Properties

Label 65.2.f.b.47.3
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 47.3
Root \(-1.49094 - 1.49094i\) of defining polynomial
Character \(\chi\) \(=\) 65.47
Dual form 65.2.f.b.18.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.134632i q^{2} +(-2.15558 + 2.15558i) q^{3} +1.98187 q^{4} +(-1.29021 + 1.82630i) q^{5} +(0.290209 + 0.290209i) q^{6} +1.90970 q^{7} -0.536087i q^{8} -6.29303i q^{9} +O(q^{10})\) \(q-0.134632i q^{2} +(-2.15558 + 2.15558i) q^{3} +1.98187 q^{4} +(-1.29021 + 1.82630i) q^{5} +(0.290209 + 0.290209i) q^{6} +1.90970 q^{7} -0.536087i q^{8} -6.29303i q^{9} +(0.245878 + 0.173703i) q^{10} +(-0.290209 + 0.290209i) q^{11} +(-4.27208 + 4.27208i) q^{12} +(0.173703 - 3.60136i) q^{13} -0.257106i q^{14} +(-1.15558 - 6.71787i) q^{15} +3.89157 q^{16} +(2.53609 - 2.53609i) q^{17} -0.847242 q^{18} +(-3.15558 + 3.15558i) q^{19} +(-2.55703 + 3.61949i) q^{20} +(-4.11651 + 4.11651i) q^{21} +(0.0390714 + 0.0390714i) q^{22} +(2.27208 + 2.27208i) q^{23} +(1.15558 + 1.15558i) q^{24} +(-1.67072 - 4.71261i) q^{25} +(-0.484858 - 0.0233860i) q^{26} +(7.09838 + 7.09838i) q^{27} +3.78478 q^{28} -2.40146i q^{29} +(-0.904440 + 0.155578i) q^{30} +(2.02095 + 2.02095i) q^{31} -1.59610i q^{32} -1.25114i q^{33} +(-0.341438 - 0.341438i) q^{34} +(-2.46391 + 3.48768i) q^{35} -12.4720i q^{36} -5.32928 q^{37} +(0.424841 + 0.424841i) q^{38} +(7.38859 + 8.13745i) q^{39} +(0.979054 + 0.691665i) q^{40} +(-1.51796 - 1.51796i) q^{41} +(0.554213 + 0.554213i) q^{42} +(-0.888754 - 0.888754i) q^{43} +(-0.575159 + 0.575159i) q^{44} +(11.4929 + 8.11933i) q^{45} +(0.305895 - 0.305895i) q^{46} -6.94562 q^{47} +(-8.38859 + 8.38859i) q^{48} -3.35305 q^{49} +(-0.634468 + 0.224932i) q^{50} +10.9335i q^{51} +(0.344258 - 7.13745i) q^{52} +(-1.09030 + 1.09030i) q^{53} +(0.955668 - 0.955668i) q^{54} +(-0.155578 - 0.904440i) q^{55} -1.02377i q^{56} -13.6042i q^{57} -0.323312 q^{58} +(-8.31642 - 8.31642i) q^{59} +(-2.29021 - 13.3140i) q^{60} +7.17300 q^{61} +(0.272084 - 0.272084i) q^{62} -12.0178i q^{63} +7.56826 q^{64} +(6.35305 + 4.96375i) q^{65} -0.168443 q^{66} -0.939983i q^{67} +(5.02621 - 5.02621i) q^{68} -9.79531 q^{69} +(0.469553 + 0.331721i) q^{70} +(-7.37643 - 7.37643i) q^{71} -3.37361 q^{72} +6.63447i q^{73} +0.717491i q^{74} +(13.7598 + 6.55703i) q^{75} +(-6.25396 + 6.25396i) q^{76} +(-0.554213 + 0.554213i) q^{77} +(1.09556 - 0.994740i) q^{78} +4.39982i q^{79} +(-5.02095 + 7.10717i) q^{80} -11.7231 q^{81} +(-0.204366 + 0.204366i) q^{82} +13.4842 q^{83} +(-8.15840 + 8.15840i) q^{84} +(1.35956 + 7.90373i) q^{85} +(-0.119655 + 0.119655i) q^{86} +(5.17652 + 5.17652i) q^{87} +(0.155578 + 0.155578i) q^{88} +(10.0238 + 10.0238i) q^{89} +(1.09312 - 1.54732i) q^{90} +(0.331721 - 6.87753i) q^{91} +(4.50298 + 4.50298i) q^{92} -8.71261 q^{93} +0.935102i q^{94} +(-1.69166 - 9.83438i) q^{95} +(3.44053 + 3.44053i) q^{96} -4.39982i q^{97} +0.451427i q^{98} +(1.82630 + 1.82630i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.134632i 0.0951991i −0.998866 0.0475996i \(-0.984843\pi\)
0.998866 0.0475996i \(-0.0151571\pi\)
\(3\) −2.15558 + 2.15558i −1.24452 + 1.24452i −0.286419 + 0.958105i \(0.592465\pi\)
−0.958105 + 0.286419i \(0.907535\pi\)
\(4\) 1.98187 0.990937
\(5\) −1.29021 + 1.82630i −0.576999 + 0.816745i
\(6\) 0.290209 + 0.290209i 0.118478 + 0.118478i
\(7\) 1.90970 0.721799 0.360899 0.932605i \(-0.382470\pi\)
0.360899 + 0.932605i \(0.382470\pi\)
\(8\) 0.536087i 0.189535i
\(9\) 6.29303i 2.09768i
\(10\) 0.245878 + 0.173703i 0.0777534 + 0.0549298i
\(11\) −0.290209 + 0.290209i −0.0875014 + 0.0875014i −0.749503 0.662001i \(-0.769707\pi\)
0.662001 + 0.749503i \(0.269707\pi\)
\(12\) −4.27208 + 4.27208i −1.23324 + 1.23324i
\(13\) 0.173703 3.60136i 0.0481766 0.998839i
\(14\) 0.257106i 0.0687146i
\(15\) −1.15558 6.71787i −0.298369 1.73455i
\(16\) 3.89157 0.972894
\(17\) 2.53609 2.53609i 0.615091 0.615091i −0.329177 0.944268i \(-0.606771\pi\)
0.944268 + 0.329177i \(0.106771\pi\)
\(18\) −0.847242 −0.199697
\(19\) −3.15558 + 3.15558i −0.723939 + 0.723939i −0.969405 0.245466i \(-0.921059\pi\)
0.245466 + 0.969405i \(0.421059\pi\)
\(20\) −2.55703 + 3.61949i −0.571770 + 0.809343i
\(21\) −4.11651 + 4.11651i −0.898295 + 0.898295i
\(22\) 0.0390714 + 0.0390714i 0.00833006 + 0.00833006i
\(23\) 2.27208 + 2.27208i 0.473762 + 0.473762i 0.903130 0.429368i \(-0.141264\pi\)
−0.429368 + 0.903130i \(0.641264\pi\)
\(24\) 1.15558 + 1.15558i 0.235881 + 0.235881i
\(25\) −1.67072 4.71261i −0.334144 0.942522i
\(26\) −0.484858 0.0233860i −0.0950886 0.00458637i
\(27\) 7.09838 + 7.09838i 1.36608 + 1.36608i
\(28\) 3.78478 0.715257
\(29\) 2.40146i 0.445939i −0.974825 0.222970i \(-0.928425\pi\)
0.974825 0.222970i \(-0.0715750\pi\)
\(30\) −0.904440 + 0.155578i −0.165127 + 0.0284045i
\(31\) 2.02095 + 2.02095i 0.362973 + 0.362973i 0.864906 0.501934i \(-0.167378\pi\)
−0.501934 + 0.864906i \(0.667378\pi\)
\(32\) 1.59610i 0.282154i
\(33\) 1.25114i 0.217795i
\(34\) −0.341438 0.341438i −0.0585562 0.0585562i
\(35\) −2.46391 + 3.48768i −0.416477 + 0.589525i
\(36\) 12.4720i 2.07867i
\(37\) −5.32928 −0.876128 −0.438064 0.898944i \(-0.644336\pi\)
−0.438064 + 0.898944i \(0.644336\pi\)
\(38\) 0.424841 + 0.424841i 0.0689184 + 0.0689184i
\(39\) 7.38859 + 8.13745i 1.18312 + 1.30304i
\(40\) 0.979054 + 0.691665i 0.154802 + 0.109362i
\(41\) −1.51796 1.51796i −0.237066 0.237066i 0.578568 0.815634i \(-0.303612\pi\)
−0.815634 + 0.578568i \(0.803612\pi\)
\(42\) 0.554213 + 0.554213i 0.0855169 + 0.0855169i
\(43\) −0.888754 0.888754i −0.135534 0.135534i 0.636085 0.771619i \(-0.280553\pi\)
−0.771619 + 0.636085i \(0.780553\pi\)
\(44\) −0.575159 + 0.575159i −0.0867084 + 0.0867084i
\(45\) 11.4929 + 8.11933i 1.71327 + 1.21036i
\(46\) 0.305895 0.305895i 0.0451017 0.0451017i
\(47\) −6.94562 −1.01312 −0.506562 0.862204i \(-0.669084\pi\)
−0.506562 + 0.862204i \(0.669084\pi\)
\(48\) −8.38859 + 8.38859i −1.21079 + 1.21079i
\(49\) −3.35305 −0.479007
\(50\) −0.634468 + 0.224932i −0.0897273 + 0.0318102i
\(51\) 10.9335i 1.53099i
\(52\) 0.344258 7.13745i 0.0477400 0.989786i
\(53\) −1.09030 + 1.09030i −0.149764 + 0.149764i −0.778013 0.628248i \(-0.783772\pi\)
0.628248 + 0.778013i \(0.283772\pi\)
\(54\) 0.955668 0.955668i 0.130050 0.130050i
\(55\) −0.155578 0.904440i −0.0209781 0.121955i
\(56\) 1.02377i 0.136806i
\(57\) 13.6042i 1.80192i
\(58\) −0.323312 −0.0424530
\(59\) −8.31642 8.31642i −1.08271 1.08271i −0.996256 0.0864488i \(-0.972448\pi\)
−0.0864488 0.996256i \(-0.527552\pi\)
\(60\) −2.29021 13.3140i −0.295665 1.71883i
\(61\) 7.17300 0.918408 0.459204 0.888331i \(-0.348135\pi\)
0.459204 + 0.888331i \(0.348135\pi\)
\(62\) 0.272084 0.272084i 0.0345547 0.0345547i
\(63\) 12.0178i 1.51410i
\(64\) 7.56826 0.946033
\(65\) 6.35305 + 4.96375i 0.787998 + 0.615677i
\(66\) −0.168443 −0.0207339
\(67\) 0.939983i 0.114837i −0.998350 0.0574186i \(-0.981713\pi\)
0.998350 0.0574186i \(-0.0182870\pi\)
\(68\) 5.02621 5.02621i 0.609517 0.609517i
\(69\) −9.79531 −1.17922
\(70\) 0.469553 + 0.331721i 0.0561223 + 0.0396483i
\(71\) −7.37643 7.37643i −0.875421 0.875421i 0.117635 0.993057i \(-0.462469\pi\)
−0.993057 + 0.117635i \(0.962469\pi\)
\(72\) −3.37361 −0.397584
\(73\) 6.63447i 0.776506i 0.921553 + 0.388253i \(0.126921\pi\)
−0.921553 + 0.388253i \(0.873079\pi\)
\(74\) 0.717491i 0.0834066i
\(75\) 13.7598 + 6.55703i 1.58884 + 0.757141i
\(76\) −6.25396 + 6.25396i −0.717378 + 0.717378i
\(77\) −0.554213 + 0.554213i −0.0631584 + 0.0631584i
\(78\) 1.09556 0.994740i 0.124048 0.112632i
\(79\) 4.39982i 0.495018i 0.968886 + 0.247509i \(0.0796120\pi\)
−0.968886 + 0.247509i \(0.920388\pi\)
\(80\) −5.02095 + 7.10717i −0.561359 + 0.794606i
\(81\) −11.7231 −1.30257
\(82\) −0.204366 + 0.204366i −0.0225684 + 0.0225684i
\(83\) 13.4842 1.48008 0.740039 0.672564i \(-0.234807\pi\)
0.740039 + 0.672564i \(0.234807\pi\)
\(84\) −8.15840 + 8.15840i −0.890154 + 0.890154i
\(85\) 1.35956 + 7.90373i 0.147465 + 0.857280i
\(86\) −0.119655 + 0.119655i −0.0129027 + 0.0129027i
\(87\) 5.17652 + 5.17652i 0.554982 + 0.554982i
\(88\) 0.155578 + 0.155578i 0.0165846 + 0.0165846i
\(89\) 10.0238 + 10.0238i 1.06252 + 1.06252i 0.997911 + 0.0646062i \(0.0205791\pi\)
0.0646062 + 0.997911i \(0.479421\pi\)
\(90\) 1.09312 1.54732i 0.115225 0.163101i
\(91\) 0.331721 6.87753i 0.0347738 0.720961i
\(92\) 4.50298 + 4.50298i 0.469469 + 0.469469i
\(93\) −8.71261 −0.903456
\(94\) 0.935102i 0.0964484i
\(95\) −1.69166 9.83438i −0.173561 1.00899i
\(96\) 3.44053 + 3.44053i 0.351147 + 0.351147i
\(97\) 4.39982i 0.446734i −0.974734 0.223367i \(-0.928295\pi\)
0.974734 0.223367i \(-0.0717048\pi\)
\(98\) 0.451427i 0.0456010i
\(99\) 1.82630 + 1.82630i 0.183550 + 0.183550i
\(100\) −3.31116 9.33980i −0.331116 0.933980i
\(101\) 3.55014i 0.353252i 0.984278 + 0.176626i \(0.0565183\pi\)
−0.984278 + 0.176626i \(0.943482\pi\)
\(102\) 1.47199 0.145749
\(103\) −7.44861 7.44861i −0.733933 0.733933i 0.237463 0.971396i \(-0.423684\pi\)
−0.971396 + 0.237463i \(0.923684\pi\)
\(104\) −1.93065 0.0931201i −0.189315 0.00913118i
\(105\) −2.20681 12.8291i −0.215362 1.25199i
\(106\) 0.146789 + 0.146789i 0.0142574 + 0.0142574i
\(107\) 9.56511 + 9.56511i 0.924694 + 0.924694i 0.997357 0.0726622i \(-0.0231495\pi\)
−0.0726622 + 0.997357i \(0.523150\pi\)
\(108\) 14.0681 + 14.0681i 1.35370 + 1.35370i
\(109\) −8.08622 + 8.08622i −0.774520 + 0.774520i −0.978893 0.204373i \(-0.934484\pi\)
0.204373 + 0.978893i \(0.434484\pi\)
\(110\) −0.121766 + 0.0209457i −0.0116100 + 0.00199709i
\(111\) 11.4877 11.4877i 1.09036 1.09036i
\(112\) 7.43174 0.702233
\(113\) 4.97943 4.97943i 0.468426 0.468426i −0.432979 0.901404i \(-0.642537\pi\)
0.901404 + 0.432979i \(0.142537\pi\)
\(114\) −1.83156 −0.171541
\(115\) −7.08096 + 1.21804i −0.660303 + 0.113582i
\(116\) 4.75938i 0.441898i
\(117\) −22.6635 1.09312i −2.09524 0.101059i
\(118\) −1.11965 + 1.11965i −0.103073 + 0.103073i
\(119\) 4.84317 4.84317i 0.443972 0.443972i
\(120\) −3.60136 + 0.619490i −0.328758 + 0.0565515i
\(121\) 10.8316i 0.984687i
\(122\) 0.965714i 0.0874316i
\(123\) 6.54417 0.590068
\(124\) 4.00526 + 4.00526i 0.359683 + 0.359683i
\(125\) 10.7622 + 3.02903i 0.962601 + 0.270924i
\(126\) −1.61798 −0.144141
\(127\) −7.01742 + 7.01742i −0.622695 + 0.622695i −0.946220 0.323525i \(-0.895132\pi\)
0.323525 + 0.946220i \(0.395132\pi\)
\(128\) 4.21114i 0.372216i
\(129\) 3.83156 0.337350
\(130\) 0.668279 0.855323i 0.0586119 0.0750168i
\(131\) −11.3052 −0.987739 −0.493869 0.869536i \(-0.664418\pi\)
−0.493869 + 0.869536i \(0.664418\pi\)
\(132\) 2.47960i 0.215821i
\(133\) −6.02621 + 6.02621i −0.522538 + 0.522538i
\(134\) −0.126552 −0.0109324
\(135\) −22.1221 + 3.80535i −1.90397 + 0.327512i
\(136\) −1.35956 1.35956i −0.116582 0.116582i
\(137\) 1.92186 0.164195 0.0820977 0.996624i \(-0.473838\pi\)
0.0820977 + 0.996624i \(0.473838\pi\)
\(138\) 1.31876i 0.112260i
\(139\) 15.2914i 1.29700i −0.761215 0.648499i \(-0.775397\pi\)
0.761215 0.648499i \(-0.224603\pi\)
\(140\) −4.88317 + 6.91214i −0.412703 + 0.584182i
\(141\) 14.9718 14.9718i 1.26086 1.26086i
\(142\) −0.993103 + 0.993103i −0.0833394 + 0.0833394i
\(143\) 0.994740 + 1.09556i 0.0831843 + 0.0916154i
\(144\) 24.4898i 2.04082i
\(145\) 4.38577 + 3.09838i 0.364218 + 0.257306i
\(146\) 0.893211 0.0739227
\(147\) 7.22775 7.22775i 0.596135 0.596135i
\(148\) −10.5620 −0.868188
\(149\) 13.8291 13.8291i 1.13293 1.13293i 0.143237 0.989688i \(-0.454249\pi\)
0.989688 0.143237i \(-0.0457511\pi\)
\(150\) 0.882786 1.85250i 0.0720791 0.151256i
\(151\) −8.55106 + 8.55106i −0.695876 + 0.695876i −0.963518 0.267643i \(-0.913755\pi\)
0.267643 + 0.963518i \(0.413755\pi\)
\(152\) 1.69166 + 1.69166i 0.137212 + 0.137212i
\(153\) −15.9597 15.9597i −1.29026 1.29026i
\(154\) 0.0746147 + 0.0746147i 0.00601263 + 0.00601263i
\(155\) −6.29829 + 1.08340i −0.505891 + 0.0870210i
\(156\) 14.6433 + 16.1274i 1.17240 + 1.29123i
\(157\) −4.00808 4.00808i −0.319880 0.319880i 0.528841 0.848721i \(-0.322627\pi\)
−0.848721 + 0.528841i \(0.822627\pi\)
\(158\) 0.592356 0.0471253
\(159\) 4.70045i 0.372770i
\(160\) 2.91496 + 2.05931i 0.230448 + 0.162803i
\(161\) 4.33900 + 4.33900i 0.341961 + 0.341961i
\(162\) 1.57831i 0.124004i
\(163\) 13.2930i 1.04119i 0.853804 + 0.520595i \(0.174290\pi\)
−0.853804 + 0.520595i \(0.825710\pi\)
\(164\) −3.00841 3.00841i −0.234917 0.234917i
\(165\) 2.28495 + 1.61423i 0.177883 + 0.125668i
\(166\) 1.81540i 0.140902i
\(167\) −12.9980 −1.00582 −0.502909 0.864339i \(-0.667737\pi\)
−0.502909 + 0.864339i \(0.667737\pi\)
\(168\) 2.20681 + 2.20681i 0.170259 + 0.170259i
\(169\) −12.9397 1.25114i −0.995358 0.0962414i
\(170\) 1.06409 0.183041i 0.0816123 0.0140386i
\(171\) 19.8581 + 19.8581i 1.51859 + 1.51859i
\(172\) −1.76140 1.76140i −0.134305 0.134305i
\(173\) −10.3052 10.3052i −0.783489 0.783489i 0.196929 0.980418i \(-0.436903\pi\)
−0.980418 + 0.196929i \(0.936903\pi\)
\(174\) 0.696925 0.696925i 0.0528338 0.0528338i
\(175\) −3.19057 8.99967i −0.241185 0.680311i
\(176\) −1.12937 + 1.12937i −0.0851296 + 0.0851296i
\(177\) 35.8534 2.69490
\(178\) 1.34952 1.34952i 0.101151 0.101151i
\(179\) 6.59094 0.492630 0.246315 0.969190i \(-0.420780\pi\)
0.246315 + 0.969190i \(0.420780\pi\)
\(180\) 22.7776 + 16.0915i 1.69774 + 1.19939i
\(181\) 15.7953i 1.17406i −0.809567 0.587028i \(-0.800298\pi\)
0.809567 0.587028i \(-0.199702\pi\)
\(182\) −0.925934 0.0446602i −0.0686348 0.00331044i
\(183\) −15.4619 + 15.4619i −1.14298 + 1.14298i
\(184\) 1.21804 1.21804i 0.0897947 0.0897947i
\(185\) 6.87589 9.73285i 0.505525 0.715573i
\(186\) 1.17300i 0.0860082i
\(187\) 1.47199i 0.107643i
\(188\) −13.7654 −1.00394
\(189\) 13.5558 + 13.5558i 0.986038 + 0.986038i
\(190\) −1.32402 + 0.227752i −0.0960546 + 0.0165229i
\(191\) −13.0116 −0.941487 −0.470743 0.882270i \(-0.656014\pi\)
−0.470743 + 0.882270i \(0.656014\pi\)
\(192\) −16.3140 + 16.3140i −1.17736 + 1.17736i
\(193\) 17.4833i 1.25847i 0.777214 + 0.629237i \(0.216632\pi\)
−0.777214 + 0.629237i \(0.783368\pi\)
\(194\) −0.592356 −0.0425287
\(195\) −24.3942 + 2.99474i −1.74691 + 0.214458i
\(196\) −6.64532 −0.474665
\(197\) 14.2749i 1.01704i 0.861049 + 0.508522i \(0.169808\pi\)
−0.861049 + 0.508522i \(0.830192\pi\)
\(198\) 0.245878 0.245878i 0.0174738 0.0174738i
\(199\) 4.76666 0.337900 0.168950 0.985625i \(-0.445962\pi\)
0.168950 + 0.985625i \(0.445962\pi\)
\(200\) −2.52637 + 0.895651i −0.178641 + 0.0633321i
\(201\) 2.02621 + 2.02621i 0.142918 + 0.142918i
\(202\) 0.477961 0.0336293
\(203\) 4.58606i 0.321878i
\(204\) 21.6688i 1.51712i
\(205\) 4.73074 0.813760i 0.330409 0.0568354i
\(206\) −1.00282 + 1.00282i −0.0698698 + 0.0698698i
\(207\) 14.2983 14.2983i 0.993800 0.993800i
\(208\) 0.675979 14.0150i 0.0468707 0.971764i
\(209\) 1.83156i 0.126691i
\(210\) −1.72721 + 0.297106i −0.119189 + 0.0205023i
\(211\) 11.6025 0.798752 0.399376 0.916787i \(-0.369227\pi\)
0.399376 + 0.916787i \(0.369227\pi\)
\(212\) −2.16084 + 2.16084i −0.148407 + 0.148407i
\(213\) 31.8009 2.17896
\(214\) 1.28777 1.28777i 0.0880301 0.0880301i
\(215\) 2.76981 0.476450i 0.188899 0.0324936i
\(216\) 3.80535 3.80535i 0.258921 0.258921i
\(217\) 3.85940 + 3.85940i 0.261993 + 0.261993i
\(218\) 1.08866 + 1.08866i 0.0737336 + 0.0737336i
\(219\) −14.3011 14.3011i −0.966379 0.966379i
\(220\) −0.308335 1.79249i −0.0207880 0.120849i
\(221\) −8.69285 9.57390i −0.584744 0.644010i
\(222\) −1.54661 1.54661i −0.103802 0.103802i
\(223\) 15.2511 1.02129 0.510646 0.859791i \(-0.329406\pi\)
0.510646 + 0.859791i \(0.329406\pi\)
\(224\) 3.04808i 0.203658i
\(225\) −29.6566 + 10.5139i −1.97711 + 0.700926i
\(226\) −0.670391 0.670391i −0.0445937 0.0445937i
\(227\) 15.4292i 1.02407i 0.858964 + 0.512037i \(0.171109\pi\)
−0.858964 + 0.512037i \(0.828891\pi\)
\(228\) 26.9618i 1.78559i
\(229\) −4.10191 4.10191i −0.271062 0.271062i 0.558466 0.829528i \(-0.311390\pi\)
−0.829528 + 0.558466i \(0.811390\pi\)
\(230\) 0.163986 + 0.953323i 0.0108129 + 0.0628603i
\(231\) 2.38930i 0.157204i
\(232\) −1.28739 −0.0845213
\(233\) 18.4776 + 18.4776i 1.21051 + 1.21051i 0.970859 + 0.239651i \(0.0770330\pi\)
0.239651 + 0.970859i \(0.422967\pi\)
\(234\) −0.147169 + 3.05123i −0.00962073 + 0.199465i
\(235\) 8.96131 12.6848i 0.584571 0.827463i
\(236\) −16.4821 16.4821i −1.07289 1.07289i
\(237\) −9.48415 9.48415i −0.616062 0.616062i
\(238\) −0.652044 0.652044i −0.0422658 0.0422658i
\(239\) 7.82819 7.82819i 0.506363 0.506363i −0.407045 0.913408i \(-0.633441\pi\)
0.913408 + 0.407045i \(0.133441\pi\)
\(240\) −4.49702 26.1431i −0.290281 1.68753i
\(241\) −9.29059 + 9.29059i −0.598459 + 0.598459i −0.939902 0.341443i \(-0.889084\pi\)
0.341443 + 0.939902i \(0.389084\pi\)
\(242\) 1.45827 0.0937413
\(243\) 3.97498 3.97498i 0.254995 0.254995i
\(244\) 14.2160 0.910085
\(245\) 4.32613 6.12366i 0.276386 0.391226i
\(246\) 0.881054i 0.0561739i
\(247\) 10.8163 + 11.9125i 0.688222 + 0.757975i
\(248\) 1.08340 1.08340i 0.0687962 0.0687962i
\(249\) −29.0661 + 29.0661i −1.84199 + 1.84199i
\(250\) 0.407803 1.44894i 0.0257918 0.0916387i
\(251\) 13.4477i 0.848810i 0.905472 + 0.424405i \(0.139517\pi\)
−0.905472 + 0.424405i \(0.860483\pi\)
\(252\) 23.8178i 1.50038i
\(253\) −1.31876 −0.0829098
\(254\) 0.944768 + 0.944768i 0.0592800 + 0.0592800i
\(255\) −19.9678 14.1065i −1.25043 0.883381i
\(256\) 14.5696 0.910598
\(257\) −2.36553 + 2.36553i −0.147558 + 0.147558i −0.777026 0.629468i \(-0.783273\pi\)
0.629468 + 0.777026i \(0.283273\pi\)
\(258\) 0.515850i 0.0321154i
\(259\) −10.1773 −0.632388
\(260\) 12.5909 + 9.83753i 0.780857 + 0.610097i
\(261\) −15.1124 −0.935436
\(262\) 1.52204i 0.0940319i
\(263\) −10.3418 + 10.3418i −0.637704 + 0.637704i −0.949989 0.312285i \(-0.898906\pi\)
0.312285 + 0.949989i \(0.398906\pi\)
\(264\) −0.670719 −0.0412799
\(265\) −0.584496 3.39793i −0.0359053 0.208733i
\(266\) 0.811319 + 0.811319i 0.0497452 + 0.0497452i
\(267\) −43.2140 −2.64465
\(268\) 1.86293i 0.113796i
\(269\) 31.6138i 1.92753i 0.266754 + 0.963765i \(0.414049\pi\)
−0.266754 + 0.963765i \(0.585951\pi\)
\(270\) 0.512322 + 2.97835i 0.0311789 + 0.181256i
\(271\) 20.1850 20.1850i 1.22615 1.22615i 0.260742 0.965409i \(-0.416033\pi\)
0.965409 0.260742i \(-0.0839671\pi\)
\(272\) 9.86937 9.86937i 0.598419 0.598419i
\(273\) 14.1100 + 15.5401i 0.853975 + 0.940529i
\(274\) 0.258743i 0.0156313i
\(275\) 1.85250 + 0.882786i 0.111710 + 0.0532340i
\(276\) −19.4131 −1.16853
\(277\) 9.04189 9.04189i 0.543275 0.543275i −0.381213 0.924487i \(-0.624493\pi\)
0.924487 + 0.381213i \(0.124493\pi\)
\(278\) −2.05871 −0.123473
\(279\) 12.7179 12.7179i 0.761399 0.761399i
\(280\) 1.86970 + 1.32087i 0.111736 + 0.0789372i
\(281\) 6.06213 6.06213i 0.361636 0.361636i −0.502779 0.864415i \(-0.667689\pi\)
0.864415 + 0.502779i \(0.167689\pi\)
\(282\) −2.01569 2.01569i −0.120032 0.120032i
\(283\) −10.6076 10.6076i −0.630554 0.630554i 0.317653 0.948207i \(-0.397105\pi\)
−0.948207 + 0.317653i \(0.897105\pi\)
\(284\) −14.6192 14.6192i −0.867488 0.867488i
\(285\) 24.8453 + 17.5522i 1.47171 + 1.03971i
\(286\) 0.147497 0.133924i 0.00872170 0.00791907i
\(287\) −2.89885 2.89885i −0.171114 0.171114i
\(288\) −10.0443 −0.591868
\(289\) 4.13652i 0.243325i
\(290\) 0.417141 0.590464i 0.0244953 0.0346733i
\(291\) 9.48415 + 9.48415i 0.555971 + 0.555971i
\(292\) 13.1487i 0.769468i
\(293\) 21.9991i 1.28520i −0.766201 0.642601i \(-0.777855\pi\)
0.766201 0.642601i \(-0.222145\pi\)
\(294\) −0.973086 0.973086i −0.0567515 0.0567515i
\(295\) 25.9182 4.45832i 1.50901 0.259574i
\(296\) 2.85696i 0.166057i
\(297\) −4.12003 −0.239069
\(298\) −1.86184 1.86184i −0.107853 0.107853i
\(299\) 8.57727 7.78793i 0.496036 0.450388i
\(300\) 27.2701 + 12.9952i 1.57444 + 0.750279i
\(301\) −1.69725 1.69725i −0.0978281 0.0978281i
\(302\) 1.15125 + 1.15125i 0.0662468 + 0.0662468i
\(303\) −7.65259 7.65259i −0.439630 0.439630i
\(304\) −12.2802 + 12.2802i −0.704316 + 0.704316i
\(305\) −9.25467 + 13.1000i −0.529921 + 0.750105i
\(306\) −2.14868 + 2.14868i −0.122832 + 0.122832i
\(307\) 9.59930 0.547861 0.273931 0.961749i \(-0.411676\pi\)
0.273931 + 0.961749i \(0.411676\pi\)
\(308\) −1.09838 + 1.09838i −0.0625860 + 0.0625860i
\(309\) 32.1121 1.82679
\(310\) 0.145861 + 0.847951i 0.00828433 + 0.0481604i
\(311\) 4.28684i 0.243084i −0.992586 0.121542i \(-0.961216\pi\)
0.992586 0.121542i \(-0.0387840\pi\)
\(312\) 4.36238 3.96093i 0.246971 0.224243i
\(313\) 5.55258 5.55258i 0.313850 0.313850i −0.532549 0.846399i \(-0.678766\pi\)
0.846399 + 0.532549i \(0.178766\pi\)
\(314\) −0.539615 + 0.539615i −0.0304523 + 0.0304523i
\(315\) 21.9481 + 15.5055i 1.23663 + 0.873635i
\(316\) 8.71989i 0.490532i
\(317\) 18.5306i 1.04078i −0.853928 0.520391i \(-0.825786\pi\)
0.853928 0.520391i \(-0.174214\pi\)
\(318\) −0.632831 −0.0354874
\(319\) 0.696925 + 0.696925i 0.0390203 + 0.0390203i
\(320\) −9.76464 + 13.8219i −0.545860 + 0.772667i
\(321\) −41.2367 −2.30161
\(322\) 0.584167 0.584167i 0.0325544 0.0325544i
\(323\) 16.0056i 0.890578i
\(324\) −23.2338 −1.29077
\(325\) −17.2620 + 5.19827i −0.957526 + 0.288348i
\(326\) 1.78967 0.0991204
\(327\) 34.8610i 1.92782i
\(328\) −0.813760 + 0.813760i −0.0449324 + 0.0449324i
\(329\) −13.2641 −0.731271
\(330\) 0.217327 0.307627i 0.0119634 0.0169343i
\(331\) 1.66302 + 1.66302i 0.0914078 + 0.0914078i 0.751332 0.659924i \(-0.229412\pi\)
−0.659924 + 0.751332i \(0.729412\pi\)
\(332\) 26.7239 1.46666
\(333\) 33.5373i 1.83783i
\(334\) 1.74995i 0.0957530i
\(335\) 1.71669 + 1.21277i 0.0937927 + 0.0662610i
\(336\) −16.0197 + 16.0197i −0.873946 + 0.873946i
\(337\) −7.30111 + 7.30111i −0.397717 + 0.397717i −0.877427 0.479710i \(-0.840742\pi\)
0.479710 + 0.877427i \(0.340742\pi\)
\(338\) −0.168443 + 1.74209i −0.00916209 + 0.0947572i
\(339\) 21.4671i 1.16593i
\(340\) 2.69448 + 15.6642i 0.146129 + 0.849511i
\(341\) −1.17300 −0.0635212
\(342\) 2.67354 2.67354i 0.144568 0.144568i
\(343\) −19.7712 −1.06755
\(344\) −0.476450 + 0.476450i −0.0256884 + 0.0256884i
\(345\) 12.6380 17.8891i 0.680407 0.963119i
\(346\) −1.38741 + 1.38741i −0.0745874 + 0.0745874i
\(347\) −9.54455 9.54455i −0.512378 0.512378i 0.402876 0.915254i \(-0.368010\pi\)
−0.915254 + 0.402876i \(0.868010\pi\)
\(348\) 10.2592 + 10.2592i 0.549952 + 0.549952i
\(349\) 18.1608 + 18.1608i 0.972127 + 0.972127i 0.999622 0.0274946i \(-0.00875290\pi\)
−0.0274946 + 0.999622i \(0.508753\pi\)
\(350\) −1.21164 + 0.429553i −0.0647650 + 0.0229606i
\(351\) 26.7969 24.3308i 1.43031 1.29868i
\(352\) 0.463205 + 0.463205i 0.0246889 + 0.0246889i
\(353\) 4.19276 0.223158 0.111579 0.993756i \(-0.464409\pi\)
0.111579 + 0.993756i \(0.464409\pi\)
\(354\) 4.82700i 0.256552i
\(355\) 22.9887 3.95441i 1.22011 0.209878i
\(356\) 19.8658 + 19.8658i 1.05289 + 1.05289i
\(357\) 20.8796i 1.10507i
\(358\) 0.887351i 0.0468979i
\(359\) −6.13909 6.13909i −0.324009 0.324009i 0.526294 0.850303i \(-0.323581\pi\)
−0.850303 + 0.526294i \(0.823581\pi\)
\(360\) 4.35267 6.16122i 0.229406 0.324725i
\(361\) 0.915340i 0.0481758i
\(362\) −2.12655 −0.111769
\(363\) −23.3483 23.3483i −1.22547 1.22547i
\(364\) 0.657430 13.6304i 0.0344587 0.714427i
\(365\) −12.1165 8.55985i −0.634207 0.448043i
\(366\) 2.08167 + 2.08167i 0.108811 + 0.108811i
\(367\) −4.59729 4.59729i −0.239976 0.239976i 0.576864 0.816840i \(-0.304276\pi\)
−0.816840 + 0.576864i \(0.804276\pi\)
\(368\) 8.84198 + 8.84198i 0.460920 + 0.460920i
\(369\) −9.55258 + 9.55258i −0.497287 + 0.497287i
\(370\) −1.31035 0.925714i −0.0681219 0.0481256i
\(371\) −2.08215 + 2.08215i −0.108100 + 0.108100i
\(372\) −17.2673 −0.895268
\(373\) 13.6188 13.6188i 0.705154 0.705154i −0.260358 0.965512i \(-0.583841\pi\)
0.965512 + 0.260358i \(0.0838407\pi\)
\(374\) 0.198177 0.0102475
\(375\) −29.7281 + 16.6695i −1.53515 + 0.860807i
\(376\) 3.72346i 0.192023i
\(377\) −8.64852 0.417141i −0.445421 0.0214838i
\(378\) 1.82504 1.82504i 0.0938699 0.0938699i
\(379\) 19.3439 19.3439i 0.993631 0.993631i −0.00634892 0.999980i \(-0.502021\pi\)
0.999980 + 0.00634892i \(0.00202094\pi\)
\(380\) −3.35267 19.4905i −0.171988 0.999841i
\(381\) 30.2532i 1.54992i
\(382\) 1.75178i 0.0896287i
\(383\) −7.13110 −0.364382 −0.182191 0.983263i \(-0.558319\pi\)
−0.182191 + 0.983263i \(0.558319\pi\)
\(384\) 9.07743 + 9.07743i 0.463231 + 0.463231i
\(385\) −0.297106 1.72721i −0.0151419 0.0880267i
\(386\) 2.35381 0.119806
\(387\) −5.59296 + 5.59296i −0.284306 + 0.284306i
\(388\) 8.71989i 0.442685i
\(389\) −25.6987 −1.30298 −0.651488 0.758659i \(-0.725855\pi\)
−0.651488 + 0.758659i \(0.725855\pi\)
\(390\) 0.403187 + 3.28424i 0.0204162 + 0.166304i
\(391\) 11.5244 0.582814
\(392\) 1.79753i 0.0907887i
\(393\) 24.3692 24.3692i 1.22926 1.22926i
\(394\) 1.92186 0.0968218
\(395\) −8.03537 5.67669i −0.404304 0.285625i
\(396\) 3.61949 + 3.61949i 0.181886 + 0.181886i
\(397\) −14.8794 −0.746777 −0.373388 0.927675i \(-0.621804\pi\)
−0.373388 + 0.927675i \(0.621804\pi\)
\(398\) 0.641744i 0.0321677i
\(399\) 25.9799i 1.30062i
\(400\) −6.50173 18.3395i −0.325086 0.916974i
\(401\) 9.52637 9.52637i 0.475724 0.475724i −0.428037 0.903761i \(-0.640795\pi\)
0.903761 + 0.428037i \(0.140795\pi\)
\(402\) 0.272792 0.272792i 0.0136056 0.0136056i
\(403\) 7.62921 6.92712i 0.380038 0.345064i
\(404\) 7.03592i 0.350050i
\(405\) 15.1253 21.4099i 0.751582 1.06387i
\(406\) −0.617430 −0.0306425
\(407\) 1.54661 1.54661i 0.0766625 0.0766625i
\(408\) 5.86129 0.290177
\(409\) 8.19410 8.19410i 0.405172 0.405172i −0.474879 0.880051i \(-0.657508\pi\)
0.880051 + 0.474879i \(0.157508\pi\)
\(410\) −0.109558 0.636908i −0.00541068 0.0314546i
\(411\) −4.14271 + 4.14271i −0.204345 + 0.204345i
\(412\) −14.7622 14.7622i −0.727282 0.727282i
\(413\) −15.8819 15.8819i −0.781495 0.781495i
\(414\) −1.92501 1.92501i −0.0946089 0.0946089i
\(415\) −17.3974 + 24.6261i −0.854004 + 1.20885i
\(416\) −5.74815 0.277249i −0.281826 0.0135932i
\(417\) 32.9618 + 32.9618i 1.61415 + 1.61415i
\(418\) −0.246586 −0.0120609
\(419\) 26.7652i 1.30757i 0.756681 + 0.653784i \(0.226819\pi\)
−0.756681 + 0.653784i \(0.773181\pi\)
\(420\) −4.37361 25.4257i −0.213410 1.24065i
\(421\) −25.6977 25.6977i −1.25243 1.25243i −0.954628 0.297800i \(-0.903747\pi\)
−0.297800 0.954628i \(-0.596253\pi\)
\(422\) 1.56207i 0.0760405i
\(423\) 43.7090i 2.12520i
\(424\) 0.584496 + 0.584496i 0.0283856 + 0.0283856i
\(425\) −16.1887 7.71450i −0.785266 0.374208i
\(426\) 4.28142i 0.207436i
\(427\) 13.6983 0.662906
\(428\) 18.9569 + 18.9569i 0.916314 + 0.916314i
\(429\) −4.50580 0.217327i −0.217542 0.0104926i
\(430\) −0.0641453 0.372904i −0.00309336 0.0179830i
\(431\) −13.6422 13.6422i −0.657120 0.657120i 0.297578 0.954698i \(-0.403821\pi\)
−0.954698 + 0.297578i \(0.903821\pi\)
\(432\) 27.6239 + 27.6239i 1.32905 + 1.32905i
\(433\) 25.0267 + 25.0267i 1.20271 + 1.20271i 0.973340 + 0.229365i \(0.0736650\pi\)
0.229365 + 0.973340i \(0.426335\pi\)
\(434\) 0.519598 0.519598i 0.0249415 0.0249415i
\(435\) −16.1327 + 2.77507i −0.773502 + 0.133054i
\(436\) −16.0259 + 16.0259i −0.767500 + 0.767500i
\(437\) −14.3395 −0.685950
\(438\) −1.92539 + 1.92539i −0.0919985 + 0.0919985i
\(439\) −32.0588 −1.53008 −0.765042 0.643981i \(-0.777282\pi\)
−0.765042 + 0.643981i \(0.777282\pi\)
\(440\) −0.484858 + 0.0834032i −0.0231147 + 0.00397609i
\(441\) 21.1008i 1.00480i
\(442\) −1.28895 + 1.17033i −0.0613092 + 0.0556671i
\(443\) 3.91063 3.91063i 0.185800 0.185800i −0.608078 0.793877i \(-0.708059\pi\)
0.793877 + 0.608078i \(0.208059\pi\)
\(444\) 22.7671 22.7671i 1.08048 1.08048i
\(445\) −31.2391 + 5.37361i −1.48088 + 0.254734i
\(446\) 2.05329i 0.0972261i
\(447\) 59.6195i 2.81990i
\(448\) 14.4531 0.682845
\(449\) 2.54173 + 2.54173i 0.119952 + 0.119952i 0.764534 0.644583i \(-0.222969\pi\)
−0.644583 + 0.764534i \(0.722969\pi\)
\(450\) 1.41550 + 3.99272i 0.0667275 + 0.188219i
\(451\) 0.881054 0.0414872
\(452\) 9.86861 9.86861i 0.464180 0.464180i
\(453\) 36.8650i 1.73207i
\(454\) 2.07727 0.0974909
\(455\) 12.1324 + 9.47927i 0.568776 + 0.444395i
\(456\) −7.29303 −0.341527
\(457\) 23.2189i 1.08613i −0.839689 0.543067i \(-0.817263\pi\)
0.839689 0.543067i \(-0.182737\pi\)
\(458\) −0.552248 + 0.552248i −0.0258048 + 0.0258048i
\(459\) 36.0042 1.68053
\(460\) −14.0336 + 2.41399i −0.654319 + 0.112553i
\(461\) 28.8356 + 28.8356i 1.34301 + 1.34301i 0.893052 + 0.449954i \(0.148560\pi\)
0.449954 + 0.893052i \(0.351440\pi\)
\(462\) −0.321676 −0.0149657
\(463\) 5.03192i 0.233853i −0.993141 0.116927i \(-0.962696\pi\)
0.993141 0.116927i \(-0.0373042\pi\)
\(464\) 9.34544i 0.433851i
\(465\) 11.2411 15.9118i 0.521293 0.737893i
\(466\) 2.48768 2.48768i 0.115239 0.115239i
\(467\) −4.64570 + 4.64570i −0.214977 + 0.214977i −0.806378 0.591401i \(-0.798575\pi\)
0.591401 + 0.806378i \(0.298575\pi\)
\(468\) −44.9162 2.16643i −2.07625 0.100143i
\(469\) 1.79509i 0.0828893i
\(470\) −1.70777 1.20648i −0.0787737 0.0556507i
\(471\) 17.2795 0.796195
\(472\) −4.45832 + 4.45832i −0.205211 + 0.205211i
\(473\) 0.515850 0.0237188
\(474\) −1.27687 + 1.27687i −0.0586485 + 0.0586485i
\(475\) 20.1431 + 9.59892i 0.924228 + 0.440429i
\(476\) 9.59854 9.59854i 0.439949 0.439949i
\(477\) 6.86129 + 6.86129i 0.314157 + 0.314157i
\(478\) −1.05392 1.05392i −0.0482053 0.0482053i
\(479\) 6.05279 + 6.05279i 0.276559 + 0.276559i 0.831734 0.555175i \(-0.187349\pi\)
−0.555175 + 0.831734i \(0.687349\pi\)
\(480\) −10.7224 + 1.84442i −0.489409 + 0.0841860i
\(481\) −0.925714 + 19.1927i −0.0422089 + 0.875111i
\(482\) 1.25081 + 1.25081i 0.0569728 + 0.0569728i
\(483\) −18.7061 −0.851157
\(484\) 21.4668i 0.975763i
\(485\) 8.03537 + 5.67669i 0.364868 + 0.257765i
\(486\) −0.535159 0.535159i −0.0242753 0.0242753i
\(487\) 8.30574i 0.376369i −0.982134 0.188184i \(-0.939740\pi\)
0.982134 0.188184i \(-0.0602603\pi\)
\(488\) 3.84535i 0.174071i
\(489\) −28.6542 28.6542i −1.29579 1.29579i
\(490\) −0.824440 0.582435i −0.0372444 0.0263117i
\(491\) 4.54905i 0.205296i 0.994718 + 0.102648i \(0.0327315\pi\)
−0.994718 + 0.102648i \(0.967269\pi\)
\(492\) 12.9697 0.584720
\(493\) −6.09030 6.09030i −0.274293 0.274293i
\(494\) 1.60380 1.45621i 0.0721586 0.0655181i
\(495\) −5.69166 + 0.979054i −0.255821 + 0.0440052i
\(496\) 7.86466 + 7.86466i 0.353134 + 0.353134i
\(497\) −14.0868 14.0868i −0.631878 0.631878i
\(498\) 3.91323 + 3.91323i 0.175356 + 0.175356i
\(499\) 10.9444 10.9444i 0.489937 0.489937i −0.418349 0.908286i \(-0.637391\pi\)
0.908286 + 0.418349i \(0.137391\pi\)
\(500\) 21.3293 + 6.00315i 0.953877 + 0.268469i
\(501\) 28.0183 28.0183i 1.25176 1.25176i
\(502\) 1.81049 0.0808060
\(503\) −9.60700 + 9.60700i −0.428355 + 0.428355i −0.888068 0.459713i \(-0.847952\pi\)
0.459713 + 0.888068i \(0.347952\pi\)
\(504\) −6.44259 −0.286976
\(505\) −6.48360 4.58042i −0.288516 0.203826i
\(506\) 0.177547i 0.00789294i
\(507\) 30.5894 25.1955i 1.35852 1.11897i
\(508\) −13.9076 + 13.9076i −0.617052 + 0.617052i
\(509\) −1.01052 + 1.01052i −0.0447905 + 0.0447905i −0.729147 0.684357i \(-0.760083\pi\)
0.684357 + 0.729147i \(0.260083\pi\)
\(510\) −1.89918 + 2.68830i −0.0840971 + 0.119040i
\(511\) 12.6698i 0.560481i
\(512\) 10.3838i 0.458904i
\(513\) −44.7990 −1.97792
\(514\) 0.318476 + 0.318476i 0.0140474 + 0.0140474i
\(515\) 23.2136 3.99310i 1.02291 0.175957i
\(516\) 7.59366 0.334292
\(517\) 2.01569 2.01569i 0.0886497 0.0886497i
\(518\) 1.37019i 0.0602028i
\(519\) 44.4273 1.95014
\(520\) 2.66100 3.40579i 0.116693 0.149354i
\(521\) 39.4816 1.72972 0.864861 0.502012i \(-0.167406\pi\)
0.864861 + 0.502012i \(0.167406\pi\)
\(522\) 2.03461i 0.0890527i
\(523\) −15.7663 + 15.7663i −0.689411 + 0.689411i −0.962102 0.272691i \(-0.912086\pi\)
0.272691 + 0.962102i \(0.412086\pi\)
\(524\) −22.4055 −0.978787
\(525\) 26.2770 + 12.5220i 1.14682 + 0.546503i
\(526\) 1.39234 + 1.39234i 0.0607088 + 0.0607088i
\(527\) 10.2506 0.446523
\(528\) 4.86890i 0.211892i
\(529\) 12.6753i 0.551099i
\(530\) −0.457469 + 0.0786918i −0.0198712 + 0.00341815i
\(531\) −52.3354 + 52.3354i −2.27116 + 2.27116i
\(532\) −11.9432 + 11.9432i −0.517803 + 0.517803i
\(533\) −5.73041 + 5.20306i −0.248212 + 0.225369i
\(534\) 5.81798i 0.251769i
\(535\) −29.8097 + 5.12773i −1.28879 + 0.221691i
\(536\) −0.503913 −0.0217657
\(537\) −14.2073 + 14.2073i −0.613089 + 0.613089i
\(538\) 4.25623 0.183499
\(539\) 0.973086 0.973086i 0.0419138 0.0419138i
\(540\) −43.8433 + 7.54173i −1.88672 + 0.324544i
\(541\) −22.2954 + 22.2954i −0.958554 + 0.958554i −0.999175 0.0406207i \(-0.987066\pi\)
0.0406207 + 0.999175i \(0.487066\pi\)
\(542\) −2.71754 2.71754i −0.116728 0.116728i
\(543\) 34.0480 + 34.0480i 1.46114 + 1.46114i
\(544\) −4.04786 4.04786i −0.173551 0.173551i
\(545\) −4.33492 25.2008i −0.185688 1.07948i
\(546\) 2.09219 1.89965i 0.0895375 0.0812977i
\(547\) 3.38779 + 3.38779i 0.144851 + 0.144851i 0.775814 0.630962i \(-0.217340\pi\)
−0.630962 + 0.775814i \(0.717340\pi\)
\(548\) 3.80888 0.162707
\(549\) 45.1399i 1.92652i
\(550\) 0.118851 0.249406i 0.00506783 0.0106347i
\(551\) 7.57798 + 7.57798i 0.322833 + 0.322833i
\(552\) 5.25114i 0.223503i
\(553\) 8.40233i 0.357304i
\(554\) −1.21733 1.21733i −0.0517193 0.0517193i
\(555\) 6.15840 + 35.8014i 0.261409 + 1.51969i
\(556\) 30.3056i 1.28524i
\(557\) −5.28065 −0.223748 −0.111874 0.993722i \(-0.535685\pi\)
−0.111874 + 0.993722i \(0.535685\pi\)
\(558\) −1.71223 1.71223i −0.0724845 0.0724845i
\(559\) −3.35511 + 3.04635i −0.141906 + 0.128847i
\(560\) −9.58850 + 13.5726i −0.405188 + 0.573545i
\(561\) −3.17300 3.17300i −0.133964 0.133964i
\(562\) −0.816156 0.816156i −0.0344275 0.0344275i
\(563\) −29.6592 29.6592i −1.24999 1.24999i −0.955725 0.294261i \(-0.904927\pi\)
−0.294261 0.955725i \(-0.595073\pi\)
\(564\) 29.6723 29.6723i 1.24943 1.24943i
\(565\) 2.66941 + 15.5184i 0.112303 + 0.652866i
\(566\) −1.42811 + 1.42811i −0.0600281 + 0.0600281i
\(567\) −22.3877 −0.940193
\(568\) −3.95441 + 3.95441i −0.165923 + 0.165923i
\(569\) 22.3322 0.936216 0.468108 0.883671i \(-0.344936\pi\)
0.468108 + 0.883671i \(0.344936\pi\)
\(570\) 2.36309 3.34497i 0.0989790 0.140105i
\(571\) 11.9099i 0.498415i −0.968450 0.249207i \(-0.919830\pi\)
0.968450 0.249207i \(-0.0801701\pi\)
\(572\) 1.97145 + 2.17126i 0.0824304 + 0.0907851i
\(573\) 28.0475 28.0475i 1.17170 1.17170i
\(574\) −0.390278 + 0.390278i −0.0162899 + 0.0162899i
\(575\) 6.91143 14.5035i 0.288227 0.604836i
\(576\) 47.6273i 1.98447i
\(577\) 31.5179i 1.31211i −0.754714 0.656053i \(-0.772225\pi\)
0.754714 0.656053i \(-0.227775\pi\)
\(578\) 0.556908 0.0231643
\(579\) −37.6866 37.6866i −1.56620 1.56620i
\(580\) 8.69204 + 6.14060i 0.360918 + 0.254975i
\(581\) 25.7507 1.06832
\(582\) 1.27687 1.27687i 0.0529279 0.0529279i
\(583\) 0.632831i 0.0262092i
\(584\) 3.55665 0.147175
\(585\) 31.2370 39.9799i 1.29149 1.65297i
\(586\) −2.96178 −0.122350
\(587\) 33.0231i 1.36301i 0.731814 + 0.681505i \(0.238674\pi\)
−0.731814 + 0.681505i \(0.761326\pi\)
\(588\) 14.3245 14.3245i 0.590732 0.590732i
\(589\) −12.7545 −0.525540
\(590\) −0.600233 3.48941i −0.0247112 0.143657i
\(591\) −30.7707 30.7707i −1.26574 1.26574i
\(592\) −20.7393 −0.852380
\(593\) 20.1991i 0.829479i −0.909940 0.414739i \(-0.863873\pi\)
0.909940 0.414739i \(-0.136127\pi\)
\(594\) 0.554688i 0.0227591i
\(595\) 2.59636 + 15.0938i 0.106440 + 0.618784i
\(596\) 27.4076 27.4076i 1.12266 1.12266i
\(597\) −10.2749 + 10.2749i −0.420524 + 0.420524i
\(598\) −1.04850 1.15477i −0.0428765 0.0472222i
\(599\) 10.8205i 0.442113i 0.975261 + 0.221057i \(0.0709505\pi\)
−0.975261 + 0.221057i \(0.929049\pi\)
\(600\) 3.51514 7.37643i 0.143505 0.301142i
\(601\) −5.12131 −0.208903 −0.104451 0.994530i \(-0.533309\pi\)
−0.104451 + 0.994530i \(0.533309\pi\)
\(602\) −0.228504 + 0.228504i −0.00931315 + 0.00931315i
\(603\) −5.91534 −0.240891
\(604\) −16.9471 + 16.9471i −0.689569 + 0.689569i
\(605\) −19.7816 13.9750i −0.804238 0.568164i
\(606\) −1.03028 + 1.03028i −0.0418524 + 0.0418524i
\(607\) 11.3669 + 11.3669i 0.461370 + 0.461370i 0.899104 0.437735i \(-0.144219\pi\)
−0.437735 + 0.899104i \(0.644219\pi\)
\(608\) 5.03663 + 5.03663i 0.204262 + 0.204262i
\(609\) 9.88561 + 9.88561i 0.400585 + 0.400585i
\(610\) 1.76368 + 1.24597i 0.0714093 + 0.0504480i
\(611\) −1.20648 + 25.0137i −0.0488089 + 1.01195i
\(612\) −31.6301 31.6301i −1.27857 1.27857i
\(613\) 31.0334 1.25343 0.626714 0.779250i \(-0.284400\pi\)
0.626714 + 0.779250i \(0.284400\pi\)
\(614\) 1.29237i 0.0521559i
\(615\) −8.44335 + 11.9516i −0.340469 + 0.481935i
\(616\) 0.297106 + 0.297106i 0.0119708 + 0.0119708i
\(617\) 39.2697i 1.58094i −0.612502 0.790469i \(-0.709837\pi\)
0.612502 0.790469i \(-0.290163\pi\)
\(618\) 4.32331i 0.173909i
\(619\) 20.7839 + 20.7839i 0.835374 + 0.835374i 0.988246 0.152872i \(-0.0488523\pi\)
−0.152872 + 0.988246i \(0.548852\pi\)
\(620\) −12.4824 + 2.14717i −0.501306 + 0.0862324i
\(621\) 32.2562i 1.29440i
\(622\) −0.577145 −0.0231414
\(623\) 19.1424 + 19.1424i 0.766923 + 0.766923i
\(624\) 28.7532 + 31.6675i 1.15105 + 1.26771i
\(625\) −19.4174 + 15.7469i −0.776696 + 0.629876i
\(626\) −0.747554 0.747554i −0.0298783 0.0298783i
\(627\) 3.94806 + 3.94806i 0.157670 + 0.157670i
\(628\) −7.94351 7.94351i −0.316981 0.316981i
\(629\) −13.5155 + 13.5155i −0.538899 + 0.538899i
\(630\) 2.08753 2.95491i 0.0831692 0.117726i
\(631\) 13.0898 13.0898i 0.521099 0.521099i −0.396805 0.917903i \(-0.629881\pi\)
0.917903 + 0.396805i \(0.129881\pi\)
\(632\) 2.35869 0.0938235
\(633\) −25.0102 + 25.0102i −0.994066 + 0.994066i
\(634\) −2.49481 −0.0990815
\(635\) −3.76195 21.8698i −0.149288 0.867878i
\(636\) 9.31571i 0.369392i
\(637\) −0.582435 + 12.0755i −0.0230769 + 0.478450i
\(638\) 0.0938283 0.0938283i 0.00371470 0.00371470i
\(639\) −46.4201 + 46.4201i −1.83635 + 1.83635i
\(640\) 7.69079 + 5.43325i 0.304005 + 0.214768i
\(641\) 41.7149i 1.64764i 0.566853 + 0.823819i \(0.308161\pi\)
−0.566853 + 0.823819i \(0.691839\pi\)
\(642\) 5.55177i 0.219111i
\(643\) 38.6757 1.52522 0.762610 0.646858i \(-0.223917\pi\)
0.762610 + 0.646858i \(0.223917\pi\)
\(644\) 8.59935 + 8.59935i 0.338862 + 0.338862i
\(645\) −4.94351 + 6.99756i −0.194651 + 0.275529i
\(646\) 2.15487 0.0847822
\(647\) 21.8936 21.8936i 0.860726 0.860726i −0.130697 0.991422i \(-0.541721\pi\)
0.991422 + 0.130697i \(0.0417214\pi\)
\(648\) 6.28462i 0.246883i
\(649\) 4.82700 0.189477
\(650\) 0.699853 + 2.32402i 0.0274505 + 0.0911556i
\(651\) −16.6385 −0.652113
\(652\) 26.3451i 1.03175i
\(653\) −21.0962 + 21.0962i −0.825558 + 0.825558i −0.986899 0.161341i \(-0.948418\pi\)
0.161341 + 0.986899i \(0.448418\pi\)
\(654\) −4.69340 −0.183526
\(655\) 14.5861 20.6466i 0.569924 0.806730i
\(656\) −5.90726 5.90726i −0.230640 0.230640i
\(657\) 41.7509 1.62886
\(658\) 1.78576i 0.0696164i
\(659\) 26.6328i 1.03747i 0.854936 + 0.518734i \(0.173596\pi\)
−0.854936 + 0.518734i \(0.826404\pi\)
\(660\) 4.52848 + 3.19920i 0.176271 + 0.124529i
\(661\) −6.53609 + 6.53609i −0.254224 + 0.254224i −0.822700 0.568476i \(-0.807533\pi\)
0.568476 + 0.822700i \(0.307533\pi\)
\(662\) 0.223895 0.223895i 0.00870194 0.00870194i
\(663\) 39.3754 + 1.89918i 1.52921 + 0.0737580i
\(664\) 7.22868i 0.280527i
\(665\) −3.23057 18.7807i −0.125276 0.728285i
\(666\) 4.51519 0.174960
\(667\) 5.45631 5.45631i 0.211269 0.211269i
\(668\) −25.7605 −0.996703
\(669\) −32.8750 + 32.8750i −1.27102 + 1.27102i
\(670\) 0.163278 0.231121i 0.00630799 0.00892898i
\(671\) −2.08167 + 2.08167i −0.0803620 + 0.0803620i
\(672\) 6.57037 + 6.57037i 0.253458 + 0.253458i
\(673\) 5.50580 + 5.50580i 0.212233 + 0.212233i 0.805215 0.592982i \(-0.202050\pi\)
−0.592982 + 0.805215i \(0.702050\pi\)
\(674\) 0.982962 + 0.982962i 0.0378623 + 0.0378623i
\(675\) 21.5925 45.3113i 0.831096 1.74403i
\(676\) −25.6448 2.47960i −0.986337 0.0953692i
\(677\) 1.67072 + 1.67072i 0.0642110 + 0.0642110i 0.738483 0.674272i \(-0.235542\pi\)
−0.674272 + 0.738483i \(0.735542\pi\)
\(678\) 2.89016 0.110996
\(679\) 8.40233i 0.322452i
\(680\) 4.23709 0.728845i 0.162485 0.0279499i
\(681\) −33.2589 33.2589i −1.27448 1.27448i
\(682\) 0.157923i 0.00604717i
\(683\) 42.2726i 1.61752i −0.588141 0.808758i \(-0.700140\pi\)
0.588141 0.808758i \(-0.299860\pi\)
\(684\) 39.3563 + 39.3563i 1.50483 + 1.50483i
\(685\) −2.47960 + 3.50988i −0.0947406 + 0.134106i
\(686\) 2.66184i 0.101629i
\(687\) 17.6840 0.674685
\(688\) −3.45865 3.45865i −0.131860 0.131860i
\(689\) 3.73718 + 4.11596i 0.142375 + 0.156805i
\(690\) −2.40845 1.70148i −0.0916880 0.0647741i
\(691\) −19.9284 19.9284i −0.758110 0.758110i 0.217868 0.975978i \(-0.430090\pi\)
−0.975978 + 0.217868i \(0.930090\pi\)
\(692\) −20.4236 20.4236i −0.776388 0.776388i
\(693\) 3.48768 + 3.48768i 0.132486 + 0.132486i
\(694\) −1.28500 + 1.28500i −0.0487779 + 0.0487779i
\(695\) 27.9266 + 19.7291i 1.05932 + 0.748367i
\(696\) 2.77507 2.77507i 0.105189 0.105189i
\(697\) −7.69937 −0.291634
\(698\) 2.44503 2.44503i 0.0925457 0.0925457i
\(699\) −79.6599 −3.01302
\(700\) −6.32331 17.8362i −0.238999 0.674146i
\(701\) 13.2327i 0.499792i 0.968273 + 0.249896i \(0.0803964\pi\)
−0.968273 + 0.249896i \(0.919604\pi\)
\(702\) −3.27571 3.60771i −0.123634 0.136164i
\(703\) 16.8170 16.8170i 0.634264 0.634264i
\(704\) −2.19638 + 2.19638i −0.0827792 + 0.0827792i
\(705\) 8.02621 + 46.6598i 0.302284 + 1.75731i
\(706\) 0.564479i 0.0212444i
\(707\) 6.77969i 0.254977i
\(708\) 71.0568 2.67048
\(709\) −5.07651 5.07651i −0.190652 0.190652i 0.605326 0.795978i \(-0.293043\pi\)
−0.795978 + 0.605326i \(0.793043\pi\)
\(710\) −0.532390 3.09501i −0.0199802 0.116154i
\(711\) 27.6882 1.03839
\(712\) 5.37361 5.37361i 0.201385 0.201385i
\(713\) 9.18352i 0.343925i
\(714\) 2.81106 0.105201
\(715\) −3.28424 + 0.403187i −0.122824 + 0.0150784i
\(716\) 13.0624 0.488165
\(717\) 33.7485i 1.26036i
\(718\) −0.826517 + 0.826517i −0.0308453 + 0.0308453i
\(719\) 21.0560 0.785257 0.392628 0.919697i \(-0.371566\pi\)
0.392628 + 0.919697i \(0.371566\pi\)
\(720\) 44.7256 + 31.5970i 1.66683 + 1.17755i
\(721\) −14.2246 14.2246i −0.529752 0.529752i
\(722\) −0.123234 −0.00458629
\(723\) 40.0532i 1.48959i
\(724\) 31.3043i 1.16342i
\(725\) −11.3171 + 4.01216i −0.420307 + 0.149008i
\(726\) −3.14342 + 3.14342i −0.116663 + 0.116663i
\(727\) 12.7325 12.7325i 0.472221 0.472221i −0.430412 0.902633i \(-0.641632\pi\)
0.902633 + 0.430412i \(0.141632\pi\)
\(728\) −3.68695 0.177831i −0.136648 0.00659087i
\(729\) 18.0326i 0.667876i
\(730\) −1.15243 + 1.63127i −0.0426533 + 0.0603759i
\(731\) −4.50792 −0.166731
\(732\) −30.6436 + 30.6436i −1.13262 + 1.13262i
\(733\) −21.9710 −0.811517 −0.405759 0.913980i \(-0.632993\pi\)
−0.405759 + 0.913980i \(0.632993\pi\)
\(734\) −0.618941 + 0.618941i −0.0228455 + 0.0228455i
\(735\) 3.87471 + 22.5253i 0.142921 + 0.830859i
\(736\) 3.62648 3.62648i 0.133674 0.133674i
\(737\) 0.272792 + 0.272792i 0.0100484 + 0.0100484i
\(738\) 1.28608 + 1.28608i 0.0473413 + 0.0473413i
\(739\) 2.55220 + 2.55220i 0.0938841 + 0.0938841i 0.752489 0.658605i \(-0.228853\pi\)
−0.658605 + 0.752489i \(0.728853\pi\)
\(740\) 13.6271 19.2893i 0.500944 0.709088i
\(741\) −48.9936 2.36309i −1.79983 0.0868104i
\(742\) 0.280323 + 0.280323i 0.0102910 + 0.0102910i
\(743\) 9.53234 0.349708 0.174854 0.984594i \(-0.444055\pi\)
0.174854 + 0.984594i \(0.444055\pi\)
\(744\) 4.67072i 0.171237i
\(745\) 7.41361 + 43.0985i 0.271614 + 1.57901i
\(746\) −1.83352 1.83352i −0.0671300 0.0671300i
\(747\) 84.8562i 3.10472i
\(748\) 2.91731i 0.106667i
\(749\) 18.2665 + 18.2665i 0.667443 + 0.667443i
\(750\) 2.24424 + 4.00234i 0.0819481 + 0.146145i
\(751\) 3.05948i 0.111642i 0.998441 + 0.0558210i \(0.0177776\pi\)
−0.998441 + 0.0558210i \(0.982222\pi\)
\(752\) −27.0294 −0.985661
\(753\) −28.9875 28.9875i −1.05636 1.05636i
\(754\) −0.0561604 + 1.16437i −0.00204524 + 0.0424037i
\(755\) −4.58412 26.6494i −0.166833 0.969873i
\(756\) 26.8658 + 26.8658i 0.977101 + 0.977101i
\(757\) −12.1746 12.1746i −0.442495 0.442495i 0.450355 0.892850i \(-0.351297\pi\)
−0.892850 + 0.450355i \(0.851297\pi\)
\(758\) −2.60431 2.60431i −0.0945928 0.0945928i
\(759\) 2.84269 2.84269i 0.103183 0.103183i
\(760\) −5.27208 + 0.906880i −0.191239 + 0.0328960i
\(761\) −32.0020 + 32.0020i −1.16007 + 1.16007i −0.175614 + 0.984459i \(0.556191\pi\)
−0.984459 + 0.175614i \(0.943809\pi\)
\(762\) −4.07304 −0.147551
\(763\) −15.4423 + 15.4423i −0.559047 + 0.559047i
\(764\) −25.7874 −0.932954
\(765\) 49.7384 8.55578i 1.79830 0.309335i
\(766\) 0.960074i 0.0346889i
\(767\) −31.3950 + 28.5059i −1.13361 + 1.02929i
\(768\) −31.4058 + 31.4058i −1.13326 + 1.13326i
\(769\) 32.4213 32.4213i 1.16914 1.16914i 0.186730 0.982411i \(-0.440211\pi\)
0.982411 0.186730i \(-0.0597891\pi\)
\(770\) −0.232537