Properties

Label 414.2.m.a.13.7
Level $414$
Weight $2$
Character 414.13
Analytic conductor $3.306$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 13.7
Character \(\chi\) \(=\) 414.13
Dual form 414.2.m.a.223.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.327068 - 0.945001i) q^{2} +(0.240116 - 1.71533i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-2.36816 - 3.32562i) q^{5} +(-1.54245 - 0.787938i) q^{6} +(0.386739 + 1.59416i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-2.88469 - 0.823754i) q^{9} +O(q^{10})\) \(q+(0.327068 - 0.945001i) q^{2} +(0.240116 - 1.71533i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-2.36816 - 3.32562i) q^{5} +(-1.54245 - 0.787938i) q^{6} +(0.386739 + 1.59416i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-2.88469 - 0.823754i) q^{9} +(-3.91726 + 1.15021i) q^{10} +(2.77764 + 0.535347i) q^{11} +(-1.24909 + 1.19991i) q^{12} +(-0.250690 + 1.03336i) q^{13} +(1.63297 + 0.155930i) q^{14} +(-6.27315 + 3.26364i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-0.904404 - 6.29027i) q^{17} +(-1.72194 + 2.45661i) q^{18} +(-0.153662 + 1.06874i) q^{19} +(-0.194260 + 4.07801i) q^{20} +(2.82737 - 0.280600i) q^{21} +(1.41438 - 2.44978i) q^{22} +(1.20904 + 4.64093i) q^{23} +(0.725377 + 1.57284i) q^{24} +(-3.81620 + 11.0262i) q^{25} +(0.894530 + 0.574880i) q^{26} +(-2.10567 + 4.75039i) q^{27} +(0.681447 - 1.49216i) q^{28} +(2.29217 - 1.80258i) q^{29} +(1.03239 + 6.99556i) q^{30} +(-0.476850 - 10.0103i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(1.58525 - 4.63602i) q^{33} +(-6.24011 - 1.20268i) q^{34} +(4.38570 - 5.06137i) q^{35} +(1.75831 + 2.43071i) q^{36} +(-1.72029 - 3.76692i) q^{37} +(0.959703 + 0.494761i) q^{38} +(1.71235 + 0.678140i) q^{39} +(3.79019 + 1.51736i) q^{40} +(-4.77712 - 6.70853i) q^{41} +(0.659573 - 2.76364i) q^{42} +(-0.235846 + 4.95101i) q^{43} +(-1.85245 - 2.13784i) q^{44} +(4.09192 + 11.5442i) q^{45} +(4.78112 + 0.375355i) q^{46} +(-3.65989 - 6.33912i) q^{47} +(1.72358 - 0.171056i) q^{48} +(3.83007 - 1.97454i) q^{49} +(9.17160 + 7.21263i) q^{50} +(-11.0070 + 0.0409542i) q^{51} +(0.835834 - 0.657307i) q^{52} +(2.55140 + 0.749160i) q^{53} +(3.80042 + 3.54356i) q^{54} +(-4.79755 - 10.5052i) q^{55} +(-1.18721 - 1.13201i) q^{56} +(1.79634 + 0.520202i) q^{57} +(-0.953746 - 2.75567i) q^{58} +(-1.22263 + 5.03976i) q^{59} +(6.94848 + 1.31241i) q^{60} +(-6.76530 - 3.48775i) q^{61} +(-9.61571 - 2.82343i) q^{62} +(0.197575 - 4.91723i) q^{63} +(0.415415 - 0.909632i) q^{64} +(4.03022 - 1.61346i) q^{65} +(-3.86256 - 3.01436i) q^{66} +(13.0791 - 2.52078i) q^{67} +(-3.17747 + 5.50355i) q^{68} +(8.25102 - 0.959538i) q^{69} +(-3.34858 - 5.79991i) q^{70} +(-3.61339 - 4.17007i) q^{71} +(2.87211 - 0.866594i) q^{72} +(-0.639331 + 4.44665i) q^{73} +(-4.12239 + 0.393641i) q^{74} +(17.9972 + 9.19359i) q^{75} +(0.781438 - 0.745099i) q^{76} +(0.220795 + 4.63505i) q^{77} +(1.20090 - 1.39637i) q^{78} +(-2.67592 - 2.55148i) q^{79} +(2.67356 - 3.08545i) q^{80} +(7.64286 + 4.75255i) q^{81} +(-7.90200 + 2.32024i) q^{82} +(7.89513 - 11.0872i) q^{83} +(-2.39592 - 1.52720i) q^{84} +(-18.7772 + 17.9041i) q^{85} +(4.60157 + 1.84219i) q^{86} +(-2.54163 - 4.36464i) q^{87} +(-2.62613 + 1.05135i) q^{88} +(10.2212 + 6.56878i) q^{89} +(12.2476 - 0.0911412i) q^{90} -1.74429 q^{91} +(1.91846 - 4.39540i) q^{92} +(-17.2854 - 1.58568i) q^{93} +(-7.18751 + 1.38528i) q^{94} +(3.91812 - 2.01993i) q^{95} +(0.402081 - 1.68473i) q^{96} +(0.740467 - 0.0707061i) q^{97} +(-0.613247 - 4.26523i) q^{98} +(-7.57164 - 3.83241i) 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 \(\left(\mathbb{Z}/414\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(235\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.327068 0.945001i 0.231272 0.668216i
\(3\) 0.240116 1.71533i 0.138631 0.990344i
\(4\) −0.786053 0.618159i −0.393027 0.309079i
\(5\) −2.36816 3.32562i −1.05907 1.48726i −0.862024 0.506868i \(-0.830803\pi\)
−0.197050 0.980393i \(-0.563136\pi\)
\(6\) −1.54245 0.787938i −0.629703 0.321674i
\(7\) 0.386739 + 1.59416i 0.146174 + 0.602536i 0.997022 + 0.0771238i \(0.0245737\pi\)
−0.850848 + 0.525412i \(0.823911\pi\)
\(8\) −0.841254 + 0.540641i −0.297428 + 0.191145i
\(9\) −2.88469 0.823754i −0.961563 0.274585i
\(10\) −3.91726 + 1.15021i −1.23875 + 0.363729i
\(11\) 2.77764 + 0.535347i 0.837491 + 0.161413i 0.589925 0.807458i \(-0.299157\pi\)
0.247566 + 0.968871i \(0.420369\pi\)
\(12\) −1.24909 + 1.19991i −0.360581 + 0.346384i
\(13\) −0.250690 + 1.03336i −0.0695288 + 0.286602i −0.995953 0.0898810i \(-0.971351\pi\)
0.926424 + 0.376482i \(0.122866\pi\)
\(14\) 1.63297 + 0.155930i 0.436430 + 0.0416740i
\(15\) −6.27315 + 3.26364i −1.61972 + 0.842667i
\(16\) 0.235759 + 0.971812i 0.0589397 + 0.242953i
\(17\) −0.904404 6.29027i −0.219350 1.52561i −0.740446 0.672116i \(-0.765386\pi\)
0.521096 0.853498i \(-0.325523\pi\)
\(18\) −1.72194 + 2.45661i −0.405865 + 0.579028i
\(19\) −0.153662 + 1.06874i −0.0352524 + 0.245186i −0.999827 0.0186262i \(-0.994071\pi\)
0.964574 + 0.263812i \(0.0849799\pi\)
\(20\) −0.194260 + 4.07801i −0.0434378 + 0.911871i
\(21\) 2.82737 0.280600i 0.616982 0.0612320i
\(22\) 1.41438 2.44978i 0.301547 0.522295i
\(23\) 1.20904 + 4.64093i 0.252102 + 0.967701i
\(24\) 0.725377 + 1.57284i 0.148067 + 0.321055i
\(25\) −3.81620 + 11.0262i −0.763240 + 2.20524i
\(26\) 0.894530 + 0.574880i 0.175432 + 0.112743i
\(27\) −2.10567 + 4.75039i −0.405236 + 0.914212i
\(28\) 0.681447 1.49216i 0.128781 0.281992i
\(29\) 2.29217 1.80258i 0.425645 0.334731i −0.382248 0.924060i \(-0.624850\pi\)
0.807893 + 0.589329i \(0.200608\pi\)
\(30\) 1.03239 + 6.99556i 0.188488 + 1.27721i
\(31\) −0.476850 10.0103i −0.0856448 1.79790i −0.478277 0.878209i \(-0.658738\pi\)
0.392632 0.919696i \(-0.371565\pi\)
\(32\) 0.995472 + 0.0950560i 0.175976 + 0.0168037i
\(33\) 1.58525 4.63602i 0.275957 0.807027i
\(34\) −6.24011 1.20268i −1.07017 0.206258i
\(35\) 4.38570 5.06137i 0.741319 0.855528i
\(36\) 1.75831 + 2.43071i 0.293051 + 0.405118i
\(37\) −1.72029 3.76692i −0.282814 0.619277i 0.713902 0.700245i \(-0.246926\pi\)
−0.996717 + 0.0809682i \(0.974199\pi\)
\(38\) 0.959703 + 0.494761i 0.155684 + 0.0802609i
\(39\) 1.71235 + 0.678140i 0.274195 + 0.108589i
\(40\) 3.79019 + 1.51736i 0.599281 + 0.239916i
\(41\) −4.77712 6.70853i −0.746061 1.04770i −0.996823 0.0796470i \(-0.974621\pi\)
0.250762 0.968049i \(-0.419319\pi\)
\(42\) 0.659573 2.76364i 0.101774 0.426439i
\(43\) −0.235846 + 4.95101i −0.0359662 + 0.755023i 0.906799 + 0.421564i \(0.138519\pi\)
−0.942765 + 0.333459i \(0.891784\pi\)
\(44\) −1.85245 2.13784i −0.279267 0.322291i
\(45\) 4.09192 + 11.5442i 0.609987 + 1.72090i
\(46\) 4.78112 + 0.375355i 0.704938 + 0.0553431i
\(47\) −3.65989 6.33912i −0.533850 0.924656i −0.999218 0.0395383i \(-0.987411\pi\)
0.465368 0.885117i \(-0.345922\pi\)
\(48\) 1.72358 0.171056i 0.248778 0.0246898i
\(49\) 3.83007 1.97454i 0.547153 0.282077i
\(50\) 9.17160 + 7.21263i 1.29706 + 1.02002i
\(51\) −11.0070 + 0.0409542i −1.54129 + 0.00573473i
\(52\) 0.835834 0.657307i 0.115909 0.0911521i
\(53\) 2.55140 + 0.749160i 0.350462 + 0.102905i 0.452225 0.891904i \(-0.350630\pi\)
−0.101763 + 0.994809i \(0.532448\pi\)
\(54\) 3.80042 + 3.54356i 0.517172 + 0.482217i
\(55\) −4.79755 10.5052i −0.646901 1.41652i
\(56\) −1.18721 1.13201i −0.158648 0.151271i
\(57\) 1.79634 + 0.520202i 0.237931 + 0.0689024i
\(58\) −0.953746 2.75567i −0.125233 0.361837i
\(59\) −1.22263 + 5.03976i −0.159173 + 0.656120i 0.835178 + 0.549980i \(0.185365\pi\)
−0.994351 + 0.106141i \(0.966151\pi\)
\(60\) 6.94848 + 1.31241i 0.897044 + 0.169432i
\(61\) −6.76530 3.48775i −0.866207 0.446561i −0.0329570 0.999457i \(-0.510492\pi\)
−0.833250 + 0.552896i \(0.813523\pi\)
\(62\) −9.61571 2.82343i −1.22120 0.358576i
\(63\) 0.197575 4.91723i 0.0248921 0.619513i
\(64\) 0.415415 0.909632i 0.0519269 0.113704i
\(65\) 4.03022 1.61346i 0.499887 0.200125i
\(66\) −3.86256 3.01436i −0.475448 0.371042i
\(67\) 13.0791 2.52078i 1.59786 0.307963i 0.688905 0.724852i \(-0.258092\pi\)
0.908957 + 0.416889i \(0.136880\pi\)
\(68\) −3.17747 + 5.50355i −0.385325 + 0.667403i
\(69\) 8.25102 0.959538i 0.993306 0.115515i
\(70\) −3.34858 5.79991i −0.400232 0.693222i
\(71\) −3.61339 4.17007i −0.428830 0.494896i 0.499677 0.866212i \(-0.333452\pi\)
−0.928507 + 0.371316i \(0.878907\pi\)
\(72\) 2.87211 0.866594i 0.338481 0.102129i
\(73\) −0.639331 + 4.44665i −0.0748281 + 0.520441i 0.917590 + 0.397529i \(0.130132\pi\)
−0.992418 + 0.122912i \(0.960777\pi\)
\(74\) −4.12239 + 0.393641i −0.479218 + 0.0457598i
\(75\) 17.9972 + 9.19359i 2.07814 + 1.06158i
\(76\) 0.781438 0.745099i 0.0896370 0.0854688i
\(77\) 0.220795 + 4.63505i 0.0251619 + 0.528213i
\(78\) 1.20090 1.39637i 0.135975 0.158108i
\(79\) −2.67592 2.55148i −0.301064 0.287064i 0.524455 0.851438i \(-0.324269\pi\)
−0.825519 + 0.564374i \(0.809118\pi\)
\(80\) 2.67356 3.08545i 0.298913 0.344964i
\(81\) 7.64286 + 4.75255i 0.849206 + 0.528061i
\(82\) −7.90200 + 2.32024i −0.872630 + 0.256227i
\(83\) 7.89513 11.0872i 0.866603 1.21697i −0.108250 0.994124i \(-0.534525\pi\)
0.974853 0.222850i \(-0.0715360\pi\)
\(84\) −2.39592 1.52720i −0.261416 0.166631i
\(85\) −18.7772 + 17.9041i −2.03668 + 1.94197i
\(86\) 4.60157 + 1.84219i 0.496201 + 0.198649i
\(87\) −2.54163 4.36464i −0.272491 0.467939i
\(88\) −2.62613 + 1.05135i −0.279947 + 0.112074i
\(89\) 10.2212 + 6.56878i 1.08345 + 0.696290i 0.955351 0.295472i \(-0.0954769\pi\)
0.128097 + 0.991762i \(0.459113\pi\)
\(90\) 12.2476 0.0911412i 1.29101 0.00960712i
\(91\) −1.74429 −0.182851
\(92\) 1.91846 4.39540i 0.200013 0.458252i
\(93\) −17.2854 1.58568i −1.79242 0.164428i
\(94\) −7.18751 + 1.38528i −0.741335 + 0.142881i
\(95\) 3.91812 2.01993i 0.401990 0.207240i
\(96\) 0.402081 1.68473i 0.0410372 0.171948i
\(97\) 0.740467 0.0707061i 0.0751831 0.00717911i −0.0573967 0.998351i \(-0.518280\pi\)
0.132580 + 0.991172i \(0.457674\pi\)
\(98\) −0.613247 4.26523i −0.0619473 0.430853i
\(99\) −7.57164 3.83241i −0.760979 0.385171i
\(100\) 9.81567 6.30815i 0.981567 0.630815i
\(101\) −7.53231 + 10.5776i −0.749492 + 1.05251i 0.247015 + 0.969012i \(0.420550\pi\)
−0.996508 + 0.0835032i \(0.973389\pi\)
\(102\) −3.56134 + 10.4150i −0.352625 + 1.03124i
\(103\) −0.265214 0.766287i −0.0261324 0.0755045i 0.931180 0.364559i \(-0.118780\pi\)
−0.957313 + 0.289055i \(0.906659\pi\)
\(104\) −0.347781 1.00485i −0.0341028 0.0985334i
\(105\) −7.62883 8.73823i −0.744497 0.852764i
\(106\) 1.54244 2.16605i 0.149815 0.210386i
\(107\) 13.8427 8.89616i 1.33822 0.860024i 0.341420 0.939911i \(-0.389092\pi\)
0.996804 + 0.0798867i \(0.0254559\pi\)
\(108\) 4.59166 2.43242i 0.441833 0.234060i
\(109\) 1.03435 + 7.19405i 0.0990726 + 0.689065i 0.977461 + 0.211117i \(0.0677102\pi\)
−0.878388 + 0.477948i \(0.841381\pi\)
\(110\) −11.4965 + 1.09778i −1.09615 + 0.104670i
\(111\) −6.87456 + 2.04637i −0.652504 + 0.194233i
\(112\) −1.45805 + 0.751675i −0.137772 + 0.0710266i
\(113\) 13.8469 2.66877i 1.30261 0.251057i 0.509675 0.860367i \(-0.329766\pi\)
0.792932 + 0.609310i \(0.208553\pi\)
\(114\) 1.07912 1.52740i 0.101069 0.143054i
\(115\) 12.5707 15.0113i 1.17223 1.39981i
\(116\) −2.91605 −0.270748
\(117\) 1.57439 2.77441i 0.145553 0.256494i
\(118\) 4.36269 + 2.80373i 0.401618 + 0.258104i
\(119\) 9.67792 3.87445i 0.887174 0.355171i
\(120\) 3.51286 6.13707i 0.320678 0.560235i
\(121\) −2.78334 1.11428i −0.253031 0.101298i
\(122\) −5.50864 + 5.25248i −0.498729 + 0.475537i
\(123\) −12.6544 + 6.58349i −1.14101 + 0.593614i
\(124\) −5.81313 + 8.16340i −0.522035 + 0.733095i
\(125\) 26.1200 7.66951i 2.33624 0.685982i
\(126\) −4.58217 1.79498i −0.408212 0.159909i
\(127\) 7.87482 9.08803i 0.698777 0.806432i −0.289810 0.957084i \(-0.593592\pi\)
0.988587 + 0.150652i \(0.0481374\pi\)
\(128\) −0.723734 0.690079i −0.0639697 0.0609949i
\(129\) 8.43597 + 1.59337i 0.742746 + 0.140288i
\(130\) −0.206562 4.33627i −0.0181167 0.380316i
\(131\) 2.96345 2.82564i 0.258918 0.246878i −0.549490 0.835500i \(-0.685178\pi\)
0.808408 + 0.588623i \(0.200330\pi\)
\(132\) −4.11189 + 2.66422i −0.357894 + 0.231891i
\(133\) −1.76317 + 0.168362i −0.152886 + 0.0145989i
\(134\) 1.89560 13.1842i 0.163755 1.13894i
\(135\) 20.7845 4.24704i 1.78885 0.365527i
\(136\) 4.16161 + 4.80275i 0.356855 + 0.411832i
\(137\) −4.25818 7.37538i −0.363801 0.630122i 0.624782 0.780799i \(-0.285188\pi\)
−0.988583 + 0.150678i \(0.951854\pi\)
\(138\) 1.79188 8.11105i 0.152535 0.690459i
\(139\) −5.14029 + 8.90325i −0.435994 + 0.755164i −0.997376 0.0723930i \(-0.976936\pi\)
0.561382 + 0.827557i \(0.310270\pi\)
\(140\) −6.57613 + 1.26745i −0.555784 + 0.107119i
\(141\) −11.7525 + 4.75579i −0.989736 + 0.400509i
\(142\) −5.12254 + 2.05076i −0.429874 + 0.172096i
\(143\) −1.24953 + 2.73609i −0.104491 + 0.228803i
\(144\) 0.120443 2.99758i 0.0100369 0.249798i
\(145\) −11.4229 3.35407i −0.948622 0.278540i
\(146\) 3.99298 + 2.05852i 0.330461 + 0.170365i
\(147\) −2.46732 7.04394i −0.203501 0.580974i
\(148\) −0.976311 + 4.02441i −0.0802523 + 0.330804i
\(149\) 2.02862 + 5.86131i 0.166191 + 0.480177i 0.997089 0.0762475i \(-0.0242939\pi\)
−0.830898 + 0.556425i \(0.812173\pi\)
\(150\) 14.5743 14.0004i 1.18998 1.14313i
\(151\) 9.17518 + 8.74851i 0.746665 + 0.711944i 0.964512 0.264039i \(-0.0850548\pi\)
−0.217847 + 0.975983i \(0.569903\pi\)
\(152\) −0.448536 0.982157i −0.0363811 0.0796635i
\(153\) −2.57271 + 18.8905i −0.207991 + 1.52720i
\(154\) 4.45234 + 1.30732i 0.358780 + 0.105347i
\(155\) −32.1612 + 25.2918i −2.58325 + 2.03149i
\(156\) −0.926799 1.59156i −0.0742033 0.127427i
\(157\) 17.5505 + 13.8019i 1.40069 + 1.10151i 0.981036 + 0.193826i \(0.0620897\pi\)
0.419650 + 0.907686i \(0.362153\pi\)
\(158\) −3.28636 + 1.69424i −0.261449 + 0.134786i
\(159\) 1.89769 4.19660i 0.150496 0.332812i
\(160\) −2.04132 3.53567i −0.161380 0.279519i
\(161\) −6.93080 + 3.72223i −0.546224 + 0.293353i
\(162\) 6.99090 5.66810i 0.549257 0.445328i
\(163\) −0.308513 0.356043i −0.0241646 0.0278874i 0.743539 0.668693i \(-0.233146\pi\)
−0.767703 + 0.640806i \(0.778600\pi\)
\(164\) −0.391866 + 8.22628i −0.0305996 + 0.642364i
\(165\) −19.1718 + 5.70690i −1.49252 + 0.444282i
\(166\) −7.89513 11.0872i −0.612781 0.860530i
\(167\) −2.00748 0.803674i −0.155344 0.0621902i 0.292688 0.956208i \(-0.405450\pi\)
−0.448031 + 0.894018i \(0.647875\pi\)
\(168\) −2.22683 + 1.76465i −0.171804 + 0.136145i
\(169\) 10.5499 + 5.43884i 0.811529 + 0.418372i
\(170\) 10.7779 + 23.6004i 0.826629 + 1.81006i
\(171\) 1.32365 2.95640i 0.101222 0.226082i
\(172\) 3.24590 3.74597i 0.247498 0.285628i
\(173\) −5.37729 1.03639i −0.408828 0.0787951i −0.0193090 0.999814i \(-0.506147\pi\)
−0.389519 + 0.921018i \(0.627359\pi\)
\(174\) −4.95588 + 0.974305i −0.375704 + 0.0738619i
\(175\) −19.0534 1.81938i −1.44030 0.137532i
\(176\) 0.134598 + 2.82556i 0.0101457 + 0.212985i
\(177\) 8.35125 + 3.30734i 0.627719 + 0.248595i
\(178\) 9.55054 7.51063i 0.715843 0.562945i
\(179\) −7.06956 + 15.4802i −0.528404 + 1.15704i 0.437755 + 0.899095i \(0.355774\pi\)
−0.966159 + 0.257949i \(0.916953\pi\)
\(180\) 3.91966 11.6038i 0.292154 0.864894i
\(181\) −4.10603 2.63878i −0.305198 0.196139i 0.379073 0.925367i \(-0.376243\pi\)
−0.684271 + 0.729228i \(0.739879\pi\)
\(182\) −0.570500 + 1.64835i −0.0422883 + 0.122184i
\(183\) −7.60709 + 10.7672i −0.562332 + 0.795936i
\(184\) −3.52619 3.25054i −0.259954 0.239633i
\(185\) −8.45339 + 14.6417i −0.621505 + 1.07648i
\(186\) −7.15199 + 15.8161i −0.524409 + 1.15970i
\(187\) 0.855363 17.9563i 0.0625504 1.31309i
\(188\) −1.04171 + 7.24528i −0.0759748 + 0.528416i
\(189\) −8.38722 1.51961i −0.610080 0.110535i
\(190\) −0.627345 4.36328i −0.0455124 0.316545i
\(191\) −2.36428 9.74569i −0.171073 0.705173i −0.991131 0.132892i \(-0.957574\pi\)
0.820057 0.572281i \(-0.193941\pi\)
\(192\) −1.46057 0.930989i −0.105407 0.0671884i
\(193\) 20.1492 + 1.92402i 1.45037 + 0.138494i 0.790306 0.612713i \(-0.209922\pi\)
0.660067 + 0.751206i \(0.270528\pi\)
\(194\) 0.175366 0.722868i 0.0125905 0.0518989i
\(195\) −1.79988 7.30056i −0.128892 0.522804i
\(196\) −4.23122 0.815500i −0.302230 0.0582500i
\(197\) −19.3068 + 5.66899i −1.37555 + 0.403899i −0.884219 0.467073i \(-0.845309\pi\)
−0.491334 + 0.870971i \(0.663490\pi\)
\(198\) −6.09807 + 5.90175i −0.433371 + 0.419419i
\(199\) −0.256471 + 0.164824i −0.0181807 + 0.0116841i −0.549700 0.835362i \(-0.685258\pi\)
0.531519 + 0.847046i \(0.321621\pi\)
\(200\) −2.75081 11.3390i −0.194512 0.801789i
\(201\) −1.18347 23.0401i −0.0834758 1.62513i
\(202\) 7.53231 + 10.5776i 0.529971 + 0.744240i
\(203\) 3.76007 + 2.95695i 0.263905 + 0.207537i
\(204\) 8.67742 + 6.77190i 0.607541 + 0.474128i
\(205\) −10.9970 + 31.7737i −0.768064 + 2.21917i
\(206\) −0.810885 −0.0564970
\(207\) 0.335281 14.3836i 0.0233036 0.999728i
\(208\) −1.06333 −0.0737287
\(209\) −0.998964 + 2.88632i −0.0690998 + 0.199651i
\(210\) −10.7528 + 4.35125i −0.742012 + 0.300265i
\(211\) 2.99683 + 2.35673i 0.206310 + 0.162244i 0.715968 0.698133i \(-0.245986\pi\)
−0.509658 + 0.860377i \(0.670228\pi\)
\(212\) −1.54244 2.16605i −0.105935 0.148765i
\(213\) −8.02066 + 5.19684i −0.549567 + 0.356081i
\(214\) −3.87938 15.9910i −0.265189 1.09312i
\(215\) 17.0237 10.9405i 1.16101 0.746134i
\(216\) −0.796852 5.13469i −0.0542189 0.349371i
\(217\) 15.7736 4.63155i 1.07078 0.314410i
\(218\) 7.13669 + 1.37548i 0.483357 + 0.0931595i
\(219\) 7.47394 + 2.16437i 0.505042 + 0.146255i
\(220\) −2.72273 + 11.2233i −0.183567 + 0.756672i
\(221\) 6.72681 + 0.642333i 0.452494 + 0.0432080i
\(222\) −0.314630 + 7.16577i −0.0211166 + 0.480935i
\(223\) 2.04180 + 8.41641i 0.136729 + 0.563605i 0.998421 + 0.0561731i \(0.0178899\pi\)
−0.861692 + 0.507432i \(0.830595\pi\)
\(224\) 0.233453 + 1.62370i 0.0155983 + 0.108488i
\(225\) 20.0914 28.6635i 1.33943 1.91090i
\(226\) 2.00689 13.9582i 0.133496 0.928486i
\(227\) −1.00630 + 21.1247i −0.0667901 + 1.40210i 0.678129 + 0.734943i \(0.262791\pi\)
−0.744919 + 0.667155i \(0.767512\pi\)
\(228\) −1.09045 1.51933i −0.0722170 0.100620i
\(229\) 6.96492 12.0636i 0.460255 0.797185i −0.538718 0.842486i \(-0.681091\pi\)
0.998973 + 0.0453010i \(0.0144247\pi\)
\(230\) −10.0742 16.7891i −0.664271 1.10704i
\(231\) 8.00364 + 0.734214i 0.526601 + 0.0483078i
\(232\) −0.953746 + 2.75567i −0.0626165 + 0.180918i
\(233\) −15.8309 10.1739i −1.03712 0.666515i −0.0928449 0.995681i \(-0.529596\pi\)
−0.944272 + 0.329166i \(0.893232\pi\)
\(234\) −2.10688 2.39522i −0.137731 0.156581i
\(235\) −12.4143 + 27.1835i −0.809818 + 1.77325i
\(236\) 4.07642 3.20573i 0.265353 0.208676i
\(237\) −5.01915 + 3.97742i −0.326029 + 0.258361i
\(238\) −0.496025 10.4129i −0.0321525 0.674965i
\(239\) −24.0336 2.29493i −1.55460 0.148446i −0.717916 0.696130i \(-0.754904\pi\)
−0.836686 + 0.547683i \(0.815510\pi\)
\(240\) −4.65059 5.32689i −0.300194 0.343849i
\(241\) −10.2973 1.98464i −0.663307 0.127842i −0.153524 0.988145i \(-0.549062\pi\)
−0.509783 + 0.860303i \(0.670274\pi\)
\(242\) −1.96334 + 2.26581i −0.126208 + 0.145652i
\(243\) 9.98735 11.9688i 0.640689 0.767801i
\(244\) 3.16190 + 6.92359i 0.202420 + 0.443237i
\(245\) −15.6368 8.06132i −0.998997 0.515019i
\(246\) 2.08257 + 14.1116i 0.132780 + 0.899725i
\(247\) −1.06587 0.426709i −0.0678196 0.0271509i
\(248\) 5.81313 + 8.16340i 0.369134 + 0.518377i
\(249\) −17.1223 16.2049i −1.08508 1.02695i
\(250\) 1.29531 27.1918i 0.0819224 1.71976i
\(251\) 5.77503 + 6.66474i 0.364517 + 0.420674i 0.908148 0.418650i \(-0.137496\pi\)
−0.543631 + 0.839324i \(0.682951\pi\)
\(252\) −3.19494 + 3.74307i −0.201262 + 0.235791i
\(253\) 0.873776 + 13.5381i 0.0549338 + 0.851133i
\(254\) −6.01259 10.4141i −0.377263 0.653440i
\(255\) 26.2026 + 36.5081i 1.64087 + 2.28623i
\(256\) −0.888835 + 0.458227i −0.0555522 + 0.0286392i
\(257\) −12.9374 10.1741i −0.807014 0.634643i 0.126991 0.991904i \(-0.459468\pi\)
−0.934004 + 0.357261i \(0.883711\pi\)
\(258\) 4.26487 7.45086i 0.265519 0.463870i
\(259\) 5.33976 4.19924i 0.331797 0.260928i
\(260\) −4.16534 1.22305i −0.258323 0.0758506i
\(261\) −8.09707 + 3.31170i −0.501196 + 0.204989i
\(262\) −1.70099 3.72464i −0.105087 0.230109i
\(263\) −2.33481 2.22624i −0.143971 0.137276i 0.614672 0.788783i \(-0.289289\pi\)
−0.758642 + 0.651507i \(0.774137\pi\)
\(264\) 1.17282 + 4.75712i 0.0721823 + 0.292780i
\(265\) −3.55072 10.2591i −0.218119 0.630213i
\(266\) −0.417574 + 1.72126i −0.0256031 + 0.105537i
\(267\) 13.7219 15.9555i 0.839766 0.976459i
\(268\) −11.8391 6.10347i −0.723187 0.372829i
\(269\) −25.1264 7.37779i −1.53199 0.449832i −0.596328 0.802741i \(-0.703374\pi\)
−0.935658 + 0.352909i \(0.885193\pi\)
\(270\) 2.78450 21.0305i 0.169459 1.27987i
\(271\) 0.945413 2.07017i 0.0574298 0.125754i −0.878741 0.477298i \(-0.841616\pi\)
0.936171 + 0.351545i \(0.114343\pi\)
\(272\) 5.89973 2.36190i 0.357724 0.143211i
\(273\) −0.418831 + 2.99202i −0.0253488 + 0.181085i
\(274\) −8.36246 + 1.61173i −0.505195 + 0.0973683i
\(275\) −16.5029 + 28.5838i −0.995161 + 1.72367i
\(276\) −7.07888 4.34619i −0.426099 0.261610i
\(277\) 13.9670 + 24.1915i 0.839193 + 1.45352i 0.890570 + 0.454845i \(0.150306\pi\)
−0.0513775 + 0.998679i \(0.516361\pi\)
\(278\) 6.73235 + 7.76955i 0.403780 + 0.465986i
\(279\) −6.87047 + 29.2694i −0.411325 + 1.75232i
\(280\) −0.953105 + 6.62899i −0.0569589 + 0.396158i
\(281\) 13.8318 1.32077i 0.825134 0.0787907i 0.326059 0.945350i \(-0.394279\pi\)
0.499075 + 0.866559i \(0.333673\pi\)
\(282\) 0.650369 + 12.6615i 0.0387289 + 0.753984i
\(283\) 13.1414 12.5303i 0.781175 0.744849i −0.190368 0.981713i \(-0.560968\pi\)
0.971543 + 0.236864i \(0.0761196\pi\)
\(284\) 0.262547 + 5.51154i 0.0155793 + 0.327050i
\(285\) −2.52404 7.20587i −0.149511 0.426839i
\(286\) 2.17693 + 2.07569i 0.128724 + 0.122738i
\(287\) 8.84696 10.2099i 0.522220 0.602674i
\(288\) −2.79332 1.09423i −0.164598 0.0644782i
\(289\) −22.4381 + 6.58843i −1.31989 + 0.387554i
\(290\) −6.90567 + 9.69766i −0.405515 + 0.569466i
\(291\) 0.0565141 1.28712i 0.00331291 0.0754524i
\(292\) 3.25128 3.10009i 0.190267 0.181419i
\(293\) 30.7241 + 12.3001i 1.79492 + 0.718578i 0.992562 + 0.121738i \(0.0388467\pi\)
0.802360 + 0.596841i \(0.203578\pi\)
\(294\) −7.46351 + 0.0277697i −0.435281 + 0.00161956i
\(295\) 19.6557 7.86895i 1.14440 0.458148i
\(296\) 3.48375 + 2.23887i 0.202489 + 0.130132i
\(297\) −8.39190 + 12.0676i −0.486947 + 0.700234i
\(298\) 6.20244 0.359298
\(299\) −5.09883 + 0.0859372i −0.294873 + 0.00496988i
\(300\) −8.46364 18.3518i −0.488648 1.05954i
\(301\) −7.98392 + 1.53877i −0.460185 + 0.0886935i
\(302\) 11.2683 5.80919i 0.648415 0.334281i
\(303\) 16.3355 + 15.4602i 0.938449 + 0.888167i
\(304\) −1.07484 + 0.102635i −0.0616464 + 0.00588652i
\(305\) 4.42238 + 30.7583i 0.253225 + 1.76122i
\(306\) 17.0101 + 8.60968i 0.972400 + 0.492183i
\(307\) 2.23976 1.43941i 0.127830 0.0821513i −0.475163 0.879898i \(-0.657611\pi\)
0.602993 + 0.797746i \(0.293975\pi\)
\(308\) 2.69164 3.77988i 0.153370 0.215379i
\(309\) −1.37811 + 0.270932i −0.0783982 + 0.0154128i
\(310\) 13.3819 + 38.6645i 0.760042 + 2.19600i
\(311\) −4.52462 13.0730i −0.256568 0.741304i −0.997562 0.0697919i \(-0.977766\pi\)
0.740994 0.671512i \(-0.234355\pi\)
\(312\) −1.80715 + 0.355278i −0.102310 + 0.0201137i
\(313\) 2.77502 3.89697i 0.156853 0.220270i −0.728670 0.684865i \(-0.759861\pi\)
0.885523 + 0.464596i \(0.153800\pi\)
\(314\) 18.7830 12.0711i 1.05999 0.681213i
\(315\) −16.8207 + 10.9877i −0.947740 + 0.619089i
\(316\) 0.526191 + 3.65974i 0.0296006 + 0.205877i
\(317\) −24.0045 + 2.29215i −1.34823 + 0.128740i −0.744058 0.668115i \(-0.767101\pi\)
−0.604170 + 0.796855i \(0.706495\pi\)
\(318\) −3.34512 3.16589i −0.187585 0.177534i
\(319\) 7.33183 3.77982i 0.410504 0.211629i
\(320\) −4.00886 + 0.772644i −0.224102 + 0.0431921i
\(321\) −11.9360 25.8808i −0.666201 1.44453i
\(322\) 1.25067 + 7.76703i 0.0696971 + 0.432840i
\(323\) 6.86163 0.381791
\(324\) −3.06986 8.46026i −0.170548 0.470014i
\(325\) −10.4373 6.70765i −0.578957 0.372073i
\(326\) −0.437365 + 0.175095i −0.0242234 + 0.00969759i
\(327\) 12.5885 0.0468385i 0.696146 0.00259017i
\(328\) 7.64567 + 3.06086i 0.422162 + 0.169008i
\(329\) 8.69015 8.28604i 0.479103 0.456824i
\(330\) −0.877439 + 19.9839i −0.0483014 + 1.10008i
\(331\) 18.3270 25.7367i 1.00734 1.41462i 0.0996312 0.995024i \(-0.468234\pi\)
0.907713 0.419592i \(-0.137827\pi\)
\(332\) −13.0596 + 3.83465i −0.716740 + 0.210454i
\(333\) 1.85950 + 12.2835i 0.101900 + 0.673130i
\(334\) −1.41606 + 1.63422i −0.0774831 + 0.0894203i
\(335\) −39.3565 37.5263i −2.15027 2.05028i
\(336\) 0.939268 + 2.68151i 0.0512412 + 0.146289i
\(337\) −0.738138 15.4954i −0.0402089 0.844090i −0.925430 0.378919i \(-0.876296\pi\)
0.885221 0.465171i \(-0.154007\pi\)
\(338\) 8.59024 8.19077i 0.467247 0.445519i
\(339\) −1.25295 24.3928i −0.0680510 1.32483i
\(340\) 25.8275 2.46622i 1.40069 0.133750i
\(341\) 4.03447 28.0604i 0.218479 1.51955i
\(342\) −2.36088 2.21779i −0.127662 0.119924i
\(343\) 12.1486 + 14.0202i 0.655963 + 0.757021i
\(344\) −2.47831 4.29257i −0.133622 0.231440i
\(345\) −22.7308 25.1674i −1.22378 1.35497i
\(346\) −2.73813 + 4.74258i −0.147203 + 0.254962i
\(347\) 27.3735 5.27580i 1.46949 0.283220i 0.609193 0.793022i \(-0.291493\pi\)
0.860292 + 0.509802i \(0.170281\pi\)
\(348\) −0.700189 + 5.00197i −0.0375341 + 0.268134i
\(349\) −15.2593 + 6.10891i −0.816812 + 0.327002i −0.742173 0.670208i \(-0.766205\pi\)
−0.0746391 + 0.997211i \(0.523780\pi\)
\(350\) −7.95106 + 17.4104i −0.425002 + 0.930625i
\(351\) −4.38097 3.36678i −0.233839 0.179705i
\(352\) 2.71418 + 0.796955i 0.144666 + 0.0424778i
\(353\) 25.0815 + 12.9304i 1.33495 + 0.688215i 0.970067 0.242837i \(-0.0780781\pi\)
0.364885 + 0.931053i \(0.381108\pi\)
\(354\) 5.85686 6.81022i 0.311289 0.361959i
\(355\) −5.31097 + 21.8921i −0.281877 + 1.16191i
\(356\) −3.97387 11.4818i −0.210615 0.608532i
\(357\) −4.32213 17.5311i −0.228751 0.927845i
\(358\) 12.3166 + 11.7438i 0.650950 + 0.620680i
\(359\) −7.36590 16.1291i −0.388757 0.851260i −0.998288 0.0584969i \(-0.981369\pi\)
0.609530 0.792763i \(-0.291358\pi\)
\(360\) −9.68358 7.49930i −0.510369 0.395248i
\(361\) 17.1118 + 5.02447i 0.900620 + 0.264446i
\(362\) −3.83660 + 3.01714i −0.201647 + 0.158577i
\(363\) −2.57968 + 4.50678i −0.135398 + 0.236544i
\(364\) 1.37110 + 1.07825i 0.0718653 + 0.0565155i
\(365\) 16.3019 8.40420i 0.853279 0.439896i
\(366\) 7.68700 + 10.7103i 0.401806 + 0.559837i
\(367\) 6.83266 + 11.8345i 0.356662 + 0.617756i 0.987401 0.158239i \(-0.0505815\pi\)
−0.630739 + 0.775995i \(0.717248\pi\)
\(368\) −4.22507 + 2.26910i −0.220247 + 0.118285i
\(369\) 8.25432 + 23.2872i 0.429703 + 1.21228i
\(370\) 11.0716 + 12.7773i 0.575584 + 0.664260i
\(371\) −0.207553 + 4.35707i −0.0107756 + 0.226208i
\(372\) 12.6071 + 11.9316i 0.653646 + 0.618624i
\(373\) 13.9028 + 19.5238i 0.719861 + 1.01090i 0.998720 + 0.0505714i \(0.0161043\pi\)
−0.278859 + 0.960332i \(0.589956\pi\)
\(374\) −16.6889 6.68125i −0.862965 0.345479i
\(375\) −6.88389 46.6458i −0.355483 2.40878i
\(376\) 6.50608 + 3.35412i 0.335526 + 0.172976i
\(377\) 1.28809 + 2.82051i 0.0663398 + 0.145264i
\(378\) −4.17922 + 7.42891i −0.214956 + 0.382102i
\(379\) −1.88201 + 2.17196i −0.0966726 + 0.111566i −0.802024 0.597291i \(-0.796244\pi\)
0.705352 + 0.708857i \(0.250789\pi\)
\(380\) −4.32848 0.834247i −0.222047 0.0427960i
\(381\) −13.6981 15.6901i −0.701773 0.803826i
\(382\) −9.98297 0.953258i −0.510773 0.0487729i
\(383\) 1.08185 + 22.7109i 0.0552800 + 1.16047i 0.840698 + 0.541505i \(0.182145\pi\)
−0.785418 + 0.618966i \(0.787552\pi\)
\(384\) −1.35749 + 1.07574i −0.0692742 + 0.0548962i
\(385\) 14.8915 11.7108i 0.758942 0.596838i
\(386\) 8.40837 18.4118i 0.427975 0.937134i
\(387\) 4.75876 14.0879i 0.241901 0.716126i
\(388\) −0.625754 0.402148i −0.0317679 0.0204160i
\(389\) 5.63539 16.2824i 0.285725 0.825550i −0.707222 0.706992i \(-0.750052\pi\)
0.992947 0.118558i \(-0.0378270\pi\)
\(390\) −7.48772 0.686887i −0.379155 0.0347819i
\(391\) 28.0992 11.8025i 1.42104 0.596876i
\(392\) −2.15454 + 3.73178i −0.108821 + 0.188483i
\(393\) −4.13533 5.76176i −0.208600 0.290643i
\(394\) −0.957438 + 20.0991i −0.0482350 + 1.01258i
\(395\) −2.14825 + 14.9414i −0.108090 + 0.751783i
\(396\) 3.58268 + 7.69295i 0.180036 + 0.386585i
\(397\) −3.16823 22.0355i −0.159009 1.10593i −0.900465 0.434929i \(-0.856773\pi\)
0.741456 0.671002i \(-0.234136\pi\)
\(398\) 0.0718752 + 0.296274i 0.00360278 + 0.0148509i
\(399\) −0.134569 + 3.06484i −0.00673687 + 0.153434i
\(400\) −11.6151 1.10911i −0.580754 0.0554553i
\(401\) −0.368146 + 1.51752i −0.0183843 + 0.0757813i −0.980265 0.197689i \(-0.936656\pi\)
0.961880 + 0.273470i \(0.0881715\pi\)
\(402\) −22.1600 6.41731i −1.10524 0.320066i
\(403\) 10.4638 + 2.01672i 0.521237 + 0.100460i
\(404\) 12.4595 3.65843i 0.619881 0.182014i
\(405\) −2.29436 36.6720i −0.114007 1.82225i
\(406\) 4.02412 2.58615i 0.199714 0.128348i
\(407\) −2.76175 11.3841i −0.136895 0.564289i
\(408\) 9.23755 5.98530i 0.457327 0.296316i
\(409\) 4.57155 + 6.41985i 0.226049 + 0.317441i 0.911987 0.410218i \(-0.134548\pi\)
−0.685939 + 0.727659i \(0.740608\pi\)
\(410\) 26.4294 + 20.7843i 1.30526 + 1.02647i
\(411\) −13.6736 + 5.53322i −0.674471 + 0.272934i
\(412\) −0.265214 + 0.766287i −0.0130662 + 0.0377522i
\(413\) −8.50702 −0.418603
\(414\) −13.4828 5.02125i −0.662646 0.246781i
\(415\) −55.5686 −2.72775
\(416\) −0.347781 + 1.00485i −0.0170514 + 0.0492667i
\(417\) 14.0377 + 10.9551i 0.687430 + 0.536473i
\(418\) 2.40084 + 1.88804i 0.117429 + 0.0923473i
\(419\) −12.6437 17.7556i −0.617684 0.867416i 0.380674 0.924709i \(-0.375692\pi\)
−0.998357 + 0.0572940i \(0.981753\pi\)
\(420\) 0.595048 + 11.5845i 0.0290354 + 0.565268i
\(421\) −4.21383 17.3697i −0.205370 0.846545i −0.977475 0.211051i \(-0.932311\pi\)
0.772105 0.635494i \(-0.219204\pi\)
\(422\) 3.20728 2.06120i 0.156128 0.100337i
\(423\) 5.33577 + 21.3012i 0.259434 + 1.03570i
\(424\) −2.55140 + 0.749160i −0.123907 + 0.0363824i
\(425\) 72.8090 + 14.0328i 3.53176 + 0.680690i
\(426\) 2.28771 + 9.27925i 0.110840 + 0.449581i
\(427\) 2.94363 12.1338i 0.142452 0.587196i
\(428\) −16.3803 1.56413i −0.791773 0.0756052i
\(429\) 4.39326 + 2.80033i 0.212108 + 0.135201i
\(430\) −4.77084 19.6657i −0.230070 0.948363i
\(431\) 2.55409 + 17.7641i 0.123026 + 0.855666i 0.954097 + 0.299499i \(0.0968194\pi\)
−0.831071 + 0.556167i \(0.812271\pi\)
\(432\) −5.11291 0.926366i −0.245995 0.0445698i
\(433\) 3.03847 21.1330i 0.146020 1.01559i −0.776632 0.629955i \(-0.783073\pi\)
0.922652 0.385635i \(-0.126017\pi\)
\(434\) 0.782225 16.4209i 0.0375480 0.788229i
\(435\) −8.49615 + 18.7887i −0.407359 + 0.900847i
\(436\) 3.63401 6.29430i 0.174038 0.301442i
\(437\) −5.14573 + 0.579017i −0.246154 + 0.0276982i
\(438\) 4.48982 6.35498i 0.214532 0.303653i
\(439\) −3.83206 + 11.0720i −0.182894 + 0.528439i −0.998759 0.0498042i \(-0.984140\pi\)
0.815865 + 0.578243i \(0.196261\pi\)
\(440\) 9.71548 + 6.24376i 0.463167 + 0.297659i
\(441\) −12.6751 + 2.54089i −0.603576 + 0.120995i
\(442\) 2.80713 6.14676i 0.133522 0.292371i
\(443\) −30.0504 + 23.6319i −1.42774 + 1.12278i −0.455102 + 0.890439i \(0.650397\pi\)
−0.972634 + 0.232345i \(0.925360\pi\)
\(444\) 6.66875 + 2.64102i 0.316485 + 0.125337i
\(445\) −2.36025 49.5478i −0.111887 2.34879i
\(446\) 8.62133 + 0.823237i 0.408232 + 0.0389814i
\(447\) 10.5412 2.07235i 0.498580 0.0980188i
\(448\) 1.61076 + 0.310448i 0.0761011 + 0.0146673i
\(449\) 9.73702 11.2371i 0.459518 0.530312i −0.477948 0.878388i \(-0.658619\pi\)
0.937466 + 0.348076i \(0.113165\pi\)
\(450\) −20.5158 28.3613i −0.967123 1.33697i
\(451\) −9.67775 21.1913i −0.455707 0.997860i
\(452\) −12.5341 6.46179i −0.589556 0.303937i
\(453\) 17.2097 13.6378i 0.808581 0.640758i
\(454\) 19.6338 + 7.86017i 0.921458 + 0.368896i
\(455\) 4.13075 + 5.80083i 0.193653 + 0.271947i
\(456\) −1.79242 + 0.533554i −0.0839378 + 0.0249860i
\(457\) −1.32114 + 27.7342i −0.0618005 + 1.29735i 0.728675 + 0.684859i \(0.240136\pi\)
−0.790476 + 0.612493i \(0.790167\pi\)
\(458\) −9.12211 10.5275i −0.426248 0.491916i
\(459\) 31.7856 + 8.94894i 1.48362 + 0.417701i
\(460\) −19.1606 + 4.02894i −0.893369 + 0.187850i
\(461\) 8.47955 + 14.6870i 0.394932 + 0.684042i 0.993093 0.117334i \(-0.0374348\pi\)
−0.598161 + 0.801376i \(0.704101\pi\)
\(462\) 3.31157 7.32330i 0.154068 0.340711i
\(463\) 2.99869 1.54593i 0.139361 0.0718454i −0.387136 0.922023i \(-0.626536\pi\)
0.526497 + 0.850177i \(0.323505\pi\)
\(464\) 2.29217 + 1.80258i 0.106411 + 0.0836827i
\(465\) 35.6614 + 61.2399i 1.65376 + 2.83993i
\(466\) −14.7921 + 11.6327i −0.685232 + 0.538872i
\(467\) 27.7624 + 8.15177i 1.28469 + 0.377219i 0.851629 0.524145i \(-0.175615\pi\)
0.433061 + 0.901364i \(0.357433\pi\)
\(468\) −2.95258 + 1.20760i −0.136483 + 0.0558215i
\(469\) 9.07671 + 19.8752i 0.419124 + 0.917753i
\(470\) 21.6281 + 20.6223i 0.997629 + 0.951237i
\(471\) 27.8889 26.7909i 1.28505 1.23446i
\(472\) −1.69615 4.90072i −0.0780718 0.225574i
\(473\) −3.30561 + 13.6259i −0.151992 + 0.626519i
\(474\) 2.11706 + 6.04399i 0.0972398 + 0.277610i
\(475\) −11.1977 5.77283i −0.513787 0.264876i
\(476\) −10.0024 2.93697i −0.458459 0.134616i
\(477\) −6.74288 4.26282i −0.308735 0.195181i
\(478\) −10.0293 + 21.9611i −0.458730 + 1.00448i
\(479\) −4.50642 + 1.80410i −0.205904 + 0.0824314i −0.472322 0.881426i \(-0.656584\pi\)
0.266418 + 0.963858i \(0.414160\pi\)
\(480\) −6.55497 + 2.65256i −0.299192 + 0.121072i
\(481\) 4.32383 0.833349i 0.197150 0.0379975i
\(482\) −5.24340 + 9.08184i −0.238831 + 0.413667i
\(483\) 4.72065 + 12.7823i 0.214797 + 0.581617i
\(484\) 1.49905 + 2.59643i 0.0681386 + 0.118020i
\(485\) −1.98869 2.29507i −0.0903016 0.104214i
\(486\) −8.04401 13.3527i −0.364884 0.605689i
\(487\) −0.0985887 + 0.685699i −0.00446748 + 0.0310720i −0.991933 0.126761i \(-0.959542\pi\)
0.987466 + 0.157833i \(0.0504509\pi\)
\(488\) 7.57695 0.723511i 0.342992 0.0327518i
\(489\) −0.684808 + 0.443708i −0.0309681 + 0.0200652i
\(490\) −12.7322 + 12.1402i −0.575184 + 0.548437i
\(491\) −0.480085 10.0782i −0.0216659 0.454824i −0.983468 0.181080i \(-0.942041\pi\)
0.961803 0.273744i \(-0.0882622\pi\)
\(492\) 14.0167 + 2.64744i 0.631920 + 0.119356i
\(493\) −13.4118 12.7881i −0.604035 0.575946i
\(494\) −0.751852 + 0.867684i −0.0338274 + 0.0390389i
\(495\) 5.18576 + 34.2561i 0.233082 + 1.53970i
\(496\) 9.61571 2.82343i 0.431758 0.126776i
\(497\) 5.25032 7.37304i 0.235509 0.330726i
\(498\) −20.9138 + 10.8805i −0.937172 + 0.487568i
\(499\) −0.240853 + 0.229653i −0.0107821 + 0.0102807i −0.695451 0.718574i \(-0.744795\pi\)
0.684669 + 0.728854i \(0.259947\pi\)
\(500\) −25.2726 10.1176i −1.13023 0.452475i
\(501\) −1.86059 + 3.25051i −0.0831251 + 0.145222i
\(502\) 8.18701 3.27758i 0.365404 0.146286i
\(503\) −20.9495 13.4635i −0.934094 0.600306i −0.0173796 0.999849i \(-0.505532\pi\)
−0.916714 + 0.399543i \(0.869169\pi\)
\(504\) 2.49225 + 4.24346i 0.111013 + 0.189019i
\(505\) 53.0149 2.35913
\(506\) 13.0793 + 3.60216i 0.581446 + 0.160136i
\(507\) 11.8626 16.7905i 0.526836 0.745694i
\(508\) −11.8079 + 2.27578i −0.523890 + 0.100971i
\(509\) 28.1292 14.5016i 1.24681 0.642773i 0.296781 0.954946i \(-0.404087\pi\)
0.950025 + 0.312172i \(0.101057\pi\)
\(510\) 43.0703 12.8208i 1.90718 0.567716i
\(511\) −7.33592 + 0.700495i −0.324522 + 0.0309881i
\(512\) 0.142315 + 0.989821i 0.00628949 + 0.0437443i
\(513\) −4.75337 2.98036i −0.209866 0.131586i
\(514\) −13.8459 + 8.89825i −0.610718 + 0.392485i
\(515\) −1.92031 + 2.69669i −0.0846188 + 0.118830i
\(516\) −5.64617 6.46725i −0.248559 0.284705i
\(517\) −6.77225 19.5671i −0.297843 0.860561i
\(518\) −2.22182 6.41951i −0.0976210 0.282057i
\(519\) −3.06892 + 8.97496i −0.134711 + 0.393957i
\(520\) −2.51814 + 3.53623i −0.110428 + 0.155074i
\(521\) −30.3962 + 19.5345i −1.33168 + 0.855821i −0.996273 0.0862517i \(-0.972511\pi\)
−0.335410 + 0.942072i \(0.608875\pi\)
\(522\) 0.481266 + 8.73489i 0.0210644 + 0.382316i
\(523\) −0.0915362 0.636649i −0.00400260 0.0278387i 0.987722 0.156220i \(-0.0499309\pi\)
−0.991725 + 0.128381i \(0.959022\pi\)
\(524\) −4.07612 + 0.389223i −0.178066 + 0.0170033i
\(525\) −7.69585 + 32.2459i −0.335874 + 1.40733i
\(526\) −2.86744 + 1.47827i −0.125026 + 0.0644556i
\(527\) −62.5362 + 12.0529i −2.72412 + 0.525031i
\(528\) 4.87908 + 0.447582i 0.212334 + 0.0194785i
\(529\) −20.0764 + 11.2221i −0.872889 + 0.487919i
\(530\) −10.8562 −0.471563
\(531\) 7.67843 13.5310i 0.333216 0.587194i
\(532\) 1.49002 + 0.957578i 0.0646006 + 0.0415163i
\(533\) 8.12987 3.25471i 0.352144 0.140977i
\(534\) −10.5899 18.1857i −0.458272 0.786973i
\(535\) −62.3669 24.9680i −2.69636 1.07946i
\(536\) −9.63997 + 9.19169i −0.416383 + 0.397021i
\(537\) 24.8561 + 15.8436i 1.07262 + 0.683704i
\(538\) −15.1901 + 21.3315i −0.654890 + 0.919665i
\(539\) 11.6956 3.43415i 0.503767 0.147919i
\(540\) −18.9631 9.50974i −0.816041 0.409234i
\(541\) −0.673468 + 0.777224i −0.0289547 + 0.0334155i −0.770042 0.637993i \(-0.779765\pi\)
0.741088 + 0.671408i \(0.234310\pi\)
\(542\) −1.64709 1.57050i −0.0707488 0.0674588i
\(543\) −5.51230 + 6.40956i −0.236555 + 0.275061i
\(544\) −0.302381 6.34775i −0.0129645 0.272158i
\(545\) 21.4752 20.4765i 0.919894 0.877118i
\(546\) 2.69048 + 1.37439i 0.115142 + 0.0588185i
\(547\) −0.725575 + 0.0692841i −0.0310234 + 0.00296237i −0.110556 0.993870i \(-0.535263\pi\)
0.0795328 + 0.996832i \(0.474657\pi\)
\(548\) −1.21200 + 8.42967i −0.0517743 + 0.360098i
\(549\) 16.6427 + 15.6340i 0.710294 + 0.667244i
\(550\) 21.6142 + 24.9441i 0.921632 + 1.06362i
\(551\) 1.57427 + 2.72672i 0.0670663 + 0.116162i
\(552\) −6.42243 + 5.26805i −0.273357 + 0.224223i
\(553\) 3.03259 5.25260i 0.128959 0.223363i
\(554\) 27.4291 5.28653i 1.16535 0.224603i
\(555\) 23.0855 + 18.0160i 0.979925 + 0.764738i
\(556\) 9.54417 3.82091i 0.404763 0.162043i
\(557\) 1.75942 3.85260i 0.0745492 0.163240i −0.868688 0.495359i \(-0.835036\pi\)
0.943237 + 0.332119i \(0.107764\pi\)
\(558\) 25.4125 + 16.0657i 1.07580 + 0.680115i
\(559\) −5.05704 1.48488i −0.213890 0.0628038i
\(560\) 5.95267 + 3.06881i 0.251546 + 0.129681i
\(561\) −30.5955 5.77882i −1.29174 0.243982i
\(562\) 3.27579 13.5030i 0.138181 0.569590i
\(563\) 12.8859 + 37.2312i 0.543074 + 1.56911i 0.798320 + 0.602233i \(0.205722\pi\)
−0.255246 + 0.966876i \(0.582156\pi\)
\(564\) 12.1779 + 3.52659i 0.512782 + 0.148496i
\(565\) −41.6670 39.7294i −1.75294 1.67143i
\(566\) −7.54301 16.5169i −0.317056 0.694257i
\(567\) −4.62053 + 14.0219i −0.194044 + 0.588866i
\(568\) 5.29428 + 1.55454i 0.222143 + 0.0652271i
\(569\) −21.2921 + 16.7443i −0.892613 + 0.701959i −0.955162 0.296083i \(-0.904319\pi\)
0.0625490 + 0.998042i \(0.480077\pi\)
\(570\) −7.63508 + 0.0284081i −0.319798 + 0.00118988i
\(571\) −17.4317 13.7085i −0.729495 0.573681i 0.182832 0.983144i \(-0.441474\pi\)
−0.912327 + 0.409463i \(0.865716\pi\)
\(572\) 2.67354 1.37830i 0.111786 0.0576298i
\(573\) −17.2847 + 1.71541i −0.722080 + 0.0716624i
\(574\) −6.75484 11.6997i −0.281942 0.488337i
\(575\) −55.7857 4.37961i −2.32642 0.182642i
\(576\) −1.94766 + 2.28181i −0.0811523 + 0.0950752i
\(577\) −3.65817 4.22175i −0.152291 0.175754i 0.674477 0.738295i \(-0.264369\pi\)
−0.826769 + 0.562542i \(0.809824\pi\)
\(578\) −1.11272 + 23.3589i −0.0462831 + 0.971602i
\(579\) 8.13847 34.1005i 0.338223 1.41717i
\(580\) 6.90567 + 9.69766i 0.286742 + 0.402673i
\(581\) 20.7281 + 8.29826i 0.859945 + 0.344270i
\(582\) −1.19785 0.474382i −0.0496523 0.0196638i
\(583\) 6.68583 + 3.44678i 0.276899 + 0.142751i
\(584\) −1.86620 4.08641i −0.0772239 0.169097i
\(585\) −12.9550 + 1.33441i −0.535624 + 0.0551710i
\(586\) 21.6725 25.0114i 0.895281 1.03321i
\(587\) 23.8140 + 4.58977i 0.982908 + 0.189440i 0.655296 0.755372i \(-0.272544\pi\)
0.327612 + 0.944812i \(0.393756\pi\)
\(588\) −2.41483 + 7.06210i −0.0995860 + 0.291236i
\(589\) 10.7717 + 1.02857i 0.443840 + 0.0423816i
\(590\) −1.00742 21.1483i −0.0414748 0.870662i
\(591\) 5.08829 + 34.4787i 0.209304 + 1.41826i
\(592\) 3.25516 2.55988i 0.133786 0.105211i
\(593\) 1.88003 4.11669i 0.0772035 0.169052i −0.867095 0.498144i \(-0.834015\pi\)
0.944298 + 0.329092i \(0.106742\pi\)
\(594\) 8.65919 + 11.8773i 0.355291 + 0.487331i
\(595\) −35.8038 23.0097i −1.46781 0.943307i
\(596\) 2.02862 5.86131i 0.0830955 0.240089i
\(597\) 0.221144 + 0.479508i 0.00905082 + 0.0196250i
\(598\) −1.58645 + 4.84650i −0.0648749 + 0.198188i
\(599\) 18.0048 31.1852i 0.735656 1.27419i −0.218779 0.975774i \(-0.570207\pi\)
0.954435 0.298419i \(-0.0964592\pi\)
\(600\) −20.1106 + 1.99587i −0.821013 + 0.0814809i
\(601\) −0.918039 + 19.2720i −0.0374476 + 0.786121i 0.899557 + 0.436804i \(0.143890\pi\)
−0.937004 + 0.349318i \(0.886413\pi\)
\(602\) −1.15714 + 8.04809i −0.0471616 + 0.328016i
\(603\) −39.8055 3.50226i −1.62101 0.142623i
\(604\) −1.80420 12.5485i −0.0734120 0.510592i
\(605\) 2.88572 + 11.8951i 0.117321 + 0.483605i
\(606\) 19.9527 10.3805i 0.810524 0.421679i
\(607\) −19.1428 1.82792i −0.776984 0.0741930i −0.300973 0.953633i \(-0.597312\pi\)
−0.476011 + 0.879440i \(0.657918\pi\)
\(608\) −0.254556 + 1.04929i −0.0103236 + 0.0425545i
\(609\) 5.97499 5.73974i 0.242119 0.232586i
\(610\) 30.5131 + 5.88091i 1.23544 + 0.238111i
\(611\) 7.46807 2.19282i 0.302126 0.0887121i
\(612\) 13.6996 13.2586i 0.553773 0.535946i
\(613\) 5.95652 3.82802i 0.240582 0.154612i −0.414794 0.909915i \(-0.636147\pi\)
0.655376 + 0.755303i \(0.272510\pi\)
\(614\) −0.627687 2.58736i −0.0253314 0.104417i
\(615\) 51.8618 + 26.4928i 2.09127 + 1.06829i
\(616\) −2.69164 3.77988i −0.108449 0.152296i
\(617\) −13.3010 10.4600i −0.535479 0.421105i 0.313456 0.949603i \(-0.398513\pi\)
−0.848935 + 0.528498i \(0.822756\pi\)
\(618\) −0.194706 + 1.39093i −0.00783224 + 0.0559515i
\(619\) 4.66797 13.4872i 0.187622 0.542097i −0.811484 0.584374i \(-0.801340\pi\)
0.999106 + 0.0422770i \(0.0134612\pi\)
\(620\) 40.9148 1.64318
\(621\) −24.5920 4.02884i −0.986845 0.161672i
\(622\) −13.8339 −0.554688
\(623\) −6.51874 + 18.8347i −0.261168 + 0.754595i
\(624\) −0.255323 + 1.82396i −0.0102211 + 0.0730168i
\(625\) −41.5041 32.6392i −1.66016 1.30557i
\(626\) −2.77502 3.89697i −0.110912 0.155754i
\(627\) 4.71111 + 2.40660i 0.188144 + 0.0961104i
\(628\) −5.26389 21.6981i −0.210052 0.865847i
\(629\) −22.1391 + 14.2279i −0.882742 + 0.567304i
\(630\) 4.88191 + 19.4893i 0.194500 + 0.776474i
\(631\) −11.3282 + 3.32625i −0.450967 + 0.132416i −0.499326 0.866414i \(-0.666419\pi\)
0.0483592 + 0.998830i \(0.484601\pi\)
\(632\) 3.63056 + 0.699733i 0.144416 + 0.0278339i
\(633\) 4.76215 4.57465i 0.189279 0.181826i
\(634\) −5.68502 + 23.4340i −0.225781 + 0.930682i
\(635\) −48.8721 4.66672i −1.93943 0.185193i
\(636\) −4.08585 + 2.12568i −0.162014 + 0.0842888i
\(637\) 1.08024 + 4.45282i 0.0428008 + 0.176427i
\(638\) −1.17393 8.16485i −0.0464762 0.323249i
\(639\) 6.98838 + 15.0059i 0.276456 + 0.593624i
\(640\) −0.581020 + 4.04108i −0.0229668 + 0.159738i
\(641\) 0.296694 6.22837i 0.0117187 0.246006i −0.985406 0.170223i \(-0.945551\pi\)
0.997124 0.0757832i \(-0.0241457\pi\)
\(642\) −28.3613 + 2.81470i −1.11933 + 0.111087i
\(643\) −8.63788 + 14.9613i −0.340645 + 0.590014i −0.984553 0.175089i \(-0.943979\pi\)
0.643908 + 0.765103i \(0.277312\pi\)
\(644\) 7.74891 + 1.35846i 0.305350 + 0.0535310i
\(645\) −14.6788 31.8282i −0.577977 1.25323i
\(646\) 2.24422 6.48425i 0.0882977 0.255119i
\(647\) 2.26705 + 1.45694i 0.0891269 + 0.0572784i 0.584445 0.811433i \(-0.301312\pi\)
−0.495318 + 0.868712i \(0.664949\pi\)
\(648\) −8.99900 + 0.133941i −0.353514 + 0.00526169i
\(649\) −6.09405 + 13.3441i −0.239212 + 0.523802i
\(650\) −9.75244 + 7.66940i −0.382522 + 0.300819i
\(651\) −4.15713 28.1690i −0.162931 1.10403i
\(652\) 0.0224164 + 0.470578i 0.000877894 + 0.0184293i
\(653\) −1.27855 0.122087i −0.0500335 0.00477762i 0.0700092 0.997546i \(-0.477697\pi\)
−0.120043 + 0.992769i \(0.538303\pi\)
\(654\) 4.07304 11.9115i 0.159268 0.465775i
\(655\) −16.4149 3.16372i −0.641384 0.123617i
\(656\) 5.39317 6.22405i 0.210568 0.243009i
\(657\) 5.50722 12.3005i 0.214857 0.479890i
\(658\) −4.98804 10.9223i −0.194454 0.425795i
\(659\) −9.86025 5.08331i −0.384101 0.198018i 0.255352 0.966848i \(-0.417809\pi\)
−0.639453 + 0.768830i \(0.720839\pi\)
\(660\) 18.5978 + 7.36526i 0.723918 + 0.286693i
\(661\) 18.8259 + 7.53675i 0.732243 + 0.293146i 0.707661 0.706552i \(-0.249750\pi\)
0.0245815 + 0.999698i \(0.492175\pi\)
\(662\) −18.3270 25.7367i −0.712300 1.00029i
\(663\) 2.71702 11.3844i 0.105520 0.442135i
\(664\) −0.647635 + 13.5955i −0.0251331 + 0.527609i
\(665\) 4.73538 + 5.46492i 0.183630 + 0.211920i
\(666\) 12.2161 + 2.26031i 0.473363 + 0.0875851i
\(667\) 11.1370 + 8.45840i 0.431225 + 0.327510i
\(668\) 1.08119 + 1.87267i 0.0418324 + 0.0724559i
\(669\) 14.9272 1.48144i 0.577118 0.0572757i
\(670\) −48.3347 + 24.9183i −1.86733 + 0.962676i
\(671\) −16.9244 13.3095i −0.653360 0.513808i
\(672\) 2.84124 0.0105715i 0.109603 0.000407804i
\(673\) −1.51038 + 1.18777i −0.0582207 + 0.0457853i −0.646845 0.762621i \(-0.723912\pi\)
0.588625 + 0.808407i \(0.299670\pi\)
\(674\) −14.8846 4.37052i −0.573334 0.168346i
\(675\) −44.3430 41.3459i −1.70676 1.59140i
\(676\) −4.93070 10.7967i −0.189642 0.415259i
\(677\) −16.2353 15.4803i −0.623973 0.594957i 0.310682 0.950514i \(-0.399443\pi\)
−0.934655 + 0.355557i \(0.884291\pi\)
\(678\) −23.4610 6.79406i −0.901014 0.260924i
\(679\) 0.399084 + 1.15308i 0.0153155 + 0.0442511i
\(680\) 6.11675 25.2136i 0.234567 0.966897i
\(681\) 35.9942 + 6.79851i 1.37930 + 0.260519i
\(682\) −25.1975 12.9902i −0.964863 0.497421i
\(683\) −18.5315 5.44133i −0.709087 0.208207i −0.0927500 0.995689i \(-0.529566\pi\)
−0.616337 + 0.787483i \(0.711384\pi\)
\(684\) −2.86798 + 1.50567i −0.109660 + 0.0575706i
\(685\) −14.4436 + 31.6272i −0.551863 + 1.20841i
\(686\) 17.2226 6.89487i 0.657560 0.263247i
\(687\) −19.0206 14.8438i −0.725682 0.566325i
\(688\) −4.86706 + 0.938048i −0.185555 + 0.0357627i
\(689\) −1.41376 + 2.44870i −0.0538599 + 0.0932881i
\(690\) −31.2177 + 13.2492i −1.18844 + 0.504387i
\(691\) 7.34130 + 12.7155i 0.279276 + 0.483721i 0.971205 0.238245i \(-0.0765722\pi\)
−0.691929 + 0.721966i \(0.743239\pi\)
\(692\) 3.58618 + 4.13868i 0.136326 + 0.157329i
\(693\) 3.18122 13.5525i 0.120844 0.514819i
\(694\) 3.96735 27.5935i 0.150598 1.04744i
\(695\) 41.7818 3.98968i 1.58488 0.151337i
\(696\) 4.49786 + 2.29766i 0.170491 + 0.0870928i
\(697\) −37.8780 + 36.1166i −1.43473 + 1.36801i
\(698\) 0.782090 + 16.4181i 0.0296025 + 0.621434i
\(699\) −21.2528 + 24.7122i −0.803855 + 0.934703i
\(700\) 13.8523 + 13.2081i 0.523568 + 0.499221i
\(701\) −10.0006 + 11.5414i −0.377719 + 0.435911i −0.912498 0.409081i \(-0.865849\pi\)
0.534779 + 0.844992i \(0.320395\pi\)
\(702\) −4.61448 + 3.03886i −0.174162 + 0.114694i
\(703\) 4.29020 1.25972i 0.161808 0.0475111i
\(704\) 1.64084 2.30424i 0.0618416 0.0868444i
\(705\) 43.6476 + 27.8217i 1.64387 + 1.04783i
\(706\) 20.4226 19.4729i 0.768614 0.732872i
\(707\) −19.7755 7.91691i −0.743734 0.297746i
\(708\) −4.52007 7.76214i −0.169875 0.291719i
\(709\) −22.9263 + 9.17832i −0.861017 + 0.344699i −0.759793 0.650165i \(-0.774700\pi\)
−0.101223 + 0.994864i \(0.532276\pi\)
\(710\) 18.9510 + 12.1791i 0.711220 + 0.457073i
\(711\) 5.61739 + 9.56453i 0.210669 + 0.358698i
\(712\) −12.1500 −0.455340
\(713\) 45.8806 14.3159i 1.71824 0.536134i
\(714\) −17.9805 1.64945i −0.672905 0.0617290i
\(715\) 12.0583 2.32404i 0.450954 0.0869143i
\(716\) 15.1263 7.79813i 0.565295 0.291430i
\(717\) −9.70739 + 40.6744i −0.362529 + 1.51901i
\(718\) −17.6511 + 1.68548i −0.658734 + 0.0629015i
\(719\) 1.69715 + 11.8039i 0.0632930 + 0.440213i 0.996685 + 0.0813548i \(0.0259247\pi\)
−0.933392 + 0.358858i \(0.883166\pi\)
\(720\) −10.2540 + 6.69821i −0.382145 + 0.249627i
\(721\) 1.11901 0.719147i 0.0416743 0.0267824i
\(722\) 10.3448 14.5273i 0.384995 0.540650i
\(723\) −5.87685 + 17.1867i −0.218563 + 0.639180i
\(724\) 1.59637 + 4.61240i 0.0593285 + 0.171418i
\(725\) 11.1282 + 32.1529i 0.413292 + 1.19413i
\(726\) 3.41518 + 3.91182i 0.126749 + 0.145181i
\(727\) 12.7364 17.8858i 0.472369 0.663349i −0.507809 0.861470i \(-0.669544\pi\)
0.980178 + 0.198121i \(0.0634838\pi\)
\(728\) 1.46739 0.943033i 0.0543850 0.0349511i
\(729\) −18.1323 20.0055i −0.671568 0.740943i
\(730\) −2.61016 18.1540i −0.0966062 0.671911i
\(731\) 31.3565 2.99418i 1.15976 0.110744i
\(732\) 12.6354 3.76122i 0.467019 0.139019i
\(733\) −4.57787 + 2.36006i −0.169087 + 0.0871706i −0.540693 0.841220i \(-0.681838\pi\)
0.371605 + 0.928391i \(0.378807\pi\)
\(734\) 13.4184 2.58618i 0.495281 0.0954575i
\(735\) −17.5824 + 24.8865i −0.648538 + 0.917953i
\(736\) 0.762417 + 4.73484i 0.0281031 + 0.174529i
\(737\) 37.6785 1.38790
\(738\) 24.7061 0.183852i 0.909445 0.00676770i
\(739\) −0.360891 0.231931i −0.0132756 0.00853170i 0.533986 0.845493i \(-0.320693\pi\)
−0.547262 + 0.836961i \(0.684330\pi\)
\(740\) 15.6957 6.28361i 0.576986 0.230990i
\(741\) −0.987878 + 1.72585i −0.0362906 + 0.0634008i
\(742\) 4.04955 + 1.62120i 0.148664 + 0.0595160i
\(743\) 14.8902 14.1978i 0.546268 0.520866i −0.365915 0.930648i \(-0.619244\pi\)
0.912183 + 0.409783i \(0.134395\pi\)
\(744\) 15.3987 8.01126i 0.564545 0.293707i
\(745\) 14.6884 20.6269i 0.538141 0.755713i
\(746\) 22.9972 6.75258i 0.841986 0.247229i
\(747\) −31.9081 + 25.4794i −1.16746 + 0.932241i
\(748\) −11.7722 + 13.5858i −0.430434 + 0.496748i
\(749\) 19.5354 + 18.6270i 0.713808 + 0.680615i
\(750\) −46.3318 8.75106i −1.69180 0.319544i
\(751\) 0.809107 + 16.9852i 0.0295247 + 0.619800i 0.964340 + 0.264666i \(0.0852618\pi\)
−0.934815 + 0.355134i \(0.884435\pi\)
\(752\) 5.29758 5.05123i 0.193183 0.184199i
\(753\) 12.8189 8.30575i 0.467146 0.302678i
\(754\) 3.08668 0.294742i 0.112410 0.0107339i
\(755\) 7.36591 51.2310i 0.268073 1.86449i
\(756\) 5.65344 + 6.37913i 0.205614 + 0.232007i
\(757\) 10.7427 + 12.3977i 0.390450 + 0.450603i 0.916610 0.399782i \(-0.130914\pi\)
−0.526160 + 0.850386i \(0.676369\pi\)
\(758\) 1.43696 + 2.48888i 0.0521927 + 0.0904003i
\(759\) 23.4321 + 1.75190i 0.850530 + 0.0635901i
\(760\) −2.20407 + 3.81757i −0.0799501 + 0.138478i
\(761\) −29.7850 + 5.74059i −1.07971 + 0.208096i −0.697935 0.716161i \(-0.745898\pi\)
−0.381770 + 0.924257i \(0.624685\pi\)
\(762\) −19.3073 + 7.81296i −0.699430 + 0.283034i
\(763\) −11.0684 + 4.43114i −0.400705 + 0.160418i
\(764\) −4.16594 + 9.12213i −0.150718 + 0.330027i
\(765\) 68.9150 36.1798i 2.49163 1.30808i
\(766\) 21.8156 + 6.40564i 0.788230 + 0.231445i
\(767\) −4.90136 2.52683i −0.176978 0.0912385i
\(768\) 0.572584 + 1.63467i 0.0206614 + 0.0589861i
\(769\) −10.7079 + 44.1384i −0.386135 + 1.59167i 0.364664 + 0.931139i \(0.381184\pi\)
−0.750799 + 0.660531i \(0.770331\pi\)
\(770\) −6.19619 17.9027i −0.223295 0.645169i
\(771\) −20.5584 + 19.7489i −0.740392 + 0.711240i
\(772\) −14.6490 13.9678i −0.527230 0.502712i
\(773\) 20.1913 + 44.2128i 0.726231 + 1.59022i 0.804960 + 0.593329i \(0.202187\pi\)
−0.0787289 + 0.996896i \(0.525086\pi\)
\(774\) −11.7566 9.10472i −0.422582 0.327262i
\(775\) 112.195 + 32.9435i 4.03017 + 1.18337i
\(776\) −0.584694 + 0.459809i −0.0209893 + 0.0165062i
\(777\) −5.92090 10.1677i −0.212411 0.364766i
\(778\) −13.5437 10.6509i −0.485565 0.381853i
\(779\) 7.90373 4.07466i 0.283181 0.145990i
\(780\) −3.09810 + 6.85124i −0.110930 + 0.245314i
\(781\) −7.80427 13.5174i −0.279259 0.483690i
\(782\) −1.96298 30.4140i −0.0701960 1.08760i
\(783\) 3.73641 + 14.6843i 0.133528 + 0.524775i
\(784\) 2.82185 + 3.25659i 0.100780 + 0.116307i
\(785\) 4.33732 91.0515i 0.154806 3.24977i
\(786\) −6.79740 + 2.02340i −0.242455 + 0.0721723i
\(787\) 4.67990 + 6.57200i 0.166820 + 0.234266i 0.889520 0.456895i \(-0.151039\pi\)
−0.722700 + 0.691162i \(0.757099\pi\)
\(788\) 18.6805 + 7.47855i 0.665466 + 0.266412i
\(789\) −4.37935 + 3.47041i −0.155909 + 0.123550i
\(790\) 13.4170 + 6.91695i 0.477356 + 0.246094i
\(791\) 9.60959 + 21.0421i 0.341678 + 0.748170i
\(792\) 8.44163 0.869514i 0.299960 0.0308968i
\(793\) 5.30008 6.11662i 0.188211 0.217208i
\(794\) −21.8598 4.21313i −0.775776 0.149519i
\(795\) −18.4503 + 3.62726i −0.654365 + 0.128646i
\(796\) 0.303487 + 0.0289795i 0.0107568 + 0.00102715i
\(797\) −0.136435 2.86413i −0.00483279 0.101453i −0.999995 0.00320585i \(-0.998980\pi\)
0.995162 0.0982469i \(-0.0313235\pi\)
\(798\) 2.85226 + 1.12958i 0.100969 + 0.0399866i
\(799\) −36.5647 + 28.7548i −1.29357 + 1.01727i
\(800\) −4.84703 + 10.6135i −0.171368 + 0.375244i
\(801\) −24.0740 27.3687i −0.850613 0.967025i
\(802\) 1.31365 + 0.844230i 0.0463865 + 0.0298108i
\(803\) −4.15633 + 12.0089i −0.146674 + 0.423786i
\(804\) −13.3122 + 18.8424i −0.469485 + 0.664518i
\(805\) 28.7920 + 14.2343i 1.01478 + 0.501695i
\(806\) 5.32817 9.22866i 0.187677 0.325066i
\(807\) −18.6886 + 41.3285i −0.657869 + 1.45483i
\(808\) 0.617873 12.9708i 0.0217367 0.456309i
\(809\) −5.63727 + 39.2081i −0.198196 + 1.37848i 0.611319 + 0.791384i \(0.290639\pi\)
−0.809515 + 0.587099i \(0.800270\pi\)
\(810\) −35.4055 9.82607i −1.24402 0.345253i
\(811\) −5.84930 40.6827i −0.205397 1.42856i −0.787934 0.615760i \(-0.788849\pi\)
0.582537 0.812804i \(-0.302060\pi\)
\(812\) −1.12775 4.64865i −0.0395762 0.163135i
\(813\) −3.32400 2.11877i −0.116578 0.0743086i
\(814\) −11.6613 1.11352i −0.408727 0.0390287i
\(815\) −0.453454 + 1.86916i −0.0158838 + 0.0654739i
\(816\) −2.63480 10.6871i −0.0922366 0.374123i
\(817\) −5.25511 1.01284i −0.183853 0.0354348i
\(818\) 7.56197 2.22040i 0.264398 0.0776343i
\(819\) 5.03172 + 1.43686i 0.175823 + 0.0502081i
\(820\) 28.2854 18.1780i 0.987771 0.634802i
\(821\) 1.66886 + 6.87914i 0.0582436 + 0.240084i 0.993491 0.113912i \(-0.0363381\pi\)
−0.935247 + 0.353995i \(0.884823\pi\)
\(822\) 0.756686 + 14.7313i 0.0263925 + 0.513815i
\(823\) −30.8114 43.2686i −1.07402 1.50825i −0.844955 0.534837i \(-0.820373\pi\)
−0.229064 0.973411i \(-0.573566\pi\)
\(824\) 0.637398 + 0.501256i 0.0222048 + 0.0174621i
\(825\) 45.0680 + 35.1713i 1.56907 + 1.22451i
\(826\) −2.78237 + 8.03914i −0.0968111 + 0.279717i
\(827\) 26.6043 0.925123 0.462562 0.886587i \(-0.346930\pi\)
0.462562 + 0.886587i \(0.346930\pi\)
\(828\) −9.15489 + 11.0990i −0.318155 + 0.385717i
\(829\) −23.3926 −0.812460 −0.406230 0.913771i \(-0.633157\pi\)
−0.406230 + 0.913771i \(0.633157\pi\)
\(830\) −18.1747 + 52.5124i −0.630853 + 1.82273i
\(831\) 44.8500 18.1491i 1.55583 0.629586i
\(832\) 0.835834 + 0.657307i 0.0289773 + 0.0227880i
\(833\) −15.8843 22.3064i −0.550358 0.772870i
\(834\) 14.9439 9.68259i 0.517463 0.335281i
\(835\) 2.08133 + 8.57934i 0.0720273 + 0.296900i
\(836\) 2.56944 1.65128i 0.0888660 0.0571107i
\(837\) 48.5569 + 18.8132i 1.67837 + 0.650278i
\(838\) −20.9144 + 6.14101i −0.722474 + 0.212138i
\(839\) 33.0921 + 6.37798i 1.14247 + 0.220192i 0.725165 0.688575i \(-0.241764\pi\)
0.417302 + 0.908768i \(0.362976\pi\)
\(840\) 11.1420 + 3.22661i 0.384436 + 0.111329i
\(841\) −4.83227 + 19.9189i −0.166630 + 0.686859i
\(842\) −17.7925 1.69898i −0.613172 0.0585508i
\(843\) 1.05567 24.0431i 0.0363592 0.828089i
\(844\) −0.898832 3.70504i −0.0309391 0.127533i
\(845\) −6.89631 47.9649i −0.237240 1.65004i
\(846\) 21.8749 + 1.92464i 0.752073 + 0.0661706i
\(847\) 0.699916 4.86802i 0.0240494 0.167267i
\(848\) −0.126526 + 2.65610i −0.00434492 + 0.0912110i
\(849\) −18.3381 25.5505i −0.629362 0.876891i
\(850\) 37.0745 64.2149i 1.27164 2.20255i
\(851\) 15.4021 12.5381i 0.527977 0.429801i
\(852\) 9.51714 + 0.873055i 0.326052 + 0.0299104i
\(853\) −5.27140 + 15.2307i −0.180489 + 0.521490i −0.998561 0.0536266i \(-0.982922\pi\)
0.818072 + 0.575116i \(0.195043\pi\)
\(854\) −10.5037 6.75032i −0.359429 0.230991i
\(855\) −12.9665 + 2.59930i −0.443444 + 0.0888942i
\(856\) −6.83559 + 14.9679i −0.233636 + 0.511591i
\(857\) 0.194981 0.153335i 0.00666042 0.00523782i −0.614823 0.788665i \(-0.710773\pi\)
0.621484 + 0.783427i \(0.286530\pi\)
\(858\) 4.08321 3.23573i 0.139398 0.110466i
\(859\) 1.42014 + 29.8123i 0.0484544 + 1.01718i 0.883919 + 0.467639i \(0.154895\pi\)
−0.835465 + 0.549544i \(0.814802\pi\)
\(860\) −20.1445 1.92356i −0.686921 0.0655930i
\(861\) −15.3891 17.6270i −0.524458 0.600726i
\(862\) 17.6224 + 3.39645i 0.600223 + 0.115683i
\(863\) −20.6330 + 23.8117i −0.702354 + 0.810560i −0.989069 0.147456i \(-0.952891\pi\)
0.286715 + 0.958016i \(0.407437\pi\)
\(864\) −2.54769 + 4.52872i −0.0866740 + 0.154070i
\(865\) 9.28766 + 20.3371i 0.315790 + 0.691484i
\(866\) −18.9770 9.78330i −0.644863 0.332450i
\(867\) 5.91355 + 40.0707i 0.200835 + 1.36087i
\(868\) −15.2619 6.10996i −0.518024 0.207385i
\(869\) −6.06682 8.51965i −0.205803 0.289009i
\(870\) 14.9765 + 14.1740i 0.507750 + 0.480545i
\(871\) −0.673918 + 14.1473i −0.0228348 + 0.479362i
\(872\) −4.75955 5.49281i −0.161179 0.186010i
\(873\) −2.19426 0.405998i −0.0742645 0.0137410i
\(874\) −1.13583 + 5.05210i −0.0384201 + 0.170890i
\(875\) 22.3280 + 38.6733i 0.754825 + 1.30740i
\(876\) −4.53698 6.32139i −0.153290 0.213580i
\(877\) 45.0735 23.2370i 1.52202 0.784658i 0.524264 0.851556i \(-0.324341\pi\)
0.997760 + 0.0668985i \(0.0213104\pi\)
\(878\) 9.20973 + 7.24261i 0.310813 + 0.244426i
\(879\) 28.4760 49.7484i 0.960472 1.67797i
\(880\) 9.07798 7.13900i 0.306019 0.240656i
\(881\) 1.70157 + 0.499626i 0.0573273 + 0.0168328i 0.310270 0.950648i \(-0.399580\pi\)
−0.252943 + 0.967481i \(0.581399\pi\)
\(882\) −1.74447 + 12.8090i −0.0587395 + 0.431302i
\(883\) 13.7682 + 30.1482i 0.463338 + 1.01457i 0.986714 + 0.162467i \(0.0519452\pi\)
−0.523376 + 0.852102i \(0.675328\pi\)
\(884\) −4.89057 4.66315i −0.164488 0.156839i
\(885\) −8.77817 35.6054i −0.295075 1.19686i
\(886\) 12.5036 + 36.1268i 0.420067 + 1.21370i
\(887\) −10.9244 + 45.0310i −0.366806 + 1.51199i 0.427242 + 0.904137i \(0.359485\pi\)
−0.794047 + 0.607856i \(0.792030\pi\)
\(888\) 4.67690 5.43818i 0.156946 0.182493i
\(889\) 17.5333 + 9.03903i 0.588047 + 0.303159i
\(890\) −47.5947 13.9751i −1.59538 0.468445i
\(891\) 18.6849 + 17.2925i 0.625967 + 0.579320i
\(892\) 3.59772 7.87791i 0.120461 0.263772i
\(893\) 7.33726 2.93740i 0.245532 0.0982962i
\(894\) 1.48931 10.6392i 0.0498098 0.355828i
\(895\) 68.2230 13.1489i 2.28044 0.439520i
\(896\) 0.820200 1.42063i 0.0274010 0.0474599i
\(897\) −1.07690 + 8.76679i −0.0359566 + 0.292715i
\(898\) −7.43442 12.8768i −0.248090 0.429704i
\(899\) −19.1374 22.0858i −0.638268 0.736601i
\(900\) −33.5115 + 10.1113i −1.11705 + 0.337045i
\(901\) 2.40491 16.7265i 0.0801193 0.557242i
\(902\) −23.1911 + 2.21448i −0.772179 + 0.0737341i
\(903\) 0.722434 + 14.0645i 0.0240411 + 0.468038i
\(904\) −10.2059 + 9.73132i −0.339444 + 0.323659i
\(905\) 0.948151 + 19.9041i 0.0315176 + 0.661636i
\(906\) −7.25897 20.7236i −0.241163 0.688496i
\(907\) −5.29092 5.04488i −0.175682 0.167513i 0.597136 0.802140i \(-0.296305\pi\)
−0.772818 + 0.634627i \(0.781154\pi\)
\(908\) 13.8494 15.9831i 0.459610 0.530418i
\(909\) 30.4417 24.3084i 1.00969 0.806260i
\(910\) 6.83283 2.00630i 0.226506 0.0665081i
\(911\) 12.1491 17.0611i 0.402519 0.565259i −0.562713 0.826652i \(-0.690242\pi\)
0.965232 + 0.261393i \(0.0841819\pi\)
\(912\) −0.0820342 + 1.86835i −0.00271642 + 0.0618672i
\(913\) 27.8653 26.5695i 0.922208 0.879324i
\(914\) 25.7768 + 10.3195i 0.852619 + 0.341337i
\(915\) 53.8225 0.200259i 1.77932 0.00662036i
\(916\) −12.9320 + 5.17720i −0.427286 + 0.171059i
\(917\) 5.65061 + 3.63142i 0.186599 + 0.119920i
\(918\) 18.8528 27.1105i 0.622235 0.894779i
\(919\) −34.0030 −1.12166 −0.560828 0.827932i \(-0.689517\pi\)
−0.560828 + 0.827932i \(0.689517\pi\)
\(920\) −2.45948 + 19.4245i −0.0810867 + 0.640408i
\(921\) −1.93125 4.18755i −0.0636369 0.137984i
\(922\) 16.6526 3.20953i 0.548425 0.105700i
\(923\) 5.21501 2.68852i 0.171654 0.0884938i
\(924\) −5.83742 5.52465i −0.192037 0.181748i
\(925\) 48.0997 4.59296i 1.58151 0.151016i
\(926\) −0.480131 3.33938i −0.0157781 0.109739i
\(927\) 0.133829 + 2.42897i 0.00439552 + 0.0797779i
\(928\) 2.45314 1.57653i 0.0805281 0.0517523i
\(929\) 18.2721 25.6595i 0.599487 0.841861i −0.397645 0.917539i \(-0.630173\pi\)
0.997132 + 0.0756776i \(0.0241120\pi\)
\(930\) 69.5355 13.6704i 2.28016 0.448270i
\(931\) 1.52173 + 4.39676i 0.0498728 + 0.144098i
\(932\) 6.15484 + 17.7832i 0.201608 + 0.582510i
\(933\) −23.5110 + 4.62216i −0.769714 + 0.151323i
\(934\) 16.7836 23.5693i 0.549177 0.771211i
\(935\) −61.7414 + 39.6788i −2.01916 + 1.29763i
\(936\) 0.175493 + 3.18516i 0.00573616 + 0.104110i
\(937\) −8.11563 56.4454i −0.265126 1.84399i −0.492660 0.870222i \(-0.663975\pi\)
0.227533 0.973770i \(-0.426934\pi\)
\(938\) 21.7508 2.07695i 0.710189 0.0678149i
\(939\) −6.01825 5.69579i −0.196398 0.185875i
\(940\) 26.5620 13.6936i 0.866356 0.446638i
\(941\) 1.08484 0.209086i 0.0353648 0.00681600i −0.171538 0.985177i \(-0.554874\pi\)
0.206903 + 0.978361i \(0.433662\pi\)
\(942\) −16.1958 35.1175i −0.527688 1.14419i
\(943\) 25.3581 30.2811i 0.825772 0.986090i
\(944\) −5.18594 −0.168788
\(945\) 14.8086 + 31.4914i 0.481725 + 1.02441i
\(946\) 11.7953 + 7.58039i 0.383499 + 0.246460i
\(947\) −6.61062 + 2.64649i −0.214816 + 0.0859994i −0.476575 0.879134i \(-0.658122\pi\)
0.261759 + 0.965133i \(0.415698\pi\)
\(948\) 6.40400 0.0238276i 0.207992 0.000773884i
\(949\) −4.43470 1.77538i −0.143956 0.0576314i
\(950\) −9.11775 + 8.69375i −0.295819 + 0.282063i
\(951\) −1.83208 + 41.7260i −0.0594092 + 1.35306i
\(952\) −6.04690 + 8.49168i −0.195981 + 0.275217i
\(953\) −51.4985 + 15.1213i −1.66820 + 0.489828i −0.973349 0.229327i \(-0.926347\pi\)
−0.694850 + 0.719155i \(0.744529\pi\)
\(954\) −6.23375 + 4.97779i −0.201825 + 0.161162i
\(955\) −26.8114 + 30.9421i −0.867598 + 1.00126i
\(956\) 17.4730 + 16.6605i 0.565118 + 0.538839i
\(957\) −4.72314 13.4841i −0.152677 0.435878i
\(958\) 0.230969 + 4.84864i 0.00746227 + 0.156652i
\(959\) 10.1107 9.64057i 0.326493 0.311310i
\(960\) 0.362746 + 7.06202i 0.0117076 + 0.227926i
\(961\) −69.1193 + 6.60009i −2.22965 + 0.212906i
\(962\) 0.626669 4.35858i 0.0202046 0.140526i
\(963\) −47.2601 + 14.2597i −1.52294 + 0.459511i
\(964\) 6.86740 + 7.92540i 0.221184 + 0.255260i
\(965\) −41.3181 71.5650i −1.33008 2.30376i
\(966\) 13.6233 0.280318i 0.438323 0.00901907i
\(967\) 23.8865 41.3726i 0.768137 1.33045i −0.170435 0.985369i \(-0.554517\pi\)
0.938572 0.345083i \(-0.112149\pi\)
\(968\) 2.94392 0.567394i 0.0946212 0.0182367i
\(969\) 1.64759 11.7699i 0.0529281 0.378105i
\(970\) −2.81928 + 1.12867i −0.0905215 + 0.0362393i
\(971\) −16.8923 + 36.9889i −0.542098 + 1.18703i 0.418277 + 0.908320i \(0.362634\pi\)
−0.960375 + 0.278710i \(0.910093\pi\)
\(972\) −15.2492 + 3.23437i −0.489119 + 0.103742i
\(973\) −16.1812 4.75121i −0.518744 0.152317i
\(974\) 0.615741 + 0.317437i 0.0197296 + 0.0101713i
\(975\) −14.0120 + 16.2928i −0.448742 + 0.521786i
\(976\) 1.79446 7.39686i 0.0574392 0.236768i
\(977\) −14.0197 40.5072i −0.448529 1.29594i −0.912132 0.409897i \(-0.865565\pi\)
0.463602 0.886043i \(-0.346557\pi\)
\(978\) 0.195326 + 0.792267i 0.00624584 + 0.0253339i
\(979\) 24.8743 + 23.7176i 0.794988 + 0.758019i
\(980\) 7.30816 + 16.0026i 0.233451 + 0.511186i
\(981\) 2.94236 21.6046i 0.0939423 0.689783i
\(982\) −9.68095 2.84258i −0.308932 0.0907105i
\(983\) −11.0189 + 8.66534i −0.351448 + 0.276382i −0.778238 0.627969i \(-0.783887\pi\)
0.426791 + 0.904350i \(0.359644\pi\)
\(984\) 7.08623 12.3799i 0.225901 0.394655i
\(985\) 64.5745 + 50.7819i 2.05751 + 1.61805i
\(986\) −16.4713 + 8.49155i −0.524553 + 0.270426i
\(987\) −12.1266 16.8960i −0.385994 0.537807i
\(988\) 0.574055 + 0.994292i 0.0182631 + 0.0316327i
\(989\) −23.2625 + 4.89143i −0.739703 + 0.155538i
\(990\) 34.0682 + 6.30354i 1.08276 + 0.200340i
\(991\) −7.28780 8.41057i −0.231505 0.267170i 0.628097 0.778135i \(-0.283834\pi\)
−0.859602 + 0.510964i \(0.829288\pi\)
\(992\) 0.476850 10.0103i 0.0151400 0.317828i
\(993\) −39.7462 37.6166i −1.26131 1.19373i
\(994\) −5.25032 7.37304i −0.166530 0.233859i
\(995\) 1.15551 + 0.462595i 0.0366320 + 0.0146652i
\(996\) 3.44185 + 23.3223i 0.109059 + 0.738994i
\(997\) 25.2017 + 12.9924i 0.798146 + 0.411473i 0.808517 0.588473i \(-0.200271\pi\)
−0.0103706 + 0.999946i \(0.503301\pi\)
\(998\) 0.138247 + 0.302719i 0.00437614 + 0.00958240i
\(999\) 21.5167 0.240182i 0.680757 0.00759903i
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.13.7 240
9.7 even 3 inner 414.2.m.a.151.2 yes 240
23.16 even 11 inner 414.2.m.a.85.2 yes 240
207.16 even 33 inner 414.2.m.a.223.7 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
414.2.m.a.13.7 240 1.1 even 1 trivial
414.2.m.a.85.2 yes 240 23.16 even 11 inner
414.2.m.a.151.2 yes 240 9.7 even 3 inner
414.2.m.a.223.7 yes 240 207.16 even 33 inner