Properties

Label 65.2.f.b.47.1
Level $65$
Weight $2$
Character 65.47
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 47.1
Root \(1.18254 + 1.18254i\) of defining polynomial
Character \(\chi\) \(=\) 65.47
Dual form 65.2.f.b.18.4

$q$-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 \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

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 \(-0.694571\pi\)
0.573903 0.818924i \(-0.305429\pi\)
\(3\) −0.240275 + 0.240275i −0.138723 + 0.138723i −0.773058 0.634335i \(-0.781274\pi\)
0.634335 + 0.773058i \(0.281274\pi\)
\(4\) −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 −0.786013 0.618210i \(-0.787858\pi\)
0.618210 + 0.786013i \(0.287858\pi\)
\(12\) 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 −0.833827 0.552025i \(-0.813855\pi\)
0.552025 + 0.833827i \(0.313855\pi\)
\(18\) 6.68135 1.57481
\(19\) −1.24027 + 1.24027i −0.284539 + 0.284539i −0.834916 0.550377i \(-0.814484\pi\)
0.550377 + 0.834916i \(0.314484\pi\)
\(20\) 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 0.350821 0.936443i \(-0.385903\pi\)
−0.936443 + 0.350821i \(0.885903\pi\)
\(24\) −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 \(0.104671\pi\)
−0.946420 + 0.322940i \(0.895329\pi\)
\(30\) 0.0271704 1.75973i 0.00496062 0.321280i
\(31\) −2.07599 2.07599i −0.372859 0.372859i 0.495659 0.868517i \(-0.334927\pi\)
−0.868517 + 0.495659i \(0.834927\pi\)
\(32\) 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 0.980874 + 0.194644i \(0.0623551\pi\)
0.194644 + 0.980874i \(0.437645\pi\)
\(42\) 2.20318 + 2.20318i 0.339959 + 0.339959i
\(43\) −7.03471 7.03471i −1.07278 1.07278i −0.997135 0.0756481i \(-0.975897\pi\)
−0.0756481 0.997135i \(-0.524103\pi\)
\(44\) 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 −0.638190 0.769879i \(-0.720316\pi\)
0.769879 + 0.638190i \(0.220316\pi\)
\(54\) −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 0.0275726 0.999620i \(-0.491222\pi\)
−0.999620 + 0.0275726i \(0.991222\pi\)
\(60\) −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 \(-0.925695\pi\)
0.972877 0.231321i \(-0.0743049\pi\)
\(68\) 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 0.454212 0.890893i \(-0.349921\pi\)
−0.890893 + 0.454212i \(0.849921\pi\)
\(72\) −9.12062 −1.07487
\(73\) 5.57581i 0.652599i −0.945266 0.326299i \(-0.894198\pi\)
0.945266 0.326299i \(-0.105802\pi\)
\(74\) 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 \(0.169617\pi\)
−0.861354 + 0.508006i \(0.830383\pi\)
\(80\) −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 0.495691 0.868499i \(-0.334915\pi\)
−0.868499 + 0.495691i \(0.834915\pi\)
\(90\) −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 \(-0.848403\pi\)
0.888718 0.458455i \(-0.151597\pi\)
\(98\) 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 \(0.0522558\pi\)
−0.986555 + 0.163430i \(0.947744\pi\)
\(102\) −1.29329 −0.128055
\(103\) 3.64426 + 3.64426i 0.359080 + 0.359080i 0.863474 0.504394i \(-0.168284\pi\)
−0.504394 + 0.863474i \(0.668284\pi\)
\(104\) 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 0.442882 0.896580i \(-0.353956\pi\)
−0.896580 + 0.442882i \(0.853956\pi\)
\(108\) 4.75791 + 4.75791i 0.457831 + 0.457831i
\(109\) −4.12300 + 4.12300i −0.394912 + 0.394912i −0.876434 0.481522i \(-0.840084\pi\)
0.481522 + 0.876434i \(0.340084\pi\)
\(110\) 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 −0.230241 + 0.973134i \(0.573951\pi\)
−0.973134 + 0.230241i \(0.926049\pi\)
\(114\) −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 −0.906253 0.422735i \(-0.861070\pi\)
0.422735 + 0.906253i \(0.361070\pi\)
\(128\) 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 \(-0.750938\pi\)
0.709187 0.705021i \(-0.249062\pi\)
\(140\) 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 −0.666968 0.745087i \(-0.732408\pi\)
0.745087 + 0.666968i \(0.232408\pi\)
\(150\) −2.86729 + 2.69546i −0.234113 + 0.220084i
\(151\) 9.13988 9.13988i 0.743793 0.743793i −0.229513 0.973306i \(-0.573713\pi\)
0.973306 + 0.229513i \(0.0737132\pi\)
\(152\) −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 0.798259 0.602314i \(-0.205754\pi\)
−0.602314 + 0.798259i \(0.705754\pi\)
\(158\) 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 \(0.0515280\pi\)
−0.986926 + 0.161174i \(0.948472\pi\)
\(164\) −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 0.825106 0.564978i \(-0.191115\pi\)
−0.564978 + 0.825106i \(0.691115\pi\)
\(174\) −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 \(-0.944709\pi\)
0.984952 0.172829i \(-0.0552908\pi\)
\(182\) −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 \(-0.688420\pi\)
0.557970 0.829861i \(-0.311580\pi\)
\(194\) −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 \(-0.997169\pi\)
0.999960 0.00889240i \(-0.00283058\pi\)
\(198\) −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 \(-0.865365\pi\)
0.911874 0.410470i \(-0.134635\pi\)
\(228\) 2.00564i 0.132827i
\(229\) 6.93888 + 6.93888i 0.458534 + 0.458534i 0.898174 0.439640i \(-0.144894\pi\)
−0.439640 + 0.898174i \(0.644894\pi\)
\(230\) 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 0.595400 0.803430i \(-0.296994\pi\)
−0.803430 + 0.595400i \(0.796994\pi\)
\(234\) 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 −0.182514 0.983203i \(-0.558424\pi\)
0.983203 + 0.182514i \(0.0584236\pi\)
\(240\) 0.450996 + 0.00696344i 0.0291117 + 0.000449488i
\(241\) 12.3115 12.3115i 0.793053 0.793053i −0.188936 0.981989i \(-0.560504\pi\)
0.981989 + 0.188936i \(0.0605039\pi\)
\(242\) 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 \(0.214603\pi\)
−0.781210 + 0.624268i \(0.785397\pi\)
\(252\) 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 −0.996209 0.0869949i \(-0.972274\pi\)
0.0869949 + 0.996209i \(0.472274\pi\)
\(258\) 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 −0.0974727 0.995238i \(-0.531076\pi\)
0.995238 + 0.0974727i \(0.0310759\pi\)
\(264\) 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 \(-0.914960\pi\)
0.964525 0.263993i \(-0.0850396\pi\)
\(270\) 10.3552 + 0.159885i 0.630195 + 0.00973031i
\(271\) −14.1589 + 14.1589i −0.860095 + 0.860095i −0.991349 0.131254i \(-0.958100\pi\)
0.131254 + 0.991349i \(0.458100\pi\)
\(272\) −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 −0.681171 0.732124i \(-0.738529\pi\)
0.732124 + 0.681171i \(0.238529\pi\)
\(278\) −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 −0.980522 0.196412i \(-0.937071\pi\)
0.196412 + 0.980522i \(0.437071\pi\)
\(282\) 5.06188 + 5.06188i 0.301430 + 0.301430i
\(283\) 7.40181 + 7.40181i 0.439992 + 0.439992i 0.892009 0.452017i \(-0.149295\pi\)
−0.452017 + 0.892009i \(0.649295\pi\)
\(284\) 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 \(0.106360\pi\)
−0.944693 + 0.327956i \(0.893640\pi\)
\(294\) 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 \(-0.912682\pi\)
0.962611 0.270889i \(-0.0873177\pi\)
\(312\) −2.76726 2.71090i −0.156665 0.153475i
\(313\) 17.7119 17.7119i 1.00113 1.00113i 0.00113436 0.999999i \(-0.499639\pi\)
0.999999 0.00113436i \(-0.000361078\pi\)
\(314\) 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 \(0.00815683\pi\)
−0.999672 + 0.0256226i \(0.991843\pi\)
\(318\) 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 0.150003 0.988685i \(-0.452072\pi\)
−0.988685 + 0.150003i \(0.952072\pi\)
\(332\) −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 −0.442483 0.896777i \(-0.645902\pi\)
0.896777 + 0.442483i \(0.145902\pi\)
\(338\) −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 0.971973 + 0.235092i \(0.0755391\pi\)
0.235092 + 0.971973i \(0.424461\pi\)
\(348\) 2.81226 + 2.81226i 0.150753 + 0.150753i
\(349\) 19.2262 + 19.2262i 1.02915 + 1.02915i 0.999562 + 0.0295907i \(0.00942039\pi\)
0.0295907 + 0.999562i \(0.490580\pi\)
\(350\) 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 0.943984 0.329992i \(-0.107046\pi\)
−0.329992 + 0.943984i \(0.607046\pi\)
\(360\) 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 0.729732 0.683734i \(-0.239645\pi\)
−0.683734 + 0.729732i \(0.739645\pi\)
\(368\) −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 −0.452415 0.891807i \(-0.649438\pi\)
0.891807 + 0.452415i \(0.149438\pi\)
\(374\) −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 −0.134918 + 0.990857i \(0.543077\pi\)
−0.990857 + 0.134918i \(0.956923\pi\)
\(380\) −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 0.149988 0.988688i \(-0.452076\pi\)
0.988688 0.149988i \(-0.0479236\pi\)
\(402\) 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 −0.626679 0.779278i \(-0.715586\pi\)
0.779278 + 0.626679i \(0.215586\pi\)
\(410\) −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 \(-0.925306\pi\)
0.972594 0.232510i \(-0.0746938\pi\)
\(420\) −10.1206 0.156264i −0.493836 0.00762489i
\(421\) 20.6718 + 20.6718i 1.00748 + 1.00748i 0.999972 + 0.00751095i \(0.00239083\pi\)
0.00751095 + 0.999972i \(0.497609\pi\)
\(422\) 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 0.173774 0.984786i \(-0.444404\pi\)
−0.984786 + 0.173774i \(0.944404\pi\)
\(432\) −0.839337 0.839337i −0.0403826 0.0403826i
\(433\) 18.0614 + 18.0614i 0.867975 + 0.867975i 0.992248 0.124273i \(-0.0396598\pi\)
−0.124273 + 0.992248i \(0.539660\pi\)
\(434\) −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 −0.924923 0.380154i \(-0.875871\pi\)
0.380154 + 0.924923i \(0.375871\pi\)
\(444\) −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 0.0526744 0.998612i \(-0.483225\pi\)
−0.998612 + 0.0526744i \(0.983225\pi\)
\(450\) −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 \(-0.976424\pi\)
0.997258 0.0739982i \(-0.0235759\pi\)
\(458\) 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 0.997820 0.0659984i \(-0.0210232\pi\)
−0.0659984 + 0.997820i \(0.521023\pi\)
\(462\) −2.45232 −0.114092
\(463\) 4.68050i 0.217521i 0.994068 + 0.108761i \(0.0346882\pi\)
−0.994068 + 0.108761i \(0.965312\pi\)
\(464\) 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 −0.819250 0.573437i \(-0.805610\pi\)
0.573437 + 0.819250i \(0.305610\pi\)
\(468\) −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 0.162125 0.986770i \(-0.448165\pi\)
−0.986770 + 0.162125i \(0.948165\pi\)
\(480\) −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 \(0.00705526\pi\)
−0.999754 + 0.0221629i \(0.992945\pi\)
\(488\) 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 \(0.142924\pi\)
−0.900878 + 0.434073i \(0.857076\pi\)
\(492\) 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 −0.971920 0.235310i \(-0.924389\pi\)
0.235310 + 0.971920i \(0.424389\pi\)
\(500\) −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 −0.360158 0.932891i \(-0.617277\pi\)
0.932891 + 0.360158i \(0.117277\pi\)
\(504\) −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 −0.844529 0.535510i \(-0.820119\pi\)
0.535510 + 0.844529i \(0.320119\pi\)
\(510\) 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 −0.956283 0.292441i \(-0.905532\pi\)
0.292441 + 0.956283i \(0.405532\pi\)
\(524\) −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 −0.954354 0.298677i \(-0.903455\pi\)
0.298677 + 0.954354i \(0.403455\pi\)
\(542\) 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 −0.977525 0.210818i \(-0.932387\pi\)
−0.210818 0.977525i \(-0.567613\pi\)
\(548\) 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 −0.961819 0.273687i \(-0.911757\pi\)
−0.273687 0.961819i \(-0.588243\pi\)
\(564\) 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 \(0.0697055\pi\)
−0.976118 + 0.217240i \(0.930295\pi\)
\(572\) 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 \(-0.918400\pi\)
0.967321 0.253556i \(-0.0816003\pi\)
\(578\) 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 \(-0.712161\pi\)
0.618258 0.785975i \(-0.287839\pi\)
\(588\) 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 \(-0.965243\pi\)
0.994045 0.108974i \(-0.0347566\pi\)
\(594\) 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 \(-0.999776\pi\)
1.00000 0.000704852i \(-0.000224361\pi\)
\(600\) 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 0.713220 0.700941i \(-0.247236\pi\)
−0.700941 + 0.713220i \(0.747236\pi\)
\(608\) −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 \(0.197529\pi\)
−0.813555 + 0.581487i \(0.802471\pi\)
\(618\) 4.05636i 0.163171i
\(619\) 21.1034 + 21.1034i 0.848216 + 0.848216i 0.989910 0.141695i \(-0.0452551\pi\)
−0.141695 + 0.989910i \(0.545255\pi\)
\(620\) 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 −0.0950787 0.995470i \(-0.530310\pi\)
0.995470 + 0.0950787i \(0.0303103\pi\)
\(632\) −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 \(-0.877650\pi\)
0.927033 0.374980i \(-0.122350\pi\)
\(642\) 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 −0.924077 0.382207i \(-0.875164\pi\)
0.382207 + 0.924077i \(0.375164\pi\)
\(648\) 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 −0.970598 0.240707i \(-0.922621\pi\)
0.240707 + 0.970598i \(0.422621\pi\)
\(654\) −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 \(0.161407\pi\)
−0.874168 + 0.485623i \(0.838593\pi\)
\(660\) 1.44479 1.40085i 0.0562382 0.0545280i
\(661\) −2.83810 + 2.83810i −0.110389 + 0.110389i −0.760144 0.649755i \(-0.774872\pi\)
0.649755 + 0.760144i \(0.274872\pi\)
\(662\) −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 0.726304 0.687374i \(-0.241237\pi\)
−0.687374 + 0.726304i \(0.741237\pi\)
\(674\) −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 0.710067 0.704134i \(-0.248665\pi\)
−0.704134 + 0.710067i \(0.748665\pi\)
\(678\) −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 \(0.120445\pi\)
−0.929261 + 0.369424i \(0.879555\pi\)
\(684\) 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 0.993157 + 0.116784i \(0.0372584\pi\)
0.116784 + 0.993157i \(0.462742\pi\)
\(692\) −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 \(-0.864400\pi\)
0.910626 0.413232i \(-0.135600\pi\)
\(702\) −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 0.280568 0.959834i \(-0.409477\pi\)
−0.959834 + 0.280568i \(0.909477\pi\)
\(710\) 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 −0.401250 0.915969i \(-0.631424\pi\)
0.915969 + 0.401250i \(0.131424\pi\)
\(728\) 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 0.890364 + 0.455250i \(0.150450\pi\)
0.455250 + 0.890364i \(0.349550\pi\)
\(740\) −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 \(0.116459\pi\)
−0.933814 + 0.357758i \(0.883541\pi\)
\(752\) 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 0.739397 0.673269i \(-0.235111\pi\)
−0.673269 + 0.739397i \(0.735111\pi\)
\(758\) 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 −0.797412 0.603436i \(-0.793798\pi\)
0.603436 + 0.797412i \(0.293798\pi\)
\(762\) −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 −0.990020 0.140924i \(-0.954993\pi\)
0.140924 + 0.990020i \(0.454993\pi\)
\(770\) 0.249137