Properties

Label 93.2.m.a.10.1
Level $93$
Weight $2$
Character 93.10
Analytic conductor $0.743$
Analytic rank $0$
Dimension $16$
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] = [93,2,Mod(7,93)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(93, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 28]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("93.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 93 = 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 93.m (of order \(15\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.742608738798\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(2\) over \(\Q(\zeta_{15})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 7 x^{15} + 24 x^{14} - 36 x^{13} + 17 x^{12} + 18 x^{11} - 52 x^{10} + 59 x^{9} + 51 x^{8} - 59 x^{7} - 52 x^{6} - 18 x^{5} + 17 x^{4} + 36 x^{3} + 24 x^{2} + 7 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 10.1
Root \(2.18323 - 2.42472i\) of defining polynomial
Character \(\chi\) \(=\) 93.10
Dual form 93.2.m.a.28.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.83063 - 1.33003i) q^{2} +(0.104528 + 0.994522i) q^{3} +(0.964190 + 2.96747i) q^{4} +(0.467963 + 0.810536i) q^{5} +(1.13139 - 1.95963i) q^{6} +(3.25038 + 0.690890i) q^{7} +(0.783275 - 2.41067i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})\) \(q+(-1.83063 - 1.33003i) q^{2} +(0.104528 + 0.994522i) q^{3} +(0.964190 + 2.96747i) q^{4} +(0.467963 + 0.810536i) q^{5} +(1.13139 - 1.95963i) q^{6} +(3.25038 + 0.690890i) q^{7} +(0.783275 - 2.41067i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(0.221370 - 2.10620i) q^{10} +(2.50394 - 2.78090i) q^{11} +(-2.85043 + 1.26909i) q^{12} +(0.0761022 + 0.0338829i) q^{13} +(-5.03134 - 5.58787i) q^{14} +(-0.757181 + 0.550124i) q^{15} +(0.408412 - 0.296728i) q^{16} +(3.15344 + 3.50225i) q^{17} +(2.06715 + 0.920356i) q^{18} +(-6.46506 + 2.87843i) q^{19} +(-1.95404 + 2.17018i) q^{20} +(-0.347348 + 3.30479i) q^{21} +(-8.28247 + 1.76049i) q^{22} +(-1.39192 + 4.28390i) q^{23} +(2.47934 + 0.527000i) q^{24} +(2.06202 - 3.57152i) q^{25} +(-0.0942497 - 0.163245i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.08379 + 10.3116i) q^{28} +(-2.72075 - 1.97674i) q^{29} +2.11780 q^{30} +(-4.48791 - 3.29525i) q^{31} -6.21177 q^{32} +(3.02740 + 2.19954i) q^{33} +(-1.11468 - 10.6055i) q^{34} +(0.961068 + 2.95786i) q^{35} +(-1.56009 - 2.70216i) q^{36} +(4.62455 - 8.00995i) q^{37} +(15.6635 + 3.32938i) q^{38} +(-0.0257424 + 0.0792270i) q^{39} +(2.32048 - 0.493233i) q^{40} +(0.814860 - 7.75287i) q^{41} +(5.03134 - 5.58787i) q^{42} +(-3.87214 + 1.72399i) q^{43} +(10.6665 + 4.74904i) q^{44} +(-0.626257 - 0.695529i) q^{45} +(8.24581 - 5.99093i) q^{46} +(-7.88472 + 5.72858i) q^{47} +(0.337794 + 0.375158i) q^{48} +(3.69283 + 1.64416i) q^{49} +(-8.52503 + 3.79559i) q^{50} +(-3.15344 + 3.50225i) q^{51} +(-0.0271695 + 0.258501i) q^{52} +(6.05080 - 1.28614i) q^{53} +(-0.699238 + 2.15203i) q^{54} +(3.42577 + 0.728171i) q^{55} +(4.21145 - 7.29445i) q^{56} +(-3.53844 - 6.12876i) q^{57} +(2.35156 + 7.23735i) q^{58} +(-1.12671 - 10.7200i) q^{59} +(-2.36254 - 1.71649i) q^{60} -8.79852 q^{61} +(3.83292 + 12.0014i) q^{62} -3.32300 q^{63} +(10.5546 + 7.66838i) q^{64} +(0.00814973 + 0.0775395i) q^{65} +(-2.61660 - 8.05307i) q^{66} +(1.39139 + 2.40996i) q^{67} +(-7.35231 + 12.7346i) q^{68} +(-4.40593 - 0.936509i) q^{69} +(2.17469 - 6.69300i) q^{70} +(5.47119 - 1.16294i) q^{71} +(-0.264951 + 2.52084i) q^{72} +(-6.19917 + 6.88488i) q^{73} +(-19.1193 + 8.51246i) q^{74} +(3.76750 + 1.67740i) q^{75} +(-14.7752 - 16.4095i) q^{76} +(10.0600 - 7.30905i) q^{77} +(0.152499 - 0.110797i) q^{78} +(5.73303 + 6.36718i) q^{79} +(0.431631 + 0.192174i) q^{80} +(0.913545 - 0.406737i) q^{81} +(-11.8033 + 13.1088i) q^{82} +(0.0799819 - 0.760977i) q^{83} +(-10.1418 + 2.15570i) q^{84} +(-1.36301 + 4.19490i) q^{85} +(9.38141 + 1.99408i) q^{86} +(1.68152 - 2.91247i) q^{87} +(-4.74257 - 8.21438i) q^{88} +(2.35056 + 7.23429i) q^{89} +(0.221370 + 2.10620i) q^{90} +(0.223952 + 0.162711i) q^{91} -14.0544 q^{92} +(2.80808 - 4.80777i) q^{93} +22.0532 q^{94} +(-5.35848 - 3.89316i) q^{95} +(-0.649307 - 6.17774i) q^{96} +(-0.977212 - 3.00755i) q^{97} +(-4.57343 - 7.92142i) q^{98} +(-1.87104 + 3.24073i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{3} + 6 q^{5} - 5 q^{6} - 9 q^{7} + 10 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{3} + 6 q^{5} - 5 q^{6} - 9 q^{7} + 10 q^{8} + 2 q^{9} - 16 q^{10} + 10 q^{11} - 10 q^{12} + 3 q^{13} - 12 q^{14} - 8 q^{15} + 6 q^{16} + 3 q^{17} - 32 q^{19} - 10 q^{20} - 6 q^{21} - 9 q^{22} - 22 q^{23} + 20 q^{24} + 12 q^{25} + 18 q^{26} + 4 q^{27} + 30 q^{28} + 38 q^{29} - 2 q^{30} - 8 q^{31} + 10 q^{33} - 52 q^{34} + 3 q^{35} - 5 q^{36} - 8 q^{37} + 7 q^{38} + 6 q^{39} + 37 q^{40} - 40 q^{41} + 12 q^{42} + q^{43} + q^{45} - 7 q^{46} - 23 q^{47} + 18 q^{48} + 25 q^{49} - 21 q^{50} - 3 q^{51} - 45 q^{52} + 30 q^{53} - 5 q^{54} + 46 q^{55} - 6 q^{56} - 8 q^{57} + 48 q^{58} - 40 q^{59} + 15 q^{60} + 26 q^{61} + 40 q^{62} - 12 q^{63} + 38 q^{64} + 12 q^{65} + 12 q^{66} - 32 q^{67} + 15 q^{68} - 11 q^{69} + 33 q^{70} + 17 q^{71} + 5 q^{72} + 27 q^{73} - 70 q^{74} + 3 q^{75} - 15 q^{76} - 9 q^{77} - 9 q^{78} + 21 q^{80} + 2 q^{81} - 32 q^{82} - 17 q^{83} - 15 q^{84} - 64 q^{85} + 26 q^{86} - 6 q^{87} - 22 q^{88} - 43 q^{89} - 16 q^{90} - 140 q^{92} - q^{93} + 88 q^{94} - 2 q^{95} - 35 q^{96} + 12 q^{97} - 32 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/93\mathbb{Z}\right)^\times\).

\(n\) \(32\) \(34\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{15}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.83063 1.33003i −1.29445 0.940473i −0.294565 0.955631i \(-0.595175\pi\)
−0.999885 + 0.0151582i \(0.995175\pi\)
\(3\) 0.104528 + 0.994522i 0.0603495 + 0.574187i
\(4\) 0.964190 + 2.96747i 0.482095 + 1.48374i
\(5\) 0.467963 + 0.810536i 0.209280 + 0.362483i 0.951488 0.307686i \(-0.0995548\pi\)
−0.742208 + 0.670169i \(0.766221\pi\)
\(6\) 1.13139 1.95963i 0.461888 0.800014i
\(7\) 3.25038 + 0.690890i 1.22853 + 0.261132i 0.776066 0.630652i \(-0.217212\pi\)
0.452463 + 0.891783i \(0.350546\pi\)
\(8\) 0.783275 2.41067i 0.276929 0.852301i
\(9\) −0.978148 + 0.207912i −0.326049 + 0.0693039i
\(10\) 0.221370 2.10620i 0.0700034 0.666038i
\(11\) 2.50394 2.78090i 0.754965 0.838474i −0.236117 0.971725i \(-0.575875\pi\)
0.991082 + 0.133251i \(0.0425415\pi\)
\(12\) −2.85043 + 1.26909i −0.822848 + 0.366356i
\(13\) 0.0761022 + 0.0338829i 0.0211070 + 0.00939742i 0.417263 0.908786i \(-0.362989\pi\)
−0.396156 + 0.918183i \(0.629656\pi\)
\(14\) −5.03134 5.58787i −1.34468 1.49342i
\(15\) −0.757181 + 0.550124i −0.195503 + 0.142041i
\(16\) 0.408412 0.296728i 0.102103 0.0741821i
\(17\) 3.15344 + 3.50225i 0.764822 + 0.849421i 0.992235 0.124378i \(-0.0396935\pi\)
−0.227413 + 0.973798i \(0.573027\pi\)
\(18\) 2.06715 + 0.920356i 0.487233 + 0.216930i
\(19\) −6.46506 + 2.87843i −1.48319 + 0.660357i −0.979115 0.203306i \(-0.934831\pi\)
−0.504070 + 0.863663i \(0.668165\pi\)
\(20\) −1.95404 + 2.17018i −0.436936 + 0.485267i
\(21\) −0.347348 + 3.30479i −0.0757975 + 0.721165i
\(22\) −8.28247 + 1.76049i −1.76583 + 0.375338i
\(23\) −1.39192 + 4.28390i −0.290236 + 0.893255i 0.694544 + 0.719450i \(0.255606\pi\)
−0.984780 + 0.173805i \(0.944394\pi\)
\(24\) 2.47934 + 0.527000i 0.506093 + 0.107573i
\(25\) 2.06202 3.57152i 0.412404 0.714305i
\(26\) −0.0942497 0.163245i −0.0184839 0.0320150i
\(27\) −0.309017 0.951057i −0.0594703 0.183031i
\(28\) 1.08379 + 10.3116i 0.204817 + 1.94870i
\(29\) −2.72075 1.97674i −0.505230 0.367071i 0.305781 0.952102i \(-0.401083\pi\)
−0.811011 + 0.585031i \(0.801083\pi\)
\(30\) 2.11780 0.386655
\(31\) −4.48791 3.29525i −0.806052 0.591844i
\(32\) −6.21177 −1.09810
\(33\) 3.02740 + 2.19954i 0.527003 + 0.382890i
\(34\) −1.11468 10.6055i −0.191166 1.81883i
\(35\) 0.961068 + 2.95786i 0.162450 + 0.499970i
\(36\) −1.56009 2.70216i −0.260015 0.450360i
\(37\) 4.62455 8.00995i 0.760271 1.31683i −0.182440 0.983217i \(-0.558400\pi\)
0.942711 0.333611i \(-0.108267\pi\)
\(38\) 15.6635 + 3.32938i 2.54096 + 0.540097i
\(39\) −0.0257424 + 0.0792270i −0.00412209 + 0.0126865i
\(40\) 2.32048 0.493233i 0.366900 0.0779870i
\(41\) 0.814860 7.75287i 0.127260 1.21080i −0.725400 0.688328i \(-0.758345\pi\)
0.852659 0.522467i \(-0.174988\pi\)
\(42\) 5.03134 5.58787i 0.776352 0.862227i
\(43\) −3.87214 + 1.72399i −0.590496 + 0.262906i −0.680157 0.733067i \(-0.738088\pi\)
0.0896609 + 0.995972i \(0.471422\pi\)
\(44\) 10.6665 + 4.74904i 1.60804 + 0.715945i
\(45\) −0.626257 0.695529i −0.0933569 0.103683i
\(46\) 8.24581 5.99093i 1.21578 0.883315i
\(47\) −7.88472 + 5.72858i −1.15010 + 0.835599i −0.988495 0.151255i \(-0.951668\pi\)
−0.161609 + 0.986855i \(0.551668\pi\)
\(48\) 0.337794 + 0.375158i 0.0487563 + 0.0541494i
\(49\) 3.69283 + 1.64416i 0.527548 + 0.234879i
\(50\) −8.52503 + 3.79559i −1.20562 + 0.536777i
\(51\) −3.15344 + 3.50225i −0.441570 + 0.490413i
\(52\) −0.0271695 + 0.258501i −0.00376773 + 0.0358476i
\(53\) 6.05080 1.28614i 0.831142 0.176665i 0.227356 0.973812i \(-0.426992\pi\)
0.603785 + 0.797147i \(0.293658\pi\)
\(54\) −0.699238 + 2.15203i −0.0951543 + 0.292855i
\(55\) 3.42577 + 0.728171i 0.461931 + 0.0981865i
\(56\) 4.21145 7.29445i 0.562779 0.974761i
\(57\) −3.53844 6.12876i −0.468678 0.811774i
\(58\) 2.35156 + 7.23735i 0.308775 + 0.950311i
\(59\) −1.12671 10.7200i −0.146686 1.39562i −0.781957 0.623332i \(-0.785779\pi\)
0.635272 0.772289i \(-0.280888\pi\)
\(60\) −2.36254 1.71649i −0.305003 0.221598i
\(61\) −8.79852 −1.12654 −0.563268 0.826274i \(-0.690456\pi\)
−0.563268 + 0.826274i \(0.690456\pi\)
\(62\) 3.83292 + 12.0014i 0.486781 + 1.52418i
\(63\) −3.32300 −0.418658
\(64\) 10.5546 + 7.66838i 1.31933 + 0.958548i
\(65\) 0.00814973 + 0.0775395i 0.00101085 + 0.00961760i
\(66\) −2.61660 8.05307i −0.322081 0.991265i
\(67\) 1.39139 + 2.40996i 0.169986 + 0.294424i 0.938415 0.345511i \(-0.112295\pi\)
−0.768429 + 0.639935i \(0.778961\pi\)
\(68\) −7.35231 + 12.7346i −0.891599 + 1.54429i
\(69\) −4.40593 0.936509i −0.530411 0.112742i
\(70\) 2.17469 6.69300i 0.259925 0.799967i
\(71\) 5.47119 1.16294i 0.649310 0.138015i 0.128530 0.991706i \(-0.458974\pi\)
0.520781 + 0.853690i \(0.325641\pi\)
\(72\) −0.264951 + 2.52084i −0.0312248 + 0.297084i
\(73\) −6.19917 + 6.88488i −0.725558 + 0.805814i −0.987223 0.159345i \(-0.949062\pi\)
0.261665 + 0.965159i \(0.415729\pi\)
\(74\) −19.1193 + 8.51246i −2.22257 + 0.989554i
\(75\) 3.76750 + 1.67740i 0.435033 + 0.193689i
\(76\) −14.7752 16.4095i −1.69483 1.88230i
\(77\) 10.0600 7.30905i 1.14645 0.832944i
\(78\) 0.152499 0.110797i 0.0172671 0.0125453i
\(79\) 5.73303 + 6.36718i 0.645016 + 0.716363i 0.973638 0.228098i \(-0.0732508\pi\)
−0.328622 + 0.944462i \(0.606584\pi\)
\(80\) 0.431631 + 0.192174i 0.0482578 + 0.0214858i
\(81\) 0.913545 0.406737i 0.101505 0.0451930i
\(82\) −11.8033 + 13.1088i −1.30345 + 1.44763i
\(83\) 0.0799819 0.760977i 0.00877916 0.0835281i −0.989255 0.146200i \(-0.953296\pi\)
0.998034 + 0.0626722i \(0.0199623\pi\)
\(84\) −10.1418 + 2.15570i −1.10656 + 0.235206i
\(85\) −1.36301 + 4.19490i −0.147839 + 0.455001i
\(86\) 9.38141 + 1.99408i 1.01162 + 0.215027i
\(87\) 1.68152 2.91247i 0.180277 0.312250i
\(88\) −4.74257 8.21438i −0.505560 0.875656i
\(89\) 2.35056 + 7.23429i 0.249159 + 0.766833i 0.994924 + 0.100625i \(0.0320841\pi\)
−0.745765 + 0.666209i \(0.767916\pi\)
\(90\) 0.221370 + 2.10620i 0.0233345 + 0.222013i
\(91\) 0.223952 + 0.162711i 0.0234765 + 0.0170567i
\(92\) −14.0544 −1.46528
\(93\) 2.80808 4.80777i 0.291185 0.498543i
\(94\) 22.0532 2.27461
\(95\) −5.35848 3.89316i −0.549768 0.399430i
\(96\) −0.649307 6.17774i −0.0662696 0.630513i
\(97\) −0.977212 3.00755i −0.0992208 0.305370i 0.889110 0.457694i \(-0.151324\pi\)
−0.988331 + 0.152324i \(0.951324\pi\)
\(98\) −4.57343 7.92142i −0.461987 0.800184i
\(99\) −1.87104 + 3.24073i −0.188046 + 0.325706i
\(100\) 12.5866 + 2.67536i 1.25866 + 0.267536i
\(101\) 0.728083 2.24081i 0.0724470 0.222969i −0.908276 0.418371i \(-0.862601\pi\)
0.980723 + 0.195402i \(0.0626012\pi\)
\(102\) 10.4309 2.21715i 1.03281 0.219531i
\(103\) 0.589520 5.60891i 0.0580872 0.552663i −0.926318 0.376744i \(-0.877044\pi\)
0.984405 0.175919i \(-0.0562896\pi\)
\(104\) 0.141289 0.156918i 0.0138546 0.0153871i
\(105\) −2.84120 + 1.26498i −0.277273 + 0.123450i
\(106\) −12.7874 5.69331i −1.24202 0.552983i
\(107\) −9.83018 10.9175i −0.950319 1.05544i −0.998397 0.0565927i \(-0.981976\pi\)
0.0480783 0.998844i \(-0.484690\pi\)
\(108\) 2.52428 1.83400i 0.242899 0.176476i
\(109\) 12.4920 9.07594i 1.19651 0.869317i 0.202575 0.979267i \(-0.435069\pi\)
0.993937 + 0.109950i \(0.0350690\pi\)
\(110\) −5.30283 5.88939i −0.505605 0.561532i
\(111\) 8.44947 + 3.76195i 0.801988 + 0.357068i
\(112\) 1.53250 0.682313i 0.144808 0.0644725i
\(113\) −2.73827 + 3.04115i −0.257594 + 0.286087i −0.858045 0.513574i \(-0.828321\pi\)
0.600451 + 0.799662i \(0.294988\pi\)
\(114\) −1.67386 + 15.9257i −0.156771 + 1.49158i
\(115\) −4.12363 + 0.876504i −0.384530 + 0.0817344i
\(116\) 3.24260 9.97969i 0.301068 0.926591i
\(117\) −0.0814838 0.0173199i −0.00753318 0.00160123i
\(118\) −12.1953 + 21.1228i −1.12267 + 1.94452i
\(119\) 7.83022 + 13.5623i 0.717795 + 1.24326i
\(120\) 0.733088 + 2.25621i 0.0669214 + 0.205963i
\(121\) −0.313912 2.98667i −0.0285375 0.271516i
\(122\) 16.1068 + 11.7023i 1.45824 + 1.05948i
\(123\) 7.79558 0.702903
\(124\) 5.45136 16.4950i 0.489547 1.48129i
\(125\) 8.53943 0.763790
\(126\) 6.08318 + 4.41969i 0.541932 + 0.393737i
\(127\) 0.722000 + 6.86937i 0.0640672 + 0.609558i 0.978703 + 0.205280i \(0.0658106\pi\)
−0.914636 + 0.404278i \(0.867523\pi\)
\(128\) −5.28334 16.2604i −0.466985 1.43723i
\(129\) −2.11929 3.67072i −0.186593 0.323189i
\(130\) 0.0882108 0.152786i 0.00773660 0.0134002i
\(131\) −12.4328 2.64268i −1.08626 0.230892i −0.370215 0.928946i \(-0.620716\pi\)
−0.716045 + 0.698055i \(0.754049\pi\)
\(132\) −3.60807 + 11.1045i −0.314042 + 0.966522i
\(133\) −23.0026 + 4.88935i −1.99458 + 0.423960i
\(134\) 0.658199 6.26234i 0.0568597 0.540984i
\(135\) 0.626257 0.695529i 0.0538996 0.0598616i
\(136\) 10.9128 4.85868i 0.935764 0.416629i
\(137\) 12.9136 + 5.74950i 1.10328 + 0.491213i 0.875851 0.482582i \(-0.160301\pi\)
0.227431 + 0.973794i \(0.426968\pi\)
\(138\) 6.82004 + 7.57442i 0.580560 + 0.644777i
\(139\) −11.8813 + 8.63225i −1.00776 + 0.732178i −0.963737 0.266853i \(-0.914016\pi\)
−0.0440192 + 0.999031i \(0.514016\pi\)
\(140\) −7.85072 + 5.70388i −0.663507 + 0.482066i
\(141\) −6.52138 7.24272i −0.549199 0.609947i
\(142\) −11.5625 5.14794i −0.970300 0.432005i
\(143\) 0.284780 0.126792i 0.0238145 0.0106029i
\(144\) −0.337794 + 0.375158i −0.0281495 + 0.0312631i
\(145\) 0.329009 3.13031i 0.0273227 0.259958i
\(146\) 20.5055 4.35858i 1.69705 0.360718i
\(147\) −1.24914 + 3.84447i −0.103028 + 0.317086i
\(148\) 28.2282 + 6.00010i 2.32035 + 0.493205i
\(149\) 2.76418 4.78771i 0.226451 0.392224i −0.730303 0.683123i \(-0.760621\pi\)
0.956754 + 0.290899i \(0.0939544\pi\)
\(150\) −4.66590 8.08158i −0.380969 0.659858i
\(151\) 5.08050 + 15.6362i 0.413445 + 1.27245i 0.913634 + 0.406537i \(0.133264\pi\)
−0.500189 + 0.865916i \(0.666736\pi\)
\(152\) 1.87503 + 17.8397i 0.152085 + 1.44699i
\(153\) −3.81269 2.77008i −0.308238 0.223948i
\(154\) −28.1375 −2.26738
\(155\) 0.570743 5.17967i 0.0458432 0.416041i
\(156\) −0.259924 −0.0208106
\(157\) 11.1917 + 8.13127i 0.893197 + 0.648946i 0.936710 0.350107i \(-0.113855\pi\)
−0.0435126 + 0.999053i \(0.513855\pi\)
\(158\) −2.02652 19.2810i −0.161221 1.53392i
\(159\) 1.91157 + 5.88322i 0.151598 + 0.466570i
\(160\) −2.90688 5.03486i −0.229809 0.398041i
\(161\) −7.48399 + 12.9626i −0.589821 + 1.02160i
\(162\) −2.21333 0.470459i −0.173896 0.0369627i
\(163\) 2.68325 8.25818i 0.210168 0.646831i −0.789293 0.614016i \(-0.789553\pi\)
0.999461 0.0328146i \(-0.0104471\pi\)
\(164\) 23.7921 5.05717i 1.85785 0.394898i
\(165\) −0.366091 + 3.48312i −0.0285001 + 0.271161i
\(166\) −1.15854 + 1.28669i −0.0899201 + 0.0998664i
\(167\) −1.78755 + 0.795868i −0.138325 + 0.0615861i −0.474732 0.880131i \(-0.657455\pi\)
0.336407 + 0.941717i \(0.390788\pi\)
\(168\) 7.69470 + 3.42590i 0.593659 + 0.264314i
\(169\) −8.69405 9.65573i −0.668773 0.742748i
\(170\) 8.07451 5.86647i 0.619286 0.449938i
\(171\) 5.72532 4.15969i 0.437826 0.318099i
\(172\) −8.84936 9.82821i −0.674757 0.749394i
\(173\) −8.80748 3.92134i −0.669620 0.298134i 0.0436257 0.999048i \(-0.486109\pi\)
−0.713246 + 0.700914i \(0.752776\pi\)
\(174\) −6.95190 + 3.09519i −0.527022 + 0.234645i
\(175\) 9.16988 10.1842i 0.693178 0.769852i
\(176\) 0.197464 1.87874i 0.0148844 0.141616i
\(177\) 10.5435 2.24108i 0.792496 0.168450i
\(178\) 5.31881 16.3696i 0.398662 1.22696i
\(179\) −22.8813 4.86358i −1.71023 0.363521i −0.754168 0.656681i \(-0.771960\pi\)
−0.956063 + 0.293160i \(0.905293\pi\)
\(180\) 1.46013 2.52902i 0.108832 0.188502i
\(181\) 4.27064 + 7.39696i 0.317434 + 0.549812i 0.979952 0.199234i \(-0.0638455\pi\)
−0.662518 + 0.749046i \(0.730512\pi\)
\(182\) −0.193563 0.595725i −0.0143478 0.0441581i
\(183\) −0.919696 8.75033i −0.0679859 0.646843i
\(184\) 9.23682 + 6.71094i 0.680947 + 0.494737i
\(185\) 8.65648 0.636437
\(186\) −11.5350 + 5.06641i −0.845790 + 0.371487i
\(187\) 17.6354 1.28963
\(188\) −24.6018 17.8742i −1.79427 1.30361i
\(189\) −0.347348 3.30479i −0.0252658 0.240388i
\(190\) 4.63137 + 14.2539i 0.335995 + 1.03409i
\(191\) −1.52056 2.63369i −0.110024 0.190567i 0.805756 0.592248i \(-0.201759\pi\)
−0.915780 + 0.401681i \(0.868426\pi\)
\(192\) −6.52311 + 11.2984i −0.470765 + 0.815389i
\(193\) −5.57785 1.18561i −0.401503 0.0853420i 0.00273443 0.999996i \(-0.499130\pi\)
−0.404237 + 0.914654i \(0.632463\pi\)
\(194\) −2.21122 + 6.80543i −0.158756 + 0.488601i
\(195\) −0.0762629 + 0.0162102i −0.00546130 + 0.00116083i
\(196\) −1.31839 + 12.5437i −0.0941708 + 0.895975i
\(197\) 2.30784 2.56312i 0.164427 0.182615i −0.655301 0.755368i \(-0.727458\pi\)
0.819728 + 0.572753i \(0.194125\pi\)
\(198\) 7.73545 3.44404i 0.549734 0.244757i
\(199\) 16.0068 + 7.12668i 1.13469 + 0.505197i 0.886138 0.463421i \(-0.153378\pi\)
0.248553 + 0.968618i \(0.420045\pi\)
\(200\) −6.99464 7.76834i −0.494596 0.549304i
\(201\) −2.25132 + 1.63568i −0.158796 + 0.115372i
\(202\) −4.31319 + 3.13372i −0.303475 + 0.220488i
\(203\) −7.47776 8.30490i −0.524836 0.582889i
\(204\) −13.4333 5.98091i −0.940522 0.418747i
\(205\) 6.66531 2.96759i 0.465525 0.207265i
\(206\) −8.53921 + 9.48376i −0.594955 + 0.660765i
\(207\) 0.470834 4.47968i 0.0327252 0.311360i
\(208\) 0.0411350 0.00874352i 0.00285220 0.000606254i
\(209\) −8.18346 + 25.1861i −0.566062 + 1.74216i
\(210\) 6.88365 + 1.46317i 0.475017 + 0.100968i
\(211\) −10.4677 + 18.1306i −0.720626 + 1.24816i 0.240123 + 0.970742i \(0.422812\pi\)
−0.960749 + 0.277419i \(0.910521\pi\)
\(212\) 9.65070 + 16.7155i 0.662813 + 1.14802i
\(213\) 1.72846 + 5.31965i 0.118432 + 0.364497i
\(214\) 3.47478 + 33.0604i 0.237531 + 2.25996i
\(215\) −3.20938 2.33175i −0.218878 0.159024i
\(216\) −2.53473 −0.172467
\(217\) −12.3108 13.8115i −0.835709 0.937584i
\(218\) −34.9394 −2.36639
\(219\) −7.49515 5.44555i −0.506476 0.367976i
\(220\) 1.14227 + 10.8680i 0.0770119 + 0.732719i
\(221\) 0.121317 + 0.373377i 0.00816069 + 0.0251160i
\(222\) −10.4643 18.1248i −0.702321 1.21646i
\(223\) 0.610850 1.05802i 0.0409055 0.0708505i −0.844848 0.535007i \(-0.820309\pi\)
0.885753 + 0.464156i \(0.153642\pi\)
\(224\) −20.1906 4.29165i −1.34904 0.286748i
\(225\) −1.27440 + 3.92220i −0.0849599 + 0.261480i
\(226\) 9.05757 1.92525i 0.602501 0.128065i
\(227\) −1.71899 + 16.3551i −0.114093 + 1.08553i 0.776309 + 0.630353i \(0.217090\pi\)
−0.890402 + 0.455174i \(0.849577\pi\)
\(228\) 14.7752 16.4095i 0.978511 1.08675i
\(229\) 3.75301 1.67095i 0.248006 0.110419i −0.278969 0.960300i \(-0.589993\pi\)
0.526975 + 0.849881i \(0.323326\pi\)
\(230\) 8.71461 + 3.87999i 0.574624 + 0.255839i
\(231\) 8.32058 + 9.24094i 0.547454 + 0.608009i
\(232\) −6.89636 + 5.01050i −0.452768 + 0.328956i
\(233\) 7.60991 5.52893i 0.498542 0.362212i −0.309918 0.950763i \(-0.600302\pi\)
0.808460 + 0.588551i \(0.200302\pi\)
\(234\) 0.126131 + 0.140082i 0.00824542 + 0.00915747i
\(235\) −8.33298 3.71008i −0.543584 0.242019i
\(236\) 30.7248 13.6796i 2.00002 0.890464i
\(237\) −5.73303 + 6.36718i −0.372400 + 0.413593i
\(238\) 3.70409 35.2420i 0.240100 2.28440i
\(239\) 24.6500 5.23953i 1.59448 0.338917i 0.676777 0.736188i \(-0.263376\pi\)
0.917701 + 0.397272i \(0.130043\pi\)
\(240\) −0.146004 + 0.449354i −0.00942452 + 0.0290057i
\(241\) −11.0599 2.35085i −0.712430 0.151432i −0.162580 0.986695i \(-0.551982\pi\)
−0.549850 + 0.835264i \(0.685315\pi\)
\(242\) −3.39771 + 5.88501i −0.218413 + 0.378302i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −8.48345 26.1094i −0.543097 1.67148i
\(245\) 0.395463 + 3.76258i 0.0252652 + 0.240382i
\(246\) −14.2708 10.3683i −0.909874 0.661062i
\(247\) −0.589534 −0.0375112
\(248\) −11.4590 + 8.23779i −0.727649 + 0.523100i
\(249\) 0.765169 0.0484906
\(250\) −15.6325 11.3577i −0.988689 0.718324i
\(251\) 2.41967 + 23.0216i 0.152728 + 1.45311i 0.755475 + 0.655177i \(0.227406\pi\)
−0.602747 + 0.797932i \(0.705927\pi\)
\(252\) −3.20400 9.86090i −0.201833 0.621178i
\(253\) 8.42782 + 14.5974i 0.529853 + 0.917732i
\(254\) 7.81476 13.5356i 0.490342 0.849296i
\(255\) −4.31440 0.917053i −0.270178 0.0574281i
\(256\) −3.89203 + 11.9784i −0.243252 + 0.748652i
\(257\) −6.11937 + 1.30071i −0.381716 + 0.0811362i −0.394773 0.918779i \(-0.629177\pi\)
0.0130575 + 0.999915i \(0.495844\pi\)
\(258\) −1.00253 + 9.53846i −0.0624149 + 0.593838i
\(259\) 20.5655 22.8403i 1.27788 1.41923i
\(260\) −0.222238 + 0.0989469i −0.0137826 + 0.00613643i
\(261\) 3.07228 + 1.36787i 0.190169 + 0.0846689i
\(262\) 19.2450 + 21.3738i 1.18896 + 1.32048i
\(263\) −9.08793 + 6.60276i −0.560386 + 0.407144i −0.831600 0.555375i \(-0.812575\pi\)
0.271214 + 0.962519i \(0.412575\pi\)
\(264\) 7.67365 5.57523i 0.472280 0.343132i
\(265\) 3.87402 + 4.30253i 0.237979 + 0.264302i
\(266\) 48.6122 + 21.6435i 2.98060 + 1.32705i
\(267\) −6.94896 + 3.09388i −0.425269 + 0.189342i
\(268\) −5.80993 + 6.45258i −0.354898 + 0.394154i
\(269\) −1.69666 + 16.1426i −0.103447 + 0.984232i 0.812508 + 0.582950i \(0.198102\pi\)
−0.915955 + 0.401282i \(0.868565\pi\)
\(270\) −2.07152 + 0.440315i −0.126069 + 0.0267967i
\(271\) 7.51413 23.1261i 0.456451 1.40481i −0.412973 0.910743i \(-0.635510\pi\)
0.869424 0.494067i \(-0.164490\pi\)
\(272\) 2.32712 + 0.494644i 0.141102 + 0.0299922i
\(273\) −0.138410 + 0.239733i −0.00837694 + 0.0145093i
\(274\) −15.9930 27.7006i −0.966171 1.67346i
\(275\) −4.76890 14.6772i −0.287575 0.885066i
\(276\) −1.46909 13.9774i −0.0884287 0.841343i
\(277\) 7.87545 + 5.72185i 0.473190 + 0.343793i 0.798683 0.601752i \(-0.205530\pi\)
−0.325493 + 0.945544i \(0.605530\pi\)
\(278\) 33.2314 1.99308
\(279\) 5.07496 + 2.29015i 0.303830 + 0.137108i
\(280\) 7.88322 0.471112
\(281\) 9.70333 + 7.04988i 0.578852 + 0.420561i 0.838310 0.545194i \(-0.183544\pi\)
−0.259458 + 0.965754i \(0.583544\pi\)
\(282\) 2.30518 + 21.9324i 0.137272 + 1.30605i
\(283\) −0.712755 2.19364i −0.0423689 0.130398i 0.927635 0.373489i \(-0.121839\pi\)
−0.970004 + 0.243091i \(0.921839\pi\)
\(284\) 8.72624 + 15.1143i 0.517807 + 0.896868i
\(285\) 3.31172 5.73607i 0.196170 0.339776i
\(286\) −0.689964 0.146656i −0.0407984 0.00867198i
\(287\) 8.00499 24.6368i 0.472519 1.45427i
\(288\) 6.07603 1.29150i 0.358033 0.0761023i
\(289\) −0.544588 + 5.18141i −0.0320346 + 0.304789i
\(290\) −4.76570 + 5.29284i −0.279851 + 0.310806i
\(291\) 2.88893 1.28623i 0.169352 0.0754003i
\(292\) −26.4079 11.7575i −1.54540 0.688058i
\(293\) 17.6066 + 19.5542i 1.02859 + 1.14237i 0.989705 + 0.143123i \(0.0457143\pi\)
0.0388862 + 0.999244i \(0.487619\pi\)
\(294\) 7.39997 5.37639i 0.431575 0.313558i
\(295\) 8.16166 5.92979i 0.475190 0.345246i
\(296\) −15.6871 17.4223i −0.911792 1.01265i
\(297\) −3.41856 1.52204i −0.198365 0.0883177i
\(298\) −11.4280 + 5.08807i −0.662006 + 0.294744i
\(299\) −0.251079 + 0.278852i −0.0145203 + 0.0161264i
\(300\) −1.34505 + 12.7973i −0.0776563 + 0.738851i
\(301\) −13.7770 + 2.92840i −0.794094 + 0.168790i
\(302\) 11.4961 35.3812i 0.661524 2.03596i
\(303\) 2.30464 + 0.489866i 0.132398 + 0.0281421i
\(304\) −1.78629 + 3.09395i −0.102451 + 0.177450i
\(305\) −4.11739 7.13152i −0.235761 0.408350i
\(306\) 3.29533 + 10.1420i 0.188381 + 0.579779i
\(307\) −1.68795 16.0597i −0.0963361 0.916577i −0.930804 0.365520i \(-0.880891\pi\)
0.834467 0.551057i \(-0.185775\pi\)
\(308\) 31.3892 + 22.8056i 1.78857 + 1.29947i
\(309\) 5.63981 0.320837
\(310\) −7.93394 + 8.72295i −0.450617 + 0.495430i
\(311\) 10.2888 0.583424 0.291712 0.956506i \(-0.405775\pi\)
0.291712 + 0.956506i \(0.405775\pi\)
\(312\) 0.170827 + 0.124113i 0.00967117 + 0.00702652i
\(313\) −1.30652 12.4307i −0.0738489 0.702625i −0.967329 0.253523i \(-0.918411\pi\)
0.893480 0.449102i \(-0.148256\pi\)
\(314\) −9.67307 29.7707i −0.545883 1.68006i
\(315\) −1.55504 2.69341i −0.0876166 0.151756i
\(316\) −13.3667 + 23.1518i −0.751934 + 1.30239i
\(317\) −5.81564 1.23615i −0.326639 0.0694292i 0.0416737 0.999131i \(-0.486731\pi\)
−0.368312 + 0.929702i \(0.620064\pi\)
\(318\) 4.32547 13.3124i 0.242561 0.746525i
\(319\) −12.3097 + 2.61651i −0.689211 + 0.146496i
\(320\) −1.27633 + 12.1434i −0.0713488 + 0.678838i
\(321\) 9.83018 10.9175i 0.548667 0.609356i
\(322\) 30.9411 13.7759i 1.72428 0.767699i
\(323\) −30.4681 13.5653i −1.69529 0.754793i
\(324\) 2.08781 + 2.31875i 0.115989 + 0.128819i
\(325\) 0.277938 0.201934i 0.0154172 0.0112013i
\(326\) −15.8957 + 11.5489i −0.880379 + 0.639633i
\(327\) 10.3320 + 11.4748i 0.571360 + 0.634559i
\(328\) −18.0514 8.03699i −0.996720 0.443768i
\(329\) −29.5862 + 13.1726i −1.63114 + 0.726229i
\(330\) 5.30283 5.88939i 0.291911 0.324200i
\(331\) 3.01750 28.7096i 0.165857 1.57802i −0.522492 0.852644i \(-0.674998\pi\)
0.688349 0.725380i \(-0.258336\pi\)
\(332\) 2.33529 0.496382i 0.128166 0.0272425i
\(333\) −2.85813 + 8.79641i −0.156624 + 0.482040i
\(334\) 4.33087 + 0.920554i 0.236975 + 0.0503705i
\(335\) −1.30224 + 2.25555i −0.0711491 + 0.123234i
\(336\) 0.838765 + 1.45278i 0.0457584 + 0.0792559i
\(337\) 1.41958 + 4.36903i 0.0773297 + 0.237996i 0.982247 0.187590i \(-0.0600678\pi\)
−0.904918 + 0.425587i \(0.860068\pi\)
\(338\) 3.07319 + 29.2394i 0.167159 + 1.59041i
\(339\) −3.31072 2.40538i −0.179814 0.130642i
\(340\) −13.7624 −0.746374
\(341\) −20.4012 + 4.22934i −1.10479 + 0.229032i
\(342\) −16.0134 −0.865908
\(343\) −7.95134 5.77699i −0.429332 0.311928i
\(344\) 1.12302 + 10.6848i 0.0605491 + 0.576087i
\(345\) −1.30274 4.00942i −0.0701371 0.215860i
\(346\) 10.9077 + 18.8927i 0.586403 + 1.01568i
\(347\) 2.02623 3.50953i 0.108773 0.188401i −0.806500 0.591234i \(-0.798641\pi\)
0.915274 + 0.402833i \(0.131974\pi\)
\(348\) 10.2640 + 2.18167i 0.550206 + 0.116950i
\(349\) −0.841273 + 2.58917i −0.0450323 + 0.138595i −0.971045 0.238898i \(-0.923214\pi\)
0.926012 + 0.377493i \(0.123214\pi\)
\(350\) −30.3319 + 6.44725i −1.62131 + 0.344620i
\(351\) 0.00870766 0.0828479i 0.000464781 0.00442209i
\(352\) −15.5539 + 17.2743i −0.829024 + 0.920725i
\(353\) −9.14415 + 4.07124i −0.486694 + 0.216690i −0.635388 0.772193i \(-0.719160\pi\)
0.148694 + 0.988883i \(0.452493\pi\)
\(354\) −22.2819 9.92054i −1.18427 0.527271i
\(355\) 3.50292 + 3.89038i 0.185916 + 0.206480i
\(356\) −19.2012 + 13.9505i −1.01766 + 0.739373i
\(357\) −12.6696 + 9.20497i −0.670544 + 0.487179i
\(358\) 35.4185 + 39.3363i 1.87193 + 2.07899i
\(359\) 10.6513 + 4.74228i 0.562155 + 0.250288i 0.668084 0.744086i \(-0.267115\pi\)
−0.105928 + 0.994374i \(0.533781\pi\)
\(360\) −2.16722 + 0.964910i −0.114223 + 0.0508552i
\(361\) 20.7981 23.0986i 1.09464 1.21572i
\(362\) 2.02023 19.2212i 0.106181 1.01024i
\(363\) 2.93750 0.624385i 0.154179 0.0327717i
\(364\) −0.266907 + 0.821454i −0.0139897 + 0.0430559i
\(365\) −8.48143 1.80278i −0.443938 0.0943620i
\(366\) −9.95457 + 17.2418i −0.520334 + 0.901245i
\(367\) 7.83091 + 13.5635i 0.408770 + 0.708011i 0.994752 0.102313i \(-0.0326244\pi\)
−0.585982 + 0.810324i \(0.699291\pi\)
\(368\) 0.702677 + 2.16262i 0.0366296 + 0.112734i
\(369\) 0.814860 + 7.75287i 0.0424199 + 0.403598i
\(370\) −15.8468 11.5134i −0.823836 0.598552i
\(371\) 20.5560 1.06721
\(372\) 16.9744 + 3.69730i 0.880084 + 0.191696i
\(373\) −29.6796 −1.53675 −0.768376 0.639999i \(-0.778935\pi\)
−0.768376 + 0.639999i \(0.778935\pi\)
\(374\) −32.2839 23.4557i −1.66936 1.21286i
\(375\) 0.892614 + 8.49265i 0.0460944 + 0.438559i
\(376\) 7.63383 + 23.4945i 0.393685 + 1.21164i
\(377\) −0.140077 0.242621i −0.00721435 0.0124956i
\(378\) −3.75961 + 6.51183i −0.193373 + 0.334933i
\(379\) 12.1369 + 2.57978i 0.623432 + 0.132514i 0.508787 0.860892i \(-0.330094\pi\)
0.114644 + 0.993407i \(0.463427\pi\)
\(380\) 6.38626 19.6549i 0.327608 1.00827i
\(381\) −6.75627 + 1.43609i −0.346134 + 0.0735731i
\(382\) −0.719303 + 6.84371i −0.0368028 + 0.350155i
\(383\) 0.302886 0.336389i 0.0154768 0.0171887i −0.735357 0.677680i \(-0.762985\pi\)
0.750834 + 0.660492i \(0.229652\pi\)
\(384\) 15.6191 6.95407i 0.797059 0.354873i
\(385\) 10.6320 + 4.73367i 0.541856 + 0.241250i
\(386\) 8.63408 + 9.58912i 0.439463 + 0.488074i
\(387\) 3.42909 2.49138i 0.174310 0.126644i
\(388\) 7.98259 5.79969i 0.405255 0.294435i
\(389\) 5.01568 + 5.57047i 0.254305 + 0.282434i 0.856756 0.515721i \(-0.172476\pi\)
−0.602452 + 0.798155i \(0.705809\pi\)
\(390\) 0.161169 + 0.0717571i 0.00816111 + 0.00363356i
\(391\) −19.3926 + 8.63416i −0.980728 + 0.436648i
\(392\) 6.85602 7.61438i 0.346281 0.384584i
\(393\) 1.32862 12.6409i 0.0670198 0.637651i
\(394\) −7.63383 + 1.62262i −0.384587 + 0.0817465i
\(395\) −2.47798 + 7.62644i −0.124681 + 0.383728i
\(396\) −11.4208 2.42757i −0.573917 0.121990i
\(397\) −5.84556 + 10.1248i −0.293380 + 0.508150i −0.974607 0.223923i \(-0.928114\pi\)
0.681227 + 0.732073i \(0.261447\pi\)
\(398\) −19.8238 34.3358i −0.993677 1.72110i
\(399\) −7.26699 22.3655i −0.363804 1.11967i
\(400\) −0.217620 2.07051i −0.0108810 0.103526i
\(401\) 0.408316 + 0.296659i 0.0203903 + 0.0148145i 0.597934 0.801546i \(-0.295989\pi\)
−0.577543 + 0.816360i \(0.695989\pi\)
\(402\) 6.29684 0.314058
\(403\) −0.229887 0.402839i −0.0114515 0.0200668i
\(404\) 7.35154 0.365753
\(405\) 0.757181 + 0.550124i 0.0376246 + 0.0273359i
\(406\) 2.64325 + 25.1488i 0.131182 + 1.24812i
\(407\) −10.6953 32.9168i −0.530148 1.63163i
\(408\) 5.97277 + 10.3451i 0.295696 + 0.512160i
\(409\) 6.06865 10.5112i 0.300075 0.519746i −0.676077 0.736831i \(-0.736321\pi\)
0.976153 + 0.217085i \(0.0696548\pi\)
\(410\) −16.1487 3.43251i −0.797527 0.169520i
\(411\) −4.36816 + 13.4438i −0.215466 + 0.663135i
\(412\) 17.2127 3.65867i 0.848008 0.180250i
\(413\) 3.74407 35.6224i 0.184234 1.75286i
\(414\) −6.82004 + 7.57442i −0.335186 + 0.372262i
\(415\) 0.654228 0.291281i 0.0321148 0.0142984i
\(416\) −0.472729 0.210473i −0.0231775 0.0103193i
\(417\) −9.82689 10.9139i −0.481225 0.534455i
\(418\) 48.4791 35.2222i 2.37119 1.72277i
\(419\) 23.9955 17.4337i 1.17225 0.851693i 0.180978 0.983487i \(-0.442074\pi\)
0.991277 + 0.131794i \(0.0420739\pi\)
\(420\) −6.49326 7.21150i −0.316839 0.351885i
\(421\) −24.7260 11.0087i −1.20507 0.536533i −0.296811 0.954936i \(-0.595923\pi\)
−0.908261 + 0.418404i \(0.862590\pi\)
\(422\) 43.2767 19.2680i 2.10668 0.937953i
\(423\) 6.52138 7.24272i 0.317080 0.352153i
\(424\) 1.63898 15.5939i 0.0795961 0.757306i
\(425\) 19.0108 4.04088i 0.922161 0.196011i
\(426\) 3.91113 12.0372i 0.189495 0.583205i
\(427\) −28.5986 6.07881i −1.38398 0.294174i
\(428\) 22.9193 39.6973i 1.10784 1.91884i
\(429\) 0.155865 + 0.269967i 0.00752525 + 0.0130341i
\(430\) 2.77388 + 8.53713i 0.133768 + 0.411697i
\(431\) 2.87530 + 27.3566i 0.138498 + 1.31772i 0.814216 + 0.580562i \(0.197167\pi\)
−0.675718 + 0.737160i \(0.736166\pi\)
\(432\) −0.408412 0.296728i −0.0196497 0.0142764i
\(433\) 24.7991 1.19177 0.595884 0.803070i \(-0.296802\pi\)
0.595884 + 0.803070i \(0.296802\pi\)
\(434\) 4.16677 + 41.6574i 0.200011 + 1.99962i
\(435\) 3.14755 0.150913
\(436\) 38.9772 + 28.3186i 1.86667 + 1.35621i
\(437\) −3.33204 31.7022i −0.159393 1.51652i
\(438\) 6.47811 + 19.9376i 0.309536 + 0.952653i
\(439\) 14.6847 + 25.4347i 0.700864 + 1.21393i 0.968163 + 0.250319i \(0.0805354\pi\)
−0.267299 + 0.963614i \(0.586131\pi\)
\(440\) 4.43870 7.68806i 0.211607 0.366514i
\(441\) −3.95398 0.840444i −0.188285 0.0400211i
\(442\) 0.274515 0.844870i 0.0130573 0.0401864i
\(443\) −27.5955 + 5.86561i −1.31110 + 0.278683i −0.809860 0.586624i \(-0.800457\pi\)
−0.501242 + 0.865307i \(0.667123\pi\)
\(444\) −3.01657 + 28.7008i −0.143160 + 1.36208i
\(445\) −4.76368 + 5.29060i −0.225820 + 0.250799i
\(446\) −2.52544 + 1.12440i −0.119583 + 0.0532418i
\(447\) 5.05042 + 2.24859i 0.238877 + 0.106355i
\(448\) 29.0085 + 32.2172i 1.37052 + 1.52212i
\(449\) −15.2056 + 11.0475i −0.717595 + 0.521363i −0.885615 0.464420i \(-0.846263\pi\)
0.168020 + 0.985784i \(0.446263\pi\)
\(450\) 7.54959 5.48510i 0.355891 0.258570i
\(451\) −19.5196 21.6787i −0.919144 1.02081i
\(452\) −11.6647 5.19347i −0.548663 0.244280i
\(453\) −15.0194 + 6.68709i −0.705675 + 0.314187i
\(454\) 24.8996 27.6538i 1.16860 1.29786i
\(455\) −0.0270815 + 0.257664i −0.00126960 + 0.0120795i
\(456\) −17.5460 + 3.72952i −0.821667 + 0.174651i
\(457\) −10.8363 + 33.3507i −0.506900 + 1.56008i 0.290652 + 0.956829i \(0.406128\pi\)
−0.797552 + 0.603250i \(0.793872\pi\)
\(458\) −9.09277 1.93273i −0.424877 0.0903105i
\(459\) 2.35637 4.08136i 0.109986 0.190501i
\(460\) −6.57696 11.3916i −0.306652 0.531137i
\(461\) −8.28285 25.4920i −0.385771 1.18728i −0.935920 0.352213i \(-0.885429\pi\)
0.550149 0.835066i \(-0.314571\pi\)
\(462\) −2.94117 27.9833i −0.136835 1.30190i
\(463\) 20.5459 + 14.9274i 0.954847 + 0.693737i 0.951948 0.306259i \(-0.0990774\pi\)
0.00289847 + 0.999996i \(0.499077\pi\)
\(464\) −1.69774 −0.0788156
\(465\) 5.21095 + 0.0261936i 0.241652 + 0.00121470i
\(466\) −21.2846 −0.985988
\(467\) 20.9267 + 15.2041i 0.968371 + 0.703563i 0.955080 0.296349i \(-0.0957692\pi\)
0.0132911 + 0.999912i \(0.495769\pi\)
\(468\) −0.0271695 0.258501i −0.00125591 0.0119492i
\(469\) 2.85754 + 8.79460i 0.131949 + 0.406097i
\(470\) 10.3201 + 17.8749i 0.476030 + 0.824508i
\(471\) −6.91687 + 11.9804i −0.318712 + 0.552026i
\(472\) −26.7248 5.68054i −1.23011 0.261468i
\(473\) −4.90135 + 15.0848i −0.225364 + 0.693600i
\(474\) 18.9636 4.03084i 0.871027 0.185142i
\(475\) −3.05070 + 29.0255i −0.139976 + 1.33178i
\(476\) −32.6960 + 36.3126i −1.49862 + 1.66438i
\(477\) −5.65117 + 2.51607i −0.258750 + 0.115203i
\(478\) −52.0938 23.1936i −2.38271 1.06085i
\(479\) 3.57361 + 3.96890i 0.163282 + 0.181344i 0.819234 0.573460i \(-0.194399\pi\)
−0.655951 + 0.754803i \(0.727732\pi\)
\(480\) 4.70343 3.41724i 0.214681 0.155975i
\(481\) 0.623338 0.452882i 0.0284218 0.0206496i
\(482\) 17.1198 + 19.0135i 0.779787 + 0.866042i
\(483\) −13.6739 6.08802i −0.622185 0.277015i
\(484\) 8.56020 3.81124i 0.389100 0.173238i
\(485\) 1.98043 2.19949i 0.0899266 0.0998736i
\(486\) 0.236525 2.25039i 0.0107290 0.102080i
\(487\) 23.6888 5.03520i 1.07344 0.228167i 0.362904 0.931827i \(-0.381785\pi\)
0.710537 + 0.703660i \(0.248452\pi\)
\(488\) −6.89166 + 21.2104i −0.311971 + 0.960147i
\(489\) 8.49342 + 1.80533i 0.384086 + 0.0816400i
\(490\) 4.28040 7.41387i 0.193369 0.334924i
\(491\) 3.33341 + 5.77364i 0.150435 + 0.260561i 0.931387 0.364030i \(-0.118599\pi\)
−0.780953 + 0.624590i \(0.785266\pi\)
\(492\) 7.51641 + 23.1331i 0.338866 + 1.04292i
\(493\) −1.65668 15.7623i −0.0746132 0.709897i
\(494\) 1.07922 + 0.784098i 0.0485563 + 0.0352783i
\(495\) −3.50231 −0.157417
\(496\) −2.81071 0.0141284i −0.126205 0.000634386i
\(497\) 18.5869 0.833737
\(498\) −1.40074 1.01770i −0.0627687 0.0456041i
\(499\) 0.294814 + 2.80497i 0.0131977 + 0.125568i 0.999137 0.0415361i \(-0.0132251\pi\)
−0.985939 + 0.167104i \(0.946558\pi\)
\(500\) 8.23363 + 25.3405i 0.368219 + 1.13326i
\(501\) −0.978358 1.69457i −0.0437098 0.0757076i
\(502\) 26.1899 45.3622i 1.16891 2.02461i
\(503\) −7.00758 1.48951i −0.312453 0.0664138i 0.0490164 0.998798i \(-0.484391\pi\)
−0.361469 + 0.932384i \(0.617725\pi\)
\(504\) −2.60282 + 8.01065i −0.115939 + 0.356823i
\(505\) 2.15697 0.458479i 0.0959841 0.0204020i
\(506\) 3.98678 37.9317i 0.177234 1.68627i
\(507\) 8.69405 9.65573i 0.386117 0.428826i
\(508\) −19.6885 + 8.76589i −0.873537 + 0.388924i
\(509\) 18.7708 + 8.35732i 0.832003 + 0.370432i 0.778120 0.628116i \(-0.216174\pi\)
0.0538830 + 0.998547i \(0.482840\pi\)
\(510\) 6.67835 + 7.41706i 0.295722 + 0.328433i
\(511\) −24.9064 + 18.0955i −1.10179 + 0.800500i
\(512\) −4.60738 + 3.34746i −0.203620 + 0.147938i
\(513\) 4.73536 + 5.25915i 0.209071 + 0.232197i
\(514\) 12.9323 + 5.75782i 0.570419 + 0.253967i
\(515\) 4.82210 2.14694i 0.212487 0.0946054i
\(516\) 8.84936 9.82821i 0.389571 0.432663i
\(517\) −3.81220 + 36.2706i −0.167660 + 1.59518i
\(518\) −68.0262 + 14.4594i −2.98890 + 0.635310i
\(519\) 2.97923 9.16912i 0.130774 0.402480i
\(520\) 0.193306 + 0.0410884i 0.00847702 + 0.00180185i
\(521\) 13.2206 22.8988i 0.579205 1.00321i −0.416366 0.909197i \(-0.636696\pi\)
0.995571 0.0940155i \(-0.0299703\pi\)
\(522\) −3.80490 6.59028i −0.166536 0.288449i
\(523\) 4.74888 + 14.6156i 0.207654 + 0.639094i 0.999594 + 0.0284946i \(0.00907134\pi\)
−0.791940 + 0.610599i \(0.790929\pi\)
\(524\) −4.14552 39.4420i −0.181098 1.72303i
\(525\) 11.0869 + 8.05511i 0.483873 + 0.351554i
\(526\) 25.4185 1.10830
\(527\) −2.61156 26.1092i −0.113761 1.13733i
\(528\) 1.88909 0.0822122
\(529\) 2.19304 + 1.59334i 0.0953497 + 0.0692756i
\(530\) −1.36939 13.0289i −0.0594826 0.565939i
\(531\) 3.33090 + 10.2515i 0.144549 + 0.444875i
\(532\) −36.6878 63.5452i −1.59062 2.75503i
\(533\) 0.324702 0.562401i 0.0140644 0.0243603i
\(534\) 16.8359 + 3.57858i 0.728561 + 0.154861i
\(535\) 4.24888 13.0767i 0.183695 0.565356i
\(536\) 6.89947 1.46653i 0.298012 0.0633444i
\(537\) 2.44518 23.2644i 0.105517 1.00393i
\(538\) 24.5761 27.2945i 1.05955 1.17675i
\(539\) 13.8189 6.15255i 0.595221 0.265009i
\(540\) 2.66779 + 1.18778i 0.114804 + 0.0511138i
\(541\) −28.3459 31.4813i −1.21869 1.35349i −0.916396 0.400273i \(-0.868915\pi\)
−0.302291 0.953216i \(-0.597751\pi\)
\(542\) −44.5140 + 32.3413i −1.91204 + 1.38918i
\(543\) −6.91003 + 5.02043i −0.296538 + 0.215447i
\(544\) −19.5884 21.7552i −0.839847 0.932745i
\(545\) 13.2022 + 5.87798i 0.565518 + 0.251785i
\(546\) 0.572229 0.254773i 0.0244891 0.0109033i
\(547\) −22.2471 + 24.7079i −0.951217 + 1.05643i 0.0471263 + 0.998889i \(0.484994\pi\)
−0.998343 + 0.0575442i \(0.981673\pi\)
\(548\) −4.61032 + 43.8643i −0.196943 + 1.87379i
\(549\) 8.60626 1.82932i 0.367306 0.0780733i
\(550\) −10.7910 + 33.2112i −0.460129 + 1.41613i
\(551\) 23.2797 + 4.94825i 0.991748 + 0.210803i
\(552\) −5.70867 + 9.88770i −0.242977 + 0.420848i
\(553\) 14.2355 + 24.6566i 0.605356 + 1.04851i
\(554\) −6.80680 20.9492i −0.289193 0.890045i
\(555\) 0.904848 + 8.60905i 0.0384087 + 0.365434i
\(556\) −37.0717 26.9342i −1.57219 1.14226i
\(557\) 13.3501 0.565663 0.282832 0.959170i \(-0.408726\pi\)
0.282832 + 0.959170i \(0.408726\pi\)
\(558\) −6.24440 10.9423i −0.264346 0.463223i
\(559\) −0.353092 −0.0149342
\(560\) 1.27019 + 0.922850i 0.0536755 + 0.0389975i
\(561\) 1.84341 + 17.5388i 0.0778286 + 0.740490i
\(562\) −8.38665 25.8114i −0.353769 1.08879i
\(563\) 4.28256 + 7.41760i 0.180488 + 0.312615i 0.942047 0.335481i \(-0.108899\pi\)
−0.761559 + 0.648096i \(0.775566\pi\)
\(564\) 15.2047 26.3353i 0.640234 1.10892i
\(565\) −3.74637 0.796316i −0.157611 0.0335013i
\(566\) −1.61281 + 4.96372i −0.0677915 + 0.208641i
\(567\) 3.25038 0.690890i 0.136503 0.0290147i
\(568\) 1.48198 14.1001i 0.0621826 0.591628i
\(569\) −19.6451 + 21.8181i −0.823564 + 0.914661i −0.997541 0.0700890i \(-0.977672\pi\)
0.173976 + 0.984750i \(0.444338\pi\)
\(570\) −13.6917 + 6.09593i −0.573482 + 0.255330i
\(571\) 23.5122 + 10.4683i 0.983955 + 0.438085i 0.834695 0.550713i \(-0.185644\pi\)
0.149260 + 0.988798i \(0.452311\pi\)
\(572\) 0.650834 + 0.722825i 0.0272127 + 0.0302228i
\(573\) 2.46032 1.78753i 0.102782 0.0746751i
\(574\) −47.4219 + 34.4540i −1.97935 + 1.43808i
\(575\) 12.4299 + 13.8048i 0.518362 + 0.575699i
\(576\) −11.9183 5.30638i −0.496597 0.221099i
\(577\) 5.54911 2.47062i 0.231013 0.102853i −0.287966 0.957641i \(-0.592979\pi\)
0.518979 + 0.854787i \(0.326312\pi\)
\(578\) 7.88837 8.76092i 0.328113 0.364406i
\(579\) 0.596070 5.67123i 0.0247718 0.235688i
\(580\) 9.60632 2.04189i 0.398881 0.0847847i
\(581\) 0.785723 2.41821i 0.0325973 0.100324i
\(582\) −6.99928 1.48774i −0.290129 0.0616689i
\(583\) 11.5742 20.0471i 0.479354 0.830266i
\(584\) 11.7415 + 20.3369i 0.485868 + 0.841548i
\(585\) −0.0240930 0.0741507i −0.000996124 0.00306575i
\(586\) −6.22362 59.2138i −0.257095 2.44610i
\(587\) −16.7055 12.1373i −0.689512 0.500960i 0.186988 0.982362i \(-0.440128\pi\)
−0.876500 + 0.481403i \(0.840128\pi\)
\(588\) −12.6127 −0.520141
\(589\) 38.4997 + 8.38585i 1.58635 + 0.345533i
\(590\) −22.8278 −0.939805
\(591\) 2.79031 + 2.02728i 0.114778 + 0.0833912i
\(592\) −0.488061 4.64359i −0.0200592 0.190850i
\(593\) 12.0524 + 37.0933i 0.494931 + 1.52324i 0.817065 + 0.576546i \(0.195600\pi\)
−0.322134 + 0.946694i \(0.604400\pi\)
\(594\) 4.23375 + 7.33307i 0.173713 + 0.300880i
\(595\) −7.32851 + 12.6933i −0.300440 + 0.520377i
\(596\) 16.8726 + 3.58638i 0.691128 + 0.146904i
\(597\) −5.41447 + 16.6640i −0.221600 + 0.682014i
\(598\) 0.830514 0.176531i 0.0339623 0.00721890i
\(599\) 0.259657 2.47047i 0.0106093 0.100941i −0.987936 0.154864i \(-0.950506\pi\)
0.998545 + 0.0539234i \(0.0171727\pi\)
\(600\) 6.99464 7.76834i 0.285555 0.317141i
\(601\) 6.22338 2.77083i 0.253857 0.113024i −0.275863 0.961197i \(-0.588964\pi\)
0.529720 + 0.848173i \(0.322297\pi\)
\(602\) 29.1155 + 12.9630i 1.18666 + 0.528334i
\(603\) −1.86205 2.06801i −0.0758284 0.0842160i
\(604\) −41.5013 + 30.1524i −1.68866 + 1.22689i
\(605\) 2.27391 1.65209i 0.0924475 0.0671671i
\(606\) −3.56740 3.96200i −0.144916 0.160945i
\(607\) −10.6075 4.72274i −0.430543 0.191690i 0.180011 0.983665i \(-0.442387\pi\)
−0.610554 + 0.791974i \(0.709053\pi\)
\(608\) 40.1594 17.8801i 1.62868 0.725135i
\(609\) 7.47776 8.30490i 0.303014 0.336531i
\(610\) −1.94773 + 18.5314i −0.0788613 + 0.750315i
\(611\) −0.794145 + 0.168801i −0.0321277 + 0.00682895i
\(612\) 4.54398 13.9849i 0.183679 0.565307i
\(613\) 1.63940 + 0.348466i 0.0662149 + 0.0140744i 0.240900 0.970550i \(-0.422557\pi\)
−0.174685 + 0.984624i \(0.555891\pi\)
\(614\) −18.2699 + 31.6444i −0.737314 + 1.27706i
\(615\) 3.64804 + 6.31860i 0.147103 + 0.254790i
\(616\) −9.73994 29.9765i −0.392434 1.20779i
\(617\) −2.50907 23.8722i −0.101011 0.961058i −0.921233 0.389012i \(-0.872817\pi\)
0.820222 0.572046i \(-0.193850\pi\)
\(618\) −10.3244 7.50111i −0.415308 0.301739i
\(619\) −16.4099 −0.659569 −0.329784 0.944056i \(-0.606976\pi\)
−0.329784 + 0.944056i \(0.606976\pi\)
\(620\) 15.9208 3.30052i 0.639396 0.132552i
\(621\) 4.50436 0.180754
\(622\) −18.8350 13.6844i −0.755213 0.548695i
\(623\) 2.64213 + 25.1382i 0.105855 + 1.00714i
\(624\) 0.0129954 + 0.0399957i 0.000520233 + 0.00160111i
\(625\) −6.31396 10.9361i −0.252558 0.437444i
\(626\) −14.1415 + 24.4937i −0.565206 + 0.978966i
\(627\) −25.9035 5.50597i −1.03449 0.219887i
\(628\) −13.3383 + 41.0512i −0.532258 + 1.63812i
\(629\) 42.6361 9.06258i 1.70001 0.361349i
\(630\) −0.735613 + 6.99889i −0.0293075 + 0.278842i
\(631\) −6.72271 + 7.46633i −0.267627 + 0.297230i −0.861947 0.506999i \(-0.830755\pi\)
0.594320 + 0.804229i \(0.297421\pi\)
\(632\) 19.8397 8.83321i 0.789181 0.351366i
\(633\) −19.1254 8.51519i −0.760168 0.338449i
\(634\) 9.00216 + 9.99791i 0.357521 + 0.397068i
\(635\) −5.23001 + 3.79982i −0.207547 + 0.150791i
\(636\) −15.6152 + 11.3451i −0.619181 + 0.449861i
\(637\) 0.225324 + 0.250248i 0.00892766 + 0.00991517i
\(638\) 26.0145 + 11.5824i 1.02993 + 0.458552i
\(639\) −5.10984 + 2.27505i −0.202142 + 0.0899995i
\(640\) 10.7073 11.8916i 0.423242 0.470058i
\(641\) −1.02323 + 9.73540i −0.0404152 + 0.384525i 0.955553 + 0.294819i \(0.0952594\pi\)
−0.995968 + 0.0897060i \(0.971407\pi\)
\(642\) −32.5160 + 6.91150i −1.28331 + 0.272775i
\(643\) 2.86045 8.80356i 0.112805 0.347178i −0.878678 0.477415i \(-0.841574\pi\)
0.991483 + 0.130237i \(0.0415738\pi\)
\(644\) −45.6822 9.71006i −1.80013 0.382630i
\(645\) 1.98350 3.43553i 0.0781004 0.135274i
\(646\) 37.7336 + 65.3566i 1.48461 + 2.57142i
\(647\) −5.01831 15.4448i −0.197290 0.607197i −0.999942 0.0107491i \(-0.996578\pi\)
0.802652 0.596448i \(-0.203422\pi\)
\(648\) −0.264951 2.52084i −0.0104083 0.0990281i
\(649\) −32.6324 23.7088i −1.28093 0.930653i
\(650\) −0.777379 −0.0304913
\(651\) 12.4490 13.6870i 0.487914 0.536436i
\(652\) 27.0931 1.06105
\(653\) −18.4578 13.4104i −0.722310 0.524789i 0.164811 0.986325i \(-0.447299\pi\)
−0.887122 + 0.461536i \(0.847299\pi\)
\(654\) −3.65216 34.7480i −0.142811 1.35875i
\(655\) −3.67612 11.3139i −0.143638 0.442071i
\(656\) −1.96770 3.40816i −0.0768257 0.133066i
\(657\) 4.63226 8.02331i 0.180722 0.313019i
\(658\) 71.6812 + 15.2363i 2.79443 + 0.593973i
\(659\) 4.63413 14.2624i 0.180520 0.555584i −0.819322 0.573333i \(-0.805650\pi\)
0.999842 + 0.0177494i \(0.00565010\pi\)
\(660\) −10.6890 + 2.27203i −0.416070 + 0.0884385i
\(661\) −0.293892 + 2.79620i −0.0114311 + 0.108759i −0.998750 0.0499924i \(-0.984080\pi\)
0.987319 + 0.158752i \(0.0507470\pi\)
\(662\) −43.7086 + 48.5433i −1.69878 + 1.88669i
\(663\) −0.358650 + 0.159681i −0.0139288 + 0.00620151i
\(664\) −1.77182 0.788864i −0.0687599 0.0306139i
\(665\) −14.7274 16.3564i −0.571102 0.634274i
\(666\) 16.9317 12.3016i 0.656089 0.476676i
\(667\) 12.2552 8.90395i 0.474524 0.344762i
\(668\) −4.08525 4.53713i −0.158063 0.175547i
\(669\) 1.11608 + 0.496910i 0.0431501 + 0.0192117i
\(670\) 5.38387 2.39705i 0.207997 0.0926062i
\(671\) −22.0310 + 24.4679i −0.850495 + 0.944571i
\(672\) 2.15764 20.5286i 0.0832329 0.791908i
\(673\) −40.1065 + 8.52489i −1.54599 + 0.328610i −0.900397 0.435070i \(-0.856724\pi\)
−0.645594 + 0.763681i \(0.723390\pi\)
\(674\) 3.21221 9.88616i 0.123730 0.380801i
\(675\) −4.03392 0.857436i −0.155266 0.0330027i
\(676\) 20.2704 35.1093i 0.779629 1.35036i
\(677\) 14.1711 + 24.5451i 0.544639 + 0.943343i 0.998630 + 0.0523363i \(0.0166668\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(678\) 2.86147 + 8.80671i 0.109894 + 0.338220i
\(679\) −1.09843 10.4508i −0.0421537 0.401066i
\(680\) 9.04492 + 6.57152i 0.346857 + 0.252006i
\(681\) −16.4452 −0.630181
\(682\) 42.9722 + 19.3919i 1.64549 + 0.742553i
\(683\) −3.06057 −0.117109 −0.0585547 0.998284i \(-0.518649\pi\)
−0.0585547 + 0.998284i \(0.518649\pi\)
\(684\) 17.8640 + 12.9790i 0.683049 + 0.496264i
\(685\) 1.38291 + 13.1575i 0.0528381 + 0.502721i
\(686\) 6.87239 + 21.1510i 0.262389 + 0.807550i
\(687\) 2.05409 + 3.55779i 0.0783684 + 0.135738i
\(688\) −1.06987 + 1.85307i −0.0407885 + 0.0706477i
\(689\) 0.504057 + 0.107141i 0.0192031 + 0.00408174i
\(690\) −2.94781 + 9.07244i −0.112221 + 0.345382i
\(691\) 19.0254 4.04397i 0.723760 0.153840i 0.168721 0.985664i \(-0.446036\pi\)
0.555040 + 0.831824i \(0.312703\pi\)
\(692\) 3.14439 29.9169i 0.119532 1.13727i
\(693\) −8.32058 + 9.24094i −0.316073 + 0.351034i
\(694\) −8.37704 + 3.72970i −0.317988 + 0.141577i
\(695\) −12.5568 5.59063i −0.476305 0.212065i
\(696\) −5.70392 6.33484i −0.216206 0.240122i
\(697\) 29.7221 21.5944i 1.12581 0.817945i
\(698\) 4.98374 3.62090i 0.188637 0.137053i
\(699\) 6.29409 + 6.99030i 0.238064 + 0.264397i
\(700\) 39.0628 + 17.3919i 1.47643 + 0.657351i
\(701\) −7.30470 + 3.25226i −0.275895 + 0.122836i −0.540020 0.841652i \(-0.681583\pi\)
0.264125 + 0.964488i \(0.414917\pi\)
\(702\) −0.126131 + 0.140082i −0.00476049 + 0.00528706i
\(703\) −6.84189 + 65.0962i −0.258047 + 2.45515i
\(704\) 47.7531 10.1502i 1.79976 0.382552i
\(705\) 2.81872 8.67514i 0.106159 0.326725i
\(706\) 22.1544 + 4.70907i 0.833793 + 0.177228i
\(707\) 3.91470 6.78046i 0.147227 0.255005i
\(708\) 16.8163 + 29.1266i 0.631993 + 1.09464i
\(709\) 6.92397 + 21.3098i 0.260035 + 0.800306i 0.992796 + 0.119819i \(0.0382316\pi\)
−0.732760 + 0.680487i \(0.761768\pi\)
\(710\) −1.23822 11.7808i −0.0464694 0.442127i
\(711\) −6.93156 5.03607i −0.259954 0.188868i
\(712\) 19.2806 0.722572
\(713\) 20.3633 14.6390i 0.762613 0.548235i
\(714\) 35.4361 1.32616
\(715\) 0.236036 + 0.171490i 0.00882726 + 0.00641338i
\(716\) −7.62942 72.5891i −0.285125 2.71278i
\(717\) 7.78745 + 23.9673i 0.290828 + 0.895076i
\(718\) −13.1913 22.8479i −0.492293 0.852677i
\(719\) 21.3907 37.0498i 0.797738 1.38172i −0.123348 0.992364i \(-0.539363\pi\)
0.921086 0.389360i \(-0.127304\pi\)
\(720\) −0.462154 0.0982339i −0.0172235 0.00366096i
\(721\) 5.79131 17.8238i 0.215680 0.663793i
\(722\) −68.7955 + 14.6229i −2.56030 + 0.544210i
\(723\) 1.18190 11.2450i 0.0439553 0.418207i
\(724\) −17.8326 + 19.8051i −0.662742 + 0.736049i
\(725\) −12.6702 + 5.64114i −0.470560 + 0.209507i
\(726\) −6.20792 2.76395i −0.230398 0.102580i
\(727\) 3.84430 + 4.26953i 0.142577 + 0.158348i 0.810204 0.586148i \(-0.199356\pi\)
−0.667627 + 0.744496i \(0.732690\pi\)
\(728\) 0.567657 0.412427i 0.0210388 0.0152856i
\(729\) −0.809017 + 0.587785i −0.0299636 + 0.0217698i
\(730\) 13.1286 + 14.5808i 0.485911 + 0.539659i
\(731\) −18.2484 8.12471i −0.674942 0.300503i
\(732\) 25.0796 11.1661i 0.926968 0.412713i
\(733\) 15.4416 17.1496i 0.570348 0.633435i −0.387101 0.922037i \(-0.626524\pi\)
0.957449 + 0.288602i \(0.0931903\pi\)
\(734\) 3.70442 35.2452i 0.136732 1.30092i
\(735\) −3.70063 + 0.786594i −0.136500 + 0.0290139i
\(736\) 8.64631 26.6106i 0.318707 0.980879i
\(737\) 10.1858 + 2.16507i 0.375200 + 0.0797512i
\(738\) 8.81985 15.2764i 0.324663 0.562333i
\(739\) −23.5981 40.8732i −0.868072 1.50354i −0.863965 0.503552i \(-0.832026\pi\)
−0.00410684 0.999992i \(-0.501307\pi\)
\(740\) 8.34648 + 25.6878i 0.306823 + 0.944304i
\(741\) −0.0616231 0.586305i −0.00226378 0.0215384i
\(742\) −37.6304 27.3401i −1.38146 1.00369i
\(743\) −28.5192 −1.04627 −0.523134 0.852250i \(-0.675237\pi\)
−0.523134 + 0.852250i \(0.675237\pi\)
\(744\) −9.39045 10.5352i −0.344271 0.386238i
\(745\) 5.17415 0.189566
\(746\) 54.3323 + 39.4748i 1.98925 + 1.44527i
\(747\) 0.0799819 + 0.760977i 0.00292639 + 0.0278427i
\(748\) 17.0039 + 52.3326i 0.621724 + 1.91347i
\(749\) −24.4090 42.2777i −0.891886 1.54479i
\(750\) 9.66144 16.7341i 0.352786 0.611043i
\(751\) −30.9879 6.58667i −1.13076 0.240351i −0.395720 0.918371i \(-0.629505\pi\)
−0.735043 + 0.678020i \(0.762838\pi\)
\(752\) −1.52038 + 4.67924i −0.0554424 + 0.170634i
\(753\) −22.6425 + 4.81282i −0.825140 + 0.175389i
\(754\) −0.0662636 + 0.630456i −0.00241318 + 0.0229599i
\(755\) −10.2962 + 11.4351i −0.374717 + 0.416165i
\(756\) 9.47197 4.21719i 0.344492 0.153378i
\(757\) 28.9003 + 12.8672i 1.05040 + 0.467668i 0.858000 0.513649i \(-0.171707\pi\)
0.192399 + 0.981317i \(0.438373\pi\)
\(758\) −18.7870 20.8651i −0.682375 0.757854i
\(759\) −13.6365 + 9.90750i −0.494974 + 0.359620i
\(760\) −13.5823 + 9.86812i −0.492682 + 0.357954i
\(761\) −28.0087 31.1068i −1.01532 1.12762i −0.991787 0.127898i \(-0.959177\pi\)
−0.0235278 0.999723i \(-0.507490\pi\)
\(762\) 14.2783 + 6.35710i 0.517247 + 0.230293i
\(763\) 46.8741 20.8697i 1.69696 0.755534i
\(764\) 6.34930 7.05161i 0.229709 0.255118i
\(765\) 0.461052 4.38662i 0.0166694 0.158599i
\(766\) −1.00188 + 0.212956i −0.0361994 + 0.00769442i
\(767\) 0.277478 0.853989i 0.0100191 0.0308358i
\(768\) −12.3196 2.61862i −0.444547 0.0944913i
\(769\) −3.55549 + 6.15828i −0.128214 + 0.222073i −0.922985 0.384837i \(-0.874258\pi\)
0.794771 + 0.606910i \(0.207591\pi\)
\(770\) −13.1673 22.8065i −0.474517 0.821887i
\(771\) −1.93324 5.94989i −0.0696238 0.214280i
\(772\) −1.85985 17.6953i −0.0669374 0.636867i
\(773\) 12.5396 + 9.11057i 0.451019 + 0.327684i 0.789998 0.613109i \(-0.210082\pi\)
−0.338979 + 0.940794i \(0.610082\pi\)
\(774\) −9.59100 −0.344741
\(775\) −21.0232 + 9.23380i −0.755177 + 0.331688i
\(776\) −8.01563 −0.287744
\(777\) 24.8649 + 18.0654i 0.892024 + 0.648093i
\(778\) −1.77295 16.8685i −0.0635632 0.604764i
\(779\) 17.0480 + 52.4683i 0.610807 + 1.87987i
\(780\) −0.121635 0.210678i −0.00435524 0.00754349i
\(781\) 10.4655 18.1268i 0.374485 0.648627i
\(782\) 46.9844 + 9.98685i 1.68016 + 0.357129i
\(783\) −1.03923 + 3.19843i −0.0371392 + 0.114303i
\(784\) 1.99606 0.424277i 0.0712880 0.0151527i
\(785\) −1.35337 + 12.8764i −0.0483038 + 0.459580i
\(786\) −19.2450 + 21.3738i −0.686447 + 0.762377i
\(787\) −22.6560 + 10.0871i −0.807598 + 0.359566i −0.768645 0.639675i \(-0.779069\pi\)
−0.0389527 + 0.999241i \(0.512402\pi\)
\(788\) 9.83118 + 4.37712i 0.350221 + 0.155929i
\(789\) −7.51654 8.34796i −0.267596 0.297195i
\(790\) 14.6797 10.6654i 0.522279 0.379458i
\(791\) −11.0015 + 7.99306i −0.391169 + 0.284201i
\(792\) 6.34680 + 7.04884i 0.225524 + 0.250470i
\(793\) −0.669587 0.298119i −0.0237777 0.0105865i
\(794\) 24.1674 10.7600i 0.857667 0.381858i
\(795\) −3.87402 + 4.30253i −0.137397 + 0.152595i
\(796\) −5.71464 + 54.3711i −0.202550 + 1.92713i
\(797\) −40.3427 + 8.57511i −1.42901 + 0.303746i −0.856499 0.516149i \(-0.827365\pi\)
−0.572514 + 0.819895i \(0.694032\pi\)
\(798\) −16.4436 + 50.6082i −0.582098 + 1.79151i
\(799\) −44.9269 9.54951i −1.58940 0.337837i
\(800\) −12.8088 + 22.1855i −0.452859 + 0.784375i
\(801\) −3.80329 6.58750i −0.134383 0.232758i
\(802\) −0.352910 1.08615i −0.0124617 0.0383531i
\(803\) 3.62385 + 34.4786i 0.127883 + 1.21672i
\(804\) −7.02453 5.10362i −0.247736 0.179991i
\(805\) −14.0089 −0.493750
\(806\) −0.114950 + 1.04321i −0.00404894 + 0.0367454i
\(807\) −16.2315 −0.571377
\(808\) −4.83157 3.51034i −0.169974 0.123493i
\(809\) −4.24310 40.3704i −0.149179 1.41935i −0.771323 0.636444i \(-0.780404\pi\)
0.622143 0.782904i \(-0.286262\pi\)
\(810\) −0.654436 2.01415i −0.0229945 0.0707699i
\(811\) 0.585304 + 1.01378i 0.0205528 + 0.0355985i 0.876119 0.482095i \(-0.160124\pi\)
−0.855566 + 0.517694i \(0.826791\pi\)
\(812\) 17.4346 30.1975i 0.611833 1.05973i
\(813\) 23.7849 + 5.05563i 0.834171 + 0.177309i
\(814\) −24.2012 + 74.4836i −0.848251 + 2.61065i
\(815\) 7.94922 1.68966i 0.278449 0.0591862i
\(816\) −0.248685 + 2.36608i −0.00870570 + 0.0828292i
\(817\) 20.0712 22.2914i 0.702203 0.779876i
\(818\) −25.0897 + 11.1706i −0.877240 + 0.390572i
\(819\) −0.252887 0.112593i −0.00883660 0.00393431i
\(820\) 15.2328 + 16.9178i 0.531954 + 0.590795i
\(821\) 26.2711 19.0871i 0.916868 0.666143i −0.0258746 0.999665i \(-0.508237\pi\)
0.942742 + 0.333522i \(0.108237\pi\)
\(822\) 25.8772 18.8009i 0.902570 0.655756i
\(823\) −20.4604 22.7236i −0.713204 0.792094i 0.272215 0.962236i \(-0.412244\pi\)
−0.985419 + 0.170143i \(0.945577\pi\)
\(824\) −13.0595 5.81446i −0.454949 0.202556i
\(825\) 14.0983 6.27695i 0.490839 0.218535i
\(826\) −54.2329 + 60.2317i −1.88700 + 2.09573i
\(827\) 1.01864 9.69167i 0.0354214 0.337012i −0.962432 0.271523i \(-0.912473\pi\)
0.997853 0.0654891i \(-0.0208607\pi\)
\(828\) 13.7473 2.92208i 0.477752 0.101549i
\(829\) 6.79674 20.9182i 0.236061 0.726520i −0.760918 0.648848i \(-0.775251\pi\)
0.996979 0.0776721i \(-0.0247487\pi\)
\(830\) −1.58506 0.336915i −0.0550183 0.0116945i
\(831\) −4.86730 + 8.43040i −0.168845 + 0.292447i
\(832\) 0.543403 + 0.941201i 0.0188391 + 0.0326303i
\(833\) 5.88689 + 18.1180i 0.203969 + 0.627751i
\(834\) 3.47362 + 33.0493i 0.120282 + 1.14440i
\(835\) −1.48159 1.07644i −0.0512724 0.0372516i
\(836\) −82.6294 −2.85780
\(837\) −1.74713 + 5.28654i −0.0603896 + 0.182730i
\(838\) −67.1141 −2.31842
\(839\) −24.0426 17.4680i −0.830043 0.603061i 0.0895287 0.995984i \(-0.471464\pi\)
−0.919571 + 0.392923i \(0.871464\pi\)
\(840\) 0.824021 + 7.84003i 0.0284314 + 0.270507i
\(841\) −5.46652 16.8242i −0.188501 0.580145i
\(842\) 30.6222 + 53.0392i 1.05531 + 1.82785i
\(843\) −5.99699 + 10.3871i −0.206547 + 0.357750i
\(844\) −63.8948 13.5813i −2.19935 0.467486i
\(845\) 3.75782 11.5654i 0.129273 0.397861i
\(846\) −21.5713 + 4.58511i −0.741635 + 0.157639i
\(847\) 1.04313 9.92471i 0.0358423 0.341017i
\(848\) 2.08958 2.32072i 0.0717566 0.0796938i
\(849\) 2.10712 0.938148i 0.0723160 0.0321972i
\(850\) −40.1763 17.8876i −1.37803 0.613541i
\(851\) 27.8768 + 30.9603i 0.955605 + 1.06131i
\(852\) −14.1194 + 10.2583i −0.483721 + 0.351444i
\(853\) 3.38030 2.45593i 0.115739 0.0840895i −0.528410 0.848989i \(-0.677212\pi\)
0.644149 + 0.764900i \(0.277212\pi\)
\(854\) 44.2684 + 49.1650i 1.51483 + 1.68239i
\(855\) 6.05082 + 2.69400i 0.206934 + 0.0921328i
\(856\) −34.0183 + 15.1459i −1.16272 + 0.517677i
\(857\) −15.2169 + 16.9000i −0.519798 + 0.577294i −0.944696 0.327947i \(-0.893643\pi\)
0.424898 + 0.905241i \(0.360310\pi\)
\(858\) 0.0737321 0.701514i 0.00251717 0.0239493i
\(859\) −33.6767 + 7.15820i −1.14903 + 0.244235i −0.742786 0.669528i \(-0.766496\pi\)
−0.406247 + 0.913763i \(0.633163\pi\)
\(860\) 3.82495 11.7720i 0.130430 0.401421i
\(861\) 25.3386 + 5.38589i 0.863537 + 0.183550i
\(862\) 31.1215 53.9040i 1.06000 1.83598i
\(863\) 9.13483 + 15.8220i 0.310953 + 0.538587i 0.978569 0.205919i \(-0.0660184\pi\)
−0.667616 + 0.744506i \(0.732685\pi\)
\(864\) 1.91954 + 5.90774i 0.0653041 + 0.200985i
\(865\) −0.943187 8.97383i −0.0320693 0.305119i
\(866\) −45.3980 32.9836i −1.54269 1.12083i
\(867\) −5.20995 −0.176939
\(868\) 29.1152 49.8487i 0.988235 1.69197i
\(869\) 32.0617 1.08762
\(870\) −5.76200 4.18634i −0.195350 0.141930i
\(871\) 0.0242316 + 0.230548i 0.000821055 + 0.00781182i
\(872\) −12.0945 37.2229i −0.409570 1.26053i
\(873\) 1.58116 + 2.73865i 0.0535142 + 0.0926893i
\(874\) −36.0652 + 62.4667i −1.21992 + 2.11297i
\(875\) 27.7564 + 5.89981i 0.938338 + 0.199450i
\(876\) 8.93275 27.4922i 0.301810 0.928875i
\(877\) 26.7079 5.67693i 0.901860 0.191696i 0.266430 0.963854i \(-0.414156\pi\)
0.635430 + 0.772158i \(0.280823\pi\)
\(878\) 6.94662 66.0927i 0.234437 2.23052i
\(879\) −17.6066 + 19.5542i −0.593857 + 0.659545i
\(880\) 1.61520 0.719131i 0.0544482 0.0242419i
\(881\) −17.5558 7.81633i −0.591469 0.263339i 0.0891004 0.996023i \(-0.471601\pi\)
−0.680569 + 0.732684i \(0.738267\pi\)
\(882\) 6.12045 + 6.79745i 0.206086 + 0.228882i
\(883\) 20.1825 14.6635i 0.679196 0.493465i −0.193895 0.981022i \(-0.562112\pi\)
0.873091 + 0.487558i \(0.162112\pi\)
\(884\) −0.991011 + 0.720012i −0.0333313 + 0.0242166i
\(885\) 6.75044 + 7.49712i 0.226913 + 0.252013i
\(886\) 58.3186 + 25.9651i 1.95925 + 0.872315i
\(887\) −29.9451 + 13.3324i −1.00546 + 0.447659i −0.842339 0.538948i \(-0.818822\pi\)
−0.163119 + 0.986606i \(0.552155\pi\)
\(888\) 15.6871 17.4223i 0.526424 0.584653i
\(889\) −2.39920 + 22.8269i −0.0804667 + 0.765590i
\(890\) 15.7572 3.34929i 0.528182 0.112269i
\(891\) 1.15636 3.55892i 0.0387397 0.119228i
\(892\) 3.72863 + 0.792544i 0.124844 + 0.0265363i
\(893\) 34.4858 59.7312i 1.15402 1.99883i
\(894\) −6.25475 10.8335i −0.209190 0.362328i
\(895\) −6.76552 20.8221i −0.226146 0.696007i
\(896\) −5.93869 56.5028i −0.198398 1.88763i
\(897\) −0.303569 0.220556i −0.0101359 0.00736415i
\(898\) 42.5293 1.41922
\(899\) 5.69662 + 17.8370i 0.189993 + 0.594896i
\(900\) −12.8678 −0.428925
\(901\) 23.5852 + 17.1357i 0.785738 + 0.570872i
\(902\) 6.89982 + 65.6474i 0.229739 + 2.18582i
\(903\) −4.35245 13.3954i −0.144840 0.445773i
\(904\) 5.18640 + 8.98311i 0.172497 + 0.298774i
\(905\) −3.99700 + 6.92301i −0.132865 + 0.230129i
\(906\) 36.3891 + 7.73474i 1.20895 + 0.256969i
\(907\) −8.23416 + 25.3421i −0.273411 + 0.841472i 0.716225 + 0.697870i \(0.245869\pi\)
−0.989636 + 0.143602i \(0.954131\pi\)
\(908\) −50.1907 + 10.6684i −1.66564 + 0.354042i
\(909\) −0.246282 + 2.34322i −0.00816867 + 0.0777197i
\(910\) 0.392277 0.435667i 0.0130038 0.0144422i
\(911\) 47.9936 21.3681i 1.59010 0.707958i 0.594717 0.803935i \(-0.297264\pi\)
0.995384 + 0.0959773i \(0.0305976\pi\)
\(912\) −3.26372 1.45310i −0.108073 0.0481170i
\(913\) −1.91593 2.12786i −0.0634082 0.0704219i
\(914\) 64.1946 46.6401i 2.12337 1.54272i
\(915\) 6.66207 4.84028i 0.220241 0.160015i
\(916\) 8.57710 + 9.52583i 0.283395 + 0.314742i
\(917\) −38.5856 17.1794i −1.27421 0.567314i
\(918\) −9.74197 + 4.33740i −0.321533 + 0.143156i
\(919\) 38.6851 42.9642i 1.27610 1.41726i 0.414200 0.910186i \(-0.364061\pi\)
0.861904 0.507071i \(-0.169272\pi\)
\(920\) −1.11697 + 10.6273i −0.0368254 + 0.350370i
\(921\) 15.7953 3.35740i 0.520473 0.110630i
\(922\) −18.7423 + 57.6828i −0.617244 + 1.89968i
\(923\) 0.455773 + 0.0968775i 0.0150019 + 0.00318876i
\(924\) −19.3996 + 33.6011i −0.638200 + 1.10539i
\(925\) −19.0718 33.0334i −0.627078 1.08613i
\(926\) −17.7579 54.6532i −0.583561 1.79602i
\(927\) 0.589520 + 5.60891i 0.0193624 + 0.184221i
\(928\) 16.9007 + 12.2790i 0.554791 + 0.403079i
\(929\) −51.9672 −1.70499 −0.852494 0.522737i \(-0.824911\pi\)
−0.852494 + 0.522737i \(0.824911\pi\)
\(930\) −9.50449 6.97868i −0.311664 0.228840i
\(931\) −28.6070 −0.937555
\(932\) 23.7443 + 17.2513i 0.777771 + 0.565084i
\(933\) 1.07547 + 10.2324i 0.0352094 + 0.334995i
\(934\) −18.0870 55.6662i −0.591826 1.82145i
\(935\) 8.25274 + 14.2942i 0.269893 + 0.467469i
\(936\) −0.105577 + 0.182864i −0.00345089 + 0.00597711i
\(937\) 43.2031 + 9.18310i 1.41138 + 0.299999i 0.849662 0.527328i \(-0.176806\pi\)
0.561721 + 0.827327i \(0.310139\pi\)
\(938\) 6.46599 19.9003i 0.211122 0.649767i
\(939\) 12.2260 2.59873i 0.398982 0.0848062i
\(940\) 2.97499 28.3051i 0.0970333 0.923210i
\(941\) 4.89259 5.43377i 0.159494 0.177136i −0.658101 0.752929i \(-0.728640\pi\)
0.817595 + 0.575794i \(0.195307\pi\)
\(942\) 28.5965 12.7320i 0.931723 0.414830i
\(943\) 32.0783 + 14.2822i 1.04461 + 0.465092i
\(944\) −3.64108 4.04383i −0.118507 0.131616i
\(945\) 2.51611 1.82806i 0.0818490 0.0594668i
\(946\) 29.0358 21.0957i 0.944035 0.685882i
\(947\) −4.81518 5.34780i −0.156472 0.173780i 0.659812 0.751431i \(-0.270636\pi\)
−0.816284 + 0.577651i \(0.803969\pi\)
\(948\) −24.4221 10.8734i −0.793194 0.353153i
\(949\) −0.705050 + 0.313909i −0.0228869 + 0.0101899i
\(950\) 44.1895 49.0774i 1.43370 1.59228i
\(951\) 0.621481 5.91299i 0.0201529 0.191742i
\(952\) 38.8275 8.25305i 1.25841 0.267483i
\(953\) −16.0592 + 49.4251i −0.520208 + 1.60104i 0.253393 + 0.967364i \(0.418454\pi\)
−0.773601 + 0.633673i \(0.781546\pi\)
\(954\) 13.6916 + 2.91025i 0.443283 + 0.0942228i
\(955\) 1.42314 2.46494i 0.0460516 0.0797637i
\(956\) 39.3154 + 68.0963i 1.27155 + 2.20239i
\(957\) −3.88889 11.9688i −0.125710 0.386895i
\(958\) −1.26320 12.0186i −0.0408123 0.388303i
\(959\) 38.0018 + 27.6099i 1.22714 + 0.891571i
\(960\) −12.2103 −0.394086
\(961\) 9.28265 + 29.5776i 0.299440 + 0.954115i
\(962\) −1.74345 −0.0562110
\(963\) 11.8852 + 8.63513i 0.382997 + 0.278263i
\(964\) −3.68774 35.0865i −0.118774 1.13006i
\(965\) −1.64925 5.07587i −0.0530913 0.163398i
\(966\) 16.9346 + 29.3316i 0.544863 + 0.943730i
\(967\) −4.51214 + 7.81526i −0.145101 + 0.251322i −0.929411 0.369048i \(-0.879684\pi\)
0.784310 + 0.620369i \(0.213017\pi\)
\(968\) −7.44577 1.58265i −0.239316 0.0508682i
\(969\) 10.3062 31.7192i 0.331083 1.01897i
\(970\) −6.55081 + 1.39242i −0.210334 + 0.0447079i
\(971\) −5.43756 + 51.7349i −0.174500 + 1.66025i 0.460440 + 0.887691i \(0.347692\pi\)
−0.634940 + 0.772562i \(0.718975\pi\)
\(972\) −2.08781 + 2.31875i −0.0669665 + 0.0743739i
\(973\) −44.5826 + 19.8495i −1.42925 + 0.636344i
\(974\) −50.0623 22.2892i −1.60410 0.714191i
\(975\) 0.229880 + 0.255307i 0.00736205 + 0.00817638i
\(976\) −3.59342 + 2.61077i −0.115023 + 0.0835688i
\(977\) −36.6807 + 26.6501i −1.17352 + 0.852612i −0.991426 0.130669i \(-0.958288\pi\)
−0.182094 + 0.983281i \(0.558288\pi\)
\(978\) −13.1472 14.6014i −0.420400 0.466901i
\(979\) 26.0035 + 11.5775i 0.831076 + 0.370019i
\(980\) −10.7840 + 4.80137i −0.344484 + 0.153374i
\(981\) −10.3320 + 11.4748i −0.329875 + 0.366363i
\(982\) 1.57687 15.0029i 0.0503200 0.478763i
\(983\) 28.2499 6.00471i 0.901033 0.191520i 0.265970 0.963981i \(-0.414308\pi\)
0.635062 + 0.772461i \(0.280974\pi\)
\(984\) 6.10608 18.7926i 0.194655 0.599085i
\(985\) 3.15749 + 0.671145i 0.100606 + 0.0213844i
\(986\) −17.9315 + 31.0583i −0.571056 + 0.989098i
\(987\) −16.1930 28.0472i −0.515430 0.892751i
\(988\) −0.568423 1.74943i −0.0180839 0.0556566i
\(989\) −1.99567 18.9875i −0.0634586 0.603768i
\(990\) 6.41143 + 4.65817i 0.203769 + 0.148047i
\(991\) 36.2495 1.15150 0.575752 0.817624i \(-0.304709\pi\)
0.575752 + 0.817624i \(0.304709\pi\)
\(992\) 27.8778 + 20.4693i 0.885123 + 0.649902i
\(993\) 28.8678 0.916091
\(994\) −34.0257 24.7211i −1.07923 0.784107i
\(995\) 1.71416 + 16.3091i 0.0543424 + 0.517033i
\(996\) 0.737768 + 2.27062i 0.0233771 + 0.0719472i
\(997\) 20.9756 + 36.3309i 0.664305 + 1.15061i 0.979473 + 0.201574i \(0.0646058\pi\)
−0.315168 + 0.949036i \(0.602061\pi\)
\(998\) 3.19100 5.52698i 0.101009 0.174953i
\(999\) −9.04698 1.92299i −0.286234 0.0608409i
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 93.2.m.a.10.1 16
3.2 odd 2 279.2.y.b.10.2 16
31.11 odd 30 2883.2.a.n.1.8 8
31.20 even 15 2883.2.a.m.1.8 8
31.28 even 15 inner 93.2.m.a.28.1 yes 16
93.11 even 30 8649.2.a.bi.1.1 8
93.20 odd 30 8649.2.a.bj.1.1 8
93.59 odd 30 279.2.y.b.28.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
93.2.m.a.10.1 16 1.1 even 1 trivial
93.2.m.a.28.1 yes 16 31.28 even 15 inner
279.2.y.b.10.2 16 3.2 odd 2
279.2.y.b.28.2 16 93.59 odd 30
2883.2.a.m.1.8 8 31.20 even 15
2883.2.a.n.1.8 8 31.11 odd 30
8649.2.a.bi.1.1 8 93.11 even 30
8649.2.a.bj.1.1 8 93.20 odd 30