Properties

Label 231.2.y.a.4.5
Level $231$
Weight $2$
Character 231.4
Analytic conductor $1.845$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [231,2,Mod(4,231)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(231, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("231.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.y (of order \(15\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.84454428669\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(8\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 4.5
Character \(\chi\) \(=\) 231.4
Dual form 231.2.y.a.58.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0140677 - 0.133845i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(1.93858 + 0.412058i) q^{4} +(3.31825 + 1.47738i) q^{5} +(-0.108880 + 0.0791057i) q^{6} +(-1.93235 + 1.80722i) q^{7} +(0.165600 - 0.509665i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\) \(q+(0.0140677 - 0.133845i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(1.93858 + 0.412058i) q^{4} +(3.31825 + 1.47738i) q^{5} +(-0.108880 + 0.0791057i) q^{6} +(-1.93235 + 1.80722i) q^{7} +(0.165600 - 0.509665i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.244421 - 0.423350i) q^{10} +(-3.26353 + 0.591061i) q^{11} +(-0.990944 - 1.71636i) q^{12} +(1.43254 + 1.04080i) q^{13} +(0.214704 + 0.284059i) q^{14} +(-1.12244 - 3.45451i) q^{15} +(3.55520 + 1.58288i) q^{16} +(-0.470621 - 4.47766i) q^{17} +(0.131642 + 0.0279813i) q^{18} +(1.63215 - 0.346925i) q^{19} +(5.82393 + 4.23133i) q^{20} +(2.63602 + 0.226747i) q^{21} +(0.0332004 + 0.445124i) q^{22} +(-3.47623 - 6.02100i) q^{23} +(-0.489563 + 0.217967i) q^{24} +(5.48250 + 6.08894i) q^{25} +(0.159459 - 0.177097i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-4.49068 + 2.70720i) q^{28} +(-1.96811 - 6.05722i) q^{29} +(-0.478160 + 0.101636i) q^{30} +(4.93764 - 2.19838i) q^{31} +(0.797768 - 1.38177i) q^{32} +(2.62297 + 2.02978i) q^{33} -0.605936 q^{34} +(-9.08197 + 3.14200i) q^{35} +(-0.612437 + 1.88489i) q^{36} +(-2.55601 + 2.83874i) q^{37} +(-0.0234737 - 0.223337i) q^{38} +(-0.185090 - 1.76101i) q^{39} +(1.30247 - 1.44654i) q^{40} +(-0.887838 + 2.73248i) q^{41} +(0.0674318 - 0.349629i) q^{42} -12.7655 q^{43} +(-6.57017 - 0.198945i) q^{44} +(-1.81614 + 3.14565i) q^{45} +(-0.854787 + 0.380575i) q^{46} +(-2.06821 + 0.439613i) q^{47} +(-1.20259 - 3.70118i) q^{48} +(0.467920 - 6.98434i) q^{49} +(0.892103 - 0.648151i) q^{50} +(-3.01265 + 3.34588i) q^{51} +(2.34822 + 2.60796i) q^{52} +(-3.91749 + 1.74418i) q^{53} +(-0.0672914 - 0.116552i) q^{54} +(-11.7025 - 2.86019i) q^{55} +(0.601079 + 1.28412i) q^{56} +(-1.34994 - 0.980789i) q^{57} +(-0.838418 + 0.178211i) q^{58} +(9.77333 + 2.07738i) q^{59} +(-0.752477 - 7.15934i) q^{60} +(-4.05171 - 1.80394i) q^{61} +(-0.224782 - 0.691807i) q^{62} +(-1.59533 - 2.11067i) q^{63} +(6.12311 + 4.44870i) q^{64} +(3.21586 + 5.57004i) q^{65} +(0.308576 - 0.322519i) q^{66} +(3.68510 - 6.38277i) q^{67} +(0.932719 - 8.87423i) q^{68} +(-2.14843 + 6.61218i) q^{69} +(0.292780 + 1.25978i) q^{70} +(-6.91873 + 5.02675i) q^{71} +(0.489563 + 0.217967i) q^{72} +(11.5843 + 2.46231i) q^{73} +(0.343995 + 0.382046i) q^{74} +(0.856451 - 8.14859i) q^{75} +3.30701 q^{76} +(5.23810 - 7.04005i) q^{77} -0.238307 q^{78} +(-1.28550 + 12.2307i) q^{79} +(9.45855 + 10.5048i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(0.353241 + 0.157273i) q^{82} +(7.26750 - 5.28015i) q^{83} +(5.01669 + 1.52576i) q^{84} +(5.05358 - 15.5533i) q^{85} +(-0.179582 + 1.70861i) q^{86} +(-3.18447 + 5.51566i) q^{87} +(-0.239198 + 1.76119i) q^{88} +(-0.907843 - 1.57243i) q^{89} +(0.395482 + 0.287334i) q^{90} +(-4.64911 + 0.577724i) q^{91} +(-4.25794 - 13.1046i) q^{92} +(-4.93764 - 2.19838i) q^{93} +(0.0297451 + 0.283005i) q^{94} +(5.92844 + 1.26013i) q^{95} +(-1.56067 + 0.331731i) q^{96} +(-6.22158 - 4.52024i) q^{97} +(-0.928240 - 0.160883i) q^{98} +(-0.246691 - 3.30744i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0140677 0.133845i 0.00994738 0.0946430i −0.988422 0.151732i \(-0.951515\pi\)
0.998369 + 0.0570886i \(0.0181817\pi\)
\(3\) −0.669131 0.743145i −0.386323 0.429055i
\(4\) 1.93858 + 0.412058i 0.969289 + 0.206029i
\(5\) 3.31825 + 1.47738i 1.48397 + 0.660705i 0.979264 0.202587i \(-0.0649349\pi\)
0.504704 + 0.863292i \(0.331602\pi\)
\(6\) −0.108880 + 0.0791057i −0.0444500 + 0.0322948i
\(7\) −1.93235 + 1.80722i −0.730358 + 0.683065i
\(8\) 0.165600 0.509665i 0.0585485 0.180194i
\(9\) −0.104528 + 0.994522i −0.0348428 + 0.331507i
\(10\) 0.244421 0.423350i 0.0772928 0.133875i
\(11\) −3.26353 + 0.591061i −0.983992 + 0.178212i
\(12\) −0.990944 1.71636i −0.286061 0.495472i
\(13\) 1.43254 + 1.04080i 0.397314 + 0.288666i 0.768446 0.639914i \(-0.221030\pi\)
−0.371132 + 0.928580i \(0.621030\pi\)
\(14\) 0.214704 + 0.284059i 0.0573821 + 0.0759180i
\(15\) −1.12244 3.45451i −0.289812 0.891949i
\(16\) 3.55520 + 1.58288i 0.888800 + 0.395719i
\(17\) −0.470621 4.47766i −0.114142 1.08599i −0.890275 0.455423i \(-0.849488\pi\)
0.776133 0.630570i \(-0.217179\pi\)
\(18\) 0.131642 + 0.0279813i 0.0310283 + 0.00659526i
\(19\) 1.63215 0.346925i 0.374442 0.0795901i −0.0168468 0.999858i \(-0.505363\pi\)
0.391289 + 0.920268i \(0.372029\pi\)
\(20\) 5.82393 + 4.23133i 1.30227 + 0.946155i
\(21\) 2.63602 + 0.226747i 0.575226 + 0.0494803i
\(22\) 0.0332004 + 0.445124i 0.00707835 + 0.0949007i
\(23\) −3.47623 6.02100i −0.724844 1.25547i −0.959038 0.283276i \(-0.908579\pi\)
0.234195 0.972190i \(-0.424755\pi\)
\(24\) −0.489563 + 0.217967i −0.0999316 + 0.0444924i
\(25\) 5.48250 + 6.08894i 1.09650 + 1.21779i
\(26\) 0.159459 0.177097i 0.0312724 0.0347315i
\(27\) 0.809017 0.587785i 0.155695 0.113119i
\(28\) −4.49068 + 2.70720i −0.848659 + 0.511612i
\(29\) −1.96811 6.05722i −0.365469 1.12480i −0.949687 0.313200i \(-0.898599\pi\)
0.584219 0.811596i \(-0.301401\pi\)
\(30\) −0.478160 + 0.101636i −0.0872997 + 0.0185561i
\(31\) 4.93764 2.19838i 0.886827 0.394841i 0.0878013 0.996138i \(-0.472016\pi\)
0.799025 + 0.601297i \(0.205349\pi\)
\(32\) 0.797768 1.38177i 0.141027 0.244266i
\(33\) 2.62297 + 2.02978i 0.456601 + 0.353339i
\(34\) −0.605936 −0.103917
\(35\) −9.08197 + 3.14200i −1.53513 + 0.531095i
\(36\) −0.612437 + 1.88489i −0.102073 + 0.314148i
\(37\) −2.55601 + 2.83874i −0.420206 + 0.466686i −0.915663 0.401946i \(-0.868334\pi\)
0.495457 + 0.868632i \(0.335001\pi\)
\(38\) −0.0234737 0.223337i −0.00380793 0.0362300i
\(39\) −0.185090 1.76101i −0.0296381 0.281988i
\(40\) 1.30247 1.44654i 0.205939 0.228718i
\(41\) −0.887838 + 2.73248i −0.138657 + 0.426742i −0.996141 0.0877685i \(-0.972026\pi\)
0.857484 + 0.514511i \(0.172026\pi\)
\(42\) 0.0674318 0.349629i 0.0104050 0.0539489i
\(43\) −12.7655 −1.94673 −0.973364 0.229265i \(-0.926368\pi\)
−0.973364 + 0.229265i \(0.926368\pi\)
\(44\) −6.57017 0.198945i −0.990490 0.0299920i
\(45\) −1.81614 + 3.14565i −0.270734 + 0.468926i
\(46\) −0.854787 + 0.380575i −0.126031 + 0.0561128i
\(47\) −2.06821 + 0.439613i −0.301680 + 0.0641241i −0.356265 0.934385i \(-0.615950\pi\)
0.0545846 + 0.998509i \(0.482617\pi\)
\(48\) −1.20259 3.70118i −0.173578 0.534220i
\(49\) 0.467920 6.98434i 0.0668456 0.997763i
\(50\) 0.892103 0.648151i 0.126162 0.0916623i
\(51\) −3.01265 + 3.34588i −0.421855 + 0.468517i
\(52\) 2.34822 + 2.60796i 0.325639 + 0.361659i
\(53\) −3.91749 + 1.74418i −0.538109 + 0.239582i −0.657751 0.753235i \(-0.728492\pi\)
0.119642 + 0.992817i \(0.461825\pi\)
\(54\) −0.0672914 0.116552i −0.00915719 0.0158607i
\(55\) −11.7025 2.86019i −1.57796 0.385668i
\(56\) 0.601079 + 1.28412i 0.0803226 + 0.171598i
\(57\) −1.34994 0.980789i −0.178804 0.129909i
\(58\) −0.838418 + 0.178211i −0.110090 + 0.0234003i
\(59\) 9.77333 + 2.07738i 1.27238 + 0.270452i 0.794117 0.607765i \(-0.207934\pi\)
0.478262 + 0.878217i \(0.341267\pi\)
\(60\) −0.752477 7.15934i −0.0971443 0.924267i
\(61\) −4.05171 1.80394i −0.518768 0.230970i 0.130613 0.991433i \(-0.458305\pi\)
−0.649381 + 0.760463i \(0.724972\pi\)
\(62\) −0.224782 0.691807i −0.0285473 0.0878596i
\(63\) −1.59533 2.11067i −0.200993 0.265919i
\(64\) 6.12311 + 4.44870i 0.765388 + 0.556087i
\(65\) 3.21586 + 5.57004i 0.398879 + 0.690878i
\(66\) 0.308576 0.322519i 0.0379831 0.0396993i
\(67\) 3.68510 6.38277i 0.450206 0.779780i −0.548192 0.836352i \(-0.684684\pi\)
0.998399 + 0.0565723i \(0.0180171\pi\)
\(68\) 0.932719 8.87423i 0.113109 1.07616i
\(69\) −2.14843 + 6.61218i −0.258640 + 0.796013i
\(70\) 0.292780 + 1.25978i 0.0349939 + 0.150573i
\(71\) −6.91873 + 5.02675i −0.821102 + 0.596566i −0.917028 0.398823i \(-0.869419\pi\)
0.0959258 + 0.995388i \(0.469419\pi\)
\(72\) 0.489563 + 0.217967i 0.0576955 + 0.0256877i
\(73\) 11.5843 + 2.46231i 1.35583 + 0.288191i 0.827796 0.561029i \(-0.189595\pi\)
0.528038 + 0.849221i \(0.322928\pi\)
\(74\) 0.343995 + 0.382046i 0.0399887 + 0.0444119i
\(75\) 0.856451 8.14859i 0.0988944 0.940918i
\(76\) 3.30701 0.379340
\(77\) 5.23810 7.04005i 0.596936 0.802289i
\(78\) −0.238307 −0.0269830
\(79\) −1.28550 + 12.2307i −0.144630 + 1.37606i 0.645800 + 0.763507i \(0.276524\pi\)
−0.790429 + 0.612553i \(0.790143\pi\)
\(80\) 9.45855 + 10.5048i 1.05750 + 1.17447i
\(81\) −0.978148 0.207912i −0.108683 0.0231013i
\(82\) 0.353241 + 0.157273i 0.0390089 + 0.0173679i
\(83\) 7.26750 5.28015i 0.797712 0.579572i −0.112530 0.993648i \(-0.535896\pi\)
0.910242 + 0.414077i \(0.135896\pi\)
\(84\) 5.01669 + 1.52576i 0.547366 + 0.166474i
\(85\) 5.05358 15.5533i 0.548138 1.68699i
\(86\) −0.179582 + 1.70861i −0.0193648 + 0.184244i
\(87\) −3.18447 + 5.51566i −0.341411 + 0.591341i
\(88\) −0.239198 + 1.76119i −0.0254986 + 0.187743i
\(89\) −0.907843 1.57243i −0.0962312 0.166677i 0.813891 0.581018i \(-0.197345\pi\)
−0.910122 + 0.414341i \(0.864012\pi\)
\(90\) 0.395482 + 0.287334i 0.0416874 + 0.0302877i
\(91\) −4.64911 + 0.577724i −0.487359 + 0.0605620i
\(92\) −4.25794 13.1046i −0.443921 1.36625i
\(93\) −4.93764 2.19838i −0.512010 0.227961i
\(94\) 0.0297451 + 0.283005i 0.00306797 + 0.0291898i
\(95\) 5.92844 + 1.26013i 0.608246 + 0.129287i
\(96\) −1.56067 + 0.331731i −0.159285 + 0.0338571i
\(97\) −6.22158 4.52024i −0.631706 0.458961i 0.225285 0.974293i \(-0.427669\pi\)
−0.856991 + 0.515332i \(0.827669\pi\)
\(98\) −0.928240 0.160883i −0.0937664 0.0162516i
\(99\) −0.246691 3.30744i −0.0247934 0.332410i
\(100\) 8.11927 + 14.0630i 0.811927 + 1.40630i
\(101\) −5.90085 + 2.62723i −0.587156 + 0.261419i −0.678740 0.734378i \(-0.737474\pi\)
0.0915837 + 0.995797i \(0.470807\pi\)
\(102\) 0.405450 + 0.450298i 0.0401455 + 0.0445861i
\(103\) −11.5129 + 12.7864i −1.13440 + 1.25988i −0.172938 + 0.984933i \(0.555326\pi\)
−0.961460 + 0.274945i \(0.911341\pi\)
\(104\) 0.767687 0.557757i 0.0752779 0.0546926i
\(105\) 8.41198 + 4.64681i 0.820925 + 0.453482i
\(106\) 0.178340 + 0.548876i 0.0173220 + 0.0533115i
\(107\) −5.20937 + 1.10729i −0.503609 + 0.107045i −0.452709 0.891658i \(-0.649542\pi\)
−0.0509000 + 0.998704i \(0.516209\pi\)
\(108\) 1.81054 0.806106i 0.174220 0.0775676i
\(109\) −2.73834 + 4.74295i −0.262286 + 0.454292i −0.966849 0.255349i \(-0.917810\pi\)
0.704563 + 0.709641i \(0.251143\pi\)
\(110\) −0.547451 + 1.52608i −0.0521974 + 0.145506i
\(111\) 3.81990 0.362569
\(112\) −9.73049 + 3.36636i −0.919444 + 0.318091i
\(113\) −2.78632 + 8.57541i −0.262115 + 0.806707i 0.730229 + 0.683202i \(0.239413\pi\)
−0.992344 + 0.123505i \(0.960587\pi\)
\(114\) −0.150265 + 0.166886i −0.0140736 + 0.0156303i
\(115\) −2.63969 25.1149i −0.246152 2.34198i
\(116\) −1.31941 12.5534i −0.122504 1.16555i
\(117\) −1.18484 + 1.31590i −0.109538 + 0.121655i
\(118\) 0.415537 1.27889i 0.0382533 0.117731i
\(119\) 9.00152 + 7.80188i 0.825168 + 0.715197i
\(120\) −1.94652 −0.177692
\(121\) 10.3013 3.85790i 0.936481 0.350718i
\(122\) −0.298447 + 0.516925i −0.0270201 + 0.0468002i
\(123\) 2.62471 1.16860i 0.236662 0.105369i
\(124\) 10.4779 2.22714i 0.940940 0.200003i
\(125\) 3.58447 + 11.0319i 0.320605 + 0.986720i
\(126\) −0.304946 + 0.183836i −0.0271667 + 0.0163774i
\(127\) 16.4807 11.9739i 1.46242 1.06251i 0.479700 0.877432i \(-0.340745\pi\)
0.982723 0.185081i \(-0.0592546\pi\)
\(128\) 2.81682 3.12839i 0.248974 0.276514i
\(129\) 8.54182 + 9.48665i 0.752065 + 0.835253i
\(130\) 0.790764 0.352071i 0.0693546 0.0308787i
\(131\) 4.14559 + 7.18037i 0.362202 + 0.627352i 0.988323 0.152374i \(-0.0486918\pi\)
−0.626121 + 0.779726i \(0.715358\pi\)
\(132\) 4.24845 + 5.01570i 0.369780 + 0.436561i
\(133\) −2.52692 + 3.62004i −0.219111 + 0.313897i
\(134\) −0.802464 0.583025i −0.0693224 0.0503656i
\(135\) 3.55291 0.755194i 0.305786 0.0649967i
\(136\) −2.36004 0.501643i −0.202372 0.0430155i
\(137\) −0.161433 1.53594i −0.0137922 0.131224i 0.985459 0.169913i \(-0.0543486\pi\)
−0.999251 + 0.0386888i \(0.987682\pi\)
\(138\) 0.854787 + 0.380575i 0.0727643 + 0.0323967i
\(139\) 3.46582 + 10.6667i 0.293967 + 0.904737i 0.983567 + 0.180546i \(0.0577865\pi\)
−0.689600 + 0.724191i \(0.742214\pi\)
\(140\) −18.9008 + 2.34872i −1.59741 + 0.198503i
\(141\) 1.71060 + 1.24282i 0.144059 + 0.104665i
\(142\) 0.575477 + 0.996755i 0.0482930 + 0.0836459i
\(143\) −5.29031 2.54996i −0.442398 0.213239i
\(144\) −1.94583 + 3.37027i −0.162152 + 0.280856i
\(145\) 2.41814 23.0070i 0.200815 1.91063i
\(146\) 0.492533 1.51586i 0.0407623 0.125453i
\(147\) −5.50348 + 4.32571i −0.453919 + 0.356778i
\(148\) −6.12476 + 4.44990i −0.503452 + 0.365779i
\(149\) 4.67914 + 2.08329i 0.383330 + 0.170669i 0.589349 0.807878i \(-0.299384\pi\)
−0.206019 + 0.978548i \(0.566051\pi\)
\(150\) −1.07860 0.229264i −0.0880676 0.0187193i
\(151\) −1.90516 2.11589i −0.155039 0.172189i 0.660621 0.750719i \(-0.270293\pi\)
−0.815661 + 0.578531i \(0.803626\pi\)
\(152\) 0.0934694 0.889302i 0.00758137 0.0721319i
\(153\) 4.50233 0.363992
\(154\) −0.868591 0.800133i −0.0699931 0.0644765i
\(155\) 19.6322 1.57690
\(156\) 0.366827 3.49013i 0.0293697 0.279434i
\(157\) −4.09768 4.55094i −0.327031 0.363204i 0.557099 0.830446i \(-0.311914\pi\)
−0.884130 + 0.467242i \(0.845248\pi\)
\(158\) 1.61894 + 0.344116i 0.128796 + 0.0273764i
\(159\) 3.91749 + 1.74418i 0.310678 + 0.138323i
\(160\) 4.68861 3.40647i 0.370667 0.269305i
\(161\) 17.5985 + 5.35235i 1.38696 + 0.421825i
\(162\) −0.0415883 + 0.127996i −0.00326749 + 0.0100563i
\(163\) 1.65819 15.7767i 0.129880 1.23572i −0.714368 0.699770i \(-0.753286\pi\)
0.844248 0.535953i \(-0.180048\pi\)
\(164\) −2.84708 + 4.93129i −0.222320 + 0.385069i
\(165\) 5.70493 + 10.6105i 0.444128 + 0.826023i
\(166\) −0.604487 1.04700i −0.0469173 0.0812631i
\(167\) −7.95253 5.77785i −0.615385 0.447103i 0.235921 0.971772i \(-0.424189\pi\)
−0.851306 + 0.524669i \(0.824189\pi\)
\(168\) 0.552090 1.30594i 0.0425947 0.100755i
\(169\) −3.04832 9.38177i −0.234486 0.721675i
\(170\) −2.01065 0.895198i −0.154210 0.0686586i
\(171\) 0.174418 + 1.65948i 0.0133381 + 0.126903i
\(172\) −24.7470 5.26014i −1.88694 0.401082i
\(173\) 9.93560 2.11188i 0.755390 0.160563i 0.185908 0.982567i \(-0.440477\pi\)
0.569482 + 0.822004i \(0.307144\pi\)
\(174\) 0.693448 + 0.503819i 0.0525701 + 0.0381944i
\(175\) −21.5981 1.85785i −1.63267 0.140440i
\(176\) −12.5381 3.06443i −0.945095 0.230990i
\(177\) −4.99583 8.65304i −0.375510 0.650402i
\(178\) −0.223234 + 0.0993902i −0.0167321 + 0.00744961i
\(179\) 15.9665 + 17.7326i 1.19339 + 1.32539i 0.932994 + 0.359891i \(0.117186\pi\)
0.260395 + 0.965502i \(0.416147\pi\)
\(180\) −4.81692 + 5.34973i −0.359032 + 0.398745i
\(181\) −4.22971 + 3.07306i −0.314392 + 0.228419i −0.733779 0.679389i \(-0.762245\pi\)
0.419387 + 0.907808i \(0.362245\pi\)
\(182\) 0.0119234 + 0.630389i 0.000883822 + 0.0467276i
\(183\) 1.37054 + 4.21808i 0.101313 + 0.311809i
\(184\) −3.64436 + 0.774632i −0.268666 + 0.0571066i
\(185\) −12.6754 + 5.64346i −0.931915 + 0.414915i
\(186\) −0.363704 + 0.629955i −0.0266681 + 0.0461905i
\(187\) 4.18246 + 14.3348i 0.305852 + 1.04827i
\(188\) −4.19054 −0.305627
\(189\) −0.501044 + 2.59788i −0.0364456 + 0.188968i
\(190\) 0.252062 0.775768i 0.0182865 0.0562801i
\(191\) 8.56835 9.51611i 0.619984 0.688562i −0.348594 0.937274i \(-0.613341\pi\)
0.968577 + 0.248712i \(0.0800073\pi\)
\(192\) −0.791131 7.52711i −0.0570950 0.543223i
\(193\) 0.800441 + 7.61569i 0.0576170 + 0.548189i 0.984814 + 0.173614i \(0.0555447\pi\)
−0.927197 + 0.374575i \(0.877789\pi\)
\(194\) −0.692538 + 0.769141i −0.0497213 + 0.0552211i
\(195\) 1.98751 6.11694i 0.142329 0.438043i
\(196\) 3.78505 13.3469i 0.270361 0.953349i
\(197\) −5.11991 −0.364778 −0.182389 0.983226i \(-0.558383\pi\)
−0.182389 + 0.983226i \(0.558383\pi\)
\(198\) −0.446156 0.0135096i −0.0317069 0.000960086i
\(199\) 6.85465 11.8726i 0.485913 0.841626i −0.513956 0.857817i \(-0.671820\pi\)
0.999869 + 0.0161905i \(0.00515383\pi\)
\(200\) 4.01122 1.78591i 0.283636 0.126283i
\(201\) −7.20914 + 1.53235i −0.508493 + 0.108084i
\(202\) 0.268631 + 0.826761i 0.0189008 + 0.0581707i
\(203\) 14.7498 + 8.14783i 1.03523 + 0.571866i
\(204\) −7.21895 + 5.24487i −0.505427 + 0.367214i
\(205\) −6.98299 + 7.75540i −0.487713 + 0.541661i
\(206\) 1.54944 + 1.72082i 0.107954 + 0.119895i
\(207\) 6.35138 2.82782i 0.441452 0.196547i
\(208\) 3.44550 + 5.96778i 0.238902 + 0.413791i
\(209\) −5.12154 + 2.09690i −0.354264 + 0.145046i
\(210\) 0.740292 1.06054i 0.0510850 0.0731839i
\(211\) 2.03761 + 1.48041i 0.140275 + 0.101916i 0.655710 0.755013i \(-0.272370\pi\)
−0.515435 + 0.856929i \(0.672370\pi\)
\(212\) −8.31307 + 1.76700i −0.570944 + 0.121358i
\(213\) 8.36514 + 1.77806i 0.573170 + 0.121831i
\(214\) 0.0749212 + 0.712828i 0.00512151 + 0.0487279i
\(215\) −42.3593 18.8596i −2.88888 1.28621i
\(216\) −0.165600 0.509665i −0.0112677 0.0346783i
\(217\) −5.56828 + 13.1714i −0.377999 + 0.894135i
\(218\) 0.596300 + 0.433237i 0.0403865 + 0.0293425i
\(219\) −5.92152 10.2564i −0.400140 0.693062i
\(220\) −21.5076 10.3668i −1.45004 0.698929i
\(221\) 3.98617 6.90424i 0.268138 0.464429i
\(222\) 0.0537374 0.511277i 0.00360662 0.0343147i
\(223\) −4.13016 + 12.7113i −0.276576 + 0.851214i 0.712222 + 0.701955i \(0.247689\pi\)
−0.988798 + 0.149260i \(0.952311\pi\)
\(224\) 0.955606 + 4.11181i 0.0638491 + 0.274732i
\(225\) −6.62866 + 4.81600i −0.441910 + 0.321067i
\(226\) 1.10858 + 0.493573i 0.0737418 + 0.0328320i
\(227\) −3.09346 0.657536i −0.205320 0.0436422i 0.104103 0.994567i \(-0.466803\pi\)
−0.309424 + 0.950924i \(0.600136\pi\)
\(228\) −2.21282 2.45759i −0.146548 0.162758i
\(229\) −0.557622 + 5.30541i −0.0368487 + 0.350592i 0.960527 + 0.278188i \(0.0897337\pi\)
−0.997375 + 0.0724039i \(0.976933\pi\)
\(230\) −3.39865 −0.224101
\(231\) −8.73675 + 0.818051i −0.574836 + 0.0538238i
\(232\) −3.41307 −0.224079
\(233\) −2.04316 + 19.4394i −0.133852 + 1.27352i 0.697019 + 0.717052i \(0.254509\pi\)
−0.830871 + 0.556465i \(0.812157\pi\)
\(234\) 0.159459 + 0.177097i 0.0104241 + 0.0115772i
\(235\) −7.51234 1.59680i −0.490051 0.104164i
\(236\) 18.0904 + 8.05435i 1.17758 + 0.524293i
\(237\) 9.94934 7.22862i 0.646279 0.469549i
\(238\) 1.17088 1.09506i 0.0758967 0.0709821i
\(239\) −1.87223 + 5.76213i −0.121104 + 0.372721i −0.993171 0.116666i \(-0.962779\pi\)
0.872067 + 0.489387i \(0.162779\pi\)
\(240\) 1.47757 14.0581i 0.0953768 0.907449i
\(241\) 10.3827 17.9834i 0.668809 1.15841i −0.309428 0.950923i \(-0.600138\pi\)
0.978237 0.207488i \(-0.0665290\pi\)
\(242\) −0.371446 1.43305i −0.0238775 0.0921201i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −7.11123 5.16661i −0.455250 0.330758i
\(245\) 11.8712 22.4845i 0.758424 1.43648i
\(246\) −0.119488 0.367745i −0.00761825 0.0234466i
\(247\) 2.69920 + 1.20176i 0.171746 + 0.0764662i
\(248\) −0.302763 2.88059i −0.0192254 0.182918i
\(249\) −8.78682 1.86770i −0.556842 0.118360i
\(250\) 1.52699 0.324572i 0.0965753 0.0205277i
\(251\) −5.82856 4.23469i −0.367895 0.267291i 0.388442 0.921473i \(-0.373013\pi\)
−0.756338 + 0.654182i \(0.773013\pi\)
\(252\) −2.22296 4.74906i −0.140034 0.299163i
\(253\) 14.9036 + 17.5951i 0.936979 + 1.10619i
\(254\) −1.37081 2.37431i −0.0860122 0.148977i
\(255\) −14.9399 + 6.65166i −0.935571 + 0.416543i
\(256\) 9.74963 + 10.8281i 0.609352 + 0.676754i
\(257\) 4.03242 4.47846i 0.251536 0.279358i −0.604132 0.796884i \(-0.706480\pi\)
0.855668 + 0.517526i \(0.173147\pi\)
\(258\) 1.38991 1.00983i 0.0865320 0.0628692i
\(259\) −0.191124 10.1047i −0.0118759 0.627876i
\(260\) 3.93903 + 12.1231i 0.244288 + 0.751841i
\(261\) 6.22976 1.32418i 0.385612 0.0819644i
\(262\) 1.01938 0.453857i 0.0629774 0.0280394i
\(263\) 3.32270 5.75508i 0.204886 0.354873i −0.745210 0.666830i \(-0.767651\pi\)
0.950096 + 0.311956i \(0.100984\pi\)
\(264\) 1.46887 1.00071i 0.0904028 0.0615892i
\(265\) −15.5761 −0.956830
\(266\) 0.448978 + 0.389142i 0.0275286 + 0.0238598i
\(267\) −0.561078 + 1.72682i −0.0343374 + 0.105680i
\(268\) 9.77392 10.8550i 0.597037 0.663077i
\(269\) 2.06486 + 19.6459i 0.125897 + 1.19783i 0.856910 + 0.515466i \(0.172381\pi\)
−0.731013 + 0.682364i \(0.760952\pi\)
\(270\) −0.0510979 0.486164i −0.00310972 0.0295870i
\(271\) 0.195497 0.217121i 0.0118756 0.0131892i −0.737178 0.675699i \(-0.763842\pi\)
0.749053 + 0.662510i \(0.230509\pi\)
\(272\) 5.41444 16.6639i 0.328299 1.01040i
\(273\) 3.54019 + 3.06839i 0.214262 + 0.185707i
\(274\) −0.207849 −0.0125566
\(275\) −21.4913 16.6309i −1.29597 1.00288i
\(276\) −6.88949 + 11.9330i −0.414699 + 0.718279i
\(277\) −16.3147 + 7.26379i −0.980258 + 0.436439i −0.833371 0.552714i \(-0.813592\pi\)
−0.146887 + 0.989153i \(0.546925\pi\)
\(278\) 1.47644 0.313828i 0.0885512 0.0188221i
\(279\) 1.67021 + 5.14039i 0.0999930 + 0.307747i
\(280\) 0.0973915 + 5.14907i 0.00582025 + 0.307716i
\(281\) −12.8119 + 9.30839i −0.764294 + 0.555292i −0.900224 0.435426i \(-0.856598\pi\)
0.135930 + 0.990718i \(0.456598\pi\)
\(282\) 0.190411 0.211473i 0.0113388 0.0125930i
\(283\) 10.5243 + 11.6885i 0.625608 + 0.694808i 0.969747 0.244111i \(-0.0784960\pi\)
−0.344140 + 0.938918i \(0.611829\pi\)
\(284\) −15.4838 + 6.89384i −0.918795 + 0.409074i
\(285\) −3.03044 5.24888i −0.179508 0.310917i
\(286\) −0.415724 + 0.672211i −0.0245823 + 0.0397487i
\(287\) −3.22259 6.88462i −0.190223 0.406386i
\(288\) 1.29082 + 0.937832i 0.0760620 + 0.0552623i
\(289\) −3.19948 + 0.680071i −0.188205 + 0.0400042i
\(290\) −3.04537 0.647313i −0.178830 0.0380115i
\(291\) 0.803855 + 7.64817i 0.0471228 + 0.448344i
\(292\) 21.4424 + 9.54676i 1.25482 + 0.558682i
\(293\) −0.400843 1.23367i −0.0234175 0.0720717i 0.938665 0.344831i \(-0.112064\pi\)
−0.962082 + 0.272759i \(0.912064\pi\)
\(294\) 0.501555 + 0.797468i 0.0292513 + 0.0465093i
\(295\) 29.3613 + 21.3322i 1.70948 + 1.24201i
\(296\) 1.02353 + 1.77281i 0.0594915 + 0.103042i
\(297\) −2.29284 + 2.39644i −0.133044 + 0.139055i
\(298\) 0.344663 0.596974i 0.0199658 0.0345818i
\(299\) 1.28683 12.2434i 0.0744193 0.708052i
\(300\) 5.01798 15.4438i 0.289713 0.891646i
\(301\) 24.6675 23.0701i 1.42181 1.32974i
\(302\) −0.310003 + 0.225231i −0.0178387 + 0.0129606i
\(303\) 5.90085 + 2.62723i 0.338995 + 0.150930i
\(304\) 6.35178 + 1.35011i 0.364299 + 0.0774342i
\(305\) −10.7795 11.9718i −0.617232 0.685506i
\(306\) 0.0633375 0.602616i 0.00362076 0.0344493i
\(307\) 15.2964 0.873012 0.436506 0.899701i \(-0.356216\pi\)
0.436506 + 0.899701i \(0.356216\pi\)
\(308\) 13.0554 11.4893i 0.743899 0.654664i
\(309\) 17.2057 0.978800
\(310\) 0.276180 2.62768i 0.0156860 0.149242i
\(311\) −17.7300 19.6912i −1.00538 1.11659i −0.993172 0.116660i \(-0.962781\pi\)
−0.0122061 0.999926i \(-0.503885\pi\)
\(312\) −0.928177 0.197290i −0.0525477 0.0111694i
\(313\) 7.32032 + 3.25922i 0.413769 + 0.184222i 0.603054 0.797700i \(-0.293950\pi\)
−0.189285 + 0.981922i \(0.560617\pi\)
\(314\) −0.666767 + 0.484435i −0.0376279 + 0.0273382i
\(315\) −2.17546 9.36064i −0.122573 0.527413i
\(316\) −7.53178 + 23.1804i −0.423696 + 1.30400i
\(317\) −1.22795 + 11.6831i −0.0689684 + 0.656190i 0.904359 + 0.426772i \(0.140349\pi\)
−0.973328 + 0.229419i \(0.926318\pi\)
\(318\) 0.288561 0.499802i 0.0161817 0.0280275i
\(319\) 10.0032 + 18.6046i 0.560070 + 1.04166i
\(320\) 13.7456 + 23.8081i 0.768402 + 1.33091i
\(321\) 4.30862 + 3.13040i 0.240484 + 0.174722i
\(322\) 0.963960 2.28019i 0.0537194 0.127070i
\(323\) −2.32154 7.14497i −0.129174 0.397557i
\(324\) −1.81054 0.806106i −0.100586 0.0447837i
\(325\) 1.51653 + 14.4288i 0.0841219 + 0.800366i
\(326\) −2.08831 0.443883i −0.115661 0.0245844i
\(327\) 5.35700 1.13867i 0.296243 0.0629684i
\(328\) 1.24562 + 0.904999i 0.0687781 + 0.0499702i
\(329\) 3.20203 4.58720i 0.176534 0.252901i
\(330\) 1.50042 0.614314i 0.0825953 0.0338169i
\(331\) −5.04652 8.74082i −0.277382 0.480439i 0.693352 0.720599i \(-0.256133\pi\)
−0.970733 + 0.240160i \(0.922800\pi\)
\(332\) 16.2643 7.24135i 0.892622 0.397421i
\(333\) −2.55601 2.83874i −0.140069 0.155562i
\(334\) −0.885213 + 0.983128i −0.0484367 + 0.0537944i
\(335\) 21.6579 15.7354i 1.18330 0.859715i
\(336\) 9.01266 + 4.97863i 0.491681 + 0.271606i
\(337\) −8.35918 25.7269i −0.455354 1.40143i −0.870719 0.491780i \(-0.836346\pi\)
0.415366 0.909655i \(-0.363654\pi\)
\(338\) −1.29859 + 0.276024i −0.0706340 + 0.0150137i
\(339\) 8.23719 3.66743i 0.447383 0.199188i
\(340\) 16.2056 28.0690i 0.878873 1.52225i
\(341\) −14.8148 + 10.0929i −0.802265 + 0.546563i
\(342\) 0.224567 0.0121432
\(343\) 11.7181 + 14.3418i 0.632716 + 0.774384i
\(344\) −2.11398 + 6.50615i −0.113978 + 0.350788i
\(345\) −16.8977 + 18.7668i −0.909744 + 1.01037i
\(346\) −0.142894 1.35954i −0.00768202 0.0730895i
\(347\) 0.465767 + 4.43147i 0.0250037 + 0.237894i 0.999885 + 0.0151688i \(0.00482857\pi\)
−0.974881 + 0.222725i \(0.928505\pi\)
\(348\) −8.44611 + 9.38035i −0.452759 + 0.502840i
\(349\) −1.96611 + 6.05107i −0.105244 + 0.323906i −0.989788 0.142550i \(-0.954470\pi\)
0.884544 + 0.466457i \(0.154470\pi\)
\(350\) −0.552501 + 2.86468i −0.0295324 + 0.153123i
\(351\) 1.77071 0.0945137
\(352\) −1.78683 + 4.98100i −0.0952383 + 0.265488i
\(353\) −5.98019 + 10.3580i −0.318294 + 0.551301i −0.980132 0.198346i \(-0.936443\pi\)
0.661838 + 0.749646i \(0.269776\pi\)
\(354\) −1.22845 + 0.546941i −0.0652914 + 0.0290696i
\(355\) −30.3845 + 6.45843i −1.61264 + 0.342778i
\(356\) −1.11199 3.42236i −0.0589355 0.181385i
\(357\) −0.225268 11.9099i −0.0119225 0.630339i
\(358\) 2.59803 1.88758i 0.137310 0.0997618i
\(359\) 24.3145 27.0039i 1.28327 1.42521i 0.430789 0.902453i \(-0.358235\pi\)
0.852479 0.522761i \(-0.175098\pi\)
\(360\) 1.30247 + 1.44654i 0.0686463 + 0.0762395i
\(361\) −14.8138 + 6.59553i −0.779673 + 0.347133i
\(362\) 0.351813 + 0.609358i 0.0184909 + 0.0320272i
\(363\) −9.75989 5.07392i −0.512261 0.266312i
\(364\) −9.25072 0.795736i −0.484869 0.0417079i
\(365\) 34.8017 + 25.2849i 1.82161 + 1.32347i
\(366\) 0.583850 0.124101i 0.0305184 0.00648688i
\(367\) −12.4043 2.63662i −0.647501 0.137631i −0.127558 0.991831i \(-0.540714\pi\)
−0.519944 + 0.854200i \(0.674047\pi\)
\(368\) −2.82818 26.9083i −0.147429 1.40269i
\(369\) −2.62471 1.16860i −0.136637 0.0608347i
\(370\) 0.577037 + 1.77594i 0.0299987 + 0.0923266i
\(371\) 4.41784 10.4501i 0.229363 0.542544i
\(372\) −8.66615 6.29632i −0.449319 0.326449i
\(373\) 18.5608 + 32.1483i 0.961042 + 1.66457i 0.719893 + 0.694085i \(0.244191\pi\)
0.241149 + 0.970488i \(0.422476\pi\)
\(374\) 1.97749 0.358145i 0.102254 0.0185192i
\(375\) 5.79979 10.0455i 0.299500 0.518749i
\(376\) −0.118442 + 1.12690i −0.00610816 + 0.0581152i
\(377\) 3.48495 10.7256i 0.179484 0.552396i
\(378\) 0.340665 + 0.103609i 0.0175219 + 0.00532905i
\(379\) −4.33612 + 3.15038i −0.222732 + 0.161824i −0.693555 0.720403i \(-0.743957\pi\)
0.470824 + 0.882227i \(0.343957\pi\)
\(380\) 10.9735 + 4.88572i 0.562929 + 0.250632i
\(381\) −19.9261 4.23542i −1.02084 0.216987i
\(382\) −1.15315 1.28070i −0.0590003 0.0655265i
\(383\) −3.61806 + 34.4235i −0.184874 + 1.75896i 0.371878 + 0.928282i \(0.378714\pi\)
−0.556752 + 0.830679i \(0.687953\pi\)
\(384\) −4.20967 −0.214824
\(385\) 27.7822 15.6220i 1.41591 0.796172i
\(386\) 1.03059 0.0524554
\(387\) 1.33436 12.6956i 0.0678295 0.645355i
\(388\) −10.1984 11.3265i −0.517747 0.575016i
\(389\) 20.9518 + 4.45344i 1.06230 + 0.225798i 0.705737 0.708474i \(-0.250616\pi\)
0.356561 + 0.934272i \(0.383949\pi\)
\(390\) −0.790764 0.352071i −0.0400419 0.0178278i
\(391\) −25.3240 + 18.3990i −1.28069 + 0.930477i
\(392\) −3.48219 1.39509i −0.175877 0.0704627i
\(393\) 2.56211 7.88538i 0.129242 0.397765i
\(394\) −0.0720255 + 0.685277i −0.00362859 + 0.0345237i
\(395\) −22.3350 + 38.6854i −1.12380 + 1.94647i
\(396\) 0.884624 6.51338i 0.0444540 0.327310i
\(397\) −4.19484 7.26567i −0.210533 0.364653i 0.741349 0.671120i \(-0.234187\pi\)
−0.951881 + 0.306467i \(0.900853\pi\)
\(398\) −1.49266 1.08448i −0.0748205 0.0543603i
\(399\) 4.38105 0.544414i 0.219327 0.0272548i
\(400\) 9.85336 + 30.3255i 0.492668 + 1.51628i
\(401\) 6.02561 + 2.68277i 0.300904 + 0.133971i 0.551635 0.834086i \(-0.314004\pi\)
−0.250731 + 0.968057i \(0.580671\pi\)
\(402\) 0.103682 + 0.986467i 0.00517118 + 0.0492005i
\(403\) 9.36142 + 1.98983i 0.466326 + 0.0991206i
\(404\) −12.5218 + 2.66160i −0.622984 + 0.132419i
\(405\) −2.93858 2.13500i −0.146019 0.106089i
\(406\) 1.29805 1.85957i 0.0644209 0.0922889i
\(407\) 6.66377 10.7751i 0.330311 0.534101i
\(408\) 1.20638 + 2.08952i 0.0597249 + 0.103447i
\(409\) 6.38320 2.84198i 0.315629 0.140527i −0.242807 0.970075i \(-0.578068\pi\)
0.558436 + 0.829548i \(0.311402\pi\)
\(410\) 0.939790 + 1.04374i 0.0464129 + 0.0515468i
\(411\) −1.03340 + 1.14771i −0.0509740 + 0.0566123i
\(412\) −27.5874 + 20.0434i −1.35913 + 0.987467i
\(413\) −22.6397 + 13.6483i −1.11403 + 0.671590i
\(414\) −0.289141 0.889885i −0.0142105 0.0437355i
\(415\) 31.9162 6.78400i 1.56671 0.333013i
\(416\) 2.58098 1.14913i 0.126543 0.0563406i
\(417\) 5.60781 9.71301i 0.274616 0.475648i
\(418\) 0.208613 + 0.714993i 0.0102036 + 0.0349714i
\(419\) −18.2877 −0.893412 −0.446706 0.894681i \(-0.647403\pi\)
−0.446706 + 0.894681i \(0.647403\pi\)
\(420\) 14.3925 + 12.4744i 0.702284 + 0.608690i
\(421\) 5.11386 15.7388i 0.249234 0.767064i −0.745677 0.666308i \(-0.767874\pi\)
0.994911 0.100756i \(-0.0321262\pi\)
\(422\) 0.226811 0.251899i 0.0110410 0.0122622i
\(423\) −0.221017 2.10284i −0.0107462 0.102243i
\(424\) 0.240210 + 2.28545i 0.0116656 + 0.110991i
\(425\) 24.6840 27.4144i 1.19735 1.32979i
\(426\) 0.355664 1.09462i 0.0172320 0.0530346i
\(427\) 11.0894 3.83649i 0.536654 0.185661i
\(428\) −10.5550 −0.510197
\(429\) 1.64491 + 5.63772i 0.0794172 + 0.272192i
\(430\) −3.12017 + 5.40429i −0.150468 + 0.260618i
\(431\) −24.5742 + 10.9412i −1.18370 + 0.527017i −0.901685 0.432394i \(-0.857669\pi\)
−0.282014 + 0.959410i \(0.591002\pi\)
\(432\) 3.80661 0.809120i 0.183146 0.0389288i
\(433\) −8.20422 25.2500i −0.394269 1.21344i −0.929529 0.368749i \(-0.879786\pi\)
0.535260 0.844688i \(-0.320214\pi\)
\(434\) 1.68460 + 0.930581i 0.0808635 + 0.0446693i
\(435\) −18.7156 + 13.5977i −0.897345 + 0.651959i
\(436\) −7.26286 + 8.06622i −0.347828 + 0.386302i
\(437\) −7.76258 8.62122i −0.371334 0.412409i
\(438\) −1.45607 + 0.648285i −0.0695738 + 0.0309763i
\(439\) 4.49707 + 7.78916i 0.214634 + 0.371756i 0.953159 0.302469i \(-0.0978110\pi\)
−0.738526 + 0.674225i \(0.764478\pi\)
\(440\) −3.39567 + 5.49068i −0.161882 + 0.261758i
\(441\) 6.89717 + 1.19542i 0.328437 + 0.0569247i
\(442\) −0.868025 0.630657i −0.0412877 0.0299973i
\(443\) 15.9468 3.38960i 0.757655 0.161045i 0.187142 0.982333i \(-0.440078\pi\)
0.570513 + 0.821288i \(0.306744\pi\)
\(444\) 7.40518 + 1.57402i 0.351434 + 0.0746997i
\(445\) −0.689374 6.55896i −0.0326795 0.310924i
\(446\) 1.64325 + 0.731623i 0.0778103 + 0.0346434i
\(447\) −1.58277 4.87127i −0.0748625 0.230403i
\(448\) −19.8717 + 2.46937i −0.938851 + 0.116667i
\(449\) −0.786378 0.571337i −0.0371115 0.0269631i 0.569075 0.822286i \(-0.307301\pi\)
−0.606186 + 0.795323i \(0.707301\pi\)
\(450\) 0.551350 + 0.954966i 0.0259909 + 0.0450175i
\(451\) 1.28242 9.44232i 0.0603869 0.444621i
\(452\) −8.93507 + 15.4760i −0.420270 + 0.727929i
\(453\) −0.297614 + 2.83161i −0.0139831 + 0.133041i
\(454\) −0.131526 + 0.404796i −0.00617283 + 0.0189980i
\(455\) −16.2804 4.95147i −0.763239 0.232129i
\(456\) −0.723424 + 0.525598i −0.0338774 + 0.0246134i
\(457\) −2.40188 1.06938i −0.112355 0.0500237i 0.349789 0.936828i \(-0.386253\pi\)
−0.462144 + 0.886805i \(0.652920\pi\)
\(458\) 0.702261 + 0.149270i 0.0328145 + 0.00697494i
\(459\) −3.01265 3.34588i −0.140618 0.156172i
\(460\) 5.23156 49.7750i 0.243923 2.32077i
\(461\) 40.9007 1.90494 0.952469 0.304637i \(-0.0985351\pi\)
0.952469 + 0.304637i \(0.0985351\pi\)
\(462\) −0.0134138 + 1.18088i −0.000624067 + 0.0549396i
\(463\) −14.1587 −0.658009 −0.329004 0.944328i \(-0.606713\pi\)
−0.329004 + 0.944328i \(0.606713\pi\)
\(464\) 2.59081 24.6499i 0.120275 1.14434i
\(465\) −13.1365 14.5896i −0.609191 0.676575i
\(466\) 2.57313 + 0.546936i 0.119198 + 0.0253363i
\(467\) −25.5734 11.3860i −1.18340 0.526881i −0.281804 0.959472i \(-0.590933\pi\)
−0.901591 + 0.432590i \(0.857600\pi\)
\(468\) −2.83913 + 2.06275i −0.131239 + 0.0953505i
\(469\) 4.41419 + 18.9935i 0.203828 + 0.877038i
\(470\) −0.319406 + 0.983029i −0.0147331 + 0.0453438i
\(471\) −0.640121 + 6.09034i −0.0294952 + 0.280628i
\(472\) 2.67723 4.63711i 0.123230 0.213440i
\(473\) 41.6608 7.54522i 1.91557 0.346930i
\(474\) −0.827553 1.43336i −0.0380108 0.0658366i
\(475\) 11.0607 + 8.03606i 0.507499 + 0.368720i
\(476\) 14.2353 + 18.8337i 0.652476 + 0.863241i
\(477\) −1.32514 4.07835i −0.0606738 0.186735i
\(478\) 0.744897 + 0.331649i 0.0340708 + 0.0151693i
\(479\) −4.05106 38.5433i −0.185098 1.76109i −0.554844 0.831955i \(-0.687222\pi\)
0.369746 0.929133i \(-0.379445\pi\)
\(480\) −5.66879 1.20494i −0.258744 0.0549977i
\(481\) −6.61614 + 1.40630i −0.301670 + 0.0641220i
\(482\) −2.26093 1.64266i −0.102983 0.0748213i
\(483\) −7.79815 16.6597i −0.354828 0.758042i
\(484\) 21.5595 3.23411i 0.979979 0.147005i
\(485\) −13.9667 24.1910i −0.634194 1.09846i
\(486\) 0.122947 0.0547397i 0.00557701 0.00248304i
\(487\) −1.02563 1.13908i −0.0464758 0.0516166i 0.719459 0.694535i \(-0.244390\pi\)
−0.765934 + 0.642919i \(0.777723\pi\)
\(488\) −1.59037 + 1.76628i −0.0719925 + 0.0799558i
\(489\) −12.8339 + 9.32437i −0.580368 + 0.421662i
\(490\) −2.84245 1.90522i −0.128409 0.0860688i
\(491\) 1.90964 + 5.87727i 0.0861808 + 0.265237i 0.984855 0.173379i \(-0.0554686\pi\)
−0.898674 + 0.438617i \(0.855469\pi\)
\(492\) 5.56974 1.18388i 0.251103 0.0533736i
\(493\) −26.1959 + 11.6632i −1.17981 + 0.525283i
\(494\) 0.198822 0.344370i 0.00894542 0.0154939i
\(495\) 4.06776 11.3394i 0.182832 0.509667i
\(496\) 21.0341 0.944458
\(497\) 4.28494 22.2171i 0.192206 0.996572i
\(498\) −0.373593 + 1.14980i −0.0167411 + 0.0515239i
\(499\) −9.78087 + 10.8628i −0.437852 + 0.486284i −0.921170 0.389161i \(-0.872765\pi\)
0.483318 + 0.875445i \(0.339432\pi\)
\(500\) 2.40301 + 22.8631i 0.107466 + 1.02247i
\(501\) 1.02750 + 9.77602i 0.0459053 + 0.436760i
\(502\) −0.648789 + 0.720553i −0.0289569 + 0.0321599i
\(503\) −5.92996 + 18.2505i −0.264404 + 0.813752i 0.727426 + 0.686186i \(0.240716\pi\)
−0.991830 + 0.127566i \(0.959284\pi\)
\(504\) −1.33992 + 0.463559i −0.0596848 + 0.0206486i
\(505\) −23.4619 −1.04404
\(506\) 2.56468 1.74725i 0.114014 0.0776748i
\(507\) −4.93229 + 8.54297i −0.219051 + 0.379407i
\(508\) 36.8830 16.4214i 1.63642 0.728581i
\(509\) −32.4744 + 6.90265i −1.43940 + 0.305955i −0.860504 0.509444i \(-0.829851\pi\)
−0.578900 + 0.815399i \(0.696518\pi\)
\(510\) 0.680124 + 2.09321i 0.0301164 + 0.0926888i
\(511\) −26.8347 + 16.1772i −1.18710 + 0.715639i
\(512\) 8.39783 6.10138i 0.371135 0.269646i
\(513\) 1.11652 1.24002i 0.0492957 0.0547484i
\(514\) −0.542694 0.602723i −0.0239372 0.0265850i
\(515\) −57.0930 + 25.4195i −2.51582 + 1.12011i
\(516\) 12.6499 + 21.9103i 0.556883 + 0.964549i
\(517\) 6.48985 2.65713i 0.285423 0.116861i
\(518\) −1.35516 0.116569i −0.0595422 0.00512175i
\(519\) −8.21764 5.97047i −0.360715 0.262074i
\(520\) 3.37140 0.716613i 0.147846 0.0314256i
\(521\) −28.2101 5.99624i −1.23591 0.262700i −0.456788 0.889576i \(-0.651000\pi\)
−0.779119 + 0.626876i \(0.784333\pi\)
\(522\) −0.0895964 0.852453i −0.00392153 0.0373108i
\(523\) 24.1977 + 10.7735i 1.05809 + 0.471093i 0.860637 0.509219i \(-0.170066\pi\)
0.197455 + 0.980312i \(0.436732\pi\)
\(524\) 5.07782 + 15.6279i 0.221826 + 0.682709i
\(525\) 13.0713 + 17.2937i 0.570479 + 0.754758i
\(526\) −0.723549 0.525689i −0.0315482 0.0229211i
\(527\) −12.1674 21.0745i −0.530019 0.918019i
\(528\) 6.11231 + 11.3681i 0.266004 + 0.494734i
\(529\) −12.6683 + 21.9422i −0.550796 + 0.954008i
\(530\) −0.219120 + 2.08479i −0.00951796 + 0.0905573i
\(531\) −3.08760 + 9.50264i −0.133990 + 0.412380i
\(532\) −6.39029 + 5.97650i −0.277054 + 0.259114i
\(533\) −4.11583 + 2.99032i −0.178276 + 0.129525i
\(534\) 0.223234 + 0.0993902i 0.00966028 + 0.00430103i
\(535\) −18.9219 4.02198i −0.818065 0.173885i
\(536\) −2.64282 2.93515i −0.114153 0.126779i
\(537\) 2.49421 23.7308i 0.107633 1.02406i
\(538\) 2.65856 0.114619
\(539\) 2.60110 + 23.0702i 0.112037 + 0.993704i
\(540\) 7.19877 0.309786
\(541\) 3.41352 32.4775i 0.146759 1.39632i −0.634893 0.772600i \(-0.718956\pi\)
0.781652 0.623715i \(-0.214377\pi\)
\(542\) −0.0263105 0.0292207i −0.00113013 0.00125514i
\(543\) 5.11396 + 1.08701i 0.219461 + 0.0466479i
\(544\) −6.56257 2.92184i −0.281368 0.125273i
\(545\) −16.0937 + 11.6927i −0.689377 + 0.500861i
\(546\) 0.460492 0.430673i 0.0197072 0.0184311i
\(547\) −1.11411 + 3.42887i −0.0476357 + 0.146608i −0.972045 0.234794i \(-0.924558\pi\)
0.924409 + 0.381402i \(0.124558\pi\)
\(548\) 0.319943 3.04405i 0.0136673 0.130035i
\(549\) 2.21757 3.84095i 0.0946437 0.163928i
\(550\) −2.52831 + 2.64255i −0.107807 + 0.112679i
\(551\) −5.31366 9.20352i −0.226369 0.392083i
\(552\) 3.01421 + 2.18995i 0.128293 + 0.0932107i
\(553\) −19.6195 25.9571i −0.834306 1.10381i
\(554\) 0.742714 + 2.28584i 0.0315549 + 0.0971160i
\(555\) 12.6754 + 5.64346i 0.538041 + 0.239551i
\(556\) 2.32347 + 22.1063i 0.0985370 + 0.937517i
\(557\) −11.6509 2.47648i −0.493666 0.104932i −0.0456502 0.998957i \(-0.514536\pi\)
−0.448016 + 0.894025i \(0.647869\pi\)
\(558\) 0.711513 0.151237i 0.0301208 0.00640237i
\(559\) −18.2871 13.2864i −0.773463 0.561953i
\(560\) −37.2616 3.20520i −1.57459 0.135445i
\(561\) 7.85425 12.7001i 0.331607 0.536197i
\(562\) 1.06565 + 1.84576i 0.0449518 + 0.0778588i
\(563\) 33.8481 15.0702i 1.42653 0.635131i 0.459125 0.888372i \(-0.348163\pi\)
0.967403 + 0.253240i \(0.0814963\pi\)
\(564\) 2.80402 + 3.11418i 0.118071 + 0.131131i
\(565\) −21.9149 + 24.3389i −0.921966 + 1.02395i
\(566\) 1.71250 1.24421i 0.0719819 0.0522979i
\(567\) 2.26586 1.36597i 0.0951572 0.0573653i
\(568\) 1.41622 + 4.35866i 0.0594231 + 0.182885i
\(569\) −31.2890 + 6.65068i −1.31170 + 0.278811i −0.810102 0.586288i \(-0.800589\pi\)
−0.501601 + 0.865099i \(0.667255\pi\)
\(570\) −0.745171 + 0.331771i −0.0312118 + 0.0138964i
\(571\) 12.6897 21.9792i 0.531047 0.919800i −0.468297 0.883571i \(-0.655132\pi\)
0.999344 0.0362289i \(-0.0115345\pi\)
\(572\) −9.20494 7.12322i −0.384878 0.297837i
\(573\) −12.8052 −0.534945
\(574\) −0.966809 + 0.334478i −0.0403538 + 0.0139608i
\(575\) 17.6031 54.1767i 0.734099 2.25932i
\(576\) −5.06436 + 5.62455i −0.211015 + 0.234356i
\(577\) 0.961625 + 9.14925i 0.0400330 + 0.380888i 0.996134 + 0.0878500i \(0.0279996\pi\)
−0.956101 + 0.293038i \(0.905334\pi\)
\(578\) 0.0460150 + 0.437804i 0.00191397 + 0.0182102i
\(579\) 5.12396 5.69074i 0.212945 0.236499i
\(580\) 14.1680 43.6045i 0.588293 1.81058i
\(581\) −4.50094 + 23.3370i −0.186730 + 0.968183i
\(582\) 1.03498 0.0429014
\(583\) 11.7540 8.00767i 0.486799 0.331644i
\(584\) 3.17331 5.49633i 0.131312 0.227440i
\(585\) −5.87568 + 2.61602i −0.242929 + 0.108159i
\(586\) −0.170760 + 0.0362961i −0.00705403 + 0.00149938i
\(587\) 10.8556 + 33.4102i 0.448060 + 1.37899i 0.879093 + 0.476650i \(0.158149\pi\)
−0.431034 + 0.902336i \(0.641851\pi\)
\(588\) −12.4514 + 6.11797i −0.513486 + 0.252301i
\(589\) 7.29632 5.30109i 0.300640 0.218427i
\(590\) 3.26827 3.62978i 0.134552 0.149436i
\(591\) 3.42589 + 3.80483i 0.140922 + 0.156510i
\(592\) −13.5805 + 6.04644i −0.558156 + 0.248507i
\(593\) 14.1710 + 24.5448i 0.581932 + 1.00793i 0.995250 + 0.0973486i \(0.0310362\pi\)
−0.413319 + 0.910586i \(0.635631\pi\)
\(594\) 0.288497 + 0.340598i 0.0118372 + 0.0139749i
\(595\) 18.3430 + 39.1873i 0.751989 + 1.60652i
\(596\) 8.21244 + 5.96669i 0.336395 + 0.244405i
\(597\) −13.4097 + 2.85032i −0.548823 + 0.116656i
\(598\) −1.62062 0.344472i −0.0662719 0.0140865i
\(599\) 1.45766 + 13.8687i 0.0595582 + 0.566659i 0.983088 + 0.183132i \(0.0586237\pi\)
−0.923530 + 0.383526i \(0.874710\pi\)
\(600\) −4.01122 1.78591i −0.163757 0.0729095i
\(601\) −11.9062 36.6434i −0.485662 1.49471i −0.831019 0.556243i \(-0.812242\pi\)
0.345357 0.938471i \(-0.387758\pi\)
\(602\) −2.74082 3.62617i −0.111707 0.147792i
\(603\) 5.96261 + 4.33209i 0.242816 + 0.176416i
\(604\) −2.82142 4.88685i −0.114802 0.198843i
\(605\) 39.8819 + 2.41747i 1.62143 + 0.0982839i
\(606\) 0.434654 0.752843i 0.0176566 0.0305821i
\(607\) −3.89130 + 37.0233i −0.157943 + 1.50273i 0.572585 + 0.819845i \(0.305941\pi\)
−0.730528 + 0.682883i \(0.760726\pi\)
\(608\) 0.822708 2.53203i 0.0333652 0.102688i
\(609\) −3.81451 16.4132i −0.154572 0.665096i
\(610\) −1.75402 + 1.27437i −0.0710182 + 0.0515977i
\(611\) −3.42034 1.52283i −0.138372 0.0616073i
\(612\) 8.72812 + 1.85522i 0.352813 + 0.0749928i
\(613\) −9.64411 10.7109i −0.389522 0.432608i 0.516208 0.856463i \(-0.327343\pi\)
−0.905730 + 0.423855i \(0.860677\pi\)
\(614\) 0.215186 2.04735i 0.00868419 0.0826245i
\(615\) 10.4359 0.420817
\(616\) −2.72064 3.83551i −0.109618 0.154537i
\(617\) −28.0965 −1.13112 −0.565562 0.824706i \(-0.691341\pi\)
−0.565562 + 0.824706i \(0.691341\pi\)
\(618\) 0.242046 2.30291i 0.00973650 0.0926366i
\(619\) 12.2489 + 13.6038i 0.492324 + 0.546781i 0.937192 0.348815i \(-0.113416\pi\)
−0.444867 + 0.895596i \(0.646749\pi\)
\(620\) 38.0586 + 8.08960i 1.52847 + 0.324886i
\(621\) −6.35138 2.82782i −0.254872 0.113476i
\(622\) −2.88500 + 2.09607i −0.115678 + 0.0840449i
\(623\) 4.59599 + 1.39781i 0.184135 + 0.0560020i
\(624\) 2.12944 6.55373i 0.0852457 0.262359i
\(625\) −0.121839 + 1.15922i −0.00487358 + 0.0463690i
\(626\) 0.539212 0.933942i 0.0215512 0.0373278i
\(627\) 4.98528 + 2.40294i 0.199093 + 0.0959642i
\(628\) −6.06843 10.5108i −0.242157 0.419428i
\(629\) 13.9138 + 10.1090i 0.554782 + 0.403072i
\(630\) −1.28348 + 0.159493i −0.0511352 + 0.00635435i
\(631\) 4.27754 + 13.1649i 0.170286 + 0.524087i 0.999387 0.0350126i \(-0.0111471\pi\)
−0.829101 + 0.559099i \(0.811147\pi\)
\(632\) 6.02067 + 2.68058i 0.239489 + 0.106628i
\(633\) −0.263268 2.50483i −0.0104640 0.0995580i
\(634\) 1.54646 + 0.328710i 0.0614178 + 0.0130548i
\(635\) 72.3771 15.3842i 2.87220 0.610505i
\(636\) 6.87567 + 4.99547i 0.272638 + 0.198083i
\(637\) 7.93961 9.51832i 0.314579 0.377129i
\(638\) 2.63087 1.07715i 0.104157 0.0426449i
\(639\) −4.27601 7.40627i −0.169156 0.292987i
\(640\) 13.9688 6.21929i 0.552164 0.245839i
\(641\) −9.73705 10.8141i −0.384590 0.427131i 0.519501 0.854470i \(-0.326118\pi\)
−0.904092 + 0.427339i \(0.859451\pi\)
\(642\) 0.479602 0.532652i 0.0189284 0.0210221i
\(643\) 37.5696 27.2959i 1.48160 1.07644i 0.504562 0.863376i \(-0.331654\pi\)
0.977037 0.213069i \(-0.0683459\pi\)
\(644\) 31.9107 + 17.6276i 1.25746 + 0.694624i
\(645\) 14.3285 + 44.0987i 0.564185 + 1.73638i
\(646\) −0.988980 + 0.210214i −0.0389109 + 0.00827077i
\(647\) 33.1864 14.7756i 1.30469 0.580887i 0.367606 0.929982i \(-0.380178\pi\)
0.937087 + 0.349095i \(0.113511\pi\)
\(648\) −0.267947 + 0.464097i −0.0105259 + 0.0182315i
\(649\) −33.1234 1.00298i −1.30021 0.0393703i
\(650\) 1.95256 0.0765859
\(651\) 13.5142 4.67537i 0.529663 0.183242i
\(652\) 9.71543 29.9010i 0.380486 1.17101i
\(653\) −2.69827 + 2.99674i −0.105592 + 0.117271i −0.793624 0.608409i \(-0.791808\pi\)
0.688032 + 0.725680i \(0.258475\pi\)
\(654\) −0.0770445 0.733029i −0.00301268 0.0286637i
\(655\) 3.14797 + 29.9509i 0.123001 + 1.17028i
\(656\) −7.48163 + 8.30919i −0.292109 + 0.324419i
\(657\) −3.65970 + 11.2634i −0.142779 + 0.439427i
\(658\) −0.568931 0.493109i −0.0221792 0.0192234i
\(659\) 6.28927 0.244995 0.122498 0.992469i \(-0.460910\pi\)
0.122498 + 0.992469i \(0.460910\pi\)
\(660\) 6.68734 + 22.9200i 0.260304 + 0.892159i
\(661\) 21.1068 36.5581i 0.820960 1.42194i −0.0840081 0.996465i \(-0.526772\pi\)
0.904968 0.425479i \(-0.139895\pi\)
\(662\) −1.24091 + 0.552490i −0.0482294 + 0.0214731i
\(663\) −7.79812 + 1.65754i −0.302854 + 0.0643735i
\(664\) −1.48761 4.57838i −0.0577303 0.177676i
\(665\) −13.7331 + 8.27899i −0.532548 + 0.321045i
\(666\) −0.415910 + 0.302176i −0.0161162 + 0.0117091i
\(667\) −29.6289 + 32.9062i −1.14724 + 1.27414i
\(668\) −13.0358 14.4777i −0.504370 0.560160i
\(669\) 12.2100 5.43624i 0.472065 0.210177i
\(670\) −1.80143 3.12017i −0.0695954 0.120543i
\(671\) 14.2891 + 3.49240i 0.551625 + 0.134823i
\(672\) 2.41624 3.46149i 0.0932086 0.133530i
\(673\) −27.3473 19.8690i −1.05416 0.765894i −0.0811631 0.996701i \(-0.525863\pi\)
−0.973000 + 0.230807i \(0.925863\pi\)
\(674\) −3.56103 + 0.756920i −0.137166 + 0.0291555i
\(675\) 8.01442 + 1.70352i 0.308475 + 0.0655685i
\(676\) −2.04358 19.4434i −0.0785993 0.747822i
\(677\) 34.4655 + 15.3450i 1.32462 + 0.589757i 0.942453 0.334337i \(-0.108513\pi\)
0.382163 + 0.924095i \(0.375179\pi\)
\(678\) −0.374991 1.15410i −0.0144014 0.0443230i
\(679\) 20.1913 2.50909i 0.774872 0.0962899i
\(680\) −7.09010 5.15126i −0.271893 0.197542i
\(681\) 1.58129 + 2.73887i 0.0605951 + 0.104954i
\(682\) 1.14248 + 2.12488i 0.0437479 + 0.0813657i
\(683\) −4.97965 + 8.62501i −0.190541 + 0.330027i −0.945430 0.325826i \(-0.894358\pi\)
0.754889 + 0.655853i \(0.227691\pi\)
\(684\) −0.345677 + 3.28890i −0.0132173 + 0.125754i
\(685\) 1.73349 5.33512i 0.0662331 0.203845i
\(686\) 2.08443 1.36665i 0.0795839 0.0521790i
\(687\) 4.31581 3.13562i 0.164659 0.119631i
\(688\) −45.3841 20.2063i −1.73025 0.770358i
\(689\) −7.42730 1.57872i −0.282957 0.0601445i
\(690\) 2.27414 + 2.52569i 0.0865752 + 0.0961515i
\(691\) 2.18744 20.8121i 0.0832140 0.791728i −0.870734 0.491755i \(-0.836356\pi\)
0.953948 0.299973i \(-0.0969778\pi\)
\(692\) 20.1312 0.765272
\(693\) 6.45396 + 5.94529i 0.245166 + 0.225843i
\(694\) 0.599685 0.0227637
\(695\) −4.25831 + 40.5151i −0.161527 + 1.53683i
\(696\) 2.28379 + 2.53640i 0.0865668 + 0.0961421i
\(697\) 12.6530 + 2.68947i 0.479266 + 0.101871i
\(698\) 0.782250 + 0.348280i 0.0296086 + 0.0131826i
\(699\) 15.8134 11.4891i 0.598119 0.434559i
\(700\) −41.1041 12.5013i −1.55359 0.472503i
\(701\) −13.9597 + 42.9636i −0.527251 + 1.62271i 0.232571 + 0.972580i \(0.425286\pi\)
−0.759821 + 0.650132i \(0.774714\pi\)
\(702\) 0.0249099 0.237002i 0.000940164 0.00894506i
\(703\) −3.18698 + 5.52001i −0.120199 + 0.208191i
\(704\) −22.6124 10.8993i −0.852237 0.410784i
\(705\) 3.84008 + 6.65122i 0.144626 + 0.250499i
\(706\) 1.30224 + 0.946135i 0.0490106 + 0.0356083i
\(707\) 6.65451 15.7408i 0.250268 0.591995i
\(708\) −6.11927 18.8332i −0.229976 0.707794i
\(709\) 10.4594 + 4.65684i 0.392812 + 0.174891i 0.593631 0.804737i \(-0.297694\pi\)
−0.200819 + 0.979628i \(0.564360\pi\)
\(710\) 0.436991 + 4.15769i 0.0164000 + 0.156035i
\(711\) −12.0293 2.55691i −0.451135 0.0958916i
\(712\) −0.951751 + 0.202301i −0.0356684 + 0.00758155i
\(713\) −30.4008 22.0875i −1.13852 0.827183i
\(714\) −1.59726 0.137394i −0.0597758 0.00514185i
\(715\) −13.7873 16.2772i −0.515616 0.608734i
\(716\) 23.6454 + 40.9551i 0.883671 + 1.53056i
\(717\) 5.53486 2.46428i 0.206703 0.0920302i
\(718\) −3.27231 3.63426i −0.122121 0.135630i
\(719\) 25.0465 27.8169i 0.934076 1.03740i −0.0651432 0.997876i \(-0.520750\pi\)
0.999219 0.0395201i \(-0.0125829\pi\)
\(720\) −11.4359 + 8.30869i −0.426192 + 0.309646i
\(721\) −0.860868 45.5140i −0.0320604 1.69503i
\(722\) 0.674385 + 2.07554i 0.0250980 + 0.0772437i
\(723\) −20.3116 + 4.31737i −0.755398 + 0.160565i
\(724\) −9.46590 + 4.21449i −0.351797 + 0.156630i
\(725\) 26.0918 45.1924i 0.969026 1.67840i
\(726\) −0.816420 + 1.23494i −0.0303002 + 0.0458328i
\(727\) 36.5013 1.35376 0.676879 0.736094i \(-0.263332\pi\)
0.676879 + 0.736094i \(0.263332\pi\)
\(728\) −0.475447 + 2.46516i −0.0176212 + 0.0913648i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 3.87385 4.30235i 0.143378 0.159237i
\(731\) 6.00774 + 57.1598i 0.222204 + 2.11413i
\(732\) 0.918801 + 8.74181i 0.0339599 + 0.323107i
\(733\) 13.9994 15.5479i 0.517078 0.574274i −0.426892 0.904302i \(-0.640392\pi\)
0.943971 + 0.330029i \(0.107058\pi\)
\(734\) −0.527401 + 1.62317i −0.0194667 + 0.0599124i
\(735\) −24.6527 + 6.22305i −0.909327 + 0.229541i
\(736\) −11.0929 −0.408889
\(737\) −8.25382 + 23.0085i −0.304033 + 0.847529i
\(738\) −0.193335 + 0.334866i −0.00711676 + 0.0123266i
\(739\) −43.2596 + 19.2604i −1.59133 + 0.708506i −0.995514 0.0946158i \(-0.969838\pi\)
−0.595816 + 0.803121i \(0.703171\pi\)
\(740\) −26.8977 + 5.71729i −0.988780 + 0.210172i
\(741\) −0.913035 2.81003i −0.0335412 0.103229i
\(742\) −1.33655 0.738317i −0.0490664 0.0271045i
\(743\) −7.86347 + 5.71314i −0.288483 + 0.209595i −0.722609 0.691257i \(-0.757057\pi\)
0.434126 + 0.900852i \(0.357057\pi\)
\(744\) −1.93811 + 2.15249i −0.0710546 + 0.0789141i
\(745\) 12.4488 + 13.8257i 0.456087 + 0.506536i
\(746\) 4.56401 2.03203i 0.167100 0.0743978i
\(747\) 4.49156 + 7.77961i 0.164338 + 0.284641i
\(748\) 2.20125 + 29.5126i 0.0804858 + 1.07909i
\(749\) 8.06520 11.5541i 0.294696 0.422179i
\(750\) −1.26296 0.917594i −0.0461168 0.0335058i
\(751\) −7.11640 + 1.51264i −0.259681 + 0.0551969i −0.335912 0.941893i \(-0.609045\pi\)
0.0762313 + 0.997090i \(0.475711\pi\)
\(752\) −8.04877 1.71082i −0.293509 0.0623872i
\(753\) 0.753074 + 7.16502i 0.0274436 + 0.261108i
\(754\) −1.38655 0.617330i −0.0504950 0.0224818i
\(755\) −3.19581 9.83570i −0.116308 0.357958i
\(756\) −2.04179 + 4.82973i −0.0742591 + 0.175655i
\(757\) −6.11513 4.44290i −0.222258 0.161480i 0.471084 0.882088i \(-0.343863\pi\)
−0.693343 + 0.720608i \(0.743863\pi\)
\(758\) 0.360664 + 0.624689i 0.0130999 + 0.0226897i
\(759\) 3.10326 22.8489i 0.112641 0.829363i
\(760\) 1.62399 2.81284i 0.0589085 0.102032i
\(761\) 1.36195 12.9581i 0.0493708 0.469732i −0.941706 0.336438i \(-0.890778\pi\)
0.991077 0.133294i \(-0.0425555\pi\)
\(762\) −0.847206 + 2.60743i −0.0306910 + 0.0944573i
\(763\) −3.28012 14.1138i −0.118748 0.510954i
\(764\) 20.5316 14.9171i 0.742807 0.539681i
\(765\) 14.9399 + 6.65166i 0.540152 + 0.240491i
\(766\) 4.55654 + 0.968522i 0.164634 + 0.0349941i
\(767\) 11.8385 + 13.1480i 0.427464 + 0.474747i
\(768\) 1.52304 14.4908i 0.0549581 0.522891i
\(769\) −12.0289 −0.433773 −0.216887 0.976197i \(-0.569590\pi\)
−0.216887 + 0.976197i \(0.569590\pi\)
\(770\) −1.70010 3.93829i −0.0612675 0.141926i
\(771\) −6.02636 −0.217034
\(772\) −1.58638 + 15.0934i −0.0570952 + 0.543225i
\(773\) 22.1140 + 24.5601i 0.795386 + 0.883365i 0.995339 0.0964402i \(-0.0307456\pi\)
−0.199953 + 0.979805i \(0.564079\pi\)
\(774\) −1.68048 0.357197i −0.0604036 0.0128392i
\(775\) 40.4564 + 18.0124i 1.45324 + 0.647023i
\(776\) −3.33410 + 2.42237i −0.119687 + 0.0869580i
\(777\) −7.38138 + 6.90340i −0.264805 + 0.247658i
\(778\) 0.890817 2.74165i 0.0319373 0.0982930i
\(779\) −0.501121 + 4.76785i −0.0179545 + 0.170826i
\(780\) 6.37348 11.0392i 0.228207 0.395266i
\(781\) 19.6084 20.4944i 0.701643 0.733346i
\(782\) 2.10637 + 3.64834i 0.0753236 + 0.130464i
\(783\) −5.15258 3.74357i −0.184138 0.133784i
\(784\) 12.7189 24.0901i 0.454247 0.860360i
\(785\) −6.87368 21.1550i −0.245332 0.755055i
\(786\) −1.01938 0.453857i −0.0363600 0.0161885i
\(787\) 4.36095 + 41.4916i 0.155451 + 1.47902i 0.742707 + 0.669616i \(0.233541\pi\)
−0.587256 + 0.809401i \(0.699792\pi\)
\(788\) −9.92535 2.10970i −0.353576 0.0751549i
\(789\) −6.50018 + 1.38166i −0.231412 + 0.0491882i
\(790\) 4.86366 + 3.53365i 0.173041 + 0.125722i
\(791\) −10.1135 21.6062i −0.359595 0.768226i
\(792\) −1.72654 0.421982i −0.0613498 0.0149945i
\(793\) −3.92669 6.80122i −0.139441 0.241518i
\(794\) −1.03149 + 0.459248i −0.0366062 + 0.0162981i
\(795\) 10.4224 + 11.5753i 0.369645 + 0.410533i
\(796\) 18.1805 20.1915i 0.644389 0.715667i
\(797\) −21.7513 + 15.8033i −0.770472 + 0.559781i −0.902104 0.431518i \(-0.857978\pi\)
0.131632 + 0.991299i \(0.457978\pi\)
\(798\) −0.0112359 0.594042i −0.000397748 0.0210289i
\(799\) 2.94178 + 9.05388i 0.104073 + 0.320303i
\(800\) 12.7873 2.71802i 0.452099 0.0960967i
\(801\) 1.65871 0.738506i 0.0586077 0.0260938i
\(802\) 0.443844 0.768760i 0.0156727 0.0271458i
\(803\) −39.2610 1.18882i −1.38549 0.0419526i
\(804\) −14.6069 −0.515145
\(805\) 50.4890 + 43.7602i 1.77950 + 1.54235i
\(806\) 0.398024 1.22499i 0.0140198 0.0431485i
\(807\) 13.2181 14.6801i 0.465298 0.516766i
\(808\) 0.361824 + 3.44252i 0.0127289 + 0.121108i
\(809\) −1.71522 16.3192i −0.0603039 0.573753i −0.982400 0.186791i \(-0.940191\pi\)
0.922096 0.386962i \(-0.126475\pi\)
\(810\) −0.327099 + 0.363281i −0.0114931 + 0.0127644i
\(811\) 0.0521602 0.160532i 0.00183159 0.00563706i −0.950137 0.311834i \(-0.899057\pi\)
0.951968 + 0.306197i \(0.0990567\pi\)
\(812\) 25.2362 + 21.8730i 0.885618 + 0.767591i
\(813\) −0.292165 −0.0102467
\(814\) −1.34845 1.04350i −0.0472632 0.0365745i
\(815\) 28.8105 49.9012i 1.00919 1.74796i
\(816\) −16.0067 + 7.12664i −0.560346 + 0.249482i
\(817\) −20.8353 + 4.42869i −0.728936 + 0.154940i
\(818\) −0.290589 0.894342i −0.0101602 0.0312699i
\(819\) −0.0885954 4.68403i −0.00309577 0.163673i
\(820\) −16.7328 + 12.1571i −0.584333 + 0.424543i
\(821\) −21.5708 + 23.9568i −0.752828 + 0.836100i −0.990823 0.135167i \(-0.956843\pi\)
0.237995 + 0.971266i \(0.423510\pi\)
\(822\) 0.139078 + 0.154462i 0.00485091 + 0.00538748i
\(823\) −4.28662 + 1.90853i −0.149422 + 0.0665270i −0.480085 0.877222i \(-0.659394\pi\)
0.330663 + 0.943749i \(0.392728\pi\)
\(824\) 4.61022 + 7.98513i 0.160605 + 0.278175i
\(825\) 2.02126 + 27.0994i 0.0703712 + 0.943480i
\(826\) 1.50828 + 3.22223i 0.0524796 + 0.112116i
\(827\) 6.12827 + 4.45245i 0.213101 + 0.154827i 0.689216 0.724556i \(-0.257955\pi\)
−0.476115 + 0.879383i \(0.657955\pi\)
\(828\) 13.4779 2.86481i 0.468389 0.0995591i
\(829\) −9.32423 1.98193i −0.323844 0.0688351i 0.0431213 0.999070i \(-0.486270\pi\)
−0.366965 + 0.930235i \(0.619603\pi\)
\(830\) −0.459019 4.36728i −0.0159328 0.151590i
\(831\) 16.3147 + 7.26379i 0.565952 + 0.251978i
\(832\) 4.14137 + 12.7458i 0.143576 + 0.441883i
\(833\) −31.4938 + 1.19180i −1.09119 + 0.0412933i
\(834\) −1.22115 0.887220i −0.0422851 0.0307219i
\(835\) −17.8524 30.9213i −0.617808 1.07008i
\(836\) −10.7925 + 1.95465i −0.373268 + 0.0676029i
\(837\) 2.70246 4.68080i 0.0934107 0.161792i
\(838\) −0.257266 + 2.44772i −0.00888711 + 0.0845552i
\(839\) −5.00569 + 15.4059i −0.172815 + 0.531871i −0.999527 0.0307548i \(-0.990209\pi\)
0.826711 + 0.562626i \(0.190209\pi\)
\(840\) 3.76134 3.51778i 0.129779 0.121375i
\(841\) −9.35492 + 6.79674i −0.322583 + 0.234370i
\(842\) −2.03463 0.905876i −0.0701180 0.0312185i
\(843\) 15.4903 + 3.29257i 0.533515 + 0.113402i
\(844\) 3.34005 + 3.70951i 0.114969 + 0.127686i
\(845\) 3.74535 35.6346i 0.128844 1.22587i
\(846\) −0.284564 −0.00978352
\(847\) −12.9336 + 26.0715i −0.444404 + 0.895827i
\(848\) −16.6883 −0.573079
\(849\) 1.64406 15.6422i 0.0564242 0.536840i
\(850\) −3.32204 3.68950i −0.113945 0.126549i
\(851\) 25.9774 + 5.52166i 0.890493 + 0.189280i
\(852\) 15.4838 + 6.89384i 0.530467 + 0.236179i
\(853\) 12.7711 9.27878i 0.437276 0.317699i −0.347276 0.937763i \(-0.612893\pi\)
0.784551 + 0.620064i \(0.212893\pi\)
\(854\) −0.357495 1.53824i −0.0122332 0.0526374i
\(855\) −1.87292 + 5.76425i −0.0640524 + 0.197133i
\(856\) −0.298328 + 2.83840i −0.0101966 + 0.0970145i
\(857\) 4.29969 7.44729i 0.146875 0.254395i −0.783196 0.621775i \(-0.786412\pi\)
0.930071 + 0.367380i \(0.119745\pi\)
\(858\) 0.777724 0.140854i 0.0265511 0.00480868i
\(859\) 0.209276 + 0.362477i 0.00714040 + 0.0123675i 0.869574 0.493803i \(-0.164394\pi\)
−0.862433 + 0.506171i \(0.831060\pi\)
\(860\) −74.3457 54.0153i −2.53517 1.84191i
\(861\) −2.95994 + 7.00156i −0.100874 + 0.238612i
\(862\) 1.11872 + 3.44307i 0.0381038 + 0.117271i
\(863\) 5.03131 + 2.24008i 0.171268 + 0.0762533i 0.490580 0.871396i \(-0.336785\pi\)
−0.319312 + 0.947650i \(0.603452\pi\)
\(864\) −0.166779 1.58680i −0.00567393 0.0539839i
\(865\) 36.0889 + 7.67093i 1.22706 + 0.260819i
\(866\) −3.49501 + 0.742887i −0.118765 + 0.0252443i
\(867\) 2.64626 + 1.92262i 0.0898719 + 0.0652957i
\(868\) −16.2219 + 23.2394i −0.550608 + 0.788797i
\(869\) −3.03382 40.6751i −0.102915 1.37981i
\(870\) 1.55670 + 2.69629i 0.0527771 + 0.0914127i
\(871\) 11.9222 5.30811i 0.403969 0.179859i
\(872\) 1.96384 + 2.18107i 0.0665041 + 0.0738603i
\(873\) 5.14581 5.71501i 0.174159 0.193424i
\(874\) −1.26311 + 0.917705i −0.0427254 + 0.0310418i
\(875\) −26.8634 14.8394i −0.908149 0.501665i
\(876\) −7.25312 22.3228i −0.245060 0.754218i
\(877\) 22.7636 4.83856i 0.768673 0.163387i 0.193147 0.981170i \(-0.438131\pi\)
0.575526 + 0.817783i \(0.304797\pi\)
\(878\) 1.10581 0.492337i 0.0373192 0.0166156i
\(879\) −0.648578 + 1.12337i −0.0218760 + 0.0378903i
\(880\) −37.0773 28.6921i −1.24987 0.967211i
\(881\) −19.0335 −0.641255 −0.320628 0.947205i \(-0.603894\pi\)
−0.320628 + 0.947205i \(0.603894\pi\)
\(882\) 0.257029 0.906338i 0.00865461 0.0305180i
\(883\) 11.4738 35.3128i 0.386124 1.18837i −0.549537 0.835469i \(-0.685196\pi\)
0.935661 0.352899i \(-0.114804\pi\)
\(884\) 10.5724 11.7419i 0.355590 0.394922i
\(885\) −3.79361 36.0937i −0.127521 1.21328i
\(886\) −0.229347 2.18209i −0.00770506 0.0733087i
\(887\) 8.09187 8.98693i 0.271698 0.301752i −0.591819 0.806071i \(-0.701590\pi\)
0.863517 + 0.504319i \(0.168257\pi\)
\(888\) 0.632577 1.94687i 0.0212279 0.0653327i
\(889\) −10.2069 + 52.9219i −0.342328 + 1.77494i
\(890\) −0.887585 −0.0297519
\(891\) 3.31511 + 0.100381i 0.111060 + 0.00336290i
\(892\) −13.2445 + 22.9401i −0.443457 + 0.768090i
\(893\) −3.22313 + 1.43503i −0.107858 + 0.0480215i
\(894\) −0.674263 + 0.143319i −0.0225507 + 0.00479331i
\(895\) 26.7830 + 82.4297i 0.895258 + 2.75532i
\(896\) 0.210626 + 11.1357i 0.00703651 + 0.372019i
\(897\) −9.95965 + 7.23611i −0.332543 + 0.241607i
\(898\) −0.0875335 + 0.0972158i −0.00292103 + 0.00324413i
\(899\) −23.0339 25.5817i −0.768223 0.853198i
\(900\) −14.8346 + 6.60481i −0.494488 + 0.220160i
\(901\) 9.65351 + 16.7204i 0.321605 + 0.557037i
\(902\) −1.24577 0.304478i −0.0414796 0.0101380i
\(903\) −33.6502 2.89455i −1.11981 0.0963247i
\(904\) 3.90917 + 2.84018i 0.130017 + 0.0944629i
\(905\) −18.5753 + 3.94831i −0.617465 + 0.131246i
\(906\) 0.374812 + 0.0796687i 0.0124523 + 0.00264681i
\(907\) −1.50354 14.3052i −0.0499241 0.474996i −0.990710 0.135994i \(-0.956577\pi\)
0.940786 0.339002i \(-0.110089\pi\)
\(908\) −5.72598 2.54937i −0.190023 0.0846039i
\(909\) −1.99603 6.14314i −0.0662041 0.203755i
\(910\) −0.891761 + 2.10941i −0.0295616 + 0.0699262i
\(911\) −24.4642 17.7743i −0.810536 0.588889i 0.103450 0.994635i \(-0.467012\pi\)
−0.913986 + 0.405746i \(0.867012\pi\)
\(912\) −3.24684 5.62369i −0.107514 0.186219i
\(913\) −20.5968 + 21.5275i −0.681656 + 0.712455i
\(914\) −0.176921 + 0.306436i −0.00585203 + 0.0101360i
\(915\) −1.68392 + 16.0215i −0.0556688 + 0.529653i
\(916\) −3.26713 + 10.0552i −0.107949 + 0.332233i
\(917\) −20.9872 6.38297i −0.693059 0.210784i
\(918\) −0.490212 + 0.356160i −0.0161794 + 0.0117550i
\(919\) −14.9745 6.66709i −0.493964 0.219927i 0.144608 0.989489i \(-0.453808\pi\)
−0.638572 + 0.769562i \(0.720475\pi\)
\(920\) −13.2373 2.81368i −0.436422 0.0927643i
\(921\) −10.2353 11.3674i −0.337264 0.374570i
\(922\) 0.575380 5.47438i 0.0189491 0.180289i
\(923\) −15.1432 −0.498444
\(924\) −17.2740 2.01419i −0.568272 0.0662619i
\(925\) −31.2983 −1.02908
\(926\) −0.199180 + 1.89507i −0.00654546 + 0.0622759i
\(927\) −11.5129 12.7864i −0.378133 0.419959i
\(928\) −9.93980 2.11277i −0.326290 0.0693551i
\(929\) −42.3546 18.8575i −1.38961 0.618694i −0.430723 0.902484i \(-0.641741\pi\)
−0.958886 + 0.283790i \(0.908408\pi\)
\(930\) −2.13755 + 1.55302i −0.0700930 + 0.0509255i
\(931\) −1.65933 11.5619i −0.0543823 0.378925i
\(932\) −11.9710 + 36.8429i −0.392123 + 1.20683i
\(933\) −2.76970 + 26.3520i −0.0906760 + 0.862725i
\(934\) −1.88372 + 3.26271i −0.0616373 + 0.106759i
\(935\) −7.29956 + 53.7457i −0.238721 + 1.75767i
\(936\) 0.474456 + 0.821783i 0.0155081 + 0.0268608i
\(937\) −14.1585 10.2868i −0.462539 0.336054i 0.331988 0.943284i \(-0.392281\pi\)
−0.794526 + 0.607230i \(0.792281\pi\)
\(938\) 2.60429 0.323624i 0.0850331 0.0105667i
\(939\) −2.47618 7.62090i −0.0808071 0.248699i
\(940\) −13.9053 6.19103i −0.453540 0.201929i
\(941\) −0.218401 2.07794i −0.00711966 0.0677391i 0.990385 0.138337i \(-0.0441758\pi\)
−0.997505 + 0.0705983i \(0.977509\pi\)
\(942\) 0.806160 + 0.171355i 0.0262661 + 0.00558303i
\(943\) 19.5386 4.15306i 0.636265 0.135242i
\(944\) 31.4579 + 22.8555i 1.02387 + 0.743883i
\(945\) −5.50065 + 7.88018i −0.178936 + 0.256342i
\(946\) −0.423821 5.68225i −0.0137796 0.184746i
\(947\) 6.45896 + 11.1873i 0.209888 + 0.363537i 0.951679 0.307094i \(-0.0993567\pi\)
−0.741791 + 0.670631i \(0.766023\pi\)
\(948\) 22.2662 9.91354i 0.723172 0.321977i
\(949\) 14.0321 + 15.5842i 0.455501 + 0.505885i
\(950\) 1.23119 1.36737i 0.0399451 0.0443635i
\(951\) 9.50392 6.90500i 0.308186 0.223910i
\(952\) 5.46700 3.29577i 0.177186 0.106816i
\(953\) −8.07001 24.8369i −0.261413 0.804547i −0.992498 0.122260i \(-0.960986\pi\)
0.731085 0.682287i \(-0.239014\pi\)
\(954\) −0.564510 + 0.119990i −0.0182767 + 0.00388483i
\(955\) 42.4909 18.9182i 1.37497 0.612177i
\(956\) −6.00379 + 10.3989i −0.194177 + 0.336324i
\(957\) 7.13252 19.8827i 0.230562 0.642718i
\(958\) −5.21583 −0.168516
\(959\) 3.08772 + 2.67621i 0.0997076 + 0.0864194i
\(960\) 8.49525 26.1457i 0.274183 0.843848i
\(961\) −1.19562 + 1.32787i −0.0385684 + 0.0428345i
\(962\) 0.0951534 + 0.905324i 0.00306787 + 0.0291888i
\(963\) −0.556693 5.29658i −0.0179392 0.170680i
\(964\) 27.5379 30.5839i 0.886935 0.985042i
\(965\) −8.59522 + 26.4534i −0.276690 + 0.851564i
\(966\) −2.33953 + 0.809383i −0.0752730 + 0.0260415i
\(967\) −47.6778 −1.53322 −0.766608 0.642116i \(-0.778057\pi\)
−0.766608 + 0.642116i \(0.778057\pi\)
\(968\) −0.260338 5.88907i −0.00836759 0.189282i
\(969\) −3.75633 + 6.50616i −0.120671 + 0.209008i
\(970\) −3.43433 + 1.52906i −0.110270 + 0.0490953i
\(971\) 16.2665 3.45754i 0.522015 0.110958i 0.0606346 0.998160i \(-0.480688\pi\)
0.461381 + 0.887202i \(0.347354\pi\)
\(972\) 0.612437 + 1.88489i 0.0196439 + 0.0604578i
\(973\) −25.9742 14.3482i −0.832695 0.459983i
\(974\) −0.166889 + 0.121252i −0.00534746 + 0.00388516i
\(975\) 9.70794 10.7818i 0.310903 0.345293i
\(976\) −11.5492 12.8267i −0.369682 0.410573i
\(977\) 51.4003 22.8849i 1.64444 0.732152i 0.644954 0.764221i \(-0.276876\pi\)
0.999486 + 0.0320696i \(0.0102098\pi\)
\(978\) 1.06748 + 1.84893i 0.0341343 + 0.0591223i
\(979\) 3.89218 + 4.59509i 0.124395 + 0.146860i
\(980\) 32.2782 38.6964i 1.03109 1.23611i
\(981\) −4.43073 3.21911i −0.141462 0.102778i
\(982\) 0.813510 0.172917i 0.0259601 0.00551800i
\(983\) −16.1416 3.43099i −0.514836 0.109432i −0.0568351 0.998384i \(-0.518101\pi\)
−0.458001 + 0.888952i \(0.651434\pi\)
\(984\) −0.160940 1.53124i −0.00513058 0.0488142i
\(985\) −16.9892 7.56406i −0.541320 0.241011i
\(986\) 1.19255 + 3.67028i 0.0379784 + 0.116886i
\(987\) −5.55153 + 0.689864i −0.176707 + 0.0219586i
\(988\) 4.73742 + 3.44193i 0.150717 + 0.109503i
\(989\) 44.3760 + 76.8614i 1.41107 + 2.44405i
\(990\) −1.46050 0.703971i −0.0464177 0.0223737i
\(991\) 10.8912 18.8641i 0.345970 0.599237i −0.639560 0.768741i \(-0.720883\pi\)
0.985529 + 0.169504i \(0.0542167\pi\)
\(992\) 0.901427 8.57650i 0.0286203 0.272304i
\(993\) −3.11892 + 9.59904i −0.0989759 + 0.304616i
\(994\) −2.91338 0.886063i −0.0924067 0.0281042i
\(995\) 40.2858 29.2694i 1.27715 0.927901i
\(996\) −16.2643 7.24135i −0.515355 0.229451i
\(997\) 42.9111 + 9.12105i 1.35901 + 0.288866i 0.829059 0.559162i \(-0.188877\pi\)
0.529951 + 0.848028i \(0.322210\pi\)
\(998\) 1.31634 + 1.46194i 0.0416679 + 0.0462769i
\(999\) −0.399289 + 3.79898i −0.0126329 + 0.120194i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 231.2.y.a.4.5 64
3.2 odd 2 693.2.by.d.235.4 64
7.2 even 3 inner 231.2.y.a.37.4 yes 64
11.3 even 5 inner 231.2.y.a.25.4 yes 64
21.2 odd 6 693.2.by.d.37.5 64
33.14 odd 10 693.2.by.d.487.5 64
77.58 even 15 inner 231.2.y.a.58.5 yes 64
231.212 odd 30 693.2.by.d.289.4 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.y.a.4.5 64 1.1 even 1 trivial
231.2.y.a.25.4 yes 64 11.3 even 5 inner
231.2.y.a.37.4 yes 64 7.2 even 3 inner
231.2.y.a.58.5 yes 64 77.58 even 15 inner
693.2.by.d.37.5 64 21.2 odd 6
693.2.by.d.235.4 64 3.2 odd 2
693.2.by.d.289.4 64 231.212 odd 30
693.2.by.d.487.5 64 33.14 odd 10