681\) 33.5274 17.8817i 1.28477 0.685230i
\(682\) −2.59533 17.2189i −0.0993802 0.659345i
\(683\) 22.7776 5.19883i 0.871559 0.198928i 0.236726 0.971577i \(-0.423926\pi\)
0.634834 + 0.772649i \(0.281069\pi\)
\(684\) −3.97674 48.1884i −0.152054 1.84253i
\(685\) 0.902975i 0.0345009i
\(686\) −44.7658 23.2558i −1.70917 0.887912i
\(687\) 0.636467 2.41165i 0.0242827 0.0920103i
\(688\) −5.24249 69.9561i −0.199868 2.66705i
\(689\) −10.5749 + 9.81206i −0.402871 + 0.373810i
\(690\) 3.78843 + 8.59465i 0.144223 + 0.327193i
\(691\) −6.70674 + 21.7427i −0.255136 + 0.827131i 0.733874 + 0.679285i \(0.237710\pi\)
−0.989010 + 0.147846i \(0.952766\pi\)
\(692\) 6.03350 26.4345i 0.229359 1.00489i
\(693\) 41.5489 7.21612i 1.57831 0.274118i
\(694\) −12.5293 54.8946i −0.475607 2.08377i
\(695\) 2.13474 + 0.159977i 0.0809753 + 0.00606826i
\(696\) 17.4262 0.717828i 0.660539 0.0272092i
\(697\) 1.47662 + 19.7042i 0.0559311 + 0.746348i
\(698\) −7.82043 1.17874i −0.296008 0.0446160i
\(699\) 8.14708 + 23.0045i 0.308151 + 0.870110i
\(700\) 16.7284 + 68.5887i 0.632274 + 2.59241i
\(701\) −0.447358 0.928948i −0.0168965 0.0350859i 0.892350 0.451344i \(-0.149055\pi\)
−0.909246 + 0.416259i \(0.863341\pi\)
\(702\) −43.0311 + 27.7218i −1.62411 + 1.04629i
\(703\) 4.91501 + 3.91959i 0.185373 + 0.147830i
\(704\) 128.858 + 74.3960i 4.85651 + 2.80390i
\(705\) −1.74994 + 1.76318i −0.0659065 + 0.0664052i
\(706\) 2.08411 13.8272i 0.0784367 0.520393i
\(707\) −5.32103 12.9882i −0.200118 0.488473i
\(708\) 51.7135 70.6249i 1.94351 2.65425i
\(709\) −1.82936 + 0.275731i −0.0687029 + 0.0103553i −0.183304 0.983056i \(-0.558679\pi\)
0.114601 + 0.993412i \(0.463441\pi\)
\(710\) −9.58701 + 4.61686i −0.359794 + 0.173268i
\(711\) 0.845930 + 0.0569844i 0.0317249 + 0.00213708i
\(712\) 88.8653 70.8677i 3.33037 2.65588i
\(713\) 8.58704 1.29429i 0.321587 0.0484714i
\(714\) −1.46633 26.1601i −0.0548759 0.979017i
\(715\) 5.24141 + 0.790015i 0.196018 + 0.0295449i
\(716\) 1.14786 0.662720i 0.0428977 0.0247670i
\(717\) 1.95536 7.40910i 0.0730243 0.276698i
\(718\) −4.43867 11.3095i −0.165650 0.422068i
\(719\) 7.02287 30.7692i 0.261909 1.14750i −0.657270 0.753656i \(-0.728289\pi\)
0.919178 0.393842i \(-0.128854\pi\)
\(720\) 5.29878 + 10.7941i 0.197474 + 0.402273i
\(721\) −5.25774 + 38.7747i −0.195808 + 1.44404i
\(722\) −15.5815 22.8538i −0.579882 0.850531i
\(723\) −3.90025 + 9.03219i −0.145052 + 0.335911i
\(724\) −42.4301 + 3.17969i −1.57690 + 0.118172i
\(725\) 1.56916 + 5.08708i 0.0582770 + 0.188929i
\(726\) 76.8195 + 26.5557i 2.85104 + 0.985575i
\(727\) −15.7139 + 50.9433i −0.582797 + 1.88938i −0.147597 + 0.989048i \(0.547154\pi\)
−0.435200 + 0.900334i \(0.643322\pi\)
\(728\) 74.3691 + 49.1051i 2.75630 + 1.81996i
\(729\) −26.4522 5.41128i −0.979711 0.200418i
\(730\) −0.978410 4.28669i −0.0362126 0.158658i
\(731\) −10.0214 + 1.51048i −0.370654 + 0.0558671i
\(732\) 48.2767 77.4787i 1.78436 2.86369i
\(733\) −50.8734 + 3.81244i −1.87905 + 0.140816i −0.964573 0.263816i \(-0.915019\pi\)
−0.914480 + 0.404631i \(0.867400\pi\)
\(734\) 13.5716 + 23.5068i 0.500938 + 0.867650i
\(735\) 0.0133181 3.34454i 0.000491244 0.123365i
\(736\) −75.6000 + 130.943i −2.78665 + 4.82663i
\(737\) −3.67981 + 7.64121i −0.135548 + 0.281467i
\(738\) −17.6814 74.8615i −0.650862 2.75569i
\(739\) −14.4004 18.0575i −0.529725 0.664255i 0.442917 0.896563i \(-0.353944\pi\)
−0.972642 + 0.232308i \(0.925372\pi\)
\(740\) −3.01957 0.931413i −0.111001 0.0342394i
\(741\) 8.64315 16.5039i 0.317514 0.606286i
\(742\) 10.8974 + 26.5997i 0.400055 + 0.976506i
\(743\) −31.4411 33.8854i −1.15346 1.24314i −0.965342 0.260990i \(-0.915951\pi\)
−0.188120 0.982146i \(-0.560239\pi\)
\(744\) 19.0583 3.68049i 0.698712 0.134933i
\(745\) −0.0626259 + 0.0674946i −0.00229443 + 0.00247281i
\(746\) 7.02800 14.5938i 0.257313 0.534317i
\(747\) 23.0523 9.24852i 0.843441 0.338386i
\(748\) 26.2233 54.4532i 0.958818 1.99101i
\(749\) −10.1228 + 21.8426i −0.369877 + 0.798112i
\(750\) −9.75762 + 8.46134i −0.356298 + 0.308964i
\(751\) 33.3882 10.2989i 1.21835 0.375812i 0.382082 0.924128i \(-0.375207\pi\)
0.836271 + 0.548316i \(0.184731\pi\)
\(752\) −74.7012 11.2594i −2.72407 0.410588i
\(753\) 22.6662 22.8377i 0.826000 0.832251i
\(754\) 9.22379 + 5.32536i 0.335911 + 0.193938i
\(755\) −1.62461 + 2.03720i −0.0591257 + 0.0741412i
\(756\) 15.7589 + 72.8170i 0.573147 + 2.64833i
\(757\) 2.04176 + 2.56029i 0.0742091 + 0.0930553i 0.817550 0.575857i \(-0.195332\pi\)
−0.743341 + 0.668912i \(0.766760\pi\)
\(758\) −4.77734 31.6956i −0.173521 1.15124i
\(759\) −21.6990 + 62.7700i −0.787623 + 2.27841i
\(760\) −6.31328 4.30432i −0.229007 0.156134i
\(761\) −13.9715 + 35.5987i −0.506465 + 1.29045i 0.417744 + 0.908565i \(0.362821\pi\)
−0.924209 + 0.381887i \(0.875274\pi\)
\(762\) −32.8735 24.0709i −1.19088 0.871996i
\(763\) −0.0266867 0.109419i −0.000966123 0.00396124i
\(764\) 13.2918 + 10.5999i 0.480881 + 0.383490i
\(765\) 1.49781 0.879881i 0.0541534 0.0318122i
\(766\) 71.9604i 2.60003i
\(767\) 31.3955 12.3218i 1.13362 0.444915i
\(768\) −30.2436 + 57.7494i −1.09132 + 2.08385i
\(769\) 5.39629 7.91491i 0.194595 0.285419i −0.716523 0.697563i \(-0.754268\pi\)
0.911119 + 0.412144i \(0.135220\pi\)
\(770\) 5.14491 9.22439i 0.185410 0.332424i
\(771\) 21.9027 + 18.7056i 0.788806 + 0.673664i
\(772\) −20.4530 52.1135i −0.736120 1.87560i
\(773\) −22.8282 10.9935i −0.821075 0.395409i −0.0243147 0.999704i \(-0.507740\pi\)
−0.796760 + 0.604296i \(0.793455\pi\)
\(774\) 37.6113 11.9128i 1.35191 0.428196i
\(775\) 2.57065 + 5.33800i 0.0923404 + 0.191747i
\(776\) 115.090 + 35.5006i 4.13150 + 1.27440i
\(777\) −8.29621 5.00016i −0.297625 0.179380i
\(778\) 27.6876 8.54051i 0.992650 0.306192i
\(779\) 19.0422 + 20.5226i 0.682257 + 0.735298i
\(780\) −1.01341 + 9.30953i −0.0362860 + 0.333335i
\(781\) −71.8981 22.1776i −2.57272 0.793578i
\(782\) 37.1777 + 17.9038i 1.32947 + 0.640240i
\(783\) 1.51530 + 5.40973i 0.0541523 + 0.193328i
\(784\) 82.3015 59.7614i 2.93934 2.13434i
\(785\) 5.06605 + 2.92489i 0.180815 + 0.104394i
\(786\) 1.98324 + 5.59997i 0.0707398 + 0.199744i
\(787\) −27.5097 29.6484i −0.980613 1.05685i −0.998374 0.0570077i \(-0.981844\pi\)
0.0177603 0.999842i \(-0.494346\pi\)
\(788\) 10.0128 + 3.92974i 0.356692 + 0.139991i
\(789\) 13.1147 + 24.5895i 0.466897 + 0.875409i
\(790\) 0.144437 0.155666i 0.00513883 0.00553834i
\(791\) 38.8372 3.49011i 1.38089 0.124094i
\(792\) −42.6857 + 142.180i −1.51677 + 5.05215i
\(793\) 31.6903 15.2612i 1.12536 0.541942i
\(794\) −49.5830 46.0063i −1.75964 1.63270i
\(795\) −1.23768 + 1.44923i −0.0438961 + 0.0513988i
\(796\) 6.10646 40.5137i 0.216438 1.43597i
\(797\) −2.33783 31.1961i −0.0828100 1.10502i −0.871554 0.490300i \(-0.836887\pi\)
0.788744 0.614722i \(-0.210732\pi\)
\(798\) −24.7339 27.6832i −0.875570 0.979973i
\(799\) −0.815576 + 10.8831i −0.0288530 + 0.385017i
\(800\) −100.571 22.9547i −3.55572 0.811569i
\(801\) 28.7958 + 22.6109i 1.01745 + 0.798915i
\(802\) −53.0123 −1.87193
\(803\) 15.5453 26.9253i 0.548583 0.950174i
\(804\) −13.7558 5.93996i −0.485128 0.209486i
\(805\) 4.60020 + 2.56576i 0.162136 + 0.0904312i
\(806\) 11.0340 + 4.33053i 0.388657 + 0.152537i
\(807\) 43.3752 + 4.72172i 1.52688 + 0.166212i
\(808\) 49.2711 + 3.69236i 1.73335 + 0.129897i
\(809\) −13.2344 27.4815i −0.465296 0.966198i −0.993148 0.116861i \(-0.962717\pi\)
0.527852 0.849336i \(-0.322998\pi\)
\(810\) −5.22293 + 4.29555i −0.183515 + 0.150930i
\(811\) −17.3439 + 13.8313i −0.609028 + 0.485684i −0.878768 0.477250i \(-0.841634\pi\)
0.269740 + 0.962933i \(0.413062\pi\)
\(812\) 11.9753 9.84390i 0.420250 0.345453i
\(813\) 19.4052 2.26054i 0.680569 0.0792806i
\(814\) −15.2951 26.4918i −0.536092 0.928538i
\(815\) 2.84321 + 4.92458i 0.0995931 + 0.172500i
\(816\) 48.4986 + 20.9425i 1.69779 + 0.733134i
\(817\) −9.76670 + 10.5260i −0.341694 + 0.368258i
\(818\) 60.1949 28.9883i 2.10466 1.01355i
\(819\) −9.88734 + 26.9495i −0.345492 + 0.941692i
\(820\) −12.6787 6.10576i −0.442761 0.213223i
\(821\) −28.3700 + 11.1344i −0.990121 + 0.388594i −0.804451 0.594019i \(-0.797541\pi\)
−0.185669 + 0.982612i \(0.559445\pi\)
\(822\) 11.7434 + 10.0292i 0.409597 + 0.349808i
\(823\) 47.4464 14.6353i 1.65388 0.510154i 0.679235 0.733921i \(-0.262312\pi\)
0.974643 + 0.223767i \(0.0718356\pi\)
\(824\) −113.809 77.5936i −3.96472 2.70310i
\(825\) −45.2863 1.52359i −1.57667 0.0530444i
\(826\) −0.996239 67.1979i −0.0346636 2.33811i
\(827\) −1.99796 0.456020i −0.0694757 0.0158574i 0.187642 0.982238i \(-0.439916\pi\)
−0.257117 + 0.966380i \(0.582773\pi\)
\(828\) −112.379 33.7387i −3.90544 1.17250i
\(829\) 17.8283 14.2176i 0.619204 0.493799i −0.262919 0.964818i \(-0.584685\pi\)
0.882123 + 0.471019i \(0.156114\pi\)
\(830\) 1.83369 5.94467i 0.0636483 0.206343i
\(831\) 8.83270 47.6647i 0.306403 1.65347i
\(832\) −87.7143 + 50.6419i −3.04095 + 1.75569i
\(833\) −9.49783 11.2113i −0.329080 0.388448i
\(834\) −25.7907 + 25.9859i −0.893059 + 0.899817i
\(835\) −3.91229 + 2.66735i −0.135390 + 0.0923075i
\(836\) −19.0550 83.4852i −0.659030 2.88740i
\(837\) 2.56489 + 5.70201i 0.0886556 + 0.197090i
\(838\) 16.2767 3.71504i 0.562268 0.128334i
\(839\) 28.6938 + 26.6240i 0.990622 + 0.919163i 0.996729 0.0808187i \(-0.0257535\pi\)
−0.00610711 + 0.999981i \(0.501944\pi\)
\(840\) 10.5096 + 5.30691i 0.362617 + 0.183106i
\(841\) −20.4016 + 18.9299i −0.703504 + 0.652756i
\(842\) 26.6086 39.0277i 0.916994 1.34498i
\(843\) 0.00126923 + 0.0308123i 4.37147e−5 + 0.00106123i
\(844\) 102.600 69.9517i 3.53165 2.40784i
\(845\) −0.0137474 + 0.0172388i −0.000472927 + 0.000593031i
\(846\) −3.49423 42.3416i −0.120134 1.45573i
\(847\) 43.3528 14.0797i 1.48962 0.483783i
\(848\) −57.7948 4.33112i −1.98468 0.148731i
\(849\) 21.1026 + 11.0515i 0.724238 + 0.379286i
\(850\) −4.19595 + 27.8383i −0.143920 + 0.954845i
\(851\) 13.2115 7.62763i 0.452883 0.261472i
\(852\) 33.9199 128.527i 1.16208 4.40325i
\(853\) −46.4083 + 18.2139i −1.58899 + 0.623632i −0.984875 0.173266i \(-0.944568\pi\)
−0.604114 + 0.796898i \(0.706473\pi\)
\(854\) −6.27317 69.8067i −0.214664 2.38874i
\(855\) 0.881899 2.29783i 0.0301603 0.0785840i
\(856\) −52.8383 66.2571i −1.80598 2.26462i
\(857\) 3.58754 47.8724i 0.122548 1.63529i −0.509578 0.860424i \(-0.670199\pi\)
0.632126 0.774865i \(-0.282182\pi\)
\(858\) −68.4897 + 59.3910i −2.33820 + 2.02757i
\(859\) 4.56689 + 1.79237i 0.155820 + 0.0611549i 0.441969 0.897030i \(-0.354280\pi\)
−0.286149 + 0.958185i \(0.592375\pi\)
\(860\) 2.63692 6.71875i 0.0899181 0.229108i
\(861\) −33.2144 27.5252i −1.13194 0.938056i
\(862\) −26.9465 68.6586i −0.917802 2.33852i
\(863\) 30.7572i 1.04699i 0.852030 + 0.523494i \(0.175372\pi\)
−0.852030 + 0.523494i \(0.824628\pi\)
\(864\) −105.463 26.9845i −3.58794 0.918031i
\(865\) 0.860533 1.07907i 0.0292590 0.0366896i
\(866\) 18.5402 + 17.2028i 0.630020 + 0.584573i
\(867\) −7.12678 + 20.6161i −0.242038 + 0.700160i
\(868\) 11.5459 12.8195i 0.391892 0.435122i
\(869\) 1.49735 0.112211i 0.0507940 0.00380649i
\(870\) 1.29179 + 0.557814i 0.0437956 + 0.0189117i
\(871\) −3.25213 4.77000i −0.110194 0.161625i
\(872\) 0.386527 + 0.0882222i 0.0130894 + 0.00298758i
\(873\) −2.60747 + 38.7077i −0.0882495 + 1.31006i
\(874\) 56.9992 13.0097i 1.92803 0.440059i
\(875\) −1.50684 + 7.08442i −0.0509407 + 0.239497i
\(876\) 48.6587 + 25.4827i 1.64402 + 0.860980i
\(877\) −30.7601 + 28.5412i −1.03869 + 0.963768i −0.999371 0.0354589i \(-0.988711\pi\)
−0.0393233 + 0.999227i \(0.512520\pi\)
\(878\) 3.11397 7.93427i 0.105092 0.267769i
\(879\) −0.852741 + 25.3465i −0.0287622 + 0.854915i
\(880\) 11.9962 + 17.5952i 0.404393 + 0.593136i
\(881\) 4.31610 0.145413 0.0727065 0.997353i \(-0.476836\pi\)
0.0727065 + 0.997353i \(0.476836\pi\)
\(882\) 43.3485 + 37.3204i 1.45962 + 1.25664i
\(883\) −6.90351 −0.232322 −0.116161 0.993230i \(-0.537059\pi\)
−0.116161 + 0.993230i \(0.537059\pi\)
\(884\) 23.1755 + 33.9922i 0.779477 + 1.14328i
\(885\) 3.93147 2.09684i 0.132155 0.0704845i
\(886\) −12.3436 + 31.4510i −0.414691 + 1.05662i
\(887\) −23.7906 + 22.0744i −0.798810 + 0.741187i −0.969752 0.244094i \(-0.921509\pi\)
0.170942 + 0.985281i \(0.445319\pi\)
\(888\) 28.8034 18.2501i 0.966578 0.612435i
\(889\) −22.8467 + 0.338712i −0.766254 + 0.0113601i
\(890\) 8.94001 2.04050i 0.299670 0.0683977i
\(891\) −47.7320 2.85410i −1.59908 0.0956158i
\(892\) −132.933 30.3410i −4.45092 1.01589i
\(893\) 8.71059 + 12.7761i 0.291489 + 0.427536i
\(894\) −0.182206 1.56411i −0.00609388 0.0523118i
\(895\) 0.0672796 0.00504191i 0.00224891 0.000168532i
\(896\) 14.8892 + 89.7360i 0.497412 + 2.99787i
\(897\) −29.6182 34.1558i −0.988924 1.14043i
\(898\) −55.5597 51.5518i −1.85405 1.72031i
\(899\) 0.811118 1.01711i 0.0270523 0.0339225i
\(900\) −0.603457 80.0498i −0.0201152 2.66833i
\(901\) 8.37275i 0.278937i
\(902\) −49.7698 126.811i −1.65715 4.22235i
\(903\) 12.8051 18.0430i 0.426126 0.600433i
\(904\) −50.1487 + 127.777i −1.66792 + 4.24979i
\(905\) −2.01614 0.791275i −0.0670186 0.0263029i
\(906\) −8.44988 43.7552i −0.280728 1.45367i
\(907\) 0.0732061 0.976868i 0.00243077 0.0324364i −0.995857 0.0909384i \(-0.971013\pi\)
0.998287 + 0.0585020i \(0.0186324\pi\)
\(908\) 74.1260 + 92.9510i 2.45996 + 3.08469i
\(909\) 2.49062 + 15.7192i 0.0826085 + 0.521372i
\(910\) 3.68678 + 6.17253i 0.122216 + 0.204617i
\(911\) 14.3803 5.64384i 0.476440 0.186989i −0.114956 0.993371i \(-0.536673\pi\)
0.591395 + 0.806382i \(0.298577\pi\)
\(912\) 72.2241 19.6445i 2.39158 0.650493i
\(913\) 38.0956 21.9945i 1.26078 0.727913i
\(914\) 1.78133 11.8184i 0.0589213 0.390917i
\(915\) 3.92522 2.48707i 0.129764 0.0822199i
\(916\) 7.78217 + 0.583193i 0.257130 + 0.0192692i
\(917\) 2.78021 + 1.83574i 0.0918105 + 0.0606215i
\(918\) −5.19288 + 29.2520i −0.171391 + 0.965459i
\(919\) −22.0251 + 27.6186i −0.726540 + 0.911052i −0.998688 0.0512030i \(-0.983694\pi\)
0.272148 + 0.962255i \(0.412266\pi\)
\(920\) −15.3202 + 10.4451i −0.505091 + 0.344365i
\(921\) 2.47729 1.56964i 0.0816295 0.0517214i
\(922\) −31.4913 + 46.1893i −1.03711 + 1.52116i
\(923\) 37.5447 34.8364i 1.23580 1.14665i
\(924\) 45.8867 + 123.709i 1.50956 + 4.06973i
\(925\) 7.62961 + 7.07924i 0.250860 + 0.232764i
\(926\) 62.4830 14.2613i 2.05332 0.468656i
\(927\) 15.8979 41.4227i 0.522156 1.36050i
\(928\) 5.04030 + 22.0830i 0.165456 + 0.724910i
\(929\) −24.6663 + 16.8172i −0.809276 + 0.551755i −0.895781 0.444496i \(-0.853383\pi\)
0.0865047 + 0.996251i \(0.472430\pi\)
\(930\) 1.51412 + 0.399597i 0.0496500 + 0.0131033i
\(931\) −20.4250 4.02886i −0.669404 0.132040i
\(932\) −66.1275 + 38.1788i −2.16608 + 1.25059i
\(933\) −38.3431 32.7462i −1.25530 1.07206i
\(934\) −10.5782 + 34.2937i −0.346129 + 1.12212i
\(935\) 2.40528 1.91815i 0.0786612 0.0627302i
\(936\) −69.2884 73.5552i −2.26476 2.40423i
\(937\) −0.340078 0.0776205i −0.0111099 0.00253575i 0.216962 0.976180i \(-0.430385\pi\)
−0.228072 + 0.973644i \(0.573242\pi\)
\(938\) −11.1762 + 2.72580i −0.364914 + 0.0890005i
\(939\) 9.26938 + 17.3796i 0.302495 + 0.567163i
\(940\) −6.42196 4.37841i −0.209461 0.142808i
\(941\) 27.8511 8.59093i 0.907920 0.280056i 0.194590 0.980885i \(-0.437662\pi\)
0.713330 + 0.700828i \(0.247186\pi\)
\(942\) −94.3065 + 33.3988i −3.07267 + 1.08819i
\(943\) 63.2407 24.8201i 2.05940 0.808255i
\(944\) 122.081 + 58.7914i 3.97341 + 1.91350i
\(945\) −0.885491 + 3.68755i −0.0288050 + 0.119956i
\(946\) 62.9518 30.3160i 2.04674 0.985658i
\(947\) −35.8827 + 38.6724i −1.16603 + 1.25668i −0.205456 + 0.978666i \(0.565868\pi\)
−0.960576 + 0.278018i \(0.910323\pi\)
\(948\) 0.306949 + 2.63494i 0.00996924 + 0.0855790i
\(949\) 10.5818 + 18.3283i 0.343501 + 0.594961i
\(950\) 19.9441 + 34.5441i 0.647071 + 1.12076i
\(951\) −6.96457 + 16.1286i −0.225842 + 0.523004i
\(952\) 50.2513 12.2560i 1.62865 0.397219i
\(953\) −29.8484 + 23.8033i −0.966886 + 0.771066i −0.973447 0.228913i \(-0.926483\pi\)
0.00656131 + 0.999978i \(0.497911\pi\)
\(954\) −5.10074 32.1926i −0.165142 1.04227i
\(955\) 0.375478 + 0.779688i 0.0121502 + 0.0252301i
\(956\) 23.9084 + 1.79169i 0.773254 + 0.0579474i
\(957\) 4.01304 + 9.10421i 0.129723 + 0.294297i
\(958\) −13.4544 5.28044i −0.434690 0.170603i
\(959\) 8.64494 + 0.519107i 0.279160 + 0.0167628i
\(960\) −10.7361 + 7.98626i −0.346505 + 0.257755i
\(961\) −14.7761 + 25.5929i −0.476648 + 0.825578i
\(962\) 20.8229 0.671358
\(963\) 16.8584 21.4699i 0.543256 0.691857i
\(964\) −30.0106 6.84971i −0.966575 0.220614i
\(965\) 0.212958 2.84173i 0.00685536 0.0914785i
\(966\) −84.4618 + 31.3289i −2.71751 + 1.00799i
\(967\) 0.609217 + 8.12944i 0.0195911 + 0.261425i 0.998395 + 0.0566273i \(0.0180347\pi\)
−0.978804 + 0.204798i \(0.934346\pi\)
\(968\) −23.9148 + 158.664i −0.768651 + 5.09967i
\(969\) −3.60973 10.1926i −0.115961 0.327434i
\(970\) 7.12289 + 6.60907i 0.228702 + 0.212205i
\(971\) −10.8616 + 5.23068i −0.348566 + 0.167861i −0.599972 0.800021i \(-0.704821\pi\)
0.251406 + 0.967882i \(0.419107\pi\)
\(972\) 1.56731 84.4637i 0.0502716 2.70917i
\(973\) −2.75882 + 20.3457i −0.0884437 + 0.652253i
\(974\) −34.3231 + 36.9916i −1.09978 + 1.18529i
\(975\) 16.3115 26.1782i 0.522387 0.838372i
\(976\) 131.544 + 51.6272i 4.21062 + 1.65255i
\(977\) 0.858277 + 0.925002i 0.0274587 + 0.0295934i 0.746632 0.665237i \(-0.231670\pi\)
−0.719173 + 0.694831i \(0.755479\pi\)
\(978\) −95.6241 17.7200i −3.05772 0.566623i
\(979\) 56.1535 + 32.4202i 1.79467 + 1.03615i
\(980\) 10.2969 1.86573i 0.328922 0.0595984i
\(981\) 0.000962691 0.127703i 3.07364e−5 0.00407724i
\(982\) −0.403459 0.194295i −0.0128749 0.00620021i
\(983\) 50.3131 + 15.5196i 1.60474 + 0.494997i 0.962449 0.271464i \(-0.0875077\pi\)
0.642291 + 0.766460i \(0.277984\pi\)
\(984\) 138.952 61.2485i 4.42962 1.95253i
\(985\) 0.372413 + 0.401365i 0.0118661 + 0.0127886i
\(986\) 5.90704 1.82208i 0.188118 0.0580269i
\(987\) −15.8744 17.7673i −0.505288 0.565538i
\(988\) 55.7008 + 17.1814i 1.77208 + 0.546614i
\(989\) 15.1186 + 31.3940i 0.480742 + 0.998272i
\(990\) −8.07959 + 8.84046i −0.256786 + 0.280968i
\(991\) −39.3569 18.9533i −1.25021 0.602071i −0.312644 0.949870i \(-0.601215\pi\)
−0.937569 + 0.347800i \(0.886929\pi\)
\(992\) 9.20976 + 23.4661i 0.292410 + 0.745049i
\(993\) 10.9444 59.0605i 0.347311 1.87423i
\(994\) −38.6897 94.4387i −1.22716 2.99541i
\(995\) 1.17483 1.72316i 0.0372446 0.0546278i
\(996\) 41.5946 + 65.6468i 1.31797 + 2.08010i
\(997\) 29.9912 11.7707i 0.949831 0.372781i 0.160698 0.987004i \(-0.448625\pi\)
0.789133 + 0.614222i \(0.210530\pi\)
\(998\) 9.93914i 0.314618i
\(999\) 7.85382 + 7.67818i 0.248484 + 0.242927i
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 441.2.bh.a.20.2 648
9.5 odd 6 inner 441.2.bh.a.167.2 yes 648
49.27 odd 14 inner 441.2.bh.a.272.2 yes 648
441.419 even 42 inner 441.2.bh.a.419.2 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.bh.a.20.2 648 1.1 even 1 trivial
441.2.bh.a.167.2 yes 648 9.5 odd 6 inner
441.2.bh.a.272.2 yes 648 49.27 odd 14 inner
441.2.bh.a.419.2 yes 648 441.419 even 42 inner