Properties

Label 224.2.be.a.115.12
Level $224$
Weight $2$
Character 224.115
Analytic conductor $1.789$
Analytic rank $0$
Dimension $240$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [224,2,Mod(3,224)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(224, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([12, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("224.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 224.be (of order \(24\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.78864900528\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(30\) over \(\Q(\zeta_{24})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label 115.12
Character \(\chi\) \(=\) 224.115
Dual form 224.2.be.a.187.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.449803 - 1.34077i) q^{2} +(0.100927 + 0.131530i) q^{3} +(-1.59535 + 1.20617i) q^{4} +(-0.463954 + 0.604637i) q^{5} +(0.130955 - 0.194483i) q^{6} +(2.49637 - 0.876446i) q^{7} +(2.33480 + 1.59647i) q^{8} +(0.769343 - 2.87123i) q^{9} +(1.01937 + 0.350091i) q^{10} +(0.485906 - 3.69082i) q^{11} +(-0.319662 - 0.0881027i) q^{12} +(1.74960 - 4.22391i) q^{13} +(-2.29799 - 2.95284i) q^{14} -0.126354 q^{15} +(1.09031 - 3.84854i) q^{16} +(-3.44670 + 5.96986i) q^{17} +(-4.19572 + 0.259971i) q^{18} +(-0.167475 - 1.27210i) q^{19} +(0.0108768 - 1.52422i) q^{20} +(0.367230 + 0.239891i) q^{21} +(-5.16712 + 1.00865i) q^{22} +(6.09119 + 1.63213i) q^{23} +(0.0256590 + 0.468224i) q^{24} +(1.14376 + 4.26858i) q^{25} +(-6.45029 - 0.445893i) q^{26} +(0.914812 - 0.378928i) q^{27} +(-2.92545 + 4.40928i) q^{28} +(-0.478719 + 1.15573i) q^{29} +(0.0568342 + 0.169412i) q^{30} +(1.64276 - 2.84535i) q^{31} +(-5.65044 + 0.269222i) q^{32} +(0.534496 - 0.308592i) q^{33} +(9.55457 + 1.93599i) q^{34} +(-0.628268 + 1.91603i) q^{35} +(2.23581 + 5.50858i) q^{36} +(-7.53920 - 5.78504i) q^{37} +(-1.63027 + 0.796740i) q^{38} +(0.732154 - 0.196180i) q^{39} +(-2.04852 + 0.671014i) q^{40} +(-7.52016 + 7.52016i) q^{41} +(0.156459 - 0.600276i) q^{42} +(5.35637 - 2.21868i) q^{43} +(3.67656 + 6.47425i) q^{44} +(1.37911 + 1.79729i) q^{45} +(-0.551519 - 8.90106i) q^{46} +(4.87523 - 2.81471i) q^{47} +(0.616241 - 0.245011i) q^{48} +(5.46368 - 4.37586i) q^{49} +(5.20874 - 3.45355i) q^{50} +(-1.13308 + 0.149173i) q^{51} +(2.30352 + 8.84895i) q^{52} +(-2.64212 - 0.347842i) q^{53} +(-0.919542 - 1.05611i) q^{54} +(2.00617 + 2.00617i) q^{55} +(7.22773 + 1.93906i) q^{56} +(0.150417 - 0.150417i) q^{57} +(1.76490 + 0.122004i) q^{58} +(-1.73785 + 13.2002i) q^{59} +(0.201579 - 0.152404i) q^{60} +(1.44512 + 10.9768i) q^{61} +(-4.55390 - 0.922729i) q^{62} +(-0.595914 - 7.84192i) q^{63} +(2.90255 + 7.45488i) q^{64} +(1.74220 + 3.01757i) q^{65} +(-0.654170 - 0.577834i) q^{66} +(-7.37852 + 5.66174i) q^{67} +(-1.70195 - 13.6813i) q^{68} +(0.400090 + 0.965903i) q^{69} +(2.85156 - 0.0194686i) q^{70} +(-5.31630 - 5.31630i) q^{71} +(6.38009 - 5.47550i) q^{72} +(1.33462 + 4.98088i) q^{73} +(-4.36527 + 12.7105i) q^{74} +(-0.446012 + 0.581254i) q^{75} +(1.80155 + 1.82744i) q^{76} +(-2.02181 - 9.63951i) q^{77} +(-0.592359 - 0.893411i) q^{78} +(3.13677 + 5.43304i) q^{79} +(1.82111 + 2.44479i) q^{80} +(-7.58065 - 4.37669i) q^{81} +(13.4654 + 6.70025i) q^{82} +(-6.31332 - 2.61506i) q^{83} +(-0.875210 + 0.0602298i) q^{84} +(-2.01049 - 4.85374i) q^{85} +(-5.38407 - 6.18372i) q^{86} +(-0.200329 + 0.0536781i) q^{87} +(7.02679 - 7.84159i) q^{88} +(-3.01639 + 11.2573i) q^{89} +(1.78944 - 2.65750i) q^{90} +(0.665615 - 12.0779i) q^{91} +(-11.6862 + 4.74319i) q^{92} +(0.540049 - 0.0710988i) q^{93} +(-5.96679 - 5.27052i) q^{94} +(0.846859 + 0.488934i) q^{95} +(-0.605692 - 0.716033i) q^{96} -0.918957i q^{97} +(-8.32462 - 5.35730i) q^{98} +(-10.2234 - 4.23466i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23}+ \cdots - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.449803 1.34077i −0.318059 0.948071i
\(3\) 0.100927 + 0.131530i 0.0582701 + 0.0759391i 0.821579 0.570094i \(-0.193093\pi\)
−0.763309 + 0.646033i \(0.776427\pi\)
\(4\) −1.59535 + 1.20617i −0.797677 + 0.603085i
\(5\) −0.463954 + 0.604637i −0.207487 + 0.270402i −0.885492 0.464656i \(-0.846178\pi\)
0.678005 + 0.735057i \(0.262845\pi\)
\(6\) 0.130955 0.194483i 0.0534623 0.0793973i
\(7\) 2.49637 0.876446i 0.943538 0.331265i
\(8\) 2.33480 + 1.59647i 0.825475 + 0.564438i
\(9\) 0.769343 2.87123i 0.256448 0.957076i
\(10\) 1.01937 + 0.350091i 0.322353 + 0.110708i
\(11\) 0.485906 3.69082i 0.146506 1.11282i −0.747337 0.664445i \(-0.768668\pi\)
0.893843 0.448380i \(-0.147999\pi\)
\(12\) −0.319662 0.0881027i −0.0922785 0.0254331i
\(13\) 1.74960 4.22391i 0.485252 1.17150i −0.471831 0.881689i \(-0.656407\pi\)
0.957083 0.289813i \(-0.0935931\pi\)
\(14\) −2.29799 2.95284i −0.614164 0.789179i
\(15\) −0.126354 −0.0326243
\(16\) 1.09031 3.84854i 0.272578 0.962134i
\(17\) −3.44670 + 5.96986i −0.835947 + 1.44790i 0.0573094 + 0.998356i \(0.481748\pi\)
−0.893257 + 0.449547i \(0.851585\pi\)
\(18\) −4.19572 + 0.259971i −0.988941 + 0.0612758i
\(19\) −0.167475 1.27210i −0.0384214 0.291839i −0.999859 0.0168150i \(-0.994647\pi\)
0.961437 0.275024i \(-0.0886860\pi\)
\(20\) 0.0108768 1.52422i 0.00243213 0.340825i
\(21\) 0.367230 + 0.239891i 0.0801361 + 0.0523485i
\(22\) −5.16712 + 1.00865i −1.10163 + 0.215046i
\(23\) 6.09119 + 1.63213i 1.27010 + 0.340323i 0.830070 0.557659i \(-0.188300\pi\)
0.440032 + 0.897982i \(0.354967\pi\)
\(24\) 0.0256590 + 0.468224i 0.00523762 + 0.0955757i
\(25\) 1.14376 + 4.26858i 0.228753 + 0.853716i
\(26\) −6.45029 0.445893i −1.26501 0.0874468i
\(27\) 0.914812 0.378928i 0.176056 0.0729246i
\(28\) −2.92545 + 4.40928i −0.552857 + 0.833276i
\(29\) −0.478719 + 1.15573i −0.0888959 + 0.214614i −0.962075 0.272787i \(-0.912055\pi\)
0.873179 + 0.487400i \(0.162055\pi\)
\(30\) 0.0568342 + 0.169412i 0.0103765 + 0.0309302i
\(31\) 1.64276 2.84535i 0.295049 0.511040i −0.679947 0.733261i \(-0.737997\pi\)
0.974996 + 0.222221i \(0.0713306\pi\)
\(32\) −5.65044 + 0.269222i −0.998867 + 0.0475921i
\(33\) 0.534496 0.308592i 0.0930439 0.0537189i
\(34\) 9.55457 + 1.93599i 1.63860 + 0.332019i
\(35\) −0.628268 + 1.91603i −0.106197 + 0.323867i
\(36\) 2.23581 + 5.50858i 0.372635 + 0.918097i
\(37\) −7.53920 5.78504i −1.23944 0.951054i −0.239634 0.970863i \(-0.577027\pi\)
−0.999804 + 0.0198094i \(0.993694\pi\)
\(38\) −1.63027 + 0.796740i −0.264464 + 0.129248i
\(39\) 0.732154 0.196180i 0.117238 0.0314140i
\(40\) −2.04852 + 0.671014i −0.323900 + 0.106097i
\(41\) −7.52016 + 7.52016i −1.17445 + 1.17445i −0.193315 + 0.981137i \(0.561924\pi\)
−0.981137 + 0.193315i \(0.938076\pi\)
\(42\) 0.156459 0.600276i 0.0241421 0.0926246i
\(43\) 5.35637 2.21868i 0.816839 0.338346i 0.0651601 0.997875i \(-0.479244\pi\)
0.751679 + 0.659529i \(0.229244\pi\)
\(44\) 3.67656 + 6.47425i 0.554263 + 0.976031i
\(45\) 1.37911 + 1.79729i 0.205586 + 0.267924i
\(46\) −0.551519 8.90106i −0.0813170 1.31239i
\(47\) 4.87523 2.81471i 0.711125 0.410568i −0.100352 0.994952i \(-0.531997\pi\)
0.811478 + 0.584384i \(0.198664\pi\)
\(48\) 0.616241 0.245011i 0.0889467 0.0353643i
\(49\) 5.46368 4.37586i 0.780526 0.625123i
\(50\) 5.20874 3.45355i 0.736627 0.488406i
\(51\) −1.13308 + 0.149173i −0.158663 + 0.0208884i
\(52\) 2.30352 + 8.84895i 0.319440 + 1.22713i
\(53\) −2.64212 0.347842i −0.362923 0.0477798i −0.0531403 0.998587i \(-0.516923\pi\)
−0.309783 + 0.950807i \(0.600256\pi\)
\(54\) −0.919542 1.05611i −0.125134 0.143719i
\(55\) 2.00617 + 2.00617i 0.270512 + 0.270512i
\(56\) 7.22773 + 1.93906i 0.965846 + 0.259117i
\(57\) 0.150417 0.150417i 0.0199232 0.0199232i
\(58\) 1.76490 + 0.122004i 0.231743 + 0.0160198i
\(59\) −1.73785 + 13.2002i −0.226248 + 1.71853i 0.381477 + 0.924378i \(0.375415\pi\)
−0.607725 + 0.794147i \(0.707918\pi\)
\(60\) 0.201579 0.152404i 0.0260237 0.0196752i
\(61\) 1.44512 + 10.9768i 0.185028 + 1.40543i 0.791910 + 0.610638i \(0.209087\pi\)
−0.606881 + 0.794793i \(0.707580\pi\)
\(62\) −4.55390 0.922729i −0.578345 0.117187i
\(63\) −0.595914 7.84192i −0.0750781 0.987989i
\(64\) 2.90255 + 7.45488i 0.362819 + 0.931860i
\(65\) 1.74220 + 3.01757i 0.216093 + 0.374284i
\(66\) −0.654170 0.577834i −0.0805227 0.0711264i
\(67\) −7.37852 + 5.66174i −0.901429 + 0.691691i −0.951695 0.307045i \(-0.900660\pi\)
0.0502656 + 0.998736i \(0.483993\pi\)
\(68\) −1.70195 13.6813i −0.206392 1.65911i
\(69\) 0.400090 + 0.965903i 0.0481652 + 0.116281i
\(70\) 2.85156 0.0194686i 0.340826 0.00232694i
\(71\) −5.31630 5.31630i −0.630929 0.630929i 0.317372 0.948301i \(-0.397200\pi\)
−0.948301 + 0.317372i \(0.897200\pi\)
\(72\) 6.38009 5.47550i 0.751901 0.645294i
\(73\) 1.33462 + 4.98088i 0.156206 + 0.582968i 0.998999 + 0.0447307i \(0.0142430\pi\)
−0.842793 + 0.538237i \(0.819090\pi\)
\(74\) −4.36527 + 12.7105i −0.507453 + 1.47757i
\(75\) −0.446012 + 0.581254i −0.0515010 + 0.0671174i
\(76\) 1.80155 + 1.82744i 0.206652 + 0.209622i
\(77\) −2.02181 9.63951i −0.230406 1.09852i
\(78\) −0.592359 0.893411i −0.0670714 0.101159i
\(79\) 3.13677 + 5.43304i 0.352914 + 0.611265i 0.986759 0.162195i \(-0.0518575\pi\)
−0.633845 + 0.773460i \(0.718524\pi\)
\(80\) 1.82111 + 2.44479i 0.203607 + 0.273335i
\(81\) −7.58065 4.37669i −0.842294 0.486299i
\(82\) 13.4654 + 6.70025i 1.48701 + 0.739919i
\(83\) −6.31332 2.61506i −0.692977 0.287040i 0.00826298 0.999966i \(-0.497370\pi\)
−0.701240 + 0.712925i \(0.747370\pi\)
\(84\) −0.875210 + 0.0602298i −0.0954933 + 0.00657161i
\(85\) −2.01049 4.85374i −0.218068 0.526462i
\(86\) −5.38407 6.18372i −0.580579 0.666808i
\(87\) −0.200329 + 0.0536781i −0.0214775 + 0.00575489i
\(88\) 7.02679 7.84159i 0.749058 0.835916i
\(89\) −3.01639 + 11.2573i −0.319736 + 1.19327i 0.599762 + 0.800178i \(0.295262\pi\)
−0.919498 + 0.393094i \(0.871405\pi\)
\(90\) 1.78944 2.65750i 0.188623 0.280125i
\(91\) 0.665615 12.0779i 0.0697754 1.26610i
\(92\) −11.6862 + 4.74319i −1.21837 + 0.494511i
\(93\) 0.540049 0.0710988i 0.0560005 0.00737260i
\(94\) −5.96679 5.27052i −0.615428 0.543612i
\(95\) 0.846859 + 0.488934i 0.0868859 + 0.0501636i
\(96\) −0.605692 0.716033i −0.0618182 0.0730799i
\(97\) 0.918957i 0.0933060i −0.998911 0.0466530i \(-0.985145\pi\)
0.998911 0.0466530i \(-0.0148555\pi\)
\(98\) −8.32462 5.35730i −0.840914 0.541169i
\(99\) −10.2234 4.23466i −1.02749 0.425599i
\(100\) −6.97334 5.43033i −0.697334 0.543033i
\(101\) 5.14716 + 0.677636i 0.512161 + 0.0674273i 0.382178 0.924089i \(-0.375174\pi\)
0.129984 + 0.991516i \(0.458508\pi\)
\(102\) 0.709671 + 1.45211i 0.0702679 + 0.143780i
\(103\) 11.7156 + 3.13918i 1.15437 + 0.309312i 0.784715 0.619857i \(-0.212809\pi\)
0.369654 + 0.929169i \(0.379476\pi\)
\(104\) 10.8283 7.06878i 1.06180 0.693151i
\(105\) −0.315425 + 0.110742i −0.0307823 + 0.0108073i
\(106\) 0.722057 + 3.69895i 0.0701324 + 0.359274i
\(107\) −5.31242 4.07636i −0.513571 0.394077i 0.319206 0.947685i \(-0.396584\pi\)
−0.832777 + 0.553608i \(0.813250\pi\)
\(108\) −1.00240 + 1.70794i −0.0964559 + 0.164347i
\(109\) 3.03629 2.32983i 0.290824 0.223157i −0.453037 0.891492i \(-0.649659\pi\)
0.743861 + 0.668335i \(0.232993\pi\)
\(110\) 1.78744 3.59220i 0.170426 0.342503i
\(111\) 1.57550i 0.149540i
\(112\) −0.651219 10.5630i −0.0615344 0.998105i
\(113\) 5.43512i 0.511293i −0.966770 0.255647i \(-0.917712\pi\)
0.966770 0.255647i \(-0.0822884\pi\)
\(114\) −0.269333 0.134017i −0.0252254 0.0125519i
\(115\) −3.81288 + 2.92573i −0.355553 + 0.272825i
\(116\) −0.630280 2.42122i −0.0585200 0.224804i
\(117\) −10.7818 8.27314i −0.996774 0.764852i
\(118\) 18.4802 3.60745i 1.70124 0.332093i
\(119\) −3.37196 + 17.9238i −0.309107 + 1.64307i
\(120\) −0.295010 0.201720i −0.0269306 0.0184144i
\(121\) −2.76088 0.739776i −0.250989 0.0672524i
\(122\) 14.0674 6.87496i 1.27360 0.622430i
\(123\) −1.74812 0.230144i −0.157622 0.0207514i
\(124\) 0.811185 + 6.52080i 0.0728465 + 0.585585i
\(125\) −6.63217 2.74713i −0.593199 0.245711i
\(126\) −10.2462 + 4.32631i −0.912805 + 0.385418i
\(127\) 8.82945i 0.783487i −0.920074 0.391744i \(-0.871872\pi\)
0.920074 0.391744i \(-0.128128\pi\)
\(128\) 8.68973 7.24490i 0.768071 0.640364i
\(129\) 0.832426 + 0.480601i 0.0732910 + 0.0423146i
\(130\) 3.26224 3.69321i 0.286118 0.323916i
\(131\) 4.66132 0.613674i 0.407261 0.0536170i 0.0758872 0.997116i \(-0.475821\pi\)
0.331374 + 0.943499i \(0.392488\pi\)
\(132\) −0.480497 + 1.13701i −0.0418219 + 0.0989637i
\(133\) −1.53300 3.02884i −0.132928 0.262634i
\(134\) 10.9100 + 7.34627i 0.942480 + 0.634621i
\(135\) −0.195317 + 0.728934i −0.0168102 + 0.0627367i
\(136\) −17.5781 + 8.43585i −1.50731 + 0.723368i
\(137\) −2.10939 + 0.565209i −0.180217 + 0.0482891i −0.347799 0.937569i \(-0.613071\pi\)
0.167582 + 0.985858i \(0.446404\pi\)
\(138\) 1.11510 0.970897i 0.0949233 0.0826482i
\(139\) −4.95117 11.9532i −0.419953 1.01386i −0.982361 0.186996i \(-0.940125\pi\)
0.562407 0.826860i \(-0.309875\pi\)
\(140\) −1.30874 3.81454i −0.110609 0.322387i
\(141\) 0.862262 + 0.357161i 0.0726155 + 0.0300783i
\(142\) −4.73667 + 9.51925i −0.397493 + 0.798838i
\(143\) −14.7396 8.50989i −1.23258 0.711633i
\(144\) −10.2112 6.09137i −0.850933 0.507615i
\(145\) −0.476693 0.825657i −0.0395872 0.0685671i
\(146\) 6.07792 4.02985i 0.503013 0.333512i
\(147\) 1.12699 + 0.276999i 0.0929526 + 0.0228465i
\(148\) 19.0054 + 0.135623i 1.56224 + 0.0111481i
\(149\) 2.32379 3.02842i 0.190372 0.248098i −0.688409 0.725323i \(-0.741691\pi\)
0.878781 + 0.477225i \(0.158357\pi\)
\(150\) 0.979948 + 0.336552i 0.0800124 + 0.0274793i
\(151\) 2.60497 + 9.72187i 0.211989 + 0.791154i 0.987205 + 0.159458i \(0.0509745\pi\)
−0.775216 + 0.631697i \(0.782359\pi\)
\(152\) 1.63985 3.23746i 0.133009 0.262593i
\(153\) 14.4891 + 14.4891i 1.17138 + 1.17138i
\(154\) −12.0150 + 7.04667i −0.968196 + 0.567837i
\(155\) 0.958237 + 2.31339i 0.0769675 + 0.185816i
\(156\) −0.931419 + 1.19608i −0.0745732 + 0.0957629i
\(157\) 4.32395 3.31788i 0.345089 0.264796i −0.421645 0.906761i \(-0.638547\pi\)
0.766734 + 0.641965i \(0.221881\pi\)
\(158\) 5.87356 6.64950i 0.467275 0.529006i
\(159\) −0.220909 0.382626i −0.0175192 0.0303442i
\(160\) 2.45877 3.54137i 0.194383 0.279970i
\(161\) 16.6363 1.26421i 1.31113 0.0996335i
\(162\) −2.45836 + 12.1326i −0.193147 + 0.953226i
\(163\) 2.89751 + 22.0087i 0.226950 + 1.72386i 0.603416 + 0.797427i \(0.293806\pi\)
−0.376465 + 0.926431i \(0.622861\pi\)
\(164\) 2.92673 21.0679i 0.228539 1.64513i
\(165\) −0.0613959 + 0.466349i −0.00477967 + 0.0363052i
\(166\) −0.666459 + 9.64100i −0.0517273 + 0.748287i
\(167\) −2.28366 + 2.28366i −0.176715 + 0.176715i −0.789922 0.613207i \(-0.789879\pi\)
0.613207 + 0.789922i \(0.289879\pi\)
\(168\) 0.474427 + 1.14637i 0.0366028 + 0.0884443i
\(169\) −5.58792 5.58792i −0.429840 0.429840i
\(170\) −5.60345 + 4.87884i −0.429765 + 0.374190i
\(171\) −3.78133 0.497822i −0.289166 0.0380694i
\(172\) −5.86921 + 10.0003i −0.447523 + 0.762514i
\(173\) 17.8137 2.34522i 1.35435 0.178304i 0.581839 0.813304i \(-0.302333\pi\)
0.772512 + 0.635001i \(0.219000\pi\)
\(174\) 0.162079 + 0.244452i 0.0122872 + 0.0185318i
\(175\) 6.59643 + 9.65349i 0.498643 + 0.729736i
\(176\) −13.6745 5.89417i −1.03075 0.444290i
\(177\) −1.91163 + 1.10368i −0.143687 + 0.0829576i
\(178\) 16.4503 1.01928i 1.23300 0.0763980i
\(179\) −3.07134 4.00265i −0.229563 0.299172i 0.664342 0.747429i \(-0.268712\pi\)
−0.893905 + 0.448256i \(0.852045\pi\)
\(180\) −4.36801 1.20388i −0.325572 0.0897316i
\(181\) −10.4866 + 4.34370i −0.779465 + 0.322865i −0.736699 0.676220i \(-0.763617\pi\)
−0.0427652 + 0.999085i \(0.513617\pi\)
\(182\) −16.4931 + 4.54022i −1.22255 + 0.336543i
\(183\) −1.29793 + 1.29793i −0.0959455 + 0.0959455i
\(184\) 11.6161 + 13.5351i 0.856347 + 0.997822i
\(185\) 6.99569 1.87449i 0.514334 0.137815i
\(186\) −0.338243 0.692104i −0.0248012 0.0507475i
\(187\) 20.3589 + 15.6219i 1.48879 + 1.14239i
\(188\) −4.38269 + 10.3708i −0.319641 + 0.756370i
\(189\) 1.95160 1.74773i 0.141958 0.127128i
\(190\) 0.274631 1.35537i 0.0199238 0.0983289i
\(191\) −5.30380 + 3.06215i −0.383769 + 0.221569i −0.679457 0.733715i \(-0.737785\pi\)
0.295688 + 0.955285i \(0.404451\pi\)
\(192\) −0.687597 + 1.13417i −0.0496231 + 0.0818517i
\(193\) 8.12985 14.0813i 0.585199 1.01359i −0.409651 0.912242i \(-0.634350\pi\)
0.994851 0.101353i \(-0.0323171\pi\)
\(194\) −1.23211 + 0.413350i −0.0884607 + 0.0296768i
\(195\) −0.221068 + 0.533706i −0.0158310 + 0.0382195i
\(196\) −3.43849 + 13.5712i −0.245606 + 0.969370i
\(197\) 7.20307 2.98361i 0.513197 0.212573i −0.111029 0.993817i \(-0.535415\pi\)
0.624226 + 0.781244i \(0.285415\pi\)
\(198\) −1.07922 + 15.6120i −0.0766968 + 1.10950i
\(199\) −0.895286 3.34125i −0.0634651 0.236855i 0.926906 0.375294i \(-0.122458\pi\)
−0.990371 + 0.138439i \(0.955792\pi\)
\(200\) −4.14422 + 11.7923i −0.293040 + 0.833838i
\(201\) −1.48938 0.399078i −0.105053 0.0281488i
\(202\) −1.40665 7.20598i −0.0989715 0.507011i
\(203\) −0.182123 + 3.30470i −0.0127825 + 0.231944i
\(204\) 1.62774 1.60467i 0.113965 0.112350i
\(205\) −1.05796 8.03598i −0.0738909 0.561257i
\(206\) −1.06077 17.1199i −0.0739073 1.19280i
\(207\) 9.37244 16.2335i 0.651429 1.12831i
\(208\) −14.3483 11.3388i −0.994873 0.786203i
\(209\) −4.77647 −0.330395
\(210\) 0.290359 + 0.373101i 0.0200367 + 0.0257464i
\(211\) −5.19732 + 12.5474i −0.357798 + 0.863801i 0.637811 + 0.770193i \(0.279840\pi\)
−0.995609 + 0.0936084i \(0.970160\pi\)
\(212\) 4.63468 2.63191i 0.318311 0.180761i
\(213\) 0.162698 1.23581i 0.0111479 0.0846765i
\(214\) −3.07594 + 8.95632i −0.210267 + 0.612242i
\(215\) −1.14361 + 4.26803i −0.0779939 + 0.291077i
\(216\) 2.74085 + 0.575753i 0.186491 + 0.0391750i
\(217\) 1.60714 8.54283i 0.109100 0.579925i
\(218\) −4.48951 3.02302i −0.304068 0.204745i
\(219\) −0.520438 + 0.678248i −0.0351679 + 0.0458318i
\(220\) −5.62033 0.780771i −0.378923 0.0526396i
\(221\) 19.1858 + 25.0034i 1.29058 + 1.68191i
\(222\) −2.11239 + 0.708665i −0.141774 + 0.0475625i
\(223\) −18.0910 −1.21146 −0.605731 0.795669i \(-0.707119\pi\)
−0.605731 + 0.795669i \(0.707119\pi\)
\(224\) −13.8696 + 5.62439i −0.926703 + 0.375795i
\(225\) 13.1360 0.875734
\(226\) −7.28728 + 2.44474i −0.484742 + 0.162621i
\(227\) −10.5180 13.7073i −0.698102 0.909784i 0.300936 0.953644i \(-0.402701\pi\)
−0.999038 + 0.0438601i \(0.986034\pi\)
\(228\) −0.0585400 + 0.421397i −0.00387691 + 0.0279077i
\(229\) −5.61518 + 7.31784i −0.371061 + 0.483577i −0.941142 0.338012i \(-0.890245\pi\)
0.570080 + 0.821589i \(0.306912\pi\)
\(230\) 5.63779 + 3.79622i 0.371745 + 0.250315i
\(231\) 1.06383 1.23881i 0.0699952 0.0815080i
\(232\) −2.96280 + 1.93413i −0.194518 + 0.126982i
\(233\) −0.832350 + 3.10637i −0.0545291 + 0.203505i −0.987816 0.155626i \(-0.950260\pi\)
0.933287 + 0.359132i \(0.116927\pi\)
\(234\) −6.24274 + 18.1772i −0.408101 + 1.18828i
\(235\) −0.560003 + 4.25364i −0.0365305 + 0.277477i
\(236\) −13.1493 23.1552i −0.855943 1.50728i
\(237\) −0.398026 + 0.960920i −0.0258546 + 0.0624184i
\(238\) 25.5485 3.54113i 1.65606 0.229538i
\(239\) 9.57247 0.619192 0.309596 0.950868i \(-0.399806\pi\)
0.309596 + 0.950868i \(0.399806\pi\)
\(240\) −0.137765 + 0.486276i −0.00889267 + 0.0313890i
\(241\) 2.51104 4.34925i 0.161750 0.280160i −0.773746 0.633496i \(-0.781619\pi\)
0.935497 + 0.353336i \(0.114953\pi\)
\(242\) 0.249980 + 4.03447i 0.0160693 + 0.259346i
\(243\) −0.577158 4.38395i −0.0370247 0.281231i
\(244\) −15.5453 15.7688i −0.995187 1.00949i
\(245\) 0.110907 + 5.33374i 0.00708556 + 0.340760i
\(246\) 0.477737 + 2.44735i 0.0304594 + 0.156037i
\(247\) −5.66624 1.51827i −0.360534 0.0966049i
\(248\) 8.37805 4.02069i 0.532006 0.255314i
\(249\) −0.293223 1.09432i −0.0185823 0.0693499i
\(250\) −0.700118 + 10.1279i −0.0442794 + 0.640546i
\(251\) 3.85388 1.59633i 0.243255 0.100759i −0.257725 0.966218i \(-0.582973\pi\)
0.500980 + 0.865459i \(0.332973\pi\)
\(252\) 10.4094 + 11.7919i 0.655729 + 0.742818i
\(253\) 8.98365 21.6885i 0.564797 1.36354i
\(254\) −11.8383 + 3.97152i −0.742802 + 0.249195i
\(255\) 0.435503 0.754313i 0.0272722 0.0472369i
\(256\) −13.6224 8.39220i −0.851403 0.524512i
\(257\) −8.95509 + 5.17022i −0.558603 + 0.322510i −0.752585 0.658495i \(-0.771193\pi\)
0.193981 + 0.981005i \(0.437860\pi\)
\(258\) 0.269950 1.33227i 0.0168064 0.0829436i
\(259\) −23.8909 7.83386i −1.48451 0.486772i
\(260\) −6.41913 2.71271i −0.398097 0.168235i
\(261\) 2.95007 + 2.26366i 0.182604 + 0.140117i
\(262\) −2.91947 5.97375i −0.180366 0.369059i
\(263\) 23.7101 6.35310i 1.46203 0.391749i 0.561837 0.827248i \(-0.310095\pi\)
0.900189 + 0.435499i \(0.143428\pi\)
\(264\) 1.74060 + 0.132810i 0.107126 + 0.00817388i
\(265\) 1.43614 1.43614i 0.0882215 0.0882215i
\(266\) −3.37144 + 3.41780i −0.206716 + 0.209559i
\(267\) −1.78511 + 0.739418i −0.109247 + 0.0452516i
\(268\) 4.94234 17.9322i 0.301901 1.09538i
\(269\) 17.1893 + 22.4015i 1.04805 + 1.36584i 0.927791 + 0.373101i \(0.121705\pi\)
0.120258 + 0.992743i \(0.461628\pi\)
\(270\) 1.06519 0.0660003i 0.0648255 0.00401665i
\(271\) −13.7220 + 7.92238i −0.833550 + 0.481250i −0.855066 0.518518i \(-0.826484\pi\)
0.0215168 + 0.999768i \(0.493150\pi\)
\(272\) 19.2172 + 19.7737i 1.16522 + 1.19896i
\(273\) 1.65578 1.13143i 0.100213 0.0684773i
\(274\) 1.70663 + 2.57398i 0.103101 + 0.155500i
\(275\) 16.3103 2.14730i 0.983550 0.129487i
\(276\) −1.80333 1.05838i −0.108548 0.0637071i
\(277\) −2.78527 0.366687i −0.167350 0.0220321i 0.0463853 0.998924i \(-0.485230\pi\)
−0.213736 + 0.976892i \(0.568563\pi\)
\(278\) −13.7995 + 12.0150i −0.827638 + 0.720611i
\(279\) −6.90580 6.90580i −0.413440 0.413440i
\(280\) −4.52576 + 3.47052i −0.270466 + 0.207403i
\(281\) −13.2850 + 13.2850i −0.792516 + 0.792516i −0.981903 0.189387i \(-0.939350\pi\)
0.189387 + 0.981903i \(0.439350\pi\)
\(282\) 0.0910238 1.31675i 0.00542039 0.0784114i
\(283\) 0.0395696 0.300561i 0.00235217 0.0178665i −0.990229 0.139454i \(-0.955465\pi\)
0.992581 + 0.121588i \(0.0387986\pi\)
\(284\) 14.8937 + 2.06902i 0.883781 + 0.122774i
\(285\) 0.0211611 + 0.160734i 0.00125347 + 0.00952107i
\(286\) −4.77994 + 23.5902i −0.282644 + 1.39492i
\(287\) −12.1821 + 25.3641i −0.719084 + 1.49719i
\(288\) −3.57413 + 16.4308i −0.210608 + 0.968196i
\(289\) −15.2595 26.4302i −0.897616 1.55472i
\(290\) −0.892602 + 1.01052i −0.0524154 + 0.0593399i
\(291\) 0.120871 0.0927474i 0.00708557 0.00543695i
\(292\) −8.13698 6.33649i −0.476181 0.370815i
\(293\) −2.40867 5.81504i −0.140716 0.339718i 0.837773 0.546019i \(-0.183857\pi\)
−0.978489 + 0.206301i \(0.933857\pi\)
\(294\) −0.135531 1.63564i −0.00790431 0.0953922i
\(295\) −7.17507 7.17507i −0.417749 0.417749i
\(296\) −8.36686 25.5430i −0.486314 1.48466i
\(297\) −0.954042 3.56053i −0.0553591 0.206603i
\(298\) −5.10568 1.75349i −0.295764 0.101577i
\(299\) 17.5511 22.8731i 1.01501 1.32278i
\(300\) 0.0104562 1.46527i 0.000603689 0.0845975i
\(301\) 11.4269 10.2332i 0.658636 0.589833i
\(302\) 11.8631 7.86560i 0.682645 0.452614i
\(303\) 0.430356 + 0.745399i 0.0247233 + 0.0428221i
\(304\) −5.07832 0.742450i −0.291261 0.0425824i
\(305\) −7.30743 4.21894i −0.418422 0.241576i
\(306\) 12.9094 25.9439i 0.737981 1.48311i
\(307\) 23.6025 + 9.77646i 1.34706 + 0.557972i 0.935474 0.353397i \(-0.114973\pi\)
0.411590 + 0.911369i \(0.364973\pi\)
\(308\) 14.8524 + 12.9398i 0.846293 + 0.737313i
\(309\) 0.769518 + 1.85778i 0.0437763 + 0.105685i
\(310\) 2.67072 2.32535i 0.151686 0.132071i
\(311\) 0.686962 0.184071i 0.0389540 0.0104377i −0.239289 0.970948i \(-0.576914\pi\)
0.278243 + 0.960511i \(0.410248\pi\)
\(312\) 2.02263 + 0.710823i 0.114509 + 0.0402424i
\(313\) 1.75489 6.54934i 0.0991923 0.370191i −0.898429 0.439118i \(-0.855291\pi\)
0.997622 + 0.0689272i \(0.0219576\pi\)
\(314\) −6.39346 4.30505i −0.360804 0.242948i
\(315\) 5.01799 + 3.27798i 0.282732 + 0.184693i
\(316\) −11.5574 4.88415i −0.650156 0.274755i
\(317\) −16.4382 + 2.16413i −0.923263 + 0.121550i −0.577146 0.816641i \(-0.695833\pi\)
−0.346118 + 0.938191i \(0.612500\pi\)
\(318\) −0.413649 + 0.468296i −0.0231963 + 0.0262607i
\(319\) 4.03298 + 2.32844i 0.225804 + 0.130368i
\(320\) −5.85415 1.70373i −0.327257 0.0952414i
\(321\) 1.11016i 0.0619630i
\(322\) −9.17809 21.7369i −0.511475 1.21135i
\(323\) 8.17148 + 3.38474i 0.454674 + 0.188332i
\(324\) 17.3728 2.16118i 0.965158 0.120065i
\(325\) 20.0312 + 2.63716i 1.11113 + 0.146283i
\(326\) 28.2055 13.7845i 1.56216 0.763453i
\(327\) 0.612887 + 0.164222i 0.0338927 + 0.00908152i
\(328\) −29.5638 + 5.55232i −1.63239 + 0.306576i
\(329\) 9.70341 11.2994i 0.534966 0.622958i
\(330\) 0.652884 0.127447i 0.0359401 0.00701572i
\(331\) 17.8756 + 13.7164i 0.982533 + 0.753924i 0.969273 0.245988i \(-0.0791124\pi\)
0.0132601 + 0.999912i \(0.495779\pi\)
\(332\) 13.2262 3.44298i 0.725881 0.188958i
\(333\) −22.4104 + 17.1961i −1.22808 + 0.942340i
\(334\) 4.08906 + 2.03467i 0.223744 + 0.111332i
\(335\) 7.08811i 0.387265i
\(336\) 1.32362 1.15174i 0.0722096 0.0628326i
\(337\) 0.915967i 0.0498959i −0.999689 0.0249479i \(-0.992058\pi\)
0.999689 0.0249479i \(-0.00794200\pi\)
\(338\) −4.97868 + 10.0056i −0.270805 + 0.544233i
\(339\) 0.714884 0.548550i 0.0388272 0.0297931i
\(340\) 9.06187 + 5.31845i 0.491449 + 0.288434i
\(341\) −9.70346 7.44573i −0.525472 0.403209i
\(342\) 1.03339 + 5.29383i 0.0558792 + 0.286258i
\(343\) 9.80415 15.7124i 0.529374 0.848388i
\(344\) 16.0481 + 3.37113i 0.865256 + 0.181759i
\(345\) −0.769644 0.206226i −0.0414362 0.0111028i
\(346\) −11.1571 22.8293i −0.599808 1.22731i
\(347\) 9.58899 + 1.26241i 0.514764 + 0.0677699i 0.383433 0.923569i \(-0.374742\pi\)
0.131331 + 0.991339i \(0.458075\pi\)
\(348\) 0.254851 0.327267i 0.0136615 0.0175433i
\(349\) −11.5729 4.79365i −0.619482 0.256598i 0.0507946 0.998709i \(-0.483825\pi\)
−0.670277 + 0.742111i \(0.733825\pi\)
\(350\) 9.97607 13.1865i 0.533243 0.704848i
\(351\) 4.52706i 0.241636i
\(352\) −1.75193 + 20.9856i −0.0933784 + 1.11854i
\(353\) −11.5041 6.64190i −0.612302 0.353513i 0.161564 0.986862i \(-0.448346\pi\)
−0.773866 + 0.633350i \(0.781680\pi\)
\(354\) 2.33964 + 2.06662i 0.124351 + 0.109840i
\(355\) 5.68095 0.747912i 0.301514 0.0396950i
\(356\) −8.76601 21.5977i −0.464598 1.14467i
\(357\) −2.69785 + 1.36548i −0.142785 + 0.0722686i
\(358\) −3.98515 + 5.91838i −0.210622 + 0.312796i
\(359\) −5.49807 + 20.5191i −0.290177 + 1.08296i 0.654796 + 0.755806i \(0.272755\pi\)
−0.944973 + 0.327149i \(0.893912\pi\)
\(360\) 0.350617 + 6.39802i 0.0184791 + 0.337205i
\(361\) 16.7624 4.49147i 0.882232 0.236393i
\(362\) 10.5408 + 12.1064i 0.554014 + 0.636298i
\(363\) −0.181344 0.437803i −0.00951809 0.0229787i
\(364\) 13.5060 + 20.0713i 0.707909 + 1.05202i
\(365\) −3.63083 1.50394i −0.190046 0.0787198i
\(366\) 2.32404 + 1.15642i 0.121479 + 0.0604468i
\(367\) −11.2214 6.47865i −0.585750 0.338183i 0.177665 0.984091i \(-0.443146\pi\)
−0.763415 + 0.645908i \(0.776479\pi\)
\(368\) 12.9226 21.6626i 0.673638 1.12924i
\(369\) 15.8065 + 27.3777i 0.822854 + 1.42523i
\(370\) −5.65995 8.53650i −0.294247 0.443791i
\(371\) −6.90057 + 1.44734i −0.358260 + 0.0751419i
\(372\) −0.775813 + 0.764819i −0.0402240 + 0.0396540i
\(373\) −1.87472 + 2.44318i −0.0970692 + 0.126503i −0.839362 0.543572i \(-0.817071\pi\)
0.742293 + 0.670075i \(0.233738\pi\)
\(374\) 11.7880 34.3235i 0.609543 1.77483i
\(375\) −0.308032 1.14959i −0.0159067 0.0593646i
\(376\) 15.8763 + 1.21138i 0.818757 + 0.0624722i
\(377\) 4.04413 + 4.04413i 0.208283 + 0.208283i
\(378\) −3.22114 1.83052i −0.165678 0.0941517i
\(379\) −13.4966 32.5837i −0.693275 1.67371i −0.738076 0.674718i \(-0.764265\pi\)
0.0448006 0.998996i \(-0.485735\pi\)
\(380\) −1.94078 + 0.241432i −0.0995597 + 0.0123852i
\(381\) 1.16134 0.891129i 0.0594973 0.0456539i
\(382\) 6.49131 + 5.73383i 0.332125 + 0.293368i
\(383\) −15.8005 27.3673i −0.807370 1.39841i −0.914680 0.404179i \(-0.867557\pi\)
0.107310 0.994226i \(-0.465776\pi\)
\(384\) 1.82995 + 0.411760i 0.0933843 + 0.0210125i
\(385\) 6.76643 + 3.24983i 0.344849 + 0.165627i
\(386\) −22.5367 4.56648i −1.14709 0.232428i
\(387\) −2.24945 17.0863i −0.114346 0.868545i
\(388\) 1.10842 + 1.46606i 0.0562714 + 0.0744280i
\(389\) −2.45833 + 18.6728i −0.124642 + 0.946750i 0.808816 + 0.588062i \(0.200109\pi\)
−0.933458 + 0.358688i \(0.883224\pi\)
\(390\) 0.815017 + 0.0563401i 0.0412700 + 0.00285289i
\(391\) −30.7381 + 30.7381i −1.55449 + 1.55449i
\(392\) 19.7425 1.49412i 0.997148 0.0754646i
\(393\) 0.551169 + 0.551169i 0.0278028 + 0.0278028i
\(394\) −7.24031 8.31565i −0.364761 0.418937i
\(395\) −4.74033 0.624077i −0.238512 0.0314007i
\(396\) 21.4176 5.57533i 1.07627 0.280171i
\(397\) −26.0615 + 3.43106i −1.30799 + 0.172200i −0.752096 0.659054i \(-0.770957\pi\)
−0.555893 + 0.831254i \(0.687624\pi\)
\(398\) −4.07716 + 2.70328i −0.204370 + 0.135503i
\(399\) 0.243663 0.507328i 0.0121984 0.0253982i
\(400\) 17.6748 + 0.252269i 0.883742 + 0.0126134i
\(401\) 12.2322 7.06227i 0.610847 0.352673i −0.162450 0.986717i \(-0.551940\pi\)
0.773297 + 0.634044i \(0.218606\pi\)
\(402\) 0.134854 + 2.17643i 0.00672590 + 0.108551i
\(403\) −9.14433 11.9171i −0.455511 0.593634i
\(404\) −9.02888 + 5.12727i −0.449204 + 0.255091i
\(405\) 6.16338 2.55296i 0.306261 0.126857i
\(406\) 4.51277 1.24228i 0.223965 0.0616532i
\(407\) −25.0149 + 25.0149i −1.23994 + 1.23994i
\(408\) −2.88367 1.46065i −0.142763 0.0723127i
\(409\) −29.4963 + 7.90351i −1.45850 + 0.390803i −0.898971 0.438009i \(-0.855684\pi\)
−0.559527 + 0.828812i \(0.689017\pi\)
\(410\) −10.2986 + 5.03309i −0.508610 + 0.248567i
\(411\) −0.287236 0.220404i −0.0141683 0.0108717i
\(412\) −22.4769 + 9.12286i −1.10736 + 0.449451i
\(413\) 7.23100 + 34.4758i 0.355814 + 1.69644i
\(414\) −25.9813 5.26443i −1.27691 0.258733i
\(415\) 4.51025 2.60400i 0.221400 0.127825i
\(416\) −8.74885 + 24.3380i −0.428948 + 1.19327i
\(417\) 1.07250 1.85763i 0.0525206 0.0909684i
\(418\) 2.14847 + 6.40417i 0.105085 + 0.313238i
\(419\) 1.09590 2.64573i 0.0535381 0.129252i −0.894847 0.446372i \(-0.852716\pi\)
0.948385 + 0.317120i \(0.102716\pi\)
\(420\) 0.369640 0.557128i 0.0180366 0.0271851i
\(421\) −10.0359 + 4.15701i −0.489120 + 0.202600i −0.613592 0.789623i \(-0.710276\pi\)
0.124473 + 0.992223i \(0.460276\pi\)
\(422\) 19.1611 + 1.32456i 0.932746 + 0.0644785i
\(423\) −4.33096 16.1634i −0.210579 0.785890i
\(424\) −5.61350 5.03021i −0.272616 0.244289i
\(425\) −29.4250 7.88441i −1.42732 0.382450i
\(426\) −1.73013 + 0.337731i −0.0838250 + 0.0163631i
\(427\) 13.2281 + 26.1355i 0.640152 + 1.26478i
\(428\) 13.3920 + 0.0955653i 0.647326 + 0.00461932i
\(429\) −0.368308 2.79758i −0.0177821 0.135068i
\(430\) 6.23687 0.386443i 0.300768 0.0186359i
\(431\) −8.83029 + 15.2945i −0.425340 + 0.736711i −0.996452 0.0841614i \(-0.973179\pi\)
0.571112 + 0.820872i \(0.306512\pi\)
\(432\) −0.460887 3.93384i −0.0221744 0.189267i
\(433\) −5.56633 −0.267501 −0.133750 0.991015i \(-0.542702\pi\)
−0.133750 + 0.991015i \(0.542702\pi\)
\(434\) −12.1769 + 1.68777i −0.584511 + 0.0810158i
\(435\) 0.0604879 0.146031i 0.00290017 0.00700163i
\(436\) −2.03379 + 7.37919i −0.0974011 + 0.353399i
\(437\) 1.05611 8.02194i 0.0505205 0.383742i
\(438\) 1.14347 + 0.392712i 0.0546372 + 0.0187645i
\(439\) 8.28467 30.9188i 0.395406 1.47567i −0.425683 0.904873i \(-0.639966\pi\)
0.821088 0.570801i \(-0.193367\pi\)
\(440\) 1.48120 + 7.88679i 0.0706137 + 0.375988i
\(441\) −8.36064 19.0540i −0.398126 0.907334i
\(442\) 24.8941 36.9704i 1.18409 1.75850i
\(443\) 6.23607 8.12701i 0.296285 0.386126i −0.621361 0.783524i \(-0.713420\pi\)
0.917646 + 0.397398i \(0.130087\pi\)
\(444\) 1.90032 + 2.51348i 0.0901852 + 0.119284i
\(445\) −5.40712 7.04669i −0.256322 0.334045i
\(446\) 8.13739 + 24.2560i 0.385316 + 1.14855i
\(447\) 0.632863 0.0299334
\(448\) 13.7796 + 16.0662i 0.651026 + 0.759055i
\(449\) 14.2000 0.670138 0.335069 0.942194i \(-0.391240\pi\)
0.335069 + 0.942194i \(0.391240\pi\)
\(450\) −5.90862 17.6124i −0.278535 0.830258i
\(451\) 24.1015 + 31.4097i 1.13489 + 1.47902i
\(452\) 6.55568 + 8.67095i 0.308353 + 0.407847i
\(453\) −1.01581 + 1.32383i −0.0477269 + 0.0621989i
\(454\) −13.6474 + 20.2678i −0.640503 + 0.951215i
\(455\) 6.99390 + 6.00603i 0.327879 + 0.281567i
\(456\) 0.591329 0.111057i 0.0276915 0.00520070i
\(457\) 1.15982 4.32849i 0.0542539 0.202478i −0.933479 0.358633i \(-0.883243\pi\)
0.987733 + 0.156154i \(0.0499097\pi\)
\(458\) 12.3373 + 4.23710i 0.576484 + 0.197987i
\(459\) −0.890938 + 6.76735i −0.0415854 + 0.315873i
\(460\) 2.55398 9.26655i 0.119080 0.432055i
\(461\) −15.0926 + 36.4369i −0.702934 + 1.69703i 0.0140091 + 0.999902i \(0.495541\pi\)
−0.716943 + 0.697131i \(0.754459\pi\)
\(462\) −2.13949 0.869140i −0.0995380 0.0404360i
\(463\) 14.3306 0.666001 0.333001 0.942927i \(-0.391939\pi\)
0.333001 + 0.942927i \(0.391939\pi\)
\(464\) 3.92592 + 3.10247i 0.182256 + 0.144029i
\(465\) −0.207569 + 0.359520i −0.00962579 + 0.0166724i
\(466\) 4.53934 0.281262i 0.210281 0.0130292i
\(467\) −1.85627 14.0998i −0.0858979 0.652459i −0.979185 0.202972i \(-0.934940\pi\)
0.893287 0.449487i \(-0.148393\pi\)
\(468\) 27.1795 + 0.193953i 1.25637 + 0.00896550i
\(469\) −13.4573 + 20.6006i −0.621399 + 0.951249i
\(470\) 5.95507 1.16246i 0.274687 0.0536205i
\(471\) 0.872805 + 0.233867i 0.0402167 + 0.0107760i
\(472\) −25.1313 + 28.0455i −1.15676 + 1.29090i
\(473\) −5.58607 20.8475i −0.256848 0.958569i
\(474\) 1.46741 + 0.101439i 0.0674004 + 0.00465923i
\(475\) 5.23851 2.16986i 0.240359 0.0995600i
\(476\) −16.2397 32.6620i −0.744343 1.49706i
\(477\) −3.03143 + 7.31852i −0.138800 + 0.335092i
\(478\) −4.30573 12.8345i −0.196939 0.587038i
\(479\) 11.1648 19.3380i 0.510133 0.883576i −0.489798 0.871836i \(-0.662930\pi\)
0.999931 0.0117402i \(-0.00373711\pi\)
\(480\) 0.713954 0.0340171i 0.0325874 0.00155266i
\(481\) −37.6261 + 21.7234i −1.71560 + 0.990503i
\(482\) −6.96084 1.41043i −0.317058 0.0642435i
\(483\) 1.84533 + 2.06059i 0.0839656 + 0.0937601i
\(484\) 5.29688 2.14989i 0.240767 0.0977221i
\(485\) 0.555635 + 0.426354i 0.0252301 + 0.0193597i
\(486\) −5.61829 + 2.74576i −0.254851 + 0.124550i
\(487\) 7.99926 2.14340i 0.362481 0.0971266i −0.0729815 0.997333i \(-0.523251\pi\)
0.435463 + 0.900207i \(0.356585\pi\)
\(488\) −14.1500 + 27.9356i −0.640542 + 1.26459i
\(489\) −2.60238 + 2.60238i −0.117684 + 0.117684i
\(490\) 7.10146 2.54784i 0.320811 0.115099i
\(491\) 3.23599 1.34039i 0.146038 0.0604910i −0.308467 0.951235i \(-0.599816\pi\)
0.454505 + 0.890744i \(0.349816\pi\)
\(492\) 3.06646 1.74136i 0.138247 0.0785067i
\(493\) −5.24955 6.84134i −0.236428 0.308118i
\(494\) 0.513042 + 8.28008i 0.0230829 + 0.372538i
\(495\) 7.30360 4.21674i 0.328272 0.189528i
\(496\) −9.15931 9.42456i −0.411265 0.423175i
\(497\) −17.9309 8.61198i −0.804310 0.386300i
\(498\) −1.33535 + 0.885376i −0.0598384 + 0.0396747i
\(499\) 2.60182 0.342537i 0.116474 0.0153340i −0.0720640 0.997400i \(-0.522959\pi\)
0.188538 + 0.982066i \(0.439625\pi\)
\(500\) 13.8942 3.61687i 0.621366 0.161751i
\(501\) −0.530852 0.0698880i −0.0237167 0.00312237i
\(502\) −3.87381 4.44915i −0.172897 0.198575i
\(503\) 6.94204 + 6.94204i 0.309530 + 0.309530i 0.844727 0.535197i \(-0.179763\pi\)
−0.535197 + 0.844727i \(0.679763\pi\)
\(504\) 11.1281 19.2607i 0.495684 0.857938i
\(505\) −2.79777 + 2.79777i −0.124499 + 0.124499i
\(506\) −33.1202 2.28952i −1.47237 0.101782i
\(507\) 0.171010 1.29895i 0.00759484 0.0576885i
\(508\) 10.6498 + 14.0861i 0.472509 + 0.624970i
\(509\) −2.43311 18.4813i −0.107846 0.819169i −0.956809 0.290717i \(-0.906106\pi\)
0.848963 0.528452i \(-0.177227\pi\)
\(510\) −1.20725 0.244619i −0.0534581 0.0108319i
\(511\) 7.69718 + 11.2644i 0.340503 + 0.498307i
\(512\) −5.12463 + 22.0395i −0.226479 + 0.974016i
\(513\) −0.635241 1.10027i −0.0280466 0.0485781i
\(514\) 10.9601 + 9.68118i 0.483431 + 0.427019i
\(515\) −7.33355 + 5.62723i −0.323155 + 0.247965i
\(516\) −1.90770 + 0.237317i −0.0839819 + 0.0104473i
\(517\) −8.01971 19.3613i −0.352706 0.851509i
\(518\) 0.242753 + 35.5560i 0.0106660 + 1.56224i
\(519\) 2.10635 + 2.10635i 0.0924584 + 0.0924584i
\(520\) −0.749796 + 9.82679i −0.0328807 + 0.430933i
\(521\) 2.02450 + 7.55554i 0.0886950 + 0.331014i 0.995988 0.0894842i \(-0.0285218\pi\)
−0.907293 + 0.420499i \(0.861855\pi\)
\(522\) 1.70812 4.97358i 0.0747622 0.217688i
\(523\) −19.3048 + 25.1584i −0.844138 + 1.10010i 0.149642 + 0.988740i \(0.452188\pi\)
−0.993780 + 0.111362i \(0.964479\pi\)
\(524\) −6.69626 + 6.60137i −0.292527 + 0.288382i
\(525\) −0.603971 + 1.84193i −0.0263595 + 0.0803883i
\(526\) −19.1829 28.9322i −0.836416 1.26151i
\(527\) 11.3242 + 19.6141i 0.493291 + 0.854406i
\(528\) −0.604858 2.39349i −0.0263231 0.104163i
\(529\) 14.5202 + 8.38325i 0.631314 + 0.364489i
\(530\) −2.57152 1.27956i −0.111700 0.0555806i
\(531\) 36.5639 + 15.1453i 1.58674 + 0.657249i
\(532\) 6.09898 + 2.98301i 0.264424 + 0.129330i
\(533\) 18.6072 + 44.9218i 0.805967 + 1.94578i
\(534\) 1.79434 + 2.06084i 0.0776488 + 0.0891813i
\(535\) 4.92944 1.32084i 0.213118 0.0571049i
\(536\) −26.2661 + 1.43941i −1.13452 + 0.0621728i
\(537\) 0.216489 0.807949i 0.00934221 0.0348656i
\(538\) 22.3036 33.1232i 0.961575 1.42804i
\(539\) −13.4957 22.2917i −0.581300 0.960174i
\(540\) −0.567618 1.39849i −0.0244264 0.0601816i
\(541\) 3.40898 0.448801i 0.146563 0.0192954i −0.0568874 0.998381i \(-0.518118\pi\)
0.203451 + 0.979085i \(0.434784\pi\)
\(542\) 16.7943 + 14.8345i 0.721377 + 0.637198i
\(543\) −1.62971 0.940914i −0.0699376 0.0403785i
\(544\) 17.8682 34.6603i 0.766091 1.48605i
\(545\) 2.91679i 0.124942i
\(546\) −2.26177 1.71111i −0.0967948 0.0732288i
\(547\) 21.7445 + 9.00687i 0.929728 + 0.385106i 0.795575 0.605855i \(-0.207169\pi\)
0.134153 + 0.990961i \(0.457169\pi\)
\(548\) 2.68349 3.44599i 0.114633 0.147205i
\(549\) 32.6286 + 4.29563i 1.39255 + 0.183333i
\(550\) −10.2155 20.9026i −0.435590 0.891291i
\(551\) 1.55038 + 0.415422i 0.0660483 + 0.0176976i
\(552\) −0.607908 + 2.89392i −0.0258743 + 0.123173i
\(553\) 12.5923 + 10.8136i 0.535478 + 0.459843i
\(554\) 0.761176 + 3.89935i 0.0323393 + 0.165668i
\(555\) 0.952605 + 0.730960i 0.0404358 + 0.0310275i
\(556\) 22.3165 + 13.0976i 0.946428 + 0.555463i
\(557\) 25.9441 19.9076i 1.09929 0.843513i 0.110654 0.993859i \(-0.464705\pi\)
0.988633 + 0.150346i \(0.0480388\pi\)
\(558\) −6.15288 + 12.3654i −0.260472 + 0.523468i
\(559\) 26.5066i 1.12111i
\(560\) 6.68889 + 4.50697i 0.282657 + 0.190454i
\(561\) 4.25449i 0.179625i
\(562\) 23.7878 + 11.8365i 1.00343 + 0.499294i
\(563\) 17.1249 13.1404i 0.721728 0.553802i −0.181276 0.983432i \(-0.558023\pi\)
0.903005 + 0.429631i \(0.141356\pi\)
\(564\) −1.80641 + 0.470236i −0.0760635 + 0.0198005i
\(565\) 3.28628 + 2.52165i 0.138255 + 0.106087i
\(566\) −0.420783 + 0.0821393i −0.0176868 + 0.00345257i
\(567\) −22.7600 4.28179i −0.955830 0.179818i
\(568\) −3.92516 20.8998i −0.164696 0.876937i
\(569\) 3.46806 + 0.929263i 0.145389 + 0.0389567i 0.330779 0.943708i \(-0.392688\pi\)
−0.185391 + 0.982665i \(0.559355\pi\)
\(570\) 0.205990 0.100671i 0.00862797 0.00421664i
\(571\) −35.0047 4.60845i −1.46490 0.192858i −0.644480 0.764621i \(-0.722926\pi\)
−0.820419 + 0.571763i \(0.806260\pi\)
\(572\) 33.7792 4.20212i 1.41238 0.175699i
\(573\) −0.938061 0.388557i −0.0391880 0.0162322i
\(574\) 39.4871 + 4.92455i 1.64816 + 0.205547i
\(575\) 27.8675i 1.16216i
\(576\) 23.6377 2.59853i 0.984904 0.108272i
\(577\) −27.3948 15.8164i −1.14046 0.658444i −0.193915 0.981018i \(-0.562119\pi\)
−0.946544 + 0.322574i \(0.895452\pi\)
\(578\) −28.5732 + 32.3479i −1.18849 + 1.34549i
\(579\) 2.67264 0.351860i 0.111071 0.0146228i
\(580\) 1.75638 + 0.742243i 0.0729296 + 0.0308200i
\(581\) −18.0523 0.994869i −0.748936 0.0412741i
\(582\) −0.178721 0.120342i −0.00740824 0.00498835i
\(583\) −2.56765 + 9.58258i −0.106341 + 0.396870i
\(584\) −4.83577 + 13.7600i −0.200105 + 0.569394i
\(585\) 10.0045 2.68069i 0.413635 0.110833i
\(586\) −6.71323 + 5.84510i −0.277321 + 0.241459i
\(587\) −17.2902 41.7421i −0.713641 1.72288i −0.690696 0.723145i \(-0.742696\pi\)
−0.0229454 0.999737i \(-0.507304\pi\)
\(588\) −2.13206 + 0.917430i −0.0879246 + 0.0378342i
\(589\) −3.89469 1.61323i −0.160478 0.0664721i
\(590\) −6.39279 + 12.8475i −0.263187 + 0.528924i
\(591\) 1.11942 + 0.646296i 0.0460467 + 0.0265851i
\(592\) −30.4840 + 22.7074i −1.25288 + 0.933269i
\(593\) −7.13623 12.3603i −0.293050 0.507577i 0.681480 0.731837i \(-0.261337\pi\)
−0.974529 + 0.224260i \(0.928003\pi\)
\(594\) −4.34474 + 2.88069i −0.178267 + 0.118196i
\(595\) −9.27295 10.3546i −0.380154 0.424499i
\(596\) −0.0544784 + 7.63430i −0.00223152 + 0.312713i
\(597\) 0.349118 0.454979i 0.0142884 0.0186211i
\(598\) −38.5622 13.2437i −1.57693 0.541577i
\(599\) −9.41520 35.1380i −0.384695 1.43570i −0.838647 0.544675i \(-0.816653\pi\)
0.453953 0.891026i \(-0.350014\pi\)
\(600\) −1.96930 + 0.645064i −0.0803964 + 0.0263346i
\(601\) 28.1564 + 28.1564i 1.14852 + 1.14852i 0.986844 + 0.161678i \(0.0516907\pi\)
0.161678 + 0.986844i \(0.448309\pi\)
\(602\) −18.8603 10.7180i −0.768688 0.436832i
\(603\) 10.5795 + 25.5412i 0.430831 + 1.04012i
\(604\) −15.8821 12.3678i −0.646232 0.503238i
\(605\) 1.72822 1.32611i 0.0702621 0.0539140i
\(606\) 0.805837 0.912294i 0.0327349 0.0370594i
\(607\) 1.97544 + 3.42156i 0.0801806 + 0.138877i 0.903327 0.428952i \(-0.141117\pi\)
−0.823147 + 0.567829i \(0.807784\pi\)
\(608\) 1.28878 + 7.14283i 0.0522671 + 0.289680i
\(609\) −0.453049 + 0.309578i −0.0183585 + 0.0125447i
\(610\) −2.36975 + 11.6953i −0.0959484 + 0.473529i
\(611\) −3.35940 25.5172i −0.135907 1.03231i
\(612\) −40.5916 5.63895i −1.64082 0.227941i
\(613\) −5.27854 + 40.0945i −0.213198 + 1.61940i 0.465544 + 0.885025i \(0.345859\pi\)
−0.678742 + 0.734377i \(0.737474\pi\)
\(614\) 2.49157 36.0431i 0.100552 1.45458i
\(615\) 0.950199 0.950199i 0.0383157 0.0383157i
\(616\) 10.6687 25.7341i 0.429854 1.03686i
\(617\) −11.3927 11.3927i −0.458653 0.458653i 0.439560 0.898213i \(-0.355134\pi\)
−0.898213 + 0.439560i \(0.855134\pi\)
\(618\) 2.14473 1.86738i 0.0862738 0.0751172i
\(619\) −8.57203 1.12853i −0.344539 0.0453594i −0.0437287 0.999043i \(-0.513924\pi\)
−0.300810 + 0.953684i \(0.597257\pi\)
\(620\) −4.31907 2.53488i −0.173458 0.101803i
\(621\) 6.19076 0.815029i 0.248427 0.0327060i
\(622\) −0.555795 0.838266i −0.0222854 0.0336114i
\(623\) 2.33642 + 30.7461i 0.0936066 + 1.23181i
\(624\) 0.0432695 3.03162i 0.00173217 0.121362i
\(625\) −14.3975 + 8.31239i −0.575899 + 0.332496i
\(626\) −9.57055 + 0.593001i −0.382516 + 0.0237011i
\(627\) −0.482074 0.628251i −0.0192522 0.0250899i
\(628\) −2.89630 + 10.5086i −0.115575 + 0.419339i
\(629\) 60.5212 25.0687i 2.41314 0.999555i
\(630\) 2.13793 8.20244i 0.0851770 0.326793i
\(631\) 22.3250 22.3250i 0.888745 0.888745i −0.105657 0.994403i \(-0.533695\pi\)
0.994403 + 0.105657i \(0.0336947\pi\)
\(632\) −1.34998 + 17.6928i −0.0536994 + 0.703782i
\(633\) −2.17492 + 0.582768i −0.0864453 + 0.0231629i
\(634\) 10.2956 + 21.0665i 0.408890 + 0.836659i
\(635\) 5.33861 + 4.09646i 0.211856 + 0.162563i
\(636\) 0.813940 + 0.343970i 0.0322748 + 0.0136393i
\(637\) −8.92397 30.7341i −0.353581 1.21773i
\(638\) 1.30787 6.45466i 0.0517791 0.255543i
\(639\) −19.3544 + 11.1743i −0.765647 + 0.442047i
\(640\) 0.348894 + 8.61543i 0.0137912 + 0.340555i
\(641\) −8.31636 + 14.4044i −0.328477 + 0.568938i −0.982210 0.187787i \(-0.939869\pi\)
0.653733 + 0.756725i \(0.273202\pi\)
\(642\) −1.48847 + 0.499353i −0.0587454 + 0.0197079i
\(643\) 18.4617 44.5706i 0.728060 1.75769i 0.0791019 0.996867i \(-0.474795\pi\)
0.648958 0.760825i \(-0.275205\pi\)
\(644\) −25.0160 + 22.0831i −0.985768 + 0.870195i
\(645\) −0.676797 + 0.280338i −0.0266489 + 0.0110383i
\(646\) 0.862615 12.4786i 0.0339391 0.490963i
\(647\) −8.85575 33.0501i −0.348155 1.29933i −0.888883 0.458135i \(-0.848518\pi\)
0.540727 0.841198i \(-0.318149\pi\)
\(648\) −10.7120 22.3210i −0.420807 0.876851i
\(649\) 47.8753 + 12.8282i 1.87927 + 0.503549i
\(650\) −5.47427 28.0436i −0.214719 1.09996i
\(651\) 1.28585 0.650813i 0.0503963 0.0255074i
\(652\) −31.1688 31.6169i −1.22067 1.23821i
\(653\) −1.84414 14.0076i −0.0721666 0.548160i −0.988891 0.148641i \(-0.952510\pi\)
0.916725 0.399520i \(-0.130823\pi\)
\(654\) −0.0554930 0.895611i −0.00216995 0.0350212i
\(655\) −1.79159 + 3.10312i −0.0700032 + 0.121249i
\(656\) 20.7423 + 37.1409i 0.809850 + 1.45011i
\(657\) 15.3280 0.598003
\(658\) −19.5146 7.92757i −0.760759 0.309049i
\(659\) −9.75158 + 23.5424i −0.379868 + 0.917081i 0.612122 + 0.790763i \(0.290316\pi\)
−0.991990 + 0.126318i \(0.959684\pi\)
\(660\) −0.464547 0.818045i −0.0180825 0.0318424i
\(661\) 2.55942 19.4407i 0.0995499 0.756157i −0.866751 0.498741i \(-0.833796\pi\)
0.966301 0.257415i \(-0.0828709\pi\)
\(662\) 10.3502 30.1369i 0.402270 1.17130i
\(663\) −1.35235 + 5.04703i −0.0525208 + 0.196010i
\(664\) −10.5654 16.1847i −0.410019 0.628087i
\(665\) 2.54259 + 0.478332i 0.0985975 + 0.0185489i
\(666\) 33.1364 + 22.3124i 1.28401 + 0.864589i
\(667\) −4.80227 + 6.25845i −0.185945 + 0.242328i
\(668\) 0.888764 6.39771i 0.0343873 0.247535i
\(669\) −1.82587 2.37952i −0.0705921 0.0919974i
\(670\) −9.50356 + 3.18825i −0.367155 + 0.123173i
\(671\) 41.2155 1.59111
\(672\) −2.13959 1.25662i −0.0825366 0.0484754i
\(673\) 4.92340 0.189783 0.0948915 0.995488i \(-0.469750\pi\)
0.0948915 + 0.995488i \(0.469750\pi\)
\(674\) −1.22811 + 0.412005i −0.0473048 + 0.0158698i
\(675\) 2.66381 + 3.47155i 0.102530 + 0.133620i
\(676\) 15.6547 + 2.17474i 0.602104 + 0.0836437i
\(677\) 23.6205 30.7828i 0.907810 1.18308i −0.0747628 0.997201i \(-0.523820\pi\)
0.982573 0.185879i \(-0.0595134\pi\)
\(678\) −1.05704 0.711759i −0.0405953 0.0273349i
\(679\) −0.805416 2.29405i −0.0309090 0.0880377i
\(680\) 3.05479 14.5422i 0.117146 0.557667i
\(681\) 0.741379 2.76687i 0.0284097 0.106026i
\(682\) −5.61840 + 16.3593i −0.215139 + 0.626429i
\(683\) −1.11245 + 8.44987i −0.0425666 + 0.323325i 0.956893 + 0.290442i \(0.0938023\pi\)
−0.999459 + 0.0328833i \(0.989531\pi\)
\(684\) 6.63302 3.76672i 0.253620 0.144024i
\(685\) 0.636914 1.53765i 0.0243352 0.0587504i
\(686\) −25.4767 6.07769i −0.972705 0.232047i
\(687\) −1.52924 −0.0583442
\(688\) −2.69857 23.0332i −0.102882 0.878134i
\(689\) −6.09191 + 10.5515i −0.232083 + 0.401980i
\(690\) 0.0696863 + 1.12468i 0.00265291 + 0.0428158i
\(691\) 0.465346 + 3.53466i 0.0177026 + 0.134465i 0.998014 0.0629934i \(-0.0200647\pi\)
−0.980311 + 0.197458i \(0.936731\pi\)
\(692\) −25.5904 + 25.2278i −0.972802 + 0.959017i
\(693\) −29.2327 1.61102i −1.11046 0.0611977i
\(694\) −2.62054 13.4245i −0.0994744 0.509587i
\(695\) 9.52446 + 2.55207i 0.361283 + 0.0968056i
\(696\) −0.553424 0.194493i −0.0209775 0.00737223i
\(697\) −18.9746 70.8140i −0.718713 2.68227i
\(698\) −1.22168 + 17.6728i −0.0462413 + 0.668926i
\(699\) −0.492589 + 0.204037i −0.0186314 + 0.00771739i
\(700\) −22.1674 7.44433i −0.837849 0.281369i
\(701\) 4.49496 10.8518i 0.169772 0.409867i −0.815978 0.578083i \(-0.803801\pi\)
0.985750 + 0.168217i \(0.0538009\pi\)
\(702\) −6.06976 + 2.03628i −0.229088 + 0.0768546i
\(703\) −6.09651 + 10.5595i −0.229934 + 0.398258i
\(704\) 28.9250 7.09044i 1.09015 0.267231i
\(705\) −0.616002 + 0.355649i −0.0232000 + 0.0133945i
\(706\) −3.73071 + 18.4120i −0.140407 + 0.692944i
\(707\) 13.4431 2.81958i 0.505580 0.106041i
\(708\) 1.71850 4.06651i 0.0645852 0.152829i
\(709\) −31.9399 24.5084i −1.19953 0.920431i −0.201277 0.979534i \(-0.564509\pi\)
−0.998252 + 0.0591038i \(0.981176\pi\)
\(710\) −3.55809 7.28047i −0.133533 0.273231i
\(711\) 18.0127 4.82650i 0.675531 0.181008i
\(712\) −25.0146 + 21.4679i −0.937463 + 0.804545i
\(713\) 14.6504 14.6504i 0.548661 0.548661i
\(714\) 3.04429 + 3.00301i 0.113930 + 0.112385i
\(715\) 11.9839 4.96388i 0.448171 0.185639i
\(716\) 9.72775 + 2.68109i 0.363543 + 0.100197i
\(717\) 0.966119 + 1.25907i 0.0360804 + 0.0470209i
\(718\) 29.9845 1.85787i 1.11901 0.0693351i
\(719\) −11.2169 + 6.47606i −0.418319 + 0.241516i −0.694358 0.719630i \(-0.744311\pi\)
0.276039 + 0.961146i \(0.410978\pi\)
\(720\) 8.42060 3.34795i 0.313817 0.124771i
\(721\) 31.9977 2.43153i 1.19165 0.0905548i
\(722\) −13.5618 20.4543i −0.504719 0.761231i
\(723\) 0.825490 0.108678i 0.0307003 0.00404177i
\(724\) 11.4906 19.5784i 0.427046 0.727625i
\(725\) −5.48087 0.721570i −0.203554 0.0267984i
\(726\) −0.505426 + 0.440067i −0.0187581 + 0.0163324i
\(727\) 9.58470 + 9.58470i 0.355477 + 0.355477i 0.862143 0.506666i \(-0.169122\pi\)
−0.506666 + 0.862143i \(0.669122\pi\)
\(728\) 20.8360 27.1367i 0.772235 1.00575i
\(729\) −18.0503 + 18.0503i −0.668531 + 0.668531i
\(730\) −0.383285 + 5.54460i −0.0141860 + 0.205215i
\(731\) −5.21659 + 39.6239i −0.192943 + 1.46554i
\(732\) 0.505134 3.63617i 0.0186703 0.134397i
\(733\) 2.15566 + 16.3739i 0.0796212 + 0.604783i 0.984015 + 0.178085i \(0.0569901\pi\)
−0.904394 + 0.426698i \(0.859677\pi\)
\(734\) −3.63901 + 17.9594i −0.134318 + 0.662895i
\(735\) −0.690356 + 0.552905i −0.0254642 + 0.0203942i
\(736\) −34.8574 7.58238i −1.28486 0.279490i
\(737\) 17.3112 + 29.9839i 0.637666 + 1.10447i
\(738\) 29.5975 33.5075i 1.08950 1.23343i
\(739\) −10.6529 + 8.17427i −0.391874 + 0.300695i −0.785840 0.618429i \(-0.787769\pi\)
0.393966 + 0.919125i \(0.371103\pi\)
\(740\) −8.89965 + 11.4285i −0.327158 + 0.420119i
\(741\) −0.372178 0.898517i −0.0136723 0.0330078i
\(742\) 5.04445 + 8.60109i 0.185188 + 0.315756i
\(743\) −37.8565 37.8565i −1.38882 1.38882i −0.827803 0.561018i \(-0.810410\pi\)
−0.561018 0.827803i \(-0.689590\pi\)
\(744\) 1.37441 + 0.696172i 0.0503884 + 0.0255229i
\(745\) 0.752964 + 2.81010i 0.0275865 + 0.102954i
\(746\) 4.11901 + 1.41462i 0.150808 + 0.0517931i
\(747\) −12.3655 + 16.1151i −0.452432 + 0.589621i
\(748\) −51.3224 0.366237i −1.87653 0.0133910i
\(749\) −16.8345 5.52005i −0.615118 0.201698i
\(750\) −1.40279 + 0.930091i −0.0512226 + 0.0339621i
\(751\) −17.6776 30.6185i −0.645064 1.11728i −0.984287 0.176578i \(-0.943497\pi\)
0.339222 0.940706i \(-0.389836\pi\)
\(752\) −5.51701 21.8314i −0.201185 0.796109i
\(753\) 0.598926 + 0.345790i 0.0218261 + 0.0126013i
\(754\) 3.60321 7.24134i 0.131221 0.263714i
\(755\) −7.08679 2.93544i −0.257915 0.106832i
\(756\) −1.00543 + 5.14220i −0.0365673 + 0.187020i
\(757\) 13.5015 + 32.5954i 0.490719 + 1.18470i 0.954355 + 0.298675i \(0.0965447\pi\)
−0.463635 + 0.886026i \(0.653455\pi\)
\(758\) −37.6166 + 32.7522i −1.36630 + 1.18961i
\(759\) 3.75938 1.00732i 0.136457 0.0365635i
\(760\) 1.19667 + 2.49355i 0.0434079 + 0.0904505i
\(761\) 13.9793 52.1715i 0.506750 1.89122i 0.0562987 0.998414i \(-0.482070\pi\)
0.450451 0.892801i \(-0.351263\pi\)
\(762\) −1.71718 1.15627i −0.0622068 0.0418871i
\(763\) 5.53773 8.47725i 0.200479 0.306897i
\(764\) 4.76796 11.2825i 0.172499 0.408186i
\(765\) −15.4830 + 2.03837i −0.559787 + 0.0736974i
\(766\) −29.5863 + 33.4949i −1.06900 + 1.21022i
\(767\) 52.7161 + 30.4357i 1.90347 + 1.09897i
\(768\) −0.271041 2.63876i −0.00978034 0.0952182i
\(769\) 12.5480i 0.452494i −0.974070 0.226247i \(-0.927354\pi\)
0.974070 0.226247i \(-0.0726457\pi\)
\(770\) 1.31373 10.5340i 0.0473437 0.379621i
\(771\) −1.58385 0.656052i −0.0570410 0.0236271i
\(772\) 4.01446 + 32.2707i 0.144483 + 1.16145i
\(773\) −5.81490 0.765546i −0.209148 0.0275348i 0.0252243 0.999682i \(-0.491970\pi\)
−0.234372 + 0.972147i \(0.575303\pi\)
\(774\) −21.8971 + 10.7015i −0.787074 + 0.384657i
\(775\) 14.0245 + 3.75787i 0.503777 + 0.134987i
\(776\) 1.46709 2.14558i 0.0526654 0.0770218i
\(777\) −1.38084 3.93302i −0.0495374 0.141096i
\(778\) 26.1418 5.10304i 0.937230 0.182953i
\(779\) 10.8258 + 8.30695i 0.387875 + 0.297627i
\(780\) −0.291058 1.11810i −0.0104215 0.0400343i
\(781\) −22.2047 + 17.0383i −0.794548 + 0.609678i
\(782\) 55.0390 + 27.3868i 1.96819 + 0.979349i
\(783\) 1.23868i 0.0442667i
\(784\) −10.8835 25.7982i −0.388698 0.921365i
\(785\) 4.15377i 0.148254i
\(786\) 0.491076 0.986911i 0.0175161 0.0352019i
\(787\) −27.2313 + 20.8953i −0.970692 + 0.744838i −0.966900 0.255154i \(-0.917874\pi\)
−0.00379200 + 0.999993i \(0.501207\pi\)
\(788\) −7.89271 + 13.4480i −0.281166 + 0.479066i
\(789\) 3.22861 + 2.47740i 0.114942 + 0.0881977i
\(790\) 1.29547 + 6.63643i 0.0460908 + 0.236114i
\(791\) −4.76359 13.5681i −0.169374 0.482424i
\(792\) −17.1090 26.2084i −0.607941 0.931274i
\(793\) 48.8932 + 13.1009i 1.73625 + 0.465227i
\(794\) 16.3228 + 33.3993i 0.579275 + 1.18530i
\(795\) 0.333841 + 0.0439511i 0.0118401 + 0.00155878i
\(796\) 5.45841 + 4.25061i 0.193468 + 0.150659i
\(797\) −24.9001 10.3139i −0.882006 0.365339i −0.104731 0.994501i \(-0.533398\pi\)
−0.777274 + 0.629162i \(0.783398\pi\)
\(798\) −0.789813 0.0985000i −0.0279591 0.00348686i
\(799\) 38.8059i 1.37285i
\(800\) −7.61196 23.8115i −0.269124 0.841862i
\(801\) 30.0017 + 17.3215i 1.06006 + 0.612024i
\(802\) −14.9710 13.2240i −0.528644 0.466956i
\(803\) 19.0321 2.50562i 0.671627 0.0884213i
\(804\) 2.85745 1.15977i 0.100774 0.0409021i
\(805\) −6.95411 + 10.6455i −0.245100 + 0.375204i
\(806\) −11.8650 + 17.6208i −0.417928 + 0.620668i
\(807\) −1.21162 + 4.52182i −0.0426510 + 0.159176i
\(808\) 10.9357 + 9.79943i 0.384718 + 0.344743i
\(809\) −51.7619 + 13.8695i −1.81985 + 0.487627i −0.996771 0.0802991i \(-0.974412\pi\)
−0.823079 + 0.567926i \(0.807746\pi\)
\(810\) −6.19525 7.11538i −0.217679 0.250009i
\(811\) 12.0724 + 29.1453i 0.423919 + 1.02343i 0.981180 + 0.193093i \(0.0618519\pi\)
−0.557262 + 0.830337i \(0.688148\pi\)
\(812\) −3.69547 5.49183i −0.129686 0.192726i
\(813\) −2.42695 1.00527i −0.0851167 0.0352565i
\(814\) 44.7911 + 22.2876i 1.56993 + 0.781178i
\(815\) −14.6516 8.45911i −0.513223 0.296310i
\(816\) −0.661314 + 4.52335i −0.0231506 + 0.158349i
\(817\) −3.71944 6.44226i −0.130127 0.225386i
\(818\) 23.8643 + 35.9929i 0.834397 + 1.25846i
\(819\) −34.1662 11.2031i −1.19386 0.391470i
\(820\) 11.3806 + 11.5442i 0.397427 + 0.403139i
\(821\) 15.0833 19.6569i 0.526411 0.686032i −0.452161 0.891936i \(-0.649347\pi\)
0.978572 + 0.205904i \(0.0660135\pi\)
\(822\) −0.166312 + 0.484257i −0.00580081 + 0.0168904i
\(823\) 0.551127 + 2.05683i 0.0192111 + 0.0716967i 0.974866 0.222792i \(-0.0715172\pi\)
−0.955655 + 0.294489i \(0.904851\pi\)
\(824\) 22.3419 + 26.0329i 0.778315 + 0.906899i
\(825\) 1.92859 + 1.92859i 0.0671447 + 0.0671447i
\(826\) 42.9717 25.2025i 1.49518 0.876906i
\(827\) −11.4984 27.7596i −0.399839 0.965297i −0.987704 0.156338i \(-0.950031\pi\)
0.587865 0.808959i \(-0.299969\pi\)
\(828\) 4.62804 + 37.2030i 0.160835 + 1.29289i
\(829\) 34.6421 26.5818i 1.20317 0.923226i 0.204718 0.978821i \(-0.434372\pi\)
0.998453 + 0.0555956i \(0.0177057\pi\)
\(830\) −5.52010 4.87595i −0.191605 0.169247i
\(831\) −0.232878 0.403356i −0.00807843 0.0139923i
\(832\) 36.5670 + 0.782934i 1.26773 + 0.0271434i
\(833\) 7.29158 + 47.6997i 0.252638 + 1.65270i
\(834\) −2.97307 0.602417i −0.102949 0.0208600i
\(835\) −0.321271 2.44029i −0.0111180 0.0844498i
\(836\) 7.62016 5.76123i 0.263549 0.199256i
\(837\) 0.424639 3.22545i 0.0146777 0.111488i
\(838\) −4.04027 0.279294i −0.139569 0.00964805i
\(839\) −24.7653 + 24.7653i −0.854993 + 0.854993i −0.990743 0.135750i \(-0.956655\pi\)
0.135750 + 0.990743i \(0.456655\pi\)
\(840\) −0.913249 0.245007i −0.0315101 0.00845353i
\(841\) 19.3996 + 19.3996i 0.668950 + 0.668950i
\(842\) 10.0878 + 11.5860i 0.347648 + 0.399282i
\(843\) −3.08819 0.406568i −0.106363 0.0140029i
\(844\) −6.84277 26.2865i −0.235538 0.904817i
\(845\) 5.97120 0.786124i 0.205416 0.0270435i
\(846\) −19.7234 + 13.0772i −0.678103 + 0.449603i
\(847\) −7.54054 + 0.573012i −0.259096 + 0.0196889i
\(848\) −4.21942 + 9.78904i −0.144895 + 0.336157i
\(849\) 0.0435265 0.0251301i 0.00149383 0.000862461i
\(850\) 2.66425 + 42.9988i 0.0913829 + 1.47485i
\(851\) −36.4808 47.5427i −1.25055 1.62974i
\(852\) 1.23104 + 2.16780i 0.0421747 + 0.0742676i
\(853\) 28.4368 11.7789i 0.973656 0.403302i 0.161584 0.986859i \(-0.448340\pi\)
0.812072 + 0.583557i \(0.198340\pi\)
\(854\) 29.0917 29.4917i 0.995498 1.00918i
\(855\) 2.05537 2.05537i 0.0702920 0.0702920i
\(856\) −5.89562 17.9986i −0.201508 0.615180i
\(857\) 11.1457 2.98648i 0.380730 0.102016i −0.0633778 0.997990i \(-0.520187\pi\)
0.444108 + 0.895973i \(0.353521\pi\)
\(858\) −3.58525 + 1.75218i −0.122399 + 0.0598183i
\(859\) −16.7224 12.8316i −0.570562 0.437807i 0.282761 0.959190i \(-0.408750\pi\)
−0.853323 + 0.521383i \(0.825416\pi\)
\(860\) −3.32349 8.18841i −0.113330 0.279223i
\(861\) −4.56564 + 0.957606i −0.155597 + 0.0326351i
\(862\) 24.4784 + 4.95991i 0.833737 + 0.168935i
\(863\) 25.2885 14.6003i 0.860830 0.497000i −0.00346028 0.999994i \(-0.501101\pi\)
0.864290 + 0.502994i \(0.167768\pi\)
\(864\) −5.06708 + 2.38740i −0.172386 + 0.0812209i
\(865\) −6.84674 + 11.8589i −0.232796 + 0.403214i
\(866\) 2.50375 + 7.46320i 0.0850810 + 0.253610i
\(867\) 1.93628 4.67460i 0.0657596 0.158758i
\(868\) 7.74014 + 15.5673i 0.262717 + 0.528390i
\(869\) 21.5766 8.93730i 0.731935 0.303177i
\(870\) −0.223002 0.0154156i −0.00756047 0.000522637i
\(871\) 11.0052 + 41.0720i 0.372897 + 1.39167i
\(872\) 10.8086 0.592321i 0.366027 0.0200585i
\(873\) −2.63854 0.706993i −0.0893009 0.0239281i
\(874\) −11.2307 + 2.19229i −0.379883 + 0.0741553i
\(875\) −18.9640 1.04511i −0.641101 0.0353313i
\(876\) 0.0122010 1.70978i 0.000412234 0.0577682i
\(877\) 5.57549 + 42.3501i 0.188271 + 1.43006i 0.780936 + 0.624611i \(0.214743\pi\)
−0.592665 + 0.805449i \(0.701924\pi\)
\(878\) −45.1816 + 2.79950i −1.52481 + 0.0944785i
\(879\) 0.521755 0.903706i 0.0175984 0.0304812i
\(880\) 9.90816 5.53347i 0.334004 0.186533i
\(881\) 21.7004 0.731104 0.365552 0.930791i \(-0.380880\pi\)
0.365552 + 0.930791i \(0.380880\pi\)
\(882\) −21.7865 + 19.7803i −0.733590 + 0.666037i
\(883\) −20.5104 + 49.5165i −0.690230 + 1.66636i 0.0540868 + 0.998536i \(0.482775\pi\)
−0.744317 + 0.667827i \(0.767225\pi\)
\(884\) −60.7665 16.7480i −2.04380 0.563296i
\(885\) 0.219583 1.66790i 0.00738120 0.0560658i
\(886\) −13.7015 4.70562i −0.460311 0.158088i
\(887\) 0.424519 1.58433i 0.0142539 0.0531965i −0.958433 0.285319i \(-0.907900\pi\)
0.972687 + 0.232123i \(0.0745671\pi\)
\(888\) 2.51524 3.67847i 0.0844060 0.123441i
\(889\) −7.73854 22.0415i −0.259542 0.739250i
\(890\) −7.01589 + 10.4194i −0.235173 + 0.349258i
\(891\) −19.8371 + 25.8522i −0.664567 + 0.866080i
\(892\) 28.8615 21.8208i 0.966356 0.730615i
\(893\) −4.39707 5.73038i −0.147142 0.191760i
\(894\) −0.284664 0.848526i −0.00952058 0.0283790i
\(895\) 3.84511 0.128528
\(896\) 15.3430 25.7020i 0.512573 0.858643i
\(897\) 4.77988 0.159596
\(898\) −6.38719 19.0390i −0.213143 0.635338i
\(899\) 2.50204 + 3.26072i 0.0834476 + 0.108751i
\(900\) −20.9566 + 15.8443i −0.698553 + 0.528142i
\(901\) 11.1832 14.5742i 0.372565 0.485536i
\(902\) 31.2724 46.4428i 1.04126 1.54638i
\(903\) 2.49926 + 0.470180i 0.0831702 + 0.0156466i
\(904\) 8.67702 12.6899i 0.288593 0.422060i
\(905\) 2.23895 8.35588i 0.0744253 0.277759i
\(906\) 2.23187 + 0.766510i 0.0741490 + 0.0254656i
\(907\) −2.89851 + 22.0164i −0.0962434 + 0.731041i 0.873484 + 0.486852i \(0.161855\pi\)
−0.969728 + 0.244189i \(0.921478\pi\)
\(908\) 33.3132 + 9.18152i 1.10554 + 0.304700i
\(909\) 5.90558 14.2573i 0.195876 0.472886i
\(910\) 4.90685 12.0788i 0.162661 0.400408i
\(911\) 19.3134 0.639882 0.319941 0.947438i \(-0.396337\pi\)
0.319941 + 0.947438i \(0.396337\pi\)
\(912\) −0.414884 0.742886i −0.0137382 0.0245994i
\(913\) −12.7194 + 22.0307i −0.420951 + 0.729109i
\(914\) −6.32522 + 0.391917i −0.209220 + 0.0129635i
\(915\) −0.182596 1.38695i −0.00603643 0.0458513i
\(916\) 0.131641 18.4474i 0.00434954 0.609520i
\(917\) 11.0985 5.61735i 0.366505 0.185501i
\(918\) 9.47424 1.84943i 0.312696 0.0610402i
\(919\) 9.82917 + 2.63372i 0.324235 + 0.0868784i 0.417265 0.908785i \(-0.362989\pi\)
−0.0930304 + 0.995663i \(0.529655\pi\)
\(920\) −13.5731 + 0.743819i −0.447493 + 0.0245230i
\(921\) 1.09622 + 4.09115i 0.0361217 + 0.134808i
\(922\) 55.6423 + 3.84642i 1.83248 + 0.126675i
\(923\) −31.7570 + 13.1542i −1.04529 + 0.432975i
\(924\) −0.202973 + 3.25951i −0.00667731 + 0.107230i
\(925\) 16.0708 38.7984i 0.528406 1.27568i
\(926\) −6.44597 19.2142i −0.211828 0.631417i
\(927\) 18.0266 31.2229i 0.592070 1.02550i
\(928\) 2.39383 6.65927i 0.0785813 0.218601i
\(929\) −33.6366 + 19.4201i −1.10358 + 0.637153i −0.937159 0.348901i \(-0.886555\pi\)
−0.166422 + 0.986055i \(0.553221\pi\)
\(930\) 0.575401 + 0.116590i 0.0188681 + 0.00382314i
\(931\) −6.48156 6.21750i −0.212424 0.203770i
\(932\) −2.41892 5.95972i −0.0792343 0.195217i
\(933\) 0.0935438 + 0.0717787i 0.00306249 + 0.00234993i
\(934\) −18.0697 + 8.83096i −0.591257 + 0.288958i
\(935\) −18.8912 + 5.06188i −0.617809 + 0.165541i
\(936\) −11.9654 36.5289i −0.391101 1.19398i
\(937\) −31.5427 + 31.5427i −1.03045 + 1.03045i −0.0309321 + 0.999521i \(0.509848\pi\)
−0.999521 + 0.0309321i \(0.990152\pi\)
\(938\) 33.6739 + 8.77694i 1.09949 + 0.286577i
\(939\) 1.03855 0.430183i 0.0338919 0.0140385i
\(940\) −4.23721 7.46152i −0.138203 0.243368i
\(941\) 8.20086 + 10.6876i 0.267341 + 0.348405i 0.907662 0.419702i \(-0.137865\pi\)
−0.640321 + 0.768107i \(0.721199\pi\)
\(942\) −0.0790269 1.27543i −0.00257483 0.0415557i
\(943\) −58.0807 + 33.5329i −1.89137 + 1.09198i
\(944\) 48.9068 + 21.0805i 1.59178 + 0.686113i
\(945\) 0.151288 + 1.99087i 0.00492140 + 0.0647631i
\(946\) −25.4392 + 16.8669i −0.827099 + 0.548391i
\(947\) 5.83197 0.767793i 0.189513 0.0249499i −0.0351720 0.999381i \(-0.511198\pi\)
0.224685 + 0.974431i \(0.427865\pi\)
\(948\) −0.524039 2.01309i −0.0170200 0.0653823i
\(949\) 23.3739 + 3.07723i 0.758747 + 0.0998910i
\(950\) −5.26559 6.04765i −0.170838 0.196212i
\(951\) −1.94371 1.94371i −0.0630290 0.0630290i
\(952\) −36.4877 + 36.4652i −1.18257 + 1.18184i
\(953\) −7.07749 + 7.07749i −0.229263 + 0.229263i −0.812385 0.583122i \(-0.801831\pi\)
0.583122 + 0.812385i \(0.301831\pi\)
\(954\) 11.1760 + 0.772573i 0.361838 + 0.0250130i
\(955\) 0.609231 4.62757i 0.0197142 0.149745i
\(956\) −15.2715 + 11.5460i −0.493915 + 0.373425i
\(957\) 0.100775 + 0.765462i 0.00325759 + 0.0247439i
\(958\) −30.9499 6.27119i −0.999945 0.202613i
\(959\) −4.77043 + 3.25973i −0.154045 + 0.105262i
\(960\) −0.366748 0.941950i −0.0118367 0.0304013i
\(961\) 10.1026 + 17.4983i 0.325892 + 0.564461i
\(962\) 46.0505 + 40.6768i 1.48473 + 1.31147i
\(963\) −15.7912 + 12.1170i −0.508866 + 0.390466i
\(964\) 1.23993 + 9.96734i 0.0399355 + 0.321026i
\(965\) 4.74220 + 11.4487i 0.152657 + 0.368546i
\(966\) 1.93275 3.40104i 0.0621852 0.109427i
\(967\) −2.01214 2.01214i −0.0647061 0.0647061i 0.674013 0.738719i \(-0.264569\pi\)
−0.738719 + 0.674013i \(0.764569\pi\)
\(968\) −5.26507 6.13490i −0.169226 0.197183i
\(969\) 0.379526 + 1.41641i 0.0121921 + 0.0455016i
\(970\) 0.321718 0.936757i 0.0103298 0.0300775i
\(971\) −19.5250 + 25.4455i −0.626589 + 0.816586i −0.993519 0.113662i \(-0.963742\pi\)
0.366931 + 0.930248i \(0.380409\pi\)
\(972\) 6.20856 + 6.29781i 0.199140 + 0.202002i
\(973\) −22.8363 25.5001i −0.732097 0.817496i
\(974\) −6.47191 9.76111i −0.207373 0.312766i
\(975\) 1.67482 + 2.90088i 0.0536372 + 0.0929024i
\(976\) 43.8201 + 6.40650i 1.40265 + 0.205067i
\(977\) −20.5849 11.8847i −0.658570 0.380225i 0.133162 0.991094i \(-0.457487\pi\)
−0.791732 + 0.610869i \(0.790820\pi\)
\(978\) 4.65977 + 2.31865i 0.149003 + 0.0741422i
\(979\) 40.0830 + 16.6029i 1.28106 + 0.530632i
\(980\) −6.61033 8.37544i −0.211159 0.267544i
\(981\) −4.35352 10.5103i −0.138997 0.335569i
\(982\) −3.25272 3.73582i −0.103799 0.119215i
\(983\) −12.6986 + 3.40257i −0.405022 + 0.108525i −0.455578 0.890196i \(-0.650567\pi\)
0.0505560 + 0.998721i \(0.483901\pi\)
\(984\) −3.71408 3.32816i −0.118400 0.106098i
\(985\) −1.53789 + 5.73950i −0.0490014 + 0.182876i
\(986\) −6.81144 + 10.1157i −0.216920 + 0.322150i
\(987\) 2.46555 + 0.135877i 0.0784794 + 0.00432503i
\(988\) 10.8710 4.41228i 0.345851 0.140373i
\(989\) 36.2479 4.77213i 1.15262 0.151745i
\(990\) −8.93888 7.89578i −0.284096 0.250944i
\(991\) −7.99556 4.61624i −0.253987 0.146640i 0.367601 0.929984i \(-0.380179\pi\)
−0.621589 + 0.783344i \(0.713512\pi\)
\(992\) −8.51632 + 16.5198i −0.270393 + 0.524503i
\(993\) 3.73554i 0.118544i
\(994\) −3.48136 + 27.9150i −0.110422 + 0.885409i
\(995\) 2.43562 + 1.00886i 0.0772142 + 0.0319832i
\(996\) 1.78773 + 1.39216i 0.0566465 + 0.0441122i
\(997\) −49.3355 6.49515i −1.56247 0.205703i −0.700870 0.713289i \(-0.747205\pi\)
−0.861601 + 0.507585i \(0.830538\pi\)
\(998\) −1.62957 3.33439i −0.0515832 0.105548i
\(999\) −9.08907 2.43541i −0.287565 0.0770529i
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 224.2.be.a.115.12 yes 240
4.3 odd 2 896.2.bi.a.367.15 240
7.5 odd 6 inner 224.2.be.a.19.9 240
28.19 even 6 896.2.bi.a.495.15 240
32.5 even 8 896.2.bi.a.143.15 240
32.27 odd 8 inner 224.2.be.a.59.9 yes 240
224.5 odd 24 896.2.bi.a.271.15 240
224.187 even 24 inner 224.2.be.a.187.12 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
224.2.be.a.19.9 240 7.5 odd 6 inner
224.2.be.a.59.9 yes 240 32.27 odd 8 inner
224.2.be.a.115.12 yes 240 1.1 even 1 trivial
224.2.be.a.187.12 yes 240 224.187 even 24 inner
896.2.bi.a.143.15 240 32.5 even 8
896.2.bi.a.271.15 240 224.5 odd 24
896.2.bi.a.367.15 240 4.3 odd 2
896.2.bi.a.495.15 240 28.19 even 6