Properties

Label 201.2.f.b.38.13
Level $201$
Weight $2$
Character 201.38
Analytic conductor $1.605$
Analytic rank $0$
Dimension $40$
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] = [201,2,Mod(38,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.38");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 201.f (of order \(6\), 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: \(1.60499308063\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 38.13
Character \(\chi\) \(=\) 201.38
Dual form 201.2.f.b.164.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.451684 - 0.782339i) q^{2} +(1.52537 - 0.820518i) q^{3} +(0.591964 + 1.02531i) q^{4} -1.39831 q^{5} +(0.0470610 - 1.56397i) q^{6} +(-0.0330810 + 0.0190993i) q^{7} +2.87626 q^{8} +(1.65350 - 2.50319i) q^{9} +O(q^{10})\) \(q+(0.451684 - 0.782339i) q^{2} +(1.52537 - 0.820518i) q^{3} +(0.591964 + 1.02531i) q^{4} -1.39831 q^{5} +(0.0470610 - 1.56397i) q^{6} +(-0.0330810 + 0.0190993i) q^{7} +2.87626 q^{8} +(1.65350 - 2.50319i) q^{9} +(-0.631592 + 1.09395i) q^{10} +(-1.29549 - 2.24386i) q^{11} +(1.74425 + 1.07826i) q^{12} +(2.41874 + 1.39646i) q^{13} +0.0345074i q^{14} +(-2.13293 + 1.14733i) q^{15} +(0.115231 - 0.199587i) q^{16} +(-3.52178 - 2.03330i) q^{17} +(-1.21148 - 2.42425i) q^{18} +(-3.93032 + 6.80752i) q^{19} +(-0.827746 - 1.43370i) q^{20} +(-0.0347893 + 0.0562770i) q^{21} -2.34061 q^{22} +(0.808503 + 0.466790i) q^{23} +(4.38735 - 2.36002i) q^{24} -3.04474 q^{25} +(2.18501 - 1.26152i) q^{26} +(0.468290 - 5.17501i) q^{27} +(-0.0391654 - 0.0226122i) q^{28} +(-7.19016 + 4.15124i) q^{29} +(-0.0658056 + 2.18691i) q^{30} +(2.33927 - 1.35058i) q^{31} +(2.77216 + 4.80152i) q^{32} +(-3.81724 - 2.35974i) q^{33} +(-3.18146 + 1.83682i) q^{34} +(0.0462573 - 0.0267066i) q^{35} +(3.54536 + 0.213558i) q^{36} +(3.92654 - 6.80097i) q^{37} +(3.55053 + 6.14969i) q^{38} +(4.83529 + 0.145497i) q^{39} -4.02188 q^{40} +(2.99340 + 5.18472i) q^{41} +(0.0283139 + 0.0526365i) q^{42} -5.14670i q^{43} +(1.53377 - 2.65657i) q^{44} +(-2.31210 + 3.50022i) q^{45} +(0.730376 - 0.421683i) q^{46} +(-2.55852 + 1.47716i) q^{47} +(0.0120060 - 0.398992i) q^{48} +(-3.49927 + 6.06091i) q^{49} +(-1.37526 + 2.38202i) q^{50} +(-7.04037 - 0.211850i) q^{51} +3.30661i q^{52} +1.55464 q^{53} +(-3.83709 - 2.70383i) q^{54} +(1.81150 + 3.13760i) q^{55} +(-0.0951493 + 0.0549345i) q^{56} +(-0.409501 + 13.6089i) q^{57} +7.50019i q^{58} -0.806637i q^{59} +(-2.43899 - 1.50774i) q^{60} +(0.740086 + 0.427289i) q^{61} -2.44014i q^{62} +(-0.00689030 + 0.114388i) q^{63} +5.46948 q^{64} +(-3.38213 - 1.95268i) q^{65} +(-3.57030 + 1.92052i) q^{66} +(-7.49778 - 3.28379i) q^{67} -4.81456i q^{68} +(1.61627 + 0.0486348i) q^{69} -0.0482518i q^{70} +(3.83615 - 2.21480i) q^{71} +(4.75589 - 7.19980i) q^{72} +(2.27011 - 3.93195i) q^{73} +(-3.54711 - 6.14378i) q^{74} +(-4.64436 + 2.49827i) q^{75} -9.30643 q^{76} +(0.0857124 + 0.0494861i) q^{77} +(2.29785 - 3.71712i) q^{78} +(12.0321 - 6.94676i) q^{79} +(-0.161129 + 0.279083i) q^{80} +(-3.53187 - 8.27804i) q^{81} +5.40828 q^{82} +(10.8858 + 6.28490i) q^{83} +(-0.0782954 - 0.00235596i) q^{84} +(4.92452 + 2.84317i) q^{85} +(-4.02647 - 2.32468i) q^{86} +(-7.56148 + 12.2318i) q^{87} +(-3.72617 - 6.45392i) q^{88} -11.8892i q^{89} +(1.69402 + 3.38984i) q^{90} -0.106686 q^{91} +1.10529i q^{92} +(2.46008 - 3.97954i) q^{93} +2.66885i q^{94} +(5.49579 - 9.51899i) q^{95} +(8.16830 + 5.04949i) q^{96} +(1.73224 + 1.00011i) q^{97} +(3.16113 + 5.47523i) q^{98} +(-7.75890 - 0.467365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 24 q^{4} - 2 q^{6} - 6 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 24 q^{4} - 2 q^{6} - 6 q^{7} + 8 q^{9} - 6 q^{10} + 9 q^{12} - 6 q^{13} - 26 q^{15} - 36 q^{16} + 6 q^{18} - 6 q^{19} + 18 q^{21} + 52 q^{22} - 26 q^{24} + 40 q^{25} - 72 q^{28} + 57 q^{30} - 36 q^{31} + 8 q^{33} - 12 q^{34} + 2 q^{36} + 12 q^{37} + 11 q^{39} - 40 q^{40} + 30 q^{46} - 78 q^{48} - 6 q^{49} - 12 q^{51} + 20 q^{54} - 16 q^{55} + 80 q^{60} + 30 q^{61} + 24 q^{63} + 136 q^{64} + 4 q^{67} - 21 q^{69} - 16 q^{73} + 52 q^{76} - 42 q^{78} - 18 q^{79} - 24 q^{81} + 104 q^{82} + 15 q^{84} - 78 q^{85} - 21 q^{87} - 62 q^{88} - 110 q^{90} - 32 q^{91} - 13 q^{93} - 9 q^{96} - 90 q^{97} + 87 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.451684 0.782339i 0.319389 0.553197i −0.660972 0.750411i \(-0.729856\pi\)
0.980361 + 0.197213i \(0.0631891\pi\)
\(3\) 1.52537 0.820518i 0.880672 0.473726i
\(4\) 0.591964 + 1.02531i 0.295982 + 0.512655i
\(5\) −1.39831 −0.625341 −0.312671 0.949862i \(-0.601224\pi\)
−0.312671 + 0.949862i \(0.601224\pi\)
\(6\) 0.0470610 1.56397i 0.0192126 0.638488i
\(7\) −0.0330810 + 0.0190993i −0.0125034 + 0.00721886i −0.506239 0.862393i \(-0.668965\pi\)
0.493735 + 0.869612i \(0.335631\pi\)
\(8\) 2.87626 1.01691
\(9\) 1.65350 2.50319i 0.551167 0.834395i
\(10\) −0.631592 + 1.09395i −0.199727 + 0.345937i
\(11\) −1.29549 2.24386i −0.390606 0.676550i 0.601923 0.798554i \(-0.294401\pi\)
−0.992530 + 0.122004i \(0.961068\pi\)
\(12\) 1.74425 + 1.07826i 0.503521 + 0.311267i
\(13\) 2.41874 + 1.39646i 0.670837 + 0.387308i 0.796394 0.604778i \(-0.206738\pi\)
−0.125556 + 0.992086i \(0.540072\pi\)
\(14\) 0.0345074i 0.00922248i
\(15\) −2.13293 + 1.14733i −0.550720 + 0.296240i
\(16\) 0.115231 0.199587i 0.0288078 0.0498966i
\(17\) −3.52178 2.03330i −0.854157 0.493148i 0.00789456 0.999969i \(-0.497487\pi\)
−0.862051 + 0.506821i \(0.830820\pi\)
\(18\) −1.21148 2.42425i −0.285549 0.571400i
\(19\) −3.93032 + 6.80752i −0.901678 + 1.56175i −0.0763630 + 0.997080i \(0.524331\pi\)
−0.825315 + 0.564672i \(0.809003\pi\)
\(20\) −0.827746 1.43370i −0.185090 0.320584i
\(21\) −0.0347893 + 0.0562770i −0.00759166 + 0.0122806i
\(22\) −2.34061 −0.499021
\(23\) 0.808503 + 0.466790i 0.168585 + 0.0973323i 0.581918 0.813247i \(-0.302302\pi\)
−0.413334 + 0.910580i \(0.635636\pi\)
\(24\) 4.38735 2.36002i 0.895564 0.481737i
\(25\) −3.04474 −0.608949
\(26\) 2.18501 1.26152i 0.428516 0.247404i
\(27\) 0.468290 5.17501i 0.0901224 0.995931i
\(28\) −0.0391654 0.0226122i −0.00740157 0.00427330i
\(29\) −7.19016 + 4.15124i −1.33518 + 0.770866i −0.986088 0.166223i \(-0.946843\pi\)
−0.349091 + 0.937089i \(0.613509\pi\)
\(30\) −0.0658056 + 2.18691i −0.0120144 + 0.399273i
\(31\) 2.33927 1.35058i 0.420145 0.242571i −0.274994 0.961446i \(-0.588676\pi\)
0.695139 + 0.718875i \(0.255343\pi\)
\(32\) 2.77216 + 4.80152i 0.490053 + 0.848797i
\(33\) −3.81724 2.35974i −0.664495 0.410778i
\(34\) −3.18146 + 1.83682i −0.545616 + 0.315011i
\(35\) 0.0462573 0.0267066i 0.00781891 0.00451425i
\(36\) 3.54536 + 0.213558i 0.590893 + 0.0355930i
\(37\) 3.92654 6.80097i 0.645520 1.11807i −0.338661 0.940908i \(-0.609974\pi\)
0.984181 0.177165i \(-0.0566926\pi\)
\(38\) 3.55053 + 6.14969i 0.575972 + 0.997612i
\(39\) 4.83529 + 0.145497i 0.774266 + 0.0232982i
\(40\) −4.02188 −0.635916
\(41\) 2.99340 + 5.18472i 0.467490 + 0.809717i 0.999310 0.0371405i \(-0.0118249\pi\)
−0.531820 + 0.846858i \(0.678492\pi\)
\(42\) 0.0283139 + 0.0526365i 0.00436893 + 0.00812198i
\(43\) 5.14670i 0.784864i −0.919781 0.392432i \(-0.871634\pi\)
0.919781 0.392432i \(-0.128366\pi\)
\(44\) 1.53377 2.65657i 0.231225 0.400493i
\(45\) −2.31210 + 3.50022i −0.344667 + 0.521781i
\(46\) 0.730376 0.421683i 0.107688 0.0621737i
\(47\) −2.55852 + 1.47716i −0.373199 + 0.215467i −0.674855 0.737950i \(-0.735794\pi\)
0.301656 + 0.953417i \(0.402461\pi\)
\(48\) 0.0120060 0.398992i 0.00173291 0.0575896i
\(49\) −3.49927 + 6.06091i −0.499896 + 0.865845i
\(50\) −1.37526 + 2.38202i −0.194491 + 0.336869i
\(51\) −7.04037 0.211850i −0.985849 0.0296649i
\(52\) 3.30661i 0.458545i
\(53\) 1.55464 0.213547 0.106773 0.994283i \(-0.465948\pi\)
0.106773 + 0.994283i \(0.465948\pi\)
\(54\) −3.83709 2.70383i −0.522162 0.367944i
\(55\) 1.81150 + 3.13760i 0.244262 + 0.423074i
\(56\) −0.0951493 + 0.0549345i −0.0127149 + 0.00734093i
\(57\) −0.409501 + 13.6089i −0.0542397 + 1.80254i
\(58\) 7.50019i 0.984823i
\(59\) 0.806637i 0.105015i −0.998621 0.0525076i \(-0.983279\pi\)
0.998621 0.0525076i \(-0.0167214\pi\)
\(60\) −2.43899 1.50774i −0.314872 0.194648i
\(61\) 0.740086 + 0.427289i 0.0947583 + 0.0547087i 0.546630 0.837374i \(-0.315910\pi\)
−0.451872 + 0.892083i \(0.649244\pi\)
\(62\) 2.44014i 0.309898i
\(63\) −0.00689030 + 0.114388i −0.000868096 + 0.0144116i
\(64\) 5.46948 0.683686
\(65\) −3.38213 1.95268i −0.419502 0.242200i
\(66\) −3.57030 + 1.92052i −0.439474 + 0.236399i
\(67\) −7.49778 3.28379i −0.916000 0.401179i
\(68\) 4.81456i 0.583851i
\(69\) 1.61627 + 0.0486348i 0.194577 + 0.00585495i
\(70\) 0.0482518i 0.00576720i
\(71\) 3.83615 2.21480i 0.455267 0.262849i −0.254785 0.966998i \(-0.582005\pi\)
0.710052 + 0.704149i \(0.248671\pi\)
\(72\) 4.75589 7.19980i 0.560487 0.848505i
\(73\) 2.27011 3.93195i 0.265696 0.460200i −0.702049 0.712128i \(-0.747731\pi\)
0.967746 + 0.251929i \(0.0810648\pi\)
\(74\) −3.54711 6.14378i −0.412344 0.714200i
\(75\) −4.64436 + 2.49827i −0.536284 + 0.288475i
\(76\) −9.30643 −1.06752
\(77\) 0.0857124 + 0.0494861i 0.00976783 + 0.00563946i
\(78\) 2.29785 3.71712i 0.260180 0.420881i
\(79\) 12.0321 6.94676i 1.35372 0.781571i 0.364953 0.931026i \(-0.381085\pi\)
0.988769 + 0.149455i \(0.0477518\pi\)
\(80\) −0.161129 + 0.279083i −0.0180147 + 0.0312024i
\(81\) −3.53187 8.27804i −0.392430 0.919782i
\(82\) 5.40828 0.597245
\(83\) 10.8858 + 6.28490i 1.19487 + 0.689857i 0.959406 0.282027i \(-0.0910067\pi\)
0.235461 + 0.971884i \(0.424340\pi\)
\(84\) −0.0782954 0.00235596i −0.00854273 0.000257057i
\(85\) 4.92452 + 2.84317i 0.534139 + 0.308385i
\(86\) −4.02647 2.32468i −0.434185 0.250677i
\(87\) −7.56148 + 12.2318i −0.810675 + 1.31139i
\(88\) −3.72617 6.45392i −0.397211 0.687990i
\(89\) 11.8892i 1.26025i −0.776492 0.630127i \(-0.783003\pi\)
0.776492 0.630127i \(-0.216997\pi\)
\(90\) 1.69402 + 3.38984i 0.178565 + 0.357320i
\(91\) −0.106686 −0.0111837
\(92\) 1.10529i 0.115234i
\(93\) 2.46008 3.97954i 0.255098 0.412659i
\(94\) 2.66885i 0.275270i
\(95\) 5.49579 9.51899i 0.563856 0.976628i
\(96\) 8.16830 + 5.04949i 0.833674 + 0.515361i
\(97\) 1.73224 + 1.00011i 0.175882 + 0.101546i 0.585356 0.810776i \(-0.300955\pi\)
−0.409474 + 0.912322i \(0.634288\pi\)
\(98\) 3.16113 + 5.47523i 0.319322 + 0.553082i
\(99\) −7.75890 0.467365i −0.779799 0.0469719i
\(100\) −1.80238 3.12181i −0.180238 0.312181i
\(101\) −2.77358 4.80399i −0.275982 0.478015i 0.694400 0.719589i \(-0.255670\pi\)
−0.970382 + 0.241574i \(0.922336\pi\)
\(102\) −3.34576 + 5.41227i −0.331279 + 0.535894i
\(103\) 5.82671 + 10.0922i 0.574123 + 0.994410i 0.996136 + 0.0878202i \(0.0279901\pi\)
−0.422014 + 0.906589i \(0.638677\pi\)
\(104\) 6.95691 + 4.01658i 0.682181 + 0.393858i
\(105\) 0.0486461 0.0786924i 0.00474737 0.00767959i
\(106\) 0.702207 1.21626i 0.0682044 0.118133i
\(107\) 10.3453i 1.00012i 0.865991 + 0.500059i \(0.166688\pi\)
−0.865991 + 0.500059i \(0.833312\pi\)
\(108\) 5.58320 2.58327i 0.537244 0.248576i
\(109\) 17.2379i 1.65109i −0.564335 0.825546i \(-0.690868\pi\)
0.564335 0.825546i \(-0.309132\pi\)
\(110\) 3.27289 0.312058
\(111\) 0.409107 13.5958i 0.0388307 1.29046i
\(112\) 0.00880335i 0.000831838i
\(113\) −2.89488 5.01408i −0.272328 0.471685i 0.697130 0.716945i \(-0.254460\pi\)
−0.969457 + 0.245260i \(0.921127\pi\)
\(114\) 10.4618 + 6.46728i 0.979837 + 0.605716i
\(115\) −1.13053 0.652714i −0.105423 0.0608659i
\(116\) −8.51262 4.91476i −0.790377 0.456324i
\(117\) 7.49498 3.74550i 0.692911 0.346272i
\(118\) −0.631064 0.364345i −0.0580941 0.0335406i
\(119\) 0.155338 0.0142398
\(120\) −6.13486 + 3.30003i −0.560033 + 0.301250i
\(121\) 2.14339 3.71246i 0.194854 0.337496i
\(122\) 0.668569 0.385999i 0.0605294 0.0349467i
\(123\) 8.82019 + 5.45247i 0.795290 + 0.491633i
\(124\) 2.76952 + 1.59899i 0.248711 + 0.143593i
\(125\) 11.2490 1.00614
\(126\) 0.0863784 + 0.0570580i 0.00769520 + 0.00508313i
\(127\) −0.307606 0.532789i −0.0272956 0.0472774i 0.852055 0.523452i \(-0.175356\pi\)
−0.879351 + 0.476175i \(0.842023\pi\)
\(128\) −3.07384 + 5.32405i −0.271692 + 0.470584i
\(129\) −4.22296 7.85062i −0.371811 0.691208i
\(130\) −3.05531 + 1.76398i −0.267968 + 0.154712i
\(131\) 10.6024i 0.926338i 0.886270 + 0.463169i \(0.153288\pi\)
−0.886270 + 0.463169i \(0.846712\pi\)
\(132\) 0.159804 5.31073i 0.0139091 0.462240i
\(133\) 0.300266i 0.0260363i
\(134\) −5.95567 + 4.38257i −0.514491 + 0.378597i
\(135\) −0.654812 + 7.23624i −0.0563572 + 0.622796i
\(136\) −10.1295 5.84829i −0.868601 0.501487i
\(137\) −17.0170 −1.45386 −0.726930 0.686712i \(-0.759053\pi\)
−0.726930 + 0.686712i \(0.759053\pi\)
\(138\) 0.768094 1.24251i 0.0653845 0.105769i
\(139\) 0.541223i 0.0459059i −0.999737 0.0229530i \(-0.992693\pi\)
0.999737 0.0229530i \(-0.00730680\pi\)
\(140\) 0.0547652 + 0.0316187i 0.00462851 + 0.00267227i
\(141\) −2.69065 + 4.35254i −0.226594 + 0.366550i
\(142\) 4.00156i 0.335804i
\(143\) 7.23642i 0.605140i
\(144\) −0.309067 0.618462i −0.0257556 0.0515385i
\(145\) 10.0540 5.80470i 0.834942 0.482054i
\(146\) −2.05074 3.55199i −0.169721 0.293965i
\(147\) −0.364589 + 12.1163i −0.0300708 + 0.999339i
\(148\) 9.29748 0.764249
\(149\) 15.1214i 1.23880i −0.785077 0.619398i \(-0.787377\pi\)
0.785077 0.619398i \(-0.212623\pi\)
\(150\) −0.143289 + 4.76189i −0.0116995 + 0.388807i
\(151\) 2.66661 4.61871i 0.217006 0.375865i −0.736885 0.676018i \(-0.763704\pi\)
0.953891 + 0.300153i \(0.0970376\pi\)
\(152\) −11.3046 + 19.5802i −0.916926 + 1.58816i
\(153\) −10.9130 + 5.45360i −0.882263 + 0.440897i
\(154\) 0.0774298 0.0447041i 0.00623947 0.00360236i
\(155\) −3.27101 + 1.88852i −0.262734 + 0.151690i
\(156\) 2.71313 + 5.04380i 0.217225 + 0.403827i
\(157\) −6.10387 + 10.5722i −0.487142 + 0.843755i −0.999891 0.0147839i \(-0.995294\pi\)
0.512749 + 0.858539i \(0.328627\pi\)
\(158\) 12.5510i 0.998500i
\(159\) 2.37140 1.27561i 0.188065 0.101163i
\(160\) −3.87633 6.71399i −0.306450 0.530788i
\(161\) −0.0356614 −0.00281051
\(162\) −8.07152 0.975932i −0.634159 0.0766765i
\(163\) 5.96713 + 10.3354i 0.467381 + 0.809528i 0.999305 0.0372637i \(-0.0118642\pi\)
−0.531924 + 0.846792i \(0.678531\pi\)
\(164\) −3.54397 + 6.13833i −0.276737 + 0.479323i
\(165\) 5.33766 + 3.29964i 0.415536 + 0.256876i
\(166\) 9.83384 5.67757i 0.763254 0.440665i
\(167\) 13.0289 7.52226i 1.00821 0.582090i 0.0975425 0.995231i \(-0.468902\pi\)
0.910667 + 0.413141i \(0.135568\pi\)
\(168\) −0.100063 + 0.161867i −0.00772003 + 0.0124883i
\(169\) −2.59980 4.50299i −0.199985 0.346384i
\(170\) 4.44865 2.56843i 0.341196 0.196990i
\(171\) 10.5417 + 21.0946i 0.806143 + 1.61314i
\(172\) 5.27697 3.04666i 0.402365 0.232306i
\(173\) 6.84785 + 3.95361i 0.520632 + 0.300587i 0.737193 0.675682i \(-0.236151\pi\)
−0.216561 + 0.976269i \(0.569484\pi\)
\(174\) 6.15404 + 11.4406i 0.466537 + 0.867306i
\(175\) 0.100723 0.0581525i 0.00761394 0.00439591i
\(176\) −0.597126 −0.0450101
\(177\) −0.661860 1.23042i −0.0497484 0.0924839i
\(178\) −9.30140 5.37017i −0.697169 0.402511i
\(179\) −7.55455 −0.564654 −0.282327 0.959318i \(-0.591106\pi\)
−0.282327 + 0.959318i \(0.591106\pi\)
\(180\) −4.95749 0.298619i −0.369509 0.0222577i
\(181\) −7.59337 13.1521i −0.564410 0.977588i −0.997104 0.0760466i \(-0.975770\pi\)
0.432694 0.901541i \(-0.357563\pi\)
\(182\) −0.0481881 + 0.0834643i −0.00357194 + 0.00618679i
\(183\) 1.47950 + 0.0445192i 0.109368 + 0.00329096i
\(184\) 2.32546 + 1.34261i 0.171435 + 0.0989783i
\(185\) −5.49051 + 9.50984i −0.403670 + 0.699177i
\(186\) −2.00218 3.72211i −0.146807 0.272918i
\(187\) 10.5365i 0.770506i
\(188\) −3.02911 1.74886i −0.220920 0.127548i
\(189\) 0.0833475 + 0.180138i 0.00606264 + 0.0131031i
\(190\) −4.96472 8.59915i −0.360179 0.623848i
\(191\) −8.84424 + 15.3187i −0.639946 + 1.10842i 0.345498 + 0.938420i \(0.387710\pi\)
−0.985444 + 0.170000i \(0.945623\pi\)
\(192\) 8.34298 4.48781i 0.602103 0.323880i
\(193\) −8.30001 −0.597447 −0.298724 0.954340i \(-0.596561\pi\)
−0.298724 + 0.954340i \(0.596561\pi\)
\(194\) 1.56485 0.903465i 0.112350 0.0648650i
\(195\) −6.76121 0.203449i −0.484180 0.0145693i
\(196\) −8.28576 −0.591840
\(197\) 13.6596 + 23.6591i 0.973204 + 1.68564i 0.685738 + 0.727849i \(0.259480\pi\)
0.287467 + 0.957791i \(0.407187\pi\)
\(198\) −3.87021 + 5.85899i −0.275044 + 0.416380i
\(199\) 0.876101 1.51745i 0.0621051 0.107569i −0.833301 0.552819i \(-0.813552\pi\)
0.895406 + 0.445250i \(0.146885\pi\)
\(200\) −8.75746 −0.619246
\(201\) −14.1313 + 1.14307i −0.996744 + 0.0806258i
\(202\) −5.01113 −0.352582
\(203\) 0.158572 0.274654i 0.0111295 0.0192769i
\(204\) −3.95043 7.34397i −0.276585 0.514181i
\(205\) −4.18569 7.24982i −0.292341 0.506349i
\(206\) 10.5273 0.733473
\(207\) 2.50532 1.25200i 0.174132 0.0870198i
\(208\) 0.557429 0.321832i 0.0386507 0.0223150i
\(209\) 20.3668 1.40880
\(210\) −0.0395915 0.0736019i −0.00273207 0.00507901i
\(211\) −12.8164 + 22.1987i −0.882318 + 1.52822i −0.0335613 + 0.999437i \(0.510685\pi\)
−0.848757 + 0.528783i \(0.822648\pi\)
\(212\) 0.920292 + 1.59399i 0.0632059 + 0.109476i
\(213\) 4.03426 6.52602i 0.276423 0.447156i
\(214\) 8.09354 + 4.67281i 0.553263 + 0.319426i
\(215\) 7.19666i 0.490808i
\(216\) 1.34692 14.8846i 0.0916464 1.01277i
\(217\) −0.0515902 + 0.0893568i −0.00350217 + 0.00606594i
\(218\) −13.4859 7.78608i −0.913379 0.527340i
\(219\) 0.236523 7.86034i 0.0159827 0.531152i
\(220\) −2.14468 + 3.71469i −0.144594 + 0.250445i
\(221\) −5.67884 9.83604i −0.382000 0.661644i
\(222\) −10.4517 6.46106i −0.701475 0.433638i
\(223\) 21.5117 1.44053 0.720265 0.693699i \(-0.244020\pi\)
0.720265 + 0.693699i \(0.244020\pi\)
\(224\) −0.183411 0.105893i −0.0122547 0.00707525i
\(225\) −5.03448 + 7.62156i −0.335632 + 0.508104i
\(226\) −5.23029 −0.347913
\(227\) −4.51735 + 2.60809i −0.299827 + 0.173105i −0.642365 0.766399i \(-0.722047\pi\)
0.342538 + 0.939504i \(0.388713\pi\)
\(228\) −14.1957 + 7.63610i −0.940136 + 0.505713i
\(229\) 1.37057 + 0.791301i 0.0905701 + 0.0522907i 0.544601 0.838695i \(-0.316681\pi\)
−0.454031 + 0.890986i \(0.650014\pi\)
\(230\) −1.02129 + 0.589641i −0.0673417 + 0.0388798i
\(231\) 0.171347 + 0.00515596i 0.0112738 + 0.000339237i
\(232\) −20.6807 + 11.9400i −1.35776 + 0.783901i
\(233\) −5.89366 10.2081i −0.386106 0.668756i 0.605816 0.795605i \(-0.292847\pi\)
−0.991922 + 0.126849i \(0.959514\pi\)
\(234\) 0.455107 7.55540i 0.0297513 0.493912i
\(235\) 3.57760 2.06553i 0.233377 0.134740i
\(236\) 0.827053 0.477499i 0.0538366 0.0310826i
\(237\) 12.6535 20.4690i 0.821934 1.32960i
\(238\) 0.0701638 0.121527i 0.00454805 0.00787745i
\(239\) 8.14101 + 14.1006i 0.526598 + 0.912095i 0.999520 + 0.0309905i \(0.00986617\pi\)
−0.472921 + 0.881105i \(0.656801\pi\)
\(240\) −0.0167880 + 0.557913i −0.00108366 + 0.0360131i
\(241\) 27.0524 1.74260 0.871299 0.490752i \(-0.163278\pi\)
0.871299 + 0.490752i \(0.163278\pi\)
\(242\) −1.93627 3.35372i −0.124468 0.215585i
\(243\) −12.1797 9.72909i −0.781327 0.624122i
\(244\) 1.01176i 0.0647711i
\(245\) 4.89305 8.47501i 0.312605 0.541448i
\(246\) 8.24962 4.43759i 0.525977 0.282930i
\(247\) −19.0129 + 10.9771i −1.20976 + 0.698455i
\(248\) 6.72834 3.88461i 0.427250 0.246673i
\(249\) 21.7617 + 0.654824i 1.37909 + 0.0414978i
\(250\) 5.08099 8.80054i 0.321350 0.556595i
\(251\) −13.6659 + 23.6700i −0.862583 + 1.49404i 0.00684431 + 0.999977i \(0.497821\pi\)
−0.869427 + 0.494061i \(0.835512\pi\)
\(252\) −0.121363 + 0.0606491i −0.00764512 + 0.00382053i
\(253\) 2.41889i 0.152074i
\(254\) −0.555763 −0.0348716
\(255\) 9.84458 + 0.296230i 0.616492 + 0.0185507i
\(256\) 8.24629 + 14.2830i 0.515393 + 0.892688i
\(257\) −2.05183 + 1.18462i −0.127989 + 0.0738947i −0.562628 0.826710i \(-0.690210\pi\)
0.434638 + 0.900605i \(0.356876\pi\)
\(258\) −8.04929 0.242209i −0.501127 0.0150793i
\(259\) 0.299977i 0.0186397i
\(260\) 4.62365i 0.286747i
\(261\) −1.49761 + 24.8624i −0.0926996 + 1.53894i
\(262\) 8.29469 + 4.78894i 0.512448 + 0.295862i
\(263\) 26.7804i 1.65135i −0.564147 0.825674i \(-0.690795\pi\)
0.564147 0.825674i \(-0.309205\pi\)
\(264\) −10.9793 6.78722i −0.675732 0.417724i
\(265\) −2.17387 −0.133539
\(266\) −0.234910 0.135625i −0.0144032 0.00831571i
\(267\) −9.75532 18.1354i −0.597016 1.10987i
\(268\) −1.07150 9.63144i −0.0654525 0.588334i
\(269\) 18.4851i 1.12706i −0.826096 0.563530i \(-0.809443\pi\)
0.826096 0.563530i \(-0.190557\pi\)
\(270\) 5.36543 + 3.78078i 0.326529 + 0.230091i
\(271\) 8.92137i 0.541935i 0.962589 + 0.270967i \(0.0873435\pi\)
−0.962589 + 0.270967i \(0.912656\pi\)
\(272\) −0.811638 + 0.468600i −0.0492128 + 0.0284130i
\(273\) −0.162735 + 0.0875374i −0.00984916 + 0.00529801i
\(274\) −7.68630 + 13.3131i −0.464346 + 0.804271i
\(275\) 3.94445 + 6.83198i 0.237859 + 0.411984i
\(276\) 0.906910 + 1.68597i 0.0545896 + 0.101484i
\(277\) 7.51079 0.451280 0.225640 0.974211i \(-0.427553\pi\)
0.225640 + 0.974211i \(0.427553\pi\)
\(278\) −0.423420 0.244462i −0.0253950 0.0146618i
\(279\) 0.487237 8.08881i 0.0291701 0.484264i
\(280\) 0.133048 0.0768152i 0.00795112 0.00459058i
\(281\) 11.3324 19.6283i 0.676033 1.17092i −0.300132 0.953898i \(-0.597031\pi\)
0.976166 0.217026i \(-0.0696358\pi\)
\(282\) 2.18984 + 4.07097i 0.130403 + 0.242423i
\(283\) −6.14219 −0.365115 −0.182558 0.983195i \(-0.558438\pi\)
−0.182558 + 0.983195i \(0.558438\pi\)
\(284\) 4.54172 + 2.62216i 0.269502 + 0.155597i
\(285\) 0.572607 19.0294i 0.0339183 1.12720i
\(286\) −5.66134 3.26857i −0.334762 0.193275i
\(287\) −0.198049 0.114344i −0.0116905 0.00674949i
\(288\) 16.6029 + 1.00009i 0.978333 + 0.0589308i
\(289\) −0.231388 0.400775i −0.0136110 0.0235750i
\(290\) 10.4876i 0.615850i
\(291\) 3.46291 + 0.104201i 0.202999 + 0.00610839i
\(292\) 5.37529 0.314565
\(293\) 18.0740i 1.05589i 0.849278 + 0.527946i \(0.177038\pi\)
−0.849278 + 0.527946i \(0.822962\pi\)
\(294\) 9.31441 + 5.75799i 0.543228 + 0.335813i
\(295\) 1.12792i 0.0656703i
\(296\) 11.2937 19.5613i 0.656436 1.13698i
\(297\) −12.2187 + 5.65341i −0.708999 + 0.328044i
\(298\) −11.8301 6.83011i −0.685299 0.395658i
\(299\) 1.30371 + 2.25808i 0.0753952 + 0.130588i
\(300\) −5.31079 3.28303i −0.306619 0.189546i
\(301\) 0.0982984 + 0.170258i 0.00566582 + 0.00981350i
\(302\) −2.40893 4.17239i −0.138618 0.240094i
\(303\) −8.17250 5.05208i −0.469498 0.290234i
\(304\) 0.905793 + 1.56888i 0.0519508 + 0.0899814i
\(305\) −1.03487 0.597480i −0.0592562 0.0342116i
\(306\) −0.662653 + 11.0010i −0.0378814 + 0.628883i
\(307\) −0.200151 + 0.346671i −0.0114232 + 0.0197856i −0.871681 0.490075i \(-0.836970\pi\)
0.860257 + 0.509860i \(0.170303\pi\)
\(308\) 0.117176i 0.00667671i
\(309\) 17.1687 + 10.6133i 0.976692 + 0.603772i
\(310\) 3.41206i 0.193792i
\(311\) −11.3177 −0.641769 −0.320884 0.947118i \(-0.603980\pi\)
−0.320884 + 0.947118i \(0.603980\pi\)
\(312\) 13.9075 + 0.418487i 0.787359 + 0.0236922i
\(313\) 20.5986i 1.16430i 0.813080 + 0.582152i \(0.197789\pi\)
−0.813080 + 0.582152i \(0.802211\pi\)
\(314\) 5.51404 + 9.55060i 0.311175 + 0.538972i
\(315\) 0.00963474 0.159950i 0.000542856 0.00901216i
\(316\) 14.2452 + 8.22445i 0.801354 + 0.462662i
\(317\) 11.5110 + 6.64589i 0.646523 + 0.373270i 0.787123 0.616796i \(-0.211570\pi\)
−0.140600 + 0.990067i \(0.544903\pi\)
\(318\) 0.0731630 2.43142i 0.00410278 0.136347i
\(319\) 18.6296 + 10.7558i 1.04306 + 0.602210i
\(320\) −7.64801 −0.427537
\(321\) 8.48851 + 15.7804i 0.473782 + 0.880776i
\(322\) −0.0161077 + 0.0278993i −0.000897646 + 0.00155477i
\(323\) 27.6835 15.9831i 1.54035 0.889321i
\(324\) 6.39682 8.52156i 0.355379 0.473420i
\(325\) −7.36444 4.25186i −0.408506 0.235851i
\(326\) 10.7810 0.597105
\(327\) −14.1440 26.2942i −0.782165 1.45407i
\(328\) 8.60978 + 14.9126i 0.475396 + 0.823410i
\(329\) 0.0564256 0.0977320i 0.00311085 0.00538814i
\(330\) 4.99237 2.68547i 0.274821 0.147830i
\(331\) 28.3236 16.3526i 1.55681 0.898823i 0.559247 0.829001i \(-0.311090\pi\)
0.997559 0.0698218i \(-0.0222431\pi\)
\(332\) 14.8817i 0.816740i
\(333\) −10.5316 21.0743i −0.577126 1.15486i
\(334\) 13.5907i 0.743652i
\(335\) 10.4842 + 4.59174i 0.572812 + 0.250874i
\(336\) 0.00722331 + 0.0134284i 0.000394064 + 0.000732577i
\(337\) −1.52050 0.877864i −0.0828271 0.0478203i 0.458014 0.888945i \(-0.348561\pi\)
−0.540842 + 0.841124i \(0.681894\pi\)
\(338\) −4.69715 −0.255492
\(339\) −8.52991 5.27302i −0.463281 0.286391i
\(340\) 6.73222i 0.365106i
\(341\) −6.06102 3.49933i −0.328223 0.189499i
\(342\) 21.2646 + 1.28089i 1.14986 + 0.0692628i
\(343\) 0.534725i 0.0288724i
\(344\) 14.8032i 0.798137i
\(345\) −2.26005 0.0680063i −0.121677 0.00366134i
\(346\) 6.18613 3.57156i 0.332568 0.192008i
\(347\) 11.6692 + 20.2117i 0.626436 + 1.08502i 0.988261 + 0.152773i \(0.0488202\pi\)
−0.361826 + 0.932246i \(0.617846\pi\)
\(348\) −17.0175 0.512070i −0.912236 0.0274498i
\(349\) −28.4938 −1.52524 −0.762618 0.646849i \(-0.776087\pi\)
−0.762618 + 0.646849i \(0.776087\pi\)
\(350\) 0.105066i 0.00561602i
\(351\) 8.35936 11.8630i 0.446190 0.633202i
\(352\) 7.18263 12.4407i 0.382836 0.663091i
\(353\) −5.88530 + 10.1936i −0.313243 + 0.542553i −0.979062 0.203560i \(-0.934749\pi\)
0.665819 + 0.746113i \(0.268082\pi\)
\(354\) −1.26156 0.0379611i −0.0670509 0.00201761i
\(355\) −5.36411 + 3.09697i −0.284697 + 0.164370i
\(356\) 12.1901 7.03798i 0.646076 0.373012i
\(357\) 0.236948 0.127458i 0.0125406 0.00674579i
\(358\) −3.41227 + 5.91022i −0.180344 + 0.312365i
\(359\) 31.0668i 1.63965i −0.572617 0.819823i \(-0.694072\pi\)
0.572617 0.819823i \(-0.305928\pi\)
\(360\) −6.65019 + 10.0675i −0.350496 + 0.530605i
\(361\) −21.3949 37.0570i −1.12605 1.95037i
\(362\) −13.7192 −0.721065
\(363\) 0.223320 7.42156i 0.0117213 0.389531i
\(364\) −0.0631540 0.109386i −0.00331017 0.00573338i
\(365\) −3.17431 + 5.49806i −0.166151 + 0.287782i
\(366\) 0.703096 1.13736i 0.0367514 0.0594510i
\(367\) −29.5339 + 17.0514i −1.54166 + 0.890077i −0.542925 + 0.839781i \(0.682683\pi\)
−0.998734 + 0.0502958i \(0.983984\pi\)
\(368\) 0.186330 0.107578i 0.00971311 0.00560787i
\(369\) 17.9279 + 1.07990i 0.933289 + 0.0562176i
\(370\) 4.95995 + 8.59088i 0.257855 + 0.446618i
\(371\) −0.0514291 + 0.0296926i −0.00267007 + 0.00154156i
\(372\) 5.53654 + 0.166598i 0.287056 + 0.00863773i
\(373\) −20.8964 + 12.0645i −1.08198 + 0.624679i −0.931429 0.363924i \(-0.881437\pi\)
−0.150547 + 0.988603i \(0.548103\pi\)
\(374\) 8.24313 + 4.75917i 0.426242 + 0.246091i
\(375\) 17.1589 9.23001i 0.886081 0.476636i
\(376\) −7.35897 + 4.24870i −0.379510 + 0.219110i
\(377\) −23.1881 −1.19425
\(378\) 0.178576 + 0.0161595i 0.00918496 + 0.000831153i
\(379\) 4.45605 + 2.57270i 0.228892 + 0.132151i 0.610061 0.792355i \(-0.291145\pi\)
−0.381169 + 0.924505i \(0.624478\pi\)
\(380\) 13.0132 0.667565
\(381\) −0.906376 0.560304i −0.0464350 0.0287052i
\(382\) 7.98960 + 13.8384i 0.408783 + 0.708033i
\(383\) 10.5418 18.2590i 0.538663 0.932991i −0.460314 0.887756i \(-0.652263\pi\)
0.998976 0.0452350i \(-0.0144037\pi\)
\(384\) −0.320264 + 10.6433i −0.0163434 + 0.543138i
\(385\) −0.119852 0.0691966i −0.00610823 0.00352659i
\(386\) −3.74898 + 6.49342i −0.190818 + 0.330506i
\(387\) −12.8831 8.51007i −0.654887 0.432591i
\(388\) 2.36811i 0.120223i
\(389\) −15.7997 9.12198i −0.801078 0.462503i 0.0427700 0.999085i \(-0.486382\pi\)
−0.843848 + 0.536582i \(0.819715\pi\)
\(390\) −3.21309 + 5.19766i −0.162701 + 0.263194i
\(391\) −1.89825 3.28786i −0.0959984 0.166274i
\(392\) −10.0648 + 17.4327i −0.508349 + 0.880487i
\(393\) 8.69948 + 16.1726i 0.438831 + 0.815800i
\(394\) 24.6792 1.24332
\(395\) −16.8246 + 9.71369i −0.846537 + 0.488749i
\(396\) −4.11379 8.23195i −0.206726 0.413671i
\(397\) −4.06140 −0.203836 −0.101918 0.994793i \(-0.532498\pi\)
−0.101918 + 0.994793i \(0.532498\pi\)
\(398\) −0.791441 1.37082i −0.0396714 0.0687128i
\(399\) −0.246373 0.458016i −0.0123341 0.0229295i
\(400\) −0.350850 + 0.607690i −0.0175425 + 0.0303845i
\(401\) −30.5036 −1.52328 −0.761639 0.648002i \(-0.775605\pi\)
−0.761639 + 0.648002i \(0.775605\pi\)
\(402\) −5.48861 + 11.5718i −0.273747 + 0.577147i
\(403\) 7.54411 0.375799
\(404\) 3.28372 5.68757i 0.163371 0.282967i
\(405\) 4.93863 + 11.5752i 0.245403 + 0.575177i
\(406\) −0.143248 0.248113i −0.00710930 0.0123137i
\(407\) −20.3473 −1.00858
\(408\) −20.2499 0.609334i −1.00252 0.0301665i
\(409\) −26.1622 + 15.1048i −1.29364 + 0.746882i −0.979297 0.202428i \(-0.935117\pi\)
−0.314341 + 0.949310i \(0.601783\pi\)
\(410\) −7.56242 −0.373482
\(411\) −25.9572 + 13.9627i −1.28037 + 0.688731i
\(412\) −6.89840 + 11.9484i −0.339860 + 0.588654i
\(413\) 0.0154062 + 0.0266843i 0.000758089 + 0.00131305i
\(414\) 0.152127 2.52552i 0.00747663 0.124122i
\(415\) −15.2216 8.78820i −0.747200 0.431396i
\(416\) 15.4848i 0.759207i
\(417\) −0.444083 0.825565i −0.0217468 0.0404281i
\(418\) 9.19937 15.9338i 0.449956 0.779347i
\(419\) −13.7470 7.93685i −0.671586 0.387740i 0.125091 0.992145i \(-0.460078\pi\)
−0.796677 + 0.604405i \(0.793411\pi\)
\(420\) 0.109481 + 0.00329436i 0.00534212 + 0.000160748i
\(421\) 7.28096 12.6110i 0.354852 0.614622i −0.632240 0.774772i \(-0.717864\pi\)
0.987093 + 0.160150i \(0.0511978\pi\)
\(422\) 11.5779 + 20.0536i 0.563605 + 0.976192i
\(423\) −0.532904 + 8.84695i −0.0259107 + 0.430154i
\(424\) 4.47155 0.217158
\(425\) 10.7229 + 6.19087i 0.520137 + 0.300302i
\(426\) −3.28335 6.10386i −0.159079 0.295733i
\(427\) −0.0326437 −0.00157974
\(428\) −10.6072 + 6.12404i −0.512716 + 0.296017i
\(429\) −5.93761 11.0382i −0.286671 0.532930i
\(430\) 5.63023 + 3.25061i 0.271514 + 0.156758i
\(431\) −18.4101 + 10.6291i −0.886784 + 0.511985i −0.872889 0.487918i \(-0.837756\pi\)
−0.0138951 + 0.999903i \(0.504423\pi\)
\(432\) −0.978900 0.689787i −0.0470974 0.0331874i
\(433\) −13.2648 + 7.65845i −0.637467 + 0.368042i −0.783638 0.621218i \(-0.786638\pi\)
0.146171 + 0.989259i \(0.453305\pi\)
\(434\) 0.0466049 + 0.0807221i 0.00223711 + 0.00387478i
\(435\) 10.5733 17.1038i 0.506949 0.820066i
\(436\) 17.6742 10.2042i 0.846441 0.488693i
\(437\) −6.35536 + 3.66927i −0.304018 + 0.175525i
\(438\) −6.04262 3.73543i −0.288727 0.178486i
\(439\) −7.83752 + 13.5750i −0.374065 + 0.647899i −0.990187 0.139752i \(-0.955370\pi\)
0.616122 + 0.787651i \(0.288703\pi\)
\(440\) 5.21033 + 9.02455i 0.248393 + 0.430229i
\(441\) 9.38555 + 18.7810i 0.446931 + 0.894336i
\(442\) −10.2602 −0.488026
\(443\) 14.8735 + 25.7616i 0.706659 + 1.22397i 0.966089 + 0.258208i \(0.0831318\pi\)
−0.259430 + 0.965762i \(0.583535\pi\)
\(444\) 14.1821 7.62875i 0.673052 0.362045i
\(445\) 16.6248i 0.788089i
\(446\) 9.71649 16.8295i 0.460089 0.796898i
\(447\) −12.4074 23.0658i −0.586850 1.09097i
\(448\) −0.180936 + 0.104463i −0.00854841 + 0.00493543i
\(449\) 25.8126 14.9029i 1.21817 0.703311i 0.253645 0.967297i \(-0.418371\pi\)
0.964526 + 0.263986i \(0.0850373\pi\)
\(450\) 3.68865 + 7.38121i 0.173885 + 0.347953i
\(451\) 7.75586 13.4335i 0.365209 0.632561i
\(452\) 3.42733 5.93631i 0.161208 0.279220i
\(453\) 0.277835 9.23324i 0.0130538 0.433815i
\(454\) 4.71213i 0.221151i
\(455\) 0.149179 0.00699362
\(456\) −1.17783 + 39.1426i −0.0551569 + 1.83302i
\(457\) −19.1529 33.1737i −0.895933 1.55180i −0.832645 0.553806i \(-0.813175\pi\)
−0.0632876 0.997995i \(-0.520159\pi\)
\(458\) 1.23813 0.714836i 0.0578541 0.0334021i
\(459\) −12.1716 + 17.2731i −0.568119 + 0.806237i
\(460\) 1.54553i 0.0720608i
\(461\) 39.8562i 1.85629i 0.372223 + 0.928143i \(0.378596\pi\)
−0.372223 + 0.928143i \(0.621404\pi\)
\(462\) 0.0814285 0.131723i 0.00378839 0.00612830i
\(463\) 11.3415 + 6.54801i 0.527083 + 0.304312i 0.739828 0.672796i \(-0.234907\pi\)
−0.212745 + 0.977108i \(0.568240\pi\)
\(464\) 1.91341i 0.0888279i
\(465\) −3.43994 + 5.56461i −0.159523 + 0.258053i
\(466\) −10.6483 −0.493272
\(467\) −29.7743 17.1902i −1.37779 0.795469i −0.385899 0.922541i \(-0.626109\pi\)
−0.991893 + 0.127073i \(0.959442\pi\)
\(468\) 8.27706 + 5.46748i 0.382607 + 0.252735i
\(469\) 0.310752 0.0345714i 0.0143492 0.00159636i
\(470\) 3.73186i 0.172138i
\(471\) −0.635963 + 21.1349i −0.0293036 + 0.973844i
\(472\) 2.32009i 0.106791i
\(473\) −11.5485 + 6.66752i −0.531000 + 0.306573i
\(474\) −10.2983 19.1448i −0.473016 0.879351i
\(475\) 11.9668 20.7272i 0.549076 0.951027i
\(476\) 0.0919547 + 0.159270i 0.00421473 + 0.00730013i
\(477\) 2.57060 3.89156i 0.117700 0.178182i
\(478\) 14.7087 0.672758
\(479\) 30.8832 + 17.8305i 1.41109 + 0.814694i 0.995491 0.0948533i \(-0.0302382\pi\)
0.415600 + 0.909547i \(0.363572\pi\)
\(480\) −11.4218 7.06072i −0.521330 0.322276i
\(481\) 18.9946 10.9665i 0.866078 0.500030i
\(482\) 12.2191 21.1642i 0.556566 0.964001i
\(483\) −0.0543968 + 0.0292608i −0.00247514 + 0.00133141i
\(484\) 5.07523 0.230692
\(485\) −2.42220 1.39846i −0.109986 0.0635006i
\(486\) −13.1128 + 5.13417i −0.594810 + 0.232891i
\(487\) 7.01892 + 4.05238i 0.318058 + 0.183631i 0.650527 0.759484i \(-0.274548\pi\)
−0.332469 + 0.943114i \(0.607882\pi\)
\(488\) 2.12868 + 1.22899i 0.0963607 + 0.0556338i
\(489\) 17.5824 + 10.8691i 0.795105 + 0.491518i
\(490\) −4.42022 7.65605i −0.199685 0.345865i
\(491\) 2.28622i 0.103176i 0.998668 + 0.0515879i \(0.0164282\pi\)
−0.998668 + 0.0515879i \(0.983572\pi\)
\(492\) −0.369246 + 12.2711i −0.0166469 + 0.553224i
\(493\) 33.7628 1.52060
\(494\) 19.8327i 0.892314i
\(495\) 10.8493 + 0.653518i 0.487640 + 0.0293735i
\(496\) 0.622516i 0.0279518i
\(497\) −0.0846024 + 0.146536i −0.00379493 + 0.00657302i
\(498\) 10.3417 16.7292i 0.463422 0.749655i
\(499\) −19.4102 11.2065i −0.868918 0.501670i −0.00192943 0.999998i \(-0.500614\pi\)
−0.866989 + 0.498328i \(0.833947\pi\)
\(500\) 6.65900 + 11.5337i 0.297800 + 0.515804i
\(501\) 13.7018 22.1647i 0.612151 0.990246i
\(502\) 12.3453 + 21.3827i 0.550998 + 0.954357i
\(503\) 2.75883 + 4.77844i 0.123010 + 0.213060i 0.920953 0.389673i \(-0.127412\pi\)
−0.797943 + 0.602733i \(0.794078\pi\)
\(504\) −0.0198183 + 0.329011i −0.000882775 + 0.0146553i
\(505\) 3.87832 + 6.71744i 0.172583 + 0.298922i
\(506\) −1.89239 1.09257i −0.0841272 0.0485709i
\(507\) −7.66044 4.73554i −0.340212 0.210313i
\(508\) 0.364183 0.630784i 0.0161580 0.0279865i
\(509\) 14.3702i 0.636950i −0.947931 0.318475i \(-0.896829\pi\)
0.947931 0.318475i \(-0.103171\pi\)
\(510\) 4.67839 7.56800i 0.207163 0.335117i
\(511\) 0.173430i 0.00767210i
\(512\) 2.60350 0.115059
\(513\) 33.3884 + 23.5273i 1.47414 + 1.03876i
\(514\) 2.14030i 0.0944045i
\(515\) −8.14752 14.1119i −0.359022 0.621845i
\(516\) 5.54948 8.97713i 0.244302 0.395196i
\(517\) 6.62911 + 3.82732i 0.291548 + 0.168325i
\(518\) 0.234684 + 0.135495i 0.0103114 + 0.00595330i
\(519\) 13.6895 + 0.411927i 0.600903 + 0.0180816i
\(520\) −9.72789 5.61640i −0.426596 0.246295i
\(521\) −1.22430 −0.0536376 −0.0268188 0.999640i \(-0.508538\pi\)
−0.0268188 + 0.999640i \(0.508538\pi\)
\(522\) 18.7744 + 12.4016i 0.821732 + 0.542802i
\(523\) 6.27415 10.8672i 0.274350 0.475187i −0.695621 0.718409i \(-0.744871\pi\)
0.969971 + 0.243221i \(0.0782041\pi\)
\(524\) −10.8708 + 6.27625i −0.474892 + 0.274179i
\(525\) 0.105925 0.171349i 0.00462293 0.00747828i
\(526\) −20.9513 12.0963i −0.913522 0.527422i
\(527\) −10.9845 −0.478493
\(528\) −0.910838 + 0.489953i −0.0396391 + 0.0213225i
\(529\) −11.0642 19.1638i −0.481053 0.833208i
\(530\) −0.981900 + 1.70070i −0.0426510 + 0.0738737i
\(531\) −2.01916 1.33377i −0.0876241 0.0578809i
\(532\) 0.307866 0.177746i 0.0133477 0.00770628i
\(533\) 16.7206i 0.724251i
\(534\) −18.5944 0.559518i −0.804658 0.0242127i
\(535\) 14.4659i 0.625415i
\(536\) −21.5655 9.44503i −0.931489 0.407963i
\(537\) −11.5235 + 6.19865i −0.497275 + 0.267491i
\(538\) −14.4617 8.34944i −0.623486 0.359970i
\(539\) 18.1331 0.781050
\(540\) −7.80702 + 3.61220i −0.335961 + 0.155444i
\(541\) 21.9246i 0.942611i 0.881970 + 0.471305i \(0.156217\pi\)
−0.881970 + 0.471305i \(0.843783\pi\)
\(542\) 6.97954 + 4.02964i 0.299797 + 0.173088i
\(543\) −22.3742 13.8313i −0.960169 0.593558i
\(544\) 22.5465i 0.966674i
\(545\) 24.1038i 1.03249i
\(546\) −0.00502073 + 0.166853i −0.000214867 + 0.00714065i
\(547\) 15.6930 9.06037i 0.670985 0.387393i −0.125465 0.992098i \(-0.540042\pi\)
0.796450 + 0.604705i \(0.206709\pi\)
\(548\) −10.0734 17.4477i −0.430316 0.745329i
\(549\) 2.29331 1.14605i 0.0978763 0.0489122i
\(550\) 7.12657 0.303878
\(551\) 65.2629i 2.78029i
\(552\) 4.64882 + 0.139886i 0.197867 + 0.00595396i
\(553\) −0.265356 + 0.459611i −0.0112841 + 0.0195446i
\(554\) 3.39250 5.87598i 0.144134 0.249647i
\(555\) −0.572056 + 19.0111i −0.0242824 + 0.806975i
\(556\) 0.554922 0.320384i 0.0235339 0.0135873i
\(557\) −10.0084 + 5.77838i −0.424071 + 0.244838i −0.696818 0.717248i \(-0.745401\pi\)
0.272746 + 0.962086i \(0.412068\pi\)
\(558\) −6.10811 4.03477i −0.258577 0.170805i
\(559\) 7.18716 12.4485i 0.303984 0.526516i
\(560\) 0.0123098i 0.000520183i
\(561\) 8.64540 + 16.0721i 0.365009 + 0.678563i
\(562\) −10.2373 17.7315i −0.431835 0.747960i
\(563\) 3.96740 0.167206 0.0836030 0.996499i \(-0.473357\pi\)
0.0836030 + 0.996499i \(0.473357\pi\)
\(564\) −6.05547 0.182213i −0.254981 0.00767257i
\(565\) 4.04793 + 7.01122i 0.170298 + 0.294964i
\(566\) −2.77433 + 4.80527i −0.116614 + 0.201981i
\(567\) 0.274942 + 0.206389i 0.0115465 + 0.00866753i
\(568\) 11.0338 6.37034i 0.462966 0.267294i
\(569\) 19.4014 11.2014i 0.813348 0.469587i −0.0347690 0.999395i \(-0.511070\pi\)
0.848117 + 0.529809i \(0.177736\pi\)
\(570\) −14.6288 9.04323i −0.612732 0.378779i
\(571\) 3.33593 + 5.77799i 0.139604 + 0.241802i 0.927347 0.374203i \(-0.122084\pi\)
−0.787743 + 0.616004i \(0.788750\pi\)
\(572\) 7.41958 4.28370i 0.310228 0.179110i
\(573\) −0.921482 + 30.6235i −0.0384955 + 1.27931i
\(574\) −0.178911 + 0.103294i −0.00746760 + 0.00431142i
\(575\) −2.46168 1.42125i −0.102659 0.0592704i
\(576\) 9.04380 13.6911i 0.376825 0.570464i
\(577\) −11.0405 + 6.37424i −0.459622 + 0.265363i −0.711885 0.702296i \(-0.752158\pi\)
0.252263 + 0.967659i \(0.418825\pi\)
\(578\) −0.418056 −0.0173888
\(579\) −12.6606 + 6.81030i −0.526155 + 0.283027i
\(580\) 11.9032 + 6.87234i 0.494255 + 0.285358i
\(581\) −0.480148 −0.0199199
\(582\) 1.64566 2.66210i 0.0682148 0.110348i
\(583\) −2.01403 3.48840i −0.0834127 0.144475i
\(584\) 6.52942 11.3093i 0.270189 0.467982i
\(585\) −10.4803 + 5.23736i −0.433306 + 0.216538i
\(586\) 14.1400 + 8.16371i 0.584117 + 0.337240i
\(587\) 8.81159 15.2621i 0.363693 0.629935i −0.624872 0.780727i \(-0.714849\pi\)
0.988566 + 0.150792i \(0.0481823\pi\)
\(588\) −12.6388 + 6.79862i −0.521217 + 0.280370i
\(589\) 21.2328i 0.874884i
\(590\) 0.882419 + 0.509465i 0.0363286 + 0.0209743i
\(591\) 40.2486 + 24.8809i 1.65561 + 1.02346i
\(592\) −0.904922 1.56737i −0.0371921 0.0644185i
\(593\) 11.7540 20.3585i 0.482679 0.836025i −0.517123 0.855911i \(-0.672997\pi\)
0.999802 + 0.0198864i \(0.00633044\pi\)
\(594\) −1.09609 + 12.1127i −0.0449730 + 0.496990i
\(595\) −0.217210 −0.00890476
\(596\) 15.5042 8.95134i 0.635076 0.366661i
\(597\) 0.0912810 3.03353i 0.00373588 0.124154i
\(598\) 2.35545 0.0963215
\(599\) 7.01169 + 12.1446i 0.286490 + 0.496215i 0.972969 0.230934i \(-0.0741781\pi\)
−0.686479 + 0.727149i \(0.740845\pi\)
\(600\) −13.3584 + 7.18565i −0.545353 + 0.293353i
\(601\) 11.1482 19.3093i 0.454745 0.787641i −0.543929 0.839131i \(-0.683064\pi\)
0.998673 + 0.0514904i \(0.0163972\pi\)
\(602\) 0.177599 0.00723840
\(603\) −20.6175 + 13.3386i −0.839610 + 0.543189i
\(604\) 6.31415 0.256919
\(605\) −2.99711 + 5.19115i −0.121850 + 0.211050i
\(606\) −7.64382 + 4.11172i −0.310509 + 0.167027i
\(607\) 3.78471 + 6.55531i 0.153617 + 0.266072i 0.932554 0.361029i \(-0.117575\pi\)
−0.778938 + 0.627101i \(0.784241\pi\)
\(608\) −43.5820 −1.76748
\(609\) 0.0165216 0.549059i 0.000669488 0.0222490i
\(610\) −0.934864 + 0.539744i −0.0378515 + 0.0218536i
\(611\) −8.25120 −0.333808
\(612\) −12.0517 7.96087i −0.487162 0.321799i
\(613\) −7.40363 + 12.8235i −0.299030 + 0.517935i −0.975914 0.218154i \(-0.929996\pi\)
0.676884 + 0.736089i \(0.263330\pi\)
\(614\) 0.180810 + 0.313172i 0.00729689 + 0.0126386i
\(615\) −12.3333 7.62422i −0.497328 0.307438i
\(616\) 0.246531 + 0.142335i 0.00993301 + 0.00573482i
\(617\) 30.6753i 1.23494i −0.786593 0.617472i \(-0.788157\pi\)
0.786593 0.617472i \(-0.211843\pi\)
\(618\) 16.0580 8.63786i 0.645949 0.347466i
\(619\) −8.15334 + 14.1220i −0.327710 + 0.567611i −0.982057 0.188584i \(-0.939610\pi\)
0.654347 + 0.756195i \(0.272944\pi\)
\(620\) −3.87264 2.23587i −0.155529 0.0897947i
\(621\) 2.79425 3.96542i 0.112130 0.159127i
\(622\) −5.11203 + 8.85429i −0.204974 + 0.355025i
\(623\) 0.227076 + 0.393307i 0.00909760 + 0.0157575i
\(624\) 0.586216 0.948293i 0.0234674 0.0379621i
\(625\) −0.505824 −0.0202329
\(626\) 16.1151 + 9.30407i 0.644090 + 0.371866i
\(627\) 31.0670 16.7114i 1.24069 0.667388i
\(628\) −14.4531 −0.576741
\(629\) −27.6568 + 15.9677i −1.10275 + 0.636673i
\(630\) −0.120783 0.0797844i −0.00481212 0.00317869i
\(631\) 9.11568 + 5.26294i 0.362890 + 0.209514i 0.670348 0.742047i \(-0.266145\pi\)
−0.307458 + 0.951562i \(0.599478\pi\)
\(632\) 34.6075 19.9807i 1.37661 0.794788i
\(633\) −1.33534 + 44.3773i −0.0530751 + 1.76384i
\(634\) 10.3987 6.00368i 0.412984 0.238437i
\(635\) 0.430127 + 0.745002i 0.0170691 + 0.0295645i
\(636\) 2.71168 + 1.67631i 0.107525 + 0.0664700i
\(637\) −16.9276 + 9.77318i −0.670698 + 0.387227i
\(638\) 16.8294 9.71645i 0.666282 0.384678i
\(639\) 0.799016 13.2648i 0.0316086 0.524746i
\(640\) 4.29817 7.44465i 0.169900 0.294276i
\(641\) 10.9089 + 18.8947i 0.430875 + 0.746297i 0.996949 0.0780571i \(-0.0248716\pi\)
−0.566074 + 0.824355i \(0.691538\pi\)
\(642\) 16.1797 + 0.486860i 0.638564 + 0.0192148i
\(643\) −42.0181 −1.65703 −0.828516 0.559965i \(-0.810815\pi\)
−0.828516 + 0.559965i \(0.810815\pi\)
\(644\) −0.0211103 0.0365640i −0.000831861 0.00144082i
\(645\) 5.90499 + 10.9776i 0.232509 + 0.432241i
\(646\) 28.8771i 1.13616i
\(647\) 20.2255 35.0316i 0.795148 1.37724i −0.127598 0.991826i \(-0.540727\pi\)
0.922745 0.385410i \(-0.125940\pi\)
\(648\) −10.1586 23.8098i −0.399066 0.935335i
\(649\) −1.80998 + 1.04499i −0.0710480 + 0.0410196i
\(650\) −6.65279 + 3.84099i −0.260944 + 0.150656i
\(651\) −0.00537519 + 0.178633i −0.000210670 + 0.00700117i
\(652\) −7.06464 + 12.2363i −0.276673 + 0.479211i
\(653\) 14.8925 25.7946i 0.582789 1.00942i −0.412358 0.911022i \(-0.635295\pi\)
0.995147 0.0983980i \(-0.0313718\pi\)
\(654\) −26.9596 0.811232i −1.05420 0.0317217i
\(655\) 14.8254i 0.579277i
\(656\) 1.37973 0.0538695
\(657\) −6.08876 12.1840i −0.237545 0.475342i
\(658\) −0.0509731 0.0882880i −0.00198714 0.00344182i
\(659\) −26.2237 + 15.1403i −1.02153 + 0.589781i −0.914547 0.404480i \(-0.867453\pi\)
−0.106984 + 0.994261i \(0.534119\pi\)
\(660\) −0.223454 + 7.42602i −0.00869795 + 0.289058i
\(661\) 37.9232i 1.47504i −0.675325 0.737520i \(-0.735997\pi\)
0.675325 0.737520i \(-0.264003\pi\)
\(662\) 29.5449i 1.14830i
\(663\) −16.7330 10.3440i −0.649855 0.401728i
\(664\) 31.3102 + 18.0770i 1.21507 + 0.701523i
\(665\) 0.419863i 0.0162816i
\(666\) −21.2442 1.27966i −0.823195 0.0495859i
\(667\) −7.75102 −0.300121
\(668\) 15.4253 + 8.90581i 0.596823 + 0.344576i
\(669\) 32.8133 17.6507i 1.26864 0.682417i
\(670\) 8.32784 6.12817i 0.321732 0.236752i
\(671\) 2.21420i 0.0854782i
\(672\) −0.366657 0.0110330i −0.0141441 0.000425606i
\(673\) 42.6809i 1.64523i −0.568601 0.822613i \(-0.692515\pi\)
0.568601 0.822613i \(-0.307485\pi\)
\(674\) −1.37357 + 0.793033i −0.0529081 + 0.0305465i
\(675\) −1.42582 + 15.7566i −0.0548799 + 0.606471i
\(676\) 3.07798 5.33121i 0.118384 0.205047i
\(677\) 13.5495 + 23.4683i 0.520748 + 0.901961i 0.999709 + 0.0241254i \(0.00768011\pi\)
−0.478961 + 0.877836i \(0.658987\pi\)
\(678\) −7.97812 + 4.29154i −0.306398 + 0.164816i
\(679\) −0.0764054 −0.00293217
\(680\) 14.1642 + 8.17769i 0.543172 + 0.313600i
\(681\) −4.75064 + 7.68487i −0.182045 + 0.294485i
\(682\) −5.47533 + 3.16118i −0.209661 + 0.121048i
\(683\) 9.47329 16.4082i 0.362485 0.627843i −0.625884 0.779916i \(-0.715262\pi\)
0.988369 + 0.152073i \(0.0485949\pi\)
\(684\) −15.3882 + 23.2957i −0.588382 + 0.890734i
\(685\) 23.7949 0.909158
\(686\) −0.418336 0.241526i −0.0159721 0.00922152i
\(687\) 2.73991 + 0.0824458i 0.104534 + 0.00314550i
\(688\) −1.02721 0.593061i −0.0391621 0.0226102i
\(689\) 3.76028 + 2.17100i 0.143255 + 0.0827084i
\(690\) −1.07403 + 1.73740i −0.0408876 + 0.0661419i
\(691\) 0.626034 + 1.08432i 0.0238155 + 0.0412496i 0.877688 0.479233i \(-0.159085\pi\)
−0.853872 + 0.520483i \(0.825752\pi\)
\(692\) 9.36157i 0.355873i
\(693\) 0.265598 0.132729i 0.0100892 0.00504195i
\(694\) 21.0832 0.800306
\(695\) 0.756795i 0.0287069i
\(696\) −21.7487 + 35.1819i −0.824384 + 1.33357i
\(697\) 24.3459i 0.922167i
\(698\) −12.8702 + 22.2918i −0.487143 + 0.843757i
\(699\) −17.3659 10.7353i −0.656840 0.406046i
\(700\) 0.119249 + 0.0688483i 0.00450718 + 0.00260222i
\(701\) 18.9154 + 32.7625i 0.714427 + 1.23742i 0.963180 + 0.268856i \(0.0866457\pi\)
−0.248754 + 0.968567i \(0.580021\pi\)
\(702\) −5.50514 11.8982i −0.207778 0.449069i
\(703\) 30.8652 + 53.4601i 1.16410 + 2.01628i
\(704\) −7.08569 12.2728i −0.267052 0.462547i
\(705\) 3.76235 6.08617i 0.141698 0.229219i
\(706\) 5.31659 + 9.20861i 0.200093 + 0.346571i
\(707\) 0.183506 + 0.105947i 0.00690144 + 0.00398455i
\(708\) 0.869765 1.40697i 0.0326878 0.0528774i
\(709\) −15.2498 + 26.4134i −0.572718 + 0.991977i 0.423567 + 0.905865i \(0.360778\pi\)
−0.996285 + 0.0861124i \(0.972556\pi\)
\(710\) 5.59540i 0.209992i
\(711\) 2.50612 41.6051i 0.0939870 1.56031i
\(712\) 34.1964i 1.28157i
\(713\) 2.52174 0.0944400
\(714\) 0.00731037 0.242945i 0.000273584 0.00909198i
\(715\) 10.1187i 0.378419i
\(716\) −4.47202 7.74577i −0.167127 0.289473i
\(717\) 23.9879 + 14.8288i 0.895844 + 0.553793i
\(718\) −24.3048 14.0324i −0.907048 0.523684i
\(719\) −23.1515 13.3666i −0.863407 0.498488i 0.00174472 0.999998i \(-0.499445\pi\)
−0.865152 + 0.501510i \(0.832778\pi\)
\(720\) 0.432170 + 0.864798i 0.0161060 + 0.0322291i
\(721\) −0.385506 0.222572i −0.0143570 0.00828902i
\(722\) −38.6549 −1.43859
\(723\) 41.2649 22.1970i 1.53466 0.825515i
\(724\) 8.98999 15.5711i 0.334110 0.578696i
\(725\) 21.8922 12.6395i 0.813055 0.469418i
\(726\) −5.70531 3.52691i −0.211744 0.130896i
\(727\) 28.3723 + 16.3808i 1.05227 + 0.607529i 0.923284 0.384118i \(-0.125494\pi\)
0.128986 + 0.991646i \(0.458828\pi\)
\(728\) −0.306855 −0.0113728
\(729\) −26.5614 4.84681i −0.983756 0.179511i
\(730\) 2.86757 + 4.96677i 0.106133 + 0.183828i
\(731\) −10.4648 + 18.1255i −0.387054 + 0.670397i
\(732\) 0.830165 + 1.54330i 0.0306838 + 0.0570421i
\(733\) −17.4627 + 10.0821i −0.645001 + 0.372391i −0.786538 0.617542i \(-0.788129\pi\)
0.141538 + 0.989933i \(0.454795\pi\)
\(734\) 30.8074i 1.13712i
\(735\) 0.509807 16.9423i 0.0188045 0.624928i
\(736\) 5.17606i 0.190792i
\(737\) 2.34495 + 21.0781i 0.0863775 + 0.776422i
\(738\) 8.94259 13.5379i 0.329181 0.498338i
\(739\) −0.562057 0.324504i −0.0206756 0.0119371i 0.489627 0.871932i \(-0.337133\pi\)
−0.510302 + 0.859995i \(0.670466\pi\)
\(740\) −13.0007 −0.477916
\(741\) −19.9947 + 32.3445i −0.734525 + 1.18820i
\(742\) 0.0536467i 0.00196943i
\(743\) 46.0127 + 26.5655i 1.68804 + 0.974592i 0.956015 + 0.293316i \(0.0947590\pi\)
0.732027 + 0.681275i \(0.238574\pi\)
\(744\) 7.07581 11.4462i 0.259412 0.419637i
\(745\) 21.1444i 0.774670i
\(746\) 21.7974i 0.798061i
\(747\) 33.7319 16.8570i 1.23418 0.616765i
\(748\) −10.8032 + 6.23723i −0.395004 + 0.228056i
\(749\) −0.197588 0.342232i −0.00721971 0.0125049i
\(750\) 0.529389 17.5931i 0.0193306 0.642410i
\(751\) 19.6415 0.716727 0.358363 0.933582i \(-0.383335\pi\)
0.358363 + 0.933582i \(0.383335\pi\)
\(752\) 0.680863i 0.0248285i
\(753\) −1.42385 + 47.3186i −0.0518880 + 1.72439i
\(754\) −10.4737 + 18.1410i −0.381430 + 0.660656i
\(755\) −3.72874 + 6.45836i −0.135703 + 0.235044i
\(756\) −0.135359 + 0.192092i −0.00492296 + 0.00698633i
\(757\) −38.1120 + 22.0040i −1.38521 + 0.799749i −0.992770 0.120031i \(-0.961701\pi\)
−0.392435 + 0.919780i \(0.628367\pi\)
\(758\) 4.02546 2.32410i 0.146211 0.0844150i
\(759\) −1.98474 3.68970i −0.0720417 0.133928i
\(760\) 15.8073 27.3791i 0.573391 0.993143i
\(761\) 17.4832i 0.633764i 0.948465 + 0.316882i \(0.102636\pi\)
−0.948465 + 0.316882i \(0.897364\pi\)
\(762\) −0.847743 + 0.456013i −0.0307105 + 0.0165196i
\(763\) 0.329232 + 0.570246i 0.0119190 + 0.0206443i
\(764\) −20.9419 −0.757650
\(765\) 15.2597 7.62580i 0.551715 0.275711i
\(766\) −9.52316 16.4946i −0.344086 0.595974i
\(767\) 1.12644 1.95104i 0.0406732 0.0704481i
\(768\) 24.2981 + 15.0206i 0.876782 + 0.542010i
\(769\) −4.59330 + 2.65194i −0.165638 + 0.0956314i −0.580528 0.814241i \(-0.697154\pi\)
0.414889 + 0.909872i \(0.363820\pi\)
\(770\) −0.108270 + 0.0625100i −0.00390180 + 0.00225270i
\(771\) −2.15779 + 3.49055i −0.0777108 + 0.125709i
\(772\) −4.91330 8.51009i −0.176834 0.306285i
\(773\) 4.49297 2.59402i 0.161601 0.0933003i −0.417019 0.908898i \(-0.636925\pi\)
0.578619 + 0.815598i \(0.303592\pi\)
\(774\) −12.4769 + 6.23513i −0.448472 + 0.224117i
\(775\) −7.12247 + 4.11216i −0.255847 + 0.147713i
\(776\) 4.98236 + 2.87657i 0.178856 + 0.103263i
\(777\) 0.246137 + 0.457576i 0.00883010 + 0.0164154i
\(778\) −14.2730 + 8.24050i −0.511710 + 0.295436i
\(779\) −47.0601 −1.68610
\(780\) −3.79379 7.05278i −0.135839 0.252530i
\(781\) −9.93942 5.73853i −0.355660 0.205341i
\(782\) −3.42963 −0.122643
\(783\) 18.1156 + 39.1531i 0.647399 + 1.39922i
\(784\) 0.806451 + 1.39681i 0.0288018 + 0.0498862i
\(785\) 8.53508 14.7832i 0.304630 0.527635i
\(786\) 16.5819 + 0.498960i 0.591456 + 0.0177973i
\(787\) −10.0302 5.79097i −0.357540 0.206426i 0.310461 0.950586i \(-0.399516\pi\)
−0.668001 + 0.744160i \(0.732850\pi\)
\(788\) −16.1719 + 28.0106i −0.576101 + 0.997837i
\(789\) −21.9738 40.8499i −0.782287 1.45430i
\(790\) 17.5501i 0.624403i
\(791\) 0.191531 + 0.110580i 0.00681006 + 0.00393179i
\(792\) −22.3166 1.34426i −0.792986 0.0477662i
\(793\) 1.19338 + 2.06700i 0.0423783 + 0.0734013i
\(794\) −1.83447 + 3.17739i −0.0651028 + 0.112761i
\(795\) −3.31595 + 1.78370i −0.117605 + 0.0632612i
\(796\) 2.07448 0.0735280
\(797\) −1.04960 + 0.605985i −0.0371786 + 0.0214651i −0.518474 0.855093i \(-0.673500\pi\)
0.481295 + 0.876558i \(0.340166\pi\)
\(798\) −0.469607 0.0141308i −0.0166239 0.000500225i
\(799\) 12.0141 0.425027
\(800\) −8.44052 14.6194i −0.298417 0.516874i
\(801\) −29.7609 19.6588i −1.05155 0.694610i
\(802\) −13.7780 + 23.8642i −0.486518 + 0.842673i
\(803\) −11.7637 −0.415131
\(804\) −9.53721 13.8123i −0.336351 0.487123i
\(805\) 0.0498655 0.00175753
\(806\) 3.40755 5.90205i 0.120026 0.207891i
\(807\) −15.1674 28.1967i −0.533918 0.992570i
\(808\) −7.97754 13.8175i −0.280649 0.486098i
\(809\) −24.7250 −0.869285 −0.434642 0.900603i \(-0.643125\pi\)
−0.434642 + 0.900603i \(0.643125\pi\)
\(810\) 11.2864 + 1.36465i 0.396565 + 0.0479490i
\(811\) −17.5965 + 10.1594i −0.617898 + 0.356743i −0.776050 0.630671i \(-0.782780\pi\)
0.158152 + 0.987415i \(0.449446\pi\)
\(812\) 0.375474 0.0131766
\(813\) 7.32014 + 13.6084i 0.256729 + 0.477267i
\(814\) −9.19053 + 15.9185i −0.322128 + 0.557942i
\(815\) −8.34386 14.4520i −0.292273 0.506231i
\(816\) −0.853553 + 1.38075i −0.0298803 + 0.0483360i
\(817\) 35.0363 + 20.2282i 1.22576 + 0.707695i
\(818\) 27.2903i 0.954183i
\(819\) −0.176405 + 0.267054i −0.00616408 + 0.00933161i
\(820\) 4.95555 8.58326i 0.173055 0.299740i
\(821\) −20.1642 11.6418i −0.703736 0.406302i 0.105001 0.994472i \(-0.466515\pi\)
−0.808737 + 0.588170i \(0.799849\pi\)
\(822\) −0.800836 + 26.6141i −0.0279324 + 0.928272i
\(823\) 20.6760 35.8119i 0.720720 1.24832i −0.239992 0.970775i \(-0.577145\pi\)
0.960712 0.277548i \(-0.0895219\pi\)
\(824\) 16.7591 + 29.0276i 0.583831 + 1.01123i
\(825\) 11.6225 + 7.18480i 0.404644 + 0.250143i
\(826\) 0.0278349 0.000968501
\(827\) 5.20647 + 3.00596i 0.181047 + 0.104527i 0.587784 0.809018i \(-0.300000\pi\)
−0.406738 + 0.913545i \(0.633334\pi\)
\(828\) 2.76674 + 1.82760i 0.0961510 + 0.0635134i
\(829\) −20.2902 −0.704709 −0.352355 0.935867i \(-0.614619\pi\)
−0.352355 + 0.935867i \(0.614619\pi\)
\(830\) −13.7507 + 7.93898i −0.477294 + 0.275566i
\(831\) 11.4567 6.16274i 0.397429 0.213783i
\(832\) 13.2293 + 7.63791i 0.458642 + 0.264797i
\(833\) 24.6473 14.2301i 0.853979 0.493045i
\(834\) −0.846457 0.0254705i −0.0293104 0.000881970i
\(835\) −18.2184 + 10.5184i −0.630475 + 0.364005i
\(836\) 12.0564 + 20.8824i 0.416980 + 0.722231i
\(837\) −5.89379 12.7382i −0.203719 0.440297i
\(838\) −12.4186 + 7.16989i −0.428994 + 0.247680i
\(839\) −11.4394 + 6.60453i −0.394931 + 0.228014i −0.684295 0.729206i \(-0.739890\pi\)
0.289363 + 0.957219i \(0.406556\pi\)
\(840\) 0.139919 0.226340i 0.00482765 0.00780946i
\(841\) 19.9656 34.5814i 0.688468 1.19246i
\(842\) −6.57738 11.3924i −0.226672 0.392607i
\(843\) 1.18072 39.2388i 0.0406662 1.35145i
\(844\) −30.3474 −1.04460
\(845\) 3.63532 + 6.29655i 0.125059 + 0.216608i
\(846\) 6.68061 + 4.41294i 0.229684 + 0.151720i
\(847\) 0.163749i 0.00562648i
\(848\) 0.179144 0.310286i 0.00615182 0.0106553i
\(849\) −9.36910 + 5.03977i −0.321547 + 0.172965i
\(850\) 9.68673 5.59263i 0.332252 0.191826i
\(851\) 6.34925 3.66574i 0.217649 0.125660i
\(852\) 9.07934 + 0.273204i 0.311053 + 0.00935980i
\(853\) −10.2045 + 17.6746i −0.349394 + 0.605168i −0.986142 0.165904i \(-0.946946\pi\)
0.636748 + 0.771072i \(0.280279\pi\)
\(854\) −0.0147446 + 0.0255384i −0.000504550 + 0.000873907i
\(855\) −14.7405 29.4966i −0.504115 1.00876i
\(856\) 29.7557i 1.01703i
\(857\) 42.8545 1.46388 0.731942 0.681367i \(-0.238614\pi\)
0.731942 + 0.681367i \(0.238614\pi\)
\(858\) −11.3175 0.340553i −0.386375 0.0116263i
\(859\) 14.9176 + 25.8380i 0.508980 + 0.881580i 0.999946 + 0.0104010i \(0.00331081\pi\)
−0.490965 + 0.871179i \(0.663356\pi\)
\(860\) −7.37881 + 4.26016i −0.251615 + 0.145270i
\(861\) −0.395919 0.0119135i −0.0134929 0.000406010i
\(862\) 19.2039i 0.654089i
\(863\) 13.9450i 0.474693i 0.971425 + 0.237346i \(0.0762777\pi\)
−0.971425 + 0.237346i \(0.923722\pi\)
\(864\) 26.1461 12.0974i 0.889508 0.411563i
\(865\) −9.57538 5.52835i −0.325573 0.187970i
\(866\) 13.8368i 0.470193i
\(867\) −0.681794 0.421472i −0.0231550 0.0143139i
\(868\) −0.122158 −0.00414631
\(869\) −31.1751 17.9990i −1.05754 0.610573i
\(870\) −8.60523 15.9974i −0.291744 0.542362i
\(871\) −13.5495 18.4130i −0.459107 0.623900i
\(872\) 49.5806i 1.67901i
\(873\) 5.36771 2.68243i 0.181670 0.0907866i
\(874\) 6.62940i 0.224243i
\(875\) −0.372128 + 0.214848i −0.0125802 + 0.00726319i
\(876\) 8.19930 4.41052i 0.277029 0.149018i
\(877\) −15.0017 + 25.9837i −0.506571 + 0.877407i 0.493400 + 0.869803i \(0.335754\pi\)
−0.999971 + 0.00760452i \(0.997579\pi\)
\(878\) 7.08017 + 12.2632i 0.238944 + 0.413863i
\(879\) 14.8300 + 27.5695i 0.500204 + 0.929895i
\(880\) 0.834964 0.0281466
\(881\) 8.84870 + 5.10880i 0.298120 + 0.172120i 0.641598 0.767041i \(-0.278272\pi\)
−0.343478 + 0.939161i \(0.611605\pi\)
\(882\) 18.9324 + 1.14041i 0.637489 + 0.0383997i
\(883\) −25.0137 + 14.4417i −0.841778 + 0.486001i −0.857868 0.513870i \(-0.828211\pi\)
0.0160901 + 0.999871i \(0.494878\pi\)
\(884\) 6.72333 11.6452i 0.226130 0.391669i
\(885\) 0.925482 + 1.72050i 0.0311097 + 0.0578340i
\(886\) 26.8724 0.902796
\(887\) −45.3843 26.2026i −1.52386 0.879799i −0.999601 0.0282371i \(-0.991011\pi\)
−0.524255 0.851562i \(-0.675656\pi\)
\(888\) 1.17670 39.1050i 0.0394874 1.31228i
\(889\) 0.0203518 + 0.0117501i 0.000682578 + 0.000394086i
\(890\) 13.0062 + 7.50913i 0.435969 + 0.251707i
\(891\) −13.9992 + 18.6492i −0.468992 + 0.624771i
\(892\) 12.7341 + 22.0562i 0.426371 + 0.738496i
\(893\) 23.2229i 0.777126i
\(894\) −23.6495 0.711629i −0.790957 0.0238004i
\(895\) 10.5636 0.353101
\(896\) 0.234833i 0.00784522i
\(897\) 3.84143 + 2.37470i 0.128262 + 0.0792888i
\(898\) 26.9256i 0.898519i
\(899\) −11.2131 + 19.4217i −0.373979 + 0.647751i
\(900\) −10.7947 0.650229i −0.359823 0.0216743i
\(901\) −5.47511 3.16106i −0.182402 0.105310i
\(902\) −7.00639 12.1354i −0.233287 0.404066i
\(903\) 0.289641 + 0.179050i 0.00963864 + 0.00595842i
\(904\) −8.32642 14.4218i −0.276933 0.479662i
\(905\) 10.6178 + 18.3906i 0.352949 + 0.611326i
\(906\) −7.09803 4.38786i −0.235816 0.145777i
\(907\) 7.11942 + 12.3312i 0.236396 + 0.409450i 0.959678 0.281103i \(-0.0907003\pi\)
−0.723281 + 0.690554i \(0.757367\pi\)
\(908\) −5.34821 3.08779i −0.177487 0.102472i
\(909\) −16.6114 1.00060i −0.550965 0.0331879i
\(910\) 0.0673817 0.116709i 0.00223368 0.00386885i
\(911\) 52.2612i 1.73149i −0.500485 0.865745i \(-0.666845\pi\)
0.500485 0.865745i \(-0.333155\pi\)
\(912\) 2.66896 + 1.64990i 0.0883782 + 0.0546337i
\(913\) 32.5682i 1.07785i
\(914\) −34.6041 −1.14460
\(915\) −2.06879 0.0622515i −0.0683922 0.00205797i
\(916\) 1.87369i 0.0619083i
\(917\) −0.202499 0.350738i −0.00668710 0.0115824i
\(918\) 8.01570 + 17.3242i 0.264557 + 0.571785i
\(919\) −2.70804 1.56349i −0.0893301 0.0515748i 0.454670 0.890660i \(-0.349757\pi\)
−0.544000 + 0.839085i \(0.683091\pi\)
\(920\) −3.25171 1.87737i −0.107206 0.0618952i
\(921\) −0.0208537 + 0.693029i −0.000687154 + 0.0228361i
\(922\) 31.1810 + 18.0024i 1.02689 + 0.592877i
\(923\) 12.3715 0.407214
\(924\) 0.0961448 + 0.178736i 0.00316293 + 0.00587999i
\(925\) −11.9553 + 20.7072i −0.393088 + 0.680849i
\(926\) 10.2455 5.91526i 0.336689 0.194387i
\(927\) 34.8970 + 2.10205i 1.14617 + 0.0690405i
\(928\) −39.8645 23.0158i −1.30862 0.755531i
\(929\) 40.8304 1.33960 0.669801 0.742540i \(-0.266379\pi\)
0.669801 + 0.742540i \(0.266379\pi\)
\(930\) 2.79965 + 5.20464i 0.0918042 + 0.170667i
\(931\) −27.5065 47.6427i −0.901490 1.56143i
\(932\) 6.97766 12.0857i 0.228561 0.395879i
\(933\) −17.2637 + 9.28639i −0.565188 + 0.304023i
\(934\) −26.8972 + 15.5291i −0.880102 + 0.508127i
\(935\) 14.7333i 0.481829i
\(936\) 21.5575 10.7730i 0.704629 0.352128i
\(937\) 25.6849i 0.839089i 0.907735 + 0.419545i \(0.137810\pi\)
−0.907735 + 0.419545i \(0.862190\pi\)
\(938\) 0.113315 0.258729i 0.00369987 0.00844779i
\(939\) 16.9016 + 31.4205i 0.551562 + 1.02537i
\(940\) 4.23561 + 2.44543i 0.138150 + 0.0797612i
\(941\) 26.9904 0.879861 0.439930 0.898032i \(-0.355003\pi\)
0.439930 + 0.898032i \(0.355003\pi\)
\(942\) 16.2474 + 10.0438i 0.529368 + 0.327245i
\(943\) 5.58915i 0.182008i
\(944\) −0.160994 0.0929498i −0.00523990 0.00302526i
\(945\) −0.116545 0.251888i −0.00379122 0.00819392i
\(946\) 12.0464i 0.391664i
\(947\) 24.5270i 0.797021i −0.917164 0.398511i \(-0.869527\pi\)
0.917164 0.398511i \(-0.130473\pi\)
\(948\) 28.4775 + 0.856907i 0.924905 + 0.0278310i
\(949\) 10.9816 6.34023i 0.356478 0.205813i
\(950\) −10.8104 18.7242i −0.350737 0.607494i
\(951\) 23.0116 + 0.692436i 0.746203 + 0.0224538i
\(952\) 0.446793 0.0144806
\(953\) 3.75142i 0.121520i 0.998152 + 0.0607602i \(0.0193525\pi\)
−0.998152 + 0.0607602i \(0.980648\pi\)
\(954\) −1.88342 3.76884i −0.0609780 0.122021i
\(955\) 12.3669 21.4202i 0.400185 0.693140i
\(956\) −9.63837 + 16.6941i −0.311727 + 0.539927i
\(957\) 37.2424 + 1.12065i 1.20387 + 0.0362254i
\(958\) 27.8989 16.1075i 0.901373 0.520408i
\(959\) 0.562938 0.325013i 0.0181782 0.0104952i
\(960\) −11.6660 + 6.27533i −0.376520 + 0.202535i
\(961\) −11.8519 + 20.5281i −0.382319 + 0.662195i
\(962\) 19.8136i 0.638816i
\(963\) 25.8962 + 17.1060i 0.834494 + 0.551232i
\(964\) 16.0140 + 27.7371i 0.515777 + 0.893353i
\(965\) 11.6059 0.373608
\(966\) −0.00167826 + 0.0557734i −5.39972e−5 + 0.00179448i
\(967\) 9.76800 + 16.9187i 0.314118 + 0.544068i 0.979250 0.202658i \(-0.0649580\pi\)
−0.665132 + 0.746726i \(0.731625\pi\)
\(968\) 6.16494 10.6780i 0.198149 0.343203i
\(969\) 29.1131 47.0948i 0.935248 1.51290i
\(970\) −2.18813 + 1.26332i −0.0702568 + 0.0405628i
\(971\) −0.278645 + 0.160875i −0.00894213 + 0.00516274i −0.504464 0.863432i \(-0.668310\pi\)
0.495522 + 0.868595i \(0.334977\pi\)
\(972\) 2.76542 18.2472i 0.0887008 0.585280i
\(973\) 0.0103370 + 0.0179042i 0.000331388 + 0.000573981i
\(974\) 6.34067 3.66079i 0.203168 0.117299i
\(975\) −14.7222 0.443002i −0.471488 0.0141874i
\(976\) 0.170562 0.0984741i 0.00545956 0.00315208i
\(977\) 50.2425 + 29.0075i 1.60740 + 0.928033i 0.989949 + 0.141423i \(0.0451677\pi\)
0.617450 + 0.786610i \(0.288166\pi\)
\(978\) 16.4450 8.84602i 0.525854 0.282864i
\(979\) −26.6778 + 15.4024i −0.852625 + 0.492263i
\(980\) 11.5860 0.370102
\(981\) −43.1496 28.5029i −1.37766 0.910027i
\(982\) 1.78860 + 1.03265i 0.0570766 + 0.0329532i
\(983\) −23.9930 −0.765258 −0.382629 0.923902i \(-0.624981\pi\)
−0.382629 + 0.923902i \(0.624981\pi\)
\(984\) 25.3691 + 15.6827i 0.808739 + 0.499946i
\(985\) −19.1003 33.0826i −0.608585 1.05410i
\(986\) 15.2501 26.4140i 0.485663 0.841193i
\(987\) 0.00587899 0.195376i 0.000187130 0.00621888i
\(988\) −22.5098 12.9961i −0.716133 0.413460i
\(989\) 2.40243 4.16112i 0.0763927 0.132316i
\(990\) 5.41173 8.19266i 0.171996 0.260380i
\(991\) 7.04730i 0.223865i −0.993716 0.111932i \(-0.964296\pi\)
0.993716 0.111932i \(-0.0357040\pi\)
\(992\) 12.9697 + 7.48804i 0.411787 + 0.237745i
\(993\) 29.7863 48.1839i 0.945240 1.52907i
\(994\) 0.0764270 + 0.132376i 0.00242412 + 0.00419870i
\(995\) −1.22506 + 2.12186i −0.0388369 + 0.0672675i
\(996\) 12.2107 + 22.7001i 0.386911 + 0.719280i
\(997\) 56.4947 1.78920 0.894602 0.446863i \(-0.147459\pi\)
0.894602 + 0.446863i \(0.147459\pi\)
\(998\) −17.5345 + 10.1236i −0.555045 + 0.320455i
\(999\) −33.3563 23.5047i −1.05535 0.743657i
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 201.2.f.b.38.13 yes 40
3.2 odd 2 inner 201.2.f.b.38.8 40
67.30 odd 6 inner 201.2.f.b.164.8 yes 40
201.164 even 6 inner 201.2.f.b.164.13 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.2.f.b.38.8 40 3.2 odd 2 inner
201.2.f.b.38.13 yes 40 1.1 even 1 trivial
201.2.f.b.164.8 yes 40 67.30 odd 6 inner
201.2.f.b.164.13 yes 40 201.164 even 6 inner