Properties

Label 169.2.h.a.12.1
Level $169$
Weight $2$
Character 169.12
Analytic conductor $1.349$
Analytic rank $0$
Dimension $168$
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] = [169,2,Mod(12,169)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(169, base_ring=CyclotomicField(26))
 
chi = DirichletCharacter(H, H._module([21]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.12");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 169.h (of order \(26\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.34947179416\)
Analytic rank: \(0\)
Dimension: \(168\)
Relative dimension: \(14\) over \(\Q(\zeta_{26})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label 12.1
Character \(\chi\) \(=\) 169.12
Dual form 169.2.h.a.155.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.11580 + 1.46043i) q^{2} +(0.527540 + 0.276874i) q^{3} +(1.63454 - 4.30994i) q^{4} +(0.267437 + 0.301873i) q^{5} +(-1.52053 + 0.184625i) q^{6} +(-1.09769 - 4.45349i) q^{7} +(1.60549 + 6.51374i) q^{8} +(-1.50256 - 2.17683i) q^{9} +O(q^{10})\) \(q+(-2.11580 + 1.46043i) q^{2} +(0.527540 + 0.276874i) q^{3} +(1.63454 - 4.30994i) q^{4} +(0.267437 + 0.301873i) q^{5} +(-1.52053 + 0.184625i) q^{6} +(-1.09769 - 4.45349i) q^{7} +(1.60549 + 6.51374i) q^{8} +(-1.50256 - 2.17683i) q^{9} +(-1.00671 - 0.248131i) q^{10} +(-3.52993 - 2.43653i) q^{11} +(2.05560 - 1.82110i) q^{12} +(2.38617 - 2.70299i) q^{13} +(8.82651 + 7.81961i) q^{14} +(0.0575024 + 0.233296i) q^{15} +(-6.00930 - 5.32377i) q^{16} +(0.317199 - 0.0781826i) q^{17} +(6.35822 + 2.41135i) q^{18} +7.41697i q^{19} +(1.73819 - 0.659209i) q^{20} +(0.653983 - 2.65331i) q^{21} +11.0270 q^{22} +4.72712 q^{23} +(-0.956526 + 3.88078i) q^{24} +(0.583078 - 4.80208i) q^{25} +(-1.10113 + 9.20384i) q^{26} +(-0.405391 - 3.33870i) q^{27} +(-20.9885 - 2.54846i) q^{28} +(1.32739 + 1.92306i) q^{29} +(-0.462377 - 0.409631i) q^{30} +(-6.98666 + 0.848334i) q^{31} +(7.16995 + 0.870590i) q^{32} +(-1.18756 - 2.26271i) q^{33} +(-0.556950 + 0.628667i) q^{34} +(1.05083 - 1.52239i) q^{35} +(-11.8380 + 2.91780i) q^{36} +(5.68052 - 0.689740i) q^{37} +(-10.8320 - 15.6928i) q^{38} +(2.00719 - 0.765267i) q^{39} +(-1.53696 + 2.22667i) q^{40} +(0.952870 - 1.81554i) q^{41} +(2.49129 + 6.56899i) q^{42} +(-0.0711358 + 0.585856i) q^{43} +(-16.2711 + 11.2311i) q^{44} +(0.255288 - 1.03574i) q^{45} +(-10.0016 + 6.90363i) q^{46} +(-3.13944 + 1.19063i) q^{47} +(-1.69613 - 4.47232i) q^{48} +(-12.4305 + 6.52402i) q^{49} +(5.77944 + 11.0118i) q^{50} +(0.188982 + 0.0465798i) q^{51} +(-7.74944 - 14.7024i) q^{52} +(2.89798 - 0.714288i) q^{53} +(5.73367 + 6.47198i) q^{54} +(-0.208507 - 1.71721i) q^{55} +(27.2466 - 14.3001i) q^{56} +(-2.05357 + 3.91275i) q^{57} +(-5.61700 - 2.13025i) q^{58} +(-1.98420 - 2.23970i) q^{59} +(1.09948 + 0.133501i) q^{60} +(5.12017 + 1.26201i) q^{61} +(13.5435 - 11.9985i) q^{62} +(-8.04515 + 9.08109i) q^{63} +(-2.22415 + 1.16732i) q^{64} +(1.45411 - 0.00255734i) q^{65} +(5.81719 + 3.05310i) q^{66} +(10.2403 - 3.88365i) q^{67} +(0.181514 - 1.49490i) q^{68} +(2.49374 + 1.30882i) q^{69} +4.75574i q^{70} +(3.85918 - 7.35306i) q^{71} +(11.7670 - 13.2821i) q^{72} +(4.85815 + 3.35334i) q^{73} +(-11.0115 + 9.75536i) q^{74} +(1.63717 - 2.37185i) q^{75} +(31.9667 + 12.1234i) q^{76} +(-6.97632 + 18.3951i) q^{77} +(-3.12920 + 4.55052i) q^{78} +(-0.0582887 - 0.153695i) q^{79} -3.23782i q^{80} +(-2.10330 + 5.54593i) q^{81} +(0.635393 + 5.23293i) q^{82} +(-1.42817 - 2.72115i) q^{83} +(-10.3667 - 7.15559i) q^{84} +(0.108432 + 0.0748451i) q^{85} +(-0.705094 - 1.34344i) q^{86} +(0.167807 + 1.38201i) q^{87} +(10.2037 - 26.9049i) q^{88} -3.71704i q^{89} +(0.972496 + 2.56426i) q^{90} +(-14.6570 - 7.65976i) q^{91} +(7.72668 - 20.3736i) q^{92} +(-3.92062 - 1.48690i) q^{93} +(4.90360 - 7.10409i) q^{94} +(-2.23899 + 1.98357i) q^{95} +(3.54139 + 2.44445i) q^{96} +(7.01212 - 7.91505i) q^{97} +(16.7725 - 31.9574i) q^{98} +11.3451i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{21}{26}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.11580 + 1.46043i −1.49610 + 1.03268i −0.511216 + 0.859452i \(0.670805\pi\)
−0.984881 + 0.173229i \(0.944580\pi\)
\(3\) 0.527540 + 0.276874i 0.304575 + 0.159853i 0.610086 0.792335i \(-0.291135\pi\)
−0.305511 + 0.952189i \(0.598827\pi\)
\(4\) 1.63454 4.30994i 0.817272 2.15497i
\(5\) 0.267437 + 0.301873i 0.119601 + 0.135002i 0.805262 0.592920i \(-0.202025\pi\)
−0.685660 + 0.727922i \(0.740486\pi\)
\(6\) −1.52053 + 0.184625i −0.620752 + 0.0753729i
\(7\) −1.09769 4.45349i −0.414887 1.68326i −0.691577 0.722302i \(-0.743084\pi\)
0.276691 0.960959i \(-0.410762\pi\)
\(8\) 1.60549 + 6.51374i 0.567628 + 2.30296i
\(9\) −1.50256 2.17683i −0.500852 0.725609i
\(10\) −1.00671 0.248131i −0.318349 0.0784660i
\(11\) −3.52993 2.43653i −1.06431 0.734642i −0.0988292 0.995104i \(-0.531510\pi\)
−0.965484 + 0.260462i \(0.916125\pi\)
\(12\) 2.05560 1.82110i 0.593400 0.525706i
\(13\) 2.38617 2.70299i 0.661805 0.749676i
\(14\) 8.82651 + 7.81961i 2.35898 + 2.08988i
\(15\) 0.0575024 + 0.233296i 0.0148471 + 0.0602369i
\(16\) −6.00930 5.32377i −1.50232 1.33094i
\(17\) 0.317199 0.0781826i 0.0769321 0.0189621i −0.200662 0.979661i \(-0.564309\pi\)
0.277594 + 0.960699i \(0.410463\pi\)
\(18\) 6.35822 + 2.41135i 1.49865 + 0.568362i
\(19\) 7.41697i 1.70157i 0.525514 + 0.850785i \(0.323873\pi\)
−0.525514 + 0.850785i \(0.676127\pi\)
\(20\) 1.73819 0.659209i 0.388672 0.147404i
\(21\) 0.653983 2.65331i 0.142711 0.579001i
\(22\) 11.0270 2.35097
\(23\) 4.72712 0.985672 0.492836 0.870122i \(-0.335960\pi\)
0.492836 + 0.870122i \(0.335960\pi\)
\(24\) −0.956526 + 3.88078i −0.195250 + 0.792161i
\(25\) 0.583078 4.80208i 0.116616 0.960416i
\(26\) −1.10113 + 9.20384i −0.215949 + 1.80502i
\(27\) −0.405391 3.33870i −0.0780176 0.642533i
\(28\) −20.9885 2.54846i −3.96645 0.481614i
\(29\) 1.32739 + 1.92306i 0.246491 + 0.357103i 0.926627 0.375982i \(-0.122695\pi\)
−0.680136 + 0.733086i \(0.738079\pi\)
\(30\) −0.462377 0.409631i −0.0844182 0.0747880i
\(31\) −6.98666 + 0.848334i −1.25484 + 0.152365i −0.720830 0.693112i \(-0.756239\pi\)
−0.534011 + 0.845477i \(0.679316\pi\)
\(32\) 7.16995 + 0.870590i 1.26748 + 0.153900i
\(33\) −1.18756 2.26271i −0.206728 0.393888i
\(34\) −0.556950 + 0.628667i −0.0955161 + 0.107815i
\(35\) 1.05083 1.52239i 0.177623 0.257331i
\(36\) −11.8380 + 2.91780i −1.97300 + 0.486300i
\(37\) 5.68052 0.689740i 0.933871 0.113392i 0.360565 0.932734i \(-0.382584\pi\)
0.573306 + 0.819341i \(0.305661\pi\)
\(38\) −10.8320 15.6928i −1.75718 2.54571i
\(39\) 2.00719 0.765267i 0.321408 0.122541i
\(40\) −1.53696 + 2.22667i −0.243014 + 0.352067i
\(41\) 0.952870 1.81554i 0.148813 0.283540i −0.799626 0.600498i \(-0.794969\pi\)
0.948440 + 0.316958i \(0.102661\pi\)
\(42\) 2.49129 + 6.56899i 0.384414 + 1.01362i
\(43\) −0.0711358 + 0.585856i −0.0108481 + 0.0893422i −0.997127 0.0757435i \(-0.975867\pi\)
0.986279 + 0.165086i \(0.0527901\pi\)
\(44\) −16.2711 + 11.2311i −2.45296 + 1.69316i
\(45\) 0.255288 1.03574i 0.0380561 0.154400i
\(46\) −10.0016 + 6.90363i −1.47466 + 1.01789i
\(47\) −3.13944 + 1.19063i −0.457935 + 0.173672i −0.572776 0.819712i \(-0.694133\pi\)
0.114841 + 0.993384i \(0.463364\pi\)
\(48\) −1.69613 4.47232i −0.244815 0.645524i
\(49\) −12.4305 + 6.52402i −1.77578 + 0.932002i
\(50\) 5.77944 + 11.0118i 0.817336 + 1.55730i
\(51\) 0.188982 + 0.0465798i 0.0264628 + 0.00652248i
\(52\) −7.74944 14.7024i −1.07465 2.03886i
\(53\) 2.89798 0.714288i 0.398068 0.0981149i −0.0351996 0.999380i \(-0.511207\pi\)
0.433268 + 0.901265i \(0.357361\pi\)
\(54\) 5.73367 + 6.47198i 0.780254 + 0.880725i
\(55\) −0.208507 1.71721i −0.0281151 0.231548i
\(56\) 27.2466 14.3001i 3.64098 1.91093i
\(57\) −2.05357 + 3.91275i −0.272002 + 0.518256i
\(58\) −5.61700 2.13025i −0.737548 0.279715i
\(59\) −1.98420 2.23970i −0.258321 0.291584i 0.605015 0.796214i \(-0.293167\pi\)
−0.863335 + 0.504631i \(0.831629\pi\)
\(60\) 1.09948 + 0.133501i 0.141943 + 0.0172350i
\(61\) 5.12017 + 1.26201i 0.655570 + 0.161583i 0.553051 0.833148i \(-0.313464\pi\)
0.102519 + 0.994731i \(0.467310\pi\)
\(62\) 13.5435 11.9985i 1.72002 1.52380i
\(63\) −8.04515 + 9.08109i −1.01359 + 1.14411i
\(64\) −2.22415 + 1.16732i −0.278019 + 0.145915i
\(65\) 1.45411 0.00255734i 0.180360 0.000317199i
\(66\) 5.81719 + 3.05310i 0.716047 + 0.375810i
\(67\) 10.2403 3.88365i 1.25106 0.474463i 0.361965 0.932192i \(-0.382106\pi\)
0.889092 + 0.457728i \(0.151337\pi\)
\(68\) 0.181514 1.49490i 0.0220118 0.181283i
\(69\) 2.49374 + 1.30882i 0.300211 + 0.157563i
\(70\) 4.75574i 0.568419i
\(71\) 3.85918 7.35306i 0.458001 0.872647i −0.541489 0.840708i \(-0.682139\pi\)
0.999490 0.0319395i \(-0.0101684\pi\)
\(72\) 11.7670 13.2821i 1.38675 1.56532i
\(73\) 4.85815 + 3.35334i 0.568604 + 0.392479i 0.817394 0.576078i \(-0.195418\pi\)
−0.248791 + 0.968557i \(0.580033\pi\)
\(74\) −11.0115 + 9.75536i −1.28006 + 1.13404i
\(75\) 1.63717 2.37185i 0.189044 0.273878i
\(76\) 31.9667 + 12.1234i 3.66683 + 1.39065i
\(77\) −6.97632 + 18.3951i −0.795026 + 2.09631i
\(78\) −3.12920 + 4.55052i −0.354312 + 0.515245i
\(79\) −0.0582887 0.153695i −0.00655800 0.0172920i 0.931697 0.363236i \(-0.118328\pi\)
−0.938255 + 0.345944i \(0.887559\pi\)
\(80\) 3.23782i 0.361999i
\(81\) −2.10330 + 5.54593i −0.233700 + 0.616215i
\(82\) 0.635393 + 5.23293i 0.0701674 + 0.577880i
\(83\) −1.42817 2.72115i −0.156762 0.298685i 0.794390 0.607408i \(-0.207791\pi\)
−0.951152 + 0.308723i \(0.900098\pi\)
\(84\) −10.3667 7.15559i −1.13109 0.780739i
\(85\) 0.108432 + 0.0748451i 0.0117611 + 0.00811809i
\(86\) −0.705094 1.34344i −0.0760322 0.144867i
\(87\) 0.167807 + 1.38201i 0.0179908 + 0.148167i
\(88\) 10.2037 26.9049i 1.08772 2.86807i
\(89\) 3.71704i 0.394006i −0.980403 0.197003i \(-0.936879\pi\)
0.980403 0.197003i \(-0.0631208\pi\)
\(90\) 0.972496 + 2.56426i 0.102510 + 0.270297i
\(91\) −14.6570 7.65976i −1.53647 0.802961i
\(92\) 7.72668 20.3736i 0.805562 2.12409i
\(93\) −3.92062 1.48690i −0.406550 0.154184i
\(94\) 4.90360 7.10409i 0.505767 0.732731i
\(95\) −2.23899 + 1.98357i −0.229715 + 0.203510i
\(96\) 3.54139 + 2.44445i 0.361442 + 0.249485i
\(97\) 7.01212 7.91505i 0.711973 0.803652i −0.275523 0.961295i \(-0.588851\pi\)
0.987496 + 0.157643i \(0.0503895\pi\)
\(98\) 16.7725 31.9574i 1.69428 3.22818i
\(99\) 11.3451i 1.14022i
\(100\) −19.7436 10.3622i −1.97436 1.03622i
\(101\) −2.03905 + 16.7931i −0.202893 + 1.67097i 0.434682 + 0.900584i \(0.356861\pi\)
−0.637575 + 0.770388i \(0.720062\pi\)
\(102\) −0.467875 + 0.177442i −0.0463265 + 0.0175693i
\(103\) −8.41005 4.41394i −0.828667 0.434918i −0.00362769 0.999993i \(-0.501155\pi\)
−0.825039 + 0.565075i \(0.808847\pi\)
\(104\) 21.4376 + 11.2033i 2.10213 + 1.09857i
\(105\) 0.975864 0.512173i 0.0952346 0.0499830i
\(106\) −5.08838 + 5.74359i −0.494227 + 0.557867i
\(107\) −10.7888 + 9.55808i −1.04300 + 0.924014i −0.997188 0.0749361i \(-0.976125\pi\)
−0.0458080 + 0.998950i \(0.514586\pi\)
\(108\) −15.0522 3.71004i −1.44840 0.356999i
\(109\) 6.21099 + 0.754151i 0.594905 + 0.0722346i 0.412451 0.910980i \(-0.364673\pi\)
0.182454 + 0.983214i \(0.441596\pi\)
\(110\) 2.94903 + 3.32876i 0.281179 + 0.317385i
\(111\) 3.18767 + 1.20892i 0.302560 + 0.114746i
\(112\) −17.1131 + 32.6062i −1.61703 + 3.08100i
\(113\) 6.00418 3.15124i 0.564826 0.296443i −0.158039 0.987433i \(-0.550517\pi\)
0.722865 + 0.690989i \(0.242825\pi\)
\(114\) −1.36936 11.2777i −0.128252 1.05625i
\(115\) 1.26420 + 1.42699i 0.117888 + 0.133068i
\(116\) 10.4580 2.57765i 0.970997 0.239329i
\(117\) −9.46931 1.13289i −0.875438 0.104735i
\(118\) 7.46909 + 1.84097i 0.687586 + 0.169475i
\(119\) −0.696371 1.32682i −0.0638362 0.121630i
\(120\) −1.42731 + 0.749112i −0.130295 + 0.0683843i
\(121\) 2.62304 + 6.91639i 0.238458 + 0.628763i
\(122\) −12.6763 + 4.80750i −1.14766 + 0.435250i
\(123\) 1.00535 0.693946i 0.0906497 0.0625710i
\(124\) −7.76373 + 31.4987i −0.697204 + 2.82867i
\(125\) 3.26510 2.25373i 0.292039 0.201580i
\(126\) 3.75961 30.9632i 0.334933 2.75842i
\(127\) 1.69508 + 4.46956i 0.150414 + 0.396610i 0.988952 0.148233i \(-0.0473586\pi\)
−0.838538 + 0.544843i \(0.816589\pi\)
\(128\) −3.71197 + 7.07257i −0.328095 + 0.625132i
\(129\) −0.199735 + 0.289367i −0.0175857 + 0.0254773i
\(130\) −3.07288 + 2.12904i −0.269509 + 0.186729i
\(131\) −12.1194 17.5580i −1.05888 1.53405i −0.827725 0.561134i \(-0.810365\pi\)
−0.231155 0.972917i \(-0.574250\pi\)
\(132\) −11.6933 + 1.41982i −1.01777 + 0.123580i
\(133\) 33.0314 8.14151i 2.86419 0.705959i
\(134\) −15.9947 + 23.1724i −1.38173 + 2.00179i
\(135\) 0.899448 1.01527i 0.0774122 0.0873803i
\(136\) 1.01852 + 1.94063i 0.0873376 + 0.166408i
\(137\) 15.3613 + 1.86520i 1.31240 + 0.159354i 0.746648 0.665220i \(-0.231662\pi\)
0.565754 + 0.824574i \(0.308585\pi\)
\(138\) −7.18770 + 0.872745i −0.611858 + 0.0742930i
\(139\) 11.4342 + 10.1299i 0.969839 + 0.859203i 0.990068 0.140593i \(-0.0449008\pi\)
−0.0202281 + 0.999795i \(0.506439\pi\)
\(140\) −4.84377 7.01742i −0.409374 0.593080i
\(141\) −1.98584 0.241124i −0.167238 0.0203063i
\(142\) 2.57338 + 21.1937i 0.215953 + 1.77853i
\(143\) −15.0090 + 3.72739i −1.25511 + 0.311700i
\(144\) −2.55963 + 21.0805i −0.213303 + 1.75671i
\(145\) −0.225528 + 0.915001i −0.0187290 + 0.0759867i
\(146\) −15.1762 −1.25599
\(147\) −8.36390 −0.689843
\(148\) 6.31232 25.6101i 0.518869 2.10514i
\(149\) 0.396349 0.150315i 0.0324702 0.0123143i −0.338316 0.941032i \(-0.609857\pi\)
0.370787 + 0.928718i \(0.379088\pi\)
\(150\) 7.40934i 0.604970i
\(151\) 12.3213 + 4.67283i 1.00269 + 0.380270i 0.800666 0.599111i \(-0.204479\pi\)
0.202023 + 0.979381i \(0.435248\pi\)
\(152\) −48.3122 + 11.9079i −3.91864 + 0.965858i
\(153\) −0.646799 0.573014i −0.0522906 0.0463254i
\(154\) −12.1042 49.1087i −0.975385 3.95729i
\(155\) −2.12458 1.88221i −0.170650 0.151183i
\(156\) −0.0174141 9.90173i −0.00139425 0.792773i
\(157\) −5.63448 + 4.99171i −0.449680 + 0.398382i −0.857339 0.514753i \(-0.827884\pi\)
0.407659 + 0.913134i \(0.366345\pi\)
\(158\) 0.347788 + 0.240061i 0.0276685 + 0.0190982i
\(159\) 1.72657 + 0.425560i 0.136926 + 0.0337491i
\(160\) 1.65470 + 2.39725i 0.130815 + 0.189519i
\(161\) −5.18889 21.0522i −0.408942 1.65914i
\(162\) −3.64931 14.8058i −0.286717 1.16325i
\(163\) 15.3470 1.86346i 1.20207 0.145957i 0.505100 0.863061i \(-0.331456\pi\)
0.696967 + 0.717103i \(0.254533\pi\)
\(164\) −6.26737 7.07440i −0.489399 0.552417i
\(165\) 0.365455 0.963626i 0.0284507 0.0750182i
\(166\) 6.99577 + 3.67166i 0.542977 + 0.284976i
\(167\) −8.77149 + 6.05453i −0.678759 + 0.468513i −0.856894 0.515493i \(-0.827609\pi\)
0.178135 + 0.984006i \(0.442994\pi\)
\(168\) 18.3330 1.41442
\(169\) −1.61236 12.8996i −0.124028 0.992279i
\(170\) −0.338727 −0.0259791
\(171\) 16.1455 11.1444i 1.23467 0.852234i
\(172\) 2.40873 + 1.26420i 0.183664 + 0.0963942i
\(173\) 3.24939 8.56795i 0.247047 0.651409i −0.752931 0.658100i \(-0.771360\pi\)
0.999978 + 0.00669062i \(0.00212971\pi\)
\(174\) −2.37338 2.67899i −0.179926 0.203094i
\(175\) −22.0261 + 2.67445i −1.66501 + 0.202169i
\(176\) 8.24084 + 33.4344i 0.621177 + 2.52021i
\(177\) −0.426629 1.73090i −0.0320674 0.130103i
\(178\) 5.42849 + 7.86452i 0.406882 + 0.589471i
\(179\) 20.3458 + 5.01479i 1.52072 + 0.374823i 0.909183 0.416396i \(-0.136707\pi\)
0.611533 + 0.791219i \(0.290553\pi\)
\(180\) −4.04672 2.79325i −0.301624 0.208196i
\(181\) −8.25204 + 7.31067i −0.613369 + 0.543398i −0.911591 0.411099i \(-0.865145\pi\)
0.298222 + 0.954497i \(0.403607\pi\)
\(182\) 42.1979 5.19908i 3.12792 0.385381i
\(183\) 2.35167 + 2.08340i 0.173841 + 0.154009i
\(184\) 7.58935 + 30.7912i 0.559495 + 2.26996i
\(185\) 1.72739 + 1.53034i 0.127000 + 0.112513i
\(186\) 10.4668 2.57983i 0.767461 0.189162i
\(187\) −1.31018 0.496887i −0.0958102 0.0363360i
\(188\) 15.4769i 1.12877i
\(189\) −14.4239 + 5.47025i −1.04918 + 0.397902i
\(190\) 1.84038 7.46673i 0.133515 0.541693i
\(191\) −17.2485 −1.24806 −0.624029 0.781401i \(-0.714505\pi\)
−0.624029 + 0.781401i \(0.714505\pi\)
\(192\) −1.49653 −0.108003
\(193\) −2.19100 + 8.88924i −0.157712 + 0.639861i 0.837862 + 0.545881i \(0.183805\pi\)
−0.995574 + 0.0939798i \(0.970041\pi\)
\(194\) −3.27686 + 26.9874i −0.235265 + 1.93758i
\(195\) 0.767810 + 0.401257i 0.0549840 + 0.0287346i
\(196\) 7.79995 + 64.2384i 0.557139 + 4.58845i
\(197\) 9.71273 + 1.17934i 0.692003 + 0.0840244i 0.458980 0.888447i \(-0.348215\pi\)
0.233023 + 0.972471i \(0.425138\pi\)
\(198\) −16.5687 24.0039i −1.17749 1.70588i
\(199\) 8.60326 + 7.62182i 0.609869 + 0.540297i 0.910535 0.413433i \(-0.135670\pi\)
−0.300666 + 0.953730i \(0.597209\pi\)
\(200\) 32.2156 3.91169i 2.27799 0.276598i
\(201\) 6.47747 + 0.786507i 0.456886 + 0.0554760i
\(202\) −20.2109 38.5087i −1.42204 2.70946i
\(203\) 7.10727 8.02245i 0.498833 0.563066i
\(204\) 0.509655 0.738363i 0.0356830 0.0516958i
\(205\) 0.802896 0.197896i 0.0560767 0.0138217i
\(206\) 24.2403 2.94330i 1.68890 0.205069i
\(207\) −7.10275 10.2901i −0.493676 0.715212i
\(208\) −28.7294 + 3.53966i −1.99202 + 0.245431i
\(209\) 18.0717 26.1814i 1.25005 1.81100i
\(210\) −1.31674 + 2.50884i −0.0908638 + 0.173126i
\(211\) −4.34990 11.4698i −0.299460 0.789610i −0.997305 0.0733622i \(-0.976627\pi\)
0.697846 0.716248i \(-0.254142\pi\)
\(212\) 1.65834 13.6576i 0.113895 0.938011i
\(213\) 4.07174 2.81052i 0.278991 0.192574i
\(214\) 8.86812 35.9794i 0.606212 2.45950i
\(215\) −0.195879 + 0.135205i −0.0133588 + 0.00922093i
\(216\) 21.0966 8.00088i 1.43544 0.544391i
\(217\) 11.4472 + 30.1838i 0.777088 + 2.04901i
\(218\) −14.2426 + 7.47510i −0.964632 + 0.506278i
\(219\) 1.63442 + 3.11412i 0.110444 + 0.210433i
\(220\) −7.74188 1.90820i −0.521957 0.128651i
\(221\) 0.545565 1.04394i 0.0366987 0.0702233i
\(222\) −8.51003 + 2.09753i −0.571156 + 0.140777i
\(223\) −3.60832 4.07296i −0.241631 0.272745i 0.615167 0.788397i \(-0.289088\pi\)
−0.856799 + 0.515651i \(0.827550\pi\)
\(224\) −3.99320 32.8870i −0.266807 2.19735i
\(225\) −11.3294 + 5.94613i −0.755294 + 0.396409i
\(226\) −8.10149 + 15.4361i −0.538903 + 1.02679i
\(227\) −6.80998 2.58268i −0.451994 0.171419i 0.118094 0.993002i \(-0.462322\pi\)
−0.570088 + 0.821584i \(0.693091\pi\)
\(228\) 13.5070 + 15.2463i 0.894526 + 1.00971i
\(229\) −1.50115 0.182273i −0.0991991 0.0120450i 0.0707866 0.997491i \(-0.477449\pi\)
−0.169986 + 0.985447i \(0.554372\pi\)
\(230\) −4.75883 1.17295i −0.313788 0.0773417i
\(231\) −8.77340 + 7.77256i −0.577248 + 0.511397i
\(232\) −10.3952 + 11.7338i −0.682479 + 0.770359i
\(233\) −3.66500 + 1.92354i −0.240102 + 0.126015i −0.580483 0.814272i \(-0.697136\pi\)
0.340381 + 0.940288i \(0.389444\pi\)
\(234\) 21.6897 11.4323i 1.41790 0.747354i
\(235\) −1.19902 0.629295i −0.0782156 0.0410507i
\(236\) −12.8962 + 4.89089i −0.839472 + 0.318370i
\(237\) 0.0118045 0.0972188i 0.000766784 0.00631504i
\(238\) 3.41112 + 1.79029i 0.221110 + 0.116047i
\(239\) 26.3416i 1.70390i 0.523626 + 0.851948i \(0.324579\pi\)
−0.523626 + 0.851948i \(0.675421\pi\)
\(240\) 0.896469 1.70808i 0.0578668 0.110256i
\(241\) −2.51536 + 2.83926i −0.162029 + 0.182893i −0.823918 0.566709i \(-0.808216\pi\)
0.661889 + 0.749602i \(0.269755\pi\)
\(242\) −15.6508 10.8029i −1.00607 0.694439i
\(243\) −10.1973 + 9.03404i −0.654158 + 0.579534i
\(244\) 13.8083 20.0048i 0.883986 1.28068i
\(245\) −5.29379 2.00767i −0.338208 0.128265i
\(246\) −1.11367 + 2.93650i −0.0710049 + 0.187225i
\(247\) 20.0480 + 17.6982i 1.27563 + 1.12611i
\(248\) −16.7429 44.1473i −1.06317 2.80336i
\(249\) 1.83094i 0.116031i
\(250\) −3.61687 + 9.53691i −0.228751 + 0.603167i
\(251\) −1.13249 9.32690i −0.0714822 0.588709i −0.983806 0.179238i \(-0.942637\pi\)
0.912323 0.409470i \(-0.134286\pi\)
\(252\) 25.9888 + 49.5175i 1.63714 + 3.11931i
\(253\) −16.6864 11.5178i −1.04906 0.724116i
\(254\) −10.1139 6.98116i −0.634606 0.438037i
\(255\) 0.0364794 + 0.0695057i 0.00228443 + 0.00435262i
\(256\) −3.08076 25.3723i −0.192547 1.58577i
\(257\) 5.77264 15.2212i 0.360087 0.949472i −0.625488 0.780234i \(-0.715100\pi\)
0.985575 0.169238i \(-0.0541308\pi\)
\(258\) 0.903943i 0.0562770i
\(259\) −9.30718 24.5410i −0.578320 1.52490i
\(260\) 2.36579 6.27131i 0.146720 0.388930i
\(261\) 2.19169 5.77901i 0.135662 0.357712i
\(262\) 51.2846 + 19.4497i 3.16837 + 1.20161i
\(263\) 4.26654 6.18115i 0.263086 0.381146i −0.669072 0.743198i \(-0.733308\pi\)
0.932158 + 0.362052i \(0.117924\pi\)
\(264\) 12.8321 11.3683i 0.789762 0.699668i
\(265\) 0.990650 + 0.683796i 0.0608551 + 0.0420053i
\(266\) −57.9978 + 65.4660i −3.55607 + 4.01398i
\(267\) 1.02915 1.96089i 0.0629831 0.120004i
\(268\) 50.4832i 3.08376i
\(269\) 16.2068 + 8.50597i 0.988145 + 0.518618i 0.879723 0.475487i \(-0.157728\pi\)
0.108422 + 0.994105i \(0.465420\pi\)
\(270\) −0.420325 + 3.46169i −0.0255802 + 0.210672i
\(271\) −16.5279 + 6.26820i −1.00400 + 0.380766i −0.801162 0.598447i \(-0.795785\pi\)
−0.202835 + 0.979213i \(0.565015\pi\)
\(272\) −2.32237 1.21887i −0.140814 0.0739051i
\(273\) −5.61138 8.09898i −0.339616 0.490173i
\(274\) −35.2254 + 18.4877i −2.12804 + 1.11688i
\(275\) −13.7587 + 15.5303i −0.829678 + 0.936513i
\(276\) 9.71705 8.60855i 0.584898 0.518174i
\(277\) 13.3074 + 3.27997i 0.799563 + 0.197074i 0.617869 0.786281i \(-0.287996\pi\)
0.181693 + 0.983355i \(0.441842\pi\)
\(278\) −38.9865 4.73382i −2.33826 0.283916i
\(279\) 12.3445 + 13.9341i 0.739047 + 0.834212i
\(280\) 11.6035 + 4.40065i 0.693445 + 0.262989i
\(281\) 14.3906 27.4191i 0.858473 1.63568i 0.0898746 0.995953i \(-0.471353\pi\)
0.768599 0.639731i \(-0.220954\pi\)
\(282\) 4.55378 2.39001i 0.271174 0.142323i
\(283\) 0.804907 + 6.62901i 0.0478468 + 0.394054i 0.996883 + 0.0788881i \(0.0251370\pi\)
−0.949037 + 0.315166i \(0.897940\pi\)
\(284\) −25.3832 28.6517i −1.50622 1.70017i
\(285\) −1.73035 + 0.426494i −0.102497 + 0.0252633i
\(286\) 26.3124 29.8060i 1.55588 1.76246i
\(287\) −9.13146 2.25070i −0.539013 0.132855i
\(288\) −8.87813 16.9159i −0.523149 0.996776i
\(289\) −14.9582 + 7.85070i −0.879897 + 0.461806i
\(290\) −0.859126 2.26533i −0.0504496 0.133025i
\(291\) 5.89065 2.23403i 0.345316 0.130961i
\(292\) 22.3936 15.4572i 1.31048 0.904562i
\(293\) −4.74195 + 19.2389i −0.277028 + 1.12395i 0.653265 + 0.757129i \(0.273399\pi\)
−0.930293 + 0.366817i \(0.880448\pi\)
\(294\) 17.6964 12.2149i 1.03207 0.712388i
\(295\) 0.145458 1.19795i 0.00846888 0.0697475i
\(296\) 13.6128 + 35.8941i 0.791229 + 2.08630i
\(297\) −6.70385 + 12.7731i −0.388997 + 0.741171i
\(298\) −0.619070 + 0.896878i −0.0358618 + 0.0519547i
\(299\) 11.2797 12.7774i 0.652323 0.738934i
\(300\) −7.54650 10.9330i −0.435697 0.631216i
\(301\) 2.68719 0.326284i 0.154887 0.0188067i
\(302\) −32.8937 + 8.10756i −1.89282 + 0.466538i
\(303\) −5.72524 + 8.29445i −0.328907 + 0.476504i
\(304\) 39.4863 44.5708i 2.26469 2.55631i
\(305\) 0.988353 + 1.88315i 0.0565929 + 0.107829i
\(306\) 2.20535 + 0.267778i 0.126071 + 0.0153078i
\(307\) 1.61650 0.196279i 0.0922585 0.0112022i −0.0742772 0.997238i \(-0.523665\pi\)
0.166536 + 0.986035i \(0.446742\pi\)
\(308\) 67.8784 + 60.1350i 3.86773 + 3.42651i
\(309\) −3.21453 4.65705i −0.182868 0.264930i
\(310\) 7.24403 + 0.879584i 0.411433 + 0.0499570i
\(311\) −1.03353 8.51185i −0.0586059 0.482663i −0.992231 0.124411i \(-0.960296\pi\)
0.933625 0.358252i \(-0.116627\pi\)
\(312\) 8.20729 + 11.8457i 0.464646 + 0.670630i
\(313\) −2.21618 + 18.2519i −0.125266 + 1.03166i 0.785536 + 0.618816i \(0.212387\pi\)
−0.910802 + 0.412843i \(0.864536\pi\)
\(314\) 4.63138 18.7902i 0.261364 1.06039i
\(315\) −4.89291 −0.275684
\(316\) −0.757691 −0.0426234
\(317\) 1.48875 6.04009i 0.0836165 0.339245i −0.914202 0.405258i \(-0.867182\pi\)
0.997819 + 0.0660128i \(0.0210278\pi\)
\(318\) −4.27457 + 1.62113i −0.239706 + 0.0909086i
\(319\) 10.0225i 0.561153i
\(320\) −0.947203 0.359227i −0.0529503 0.0200814i
\(321\) −8.33793 + 2.05511i −0.465378 + 0.114705i
\(322\) 41.7239 + 36.9642i 2.32518 + 2.05993i
\(323\) 0.579878 + 2.35266i 0.0322653 + 0.130905i
\(324\) 20.4647 + 18.1301i 1.13693 + 1.00723i
\(325\) −11.5887 13.0347i −0.642824 0.723032i
\(326\) −29.7497 + 26.3559i −1.64768 + 1.45972i
\(327\) 3.06774 + 2.11751i 0.169646 + 0.117099i
\(328\) 13.3558 + 3.29191i 0.737451 + 0.181765i
\(329\) 8.74860 + 12.6745i 0.482326 + 0.698770i
\(330\) 0.634080 + 2.57256i 0.0349050 + 0.141615i
\(331\) −3.55253 14.4132i −0.195265 0.792220i −0.984100 0.177616i \(-0.943162\pi\)
0.788835 0.614605i \(-0.210685\pi\)
\(332\) −14.0624 + 1.70748i −0.771773 + 0.0937102i
\(333\) −10.0367 11.3291i −0.550010 0.620833i
\(334\) 9.71652 25.6203i 0.531664 1.40188i
\(335\) 3.91101 + 2.05266i 0.213681 + 0.112149i
\(336\) −18.0556 + 12.4629i −0.985015 + 0.679907i
\(337\) 12.8480 0.699875 0.349937 0.936773i \(-0.386203\pi\)
0.349937 + 0.936773i \(0.386203\pi\)
\(338\) 22.2505 + 24.9383i 1.21027 + 1.35646i
\(339\) 4.03994 0.219419
\(340\) 0.499814 0.344997i 0.0271062 0.0187101i
\(341\) 26.7294 + 14.0287i 1.44748 + 0.759695i
\(342\) −17.8849 + 47.1587i −0.967107 + 2.55005i
\(343\) 21.4083 + 24.1649i 1.15594 + 1.30478i
\(344\) −3.93032 + 0.477228i −0.211909 + 0.0257304i
\(345\) 0.271821 + 1.10282i 0.0146343 + 0.0593738i
\(346\) 5.63784 + 22.8736i 0.303092 + 1.22969i
\(347\) −14.6281 21.1924i −0.785276 1.13767i −0.987390 0.158306i \(-0.949397\pi\)
0.202114 0.979362i \(-0.435219\pi\)
\(348\) 6.23067 + 1.53572i 0.333999 + 0.0823234i
\(349\) −4.36026 3.00967i −0.233399 0.161104i 0.445625 0.895220i \(-0.352982\pi\)
−0.679024 + 0.734116i \(0.737597\pi\)
\(350\) 42.6969 37.8262i 2.28225 2.02189i
\(351\) −9.99182 6.87094i −0.533324 0.366744i
\(352\) −23.1882 20.5429i −1.23593 1.09494i
\(353\) 1.52664 + 6.19382i 0.0812548 + 0.329664i 0.997476 0.0710100i \(-0.0226222\pi\)
−0.916221 + 0.400674i \(0.868776\pi\)
\(354\) 3.43053 + 3.03918i 0.182330 + 0.161531i
\(355\) 3.25178 0.801491i 0.172586 0.0425387i
\(356\) −16.0202 6.07567i −0.849070 0.322010i
\(357\) 0.892759i 0.0472498i
\(358\) −50.3714 + 19.1034i −2.66221 + 1.00964i
\(359\) 0.614544 2.49330i 0.0324344 0.131592i −0.952493 0.304561i \(-0.901490\pi\)
0.984927 + 0.172970i \(0.0553363\pi\)
\(360\) 7.15644 0.377177
\(361\) −36.0115 −1.89534
\(362\) 6.78294 27.5195i 0.356503 1.44639i
\(363\) −0.531212 + 4.37493i −0.0278814 + 0.229624i
\(364\) −56.9706 + 50.6507i −2.98607 + 2.65482i
\(365\) 0.286963 + 2.36335i 0.0150203 + 0.123704i
\(366\) −8.01834 0.973603i −0.419125 0.0508910i
\(367\) 4.49098 + 6.50631i 0.234427 + 0.339626i 0.922487 0.386027i \(-0.126153\pi\)
−0.688060 + 0.725654i \(0.741538\pi\)
\(368\) −28.4067 25.1661i −1.48080 1.31187i
\(369\) −5.38386 + 0.653719i −0.280273 + 0.0340313i
\(370\) −5.88977 0.715147i −0.306195 0.0371787i
\(371\) −6.36215 12.1221i −0.330306 0.629346i
\(372\) −12.8169 + 14.4672i −0.664523 + 0.750092i
\(373\) 7.91941 11.4732i 0.410051 0.594062i −0.562487 0.826806i \(-0.690155\pi\)
0.972538 + 0.232744i \(0.0747706\pi\)
\(374\) 3.49776 0.862121i 0.180865 0.0445792i
\(375\) 2.34647 0.284913i 0.121171 0.0147128i
\(376\) −12.7958 18.5380i −0.659895 0.956023i
\(377\) 8.36541 + 1.00082i 0.430841 + 0.0515448i
\(378\) 22.5291 32.6391i 1.15877 1.67877i
\(379\) 9.89476 18.8529i 0.508260 0.968408i −0.487206 0.873287i \(-0.661984\pi\)
0.995466 0.0951209i \(-0.0303238\pi\)
\(380\) 4.88934 + 12.8921i 0.250818 + 0.661352i
\(381\) −0.343284 + 2.82720i −0.0175870 + 0.144842i
\(382\) 36.4944 25.1903i 1.86722 1.28885i
\(383\) 2.68469 10.8922i 0.137181 0.556567i −0.861617 0.507559i \(-0.830548\pi\)
0.998798 0.0490077i \(-0.0156059\pi\)
\(384\) −3.91642 + 2.70331i −0.199859 + 0.137953i
\(385\) −7.41870 + 2.81354i −0.378092 + 0.143391i
\(386\) −8.34641 22.0077i −0.424821 1.12016i
\(387\) 1.38219 0.725431i 0.0702608 0.0368757i
\(388\) −22.6518 43.1593i −1.14997 2.19108i
\(389\) −33.1019 8.15888i −1.67833 0.413671i −0.718787 0.695230i \(-0.755302\pi\)
−0.959544 + 0.281559i \(0.909149\pi\)
\(390\) −2.21054 + 0.272354i −0.111935 + 0.0137912i
\(391\) 1.49944 0.369578i 0.0758298 0.0186904i
\(392\) −62.4528 70.4947i −3.15434 3.56052i
\(393\) −1.53212 12.6181i −0.0772850 0.636499i
\(394\) −22.2725 + 11.6895i −1.12207 + 0.588910i
\(395\) 0.0308078 0.0586994i 0.00155011 0.00295349i
\(396\) 48.8965 + 18.5440i 2.45714 + 0.931872i
\(397\) −20.6396 23.2973i −1.03587 1.16926i −0.985351 0.170537i \(-0.945450\pi\)
−0.0505225 0.998723i \(-0.516089\pi\)
\(398\) −29.3339 3.56179i −1.47038 0.178536i
\(399\) 19.6796 + 4.85057i 0.985210 + 0.242832i
\(400\) −29.0691 + 25.7530i −1.45345 + 1.28765i
\(401\) −14.8870 + 16.8039i −0.743420 + 0.839148i −0.991570 0.129574i \(-0.958639\pi\)
0.248149 + 0.968722i \(0.420178\pi\)
\(402\) −14.8537 + 7.79582i −0.740834 + 0.388820i
\(403\) −14.3783 + 20.9092i −0.716236 + 1.04156i
\(404\) 69.0442 + 36.2372i 3.43507 + 1.80287i
\(405\) −2.23667 + 0.848256i −0.111141 + 0.0421502i
\(406\) −3.32133 + 27.3536i −0.164835 + 1.35754i
\(407\) −21.7324 11.4060i −1.07723 0.565376i
\(408\) 1.30576i 0.0646449i
\(409\) −6.71602 + 12.7963i −0.332086 + 0.632737i −0.993052 0.117679i \(-0.962455\pi\)
0.660966 + 0.750416i \(0.270147\pi\)
\(410\) −1.40976 + 1.59128i −0.0696229 + 0.0785880i
\(411\) 7.58725 + 5.23710i 0.374252 + 0.258327i
\(412\) −32.7704 + 29.0320i −1.61448 + 1.43031i
\(413\) −7.79644 + 11.2951i −0.383638 + 0.555795i
\(414\) 30.0560 + 11.3988i 1.47717 + 0.560218i
\(415\) 0.439497 1.15886i 0.0215741 0.0568862i
\(416\) 19.4619 17.3030i 0.954200 0.848348i
\(417\) 3.22732 + 8.50974i 0.158043 + 0.416724i
\(418\) 81.7871i 4.00034i
\(419\) 9.49406 25.0338i 0.463815 1.22298i −0.475436 0.879750i \(-0.657710\pi\)
0.939251 0.343230i \(-0.111521\pi\)
\(420\) −0.612341 5.04308i −0.0298792 0.246077i
\(421\) −3.93535 7.49819i −0.191797 0.365439i 0.770500 0.637441i \(-0.220007\pi\)
−0.962297 + 0.272001i \(0.912315\pi\)
\(422\) 25.9543 + 17.9150i 1.26344 + 0.872088i
\(423\) 7.30899 + 5.04503i 0.355375 + 0.245298i
\(424\) 9.30537 + 17.7299i 0.451909 + 0.861040i
\(425\) −0.190487 1.56880i −0.00923998 0.0760981i
\(426\) −4.51042 + 11.8930i −0.218531 + 0.576218i
\(427\) 24.1879i 1.17053i
\(428\) 23.5599 + 62.1223i 1.13881 + 3.00280i
\(429\) −8.94984 2.18925i −0.432102 0.105698i
\(430\) 0.216982 0.572135i 0.0104638 0.0275908i
\(431\) 14.7781 + 5.60458i 0.711835 + 0.269963i 0.683827 0.729644i \(-0.260314\pi\)
0.0280080 + 0.999608i \(0.491084\pi\)
\(432\) −15.3384 + 22.2215i −0.737967 + 1.06913i
\(433\) 0.843193 0.747004i 0.0405213 0.0358987i −0.642619 0.766186i \(-0.722152\pi\)
0.683140 + 0.730287i \(0.260614\pi\)
\(434\) −68.3015 47.1451i −3.27858 2.26304i
\(435\) −0.372315 + 0.420257i −0.0178511 + 0.0201498i
\(436\) 13.4025 25.5363i 0.641863 1.22297i
\(437\) 35.0609i 1.67719i
\(438\) −8.00606 4.20190i −0.382544 0.200775i
\(439\) 0.637030 5.24641i 0.0304038 0.250398i −0.969580 0.244773i \(-0.921287\pi\)
0.999984 0.00562458i \(-0.00179037\pi\)
\(440\) 10.8507 4.11513i 0.517287 0.196181i
\(441\) 32.8791 + 17.2563i 1.56567 + 0.821729i
\(442\) 0.370304 + 3.00554i 0.0176135 + 0.142959i
\(443\) 37.2160 19.5325i 1.76819 0.928016i 0.858321 0.513113i \(-0.171508\pi\)
0.909865 0.414903i \(-0.136185\pi\)
\(444\) 10.4208 11.7626i 0.494548 0.558229i
\(445\) 1.12208 0.994072i 0.0531915 0.0471235i
\(446\) 13.5828 + 3.34785i 0.643163 + 0.158525i
\(447\) 0.250708 + 0.0304415i 0.0118581 + 0.00143983i
\(448\) 7.64009 + 8.62388i 0.360960 + 0.407440i
\(449\) 37.0200 + 14.0398i 1.74708 + 0.662581i 0.999998 0.00214786i \(-0.000683686\pi\)
0.747085 + 0.664729i \(0.231453\pi\)
\(450\) 15.2869 29.1267i 0.720629 1.37304i
\(451\) −7.78719 + 4.08703i −0.366685 + 0.192451i
\(452\) −3.76754 31.0285i −0.177210 1.45946i
\(453\) 5.20616 + 5.87654i 0.244607 + 0.276104i
\(454\) 18.1804 4.48106i 0.853248 0.210307i
\(455\) −1.60755 6.47307i −0.0753631 0.303462i
\(456\) −28.7836 7.09452i −1.34792 0.332232i
\(457\) −17.7824 33.8816i −0.831826 1.58491i −0.810939 0.585130i \(-0.801043\pi\)
−0.0208867 0.999782i \(-0.506649\pi\)
\(458\) 3.44234 1.80668i 0.160850 0.0844207i
\(459\) −0.389618 1.02734i −0.0181858 0.0479520i
\(460\) 8.21664 3.11616i 0.383103 0.145292i
\(461\) −1.41797 + 0.978752i −0.0660413 + 0.0455850i −0.600628 0.799529i \(-0.705083\pi\)
0.534587 + 0.845114i \(0.320467\pi\)
\(462\) 7.21149 29.2582i 0.335509 1.36121i
\(463\) −27.4191 + 18.9261i −1.27427 + 0.879568i −0.996703 0.0811365i \(-0.974145\pi\)
−0.277572 + 0.960705i \(0.589530\pi\)
\(464\) 2.26124 18.6230i 0.104975 0.864551i
\(465\) −0.599663 1.58118i −0.0278087 0.0733256i
\(466\) 4.94522 9.42233i 0.229083 0.436481i
\(467\) −9.64493 + 13.9731i −0.446314 + 0.646597i −0.979980 0.199098i \(-0.936199\pi\)
0.533666 + 0.845696i \(0.320814\pi\)
\(468\) −20.3607 + 38.9604i −0.941172 + 1.80094i
\(469\) −28.5365 41.3423i −1.31769 1.90901i
\(470\) 3.45594 0.419627i 0.159410 0.0193559i
\(471\) −4.35449 + 1.07328i −0.200644 + 0.0494543i
\(472\) 11.4032 16.5204i 0.524874 0.760412i
\(473\) 1.67856 1.89471i 0.0771804 0.0871186i
\(474\) 0.117005 + 0.222935i 0.00537424 + 0.0102398i
\(475\) 35.6169 + 4.32467i 1.63421 + 0.198430i
\(476\) −6.85678 + 0.832563i −0.314280 + 0.0381605i
\(477\) −5.90925 5.23514i −0.270566 0.239701i
\(478\) −38.4701 55.7336i −1.75958 2.54920i
\(479\) 41.9110 + 5.08891i 1.91496 + 0.232518i 0.989306 0.145852i \(-0.0465922\pi\)
0.925654 + 0.378370i \(0.123515\pi\)
\(480\) 0.209184 + 1.72279i 0.00954790 + 0.0786340i
\(481\) 11.6903 17.0002i 0.533033 0.775144i
\(482\) 1.17547 9.68083i 0.0535410 0.440950i
\(483\) 3.09146 12.5425i 0.140666 0.570705i
\(484\) 34.0967 1.54985
\(485\) 4.26464 0.193647
\(486\) 8.38190 34.0067i 0.380211 1.54258i
\(487\) 0.925020 0.350814i 0.0419167 0.0158969i −0.333557 0.942730i \(-0.608249\pi\)
0.375474 + 0.926833i \(0.377480\pi\)
\(488\) 35.3776i 1.60147i
\(489\) 8.61207 + 3.26613i 0.389451 + 0.147699i
\(490\) 14.1327 3.48339i 0.638449 0.157364i
\(491\) 5.95750 + 5.27788i 0.268858 + 0.238187i 0.786770 0.617247i \(-0.211752\pi\)
−0.517912 + 0.855434i \(0.673290\pi\)
\(492\) −1.34757 5.46730i −0.0607530 0.246485i
\(493\) 0.571398 + 0.506214i 0.0257345 + 0.0227987i
\(494\) −68.2646 8.16703i −3.07137 0.367452i
\(495\) −3.42477 + 3.03409i −0.153932 + 0.136372i
\(496\) 46.5013 + 32.0975i 2.08797 + 1.44122i
\(497\) −36.9829 9.11548i −1.65891 0.408885i
\(498\) 2.67396 + 3.87390i 0.119823 + 0.173593i
\(499\) 0.864910 + 3.50908i 0.0387187 + 0.157088i 0.987119 0.159987i \(-0.0511454\pi\)
−0.948400 + 0.317075i \(0.897299\pi\)
\(500\) −4.37651 17.7562i −0.195723 0.794081i
\(501\) −6.30365 + 0.765402i −0.281626 + 0.0341956i
\(502\) 16.0174 + 18.0799i 0.714893 + 0.806947i
\(503\) −8.02702 + 21.1655i −0.357907 + 0.943724i 0.628265 + 0.777999i \(0.283765\pi\)
−0.986172 + 0.165724i \(0.947004\pi\)
\(504\) −72.0683 37.8244i −3.21018 1.68483i
\(505\) −5.61470 + 3.87554i −0.249851 + 0.172459i
\(506\) 52.1260 2.31728
\(507\) 2.72099 7.25148i 0.120843 0.322050i
\(508\) 22.0342 0.977610
\(509\) −15.1557 + 10.4612i −0.671764 + 0.463685i −0.854482 0.519480i \(-0.826126\pi\)
0.182719 + 0.983165i \(0.441510\pi\)
\(510\) −0.178692 0.0937846i −0.00791260 0.00415285i
\(511\) 9.60134 25.3167i 0.424738 1.11994i
\(512\) 32.9795 + 37.2262i 1.45750 + 1.64518i
\(513\) 24.7630 3.00678i 1.09331 0.132752i
\(514\) 10.0158 + 40.6356i 0.441777 + 1.79236i
\(515\) −0.916705 3.71922i −0.0403948 0.163888i
\(516\) 0.920676 + 1.33383i 0.0405305 + 0.0587186i
\(517\) 13.9830 + 3.44650i 0.614973 + 0.151577i
\(518\) 55.5326 + 38.3314i 2.43996 + 1.68419i
\(519\) 4.08643 3.62026i 0.179374 0.158912i
\(520\) 2.35123 + 9.46761i 0.103108 + 0.415182i
\(521\) −11.2013 9.92353i −0.490740 0.434758i 0.381111 0.924529i \(-0.375542\pi\)
−0.871851 + 0.489772i \(0.837080\pi\)
\(522\) 3.80267 + 15.4281i 0.166439 + 0.675268i
\(523\) 26.1307 + 23.1497i 1.14261 + 1.01227i 0.999746 + 0.0225255i \(0.00717071\pi\)
0.142867 + 0.989742i \(0.454368\pi\)
\(524\) −95.4837 + 23.5346i −4.17123 + 1.02811i
\(525\) −12.3601 4.68757i −0.539439 0.204582i
\(526\) 19.3091i 0.841916i
\(527\) −2.14984 + 0.815326i −0.0936484 + 0.0355161i
\(528\) −4.90975 + 19.9196i −0.213670 + 0.866891i
\(529\) −0.654374 −0.0284511
\(530\) −3.09466 −0.134423
\(531\) −1.89406 + 7.68452i −0.0821954 + 0.333480i
\(532\) 18.9019 155.671i 0.819500 6.74919i
\(533\) −2.63369 6.90780i −0.114078 0.299210i
\(534\) 0.686259 + 5.65185i 0.0296973 + 0.244580i
\(535\) −5.77066 0.700685i −0.249487 0.0302932i
\(536\) 41.7379 + 60.4678i 1.80280 + 2.61181i
\(537\) 9.34475 + 8.27873i 0.403256 + 0.357253i
\(538\) −46.7127 + 5.67195i −2.01393 + 0.244535i
\(539\) 59.7747 + 7.25796i 2.57468 + 0.312622i
\(540\) −2.90555 5.53606i −0.125035 0.238234i
\(541\) 6.61857 7.47083i 0.284555 0.321196i −0.588802 0.808277i \(-0.700400\pi\)
0.873356 + 0.487082i \(0.161939\pi\)
\(542\) 25.8154 37.4001i 1.10887 1.60647i
\(543\) −6.37741 + 1.57189i −0.273681 + 0.0674563i
\(544\) 2.34237 0.284415i 0.100428 0.0121942i
\(545\) 1.43339 + 2.07662i 0.0613996 + 0.0889527i
\(546\) 23.7006 + 8.94080i 1.01429 + 0.382631i
\(547\) −5.88495 + 8.52582i −0.251622 + 0.364538i −0.928357 0.371689i \(-0.878779\pi\)
0.676735 + 0.736227i \(0.263394\pi\)
\(548\) 33.1475 63.1574i 1.41599 2.69795i
\(549\) −4.94616 13.0420i −0.211097 0.556617i
\(550\) 6.42961 52.9526i 0.274160 2.25791i
\(551\) −14.2633 + 9.84524i −0.607636 + 0.419421i
\(552\) −4.52161 + 18.3449i −0.192452 + 0.780810i
\(553\) −0.620496 + 0.428297i −0.0263862 + 0.0182130i
\(554\) −32.9459 + 12.4947i −1.39974 + 0.530851i
\(555\) 0.487557 + 1.28558i 0.0206957 + 0.0545700i
\(556\) 62.3488 32.7232i 2.64418 1.38777i
\(557\) −9.16269 17.4580i −0.388236 0.739721i 0.610392 0.792100i \(-0.291012\pi\)
−0.998627 + 0.0523786i \(0.983320\pi\)
\(558\) −46.4683 11.4534i −1.96716 0.484862i
\(559\) 1.41382 + 1.59023i 0.0597984 + 0.0672597i
\(560\) −14.4196 + 3.55411i −0.609339 + 0.150189i
\(561\) −0.553599 0.624884i −0.0233730 0.0263826i
\(562\) 9.59596 + 79.0299i 0.404781 + 3.33367i
\(563\) 23.3976 12.2800i 0.986092 0.517541i 0.107034 0.994255i \(-0.465865\pi\)
0.879058 + 0.476714i \(0.158172\pi\)
\(564\) −4.28517 + 8.16470i −0.180438 + 0.343796i
\(565\) 2.55701 + 0.969747i 0.107574 + 0.0407976i
\(566\) −11.3842 12.8502i −0.478515 0.540132i
\(567\) 27.0075 + 3.27931i 1.13421 + 0.137718i
\(568\) 54.0918 + 13.3324i 2.26964 + 0.559416i
\(569\) −13.4494 + 11.9152i −0.563830 + 0.499510i −0.896207 0.443637i \(-0.853688\pi\)
0.332377 + 0.943147i \(0.392149\pi\)
\(570\) 3.03822 3.42944i 0.127257 0.143643i
\(571\) −27.5574 + 14.4633i −1.15324 + 0.605269i −0.929297 0.369333i \(-0.879586\pi\)
−0.223946 + 0.974602i \(0.571894\pi\)
\(572\) −8.46799 + 70.7802i −0.354064 + 2.95947i
\(573\) −9.09927 4.77567i −0.380128 0.199506i
\(574\) 22.6073 8.57384i 0.943612 0.357865i
\(575\) 2.75628 22.7000i 0.114945 0.946655i
\(576\) 5.88297 + 3.08762i 0.245124 + 0.128651i
\(577\) 2.27082i 0.0945354i 0.998882 + 0.0472677i \(0.0150514\pi\)
−0.998882 + 0.0472677i \(0.984949\pi\)
\(578\) 20.1833 38.4560i 0.839514 1.59956i
\(579\) −3.61704 + 4.08279i −0.150319 + 0.169675i
\(580\) 3.57496 + 2.46762i 0.148442 + 0.102462i
\(581\) −10.5509 + 9.34730i −0.437726 + 0.387791i
\(582\) −9.20079 + 13.3297i −0.381385 + 0.552532i
\(583\) −11.9700 4.53964i −0.495748 0.188013i
\(584\) −14.0431 + 37.0285i −0.581106 + 1.53225i
\(585\) −2.19045 3.16151i −0.0905640 0.130712i
\(586\) −18.0640 47.6309i −0.746218 1.96761i
\(587\) 32.2846i 1.33253i −0.745716 0.666264i \(-0.767892\pi\)
0.745716 0.666264i \(-0.232108\pi\)
\(588\) −13.6712 + 36.0479i −0.563789 + 1.48659i
\(589\) −6.29207 51.8198i −0.259260 2.13520i
\(590\) 1.44177 + 2.74706i 0.0593567 + 0.113095i
\(591\) 4.79732 + 3.31135i 0.197335 + 0.136211i
\(592\) −37.8079 26.0969i −1.55390 1.07258i
\(593\) 0.902600 + 1.71976i 0.0370653 + 0.0706221i 0.903284 0.429042i \(-0.141149\pi\)
−0.866219 + 0.499665i \(0.833457\pi\)
\(594\) −4.47026 36.8159i −0.183417 1.51057i
\(595\) 0.214298 0.565057i 0.00878535 0.0231651i
\(596\) 1.95394i 0.0800363i
\(597\) 2.42827 + 6.40283i 0.0993827 + 0.262051i
\(598\) −5.20516 + 43.5076i −0.212855 + 1.77916i
\(599\) −8.77057 + 23.1261i −0.358356 + 0.944907i 0.627695 + 0.778460i \(0.283999\pi\)
−0.986050 + 0.166447i \(0.946771\pi\)
\(600\) 18.0781 + 6.85611i 0.738035 + 0.279900i
\(601\) −16.3263 + 23.6528i −0.665966 + 0.964818i 0.333789 + 0.942648i \(0.391673\pi\)
−0.999754 + 0.0221698i \(0.992943\pi\)
\(602\) −5.20905 + 4.61481i −0.212305 + 0.188086i
\(603\) −23.8407 16.4561i −0.970869 0.670143i
\(604\) 40.2792 45.4659i 1.63894 1.84998i
\(605\) −1.38638 + 2.64152i −0.0563643 + 0.107393i
\(606\) 25.9107i 1.05255i
\(607\) 33.2627 + 17.4576i 1.35009 + 0.708582i 0.975787 0.218724i \(-0.0701896\pi\)
0.374303 + 0.927306i \(0.377882\pi\)
\(608\) −6.45714 + 53.1793i −0.261872 + 2.15671i
\(609\) 5.97058 2.26434i 0.241940 0.0917558i
\(610\) −4.84137 2.54095i −0.196021 0.102880i
\(611\) −4.27298 + 11.3270i −0.172866 + 0.458239i
\(612\) −3.52688 + 1.85105i −0.142566 + 0.0748242i
\(613\) −4.76109 + 5.37416i −0.192299 + 0.217060i −0.836750 0.547585i \(-0.815547\pi\)
0.644451 + 0.764645i \(0.277086\pi\)
\(614\) −3.13354 + 2.77607i −0.126459 + 0.112033i
\(615\) 0.478352 + 0.117903i 0.0192890 + 0.00475432i
\(616\) −131.021 15.9088i −5.27899 0.640986i
\(617\) 17.0200 + 19.2116i 0.685199 + 0.773430i 0.983474 0.181050i \(-0.0579496\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(618\) 13.6026 + 5.15879i 0.547178 + 0.207517i
\(619\) −18.2133 + 34.7026i −0.732056 + 1.39482i 0.179549 + 0.983749i \(0.442536\pi\)
−0.911605 + 0.411067i \(0.865156\pi\)
\(620\) −11.5849 + 6.08024i −0.465262 + 0.244188i
\(621\) −1.91633 15.7824i −0.0768998 0.633327i
\(622\) 14.6177 + 16.5000i 0.586117 + 0.661590i
\(623\) −16.5538 + 4.08015i −0.663214 + 0.163468i
\(624\) −16.1359 6.08711i −0.645954 0.243679i
\(625\) −21.9304 5.40535i −0.877215 0.216214i
\(626\) −21.9667 41.8540i −0.877965 1.67282i
\(627\) 16.7825 8.80813i 0.670228 0.351763i
\(628\) 12.3042 + 32.4434i 0.490990 + 1.29463i
\(629\) 1.74793 0.662902i 0.0696945 0.0264316i
\(630\) 10.3524 7.14576i 0.412450 0.284694i
\(631\) −3.68955 + 14.9691i −0.146879 + 0.595910i 0.850655 + 0.525724i \(0.176206\pi\)
−0.997534 + 0.0701864i \(0.977641\pi\)
\(632\) 0.907546 0.626434i 0.0361003 0.0249182i
\(633\) 0.880932 7.25513i 0.0350139 0.288365i
\(634\) 5.67125 + 14.9539i 0.225234 + 0.593893i
\(635\) −0.895915 + 1.70702i −0.0355533 + 0.0677412i
\(636\) 4.65629 6.74580i 0.184634 0.267488i
\(637\) −12.0269 + 49.1669i −0.476522 + 1.94806i
\(638\) 14.6372 + 21.2056i 0.579492 + 0.839539i
\(639\) −21.8050 + 2.64760i −0.862591 + 0.104738i
\(640\) −3.12774 + 0.770918i −0.123635 + 0.0304732i
\(641\) −4.03488 + 5.84554i −0.159368 + 0.230885i −0.894531 0.447006i \(-0.852490\pi\)
0.735163 + 0.677891i \(0.237106\pi\)
\(642\) 14.6400 16.5252i 0.577796 0.652197i
\(643\) −3.78725 7.21600i −0.149354 0.284571i 0.799272 0.600969i \(-0.205219\pi\)
−0.948626 + 0.316398i \(0.897526\pi\)
\(644\) −99.2150 12.0469i −3.90962 0.474714i
\(645\) −0.140769 + 0.0170924i −0.00554276 + 0.000673013i
\(646\) −4.66280 4.13088i −0.183455 0.162527i
\(647\) 17.2728 + 25.0240i 0.679065 + 0.983795i 0.999335 + 0.0364689i \(0.0116110\pi\)
−0.320270 + 0.947326i \(0.603774\pi\)
\(648\) −39.5016 4.79637i −1.55177 0.188419i
\(649\) 1.54698 + 12.7405i 0.0607243 + 0.500110i
\(650\) 43.5556 + 10.6543i 1.70839 + 0.417895i
\(651\) −2.31826 + 19.0926i −0.0908598 + 0.748298i
\(652\) 17.0539 69.1904i 0.667882 2.70970i
\(653\) 19.7265 0.771957 0.385978 0.922508i \(-0.373864\pi\)
0.385978 + 0.922508i \(0.373864\pi\)
\(654\) −9.58321 −0.374733
\(655\) 2.05912 8.35419i 0.0804566 0.326425i
\(656\) −15.3916 + 5.83727i −0.600942 + 0.227907i
\(657\) 15.6139i 0.609158i
\(658\) −37.0206 14.0401i −1.44321 0.547339i
\(659\) −8.02027 + 1.97682i −0.312425 + 0.0770059i −0.392411 0.919790i \(-0.628359\pi\)
0.0799854 + 0.996796i \(0.474513\pi\)
\(660\) −3.55582 3.15018i −0.138410 0.122621i
\(661\) 5.19897 + 21.0930i 0.202216 + 0.820424i 0.981139 + 0.193304i \(0.0619203\pi\)
−0.778923 + 0.627120i \(0.784234\pi\)
\(662\) 28.5659 + 25.3072i 1.11025 + 0.983593i
\(663\) 0.576848 0.399669i 0.0224029 0.0155219i
\(664\) 15.4319 13.6715i 0.598875 0.530557i
\(665\) 11.2915 + 7.79397i 0.437866 + 0.302237i
\(666\) 37.7812 + 9.31222i 1.46399 + 0.360841i
\(667\) 6.27474 + 9.09053i 0.242959 + 0.351987i
\(668\) 11.7572 + 47.7010i 0.454901 + 1.84561i
\(669\) −0.775838 3.14770i −0.0299956 0.121697i
\(670\) −11.2727 + 1.36875i −0.435502 + 0.0528795i
\(671\) −14.9989 16.9302i −0.579026 0.653585i
\(672\) 6.99898 18.4548i 0.269991 0.711909i
\(673\) 3.19351 + 1.67609i 0.123101 + 0.0646083i 0.525149 0.851010i \(-0.324009\pi\)
−0.402049 + 0.915618i \(0.631702\pi\)
\(674\) −27.1838 + 18.7636i −1.04708 + 0.722748i
\(675\) −16.2691 −0.626197
\(676\) −58.2321 14.1358i −2.23969 0.543686i
\(677\) −0.279497 −0.0107420 −0.00537098 0.999986i \(-0.501710\pi\)
−0.00537098 + 0.999986i \(0.501710\pi\)
\(678\) −8.54771 + 5.90006i −0.328273 + 0.226590i
\(679\) −42.9467 22.5402i −1.64814 0.865013i
\(680\) −0.313435 + 0.826461i −0.0120197 + 0.0316933i
\(681\) −2.87745 3.24797i −0.110264 0.124463i
\(682\) −77.0420 + 9.35460i −2.95009 + 0.358206i
\(683\) −4.67466 18.9658i −0.178871 0.725708i −0.990027 0.140878i \(-0.955007\pi\)
0.811156 0.584830i \(-0.198839\pi\)
\(684\) −21.6412 87.8020i −0.827474 3.35719i
\(685\) 3.54511 + 5.13598i 0.135452 + 0.196236i
\(686\) −80.5869 19.8629i −3.07682 0.758368i
\(687\) −0.741452 0.511787i −0.0282882 0.0195259i
\(688\) 3.54644 3.14187i 0.135207 0.119783i
\(689\) 4.98436 9.53763i 0.189889 0.363355i
\(690\) −2.18571 1.93637i −0.0832086 0.0737164i
\(691\) 10.0198 + 40.6519i 0.381171 + 1.54647i 0.777811 + 0.628498i \(0.216330\pi\)
−0.396640 + 0.917974i \(0.629824\pi\)
\(692\) −31.6161 28.0094i −1.20186 1.06476i
\(693\) 50.5252 12.4533i 1.91929 0.473063i
\(694\) 61.9002 + 23.4756i 2.34970 + 0.891123i
\(695\) 6.16078i 0.233692i
\(696\) −8.73266 + 3.31186i −0.331011 + 0.125536i
\(697\) 0.160306 0.650386i 0.00607202 0.0246351i
\(698\) 13.6209 0.515558
\(699\) −2.46601 −0.0932732
\(700\) −24.4759 + 99.3025i −0.925100 + 3.75328i
\(701\) 3.98495 32.8190i 0.150509 1.23956i −0.700210 0.713937i \(-0.746910\pi\)
0.850719 0.525620i \(-0.176167\pi\)
\(702\) 31.1753 0.0548278i 1.17663 0.00206934i
\(703\) 5.11578 + 42.1322i 0.192945 + 1.58905i
\(704\) 10.6953 + 1.29865i 0.403095 + 0.0489446i
\(705\) −0.458296 0.663956i −0.0172604 0.0250060i
\(706\) −12.2757 10.8753i −0.462003 0.409299i
\(707\) 77.0260 9.35265i 2.89686 0.351743i
\(708\) −8.15742 0.990490i −0.306575 0.0372249i
\(709\) 16.0773 + 30.6327i 0.603796 + 1.15044i 0.975067 + 0.221912i \(0.0712297\pi\)
−0.371271 + 0.928525i \(0.621078\pi\)
\(710\) −5.70959 + 6.44480i −0.214277 + 0.241869i
\(711\) −0.246985 + 0.357819i −0.00926266 + 0.0134193i
\(712\) 24.2118 5.96769i 0.907377 0.223648i
\(713\) −33.0268 + 4.01017i −1.23686 + 0.150182i
\(714\) 1.30381 + 1.88890i 0.0487940 + 0.0706904i
\(715\) −5.13914 3.53396i −0.192193 0.132163i
\(716\) 54.8695 79.4922i 2.05057 2.97076i
\(717\) −7.29331 + 13.8962i −0.272374 + 0.518965i
\(718\) 2.34105 + 6.17284i 0.0873671 + 0.230368i
\(719\) −1.93598 + 15.9442i −0.0721998 + 0.594619i 0.911042 + 0.412313i \(0.135279\pi\)
−0.983242 + 0.182306i \(0.941644\pi\)
\(720\) −7.04817 + 4.86500i −0.262670 + 0.181308i
\(721\) −10.4258 + 42.2992i −0.388278 + 1.57530i
\(722\) 76.1931 52.5923i 2.83561 1.95728i
\(723\) −2.11307 + 0.801382i −0.0785860 + 0.0298037i
\(724\) 18.0202 + 47.5154i 0.669716 + 1.76590i
\(725\) 10.0087 5.25295i 0.371713 0.195090i
\(726\) −5.26534 10.0323i −0.195415 0.372333i
\(727\) 15.0733 + 3.71525i 0.559039 + 0.137791i 0.508704 0.860942i \(-0.330125\pi\)
0.0503355 + 0.998732i \(0.483971\pi\)
\(728\) 26.3619 107.770i 0.977038 3.99422i
\(729\) 9.39629 2.31598i 0.348011 0.0857769i
\(730\) −4.05867 4.58130i −0.150218 0.169561i
\(731\) 0.0232395 + 0.191395i 0.000859545 + 0.00707899i
\(732\) 12.8232 6.73016i 0.473961 0.248754i
\(733\) 15.8337 30.1685i 0.584830 1.11430i −0.395783 0.918344i \(-0.629527\pi\)
0.980613 0.195956i \(-0.0627810\pi\)
\(734\) −19.0040 7.20728i −0.701452 0.266026i
\(735\) −2.23681 2.52484i −0.0825061 0.0931301i
\(736\) 33.8932 + 4.11538i 1.24932 + 0.151695i
\(737\) −45.6103 11.2419i −1.68008 0.414102i
\(738\) 10.4365 9.24591i 0.384172 0.340347i
\(739\) 27.6003 31.1543i 1.01529 1.14603i 0.0260631 0.999660i \(-0.491703\pi\)
0.989230 0.146369i \(-0.0467586\pi\)
\(740\) 9.41915 4.94355i 0.346255 0.181729i
\(741\) 5.67597 + 14.8873i 0.208512 + 0.546898i
\(742\) 31.1645 + 16.3564i 1.14408 + 0.600462i
\(743\) −0.819364 + 0.310744i −0.0300595 + 0.0114001i −0.369589 0.929195i \(-0.620501\pi\)
0.339529 + 0.940595i \(0.389732\pi\)
\(744\) 3.39072 27.9251i 0.124310 1.02378i
\(745\) 0.151374 + 0.0794474i 0.00554593 + 0.00291073i
\(746\) 35.8409i 1.31223i
\(747\) −3.77756 + 7.19755i −0.138214 + 0.263344i
\(748\) −4.28311 + 4.83463i −0.156606 + 0.176772i
\(749\) 54.4096 + 37.5562i 1.98808 + 1.37227i
\(750\) −4.54857 + 4.02968i −0.166090 + 0.147143i
\(751\) −17.2838 + 25.0399i −0.630695 + 0.913720i −0.999878 0.0156370i \(-0.995022\pi\)
0.369182 + 0.929357i \(0.379638\pi\)
\(752\) 25.2045 + 9.55881i 0.919114 + 0.348574i
\(753\) 1.98494 5.23387i 0.0723354 0.190733i
\(754\) −19.1612 + 10.0996i −0.697809 + 0.367805i
\(755\) 1.88455 + 4.96914i 0.0685857 + 0.180846i
\(756\) 71.1074i 2.58615i
\(757\) −0.133653 + 0.352415i −0.00485771 + 0.0128087i −0.937423 0.348192i \(-0.886796\pi\)
0.932565 + 0.361001i \(0.117565\pi\)
\(758\) 6.59802 + 54.3396i 0.239651 + 1.97370i
\(759\) −5.61375 10.6961i −0.203766 0.388244i
\(760\) −16.5151 11.3996i −0.599067 0.413506i
\(761\) −20.4697 14.1292i −0.742026 0.512183i 0.136052 0.990702i \(-0.456559\pi\)
−0.878078 + 0.478518i \(0.841174\pi\)
\(762\) −3.40261 6.48313i −0.123263 0.234859i
\(763\) −3.45912 28.4884i −0.125229 1.03135i
\(764\) −28.1934 + 74.3400i −1.02000 + 2.68953i
\(765\) 0.348496i 0.0125999i
\(766\) 10.2271 + 26.9666i 0.369519 + 0.974343i
\(767\) −10.7885 + 0.0189737i −0.389551 + 0.000685102i
\(768\) 5.39972 14.2379i 0.194846 0.513766i
\(769\) −41.5016 15.7395i −1.49659 0.567581i −0.535672 0.844426i \(-0.679942\pi\)
−0.960915 + 0.276845i \(0.910711\pi\)
\(770\) 11.5875 16.7874i 0.417585 0.604976i
\(771\) 7.25965 6.43149i 0.261450 0.231625i
\(772\) 34.7308 + 23.9729i 1.24999 + 0.862804i
\(773\) −8.14448 + 9.19322i −0.292937 + 0.330657i −0.876492 0.481416i \(-0.840123\pi\)
0.583556 + 0.812073i \(0.301661\pi\)
\(774\) −1.86500 + 3.55347i −0.0670362 + 0.127727i
\(775\) 34.0451i 1.22294i
\(776\) 62.8145 + 32.9676i 2.25491 + 1.18347i
\(777\) 1.88487 15.5233i 0.0676192 0.556894i
\(778\) 81.9525 31.0805i 2.93814 1.11429i
\(779\) 13.4658 + 7.06741i 0.482463 + 0.253216i
\(780\) 2.98441 2.65334i 0.106859 0.0950048i
\(781\) −31.5386 + 16.5527i −1.12854 + 0.592303i
\(782\) −2.63277 + 2.97178i −0.0941476 + 0.106271i
\(783\) 5.88241 5.21136i 0.210220 0.186239i
\(784\) 109.431 + 26.9723i 3.90824 + 0.963296i
\(785\) −3.01373 0.365933i −0.107565 0.0130607i
\(786\) 21.6696 + 24.4599i 0.772927 + 0.872455i
\(787\) −10.8710 4.12283i −0.387510 0.146963i 0.153153 0.988202i \(-0.451057\pi\)
−0.540663 + 0.841239i \(0.681826\pi\)
\(788\) 20.9588 39.9336i 0.746625 1.42257i
\(789\) 3.96217 2.07951i 0.141057 0.0740324i
\(790\) 0.0205433 + 0.169189i 0.000730897 + 0.00601948i
\(791\) −20.6247 23.2805i −0.733331 0.827759i
\(792\) −73.8989 + 18.2144i −2.62588 + 0.647222i
\(793\) 15.6288 10.8284i 0.554995 0.384528i
\(794\) 77.6936 + 19.1497i 2.75724 + 0.679599i
\(795\) 0.333282 + 0.635015i 0.0118203 + 0.0225217i
\(796\) 46.9120 24.6213i 1.66275 0.872679i
\(797\) 0.170181 + 0.448729i 0.00602811 + 0.0158948i 0.937997 0.346645i \(-0.112679\pi\)
−0.931968 + 0.362539i \(0.881910\pi\)
\(798\) −48.7220 + 18.4778i −1.72474 + 0.654107i
\(799\) −0.902741 + 0.623117i −0.0319367 + 0.0220443i
\(800\) 8.36128 33.9231i 0.295616 1.19936i
\(801\) −8.09136 + 5.58506i −0.285894 + 0.197338i
\(802\) 6.95690 57.2952i 0.245657 2.02316i
\(803\) −8.97840 23.6741i −0.316841 0.835441i
\(804\) 13.9775 26.6319i 0.492949 0.939235i
\(805\) 4.96739 7.19651i 0.175078 0.253644i
\(806\) −0.114734 65.2383i −0.00404134 2.29792i
\(807\) 6.19463 + 8.97448i 0.218061 + 0.315917i
\(808\) −112.659 + 13.6793i −3.96334 + 0.481237i
\(809\) −13.8235 + 3.40719i −0.486009 + 0.119790i −0.474704 0.880146i \(-0.657445\pi\)
−0.0113053 + 0.999936i \(0.503599\pi\)
\(810\) 3.49353 5.06124i 0.122750 0.177834i
\(811\) −9.89642 + 11.1707i −0.347510 + 0.392258i −0.896114 0.443825i \(-0.853621\pi\)
0.548603 + 0.836083i \(0.315160\pi\)
\(812\) −22.9591 43.7450i −0.805707 1.53515i
\(813\) −10.4546 1.26942i −0.366659 0.0445205i
\(814\) 62.6392 7.60577i 2.19550 0.266582i
\(815\) 4.66687 + 4.13448i 0.163473 + 0.144825i
\(816\) −0.887668 1.28601i −0.0310746 0.0450193i
\(817\) −4.34528 0.527612i −0.152022 0.0184588i
\(818\) −4.47838 36.8828i −0.156583 1.28958i
\(819\) 5.34904 + 43.4150i 0.186910 + 1.51704i
\(820\) 0.459449 3.78390i 0.0160447 0.132140i
\(821\) −6.64187 + 26.9471i −0.231803 + 0.940461i 0.733576 + 0.679608i \(0.237850\pi\)
−0.965378 + 0.260853i \(0.915996\pi\)
\(822\) −23.7016 −0.826687
\(823\) −21.9186 −0.764034 −0.382017 0.924155i \(-0.624770\pi\)
−0.382017 + 0.924155i \(0.624770\pi\)
\(824\) 15.2490 61.8675i 0.531223 2.15526i
\(825\) −11.5582 + 4.38344i −0.402404 + 0.152612i
\(826\) 35.2843i 1.22770i
\(827\) −26.3308 9.98596i −0.915612 0.347246i −0.148614 0.988895i \(-0.547481\pi\)
−0.766998 + 0.641649i \(0.778251\pi\)
\(828\) −55.9595 + 13.7928i −1.94473 + 0.479332i
\(829\) 12.9483 + 11.4712i 0.449714 + 0.398412i 0.857351 0.514732i \(-0.172109\pi\)
−0.407637 + 0.913144i \(0.633647\pi\)
\(830\) 0.762547 + 3.09377i 0.0264684 + 0.107386i
\(831\) 6.11203 + 5.41478i 0.212024 + 0.187837i
\(832\) −2.15194 + 8.79730i −0.0746049 + 0.304992i
\(833\) −3.43287 + 3.04126i −0.118942 + 0.105373i
\(834\) −19.2563 13.2916i −0.666790 0.460252i
\(835\) −4.17352 1.02868i −0.144431 0.0355989i
\(836\) −83.3011 120.682i −2.88103 4.17389i
\(837\) 5.66466 + 22.9824i 0.195799 + 0.794390i
\(838\) 16.4726 + 66.8320i 0.569037 + 2.30867i
\(839\) −20.8963 + 2.53727i −0.721419 + 0.0875961i −0.473007 0.881058i \(-0.656832\pi\)
−0.248412 + 0.968655i \(0.579909\pi\)
\(840\) 4.90291 + 5.53424i 0.169166 + 0.190949i
\(841\) 8.34735 22.0102i 0.287840 0.758971i
\(842\) 19.2770 + 10.1174i 0.664330 + 0.348667i
\(843\) 15.1833 10.4802i 0.522939 0.360959i
\(844\) −56.5440 −1.94633
\(845\) 3.46285 3.93656i 0.119126 0.135422i
\(846\) −22.8323 −0.784990
\(847\) 27.9228 19.2737i 0.959439 0.662253i
\(848\) −21.2175 11.1358i −0.728613 0.382406i
\(849\) −1.41078 + 3.71992i −0.0484179 + 0.127667i
\(850\) 2.69416 + 3.04108i 0.0924090 + 0.104308i
\(851\) 26.8525 3.26048i 0.920491 0.111768i
\(852\) −5.45773 22.1429i −0.186979 0.758602i
\(853\) 9.55433 + 38.7634i 0.327134 + 1.32723i 0.872327 + 0.488924i \(0.162610\pi\)
−0.545193 + 0.838311i \(0.683544\pi\)
\(854\) 35.3248 + 51.1768i 1.20879 + 1.75123i
\(855\) 7.68209 + 1.89346i 0.262722 + 0.0647551i
\(856\) −79.5803 54.9303i −2.72000 1.87748i
\(857\) 20.4879 18.1507i 0.699854 0.620017i −0.236269 0.971688i \(-0.575925\pi\)
0.936124 + 0.351671i \(0.114386\pi\)
\(858\) 22.1333 8.43862i 0.755619 0.288090i
\(859\) 22.1799 + 19.6497i 0.756770 + 0.670439i 0.950538 0.310608i \(-0.100533\pi\)
−0.193769 + 0.981047i \(0.562071\pi\)
\(860\) 0.262554 + 1.06522i 0.00895302 + 0.0363238i
\(861\) −4.19404 3.71560i −0.142933 0.126627i
\(862\) −39.4526 + 9.72419i −1.34376 + 0.331207i
\(863\) 52.7117 + 19.9909i 1.79433 + 0.680498i 0.997039 + 0.0768975i \(0.0245014\pi\)
0.797287 + 0.603601i \(0.206268\pi\)
\(864\) 24.2912i 0.826405i
\(865\) 3.45544 1.31048i 0.117489 0.0445575i
\(866\) −0.693081 + 2.81194i −0.0235518 + 0.0955536i
\(867\) −10.0647 −0.341816
\(868\) 148.801 5.05065
\(869\) −0.168727 + 0.684554i −0.00572368 + 0.0232219i
\(870\) 0.173988 1.43292i 0.00589875 0.0485806i
\(871\) 13.9377 36.9467i 0.472262 1.25189i
\(872\) 5.05936 + 41.6676i 0.171332 + 1.41104i
\(873\) −27.7658 3.37138i −0.939730 0.114104i
\(874\) −51.2040 74.1819i −1.73200 2.50924i
\(875\) −13.6210 12.0672i −0.460475 0.407946i
\(876\) 16.0932 1.95407i 0.543738 0.0660218i
\(877\) −27.7664 3.37145i −0.937605 0.113846i −0.362553 0.931963i \(-0.618095\pi\)
−0.575051 + 0.818117i \(0.695018\pi\)
\(878\) 6.31420 + 12.0307i 0.213094 + 0.406017i
\(879\) −7.82831 + 8.83634i −0.264042 + 0.298042i
\(880\) −7.88905 + 11.4293i −0.265940 + 0.385281i
\(881\) −30.0556 + 7.40804i −1.01260 + 0.249583i −0.710503 0.703694i \(-0.751532\pi\)
−0.302096 + 0.953278i \(0.597686\pi\)
\(882\) −94.7674 + 11.5068i −3.19098 + 0.387456i
\(883\) 4.96950 + 7.19957i 0.167237 + 0.242285i 0.897638 0.440734i \(-0.145282\pi\)
−0.730400 + 0.683019i \(0.760667\pi\)
\(884\) −3.60759 4.05772i −0.121336 0.136476i
\(885\) 0.408417 0.591694i 0.0137288 0.0198896i
\(886\) −50.2159 + 95.6783i −1.68703 + 3.21438i
\(887\) −13.8269 36.4584i −0.464260 1.22415i −0.938966 0.344009i \(-0.888215\pi\)
0.474706 0.880144i \(-0.342554\pi\)
\(888\) −2.75684 + 22.7046i −0.0925133 + 0.761916i
\(889\) 18.0445 12.4552i 0.605193 0.417734i
\(890\) −0.922314 + 3.74198i −0.0309160 + 0.125431i
\(891\) 20.9373 14.4520i 0.701427 0.484160i
\(892\) −23.4521 + 8.89423i −0.785236 + 0.297801i
\(893\) −8.83089 23.2851i −0.295515 0.779208i
\(894\) −0.574906 + 0.301734i −0.0192277 + 0.0100915i
\(895\) 3.92738 + 7.48299i 0.131278 + 0.250129i
\(896\) 35.5722 + 8.76776i 1.18838 + 0.292910i
\(897\) 9.48822 3.61751i 0.316802 0.120785i
\(898\) −98.8312 + 24.3597i −3.29804 + 0.812894i
\(899\) −10.9054 12.3097i −0.363717 0.410552i
\(900\) 7.10905 + 58.5483i 0.236968 + 1.95161i
\(901\) 0.863391 0.453143i 0.0287637 0.0150964i
\(902\) 10.5073 20.0200i 0.349855 0.666594i
\(903\) 1.50794 + 0.571886i 0.0501811 + 0.0190312i
\(904\) 30.1660 + 34.0504i 1.00331 + 1.13250i
\(905\) −4.41379 0.535931i −0.146719 0.0178150i
\(906\) −19.5975 4.83035i −0.651083 0.160478i
\(907\) −1.42072 + 1.25865i −0.0471744 + 0.0417928i −0.686381 0.727243i \(-0.740802\pi\)
0.639206 + 0.769035i \(0.279263\pi\)
\(908\) −22.2624 + 25.1291i −0.738804 + 0.833937i
\(909\) 39.6194 20.7939i 1.31409 0.689689i
\(910\) 12.8547 + 11.3480i 0.426130 + 0.376183i
\(911\) 1.08743 + 0.570726i 0.0360281 + 0.0189090i 0.482641 0.875818i \(-0.339678\pi\)
−0.446613 + 0.894727i \(0.647370\pi\)
\(912\) 33.1711 12.5801i 1.09840 0.416570i
\(913\) −1.58883 + 13.0852i −0.0525827 + 0.433058i
\(914\) 87.1058 + 45.7166i 2.88120 + 1.51217i
\(915\) 1.26708i 0.0418885i
\(916\) −3.23929 + 6.17195i −0.107029 + 0.203927i
\(917\) −64.8912 + 73.2470i −2.14289 + 2.41883i
\(918\) 2.32471 + 1.60463i 0.0767269 + 0.0529608i
\(919\) −1.95734 + 1.73405i −0.0645665 + 0.0572010i −0.694789 0.719214i \(-0.744502\pi\)
0.630222 + 0.776415i \(0.282964\pi\)
\(920\) −7.26538 + 10.5257i −0.239533 + 0.347023i
\(921\) 0.907112 + 0.344022i 0.0298904 + 0.0113359i
\(922\) 1.57074 4.14169i 0.0517294 0.136399i
\(923\) −10.6666 27.9770i −0.351095 0.920874i
\(924\) 19.1587 + 50.5174i 0.630276 + 1.66190i
\(925\) 27.6805i 0.910128i
\(926\) 30.3732 80.0876i 0.998125 2.63184i
\(927\) 3.02819 + 24.9394i 0.0994589 + 0.819118i
\(928\) 7.84315 + 14.9439i 0.257464 + 0.490557i
\(929\) −29.8107 20.5768i −0.978056 0.675103i −0.0321292 0.999484i \(-0.510229\pi\)
−0.945927 + 0.324381i \(0.894844\pi\)
\(930\) 3.57798 + 2.46970i 0.117327 + 0.0809846i
\(931\) −48.3884 92.1965i −1.58587 3.02162i
\(932\) 2.29974 + 18.9401i 0.0753305 + 0.620402i
\(933\) 1.81149 4.77650i 0.0593054 0.156375i
\(934\) 43.6501i 1.42827i
\(935\) −0.200394 0.528396i −0.00655359 0.0172804i
\(936\) −7.82358 63.4995i −0.255722 2.07555i
\(937\) 9.65364 25.4545i 0.315371 0.831564i −0.679800 0.733398i \(-0.737933\pi\)
0.995170 0.0981658i \(-0.0312976\pi\)
\(938\) 120.755 + 45.7964i 3.94279 + 1.49530i
\(939\) −6.22261 + 9.01500i −0.203067 + 0.294194i
\(940\) −4.67208 + 4.13910i −0.152386 + 0.135003i
\(941\) 12.0793 + 8.33776i 0.393775 + 0.271803i 0.748456 0.663184i \(-0.230795\pi\)
−0.354682 + 0.934987i \(0.615411\pi\)
\(942\) 7.64577 8.63029i 0.249113 0.281190i
\(943\) 4.50433 8.58228i 0.146681 0.279478i
\(944\) 24.0224i 0.781863i
\(945\) −5.50879 2.89124i −0.179201 0.0940520i
\(946\) −0.784416 + 6.46025i −0.0255036 + 0.210041i
\(947\) 7.56511 2.86907i 0.245833 0.0932322i −0.228611 0.973518i \(-0.573418\pi\)
0.474444 + 0.880286i \(0.342649\pi\)
\(948\) −0.399712 0.209785i −0.0129820 0.00681350i
\(949\) 20.6565 5.12991i 0.670537 0.166524i
\(950\) −81.6742 + 42.8659i −2.64986 + 1.39075i
\(951\) 2.45772 2.77419i 0.0796970 0.0899593i
\(952\) 7.52457 6.66619i 0.243873 0.216052i
\(953\) −22.0319 5.43038i −0.713684 0.175907i −0.134275 0.990944i \(-0.542871\pi\)
−0.579409 + 0.815037i \(0.696717\pi\)
\(954\) 20.1484 + 2.44646i 0.652328 + 0.0792070i
\(955\) −4.61288 5.20687i −0.149269 0.168490i
\(956\) 113.531 + 43.0565i 3.67184 + 1.39255i
\(957\) 2.77497 5.28727i 0.0897021 0.170913i
\(958\) −96.1073 + 50.4410i −3.10509 + 1.62967i
\(959\) −8.55523 70.4587i −0.276263 2.27523i
\(960\) −0.400227 0.451762i −0.0129173 0.0145806i
\(961\) 17.9945 4.43526i 0.580469 0.143073i
\(962\) 0.0932850 + 53.0421i 0.00300763 + 1.71015i
\(963\) 37.0171 + 9.12390i 1.19286 + 0.294014i
\(964\) 8.12556 + 15.4820i 0.261707 + 0.498640i
\(965\) −3.26938 + 1.71590i −0.105245 + 0.0552368i
\(966\) 11.7766 + 31.0524i 0.378906 + 0.999093i
\(967\) −32.1734 + 12.2018i −1.03463 + 0.392382i −0.812701 0.582682i \(-0.802004\pi\)
−0.221926 + 0.975064i \(0.571234\pi\)
\(968\) −40.8403 + 28.1901i −1.31266 + 0.906063i
\(969\) −0.345481 + 1.40167i −0.0110985 + 0.0450282i
\(970\) −9.02314 + 6.22822i −0.289715 + 0.199976i
\(971\) −0.186729 + 1.53785i −0.00599242 + 0.0493520i −0.995398 0.0958234i \(-0.969452\pi\)
0.989406 + 0.145175i \(0.0463747\pi\)
\(972\) 22.2682 + 58.7163i 0.714252 + 1.88333i
\(973\) 32.5620 62.0417i 1.04389 1.98897i
\(974\) −1.44482 + 2.09318i −0.0462950 + 0.0670699i
\(975\) −2.50453 10.0849i −0.0802090 0.322975i
\(976\) −24.0500 34.8424i −0.769820 1.11528i
\(977\) 37.4231 4.54398i 1.19727 0.145375i 0.502481 0.864588i \(-0.332421\pi\)
0.694789 + 0.719213i \(0.255498\pi\)
\(978\) −22.9914 + 5.66687i −0.735184 + 0.181207i
\(979\) −9.05669 + 13.1209i −0.289453 + 0.419345i
\(980\) −17.3059 + 19.5343i −0.552816 + 0.624000i
\(981\) −7.69071 14.6534i −0.245545 0.467848i
\(982\) −20.3129 2.46643i −0.648210 0.0787069i
\(983\) −16.4398 + 1.99616i −0.524349 + 0.0636675i −0.378432 0.925629i \(-0.623536\pi\)
−0.145918 + 0.989297i \(0.546613\pi\)
\(984\) 6.13427 + 5.43449i 0.195553 + 0.173245i
\(985\) 2.24153 + 3.24741i 0.0714210 + 0.103471i
\(986\) −1.94826 0.236561i −0.0620451 0.00753364i
\(987\) 1.10598 + 9.10858i 0.0352038 + 0.289929i
\(988\) 109.047 57.4773i 3.46926 1.82860i
\(989\) −0.336267 + 2.76941i −0.0106927 + 0.0880621i
\(990\) 2.81507 11.4212i 0.0894687 0.362989i
\(991\) 36.5566 1.16126 0.580630 0.814168i \(-0.302806\pi\)
0.580630 + 0.814168i \(0.302806\pi\)
\(992\) −50.8326 −1.61394
\(993\) 2.11654 8.58713i 0.0671663 0.272504i
\(994\) 91.5611 34.7245i 2.90414 1.10140i
\(995\) 4.63545i 0.146954i
\(996\) −7.89122 2.99274i −0.250043 0.0948287i
\(997\) −6.05702 + 1.49292i −0.191828 + 0.0472813i −0.334059 0.942552i \(-0.608418\pi\)
0.142231 + 0.989833i \(0.454572\pi\)
\(998\) −6.95475 6.16137i −0.220149 0.195035i
\(999\) −4.60567 18.6859i −0.145717 0.591196i
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 169.2.h.a.12.1 168
169.155 even 26 inner 169.2.h.a.155.1 yes 168
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
169.2.h.a.12.1 168 1.1 even 1 trivial
169.2.h.a.155.1 yes 168 169.155 even 26 inner