Properties

Label 287.2.r.c.9.1
Level $287$
Weight $2$
Character 287.9
Analytic conductor $2.292$
Analytic rank $0$
Dimension $96$
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] = [287,2,Mod(9,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([4, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 287.r (of order \(12\), degree \(4\), 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: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(24\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 9.1
Character \(\chi\) \(=\) 287.9
Dual form 287.2.r.c.32.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.36599 - 1.36600i) q^{2} +(0.327392 - 1.22184i) q^{3} +(2.73193 + 4.73184i) q^{4} +(0.808637 + 0.466867i) q^{5} +(-2.44364 + 2.44364i) q^{6} +(-2.58896 + 0.545252i) q^{7} -9.46328i q^{8} +(1.21236 + 0.699958i) q^{9} +O(q^{10})\) \(q+(-2.36599 - 1.36600i) q^{2} +(0.327392 - 1.22184i) q^{3} +(2.73193 + 4.73184i) q^{4} +(0.808637 + 0.466867i) q^{5} +(-2.44364 + 2.44364i) q^{6} +(-2.58896 + 0.545252i) q^{7} -9.46328i q^{8} +(1.21236 + 0.699958i) q^{9} +(-1.27548 - 2.20920i) q^{10} +(-0.360339 + 1.34480i) q^{11} +(6.67597 - 1.78882i) q^{12} +(4.72910 + 4.72910i) q^{13} +(6.87025 + 2.24647i) q^{14} +(0.835178 - 0.835178i) q^{15} +(-7.46301 + 12.9263i) q^{16} +(0.940870 + 0.252105i) q^{17} +(-1.91229 - 3.31218i) q^{18} +(1.07639 + 4.01714i) q^{19} +5.10179i q^{20} +(-0.181391 + 3.34181i) q^{21} +(2.68957 - 2.68957i) q^{22} +(2.70927 - 4.69259i) q^{23} +(-11.5626 - 3.09820i) q^{24} +(-2.06407 - 3.57508i) q^{25} +(-4.72903 - 17.6490i) q^{26} +(3.93551 - 3.93551i) q^{27} +(-9.65289 - 10.7609i) q^{28} +(6.53121 + 6.53121i) q^{29} +(-3.11688 + 0.835164i) q^{30} +(-1.81764 - 3.14824i) q^{31} +(18.9239 - 10.9257i) q^{32} +(1.52517 + 0.880556i) q^{33} +(-1.88171 - 1.88171i) q^{34} +(-2.34809 - 0.767787i) q^{35} +7.64895i q^{36} +(-2.23860 + 3.87737i) q^{37} +(2.94070 - 10.9749i) q^{38} +(7.32649 - 4.22995i) q^{39} +(4.41809 - 7.65235i) q^{40} +(-4.82583 - 4.20849i) q^{41} +(4.99409 - 7.65889i) q^{42} +1.62126i q^{43} +(-7.34782 + 1.96884i) q^{44} +(0.653575 + 1.13202i) q^{45} +(-12.8202 + 7.40173i) q^{46} +(-1.08681 - 4.05603i) q^{47} +(13.3506 + 13.3506i) q^{48} +(6.40540 - 2.82327i) q^{49} +11.2781i q^{50} +(0.616066 - 1.06706i) q^{51} +(-9.45778 + 35.2969i) q^{52} +(0.297991 - 1.11212i) q^{53} +(-14.6873 + 3.93544i) q^{54} +(-0.919228 + 0.919228i) q^{55} +(5.15987 + 24.5000i) q^{56} +5.26071 q^{57} +(-6.53110 - 24.3744i) q^{58} +(0.186684 + 0.323347i) q^{59} +(6.23358 + 1.67028i) q^{60} +(6.08726 + 3.51448i) q^{61} +9.93160i q^{62} +(-3.52041 - 1.15112i) q^{63} -29.8462 q^{64} +(1.61627 + 6.03199i) q^{65} +(-2.40568 - 4.16677i) q^{66} +(7.86595 + 2.10768i) q^{67} +(1.37747 + 5.14078i) q^{68} +(-4.84661 - 4.84661i) q^{69} +(4.50674 + 5.02407i) q^{70} +(5.71734 + 5.71734i) q^{71} +(6.62390 - 11.4729i) q^{72} +(2.44324 - 1.41060i) q^{73} +(10.5930 - 6.11588i) q^{74} +(-5.04394 + 1.35152i) q^{75} +(-16.0678 + 16.0678i) q^{76} +(0.199646 - 3.67812i) q^{77} -23.1125 q^{78} +(-14.9108 + 3.99535i) q^{79} +(-12.0697 + 6.96846i) q^{80} +(-1.42024 - 2.45993i) q^{81} +(5.66903 + 16.5493i) q^{82} -2.94509 q^{83} +(-16.3084 + 8.27126i) q^{84} +(0.643123 + 0.643123i) q^{85} +(2.21465 - 3.83588i) q^{86} +(10.1184 - 5.84184i) q^{87} +(12.7263 + 3.40999i) q^{88} +(-0.244955 + 0.0656355i) q^{89} -3.57114i q^{90} +(-14.8220 - 9.66490i) q^{91} +29.6061 q^{92} +(-4.44173 + 1.19016i) q^{93} +(-2.96917 + 11.0811i) q^{94} +(-1.00506 + 3.75094i) q^{95} +(-7.15397 - 26.6990i) q^{96} +(-0.715909 + 0.715909i) q^{97} +(-19.0117 - 2.06999i) q^{98} +(-1.37817 + 1.37817i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q - 4 q^{3} + 48 q^{4} - 28 q^{6} - 14 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 4 q^{3} + 48 q^{4} - 28 q^{6} - 14 q^{7} - 28 q^{10} + 12 q^{12} - 8 q^{13} + 8 q^{14} - 20 q^{15} - 40 q^{16} - 20 q^{17} - 16 q^{18} - 8 q^{19} - 12 q^{22} + 12 q^{23} - 30 q^{24} + 40 q^{25} + 8 q^{26} - 4 q^{27} - 20 q^{28} - 72 q^{29} + 14 q^{30} + 24 q^{31} + 40 q^{34} + 20 q^{35} + 16 q^{37} - 18 q^{38} + 80 q^{40} - 88 q^{41} - 76 q^{42} + 4 q^{44} - 16 q^{45} + 14 q^{47} - 24 q^{48} - 8 q^{51} + 10 q^{52} - 4 q^{53} + 16 q^{54} - 60 q^{55} + 36 q^{56} + 128 q^{57} - 16 q^{58} - 8 q^{59} + 54 q^{60} + 30 q^{63} - 16 q^{64} + 48 q^{66} + 14 q^{67} - 30 q^{68} + 56 q^{69} - 34 q^{70} - 68 q^{71} + 112 q^{72} - 62 q^{75} - 84 q^{76} - 96 q^{78} - 26 q^{79} - 32 q^{81} + 14 q^{82} + 56 q^{83} - 92 q^{85} + 36 q^{86} + 6 q^{88} + 40 q^{89} - 160 q^{92} - 78 q^{93} + 96 q^{94} + 72 q^{95} + 24 q^{96} + 60 q^{97} - 116 q^{98} - 128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.36599 1.36600i −1.67301 0.965910i −0.965942 0.258760i \(-0.916686\pi\)
−0.707064 0.707150i \(-0.749981\pi\)
\(3\) 0.327392 1.22184i 0.189020 0.705431i −0.804715 0.593662i \(-0.797682\pi\)
0.993734 0.111769i \(-0.0356517\pi\)
\(4\) 2.73193 + 4.73184i 1.36596 + 2.36592i
\(5\) 0.808637 + 0.466867i 0.361633 + 0.208789i 0.669797 0.742544i \(-0.266381\pi\)
−0.308164 + 0.951333i \(0.599714\pi\)
\(6\) −2.44364 + 2.44364i −0.997613 + 0.997613i
\(7\) −2.58896 + 0.545252i −0.978534 + 0.206086i
\(8\) 9.46328i 3.34577i
\(9\) 1.21236 + 0.699958i 0.404121 + 0.233319i
\(10\) −1.27548 2.20920i −0.403343 0.698611i
\(11\) −0.360339 + 1.34480i −0.108646 + 0.405474i −0.998733 0.0503170i \(-0.983977\pi\)
0.890087 + 0.455791i \(0.150644\pi\)
\(12\) 6.67597 1.78882i 1.92719 0.516388i
\(13\) 4.72910 + 4.72910i 1.31162 + 1.31162i 0.920223 + 0.391394i \(0.128007\pi\)
0.391394 + 0.920223i \(0.371993\pi\)
\(14\) 6.87025 + 2.24647i 1.83615 + 0.600393i
\(15\) 0.835178 0.835178i 0.215642 0.215642i
\(16\) −7.46301 + 12.9263i −1.86575 + 3.23158i
\(17\) 0.940870 + 0.252105i 0.228195 + 0.0611445i 0.371104 0.928591i \(-0.378979\pi\)
−0.142910 + 0.989736i \(0.545646\pi\)
\(18\) −1.91229 3.31218i −0.450731 0.780689i
\(19\) 1.07639 + 4.01714i 0.246941 + 0.921596i 0.972398 + 0.233328i \(0.0749617\pi\)
−0.725457 + 0.688267i \(0.758372\pi\)
\(20\) 5.10179i 1.14079i
\(21\) −0.181391 + 3.34181i −0.0395828 + 0.729242i
\(22\) 2.68957 2.68957i 0.573417 0.573417i
\(23\) 2.70927 4.69259i 0.564921 0.978472i −0.432136 0.901808i \(-0.642240\pi\)
0.997057 0.0766634i \(-0.0244267\pi\)
\(24\) −11.5626 3.09820i −2.36021 0.632417i
\(25\) −2.06407 3.57508i −0.412814 0.715015i
\(26\) −4.72903 17.6490i −0.927438 3.46125i
\(27\) 3.93551 3.93551i 0.757389 0.757389i
\(28\) −9.65289 10.7609i −1.82422 2.03363i
\(29\) 6.53121 + 6.53121i 1.21281 + 1.21281i 0.970097 + 0.242718i \(0.0780390\pi\)
0.242718 + 0.970097i \(0.421961\pi\)
\(30\) −3.11688 + 0.835164i −0.569061 + 0.152479i
\(31\) −1.81764 3.14824i −0.326458 0.565441i 0.655349 0.755326i \(-0.272522\pi\)
−0.981806 + 0.189885i \(0.939188\pi\)
\(32\) 18.9239 10.9257i 3.34530 1.93141i
\(33\) 1.52517 + 0.880556i 0.265498 + 0.153285i
\(34\) −1.88171 1.88171i −0.322710 0.322710i
\(35\) −2.34809 0.767787i −0.396899 0.129780i
\(36\) 7.64895i 1.27482i
\(37\) −2.23860 + 3.87737i −0.368024 + 0.637436i −0.989257 0.146190i \(-0.953299\pi\)
0.621232 + 0.783626i \(0.286632\pi\)
\(38\) 2.94070 10.9749i 0.477045 1.78036i
\(39\) 7.32649 4.22995i 1.17318 0.677334i
\(40\) 4.41809 7.65235i 0.698561 1.20994i
\(41\) −4.82583 4.20849i −0.753668 0.657256i
\(42\) 4.99409 7.65889i 0.770605 1.18179i
\(43\) 1.62126i 0.247240i 0.992330 + 0.123620i \(0.0394504\pi\)
−0.992330 + 0.123620i \(0.960550\pi\)
\(44\) −7.34782 + 1.96884i −1.10773 + 0.296814i
\(45\) 0.653575 + 1.13202i 0.0974291 + 0.168752i
\(46\) −12.8202 + 7.40173i −1.89023 + 1.09133i
\(47\) −1.08681 4.05603i −0.158528 0.591633i −0.998777 0.0494335i \(-0.984258\pi\)
0.840250 0.542199i \(-0.182408\pi\)
\(48\) 13.3506 + 13.3506i 1.92699 + 1.92699i
\(49\) 6.40540 2.82327i 0.915057 0.403324i
\(50\) 11.2781i 1.59497i
\(51\) 0.616066 1.06706i 0.0862665 0.149418i
\(52\) −9.45778 + 35.2969i −1.31156 + 4.89480i
\(53\) 0.297991 1.11212i 0.0409322 0.152761i −0.942435 0.334389i \(-0.891470\pi\)
0.983367 + 0.181628i \(0.0581367\pi\)
\(54\) −14.6873 + 3.93544i −1.99868 + 0.535546i
\(55\) −0.919228 + 0.919228i −0.123949 + 0.123949i
\(56\) 5.15987 + 24.5000i 0.689516 + 3.27395i
\(57\) 5.26071 0.696799
\(58\) −6.53110 24.3744i −0.857576 3.20052i
\(59\) 0.186684 + 0.323347i 0.0243042 + 0.0420962i 0.877922 0.478804i \(-0.158930\pi\)
−0.853617 + 0.520900i \(0.825596\pi\)
\(60\) 6.23358 + 1.67028i 0.804751 + 0.215632i
\(61\) 6.08726 + 3.51448i 0.779394 + 0.449984i 0.836216 0.548401i \(-0.184763\pi\)
−0.0568212 + 0.998384i \(0.518097\pi\)
\(62\) 9.93160i 1.26131i
\(63\) −3.52041 1.15112i −0.443530 0.145027i
\(64\) −29.8462 −3.73077
\(65\) 1.61627 + 6.03199i 0.200473 + 0.748176i
\(66\) −2.40568 4.16677i −0.296119 0.512893i
\(67\) 7.86595 + 2.10768i 0.960979 + 0.257494i 0.705015 0.709193i \(-0.250940\pi\)
0.255964 + 0.966686i \(0.417607\pi\)
\(68\) 1.37747 + 5.14078i 0.167042 + 0.623411i
\(69\) −4.84661 4.84661i −0.583463 0.583463i
\(70\) 4.50674 + 5.02407i 0.538659 + 0.600491i
\(71\) 5.71734 + 5.71734i 0.678524 + 0.678524i 0.959666 0.281142i \(-0.0907133\pi\)
−0.281142 + 0.959666i \(0.590713\pi\)
\(72\) 6.62390 11.4729i 0.780634 1.35210i
\(73\) 2.44324 1.41060i 0.285959 0.165099i −0.350159 0.936690i \(-0.613872\pi\)
0.636118 + 0.771592i \(0.280539\pi\)
\(74\) 10.5930 6.11588i 1.23141 0.710956i
\(75\) −5.04394 + 1.35152i −0.582424 + 0.156060i
\(76\) −16.0678 + 16.0678i −1.84311 + 1.84311i
\(77\) 0.199646 3.67812i 0.0227518 0.419160i
\(78\) −23.1125 −2.61697
\(79\) −14.9108 + 3.99535i −1.67760 + 0.449512i −0.967144 0.254230i \(-0.918178\pi\)
−0.710456 + 0.703741i \(0.751511\pi\)
\(80\) −12.0697 + 6.96846i −1.34944 + 0.779098i
\(81\) −1.42024 2.45993i −0.157805 0.273325i
\(82\) 5.66903 + 16.5493i 0.626040 + 1.82757i
\(83\) −2.94509 −0.323265 −0.161633 0.986851i \(-0.551676\pi\)
−0.161633 + 0.986851i \(0.551676\pi\)
\(84\) −16.3084 + 8.27126i −1.77940 + 0.902469i
\(85\) 0.643123 + 0.643123i 0.0697564 + 0.0697564i
\(86\) 2.21465 3.83588i 0.238812 0.413634i
\(87\) 10.1184 5.84184i 1.08480 0.626311i
\(88\) 12.7263 + 3.40999i 1.35662 + 0.363506i
\(89\) −0.244955 + 0.0656355i −0.0259652 + 0.00695735i −0.271778 0.962360i \(-0.587612\pi\)
0.245813 + 0.969317i \(0.420945\pi\)
\(90\) 3.57114i 0.376431i
\(91\) −14.8220 9.66490i −1.55377 1.01316i
\(92\) 29.6061 3.08665
\(93\) −4.44173 + 1.19016i −0.460586 + 0.123414i
\(94\) −2.96917 + 11.0811i −0.306247 + 1.14293i
\(95\) −1.00506 + 3.75094i −0.103117 + 0.384838i
\(96\) −7.15397 26.6990i −0.730149 2.72495i
\(97\) −0.715909 + 0.715909i −0.0726895 + 0.0726895i −0.742517 0.669827i \(-0.766368\pi\)
0.669827 + 0.742517i \(0.266368\pi\)
\(98\) −19.0117 2.06999i −1.92047 0.209100i
\(99\) −1.37817 + 1.37817i −0.138511 + 0.138511i
\(100\) 11.2778 19.5337i 1.12778 1.95337i
\(101\) 5.15212 + 1.38051i 0.512655 + 0.137366i 0.505867 0.862611i \(-0.331173\pi\)
0.00678811 + 0.999977i \(0.497839\pi\)
\(102\) −2.91521 + 1.68310i −0.288649 + 0.166651i
\(103\) 8.50746 + 4.91179i 0.838265 + 0.483973i 0.856674 0.515858i \(-0.172527\pi\)
−0.0184088 + 0.999831i \(0.505860\pi\)
\(104\) 44.7528 44.7528i 4.38837 4.38837i
\(105\) −1.70686 + 2.61762i −0.166572 + 0.255454i
\(106\) −2.22420 + 2.22420i −0.216033 + 0.216033i
\(107\) −2.96666 + 5.13841i −0.286798 + 0.496749i −0.973044 0.230621i \(-0.925924\pi\)
0.686246 + 0.727370i \(0.259257\pi\)
\(108\) 29.3737 + 7.87066i 2.82649 + 0.757355i
\(109\) −2.87437 0.770185i −0.275315 0.0737704i 0.118520 0.992952i \(-0.462185\pi\)
−0.393835 + 0.919181i \(0.628852\pi\)
\(110\) 3.43055 0.919213i 0.327090 0.0876435i
\(111\) 4.00464 + 4.00464i 0.380103 + 0.380103i
\(112\) 12.2733 37.5349i 1.15972 3.54671i
\(113\) −11.4574 −1.07782 −0.538909 0.842364i \(-0.681163\pi\)
−0.538909 + 0.842364i \(0.681163\pi\)
\(114\) −12.4468 7.18615i −1.16575 0.673045i
\(115\) 4.38162 2.52973i 0.408589 0.235899i
\(116\) −13.0618 + 48.7474i −1.21276 + 4.52608i
\(117\) 2.42322 + 9.04357i 0.224026 + 0.836078i
\(118\) 1.02005i 0.0939028i
\(119\) −2.57333 0.139679i −0.235897 0.0128044i
\(120\) −7.90352 7.90352i −0.721490 0.721490i
\(121\) 7.84762 + 4.53083i 0.713420 + 0.411893i
\(122\) −9.60159 16.6304i −0.869287 1.50565i
\(123\) −6.72205 + 4.51857i −0.606106 + 0.407426i
\(124\) 9.93132 17.2015i 0.891859 1.54474i
\(125\) 8.52325i 0.762343i
\(126\) 6.75681 + 7.53243i 0.601945 + 0.671042i
\(127\) −1.46158 −0.129695 −0.0648473 0.997895i \(-0.520656\pi\)
−0.0648473 + 0.997895i \(0.520656\pi\)
\(128\) 32.7679 + 18.9185i 2.89630 + 1.67218i
\(129\) 1.98093 + 0.530787i 0.174411 + 0.0467332i
\(130\) 4.41565 16.4794i 0.387278 1.44534i
\(131\) −13.5843 7.84289i −1.18686 0.685236i −0.229272 0.973362i \(-0.573634\pi\)
−0.957593 + 0.288126i \(0.906968\pi\)
\(132\) 9.62246i 0.837528i
\(133\) −4.97708 9.81331i −0.431568 0.850922i
\(134\) −15.7316 15.7316i −1.35901 1.35901i
\(135\) 5.01975 1.34504i 0.432032 0.115763i
\(136\) 2.38574 8.90371i 0.204576 0.763487i
\(137\) −17.4456 4.67454i −1.49048 0.399373i −0.580581 0.814203i \(-0.697174\pi\)
−0.909899 + 0.414830i \(0.863841\pi\)
\(138\) 4.84653 + 18.0875i 0.412564 + 1.53971i
\(139\) 3.86071 0.327461 0.163731 0.986505i \(-0.447647\pi\)
0.163731 + 0.986505i \(0.447647\pi\)
\(140\) −2.78176 13.2083i −0.235101 1.11631i
\(141\) −5.31164 −0.447321
\(142\) −5.71725 21.3371i −0.479781 1.79057i
\(143\) −8.06380 + 4.65564i −0.674329 + 0.389324i
\(144\) −18.0958 + 10.4476i −1.50798 + 0.870633i
\(145\) 2.23217 + 8.33058i 0.185372 + 0.691817i
\(146\) −7.70755 −0.637882
\(147\) −1.35251 8.75070i −0.111553 0.721746i
\(148\) −24.4628 −2.01083
\(149\) 2.68175 + 10.0084i 0.219697 + 0.819921i 0.984460 + 0.175609i \(0.0561895\pi\)
−0.764763 + 0.644312i \(0.777144\pi\)
\(150\) 13.7801 + 3.69236i 1.12514 + 0.301480i
\(151\) 2.78222 10.3834i 0.226414 0.844988i −0.755419 0.655242i \(-0.772567\pi\)
0.981833 0.189746i \(-0.0607665\pi\)
\(152\) 38.0153 10.1862i 3.08345 0.826208i
\(153\) 0.964213 + 0.964213i 0.0779520 + 0.0779520i
\(154\) −5.49668 + 8.42966i −0.442935 + 0.679281i
\(155\) 3.39438i 0.272643i
\(156\) 40.0309 + 23.1118i 3.20503 + 1.85043i
\(157\) 6.20123 23.1433i 0.494912 1.84704i −0.0356095 0.999366i \(-0.511337\pi\)
0.530522 0.847671i \(-0.321996\pi\)
\(158\) 40.7365 + 10.9153i 3.24082 + 0.868376i
\(159\) −1.26127 0.728196i −0.100025 0.0577497i
\(160\) 20.4034 1.61303
\(161\) −4.45553 + 13.6261i −0.351145 + 1.07389i
\(162\) 7.76021i 0.609700i
\(163\) −5.29986 + 9.17963i −0.415117 + 0.719004i −0.995441 0.0953820i \(-0.969593\pi\)
0.580324 + 0.814386i \(0.302926\pi\)
\(164\) 6.73008 34.3323i 0.525531 2.68090i
\(165\) 0.822204 + 1.42410i 0.0640085 + 0.110866i
\(166\) 6.96804 + 4.02300i 0.540825 + 0.312245i
\(167\) 0.618667 + 0.618667i 0.0478739 + 0.0478739i 0.730638 0.682765i \(-0.239223\pi\)
−0.682765 + 0.730638i \(0.739223\pi\)
\(168\) 31.6245 + 1.71656i 2.43988 + 0.132435i
\(169\) 31.7288i 2.44068i
\(170\) −0.643112 2.40013i −0.0493244 0.184081i
\(171\) −1.50686 + 5.62366i −0.115232 + 0.430052i
\(172\) −7.67155 + 4.42917i −0.584950 + 0.337721i
\(173\) −16.7337 9.66123i −1.27224 0.734530i −0.296834 0.954929i \(-0.595931\pi\)
−0.975410 + 0.220399i \(0.929264\pi\)
\(174\) −31.9199 −2.41984
\(175\) 7.29311 + 8.13028i 0.551307 + 0.614591i
\(176\) −14.6942 14.6942i −1.10761 1.10761i
\(177\) 0.456198 0.122238i 0.0342899 0.00918795i
\(178\) 0.669218 + 0.179317i 0.0501600 + 0.0134403i
\(179\) −7.97996 2.13822i −0.596450 0.159818i −0.0520506 0.998644i \(-0.516576\pi\)
−0.544399 + 0.838826i \(0.683242\pi\)
\(180\) −3.57104 + 6.18522i −0.266169 + 0.461019i
\(181\) 15.0164 15.0164i 1.11616 1.11616i 0.123861 0.992300i \(-0.460472\pi\)
0.992300 0.123861i \(-0.0395278\pi\)
\(182\) 21.8664 + 43.1139i 1.62084 + 3.19582i
\(183\) 6.28706 6.28706i 0.464753 0.464753i
\(184\) −44.4072 25.6385i −3.27375 1.89010i
\(185\) −3.62043 + 2.09026i −0.266180 + 0.153679i
\(186\) 12.1348 + 3.25152i 0.889770 + 0.238413i
\(187\) −0.678065 + 1.17444i −0.0495850 + 0.0858838i
\(188\) 16.2234 16.2234i 1.18321 1.18321i
\(189\) −8.04302 + 12.3347i −0.585044 + 0.897218i
\(190\) 7.50176 7.50176i 0.544235 0.544235i
\(191\) −4.27210 15.9437i −0.309118 1.15365i −0.929342 0.369221i \(-0.879625\pi\)
0.620223 0.784425i \(-0.287042\pi\)
\(192\) −9.77138 + 36.4673i −0.705189 + 2.63180i
\(193\) 2.17401 8.11352i 0.156489 0.584024i −0.842485 0.538720i \(-0.818908\pi\)
0.998973 0.0453032i \(-0.0144254\pi\)
\(194\) 2.67176 0.715897i 0.191821 0.0513984i
\(195\) 7.89929 0.565680
\(196\) 30.8583 + 22.5964i 2.20417 + 1.61403i
\(197\) 18.7118i 1.33316i 0.745432 + 0.666581i \(0.232243\pi\)
−0.745432 + 0.666581i \(0.767757\pi\)
\(198\) 5.14332 1.37815i 0.365520 0.0979407i
\(199\) 9.33565 + 2.50148i 0.661787 + 0.177325i 0.574052 0.818819i \(-0.305371\pi\)
0.0877345 + 0.996144i \(0.472037\pi\)
\(200\) −33.8319 + 19.5329i −2.39228 + 1.38118i
\(201\) 5.15049 8.92092i 0.363288 0.629233i
\(202\) −10.3041 10.3041i −0.724992 0.724992i
\(203\) −20.4702 13.3479i −1.43672 0.936837i
\(204\) 6.73219 0.471348
\(205\) −1.93754 5.65616i −0.135323 0.395043i
\(206\) −13.4190 23.2424i −0.934948 1.61938i
\(207\) 6.56923 3.79275i 0.456593 0.263614i
\(208\) −96.4232 + 25.8365i −6.68575 + 1.79144i
\(209\) −5.79014 −0.400512
\(210\) 7.61409 3.86169i 0.525422 0.266482i
\(211\) 6.48435 6.48435i 0.446401 0.446401i −0.447755 0.894156i \(-0.647776\pi\)
0.894156 + 0.447755i \(0.147776\pi\)
\(212\) 6.07645 1.62818i 0.417332 0.111824i
\(213\) 8.85750 5.11388i 0.606906 0.350397i
\(214\) 14.0382 8.10494i 0.959629 0.554042i
\(215\) −0.756913 + 1.31101i −0.0516210 + 0.0894103i
\(216\) −37.2428 37.2428i −2.53405 2.53405i
\(217\) 6.42237 + 7.15959i 0.435979 + 0.486025i
\(218\) 5.74865 + 5.74865i 0.389348 + 0.389348i
\(219\) −0.923639 3.44707i −0.0624138 0.232931i
\(220\) −6.86091 1.83837i −0.462562 0.123943i
\(221\) 3.25724 + 5.64170i 0.219106 + 0.379502i
\(222\) −4.00457 14.9453i −0.268769 1.00306i
\(223\) −9.01754 −0.603859 −0.301929 0.953330i \(-0.597631\pi\)
−0.301929 + 0.953330i \(0.597631\pi\)
\(224\) −43.0359 + 38.6045i −2.87545 + 2.57937i
\(225\) 5.77906i 0.385270i
\(226\) 27.1080 + 15.6508i 1.80319 + 1.04107i
\(227\) −27.0604 7.25081i −1.79606 0.481253i −0.802710 0.596369i \(-0.796609\pi\)
−0.993352 + 0.115116i \(0.963276\pi\)
\(228\) 14.3719 + 24.8928i 0.951802 + 1.64857i
\(229\) −0.630750 2.35399i −0.0416812 0.155556i 0.941949 0.335757i \(-0.108992\pi\)
−0.983630 + 0.180201i \(0.942325\pi\)
\(230\) −13.8225 −0.911428
\(231\) −4.42872 1.44812i −0.291388 0.0952794i
\(232\) 61.8066 61.8066i 4.05780 4.05780i
\(233\) −5.88079 + 1.57575i −0.385263 + 0.103231i −0.446252 0.894907i \(-0.647241\pi\)
0.0609884 + 0.998138i \(0.480575\pi\)
\(234\) 6.62024 24.7071i 0.432779 1.61515i
\(235\) 1.01479 3.78725i 0.0661977 0.247053i
\(236\) −1.02002 + 1.76672i −0.0663974 + 0.115004i
\(237\) 19.5267i 1.26840i
\(238\) 5.89767 + 3.84566i 0.382289 + 0.249277i
\(239\) −2.33498 2.33498i −0.151037 0.151037i 0.627544 0.778581i \(-0.284060\pi\)
−0.778581 + 0.627544i \(0.784060\pi\)
\(240\) 4.56283 + 17.0287i 0.294529 + 1.09920i
\(241\) −22.0045 + 12.7043i −1.41744 + 0.818357i −0.996073 0.0885356i \(-0.971781\pi\)
−0.421362 + 0.906892i \(0.638448\pi\)
\(242\) −12.3782 21.4398i −0.795704 1.37820i
\(243\) 12.6574 3.39154i 0.811972 0.217567i
\(244\) 38.4053i 2.45865i
\(245\) 6.49773 + 0.707471i 0.415125 + 0.0451986i
\(246\) 22.0767 1.50855i 1.40756 0.0961817i
\(247\) −13.9071 + 24.0878i −0.884889 + 1.53267i
\(248\) −29.7927 + 17.2008i −1.89184 + 1.09225i
\(249\) −0.964197 + 3.59843i −0.0611035 + 0.228041i
\(250\) −11.6428 + 20.1659i −0.736354 + 1.27540i
\(251\) 18.4075i 1.16187i −0.813950 0.580934i \(-0.802687\pi\)
0.813950 0.580934i \(-0.197313\pi\)
\(252\) −4.17060 19.8028i −0.262723 1.24746i
\(253\) 5.33436 + 5.33436i 0.335368 + 0.335368i
\(254\) 3.45809 + 1.99653i 0.216980 + 0.125273i
\(255\) 0.996347 0.575241i 0.0623937 0.0360230i
\(256\) −21.8394 37.8269i −1.36496 2.36418i
\(257\) 14.1237 3.78442i 0.881010 0.236066i 0.210167 0.977665i \(-0.432599\pi\)
0.670843 + 0.741600i \(0.265933\pi\)
\(258\) −3.96179 3.96179i −0.246650 0.246650i
\(259\) 3.68150 11.2590i 0.228757 0.699598i
\(260\) −24.1269 + 24.1269i −1.49628 + 1.49628i
\(261\) 3.34662 + 12.4898i 0.207151 + 0.773098i
\(262\) 21.4268 + 37.1123i 1.32375 + 2.29281i
\(263\) −2.59688 0.695832i −0.160131 0.0429068i 0.177863 0.984055i \(-0.443082\pi\)
−0.337994 + 0.941148i \(0.609748\pi\)
\(264\) 8.33294 14.4331i 0.512857 0.888295i
\(265\) 0.760177 0.760177i 0.0466973 0.0466973i
\(266\) −1.62930 + 30.0169i −0.0998986 + 1.84045i
\(267\) 0.320785i 0.0196317i
\(268\) 11.5160 + 42.9784i 0.703454 + 2.62533i
\(269\) 1.38972 + 2.40706i 0.0847325 + 0.146761i 0.905277 0.424821i \(-0.139663\pi\)
−0.820545 + 0.571582i \(0.806330\pi\)
\(270\) −13.7140 3.67465i −0.834607 0.223632i
\(271\) 11.6771 20.2253i 0.709332 1.22860i −0.255773 0.966737i \(-0.582330\pi\)
0.965105 0.261863i \(-0.0843368\pi\)
\(272\) −10.2805 + 10.2805i −0.623348 + 0.623348i
\(273\) −16.6616 + 14.9459i −1.00840 + 0.904569i
\(274\) 34.8907 + 34.8907i 2.10782 + 2.10782i
\(275\) 5.55155 1.48753i 0.334771 0.0897016i
\(276\) 9.69278 36.1740i 0.583437 2.17742i
\(277\) −1.89619 3.28431i −0.113931 0.197335i 0.803421 0.595412i \(-0.203011\pi\)
−0.917352 + 0.398077i \(0.869678\pi\)
\(278\) −9.13439 5.27374i −0.547844 0.316298i
\(279\) 5.08909i 0.304676i
\(280\) −7.26578 + 22.2206i −0.434214 + 1.32793i
\(281\) 7.49035 7.49035i 0.446837 0.446837i −0.447465 0.894301i \(-0.647673\pi\)
0.894301 + 0.447465i \(0.147673\pi\)
\(282\) 12.5673 + 7.25572i 0.748370 + 0.432072i
\(283\) 8.42584 + 14.5940i 0.500864 + 0.867522i 1.00000 0.000998346i \(0.000317783\pi\)
−0.499135 + 0.866524i \(0.666349\pi\)
\(284\) −11.4342 + 42.6729i −0.678493 + 2.53217i
\(285\) 4.25401 + 2.45605i 0.251986 + 0.145484i
\(286\) 25.4385 1.50421
\(287\) 14.7885 + 8.26431i 0.872940 + 0.487827i
\(288\) 30.5902 1.80254
\(289\) −13.9008 8.02560i −0.817691 0.472094i
\(290\) 6.09831 22.7592i 0.358105 1.33647i
\(291\) 0.640345 + 1.10911i 0.0375377 + 0.0650172i
\(292\) 13.3495 + 7.70733i 0.781220 + 0.451038i
\(293\) 7.00619 7.00619i 0.409306 0.409306i −0.472191 0.881497i \(-0.656537\pi\)
0.881497 + 0.472191i \(0.156537\pi\)
\(294\) −8.75346 + 22.5516i −0.510512 + 1.31523i
\(295\) 0.348627i 0.0202978i
\(296\) 36.6927 + 21.1845i 2.13272 + 1.23133i
\(297\) 3.87437 + 6.71061i 0.224814 + 0.389389i
\(298\) 7.32655 27.3430i 0.424416 1.58394i
\(299\) 35.0041 9.37933i 2.02434 0.542420i
\(300\) −20.1748 20.1748i −1.16480 1.16480i
\(301\) −0.883996 4.19738i −0.0509527 0.241933i
\(302\) −20.7664 + 20.7664i −1.19497 + 1.19497i
\(303\) 3.37352 5.84311i 0.193804 0.335678i
\(304\) −59.9599 16.0662i −3.43894 0.921461i
\(305\) 3.28159 + 5.68388i 0.187903 + 0.325458i
\(306\) −0.964198 3.59843i −0.0551195 0.205709i
\(307\) 21.3343i 1.21761i −0.793320 0.608805i \(-0.791649\pi\)
0.793320 0.608805i \(-0.208351\pi\)
\(308\) 17.9497 9.10366i 1.02278 0.518729i
\(309\) 8.78670 8.78670i 0.499858 0.499858i
\(310\) −4.63673 + 8.03106i −0.263349 + 0.456133i
\(311\) 28.5739 + 7.65634i 1.62027 + 0.434151i 0.951082 0.308938i \(-0.0999734\pi\)
0.669193 + 0.743089i \(0.266640\pi\)
\(312\) −40.0292 69.3326i −2.26621 3.92518i
\(313\) −5.24100 19.5597i −0.296239 1.10558i −0.940229 0.340544i \(-0.889389\pi\)
0.643990 0.765034i \(-0.277278\pi\)
\(314\) −46.2859 + 46.2859i −2.61206 + 2.61206i
\(315\) −2.30931 2.57440i −0.130115 0.145051i
\(316\) −59.6407 59.6407i −3.35505 3.35505i
\(317\) −23.6560 + 6.33860i −1.32865 + 0.356011i −0.852212 0.523196i \(-0.824740\pi\)
−0.476439 + 0.879207i \(0.658073\pi\)
\(318\) 1.98943 + 3.44580i 0.111562 + 0.193231i
\(319\) −11.1367 + 6.42975i −0.623533 + 0.359997i
\(320\) −24.1347 13.9342i −1.34917 0.778944i
\(321\) 5.30706 + 5.30706i 0.296211 + 0.296211i
\(322\) 29.1551 26.1530i 1.62475 1.45745i
\(323\) 4.05097i 0.225402i
\(324\) 7.75999 13.4407i 0.431111 0.746706i
\(325\) 7.14570 26.6681i 0.396372 1.47928i
\(326\) 25.0788 14.4793i 1.38899 0.801932i
\(327\) −1.88209 + 3.25988i −0.104080 + 0.180272i
\(328\) −39.8261 + 45.6681i −2.19903 + 2.52160i
\(329\) 5.02526 + 9.90830i 0.277052 + 0.546263i
\(330\) 4.49253i 0.247306i
\(331\) 7.60273 2.03715i 0.417884 0.111972i −0.0437493 0.999043i \(-0.513930\pi\)
0.461633 + 0.887071i \(0.347264\pi\)
\(332\) −8.04577 13.9357i −0.441569 0.764820i
\(333\) −5.42800 + 3.13386i −0.297453 + 0.171734i
\(334\) −0.618657 2.30886i −0.0338514 0.126335i
\(335\) 5.37669 + 5.37669i 0.293760 + 0.293760i
\(336\) −41.8435 27.2847i −2.28275 1.48850i
\(337\) 4.98392i 0.271491i −0.990744 0.135746i \(-0.956657\pi\)
0.990744 0.135746i \(-0.0433430\pi\)
\(338\) 43.3417 75.0700i 2.35748 4.08327i
\(339\) −3.75104 + 13.9991i −0.203729 + 0.760326i
\(340\) −1.28619 + 4.80012i −0.0697533 + 0.260323i
\(341\) 4.88874 1.30993i 0.264740 0.0709369i
\(342\) 11.2471 11.2471i 0.608176 0.608176i
\(343\) −15.0439 + 10.8019i −0.812295 + 0.583246i
\(344\) 15.3424 0.827209
\(345\) −1.65643 6.18186i −0.0891790 0.332820i
\(346\) 26.3946 + 45.7167i 1.41898 + 2.45775i
\(347\) 0.415562 + 0.111349i 0.0223085 + 0.00597755i 0.269956 0.962873i \(-0.412991\pi\)
−0.247648 + 0.968850i \(0.579657\pi\)
\(348\) 55.2853 + 31.9190i 2.96360 + 1.71104i
\(349\) 20.3213i 1.08778i −0.839158 0.543888i \(-0.816952\pi\)
0.839158 0.543888i \(-0.183048\pi\)
\(350\) −6.14941 29.1985i −0.328700 1.56073i
\(351\) 37.2228 1.98681
\(352\) 7.87393 + 29.3859i 0.419682 + 1.56627i
\(353\) −7.32336 12.6844i −0.389783 0.675125i 0.602637 0.798016i \(-0.294117\pi\)
−0.992420 + 0.122891i \(0.960783\pi\)
\(354\) −1.24633 0.333954i −0.0662419 0.0177495i
\(355\) 1.95402 + 7.29249i 0.103708 + 0.387045i
\(356\) −0.979776 0.979776i −0.0519280 0.0519280i
\(357\) −1.01315 + 3.09848i −0.0536218 + 0.163989i
\(358\) 15.9597 + 15.9597i 0.843494 + 0.843494i
\(359\) 17.2037 29.7977i 0.907978 1.57266i 0.0911080 0.995841i \(-0.470959\pi\)
0.816870 0.576822i \(-0.195708\pi\)
\(360\) 10.7127 6.18496i 0.564607 0.325976i
\(361\) 1.47567 0.851978i 0.0776668 0.0448410i
\(362\) −56.0411 + 15.0162i −2.94545 + 0.789232i
\(363\) 8.10520 8.10520i 0.425413 0.425413i
\(364\) 5.24009 96.5391i 0.274655 5.06002i
\(365\) 2.63425 0.137883
\(366\) −23.4633 + 6.28696i −1.22644 + 0.328625i
\(367\) −1.23300 + 0.711873i −0.0643621 + 0.0371595i −0.531836 0.846848i \(-0.678498\pi\)
0.467474 + 0.884007i \(0.345164\pi\)
\(368\) 40.4385 + 70.0416i 2.10801 + 3.65117i
\(369\) −2.90489 8.48010i −0.151222 0.441456i
\(370\) 11.4212 0.593760
\(371\) −0.165102 + 3.04170i −0.00857166 + 0.157917i
\(372\) −17.7661 17.7661i −0.921132 0.921132i
\(373\) −12.2063 + 21.1419i −0.632018 + 1.09469i 0.355120 + 0.934821i \(0.384440\pi\)
−0.987139 + 0.159867i \(0.948893\pi\)
\(374\) 3.20859 1.85248i 0.165912 0.0957894i
\(375\) −10.4141 2.79044i −0.537780 0.144098i
\(376\) −38.3833 + 10.2848i −1.97947 + 0.530397i
\(377\) 61.7735i 3.18150i
\(378\) 35.8789 18.1970i 1.84541 0.935950i
\(379\) −34.1500 −1.75417 −0.877085 0.480336i \(-0.840515\pi\)
−0.877085 + 0.480336i \(0.840515\pi\)
\(380\) −20.4946 + 5.49151i −1.05135 + 0.281709i
\(381\) −0.478510 + 1.78583i −0.0245148 + 0.0914906i
\(382\) −11.6714 + 43.5583i −0.597161 + 2.22864i
\(383\) 0.327322 + 1.22158i 0.0167254 + 0.0624200i 0.973784 0.227474i \(-0.0730466\pi\)
−0.957059 + 0.289894i \(0.906380\pi\)
\(384\) 33.8434 33.8434i 1.72706 1.72706i
\(385\) 1.87863 2.88105i 0.0957440 0.146832i
\(386\) −16.2268 + 16.2268i −0.825921 + 0.825921i
\(387\) −1.13482 + 1.96556i −0.0576859 + 0.0999150i
\(388\) −5.34338 1.43175i −0.271269 0.0726863i
\(389\) −3.64580 + 2.10490i −0.184849 + 0.106723i −0.589569 0.807718i \(-0.700702\pi\)
0.404720 + 0.914441i \(0.367369\pi\)
\(390\) −18.6896 10.7905i −0.946385 0.546396i
\(391\) 3.73209 3.73209i 0.188740 0.188740i
\(392\) −26.7174 60.6161i −1.34943 3.06157i
\(393\) −14.0302 + 14.0302i −0.707728 + 0.707728i
\(394\) 25.5604 44.2719i 1.28772 2.23039i
\(395\) −13.9227 3.73059i −0.700529 0.187706i
\(396\) −10.2863 2.75622i −0.516908 0.138505i
\(397\) 15.7248 4.21345i 0.789205 0.211467i 0.158366 0.987380i \(-0.449377\pi\)
0.630839 + 0.775914i \(0.282711\pi\)
\(398\) −18.6710 18.6710i −0.935892 0.935892i
\(399\) −13.6198 + 2.86841i −0.681841 + 0.143600i
\(400\) 61.6167 3.08084
\(401\) 6.31018 + 3.64318i 0.315115 + 0.181932i 0.649213 0.760606i \(-0.275098\pi\)
−0.334098 + 0.942538i \(0.608432\pi\)
\(402\) −24.3720 + 14.0712i −1.21556 + 0.701807i
\(403\) 6.29256 23.4842i 0.313455 1.16983i
\(404\) 7.54289 + 28.1505i 0.375273 + 1.40054i
\(405\) 2.65225i 0.131791i
\(406\) 30.1989 + 59.5432i 1.49875 + 2.95508i
\(407\) −4.40766 4.40766i −0.218479 0.218479i
\(408\) −10.0979 5.83000i −0.499919 0.288628i
\(409\) −3.31222 5.73693i −0.163779 0.283673i 0.772442 0.635085i \(-0.219035\pi\)
−0.936221 + 0.351412i \(0.885702\pi\)
\(410\) −3.14214 + 16.0291i −0.155179 + 0.791620i
\(411\) −11.4231 + 19.7854i −0.563460 + 0.975941i
\(412\) 53.6746i 2.64436i
\(413\) −0.659623 0.735341i −0.0324579 0.0361838i
\(414\) −20.7236 −1.01851
\(415\) −2.38151 1.37496i −0.116904 0.0674943i
\(416\) 141.162 + 37.8242i 6.92103 + 1.85448i
\(417\) 1.26396 4.71718i 0.0618966 0.231001i
\(418\) 13.6994 + 7.90935i 0.670059 + 0.386859i
\(419\) 28.2365i 1.37944i −0.724075 0.689721i \(-0.757733\pi\)
0.724075 0.689721i \(-0.242267\pi\)
\(420\) −17.0492 0.925420i −0.831915 0.0451559i
\(421\) 7.29391 + 7.29391i 0.355484 + 0.355484i 0.862145 0.506662i \(-0.169121\pi\)
−0.506662 + 0.862145i \(0.669121\pi\)
\(422\) −24.1995 + 6.48424i −1.17801 + 0.315648i
\(423\) 1.52144 5.67811i 0.0739751 0.276079i
\(424\) −10.5243 2.81997i −0.511104 0.136950i
\(425\) −1.04073 3.88405i −0.0504827 0.188404i
\(426\) −27.9423 −1.35381
\(427\) −17.6759 5.77976i −0.855399 0.279702i
\(428\) −32.4188 −1.56702
\(429\) 3.04843 + 11.3769i 0.147180 + 0.549282i
\(430\) 3.58169 2.06789i 0.172725 0.0997225i
\(431\) 5.69115 3.28579i 0.274133 0.158271i −0.356631 0.934245i \(-0.616075\pi\)
0.630764 + 0.775974i \(0.282741\pi\)
\(432\) 21.5009 + 80.2423i 1.03446 + 3.86066i
\(433\) −34.8748 −1.67598 −0.837989 0.545688i \(-0.816268\pi\)
−0.837989 + 0.545688i \(0.816268\pi\)
\(434\) −5.41522 25.7125i −0.259939 1.23424i
\(435\) 10.9094 0.523068
\(436\) −4.20818 15.7052i −0.201535 0.752140i
\(437\) 21.7670 + 5.83245i 1.04126 + 0.279004i
\(438\) −2.52339 + 9.41741i −0.120572 + 0.449981i
\(439\) 15.4272 4.13371i 0.736301 0.197291i 0.128868 0.991662i \(-0.458866\pi\)
0.607433 + 0.794371i \(0.292199\pi\)
\(440\) 8.69891 + 8.69891i 0.414704 + 0.414704i
\(441\) 9.74185 + 1.06069i 0.463897 + 0.0505090i
\(442\) 17.7976i 0.846545i
\(443\) 9.33765 + 5.39109i 0.443645 + 0.256139i 0.705143 0.709066i \(-0.250883\pi\)
−0.261498 + 0.965204i \(0.584216\pi\)
\(444\) −8.00892 + 29.8897i −0.380086 + 1.41850i
\(445\) −0.228723 0.0612860i −0.0108425 0.00290524i
\(446\) 21.3354 + 12.3180i 1.01026 + 0.583273i
\(447\) 13.1067 0.619925
\(448\) 77.2704 16.2737i 3.65069 0.768859i
\(449\) 0.416951i 0.0196771i −0.999952 0.00983856i \(-0.996868\pi\)
0.999952 0.00983856i \(-0.00313176\pi\)
\(450\) −7.89421 + 13.6732i −0.372137 + 0.644559i
\(451\) 7.39853 4.97331i 0.348383 0.234184i
\(452\) −31.3007 54.2144i −1.47226 2.55003i
\(453\) −11.7760 6.79887i −0.553284 0.319439i
\(454\) 54.1199 + 54.1199i 2.53997 + 2.53997i
\(455\) −7.47340 14.7353i −0.350358 0.690801i
\(456\) 49.7836i 2.33133i
\(457\) 2.56046 + 9.55576i 0.119773 + 0.447000i 0.999600 0.0282955i \(-0.00900795\pi\)
−0.879826 + 0.475295i \(0.842341\pi\)
\(458\) −1.72321 + 6.43112i −0.0805205 + 0.300507i
\(459\) 4.69496 2.71064i 0.219142 0.126522i
\(460\) 23.9406 + 13.8221i 1.11623 + 0.644458i
\(461\) 21.6018 1.00610 0.503048 0.864258i \(-0.332212\pi\)
0.503048 + 0.864258i \(0.332212\pi\)
\(462\) 8.50015 + 9.47588i 0.395463 + 0.440858i
\(463\) −4.65017 4.65017i −0.216112 0.216112i 0.590746 0.806858i \(-0.298834\pi\)
−0.806858 + 0.590746i \(0.798834\pi\)
\(464\) −133.167 + 35.6820i −6.18212 + 1.65649i
\(465\) −4.14740 1.11129i −0.192331 0.0515349i
\(466\) 16.0664 + 4.30497i 0.744259 + 0.199424i
\(467\) −11.1212 + 19.2625i −0.514628 + 0.891361i 0.485228 + 0.874387i \(0.338736\pi\)
−0.999856 + 0.0169737i \(0.994597\pi\)
\(468\) −36.1727 + 36.1727i −1.67208 + 1.67208i
\(469\) −21.5138 1.16776i −0.993416 0.0539221i
\(470\) −7.57438 + 7.57438i −0.349380 + 0.349380i
\(471\) −26.2472 15.1538i −1.20941 0.698253i
\(472\) 3.05992 1.76665i 0.140844 0.0813165i
\(473\) −2.18028 0.584204i −0.100249 0.0268617i
\(474\) 26.6736 46.2000i 1.22516 2.12204i
\(475\) 12.1398 12.1398i 0.557014 0.557014i
\(476\) −6.36922 12.5582i −0.291933 0.575604i
\(477\) 1.13971 1.13971i 0.0521837 0.0521837i
\(478\) 2.33494 + 8.71413i 0.106798 + 0.398575i
\(479\) −5.68661 + 21.2227i −0.259828 + 0.969690i 0.705513 + 0.708697i \(0.250717\pi\)
−0.965341 + 0.260993i \(0.915950\pi\)
\(480\) 6.67990 24.9297i 0.304894 1.13788i
\(481\) −28.9231 + 7.74992i −1.31878 + 0.353366i
\(482\) 69.4165 3.16184
\(483\) 15.1903 + 9.90504i 0.691182 + 0.450695i
\(484\) 49.5116i 2.25053i
\(485\) −0.913144 + 0.244676i −0.0414637 + 0.0111102i
\(486\) −34.5801 9.26570i −1.56858 0.420301i
\(487\) −10.0525 + 5.80383i −0.455523 + 0.262997i −0.710160 0.704040i \(-0.751377\pi\)
0.254637 + 0.967037i \(0.418044\pi\)
\(488\) 33.2585 57.6055i 1.50554 2.60768i
\(489\) 9.48093 + 9.48093i 0.428742 + 0.428742i
\(490\) −14.4071 10.5498i −0.650848 0.476591i
\(491\) −39.6607 −1.78986 −0.894930 0.446206i \(-0.852775\pi\)
−0.894930 + 0.446206i \(0.852775\pi\)
\(492\) −39.7453 19.4632i −1.79186 0.877469i
\(493\) 4.49847 + 7.79157i 0.202601 + 0.350915i
\(494\) 65.8081 37.9943i 2.96085 1.70945i
\(495\) −1.75786 + 0.471017i −0.0790100 + 0.0211707i
\(496\) 54.2602 2.43636
\(497\) −17.9193 11.6846i −0.803792 0.524124i
\(498\) 7.19675 7.19675i 0.322494 0.322494i
\(499\) −23.7101 + 6.35311i −1.06141 + 0.284404i −0.746960 0.664869i \(-0.768487\pi\)
−0.314451 + 0.949274i \(0.601821\pi\)
\(500\) 40.3306 23.2849i 1.80364 1.04133i
\(501\) 0.958459 0.553367i 0.0428208 0.0247226i
\(502\) −25.1446 + 43.5518i −1.12226 + 1.94381i
\(503\) −4.27086 4.27086i −0.190428 0.190428i 0.605453 0.795881i \(-0.292992\pi\)
−0.795881 + 0.605453i \(0.792992\pi\)
\(504\) −10.8934 + 33.3146i −0.485229 + 1.48395i
\(505\) 3.52168 + 3.52168i 0.156713 + 0.156713i
\(506\) −5.33427 19.9078i −0.237137 0.885008i
\(507\) 38.7676 + 10.3878i 1.72173 + 0.461336i
\(508\) −3.99294 6.91598i −0.177158 0.306847i
\(509\) −1.98975 7.42583i −0.0881939 0.329144i 0.907706 0.419607i \(-0.137832\pi\)
−0.995900 + 0.0904627i \(0.971165\pi\)
\(510\) −3.14313 −0.139180
\(511\) −5.55630 + 4.98417i −0.245796 + 0.220487i
\(512\) 43.6565i 1.92936i
\(513\) 20.0456 + 11.5734i 0.885036 + 0.510976i
\(514\) −38.5859 10.3391i −1.70195 0.456037i
\(515\) 4.58630 + 7.94370i 0.202096 + 0.350041i
\(516\) 2.90015 + 10.8235i 0.127672 + 0.476478i
\(517\) 5.84619 0.257115
\(518\) −24.0902 + 21.6096i −1.05846 + 0.949471i
\(519\) −17.2830 + 17.2830i −0.758639 + 0.758639i
\(520\) 57.0824 15.2952i 2.50323 0.670738i
\(521\) −6.08798 + 22.7207i −0.266719 + 0.995410i 0.694470 + 0.719521i \(0.255639\pi\)
−0.961190 + 0.275889i \(0.911028\pi\)
\(522\) 9.14300 34.1221i 0.400178 1.49349i
\(523\) −7.41375 + 12.8410i −0.324181 + 0.561498i −0.981346 0.192249i \(-0.938422\pi\)
0.657165 + 0.753746i \(0.271755\pi\)
\(524\) 85.7049i 3.74403i
\(525\) 12.3216 6.24924i 0.537760 0.272739i
\(526\) 5.19368 + 5.19368i 0.226455 + 0.226455i
\(527\) −0.916473 3.42032i −0.0399222 0.148992i
\(528\) −22.7647 + 13.1432i −0.990705 + 0.571984i
\(529\) −3.18024 5.50834i −0.138271 0.239493i
\(530\) −2.83697 + 0.760164i −0.123230 + 0.0330194i
\(531\) 0.522685i 0.0226826i
\(532\) 32.8380 50.3600i 1.42371 2.18338i
\(533\) −2.91945 42.7242i −0.126455 1.85059i
\(534\) 0.438193 0.758972i 0.0189625 0.0328439i
\(535\) −4.79790 + 2.77007i −0.207431 + 0.119761i
\(536\) 19.9455 74.4377i 0.861515 3.21522i
\(537\) −5.22514 + 9.05021i −0.225482 + 0.390545i
\(538\) 7.59343i 0.327376i
\(539\) 1.48863 + 9.63135i 0.0641196 + 0.414852i
\(540\) 20.0781 + 20.0781i 0.864024 + 0.864024i
\(541\) 15.4113 + 8.89770i 0.662582 + 0.382542i 0.793260 0.608883i \(-0.208382\pi\)
−0.130678 + 0.991425i \(0.541715\pi\)
\(542\) −55.2557 + 31.9019i −2.37343 + 1.37030i
\(543\) −13.4314 23.2639i −0.576398 0.998351i
\(544\) 20.5593 5.50886i 0.881475 0.236190i
\(545\) −1.96475 1.96475i −0.0841606 0.0841606i
\(546\) 59.8372 12.6021i 2.56080 0.539321i
\(547\) 0.892822 0.892822i 0.0381743 0.0381743i −0.687762 0.725936i \(-0.741407\pi\)
0.725936 + 0.687762i \(0.241407\pi\)
\(548\) −25.5410 95.3204i −1.09106 4.07188i
\(549\) 4.91999 + 8.52166i 0.209980 + 0.363696i
\(550\) −15.1669 4.06395i −0.646717 0.173287i
\(551\) −19.2067 + 33.2669i −0.818231 + 1.41722i
\(552\) −45.8648 + 45.8648i −1.95214 + 1.95214i
\(553\) 36.4251 18.4739i 1.54895 0.785592i
\(554\) 10.3608i 0.440190i
\(555\) 1.36867 + 5.10793i 0.0580966 + 0.216820i
\(556\) 10.5472 + 18.2683i 0.447300 + 0.774747i
\(557\) 14.5959 + 3.91096i 0.618448 + 0.165713i 0.554422 0.832236i \(-0.312939\pi\)
0.0640258 + 0.997948i \(0.479606\pi\)
\(558\) −6.95171 + 12.0407i −0.294289 + 0.509724i
\(559\) −7.66711 + 7.66711i −0.324284 + 0.324284i
\(560\) 27.4484 24.6221i 1.15991 1.04047i
\(561\) 1.21299 + 1.21299i 0.0512125 + 0.0512125i
\(562\) −27.9539 + 7.49022i −1.17916 + 0.315956i
\(563\) 4.84773 18.0920i 0.204308 0.762486i −0.785352 0.619050i \(-0.787518\pi\)
0.989659 0.143437i \(-0.0458154\pi\)
\(564\) −14.5110 25.1338i −0.611024 1.05833i
\(565\) −9.26484 5.34906i −0.389775 0.225037i
\(566\) 46.0389i 1.93516i
\(567\) 5.01822 + 5.59426i 0.210746 + 0.234937i
\(568\) 54.1048 54.1048i 2.27019 2.27019i
\(569\) −4.57595 2.64192i −0.191834 0.110755i 0.401007 0.916075i \(-0.368660\pi\)
−0.592841 + 0.805320i \(0.701994\pi\)
\(570\) −6.70995 11.6220i −0.281049 0.486791i
\(571\) −2.79809 + 10.4426i −0.117097 + 0.437010i −0.999435 0.0336048i \(-0.989301\pi\)
0.882339 + 0.470615i \(0.155968\pi\)
\(572\) −44.0595 25.4377i −1.84222 1.06361i
\(573\) −20.8793 −0.872247
\(574\) −23.7004 39.7545i −0.989237 1.65932i
\(575\) −22.3685 −0.932830
\(576\) −36.1844 20.8911i −1.50768 0.870461i
\(577\) 9.21226 34.3806i 0.383511 1.43128i −0.456988 0.889473i \(-0.651072\pi\)
0.840500 0.541812i \(-0.182261\pi\)
\(578\) 21.9260 + 37.9769i 0.912001 + 1.57963i
\(579\) −9.20168 5.31259i −0.382409 0.220784i
\(580\) −33.3208 + 33.3208i −1.38357 + 1.38357i
\(581\) 7.62471 1.60581i 0.316326 0.0666204i
\(582\) 3.49885i 0.145032i
\(583\) 1.38820 + 0.801479i 0.0574935 + 0.0331939i
\(584\) −13.3489 23.1210i −0.552383 0.956755i
\(585\) −2.26264 + 8.44428i −0.0935486 + 0.349128i
\(586\) −26.1470 + 7.00607i −1.08012 + 0.289418i
\(587\) 19.3887 + 19.3887i 0.800257 + 0.800257i 0.983136 0.182878i \(-0.0585414\pi\)
−0.182878 + 0.983136i \(0.558541\pi\)
\(588\) 37.7119 30.3062i 1.55521 1.24980i
\(589\) 10.6904 10.6904i 0.440492 0.440492i
\(590\) 0.476225 0.824847i 0.0196059 0.0339584i
\(591\) 22.8629 + 6.12610i 0.940454 + 0.251994i
\(592\) −33.4134 57.8738i −1.37328 2.37860i
\(593\) −8.15983 30.4529i −0.335084 1.25055i −0.903778 0.428001i \(-0.859218\pi\)
0.568694 0.822549i \(-0.307449\pi\)
\(594\) 21.1696i 0.868600i
\(595\) −2.01568 1.31435i −0.0826348 0.0538832i
\(596\) −40.0319 + 40.0319i −1.63977 + 1.63977i
\(597\) 6.11283 10.5877i 0.250181 0.433327i
\(598\) −95.6315 25.6244i −3.91066 1.04786i
\(599\) 23.5361 + 40.7657i 0.961659 + 1.66564i 0.718336 + 0.695697i \(0.244904\pi\)
0.243323 + 0.969945i \(0.421762\pi\)
\(600\) 12.7898 + 47.7322i 0.522141 + 1.94866i
\(601\) −21.3978 + 21.3978i −0.872833 + 0.872833i −0.992780 0.119947i \(-0.961727\pi\)
0.119947 + 0.992780i \(0.461727\pi\)
\(602\) −3.64211 + 11.1385i −0.148441 + 0.453970i
\(603\) 8.06111 + 8.06111i 0.328274 + 0.328274i
\(604\) 56.7333 15.2017i 2.30845 0.618546i
\(605\) 4.23058 + 7.32759i 0.171998 + 0.297909i
\(606\) −15.9634 + 9.21648i −0.648470 + 0.374394i
\(607\) 11.7582 + 6.78858i 0.477249 + 0.275540i 0.719270 0.694731i \(-0.244477\pi\)
−0.242020 + 0.970271i \(0.577810\pi\)
\(608\) 64.2596 + 64.2596i 2.60607 + 2.60607i
\(609\) −23.0107 + 20.6413i −0.932442 + 0.836429i
\(610\) 17.9307i 0.725991i
\(611\) 14.0417 24.3210i 0.568068 0.983923i
\(612\) −1.92834 + 7.19666i −0.0779485 + 0.290908i
\(613\) −0.194608 + 0.112357i −0.00786015 + 0.00453806i −0.503925 0.863747i \(-0.668111\pi\)
0.496065 + 0.868286i \(0.334778\pi\)
\(614\) −29.1427 + 50.4766i −1.17610 + 2.03707i
\(615\) −7.54526 + 0.515586i −0.304254 + 0.0207904i
\(616\) −34.8071 1.88931i −1.40242 0.0761223i
\(617\) 15.5281i 0.625139i 0.949895 + 0.312569i \(0.101190\pi\)
−0.949895 + 0.312569i \(0.898810\pi\)
\(618\) −32.7919 + 8.78656i −1.31908 + 0.353447i
\(619\) 5.32577 + 9.22451i 0.214061 + 0.370764i 0.952982 0.303028i \(-0.0979976\pi\)
−0.738921 + 0.673792i \(0.764664\pi\)
\(620\) 16.0617 9.27320i 0.645052 0.372421i
\(621\) −7.80537 29.1300i −0.313219 1.16895i
\(622\) −57.1468 57.1468i −2.29138 2.29138i
\(623\) 0.598390 0.303490i 0.0239740 0.0121591i
\(624\) 126.273i 5.05495i
\(625\) −6.34113 + 10.9832i −0.253645 + 0.439327i
\(626\) −14.3184 + 53.4371i −0.572280 + 2.13578i
\(627\) −1.89564 + 7.07463i −0.0757047 + 0.282534i
\(628\) 126.452 33.8826i 5.04597 1.35206i
\(629\) −3.08374 + 3.08374i −0.122957 + 0.122957i
\(630\) 1.94717 + 9.24553i 0.0775771 + 0.368351i
\(631\) −15.5948 −0.620820 −0.310410 0.950603i \(-0.600466\pi\)
−0.310410 + 0.950603i \(0.600466\pi\)
\(632\) 37.8091 + 141.105i 1.50396 + 5.61287i
\(633\) −5.79993 10.0458i −0.230526 0.399283i
\(634\) 64.6283 + 17.3171i 2.56672 + 0.687750i
\(635\) −1.18189 0.682365i −0.0469019 0.0270788i
\(636\) 7.95751i 0.315536i
\(637\) 43.6433 + 16.9403i 1.72921 + 0.671198i
\(638\) 35.1322 1.39090
\(639\) 2.92960 + 10.9334i 0.115893 + 0.432519i
\(640\) 17.6649 + 30.5964i 0.698265 + 1.20943i
\(641\) 13.6296 + 3.65205i 0.538339 + 0.144247i 0.517736 0.855540i \(-0.326775\pi\)
0.0206025 + 0.999788i \(0.493442\pi\)
\(642\) −5.30698 19.8059i −0.209450 0.781677i
\(643\) 4.78199 + 4.78199i 0.188583 + 0.188583i 0.795083 0.606500i \(-0.207427\pi\)
−0.606500 + 0.795083i \(0.707427\pi\)
\(644\) −76.6489 + 16.1428i −3.02039 + 0.636114i
\(645\) 1.35404 + 1.35404i 0.0533154 + 0.0533154i
\(646\) 5.53364 9.58455i 0.217718 0.377099i
\(647\) −9.95932 + 5.75002i −0.391541 + 0.226057i −0.682828 0.730579i \(-0.739250\pi\)
0.291286 + 0.956636i \(0.405917\pi\)
\(648\) −23.2790 + 13.4401i −0.914485 + 0.527978i
\(649\) −0.502108 + 0.134539i −0.0197095 + 0.00528114i
\(650\) −53.3353 + 53.3353i −2.09198 + 2.09198i
\(651\) 10.8505 5.50313i 0.425266 0.215685i
\(652\) −57.9154 −2.26814
\(653\) −15.9848 + 4.28311i −0.625532 + 0.167611i −0.557641 0.830082i \(-0.688294\pi\)
−0.0678907 + 0.997693i \(0.521627\pi\)
\(654\) 8.90600 5.14188i 0.348252 0.201063i
\(655\) −7.32317 12.6841i −0.286140 0.495609i
\(656\) 90.4154 30.9721i 3.53013 1.20926i
\(657\) 3.94945 0.154083
\(658\) 1.64507 30.3074i 0.0641315 1.18151i
\(659\) 24.9047 + 24.9047i 0.970148 + 0.970148i 0.999567 0.0294195i \(-0.00936587\pi\)
−0.0294195 + 0.999567i \(0.509366\pi\)
\(660\) −4.49241 + 7.78107i −0.174867 + 0.302878i
\(661\) 8.05623 4.65127i 0.313351 0.180913i −0.335074 0.942192i \(-0.608761\pi\)
0.648425 + 0.761278i \(0.275428\pi\)
\(662\) −20.7707 5.56549i −0.807277 0.216309i
\(663\) 7.95966 2.13279i 0.309128 0.0828305i
\(664\) 27.8702i 1.08157i
\(665\) 0.556854 10.2590i 0.0215939 0.397828i
\(666\) 17.1234 0.663520
\(667\) 48.3430 12.9535i 1.87185 0.501561i
\(668\) −1.23728 + 4.61758i −0.0478717 + 0.178660i
\(669\) −2.95227 + 11.0180i −0.114141 + 0.425981i
\(670\) −5.37661 20.0658i −0.207716 0.775208i
\(671\) −6.91978 + 6.91978i −0.267135 + 0.267135i
\(672\) 33.0790 + 65.2218i 1.27605 + 2.51599i
\(673\) 32.1465 32.1465i 1.23916 1.23916i 0.278813 0.960345i \(-0.410059\pi\)
0.960345 0.278813i \(-0.0899409\pi\)
\(674\) −6.80805 + 11.7919i −0.262236 + 0.454206i
\(675\) −22.1929 5.94657i −0.854205 0.228884i
\(676\) −150.136 + 86.6809i −5.77445 + 3.33388i
\(677\) 37.6344 + 21.7282i 1.44641 + 0.835083i 0.998265 0.0588792i \(-0.0187527\pi\)
0.448142 + 0.893963i \(0.352086\pi\)
\(678\) 27.9977 27.9977i 1.07525 1.07525i
\(679\) 1.46311 2.24381i 0.0561489 0.0861094i
\(680\) 6.08605 6.08605i 0.233389 0.233389i
\(681\) −17.7187 + 30.6897i −0.678982 + 1.17603i
\(682\) −13.3561 3.57875i −0.511430 0.137037i
\(683\) 18.9171 + 5.06883i 0.723845 + 0.193954i 0.601886 0.798582i \(-0.294416\pi\)
0.121958 + 0.992535i \(0.461083\pi\)
\(684\) −30.7269 + 8.23325i −1.17487 + 0.314806i
\(685\) −11.9248 11.9248i −0.455623 0.455623i
\(686\) 50.3491 5.00705i 1.92234 0.191170i
\(687\) −3.08271 −0.117613
\(688\) −20.9569 12.0995i −0.798975 0.461289i
\(689\) 6.66855 3.85009i 0.254051 0.146677i
\(690\) −4.52536 + 16.8889i −0.172278 + 0.642949i
\(691\) −6.19134 23.1064i −0.235530 0.879009i −0.977909 0.209030i \(-0.932969\pi\)
0.742379 0.669980i \(-0.233697\pi\)
\(692\) 105.575i 4.01337i
\(693\) 2.81657 4.31947i 0.106993 0.164083i
\(694\) −0.831110 0.831110i −0.0315485 0.0315485i
\(695\) 3.12191 + 1.80244i 0.118421 + 0.0683703i
\(696\) −55.2830 95.7529i −2.09550 3.62950i
\(697\) −3.47949 5.17626i −0.131795 0.196065i
\(698\) −27.7590 + 48.0800i −1.05069 + 1.81986i
\(699\) 7.70128i 0.291289i
\(700\) −18.5469 + 56.7212i −0.701008 + 2.14386i
\(701\) 2.97908 0.112518 0.0562592 0.998416i \(-0.482083\pi\)
0.0562592 + 0.998416i \(0.482083\pi\)
\(702\) −88.0687 50.8465i −3.32394 1.91908i
\(703\) −17.9856 4.81922i −0.678339 0.181760i
\(704\) 10.7547 40.1373i 0.405335 1.51273i
\(705\) −4.29519 2.47983i −0.161766 0.0933957i
\(706\) 40.0149i 1.50598i
\(707\) −14.0913 0.764870i −0.529960 0.0287659i
\(708\) 1.82471 + 1.82471i 0.0685768 + 0.0685768i
\(709\) 24.1959 6.48326i 0.908695 0.243484i 0.225948 0.974139i \(-0.427452\pi\)
0.682746 + 0.730655i \(0.260785\pi\)
\(710\) 5.33838 19.9231i 0.200346 0.747701i
\(711\) −20.8739 5.59315i −0.782834 0.209760i
\(712\) 0.621127 + 2.31808i 0.0232777 + 0.0868736i
\(713\) −19.6979 −0.737691
\(714\) 6.62964 5.94698i 0.248108 0.222560i
\(715\) −8.69425 −0.325147
\(716\) −11.6829 43.6013i −0.436612 1.62946i
\(717\) −3.61743 + 2.08853i −0.135096 + 0.0779974i
\(718\) −81.4075 + 47.0007i −3.03810 + 1.75405i
\(719\) 4.22685 + 15.7748i 0.157635 + 0.588301i 0.998865 + 0.0476244i \(0.0151650\pi\)
−0.841231 + 0.540677i \(0.818168\pi\)
\(720\) −19.5105 −0.727115
\(721\) −24.7036 8.07770i −0.920011 0.300829i
\(722\) −4.65522 −0.173249
\(723\) 8.31857 + 31.0453i 0.309371 + 1.15459i
\(724\) 112.079 + 30.0315i 4.16538 + 1.11611i
\(725\) 9.86869 36.8304i 0.366514 1.36785i
\(726\) −30.2485 + 8.10507i −1.12263 + 0.300807i
\(727\) 13.6361 + 13.6361i 0.505734 + 0.505734i 0.913214 0.407480i \(-0.133593\pi\)
−0.407480 + 0.913214i \(0.633593\pi\)
\(728\) −91.4616 + 140.265i −3.38979 + 5.19856i
\(729\) 25.0971i 0.929524i
\(730\) −6.23261 3.59840i −0.230679 0.133183i
\(731\) −0.408729 + 1.52540i −0.0151174 + 0.0564188i
\(732\) 46.9252 + 12.5736i 1.73440 + 0.464732i
\(733\) −32.7391 18.9019i −1.20925 0.698158i −0.246651 0.969104i \(-0.579330\pi\)
−0.962595 + 0.270946i \(0.912663\pi\)
\(734\) 3.88968 0.143571
\(735\) 2.99172 7.70758i 0.110351 0.284298i
\(736\) 118.403i 4.36438i
\(737\) −5.66882 + 9.81869i −0.208814 + 0.361676i
\(738\) −4.71091 + 24.0319i −0.173411 + 0.884626i
\(739\) 10.7458 + 18.6122i 0.395290 + 0.684662i 0.993138 0.116948i \(-0.0373109\pi\)
−0.597849 + 0.801609i \(0.703978\pi\)
\(740\) −19.7815 11.4209i −0.727184 0.419840i
\(741\) 24.8785 + 24.8785i 0.913933 + 0.913933i
\(742\) 4.54561 6.97110i 0.166874 0.255917i
\(743\) 31.7689i 1.16549i −0.812656 0.582744i \(-0.801979\pi\)
0.812656 0.582744i \(-0.198021\pi\)
\(744\) 11.2628 + 42.0334i 0.412915 + 1.54102i
\(745\) −2.50404 + 9.34519i −0.0917408 + 0.342381i
\(746\) 57.7599 33.3477i 2.11474 1.22095i
\(747\) −3.57052 2.06144i −0.130638 0.0754241i
\(748\) −7.40970 −0.270926
\(749\) 4.87883 14.9207i 0.178269 0.545190i
\(750\) 20.8278 + 20.8278i 0.760523 + 0.760523i
\(751\) −36.2615 + 9.71625i −1.32320 + 0.354551i −0.850177 0.526498i \(-0.823505\pi\)
−0.473026 + 0.881049i \(0.656838\pi\)
\(752\) 60.5404 + 16.2217i 2.20768 + 0.591546i
\(753\) −22.4910 6.02645i −0.819618 0.219616i
\(754\) 84.3828 146.155i 3.07304 5.32266i
\(755\) 7.09746 7.09746i 0.258303 0.258303i
\(756\) −80.3388 4.36074i −2.92189 0.158599i
\(757\) 33.3752 33.3752i 1.21304 1.21304i 0.243022 0.970021i \(-0.421861\pi\)
0.970021 0.243022i \(-0.0781386\pi\)
\(758\) 80.7985 + 46.6490i 2.93473 + 1.69437i
\(759\) 8.26417 4.77132i 0.299970 0.173188i
\(760\) 35.4962 + 9.51117i 1.28758 + 0.345006i
\(761\) 16.2745 28.1882i 0.589949 1.02182i −0.404290 0.914631i \(-0.632481\pi\)
0.994239 0.107190i \(-0.0341854\pi\)
\(762\) 3.57159 3.57159i 0.129385 0.129385i
\(763\) 7.86157 + 0.426721i 0.284608 + 0.0154484i
\(764\) 63.7720 63.7720i 2.30719 2.30719i
\(765\) 0.329539 + 1.22986i 0.0119145 + 0.0444656i
\(766\) 0.894246 3.33737i 0.0323104 0.120584i
\(767\) −0.646291 + 2.41199i −0.0233362 + 0.0870919i
\(768\) −53.3685 + 14.3001i −1.92577 + 0.516009i
\(769\) 32.3717 1.16735 0.583676 0.811986i \(-0.301614\pi\)
0.583676 + 0.811986i \(0.301614\pi\)
\(770\) −8.38035 + 4.25032i −0.302007 + 0.153171i
\(771\) 18.4959i 0.666112i
\(772\) 44.3311 11.8785i 1.59551 0.427516i
\(773\) −22.5931 6.05380i −0.812618 0.217740i −0.171501 0.985184i \(-0.554862\pi\)
−0.641116 + 0.767444i \(0.721528\pi\)
\(774\) 5.36992 3.10032i 0.193018 0.111439i
\(775\) −7.50347 + 12.9964i −0.269533 + 0.466844i
\(776\) 6.77484 + 6.77484i 0.243203 + 0.243203i
\(777\) −12.5514 8.18430i −0.450278 0.293610i
\(778\) 11.5012 0.412339
\(779\) 11.7116 23.9160i 0.419613 0.856880i
\(780\) 21.5803 + 37.3782i 0.772698 + 1.33835i
\(781\) −9.74889 + 5.62853i −0.348843 + 0.201404i
\(782\) −13.9281 + 3.73203i −0.498069 + 0.133457i
\(783\) 51.4072 1.83714
\(784\) −11.3091 + 103.868i −0.403898 + 3.70958i
\(785\) 15.8194 15.8194i 0.564618 0.564618i
\(786\) 52.3604 14.0299i 1.86763 0.500431i
\(787\) −41.7807 + 24.1221i −1.48932 + 0.859861i −0.999926 0.0122008i \(-0.996116\pi\)
−0.489397 + 0.872061i \(0.662783\pi\)
\(788\) −88.5414 + 51.1194i −3.15416 + 1.82105i
\(789\) −1.70039 + 2.94517i −0.0605356 + 0.104851i
\(790\) 27.8450 + 27.8450i 0.990682 + 0.990682i
\(791\) 29.6626 6.24714i 1.05468 0.222123i
\(792\) 13.0420 + 13.0420i 0.463427 + 0.463427i
\(793\) 12.1669 + 45.4077i 0.432061 + 1.61247i
\(794\) −42.9603 11.5112i −1.52460 0.408516i
\(795\) −0.679940 1.17769i −0.0241150 0.0417684i
\(796\) 13.6677 + 51.0087i 0.484440 + 1.80795i
\(797\) −6.95547 −0.246375 −0.123188 0.992383i \(-0.539312\pi\)
−0.123188 + 0.992383i \(0.539312\pi\)
\(798\) 36.1424 + 11.8180i 1.27943 + 0.418353i
\(799\) 4.09019i 0.144700i
\(800\) −78.1205 45.1029i −2.76198 1.59463i
\(801\) −0.342917 0.0918842i −0.0121164 0.00324657i
\(802\) −9.95320 17.2394i −0.351460 0.608746i
\(803\) 1.01659 + 3.79397i 0.0358747 + 0.133886i
\(804\) 56.2831 1.98495
\(805\) −9.96450 + 8.93846i −0.351202 + 0.315039i
\(806\) −46.9676 + 46.9676i −1.65436 + 1.65436i
\(807\) 3.39603 0.909963i 0.119546 0.0320322i
\(808\) 13.0641 48.7560i 0.459594 1.71523i
\(809\) −6.44564 + 24.0555i −0.226617 + 0.845745i 0.755134 + 0.655571i \(0.227572\pi\)
−0.981750 + 0.190174i \(0.939095\pi\)
\(810\) −3.62298 + 6.27519i −0.127299 + 0.220488i
\(811\) 14.6411i 0.514120i −0.966395 0.257060i \(-0.917246\pi\)
0.966395 0.257060i \(-0.0827538\pi\)
\(812\) 7.23691 133.327i 0.253966 4.67886i
\(813\) −20.8891 20.8891i −0.732614 0.732614i
\(814\) 4.40758 + 16.4493i 0.154486 + 0.576548i
\(815\) −8.57133 + 4.94866i −0.300240 + 0.173344i
\(816\) 9.19541 + 15.9269i 0.321904 + 0.557554i
\(817\) −6.51284 + 1.74511i −0.227855 + 0.0610537i
\(818\) 18.0980i 0.632782i
\(819\) −11.2046 22.0922i −0.391521 0.771962i
\(820\) 21.4708 24.6203i 0.749793 0.859779i
\(821\) 14.3436 24.8438i 0.500595 0.867055i −0.499405 0.866369i \(-0.666448\pi\)
1.00000 0.000686765i \(-0.000218604\pi\)
\(822\) 54.0538 31.2080i 1.88534 1.08850i
\(823\) 2.99293 11.1698i 0.104327 0.389354i −0.893941 0.448185i \(-0.852071\pi\)
0.998268 + 0.0588309i \(0.0187373\pi\)
\(824\) 46.4816 80.5085i 1.61926 2.80465i
\(825\) 7.27012i 0.253113i
\(826\) 0.556182 + 2.64086i 0.0193520 + 0.0918871i
\(827\) 7.42878 + 7.42878i 0.258324 + 0.258324i 0.824372 0.566048i \(-0.191528\pi\)
−0.566048 + 0.824372i \(0.691528\pi\)
\(828\) 35.8933 + 20.7230i 1.24738 + 0.720175i
\(829\) −13.9854 + 8.07447i −0.485733 + 0.280438i −0.722802 0.691055i \(-0.757146\pi\)
0.237070 + 0.971493i \(0.423813\pi\)
\(830\) 3.75641 + 6.50629i 0.130387 + 0.225837i
\(831\) −4.63370 + 1.24160i −0.160741 + 0.0430705i
\(832\) −141.146 141.146i −4.89334 4.89334i
\(833\) 6.73841 1.04149i 0.233472 0.0360855i
\(834\) −9.43420 + 9.43420i −0.326680 + 0.326680i
\(835\) 0.211442 + 0.789112i 0.00731725 + 0.0273083i
\(836\) −15.8182 27.3980i −0.547085 0.947580i
\(837\) −19.5433 5.23660i −0.675514 0.181003i
\(838\) −38.5711 + 66.8071i −1.33242 + 2.30781i
\(839\) −6.35304 + 6.35304i −0.219331 + 0.219331i −0.808217 0.588885i \(-0.799567\pi\)
0.588885 + 0.808217i \(0.299567\pi\)
\(840\) 24.7713 + 16.1525i 0.854691 + 0.557313i
\(841\) 56.3134i 1.94184i
\(842\) −7.29379 27.2208i −0.251361 0.938091i
\(843\) −6.69974 11.6043i −0.230751 0.399673i
\(844\) 48.3977 + 12.9681i 1.66592 + 0.446381i
\(845\) −14.8131 + 25.6571i −0.509587 + 0.882631i
\(846\) −11.3560 + 11.3560i −0.390428 + 0.390428i
\(847\) −22.7876 7.45119i −0.782991 0.256026i
\(848\) 12.1517 + 12.1517i 0.417290 + 0.417290i
\(849\) 20.5901 5.51710i 0.706650 0.189346i
\(850\) −2.84327 + 10.6112i −0.0975234 + 0.363962i
\(851\) 12.1299 + 21.0097i 0.415809 + 0.720202i
\(852\) 48.3961 + 27.9415i 1.65802 + 0.957260i
\(853\) 20.7069i 0.708991i −0.935058 0.354495i \(-0.884653\pi\)
0.935058 0.354495i \(-0.115347\pi\)
\(854\) 33.9259 + 37.8202i 1.16092 + 1.29418i
\(855\) −3.84400 + 3.84400i −0.131462 + 0.131462i
\(856\) 48.6262 + 28.0743i 1.66201 + 0.959561i
\(857\) −12.9343 22.4029i −0.441827 0.765267i 0.555998 0.831184i \(-0.312336\pi\)
−0.997825 + 0.0659167i \(0.979003\pi\)
\(858\) 8.32834 31.0818i 0.284325 1.06111i
\(859\) 21.1301 + 12.1995i 0.720949 + 0.416240i 0.815102 0.579317i \(-0.196681\pi\)
−0.0941526 + 0.995558i \(0.530014\pi\)
\(860\) −8.27133 −0.282050
\(861\) 14.9393 15.3636i 0.509131 0.523590i
\(862\) −17.9536 −0.611501
\(863\) 21.4346 + 12.3753i 0.729641 + 0.421259i 0.818291 0.574804i \(-0.194922\pi\)
−0.0886497 + 0.996063i \(0.528255\pi\)
\(864\) 31.4769 117.473i 1.07086 3.99652i
\(865\) −9.02102 15.6249i −0.306724 0.531261i
\(866\) 82.5134 + 47.6391i 2.80392 + 1.61884i
\(867\) −14.3570 + 14.3570i −0.487590 + 0.487590i
\(868\) −16.3326 + 49.9491i −0.554364 + 1.69538i
\(869\) 21.4918i 0.729061i
\(870\) −25.8116 14.9023i −0.875095 0.505236i
\(871\) 27.2315 + 47.1663i 0.922704 + 1.59817i
\(872\) −7.28848 + 27.2010i −0.246819 + 0.921141i
\(873\) −1.36905 + 0.366835i −0.0463353 + 0.0124155i
\(874\) −43.5333 43.5333i −1.47254 1.47254i
\(875\) 4.64732 + 22.0663i 0.157108 + 0.745978i
\(876\) 13.7877 13.7877i 0.465842 0.465842i
\(877\) 16.4119 28.4262i 0.554189 0.959883i −0.443777 0.896137i \(-0.646362\pi\)
0.997966 0.0637463i \(-0.0203048\pi\)
\(878\) −42.1473 11.2933i −1.42240 0.381131i
\(879\) −6.26669 10.8542i −0.211370 0.366104i
\(880\) −5.02202 18.7424i −0.169292 0.631808i
\(881\) 27.8914i 0.939687i −0.882750 0.469843i \(-0.844310\pi\)
0.882750 0.469843i \(-0.155690\pi\)
\(882\) −21.6002 15.8170i −0.727316 0.532585i
\(883\) −34.1842 + 34.1842i −1.15039 + 1.15039i −0.163914 + 0.986475i \(0.552412\pi\)
−0.986475 + 0.163914i \(0.947588\pi\)
\(884\) −17.7971 + 30.8255i −0.598581 + 1.03677i
\(885\) 0.425967 + 0.114138i 0.0143187 + 0.00383669i
\(886\) −14.7285 25.5105i −0.494813 0.857042i
\(887\) 6.87401 + 25.6541i 0.230807 + 0.861382i 0.979995 + 0.199024i \(0.0637773\pi\)
−0.749188 + 0.662358i \(0.769556\pi\)
\(888\) 37.8970 37.8970i 1.27174 1.27174i
\(889\) 3.78398 0.796931i 0.126911 0.0267282i
\(890\) 0.457438 + 0.457438i 0.0153333 + 0.0153333i
\(891\) 3.81989 1.02354i 0.127971 0.0342898i
\(892\) −24.6353 42.6695i −0.824850 1.42868i
\(893\) 15.1238 8.73174i 0.506099 0.292197i
\(894\) −31.0102 17.9038i −1.03714 0.598792i
\(895\) −5.45462 5.45462i −0.182328 0.182328i
\(896\) −95.1500 31.1125i −3.17874 1.03940i
\(897\) 45.8402i 1.53056i
\(898\) −0.569556 + 0.986500i −0.0190063 + 0.0329199i
\(899\) 8.69045 32.4332i 0.289843 1.08171i
\(900\) 27.3456 15.7880i 0.911519 0.526266i
\(901\) 0.560741 0.971233i 0.0186810 0.0323564i
\(902\) −24.2984 + 1.66037i −0.809048 + 0.0552842i
\(903\) −5.41794 0.294083i −0.180298 0.00978646i
\(904\) 108.424i 3.60613i
\(905\) 19.1535 5.13216i 0.636683 0.170599i
\(906\) 18.5745 + 32.1721i 0.617098 + 1.06884i
\(907\) 9.00056 5.19647i 0.298859 0.172546i −0.343071 0.939309i \(-0.611467\pi\)
0.641930 + 0.766763i \(0.278134\pi\)
\(908\) −39.6174 147.854i −1.31475 4.90671i
\(909\) 5.27995 + 5.27995i 0.175125 + 0.175125i
\(910\) −2.44649 + 45.0722i −0.0811004 + 1.49413i
\(911\) 22.7206i 0.752767i −0.926464 0.376384i \(-0.877167\pi\)
0.926464 0.376384i \(-0.122833\pi\)
\(912\) −39.2608 + 68.0016i −1.30005 + 2.25176i
\(913\) 1.06123 3.96057i 0.0351216 0.131076i
\(914\) 6.99519 26.1064i 0.231380 0.863523i
\(915\) 8.01917 2.14873i 0.265106 0.0710348i
\(916\) 9.41555 9.41555i 0.311098 0.311098i
\(917\) 39.4455 + 12.8981i 1.30260 + 0.425931i
\(918\) −14.8110 −0.488835
\(919\) −3.23622 12.0777i −0.106753 0.398407i 0.891785 0.452459i \(-0.149453\pi\)
−0.998538 + 0.0540517i \(0.982786\pi\)
\(920\) −23.9396 41.4645i −0.789264 1.36704i
\(921\) −26.0671 6.98465i −0.858940 0.230152i
\(922\) −51.1096 29.5081i −1.68321 0.971799i
\(923\) 54.0758i 1.77993i
\(924\) −5.24666 24.9121i −0.172603 0.819549i
\(925\) 18.4825 0.607702
\(926\) 4.65009 + 17.3544i 0.152811 + 0.570300i
\(927\) 6.87609 + 11.9097i 0.225841 + 0.391167i
\(928\) 194.954 + 52.2377i 6.39967 + 1.71479i
\(929\) −3.93213 14.6749i −0.129009 0.481468i 0.870942 0.491386i \(-0.163510\pi\)
−0.999951 + 0.00991808i \(0.996843\pi\)
\(930\) 8.29465 + 8.29465i 0.271992 + 0.271992i
\(931\) 18.2362 + 22.6925i 0.597666 + 0.743716i
\(932\) −23.5221 23.5221i −0.770492 0.770492i
\(933\) 18.7097 32.4061i 0.612527 1.06093i
\(934\) 52.6252 30.3832i 1.72195 0.994168i
\(935\) −1.09662 + 0.633132i −0.0358632 + 0.0207056i
\(936\) 85.5818 22.9316i 2.79733 0.749542i
\(937\) −4.75775 + 4.75775i −0.155429 + 0.155429i −0.780538 0.625109i \(-0.785055\pi\)
0.625109 + 0.780538i \(0.285055\pi\)
\(938\) 49.3063 + 32.1509i 1.60991 + 1.04976i
\(939\) −25.6147 −0.835903
\(940\) 20.6930 5.54467i 0.674931 0.180847i
\(941\) −35.3176 + 20.3906i −1.15132 + 0.664716i −0.949209 0.314646i \(-0.898114\pi\)
−0.202113 + 0.979362i \(0.564781\pi\)
\(942\) 41.4004 + 71.7076i 1.34890 + 2.33636i
\(943\) −32.8232 + 11.2437i −1.06887 + 0.366145i
\(944\) −5.57291 −0.181383
\(945\) −12.2625 + 6.21928i −0.398901 + 0.202313i
\(946\) 4.36049 + 4.36049i 0.141772 + 0.141772i
\(947\) 6.33004 10.9639i 0.205699 0.356280i −0.744657 0.667448i \(-0.767387\pi\)
0.950355 + 0.311168i \(0.100720\pi\)
\(948\) −92.3973 + 53.3456i −3.00093 + 1.73259i
\(949\) 18.2252 + 4.88343i 0.591615 + 0.158523i
\(950\) −45.3058 + 12.1396i −1.46991 + 0.393862i
\(951\) 30.9791i 1.00456i
\(952\) −1.32182 + 24.3522i −0.0428405 + 0.789258i
\(953\) 14.4583 0.468350 0.234175 0.972194i \(-0.424761\pi\)
0.234175 + 0.972194i \(0.424761\pi\)
\(954\) −4.25338 + 1.13969i −0.137708 + 0.0368988i
\(955\) 3.98900 14.8872i 0.129081 0.481737i
\(956\) 4.66976 17.4278i 0.151031 0.563654i
\(957\) 4.21009 + 15.7123i 0.136093 + 0.507906i
\(958\) 42.4447 42.4447i 1.37133 1.37133i
\(959\) 47.7148 + 2.58993i 1.54079 + 0.0836332i
\(960\) −24.9269 + 24.9269i −0.804511 + 0.804511i
\(961\) 8.89238 15.4021i 0.286851 0.496840i
\(962\) 79.0180 + 21.1728i 2.54764 + 0.682639i
\(963\) −7.19334 + 4.15308i −0.231802 + 0.133831i
\(964\) −120.230 69.4145i −3.87233 2.23569i
\(965\) 5.54591 5.54591i 0.178529 0.178529i
\(966\) −22.4097 44.1852i −0.721020 1.42163i
\(967\) 14.1690 14.1690i 0.455643 0.455643i −0.441579 0.897222i \(-0.645582\pi\)
0.897222 + 0.441579i \(0.145582\pi\)
\(968\) 42.8765 74.2642i 1.37810 2.38694i
\(969\) 4.94965 + 1.32625i 0.159006 + 0.0426054i
\(970\) 2.49471 + 0.668457i 0.0801005 + 0.0214629i
\(971\) −1.94156 + 0.520239i −0.0623076 + 0.0166953i −0.289838 0.957076i \(-0.593601\pi\)
0.227531 + 0.973771i \(0.426935\pi\)
\(972\) 50.6273 + 50.6273i 1.62387 + 1.62387i
\(973\) −9.99522 + 2.10506i −0.320432 + 0.0674851i
\(974\) 31.7122 1.01612
\(975\) −30.2448 17.4618i −0.968608 0.559226i
\(976\) −90.8586 + 52.4572i −2.90831 + 1.67912i
\(977\) −6.71495 + 25.0605i −0.214830 + 0.801758i 0.771396 + 0.636356i \(0.219559\pi\)
−0.986226 + 0.165402i \(0.947108\pi\)
\(978\) −9.48077 35.3827i −0.303162 1.13141i
\(979\) 0.353068i 0.0112841i
\(980\) 14.4037 + 32.6790i 0.460109 + 1.04389i
\(981\) −2.94569 2.94569i −0.0940485 0.0940485i
\(982\) 93.8366 + 54.1766i 2.99445 + 1.72884i
\(983\) 11.7292 + 20.3155i 0.374102 + 0.647963i 0.990192 0.139712i \(-0.0446177\pi\)
−0.616090 + 0.787676i \(0.711284\pi\)
\(984\) 42.7605 + 63.6126i 1.36316 + 2.02790i
\(985\) −8.73593 + 15.1311i −0.278350 + 0.482116i
\(986\) 24.5797i 0.782776i
\(987\) 13.7516 2.89618i 0.437719 0.0921865i
\(988\) −151.973 −4.83491
\(989\) 7.60791 + 4.39243i 0.241917 + 0.139671i
\(990\) 4.80249 + 1.28682i 0.152633 + 0.0408979i
\(991\) 4.75063 17.7296i 0.150909 0.563199i −0.848512 0.529176i \(-0.822501\pi\)
0.999421 0.0340236i \(-0.0108321\pi\)
\(992\) −68.7936 39.7180i −2.18420 1.26105i
\(993\) 9.95628i 0.315953i
\(994\) 26.4358 + 52.1234i 0.838492 + 1.65325i
\(995\) 6.38129 + 6.38129i 0.202301 + 0.202301i
\(996\) −19.6613 + 5.26823i −0.622993 + 0.166930i
\(997\) −5.22751 + 19.5093i −0.165557 + 0.617867i 0.832411 + 0.554158i \(0.186960\pi\)
−0.997969 + 0.0637092i \(0.979707\pi\)
\(998\) 64.7762 + 17.3567i 2.05046 + 0.549418i
\(999\) 6.44940 + 24.0695i 0.204050 + 0.761524i
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 287.2.r.c.9.1 96
7.4 even 3 inner 287.2.r.c.214.24 yes 96
41.32 even 4 inner 287.2.r.c.114.24 yes 96
287.32 even 12 inner 287.2.r.c.32.1 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.2.r.c.9.1 96 1.1 even 1 trivial
287.2.r.c.32.1 yes 96 287.32 even 12 inner
287.2.r.c.114.24 yes 96 41.32 even 4 inner
287.2.r.c.214.24 yes 96 7.4 even 3 inner