Properties

Label 966.2.q.e.169.1
Level $966$
Weight $2$
Character 966.169
Analytic conductor $7.714$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [966,2,Mod(85,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("966.85");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.q (of order \(11\), degree \(10\), 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: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 9 x^{19} + 42 x^{18} - 126 x^{17} + 277 x^{16} - 538 x^{15} + 1046 x^{14} - 1170 x^{13} - 619 x^{12} + 2218 x^{11} + 1660 x^{10} - 3225 x^{9} + 2719 x^{8} + 8761 x^{7} + \cdots + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 169.1
Root \(2.33806 - 1.50258i\) of defining polynomial
Character \(\chi\) \(=\) 966.169
Dual form 966.2.q.e.463.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.142315 - 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.18479 - 1.36732i) q^{5} +(0.959493 - 0.281733i) q^{6} +(0.841254 + 0.540641i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\) \(q+(0.142315 - 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.18479 - 1.36732i) q^{5} +(0.959493 - 0.281733i) q^{6} +(0.841254 + 0.540641i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-1.52202 + 0.978140i) q^{10} +(0.294035 + 2.04506i) q^{11} +(-0.142315 - 0.989821i) q^{12} +(4.53425 - 2.91398i) q^{13} +(0.654861 - 0.755750i) q^{14} +(0.751578 - 1.64573i) q^{15} +(0.841254 + 0.540641i) q^{16} +(0.123350 - 0.0362190i) q^{17} +(0.654861 + 0.755750i) q^{18} +(2.21858 + 0.651433i) q^{19} +(0.751578 + 1.64573i) q^{20} +(-0.142315 + 0.989821i) q^{21} +2.06609 q^{22} +(-3.43390 + 3.34789i) q^{23} -1.00000 q^{24} +(0.245737 - 1.70914i) q^{25} +(-2.23903 - 4.90280i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(-0.654861 - 0.755750i) q^{28} +(9.94663 - 2.92059i) q^{29} +(-1.52202 - 0.978140i) q^{30} +(2.42664 - 5.31359i) q^{31} +(0.654861 - 0.755750i) q^{32} +(-1.73810 + 1.11701i) q^{33} +(-0.0182957 - 0.127249i) q^{34} +(-0.257479 - 1.79081i) q^{35} +(0.841254 - 0.540641i) q^{36} +(4.33411 - 5.00183i) q^{37} +(0.960539 - 2.10329i) q^{38} +(4.53425 + 2.91398i) q^{39} +(1.73594 - 0.509717i) q^{40} +(4.31152 + 4.97576i) q^{41} +(0.959493 + 0.281733i) q^{42} +(-3.36354 - 7.36513i) q^{43} +(0.294035 - 2.04506i) q^{44} +1.80922 q^{45} +(2.82512 + 3.87540i) q^{46} -3.45576 q^{47} +(-0.142315 + 0.989821i) q^{48} +(0.415415 + 0.909632i) q^{49} +(-1.65677 - 0.486471i) q^{50} +(0.0841876 + 0.0971576i) q^{51} +(-5.17154 + 1.51850i) q^{52} +(3.47673 + 2.23436i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(2.44788 - 2.82500i) q^{55} +(-0.841254 + 0.540641i) q^{56} +(0.329066 + 2.28870i) q^{57} +(-1.47531 - 10.2610i) q^{58} +(-4.12860 + 2.65329i) q^{59} +(-1.18479 + 1.36732i) q^{60} +(3.97146 - 8.69629i) q^{61} +(-4.91416 - 3.15814i) q^{62} +(-0.959493 + 0.281733i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-9.35647 - 2.74731i) q^{65} +(0.858284 + 1.87938i) q^{66} +(-1.21827 + 8.47327i) q^{67} -0.128558 q^{68} +(-4.47184 - 1.73282i) q^{69} -1.80922 q^{70} +(0.419758 - 2.91948i) q^{71} +(-0.415415 - 0.909632i) q^{72} +(11.4515 + 3.36247i) q^{73} +(-4.33411 - 5.00183i) q^{74} +(1.65677 - 0.486471i) q^{75} +(-1.94518 - 1.25009i) q^{76} +(-0.858284 + 1.87938i) q^{77} +(3.52961 - 4.07339i) q^{78} +(-1.66985 + 1.07315i) q^{79} +(-0.257479 - 1.79081i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(5.53871 - 3.55951i) q^{82} +(4.11967 - 4.75436i) q^{83} +(0.415415 - 0.909632i) q^{84} +(-0.195667 - 0.125748i) q^{85} +(-7.76884 + 2.28114i) q^{86} +(6.78864 + 7.83451i) q^{87} +(-1.98240 - 0.582084i) q^{88} +(5.19257 + 11.3701i) q^{89} +(0.257479 - 1.79081i) q^{90} +5.38987 q^{91} +(4.23801 - 2.24484i) q^{92} +5.84147 q^{93} +(-0.491807 + 3.42059i) q^{94} +(-1.73783 - 3.80531i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-0.372464 - 0.429846i) q^{97} +(0.959493 - 0.281733i) q^{98} +(-1.73810 - 1.11701i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 10 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 10 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 10 q^{10} - 3 q^{11} - 2 q^{12} + 6 q^{13} + 2 q^{14} - 12 q^{15} - 2 q^{16} + 14 q^{17} + 2 q^{18} - 13 q^{19} - 12 q^{20} - 2 q^{21} - 8 q^{22} - 2 q^{23} - 20 q^{24} + 22 q^{25} - 28 q^{26} - 2 q^{27} - 2 q^{28} + 26 q^{29} - 10 q^{30} + 15 q^{31} + 2 q^{32} - 14 q^{33} - 3 q^{34} - q^{35} - 2 q^{36} - 26 q^{37} + 2 q^{38} + 6 q^{39} + q^{40} + 40 q^{41} + 2 q^{42} + 8 q^{43} - 3 q^{44} - 12 q^{45} - 20 q^{46} + 36 q^{47} - 2 q^{48} - 2 q^{49} + 11 q^{50} + 3 q^{51} - 27 q^{52} - 5 q^{53} + 2 q^{54} - 7 q^{55} + 2 q^{56} + 9 q^{57} - 15 q^{58} + 13 q^{59} + 10 q^{60} + 59 q^{61} - 4 q^{62} - 2 q^{63} - 2 q^{64} - q^{65} - 8 q^{66} - 26 q^{67} - 8 q^{68} - 35 q^{69} + 12 q^{70} + 13 q^{71} + 2 q^{72} - 34 q^{73} + 26 q^{74} - 11 q^{75} - 2 q^{76} + 8 q^{77} - 6 q^{78} - 27 q^{79} - q^{80} - 2 q^{81} - 40 q^{82} + 41 q^{83} - 2 q^{84} + 51 q^{85} + 14 q^{86} - 7 q^{87} - 8 q^{88} + 43 q^{89} + q^{90} - 16 q^{91} + 9 q^{92} + 4 q^{93} - 3 q^{94} - 26 q^{95} + 2 q^{96} - 8 q^{97} + 2 q^{98} - 14 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.142315 0.989821i 0.100632 0.699909i
\(3\) 0.415415 + 0.909632i 0.239840 + 0.525176i
\(4\) −0.959493 0.281733i −0.479746 0.140866i
\(5\) −1.18479 1.36732i −0.529854 0.611484i 0.426217 0.904621i \(-0.359846\pi\)
−0.956070 + 0.293137i \(0.905301\pi\)
\(6\) 0.959493 0.281733i 0.391711 0.115017i
\(7\) 0.841254 + 0.540641i 0.317964 + 0.204343i
\(8\) −0.415415 + 0.909632i −0.146871 + 0.321603i
\(9\) −0.654861 + 0.755750i −0.218287 + 0.251917i
\(10\) −1.52202 + 0.978140i −0.481303 + 0.309315i
\(11\) 0.294035 + 2.04506i 0.0886549 + 0.616608i 0.984910 + 0.173069i \(0.0553683\pi\)
−0.896255 + 0.443539i \(0.853723\pi\)
\(12\) −0.142315 0.989821i −0.0410828 0.285737i
\(13\) 4.53425 2.91398i 1.25757 0.808193i 0.269623 0.962966i \(-0.413101\pi\)
0.987950 + 0.154772i \(0.0494644\pi\)
\(14\) 0.654861 0.755750i 0.175019 0.201983i
\(15\) 0.751578 1.64573i 0.194057 0.424925i
\(16\) 0.841254 + 0.540641i 0.210313 + 0.135160i
\(17\) 0.123350 0.0362190i 0.0299169 0.00878439i −0.266740 0.963769i \(-0.585946\pi\)
0.296657 + 0.954984i \(0.404128\pi\)
\(18\) 0.654861 + 0.755750i 0.154352 + 0.178132i
\(19\) 2.21858 + 0.651433i 0.508976 + 0.149449i 0.526130 0.850404i \(-0.323642\pi\)
−0.0171540 + 0.999853i \(0.505461\pi\)
\(20\) 0.751578 + 1.64573i 0.168058 + 0.367996i
\(21\) −0.142315 + 0.989821i −0.0310556 + 0.215997i
\(22\) 2.06609 0.440492
\(23\) −3.43390 + 3.34789i −0.716017 + 0.698083i
\(24\) −1.00000 −0.204124
\(25\) 0.245737 1.70914i 0.0491474 0.341827i
\(26\) −2.23903 4.90280i −0.439110 0.961518i
\(27\) −0.959493 0.281733i −0.184655 0.0542195i
\(28\) −0.654861 0.755750i −0.123757 0.142823i
\(29\) 9.94663 2.92059i 1.84704 0.542340i 0.847102 0.531431i \(-0.178346\pi\)
0.999940 0.0109094i \(-0.00347263\pi\)
\(30\) −1.52202 0.978140i −0.277881 0.178583i
\(31\) 2.42664 5.31359i 0.435837 0.954349i −0.556507 0.830843i \(-0.687859\pi\)
0.992344 0.123506i \(-0.0394139\pi\)
\(32\) 0.654861 0.755750i 0.115764 0.133599i
\(33\) −1.73810 + 1.11701i −0.302565 + 0.194447i
\(34\) −0.0182957 0.127249i −0.00313769 0.0218231i
\(35\) −0.257479 1.79081i −0.0435219 0.302702i
\(36\) 0.841254 0.540641i 0.140209 0.0901068i
\(37\) 4.33411 5.00183i 0.712524 0.822296i −0.277863 0.960621i \(-0.589626\pi\)
0.990387 + 0.138324i \(0.0441716\pi\)
\(38\) 0.960539 2.10329i 0.155820 0.341198i
\(39\) 4.53425 + 2.91398i 0.726060 + 0.466611i
\(40\) 1.73594 0.509717i 0.274476 0.0805933i
\(41\) 4.31152 + 4.97576i 0.673347 + 0.777083i 0.984896 0.173147i \(-0.0553934\pi\)
−0.311550 + 0.950230i \(0.600848\pi\)
\(42\) 0.959493 + 0.281733i 0.148053 + 0.0434723i
\(43\) −3.36354 7.36513i −0.512935 1.12317i −0.972046 0.234792i \(-0.924559\pi\)
0.459110 0.888379i \(-0.348168\pi\)
\(44\) 0.294035 2.04506i 0.0443274 0.308304i
\(45\) 1.80922 0.269703
\(46\) 2.82512 + 3.87540i 0.416541 + 0.571396i
\(47\) −3.45576 −0.504075 −0.252038 0.967717i \(-0.581101\pi\)
−0.252038 + 0.967717i \(0.581101\pi\)
\(48\) −0.142315 + 0.989821i −0.0205414 + 0.142868i
\(49\) 0.415415 + 0.909632i 0.0593450 + 0.129947i
\(50\) −1.65677 0.486471i −0.234302 0.0687974i
\(51\) 0.0841876 + 0.0971576i 0.0117886 + 0.0136048i
\(52\) −5.17154 + 1.51850i −0.717164 + 0.210578i
\(53\) 3.47673 + 2.23436i 0.477566 + 0.306913i 0.757188 0.653197i \(-0.226573\pi\)
−0.279622 + 0.960110i \(0.590209\pi\)
\(54\) −0.415415 + 0.909632i −0.0565308 + 0.123785i
\(55\) 2.44788 2.82500i 0.330072 0.380923i
\(56\) −0.841254 + 0.540641i −0.112417 + 0.0722462i
\(57\) 0.329066 + 2.28870i 0.0435858 + 0.303146i
\(58\) −1.47531 10.2610i −0.193718 1.34734i
\(59\) −4.12860 + 2.65329i −0.537498 + 0.345429i −0.781060 0.624456i \(-0.785321\pi\)
0.243561 + 0.969885i \(0.421684\pi\)
\(60\) −1.18479 + 1.36732i −0.152956 + 0.176520i
\(61\) 3.97146 8.69629i 0.508494 1.11345i −0.465121 0.885247i \(-0.653989\pi\)
0.973615 0.228199i \(-0.0732836\pi\)
\(62\) −4.91416 3.15814i −0.624099 0.401084i
\(63\) −0.959493 + 0.281733i −0.120885 + 0.0354950i
\(64\) −0.654861 0.755750i −0.0818576 0.0944687i
\(65\) −9.35647 2.74731i −1.16053 0.340762i
\(66\) 0.858284 + 1.87938i 0.105647 + 0.231336i
\(67\) −1.21827 + 8.47327i −0.148836 + 1.03517i 0.769294 + 0.638895i \(0.220608\pi\)
−0.918130 + 0.396280i \(0.870301\pi\)
\(68\) −0.128558 −0.0155899
\(69\) −4.47184 1.73282i −0.538346 0.208607i
\(70\) −1.80922 −0.216243
\(71\) 0.419758 2.91948i 0.0498161 0.346479i −0.949635 0.313357i \(-0.898546\pi\)
0.999451 0.0331211i \(-0.0105447\pi\)
\(72\) −0.415415 0.909632i −0.0489571 0.107201i
\(73\) 11.4515 + 3.36247i 1.34030 + 0.393547i 0.871776 0.489904i \(-0.162968\pi\)
0.468523 + 0.883451i \(0.344786\pi\)
\(74\) −4.33411 5.00183i −0.503830 0.581451i
\(75\) 1.65677 0.486471i 0.191307 0.0561729i
\(76\) −1.94518 1.25009i −0.223127 0.143395i
\(77\) −0.858284 + 1.87938i −0.0978106 + 0.214175i
\(78\) 3.52961 4.07339i 0.399650 0.461221i
\(79\) −1.66985 + 1.07315i −0.187872 + 0.120738i −0.631196 0.775623i \(-0.717436\pi\)
0.443324 + 0.896362i \(0.353799\pi\)
\(80\) −0.257479 1.79081i −0.0287871 0.200218i
\(81\) −0.142315 0.989821i −0.0158128 0.109980i
\(82\) 5.53871 3.55951i 0.611648 0.393082i
\(83\) 4.11967 4.75436i 0.452193 0.521858i −0.483180 0.875521i \(-0.660518\pi\)
0.935373 + 0.353663i \(0.115064\pi\)
\(84\) 0.415415 0.909632i 0.0453255 0.0992490i
\(85\) −0.195667 0.125748i −0.0212231 0.0136392i
\(86\) −7.76884 + 2.28114i −0.837736 + 0.245981i
\(87\) 6.78864 + 7.83451i 0.727819 + 0.839948i
\(88\) −1.98240 0.582084i −0.211324 0.0620504i
\(89\) 5.19257 + 11.3701i 0.550411 + 1.20523i 0.956589 + 0.291439i \(0.0941339\pi\)
−0.406178 + 0.913794i \(0.633139\pi\)
\(90\) 0.257479 1.79081i 0.0271407 0.188768i
\(91\) 5.38987 0.565012
\(92\) 4.23801 2.24484i 0.441843 0.234040i
\(93\) 5.84147 0.605732
\(94\) −0.491807 + 3.42059i −0.0507260 + 0.352807i
\(95\) −1.73783 3.80531i −0.178297 0.390417i
\(96\) 0.959493 + 0.281733i 0.0979278 + 0.0287542i
\(97\) −0.372464 0.429846i −0.0378179 0.0436442i 0.736525 0.676410i \(-0.236465\pi\)
−0.774343 + 0.632766i \(0.781920\pi\)
\(98\) 0.959493 0.281733i 0.0969234 0.0284593i
\(99\) −1.73810 1.11701i −0.174686 0.112264i
\(100\) −0.717302 + 1.57067i −0.0717302 + 0.157067i
\(101\) 3.00135 3.46374i 0.298645 0.344655i −0.586517 0.809937i \(-0.699501\pi\)
0.885163 + 0.465281i \(0.154047\pi\)
\(102\) 0.108150 0.0695037i 0.0107084 0.00688189i
\(103\) 1.68723 + 11.7349i 0.166247 + 1.15628i 0.886556 + 0.462622i \(0.153091\pi\)
−0.720309 + 0.693654i \(0.756000\pi\)
\(104\) 0.767058 + 5.33501i 0.0752163 + 0.523141i
\(105\) 1.52202 0.978140i 0.148533 0.0954567i
\(106\) 2.70641 3.12336i 0.262870 0.303368i
\(107\) −1.76283 + 3.86007i −0.170420 + 0.373167i −0.975500 0.219999i \(-0.929395\pi\)
0.805081 + 0.593165i \(0.202122\pi\)
\(108\) 0.841254 + 0.540641i 0.0809497 + 0.0520232i
\(109\) −12.4296 + 3.64965i −1.19054 + 0.349573i −0.816228 0.577730i \(-0.803939\pi\)
−0.374310 + 0.927304i \(0.622120\pi\)
\(110\) −2.44788 2.82500i −0.233396 0.269353i
\(111\) 6.35028 + 1.86461i 0.602742 + 0.176981i
\(112\) 0.415415 + 0.909632i 0.0392530 + 0.0859521i
\(113\) 0.0983203 0.683833i 0.00924920 0.0643296i −0.984674 0.174404i \(-0.944200\pi\)
0.993923 + 0.110075i \(0.0351091\pi\)
\(114\) 2.31224 0.216561
\(115\) 8.64608 + 0.728691i 0.806251 + 0.0679508i
\(116\) −10.3665 −0.962509
\(117\) −0.767058 + 5.33501i −0.0709146 + 0.493222i
\(118\) 2.03872 + 4.46418i 0.187680 + 0.410961i
\(119\) 0.123350 + 0.0362190i 0.0113075 + 0.00332019i
\(120\) 1.18479 + 1.36732i 0.108156 + 0.124819i
\(121\) 6.45862 1.89642i 0.587147 0.172402i
\(122\) −8.04258 5.16865i −0.728141 0.467948i
\(123\) −2.73504 + 5.98890i −0.246610 + 0.540001i
\(124\) −3.82535 + 4.41469i −0.343527 + 0.396451i
\(125\) −10.2382 + 6.57966i −0.915729 + 0.588503i
\(126\) 0.142315 + 0.989821i 0.0126784 + 0.0881803i
\(127\) −2.33868 16.2659i −0.207524 1.44336i −0.781199 0.624282i \(-0.785392\pi\)
0.573675 0.819083i \(-0.305517\pi\)
\(128\) −0.841254 + 0.540641i −0.0743570 + 0.0477863i
\(129\) 5.30229 6.11917i 0.466841 0.538763i
\(130\) −4.05091 + 8.87025i −0.355288 + 0.777973i
\(131\) −7.86210 5.05266i −0.686915 0.441453i 0.150073 0.988675i \(-0.452049\pi\)
−0.836988 + 0.547222i \(0.815685\pi\)
\(132\) 1.98240 0.582084i 0.172546 0.0506639i
\(133\) 1.51419 + 1.74747i 0.131297 + 0.151525i
\(134\) 8.21364 + 2.41174i 0.709551 + 0.208343i
\(135\) 0.751578 + 1.64573i 0.0646856 + 0.141642i
\(136\) −0.0182957 + 0.127249i −0.00156884 + 0.0109115i
\(137\) −22.1289 −1.89060 −0.945301 0.326200i \(-0.894232\pi\)
−0.945301 + 0.326200i \(0.894232\pi\)
\(138\) −2.35159 + 4.17972i −0.200181 + 0.355801i
\(139\) −16.1409 −1.36905 −0.684526 0.728989i \(-0.739991\pi\)
−0.684526 + 0.728989i \(0.739991\pi\)
\(140\) −0.257479 + 1.79081i −0.0217610 + 0.151351i
\(141\) −1.43558 3.14347i −0.120897 0.264728i
\(142\) −2.83003 0.830971i −0.237491 0.0697335i
\(143\) 7.29249 + 8.41599i 0.609829 + 0.703780i
\(144\) −0.959493 + 0.281733i −0.0799577 + 0.0234777i
\(145\) −15.7780 10.1399i −1.31029 0.842075i
\(146\) 4.95797 10.8564i 0.410324 0.898485i
\(147\) −0.654861 + 0.755750i −0.0540120 + 0.0623332i
\(148\) −5.56773 + 3.57816i −0.457665 + 0.294123i
\(149\) −1.97387 13.7286i −0.161706 1.12469i −0.895418 0.445227i \(-0.853123\pi\)
0.733712 0.679460i \(-0.237786\pi\)
\(150\) −0.245737 1.70914i −0.0200643 0.139550i
\(151\) −14.2980 + 9.18877i −1.16356 + 0.747772i −0.972293 0.233767i \(-0.924895\pi\)
−0.191263 + 0.981539i \(0.561258\pi\)
\(152\) −1.51419 + 1.74747i −0.122817 + 0.141739i
\(153\) −0.0534049 + 0.116940i −0.00431753 + 0.00945408i
\(154\) 1.73810 + 1.11701i 0.140060 + 0.0900114i
\(155\) −10.1404 + 2.97750i −0.814499 + 0.239158i
\(156\) −3.52961 4.07339i −0.282595 0.326132i
\(157\) 12.1539 + 3.56870i 0.969986 + 0.284814i 0.728085 0.685487i \(-0.240411\pi\)
0.241901 + 0.970301i \(0.422229\pi\)
\(158\) 0.824578 + 1.80557i 0.0655999 + 0.143644i
\(159\) −0.588159 + 4.09074i −0.0466441 + 0.324417i
\(160\) −1.80922 −0.143032
\(161\) −4.69878 + 0.959919i −0.370316 + 0.0756522i
\(162\) −1.00000 −0.0785674
\(163\) −2.15142 + 14.9634i −0.168512 + 1.17203i 0.713450 + 0.700706i \(0.247132\pi\)
−0.881962 + 0.471321i \(0.843778\pi\)
\(164\) −2.73504 5.98890i −0.213571 0.467655i
\(165\) 3.58660 + 1.05312i 0.279216 + 0.0819853i
\(166\) −4.11967 4.75436i −0.319749 0.369010i
\(167\) 1.28053 0.375998i 0.0990906 0.0290956i −0.231811 0.972761i \(-0.574465\pi\)
0.330902 + 0.943665i \(0.392647\pi\)
\(168\) −0.841254 0.540641i −0.0649041 0.0417113i
\(169\) 6.66770 14.6002i 0.512900 1.12309i
\(170\) −0.152314 + 0.175780i −0.0116820 + 0.0134817i
\(171\) −1.94518 + 1.25009i −0.148752 + 0.0955968i
\(172\) 1.15230 + 8.01441i 0.0878619 + 0.611093i
\(173\) 2.32587 + 16.1768i 0.176833 + 1.22990i 0.864035 + 0.503433i \(0.167930\pi\)
−0.687202 + 0.726467i \(0.741161\pi\)
\(174\) 8.72089 5.60458i 0.661129 0.424882i
\(175\) 1.13076 1.30496i 0.0854771 0.0986459i
\(176\) −0.858284 + 1.87938i −0.0646956 + 0.141664i
\(177\) −4.12860 2.65329i −0.310325 0.199434i
\(178\) 11.9934 3.52158i 0.898943 0.263953i
\(179\) −4.21335 4.86247i −0.314921 0.363438i 0.576117 0.817367i \(-0.304567\pi\)
−0.891038 + 0.453929i \(0.850022\pi\)
\(180\) −1.73594 0.509717i −0.129389 0.0379921i
\(181\) 7.33807 + 16.0681i 0.545434 + 1.19433i 0.958882 + 0.283806i \(0.0915972\pi\)
−0.413448 + 0.910528i \(0.635675\pi\)
\(182\) 0.767058 5.33501i 0.0568581 0.395457i
\(183\) 9.56023 0.706713
\(184\) −1.61885 4.51434i −0.119344 0.332802i
\(185\) −11.9741 −0.880354
\(186\) 0.831328 5.78201i 0.0609559 0.423958i
\(187\) 0.110339 + 0.241609i 0.00806881 + 0.0176682i
\(188\) 3.31578 + 0.973601i 0.241828 + 0.0710072i
\(189\) −0.654861 0.755750i −0.0476341 0.0549727i
\(190\) −4.01390 + 1.17859i −0.291199 + 0.0855037i
\(191\) −4.12348 2.65000i −0.298365 0.191747i 0.382890 0.923794i \(-0.374929\pi\)
−0.681254 + 0.732047i \(0.738565\pi\)
\(192\) 0.415415 0.909632i 0.0299800 0.0656470i
\(193\) 6.11262 7.05434i 0.439996 0.507783i −0.491828 0.870692i \(-0.663671\pi\)
0.931824 + 0.362910i \(0.118217\pi\)
\(194\) −0.478478 + 0.307499i −0.0343527 + 0.0220771i
\(195\) −1.38778 9.65222i −0.0993809 0.691210i
\(196\) −0.142315 0.989821i −0.0101653 0.0707015i
\(197\) −18.5481 + 11.9201i −1.32150 + 0.849275i −0.995376 0.0960522i \(-0.969378\pi\)
−0.326122 + 0.945328i \(0.605742\pi\)
\(198\) −1.35300 + 1.56145i −0.0961535 + 0.110967i
\(199\) −9.57124 + 20.9581i −0.678488 + 1.48568i 0.185750 + 0.982597i \(0.440528\pi\)
−0.864238 + 0.503083i \(0.832199\pi\)
\(200\) 1.45260 + 0.933531i 0.102715 + 0.0660106i
\(201\) −8.21364 + 2.41174i −0.579346 + 0.170111i
\(202\) −3.00135 3.46374i −0.211174 0.243708i
\(203\) 9.94663 + 2.92059i 0.698116 + 0.204985i
\(204\) −0.0534049 0.116940i −0.00373909 0.00818747i
\(205\) 1.69521 11.7905i 0.118399 0.823481i
\(206\) 11.8556 0.826018
\(207\) −0.281442 4.78757i −0.0195615 0.332759i
\(208\) 5.38987 0.373720
\(209\) −0.679879 + 4.72866i −0.0470282 + 0.327088i
\(210\) −0.751578 1.64573i −0.0518638 0.113566i
\(211\) 4.46823 + 1.31199i 0.307606 + 0.0903212i 0.431892 0.901925i \(-0.357846\pi\)
−0.124287 + 0.992246i \(0.539664\pi\)
\(212\) −2.70641 3.12336i −0.185877 0.214514i
\(213\) 2.83003 0.830971i 0.193910 0.0569372i
\(214\) 3.56990 + 2.29424i 0.244033 + 0.156831i
\(215\) −6.08540 + 13.3252i −0.415021 + 0.908768i
\(216\) 0.654861 0.755750i 0.0445576 0.0514222i
\(217\) 4.91416 3.15814i 0.333595 0.214388i
\(218\) 1.84359 + 12.8225i 0.124864 + 0.868447i
\(219\) 1.69852 + 11.8135i 0.114776 + 0.798282i
\(220\) −3.14462 + 2.02092i −0.212010 + 0.136251i
\(221\) 0.453760 0.523667i 0.0305232 0.0352256i
\(222\) 2.74937 6.02029i 0.184526 0.404055i
\(223\) 19.2297 + 12.3582i 1.28772 + 0.827567i 0.991819 0.127653i \(-0.0407442\pi\)
0.295900 + 0.955219i \(0.404381\pi\)
\(224\) 0.959493 0.281733i 0.0641088 0.0188240i
\(225\) 1.13076 + 1.30496i 0.0753838 + 0.0869975i
\(226\) −0.662880 0.194639i −0.0440941 0.0129472i
\(227\) −4.45679 9.75902i −0.295808 0.647729i 0.702121 0.712058i \(-0.252237\pi\)
−0.997929 + 0.0643289i \(0.979509\pi\)
\(228\) 0.329066 2.28870i 0.0217929 0.151573i
\(229\) 12.8645 0.850107 0.425054 0.905168i \(-0.360255\pi\)
0.425054 + 0.905168i \(0.360255\pi\)
\(230\) 1.95174 8.45437i 0.128694 0.557464i
\(231\) −2.06609 −0.135939
\(232\) −1.47531 + 10.2610i −0.0968590 + 0.673669i
\(233\) −8.87064 19.4240i −0.581135 1.27251i −0.940653 0.339369i \(-0.889786\pi\)
0.359519 0.933138i \(-0.382941\pi\)
\(234\) 5.17154 + 1.51850i 0.338074 + 0.0992676i
\(235\) 4.09435 + 4.72513i 0.267086 + 0.308234i
\(236\) 4.70888 1.38265i 0.306522 0.0900030i
\(237\) −1.66985 1.07315i −0.108468 0.0697083i
\(238\) 0.0534049 0.116940i 0.00346173 0.00758012i
\(239\) 14.9441 17.2464i 0.966653 1.11558i −0.0266038 0.999646i \(-0.508469\pi\)
0.993257 0.115931i \(-0.0369853\pi\)
\(240\) 1.52202 0.978140i 0.0982457 0.0631386i
\(241\) −1.26863 8.82348i −0.0817193 0.568370i −0.989008 0.147862i \(-0.952761\pi\)
0.907289 0.420508i \(-0.138148\pi\)
\(242\) −0.957961 6.66276i −0.0615801 0.428299i
\(243\) 0.841254 0.540641i 0.0539664 0.0346821i
\(244\) −6.26062 + 7.22514i −0.400795 + 0.462542i
\(245\) 0.751578 1.64573i 0.0480166 0.105142i
\(246\) 5.53871 + 3.55951i 0.353135 + 0.226946i
\(247\) 11.9578 3.51114i 0.760859 0.223408i
\(248\) 3.82535 + 4.41469i 0.242910 + 0.280333i
\(249\) 6.03609 + 1.77236i 0.382522 + 0.112318i
\(250\) 5.05565 + 11.0703i 0.319747 + 0.700149i
\(251\) −1.78358 + 12.4050i −0.112578 + 0.783000i 0.852817 + 0.522210i \(0.174892\pi\)
−0.965396 + 0.260790i \(0.916017\pi\)
\(252\) 1.00000 0.0629941
\(253\) −7.85631 6.03812i −0.493922 0.379613i
\(254\) −16.4332 −1.03111
\(255\) 0.0331010 0.230223i 0.00207287 0.0144171i
\(256\) 0.415415 + 0.909632i 0.0259634 + 0.0568520i
\(257\) −11.7141 3.43956i −0.730704 0.214554i −0.104843 0.994489i \(-0.533434\pi\)
−0.625861 + 0.779935i \(0.715252\pi\)
\(258\) −5.30229 6.11917i −0.330106 0.380963i
\(259\) 6.35028 1.86461i 0.394587 0.115861i
\(260\) 8.20346 + 5.27204i 0.508757 + 0.326958i
\(261\) −4.30642 + 9.42974i −0.266561 + 0.583686i
\(262\) −6.12013 + 7.06300i −0.378103 + 0.436354i
\(263\) −5.49409 + 3.53084i −0.338780 + 0.217721i −0.698958 0.715163i \(-0.746352\pi\)
0.360178 + 0.932884i \(0.382716\pi\)
\(264\) −0.294035 2.04506i −0.0180966 0.125865i
\(265\) −1.06411 7.40105i −0.0653678 0.454643i
\(266\) 1.94518 1.25009i 0.119267 0.0766480i
\(267\) −8.18557 + 9.44666i −0.500949 + 0.578126i
\(268\) 3.55612 7.78681i 0.217225 0.475655i
\(269\) 18.3984 + 11.8239i 1.12177 + 0.720918i 0.963827 0.266530i \(-0.0858772\pi\)
0.157944 + 0.987448i \(0.449514\pi\)
\(270\) 1.73594 0.509717i 0.105646 0.0310204i
\(271\) −0.124856 0.144092i −0.00758446 0.00875294i 0.751945 0.659226i \(-0.229116\pi\)
−0.759529 + 0.650473i \(0.774571\pi\)
\(272\) 0.123350 + 0.0362190i 0.00747922 + 0.00219610i
\(273\) 2.23903 + 4.90280i 0.135512 + 0.296731i
\(274\) −3.14927 + 21.9037i −0.190255 + 1.32325i
\(275\) 3.56754 0.215131
\(276\) 3.80251 + 2.92249i 0.228884 + 0.175913i
\(277\) −22.1850 −1.33297 −0.666483 0.745521i \(-0.732201\pi\)
−0.666483 + 0.745521i \(0.732201\pi\)
\(278\) −2.29709 + 15.9766i −0.137770 + 0.958212i
\(279\) 2.42664 + 5.31359i 0.145279 + 0.318116i
\(280\) 1.73594 + 0.509717i 0.103742 + 0.0304614i
\(281\) 2.37547 + 2.74144i 0.141709 + 0.163540i 0.822167 0.569246i \(-0.192765\pi\)
−0.680459 + 0.732787i \(0.738219\pi\)
\(282\) −3.31578 + 0.973601i −0.197452 + 0.0579771i
\(283\) 6.86802 + 4.41381i 0.408261 + 0.262374i 0.728614 0.684925i \(-0.240165\pi\)
−0.320352 + 0.947298i \(0.603801\pi\)
\(284\) −1.22527 + 2.68296i −0.0727063 + 0.159204i
\(285\) 2.73951 3.16157i 0.162275 0.187275i
\(286\) 9.36815 6.02055i 0.553951 0.356002i
\(287\) 0.936983 + 6.51686i 0.0553084 + 0.384678i
\(288\) 0.142315 + 0.989821i 0.00838598 + 0.0583258i
\(289\) −14.2874 + 9.18196i −0.840436 + 0.540115i
\(290\) −12.2822 + 14.1744i −0.721234 + 0.832348i
\(291\) 0.236275 0.517369i 0.0138507 0.0303287i
\(292\) −10.0403 6.45253i −0.587566 0.377606i
\(293\) −0.402531 + 0.118194i −0.0235161 + 0.00690495i −0.293469 0.955968i \(-0.594810\pi\)
0.269953 + 0.962873i \(0.412992\pi\)
\(294\) 0.654861 + 0.755750i 0.0381923 + 0.0440762i
\(295\) 8.51942 + 2.50153i 0.496020 + 0.145645i
\(296\) 2.74937 + 6.02029i 0.159804 + 0.349922i
\(297\) 0.294035 2.04506i 0.0170616 0.118666i
\(298\) −13.8697 −0.803452
\(299\) −5.81444 + 25.1865i −0.336258 + 1.45657i
\(300\) −1.72671 −0.0996918
\(301\) 1.15230 8.01441i 0.0664173 0.461943i
\(302\) 7.06043 + 15.4602i 0.406282 + 0.889633i
\(303\) 4.39754 + 1.29123i 0.252632 + 0.0741794i
\(304\) 1.51419 + 1.74747i 0.0868450 + 0.100224i
\(305\) −16.5960 + 4.87301i −0.950282 + 0.279028i
\(306\) 0.108150 + 0.0695037i 0.00618252 + 0.00397326i
\(307\) 3.17371 6.94945i 0.181133 0.396626i −0.797185 0.603735i \(-0.793678\pi\)
0.978318 + 0.207109i \(0.0664056\pi\)
\(308\) 1.35300 1.56145i 0.0770943 0.0889716i
\(309\) −9.97355 + 6.40961i −0.567376 + 0.364630i
\(310\) 1.50406 + 10.4610i 0.0854248 + 0.594142i
\(311\) −2.84242 19.7695i −0.161179 1.12102i −0.896416 0.443214i \(-0.853838\pi\)
0.735237 0.677810i \(-0.237071\pi\)
\(312\) −4.53425 + 2.91398i −0.256701 + 0.164972i
\(313\) −9.34155 + 10.7807i −0.528016 + 0.609363i −0.955620 0.294604i \(-0.904812\pi\)
0.427604 + 0.903966i \(0.359358\pi\)
\(314\) 5.26206 11.5223i 0.296955 0.650241i
\(315\) 1.52202 + 0.978140i 0.0857558 + 0.0551119i
\(316\) 1.90455 0.559225i 0.107139 0.0314589i
\(317\) −8.18540 9.44646i −0.459738 0.530566i 0.477791 0.878474i \(-0.341438\pi\)
−0.937529 + 0.347908i \(0.886892\pi\)
\(318\) 3.96540 + 1.16435i 0.222368 + 0.0652932i
\(319\) 8.89744 + 19.4827i 0.498161 + 1.09082i
\(320\) −0.257479 + 1.79081i −0.0143935 + 0.100109i
\(321\) −4.24355 −0.236852
\(322\) 0.281442 + 4.78757i 0.0156841 + 0.266801i
\(323\) 0.297257 0.0165398
\(324\) −0.142315 + 0.989821i −0.00790638 + 0.0549901i
\(325\) −3.86617 8.46572i −0.214456 0.469594i
\(326\) 14.5050 + 4.25904i 0.803355 + 0.235886i
\(327\) −8.48328 9.79022i −0.469126 0.541401i
\(328\) −6.31718 + 1.85489i −0.348808 + 0.102419i
\(329\) −2.90717 1.86833i −0.160278 0.103004i
\(330\) 1.55283 3.40022i 0.0854803 0.187176i
\(331\) 6.56517 7.57661i 0.360855 0.416448i −0.546071 0.837739i \(-0.683877\pi\)
0.906926 + 0.421290i \(0.138423\pi\)
\(332\) −5.29225 + 3.40112i −0.290450 + 0.186661i
\(333\) 0.941893 + 6.55101i 0.0516154 + 0.358993i
\(334\) −0.189932 1.32101i −0.0103926 0.0722824i
\(335\) 13.0291 8.37327i 0.711853 0.457480i
\(336\) −0.654861 + 0.755750i −0.0357256 + 0.0412295i
\(337\) 6.85683 15.0144i 0.373515 0.817884i −0.625767 0.780010i \(-0.715214\pi\)
0.999283 0.0378743i \(-0.0120587\pi\)
\(338\) −13.5027 8.67766i −0.734450 0.472002i
\(339\) 0.662880 0.194639i 0.0360027 0.0105713i
\(340\) 0.152314 + 0.175780i 0.00826039 + 0.00953300i
\(341\) 11.5801 + 3.40023i 0.627099 + 0.184133i
\(342\) 0.960539 + 2.10329i 0.0519400 + 0.113733i
\(343\) −0.142315 + 0.989821i −0.00768428 + 0.0534453i
\(344\) 8.09682 0.436551
\(345\) 2.92887 + 8.16746i 0.157685 + 0.439721i
\(346\) 16.3431 0.878613
\(347\) −3.81138 + 26.5087i −0.204606 + 1.42306i 0.585788 + 0.810464i \(0.300785\pi\)
−0.790394 + 0.612599i \(0.790124\pi\)
\(348\) −4.30642 9.42974i −0.230848 0.505487i
\(349\) 29.1975 + 8.57317i 1.56291 + 0.458911i 0.944927 0.327281i \(-0.106132\pi\)
0.617982 + 0.786193i \(0.287951\pi\)
\(350\) −1.13076 1.30496i −0.0604415 0.0697532i
\(351\) −5.17154 + 1.51850i −0.276036 + 0.0810516i
\(352\) 1.73810 + 1.11701i 0.0926413 + 0.0595369i
\(353\) 13.8061 30.2311i 0.734825 1.60904i −0.0570601 0.998371i \(-0.518173\pi\)
0.791885 0.610671i \(-0.209100\pi\)
\(354\) −3.21385 + 3.70898i −0.170814 + 0.197130i
\(355\) −4.48919 + 2.88503i −0.238261 + 0.153121i
\(356\) −1.77890 12.3725i −0.0942813 0.655740i
\(357\) 0.0182957 + 0.127249i 0.000968312 + 0.00673475i
\(358\) −5.41260 + 3.47846i −0.286065 + 0.183843i
\(359\) 8.89583 10.2663i 0.469504 0.541836i −0.470770 0.882256i \(-0.656024\pi\)
0.940274 + 0.340420i \(0.110569\pi\)
\(360\) −0.751578 + 1.64573i −0.0396117 + 0.0867374i
\(361\) −11.4861 7.38167i −0.604532 0.388509i
\(362\) 16.9489 4.97664i 0.890814 0.261567i
\(363\) 4.40805 + 5.08716i 0.231363 + 0.267007i
\(364\) −5.17154 1.51850i −0.271062 0.0795911i
\(365\) −8.97007 19.6417i −0.469515 1.02809i
\(366\) 1.36056 9.46292i 0.0711178 0.494635i
\(367\) −10.0244 −0.523271 −0.261636 0.965167i \(-0.584262\pi\)
−0.261636 + 0.965167i \(0.584262\pi\)
\(368\) −4.69878 + 0.959919i −0.244941 + 0.0500392i
\(369\) −6.58388 −0.342743
\(370\) −1.70409 + 11.8522i −0.0885916 + 0.616168i
\(371\) 1.71683 + 3.75933i 0.0891333 + 0.195175i
\(372\) −5.60485 1.64573i −0.290598 0.0853273i
\(373\) 4.95414 + 5.71738i 0.256515 + 0.296035i 0.869371 0.494161i \(-0.164525\pi\)
−0.612855 + 0.790195i \(0.709979\pi\)
\(374\) 0.254853 0.0748316i 0.0131781 0.00386945i
\(375\) −10.2382 6.57966i −0.528696 0.339772i
\(376\) 1.43558 3.14347i 0.0740342 0.162112i
\(377\) 36.5899 42.2270i 1.88448 2.17480i
\(378\) −0.841254 + 0.540641i −0.0432694 + 0.0278076i
\(379\) 4.40274 + 30.6217i 0.226154 + 1.57293i 0.714090 + 0.700054i \(0.246841\pi\)
−0.487936 + 0.872879i \(0.662250\pi\)
\(380\) 0.595353 + 4.14077i 0.0305410 + 0.212417i
\(381\) 13.8245 8.88444i 0.708248 0.455163i
\(382\) −3.20986 + 3.70438i −0.164231 + 0.189532i
\(383\) −2.82079 + 6.17667i −0.144136 + 0.315613i −0.967907 0.251309i \(-0.919139\pi\)
0.823771 + 0.566923i \(0.191866\pi\)
\(384\) −0.841254 0.540641i −0.0429300 0.0275895i
\(385\) 3.58660 1.05312i 0.182790 0.0536720i
\(386\) −6.11262 7.05434i −0.311124 0.359057i
\(387\) 7.76884 + 2.28114i 0.394913 + 0.115957i
\(388\) 0.236275 + 0.517369i 0.0119950 + 0.0262654i
\(389\) −0.0517605 + 0.360003i −0.00262436 + 0.0182529i −0.991092 0.133182i \(-0.957480\pi\)
0.988467 + 0.151435i \(0.0483895\pi\)
\(390\) −9.75147 −0.493785
\(391\) −0.302316 + 0.537336i −0.0152888 + 0.0271742i
\(392\) −1.00000 −0.0505076
\(393\) 1.33003 9.25057i 0.0670912 0.466629i
\(394\) 9.15915 + 20.0557i 0.461431 + 1.01039i
\(395\) 3.44575 + 1.01176i 0.173374 + 0.0509073i
\(396\) 1.35300 + 1.56145i 0.0679908 + 0.0784656i
\(397\) −14.5535 + 4.27329i −0.730419 + 0.214470i −0.625736 0.780035i \(-0.715201\pi\)
−0.104683 + 0.994506i \(0.533383\pi\)
\(398\) 19.3826 + 12.4565i 0.971564 + 0.624387i
\(399\) −0.960539 + 2.10329i −0.0480871 + 0.105296i
\(400\) 1.13076 1.30496i 0.0565378 0.0652481i
\(401\) −21.5394 + 13.8426i −1.07563 + 0.691264i −0.953543 0.301256i \(-0.902594\pi\)
−0.122085 + 0.992520i \(0.538958\pi\)
\(402\) 1.21827 + 8.47327i 0.0607619 + 0.422608i
\(403\) −4.48075 31.1643i −0.223202 1.55240i
\(404\) −3.85562 + 2.47786i −0.191824 + 0.123278i
\(405\) −1.18479 + 1.36732i −0.0588726 + 0.0679426i
\(406\) 4.30642 9.42974i 0.213724 0.467990i
\(407\) 11.5034 + 7.39280i 0.570204 + 0.366448i
\(408\) −0.123350 + 0.0362190i −0.00610676 + 0.00179311i
\(409\) −24.1119 27.8266i −1.19226 1.37594i −0.908948 0.416909i \(-0.863114\pi\)
−0.283308 0.959029i \(-0.591432\pi\)
\(410\) −11.4292 3.35591i −0.564447 0.165737i
\(411\) −9.19269 20.1292i −0.453442 0.992899i
\(412\) 1.68723 11.7349i 0.0831236 0.578138i
\(413\) −4.90768 −0.241491
\(414\) −4.77889 0.402765i −0.234870 0.0197948i
\(415\) −11.3817 −0.558704
\(416\) 0.767058 5.33501i 0.0376081 0.261570i
\(417\) −6.70516 14.6823i −0.328353 0.718993i
\(418\) 4.58378 + 1.34592i 0.224200 + 0.0658310i
\(419\) −7.08420 8.17561i −0.346086 0.399405i 0.555844 0.831287i \(-0.312395\pi\)
−0.901930 + 0.431882i \(0.857850\pi\)
\(420\) −1.73594 + 0.509717i −0.0847050 + 0.0248716i
\(421\) −11.4568 7.36284i −0.558371 0.358843i 0.230815 0.972998i \(-0.425861\pi\)
−0.789186 + 0.614155i \(0.789497\pi\)
\(422\) 1.93453 4.23603i 0.0941715 0.206207i
\(423\) 2.26304 2.61169i 0.110033 0.126985i
\(424\) −3.47673 + 2.23436i −0.168845 + 0.108510i
\(425\) −0.0315914 0.219723i −0.00153241 0.0106581i
\(426\) −0.419758 2.91948i −0.0203373 0.141449i
\(427\) 8.04258 5.16865i 0.389208 0.250129i
\(428\) 2.77893 3.20706i 0.134325 0.155019i
\(429\) −4.62604 + 10.1296i −0.223347 + 0.489062i
\(430\) 12.3235 + 7.91982i 0.594291 + 0.381928i
\(431\) −9.76676 + 2.86778i −0.470448 + 0.138136i −0.508359 0.861145i \(-0.669748\pi\)
0.0379111 + 0.999281i \(0.487930\pi\)
\(432\) −0.654861 0.755750i −0.0315070 0.0363610i
\(433\) −23.7289 6.96743i −1.14034 0.334834i −0.343575 0.939125i \(-0.611638\pi\)
−0.796763 + 0.604292i \(0.793456\pi\)
\(434\) −2.42664 5.31359i −0.116482 0.255061i
\(435\) 2.66917 18.5645i 0.127977 0.890099i
\(436\) 12.9543 0.620399
\(437\) −9.79929 + 5.19059i −0.468763 + 0.248300i
\(438\) 11.9350 0.570275
\(439\) 1.01289 7.04479i 0.0483425 0.336230i −0.951269 0.308362i \(-0.900219\pi\)
0.999612 0.0278677i \(-0.00887171\pi\)
\(440\) 1.55283 + 3.40022i 0.0740281 + 0.162099i
\(441\) −0.959493 0.281733i −0.0456901 0.0134158i
\(442\) −0.453760 0.523667i −0.0215832 0.0249083i
\(443\) 36.5863 10.7427i 1.73827 0.510401i 0.749777 0.661690i \(-0.230161\pi\)
0.988490 + 0.151289i \(0.0483424\pi\)
\(444\) −5.56773 3.57816i −0.264233 0.169812i
\(445\) 9.39452 20.5711i 0.445343 0.975165i
\(446\) 14.9691 17.2753i 0.708807 0.818007i
\(447\) 11.6680 7.49854i 0.551875 0.354669i
\(448\) −0.142315 0.989821i −0.00672374 0.0467647i
\(449\) 1.43434 + 9.97607i 0.0676908 + 0.470800i 0.995268 + 0.0971682i \(0.0309785\pi\)
−0.927577 + 0.373632i \(0.878112\pi\)
\(450\) 1.45260 0.933531i 0.0684764 0.0440071i
\(451\) −8.90798 + 10.2804i −0.419461 + 0.484083i
\(452\) −0.286996 + 0.628433i −0.0134991 + 0.0295590i
\(453\) −14.2980 9.18877i −0.671779 0.431726i
\(454\) −10.2940 + 3.02258i −0.483119 + 0.141857i
\(455\) −6.38586 7.36967i −0.299374 0.345496i
\(456\) −2.21858 0.651433i −0.103894 0.0305061i
\(457\) −1.43115 3.13378i −0.0669464 0.146592i 0.873201 0.487360i \(-0.162040\pi\)
−0.940147 + 0.340768i \(0.889313\pi\)
\(458\) 1.83080 12.7335i 0.0855478 0.594998i
\(459\) −0.128558 −0.00600057
\(460\) −8.09055 3.13506i −0.377224 0.146173i
\(461\) 3.57779 0.166634 0.0833172 0.996523i \(-0.473449\pi\)
0.0833172 + 0.996523i \(0.473449\pi\)
\(462\) −0.294035 + 2.04506i −0.0136797 + 0.0951447i
\(463\) −7.81722 17.1173i −0.363297 0.795509i −0.999708 0.0241592i \(-0.992309\pi\)
0.636411 0.771350i \(-0.280418\pi\)
\(464\) 9.94663 + 2.92059i 0.461761 + 0.135585i
\(465\) −6.92091 7.98716i −0.320950 0.370396i
\(466\) −20.4887 + 6.01602i −0.949121 + 0.278687i
\(467\) 19.8494 + 12.7564i 0.918522 + 0.590298i 0.912228 0.409682i \(-0.134360\pi\)
0.00629322 + 0.999980i \(0.497997\pi\)
\(468\) 2.23903 4.90280i 0.103499 0.226632i
\(469\) −5.60587 + 6.46952i −0.258855 + 0.298735i
\(470\) 5.25973 3.38022i 0.242613 0.155918i
\(471\) 1.80270 + 12.5381i 0.0830641 + 0.577723i
\(472\) −0.698436 4.85773i −0.0321481 0.223595i
\(473\) 14.0731 9.04424i 0.647083 0.415855i
\(474\) −1.29987 + 1.50013i −0.0597048 + 0.0689031i
\(475\) 1.65857 3.63177i 0.0761006 0.166637i
\(476\) −0.108150 0.0695037i −0.00495704 0.00318570i
\(477\) −3.96540 + 1.16435i −0.181563 + 0.0533117i
\(478\) −14.9441 17.2464i −0.683527 0.788832i
\(479\) 13.5712 + 3.98485i 0.620082 + 0.182073i 0.576660 0.816984i \(-0.304356\pi\)
0.0434222 + 0.999057i \(0.486174\pi\)
\(480\) −0.751578 1.64573i −0.0343047 0.0751168i
\(481\) 5.07668 35.3091i 0.231477 1.60996i
\(482\) −8.91422 −0.406031
\(483\) −2.82512 3.87540i −0.128547 0.176337i
\(484\) −6.73128 −0.305967
\(485\) −0.146446 + 1.01855i −0.00664976 + 0.0462501i
\(486\) −0.415415 0.909632i −0.0188436 0.0412617i
\(487\) −0.968295 0.284317i −0.0438776 0.0128836i 0.259720 0.965684i \(-0.416370\pi\)
−0.303598 + 0.952800i \(0.598188\pi\)
\(488\) 6.26062 + 7.22514i 0.283405 + 0.327067i
\(489\) −14.5050 + 4.25904i −0.655937 + 0.192600i
\(490\) −1.52202 0.978140i −0.0687576 0.0441878i
\(491\) 3.24497 7.10550i 0.146444 0.320667i −0.822168 0.569244i \(-0.807236\pi\)
0.968612 + 0.248578i \(0.0799631\pi\)
\(492\) 4.31152 4.97576i 0.194378 0.224325i
\(493\) 1.12114 0.720513i 0.0504936 0.0324503i
\(494\) −1.77362 12.3358i −0.0797990 0.555014i
\(495\) 0.531975 + 3.69997i 0.0239105 + 0.166301i
\(496\) 4.91416 3.15814i 0.220652 0.141805i
\(497\) 1.93151 2.22909i 0.0866402 0.0999881i
\(498\) 2.61334 5.72242i 0.117107 0.256428i
\(499\) 10.6486 + 6.84345i 0.476698 + 0.306355i 0.756836 0.653605i \(-0.226744\pi\)
−0.280139 + 0.959960i \(0.590380\pi\)
\(500\) 11.6771 3.42872i 0.522218 0.153337i
\(501\) 0.873973 + 1.00862i 0.0390462 + 0.0450618i
\(502\) 12.0250 + 3.53084i 0.536700 + 0.157589i
\(503\) −5.00206 10.9530i −0.223031 0.488370i 0.764729 0.644352i \(-0.222873\pi\)
−0.987760 + 0.155983i \(0.950146\pi\)
\(504\) 0.142315 0.989821i 0.00633921 0.0440902i
\(505\) −8.29201 −0.368990
\(506\) −7.09473 + 6.91703i −0.315399 + 0.307500i
\(507\) 16.0507 0.712836
\(508\) −2.33868 + 16.2659i −0.103762 + 0.721682i
\(509\) 8.11282 + 17.7646i 0.359594 + 0.787402i 0.999815 + 0.0192110i \(0.00611542\pi\)
−0.640221 + 0.768191i \(0.721157\pi\)
\(510\) −0.223169 0.0655282i −0.00988207 0.00290164i
\(511\) 7.81574 + 9.01985i 0.345748 + 0.399015i
\(512\) 0.959493 0.281733i 0.0424040 0.0124509i
\(513\) −1.94518 1.25009i −0.0858817 0.0551928i
\(514\) −5.07164 + 11.1053i −0.223700 + 0.489836i
\(515\) 14.0464 16.2104i 0.618957 0.714314i
\(516\) −6.81148 + 4.37747i −0.299859 + 0.192707i
\(517\) −1.01612 7.06724i −0.0446887 0.310817i
\(518\) −0.941893 6.55101i −0.0413844 0.287835i
\(519\) −13.7487 + 8.83577i −0.603502 + 0.387847i
\(520\) 6.38586 7.36967i 0.280038 0.323182i
\(521\) −0.0702635 + 0.153856i −0.00307830 + 0.00674054i −0.911165 0.412042i \(-0.864816\pi\)
0.908087 + 0.418782i \(0.137543\pi\)
\(522\) 8.72089 + 5.60458i 0.381703 + 0.245306i
\(523\) −38.8039 + 11.3939i −1.69678 + 0.498218i −0.979985 0.199070i \(-0.936208\pi\)
−0.716791 + 0.697288i \(0.754390\pi\)
\(524\) 6.12013 + 7.06300i 0.267359 + 0.308549i
\(525\) 1.65677 + 0.486471i 0.0723073 + 0.0212313i
\(526\) 2.71301 + 5.94066i 0.118293 + 0.259025i
\(527\) 0.106874 0.743324i 0.00465550 0.0323797i
\(528\) −2.06609 −0.0899150
\(529\) 0.583286 22.9926i 0.0253602 0.999678i
\(530\) −7.47716 −0.324787
\(531\) 0.698436 4.85773i 0.0303095 0.210807i
\(532\) −0.960539 2.10329i −0.0416446 0.0911890i
\(533\) 34.0488 + 9.99762i 1.47482 + 0.433045i
\(534\) 8.18557 + 9.44666i 0.354224 + 0.408797i
\(535\) 7.36653 2.16301i 0.318483 0.0935150i
\(536\) −7.20147 4.62810i −0.311056 0.199904i
\(537\) 2.67277 5.85254i 0.115338 0.252556i
\(538\) 14.3219 16.5284i 0.617463 0.712590i
\(539\) −1.73810 + 1.11701i −0.0748654 + 0.0481131i
\(540\) −0.257479 1.79081i −0.0110801 0.0770641i
\(541\) 1.23750 + 8.60702i 0.0532044 + 0.370045i 0.998977 + 0.0452158i \(0.0143976\pi\)
−0.945773 + 0.324829i \(0.894693\pi\)
\(542\) −0.160394 + 0.103079i −0.00688950 + 0.00442761i
\(543\) −11.5677 + 13.3499i −0.496419 + 0.572898i
\(544\) 0.0534049 0.116940i 0.00228972 0.00501378i
\(545\) 19.7167 + 12.6711i 0.844569 + 0.542772i
\(546\) 5.17154 1.51850i 0.221322 0.0649859i
\(547\) −22.7769 26.2860i −0.973871 1.12391i −0.992273 0.124076i \(-0.960403\pi\)
0.0184017 0.999831i \(-0.494142\pi\)
\(548\) 21.2325 + 6.23444i 0.907009 + 0.266322i
\(549\) 3.97146 + 8.69629i 0.169498 + 0.371149i
\(550\) 0.507714 3.53123i 0.0216490 0.150572i
\(551\) 23.9699 1.02115
\(552\) 3.43390 3.34789i 0.146156 0.142496i
\(553\) −1.98495 −0.0844087
\(554\) −3.15725 + 21.9592i −0.134139 + 0.932955i
\(555\) −4.97423 10.8920i −0.211144 0.462341i
\(556\) 15.4871 + 4.54741i 0.656798 + 0.192853i
\(557\) −19.8853 22.9489i −0.842567 0.972374i 0.157318 0.987548i \(-0.449715\pi\)
−0.999885 + 0.0151737i \(0.995170\pi\)
\(558\) 5.60485 1.64573i 0.237272 0.0696694i
\(559\) −36.7130 23.5940i −1.55279 0.997920i
\(560\) 0.751578 1.64573i 0.0317600 0.0695447i
\(561\) −0.173939 + 0.200736i −0.00734371 + 0.00847509i
\(562\) 3.05160 1.96114i 0.128724 0.0827258i
\(563\) −4.67196 32.4942i −0.196900 1.36947i −0.813213 0.581966i \(-0.802284\pi\)
0.616314 0.787501i \(-0.288625\pi\)
\(564\) 0.491807 + 3.42059i 0.0207088 + 0.144033i
\(565\) −1.05151 + 0.675763i −0.0442372 + 0.0284295i
\(566\) 5.34630 6.16996i 0.224722 0.259343i
\(567\) 0.415415 0.909632i 0.0174458 0.0382010i
\(568\) 2.48128 + 1.59462i 0.104112 + 0.0669088i
\(569\) −22.3732 + 6.56935i −0.937931 + 0.275401i −0.714754 0.699376i \(-0.753461\pi\)
−0.223178 + 0.974778i \(0.571643\pi\)
\(570\) −2.73951 3.16157i −0.114746 0.132424i
\(571\) 31.1445 + 9.14486i 1.30336 + 0.382701i 0.858460 0.512880i \(-0.171422\pi\)
0.444899 + 0.895581i \(0.353240\pi\)
\(572\) −4.62604 10.1296i −0.193424 0.423540i
\(573\) 0.697570 4.85170i 0.0291414 0.202683i
\(574\) 6.58388 0.274806
\(575\) 4.87817 + 6.69170i 0.203434 + 0.279063i
\(576\) 1.00000 0.0416667
\(577\) 1.36048 9.46232i 0.0566374 0.393921i −0.941709 0.336430i \(-0.890781\pi\)
0.998346 0.0574919i \(-0.0183103\pi\)
\(578\) 7.05519 + 15.4487i 0.293457 + 0.642582i
\(579\) 8.95613 + 2.62976i 0.372204 + 0.109289i
\(580\) 12.2822 + 14.1744i 0.509989 + 0.588559i
\(581\) 6.03609 1.77236i 0.250419 0.0735297i
\(582\) −0.478478 0.307499i −0.0198335 0.0127462i
\(583\) −3.54712 + 7.76711i −0.146907 + 0.321681i
\(584\) −7.81574 + 9.01985i −0.323418 + 0.373244i
\(585\) 8.20346 5.27204i 0.339171 0.217972i
\(586\) 0.0597045 + 0.415254i 0.00246637 + 0.0171540i
\(587\) 0.909428 + 6.32521i 0.0375361 + 0.261069i 0.999944 0.0105372i \(-0.00335414\pi\)
−0.962408 + 0.271607i \(0.912445\pi\)
\(588\) 0.841254 0.540641i 0.0346927 0.0222957i
\(589\) 8.84512 10.2078i 0.364457 0.420606i
\(590\) 3.68851 8.07670i 0.151853 0.332512i
\(591\) −18.5481 11.9201i −0.762967 0.490329i
\(592\) 6.35028 1.86461i 0.260995 0.0766351i
\(593\) 23.2283 + 26.8069i 0.953873 + 1.10083i 0.994818 + 0.101667i \(0.0324177\pi\)
−0.0409450 + 0.999161i \(0.513037\pi\)
\(594\) −1.98240 0.582084i −0.0813387 0.0238832i
\(595\) −0.0966214 0.211571i −0.00396109 0.00867358i
\(596\) −1.97387 + 13.7286i −0.0808528 + 0.562343i
\(597\) −23.0402 −0.942973
\(598\) 24.1026 + 9.33967i 0.985630 + 0.381927i
\(599\) −2.91998 −0.119307 −0.0596537 0.998219i \(-0.519000\pi\)
−0.0596537 + 0.998219i \(0.519000\pi\)
\(600\) −0.245737 + 1.70914i −0.0100322 + 0.0697752i
\(601\) 5.04080 + 11.0378i 0.205618 + 0.450242i 0.984144 0.177371i \(-0.0567593\pi\)
−0.778526 + 0.627613i \(0.784032\pi\)
\(602\) −7.76884 2.28114i −0.316634 0.0929723i
\(603\) −5.60587 6.46952i −0.228289 0.263459i
\(604\) 16.3076 4.78835i 0.663548 0.194835i
\(605\) −10.2451 6.58413i −0.416523 0.267683i
\(606\) 1.90393 4.16901i 0.0773417 0.169355i
\(607\) 5.99321 6.91654i 0.243257 0.280734i −0.620971 0.783833i \(-0.713262\pi\)
0.864228 + 0.503100i \(0.167807\pi\)
\(608\) 1.94518 1.25009i 0.0788874 0.0506979i
\(609\) 1.47531 + 10.2610i 0.0597827 + 0.415798i
\(610\) 2.46156 + 17.1205i 0.0996657 + 0.693190i
\(611\) −15.6693 + 10.0700i −0.633911 + 0.407390i
\(612\) 0.0841876 0.0971576i 0.00340308 0.00392736i
\(613\) −11.2717 + 24.6816i −0.455260 + 0.996880i 0.533283 + 0.845937i \(0.320958\pi\)
−0.988542 + 0.150943i \(0.951769\pi\)
\(614\) −6.42705 4.13041i −0.259374 0.166690i
\(615\) 11.4292 3.35591i 0.460869 0.135323i
\(616\) −1.35300 1.56145i −0.0545139 0.0629124i
\(617\) −13.5982 3.99278i −0.547442 0.160743i −0.00369566 0.999993i \(-0.501176\pi\)
−0.543746 + 0.839250i \(0.682995\pi\)
\(618\) 4.92499 + 10.7842i 0.198112 + 0.433805i
\(619\) 2.57847 17.9337i 0.103638 0.720815i −0.870056 0.492953i \(-0.835917\pi\)
0.973693 0.227862i \(-0.0731735\pi\)
\(620\) 10.5685 0.424442
\(621\) 4.23801 2.24484i 0.170065 0.0900821i
\(622\) −19.9728 −0.800835
\(623\) −1.77890 + 12.3725i −0.0712699 + 0.495693i
\(624\) 2.23903 + 4.90280i 0.0896330 + 0.196269i
\(625\) 12.8427 + 3.77096i 0.513709 + 0.150838i
\(626\) 9.34155 + 10.7807i 0.373363 + 0.430884i
\(627\) −4.58378 + 1.34592i −0.183058 + 0.0537508i
\(628\) −10.6562 6.84829i −0.425227 0.273277i
\(629\) 0.353454 0.773956i 0.0140931 0.0308596i
\(630\) 1.18479 1.36732i 0.0472031 0.0544753i
\(631\) 39.2413 25.2188i 1.56217 1.00395i 0.580298 0.814404i \(-0.302936\pi\)
0.981873 0.189542i \(-0.0607003\pi\)
\(632\) −0.282488 1.96475i −0.0112368 0.0781534i
\(633\) 0.662741 + 4.60947i 0.0263416 + 0.183210i
\(634\) −10.5152 + 6.75772i −0.417612 + 0.268383i
\(635\) −19.4698 + 22.4694i −0.772636 + 0.891670i
\(636\) 1.71683 3.75933i 0.0680767 0.149067i
\(637\) 4.53425 + 2.91398i 0.179653 + 0.115456i
\(638\) 20.5506 6.03420i 0.813606 0.238896i
\(639\) 1.93151 + 2.22909i 0.0764095 + 0.0881812i
\(640\) 1.73594 + 0.509717i 0.0686189 + 0.0201483i
\(641\) −12.5186 27.4120i −0.494457 1.08271i −0.978231 0.207517i \(-0.933462\pi\)
0.483775 0.875193i \(-0.339265\pi\)
\(642\) −0.603920 + 4.20036i −0.0238348 + 0.165775i
\(643\) −9.12720 −0.359942 −0.179971 0.983672i \(-0.557600\pi\)
−0.179971 + 0.983672i \(0.557600\pi\)
\(644\) 4.77889 + 0.402765i 0.188315 + 0.0158712i
\(645\) −14.6490 −0.576802
\(646\) 0.0423040 0.294231i 0.00166443 0.0115764i
\(647\) −10.7366 23.5098i −0.422098 0.924266i −0.994543 0.104323i \(-0.966732\pi\)
0.572445 0.819943i \(-0.305995\pi\)
\(648\) 0.959493 + 0.281733i 0.0376924 + 0.0110675i
\(649\) −6.64009 7.66307i −0.260646 0.300802i
\(650\) −8.92977 + 2.62202i −0.350254 + 0.102844i
\(651\) 4.91416 + 3.15814i 0.192601 + 0.123777i
\(652\) 6.27996 13.7512i 0.245942 0.538538i
\(653\) −23.9105 + 27.5942i −0.935689 + 1.07984i 0.0609674 + 0.998140i \(0.480581\pi\)
−0.996657 + 0.0817033i \(0.973964\pi\)
\(654\) −10.8979 + 7.00364i −0.426140 + 0.273864i
\(655\) 2.40632 + 16.7363i 0.0940228 + 0.653943i
\(656\) 0.936983 + 6.51686i 0.0365830 + 0.254441i
\(657\) −10.0403 + 6.45253i −0.391711 + 0.251737i
\(658\) −2.26304 + 2.61169i −0.0882227 + 0.101814i
\(659\) −0.00159036 + 0.00348240i −6.19515e−5 + 0.000135655i −0.909663 0.415347i \(-0.863660\pi\)
0.909601 + 0.415483i \(0.136387\pi\)
\(660\) −3.14462 2.02092i −0.122404 0.0786643i
\(661\) −41.4154 + 12.1606i −1.61087 + 0.472994i −0.958544 0.284943i \(-0.908025\pi\)
−0.652327 + 0.757938i \(0.726207\pi\)
\(662\) −6.56517 7.57661i −0.255163 0.294473i
\(663\) 0.664843 + 0.195215i 0.0258204 + 0.00758154i
\(664\) 2.61334 + 5.72242i 0.101417 + 0.222073i
\(665\) 0.595353 4.14077i 0.0230868 0.160572i
\(666\) 6.61837 0.256457
\(667\) −24.3779 + 43.3292i −0.943915 + 1.67771i
\(668\) −1.33459 −0.0516370
\(669\) −3.25309 + 22.6258i −0.125772 + 0.874763i
\(670\) −6.43381 14.0881i −0.248560 0.544270i
\(671\) 18.9522 + 5.56486i 0.731641 + 0.214829i
\(672\) 0.654861 + 0.755750i 0.0252618 + 0.0291537i
\(673\) 21.3008 6.25448i 0.821085 0.241092i 0.155902 0.987773i \(-0.450172\pi\)
0.665183 + 0.746680i \(0.268353\pi\)
\(674\) −13.8857 8.92380i −0.534857 0.343732i
\(675\) −0.717302 + 1.57067i −0.0276090 + 0.0604552i
\(676\) −10.5110 + 12.1303i −0.404268 + 0.466550i
\(677\) 15.6455 10.0548i 0.601306 0.386436i −0.204282 0.978912i \(-0.565486\pi\)
0.805588 + 0.592476i \(0.201849\pi\)
\(678\) −0.0983203 0.683833i −0.00377597 0.0262624i
\(679\) −0.0809441 0.562978i −0.00310635 0.0216051i
\(680\) 0.195667 0.125748i 0.00750349 0.00482220i
\(681\) 7.02570 8.10809i 0.269225 0.310703i
\(682\) 5.01364 10.9783i 0.191982 0.420383i
\(683\) −36.9699 23.7591i −1.41462 0.909118i −0.414616 0.909997i \(-0.636084\pi\)
−1.00000 0.000878515i \(0.999720\pi\)
\(684\) 2.21858 0.651433i 0.0848294 0.0249082i
\(685\) 26.2181 + 30.2573i 1.00174 + 1.15607i
\(686\) 0.959493 + 0.281733i 0.0366336 + 0.0107566i
\(687\) 5.34409 + 11.7019i 0.203890 + 0.446456i
\(688\) 1.15230 8.01441i 0.0439309 0.305546i
\(689\) 22.2753 0.848620
\(690\) 8.50114 1.73671i 0.323633 0.0661153i
\(691\) 8.67012 0.329827 0.164913 0.986308i \(-0.447266\pi\)
0.164913 + 0.986308i \(0.447266\pi\)
\(692\) 2.32587 16.1768i 0.0884164 0.614950i
\(693\) −0.858284 1.87938i −0.0326035 0.0713917i
\(694\) 25.6965 + 7.54517i 0.975426 + 0.286411i
\(695\) 19.1235 + 22.0697i 0.725397 + 0.837153i
\(696\) −9.94663 + 2.92059i −0.377026 + 0.110705i
\(697\) 0.712045 + 0.457604i 0.0269706 + 0.0173330i
\(698\) 12.6412 27.6803i 0.478475 1.04771i
\(699\) 13.9837 16.1380i 0.528911 0.610396i
\(700\) −1.45260 + 0.933531i −0.0549032 + 0.0352842i
\(701\) 4.81427 + 33.4840i 0.181832 + 1.26467i 0.852426 + 0.522847i \(0.175130\pi\)
−0.670594 + 0.741824i \(0.733961\pi\)
\(702\) 0.767058 + 5.33501i 0.0289508 + 0.201357i
\(703\) 12.8739 8.27357i 0.485549 0.312044i
\(704\) 1.35300 1.56145i 0.0509931 0.0588492i
\(705\) −2.59728 + 5.68724i −0.0978191 + 0.214194i
\(706\) −27.9586 17.9679i −1.05224 0.676231i
\(707\) 4.39754 1.29123i 0.165386 0.0485618i
\(708\) 3.21385 + 3.70898i 0.120784 + 0.139392i
\(709\) 35.1242 + 10.3134i 1.31912 + 0.387327i 0.864174 0.503194i \(-0.167842\pi\)
0.454942 + 0.890521i \(0.349660\pi\)
\(710\) 2.21678 + 4.85408i 0.0831943 + 0.182170i
\(711\) 0.282488 1.96475i 0.0105941 0.0736838i
\(712\) −12.4997 −0.468447
\(713\) 9.45649 + 26.3704i 0.354148 + 0.987580i
\(714\) 0.128558 0.00481116
\(715\) 2.86727 19.9423i 0.107230 0.745801i
\(716\) 2.67277 + 5.85254i 0.0998859 + 0.218720i
\(717\) 21.8959 + 6.42921i 0.817717 + 0.240103i
\(718\) −8.89583 10.2663i −0.331989 0.383136i
\(719\) 27.5548 8.09082i 1.02762 0.301737i 0.275878 0.961193i \(-0.411031\pi\)
0.751743 + 0.659456i \(0.229213\pi\)
\(720\) 1.52202 + 0.978140i 0.0567222 + 0.0364531i
\(721\) −4.92499 + 10.7842i −0.183416 + 0.401625i
\(722\) −8.94118 + 10.3187i −0.332756 + 0.384021i
\(723\) 7.49912 4.81939i 0.278895 0.179235i
\(724\) −2.51391 17.4846i −0.0934287 0.649811i
\(725\) −2.54744 17.7178i −0.0946096 0.658024i
\(726\) 5.66271 3.63920i 0.210163 0.135064i
\(727\) −33.4915 + 38.6513i −1.24213 + 1.43350i −0.381420 + 0.924402i \(0.624565\pi\)
−0.860711 + 0.509094i \(0.829980\pi\)
\(728\) −2.23903 + 4.90280i −0.0829841 + 0.181710i
\(729\) 0.841254 + 0.540641i 0.0311575 + 0.0200237i
\(730\) −20.7184 + 6.08346i −0.766821 + 0.225159i
\(731\) −0.681652 0.786668i −0.0252118 0.0290960i
\(732\) −9.17297 2.69343i −0.339043 0.0995520i
\(733\) −4.70301 10.2982i −0.173710 0.380371i 0.802673 0.596419i \(-0.203410\pi\)
−0.976383 + 0.216048i \(0.930683\pi\)
\(734\) −1.42663 + 9.92240i −0.0526577 + 0.366242i
\(735\) 1.80922 0.0667342
\(736\) 0.281442 + 4.78757i 0.0103741 + 0.176472i
\(737\) −17.6865 −0.651492
\(738\) −0.936983 + 6.51686i −0.0344908 + 0.239889i
\(739\) 2.99416 + 6.55630i 0.110142 + 0.241178i 0.956674 0.291160i \(-0.0940411\pi\)
−0.846532 + 0.532337i \(0.821314\pi\)
\(740\) 11.4891 + 3.37350i 0.422347 + 0.124012i
\(741\) 8.16131 + 9.41865i 0.299813 + 0.346003i
\(742\) 3.96540 1.16435i 0.145574 0.0427445i
\(743\) 23.4561 + 15.0743i 0.860521 + 0.553023i 0.894840 0.446387i \(-0.147290\pi\)
−0.0343184 + 0.999411i \(0.510926\pi\)
\(744\) −2.42664 + 5.31359i −0.0889648 + 0.194806i
\(745\) −16.4327 + 18.9643i −0.602047 + 0.694800i
\(746\) 6.36423 4.09004i 0.233011 0.149747i
\(747\) 0.895290 + 6.22688i 0.0327570 + 0.227830i
\(748\) −0.0378005 0.262909i −0.00138212 0.00961289i
\(749\) −3.56990 + 2.29424i −0.130441 + 0.0838296i
\(750\) −7.96974 + 9.19756i −0.291014 + 0.335848i
\(751\) −4.40620 + 9.64824i −0.160785 + 0.352069i −0.972828 0.231527i \(-0.925628\pi\)
0.812044 + 0.583597i \(0.198355\pi\)
\(752\) −2.90717 1.86833i −0.106014 0.0681309i
\(753\) −12.0250 + 3.53084i −0.438214 + 0.128671i
\(754\) −36.5899 42.2270i −1.33253 1.53782i
\(755\) 29.5041 + 8.66319i 1.07376 + 0.315286i
\(756\) 0.415415 + 0.909632i 0.0151085 + 0.0330830i
\(757\) 1.39355 9.69235i 0.0506494 0.352275i −0.948699 0.316181i \(-0.897599\pi\)
0.999348 0.0360938i \(-0.0114915\pi\)
\(758\) 30.9366 1.12367
\(759\) 2.22884 9.65468i 0.0809017 0.350443i
\(760\) 4.18335 0.151746
\(761\) 1.74859 12.1617i 0.0633865 0.440863i −0.933271 0.359172i \(-0.883059\pi\)
0.996658 0.0816904i \(-0.0260319\pi\)
\(762\) −6.82658 14.9481i −0.247301 0.541513i
\(763\) −12.4296 3.64965i −0.449981 0.132126i
\(764\) 3.20986 + 3.70438i 0.116129 + 0.134020i
\(765\) 0.223169 0.0655282i 0.00806867 0.00236918i
\(766\) 5.71236 + 3.67111i 0.206396 + 0.132643i
\(767\) −10.9885 + 24.0614i −0.396770 + 0.868805i
\(768\) −0.654861 + 0.755750i −0.0236303 + 0.0272708i
\(769\) 23.5165 15.1131i 0.848027 0.544994i −0.0429316 0.999078i \(-0.513670\pi\)
0.890959 + 0.454084i \(0.150033\pi\)
\(770\) −0.531975 3.69997i −0.0191710 0.133338i
\(771\) −1.73747 12.0843i −0.0625733 0.435207i
\(772\) −7.85245 + 5.04647i −0.282616 + 0.181626i
\(773\) −31.6852 + 36.5667i −1.13964 + 1.31521i −0.197377 + 0.980328i \(0.563242\pi\)
−0.942260 + 0.334883i \(0.891303\pi\)
\(774\) 3.36354 7.36513i 0.120900 0.264734i
\(775\) −8.48534 5.45320i −0.304802 0.195885i
\(776\) 0.545729 0.160240i 0.0195905 0.00575229i
\(777\) 4.33411 + 5.00183i 0.155485 + 0.179440i
\(778\) 0.348972 + 0.102467i 0.0125112 + 0.00367363i
\(779\) 6.32407 + 13.8478i 0.226583 + 0.496148i
\(780\) −1.38778 + 9.65222i −0.0496905 + 0.345605i
\(781\) 6.09393 0.218058
\(782\) 0.488843 + 0.375709i 0.0174810 + 0.0134353i
\(783\) −10.3665 −0.370470
\(784\) −0.142315 + 0.989821i −0.00508267 + 0.0353508i
\(785\) −9.52024 20.8464i −0.339792 0.744040i
\(786\) −8.96713 2.63299i −0.319847 0.0939155i
\(787\) −9.83127 11.3459i −0.350447 0.404437i 0.552970 0.833201i \(-0.313495\pi\)
−0.903416 + 0.428764i \(0.858949\pi\)
\(788\) 21.1551 6.21169i 0.753619 0.221282i
\(789\) −5.49409 3.53084i −0.195595 0.125701i
\(790\) 1.49185 3.26669i 0.0530775 0.116224i
\(791\) 0.452420 0.522121i 0.0160862 0.0185645i
\(792\) 1.73810 1.11701i 0.0617608 0.0396913i
\(793\) −7.33325 51.0039i −0.260412 1.81120i
\(794\) 2.15862 + 15.0135i 0.0766065 + 0.532810i
\(795\) 6.29019 4.04246i 0.223090 0.143371i
\(796\) 15.0881 17.4126i 0.534784 0.617174i
\(797\) −9.82425 + 21.5121i −0.347993 + 0.761998i 0.652000 + 0.758219i \(0.273930\pi\)
−0.999993 + 0.00377918i \(0.998797\pi\)
\(798\) 1.94518 + 1.25009i 0.0688586 + 0.0442527i
\(799\) −0.426270 + 0.125164i −0.0150804 + 0.00442799i
\(800\) −1.13076 1.30496i −0.0399783 0.0461374i
\(801\) −11.9934 3.52158i −0.423766 0.124429i
\(802\) 10.6363 + 23.2902i 0.375580 + 0.822405i
\(803\) −3.50930 + 24.4077i −0.123840 + 0.861330i
\(804\) 8.56040 0.301902
\(805\) 6.87958 + 5.28744i 0.242473 + 0.186358i
\(806\) −31.4848 −1.10900
\(807\) −3.11246 + 21.6476i −0.109564 + 0.762032i
\(808\) 1.90393 + 4.16901i 0.0669798 + 0.146665i
\(809\) 46.1470 + 13.5500i 1.62244 + 0.476392i 0.961673 0.274198i \(-0.0884122\pi\)
0.660769 + 0.750590i \(0.270230\pi\)
\(810\) 1.18479 + 1.36732i 0.0416292 + 0.0480427i
\(811\) 11.7111 3.43869i 0.411232 0.120749i −0.0695713 0.997577i \(-0.522163\pi\)
0.480804 + 0.876828i \(0.340345\pi\)
\(812\) −8.72089 5.60458i −0.306043 0.196682i
\(813\) 0.0792032 0.173431i 0.00277778 0.00608249i
\(814\) 8.95466 10.3342i 0.313861 0.362215i
\(815\) 23.0088 14.7868i 0.805962 0.517960i
\(816\) 0.0182957 + 0.127249i 0.000640478 + 0.00445462i
\(817\) −2.66439 18.5312i −0.0932151 0.648325i
\(818\) −30.9749 + 19.9063i −1.08301 + 0.696009i
\(819\) −3.52961 + 4.07339i −0.123335 + 0.142336i
\(820\) −4.94830 + 10.8353i −0.172802 + 0.378384i
\(821\) 6.44582 + 4.14248i 0.224961 + 0.144574i 0.648267 0.761413i \(-0.275494\pi\)
−0.423306 + 0.905987i \(0.639130\pi\)
\(822\) −21.2325 + 6.23444i −0.740570 + 0.217451i
\(823\) 19.8682 + 22.9292i 0.692563 + 0.799260i 0.987728 0.156186i \(-0.0499200\pi\)
−0.295165 + 0.955446i \(0.595375\pi\)
\(824\) −11.3754 3.34010i −0.396279 0.116358i
\(825\) 1.48201 + 3.24515i 0.0515970 + 0.112982i
\(826\) −0.698436 + 4.85773i −0.0243017 + 0.169022i
\(827\) 25.7802 0.896466 0.448233 0.893917i \(-0.352053\pi\)
0.448233 + 0.893917i \(0.352053\pi\)
\(828\) −1.07877 + 4.67293i −0.0374899 + 0.162395i
\(829\) −23.3305 −0.810302 −0.405151 0.914250i \(-0.632781\pi\)
−0.405151 + 0.914250i \(0.632781\pi\)
\(830\) −1.61978 + 11.2658i −0.0562234 + 0.391042i
\(831\) −9.21597 20.1802i −0.319698 0.700042i
\(832\) −5.17154 1.51850i −0.179291 0.0526446i
\(833\) 0.0841876 + 0.0971576i 0.00291693 + 0.00336631i
\(834\) −15.4871 + 4.54741i −0.536273 + 0.157464i
\(835\) −2.03127 1.30542i −0.0702951 0.0451759i
\(836\) 1.98456 4.34557i 0.0686374 0.150295i
\(837\) −3.82535 + 4.41469i −0.132223 + 0.152594i
\(838\) −9.10058 + 5.84859i −0.314374 + 0.202036i
\(839\) 0.307806 + 2.14084i 0.0106267 + 0.0739100i 0.994445 0.105261i \(-0.0335677\pi\)
−0.983818 + 0.179171i \(0.942659\pi\)
\(840\) 0.257479 + 1.79081i 0.00888388 + 0.0617887i
\(841\) 66.0091 42.4215i 2.27618 1.46281i
\(842\) −8.91837 + 10.2924i −0.307347 + 0.354698i
\(843\) −1.50689 + 3.29964i −0.0519002 + 0.113645i
\(844\) −3.91760 2.51769i −0.134850 0.0866625i
\(845\) −27.8630 + 8.18131i −0.958515 + 0.281446i
\(846\) −2.26304 2.61169i −0.0778051 0.0897918i
\(847\) 6.45862 + 1.89642i 0.221921 + 0.0651618i
\(848\) 1.71683 + 3.75933i 0.0589561 + 0.129096i
\(849\) −1.16186 + 8.08093i −0.0398750 + 0.277337i
\(850\) −0.221983 −0.00761394
\(851\) 1.86269 + 31.6859i 0.0638520 + 1.08618i
\(852\) −2.94950 −0.101048
\(853\) 0.370028 2.57360i 0.0126695 0.0881184i −0.982506 0.186233i \(-0.940372\pi\)
0.995175 + 0.0981146i \(0.0312812\pi\)
\(854\) −3.97146 8.69629i −0.135901 0.297581i
\(855\) 4.01390 + 1.17859i 0.137272 + 0.0403068i
\(856\) −2.77893 3.20706i −0.0949820 0.109615i
\(857\) −28.6744 + 8.41955i −0.979498 + 0.287606i −0.732017 0.681286i \(-0.761421\pi\)
−0.247481 + 0.968893i \(0.579603\pi\)
\(858\) 9.36815 + 6.02055i 0.319823 + 0.205538i
\(859\) −7.92986 + 17.3640i −0.270563 + 0.592451i −0.995329 0.0965449i \(-0.969221\pi\)
0.724765 + 0.688996i \(0.241948\pi\)
\(860\) 9.59303 11.0709i 0.327119 0.377516i
\(861\) −5.53871 + 3.55951i −0.188759 + 0.121308i
\(862\) 1.44863 + 10.0755i 0.0493407 + 0.343172i
\(863\) 6.64147 + 46.1924i 0.226078 + 1.57241i 0.714396 + 0.699742i \(0.246702\pi\)
−0.488318 + 0.872666i \(0.662389\pi\)
\(864\) −0.841254 + 0.540641i −0.0286200 + 0.0183930i
\(865\) 19.3632 22.3463i 0.658368 0.759797i
\(866\) −10.2735 + 22.4958i −0.349107 + 0.764439i
\(867\) −14.2874 9.18196i −0.485226 0.311836i
\(868\) −5.60485 + 1.64573i −0.190241 + 0.0558598i
\(869\) −2.68564 3.09939i −0.0911041 0.105140i
\(870\) −17.9957 5.28400i −0.610110 0.179144i
\(871\) 19.1670 + 41.9699i 0.649449 + 1.42210i
\(872\) 1.84359 12.8225i 0.0624319 0.434223i
\(873\) 0.568768 0.0192499
\(874\) 3.74318 + 10.4382i 0.126615 + 0.353079i
\(875\) −12.1701 −0.411425
\(876\) 1.69852 11.8135i 0.0573878 0.399141i
\(877\) 6.24729 + 13.6797i 0.210956 + 0.461929i 0.985299 0.170836i \(-0.0546470\pi\)
−0.774343 + 0.632766i \(0.781920\pi\)
\(878\) −6.82894 2.00516i −0.230466 0.0676708i
\(879\) −0.274730 0.317055i −0.00926641 0.0106940i
\(880\) 3.58660 1.05312i 0.120904 0.0355007i
\(881\) 33.3749 + 21.4488i 1.12443 + 0.722627i 0.964390 0.264484i \(-0.0852015\pi\)
0.160039 + 0.987111i \(0.448838\pi\)
\(882\) −0.415415 + 0.909632i −0.0139878 + 0.0306289i
\(883\) −25.5419 + 29.4769i −0.859554 + 0.991978i 0.140444 + 0.990089i \(0.455147\pi\)
−0.999998 + 0.00188962i \(0.999399\pi\)
\(884\) −0.582914 + 0.374616i −0.0196055 + 0.0125997i
\(885\) 1.26363 + 8.78871i 0.0424763 + 0.295429i
\(886\) −5.42659 37.7427i −0.182310 1.26799i
\(887\) 29.3858 18.8851i 0.986678 0.634100i 0.0554215 0.998463i \(-0.482350\pi\)
0.931257 + 0.364363i \(0.118713\pi\)
\(888\) −4.33411 + 5.00183i −0.145443 + 0.167851i
\(889\) 6.82658 14.9481i 0.228956 0.501344i
\(890\) −19.0248 12.2265i −0.637711 0.409832i
\(891\) 1.98240 0.582084i 0.0664128 0.0195006i
\(892\) −14.9691 17.2753i −0.501202 0.578418i
\(893\) −7.66688 2.25120i −0.256562 0.0753335i
\(894\) −5.76169 12.6163i −0.192700 0.421954i
\(895\) −1.65661 + 11.5220i −0.0553745 + 0.385138i
\(896\) −1.00000 −0.0334077
\(897\) −25.3258 + 5.17384i −0.845605 + 0.172749i
\(898\) 10.0787 0.336329
\(899\) 8.61800 59.9395i 0.287426 1.99909i
\(900\) −0.717302 1.57067i −0.0239101 0.0523558i
\(901\) 0.509783 + 0.149686i 0.0169833 + 0.00498676i
\(902\) 8.90798 + 10.2804i 0.296603 + 0.342299i
\(903\) 7.76884 2.28114i 0.258531 0.0759115i
\(904\) 0.581193 + 0.373510i 0.0193302 + 0.0124228i
\(905\) 13.2762 29.0708i 0.441316 0.966347i
\(906\) −11.1301 + 12.8448i −0.369772 + 0.426739i
\(907\) −40.6227 + 26.1066i −1.34886 + 0.866857i −0.997588 0.0694178i \(-0.977886\pi\)
−0.351268 + 0.936275i \(0.614249\pi\)
\(908\) 1.52683 + 10.6193i 0.0506696 + 0.352415i
\(909\) 0.652256 + 4.53654i 0.0216340 + 0.150467i
\(910\) −8.20346 + 5.27204i −0.271942 + 0.174767i
\(911\) 2.11881 2.44524i 0.0701994 0.0810145i −0.719564 0.694427i \(-0.755658\pi\)
0.789763 + 0.613412i \(0.210204\pi\)
\(912\) −0.960539 + 2.10329i −0.0318066 + 0.0696468i
\(913\) 10.9343 + 7.02702i 0.361871 + 0.232561i
\(914\) −3.30556 + 0.970600i −0.109338 + 0.0321046i
\(915\) −11.3269 13.0719i −0.374454 0.432143i
\(916\) −12.3434 3.62434i −0.407836 0.119751i
\(917\) −3.88234 8.50114i −0.128206 0.280732i
\(918\) −0.0182957 + 0.127249i −0.000603848 + 0.00419986i
\(919\) −38.2696 −1.26240 −0.631200 0.775621i \(-0.717437\pi\)
−0.631200 + 0.775621i \(0.717437\pi\)
\(920\) −4.25455 + 7.56204i −0.140268 + 0.249313i
\(921\) 7.63984 0.251741
\(922\) 0.509173 3.54138i 0.0167687 0.116629i
\(923\) −6.60403 14.4608i −0.217374 0.475983i
\(924\) 1.98240 + 0.582084i 0.0652161 + 0.0191492i
\(925\) −7.48377 8.63673i −0.246065 0.283974i
\(926\) −18.0556 + 5.30160i −0.593344 + 0.174221i
\(927\) −9.97355 6.40961i −0.327574 0.210519i
\(928\) 4.30642 9.42974i 0.141365 0.309546i
\(929\) 17.8291 20.5759i 0.584955 0.675074i −0.383708 0.923455i \(-0.625353\pi\)
0.968662 + 0.248381i \(0.0798984\pi\)
\(930\) −8.89081 + 5.71378i −0.291541 + 0.187362i
\(931\) 0.329066 + 2.28870i 0.0107847 + 0.0750092i
\(932\) 3.03894 + 21.1363i 0.0995439 + 0.692343i
\(933\) 16.8022 10.7981i 0.550078 0.353514i
\(934\) 15.4515 17.8319i 0.505588 0.583479i
\(935\) 0.199628 0.437125i 0.00652854 0.0142955i
\(936\) −4.53425 2.91398i −0.148206 0.0952465i
\(937\) −56.5359 + 16.6004i −1.84695 + 0.542313i −0.847004 + 0.531586i \(0.821596\pi\)
−0.999942 + 0.0107267i \(0.996586\pi\)
\(938\) 5.60587 + 6.46952i 0.183038 + 0.211237i
\(939\) −13.6871 4.01890i −0.446662 0.131152i
\(940\) −2.59728 5.68724i −0.0847138 0.185497i
\(941\) −0.559297 + 3.88999i −0.0182325 + 0.126810i −0.996905 0.0786175i \(-0.974949\pi\)
0.978672 + 0.205428i \(0.0658585\pi\)
\(942\) 12.6670 0.412713
\(943\) −31.4636 2.65175i −1.02460 0.0863530i
\(944\) −4.90768 −0.159731
\(945\) −0.257479 + 1.79081i −0.00837580 + 0.0582550i
\(946\) −6.94937 15.2170i −0.225944 0.494748i
\(947\) −5.56176 1.63308i −0.180733 0.0530680i 0.190114 0.981762i \(-0.439114\pi\)
−0.370847 + 0.928694i \(0.620932\pi\)
\(948\) 1.29987 + 1.50013i 0.0422177 + 0.0487218i
\(949\) 61.7222 18.1233i 2.00359 0.588306i
\(950\) −3.35877 2.15855i −0.108973 0.0700325i
\(951\) 5.19246 11.3699i 0.168377 0.368694i
\(952\) −0.0841876 + 0.0971576i −0.00272853 + 0.00314890i
\(953\) −46.6806 + 29.9998i −1.51213 + 0.971788i −0.519002 + 0.854773i \(0.673696\pi\)
−0.993130 + 0.117015i \(0.962667\pi\)
\(954\) 0.588159 + 4.09074i 0.0190424 + 0.132442i
\(955\) 1.26206 + 8.77781i 0.0408393 + 0.284043i
\(956\) −19.1976 + 12.3376i −0.620896 + 0.399026i
\(957\) −14.0259 + 16.1868i −0.453394 + 0.523245i
\(958\) 5.87567 12.8659i 0.189834 0.415679i
\(959\) −18.6160 11.9638i −0.601143 0.386331i
\(960\) −1.73594 + 0.509717i −0.0560271 + 0.0164510i
\(961\) −2.04500 2.36006i −0.0659678 0.0761309i
\(962\) −34.2272 10.0500i −1.10353 0.324025i
\(963\) −1.76283 3.86007i −0.0568065 0.124389i
\(964\) −1.26863 + 8.82348i −0.0408597 + 0.284185i
\(965\) −16.8877 −0.543634
\(966\) −4.23801 + 2.24484i −0.136356 + 0.0722264i
\(967\) −43.2208 −1.38989 −0.694944 0.719063i \(-0.744571\pi\)
−0.694944 + 0.719063i \(0.744571\pi\)
\(968\) −0.957961 + 6.66276i −0.0307900 + 0.214149i
\(969\) 0.123485 + 0.270394i 0.00396691 + 0.00868631i
\(970\) 0.987345 + 0.289911i 0.0317017 + 0.00930847i
\(971\) 31.3796 + 36.2140i 1.00702 + 1.16216i 0.986730 + 0.162368i \(0.0519130\pi\)
0.0202885 + 0.999794i \(0.493542\pi\)
\(972\) −0.959493 + 0.281733i −0.0307758 + 0.00903658i
\(973\) −13.5786 8.72642i −0.435309 0.279756i
\(974\) −0.419226 + 0.917977i −0.0134329 + 0.0294139i
\(975\) 6.09463 7.03358i 0.195184 0.225255i
\(976\) 8.04258 5.16865i 0.257437 0.165444i
\(977\) −4.00920 27.8846i −0.128266 0.892107i −0.947752 0.319008i \(-0.896650\pi\)
0.819486 0.573099i \(-0.194259\pi\)
\(978\) 2.15142 + 14.9634i 0.0687947 + 0.478478i
\(979\) −21.7258 + 13.9623i −0.694360 + 0.446238i
\(980\) −1.18479 + 1.36732i −0.0378467 + 0.0436774i
\(981\) 5.38142 11.7837i 0.171816 0.376223i
\(982\) −6.57137 4.22316i −0.209701 0.134766i
\(983\) −32.0853 + 9.42108i −1.02336 + 0.300486i −0.750009 0.661428i \(-0.769951\pi\)
−0.273352 + 0.961914i \(0.588132\pi\)
\(984\) −4.31152 4.97576i −0.137446 0.158621i
\(985\) 38.2743 + 11.2383i 1.21952 + 0.358083i
\(986\) −0.553624 1.21227i −0.0176310 0.0386065i
\(987\) 0.491807 3.42059i 0.0156544 0.108879i
\(988\) −12.4627 −0.396490
\(989\) 36.2077 + 14.0303i 1.15134 + 0.446138i
\(990\) 3.73801 0.118802
\(991\) −4.67433 + 32.5107i −0.148485 + 1.03274i 0.770216 + 0.637783i \(0.220148\pi\)
−0.918701 + 0.394953i \(0.870761\pi\)
\(992\) −2.42664 5.31359i −0.0770458 0.168707i
\(993\) 9.61920 + 2.82445i 0.305256 + 0.0896313i
\(994\) −1.93151 2.22909i −0.0612639 0.0707023i
\(995\) 39.9963 11.7440i 1.26797 0.372309i
\(996\) −5.29225 3.40112i −0.167691 0.107769i
\(997\) −1.00407 + 2.19860i −0.0317991 + 0.0696302i −0.924865 0.380296i \(-0.875822\pi\)
0.893066 + 0.449926i \(0.148550\pi\)
\(998\) 8.28925 9.56630i 0.262392 0.302816i
\(999\) −5.56773 + 3.57816i −0.176155 + 0.113208i
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 966.2.q.e.169.1 20
23.3 even 11 inner 966.2.q.e.463.1 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.q.e.169.1 20 1.1 even 1 trivial
966.2.q.e.463.1 yes 20 23.3 even 11 inner