Properties

Label 65.2.f.b.18.4
Level $65$
Weight $2$
Character 65.18
Analytic conductor $0.519$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [65,2,Mod(18,65)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(65, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("65.18");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 65 = 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 65.f (of order \(4\), degree \(2\), 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: \(0.519027613138\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.619810816.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 18.4
Root \(1.18254 - 1.18254i\) of defining polynomial
Character \(\chi\) \(=\) 65.18
Dual form 65.2.f.b.47.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.31627i q^{2} +(-0.240275 - 0.240275i) q^{3} -3.36509 q^{4} +(-1.55654 + 1.60536i) q^{5} +(0.556540 - 0.556540i) q^{6} +3.95872 q^{7} -3.16190i q^{8} -2.88454i q^{9} +O(q^{10})\) \(q+2.31627i q^{2} +(-0.240275 - 0.240275i) q^{3} -3.36509 q^{4} +(-1.55654 + 1.60536i) q^{5} +(0.556540 - 0.556540i) q^{6} +3.95872 q^{7} -3.16190i q^{8} -2.88454i q^{9} +(-3.71844 - 3.60536i) q^{10} +(-0.556540 - 0.556540i) q^{11} +(0.808545 + 0.808545i) q^{12} +(3.60536 + 0.0370899i) q^{13} +9.16944i q^{14} +(0.759725 - 0.0117303i) q^{15} +0.593630 q^{16} +(-1.16190 - 1.16190i) q^{17} +6.68135 q^{18} +(-1.24027 - 1.24027i) q^{19} +(5.23789 - 5.40218i) q^{20} +(-0.951180 - 0.951180i) q^{21} +(1.28910 - 1.28910i) q^{22} +(-2.80855 + 2.80855i) q^{23} +(-0.759725 + 0.759725i) q^{24} +(-0.154365 - 4.99762i) q^{25} +(-0.0859102 + 8.35097i) q^{26} +(-1.41391 + 1.41391i) q^{27} -13.3214 q^{28} -3.47817i q^{29} +(0.0271704 + 1.75973i) q^{30} +(-2.07599 + 2.07599i) q^{31} -4.94880i q^{32} +0.267445i q^{33} +(2.69127 - 2.69127i) q^{34} +(-6.16190 + 6.35517i) q^{35} +9.70671i q^{36} -6.84564 q^{37} +(2.87281 - 2.87281i) q^{38} +(-0.857366 - 0.875189i) q^{39} +(5.07599 + 4.92163i) q^{40} +(7.52699 - 7.52699i) q^{41} +(2.20318 - 2.20318i) q^{42} +(-7.03471 + 7.03471i) q^{43} +(1.87281 + 1.87281i) q^{44} +(4.63072 + 4.48990i) q^{45} +(-6.50534 - 6.50534i) q^{46} +9.09526 q^{47} +(-0.142634 - 0.142634i) q^{48} +8.67143 q^{49} +(11.5758 - 0.357550i) q^{50} +0.558351i q^{51} +(-12.1323 - 0.124811i) q^{52} +(0.958716 + 0.958716i) q^{53} +(-3.27498 - 3.27498i) q^{54} +(1.75973 - 0.0271704i) q^{55} -12.5171i q^{56} +0.596014i q^{57} +8.05636 q^{58} +(-7.46644 + 7.46644i) q^{59} +(-2.55654 + 0.0394734i) q^{60} +3.68926 q^{61} +(-4.80855 - 4.80855i) q^{62} -11.4191i q^{63} +12.6500 q^{64} +(-5.67143 + 5.73017i) q^{65} -0.619474 q^{66} +3.78690i q^{67} +(3.90990 + 3.90990i) q^{68} +1.34965 q^{69} +(-14.7203 - 14.2726i) q^{70} +(-3.67954 + 3.67954i) q^{71} -9.12062 q^{72} +5.57581i q^{73} -15.8563i q^{74} +(-1.16371 + 1.23789i) q^{75} +(4.17363 + 4.17363i) q^{76} +(-2.20318 - 2.20318i) q^{77} +(2.02717 - 1.98589i) q^{78} -9.03051i q^{79} +(-0.924009 + 0.952991i) q^{80} -7.97416 q^{81} +(17.4345 + 17.4345i) q^{82} +6.16980 q^{83} +(3.20080 + 3.20080i) q^{84} +(3.67382 - 0.0567242i) q^{85} +(-16.2942 - 16.2942i) q^{86} +(-0.835716 + 0.835716i) q^{87} +(-1.75973 + 1.75973i) q^{88} +(-3.51707 + 3.51707i) q^{89} +(-10.3998 + 10.7260i) q^{90} +(14.2726 + 0.146829i) q^{91} +(9.45100 - 9.45100i) q^{92} +0.997617 q^{93} +21.0670i q^{94} +(3.92163 - 0.0605505i) q^{95} +(-1.18907 + 1.18907i) q^{96} +9.03051i q^{97} +20.0853i q^{98} +(-1.60536 + 1.60536i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{10} + 6 q^{11} - 2 q^{12} + 14 q^{13} + 2 q^{15} - 8 q^{16} + 16 q^{17} + 20 q^{18} - 14 q^{19} - 2 q^{20} - 12 q^{21} + 10 q^{22} - 14 q^{23} - 2 q^{24} - 12 q^{25} + 6 q^{26} + 12 q^{27} - 8 q^{28} - 14 q^{30} + 2 q^{31} - 24 q^{35} - 44 q^{37} - 2 q^{38} + 6 q^{39} + 22 q^{40} + 16 q^{41} + 24 q^{42} - 6 q^{43} - 10 q^{44} + 22 q^{45} + 2 q^{46} + 16 q^{47} - 14 q^{48} + 24 q^{49} + 44 q^{50} - 38 q^{52} - 24 q^{53} + 20 q^{54} + 10 q^{55} + 24 q^{58} - 22 q^{59} - 10 q^{60} + 20 q^{61} - 30 q^{62} + 48 q^{64} - 36 q^{66} + 4 q^{68} + 4 q^{69} - 68 q^{70} - 10 q^{71} - 16 q^{72} + 30 q^{75} + 6 q^{76} - 24 q^{77} + 2 q^{78} - 26 q^{80} - 20 q^{81} + 20 q^{82} + 48 q^{83} - 16 q^{84} + 32 q^{85} - 46 q^{86} + 16 q^{87} - 10 q^{88} + 28 q^{89} - 14 q^{90} + 20 q^{91} + 50 q^{92} - 40 q^{93} + 2 q^{95} + 30 q^{96} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.31627i 1.63785i 0.573903 + 0.818924i \(0.305429\pi\)
−0.573903 + 0.818924i \(0.694571\pi\)
\(3\) −0.240275 0.240275i −0.138723 0.138723i 0.634335 0.773058i \(-0.281274\pi\)
−0.773058 + 0.634335i \(0.781274\pi\)
\(4\) −3.36509 −1.68254
\(5\) −1.55654 + 1.60536i −0.696106 + 0.717939i
\(6\) 0.556540 0.556540i 0.227207 0.227207i
\(7\) 3.95872 1.49625 0.748127 0.663556i \(-0.230953\pi\)
0.748127 + 0.663556i \(0.230953\pi\)
\(8\) 3.16190i 1.11790i
\(9\) 2.88454i 0.961512i
\(10\) −3.71844 3.60536i −1.17587 1.14012i
\(11\) −0.556540 0.556540i −0.167803 0.167803i 0.618210 0.786013i \(-0.287858\pi\)
−0.786013 + 0.618210i \(0.787858\pi\)
\(12\) 0.808545 + 0.808545i 0.233407 + 0.233407i
\(13\) 3.60536 + 0.0370899i 0.999947 + 0.0102869i
\(14\) 9.16944i 2.45064i
\(15\) 0.759725 0.0117303i 0.196160 0.00302874i
\(16\) 0.593630 0.148408
\(17\) −1.16190 1.16190i −0.281802 0.281802i 0.552025 0.833827i \(-0.313855\pi\)
−0.833827 + 0.552025i \(0.813855\pi\)
\(18\) 6.68135 1.57481
\(19\) −1.24027 1.24027i −0.284539 0.284539i 0.550377 0.834916i \(-0.314484\pi\)
−0.834916 + 0.550377i \(0.814484\pi\)
\(20\) 5.23789 5.40218i 1.17123 1.20796i
\(21\) −0.951180 0.951180i −0.207564 0.207564i
\(22\) 1.28910 1.28910i 0.274836 0.274836i
\(23\) −2.80855 + 2.80855i −0.585622 + 0.585622i −0.936443 0.350821i \(-0.885903\pi\)
0.350821 + 0.936443i \(0.385903\pi\)
\(24\) −0.759725 + 0.759725i −0.155078 + 0.155078i
\(25\) −0.154365 4.99762i −0.0308729 0.999523i
\(26\) −0.0859102 + 8.35097i −0.0168484 + 1.63776i
\(27\) −1.41391 + 1.41391i −0.272106 + 0.272106i
\(28\) −13.3214 −2.51751
\(29\) 3.47817i 0.645879i −0.946420 0.322940i \(-0.895329\pi\)
0.946420 0.322940i \(-0.104671\pi\)
\(30\) 0.0271704 + 1.75973i 0.00496062 + 0.321280i
\(31\) −2.07599 + 2.07599i −0.372859 + 0.372859i −0.868517 0.495659i \(-0.834927\pi\)
0.495659 + 0.868517i \(0.334927\pi\)
\(32\) 4.94880i 0.874832i
\(33\) 0.267445i 0.0465562i
\(34\) 2.69127 2.69127i 0.461549 0.461549i
\(35\) −6.16190 + 6.35517i −1.04155 + 1.07422i
\(36\) 9.70671i 1.61779i
\(37\) −6.84564 −1.12542 −0.562708 0.826656i \(-0.690240\pi\)
−0.562708 + 0.826656i \(0.690240\pi\)
\(38\) 2.87281 2.87281i 0.466031 0.466031i
\(39\) −0.857366 0.875189i −0.137288 0.140142i
\(40\) 5.07599 + 4.92163i 0.802585 + 0.778177i
\(41\) 7.52699 7.52699i 1.17552 1.17552i 0.194644 0.980874i \(-0.437645\pi\)
0.980874 0.194644i \(-0.0623551\pi\)
\(42\) 2.20318 2.20318i 0.339959 0.339959i
\(43\) −7.03471 + 7.03471i −1.07278 + 1.07278i −0.0756481 + 0.997135i \(0.524103\pi\)
−0.997135 + 0.0756481i \(0.975897\pi\)
\(44\) 1.87281 + 1.87281i 0.282336 + 0.282336i
\(45\) 4.63072 + 4.48990i 0.690307 + 0.669314i
\(46\) −6.50534 6.50534i −0.959160 0.959160i
\(47\) 9.09526 1.32668 0.663340 0.748318i \(-0.269138\pi\)
0.663340 + 0.748318i \(0.269138\pi\)
\(48\) −0.142634 0.142634i −0.0205875 0.0205875i
\(49\) 8.67143 1.23878
\(50\) 11.5758 0.357550i 1.63707 0.0505651i
\(51\) 0.558351i 0.0781848i
\(52\) −12.1323 0.124811i −1.68245 0.0173081i
\(53\) 0.958716 + 0.958716i 0.131690 + 0.131690i 0.769879 0.638190i \(-0.220316\pi\)
−0.638190 + 0.769879i \(0.720316\pi\)
\(54\) −3.27498 3.27498i −0.445669 0.445669i
\(55\) 1.75973 0.0271704i 0.237281 0.00366366i
\(56\) 12.5171i 1.67266i
\(57\) 0.596014i 0.0789439i
\(58\) 8.05636 1.05785
\(59\) −7.46644 + 7.46644i −0.972047 + 0.972047i −0.999620 0.0275726i \(-0.991222\pi\)
0.0275726 + 0.999620i \(0.491222\pi\)
\(60\) −2.55654 + 0.0394734i −0.330048 + 0.00509599i
\(61\) 3.68926 0.472361 0.236180 0.971709i \(-0.424104\pi\)
0.236180 + 0.971709i \(0.424104\pi\)
\(62\) −4.80855 4.80855i −0.610686 0.610686i
\(63\) 11.4191i 1.43867i
\(64\) 12.6500 1.58125
\(65\) −5.67143 + 5.73017i −0.703455 + 0.710740i
\(66\) −0.619474 −0.0762520
\(67\) 3.78690i 0.462643i 0.972877 + 0.231321i \(0.0743049\pi\)
−0.972877 + 0.231321i \(0.925695\pi\)
\(68\) 3.90990 + 3.90990i 0.474144 + 0.474144i
\(69\) 1.34965 0.162478
\(70\) −14.7203 14.2726i −1.75941 1.70590i
\(71\) −3.67954 + 3.67954i −0.436681 + 0.436681i −0.890893 0.454212i \(-0.849921\pi\)
0.454212 + 0.890893i \(0.349921\pi\)
\(72\) −9.12062 −1.07487
\(73\) 5.57581i 0.652599i 0.945266 + 0.326299i \(0.105802\pi\)
−0.945266 + 0.326299i \(0.894198\pi\)
\(74\) 15.8563i 1.84326i
\(75\) −1.16371 + 1.23789i −0.134374 + 0.142939i
\(76\) 4.17363 + 4.17363i 0.478748 + 0.478748i
\(77\) −2.20318 2.20318i −0.251076 0.251076i
\(78\) 2.02717 1.98589i 0.229532 0.224857i
\(79\) 9.03051i 1.01601i −0.861354 0.508006i \(-0.830383\pi\)
0.861354 0.508006i \(-0.169617\pi\)
\(80\) −0.924009 + 0.952991i −0.103307 + 0.106548i
\(81\) −7.97416 −0.886017
\(82\) 17.4345 + 17.4345i 1.92532 + 1.92532i
\(83\) 6.16980 0.677224 0.338612 0.940926i \(-0.390043\pi\)
0.338612 + 0.940926i \(0.390043\pi\)
\(84\) 3.20080 + 3.20080i 0.349236 + 0.349236i
\(85\) 3.67382 0.0567242i 0.398481 0.00615261i
\(86\) −16.2942 16.2942i −1.75705 1.75705i
\(87\) −0.835716 + 0.835716i −0.0895981 + 0.0895981i
\(88\) −1.75973 + 1.75973i −0.187587 + 0.187587i
\(89\) −3.51707 + 3.51707i −0.372808 + 0.372808i −0.868499 0.495691i \(-0.834915\pi\)
0.495691 + 0.868499i \(0.334915\pi\)
\(90\) −10.3998 + 10.7260i −1.09623 + 1.13062i
\(91\) 14.2726 + 0.146829i 1.49617 + 0.0153918i
\(92\) 9.45100 9.45100i 0.985334 0.985334i
\(93\) 0.997617 0.103448
\(94\) 21.0670i 2.17290i
\(95\) 3.92163 0.0605505i 0.402350 0.00621235i
\(96\) −1.18907 + 1.18907i −0.121359 + 0.121359i
\(97\) 9.03051i 0.916910i 0.888718 + 0.458455i \(0.151597\pi\)
−0.888718 + 0.458455i \(0.848403\pi\)
\(98\) 20.0853i 2.02893i
\(99\) −1.60536 + 1.60536i −0.161345 + 0.161345i
\(100\) 0.519450 + 16.8174i 0.0519450 + 1.68174i
\(101\) 3.28490i 0.326860i −0.986555 0.163430i \(-0.947744\pi\)
0.986555 0.163430i \(-0.0522558\pi\)
\(102\) −1.29329 −0.128055
\(103\) 3.64426 3.64426i 0.359080 0.359080i −0.504394 0.863474i \(-0.668284\pi\)
0.863474 + 0.504394i \(0.168284\pi\)
\(104\) 0.117275 11.3998i 0.0114997 1.11784i
\(105\) 3.00754 0.0464368i 0.293505 0.00453177i
\(106\) −2.22064 + 2.22064i −0.215688 + 0.215688i
\(107\) −4.69308 + 4.69308i −0.453697 + 0.453697i −0.896580 0.442882i \(-0.853956\pi\)
0.442882 + 0.896580i \(0.353956\pi\)
\(108\) 4.75791 4.75791i 0.457831 0.457831i
\(109\) −4.12300 4.12300i −0.394912 0.394912i 0.481522 0.876434i \(-0.340084\pi\)
−0.876434 + 0.481522i \(0.840084\pi\)
\(110\) 0.0629339 + 4.07599i 0.00600051 + 0.388630i
\(111\) 1.64483 + 1.64483i 0.156121 + 0.156121i
\(112\) 2.35001 0.222055
\(113\) −12.7920 12.7920i −1.20337 1.20337i −0.973134 0.230241i \(-0.926049\pi\)
−0.230241 0.973134i \(-0.573951\pi\)
\(114\) −1.38053 −0.129298
\(115\) −0.137114 8.88034i −0.0127859 0.828096i
\(116\) 11.7043i 1.08672i
\(117\) 0.106987 10.3998i 0.00989098 0.961461i
\(118\) −17.2942 17.2942i −1.59206 1.59206i
\(119\) −4.59964 4.59964i −0.421648 0.421648i
\(120\) −0.0370899 2.40218i −0.00338583 0.219288i
\(121\) 10.3805i 0.943684i
\(122\) 8.54529i 0.773655i
\(123\) −3.61709 −0.326142
\(124\) 6.98589 6.98589i 0.627351 0.627351i
\(125\) 8.26325 + 7.53118i 0.739088 + 0.673609i
\(126\) 26.4496 2.35632
\(127\) −5.44898 5.44898i −0.483519 0.483519i 0.422735 0.906253i \(-0.361070\pi\)
−0.906253 + 0.422735i \(0.861070\pi\)
\(128\) 19.4031i 1.71501i
\(129\) 3.38053 0.297639
\(130\) −13.2726 13.1365i −1.16408 1.15215i
\(131\) 2.42144 0.211562 0.105781 0.994389i \(-0.466266\pi\)
0.105781 + 0.994389i \(0.466266\pi\)
\(132\) 0.899976i 0.0783329i
\(133\) −4.90990 4.90990i −0.425742 0.425742i
\(134\) −8.77146 −0.757738
\(135\) −0.0690272 4.47063i −0.00594091 0.384771i
\(136\) −3.67382 + 3.67382i −0.315027 + 0.315027i
\(137\) −0.578190 −0.0493981 −0.0246991 0.999695i \(-0.507863\pi\)
−0.0246991 + 0.999695i \(0.507863\pi\)
\(138\) 3.12614i 0.266114i
\(139\) 16.6241i 1.41004i 0.709187 + 0.705021i \(0.249062\pi\)
−0.709187 + 0.705021i \(0.750938\pi\)
\(140\) 20.7353 21.3857i 1.75245 1.80742i
\(141\) −2.18536 2.18536i −0.184041 0.184041i
\(142\) −8.52279 8.52279i −0.715217 0.715217i
\(143\) −1.98589 2.02717i −0.166068 0.169521i
\(144\) 1.71235i 0.142696i
\(145\) 5.58371 + 5.41391i 0.463702 + 0.449600i
\(146\) −12.9150 −1.06886
\(147\) −2.08353 2.08353i −0.171846 0.171846i
\(148\) 23.0361 1.89356
\(149\) 0.953563 + 0.953563i 0.0781189 + 0.0781189i 0.745087 0.666968i \(-0.232408\pi\)
−0.666968 + 0.745087i \(0.732408\pi\)
\(150\) −2.86729 2.69546i −0.234113 0.220084i
\(151\) 9.13988 + 9.13988i 0.743793 + 0.743793i 0.973306 0.229513i \(-0.0737132\pi\)
−0.229513 + 0.973306i \(0.573713\pi\)
\(152\) −3.92163 + 3.92163i −0.318086 + 0.318086i
\(153\) −3.35154 + 3.35154i −0.270956 + 0.270956i
\(154\) 5.10316 5.10316i 0.411224 0.411224i
\(155\) −0.101350 6.56408i −0.00814065 0.527239i
\(156\) 2.88511 + 2.94509i 0.230994 + 0.235796i
\(157\) 2.45519 2.45519i 0.195945 0.195945i −0.602314 0.798259i \(-0.705754\pi\)
0.798259 + 0.602314i \(0.205754\pi\)
\(158\) 20.9171 1.66407
\(159\) 0.460711i 0.0365367i
\(160\) 7.94460 + 7.70300i 0.628076 + 0.608976i
\(161\) −11.1182 + 11.1182i −0.876240 + 0.876240i
\(162\) 18.4703i 1.45116i
\(163\) 4.11546i 0.322348i −0.986926 0.161174i \(-0.948472\pi\)
0.986926 0.161174i \(-0.0515280\pi\)
\(164\) −25.3290 + 25.3290i −1.97786 + 1.97786i
\(165\) −0.429346 0.416289i −0.0334245 0.0324081i
\(166\) 14.2909i 1.10919i
\(167\) 5.27547 0.408228 0.204114 0.978947i \(-0.434569\pi\)
0.204114 + 0.978947i \(0.434569\pi\)
\(168\) −3.00754 + 3.00754i −0.232036 + 0.232036i
\(169\) 12.9972 + 0.267445i 0.999788 + 0.0205727i
\(170\) 0.131388 + 8.50953i 0.0100770 + 0.652651i
\(171\) −3.57762 + 3.57762i −0.273587 + 0.273587i
\(172\) 23.6724 23.6724i 1.80500 1.80500i
\(173\) 3.42144 3.42144i 0.260127 0.260127i −0.564978 0.825106i \(-0.691115\pi\)
0.825106 + 0.564978i \(0.191115\pi\)
\(174\) −1.93574 1.93574i −0.146748 0.146748i
\(175\) −0.611086 19.7841i −0.0461938 1.49554i
\(176\) −0.330379 0.330379i −0.0249033 0.0249033i
\(177\) 3.58799 0.269690
\(178\) −8.14646 8.14646i −0.610603 0.610603i
\(179\) 13.0849 0.978008 0.489004 0.872282i \(-0.337360\pi\)
0.489004 + 0.872282i \(0.337360\pi\)
\(180\) −15.5828 15.1089i −1.16147 1.12615i
\(181\) 4.65035i 0.345658i 0.984952 + 0.172829i \(0.0552908\pi\)
−0.984952 + 0.172829i \(0.944709\pi\)
\(182\) −0.340094 + 33.0591i −0.0252094 + 2.45051i
\(183\) −0.886435 0.886435i −0.0655272 0.0655272i
\(184\) 8.88034 + 8.88034i 0.654667 + 0.654667i
\(185\) 10.6555 10.9897i 0.783408 0.807980i
\(186\) 2.31074i 0.169432i
\(187\) 1.29329i 0.0945747i
\(188\) −30.6063 −2.23220
\(189\) −5.59725 + 5.59725i −0.407140 + 0.407140i
\(190\) 0.140251 + 9.08353i 0.0101749 + 0.658988i
\(191\) −4.01984 −0.290865 −0.145433 0.989368i \(-0.546457\pi\)
−0.145433 + 0.989368i \(0.546457\pi\)
\(192\) −3.03947 3.03947i −0.219355 0.219355i
\(193\) 23.0576i 1.65972i 0.557970 + 0.829861i \(0.311580\pi\)
−0.557970 + 0.829861i \(0.688420\pi\)
\(194\) −20.9171 −1.50176
\(195\) 2.73952 0.0141137i 0.196181 0.00101070i
\(196\) −29.1801 −2.08429
\(197\) 0.249622i 0.0177848i 0.999960 + 0.00889240i \(0.00283058\pi\)
−0.999960 + 0.00889240i \(0.997169\pi\)
\(198\) −3.71844 3.71844i −0.264258 0.264258i
\(199\) −17.6865 −1.25376 −0.626882 0.779115i \(-0.715669\pi\)
−0.626882 + 0.779115i \(0.715669\pi\)
\(200\) −15.8020 + 0.488086i −1.11737 + 0.0345129i
\(201\) 0.909896 0.909896i 0.0641791 0.0641791i
\(202\) 7.60870 0.535346
\(203\) 13.7691i 0.966399i
\(204\) 1.87890i 0.131549i
\(205\) 0.367469 + 23.7996i 0.0256652 + 1.66224i
\(206\) 8.44108 + 8.44108i 0.588118 + 0.588118i
\(207\) 8.10135 + 8.10135i 0.563083 + 0.563083i
\(208\) 2.14025 + 0.0220177i 0.148400 + 0.00152665i
\(209\) 1.38053i 0.0954930i
\(210\) 0.107560 + 6.96625i 0.00742234 + 0.480717i
\(211\) 9.10469 0.626793 0.313396 0.949622i \(-0.398533\pi\)
0.313396 + 0.949622i \(0.398533\pi\)
\(212\) −3.22616 3.22616i −0.221574 0.221574i
\(213\) 1.76820 0.121155
\(214\) −10.8704 10.8704i −0.743087 0.743087i
\(215\) −0.343436 22.2430i −0.0234221 1.51696i
\(216\) 4.47063 + 4.47063i 0.304188 + 0.304188i
\(217\) −8.21826 + 8.21826i −0.557892 + 0.557892i
\(218\) 9.54996 9.54996i 0.646805 0.646805i
\(219\) 1.33973 1.33973i 0.0905303 0.0905303i
\(220\) −5.92163 + 0.0914308i −0.399236 + 0.00616426i
\(221\) −4.14598 4.23217i −0.278889 0.284686i
\(222\) −3.80987 + 3.80987i −0.255702 + 0.255702i
\(223\) 14.2674 0.955419 0.477709 0.878518i \(-0.341467\pi\)
0.477709 + 0.878518i \(0.341467\pi\)
\(224\) 19.5909i 1.30897i
\(225\) −14.4158 + 0.445270i −0.961054 + 0.0296847i
\(226\) 29.6298 29.6298i 1.97094 1.97094i
\(227\) 12.3687i 0.820940i 0.911874 + 0.410470i \(0.134635\pi\)
−0.911874 + 0.410470i \(0.865365\pi\)
\(228\) 2.00564i 0.132827i
\(229\) 6.93888 6.93888i 0.458534 0.458534i −0.439640 0.898174i \(-0.644894\pi\)
0.898174 + 0.439640i \(0.144894\pi\)
\(230\) 20.5692 0.317592i 1.35629 0.0209414i
\(231\) 1.05874i 0.0696600i
\(232\) −10.9976 −0.722029
\(233\) −3.17544 + 3.17544i −0.208030 + 0.208030i −0.803430 0.595400i \(-0.796994\pi\)
0.595400 + 0.803430i \(0.296994\pi\)
\(234\) 24.0887 + 0.247811i 1.57473 + 0.0161999i
\(235\) −14.1571 + 14.6012i −0.923510 + 0.952475i
\(236\) 25.1252 25.1252i 1.63551 1.63551i
\(237\) −2.16980 + 2.16980i −0.140944 + 0.140944i
\(238\) 10.6540 10.6540i 0.690595 0.690595i
\(239\) 12.3783 + 12.3783i 0.800689 + 0.800689i 0.983203 0.182514i \(-0.0584236\pi\)
−0.182514 + 0.983203i \(0.558424\pi\)
\(240\) 0.450996 0.00696344i 0.0291117 0.000449488i
\(241\) 12.3115 + 12.3115i 0.793053 + 0.793053i 0.981989 0.188936i \(-0.0605039\pi\)
−0.188936 + 0.981989i \(0.560504\pi\)
\(242\) 24.0441 1.54561
\(243\) 6.15771 + 6.15771i 0.395017 + 0.395017i
\(244\) −12.4147 −0.794767
\(245\) −13.4974 + 13.9208i −0.862319 + 0.889366i
\(246\) 8.37814i 0.534171i
\(247\) −4.42564 4.51764i −0.281596 0.287451i
\(248\) 6.56408 + 6.56408i 0.416819 + 0.416819i
\(249\) −1.48245 1.48245i −0.0939464 0.0939464i
\(250\) −17.4442 + 19.1399i −1.10327 + 1.21051i
\(251\) 19.7805i 1.24854i −0.781210 0.624268i \(-0.785397\pi\)
0.781210 0.624268i \(-0.214603\pi\)
\(252\) 38.4261i 2.42062i
\(253\) 3.12614 0.196539
\(254\) 12.6213 12.6213i 0.791930 0.791930i
\(255\) −0.896355 0.869096i −0.0561319 0.0544249i
\(256\) −19.6428 −1.22768
\(257\) −14.5758 14.5758i −0.909214 0.909214i 0.0869949 0.996209i \(-0.472274\pi\)
−0.996209 + 0.0869949i \(0.972274\pi\)
\(258\) 7.83020i 0.487487i
\(259\) −27.0999 −1.68391
\(260\) 19.0849 19.2825i 1.18359 1.19585i
\(261\) −10.0329 −0.621021
\(262\) 5.60870i 0.346507i
\(263\) 14.5593 + 14.5593i 0.897765 + 0.897765i 0.995238 0.0974727i \(-0.0310759\pi\)
−0.0974727 + 0.995238i \(0.531076\pi\)
\(264\) 0.845635 0.0520453
\(265\) −3.03136 + 0.0468047i −0.186215 + 0.00287519i
\(266\) 11.3726 11.3726i 0.697300 0.697300i
\(267\) 1.69013 0.103434
\(268\) 12.7432i 0.778417i
\(269\) 8.65961i 0.527986i 0.964525 + 0.263993i \(0.0850396\pi\)
−0.964525 + 0.263993i \(0.914960\pi\)
\(270\) 10.3552 0.159885i 0.630195 0.00973031i
\(271\) −14.1589 14.1589i −0.860095 0.860095i 0.131254 0.991349i \(-0.458100\pi\)
−0.991349 + 0.131254i \(0.958100\pi\)
\(272\) −0.689739 0.689739i −0.0418216 0.0418216i
\(273\) −3.39407 3.46463i −0.205418 0.209689i
\(274\) 1.33924i 0.0809066i
\(275\) −2.69546 + 2.86729i −0.162543 + 0.172904i
\(276\) −4.54167 −0.273377
\(277\) 0.848019 + 0.848019i 0.0509525 + 0.0509525i 0.732124 0.681171i \(-0.238529\pi\)
−0.681171 + 0.732124i \(0.738529\pi\)
\(278\) −38.5059 −2.30943
\(279\) 5.98827 + 5.98827i 0.358508 + 0.358508i
\(280\) 20.0944 + 19.4833i 1.20087 + 1.16435i
\(281\) −13.1441 13.1441i −0.784110 0.784110i 0.196412 0.980522i \(-0.437071\pi\)
−0.980522 + 0.196412i \(0.937071\pi\)
\(282\) 5.06188 5.06188i 0.301430 0.301430i
\(283\) 7.40181 7.40181i 0.439992 0.439992i −0.452017 0.892009i \(-0.649295\pi\)
0.892009 + 0.452017i \(0.149295\pi\)
\(284\) 12.3820 12.3820i 0.734735 0.734735i
\(285\) −0.956817 0.927719i −0.0566769 0.0549533i
\(286\) 4.69546 4.59984i 0.277649 0.271994i
\(287\) 29.7972 29.7972i 1.75887 1.75887i
\(288\) −14.2750 −0.841161
\(289\) 14.3000i 0.841175i
\(290\) −12.5400 + 12.9334i −0.736377 + 0.759473i
\(291\) 2.16980 2.16980i 0.127196 0.127196i
\(292\) 18.7631i 1.09803i
\(293\) 11.2274i 0.655912i −0.944693 0.327956i \(-0.893640\pi\)
0.944693 0.327956i \(-0.106360\pi\)
\(294\) 4.82600 4.82600i 0.281458 0.281458i
\(295\) −0.364513 23.6081i −0.0212228 1.37452i
\(296\) 21.6452i 1.25810i
\(297\) 1.57379 0.0913206
\(298\) −2.20871 + 2.20871i −0.127947 + 0.127947i
\(299\) −10.2300 + 10.0216i −0.591615 + 0.579567i
\(300\) 3.91599 4.16561i 0.226090 0.240502i
\(301\) −27.8484 + 27.8484i −1.60516 + 1.60516i
\(302\) −21.1704 + 21.1704i −1.21822 + 1.21822i
\(303\) −0.789279 + 0.789279i −0.0453429 + 0.0453429i
\(304\) −0.736265 0.736265i −0.0422277 0.0422277i
\(305\) −5.74247 + 5.92258i −0.328813 + 0.339126i
\(306\) −7.76307 7.76307i −0.443785 0.443785i
\(307\) −28.2579 −1.61276 −0.806382 0.591395i \(-0.798577\pi\)
−0.806382 + 0.591395i \(0.798577\pi\)
\(308\) 7.41391 + 7.41391i 0.422446 + 0.422446i
\(309\) −1.75125 −0.0996250
\(310\) 15.2041 0.234754i 0.863537 0.0133331i
\(311\) 9.55436i 0.541778i 0.962611 + 0.270889i \(0.0873177\pi\)
−0.962611 + 0.270889i \(0.912682\pi\)
\(312\) −2.76726 + 2.71090i −0.156665 + 0.153475i
\(313\) 17.7119 + 17.7119i 1.00113 + 1.00113i 0.999999 + 0.00113436i \(0.000361078\pi\)
0.00113436 + 0.999999i \(0.499639\pi\)
\(314\) 5.68687 + 5.68687i 0.320929 + 0.320929i
\(315\) 18.3317 + 17.7742i 1.03287 + 1.00146i
\(316\) 30.3884i 1.70948i
\(317\) 0.912395i 0.0512452i −0.999672 0.0256226i \(-0.991843\pi\)
0.999672 0.0256226i \(-0.00815683\pi\)
\(318\) 1.06713 0.0598416
\(319\) −1.93574 + 1.93574i −0.108381 + 0.108381i
\(320\) −19.6902 + 20.3078i −1.10072 + 1.13524i
\(321\) 2.25526 0.125876
\(322\) −25.7528 25.7528i −1.43515 1.43515i
\(323\) 2.88215i 0.160367i
\(324\) 26.8337 1.49076
\(325\) −0.371179 18.0239i −0.0205893 0.999788i
\(326\) 9.53251 0.527957
\(327\) 1.98131i 0.109566i
\(328\) −23.7996 23.7996i −1.31411 1.31411i
\(329\) 36.0055 1.98505
\(330\) 0.964237 0.994479i 0.0530795 0.0547443i
\(331\) −15.2585 + 15.2585i −0.838682 + 0.838682i −0.988685 0.150003i \(-0.952072\pi\)
0.150003 + 0.988685i \(0.452072\pi\)
\(332\) −20.7619 −1.13946
\(333\) 19.7465i 1.08210i
\(334\) 12.2194i 0.668615i
\(335\) −6.07933 5.89446i −0.332149 0.322049i
\(336\) −0.564649 0.564649i −0.0308041 0.0308041i
\(337\) 8.33973 + 8.33973i 0.454294 + 0.454294i 0.896777 0.442483i \(-0.145902\pi\)
−0.442483 + 0.896777i \(0.645902\pi\)
\(338\) −0.619474 + 30.1051i −0.0336950 + 1.63750i
\(339\) 6.14721i 0.333871i
\(340\) −12.3627 + 0.190882i −0.670462 + 0.0103520i
\(341\) 2.31074 0.125134
\(342\) −8.28671 8.28671i −0.448094 0.448094i
\(343\) 6.61672 0.357269
\(344\) 22.2430 + 22.2430i 1.19926 + 1.19926i
\(345\) −2.10078 + 2.16667i −0.113102 + 0.116649i
\(346\) 7.92497 + 7.92497i 0.426049 + 0.426049i
\(347\) 22.4851 22.4851i 1.20707 1.20707i 0.235092 0.971973i \(-0.424461\pi\)
0.971973 0.235092i \(-0.0755391\pi\)
\(348\) 2.81226 2.81226i 0.150753 0.150753i
\(349\) 19.2262 19.2262i 1.02915 1.02915i 0.0295907 0.999562i \(-0.490580\pi\)
0.999562 0.0295907i \(-0.00942039\pi\)
\(350\) 45.8253 1.41544i 2.44947 0.0756583i
\(351\) −5.15008 + 5.04520i −0.274891 + 0.269293i
\(352\) −2.75420 + 2.75420i −0.146800 + 0.146800i
\(353\) −4.45434 −0.237080 −0.118540 0.992949i \(-0.537821\pi\)
−0.118540 + 0.992949i \(0.537821\pi\)
\(354\) 8.31074i 0.441711i
\(355\) −0.179636 11.6343i −0.00953409 0.617487i
\(356\) 11.8352 11.8352i 0.627266 0.627266i
\(357\) 2.21035i 0.116984i
\(358\) 30.3080i 1.60183i
\(359\) 11.6335 11.6335i 0.613992 0.613992i −0.329992 0.943984i \(-0.607046\pi\)
0.943984 + 0.329992i \(0.107046\pi\)
\(360\) 14.1966 14.6419i 0.748227 0.771695i
\(361\) 15.9234i 0.838076i
\(362\) −10.7715 −0.566135
\(363\) −2.49418 + 2.49418i −0.130910 + 0.130910i
\(364\) −48.0285 0.494091i −2.51738 0.0258974i
\(365\) −8.95118 8.67897i −0.468526 0.454278i
\(366\) 2.05322 2.05322i 0.107323 0.107323i
\(367\) 0.881194 0.881194i 0.0459980 0.0459980i −0.683734 0.729732i \(-0.739645\pi\)
0.729732 + 0.683734i \(0.239645\pi\)
\(368\) −1.66724 + 1.66724i −0.0869108 + 0.0869108i
\(369\) −21.7119 21.7119i −1.13027 1.13027i
\(370\) 25.4551 + 24.6810i 1.32335 + 1.28310i
\(371\) 3.79528 + 3.79528i 0.197041 + 0.197041i
\(372\) −3.35707 −0.174056
\(373\) 8.48607 + 8.48607i 0.439392 + 0.439392i 0.891807 0.452415i \(-0.149438\pi\)
−0.452415 + 0.891807i \(0.649438\pi\)
\(374\) −2.99560 −0.154899
\(375\) −0.175898 3.79500i −0.00908334 0.195973i
\(376\) 28.7583i 1.48310i
\(377\) 0.129005 12.5400i 0.00664410 0.645845i
\(378\) −12.9647 12.9647i −0.666833 0.666833i
\(379\) −21.9165 21.9165i −1.12577 1.12577i −0.990857 0.134918i \(-0.956923\pi\)
−0.134918 0.990857i \(-0.543077\pi\)
\(380\) −13.1966 + 0.203758i −0.676972 + 0.0104525i
\(381\) 2.61851i 0.134150i
\(382\) 9.31101i 0.476393i
\(383\) −11.8412 −0.605059 −0.302529 0.953140i \(-0.597831\pi\)
−0.302529 + 0.953140i \(0.597831\pi\)
\(384\) 4.66208 4.66208i 0.237911 0.237911i
\(385\) 6.96625 0.107560i 0.355033 0.00548176i
\(386\) −53.4075 −2.71837
\(387\) 20.2919 + 20.2919i 1.03149 + 1.03149i
\(388\) 30.3884i 1.54274i
\(389\) 22.0771 1.11935 0.559676 0.828712i \(-0.310926\pi\)
0.559676 + 0.828712i \(0.310926\pi\)
\(390\) 0.0326910 + 6.34545i 0.00165537 + 0.321314i
\(391\) 6.52650 0.330059
\(392\) 27.4182i 1.38483i
\(393\) −0.581812 0.581812i −0.0293485 0.0293485i
\(394\) −0.578190 −0.0291288
\(395\) 14.4972 + 14.0564i 0.729435 + 0.707252i
\(396\) 5.40218 5.40218i 0.271470 0.271470i
\(397\) −16.1305 −0.809568 −0.404784 0.914412i \(-0.632653\pi\)
−0.404784 + 0.914412i \(0.632653\pi\)
\(398\) 40.9666i 2.05347i
\(399\) 2.35945i 0.118120i
\(400\) −0.0916355 2.96674i −0.00458178 0.148337i
\(401\) 22.8020 + 22.8020i 1.13868 + 1.13868i 0.988688 + 0.149988i \(0.0479236\pi\)
0.149988 + 0.988688i \(0.452076\pi\)
\(402\) 2.10756 + 2.10756i 0.105116 + 0.105116i
\(403\) −7.56169 + 7.40770i −0.376675 + 0.369004i
\(404\) 11.0540i 0.549956i
\(405\) 12.4121 12.8014i 0.616762 0.636106i
\(406\) 31.8928 1.58281
\(407\) 3.80987 + 3.80987i 0.188848 + 0.188848i
\(408\) 1.76545 0.0874028
\(409\) 3.08611 + 3.08611i 0.152599 + 0.152599i 0.779278 0.626679i \(-0.215586\pi\)
−0.626679 + 0.779278i \(0.715586\pi\)
\(410\) −55.1262 + 0.851156i −2.72249 + 0.0420356i
\(411\) 0.138925 + 0.138925i 0.00685264 + 0.00685264i
\(412\) −12.2633 + 12.2633i −0.604167 + 0.604167i
\(413\) −29.5575 + 29.5575i −1.45443 + 1.45443i
\(414\) −18.7649 + 18.7649i −0.922243 + 0.922243i
\(415\) −9.60355 + 9.90476i −0.471420 + 0.486206i
\(416\) 0.183551 17.8422i 0.00899931 0.874786i
\(417\) 3.99436 3.99436i 0.195605 0.195605i
\(418\) −3.19766 −0.156403
\(419\) 9.51871i 0.465020i 0.972594 + 0.232510i \(0.0746938\pi\)
−0.972594 + 0.232510i \(0.925306\pi\)
\(420\) −10.1206 + 0.156264i −0.493836 + 0.00762489i
\(421\) 20.6718 20.6718i 1.00748 1.00748i 0.00751095 0.999972i \(-0.497609\pi\)
0.999972 0.00751095i \(-0.00239083\pi\)
\(422\) 21.0889i 1.02659i
\(423\) 26.2356i 1.27562i
\(424\) 3.03136 3.03136i 0.147216 0.147216i
\(425\) −5.62738 + 5.98609i −0.272968 + 0.290368i
\(426\) 4.09562i 0.198434i
\(427\) 14.6047 0.706772
\(428\) 15.7926 15.7926i 0.763365 0.763365i
\(429\) −0.00991953 + 0.964237i −0.000478919 + 0.0465538i
\(430\) 51.5208 0.795489i 2.48455 0.0383619i
\(431\) −16.8370 + 16.8370i −0.811012 + 0.811012i −0.984786 0.173774i \(-0.944404\pi\)
0.173774 + 0.984786i \(0.444404\pi\)
\(432\) −0.839337 + 0.839337i −0.0403826 + 0.0403826i
\(433\) 18.0614 18.0614i 0.867975 0.867975i −0.124273 0.992248i \(-0.539660\pi\)
0.992248 + 0.124273i \(0.0396598\pi\)
\(434\) −19.0357 19.0357i −0.913741 0.913741i
\(435\) −0.0407998 2.64245i −0.00195620 0.126696i
\(436\) 13.8742 + 13.8742i 0.664456 + 0.664456i
\(437\) 6.96674 0.333264
\(438\) 3.10316 + 3.10316i 0.148275 + 0.148275i
\(439\) 32.7984 1.56538 0.782692 0.622409i \(-0.213846\pi\)
0.782692 + 0.622409i \(0.213846\pi\)
\(440\) −0.0859102 5.56408i −0.00409561 0.265257i
\(441\) 25.0131i 1.19110i
\(442\) 9.80282 9.60318i 0.466273 0.456777i
\(443\) −11.4661 11.4661i −0.544769 0.544769i 0.380154 0.924923i \(-0.375871\pi\)
−0.924923 + 0.380154i \(0.875871\pi\)
\(444\) −5.53501 5.53501i −0.262680 0.262680i
\(445\) −0.171704 11.1206i −0.00813955 0.527168i
\(446\) 33.0472i 1.56483i
\(447\) 0.458234i 0.0216737i
\(448\) 50.0777 2.36595
\(449\) −20.0441 + 20.0441i −0.945937 + 0.945937i −0.998612 0.0526744i \(-0.983225\pi\)
0.0526744 + 0.998612i \(0.483225\pi\)
\(450\) −1.03136 33.3908i −0.0486190 1.57406i
\(451\) −8.37814 −0.394511
\(452\) 43.0463 + 43.0463i 2.02473 + 2.02473i
\(453\) 4.39217i 0.206362i
\(454\) −28.6492 −1.34457
\(455\) −22.4516 + 22.6841i −1.05255 + 1.06345i
\(456\) 1.88454 0.0882515
\(457\) 3.16380i 0.147996i 0.997258 + 0.0739982i \(0.0235759\pi\)
−0.997258 + 0.0739982i \(0.976424\pi\)
\(458\) 16.0723 + 16.0723i 0.751008 + 0.751008i
\(459\) 3.28564 0.153360
\(460\) 0.461400 + 29.8831i 0.0215129 + 1.39331i
\(461\) 20.0071 20.0071i 0.931821 0.931821i −0.0659984 0.997820i \(-0.521023\pi\)
0.997820 + 0.0659984i \(0.0210232\pi\)
\(462\) −2.45232 −0.114092
\(463\) 4.68050i 0.217521i −0.994068 0.108761i \(-0.965312\pi\)
0.994068 0.108761i \(-0.0346882\pi\)
\(464\) 2.06474i 0.0958534i
\(465\) −1.55283 + 1.60153i −0.0720108 + 0.0742694i
\(466\) −7.35517 7.35517i −0.340721 0.340721i
\(467\) −5.31207 5.31207i −0.245813 0.245813i 0.573437 0.819250i \(-0.305610\pi\)
−0.819250 + 0.573437i \(0.805610\pi\)
\(468\) −0.360021 + 34.9962i −0.0166420 + 1.61770i
\(469\) 14.9912i 0.692231i
\(470\) −33.8202 32.7917i −1.56001 1.51257i
\(471\) −1.17984 −0.0543642
\(472\) 23.6081 + 23.6081i 1.08665 + 1.08665i
\(473\) 7.83020 0.360033
\(474\) −5.02584 5.02584i −0.230845 0.230845i
\(475\) −6.00696 + 6.38987i −0.275618 + 0.293187i
\(476\) 15.4782 + 15.4782i 0.709441 + 0.709441i
\(477\) 2.76545 2.76545i 0.126621 0.126621i
\(478\) −28.6715 + 28.6715i −1.31141 + 1.31141i
\(479\) −18.0482 + 18.0482i −0.824645 + 0.824645i −0.986770 0.162125i \(-0.948165\pi\)
0.162125 + 0.986770i \(0.448165\pi\)
\(480\) −0.0580507 3.75973i −0.00264964 0.171607i
\(481\) −24.6810 0.253904i −1.12536 0.0115770i
\(482\) −28.5167 + 28.5167i −1.29890 + 1.29890i
\(483\) 5.34286 0.243109
\(484\) 34.9314i 1.58779i
\(485\) −14.4972 14.0564i −0.658285 0.638266i
\(486\) −14.2629 + 14.2629i −0.646978 + 0.646978i
\(487\) 0.978187i 0.0443259i −0.999754 0.0221629i \(-0.992945\pi\)
0.999754 0.0221629i \(-0.00705526\pi\)
\(488\) 11.6651i 0.528052i
\(489\) −0.988842 + 0.988842i −0.0447170 + 0.0447170i
\(490\) −32.2442 31.2636i −1.45664 1.41235i
\(491\) 19.2368i 0.868146i −0.900878 0.434073i \(-0.857076\pi\)
0.900878 0.434073i \(-0.142924\pi\)
\(492\) 12.1718 0.548748
\(493\) −4.04128 + 4.04128i −0.182010 + 0.182010i
\(494\) 10.4641 10.2509i 0.470800 0.461212i
\(495\) −0.0783740 5.07599i −0.00352265 0.228149i
\(496\) −1.23237 + 1.23237i −0.0553351 + 0.0553351i
\(497\) −14.5663 + 14.5663i −0.653386 + 0.653386i
\(498\) 3.43374 3.43374i 0.153870 0.153870i
\(499\) −16.4546 16.4546i −0.736610 0.736610i 0.235310 0.971920i \(-0.424389\pi\)
−0.971920 + 0.235310i \(0.924389\pi\)
\(500\) −27.8065 25.3431i −1.24355 1.13338i
\(501\) −1.26756 1.26756i −0.0566305 0.0566305i
\(502\) 45.8169 2.04491
\(503\) 12.8451 + 12.8451i 0.572733 + 0.572733i 0.932891 0.360158i \(-0.117277\pi\)
−0.360158 + 0.932891i \(0.617277\pi\)
\(504\) −36.1059 −1.60829
\(505\) 5.27345 + 5.11308i 0.234665 + 0.227529i
\(506\) 7.24096i 0.321900i
\(507\) −3.05865 3.18717i −0.135839 0.141547i
\(508\) 18.3363 + 18.3363i 0.813541 + 0.813541i
\(509\) −6.97177 6.97177i −0.309018 0.309018i 0.535510 0.844529i \(-0.320119\pi\)
−0.844529 + 0.535510i \(0.820119\pi\)
\(510\) 2.01306 2.07620i 0.0891397 0.0919355i
\(511\) 22.0730i 0.976454i
\(512\) 6.69175i 0.295737i
\(513\) 3.50726 0.154849
\(514\) 33.7614 33.7614i 1.48915 1.48915i
\(515\) 0.177914 + 11.5228i 0.00783981 + 0.507755i
\(516\) −11.3758 −0.500790
\(517\) −5.06188 5.06188i −0.222621 0.222621i
\(518\) 62.7706i 2.75798i
\(519\) −1.64417 −0.0721712
\(520\) 18.1182 + 17.9325i 0.794537 + 0.786392i
\(521\) 9.45108 0.414060 0.207030 0.978335i \(-0.433620\pi\)
0.207030 + 0.978335i \(0.433620\pi\)
\(522\) 23.2388i 1.01714i
\(523\) −15.1815 15.1815i −0.663842 0.663842i 0.292441 0.956283i \(-0.405532\pi\)
−0.956283 + 0.292441i \(0.905532\pi\)
\(524\) −8.14836 −0.355963
\(525\) −4.60680 + 4.90046i −0.201057 + 0.213874i
\(526\) −33.7232 + 33.7232i −1.47040 + 1.47040i
\(527\) 4.82419 0.210145
\(528\) 0.158764i 0.00690930i
\(529\) 7.22415i 0.314093i
\(530\) −0.108412 7.02145i −0.00470912 0.304992i
\(531\) 21.5372 + 21.5372i 0.934635 + 0.934635i
\(532\) 16.5222 + 16.5222i 0.716329 + 0.716329i
\(533\) 27.4167 26.8583i 1.18755 1.16336i
\(534\) 3.91478i 0.169409i
\(535\) −0.229117 14.8391i −0.00990560 0.641548i
\(536\) 11.9738 0.517189
\(537\) −3.14396 3.14396i −0.135672 0.135672i
\(538\) −20.0580 −0.864760
\(539\) −4.82600 4.82600i −0.207871 0.207871i
\(540\) 0.232282 + 15.0441i 0.00999584 + 0.647393i
\(541\) −15.2507 15.2507i −0.655677 0.655677i 0.298677 0.954354i \(-0.403455\pi\)
−0.954354 + 0.298677i \(0.903455\pi\)
\(542\) 32.7959 32.7959i 1.40870 1.40870i
\(543\) 1.11736 1.11736i 0.0479506 0.0479506i
\(544\) −5.75001 + 5.75001i −0.246530 + 0.246530i
\(545\) 13.0365 0.201286i 0.558423 0.00862213i
\(546\) 8.02499 7.86156i 0.343438 0.336444i
\(547\) −27.7930 + 27.7930i −1.18834 + 1.18834i −0.210818 + 0.977525i \(0.567613\pi\)
−0.977525 + 0.210818i \(0.932387\pi\)
\(548\) 1.94566 0.0831144
\(549\) 10.6418i 0.454181i
\(550\) −6.64139 6.24341i −0.283190 0.266220i
\(551\) −4.31388 + 4.31388i −0.183778 + 0.183778i
\(552\) 4.26745i 0.181635i
\(553\) 35.7492i 1.52021i
\(554\) −1.96424 + 1.96424i −0.0834524 + 0.0834524i
\(555\) −5.20080 + 0.0803011i −0.220762 + 0.00340859i
\(556\) 55.9417i 2.37246i
\(557\) −24.9933 −1.05900 −0.529499 0.848310i \(-0.677620\pi\)
−0.529499 + 0.848310i \(0.677620\pi\)
\(558\) −13.8704 + 13.8704i −0.587182 + 0.587182i
\(559\) −25.6236 + 25.1017i −1.08376 + 1.06169i
\(560\) −3.65789 + 3.77262i −0.154574 + 0.159422i
\(561\) 0.310745 0.310745i 0.0131197 0.0131197i
\(562\) 30.4452 30.4452i 1.28425 1.28425i
\(563\) −29.3156 + 29.3156i −1.23551 + 1.23551i −0.273687 + 0.961819i \(0.588243\pi\)
−0.961819 + 0.273687i \(0.911757\pi\)
\(564\) 7.35393 + 7.35393i 0.309656 + 0.309656i
\(565\) 40.4472 0.624511i 1.70163 0.0262734i
\(566\) 17.1446 + 17.1446i 0.720639 + 0.720639i
\(567\) −31.5674 −1.32571
\(568\) 11.6343 + 11.6343i 0.488166 + 0.488166i
\(569\) −25.9559 −1.08813 −0.544063 0.839044i \(-0.683115\pi\)
−0.544063 + 0.839044i \(0.683115\pi\)
\(570\) 2.14884 2.21624i 0.0900052 0.0928281i
\(571\) 10.3822i 0.434480i −0.976118 0.217240i \(-0.930295\pi\)
0.976118 0.217240i \(-0.0697055\pi\)
\(572\) 6.68268 + 6.82160i 0.279417 + 0.285226i
\(573\) 0.965866 + 0.965866i 0.0403496 + 0.0403496i
\(574\) 69.0182 + 69.0182i 2.88077 + 2.88077i
\(575\) 14.4696 + 13.6025i 0.603423 + 0.567263i
\(576\) 36.4893i 1.52039i
\(577\) 12.1813i 0.507112i 0.967321 + 0.253556i \(0.0816003\pi\)
−0.967321 + 0.253556i \(0.918400\pi\)
\(578\) 33.1225 1.37772
\(579\) 5.54016 5.54016i 0.230241 0.230241i
\(580\) −18.7897 18.2183i −0.780198 0.756472i
\(581\) 24.4245 1.01330
\(582\) 5.02584 + 5.02584i 0.208328 + 0.208328i
\(583\) 1.06713i 0.0441959i
\(584\) 17.6301 0.729541
\(585\) 16.5289 + 16.3594i 0.683385 + 0.676380i
\(586\) 26.0056 1.07428
\(587\) 38.0854i 1.57195i 0.618258 + 0.785975i \(0.287839\pi\)
−0.618258 + 0.785975i \(0.712161\pi\)
\(588\) 7.01125 + 7.01125i 0.289139 + 0.289139i
\(589\) 5.14960 0.212185
\(590\) 54.6827 0.844309i 2.25125 0.0347596i
\(591\) 0.0599778 0.0599778i 0.00246716 0.00246716i
\(592\) −4.06378 −0.167020
\(593\) 5.30739i 0.217949i 0.994045 + 0.108974i \(0.0347566\pi\)
−0.994045 + 0.108974i \(0.965243\pi\)
\(594\) 3.64532i 0.149569i
\(595\) 14.5436 0.224555i 0.596229 0.00920586i
\(596\) −3.20882 3.20882i −0.131438 0.131438i
\(597\) 4.24962 + 4.24962i 0.173925 + 0.173925i
\(598\) −23.2128 23.6954i −0.949242 0.968976i
\(599\) 0.0345018i 0.00140970i 1.00000 0.000704852i \(0.000224361\pi\)
−1.00000 0.000704852i \(0.999776\pi\)
\(600\) 3.91409 + 3.67954i 0.159792 + 0.150217i
\(601\) −16.5133 −0.673593 −0.336797 0.941577i \(-0.609344\pi\)
−0.336797 + 0.941577i \(0.609344\pi\)
\(602\) −64.5043 64.5043i −2.62900 2.62900i
\(603\) 10.9234 0.444837
\(604\) −30.7565 30.7565i −1.25146 1.25146i
\(605\) 16.6645 + 16.1577i 0.677508 + 0.656904i
\(606\) −1.82818 1.82818i −0.0742647 0.0742647i
\(607\) 0.302520 0.302520i 0.0122789 0.0122789i −0.700941 0.713220i \(-0.747236\pi\)
0.713220 + 0.700941i \(0.247236\pi\)
\(608\) −6.13787 + 6.13787i −0.248923 + 0.248923i
\(609\) −3.30836 + 3.30836i −0.134062 + 0.134062i
\(610\) −13.7183 13.3011i −0.555437 0.538546i
\(611\) 32.7917 + 0.337343i 1.32661 + 0.0136474i
\(612\) 11.2782 11.2782i 0.455896 0.455896i
\(613\) −9.77269 −0.394715 −0.197358 0.980332i \(-0.563236\pi\)
−0.197358 + 0.980332i \(0.563236\pi\)
\(614\) 65.4528i 2.64146i
\(615\) 5.63015 5.80673i 0.227029 0.234150i
\(616\) −6.96625 + 6.96625i −0.280678 + 0.280678i
\(617\) 28.8877i 1.16297i −0.813555 0.581487i \(-0.802471\pi\)
0.813555 0.581487i \(-0.197529\pi\)
\(618\) 4.05636i 0.163171i
\(619\) 21.1034 21.1034i 0.848216 0.848216i −0.141695 0.989910i \(-0.545255\pi\)
0.989910 + 0.141695i \(0.0452551\pi\)
\(620\) 0.341052 + 22.0887i 0.0136970 + 0.887103i
\(621\) 7.94204i 0.318703i
\(622\) −22.1304 −0.887350
\(623\) −13.9231 + 13.9231i −0.557816 + 0.557816i
\(624\) −0.508958 0.519539i −0.0203746 0.0207982i
\(625\) −24.9523 + 1.54291i −0.998094 + 0.0617164i
\(626\) −41.0254 + 41.0254i −1.63970 + 1.63970i
\(627\) 0.331706 0.331706i 0.0132470 0.0132470i
\(628\) −8.26192 + 8.26192i −0.329687 + 0.329687i
\(629\) 7.95395 + 7.95395i 0.317145 + 0.317145i
\(630\) −41.1698 + 42.4611i −1.64025 + 1.69169i
\(631\) 22.6176 + 22.6176i 0.900391 + 0.900391i 0.995470 0.0950787i \(-0.0303103\pi\)
−0.0950787 + 0.995470i \(0.530310\pi\)
\(632\) −28.5536 −1.13580
\(633\) −2.18763 2.18763i −0.0869504 0.0869504i
\(634\) 2.11335 0.0839319
\(635\) 17.2291 0.266020i 0.683717 0.0105567i
\(636\) 1.55033i 0.0614746i
\(637\) 31.2636 + 0.321623i 1.23871 + 0.0127432i
\(638\) −4.48369 4.48369i −0.177511 0.177511i
\(639\) 10.6138 + 10.6138i 0.419874 + 0.419874i
\(640\) −31.1490 30.2018i −1.23127 1.19383i
\(641\) 18.9874i 0.749959i 0.927033 + 0.374980i \(0.122350\pi\)
−0.927033 + 0.374980i \(0.877650\pi\)
\(642\) 5.22378i 0.206166i
\(643\) −39.2961 −1.54969 −0.774843 0.632154i \(-0.782171\pi\)
−0.774843 + 0.632154i \(0.782171\pi\)
\(644\) 37.4138 37.4138i 1.47431 1.47431i
\(645\) −5.26192 + 5.42696i −0.207188 + 0.213686i
\(646\) −6.67583 −0.262657
\(647\) −13.7831 13.7831i −0.541869 0.541869i 0.382207 0.924077i \(-0.375164\pi\)
−0.924077 + 0.382207i \(0.875164\pi\)
\(648\) 25.2135i 0.990479i
\(649\) 8.31074 0.326225
\(650\) 41.7482 0.859749i 1.63750 0.0337221i
\(651\) 3.94928 0.154785
\(652\) 13.8489i 0.542364i
\(653\) −18.6515 18.6515i −0.729890 0.729890i 0.240707 0.970598i \(-0.422621\pi\)
−0.970598 + 0.240707i \(0.922621\pi\)
\(654\) −4.58923 −0.179453
\(655\) −3.76907 + 3.88729i −0.147270 + 0.151889i
\(656\) 4.46825 4.46825i 0.174456 0.174456i
\(657\) 16.0836 0.627482
\(658\) 83.3984i 3.25121i
\(659\) 24.9329i 0.971247i −0.874168 0.485623i \(-0.838593\pi\)
0.874168 0.485623i \(-0.161407\pi\)
\(660\) 1.44479 + 1.40085i 0.0562382 + 0.0545280i
\(661\) −2.83810 2.83810i −0.110389 0.110389i 0.649755 0.760144i \(-0.274872\pi\)
−0.760144 + 0.649755i \(0.774872\pi\)
\(662\) −35.3427 35.3427i −1.37363 1.37363i
\(663\) −0.0207092 + 2.01306i −0.000804279 + 0.0781806i
\(664\) 19.5083i 0.757069i
\(665\) 15.5246 0.239702i 0.602018 0.00929525i
\(666\) −45.7381 −1.77232
\(667\) 9.76859 + 9.76859i 0.378241 + 0.378241i
\(668\) −17.7524 −0.686861
\(669\) −3.42811 3.42811i −0.132538 0.132538i
\(670\) 13.6531 14.0813i 0.527466 0.544010i
\(671\) −2.05322 2.05322i −0.0792636 0.0792636i
\(672\) −4.70720 + 4.70720i −0.181584 + 0.181584i
\(673\) 1.00992 1.00992i 0.0389295 0.0389295i −0.687374 0.726304i \(-0.741237\pi\)
0.726304 + 0.687374i \(0.241237\pi\)
\(674\) −19.3170 + 19.3170i −0.744064 + 0.744064i
\(675\) 7.28442 + 6.84790i 0.280377 + 0.263576i
\(676\) −43.7369 0.899976i −1.68219 0.0346145i
\(677\) 0.154365 0.154365i 0.00593272 0.00593272i −0.704134 0.710067i \(-0.748665\pi\)
0.710067 + 0.704134i \(0.248665\pi\)
\(678\) −14.2386 −0.546829
\(679\) 35.7492i 1.37193i
\(680\) −0.179356 11.6162i −0.00687801 0.445462i
\(681\) 2.97189 2.97189i 0.113883 0.113883i
\(682\) 5.35230i 0.204950i
\(683\) 19.3092i 0.738847i −0.929261 0.369424i \(-0.879555\pi\)
0.929261 0.369424i \(-0.120445\pi\)
\(684\) 12.0390 12.0390i 0.460322 0.460322i
\(685\) 0.899976 0.928204i 0.0343863 0.0354648i
\(686\) 15.3261i 0.585153i
\(687\) −3.33447 −0.127218
\(688\) −4.17601 + 4.17601i −0.159209 + 0.159209i
\(689\) 3.42096 + 3.49208i 0.130328 + 0.133037i
\(690\) −5.01858 4.86596i −0.191054 0.185244i
\(691\) 29.1769 29.1769i 1.10994 1.10994i 0.116784 0.993157i \(-0.462742\pi\)
0.993157 0.116784i \(-0.0372584\pi\)
\(692\) −11.5134 + 11.5134i −0.437676 + 0.437676i
\(693\) −6.35517 + 6.35517i −0.241413 + 0.241413i
\(694\) 52.0815 + 52.0815i 1.97699 + 1.97699i
\(695\) −26.6877 25.8761i −1.01232 0.981538i
\(696\) 2.64245 + 2.64245i 0.100162 + 0.100162i
\(697\) −17.4912 −0.662527
\(698\) 44.5329 + 44.5329i 1.68559 + 1.68559i
\(699\) 1.52596 0.0577170
\(700\) 2.05636 + 66.5753i 0.0777230 + 2.51631i
\(701\) 21.8818i 0.826464i 0.910626 + 0.413232i \(0.135600\pi\)
−0.910626 + 0.413232i \(0.864400\pi\)
\(702\) −11.6860 11.9290i −0.441060 0.450229i
\(703\) 8.49047 + 8.49047i 0.320224 + 0.320224i
\(704\) −7.04023 7.04023i −0.265339 0.265339i
\(705\) 6.90990 0.106690i 0.260242 0.00401817i
\(706\) 10.3174i 0.388302i
\(707\) 13.0040i 0.489065i
\(708\) −12.0739 −0.453765
\(709\) −18.0869 + 18.0869i −0.679267 + 0.679267i −0.959834 0.280568i \(-0.909477\pi\)
0.280568 + 0.959834i \(0.409477\pi\)
\(710\) 26.9482 0.416085i 1.01135 0.0156154i
\(711\) −26.0488 −0.976908
\(712\) 11.1206 + 11.1206i 0.416763 + 0.416763i
\(713\) 11.6610i 0.436709i
\(714\) −5.11976 −0.191602
\(715\) 6.34545 0.0326910i 0.237306 0.00122258i
\(716\) −44.0317 −1.64554
\(717\) 5.94841i 0.222147i
\(718\) 26.9462 + 26.9462i 1.00563 + 1.00563i
\(719\) 26.5866 0.991512 0.495756 0.868462i \(-0.334891\pi\)
0.495756 + 0.868462i \(0.334891\pi\)
\(720\) 2.74894 + 2.66534i 0.102447 + 0.0993313i
\(721\) 14.4266 14.4266i 0.537274 0.537274i
\(722\) 36.8829 1.37264
\(723\) 5.91629i 0.220029i
\(724\) 15.6488i 0.581585i
\(725\) −17.3825 + 0.536906i −0.645571 + 0.0199402i
\(726\) −5.77718 5.77718i −0.214411 0.214411i
\(727\) 13.8783 + 13.8783i 0.514719 + 0.514719i 0.915969 0.401250i \(-0.131424\pi\)
−0.401250 + 0.915969i \(0.631424\pi\)
\(728\) 0.464257 45.1285i 0.0172065 1.67257i
\(729\) 20.9634i 0.776422i
\(730\) 20.1028 20.7333i 0.744038 0.767374i
\(731\) 16.3473 0.604625
\(732\) 2.98293 + 2.98293i 0.110252 + 0.110252i
\(733\) −38.2590 −1.41313 −0.706563 0.707650i \(-0.749756\pi\)
−0.706563 + 0.707650i \(0.749756\pi\)
\(734\) 2.04108 + 2.04108i 0.0753376 + 0.0753376i
\(735\) 6.58790 0.101718i 0.242999 0.00375193i
\(736\) 13.8989 + 13.8989i 0.512321 + 0.512321i
\(737\) 2.10756 2.10756i 0.0776330 0.0776330i
\(738\) 50.2904 50.2904i 1.85122 1.85122i
\(739\) 36.5799 36.5799i 1.34561 1.34561i 0.455250 0.890364i \(-0.349550\pi\)
0.890364 0.455250i \(-0.150450\pi\)
\(740\) −35.8567 + 36.9813i −1.31812 + 1.35946i
\(741\) −0.0221061 + 2.14884i −0.000812088 + 0.0789398i
\(742\) −8.79088 + 8.79088i −0.322724 + 0.322724i
\(743\) 32.7040 1.19979 0.599896 0.800078i \(-0.295209\pi\)
0.599896 + 0.800078i \(0.295209\pi\)
\(744\) 3.15436i 0.115645i
\(745\) −3.01507 + 0.0465532i −0.110464 + 0.00170558i
\(746\) −19.6560 + 19.6560i −0.719657 + 0.719657i
\(747\) 17.7970i 0.651159i
\(748\) 4.35203i 0.159126i
\(749\) −18.5786 + 18.5786i −0.678846 + 0.678846i
\(750\) 8.79024 0.407427i 0.320974 0.0148771i
\(751\) 19.6083i 0.715517i −0.933814 0.357758i \(-0.883541\pi\)
0.933814 0.357758i \(-0.116459\pi\)
\(752\) 5.39922 0.196889
\(753\) −4.75276 + 4.75276i −0.173200 + 0.173200i
\(754\) 29.0461 + 0.298810i 1.05780 + 0.0108820i
\(755\) −28.8994 + 0.446211i −1.05176 + 0.0162393i
\(756\) 18.8352 18.8352i 0.685031 0.685031i
\(757\) 1.81942 1.81942i 0.0661281 0.0661281i −0.673269 0.739397i \(-0.735111\pi\)
0.739397 + 0.673269i \(0.235111\pi\)
\(758\) 50.7644 50.7644i 1.84385 1.84385i
\(759\) −0.751132 0.751132i −0.0272644 0.0272644i
\(760\) −0.191455 12.3998i −0.00694479 0.449788i
\(761\) −5.35106 5.35106i −0.193976 0.193976i 0.603436 0.797412i \(-0.293798\pi\)
−0.797412 + 0.603436i \(0.793798\pi\)
\(762\) −6.06515 −0.219717
\(763\) −16.3218 16.3218i −0.590888 0.590888i
\(764\) 13.5271 0.489393
\(765\) −0.163623 10.5973i −0.00591581 0.383144i
\(766\) 27.4274i 0.990994i
\(767\) −27.1961 + 26.6423i −0.981995 + 0.961996i
\(768\) 4.71968 + 4.71968i 0.170307 + 0.170307i
\(769\) −23.5462 23.5462i −0.849096 0.849096i 0.140924 0.990020i \(-0.454993\pi\)
−0.990020 + 0.140924i \(0.954993\pi\)
\(770\)