Properties

Label 966.2.q.e.673.2
Level $966$
Weight $2$
Character 966.673
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 673.2
Root \(0.130037 + 0.904424i\) of defining polynomial
Character \(\chi\) \(=\) 966.673
Dual form 966.2.q.e.211.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(2.06640 - 1.32799i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\) \(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(2.06640 - 1.32799i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(0.349573 + 2.43133i) q^{10} +(0.555075 + 1.21544i) q^{11} +(0.415415 + 0.909632i) q^{12} +(0.0102349 + 0.0711851i) q^{13} +(-0.841254 - 0.540641i) q^{14} +(-2.35683 + 0.692029i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-1.88951 + 2.18061i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(1.17198 + 1.35254i) q^{19} +(-2.35683 - 0.692029i) q^{20} +(0.415415 - 0.909632i) q^{21} -1.33619 q^{22} +(4.51632 - 1.61332i) q^{23} -1.00000 q^{24} +(0.429362 - 0.940171i) q^{25} +(-0.0690040 - 0.0202614i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(0.841254 - 0.540641i) q^{28} +(1.94443 - 2.24399i) q^{29} +(0.349573 - 2.43133i) q^{30} +(8.06752 - 2.36884i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-0.190160 - 1.32259i) q^{33} +(-1.19862 - 2.62461i) q^{34} +(1.02040 + 2.23436i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-7.27320 - 4.67420i) q^{37} +(-1.71717 + 0.504207i) q^{38} +(0.0102349 - 0.0711851i) q^{39} +(1.60856 - 1.85637i) q^{40} +(-4.03089 + 2.59049i) q^{41} +(0.654861 + 0.755750i) q^{42} +(9.61032 + 2.82185i) q^{43} +(0.555075 - 1.21544i) q^{44} +2.45633 q^{45} +(-0.408619 + 4.77839i) q^{46} +12.0588 q^{47} +(0.415415 - 0.909632i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(0.676847 + 0.781123i) q^{50} +(2.42732 - 1.55994i) q^{51} +(0.0470957 - 0.0543513i) q^{52} +(0.145353 - 1.01095i) q^{53} +(0.959493 - 0.281733i) q^{54} +(2.76111 + 1.77446i) q^{55} +(0.142315 + 0.989821i) q^{56} +(-0.743455 - 1.62794i) q^{57} +(1.23346 + 2.70090i) q^{58} +(1.84792 + 12.8526i) q^{59} +(2.06640 + 1.32799i) q^{60} +(13.3971 - 3.93375i) q^{61} +(-1.19660 + 8.32253i) q^{62} +(-0.654861 + 0.755750i) q^{63} +(0.841254 - 0.540641i) q^{64} +(0.115683 + 0.133505i) q^{65} +(1.28207 + 0.376449i) q^{66} +(0.848269 - 1.85745i) q^{67} +2.88536 q^{68} +(-4.78791 + 0.275576i) q^{69} -2.45633 q^{70} +(-4.29109 + 9.39618i) q^{71} +(0.959493 + 0.281733i) q^{72} +(-6.76030 - 7.80180i) q^{73} +(7.27320 - 4.67420i) q^{74} +(-0.676847 + 0.781123i) q^{75} +(0.254696 - 1.77145i) q^{76} +(-1.28207 + 0.376449i) q^{77} +(0.0605005 + 0.0388813i) q^{78} +(-0.747893 - 5.20171i) q^{79} +(1.02040 + 2.23436i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.681905 - 4.74275i) q^{82} +(7.67818 + 4.93446i) q^{83} +(-0.959493 + 0.281733i) q^{84} +(-1.00864 + 7.01526i) q^{85} +(-6.55911 + 7.56962i) q^{86} +(-2.49787 + 1.60528i) q^{87} +(0.875021 + 1.00983i) q^{88} +(7.76701 + 2.28060i) q^{89} +(-1.02040 + 2.23436i) q^{90} -0.0719171 q^{91} +(-4.17683 - 2.35671i) q^{92} -8.40811 q^{93} +(-5.00941 + 10.9691i) q^{94} +(4.21795 + 1.23850i) q^{95} +(0.654861 + 0.755750i) q^{96} +(-9.89607 + 6.35982i) q^{97} +(0.654861 - 0.755750i) q^{98} +(-0.190160 + 1.32259i) 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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{9}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.415415 + 0.909632i −0.293743 + 0.643207i
\(3\) −0.959493 0.281733i −0.553964 0.162658i
\(4\) −0.654861 0.755750i −0.327430 0.377875i
\(5\) 2.06640 1.32799i 0.924122 0.593897i 0.0102710 0.999947i \(-0.496731\pi\)
0.913851 + 0.406050i \(0.133094\pi\)
\(6\) 0.654861 0.755750i 0.267346 0.308533i
\(7\) −0.142315 + 0.989821i −0.0537900 + 0.374117i
\(8\) 0.959493 0.281733i 0.339232 0.0996075i
\(9\) 0.841254 + 0.540641i 0.280418 + 0.180214i
\(10\) 0.349573 + 2.43133i 0.110545 + 0.768854i
\(11\) 0.555075 + 1.21544i 0.167361 + 0.366470i 0.974666 0.223664i \(-0.0718019\pi\)
−0.807305 + 0.590135i \(0.799075\pi\)
\(12\) 0.415415 + 0.909632i 0.119920 + 0.262588i
\(13\) 0.0102349 + 0.0711851i 0.00283864 + 0.0197432i 0.991192 0.132436i \(-0.0422800\pi\)
−0.988353 + 0.152179i \(0.951371\pi\)
\(14\) −0.841254 0.540641i −0.224834 0.144492i
\(15\) −2.35683 + 0.692029i −0.608532 + 0.178681i
\(16\) −0.142315 + 0.989821i −0.0355787 + 0.247455i
\(17\) −1.88951 + 2.18061i −0.458273 + 0.528875i −0.937113 0.349027i \(-0.886512\pi\)
0.478840 + 0.877902i \(0.341058\pi\)
\(18\) −0.841254 + 0.540641i −0.198285 + 0.127430i
\(19\) 1.17198 + 1.35254i 0.268871 + 0.310294i 0.874089 0.485766i \(-0.161459\pi\)
−0.605218 + 0.796060i \(0.706914\pi\)
\(20\) −2.35683 0.692029i −0.527004 0.154742i
\(21\) 0.415415 0.909632i 0.0906510 0.198498i
\(22\) −1.33619 −0.284878
\(23\) 4.51632 1.61332i 0.941719 0.336401i
\(24\) −1.00000 −0.204124
\(25\) 0.429362 0.940171i 0.0858724 0.188034i
\(26\) −0.0690040 0.0202614i −0.0135328 0.00397359i
\(27\) −0.654861 0.755750i −0.126028 0.145444i
\(28\) 0.841254 0.540641i 0.158982 0.102172i
\(29\) 1.94443 2.24399i 0.361071 0.416698i −0.545927 0.837833i \(-0.683823\pi\)
0.906998 + 0.421135i \(0.138368\pi\)
\(30\) 0.349573 2.43133i 0.0638229 0.443898i
\(31\) 8.06752 2.36884i 1.44897 0.425456i 0.539769 0.841813i \(-0.318512\pi\)
0.909201 + 0.416358i \(0.136694\pi\)
\(32\) −0.841254 0.540641i −0.148714 0.0955727i
\(33\) −0.190160 1.32259i −0.0331027 0.230234i
\(34\) −1.19862 2.62461i −0.205562 0.450118i
\(35\) 1.02040 + 2.23436i 0.172479 + 0.377676i
\(36\) −0.142315 0.989821i −0.0237191 0.164970i
\(37\) −7.27320 4.67420i −1.19571 0.768434i −0.217499 0.976061i \(-0.569790\pi\)
−0.978208 + 0.207627i \(0.933426\pi\)
\(38\) −1.71717 + 0.504207i −0.278562 + 0.0817933i
\(39\) 0.0102349 0.0711851i 0.00163889 0.0113987i
\(40\) 1.60856 1.85637i 0.254335 0.293518i
\(41\) −4.03089 + 2.59049i −0.629519 + 0.404567i −0.816131 0.577867i \(-0.803885\pi\)
0.186613 + 0.982434i \(0.440249\pi\)
\(42\) 0.654861 + 0.755750i 0.101047 + 0.116615i
\(43\) 9.61032 + 2.82185i 1.46556 + 0.430327i 0.914653 0.404239i \(-0.132464\pi\)
0.550907 + 0.834566i \(0.314282\pi\)
\(44\) 0.555075 1.21544i 0.0836807 0.183235i
\(45\) 2.45633 0.366169
\(46\) −0.408619 + 4.77839i −0.0602476 + 0.704535i
\(47\) 12.0588 1.75896 0.879479 0.475938i \(-0.157891\pi\)
0.879479 + 0.475938i \(0.157891\pi\)
\(48\) 0.415415 0.909632i 0.0599600 0.131294i
\(49\) −0.959493 0.281733i −0.137070 0.0402475i
\(50\) 0.676847 + 0.781123i 0.0957206 + 0.110467i
\(51\) 2.42732 1.55994i 0.339893 0.218436i
\(52\) 0.0470957 0.0543513i 0.00653100 0.00753717i
\(53\) 0.145353 1.01095i 0.0199657 0.138865i −0.977400 0.211397i \(-0.932199\pi\)
0.997366 + 0.0725319i \(0.0231079\pi\)
\(54\) 0.959493 0.281733i 0.130570 0.0383389i
\(55\) 2.76111 + 1.77446i 0.372308 + 0.239268i
\(56\) 0.142315 + 0.989821i 0.0190176 + 0.132270i
\(57\) −0.743455 1.62794i −0.0984730 0.215626i
\(58\) 1.23346 + 2.70090i 0.161961 + 0.354645i
\(59\) 1.84792 + 12.8526i 0.240579 + 1.67326i 0.649247 + 0.760578i \(0.275084\pi\)
−0.408668 + 0.912683i \(0.634007\pi\)
\(60\) 2.06640 + 1.32799i 0.266771 + 0.171443i
\(61\) 13.3971 3.93375i 1.71533 0.503665i 0.731355 0.681997i \(-0.238888\pi\)
0.983970 + 0.178332i \(0.0570702\pi\)
\(62\) −1.19660 + 8.32253i −0.151968 + 1.05696i
\(63\) −0.654861 + 0.755750i −0.0825047 + 0.0952155i
\(64\) 0.841254 0.540641i 0.105157 0.0675801i
\(65\) 0.115683 + 0.133505i 0.0143487 + 0.0165593i
\(66\) 1.28207 + 0.376449i 0.157812 + 0.0463377i
\(67\) 0.848269 1.85745i 0.103633 0.226924i −0.850712 0.525633i \(-0.823829\pi\)
0.954344 + 0.298709i \(0.0965560\pi\)
\(68\) 2.88536 0.349901
\(69\) −4.78791 + 0.275576i −0.576396 + 0.0331755i
\(70\) −2.45633 −0.293588
\(71\) −4.29109 + 9.39618i −0.509259 + 1.11512i 0.464089 + 0.885788i \(0.346382\pi\)
−0.973348 + 0.229333i \(0.926346\pi\)
\(72\) 0.959493 + 0.281733i 0.113077 + 0.0332025i
\(73\) −6.76030 7.80180i −0.791233 0.913132i 0.206633 0.978418i \(-0.433749\pi\)
−0.997867 + 0.0652866i \(0.979204\pi\)
\(74\) 7.27320 4.67420i 0.845492 0.543365i
\(75\) −0.676847 + 0.781123i −0.0781555 + 0.0901963i
\(76\) 0.254696 1.77145i 0.0292157 0.203199i
\(77\) −1.28207 + 0.376449i −0.146105 + 0.0429004i
\(78\) 0.0605005 + 0.0388813i 0.00685034 + 0.00440244i
\(79\) −0.747893 5.20171i −0.0841446 0.585238i −0.987652 0.156665i \(-0.949926\pi\)
0.903507 0.428573i \(-0.140983\pi\)
\(80\) 1.02040 + 2.23436i 0.114084 + 0.249809i
\(81\) 0.415415 + 0.909632i 0.0461572 + 0.101070i
\(82\) −0.681905 4.74275i −0.0753038 0.523749i
\(83\) 7.67818 + 4.93446i 0.842789 + 0.541628i 0.889318 0.457289i \(-0.151180\pi\)
−0.0465288 + 0.998917i \(0.514816\pi\)
\(84\) −0.959493 + 0.281733i −0.104689 + 0.0307395i
\(85\) −1.00864 + 7.01526i −0.109403 + 0.760912i
\(86\) −6.55911 + 7.56962i −0.707287 + 0.816253i
\(87\) −2.49787 + 1.60528i −0.267799 + 0.172104i
\(88\) 0.875021 + 1.00983i 0.0932776 + 0.107648i
\(89\) 7.76701 + 2.28060i 0.823301 + 0.241743i 0.666137 0.745829i \(-0.267947\pi\)
0.157164 + 0.987572i \(0.449765\pi\)
\(90\) −1.02040 + 2.23436i −0.107559 + 0.235522i
\(91\) −0.0719171 −0.00753896
\(92\) −4.17683 2.35671i −0.435465 0.245704i
\(93\) −8.40811 −0.871880
\(94\) −5.00941 + 10.9691i −0.516681 + 1.13137i
\(95\) 4.21795 + 1.23850i 0.432752 + 0.127068i
\(96\) 0.654861 + 0.755750i 0.0668364 + 0.0771334i
\(97\) −9.89607 + 6.35982i −1.00479 + 0.645742i −0.936041 0.351892i \(-0.885538\pi\)
−0.0687533 + 0.997634i \(0.521902\pi\)
\(98\) 0.654861 0.755750i 0.0661509 0.0763422i
\(99\) −0.190160 + 1.32259i −0.0191118 + 0.132926i
\(100\) −0.991706 + 0.291191i −0.0991706 + 0.0291191i
\(101\) 7.87163 + 5.05879i 0.783256 + 0.503368i 0.870113 0.492853i \(-0.164046\pi\)
−0.0868565 + 0.996221i \(0.527682\pi\)
\(102\) 0.410629 + 2.85599i 0.0406584 + 0.282785i
\(103\) −0.503118 1.10168i −0.0495737 0.108551i 0.883224 0.468951i \(-0.155368\pi\)
−0.932798 + 0.360399i \(0.882640\pi\)
\(104\) 0.0298755 + 0.0654181i 0.00292953 + 0.00641477i
\(105\) −0.349573 2.43133i −0.0341148 0.237274i
\(106\) 0.859212 + 0.552182i 0.0834540 + 0.0536326i
\(107\) −5.30368 + 1.55730i −0.512726 + 0.150550i −0.527853 0.849336i \(-0.677003\pi\)
0.0151273 + 0.999886i \(0.495185\pi\)
\(108\) −0.142315 + 0.989821i −0.0136943 + 0.0952456i
\(109\) 10.6387 12.2777i 1.01900 1.17599i 0.0347170 0.999397i \(-0.488947\pi\)
0.984284 0.176593i \(-0.0565075\pi\)
\(110\) −2.76111 + 1.77446i −0.263262 + 0.169188i
\(111\) 5.66171 + 6.53396i 0.537386 + 0.620176i
\(112\) −0.959493 0.281733i −0.0906636 0.0266212i
\(113\) −4.78954 + 10.4876i −0.450562 + 0.986592i 0.538977 + 0.842321i \(0.318811\pi\)
−0.989538 + 0.144272i \(0.953916\pi\)
\(114\) 1.78967 0.167618
\(115\) 7.19005 9.33142i 0.670475 0.870160i
\(116\) −2.96922 −0.275685
\(117\) −0.0298755 + 0.0654181i −0.00276199 + 0.00604791i
\(118\) −12.4588 3.65822i −1.14692 0.336766i
\(119\) −1.88951 2.18061i −0.173211 0.199896i
\(120\) −2.06640 + 1.32799i −0.188636 + 0.121229i
\(121\) 6.03427 6.96392i 0.548570 0.633084i
\(122\) −1.98710 + 13.8206i −0.179904 + 1.25126i
\(123\) 4.59743 1.34993i 0.414537 0.121719i
\(124\) −7.07335 4.54577i −0.635206 0.408222i
\(125\) 1.38655 + 9.64370i 0.124017 + 0.862559i
\(126\) −0.415415 0.909632i −0.0370081 0.0810365i
\(127\) −3.90285 8.54605i −0.346322 0.758340i −0.999999 0.00156574i \(-0.999502\pi\)
0.653677 0.756774i \(-0.273226\pi\)
\(128\) 0.142315 + 0.989821i 0.0125790 + 0.0874887i
\(129\) −8.42603 5.41508i −0.741871 0.476771i
\(130\) −0.169497 + 0.0497687i −0.0148658 + 0.00436501i
\(131\) −0.558841 + 3.88683i −0.0488262 + 0.339594i 0.950736 + 0.310002i \(0.100330\pi\)
−0.999562 + 0.0295916i \(0.990579\pi\)
\(132\) −0.875021 + 1.00983i −0.0761608 + 0.0878943i
\(133\) −1.50556 + 0.967567i −0.130549 + 0.0838987i
\(134\) 1.33721 + 1.54323i 0.115518 + 0.133314i
\(135\) −2.35683 0.692029i −0.202844 0.0595604i
\(136\) −1.19862 + 2.62461i −0.102781 + 0.225059i
\(137\) −6.62947 −0.566393 −0.283197 0.959062i \(-0.591395\pi\)
−0.283197 + 0.959062i \(0.591395\pi\)
\(138\) 1.73830 4.46971i 0.147974 0.380487i
\(139\) −8.30187 −0.704155 −0.352078 0.935971i \(-0.614525\pi\)
−0.352078 + 0.935971i \(0.614525\pi\)
\(140\) 1.02040 2.23436i 0.0862393 0.188838i
\(141\) −11.5703 3.39736i −0.974399 0.286109i
\(142\) −6.76448 7.80663i −0.567663 0.655118i
\(143\) −0.0808405 + 0.0519530i −0.00676022 + 0.00434453i
\(144\) −0.654861 + 0.755750i −0.0545717 + 0.0629791i
\(145\) 1.03796 7.21916i 0.0861977 0.599518i
\(146\) 9.90510 2.90840i 0.819752 0.240701i
\(147\) 0.841254 + 0.540641i 0.0693854 + 0.0445913i
\(148\) 1.23041 + 8.55767i 0.101139 + 0.703436i
\(149\) −3.81994 8.36450i −0.312942 0.685246i 0.686168 0.727443i \(-0.259292\pi\)
−0.999109 + 0.0421969i \(0.986564\pi\)
\(150\) −0.429362 0.940171i −0.0350572 0.0767647i
\(151\) 1.74671 + 12.1486i 0.142145 + 0.988643i 0.928623 + 0.371024i \(0.120993\pi\)
−0.786478 + 0.617618i \(0.788098\pi\)
\(152\) 1.50556 + 0.967567i 0.122117 + 0.0784800i
\(153\) −2.76848 + 0.812900i −0.223818 + 0.0657190i
\(154\) 0.190160 1.32259i 0.0153235 0.106578i
\(155\) 13.5249 15.6086i 1.08635 1.25371i
\(156\) −0.0605005 + 0.0388813i −0.00484392 + 0.00311300i
\(157\) −1.40772 1.62460i −0.112348 0.129657i 0.696790 0.717275i \(-0.254611\pi\)
−0.809138 + 0.587618i \(0.800066\pi\)
\(158\) 5.04233 + 1.48056i 0.401146 + 0.117787i
\(159\) −0.424283 + 0.929050i −0.0336478 + 0.0736784i
\(160\) −2.45633 −0.194190
\(161\) 0.954162 + 4.69995i 0.0751985 + 0.370408i
\(162\) −1.00000 −0.0785674
\(163\) 3.84170 8.41214i 0.300905 0.658890i −0.697425 0.716658i \(-0.745671\pi\)
0.998330 + 0.0577678i \(0.0183983\pi\)
\(164\) 4.59743 + 1.34993i 0.358999 + 0.105412i
\(165\) −2.14934 2.48047i −0.167326 0.193105i
\(166\) −7.67818 + 4.93446i −0.595942 + 0.382989i
\(167\) 6.38104 7.36411i 0.493779 0.569852i −0.453092 0.891464i \(-0.649679\pi\)
0.946872 + 0.321612i \(0.104225\pi\)
\(168\) 0.142315 0.989821i 0.0109798 0.0763664i
\(169\) 12.4684 3.66107i 0.959111 0.281620i
\(170\) −5.96230 3.83174i −0.457288 0.293881i
\(171\) 0.254696 + 1.77145i 0.0194771 + 0.135466i
\(172\) −4.16082 9.11091i −0.317259 0.694701i
\(173\) −3.14583 6.88841i −0.239173 0.523716i 0.751540 0.659688i \(-0.229312\pi\)
−0.990713 + 0.135972i \(0.956584\pi\)
\(174\) −0.422564 2.93900i −0.0320345 0.222805i
\(175\) 0.869497 + 0.558792i 0.0657278 + 0.0422407i
\(176\) −1.28207 + 0.376449i −0.0966396 + 0.0283759i
\(177\) 1.84792 12.8526i 0.138898 0.966057i
\(178\) −5.30104 + 6.11772i −0.397330 + 0.458543i
\(179\) 1.35958 0.873750i 0.101620 0.0653071i −0.488844 0.872371i \(-0.662581\pi\)
0.590464 + 0.807064i \(0.298945\pi\)
\(180\) −1.60856 1.85637i −0.119895 0.138366i
\(181\) −22.9389 6.73546i −1.70503 0.500643i −0.723240 0.690597i \(-0.757348\pi\)
−0.981793 + 0.189954i \(0.939166\pi\)
\(182\) 0.0298755 0.0654181i 0.00221452 0.00484911i
\(183\) −13.9627 −1.03215
\(184\) 3.87886 2.82037i 0.285953 0.207920i
\(185\) −21.2366 −1.56135
\(186\) 3.49285 7.64828i 0.256109 0.560799i
\(187\) −3.69923 1.08619i −0.270514 0.0794302i
\(188\) −7.89684 9.11344i −0.575936 0.664666i
\(189\) 0.841254 0.540641i 0.0611922 0.0393258i
\(190\) −2.87878 + 3.32229i −0.208849 + 0.241024i
\(191\) 0.0992731 0.690459i 0.00718315 0.0499599i −0.985915 0.167249i \(-0.946511\pi\)
0.993098 + 0.117290i \(0.0374206\pi\)
\(192\) −0.959493 + 0.281733i −0.0692454 + 0.0203323i
\(193\) −5.65719 3.63566i −0.407214 0.261700i 0.320960 0.947093i \(-0.395994\pi\)
−0.728174 + 0.685392i \(0.759631\pi\)
\(194\) −1.67412 11.6437i −0.120195 0.835972i
\(195\) −0.0733841 0.160689i −0.00525514 0.0115072i
\(196\) 0.415415 + 0.909632i 0.0296725 + 0.0649737i
\(197\) −1.61778 11.2519i −0.115262 0.801667i −0.962661 0.270710i \(-0.912742\pi\)
0.847399 0.530957i \(-0.178167\pi\)
\(198\) −1.12408 0.722401i −0.0798847 0.0513388i
\(199\) 1.62508 0.477167i 0.115199 0.0338254i −0.223625 0.974675i \(-0.571789\pi\)
0.338824 + 0.940850i \(0.389971\pi\)
\(200\) 0.147093 1.02305i 0.0104010 0.0723408i
\(201\) −1.33721 + 1.54323i −0.0943197 + 0.108851i
\(202\) −7.87163 + 5.05879i −0.553846 + 0.355935i
\(203\) 1.94443 + 2.24399i 0.136472 + 0.157497i
\(204\) −2.76848 0.812900i −0.193832 0.0569144i
\(205\) −4.88926 + 10.7060i −0.341481 + 0.747738i
\(206\) 1.21112 0.0843829
\(207\) 4.67160 + 1.08450i 0.324699 + 0.0753777i
\(208\) −0.0719171 −0.00498656
\(209\) −0.993400 + 2.17524i −0.0687149 + 0.150465i
\(210\) 2.35683 + 0.692029i 0.162637 + 0.0477545i
\(211\) −9.93121 11.4612i −0.683693 0.789024i 0.302760 0.953067i \(-0.402092\pi\)
−0.986453 + 0.164043i \(0.947546\pi\)
\(212\) −0.859212 + 0.552182i −0.0590109 + 0.0379240i
\(213\) 6.76448 7.80663i 0.463495 0.534901i
\(214\) 0.786657 5.47132i 0.0537748 0.374012i
\(215\) 23.6062 6.93139i 1.60993 0.472717i
\(216\) −0.841254 0.540641i −0.0572401 0.0367859i
\(217\) 1.19660 + 8.32253i 0.0812304 + 0.564970i
\(218\) 6.74872 + 14.7776i 0.457081 + 1.00087i
\(219\) 4.28844 + 9.39037i 0.289786 + 0.634542i
\(220\) −0.467097 3.24873i −0.0314917 0.219029i
\(221\) −0.174566 0.112187i −0.0117426 0.00754649i
\(222\) −8.29546 + 2.43577i −0.556755 + 0.163478i
\(223\) −1.64934 + 11.4714i −0.110448 + 0.768183i 0.857037 + 0.515255i \(0.172303\pi\)
−0.967485 + 0.252928i \(0.918606\pi\)
\(224\) 0.654861 0.755750i 0.0437547 0.0504956i
\(225\) 0.869497 0.558792i 0.0579665 0.0372528i
\(226\) −7.55023 8.71343i −0.502234 0.579609i
\(227\) −9.48159 2.78405i −0.629315 0.184784i −0.0485055 0.998823i \(-0.515446\pi\)
−0.580810 + 0.814039i \(0.697264\pi\)
\(228\) −0.743455 + 1.62794i −0.0492365 + 0.107813i
\(229\) 10.1527 0.670910 0.335455 0.942056i \(-0.391110\pi\)
0.335455 + 0.942056i \(0.391110\pi\)
\(230\) 5.50131 + 10.4167i 0.362745 + 0.686857i
\(231\) 1.33619 0.0879151
\(232\) 1.23346 2.70090i 0.0809805 0.177323i
\(233\) −6.94261 2.03853i −0.454825 0.133549i 0.0462923 0.998928i \(-0.485259\pi\)
−0.501118 + 0.865379i \(0.667078\pi\)
\(234\) −0.0470957 0.0543513i −0.00307874 0.00355306i
\(235\) 24.9183 16.0140i 1.62549 1.04464i
\(236\) 8.50319 9.81320i 0.553510 0.638785i
\(237\) −0.747893 + 5.20171i −0.0485809 + 0.337887i
\(238\) 2.76848 0.812900i 0.179454 0.0526925i
\(239\) −19.3311 12.4233i −1.25042 0.803599i −0.263480 0.964665i \(-0.584870\pi\)
−0.986944 + 0.161066i \(0.948507\pi\)
\(240\) −0.349573 2.43133i −0.0225648 0.156942i
\(241\) 4.75078 + 10.4028i 0.306024 + 0.670100i 0.998691 0.0511583i \(-0.0162913\pi\)
−0.692666 + 0.721258i \(0.743564\pi\)
\(242\) 3.82788 + 8.38188i 0.246065 + 0.538808i
\(243\) −0.142315 0.989821i −0.00912950 0.0634971i
\(244\) −11.7462 7.54881i −0.751972 0.483263i
\(245\) −2.35683 + 0.692029i −0.150573 + 0.0442121i
\(246\) −0.681905 + 4.74275i −0.0434767 + 0.302387i
\(247\) −0.0842856 + 0.0972708i −0.00536297 + 0.00618919i
\(248\) 7.07335 4.54577i 0.449158 0.288656i
\(249\) −5.97696 6.89778i −0.378774 0.437129i
\(250\) −9.34821 2.74488i −0.591233 0.173602i
\(251\) −8.65096 + 18.9430i −0.546044 + 1.19567i 0.412561 + 0.910930i \(0.364634\pi\)
−0.958605 + 0.284740i \(0.908093\pi\)
\(252\) 1.00000 0.0629941
\(253\) 4.46780 + 4.59383i 0.280888 + 0.288812i
\(254\) 9.39507 0.589499
\(255\) 2.94421 6.44693i 0.184374 0.403722i
\(256\) −0.959493 0.281733i −0.0599683 0.0176083i
\(257\) 0.955244 + 1.10241i 0.0595865 + 0.0687665i 0.784760 0.619799i \(-0.212786\pi\)
−0.725174 + 0.688566i \(0.758241\pi\)
\(258\) 8.42603 5.41508i 0.524582 0.337128i
\(259\) 5.66171 6.53396i 0.351802 0.406001i
\(260\) 0.0251403 0.174854i 0.00155913 0.0108440i
\(261\) 2.84895 0.836526i 0.176345 0.0517797i
\(262\) −3.30343 2.12299i −0.204087 0.131159i
\(263\) −2.77855 19.3252i −0.171333 1.19164i −0.876073 0.482179i \(-0.839846\pi\)
0.704740 0.709465i \(-0.251064\pi\)
\(264\) −0.555075 1.21544i −0.0341625 0.0748055i
\(265\) −1.04218 2.28206i −0.0640206 0.140186i
\(266\) −0.254696 1.77145i −0.0156164 0.108615i
\(267\) −6.80987 4.37644i −0.416757 0.267834i
\(268\) −1.95927 + 0.575292i −0.119681 + 0.0351416i
\(269\) −2.33149 + 16.2159i −0.142153 + 0.988699i 0.786458 + 0.617644i \(0.211913\pi\)
−0.928611 + 0.371055i \(0.878996\pi\)
\(270\) 1.60856 1.85637i 0.0978936 0.112975i
\(271\) −25.3033 + 16.2615i −1.53707 + 0.987814i −0.548651 + 0.836051i \(0.684859\pi\)
−0.988417 + 0.151763i \(0.951505\pi\)
\(272\) −1.88951 2.18061i −0.114568 0.132219i
\(273\) 0.0690040 + 0.0202614i 0.00417631 + 0.00122628i
\(274\) 2.75398 6.03037i 0.166374 0.364308i
\(275\) 1.38105 0.0832807
\(276\) 3.34368 + 3.43799i 0.201266 + 0.206943i
\(277\) 6.16646 0.370507 0.185253 0.982691i \(-0.440689\pi\)
0.185253 + 0.982691i \(0.440689\pi\)
\(278\) 3.44872 7.55165i 0.206841 0.452918i
\(279\) 8.06752 + 2.36884i 0.482990 + 0.141819i
\(280\) 1.60856 + 1.85637i 0.0961296 + 0.110939i
\(281\) −0.965321 + 0.620374i −0.0575862 + 0.0370084i −0.569117 0.822256i \(-0.692715\pi\)
0.511531 + 0.859265i \(0.329079\pi\)
\(282\) 7.89684 9.11344i 0.470250 0.542697i
\(283\) 2.47274 17.1983i 0.146989 1.02233i −0.774123 0.633036i \(-0.781809\pi\)
0.921112 0.389298i \(-0.127282\pi\)
\(284\) 9.91122 2.91020i 0.588123 0.172688i
\(285\) −3.69817 2.37667i −0.219060 0.140782i
\(286\) −0.0136758 0.0951171i −0.000808666 0.00562439i
\(287\) −1.99047 4.35852i −0.117494 0.257275i
\(288\) −0.415415 0.909632i −0.0244786 0.0536006i
\(289\) 1.23454 + 8.58641i 0.0726199 + 0.505083i
\(290\) 6.13559 + 3.94311i 0.360294 + 0.231547i
\(291\) 11.2870 3.31416i 0.661655 0.194279i
\(292\) −1.46915 + 10.2182i −0.0859757 + 0.597974i
\(293\) 1.49534 1.72571i 0.0873586 0.100817i −0.710387 0.703811i \(-0.751480\pi\)
0.797746 + 0.602994i \(0.206026\pi\)
\(294\) −0.841254 + 0.540641i −0.0490629 + 0.0315308i
\(295\) 20.8867 + 24.1045i 1.21607 + 1.40342i
\(296\) −8.29546 2.43577i −0.482164 0.141576i
\(297\) 0.555075 1.21544i 0.0322087 0.0705273i
\(298\) 9.19547 0.532680
\(299\) 0.161069 + 0.304983i 0.00931484 + 0.0176376i
\(300\) 1.03357 0.0596734
\(301\) −4.16082 + 9.11091i −0.239825 + 0.525144i
\(302\) −11.7764 3.45786i −0.677656 0.198978i
\(303\) −6.12755 7.07157i −0.352018 0.406251i
\(304\) −1.50556 + 0.967567i −0.0863500 + 0.0554938i
\(305\) 22.4598 25.9200i 1.28604 1.48417i
\(306\) 0.410629 2.85599i 0.0234741 0.163266i
\(307\) −10.4796 + 3.07709i −0.598103 + 0.175619i −0.566750 0.823890i \(-0.691800\pi\)
−0.0313524 + 0.999508i \(0.509981\pi\)
\(308\) 1.12408 + 0.722401i 0.0640503 + 0.0411626i
\(309\) 0.172361 + 1.19880i 0.00980526 + 0.0681971i
\(310\) 8.57961 + 18.7867i 0.487289 + 1.06701i
\(311\) −0.0533751 0.116875i −0.00302662 0.00662738i 0.908113 0.418726i \(-0.137523\pi\)
−0.911139 + 0.412099i \(0.864796\pi\)
\(312\) −0.0102349 0.0711851i −0.000579436 0.00403006i
\(313\) 0.498360 + 0.320277i 0.0281690 + 0.0181031i 0.554650 0.832084i \(-0.312852\pi\)
−0.526481 + 0.850187i \(0.676489\pi\)
\(314\) 2.06257 0.605626i 0.116398 0.0341775i
\(315\) −0.349573 + 2.43133i −0.0196962 + 0.136990i
\(316\) −3.44143 + 3.97162i −0.193595 + 0.223421i
\(317\) −7.17604 + 4.61176i −0.403047 + 0.259022i −0.726423 0.687248i \(-0.758819\pi\)
0.323376 + 0.946271i \(0.395182\pi\)
\(318\) −0.668840 0.771882i −0.0375067 0.0432850i
\(319\) 3.80674 + 1.11776i 0.213137 + 0.0625826i
\(320\) 1.02040 2.23436i 0.0570420 0.124904i
\(321\) 5.52758 0.308520
\(322\) −4.67160 1.08450i −0.260338 0.0604366i
\(323\) −5.16383 −0.287323
\(324\) 0.415415 0.909632i 0.0230786 0.0505351i
\(325\) 0.0713207 + 0.0209416i 0.00395616 + 0.00116163i
\(326\) 6.05606 + 6.98906i 0.335414 + 0.387088i
\(327\) −13.6668 + 8.78310i −0.755774 + 0.485706i
\(328\) −3.13778 + 3.62119i −0.173255 + 0.199947i
\(329\) −1.71615 + 11.9361i −0.0946143 + 0.658057i
\(330\) 3.14919 0.924685i 0.173357 0.0509022i
\(331\) 10.3559 + 6.65536i 0.569214 + 0.365811i 0.793368 0.608742i \(-0.208326\pi\)
−0.224154 + 0.974554i \(0.571962\pi\)
\(332\) −1.29892 9.03416i −0.0712873 0.495814i
\(333\) −3.59154 7.86438i −0.196815 0.430965i
\(334\) 4.04785 + 8.86356i 0.221489 + 0.484992i
\(335\) −0.713820 4.96473i −0.0390002 0.271252i
\(336\) 0.841254 + 0.540641i 0.0458941 + 0.0294944i
\(337\) −31.8669 + 9.35697i −1.73590 + 0.509707i −0.988047 0.154155i \(-0.950735\pi\)
−0.747855 + 0.663862i \(0.768916\pi\)
\(338\) −1.84936 + 12.8626i −0.100592 + 0.699631i
\(339\) 7.55023 8.71343i 0.410072 0.473249i
\(340\) 5.96230 3.83174i 0.323351 0.207805i
\(341\) 7.35727 + 8.49074i 0.398419 + 0.459800i
\(342\) −1.71717 0.504207i −0.0928541 0.0272644i
\(343\) 0.415415 0.909632i 0.0224303 0.0491155i
\(344\) 10.0160 0.540029
\(345\) −9.52776 + 6.92776i −0.512958 + 0.372978i
\(346\) 7.57274 0.407113
\(347\) −9.63143 + 21.0899i −0.517042 + 1.13216i 0.453505 + 0.891254i \(0.350173\pi\)
−0.970547 + 0.240911i \(0.922554\pi\)
\(348\) 2.84895 + 0.836526i 0.152720 + 0.0448425i
\(349\) −10.2668 11.8485i −0.549567 0.634234i 0.411215 0.911538i \(-0.365104\pi\)
−0.960782 + 0.277304i \(0.910559\pi\)
\(350\) −0.869497 + 0.558792i −0.0464766 + 0.0298687i
\(351\) 0.0470957 0.0543513i 0.00251378 0.00290106i
\(352\) 0.190160 1.32259i 0.0101356 0.0704945i
\(353\) −30.5298 + 8.96436i −1.62494 + 0.477125i −0.962340 0.271850i \(-0.912365\pi\)
−0.662599 + 0.748975i \(0.730546\pi\)
\(354\) 10.9234 + 7.02007i 0.580575 + 0.373113i
\(355\) 3.61096 + 25.1148i 0.191650 + 1.33295i
\(356\) −3.36275 7.36339i −0.178225 0.390259i
\(357\) 1.19862 + 2.62461i 0.0634378 + 0.138909i
\(358\) 0.230000 + 1.59969i 0.0121559 + 0.0845461i
\(359\) 1.91245 + 1.22905i 0.100935 + 0.0648670i 0.590135 0.807305i \(-0.299075\pi\)
−0.489200 + 0.872172i \(0.662711\pi\)
\(360\) 2.35683 0.692029i 0.124216 0.0364731i
\(361\) 2.24816 15.6363i 0.118324 0.822963i
\(362\) 15.6559 18.0679i 0.822858 0.949629i
\(363\) −7.75180 + 4.98178i −0.406864 + 0.261476i
\(364\) 0.0470957 + 0.0543513i 0.00246849 + 0.00284878i
\(365\) −24.3302 7.14400i −1.27350 0.373934i
\(366\) 5.80032 12.7009i 0.303187 0.663888i
\(367\) −16.5705 −0.864972 −0.432486 0.901641i \(-0.642363\pi\)
−0.432486 + 0.901641i \(0.642363\pi\)
\(368\) 0.954162 + 4.69995i 0.0497391 + 0.245002i
\(369\) −4.79152 −0.249437
\(370\) 8.82202 19.3175i 0.458635 1.00427i
\(371\) 0.979975 + 0.287747i 0.0508778 + 0.0149391i
\(372\) 5.50614 + 6.35442i 0.285480 + 0.329462i
\(373\) 14.2058 9.12952i 0.735549 0.472708i −0.118465 0.992958i \(-0.537797\pi\)
0.854014 + 0.520250i \(0.174161\pi\)
\(374\) 2.52475 2.91372i 0.130552 0.150665i
\(375\) 1.38655 9.64370i 0.0716014 0.497998i
\(376\) 11.5703 3.39736i 0.596695 0.175205i
\(377\) 0.179639 + 0.115447i 0.00925190 + 0.00594583i
\(378\) 0.142315 + 0.989821i 0.00731989 + 0.0509109i
\(379\) 4.64446 + 10.1699i 0.238570 + 0.522395i 0.990609 0.136723i \(-0.0436570\pi\)
−0.752039 + 0.659118i \(0.770930\pi\)
\(380\) −1.82617 3.99876i −0.0936807 0.205132i
\(381\) 1.33706 + 9.29944i 0.0684995 + 0.476425i
\(382\) 0.586824 + 0.377129i 0.0300246 + 0.0192956i
\(383\) −21.4653 + 6.30279i −1.09683 + 0.322057i −0.779591 0.626289i \(-0.784573\pi\)
−0.317236 + 0.948347i \(0.602755\pi\)
\(384\) 0.142315 0.989821i 0.00726247 0.0505116i
\(385\) −2.14934 + 2.48047i −0.109541 + 0.126417i
\(386\) 5.65719 3.63566i 0.287943 0.185050i
\(387\) 6.55911 + 7.56962i 0.333419 + 0.384785i
\(388\) 11.2870 + 3.31416i 0.573010 + 0.168251i
\(389\) 2.44736 5.35896i 0.124086 0.271710i −0.837387 0.546611i \(-0.815918\pi\)
0.961473 + 0.274901i \(0.0886450\pi\)
\(390\) 0.176652 0.00894514
\(391\) −5.01561 + 12.8967i −0.253650 + 0.652215i
\(392\) −1.00000 −0.0505076
\(393\) 1.63125 3.57194i 0.0822857 0.180181i
\(394\) 10.9072 + 3.20263i 0.549495 + 0.161346i
\(395\) −8.45329 9.75561i −0.425331 0.490858i
\(396\) 1.12408 0.722401i 0.0564870 0.0363020i
\(397\) −12.7534 + 14.7182i −0.640075 + 0.738686i −0.979388 0.201987i \(-0.935260\pi\)
0.339313 + 0.940674i \(0.389806\pi\)
\(398\) −0.241037 + 1.67645i −0.0120821 + 0.0840327i
\(399\) 1.71717 0.504207i 0.0859662 0.0252419i
\(400\) 0.869497 + 0.558792i 0.0434749 + 0.0279396i
\(401\) −0.551015 3.83239i −0.0275164 0.191380i 0.971427 0.237338i \(-0.0762750\pi\)
−0.998943 + 0.0459580i \(0.985366\pi\)
\(402\) −0.848269 1.85745i −0.0423078 0.0926412i
\(403\) 0.251196 + 0.550043i 0.0125130 + 0.0273996i
\(404\) −1.33164 9.26178i −0.0662517 0.460791i
\(405\) 2.06640 + 1.32799i 0.102680 + 0.0659886i
\(406\) −2.84895 + 0.836526i −0.141391 + 0.0415161i
\(407\) 1.64406 11.4347i 0.0814932 0.566797i
\(408\) 1.88951 2.18061i 0.0935446 0.107956i
\(409\) −6.15668 + 3.95666i −0.304428 + 0.195644i −0.683932 0.729546i \(-0.739731\pi\)
0.379503 + 0.925190i \(0.376095\pi\)
\(410\) −7.70743 8.89485i −0.380643 0.439285i
\(411\) 6.36093 + 1.86774i 0.313761 + 0.0921286i
\(412\) −0.503118 + 1.10168i −0.0247869 + 0.0542757i
\(413\) −12.9847 −0.638937
\(414\) −2.92715 + 3.79892i −0.143861 + 0.186707i
\(415\) 22.4191 1.10051
\(416\) 0.0298755 0.0654181i 0.00146476 0.00320739i
\(417\) 7.96558 + 2.33891i 0.390076 + 0.114537i
\(418\) −1.56600 1.80726i −0.0765954 0.0883958i
\(419\) −11.8172 + 7.59444i −0.577307 + 0.371013i −0.796472 0.604675i \(-0.793303\pi\)
0.219165 + 0.975688i \(0.429667\pi\)
\(420\) −1.60856 + 1.85637i −0.0784895 + 0.0905817i
\(421\) −0.756545 + 5.26189i −0.0368717 + 0.256449i −0.999917 0.0128914i \(-0.995896\pi\)
0.963045 + 0.269340i \(0.0868055\pi\)
\(422\) 14.5511 4.27258i 0.708335 0.207986i
\(423\) 10.1445 + 6.51948i 0.493243 + 0.316988i
\(424\) −0.145353 1.01095i −0.00705896 0.0490961i
\(425\) 1.23886 + 2.71273i 0.0600937 + 0.131587i
\(426\) 4.29109 + 9.39618i 0.207904 + 0.455246i
\(427\) 1.98710 + 13.8206i 0.0961625 + 0.668825i
\(428\) 4.65010 + 2.98844i 0.224771 + 0.144452i
\(429\) 0.0922027 0.0270732i 0.00445159 0.00130710i
\(430\) −3.50134 + 24.3523i −0.168849 + 1.17437i
\(431\) 11.7789 13.5936i 0.567371 0.654781i −0.397470 0.917615i \(-0.630112\pi\)
0.964841 + 0.262834i \(0.0846573\pi\)
\(432\) 0.841254 0.540641i 0.0404748 0.0260116i
\(433\) 14.7940 + 17.0732i 0.710955 + 0.820486i 0.990189 0.139738i \(-0.0446259\pi\)
−0.279234 + 0.960223i \(0.590080\pi\)
\(434\) −8.06752 2.36884i −0.387253 0.113708i
\(435\) −3.02979 + 6.63430i −0.145267 + 0.318091i
\(436\) −16.2457 −0.778029
\(437\) 7.47514 + 4.21772i 0.357584 + 0.201761i
\(438\) −10.3233 −0.493265
\(439\) 10.4314 22.8415i 0.497862 1.09017i −0.479296 0.877653i \(-0.659108\pi\)
0.977158 0.212513i \(-0.0681647\pi\)
\(440\) 3.14919 + 0.924685i 0.150132 + 0.0440826i
\(441\) −0.654861 0.755750i −0.0311838 0.0359881i
\(442\) 0.174566 0.112187i 0.00830325 0.00533617i
\(443\) 14.1875 16.3732i 0.674068 0.777916i −0.310939 0.950430i \(-0.600644\pi\)
0.985007 + 0.172514i \(0.0551890\pi\)
\(444\) 1.23041 8.55767i 0.0583925 0.406129i
\(445\) 19.0784 5.60191i 0.904401 0.265556i
\(446\) −9.74961 6.26569i −0.461657 0.296689i
\(447\) 1.30865 + 9.10188i 0.0618971 + 0.430504i
\(448\) 0.415415 + 0.909632i 0.0196265 + 0.0429761i
\(449\) −8.73908 19.1359i −0.412423 0.903080i −0.995858 0.0909201i \(-0.971019\pi\)
0.583436 0.812159i \(-0.301708\pi\)
\(450\) 0.147093 + 1.02305i 0.00693402 + 0.0482272i
\(451\) −5.38605 3.46140i −0.253619 0.162991i
\(452\) 11.0625 3.24824i 0.520336 0.152784i
\(453\) 1.74671 12.1486i 0.0820676 0.570793i
\(454\) 6.47125 7.46823i 0.303711 0.350501i
\(455\) −0.148609 + 0.0955055i −0.00696692 + 0.00447737i
\(456\) −1.17198 1.35254i −0.0548831 0.0633385i
\(457\) −6.70425 1.96854i −0.313611 0.0920846i 0.121139 0.992636i \(-0.461345\pi\)
−0.434751 + 0.900551i \(0.643163\pi\)
\(458\) −4.21759 + 9.23523i −0.197075 + 0.431534i
\(459\) 2.88536 0.134677
\(460\) −11.7607 + 0.676907i −0.548345 + 0.0315610i
\(461\) 15.8865 0.739910 0.369955 0.929050i \(-0.379373\pi\)
0.369955 + 0.929050i \(0.379373\pi\)
\(462\) −0.555075 + 1.21544i −0.0258244 + 0.0565476i
\(463\) −22.6903 6.66248i −1.05451 0.309632i −0.291871 0.956458i \(-0.594278\pi\)
−0.762637 + 0.646826i \(0.776096\pi\)
\(464\) 1.94443 + 2.24399i 0.0902677 + 0.104174i
\(465\) −17.3745 + 11.1659i −0.805723 + 0.517807i
\(466\) 4.73838 5.46838i 0.219501 0.253318i
\(467\) −5.90397 + 41.0630i −0.273203 + 1.90017i 0.141040 + 0.990004i \(0.454955\pi\)
−0.414243 + 0.910166i \(0.635954\pi\)
\(468\) 0.0690040 0.0202614i 0.00318971 0.000936583i
\(469\) 1.71782 + 1.10398i 0.0793217 + 0.0509770i
\(470\) 4.21543 + 29.3190i 0.194443 + 1.35238i
\(471\) 0.892997 + 1.95539i 0.0411471 + 0.0900996i
\(472\) 5.39405 + 11.8113i 0.248281 + 0.543660i
\(473\) 1.90465 + 13.2472i 0.0875761 + 0.609105i
\(474\) −4.42096 2.84118i −0.203061 0.130500i
\(475\) 1.77482 0.521135i 0.0814345 0.0239113i
\(476\) −0.410629 + 2.85599i −0.0188212 + 0.130904i
\(477\) 0.668840 0.771882i 0.0306241 0.0353421i
\(478\) 19.3311 12.4233i 0.884183 0.568230i
\(479\) −0.0662485 0.0764549i −0.00302697 0.00349331i 0.754234 0.656606i \(-0.228008\pi\)
−0.757261 + 0.653112i \(0.773463\pi\)
\(480\) 2.35683 + 0.692029i 0.107574 + 0.0315867i
\(481\) 0.258293 0.565583i 0.0117772 0.0257884i
\(482\) −11.4362 −0.520906
\(483\) 0.408619 4.77839i 0.0185928 0.217424i
\(484\) −9.21459 −0.418845
\(485\) −12.0034 + 26.2839i −0.545048 + 1.19349i
\(486\) 0.959493 + 0.281733i 0.0435235 + 0.0127796i
\(487\) −27.0804 31.2525i −1.22713 1.41618i −0.877692 0.479225i \(-0.840918\pi\)
−0.349438 0.936959i \(-0.613628\pi\)
\(488\) 11.7462 7.54881i 0.531724 0.341719i
\(489\) −6.05606 + 6.98906i −0.273864 + 0.316056i
\(490\) 0.349573 2.43133i 0.0157921 0.109836i
\(491\) 39.2927 11.5374i 1.77325 0.520675i 0.778935 0.627105i \(-0.215760\pi\)
0.994320 + 0.106431i \(0.0339422\pi\)
\(492\) −4.03089 2.59049i −0.181726 0.116788i
\(493\) 1.21925 + 8.48006i 0.0549122 + 0.381923i
\(494\) −0.0534671 0.117077i −0.00240560 0.00526753i
\(495\) 1.36345 + 2.98554i 0.0612825 + 0.134190i
\(496\) 1.19660 + 8.32253i 0.0537289 + 0.373692i
\(497\) −8.68985 5.58463i −0.389793 0.250505i
\(498\) 8.75735 2.57139i 0.392426 0.115227i
\(499\) −3.49531 + 24.3104i −0.156471 + 1.08828i 0.748599 + 0.663023i \(0.230727\pi\)
−0.905071 + 0.425261i \(0.860182\pi\)
\(500\) 6.38022 7.36317i 0.285332 0.329291i
\(501\) −8.19727 + 5.26806i −0.366227 + 0.235360i
\(502\) −13.6374 15.7384i −0.608666 0.702439i
\(503\) −10.9179 3.20577i −0.486803 0.142938i 0.0291150 0.999576i \(-0.490731\pi\)
−0.515919 + 0.856638i \(0.672549\pi\)
\(504\) −0.415415 + 0.909632i −0.0185041 + 0.0405182i
\(505\) 22.9840 1.02277
\(506\) −6.03469 + 2.15571i −0.268275 + 0.0958331i
\(507\) −12.9948 −0.577121
\(508\) −3.90285 + 8.54605i −0.173161 + 0.379170i
\(509\) 41.4301 + 12.1650i 1.83636 + 0.539203i 0.999960 0.00892132i \(-0.00283978\pi\)
0.836397 + 0.548124i \(0.184658\pi\)
\(510\) 4.64126 + 5.35630i 0.205519 + 0.237181i
\(511\) 8.68448 5.58118i 0.384179 0.246897i
\(512\) 0.654861 0.755750i 0.0289410 0.0333997i
\(513\) 0.254696 1.77145i 0.0112451 0.0782115i
\(514\) −1.39961 + 0.410963i −0.0617342 + 0.0181268i
\(515\) −2.50266 1.60836i −0.110280 0.0708730i
\(516\) 1.42543 + 9.91410i 0.0627511 + 0.436444i
\(517\) 6.69354 + 14.6568i 0.294382 + 0.644606i
\(518\) 3.59154 + 7.86438i 0.157803 + 0.345541i
\(519\) 1.07771 + 7.49566i 0.0473064 + 0.329023i
\(520\) 0.148609 + 0.0955055i 0.00651696 + 0.00418819i
\(521\) −32.2970 + 9.48327i −1.41496 + 0.415469i −0.897794 0.440416i \(-0.854831\pi\)
−0.517165 + 0.855886i \(0.673013\pi\)
\(522\) −0.422564 + 2.93900i −0.0184951 + 0.128636i
\(523\) 22.8198 26.3355i 0.997841 1.15157i 0.00940098 0.999956i \(-0.497008\pi\)
0.988440 0.151614i \(-0.0484470\pi\)
\(524\) 3.30343 2.12299i 0.144311 0.0927431i
\(525\) −0.676847 0.781123i −0.0295400 0.0340910i
\(526\) 18.7331 + 5.50053i 0.816801 + 0.239835i
\(527\) −10.0781 + 22.0680i −0.439011 + 0.961299i
\(528\) 1.33619 0.0581504
\(529\) 17.7944 14.5726i 0.773669 0.633590i
\(530\) 2.50877 0.108974
\(531\) −5.39405 + 11.8113i −0.234082 + 0.512568i
\(532\) 1.71717 + 0.504207i 0.0744489 + 0.0218602i
\(533\) −0.225660 0.260426i −0.00977443 0.0112803i
\(534\) 6.80987 4.37644i 0.294692 0.189387i
\(535\) −8.89143 + 10.2613i −0.384410 + 0.443633i
\(536\) 0.290604 2.02120i 0.0125522 0.0873024i
\(537\) −1.55067 + 0.455319i −0.0669165 + 0.0196484i
\(538\) −13.7819 8.85711i −0.594181 0.381857i
\(539\) −0.190160 1.32259i −0.00819078 0.0569681i
\(540\) 1.02040 + 2.23436i 0.0439109 + 0.0961515i
\(541\) 8.14409 + 17.8331i 0.350142 + 0.766704i 0.999978 + 0.00662930i \(0.00211019\pi\)
−0.649836 + 0.760074i \(0.725163\pi\)
\(542\) −4.28057 29.7720i −0.183866 1.27882i
\(543\) 20.1121 + 12.9253i 0.863092 + 0.554676i
\(544\) 2.76848 0.812900i 0.118698 0.0348528i
\(545\) 5.67906 39.4987i 0.243264 1.69194i
\(546\) −0.0470957 + 0.0543513i −0.00201551 + 0.00232602i
\(547\) −31.9087 + 20.5065i −1.36432 + 0.876794i −0.998546 0.0539102i \(-0.982832\pi\)
−0.365772 + 0.930704i \(0.619195\pi\)
\(548\) 4.34138 + 5.01022i 0.185454 + 0.214026i
\(549\) 13.3971 + 3.93375i 0.571775 + 0.167888i
\(550\) −0.573711 + 1.25625i −0.0244631 + 0.0535667i
\(551\) 5.31392 0.226380
\(552\) −4.51632 + 1.61332i −0.192228 + 0.0686676i
\(553\) 5.25520 0.223474
\(554\) −2.56164 + 5.60921i −0.108834 + 0.238313i
\(555\) 20.3764 + 5.98306i 0.864931 + 0.253967i
\(556\) 5.43657 + 6.27413i 0.230562 + 0.266083i
\(557\) −26.6767 + 17.1441i −1.13033 + 0.726418i −0.965629 0.259926i \(-0.916302\pi\)
−0.164700 + 0.986344i \(0.552666\pi\)
\(558\) −5.50614 + 6.35442i −0.233093 + 0.269004i
\(559\) −0.102513 + 0.712993i −0.00433584 + 0.0301564i
\(560\) −2.35683 + 0.692029i −0.0995944 + 0.0292436i
\(561\) 3.24337 + 2.08439i 0.136935 + 0.0880029i
\(562\) −0.163303 1.13580i −0.00688853 0.0479108i
\(563\) 14.4467 + 31.6339i 0.608857 + 1.33321i 0.923353 + 0.383953i \(0.125437\pi\)
−0.314495 + 0.949259i \(0.601835\pi\)
\(564\) 5.00941 + 10.9691i 0.210934 + 0.461882i
\(565\) 4.03041 + 28.0321i 0.169560 + 1.17932i
\(566\) 14.6169 + 9.39372i 0.614395 + 0.394848i
\(567\) −0.959493 + 0.281733i −0.0402949 + 0.0118317i
\(568\) −1.47006 + 10.2245i −0.0616824 + 0.429011i
\(569\) 4.34974 5.01987i 0.182351 0.210444i −0.657213 0.753705i \(-0.728265\pi\)
0.839564 + 0.543261i \(0.182810\pi\)
\(570\) 3.69817 2.37667i 0.154899 0.0995476i
\(571\) 10.5471 + 12.1720i 0.441383 + 0.509383i 0.932232 0.361861i \(-0.117859\pi\)
−0.490849 + 0.871245i \(0.663313\pi\)
\(572\) 0.0922027 + 0.0270732i 0.00385519 + 0.00113199i
\(573\) −0.289777 + 0.634522i −0.0121056 + 0.0265076i
\(574\) 4.79152 0.199994
\(575\) 0.422338 4.93882i 0.0176127 0.205963i
\(576\) 1.00000 0.0416667
\(577\) 15.0930 33.0491i 0.628330 1.37585i −0.280973 0.959716i \(-0.590657\pi\)
0.909303 0.416135i \(-0.136616\pi\)
\(578\) −8.32332 2.44395i −0.346204 0.101655i
\(579\) 4.40375 + 5.08220i 0.183014 + 0.211209i
\(580\) −6.13559 + 3.94311i −0.254767 + 0.163729i
\(581\) −5.97696 + 6.89778i −0.247966 + 0.286168i
\(582\) −1.67412 + 11.6437i −0.0693944 + 0.482649i
\(583\) 1.30944 0.384485i 0.0542313 0.0159238i
\(584\) −8.68448 5.58118i −0.359366 0.230951i
\(585\) 0.0251403 + 0.174854i 0.00103942 + 0.00722934i
\(586\) 0.948577 + 2.07709i 0.0391854 + 0.0858040i
\(587\) −0.269284 0.589649i −0.0111145 0.0243374i 0.903993 0.427547i \(-0.140622\pi\)
−0.915108 + 0.403209i \(0.867895\pi\)
\(588\) −0.142315 0.989821i −0.00586897 0.0408195i
\(589\) 12.6589 + 8.13541i 0.521603 + 0.335214i
\(590\) −30.6028 + 8.98581i −1.25990 + 0.369940i
\(591\) −1.61778 + 11.2519i −0.0665467 + 0.462843i
\(592\) 5.66171 6.53396i 0.232695 0.268544i
\(593\) 25.9909 16.7033i 1.06732 0.685923i 0.115723 0.993282i \(-0.463082\pi\)
0.951594 + 0.307359i \(0.0994452\pi\)
\(594\) 0.875021 + 1.00983i 0.0359025 + 0.0414338i
\(595\) −6.80031 1.99675i −0.278786 0.0818589i
\(596\) −3.81994 + 8.36450i −0.156471 + 0.342623i
\(597\) −1.69369 −0.0693180
\(598\) −0.344333 + 0.0198187i −0.0140808 + 0.000810445i
\(599\) 4.65195 0.190074 0.0950369 0.995474i \(-0.469703\pi\)
0.0950369 + 0.995474i \(0.469703\pi\)
\(600\) −0.429362 + 0.940171i −0.0175286 + 0.0383823i
\(601\) 14.9171 + 4.38006i 0.608481 + 0.178666i 0.571435 0.820647i \(-0.306387\pi\)
0.0370464 + 0.999314i \(0.488205\pi\)
\(602\) −6.55911 7.56962i −0.267330 0.308515i
\(603\) 1.71782 1.10398i 0.0699552 0.0449574i
\(604\) 8.03748 9.27575i 0.327040 0.377425i
\(605\) 3.22117 22.4037i 0.130959 0.910840i
\(606\) 8.97800 2.63618i 0.364706 0.107087i
\(607\) 10.0268 + 6.44384i 0.406976 + 0.261547i 0.728074 0.685498i \(-0.240416\pi\)
−0.321098 + 0.947046i \(0.604052\pi\)
\(608\) −0.254696 1.77145i −0.0103293 0.0718418i
\(609\) −1.23346 2.70090i −0.0499823 0.109446i
\(610\) 14.2475 + 31.1977i 0.576865 + 1.26316i
\(611\) 0.123420 + 0.858408i 0.00499305 + 0.0347275i
\(612\) 2.42732 + 1.55994i 0.0981185 + 0.0630569i
\(613\) −4.70161 + 1.38052i −0.189896 + 0.0557586i −0.375298 0.926904i \(-0.622460\pi\)
0.185402 + 0.982663i \(0.440641\pi\)
\(614\) 1.55437 10.8109i 0.0627291 0.436291i
\(615\) 7.70743 8.89485i 0.310794 0.358675i
\(616\) −1.12408 + 0.722401i −0.0452904 + 0.0291064i
\(617\) −12.4724 14.3939i −0.502119 0.579476i 0.446944 0.894562i \(-0.352512\pi\)
−0.949063 + 0.315086i \(0.897967\pi\)
\(618\) −1.16206 0.341213i −0.0467451 0.0137256i
\(619\) 6.70937 14.6915i 0.269672 0.590500i −0.725546 0.688174i \(-0.758413\pi\)
0.995219 + 0.0976733i \(0.0311400\pi\)
\(620\) −20.6531 −0.829449
\(621\) −4.17683 2.35671i −0.167610 0.0945715i
\(622\) 0.128486 0.00515183
\(623\) −3.36275 + 7.36339i −0.134726 + 0.295008i
\(624\) 0.0690040 + 0.0202614i 0.00276237 + 0.000811105i
\(625\) 19.0562 + 21.9920i 0.762247 + 0.879680i
\(626\) −0.498360 + 0.320277i −0.0199185 + 0.0128008i
\(627\) 1.56600 1.80726i 0.0625399 0.0721749i
\(628\) −0.305927 + 2.12777i −0.0122078 + 0.0849072i
\(629\) 23.9354 7.02806i 0.954366 0.280227i
\(630\) −2.06640 1.32799i −0.0823273 0.0529085i
\(631\) −5.23441 36.4061i −0.208379 1.44930i −0.778448 0.627709i \(-0.783993\pi\)
0.570070 0.821596i \(-0.306916\pi\)
\(632\) −2.18309 4.78030i −0.0868386 0.190150i
\(633\) 6.29993 + 13.7949i 0.250400 + 0.548299i
\(634\) −1.21397 8.44336i −0.0482130 0.335328i
\(635\) −19.4140 12.4766i −0.770420 0.495119i
\(636\) 0.979975 0.287747i 0.0388585 0.0114099i
\(637\) 0.0102349 0.0711851i 0.000405520 0.00282046i
\(638\) −2.59813 + 2.99840i −0.102861 + 0.118708i
\(639\) −8.68985 + 5.58463i −0.343765 + 0.220924i
\(640\) 1.60856 + 1.85637i 0.0635838 + 0.0733796i
\(641\) −32.6644 9.59112i −1.29016 0.378826i −0.436525 0.899692i \(-0.643791\pi\)
−0.853639 + 0.520865i \(0.825609\pi\)
\(642\) −2.29624 + 5.02807i −0.0906254 + 0.198442i
\(643\) 9.71405 0.383085 0.191542 0.981484i \(-0.438651\pi\)
0.191542 + 0.981484i \(0.438651\pi\)
\(644\) 2.92715 3.79892i 0.115346 0.149699i
\(645\) −24.6027 −0.968732
\(646\) 2.14513 4.69719i 0.0843991 0.184808i
\(647\) 45.7503 + 13.4335i 1.79863 + 0.528126i 0.997520 0.0703902i \(-0.0224244\pi\)
0.801111 + 0.598516i \(0.204243\pi\)
\(648\) 0.654861 + 0.755750i 0.0257254 + 0.0296886i
\(649\) −14.5958 + 9.38018i −0.572937 + 0.368204i
\(650\) −0.0486769 + 0.0561761i −0.00190926 + 0.00220341i
\(651\) 1.19660 8.32253i 0.0468984 0.326186i
\(652\) −8.87325 + 2.60542i −0.347503 + 0.102036i
\(653\) −12.6420 8.12455i −0.494721 0.317938i 0.269380 0.963034i \(-0.413181\pi\)
−0.764102 + 0.645096i \(0.776817\pi\)
\(654\) −2.31201 16.0804i −0.0904066 0.628792i
\(655\) 4.00689 + 8.77387i 0.156562 + 0.342824i
\(656\) −1.99047 4.35852i −0.0777148 0.170172i
\(657\) −1.46915 10.2182i −0.0573171 0.398649i
\(658\) −10.1445 6.51948i −0.395474 0.254156i
\(659\) 30.1891 8.86431i 1.17600 0.345304i 0.365369 0.930863i \(-0.380943\pi\)
0.810630 + 0.585558i \(0.199125\pi\)
\(660\) −0.467097 + 3.24873i −0.0181817 + 0.126457i
\(661\) 11.5924 13.3783i 0.450892 0.520357i −0.484107 0.875009i \(-0.660855\pi\)
0.934998 + 0.354652i \(0.115401\pi\)
\(662\) −10.3559 + 6.65536i −0.402495 + 0.258668i
\(663\) 0.135888 + 0.156823i 0.00527745 + 0.00609050i
\(664\) 8.75735 + 2.57139i 0.339851 + 0.0997893i
\(665\) −1.82617 + 3.99876i −0.0708159 + 0.155065i
\(666\) 8.64567 0.335013
\(667\) 5.16138 13.2716i 0.199850 0.513877i
\(668\) −9.74411 −0.377011
\(669\) 4.81440 10.5421i 0.186136 0.407580i
\(670\) 4.81261 + 1.41311i 0.185927 + 0.0545932i
\(671\) 12.2177 + 14.0999i 0.471658 + 0.544322i
\(672\) −0.841254 + 0.540641i −0.0324521 + 0.0208557i
\(673\) 2.46490 2.84464i 0.0950148 0.109653i −0.706251 0.707962i \(-0.749615\pi\)
0.801266 + 0.598309i \(0.204160\pi\)
\(674\) 4.72660 32.8742i 0.182062 1.26627i
\(675\) −0.991706 + 0.291191i −0.0381708 + 0.0112080i
\(676\) −10.9319 7.02553i −0.420459 0.270213i
\(677\) −6.93624 48.2426i −0.266581 1.85411i −0.480150 0.877187i \(-0.659418\pi\)
0.213568 0.976928i \(-0.431491\pi\)
\(678\) 4.78954 + 10.4876i 0.183941 + 0.402775i
\(679\) −4.88673 10.7004i −0.187535 0.410645i
\(680\) 1.00864 + 7.01526i 0.0386797 + 0.269023i
\(681\) 8.31316 + 5.34255i 0.318561 + 0.204727i
\(682\) −10.7798 + 3.16523i −0.412779 + 0.121203i
\(683\) −4.10894 + 28.5783i −0.157224 + 1.09352i 0.746494 + 0.665392i \(0.231736\pi\)
−0.903719 + 0.428127i \(0.859174\pi\)
\(684\) 1.17198 1.35254i 0.0448119 0.0517157i
\(685\) −13.6991 + 8.80389i −0.523417 + 0.336379i
\(686\) 0.654861 + 0.755750i 0.0250027 + 0.0288547i
\(687\) −9.74145 2.86035i −0.371659 0.109129i
\(688\) −4.16082 + 9.11091i −0.158630 + 0.347350i
\(689\) 0.0734523 0.00279831
\(690\) −2.34374 11.5447i −0.0892246 0.439498i
\(691\) −0.697433 −0.0265316 −0.0132658 0.999912i \(-0.504223\pi\)
−0.0132658 + 0.999912i \(0.504223\pi\)
\(692\) −3.14583 + 6.88841i −0.119587 + 0.261858i
\(693\) −1.28207 0.376449i −0.0487018 0.0143001i
\(694\) −15.1830 17.5221i −0.576339 0.665130i
\(695\) −17.1550 + 11.0248i −0.650725 + 0.418196i
\(696\) −1.94443 + 2.24399i −0.0737033 + 0.0850581i
\(697\) 1.96754 13.6845i 0.0745259 0.518339i
\(698\) 15.0427 4.41694i 0.569375 0.167184i
\(699\) 6.08706 + 3.91192i 0.230234 + 0.147962i
\(700\) −0.147093 1.02305i −0.00555959 0.0386678i
\(701\) 8.61883 + 18.8726i 0.325529 + 0.712808i 0.999667 0.0257965i \(-0.00821220\pi\)
−0.674139 + 0.738605i \(0.735485\pi\)
\(702\) 0.0298755 + 0.0654181i 0.00112758 + 0.00246905i
\(703\) −2.20202 15.3154i −0.0830507 0.577630i
\(704\) 1.12408 + 0.722401i 0.0423653 + 0.0272265i
\(705\) −28.4206 + 8.34505i −1.07038 + 0.314293i
\(706\) 4.52827 31.4948i 0.170424 1.18532i
\(707\) −6.12755 + 7.07157i −0.230450 + 0.265954i
\(708\) −10.9234 + 7.02007i −0.410528 + 0.263830i
\(709\) 5.46890 + 6.31145i 0.205389 + 0.237031i 0.849093 0.528243i \(-0.177149\pi\)
−0.643705 + 0.765274i \(0.722603\pi\)
\(710\) −24.3453 7.14842i −0.913662 0.268275i
\(711\) 2.18309 4.78030i 0.0818723 0.179275i
\(712\) 8.09491 0.303369
\(713\) 32.6138 23.7140i 1.22140 0.888095i
\(714\) −2.88536 −0.107982
\(715\) −0.0980554 + 0.214711i −0.00366706 + 0.00802975i
\(716\) −1.55067 0.455319i −0.0579514 0.0170161i
\(717\) 15.0480 + 17.3663i 0.561977 + 0.648556i
\(718\) −1.91245 + 1.22905i −0.0713718 + 0.0458679i
\(719\) 16.2764 18.7839i 0.607006 0.700523i −0.366179 0.930544i \(-0.619334\pi\)
0.973185 + 0.230022i \(0.0738797\pi\)
\(720\) −0.349573 + 2.43133i −0.0130278 + 0.0906104i
\(721\) 1.16206 0.341213i 0.0432775 0.0127074i
\(722\) 13.2894 + 8.54055i 0.494579 + 0.317846i
\(723\) −1.62754 11.3198i −0.0605290 0.420988i
\(724\) 9.93145 + 21.7468i 0.369099 + 0.808215i
\(725\) −1.27487 2.79158i −0.0473475 0.103677i
\(726\) −1.31137 9.12079i −0.0486696 0.338504i
\(727\) −18.4561 11.8610i −0.684500 0.439901i 0.151627 0.988438i \(-0.451549\pi\)
−0.836127 + 0.548537i \(0.815185\pi\)
\(728\) −0.0690040 + 0.0202614i −0.00255746 + 0.000750937i
\(729\) −0.142315 + 0.989821i −0.00527092 + 0.0366601i
\(730\) 16.6055 19.1638i 0.614599 0.709285i
\(731\) −24.3121 + 15.6245i −0.899217 + 0.577891i
\(732\) 9.14363 + 10.5523i 0.337958 + 0.390025i
\(733\) −21.2402 6.23668i −0.784524 0.230357i −0.135149 0.990825i \(-0.543151\pi\)
−0.649375 + 0.760468i \(0.724969\pi\)
\(734\) 6.88362 15.0730i 0.254079 0.556356i
\(735\) 2.45633 0.0906032
\(736\) −4.67160 1.08450i −0.172198 0.0399750i
\(737\) 2.72848 0.100505
\(738\) 1.99047 4.35852i 0.0732702 0.160439i
\(739\) −19.6563 5.77161i −0.723069 0.212312i −0.100567 0.994930i \(-0.532066\pi\)
−0.622502 + 0.782618i \(0.713884\pi\)
\(740\) 13.9070 + 16.0496i 0.511233 + 0.589995i
\(741\) 0.108276 0.0695846i 0.00397761 0.00255626i
\(742\) −0.668840 + 0.771882i −0.0245539 + 0.0283367i
\(743\) 6.24847 43.4590i 0.229234 1.59436i −0.472113 0.881538i \(-0.656509\pi\)
0.701347 0.712820i \(-0.252582\pi\)
\(744\) −8.06752 + 2.36884i −0.295770 + 0.0868458i
\(745\) −19.0015 12.2115i −0.696162 0.447396i
\(746\) 2.40320 + 16.7146i 0.0879873 + 0.611965i
\(747\) 3.79152 + 8.30227i 0.138724 + 0.303764i
\(748\) 1.60159 + 3.50699i 0.0585600 + 0.128228i
\(749\) −0.786657 5.47132i −0.0287438 0.199918i
\(750\) 8.19622 + 5.26739i 0.299284 + 0.192338i
\(751\) −5.17151 + 1.51849i −0.188711 + 0.0554105i −0.374722 0.927137i \(-0.622262\pi\)
0.186011 + 0.982548i \(0.440444\pi\)
\(752\) −1.71615 + 11.9361i −0.0625815 + 0.435264i
\(753\) 13.6374 15.7384i 0.496974 0.573539i
\(754\) −0.179639 + 0.115447i −0.00654208 + 0.00420434i
\(755\) 19.7427 + 22.7843i 0.718511 + 0.829206i
\(756\) −0.959493 0.281733i −0.0348964 0.0102465i
\(757\) 17.7306 38.8245i 0.644428 1.41110i −0.251919 0.967748i \(-0.581062\pi\)
0.896347 0.443353i \(-0.146211\pi\)
\(758\) −11.1803 −0.406086
\(759\) −2.99260 5.66647i −0.108624 0.205680i
\(760\) 4.39602 0.159460
\(761\) 13.3391 29.2086i 0.483542 1.05881i −0.497932 0.867216i \(-0.665907\pi\)
0.981474 0.191594i \(-0.0613656\pi\)
\(762\) −9.01450 2.64690i −0.326561 0.0958869i
\(763\) 10.6387 + 12.2777i 0.385146 + 0.444482i
\(764\) −0.586824 + 0.377129i −0.0212306 + 0.0136441i
\(765\) −4.64126 + 5.35630i −0.167805 + 0.193658i
\(766\) 3.18380 22.1438i 0.115035 0.800088i
\(767\) −0.895998 + 0.263089i −0.0323526 + 0.00949958i
\(768\) 0.841254 + 0.540641i 0.0303561 + 0.0195087i
\(769\) −0.328262 2.28311i −0.0118374 0.0823311i 0.983046 0.183357i \(-0.0586965\pi\)
−0.994884 + 0.101026i \(0.967787\pi\)
\(770\) −1.36345 2.98554i −0.0491353 0.107591i
\(771\) −0.605965 1.32688i −0.0218233 0.0477864i
\(772\) 0.957027 + 6.65627i 0.0344442 + 0.239564i
\(773\) −39.9131 25.6506i −1.43557 0.922588i −0.999746 0.0225581i \(-0.992819\pi\)
−0.435829 0.900030i \(-0.643545\pi\)
\(774\) −9.61032 + 2.82185i −0.345436 + 0.101429i
\(775\) 1.23677 8.60194i 0.0444262 0.308991i
\(776\) −7.70344 + 8.89025i −0.276538 + 0.319141i
\(777\) −7.27320 + 4.67420i −0.260925 + 0.167686i
\(778\) 3.85802 + 4.45239i 0.138317 + 0.159626i
\(779\) −8.22787 2.41592i −0.294794 0.0865594i
\(780\) −0.0733841 + 0.160689i −0.00262757 + 0.00575358i
\(781\) −13.8024 −0.493889
\(782\) −9.64771 9.91985i −0.345002 0.354733i
\(783\) −2.96922 −0.106111
\(784\) 0.415415 0.909632i 0.0148363 0.0324869i
\(785\) −5.06637 1.48762i −0.180826 0.0530954i
\(786\) 2.57150 + 2.96767i 0.0917225 + 0.105853i
\(787\) −12.2360 + 7.86361i −0.436167 + 0.280307i −0.740242 0.672341i \(-0.765289\pi\)
0.304075 + 0.952648i \(0.401653\pi\)
\(788\) −7.44422 + 8.59109i −0.265189 + 0.306045i
\(789\) −2.77855 + 19.3252i −0.0989189 + 0.687996i
\(790\) 12.3856 3.63675i 0.440661 0.129390i
\(791\) −9.69925 6.23333i −0.344866 0.221632i
\(792\) 0.190160 + 1.32259i 0.00675705 + 0.0469963i
\(793\) 0.417142 + 0.913414i 0.0148132 + 0.0324363i
\(794\) −8.09021 17.7151i −0.287111 0.628685i
\(795\) 0.357035 + 2.48323i 0.0126627 + 0.0880712i
\(796\) −1.42482 0.915676i −0.0505014 0.0324553i
\(797\) −38.6117 + 11.3374i −1.36770 + 0.401592i −0.881469 0.472241i \(-0.843445\pi\)
−0.486226 + 0.873833i \(0.661627\pi\)
\(798\) −0.254696 + 1.77145i −0.00901615 + 0.0627087i
\(799\) −22.7852 + 26.2955i −0.806083 + 0.930269i
\(800\) −0.869497 + 0.558792i −0.0307414 + 0.0197563i
\(801\) 5.30104 + 6.11772i 0.187303 + 0.216159i
\(802\) 3.71497 + 1.09081i 0.131180 + 0.0385179i
\(803\) 5.73019 12.5474i 0.202214 0.442787i
\(804\) 2.04198 0.0720151
\(805\) 8.21319 + 8.44486i 0.289477 + 0.297642i
\(806\) −0.604687 −0.0212992
\(807\) 6.80559 14.9022i 0.239568 0.524581i
\(808\) 8.97800 + 2.63618i 0.315845 + 0.0927404i
\(809\) −27.8408 32.1300i −0.978830 1.12963i −0.991552 0.129711i \(-0.958595\pi\)
0.0127214 0.999919i \(-0.495951\pi\)
\(810\) −2.06640 + 1.32799i −0.0726059 + 0.0466610i
\(811\) 28.1414 32.4769i 0.988177 1.14042i −0.00191544 0.999998i \(-0.500610\pi\)
0.990092 0.140419i \(-0.0448448\pi\)
\(812\) 0.422564 2.93900i 0.0148291 0.103139i
\(813\) 28.8598 8.47399i 1.01216 0.297196i
\(814\) 9.71841 + 6.24564i 0.340630 + 0.218910i
\(815\) −3.23280 22.4846i −0.113240 0.787601i
\(816\) 1.19862 + 2.62461i 0.0419601 + 0.0918799i
\(817\) 7.44647 + 16.3055i 0.260519 + 0.570457i
\(818\) −1.04153 7.24397i −0.0364161 0.253280i
\(819\) −0.0605005 0.0388813i −0.00211406 0.00135862i
\(820\) 11.2928 3.31587i 0.394363 0.115795i
\(821\) −0.638145 + 4.43840i −0.0222714 + 0.154901i −0.997922 0.0644279i \(-0.979478\pi\)
0.975651 + 0.219329i \(0.0703868\pi\)
\(822\) −4.34138 + 5.01022i −0.151423 + 0.174751i
\(823\) −20.4162 + 13.1207i −0.711664 + 0.457359i −0.845728 0.533614i \(-0.820833\pi\)
0.134064 + 0.990973i \(0.457197\pi\)
\(824\) −0.793117 0.915305i −0.0276295 0.0318862i
\(825\) −1.32511 0.389088i −0.0461345 0.0135463i
\(826\) 5.39405 11.8113i 0.187683 0.410968i
\(827\) 26.6919 0.928167 0.464083 0.885792i \(-0.346384\pi\)
0.464083 + 0.885792i \(0.346384\pi\)
\(828\) −2.23964 4.24076i −0.0778329 0.147376i
\(829\) −10.0282 −0.348295 −0.174147 0.984720i \(-0.555717\pi\)
−0.174147 + 0.984720i \(0.555717\pi\)
\(830\) −9.31324 + 20.3931i −0.323267 + 0.707856i
\(831\) −5.91668 1.73729i −0.205247 0.0602660i
\(832\) 0.0470957 + 0.0543513i 0.00163275 + 0.00188429i
\(833\) 2.42732 1.55994i 0.0841016 0.0540488i
\(834\) −5.43657 + 6.27413i −0.188253 + 0.217255i
\(835\) 3.40628 23.6912i 0.117879 0.819867i
\(836\) 2.29448 0.673719i 0.0793561 0.0233011i
\(837\) −7.07335 4.54577i −0.244491 0.157125i
\(838\) −1.99911 13.9041i −0.0690582 0.480310i
\(839\) 9.62546 + 21.0768i 0.332308 + 0.727652i 0.999857 0.0169133i \(-0.00538393\pi\)
−0.667549 + 0.744566i \(0.732657\pi\)
\(840\) −1.02040 2.23436i −0.0352071 0.0770927i
\(841\) 2.87244 + 19.9783i 0.0990498 + 0.688907i
\(842\) −4.47210 2.87404i −0.154119 0.0990461i
\(843\) 1.10100 0.323282i 0.0379204 0.0111344i
\(844\) −2.15826 + 15.0110i −0.0742903 + 0.516701i
\(845\) 20.9029 24.1232i 0.719082 0.829865i
\(846\) −10.1445 + 6.51948i −0.348776 + 0.224144i
\(847\) 6.03427 + 6.96392i 0.207340 + 0.239283i
\(848\) 0.979975 + 0.287747i 0.0336525 + 0.00988126i
\(849\) −7.21790 + 15.8050i −0.247718 + 0.542426i
\(850\) −2.98223 −0.102290
\(851\) −40.3891 9.37619i −1.38452 0.321412i
\(852\) −10.3296 −0.353888
\(853\) −7.99976 + 17.5170i −0.273907 + 0.599772i −0.995731 0.0923047i \(-0.970577\pi\)
0.721824 + 0.692076i \(0.243304\pi\)
\(854\) −13.3971 3.93375i −0.458440 0.134610i
\(855\) 2.87878 + 3.32229i 0.0984522 + 0.113620i
\(856\) −4.65010 + 2.98844i −0.158937 + 0.102143i
\(857\) −7.46109 + 8.61056i −0.254866 + 0.294131i −0.868735 0.495277i \(-0.835067\pi\)
0.613869 + 0.789408i \(0.289612\pi\)
\(858\) −0.0136758 + 0.0951171i −0.000466883 + 0.00324725i
\(859\) −5.02668 + 1.47597i −0.171508 + 0.0503593i −0.366359 0.930474i \(-0.619396\pi\)
0.194851 + 0.980833i \(0.437578\pi\)
\(860\) −20.6971 13.3012i −0.705767 0.453569i
\(861\) 0.681905 + 4.74275i 0.0232393 + 0.161633i
\(862\) 7.47203 + 16.3615i 0.254498 + 0.557274i
\(863\) 1.66917 + 3.65497i 0.0568191 + 0.124417i 0.935912 0.352234i \(-0.114578\pi\)
−0.879093 + 0.476651i \(0.841851\pi\)
\(864\) 0.142315 + 0.989821i 0.00484165 + 0.0336744i
\(865\) −15.6483 10.0566i −0.532059 0.341933i
\(866\) −21.6760 + 6.36464i −0.736580 + 0.216279i
\(867\) 1.23454 8.58641i 0.0419271 0.291610i
\(868\) 5.50614 6.35442i 0.186891 0.215683i
\(869\) 5.90726 3.79636i 0.200390 0.128783i
\(870\) −4.77616 5.51198i −0.161927 0.186874i
\(871\) 0.140905 + 0.0413734i 0.00477437 + 0.00140188i
\(872\) 6.74872 14.7776i 0.228540 0.500434i
\(873\) −11.7635 −0.398134
\(874\) −6.94186 + 5.04752i −0.234812 + 0.170735i
\(875\) −9.74287 −0.329369
\(876\) 4.28844 9.39037i 0.144893 0.317271i
\(877\) 16.7651 + 4.92267i 0.566116 + 0.166227i 0.552252 0.833677i \(-0.313769\pi\)
0.0138640 + 0.999904i \(0.495587\pi\)
\(878\) 16.4440 + 18.9774i 0.554959 + 0.640457i
\(879\) −1.92096 + 1.23452i −0.0647922 + 0.0416394i
\(880\) −2.14934 + 2.48047i −0.0724544 + 0.0836168i
\(881\) 1.01419 7.05382i 0.0341688 0.237649i −0.965579 0.260110i \(-0.916241\pi\)
0.999748 + 0.0224611i \(0.00715018\pi\)
\(882\) 0.959493 0.281733i 0.0323078 0.00948643i
\(883\) −33.3556 21.4364i −1.12251 0.721391i −0.158523 0.987355i \(-0.550673\pi\)
−0.963983 + 0.265964i \(0.914310\pi\)
\(884\) 0.0295313 + 0.205395i 0.000993245 + 0.00690817i
\(885\) −13.2496 29.0125i −0.445380 0.975246i
\(886\) 8.99992 + 19.7071i 0.302358 + 0.662072i
\(887\) −0.128992 0.897160i −0.00433113 0.0301237i 0.987541 0.157360i \(-0.0502984\pi\)
−0.991872 + 0.127237i \(0.959389\pi\)
\(888\) 7.27320 + 4.67420i 0.244073 + 0.156856i
\(889\) 9.01450 2.64690i 0.302337 0.0887741i
\(890\) −2.82976 + 19.6814i −0.0948537 + 0.659722i
\(891\) −0.875021 + 1.00983i −0.0293143 + 0.0338305i
\(892\) 9.74961 6.26569i 0.326441 0.209791i
\(893\) 14.1327 + 16.3100i 0.472933 + 0.545794i
\(894\) −8.82299 2.59066i −0.295085 0.0866448i
\(895\) 1.64910 3.61103i 0.0551234 0.120703i
\(896\) −1.00000 −0.0334077
\(897\) −0.0686206 0.338007i −0.00229117 0.0112857i
\(898\) 21.0370 0.702013
\(899\) 10.3711 22.7094i 0.345894 0.757402i
\(900\) −0.991706 0.291191i −0.0330569 0.00970637i
\(901\) 1.92984 + 2.22716i 0.0642924 + 0.0741974i
\(902\) 5.38605 3.46140i 0.179336 0.115252i
\(903\) 6.55911 7.56962i 0.218274 0.251901i
\(904\) −1.64082 + 11.4122i −0.0545729 + 0.379563i
\(905\) −56.3455 + 16.5445i −1.87299 + 0.549959i
\(906\) 10.3252 + 6.63559i 0.343031 + 0.220453i
\(907\) 2.76823 + 19.2534i 0.0919175 + 0.639300i 0.982746 + 0.184960i \(0.0592157\pi\)
−0.890829 + 0.454340i \(0.849875\pi\)
\(908\) 4.10508 + 8.98887i 0.136232 + 0.298306i
\(909\) 3.88705 + 8.51145i 0.128925 + 0.282307i
\(910\) −0.0251403 0.174854i −0.000833392 0.00579637i
\(911\) 11.4144 + 7.33557i 0.378175 + 0.243038i 0.715894 0.698209i \(-0.246019\pi\)
−0.337720 + 0.941247i \(0.609656\pi\)
\(912\) 1.71717 0.504207i 0.0568613 0.0166960i
\(913\) −1.73561 + 12.0714i −0.0574401 + 0.399505i
\(914\) 4.57569 5.28063i 0.151351 0.174668i
\(915\) −28.8525 + 18.5424i −0.953835 + 0.612992i
\(916\) −6.64861 7.67290i −0.219676 0.253520i
\(917\) −3.76773 1.10631i −0.124422 0.0365335i
\(918\) −1.19862 + 2.62461i −0.0395604 + 0.0866252i
\(919\) 43.9635 1.45022 0.725110 0.688633i \(-0.241789\pi\)
0.725110 + 0.688633i \(0.241789\pi\)
\(920\) 4.26983 10.9791i 0.140772 0.361970i
\(921\) 10.9220 0.359893
\(922\) −6.59951 + 14.4509i −0.217343 + 0.475915i
\(923\) −0.712787 0.209293i −0.0234617 0.00688896i
\(924\) −0.875021 1.00983i −0.0287861 0.0332209i
\(925\) −7.51739 + 4.83113i −0.247170 + 0.158847i
\(926\) 15.4863 17.8721i 0.508911 0.587315i
\(927\) 0.172361 1.19880i 0.00566107 0.0393736i
\(928\) −2.84895 + 0.836526i −0.0935212 + 0.0274603i
\(929\) 0.709841 + 0.456187i 0.0232891 + 0.0149670i 0.552234 0.833689i \(-0.313776\pi\)
−0.528944 + 0.848656i \(0.677412\pi\)
\(930\) −2.93924 20.4429i −0.0963816 0.670349i
\(931\) −0.743455 1.62794i −0.0243657 0.0533535i
\(932\) 3.00582 + 6.58183i 0.0984589 + 0.215595i
\(933\) 0.0182855 + 0.127178i 0.000598640 + 0.00416363i
\(934\) −34.8996 22.4286i −1.14195 0.733887i
\(935\) −9.08654 + 2.66805i −0.297162 + 0.0872545i
\(936\) −0.0102349 + 0.0711851i −0.000334537 + 0.00232676i
\(937\) −0.991379 + 1.14411i −0.0323870 + 0.0373765i −0.771712 0.635972i \(-0.780599\pi\)
0.739325 + 0.673349i \(0.235145\pi\)
\(938\) −1.71782 + 1.10398i −0.0560889 + 0.0360462i
\(939\) −0.387941 0.447707i −0.0126600 0.0146104i
\(940\) −28.4206 8.34505i −0.926978 0.272185i
\(941\) −4.27194 + 9.35424i −0.139261 + 0.304940i −0.966393 0.257068i \(-0.917244\pi\)
0.827132 + 0.562008i \(0.189971\pi\)
\(942\) −2.14965 −0.0700394
\(943\) −14.0255 + 18.2026i −0.456733 + 0.592759i
\(944\) −12.9847 −0.422617
\(945\) 1.02040 2.23436i 0.0331935 0.0726837i
\(946\) −12.8413 3.77053i −0.417505 0.122591i
\(947\) 24.2159 + 27.9467i 0.786912 + 0.908145i 0.997588 0.0694111i \(-0.0221120\pi\)
−0.210676 + 0.977556i \(0.567567\pi\)
\(948\) 4.42096 2.84118i 0.143586 0.0922771i
\(949\) 0.486181 0.561083i 0.0157821 0.0182135i
\(950\) −0.263247 + 1.83092i −0.00854087 + 0.0594030i
\(951\) 8.18465 2.40323i 0.265405 0.0779301i
\(952\) −2.42732 1.55994i −0.0786698 0.0505580i
\(953\) −8.44273 58.7205i −0.273487 1.90214i −0.410986 0.911642i \(-0.634815\pi\)
0.137499 0.990502i \(-0.456094\pi\)
\(954\) 0.424283 + 0.929050i 0.0137367 + 0.0300791i
\(955\) −0.711788 1.55860i −0.0230329 0.0504351i
\(956\) 3.27024 + 22.7450i 0.105767 + 0.735626i
\(957\) −3.33764 2.14497i −0.107890 0.0693370i
\(958\) 0.0970665 0.0285013i 0.00313607 0.000920835i
\(959\) 0.943471 6.56199i 0.0304663 0.211898i
\(960\) −1.60856 + 1.85637i −0.0519159 + 0.0599142i
\(961\) 33.3946 21.4614i 1.07725 0.692304i
\(962\) 0.407174 + 0.469904i 0.0131278 + 0.0151503i
\(963\) −5.30368 1.55730i −0.170909 0.0501833i
\(964\) 4.75078 10.4028i 0.153012 0.335050i
\(965\) −16.5181 −0.531738
\(966\) 4.17683 + 2.35671i 0.134387 + 0.0758259i
\(967\) 19.9606 0.641889 0.320945 0.947098i \(-0.396000\pi\)
0.320945 + 0.947098i \(0.396000\pi\)
\(968\) 3.82788 8.38188i 0.123033 0.269404i
\(969\) 4.95466 + 1.45482i 0.159167 + 0.0467355i
\(970\) −18.9222 21.8374i −0.607556 0.701157i
\(971\) −31.5559 + 20.2798i −1.01268 + 0.650808i −0.938085 0.346406i \(-0.887402\pi\)
−0.0745928 + 0.997214i \(0.523766\pi\)
\(972\) −0.654861 + 0.755750i −0.0210047 + 0.0242407i
\(973\) 1.18148 8.21737i 0.0378765 0.263437i
\(974\) 39.6778 11.6505i 1.27136 0.373305i
\(975\) −0.0625317 0.0401867i −0.00200262 0.00128700i
\(976\) 1.98710 + 13.8206i 0.0636055 + 0.442386i
\(977\) 0.426743 + 0.934438i 0.0136527 + 0.0298953i 0.916336 0.400411i \(-0.131133\pi\)
−0.902683 + 0.430307i \(0.858405\pi\)
\(978\) −3.84170 8.41214i −0.122844 0.268991i
\(979\) 1.53933 + 10.7063i 0.0491972 + 0.342174i
\(980\) 2.06640 + 1.32799i 0.0660087 + 0.0424212i
\(981\) 15.5877 4.57695i 0.497675 0.146131i
\(982\) −5.82801 + 40.5347i −0.185979 + 1.29351i
\(983\) −10.3362 + 11.9286i −0.329674 + 0.380464i −0.896253 0.443544i \(-0.853721\pi\)
0.566579 + 0.824007i \(0.308267\pi\)
\(984\) 4.03089 2.59049i 0.128500 0.0825819i
\(985\) −18.2855 21.1026i −0.582624 0.672384i
\(986\) −8.22023 2.41368i −0.261785 0.0768672i
\(987\) 5.00941 10.9691i 0.159451 0.349150i
\(988\) 0.128708 0.00409474
\(989\) 47.9559 2.76018i 1.52491 0.0877688i
\(990\) −3.28214 −0.104313
\(991\) −23.9001 + 52.3339i −0.759211 + 1.66244i −0.0101430 + 0.999949i \(0.503229\pi\)
−0.749068 + 0.662493i \(0.769499\pi\)
\(992\) −8.06752 2.36884i −0.256144 0.0752107i
\(993\) −8.06142 9.30337i −0.255821 0.295234i
\(994\) 8.68985 5.58463i 0.275625 0.177134i
\(995\) 2.72439 3.14411i 0.0863689 0.0996751i
\(996\) −1.29892 + 9.03416i −0.0411578 + 0.286258i
\(997\) −29.9817 + 8.80341i −0.949529 + 0.278807i −0.719591 0.694399i \(-0.755671\pi\)
−0.229938 + 0.973205i \(0.573852\pi\)
\(998\) −20.6615 13.2784i −0.654029 0.420319i
\(999\) 1.23041 + 8.55767i 0.0389284 + 0.270753i
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.673.2 yes 20
23.4 even 11 inner 966.2.q.e.211.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.q.e.211.2 20 23.4 even 11 inner
966.2.q.e.673.2 yes 20 1.1 even 1 trivial