Properties

Label 69.2.g.a.44.6
Level $69$
Weight $2$
Character 69.44
Analytic conductor $0.551$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [69,2,Mod(5,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 69.g (of order \(22\), 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: \(0.550967773947\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 44.6
Character \(\chi\) \(=\) 69.44
Dual form 69.2.g.a.11.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.13923 - 1.77267i) q^{2} +(0.180745 + 1.72259i) q^{3} +(-1.01370 - 2.21969i) q^{4} +(-1.10513 - 0.324494i) q^{5} +(3.25951 + 1.64203i) q^{6} +(-1.21996 - 1.05710i) q^{7} +(-0.918158 - 0.132011i) q^{8} +(-2.93466 + 0.622700i) q^{9} +O(q^{10})\) \(q+(1.13923 - 1.77267i) q^{2} +(0.180745 + 1.72259i) q^{3} +(-1.01370 - 2.21969i) q^{4} +(-1.10513 - 0.324494i) q^{5} +(3.25951 + 1.64203i) q^{6} +(-1.21996 - 1.05710i) q^{7} +(-0.918158 - 0.132011i) q^{8} +(-2.93466 + 0.622700i) q^{9} +(-1.83421 + 1.58935i) q^{10} +(-4.10123 + 2.63570i) q^{11} +(3.64041 - 2.14739i) q^{12} +(2.30778 + 2.66332i) q^{13} +(-3.26371 + 0.958312i) q^{14} +(0.359226 - 1.96233i) q^{15} +(1.91599 - 2.21117i) q^{16} +(2.44661 - 5.35733i) q^{17} +(-2.23941 + 5.91159i) q^{18} +(3.45437 - 1.57756i) q^{19} +(0.399988 + 2.78198i) q^{20} +(1.60046 - 2.29256i) q^{21} +10.2728i q^{22} +(-2.74840 + 3.93018i) q^{23} +(0.0614494 - 1.60547i) q^{24} +(-3.09026 - 1.98599i) q^{25} +(7.35029 - 1.05681i) q^{26} +(-1.60308 - 4.94268i) q^{27} +(-1.10977 + 3.77952i) q^{28} +(4.87704 + 2.22727i) q^{29} +(-3.06934 - 2.87234i) q^{30} +(-0.200482 + 1.39439i) q^{31} +(-2.25960 - 7.69550i) q^{32} +(-5.28152 - 6.58837i) q^{33} +(-6.70954 - 10.4403i) q^{34} +(1.00519 + 1.56410i) q^{35} +(4.35707 + 5.88282i) q^{36} +(-0.670140 - 2.28229i) q^{37} +(1.13882 - 7.92067i) q^{38} +(-4.17071 + 4.45676i) q^{39} +(0.971844 + 0.443826i) q^{40} +(0.848837 - 2.89087i) q^{41} +(-2.24068 - 5.44884i) q^{42} +(1.65948 - 0.238597i) q^{43} +(10.0079 + 6.43166i) q^{44} +(3.44524 + 0.264119i) q^{45} +(3.83586 + 9.34938i) q^{46} +11.0600i q^{47} +(4.15526 + 2.90082i) q^{48} +(-0.625364 - 4.34950i) q^{49} +(-7.04102 + 3.21553i) q^{50} +(9.67071 + 3.24621i) q^{51} +(3.57236 - 7.82238i) q^{52} +(-4.00477 + 4.62175i) q^{53} +(-10.5880 - 2.78910i) q^{54} +(5.38765 - 1.58196i) q^{55} +(0.980568 + 1.13164i) q^{56} +(3.34185 + 5.66535i) q^{57} +(9.50428 - 6.10803i) q^{58} +(4.12273 - 3.57237i) q^{59} +(-4.71993 + 1.19185i) q^{60} +(-3.50095 - 0.503360i) q^{61} +(2.24339 + 1.94391i) q^{62} +(4.23843 + 2.34257i) q^{63} +(-10.6012 - 3.11281i) q^{64} +(-1.68616 - 3.69217i) q^{65} +(-17.6959 + 1.85676i) q^{66} +(-7.43518 + 11.5694i) q^{67} -14.3717 q^{68} +(-7.26686 - 4.02402i) q^{69} +3.91778 q^{70} +(-0.504000 + 0.784239i) q^{71} +(2.77669 - 0.184329i) q^{72} +(2.17260 + 4.75733i) q^{73} +(-4.80919 - 1.41211i) q^{74} +(2.86251 - 5.68222i) q^{75} +(-7.00339 - 6.06847i) q^{76} +(7.78955 + 1.11997i) q^{77} +(3.14899 + 12.4706i) q^{78} +(-0.834060 + 0.722717i) q^{79} +(-2.83492 + 1.82189i) q^{80} +(8.22449 - 3.65483i) q^{81} +(-4.15755 - 4.79807i) q^{82} +(9.84410 - 2.89049i) q^{83} +(-6.71117 - 1.22855i) q^{84} +(-4.44223 + 5.12661i) q^{85} +(1.46757 - 3.21353i) q^{86} +(-2.95518 + 8.80373i) q^{87} +(4.11352 - 1.87858i) q^{88} +(-0.477689 - 3.32240i) q^{89} +(4.39310 - 5.80638i) q^{90} -5.68871i q^{91} +(11.5098 + 2.11659i) q^{92} +(-2.43820 - 0.0933217i) q^{93} +(19.6058 + 12.5999i) q^{94} +(-4.32943 + 0.622478i) q^{95} +(12.8478 - 5.28330i) q^{96} +(-3.01650 + 10.2733i) q^{97} +(-8.42268 - 3.84651i) q^{98} +(10.3945 - 10.2887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q - 11 q^{3} - 10 q^{4} - 14 q^{6} - 22 q^{7} - 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q - 11 q^{3} - 10 q^{4} - 14 q^{6} - 22 q^{7} - 11 q^{9} - 22 q^{10} + 4 q^{12} - 22 q^{13} - 46 q^{16} + 12 q^{18} - 22 q^{19} + 22 q^{21} + 50 q^{24} + 8 q^{25} + 10 q^{27} - 22 q^{28} + 33 q^{30} - 22 q^{31} + 22 q^{36} + 22 q^{37} + 13 q^{39} + 132 q^{40} - 11 q^{42} + 22 q^{43} + 66 q^{46} - 58 q^{48} + 68 q^{49} - 11 q^{51} + 94 q^{52} - 33 q^{54} - 44 q^{57} - 8 q^{58} - 121 q^{60} - 66 q^{61} - 66 q^{63} - 20 q^{64} - 66 q^{66} - 44 q^{67} - 66 q^{69} - 132 q^{70} - 101 q^{72} - 44 q^{73} - 44 q^{75} - 110 q^{76} + 84 q^{78} - 66 q^{79} + 77 q^{81} - 132 q^{82} + 77 q^{84} - 44 q^{85} + 73 q^{87} + 66 q^{88} + 176 q^{90} + 116 q^{93} + 100 q^{94} + 85 q^{96} + 44 q^{97} + 121 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{13}{22}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.13923 1.77267i 0.805556 1.25347i −0.158392 0.987376i \(-0.550631\pi\)
0.963947 0.266093i \(-0.0857327\pi\)
\(3\) 0.180745 + 1.72259i 0.104353 + 0.994540i
\(4\) −1.01370 2.21969i −0.506850 1.10985i
\(5\) −1.10513 0.324494i −0.494227 0.145118i 0.0251149 0.999685i \(-0.492005\pi\)
−0.519342 + 0.854566i \(0.673823\pi\)
\(6\) 3.25951 + 1.64203i 1.33069 + 0.670354i
\(7\) −1.21996 1.05710i −0.461102 0.399547i 0.393094 0.919498i \(-0.371405\pi\)
−0.854196 + 0.519951i \(0.825950\pi\)
\(8\) −0.918158 0.132011i −0.324618 0.0466730i
\(9\) −2.93466 + 0.622700i −0.978221 + 0.207567i
\(10\) −1.83421 + 1.58935i −0.580029 + 0.502598i
\(11\) −4.10123 + 2.63570i −1.23657 + 0.794694i −0.984901 0.173120i \(-0.944615\pi\)
−0.251667 + 0.967814i \(0.580979\pi\)
\(12\) 3.64041 2.14739i 1.05090 0.619898i
\(13\) 2.30778 + 2.66332i 0.640064 + 0.738673i 0.979386 0.201997i \(-0.0647432\pi\)
−0.339322 + 0.940670i \(0.610198\pi\)
\(14\) −3.26371 + 0.958312i −0.872263 + 0.256120i
\(15\) 0.359226 1.96233i 0.0927518 0.506673i
\(16\) 1.91599 2.21117i 0.478998 0.552793i
\(17\) 2.44661 5.35733i 0.593390 1.29934i −0.339982 0.940432i \(-0.610421\pi\)
0.933372 0.358910i \(-0.116852\pi\)
\(18\) −2.23941 + 5.91159i −0.527833 + 1.39338i
\(19\) 3.45437 1.57756i 0.792488 0.361917i 0.0223137 0.999751i \(-0.492897\pi\)
0.770174 + 0.637834i \(0.220169\pi\)
\(20\) 0.399988 + 2.78198i 0.0894401 + 0.622070i
\(21\) 1.60046 2.29256i 0.349248 0.500278i
\(22\) 10.2728i 2.19017i
\(23\) −2.74840 + 3.93018i −0.573082 + 0.819498i
\(24\) 0.0614494 1.60547i 0.0125433 0.327716i
\(25\) −3.09026 1.98599i −0.618052 0.397198i
\(26\) 7.35029 1.05681i 1.44151 0.207258i
\(27\) −1.60308 4.94268i −0.308514 0.951220i
\(28\) −1.10977 + 3.77952i −0.209726 + 0.714263i
\(29\) 4.87704 + 2.22727i 0.905643 + 0.413593i 0.813106 0.582116i \(-0.197775\pi\)
0.0925373 + 0.995709i \(0.470502\pi\)
\(30\) −3.06934 2.87234i −0.560382 0.524415i
\(31\) −0.200482 + 1.39439i −0.0360077 + 0.250439i −0.999873 0.0159520i \(-0.994922\pi\)
0.963865 + 0.266391i \(0.0858312\pi\)
\(32\) −2.25960 7.69550i −0.399445 1.36039i
\(33\) −5.28152 6.58837i −0.919395 1.14689i
\(34\) −6.70954 10.4403i −1.15068 1.79049i
\(35\) 1.00519 + 1.56410i 0.169908 + 0.264381i
\(36\) 4.35707 + 5.88282i 0.726178 + 0.980470i
\(37\) −0.670140 2.28229i −0.110170 0.375206i 0.885889 0.463898i \(-0.153549\pi\)
−0.996059 + 0.0886921i \(0.971731\pi\)
\(38\) 1.13882 7.92067i 0.184741 1.28490i
\(39\) −4.17071 + 4.45676i −0.667847 + 0.713652i
\(40\) 0.971844 + 0.443826i 0.153662 + 0.0701751i
\(41\) 0.848837 2.89087i 0.132566 0.451479i −0.866277 0.499564i \(-0.833494\pi\)
0.998843 + 0.0480851i \(0.0153119\pi\)
\(42\) −2.24068 5.44884i −0.345745 0.840774i
\(43\) 1.65948 0.238597i 0.253068 0.0363857i −0.0146131 0.999893i \(-0.504652\pi\)
0.267681 + 0.963508i \(0.413743\pi\)
\(44\) 10.0079 + 6.43166i 1.50874 + 0.969610i
\(45\) 3.44524 + 0.264119i 0.513585 + 0.0393726i
\(46\) 3.83586 + 9.34938i 0.565567 + 1.37849i
\(47\) 11.0600i 1.61327i 0.591049 + 0.806636i \(0.298714\pi\)
−0.591049 + 0.806636i \(0.701286\pi\)
\(48\) 4.15526 + 2.90082i 0.599759 + 0.418697i
\(49\) −0.625364 4.34950i −0.0893377 0.621358i
\(50\) −7.04102 + 3.21553i −0.995751 + 0.454744i
\(51\) 9.67071 + 3.24621i 1.35417 + 0.454560i
\(52\) 3.57236 7.82238i 0.495397 1.08477i
\(53\) −4.00477 + 4.62175i −0.550097 + 0.634846i −0.960906 0.276876i \(-0.910701\pi\)
0.410809 + 0.911721i \(0.365246\pi\)
\(54\) −10.5880 2.78910i −1.44085 0.379548i
\(55\) 5.38765 1.58196i 0.726470 0.213311i
\(56\) 0.980568 + 1.13164i 0.131034 + 0.151221i
\(57\) 3.34185 + 5.66535i 0.442639 + 0.750394i
\(58\) 9.50428 6.10803i 1.24797 0.802023i
\(59\) 4.12273 3.57237i 0.536734 0.465083i −0.343815 0.939037i \(-0.611719\pi\)
0.880549 + 0.473955i \(0.157174\pi\)
\(60\) −4.71993 + 1.19185i −0.609340 + 0.153867i
\(61\) −3.50095 0.503360i −0.448250 0.0644486i −0.0855065 0.996338i \(-0.527251\pi\)
−0.362744 + 0.931889i \(0.618160\pi\)
\(62\) 2.24339 + 1.94391i 0.284911 + 0.246877i
\(63\) 4.23843 + 2.34257i 0.533992 + 0.295136i
\(64\) −10.6012 3.11281i −1.32516 0.389101i
\(65\) −1.68616 3.69217i −0.209142 0.457957i
\(66\) −17.6959 + 1.85676i −2.17821 + 0.228551i
\(67\) −7.43518 + 11.5694i −0.908351 + 1.41342i 0.00218686 + 0.999998i \(0.499304\pi\)
−0.910538 + 0.413425i \(0.864332\pi\)
\(68\) −14.3717 −1.74283
\(69\) −7.26686 4.02402i −0.874827 0.484436i
\(70\) 3.91778 0.468264
\(71\) −0.504000 + 0.784239i −0.0598138 + 0.0930720i −0.869872 0.493277i \(-0.835799\pi\)
0.810059 + 0.586349i \(0.199435\pi\)
\(72\) 2.77669 0.184329i 0.327236 0.0217234i
\(73\) 2.17260 + 4.75733i 0.254284 + 0.556804i 0.993123 0.117078i \(-0.0373529\pi\)
−0.738839 + 0.673882i \(0.764626\pi\)
\(74\) −4.80919 1.41211i −0.559057 0.164154i
\(75\) 2.86251 5.68222i 0.330534 0.656127i
\(76\) −7.00339 6.06847i −0.803344 0.696102i
\(77\) 7.78955 + 1.11997i 0.887701 + 0.127632i
\(78\) 3.14899 + 12.4706i 0.356552 + 1.41201i
\(79\) −0.834060 + 0.722717i −0.0938390 + 0.0813120i −0.700517 0.713636i \(-0.747047\pi\)
0.606678 + 0.794948i \(0.292502\pi\)
\(80\) −2.83492 + 1.82189i −0.316954 + 0.203694i
\(81\) 8.22449 3.65483i 0.913832 0.406092i
\(82\) −4.15755 4.79807i −0.459125 0.529859i
\(83\) 9.84410 2.89049i 1.08053 0.317272i 0.307439 0.951568i \(-0.400528\pi\)
0.773091 + 0.634295i \(0.218710\pi\)
\(84\) −6.71117 1.22855i −0.732249 0.134046i
\(85\) −4.44223 + 5.12661i −0.481828 + 0.556059i
\(86\) 1.46757 3.21353i 0.158252 0.346524i
\(87\) −2.95518 + 8.80373i −0.316829 + 0.943858i
\(88\) 4.11352 1.87858i 0.438503 0.200258i
\(89\) −0.477689 3.32240i −0.0506349 0.352174i −0.999350 0.0360421i \(-0.988525\pi\)
0.948715 0.316132i \(-0.102384\pi\)
\(90\) 4.39310 5.80638i 0.463074 0.612047i
\(91\) 5.68871i 0.596339i
\(92\) 11.5098 + 2.11659i 1.19998 + 0.220670i
\(93\) −2.43820 0.0933217i −0.252829 0.00967701i
\(94\) 19.6058 + 12.5999i 2.02219 + 1.29958i
\(95\) −4.32943 + 0.622478i −0.444190 + 0.0638649i
\(96\) 12.8478 5.28330i 1.31127 0.539225i
\(97\) −3.01650 + 10.2733i −0.306279 + 1.04309i 0.652228 + 0.758023i \(0.273835\pi\)
−0.958507 + 0.285068i \(0.907984\pi\)
\(98\) −8.42268 3.84651i −0.850819 0.388556i
\(99\) 10.3945 10.2887i 1.04468 1.03406i
\(100\) −1.27569 + 8.87262i −0.127569 + 0.887262i
\(101\) −2.20019 7.49317i −0.218928 0.745599i −0.993572 0.113202i \(-0.963889\pi\)
0.774644 0.632397i \(-0.217929\pi\)
\(102\) 16.7716 13.4448i 1.66064 1.33124i
\(103\) −4.97262 7.73756i −0.489967 0.762404i 0.504945 0.863152i \(-0.331513\pi\)
−0.994912 + 0.100748i \(0.967877\pi\)
\(104\) −1.76732 2.75001i −0.173300 0.269660i
\(105\) −2.51263 + 2.01423i −0.245208 + 0.196569i
\(106\) 3.63050 + 12.3644i 0.352626 + 1.20093i
\(107\) −0.999645 + 6.95268i −0.0966393 + 0.672141i 0.882703 + 0.469931i \(0.155721\pi\)
−0.979342 + 0.202210i \(0.935188\pi\)
\(108\) −9.34619 + 8.56875i −0.899338 + 0.824528i
\(109\) 4.60395 + 2.10255i 0.440978 + 0.201388i 0.623516 0.781811i \(-0.285704\pi\)
−0.182537 + 0.983199i \(0.558431\pi\)
\(110\) 3.33347 11.3527i 0.317834 1.08244i
\(111\) 3.81033 1.56689i 0.361661 0.148723i
\(112\) −4.67487 + 0.672144i −0.441733 + 0.0635117i
\(113\) −13.2115 8.49053i −1.24284 0.798722i −0.256996 0.966413i \(-0.582733\pi\)
−0.985840 + 0.167691i \(0.946369\pi\)
\(114\) 13.8499 + 0.530105i 1.29717 + 0.0496489i
\(115\) 4.31265 3.45150i 0.402157 0.321854i
\(116\) 13.0833i 1.21475i
\(117\) −8.43102 6.37890i −0.779448 0.589729i
\(118\) −1.63591 11.3780i −0.150598 1.04743i
\(119\) −8.64801 + 3.94941i −0.792762 + 0.362042i
\(120\) −0.588877 + 1.75431i −0.0537569 + 0.160146i
\(121\) 5.30361 11.6133i 0.482146 1.05575i
\(122\) −4.88067 + 5.63259i −0.441875 + 0.509951i
\(123\) 5.13323 + 0.939691i 0.462847 + 0.0847291i
\(124\) 3.29833 0.968478i 0.296199 0.0869719i
\(125\) 6.54197 + 7.54983i 0.585131 + 0.675278i
\(126\) 8.98115 4.84463i 0.800104 0.431594i
\(127\) −6.74790 + 4.33661i −0.598779 + 0.384812i −0.804634 0.593770i \(-0.797639\pi\)
0.205855 + 0.978582i \(0.434002\pi\)
\(128\) −5.47242 + 4.74188i −0.483698 + 0.419127i
\(129\) 0.710948 + 2.81548i 0.0625955 + 0.247890i
\(130\) −8.46593 1.21722i −0.742511 0.106757i
\(131\) −6.43807 5.57862i −0.562497 0.487406i 0.326577 0.945171i \(-0.394105\pi\)
−0.889074 + 0.457764i \(0.848650\pi\)
\(132\) −9.27028 + 18.4020i −0.806874 + 1.60169i
\(133\) −5.88184 1.72706i −0.510020 0.149756i
\(134\) 12.0383 + 26.3603i 1.03995 + 2.27718i
\(135\) 0.167738 + 5.98248i 0.0144366 + 0.514890i
\(136\) −2.95360 + 4.59589i −0.253269 + 0.394095i
\(137\) 9.88214 0.844288 0.422144 0.906529i \(-0.361278\pi\)
0.422144 + 0.906529i \(0.361278\pi\)
\(138\) −15.4119 + 8.29748i −1.31195 + 0.706329i
\(139\) −1.52932 −0.129715 −0.0648576 0.997895i \(-0.520659\pi\)
−0.0648576 + 0.997895i \(0.520659\pi\)
\(140\) 2.45287 3.81674i 0.207305 0.322573i
\(141\) −19.0519 + 1.99904i −1.60446 + 0.168350i
\(142\) 0.816029 + 1.78685i 0.0684796 + 0.149949i
\(143\) −16.4845 4.84028i −1.37850 0.404764i
\(144\) −4.24589 + 7.68213i −0.353824 + 0.640177i
\(145\) −4.66701 4.04398i −0.387574 0.335835i
\(146\) 10.9083 + 1.56837i 0.902776 + 0.129800i
\(147\) 7.37940 1.86340i 0.608642 0.153691i
\(148\) −4.38665 + 3.80106i −0.360581 + 0.312445i
\(149\) 4.03130 2.59076i 0.330257 0.212243i −0.364995 0.931009i \(-0.618929\pi\)
0.695252 + 0.718766i \(0.255293\pi\)
\(150\) −6.81168 11.5476i −0.556171 0.942860i
\(151\) −3.37353 3.89326i −0.274534 0.316829i 0.601693 0.798727i \(-0.294493\pi\)
−0.876227 + 0.481898i \(0.839947\pi\)
\(152\) −3.37992 + 0.992433i −0.274147 + 0.0804970i
\(153\) −3.84396 + 17.2454i −0.310766 + 1.39421i
\(154\) 10.8594 12.5324i 0.875076 1.00989i
\(155\) 0.674028 1.47592i 0.0541393 0.118548i
\(156\) 14.1205 + 4.73987i 1.13054 + 0.379494i
\(157\) 16.4337 7.50501i 1.31155 0.598965i 0.367887 0.929871i \(-0.380081\pi\)
0.943664 + 0.330905i \(0.107354\pi\)
\(158\) 0.330957 + 2.30185i 0.0263295 + 0.183126i
\(159\) −8.68523 6.06323i −0.688784 0.480845i
\(160\) 9.23773i 0.730307i
\(161\) 7.50754 1.88932i 0.591677 0.148899i
\(162\) 2.89075 18.7430i 0.227119 1.47259i
\(163\) −3.88463 2.49650i −0.304268 0.195541i 0.379593 0.925154i \(-0.376064\pi\)
−0.683861 + 0.729613i \(0.739700\pi\)
\(164\) −7.27732 + 1.04632i −0.568263 + 0.0817039i
\(165\) 3.69886 + 8.99480i 0.287956 + 0.700244i
\(166\) 6.09078 20.7433i 0.472736 1.60999i
\(167\) −14.9427 6.82411i −1.15630 0.528065i −0.257439 0.966295i \(-0.582878\pi\)
−0.898863 + 0.438229i \(0.855606\pi\)
\(168\) −1.77212 + 1.89366i −0.136722 + 0.146099i
\(169\) 0.0826631 0.574935i 0.00635870 0.0442258i
\(170\) 4.02709 + 13.7150i 0.308864 + 1.05189i
\(171\) −9.15507 + 6.78064i −0.700106 + 0.518529i
\(172\) −2.21182 3.44167i −0.168650 0.262425i
\(173\) 8.24849 + 12.8349i 0.627121 + 0.975819i 0.998872 + 0.0474868i \(0.0151212\pi\)
−0.371751 + 0.928333i \(0.621242\pi\)
\(174\) 12.2395 + 15.2680i 0.927874 + 1.15747i
\(175\) 1.67060 + 5.68955i 0.126286 + 0.430090i
\(176\) −2.02993 + 14.1185i −0.153012 + 1.06422i
\(177\) 6.89891 + 6.45611i 0.518553 + 0.485271i
\(178\) −6.43373 2.93818i −0.482228 0.220226i
\(179\) 5.70031 19.4135i 0.426061 1.45103i −0.414866 0.909882i \(-0.636172\pi\)
0.840927 0.541148i \(-0.182010\pi\)
\(180\) −2.90617 7.91510i −0.216613 0.589957i
\(181\) 17.3467 2.49409i 1.28937 0.185384i 0.536697 0.843775i \(-0.319672\pi\)
0.752676 + 0.658391i \(0.228763\pi\)
\(182\) −10.0842 6.48074i −0.747493 0.480384i
\(183\) 0.234307 6.12169i 0.0173205 0.452528i
\(184\) 3.04230 3.24570i 0.224281 0.239276i
\(185\) 2.73967i 0.201425i
\(186\) −2.94309 + 4.21581i −0.215798 + 0.309118i
\(187\) 4.08620 + 28.4202i 0.298813 + 2.07829i
\(188\) 24.5499 11.2115i 1.79048 0.817686i
\(189\) −3.26922 + 7.72451i −0.237801 + 0.561875i
\(190\) −3.82875 + 8.38380i −0.277767 + 0.608225i
\(191\) 2.90913 3.35732i 0.210497 0.242927i −0.640676 0.767811i \(-0.721346\pi\)
0.851174 + 0.524884i \(0.175891\pi\)
\(192\) 3.44598 18.8243i 0.248692 1.35852i
\(193\) −15.6259 + 4.58817i −1.12477 + 0.330264i −0.790652 0.612266i \(-0.790258\pi\)
−0.334123 + 0.942530i \(0.608440\pi\)
\(194\) 14.7746 + 17.0509i 1.06076 + 1.22418i
\(195\) 6.05535 3.57191i 0.433633 0.255790i
\(196\) −9.02063 + 5.79720i −0.644330 + 0.414086i
\(197\) 8.26866 7.16484i 0.589118 0.510473i −0.308514 0.951220i \(-0.599832\pi\)
0.897632 + 0.440746i \(0.145286\pi\)
\(198\) −6.39688 30.1472i −0.454606 2.14247i
\(199\) 14.8212 + 2.13097i 1.05065 + 0.151061i 0.645942 0.763386i \(-0.276465\pi\)
0.404706 + 0.914447i \(0.367374\pi\)
\(200\) 2.57518 + 2.23140i 0.182092 + 0.157784i
\(201\) −21.2732 10.7167i −1.50049 0.755897i
\(202\) −15.7895 4.63621i −1.11094 0.326202i
\(203\) −3.59535 7.87271i −0.252344 0.552556i
\(204\) −2.59762 24.7567i −0.181870 1.73331i
\(205\) −1.87614 + 2.91934i −0.131036 + 0.203895i
\(206\) −19.3811 −1.35035
\(207\) 5.61831 13.2452i 0.390500 0.920603i
\(208\) 10.3108 0.714922
\(209\) −10.0092 + 15.5746i −0.692351 + 1.07732i
\(210\) 0.708118 + 6.74874i 0.0488648 + 0.465708i
\(211\) −8.96001 19.6197i −0.616833 1.35067i −0.917801 0.397041i \(-0.870037\pi\)
0.300968 0.953634i \(-0.402690\pi\)
\(212\) 14.3185 + 4.20429i 0.983397 + 0.288752i
\(213\) −1.44202 0.726440i −0.0988057 0.0497749i
\(214\) 11.1860 + 9.69273i 0.764660 + 0.662581i
\(215\) −1.91136 0.274812i −0.130353 0.0187420i
\(216\) 0.819396 + 4.74979i 0.0557528 + 0.323182i
\(217\) 1.71859 1.48917i 0.116665 0.101091i
\(218\) 8.97209 5.76601i 0.607667 0.390524i
\(219\) −7.80227 + 4.60237i −0.527228 + 0.311000i
\(220\) −8.97291 10.3553i −0.604954 0.698154i
\(221\) 19.9145 5.84743i 1.33960 0.393341i
\(222\) 1.56325 8.53951i 0.104918 0.573135i
\(223\) 1.96233 2.26465i 0.131407 0.151652i −0.686232 0.727382i \(-0.740737\pi\)
0.817640 + 0.575730i \(0.195282\pi\)
\(224\) −5.37830 + 11.7768i −0.359353 + 0.786874i
\(225\) 10.3055 + 3.90390i 0.687036 + 0.260260i
\(226\) −30.1019 + 13.7471i −2.00235 + 0.914441i
\(227\) 0.473354 + 3.29225i 0.0314176 + 0.218514i 0.999482 0.0321880i \(-0.0102475\pi\)
−0.968064 + 0.250702i \(0.919338\pi\)
\(228\) 9.18769 13.1608i 0.608470 0.871599i
\(229\) 14.4101i 0.952245i 0.879379 + 0.476123i \(0.157958\pi\)
−0.879379 + 0.476123i \(0.842042\pi\)
\(230\) −1.20529 11.5770i −0.0794742 0.763362i
\(231\) −0.521330 + 13.6207i −0.0343010 + 0.896174i
\(232\) −4.18387 2.68881i −0.274684 0.176529i
\(233\) 12.7966 1.83987i 0.838334 0.120534i 0.290243 0.956953i \(-0.406264\pi\)
0.548091 + 0.836419i \(0.315355\pi\)
\(234\) −20.9125 + 7.67842i −1.36710 + 0.501954i
\(235\) 3.58892 12.2227i 0.234115 0.797323i
\(236\) −12.1088 5.52989i −0.788214 0.359965i
\(237\) −1.39570 1.30612i −0.0906604 0.0848416i
\(238\) −2.85103 + 19.8294i −0.184805 + 1.28535i
\(239\) 1.21215 + 4.12821i 0.0784077 + 0.267032i 0.989362 0.145476i \(-0.0464712\pi\)
−0.910954 + 0.412508i \(0.864653\pi\)
\(240\) −3.65078 4.55412i −0.235657 0.293967i
\(241\) 11.2648 + 17.5284i 0.725631 + 1.12910i 0.986505 + 0.163731i \(0.0523528\pi\)
−0.260874 + 0.965373i \(0.584011\pi\)
\(242\) −14.5445 22.6317i −0.934959 1.45482i
\(243\) 7.78232 + 13.5069i 0.499236 + 0.866466i
\(244\) 2.43160 + 8.28128i 0.155667 + 0.530154i
\(245\) −0.720283 + 5.00968i −0.0460172 + 0.320056i
\(246\) 7.51368 8.02901i 0.479055 0.511911i
\(247\) 12.1735 + 5.55945i 0.774581 + 0.353739i
\(248\) 0.368149 1.25380i 0.0233775 0.0796164i
\(249\) 6.75841 + 16.4350i 0.428297 + 1.04152i
\(250\) 20.8362 2.99579i 1.31780 0.189470i
\(251\) 6.46799 + 4.15672i 0.408256 + 0.262370i 0.728611 0.684927i \(-0.240166\pi\)
−0.320356 + 0.947297i \(0.603802\pi\)
\(252\) 0.903285 11.7827i 0.0569016 0.742239i
\(253\) 0.913067 23.3625i 0.0574040 1.46879i
\(254\) 16.9022i 1.06054i
\(255\) −9.63398 6.72556i −0.603303 0.421171i
\(256\) −0.973349 6.76979i −0.0608343 0.423112i
\(257\) −9.89851 + 4.52050i −0.617452 + 0.281981i −0.699483 0.714649i \(-0.746587\pi\)
0.0820313 + 0.996630i \(0.473859\pi\)
\(258\) 5.80086 + 1.94720i 0.361146 + 0.121227i
\(259\) −1.59507 + 3.49271i −0.0991126 + 0.217026i
\(260\) −6.48623 + 7.48550i −0.402259 + 0.464231i
\(261\) −15.6994 3.49935i −0.971767 0.216604i
\(262\) −17.2235 + 5.05728i −1.06407 + 0.312440i
\(263\) −4.11436 4.74823i −0.253703 0.292788i 0.614584 0.788851i \(-0.289324\pi\)
−0.868286 + 0.496063i \(0.834778\pi\)
\(264\) 3.97953 + 6.74639i 0.244923 + 0.415211i
\(265\) 5.92550 3.80809i 0.364001 0.233929i
\(266\) −9.76228 + 8.45906i −0.598564 + 0.518658i
\(267\) 5.63681 1.42337i 0.344967 0.0871089i
\(268\) 33.2175 + 4.77595i 2.02908 + 0.291738i
\(269\) −3.93980 3.41386i −0.240214 0.208147i 0.526431 0.850218i \(-0.323530\pi\)
−0.766645 + 0.642071i \(0.778075\pi\)
\(270\) 10.7961 + 6.51806i 0.657028 + 0.396677i
\(271\) 14.5378 + 4.26869i 0.883110 + 0.259305i 0.691682 0.722202i \(-0.256870\pi\)
0.191428 + 0.981507i \(0.438688\pi\)
\(272\) −7.15828 15.6745i −0.434035 0.950403i
\(273\) 9.79935 1.02821i 0.593083 0.0622298i
\(274\) 11.2580 17.5178i 0.680121 1.05829i
\(275\) 17.9083 1.07991
\(276\) −1.56568 + 20.2093i −0.0942432 + 1.21646i
\(277\) −25.5985 −1.53806 −0.769031 0.639211i \(-0.779261\pi\)
−0.769031 + 0.639211i \(0.779261\pi\)
\(278\) −1.74224 + 2.71099i −0.104493 + 0.162594i
\(279\) −0.279936 4.21689i −0.0167593 0.252459i
\(280\) −0.716442 1.56879i −0.0428156 0.0937531i
\(281\) −2.87252 0.843447i −0.171360 0.0503158i 0.194927 0.980818i \(-0.437553\pi\)
−0.366287 + 0.930502i \(0.619371\pi\)
\(282\) −18.1609 + 36.0502i −1.08146 + 2.14676i
\(283\) −8.46660 7.33635i −0.503287 0.436101i 0.365848 0.930674i \(-0.380779\pi\)
−0.869136 + 0.494573i \(0.835324\pi\)
\(284\) 2.25167 + 0.323742i 0.133612 + 0.0192105i
\(285\) −1.85480 7.34534i −0.109869 0.435100i
\(286\) −27.3598 + 23.7074i −1.61782 + 1.40185i
\(287\) −4.09150 + 2.62945i −0.241513 + 0.155211i
\(288\) 11.4232 + 21.1766i 0.673116 + 1.24785i
\(289\) −11.5824 13.3668i −0.681318 0.786283i
\(290\) −12.4854 + 3.66606i −0.733171 + 0.215278i
\(291\) −18.2419 3.33937i −1.06936 0.195757i
\(292\) 8.35745 9.64501i 0.489083 0.564432i
\(293\) −2.74244 + 6.00510i −0.160215 + 0.350822i −0.972666 0.232207i \(-0.925405\pi\)
0.812451 + 0.583029i \(0.198133\pi\)
\(294\) 5.10362 15.2041i 0.297649 0.886721i
\(295\) −5.71535 + 2.61011i −0.332761 + 0.151967i
\(296\) 0.314007 + 2.18397i 0.0182513 + 0.126940i
\(297\) 19.6021 + 16.0458i 1.13743 + 0.931074i
\(298\) 10.0976i 0.584940i
\(299\) −16.8100 + 1.75011i −0.972150 + 0.101211i
\(300\) −15.5145 0.593816i −0.895730 0.0342840i
\(301\) −2.27672 1.46316i −0.131228 0.0843351i
\(302\) −10.7447 + 1.54485i −0.618288 + 0.0888963i
\(303\) 12.5100 5.14440i 0.718682 0.295538i
\(304\) 3.13029 10.6608i 0.179535 0.611439i
\(305\) 3.70565 + 1.69231i 0.212185 + 0.0969016i
\(306\) 26.1914 + 26.4606i 1.49726 + 1.51265i
\(307\) 2.52687 17.5748i 0.144216 1.00305i −0.781250 0.624218i \(-0.785418\pi\)
0.925467 0.378829i \(-0.123673\pi\)
\(308\) −5.41028 18.4257i −0.308279 1.04990i
\(309\) 12.4299 9.96434i 0.707112 0.566851i
\(310\) −1.84844 2.87624i −0.104985 0.163359i
\(311\) 8.83560 + 13.7485i 0.501021 + 0.779604i 0.996005 0.0892980i \(-0.0284624\pi\)
−0.494984 + 0.868902i \(0.664826\pi\)
\(312\) 4.41771 3.54143i 0.250104 0.200494i
\(313\) 0.0389593 + 0.132683i 0.00220211 + 0.00749969i 0.960587 0.277981i \(-0.0896651\pi\)
−0.958385 + 0.285480i \(0.907847\pi\)
\(314\) 5.41778 37.6815i 0.305743 2.12649i
\(315\) −3.92385 3.96418i −0.221084 0.223356i
\(316\) 2.44969 + 1.11874i 0.137806 + 0.0629339i
\(317\) −9.10251 + 31.0003i −0.511248 + 1.74115i 0.147768 + 0.989022i \(0.452791\pi\)
−0.659016 + 0.752129i \(0.729027\pi\)
\(318\) −20.6426 + 8.48868i −1.15758 + 0.476022i
\(319\) −25.8723 + 3.71987i −1.44857 + 0.208273i
\(320\) 10.7056 + 6.88009i 0.598463 + 0.384609i
\(321\) −12.1573 0.465321i −0.678556 0.0259717i
\(322\) 5.20366 15.4608i 0.289988 0.861596i
\(323\) 22.3659i 1.24447i
\(324\) −16.4498 14.5509i −0.913875 0.808385i
\(325\) −1.84232 12.8136i −0.102193 0.710770i
\(326\) −8.85095 + 4.04209i −0.490209 + 0.223871i
\(327\) −2.78971 + 8.31077i −0.154271 + 0.459586i
\(328\) −1.16099 + 2.54222i −0.0641052 + 0.140371i
\(329\) 11.6916 13.4928i 0.644578 0.743882i
\(330\) 20.1587 + 3.69026i 1.10970 + 0.203142i
\(331\) 12.6002 3.69974i 0.692568 0.203356i 0.0835394 0.996504i \(-0.473378\pi\)
0.609029 + 0.793148i \(0.291559\pi\)
\(332\) −16.3950 18.9208i −0.899790 1.03841i
\(333\) 3.38781 + 6.28045i 0.185651 + 0.344166i
\(334\) −29.1201 + 18.7143i −1.59338 + 1.02400i
\(335\) 11.9710 10.3729i 0.654046 0.566734i
\(336\) −2.00279 7.93141i −0.109261 0.432694i
\(337\) 27.5905 + 3.96691i 1.50295 + 0.216091i 0.844100 0.536185i \(-0.180135\pi\)
0.658847 + 0.752277i \(0.271044\pi\)
\(338\) −0.924999 0.801516i −0.0503133 0.0435967i
\(339\) 12.2378 24.2927i 0.664667 1.31940i
\(340\) 15.8826 + 4.66355i 0.861354 + 0.252916i
\(341\) −2.85296 6.24711i −0.154496 0.338300i
\(342\) 1.59015 + 23.9536i 0.0859854 + 1.29526i
\(343\) −9.94402 + 15.4732i −0.536926 + 0.835474i
\(344\) −1.55516 −0.0838487
\(345\) 6.72502 + 6.80511i 0.362063 + 0.366375i
\(346\) 32.1490 1.72834
\(347\) 6.69478 10.4173i 0.359395 0.559229i −0.613728 0.789518i \(-0.710331\pi\)
0.973122 + 0.230289i \(0.0739671\pi\)
\(348\) 22.5372 2.36474i 1.20812 0.126763i
\(349\) 3.03180 + 6.63872i 0.162289 + 0.355362i 0.973254 0.229732i \(-0.0737848\pi\)
−0.810965 + 0.585094i \(0.801058\pi\)
\(350\) 11.9889 + 3.52026i 0.640834 + 0.188166i
\(351\) 9.46439 15.6762i 0.505172 0.836732i
\(352\) 29.5502 + 25.6054i 1.57503 + 1.36477i
\(353\) −4.59822 0.661124i −0.244739 0.0351881i 0.0188538 0.999822i \(-0.493998\pi\)
−0.263592 + 0.964634i \(0.584907\pi\)
\(354\) 19.3040 4.87452i 1.02600 0.259078i
\(355\) 0.811464 0.703138i 0.0430681 0.0373187i
\(356\) −6.89047 + 4.42824i −0.365194 + 0.234696i
\(357\) −8.36632 14.1832i −0.442793 0.750653i
\(358\) −27.9198 32.2211i −1.47561 1.70294i
\(359\) −36.2436 + 10.6421i −1.91286 + 0.561667i −0.933940 + 0.357429i \(0.883653\pi\)
−0.978921 + 0.204238i \(0.934528\pi\)
\(360\) −3.12840 0.697313i −0.164881 0.0367516i
\(361\) −2.99835 + 3.46029i −0.157808 + 0.182120i
\(362\) 15.3407 33.5914i 0.806289 1.76553i
\(363\) 20.9636 + 7.03693i 1.10030 + 0.369343i
\(364\) −12.6272 + 5.76665i −0.661845 + 0.302254i
\(365\) −0.857271 5.96245i −0.0448716 0.312089i
\(366\) −10.5848 7.38935i −0.553278 0.386247i
\(367\) 33.5080i 1.74910i −0.484931 0.874552i \(-0.661155\pi\)
0.484931 0.874552i \(-0.338845\pi\)
\(368\) 3.42438 + 13.6074i 0.178508 + 0.709333i
\(369\) −0.690903 + 9.01231i −0.0359670 + 0.469162i
\(370\) 4.85654 + 3.12111i 0.252480 + 0.162259i
\(371\) 9.77132 1.40490i 0.507301 0.0729389i
\(372\) 2.26445 + 5.50664i 0.117406 + 0.285506i
\(373\) −9.21175 + 31.3723i −0.476966 + 1.62440i 0.272359 + 0.962196i \(0.412196\pi\)
−0.749325 + 0.662202i \(0.769622\pi\)
\(374\) 55.0348 + 25.1335i 2.84578 + 1.29962i
\(375\) −11.8229 + 12.6337i −0.610531 + 0.652404i
\(376\) 1.46005 10.1549i 0.0752962 0.523697i
\(377\) 5.32321 + 18.1292i 0.274159 + 0.933700i
\(378\) 9.96864 + 14.5952i 0.512731 + 0.750698i
\(379\) 9.12285 + 14.1954i 0.468609 + 0.729170i 0.992451 0.122646i \(-0.0391378\pi\)
−0.523841 + 0.851816i \(0.675501\pi\)
\(380\) 5.77045 + 8.97899i 0.296018 + 0.460613i
\(381\) −8.68987 10.8401i −0.445196 0.555354i
\(382\) −2.63726 8.98168i −0.134934 0.459543i
\(383\) 0.766927 5.33409i 0.0391881 0.272560i −0.960801 0.277239i \(-0.910581\pi\)
0.999989 + 0.00467976i \(0.00148962\pi\)
\(384\) −9.15744 8.56968i −0.467314 0.437320i
\(385\) −8.24501 3.76537i −0.420205 0.191901i
\(386\) −9.66810 + 32.9265i −0.492093 + 1.67592i
\(387\) −4.72144 + 1.73356i −0.240004 + 0.0881218i
\(388\) 25.8613 3.71829i 1.31291 0.188768i
\(389\) −9.42018 6.05398i −0.477622 0.306949i 0.279588 0.960120i \(-0.409802\pi\)
−0.757211 + 0.653171i \(0.773438\pi\)
\(390\) 0.566598 14.8034i 0.0286908 0.749598i
\(391\) 14.3310 + 24.3397i 0.724748 + 1.23091i
\(392\) 4.07609i 0.205873i
\(393\) 8.44605 12.0985i 0.426047 0.610288i
\(394\) −3.28102 22.8200i −0.165295 1.14966i
\(395\) 1.15626 0.528046i 0.0581777 0.0265689i
\(396\) −33.3747 12.6429i −1.67714 0.635328i
\(397\) −13.3334 + 29.1961i −0.669185 + 1.46531i 0.204524 + 0.978861i \(0.434435\pi\)
−0.873709 + 0.486449i \(0.838292\pi\)
\(398\) 20.6623 23.8455i 1.03571 1.19527i
\(399\) 1.91192 10.4442i 0.0957157 0.522863i
\(400\) −10.3123 + 3.02796i −0.515613 + 0.151398i
\(401\) −17.7005 20.4275i −0.883923 1.02010i −0.999640 0.0268193i \(-0.991462\pi\)
0.115717 0.993282i \(-0.463083\pi\)
\(402\) −43.2322 + 25.5016i −2.15623 + 1.27191i
\(403\) −4.17637 + 2.68399i −0.208040 + 0.133699i
\(404\) −14.4022 + 12.4796i −0.716537 + 0.620882i
\(405\) −10.2751 + 1.37025i −0.510572 + 0.0680882i
\(406\) −18.0517 2.59544i −0.895889 0.128809i
\(407\) 8.76382 + 7.59390i 0.434407 + 0.376416i
\(408\) −8.45071 4.25717i −0.418372 0.210761i
\(409\) −15.4507 4.53673i −0.763988 0.224327i −0.123551 0.992338i \(-0.539428\pi\)
−0.640436 + 0.768011i \(0.721247\pi\)
\(410\) 3.03767 + 6.65158i 0.150020 + 0.328498i
\(411\) 1.78615 + 17.0229i 0.0881041 + 0.839678i
\(412\) −12.1342 + 18.8813i −0.597811 + 0.930213i
\(413\) −8.80593 −0.433312
\(414\) −17.0788 25.0487i −0.839378 1.23108i
\(415\) −11.8169 −0.580070
\(416\) 15.2809 23.7776i 0.749210 1.16579i
\(417\) −0.276417 2.63440i −0.0135362 0.129007i
\(418\) 16.2060 + 35.4861i 0.792659 + 1.73568i
\(419\) 7.13619 + 2.09537i 0.348626 + 0.102366i 0.451357 0.892343i \(-0.350940\pi\)
−0.102732 + 0.994709i \(0.532758\pi\)
\(420\) 7.01803 + 3.53544i 0.342445 + 0.172512i
\(421\) −3.58919 3.11005i −0.174926 0.151575i 0.562997 0.826459i \(-0.309648\pi\)
−0.737924 + 0.674884i \(0.764194\pi\)
\(422\) −44.9868 6.46812i −2.18992 0.314863i
\(423\) −6.88708 32.4575i −0.334861 1.57814i
\(424\) 4.28713 3.71482i 0.208201 0.180408i
\(425\) −18.2003 + 11.6966i −0.882842 + 0.567368i
\(426\) −2.93053 + 1.72865i −0.141985 + 0.0837534i
\(427\) 3.73891 + 4.31494i 0.180939 + 0.208814i
\(428\) 16.4462 4.82903i 0.794955 0.233420i
\(429\) 5.35835 29.2709i 0.258704 1.41321i
\(430\) −2.66462 + 3.07514i −0.128499 + 0.148296i
\(431\) −12.0473 + 26.3800i −0.580299 + 1.27068i 0.360830 + 0.932632i \(0.382493\pi\)
−0.941129 + 0.338047i \(0.890234\pi\)
\(432\) −14.0006 5.92544i −0.673605 0.285088i
\(433\) −1.42394 + 0.650293i −0.0684303 + 0.0312511i −0.449336 0.893363i \(-0.648339\pi\)
0.380906 + 0.924614i \(0.375612\pi\)
\(434\) −0.681939 4.74299i −0.0327341 0.227671i
\(435\) 6.12261 8.77029i 0.293557 0.420503i
\(436\) 12.3507i 0.591492i
\(437\) −3.29392 + 17.9121i −0.157570 + 0.856850i
\(438\) −0.730056 + 19.0740i −0.0348834 + 0.911392i
\(439\) −13.9049 8.93611i −0.663643 0.426497i 0.164986 0.986296i \(-0.447242\pi\)
−0.828629 + 0.559799i \(0.810878\pi\)
\(440\) −5.15555 + 0.741256i −0.245781 + 0.0353380i
\(441\) 4.54367 + 12.3749i 0.216365 + 0.589281i
\(442\) 12.3216 41.9635i 0.586079 1.99600i
\(443\) 36.9045 + 16.8537i 1.75338 + 0.800744i 0.987471 + 0.157800i \(0.0504400\pi\)
0.765913 + 0.642944i \(0.222287\pi\)
\(444\) −7.34055 6.86940i −0.348367 0.326007i
\(445\) −0.550194 + 3.82668i −0.0260817 + 0.181402i
\(446\) −1.77894 6.05851i −0.0842353 0.286879i
\(447\) 5.19146 + 6.47602i 0.245548 + 0.306305i
\(448\) 9.64255 + 15.0041i 0.455568 + 0.708877i
\(449\) −6.14859 9.56739i −0.290170 0.451513i 0.665311 0.746566i \(-0.268299\pi\)
−0.955481 + 0.295053i \(0.904663\pi\)
\(450\) 18.6607 13.8209i 0.879674 0.651525i
\(451\) 4.13820 + 14.0934i 0.194860 + 0.663633i
\(452\) −5.45385 + 37.9323i −0.256527 + 1.78419i
\(453\) 6.09676 6.51491i 0.286451 0.306097i
\(454\) 6.37534 + 2.91152i 0.299210 + 0.136645i
\(455\) −1.84596 + 6.28675i −0.0865397 + 0.294727i
\(456\) −2.32046 5.64285i −0.108666 0.264251i
\(457\) 19.0145 2.73387i 0.889458 0.127885i 0.317588 0.948229i \(-0.397127\pi\)
0.571870 + 0.820344i \(0.306218\pi\)
\(458\) 25.5444 + 16.4164i 1.19361 + 0.767087i
\(459\) −30.4017 3.50456i −1.41903 0.163579i
\(460\) −12.0330 6.07398i −0.561041 0.283201i
\(461\) 2.64425i 0.123155i 0.998102 + 0.0615776i \(0.0196132\pi\)
−0.998102 + 0.0615776i \(0.980387\pi\)
\(462\) 23.5511 + 16.4412i 1.09569 + 0.764913i
\(463\) 2.69828 + 18.7669i 0.125400 + 0.872173i 0.951280 + 0.308328i \(0.0997695\pi\)
−0.825880 + 0.563845i \(0.809321\pi\)
\(464\) 14.2692 6.51654i 0.662432 0.302523i
\(465\) 2.66423 + 0.894313i 0.123551 + 0.0414728i
\(466\) 11.3168 24.7802i 0.524239 1.14792i
\(467\) −21.7892 + 25.1460i −1.00828 + 1.16362i −0.0217982 + 0.999762i \(0.506939\pi\)
−0.986484 + 0.163857i \(0.947606\pi\)
\(468\) −5.61268 + 25.1805i −0.259446 + 1.16397i
\(469\) 21.3006 6.25443i 0.983571 0.288803i
\(470\) −17.5783 20.2864i −0.810827 0.935744i
\(471\) 15.8984 + 26.9521i 0.732559 + 1.24189i
\(472\) −4.25691 + 2.73575i −0.195940 + 0.125923i
\(473\) −6.17704 + 5.35243i −0.284020 + 0.246105i
\(474\) −3.90534 + 0.986152i −0.179378 + 0.0452955i
\(475\) −13.8079 1.98528i −0.633551 0.0910909i
\(476\) 17.5330 + 15.1924i 0.803622 + 0.696343i
\(477\) 8.87467 16.0570i 0.406343 0.735201i
\(478\) 8.69889 + 2.55422i 0.397878 + 0.116828i
\(479\) −1.71798 3.76184i −0.0784963 0.171883i 0.866315 0.499498i \(-0.166482\pi\)
−0.944811 + 0.327615i \(0.893755\pi\)
\(480\) −15.9129 + 1.66967i −0.726319 + 0.0762098i
\(481\) 4.53193 7.05182i 0.206638 0.321535i
\(482\) 43.9053 1.99983
\(483\) 4.61148 + 12.5910i 0.209830 + 0.572909i
\(484\) −31.1542 −1.41610
\(485\) 6.66723 10.3744i 0.302743 0.471078i
\(486\) 32.8091 + 1.59188i 1.48825 + 0.0722093i
\(487\) −3.22113 7.05330i −0.145963 0.319615i 0.822502 0.568762i \(-0.192577\pi\)
−0.968466 + 0.249146i \(0.919850\pi\)
\(488\) 3.14797 + 0.924328i 0.142502 + 0.0418424i
\(489\) 3.59833 7.14287i 0.162722 0.323012i
\(490\) 8.05995 + 6.98399i 0.364112 + 0.315504i
\(491\) −8.12547 1.16827i −0.366697 0.0527231i −0.0434967 0.999054i \(-0.513850\pi\)
−0.323201 + 0.946330i \(0.604759\pi\)
\(492\) −3.11772 12.3467i −0.140558 0.556634i
\(493\) 23.8644 20.6786i 1.07480 0.931318i
\(494\) 23.7235 15.2461i 1.06737 0.685956i
\(495\) −14.8258 + 7.99740i −0.666372 + 0.359456i
\(496\) 2.69910 + 3.11493i 0.121193 + 0.139864i
\(497\) 1.44388 0.423962i 0.0647669 0.0190173i
\(498\) 36.8332 + 6.74270i 1.65053 + 0.302148i
\(499\) 6.73627 7.77406i 0.301557 0.348015i −0.584666 0.811274i \(-0.698775\pi\)
0.886223 + 0.463259i \(0.153320\pi\)
\(500\) 10.1267 22.1744i 0.452881 0.991670i
\(501\) 9.05435 26.9737i 0.404519 1.20509i
\(502\) 14.7370 6.73018i 0.657746 0.300382i
\(503\) −3.33265 23.1791i −0.148596 1.03351i −0.918521 0.395372i \(-0.870616\pi\)
0.769926 0.638134i \(-0.220293\pi\)
\(504\) −3.58231 2.71037i −0.159569 0.120729i
\(505\) 8.99485i 0.400266i
\(506\) −40.3739 28.2338i −1.79484 1.25515i
\(507\) 1.00532 + 0.0384786i 0.0446478 + 0.00170889i
\(508\) 16.4663 + 10.5822i 0.730573 + 0.469511i
\(509\) 15.8196 2.27451i 0.701190 0.100816i 0.217506 0.976059i \(-0.430208\pi\)
0.483684 + 0.875243i \(0.339299\pi\)
\(510\) −22.8975 + 9.41596i −1.01392 + 0.416946i
\(511\) 2.37850 8.10042i 0.105219 0.358342i
\(512\) −26.2829 12.0030i −1.16155 0.530462i
\(513\) −13.3350 14.5449i −0.588756 0.642173i
\(514\) −3.26329 + 22.6967i −0.143938 + 1.00111i
\(515\) 2.98459 + 10.1646i 0.131517 + 0.447904i
\(516\) 5.52882 4.43214i 0.243393 0.195114i
\(517\) −29.1509 45.3597i −1.28206 1.99492i
\(518\) 4.37428 + 6.80652i 0.192195 + 0.299061i
\(519\) −20.6185 + 16.5286i −0.905050 + 0.725527i
\(520\) 1.06075 + 3.61259i 0.0465170 + 0.158423i
\(521\) 5.76008 40.0622i 0.252354 1.75516i −0.331646 0.943404i \(-0.607604\pi\)
0.583999 0.811754i \(-0.301487\pi\)
\(522\) −24.0884 + 23.8433i −1.05432 + 1.04359i
\(523\) −25.4670 11.6304i −1.11359 0.508561i −0.228299 0.973591i \(-0.573316\pi\)
−0.885295 + 0.465030i \(0.846043\pi\)
\(524\) −5.85655 + 19.9456i −0.255845 + 0.871327i
\(525\) −9.49884 + 3.90613i −0.414563 + 0.170477i
\(526\) −13.1043 + 1.88411i −0.571373 + 0.0821510i
\(527\) 6.97967 + 4.48556i 0.304039 + 0.195394i
\(528\) −24.6873 0.944906i −1.07438 0.0411218i
\(529\) −7.89256 21.6034i −0.343155 0.939279i
\(530\) 14.8423i 0.644706i
\(531\) −9.87432 + 13.0509i −0.428509 + 0.566362i
\(532\) 2.12887 + 14.8066i 0.0922981 + 0.641948i
\(533\) 9.65826 4.41078i 0.418346 0.191052i
\(534\) 3.89844 11.6138i 0.168702 0.502577i
\(535\) 3.36084 7.35921i 0.145302 0.318166i
\(536\) 8.35395 9.64098i 0.360836 0.416427i
\(537\) 34.4718 + 6.31043i 1.48757 + 0.272315i
\(538\) −10.5400 + 3.09482i −0.454411 + 0.133427i
\(539\) 14.0288 + 16.1900i 0.604261 + 0.697355i
\(540\) 13.1092 6.43677i 0.564131 0.276994i
\(541\) −17.2465 + 11.0837i −0.741486 + 0.476524i −0.856051 0.516892i \(-0.827089\pi\)
0.114565 + 0.993416i \(0.463453\pi\)
\(542\) 24.1289 20.9078i 1.03642 0.898067i
\(543\) 7.43163 + 29.4306i 0.318922 + 1.26299i
\(544\) −46.7557 6.72245i −2.00463 0.288223i
\(545\) −4.40568 3.81754i −0.188719 0.163526i
\(546\) 9.34101 18.5424i 0.399758 0.793541i
\(547\) 4.54550 + 1.33468i 0.194352 + 0.0570668i 0.377460 0.926026i \(-0.376798\pi\)
−0.183108 + 0.983093i \(0.558616\pi\)
\(548\) −10.0175 21.9353i −0.427927 0.937030i
\(549\) 10.5875 0.702848i 0.451865 0.0299968i
\(550\) 20.4017 31.7456i 0.869931 1.35364i
\(551\) 20.3608 0.867397
\(552\) 6.14091 + 4.65400i 0.261374 + 0.198087i
\(553\) 1.78151 0.0757573
\(554\) −29.1625 + 45.3777i −1.23899 + 1.92791i
\(555\) −4.71934 + 0.495182i −0.200325 + 0.0210193i
\(556\) 1.55027 + 3.39462i 0.0657462 + 0.143964i
\(557\) 25.0638 + 7.35938i 1.06199 + 0.311827i 0.765650 0.643257i \(-0.222417\pi\)
0.296335 + 0.955084i \(0.404236\pi\)
\(558\) −7.79408 4.30776i −0.329950 0.182362i
\(559\) 4.46518 + 3.86910i 0.188857 + 0.163645i
\(560\) 5.38442 + 0.774163i 0.227533 + 0.0327144i
\(561\) −48.2178 + 12.1757i −2.03576 + 0.514057i
\(562\) −4.76761 + 4.13116i −0.201109 + 0.174262i
\(563\) 7.00657 4.50285i 0.295292 0.189772i −0.384603 0.923082i \(-0.625662\pi\)
0.679895 + 0.733310i \(0.262025\pi\)
\(564\) 23.7502 + 40.2630i 1.00006 + 1.69538i
\(565\) 11.8453 + 13.6702i 0.498334 + 0.575108i
\(566\) −22.6503 + 6.65074i −0.952065 + 0.279552i
\(567\) −13.8971 4.23538i −0.583623 0.177869i
\(568\) 0.566280 0.653522i 0.0237606 0.0274212i
\(569\) −13.7359 + 30.0775i −0.575840 + 1.26091i 0.367789 + 0.929909i \(0.380115\pi\)
−0.943629 + 0.331004i \(0.892613\pi\)
\(570\) −15.1339 5.08006i −0.633890 0.212780i
\(571\) 19.3054 8.81649i 0.807907 0.368959i 0.0317480 0.999496i \(-0.489893\pi\)
0.776159 + 0.630537i \(0.217165\pi\)
\(572\) 5.96638 + 41.4971i 0.249467 + 1.73508i
\(573\) 6.30910 + 4.40443i 0.263567 + 0.183998i
\(574\) 10.2484i 0.427761i
\(575\) 16.2986 6.68697i 0.679697 0.278866i
\(576\) 33.0494 + 2.53364i 1.37706 + 0.105568i
\(577\) 9.95072 + 6.39494i 0.414254 + 0.266225i 0.731125 0.682244i \(-0.238996\pi\)
−0.316871 + 0.948469i \(0.602632\pi\)
\(578\) −36.8900 + 5.30398i −1.53442 + 0.220617i
\(579\) −10.7279 26.0877i −0.445834 1.08417i
\(580\) −4.24546 + 14.4587i −0.176283 + 0.600365i
\(581\) −15.0650 6.87994i −0.625000 0.285428i
\(582\) −26.7013 + 28.5326i −1.10680 + 1.18271i
\(583\) 4.24293 29.5102i 0.175724 1.22219i
\(584\) −1.36677 4.65479i −0.0565574 0.192617i
\(585\) 7.24742 + 9.78531i 0.299644 + 0.404573i
\(586\) 7.52082 + 11.7026i 0.310682 + 0.483431i
\(587\) −15.2028 23.6560i −0.627485 0.976386i −0.998852 0.0479001i \(-0.984747\pi\)
0.371367 0.928486i \(-0.378889\pi\)
\(588\) −11.6167 14.4911i −0.479063 0.597601i
\(589\) 1.50718 + 5.13300i 0.0621025 + 0.211502i
\(590\) −1.88421 + 13.1050i −0.0775717 + 0.539523i
\(591\) 13.8366 + 12.9485i 0.569163 + 0.532632i
\(592\) −6.33051 2.89105i −0.260182 0.118821i
\(593\) 2.46287 8.38778i 0.101138 0.344445i −0.893341 0.449379i \(-0.851645\pi\)
0.994479 + 0.104935i \(0.0334633\pi\)
\(594\) 50.7752 16.4682i 2.08333 0.675698i
\(595\) 10.8387 1.55837i 0.444344 0.0638870i
\(596\) −9.83721 6.32199i −0.402948 0.258959i
\(597\) −0.991937 + 25.9161i −0.0405973 + 1.06068i
\(598\) −16.0481 + 31.7925i −0.656256 + 1.30009i
\(599\) 3.55017i 0.145056i −0.997366 0.0725281i \(-0.976893\pi\)
0.997366 0.0725281i \(-0.0231067\pi\)
\(600\) −3.37835 + 4.83930i −0.137921 + 0.197563i
\(601\) 2.04995 + 14.2577i 0.0836194 + 0.581585i 0.987952 + 0.154758i \(0.0494598\pi\)
−0.904333 + 0.426827i \(0.859631\pi\)
\(602\) −5.18741 + 2.36901i −0.211423 + 0.0965536i
\(603\) 14.6155 38.5821i 0.595189 1.57118i
\(604\) −5.22209 + 11.4348i −0.212484 + 0.465275i
\(605\) −9.62961 + 11.1132i −0.391499 + 0.451814i
\(606\) 5.13244 28.0368i 0.208491 1.13892i
\(607\) 35.0641 10.2957i 1.42321 0.417891i 0.522619 0.852566i \(-0.324955\pi\)
0.900587 + 0.434675i \(0.143137\pi\)
\(608\) −19.9456 23.0185i −0.808902 0.933522i
\(609\) 12.9116 7.61627i 0.523206 0.308627i
\(610\) 7.22150 4.64097i 0.292390 0.187908i
\(611\) −29.4564 + 25.5241i −1.19168 + 1.03260i
\(612\) 42.1762 8.94928i 1.70487 0.361753i
\(613\) 21.8812 + 3.14605i 0.883775 + 0.127068i 0.569233 0.822176i \(-0.307240\pi\)
0.314542 + 0.949244i \(0.398149\pi\)
\(614\) −28.2757 24.5010i −1.14111 0.988781i
\(615\) −5.36794 2.70418i −0.216456 0.109043i
\(616\) −7.00419 2.05662i −0.282207 0.0828634i
\(617\) −11.1814 24.4839i −0.450146 0.985683i −0.989624 0.143683i \(-0.954105\pi\)
0.539477 0.842000i \(-0.318622\pi\)
\(618\) −3.50304 33.3858i −0.140913 1.34297i
\(619\) −15.3856 + 23.9405i −0.618401 + 0.962251i 0.380890 + 0.924620i \(0.375618\pi\)
−0.999292 + 0.0376310i \(0.988019\pi\)
\(620\) −3.95934 −0.159011
\(621\) 23.8315 + 7.28408i 0.956327 + 0.292300i
\(622\) 34.4373 1.38081
\(623\) −2.92936 + 4.55817i −0.117362 + 0.182619i
\(624\) 1.86362 + 17.7612i 0.0746043 + 0.711019i
\(625\) 2.85010 + 6.24086i 0.114004 + 0.249634i
\(626\) 0.279587 + 0.0820942i 0.0111746 + 0.00328115i
\(627\) −28.6379 14.4268i −1.14369 0.576150i
\(628\) −33.3176 28.8699i −1.32952 1.15203i
\(629\) −13.8665 1.99371i −0.552895 0.0794942i
\(630\) −11.4974 + 2.43960i −0.458066 + 0.0971960i
\(631\) −20.3896 + 17.6677i −0.811696 + 0.703339i −0.958271 0.285861i \(-0.907720\pi\)
0.146575 + 0.989200i \(0.453175\pi\)
\(632\) 0.861206 0.553463i 0.0342569 0.0220156i
\(633\) 32.1773 18.9806i 1.27893 0.754412i
\(634\) 44.5836 + 51.4522i 1.77064 + 2.04343i
\(635\) 8.86449 2.60285i 0.351776 0.103291i
\(636\) −4.65429 + 25.4248i −0.184554 + 1.00816i
\(637\) 10.1409 11.7033i 0.401798 0.463700i
\(638\) −22.8803 + 50.1009i −0.905840 + 1.98351i
\(639\) 0.990724 2.61532i 0.0391924 0.103460i
\(640\) 7.58642 3.46460i 0.299880 0.136950i
\(641\) −2.99677 20.8430i −0.118365 0.823248i −0.959356 0.282198i \(-0.908936\pi\)
0.840991 0.541049i \(-0.181973\pi\)
\(642\) −14.6748 + 21.0209i −0.579169 + 0.829627i
\(643\) 25.0372i 0.987369i 0.869641 + 0.493685i \(0.164350\pi\)
−0.869641 + 0.493685i \(0.835650\pi\)
\(644\) −11.8041 14.7492i −0.465147 0.581201i
\(645\) 0.127921 3.34216i 0.00503689 0.131598i
\(646\) −39.6474 25.4798i −1.55991 1.00249i
\(647\) 27.4628 3.94856i 1.07968 0.155234i 0.420552 0.907268i \(-0.361836\pi\)
0.659124 + 0.752035i \(0.270927\pi\)
\(648\) −8.03386 + 2.26999i −0.315600 + 0.0891735i
\(649\) −7.49259 + 25.5174i −0.294110 + 1.00165i
\(650\) −24.8131 11.3318i −0.973251 0.444469i
\(651\) 2.87585 + 2.69127i 0.112714 + 0.105479i
\(652\) −1.60361 + 11.1534i −0.0628024 + 0.436800i
\(653\) 10.0608 + 34.2639i 0.393709 + 1.34085i 0.883264 + 0.468876i \(0.155341\pi\)
−0.489555 + 0.871972i \(0.662841\pi\)
\(654\) 11.5542 + 14.4131i 0.451803 + 0.563596i
\(655\) 5.30465 + 8.25420i 0.207270 + 0.322518i
\(656\) −4.76585 7.41581i −0.186075 0.289539i
\(657\) −9.33824 12.6083i −0.364320 0.491896i
\(658\) −10.5990 36.0967i −0.413190 1.40720i
\(659\) −3.20230 + 22.2725i −0.124744 + 0.867614i 0.827323 + 0.561726i \(0.189862\pi\)
−0.952067 + 0.305888i \(0.901047\pi\)
\(660\) 16.2162 17.3284i 0.631213 0.674505i
\(661\) −0.940765 0.429633i −0.0365915 0.0167108i 0.397035 0.917803i \(-0.370039\pi\)
−0.433627 + 0.901093i \(0.642766\pi\)
\(662\) 7.79603 26.5508i 0.303001 1.03193i
\(663\) 13.6722 + 33.2478i 0.530985 + 1.29124i
\(664\) −9.42002 + 1.35439i −0.365568 + 0.0525607i
\(665\) 5.93976 + 3.81725i 0.230334 + 0.148027i
\(666\) 14.9927 + 1.14937i 0.580954 + 0.0445372i
\(667\) −22.1576 + 13.0462i −0.857947 + 0.505150i
\(668\) 40.0858i 1.55097i
\(669\) 4.25575 + 2.97097i 0.164537 + 0.114864i
\(670\) −4.75012 33.0378i −0.183513 1.27636i
\(671\) 15.6849 7.16305i 0.605509 0.276527i
\(672\) −21.2588 7.13603i −0.820077 0.275278i
\(673\) −3.92848 + 8.60218i −0.151432 + 0.331590i −0.970111 0.242662i \(-0.921980\pi\)
0.818679 + 0.574251i \(0.194707\pi\)
\(674\) 38.4638 44.3896i 1.48157 1.70982i
\(675\) −4.86217 + 18.4579i −0.187145 + 0.710444i
\(676\) −1.35997 + 0.399324i −0.0523067 + 0.0153586i
\(677\) 7.32061 + 8.44843i 0.281354 + 0.324700i 0.878783 0.477222i \(-0.158356\pi\)
−0.597429 + 0.801922i \(0.703811\pi\)
\(678\) −29.1214 49.3686i −1.11840 1.89599i
\(679\) 14.5399 9.34423i 0.557990 0.358599i
\(680\) 4.75544 4.12062i 0.182363 0.158018i
\(681\) −5.58566 + 1.41046i −0.214043 + 0.0540488i
\(682\) −14.3242 2.05952i −0.548504 0.0788629i
\(683\) 3.11627 + 2.70027i 0.119241 + 0.103323i 0.712440 0.701733i \(-0.247590\pi\)
−0.593199 + 0.805056i \(0.702135\pi\)
\(684\) 24.3314 + 13.4479i 0.930336 + 0.514194i
\(685\) −10.9210 3.20670i −0.417270 0.122522i
\(686\) 16.1004 + 35.2550i 0.614717 + 1.34604i
\(687\) −24.8227 + 2.60455i −0.947046 + 0.0993697i
\(688\) 2.65197 4.12654i 0.101105 0.157323i
\(689\) −21.5513 −0.821040
\(690\) 19.7246 4.16870i 0.750901 0.158700i
\(691\) 15.2318 0.579443 0.289722 0.957111i \(-0.406437\pi\)
0.289722 + 0.957111i \(0.406437\pi\)
\(692\) 20.1280 31.3198i 0.765153 1.19060i
\(693\) −23.5571 + 1.56382i −0.894860 + 0.0594048i
\(694\) −10.8396 23.7353i −0.411464 0.900980i
\(695\) 1.69009 + 0.496256i 0.0641089 + 0.0188241i
\(696\) 3.87551 7.69310i 0.146901 0.291606i
\(697\) −13.4106 11.6203i −0.507962 0.440151i
\(698\) 15.2222 + 2.18862i 0.576168 + 0.0828405i
\(699\) 5.48228 + 21.7108i 0.207359 + 0.821179i
\(700\) 10.9356 9.47572i 0.413325 0.358149i
\(701\) 28.6840 18.4341i 1.08338 0.696247i 0.128045 0.991768i \(-0.459130\pi\)
0.955336 + 0.295521i \(0.0954934\pi\)
\(702\) −17.0066 34.6360i −0.641874 1.30725i
\(703\) −5.91536 6.82668i −0.223102 0.257473i
\(704\) 51.6826 15.1754i 1.94786 0.571944i
\(705\) 21.7035 + 3.97305i 0.817400 + 0.149634i
\(706\) −6.41038 + 7.39797i −0.241258 + 0.278426i
\(707\) −5.23690 + 11.4672i −0.196954 + 0.431269i
\(708\) 7.33716 21.8580i 0.275747 0.821474i
\(709\) 8.16470 3.72870i 0.306632 0.140034i −0.256156 0.966635i \(-0.582456\pi\)
0.562788 + 0.826601i \(0.309729\pi\)
\(710\) −0.321991 2.23950i −0.0120841 0.0840468i
\(711\) 1.99765 2.64030i 0.0749176 0.0990190i
\(712\) 3.11355i 0.116685i
\(713\) −4.92917 4.62026i −0.184599 0.173030i
\(714\) −34.6733 1.32712i −1.29761 0.0496661i
\(715\) 16.6468 + 10.6982i 0.622554 + 0.400091i
\(716\) −48.8703 + 7.02649i −1.82637 + 0.262592i
\(717\) −6.89215 + 2.83420i −0.257392 + 0.105845i
\(718\) −22.4248 + 76.3717i −0.836884 + 2.85017i
\(719\) 2.45425 + 1.12082i 0.0915281 + 0.0417995i 0.460653 0.887580i \(-0.347615\pi\)
−0.369125 + 0.929380i \(0.620343\pi\)
\(720\) 7.18505 7.11195i 0.267771 0.265047i
\(721\) −2.11298 + 14.6961i −0.0786914 + 0.547311i
\(722\) 2.71815 + 9.25715i 0.101159 + 0.344516i
\(723\) −28.1583 + 22.5729i −1.04722 + 0.839494i
\(724\) −23.1205 35.9762i −0.859266 1.33704i
\(725\) −10.6480 16.5686i −0.395456 0.615342i
\(726\) 36.3565 29.1449i 1.34932 1.08167i
\(727\) −7.11750 24.2400i −0.263973 0.899011i −0.979673 0.200602i \(-0.935710\pi\)
0.715699 0.698409i \(-0.246108\pi\)
\(728\) −0.750974 + 5.22314i −0.0278330 + 0.193582i
\(729\) −21.8602 + 15.8471i −0.809638 + 0.586929i
\(730\) −11.5461 5.27293i −0.427340 0.195160i
\(731\) 2.78185 9.47412i 0.102891 0.350413i
\(732\) −13.8258 + 5.68546i −0.511016 + 0.210141i
\(733\) −0.969789 + 0.139435i −0.0358200 + 0.00515013i −0.160202 0.987084i \(-0.551214\pi\)
0.124382 + 0.992234i \(0.460305\pi\)
\(734\) −59.3988 38.1733i −2.19245 1.40900i
\(735\) −8.75983 0.335282i −0.323111 0.0123671i
\(736\) 36.4550 + 12.2697i 1.34375 + 0.452267i
\(737\) 67.0455i 2.46965i
\(738\) 15.1888 + 11.4918i 0.559107 + 0.423020i
\(739\) 1.44703 + 10.0643i 0.0532300 + 0.370223i 0.998973 + 0.0453075i \(0.0144268\pi\)
−0.945743 + 0.324916i \(0.894664\pi\)
\(740\) 6.08123 2.77720i 0.223550 0.102092i
\(741\) −7.37638 + 21.9748i −0.270978 + 0.807266i
\(742\) 8.64132 18.9219i 0.317233 0.694643i
\(743\) 15.2016 17.5435i 0.557691 0.643610i −0.404966 0.914332i \(-0.632717\pi\)
0.962658 + 0.270722i \(0.0872623\pi\)
\(744\) 2.22633 + 0.407553i 0.0816212 + 0.0149416i
\(745\) −5.29578 + 1.55498i −0.194022 + 0.0569701i
\(746\) 45.1186 + 52.0697i 1.65191 + 1.90641i
\(747\) −27.0892 + 14.6125i −0.991142 + 0.534645i
\(748\) 58.9418 37.8796i 2.15513 1.38502i
\(749\) 8.56922 7.42527i 0.313113 0.271314i
\(750\) 8.92656 + 35.3508i 0.325952 + 1.29083i
\(751\) −29.9082 4.30016i −1.09137 0.156915i −0.426949 0.904276i \(-0.640412\pi\)
−0.664418 + 0.747361i \(0.731321\pi\)
\(752\) 24.4556 + 21.1909i 0.891804 + 0.772753i
\(753\) −5.99129 + 11.8930i −0.218335 + 0.433406i
\(754\) 38.2015 + 11.2170i 1.39121 + 0.408498i
\(755\) 2.46483 + 5.39723i 0.0897045 + 0.196425i
\(756\) 20.4600 0.573664i 0.744124 0.0208640i
\(757\) 11.1727 17.3851i 0.406079 0.631871i −0.576635 0.817002i \(-0.695634\pi\)
0.982714 + 0.185131i \(0.0592709\pi\)
\(758\) 35.5569 1.29148
\(759\) 40.4092 2.64981i 1.46676 0.0961821i
\(760\) 4.05727 0.147173
\(761\) 0.279525 0.434950i 0.0101328 0.0157669i −0.836150 0.548501i \(-0.815199\pi\)
0.846283 + 0.532734i \(0.178835\pi\)
\(762\) −29.1156 + 3.05499i −1.05475 + 0.110670i
\(763\) −3.39403 7.43188i −0.122872 0.269052i
\(764\) −10.4012 3.05407i −0.376302 0.110492i
\(765\) 9.84411 17.8111i 0.355915 0.643960i
\(766\) −8.58190 7.43626i −0.310077 0.268683i
\(767\) 19.0287 + 2.73592i 0.687088 + 0.0987884i
\(768\) 11.4857 2.90029i 0.414454 0.104655i
\(769\) 24.4911 21.2216i 0.883171 0.765272i −0.0898581 0.995955i \(-0.528641\pi\)
0.973029 + 0.230683i \(0.0740959\pi\)
\(770\) −16.0677 + 10.3261i −0.579040 + 0.372127i
\(771\) −9.57609 16.2341i −0.344874 0.584655i
\(772\) 26.0243 + 30.0336i 0.936634 + 1.08093i
\(773\) −46.8885 + 13.7677i −1.68646 + 0.495190i −0.977656 0.210212i \(-0.932585\pi\)
−0.708807 + 0.705402i \(0.750766\pi\)
\(774\) −2.30576 + 10.3445i −0.0828787 + 0.371825i
\(775\) 3.38878 3.91086i 0.121728 0.140482i
\(776\) 4.12581 9.03427i 0.148108 0.324311i
\(777\) −6.30482 2.11636i −0.226184 0.0759241i
\(778\) −21.4635 + 9.80204i −0.769503 + 0.351420i
\(779\) −1.62832 11.3252i −0.0583408 0.405769i
\(780\) −14.0668 9.82017i −0.503674 0.351618i
\(781\) 4.54474i 0.162624i
\(782\) 59.4725 + 2.32434i 2.12673 + 0.0831181i
\(783\) 3.19038 27.6762i 0.114015 0.989065i
\(784\) −10.8157 6.95082i −0.386274 0.248243i
\(785\) −20.5966 + 2.96135i −0.735125 + 0.105695i
\(786\) −11.8247 28.7550i −0.421773 1.02566i
\(787\) 6.58438 22.4244i 0.234708 0.799342i −0.754936 0.655798i \(-0.772332\pi\)
0.989644 0.143543i \(-0.0458497\pi\)
\(788\) −24.2857 11.0909i −0.865141 0.395097i
\(789\) 7.43562 7.94560i 0.264715 0.282871i
\(790\) 0.381190 2.65123i 0.0135621 0.0943266i
\(791\) 7.14218 + 24.3240i 0.253947 + 0.864863i
\(792\) −10.9020 + 8.07450i −0.387386 + 0.286915i
\(793\) −6.73881 10.4858i −0.239302 0.372362i
\(794\) 36.5653 + 56.8968i 1.29766 + 2.01919i
\(795\) 7.63080 + 9.51894i 0.270636 + 0.337602i
\(796\) −10.2942 35.0587i −0.364867 1.24262i
\(797\) −6.97531 + 48.5144i −0.247078 + 1.71847i 0.367851 + 0.929885i \(0.380094\pi\)
−0.614929 + 0.788582i \(0.710815\pi\)
\(798\) −16.3360 15.2875i −0.578289 0.541172i
\(799\) 59.2522 + 27.0596i 2.09619 + 0.957299i
\(800\) −8.30043 + 28.2687i −0.293464 + 0.999448i
\(801\) 3.47072 + 9.45267i 0.122632 + 0.333994i
\(802\) −56.3763 + 8.10568i −1.99071 + 0.286222i
\(803\) −21.4492 13.7846i −0.756927 0.486448i
\(804\) −2.22314 + 58.0834i −0.0784040 + 2.04844i
\(805\) −8.90986 0.348220i −0.314031 0.0122731i
\(806\) 10.4610i 0.368473i
\(807\) 5.16859 7.40371i 0.181943 0.260623i
\(808\) 1.03094 + 7.17037i 0.0362685 + 0.252253i
\(809\) 20.9802 9.58133i 0.737624 0.336862i −0.0109255 0.999940i \(-0.503478\pi\)
0.748550 + 0.663079i \(0.230750\pi\)
\(810\) −9.27664 + 19.7754i −0.325948 + 0.694835i
\(811\) 2.69626 5.90398i 0.0946784 0.207317i −0.856367 0.516367i \(-0.827284\pi\)
0.951046 + 0.309050i \(0.100011\pi\)
\(812\) −13.8304 + 15.9611i −0.485352 + 0.560126i
\(813\) −4.72559 + 25.8143i −0.165734 + 0.905348i
\(814\) 23.4455 6.88422i 0.821764 0.241292i
\(815\) 3.48290 + 4.01949i 0.122001 + 0.140796i
\(816\) 25.7069 15.1639i 0.899921 0.530842i
\(817\) 5.35606 3.44213i 0.187385 0.120425i
\(818\) −25.6440 + 22.2207i −0.896622 + 0.776927i
\(819\) 3.54236 + 16.6945i 0.123780 + 0.583351i
\(820\) 8.38188 + 1.20513i 0.292708 + 0.0420850i
\(821\) −19.1441 16.5884i −0.668132 0.578940i 0.253343 0.967376i \(-0.418470\pi\)
−0.921475 + 0.388437i \(0.873015\pi\)
\(822\) 32.2109 + 16.2267i 1.12348 + 0.565972i
\(823\) −32.3375 9.49515i −1.12722 0.330980i −0.335603 0.942004i \(-0.608940\pi\)
−0.791612 + 0.611023i \(0.790758\pi\)
\(824\) 3.54421 + 7.76074i 0.123468 + 0.270358i
\(825\) 3.23684 + 30.8488i 0.112692 + 1.07402i
\(826\) −10.0320 + 15.6100i −0.349057 + 0.543143i
\(827\) −16.9340 −0.588853 −0.294426 0.955674i \(-0.595129\pi\)
−0.294426 + 0.955674i \(0.595129\pi\)
\(828\) −35.0955 + 0.955694i −1.21965 + 0.0332127i
\(829\) −42.4912 −1.47578 −0.737890 0.674921i \(-0.764178\pi\)
−0.737890 + 0.674921i \(0.764178\pi\)
\(830\) −13.4622 + 20.9475i −0.467279 + 0.727100i
\(831\) −4.62679 44.0958i −0.160502 1.52967i
\(832\) −16.1750 35.4182i −0.560766 1.22791i
\(833\) −24.8317 7.29125i −0.860368 0.252627i
\(834\) −4.98483 2.51118i −0.172611 0.0869552i
\(835\) 14.2992 + 12.3903i 0.494844 + 0.428785i
\(836\) 44.7172 + 6.42937i 1.54658 + 0.222364i
\(837\) 7.21339 1.24440i 0.249331 0.0430127i
\(838\) 11.8442 10.2630i 0.409149 0.354530i
\(839\) 31.1026 19.9884i 1.07378 0.690077i 0.120669 0.992693i \(-0.461496\pi\)
0.953113 + 0.302615i \(0.0978597\pi\)
\(840\) 2.57289 1.51769i 0.0887733 0.0523653i
\(841\) −0.166187 0.191790i −0.00573058 0.00661344i
\(842\) −9.60201 + 2.81940i −0.330907 + 0.0971631i
\(843\) 0.933725 5.10063i 0.0321592 0.175675i
\(844\) −34.4669 + 39.7769i −1.18640 + 1.36918i
\(845\) −0.277916 + 0.608552i −0.00956061 + 0.0209348i
\(846\) −65.3824 24.7679i −2.24789 0.851538i
\(847\) −18.7466 + 8.56130i −0.644142 + 0.294170i
\(848\) 2.54638 + 17.7104i 0.0874429 + 0.608179i
\(849\) 11.1073 15.9105i 0.381200 0.546048i
\(850\) 45.5882i 1.56366i
\(851\) 10.8116 + 3.63888i 0.370617 + 0.124739i
\(852\) −0.150697 + 3.93723i −0.00516281 + 0.134887i
\(853\) −6.63437 4.26365i −0.227157 0.145985i 0.422112 0.906543i \(-0.361289\pi\)
−0.649269 + 0.760559i \(0.724925\pi\)
\(854\) 11.9084 1.71218i 0.407499 0.0585895i
\(855\) 12.3178 4.52270i 0.421260 0.154673i
\(856\) 1.83566 6.25170i 0.0627417 0.213679i
\(857\) −24.7100 11.2847i −0.844078 0.385477i −0.0540423 0.998539i \(-0.517211\pi\)
−0.790035 + 0.613061i \(0.789938\pi\)
\(858\) −45.7834 42.8449i −1.56302 1.46270i
\(859\) 3.49540 24.3110i 0.119261 0.829481i −0.839111 0.543960i \(-0.816924\pi\)
0.958372 0.285521i \(-0.0921667\pi\)
\(860\) 1.32754 + 4.52120i 0.0452689 + 0.154172i
\(861\) −5.26899 6.57273i −0.179567 0.223998i
\(862\) 33.0384 + 51.4088i 1.12529 + 1.75099i
\(863\) −13.8320 21.5231i −0.470848 0.732654i 0.521882 0.853018i \(-0.325230\pi\)
−0.992730 + 0.120364i \(0.961594\pi\)
\(864\) −34.4141 + 23.5050i −1.17079 + 0.799658i
\(865\) −4.95077 16.8608i −0.168331 0.573283i
\(866\) −0.469439 + 3.26502i −0.0159522 + 0.110950i
\(867\) 20.9321 22.3678i 0.710893 0.759650i
\(868\) −5.04762 2.30517i −0.171327 0.0782426i
\(869\) 1.51581 5.16236i 0.0514202 0.175121i
\(870\) −8.57181 20.8447i −0.290612 0.706703i
\(871\) −47.9717 + 6.89729i −1.62546 + 0.233706i
\(872\) −3.94959 2.53825i −0.133750 0.0859560i
\(873\) 2.45525 32.0269i 0.0830977 1.08395i
\(874\) 27.9997 + 26.2450i 0.947104 + 0.887749i
\(875\) 16.1260i 0.545159i
\(876\) 18.1250 + 12.6532i 0.612387 + 0.427512i
\(877\) −2.94421 20.4774i −0.0994189 0.691474i −0.977186 0.212386i \(-0.931877\pi\)
0.877767 0.479088i \(-0.159033\pi\)
\(878\) −31.6816 + 14.4685i −1.06920 + 0.488288i
\(879\) −10.8400 3.63872i −0.365625 0.122731i
\(880\) 6.82471 14.9440i 0.230061 0.503763i
\(881\) −22.7242 + 26.2251i −0.765598 + 0.883548i −0.995982 0.0895523i \(-0.971456\pi\)
0.230384 + 0.973100i \(0.426002\pi\)
\(882\) 27.1129 + 6.04340i 0.912940 + 0.203492i
\(883\) −38.3258 + 11.2535i −1.28976 + 0.378709i −0.853492 0.521105i \(-0.825520\pi\)
−0.436273 + 0.899815i \(0.643702\pi\)
\(884\) −33.1669 38.2766i −1.11552 1.28738i
\(885\) −5.52919 9.37347i −0.185862 0.315086i
\(886\) 71.9187 46.2193i 2.41616 1.55277i
\(887\) 25.8278 22.3799i 0.867213 0.751444i −0.102747 0.994707i \(-0.532763\pi\)
0.969960 + 0.243263i \(0.0782179\pi\)
\(888\) −3.70533 + 0.935647i −0.124343 + 0.0313983i
\(889\) 12.8164 + 1.84272i 0.429849 + 0.0618029i
\(890\) 6.15666 + 5.33477i 0.206372 + 0.178822i
\(891\) −24.0975 + 36.6666i −0.807296 + 1.22838i
\(892\) −7.01603 2.06009i −0.234914 0.0689770i
\(893\) 17.4479 + 38.2055i 0.583870 + 1.27850i
\(894\) 17.3941 1.82510i 0.581747 0.0610403i
\(895\) −12.5991 + 19.6046i −0.421142 + 0.655310i
\(896\) 11.6888 0.390495
\(897\) −6.05305 28.6406i −0.202106 0.956281i
\(898\) −23.9645 −0.799706
\(899\) −4.08343 + 6.35394i −0.136190 + 0.211916i
\(900\) −1.78126 26.8325i −0.0593754 0.894418i
\(901\) 14.9621 + 32.7624i 0.498460 + 1.09147i
\(902\) 29.6974 + 8.71994i 0.988815 + 0.290342i
\(903\) 2.10893 4.18633i 0.0701806 0.139312i
\(904\) 11.0094 + 9.53972i 0.366168 + 0.317286i
\(905\) −19.9797 2.87264i −0.664146 0.0954898i
\(906\) −4.60320 18.2295i −0.152931 0.605635i
\(907\) −3.14593 + 2.72596i −0.104459 + 0.0905142i −0.705524 0.708686i \(-0.749289\pi\)
0.601066 + 0.799200i \(0.294743\pi\)
\(908\) 6.82795 4.38806i 0.226593 0.145623i
\(909\) 11.1228 + 20.6199i 0.368921 + 0.683918i
\(910\) 9.04138 + 10.4343i 0.299719 + 0.345894i
\(911\) 38.2480 11.2306i 1.26721 0.372087i 0.422039 0.906578i \(-0.361315\pi\)
0.845175 + 0.534490i \(0.179496\pi\)
\(912\) 18.9300 + 3.46534i 0.626835 + 0.114749i
\(913\) −32.7545 + 37.8007i −1.08401 + 1.25102i
\(914\) 16.8155 36.8209i 0.556209 1.21793i
\(915\) −2.24539 + 6.68921i −0.0742304 + 0.221138i
\(916\) 31.9860 14.6075i 1.05685 0.482645i
\(917\) 1.95702 + 13.6114i 0.0646266 + 0.449488i
\(918\) −40.8469 + 49.8997i −1.34815 + 1.64694i
\(919\) 25.0714i 0.827029i −0.910498 0.413514i \(-0.864301\pi\)
0.910498 0.413514i \(-0.135699\pi\)
\(920\) −4.41533 + 2.59970i −0.145569 + 0.0857097i
\(921\) 30.7310 + 1.17623i 1.01262 + 0.0387579i
\(922\) 4.68740 + 3.01241i 0.154371 + 0.0992083i
\(923\) −3.25180 + 0.467539i −0.107034 + 0.0153892i
\(924\) 30.7621 12.6501i 1.01200 0.416157i
\(925\) −2.46169 + 8.38375i −0.0809399 + 0.275656i
\(926\) 36.3416 + 16.5966i 1.19426 + 0.545400i
\(927\) 19.4112 + 19.6107i 0.637546 + 0.644099i
\(928\) 6.11978 42.5640i 0.200892 1.39723i
\(929\) −9.79787 33.3685i −0.321458 1.09478i −0.948757 0.316006i \(-0.897658\pi\)
0.627299 0.778778i \(-0.284160\pi\)
\(930\) 4.62049 3.70399i 0.151512 0.121458i
\(931\) −9.02184 14.0383i −0.295679 0.460085i
\(932\) −17.0559 26.5395i −0.558684 0.869329i
\(933\) −22.0860 + 17.7051i −0.723065 + 0.579640i
\(934\) 19.7529 + 67.2721i 0.646334 + 2.20121i
\(935\) 4.70641 32.7338i 0.153916 1.07051i
\(936\) 6.89892 + 6.96983i 0.225498 + 0.227816i
\(937\) 29.0588 + 13.2707i 0.949310 + 0.433536i 0.829030 0.559204i \(-0.188893\pi\)
0.120281 + 0.992740i \(0.461621\pi\)
\(938\) 13.1792 44.8843i 0.430316 1.46552i
\(939\) −0.221518 + 0.0910928i −0.00722895 + 0.00297270i
\(940\) −30.7688 + 4.42388i −1.00357 + 0.144291i
\(941\) 37.4172 + 24.0466i 1.21977 + 0.783896i 0.982266 0.187492i \(-0.0600358\pi\)
0.237500 + 0.971388i \(0.423672\pi\)
\(942\) 65.8891 + 2.52190i 2.14678 + 0.0821680i
\(943\) 9.02869 + 11.2814i 0.294015 + 0.367372i
\(944\) 15.9607i 0.519476i
\(945\) 6.11946 7.47571i 0.199066 0.243185i
\(946\) 2.45106 + 17.0475i 0.0796909 + 0.554262i
\(947\) −27.8050 + 12.6981i −0.903541 + 0.412633i −0.812330 0.583198i \(-0.801801\pi\)
−0.0912109 + 0.995832i \(0.529074\pi\)
\(948\) −1.48436 + 4.42204i −0.0482098 + 0.143621i
\(949\) −7.65642 + 16.7652i −0.248538 + 0.544222i
\(950\) −19.2496 + 22.2153i −0.624540 + 0.720758i
\(951\) −55.0462 10.0768i −1.78500 0.326762i
\(952\) 8.46161 2.48455i 0.274242 0.0805248i
\(953\) 28.3870 + 32.7603i 0.919544 + 1.06121i 0.997931 + 0.0642872i \(0.0204774\pi\)
−0.0783876 + 0.996923i \(0.524977\pi\)
\(954\) −18.3536 34.0245i −0.594219 1.10158i
\(955\) −4.30439 + 2.76626i −0.139287 + 0.0895141i
\(956\) 7.93461 6.87537i 0.256623 0.222366i
\(957\) −11.0841 43.8951i −0.358298 1.41893i
\(958\) −8.62568 1.24019i −0.278683 0.0400686i
\(959\) −12.0558 10.4464i −0.389303 0.337333i
\(960\) −9.91661 + 19.6850i −0.320057 + 0.635330i
\(961\) 27.8402 + 8.17461i 0.898070 + 0.263697i
\(962\) −7.33767 16.0673i −0.236576 0.518029i
\(963\) −1.39582 21.0263i −0.0449795 0.677562i
\(964\) 27.4885 42.7730i 0.885345 1.37762i
\(965\) 18.7574 0.603822
\(966\) 27.5732 + 6.16933i 0.887153 + 0.198495i
\(967\) 48.2618 1.55200 0.775998 0.630735i \(-0.217247\pi\)
0.775998 + 0.630735i \(0.217247\pi\)
\(968\) −6.40264 + 9.96270i −0.205789 + 0.320213i
\(969\) 38.5273 4.04252i 1.23768 0.129864i
\(970\) −10.7949 23.6376i −0.346605 0.758959i
\(971\) −10.7524 3.15720i −0.345063 0.101320i 0.104609 0.994513i \(-0.466641\pi\)
−0.449672 + 0.893194i \(0.648459\pi\)
\(972\) 22.0922 30.9663i 0.708606 0.993243i
\(973\) 1.86571 + 1.61665i 0.0598120 + 0.0518274i
\(974\) −16.1728 2.32530i −0.518210 0.0745073i
\(975\) 21.7396 5.48956i 0.696226 0.175807i
\(976\) −7.82079 + 6.77675i −0.250337 + 0.216919i
\(977\) −25.9832 + 16.6984i −0.831277 + 0.534229i −0.885684 0.464289i \(-0.846310\pi\)
0.0544063 + 0.998519i \(0.482673\pi\)
\(978\) −8.56265 14.5160i −0.273803 0.464171i
\(979\) 10.7160 + 12.3669i 0.342484 + 0.395247i
\(980\) 11.8501 3.47950i 0.378537 0.111149i
\(981\) −14.8203 3.30341i −0.473176 0.105470i
\(982\) −11.3277 + 13.0729i −0.361482 + 0.417172i
\(983\) 21.5590 47.2077i 0.687626 1.50569i −0.166730 0.986003i \(-0.553321\pi\)
0.854356 0.519688i \(-0.173952\pi\)
\(984\) −4.58906 1.54043i −0.146294 0.0491071i
\(985\) −11.4629 + 5.23491i −0.365237 + 0.166798i
\(986\) −9.46945 65.8615i −0.301569 2.09746i
\(987\) 25.3558 + 17.7011i 0.807085 + 0.563432i
\(988\) 32.6570i 1.03896i
\(989\) −3.62319 + 7.17780i −0.115211 + 0.228241i
\(990\) −2.71324 + 35.3922i −0.0862326 + 1.12484i
\(991\) 21.2430 + 13.6520i 0.674806 + 0.433672i 0.832655 0.553792i \(-0.186820\pi\)
−0.157849 + 0.987463i \(0.550456\pi\)
\(992\) 11.1835 1.60794i 0.355077 0.0510523i
\(993\) 8.65058 + 21.0363i 0.274518 + 0.667566i
\(994\) 0.893364 3.04252i 0.0283358 0.0965028i
\(995\) −15.6878 7.16440i −0.497338 0.227127i
\(996\) 29.6295 31.6617i 0.938848 1.00324i
\(997\) −4.09241 + 28.4634i −0.129608 + 0.901444i 0.816443 + 0.577426i \(0.195943\pi\)
−0.946051 + 0.324018i \(0.894966\pi\)
\(998\) −6.10673 20.7976i −0.193305 0.658337i
\(999\) −10.2063 + 6.97099i −0.322914 + 0.220552i
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 69.2.g.a.44.6 yes 60
3.2 odd 2 inner 69.2.g.a.44.1 yes 60
23.11 odd 22 inner 69.2.g.a.11.1 60
69.11 even 22 inner 69.2.g.a.11.6 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.2.g.a.11.1 60 23.11 odd 22 inner
69.2.g.a.11.6 yes 60 69.11 even 22 inner
69.2.g.a.44.1 yes 60 3.2 odd 2 inner
69.2.g.a.44.6 yes 60 1.1 even 1 trivial