Properties

Label 1183.2.e.g.170.4
Level $1183$
Weight $2$
Character 1183.170
Analytic conductor $9.446$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1183,2,Mod(170,1183)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1183.170");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 170.4
Root \(-0.437442 - 0.757672i\) of defining polynomial
Character \(\chi\) \(=\) 1183.170
Dual form 1183.2.e.g.508.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.134063 + 0.232203i) q^{2} +(0.571504 + 0.989875i) q^{3} +(0.964054 + 1.66979i) q^{4} +(-1.28088 + 2.21854i) q^{5} -0.306470 q^{6} +(2.57801 + 0.594848i) q^{7} -1.05323 q^{8} +(0.846765 - 1.46664i) q^{9} +O(q^{10})\) \(q+(-0.134063 + 0.232203i) q^{2} +(0.571504 + 0.989875i) q^{3} +(0.964054 + 1.66979i) q^{4} +(-1.28088 + 2.21854i) q^{5} -0.306470 q^{6} +(2.57801 + 0.594848i) q^{7} -1.05323 q^{8} +(0.846765 - 1.46664i) q^{9} +(-0.343436 - 0.594848i) q^{10} +(1.97300 + 3.41734i) q^{11} +(-1.10192 + 1.90859i) q^{12} +(-0.483741 + 0.518876i) q^{14} -2.92811 q^{15} +(-1.78691 + 3.09502i) q^{16} +(-0.392550 - 0.679916i) q^{17} +(0.227039 + 0.393243i) q^{18} +(-3.74764 + 6.49110i) q^{19} -4.93934 q^{20} +(0.884522 + 2.89187i) q^{21} -1.05802 q^{22} +(3.97759 - 6.88938i) q^{23} +(-0.601923 - 1.04256i) q^{24} +(-0.781294 - 1.35324i) q^{25} +5.36475 q^{27} +(1.49207 + 4.87821i) q^{28} +2.35173 q^{29} +(0.392550 - 0.679916i) q^{30} +(-1.27718 - 2.21215i) q^{31} +(-1.53234 - 2.65409i) q^{32} +(-2.25516 + 3.90605i) q^{33} +0.210505 q^{34} +(-4.62182 + 4.95751i) q^{35} +3.26531 q^{36} +(3.37858 - 5.85187i) q^{37} +(-1.00484 - 1.74043i) q^{38} +(1.34905 - 2.33663i) q^{40} +2.43747 q^{41} +(-0.790083 - 0.182303i) q^{42} -2.24946 q^{43} +(-3.80416 + 6.58900i) q^{44} +(2.16920 + 3.75717i) q^{45} +(1.06649 + 1.84722i) q^{46} +(0.658276 - 1.14017i) q^{47} -4.08491 q^{48} +(6.29231 + 3.06705i) q^{49} +0.418969 q^{50} +(0.448688 - 0.777151i) q^{51} +(-4.63977 - 8.03632i) q^{53} +(-0.719212 + 1.24571i) q^{54} -10.1087 q^{55} +(-2.71523 - 0.626509i) q^{56} -8.56716 q^{57} +(-0.315279 + 0.546079i) q^{58} +(-4.48335 - 7.76540i) q^{59} +(-2.82286 - 4.88933i) q^{60} +(-4.72273 + 8.18002i) q^{61} +0.684890 q^{62} +(3.05540 - 3.27732i) q^{63} -6.32592 q^{64} +(-0.604665 - 1.04731i) q^{66} +(-0.676281 - 1.17135i) q^{67} +(0.756879 - 1.31095i) q^{68} +9.09284 q^{69} +(-0.531538 - 1.73782i) q^{70} -12.3162 q^{71} +(-0.891834 + 1.54470i) q^{72} +(0.384295 + 0.665619i) q^{73} +(0.905882 + 1.56903i) q^{74} +(0.893026 - 1.54677i) q^{75} -14.4517 q^{76} +(3.05363 + 9.98358i) q^{77} +(-3.09642 + 5.36316i) q^{79} +(-4.57763 - 7.92868i) q^{80} +(0.525682 + 0.910507i) q^{81} +(-0.326774 + 0.565989i) q^{82} +1.07292 q^{83} +(-3.97609 + 4.26489i) q^{84} +2.01123 q^{85} +(0.301568 - 0.522332i) q^{86} +(1.34402 + 2.32792i) q^{87} +(-2.07801 - 3.59923i) q^{88} +(3.83149 - 6.63634i) q^{89} -1.16324 q^{90} +15.3384 q^{92} +(1.45983 - 2.52850i) q^{93} +(0.176501 + 0.305708i) q^{94} +(-9.60052 - 16.6286i) q^{95} +(1.75148 - 3.03365i) q^{96} +2.37202 q^{97} +(-1.55574 + 1.04992i) q^{98} +6.68267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} + 5 q^{12} - 2 q^{14} - 4 q^{15} + 8 q^{16} + 5 q^{17} - 3 q^{18} + q^{19} - 2 q^{20} + 9 q^{21} + 10 q^{22} - q^{23} + 11 q^{24} + 7 q^{25} - 8 q^{27} - 8 q^{28} - 6 q^{29} - 5 q^{30} - 16 q^{31} - 8 q^{32} - 16 q^{33} - 32 q^{34} - 28 q^{35} + 42 q^{36} + 13 q^{37} - 17 q^{38} - 5 q^{40} - 16 q^{41} - 52 q^{42} + 22 q^{43} - 21 q^{44} + 7 q^{45} - 16 q^{46} + q^{47} - 42 q^{48} + 6 q^{49} + 12 q^{50} - 20 q^{51} - 2 q^{53} + 18 q^{54} - 18 q^{55} + 9 q^{56} - 42 q^{57} + 8 q^{58} - 13 q^{59} - 20 q^{60} - 5 q^{61} - 10 q^{62} - 8 q^{63} - 30 q^{64} + 18 q^{66} + 11 q^{67} + 29 q^{68} - 46 q^{69} + 39 q^{70} + 12 q^{71} - 25 q^{72} + 30 q^{73} - 3 q^{74} - 3 q^{75} - 18 q^{76} + 11 q^{77} + 7 q^{79} + 7 q^{80} - 6 q^{81} + q^{82} + 54 q^{83} - 41 q^{84} - 2 q^{85} + 7 q^{86} + 16 q^{87} - 4 q^{89} - 16 q^{90} + 54 q^{92} + 7 q^{93} + 45 q^{94} - 6 q^{95} - 19 q^{96} - 70 q^{97} + 82 q^{98} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.134063 + 0.232203i −0.0947966 + 0.164193i −0.909524 0.415652i \(-0.863553\pi\)
0.814727 + 0.579845i \(0.196887\pi\)
\(3\) 0.571504 + 0.989875i 0.329958 + 0.571504i 0.982503 0.186246i \(-0.0596320\pi\)
−0.652545 + 0.757750i \(0.726299\pi\)
\(4\) 0.964054 + 1.66979i 0.482027 + 0.834896i
\(5\) −1.28088 + 2.21854i −0.572826 + 0.992163i 0.423448 + 0.905920i \(0.360820\pi\)
−0.996274 + 0.0862431i \(0.972514\pi\)
\(6\) −0.306470 −0.125116
\(7\) 2.57801 + 0.594848i 0.974398 + 0.224831i
\(8\) −1.05323 −0.372371
\(9\) 0.846765 1.46664i 0.282255 0.488880i
\(10\) −0.343436 0.594848i −0.108604 0.188107i
\(11\) 1.97300 + 3.41734i 0.594882 + 1.03037i 0.993563 + 0.113277i \(0.0361346\pi\)
−0.398681 + 0.917090i \(0.630532\pi\)
\(12\) −1.10192 + 1.90859i −0.318098 + 0.550961i
\(13\) 0 0
\(14\) −0.483741 + 0.518876i −0.129285 + 0.138676i
\(15\) −2.92811 −0.756034
\(16\) −1.78691 + 3.09502i −0.446728 + 0.773755i
\(17\) −0.392550 0.679916i −0.0952073 0.164904i 0.814488 0.580181i \(-0.197018\pi\)
−0.909695 + 0.415277i \(0.863685\pi\)
\(18\) 0.227039 + 0.393243i 0.0535136 + 0.0926883i
\(19\) −3.74764 + 6.49110i −0.859767 + 1.48916i 0.0123849 + 0.999923i \(0.496058\pi\)
−0.872151 + 0.489236i \(0.837276\pi\)
\(20\) −4.93934 −1.10447
\(21\) 0.884522 + 2.89187i 0.193018 + 0.631058i
\(22\) −1.05802 −0.225571
\(23\) 3.97759 6.88938i 0.829384 1.43654i −0.0691375 0.997607i \(-0.522025\pi\)
0.898522 0.438929i \(-0.144642\pi\)
\(24\) −0.601923 1.04256i −0.122867 0.212812i
\(25\) −0.781294 1.35324i −0.156259 0.270648i
\(26\) 0 0
\(27\) 5.36475 1.03245
\(28\) 1.49207 + 4.87821i 0.281975 + 0.921895i
\(29\) 2.35173 0.436705 0.218353 0.975870i \(-0.429932\pi\)
0.218353 + 0.975870i \(0.429932\pi\)
\(30\) 0.392550 0.679916i 0.0716695 0.124135i
\(31\) −1.27718 2.21215i −0.229389 0.397313i 0.728238 0.685324i \(-0.240339\pi\)
−0.957627 + 0.288011i \(0.907006\pi\)
\(32\) −1.53234 2.65409i −0.270882 0.469182i
\(33\) −2.25516 + 3.90605i −0.392573 + 0.679956i
\(34\) 0.210505 0.0361013
\(35\) −4.62182 + 4.95751i −0.781230 + 0.837973i
\(36\) 3.26531 0.544219
\(37\) 3.37858 5.85187i 0.555435 0.962041i −0.442435 0.896801i \(-0.645885\pi\)
0.997870 0.0652406i \(-0.0207815\pi\)
\(38\) −1.00484 1.74043i −0.163006 0.282334i
\(39\) 0 0
\(40\) 1.34905 2.33663i 0.213304 0.369453i
\(41\) 2.43747 0.380669 0.190335 0.981719i \(-0.439043\pi\)
0.190335 + 0.981719i \(0.439043\pi\)
\(42\) −0.790083 0.182303i −0.121912 0.0281299i
\(43\) −2.24946 −0.343039 −0.171520 0.985181i \(-0.554868\pi\)
−0.171520 + 0.985181i \(0.554868\pi\)
\(44\) −3.80416 + 6.58900i −0.573499 + 0.993329i
\(45\) 2.16920 + 3.75717i 0.323366 + 0.560086i
\(46\) 1.06649 + 1.84722i 0.157246 + 0.272357i
\(47\) 0.658276 1.14017i 0.0960195 0.166311i −0.814014 0.580845i \(-0.802722\pi\)
0.910034 + 0.414534i \(0.136056\pi\)
\(48\) −4.08491 −0.589606
\(49\) 6.29231 + 3.06705i 0.898902 + 0.438150i
\(50\) 0.418969 0.0592512
\(51\) 0.448688 0.777151i 0.0628289 0.108823i
\(52\) 0 0
\(53\) −4.63977 8.03632i −0.637321 1.10387i −0.986018 0.166637i \(-0.946709\pi\)
0.348697 0.937236i \(-0.386624\pi\)
\(54\) −0.719212 + 1.24571i −0.0978724 + 0.169520i
\(55\) −10.1087 −1.36306
\(56\) −2.71523 0.626509i −0.362838 0.0837207i
\(57\) −8.56716 −1.13475
\(58\) −0.315279 + 0.546079i −0.0413981 + 0.0717037i
\(59\) −4.48335 7.76540i −0.583683 1.01097i −0.995038 0.0994935i \(-0.968278\pi\)
0.411355 0.911475i \(-0.365056\pi\)
\(60\) −2.82286 4.88933i −0.364429 0.631210i
\(61\) −4.72273 + 8.18002i −0.604684 + 1.04734i 0.387417 + 0.921905i \(0.373367\pi\)
−0.992101 + 0.125439i \(0.959966\pi\)
\(62\) 0.684890 0.0869811
\(63\) 3.05540 3.27732i 0.384944 0.412904i
\(64\) −6.32592 −0.790741
\(65\) 0 0
\(66\) −0.604665 1.04731i −0.0744291 0.128915i
\(67\) −0.676281 1.17135i −0.0826209 0.143104i 0.821754 0.569842i \(-0.192996\pi\)
−0.904375 + 0.426739i \(0.859662\pi\)
\(68\) 0.756879 1.31095i 0.0917851 0.158976i
\(69\) 9.09284 1.09465
\(70\) −0.531538 1.73782i −0.0635309 0.207709i
\(71\) −12.3162 −1.46166 −0.730829 0.682560i \(-0.760867\pi\)
−0.730829 + 0.682560i \(0.760867\pi\)
\(72\) −0.891834 + 1.54470i −0.105104 + 0.182045i
\(73\) 0.384295 + 0.665619i 0.0449783 + 0.0779048i 0.887638 0.460542i \(-0.152345\pi\)
−0.842660 + 0.538446i \(0.819011\pi\)
\(74\) 0.905882 + 1.56903i 0.105307 + 0.182396i
\(75\) 0.893026 1.54677i 0.103118 0.178605i
\(76\) −14.4517 −1.65772
\(77\) 3.05363 + 9.98358i 0.347993 + 1.13773i
\(78\) 0 0
\(79\) −3.09642 + 5.36316i −0.348375 + 0.603402i −0.985961 0.166976i \(-0.946600\pi\)
0.637586 + 0.770379i \(0.279933\pi\)
\(80\) −4.57763 7.92868i −0.511794 0.886454i
\(81\) 0.525682 + 0.910507i 0.0584091 + 0.101167i
\(82\) −0.326774 + 0.565989i −0.0360861 + 0.0625030i
\(83\) 1.07292 0.117768 0.0588841 0.998265i \(-0.481246\pi\)
0.0588841 + 0.998265i \(0.481246\pi\)
\(84\) −3.97609 + 4.26489i −0.433827 + 0.465337i
\(85\) 2.01123 0.218149
\(86\) 0.301568 0.522332i 0.0325190 0.0563245i
\(87\) 1.34402 + 2.32792i 0.144094 + 0.249579i
\(88\) −2.07801 3.59923i −0.221517 0.383679i
\(89\) 3.83149 6.63634i 0.406138 0.703451i −0.588316 0.808631i \(-0.700209\pi\)
0.994453 + 0.105180i \(0.0335420\pi\)
\(90\) −1.16324 −0.122616
\(91\) 0 0
\(92\) 15.3384 1.59914
\(93\) 1.45983 2.52850i 0.151378 0.262194i
\(94\) 0.176501 + 0.305708i 0.0182046 + 0.0315314i
\(95\) −9.60052 16.6286i −0.984993 1.70606i
\(96\) 1.75148 3.03365i 0.178760 0.309621i
\(97\) 2.37202 0.240842 0.120421 0.992723i \(-0.461576\pi\)
0.120421 + 0.992723i \(0.461576\pi\)
\(98\) −1.55574 + 1.04992i −0.157154 + 0.106058i
\(99\) 6.68267 0.671634
\(100\) 1.50642 2.60920i 0.150642 0.260920i
\(101\) 0.398665 + 0.690508i 0.0396686 + 0.0687081i 0.885178 0.465252i \(-0.154036\pi\)
−0.845509 + 0.533961i \(0.820703\pi\)
\(102\) 0.120305 + 0.208374i 0.0119119 + 0.0206321i
\(103\) −1.08309 + 1.87597i −0.106720 + 0.184844i −0.914440 0.404722i \(-0.867368\pi\)
0.807720 + 0.589567i \(0.200701\pi\)
\(104\) 0 0
\(105\) −7.54871 1.74178i −0.736678 0.169980i
\(106\) 2.48808 0.241664
\(107\) 5.76311 9.98201i 0.557141 0.964997i −0.440592 0.897707i \(-0.645232\pi\)
0.997733 0.0672896i \(-0.0214351\pi\)
\(108\) 5.17191 + 8.95801i 0.497667 + 0.861985i
\(109\) 4.03912 + 6.99595i 0.386877 + 0.670091i 0.992028 0.126020i \(-0.0402204\pi\)
−0.605151 + 0.796111i \(0.706887\pi\)
\(110\) 1.35520 2.34727i 0.129213 0.223803i
\(111\) 7.72349 0.733081
\(112\) −6.44775 + 6.91607i −0.609255 + 0.653507i
\(113\) 8.04135 0.756467 0.378233 0.925710i \(-0.376532\pi\)
0.378233 + 0.925710i \(0.376532\pi\)
\(114\) 1.14854 1.98932i 0.107570 0.186317i
\(115\) 10.1896 + 17.6489i 0.950186 + 1.64577i
\(116\) 2.26719 + 3.92690i 0.210504 + 0.364603i
\(117\) 0 0
\(118\) 2.40420 0.221325
\(119\) −0.607552 1.98634i −0.0556942 0.182088i
\(120\) 3.08396 0.281526
\(121\) −2.28546 + 3.95854i −0.207769 + 0.359867i
\(122\) −1.26628 2.19327i −0.114644 0.198569i
\(123\) 1.39303 + 2.41279i 0.125605 + 0.217554i
\(124\) 2.46255 4.26526i 0.221143 0.383032i
\(125\) −8.80581 −0.787615
\(126\) 0.351390 + 1.14884i 0.0313043 + 0.102347i
\(127\) 1.78805 0.158663 0.0793317 0.996848i \(-0.474721\pi\)
0.0793317 + 0.996848i \(0.474721\pi\)
\(128\) 3.91275 6.77709i 0.345842 0.599015i
\(129\) −1.28558 2.22668i −0.113189 0.196049i
\(130\) 0 0
\(131\) 3.19545 5.53469i 0.279188 0.483568i −0.691995 0.721902i \(-0.743268\pi\)
0.971183 + 0.238334i \(0.0766014\pi\)
\(132\) −8.69638 −0.756923
\(133\) −13.5227 + 14.5049i −1.17256 + 1.25773i
\(134\) 0.362656 0.0313287
\(135\) −6.87158 + 11.9019i −0.591412 + 1.02436i
\(136\) 0.413443 + 0.716105i 0.0354525 + 0.0614055i
\(137\) 5.01827 + 8.69190i 0.428740 + 0.742599i 0.996762 0.0804144i \(-0.0256244\pi\)
−0.568022 + 0.823014i \(0.692291\pi\)
\(138\) −1.21901 + 2.11139i −0.103769 + 0.179733i
\(139\) −5.54557 −0.470369 −0.235184 0.971951i \(-0.575569\pi\)
−0.235184 + 0.971951i \(0.575569\pi\)
\(140\) −12.7337 2.93816i −1.07619 0.248320i
\(141\) 1.50483 0.126730
\(142\) 1.65114 2.85985i 0.138560 0.239993i
\(143\) 0 0
\(144\) 3.02619 + 5.24151i 0.252182 + 0.436793i
\(145\) −3.01228 + 5.21742i −0.250156 + 0.433283i
\(146\) −0.206078 −0.0170552
\(147\) 0.560087 + 7.98144i 0.0461952 + 0.658298i
\(148\) 13.0285 1.07094
\(149\) 9.23254 15.9912i 0.756359 1.31005i −0.188337 0.982104i \(-0.560310\pi\)
0.944696 0.327947i \(-0.106357\pi\)
\(150\) 0.239443 + 0.414727i 0.0195504 + 0.0338623i
\(151\) 0.803678 + 1.39201i 0.0654024 + 0.113280i 0.896872 0.442289i \(-0.145834\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(152\) 3.94710 6.83658i 0.320152 0.554520i
\(153\) −1.32959 −0.107491
\(154\) −2.72760 0.629362i −0.219796 0.0507155i
\(155\) 6.54366 0.525600
\(156\) 0 0
\(157\) 0.822967 + 1.42542i 0.0656799 + 0.113761i 0.896995 0.442040i \(-0.145745\pi\)
−0.831315 + 0.555801i \(0.812412\pi\)
\(158\) −0.830229 1.43800i −0.0660494 0.114401i
\(159\) 5.30330 9.18558i 0.420579 0.728464i
\(160\) 7.85096 0.620673
\(161\) 14.3524 15.3949i 1.13113 1.21329i
\(162\) −0.281897 −0.0221479
\(163\) −3.27409 + 5.67090i −0.256447 + 0.444179i −0.965287 0.261190i \(-0.915885\pi\)
0.708841 + 0.705369i \(0.249218\pi\)
\(164\) 2.34986 + 4.07007i 0.183493 + 0.317819i
\(165\) −5.77716 10.0063i −0.449751 0.778992i
\(166\) −0.143838 + 0.249135i −0.0111640 + 0.0193367i
\(167\) −9.54880 −0.738908 −0.369454 0.929249i \(-0.620455\pi\)
−0.369454 + 0.929249i \(0.620455\pi\)
\(168\) −0.931600 3.04579i −0.0718745 0.234988i
\(169\) 0 0
\(170\) −0.269631 + 0.467015i −0.0206798 + 0.0358184i
\(171\) 6.34673 + 10.9929i 0.485347 + 0.840646i
\(172\) −2.16860 3.75613i −0.165354 0.286402i
\(173\) −5.56582 + 9.64028i −0.423161 + 0.732937i −0.996247 0.0865588i \(-0.972413\pi\)
0.573085 + 0.819496i \(0.305746\pi\)
\(174\) −0.720733 −0.0546386
\(175\) −1.20921 3.95343i −0.0914080 0.298851i
\(176\) −14.1023 −1.06300
\(177\) 5.12451 8.87592i 0.385182 0.667155i
\(178\) 1.02732 + 1.77937i 0.0770009 + 0.133369i
\(179\) 6.32173 + 10.9496i 0.472508 + 0.818409i 0.999505 0.0314588i \(-0.0100153\pi\)
−0.526997 + 0.849867i \(0.676682\pi\)
\(180\) −4.18246 + 7.24424i −0.311742 + 0.539954i
\(181\) 14.9158 1.10868 0.554341 0.832289i \(-0.312970\pi\)
0.554341 + 0.832289i \(0.312970\pi\)
\(182\) 0 0
\(183\) −10.7963 −0.798082
\(184\) −4.18930 + 7.25607i −0.308839 + 0.534925i
\(185\) 8.65509 + 14.9911i 0.636335 + 1.10216i
\(186\) 0.391418 + 0.677956i 0.0287001 + 0.0497101i
\(187\) 1.54900 2.68295i 0.113274 0.196197i
\(188\) 2.53846 0.185136
\(189\) 13.8304 + 3.19121i 1.00601 + 0.232126i
\(190\) 5.14829 0.373496
\(191\) 7.06528 12.2374i 0.511226 0.885469i −0.488690 0.872458i \(-0.662525\pi\)
0.999915 0.0130110i \(-0.00414165\pi\)
\(192\) −3.61529 6.26187i −0.260911 0.451912i
\(193\) 1.94727 + 3.37277i 0.140167 + 0.242777i 0.927560 0.373675i \(-0.121903\pi\)
−0.787392 + 0.616452i \(0.788569\pi\)
\(194\) −0.317999 + 0.550790i −0.0228310 + 0.0395444i
\(195\) 0 0
\(196\) 0.944795 + 13.4637i 0.0674853 + 0.961689i
\(197\) 11.7089 0.834224 0.417112 0.908855i \(-0.363042\pi\)
0.417112 + 0.908855i \(0.363042\pi\)
\(198\) −0.895897 + 1.55174i −0.0636686 + 0.110277i
\(199\) −1.74842 3.02835i −0.123942 0.214674i 0.797377 0.603482i \(-0.206220\pi\)
−0.921319 + 0.388808i \(0.872887\pi\)
\(200\) 0.822878 + 1.42527i 0.0581863 + 0.100782i
\(201\) 0.772995 1.33887i 0.0545229 0.0944364i
\(202\) −0.213784 −0.0150418
\(203\) 6.06279 + 1.39892i 0.425524 + 0.0981850i
\(204\) 1.73024 0.121141
\(205\) −3.12210 + 5.40764i −0.218057 + 0.377686i
\(206\) −0.290403 0.502994i −0.0202334 0.0350452i
\(207\) −6.73617 11.6674i −0.468196 0.810939i
\(208\) 0 0
\(209\) −29.5764 −2.04584
\(210\) 1.41645 1.51933i 0.0977441 0.104843i
\(211\) 19.0052 1.30837 0.654184 0.756335i \(-0.273012\pi\)
0.654184 + 0.756335i \(0.273012\pi\)
\(212\) 8.94598 15.4949i 0.614412 1.06419i
\(213\) −7.03874 12.1915i −0.482286 0.835345i
\(214\) 1.54524 + 2.67643i 0.105630 + 0.182957i
\(215\) 2.88128 4.99053i 0.196502 0.340351i
\(216\) −5.65029 −0.384453
\(217\) −1.97671 6.46267i −0.134188 0.438715i
\(218\) −2.16598 −0.146698
\(219\) −0.439253 + 0.760808i −0.0296820 + 0.0514106i
\(220\) −9.74533 16.8794i −0.657030 1.13801i
\(221\) 0 0
\(222\) −1.03543 + 1.79342i −0.0694936 + 0.120366i
\(223\) 11.9662 0.801317 0.400658 0.916228i \(-0.368781\pi\)
0.400658 + 0.916228i \(0.368781\pi\)
\(224\) −2.37162 7.75380i −0.158460 0.518072i
\(225\) −2.64629 −0.176419
\(226\) −1.07804 + 1.86723i −0.0717104 + 0.124206i
\(227\) 7.69209 + 13.3231i 0.510542 + 0.884284i 0.999925 + 0.0122157i \(0.00388847\pi\)
−0.489384 + 0.872069i \(0.662778\pi\)
\(228\) −8.25921 14.3054i −0.546980 0.947396i
\(229\) 4.33084 7.50123i 0.286190 0.495695i −0.686707 0.726934i \(-0.740945\pi\)
0.972897 + 0.231239i \(0.0742779\pi\)
\(230\) −5.46418 −0.360297
\(231\) −8.13733 + 8.72837i −0.535397 + 0.574285i
\(232\) −2.47690 −0.162616
\(233\) −10.1253 + 17.5376i −0.663333 + 1.14893i 0.316402 + 0.948625i \(0.397525\pi\)
−0.979734 + 0.200301i \(0.935808\pi\)
\(234\) 0 0
\(235\) 1.68634 + 2.92083i 0.110005 + 0.190534i
\(236\) 8.64440 14.9725i 0.562702 0.974629i
\(237\) −7.07847 −0.459796
\(238\) 0.542685 + 0.125218i 0.0351770 + 0.00811671i
\(239\) −16.5526 −1.07070 −0.535350 0.844630i \(-0.679820\pi\)
−0.535350 + 0.844630i \(0.679820\pi\)
\(240\) 5.23227 9.06256i 0.337742 0.584985i
\(241\) −8.20038 14.2035i −0.528233 0.914926i −0.999458 0.0329132i \(-0.989522\pi\)
0.471225 0.882013i \(-0.343812\pi\)
\(242\) −0.612791 1.06138i −0.0393917 0.0682284i
\(243\) 7.44626 12.8973i 0.477678 0.827362i
\(244\) −18.2119 −1.16590
\(245\) −14.8641 + 10.0313i −0.949631 + 0.640874i
\(246\) −0.747011 −0.0476277
\(247\) 0 0
\(248\) 1.34516 + 2.32989i 0.0854178 + 0.147948i
\(249\) 0.613178 + 1.06206i 0.0388586 + 0.0673051i
\(250\) 1.18053 2.04474i 0.0746632 0.129321i
\(251\) −20.4307 −1.28958 −0.644788 0.764362i \(-0.723054\pi\)
−0.644788 + 0.764362i \(0.723054\pi\)
\(252\) 8.41802 + 1.94236i 0.530285 + 0.122357i
\(253\) 31.3911 1.97354
\(254\) −0.239710 + 0.415190i −0.0150407 + 0.0260513i
\(255\) 1.14943 + 1.99087i 0.0719800 + 0.124673i
\(256\) −5.27682 9.13972i −0.329801 0.571232i
\(257\) −6.88895 + 11.9320i −0.429721 + 0.744299i −0.996848 0.0793315i \(-0.974721\pi\)
0.567127 + 0.823630i \(0.308055\pi\)
\(258\) 0.689391 0.0429196
\(259\) 12.1910 13.0765i 0.757511 0.812532i
\(260\) 0 0
\(261\) 1.99136 3.44914i 0.123262 0.213496i
\(262\) 0.856782 + 1.48399i 0.0529321 + 0.0916812i
\(263\) −12.9587 22.4451i −0.799065 1.38402i −0.920225 0.391389i \(-0.871995\pi\)
0.121160 0.992633i \(-0.461338\pi\)
\(264\) 2.37519 4.11395i 0.146183 0.253196i
\(265\) 23.7719 1.46030
\(266\) −1.55519 5.08457i −0.0953549 0.311755i
\(267\) 8.75887 0.536034
\(268\) 1.30394 2.25850i 0.0796510 0.137960i
\(269\) 15.0333 + 26.0384i 0.916596 + 1.58759i 0.804547 + 0.593889i \(0.202408\pi\)
0.112050 + 0.993703i \(0.464258\pi\)
\(270\) −1.84245 3.19121i −0.112128 0.194211i
\(271\) 7.22527 12.5145i 0.438904 0.760204i −0.558701 0.829369i \(-0.688700\pi\)
0.997605 + 0.0691651i \(0.0220335\pi\)
\(272\) 2.80581 0.170127
\(273\) 0 0
\(274\) −2.69105 −0.162572
\(275\) 3.08299 5.33989i 0.185911 0.322008i
\(276\) 8.76599 + 15.1831i 0.527651 + 0.913918i
\(277\) 7.66274 + 13.2723i 0.460409 + 0.797452i 0.998981 0.0451272i \(-0.0143693\pi\)
−0.538572 + 0.842580i \(0.681036\pi\)
\(278\) 0.743453 1.28770i 0.0445894 0.0772310i
\(279\) −4.32590 −0.258985
\(280\) 4.86781 5.22138i 0.290907 0.312037i
\(281\) −5.29279 −0.315741 −0.157871 0.987460i \(-0.550463\pi\)
−0.157871 + 0.987460i \(0.550463\pi\)
\(282\) −0.201742 + 0.349427i −0.0120135 + 0.0208081i
\(283\) 15.3923 + 26.6602i 0.914975 + 1.58478i 0.806938 + 0.590636i \(0.201123\pi\)
0.108036 + 0.994147i \(0.465544\pi\)
\(284\) −11.8734 20.5654i −0.704559 1.22033i
\(285\) 10.9735 19.0066i 0.650013 1.12586i
\(286\) 0 0
\(287\) 6.28384 + 1.44992i 0.370923 + 0.0855864i
\(288\) −5.19013 −0.305831
\(289\) 8.19181 14.1886i 0.481871 0.834625i
\(290\) −0.807667 1.39892i −0.0474279 0.0821474i
\(291\) 1.35562 + 2.34800i 0.0794677 + 0.137642i
\(292\) −0.740963 + 1.28339i −0.0433616 + 0.0751044i
\(293\) 17.5173 1.02337 0.511685 0.859173i \(-0.329021\pi\)
0.511685 + 0.859173i \(0.329021\pi\)
\(294\) −1.92840 0.939958i −0.112467 0.0548195i
\(295\) 22.9705 1.33739
\(296\) −3.55840 + 6.16333i −0.206828 + 0.358237i
\(297\) 10.5847 + 18.3332i 0.614184 + 1.06380i
\(298\) 2.47548 + 4.28765i 0.143400 + 0.248377i
\(299\) 0 0
\(300\) 3.44370 0.198822
\(301\) −5.79914 1.33809i −0.334257 0.0771260i
\(302\) −0.430973 −0.0247997
\(303\) −0.455678 + 0.789257i −0.0261780 + 0.0453416i
\(304\) −13.3934 23.1980i −0.768163 1.33050i
\(305\) −12.0985 20.9552i −0.692757 1.19989i
\(306\) 0.178248 0.308735i 0.0101898 0.0176492i
\(307\) 8.63573 0.492867 0.246434 0.969160i \(-0.420741\pi\)
0.246434 + 0.969160i \(0.420741\pi\)
\(308\) −13.7266 + 14.7236i −0.782147 + 0.838957i
\(309\) −2.47596 −0.140852
\(310\) −0.877260 + 1.51946i −0.0498250 + 0.0862995i
\(311\) 8.21130 + 14.2224i 0.465620 + 0.806478i 0.999229 0.0392535i \(-0.0124980\pi\)
−0.533609 + 0.845731i \(0.679165\pi\)
\(312\) 0 0
\(313\) −5.02308 + 8.70024i −0.283921 + 0.491766i −0.972347 0.233541i \(-0.924969\pi\)
0.688426 + 0.725307i \(0.258302\pi\)
\(314\) −0.441316 −0.0249049
\(315\) 3.35729 + 10.9764i 0.189162 + 0.618450i
\(316\) −11.9405 −0.671704
\(317\) 5.07249 8.78581i 0.284899 0.493460i −0.687685 0.726009i \(-0.741373\pi\)
0.972585 + 0.232549i \(0.0747064\pi\)
\(318\) 1.42195 + 2.46289i 0.0797389 + 0.138112i
\(319\) 4.63996 + 8.03665i 0.259788 + 0.449966i
\(320\) 8.10273 14.0343i 0.452957 0.784544i
\(321\) 13.1746 0.735333
\(322\) 1.65062 + 5.39655i 0.0919853 + 0.300738i
\(323\) 5.88454 0.327424
\(324\) −1.01357 + 1.75556i −0.0563095 + 0.0975310i
\(325\) 0 0
\(326\) −0.877867 1.52051i −0.0486206 0.0842133i
\(327\) −4.61674 + 7.99644i −0.255307 + 0.442204i
\(328\) −2.56721 −0.141750
\(329\) 2.37527 2.54780i 0.130953 0.140464i
\(330\) 3.09801 0.170540
\(331\) 1.15958 2.00845i 0.0637363 0.110395i −0.832396 0.554181i \(-0.813032\pi\)
0.896133 + 0.443786i \(0.146365\pi\)
\(332\) 1.03435 + 1.79155i 0.0567675 + 0.0983242i
\(333\) −5.72172 9.91032i −0.313549 0.543082i
\(334\) 1.28014 2.21726i 0.0700460 0.121323i
\(335\) 3.46493 0.189309
\(336\) −10.5310 2.42990i −0.574511 0.132562i
\(337\) −15.9998 −0.871565 −0.435783 0.900052i \(-0.643528\pi\)
−0.435783 + 0.900052i \(0.643528\pi\)
\(338\) 0 0
\(339\) 4.59567 + 7.95993i 0.249602 + 0.432324i
\(340\) 1.93894 + 3.35834i 0.105154 + 0.182132i
\(341\) 5.03977 8.72913i 0.272919 0.472709i
\(342\) −3.40344 −0.184037
\(343\) 14.3972 + 11.6499i 0.777378 + 0.629034i
\(344\) 2.36919 0.127738
\(345\) −11.6468 + 20.1729i −0.627043 + 1.08607i
\(346\) −1.49234 2.58480i −0.0802285 0.138960i
\(347\) 11.4104 + 19.7634i 0.612543 + 1.06096i 0.990810 + 0.135259i \(0.0431867\pi\)
−0.378267 + 0.925696i \(0.623480\pi\)
\(348\) −2.59142 + 4.48848i −0.138915 + 0.240608i
\(349\) 22.7022 1.21522 0.607612 0.794234i \(-0.292128\pi\)
0.607612 + 0.794234i \(0.292128\pi\)
\(350\) 1.08011 + 0.249223i 0.0577342 + 0.0133215i
\(351\) 0 0
\(352\) 6.04662 10.4731i 0.322286 0.558216i
\(353\) −13.6322 23.6116i −0.725568 1.25672i −0.958740 0.284286i \(-0.908244\pi\)
0.233171 0.972436i \(-0.425090\pi\)
\(354\) 1.37401 + 2.37986i 0.0730279 + 0.126488i
\(355\) 15.7755 27.3239i 0.837276 1.45020i
\(356\) 14.7751 0.783077
\(357\) 1.61901 1.73660i 0.0856871 0.0919108i
\(358\) −3.39003 −0.179169
\(359\) −7.21309 + 12.4934i −0.380692 + 0.659378i −0.991161 0.132662i \(-0.957648\pi\)
0.610469 + 0.792040i \(0.290981\pi\)
\(360\) −2.28466 3.95715i −0.120412 0.208560i
\(361\) −18.5895 32.1980i −0.978397 1.69463i
\(362\) −1.99965 + 3.46350i −0.105099 + 0.182037i
\(363\) −5.22461 −0.274221
\(364\) 0 0
\(365\) −1.96894 −0.103059
\(366\) 1.44737 2.50693i 0.0756555 0.131039i
\(367\) 5.69586 + 9.86553i 0.297322 + 0.514976i 0.975522 0.219901i \(-0.0705733\pi\)
−0.678201 + 0.734877i \(0.737240\pi\)
\(368\) 14.2152 + 24.6214i 0.741018 + 1.28348i
\(369\) 2.06397 3.57489i 0.107446 0.186102i
\(370\) −4.64130 −0.241289
\(371\) −7.18100 23.4777i −0.372819 1.21890i
\(372\) 5.62943 0.291872
\(373\) 15.4815 26.8147i 0.801599 1.38841i −0.116964 0.993136i \(-0.537316\pi\)
0.918563 0.395274i \(-0.129351\pi\)
\(374\) 0.415327 + 0.719367i 0.0214760 + 0.0371976i
\(375\) −5.03256 8.71665i −0.259880 0.450126i
\(376\) −0.693313 + 1.20085i −0.0357549 + 0.0619293i
\(377\) 0 0
\(378\) −2.59515 + 2.78364i −0.133480 + 0.143175i
\(379\) −10.5866 −0.543797 −0.271898 0.962326i \(-0.587651\pi\)
−0.271898 + 0.962326i \(0.587651\pi\)
\(380\) 18.5109 32.0617i 0.949587 1.64473i
\(381\) 1.02188 + 1.76994i 0.0523523 + 0.0906768i
\(382\) 1.89438 + 3.28116i 0.0969249 + 0.167879i
\(383\) 15.3758 26.6317i 0.785668 1.36082i −0.142931 0.989733i \(-0.545653\pi\)
0.928599 0.371084i \(-0.121014\pi\)
\(384\) 8.94462 0.456453
\(385\) −26.0603 6.01313i −1.32816 0.306458i
\(386\) −1.04422 −0.0531496
\(387\) −1.90476 + 3.29915i −0.0968246 + 0.167705i
\(388\) 2.28675 + 3.96077i 0.116092 + 0.201078i
\(389\) 8.18978 + 14.1851i 0.415239 + 0.719214i 0.995453 0.0952492i \(-0.0303648\pi\)
−0.580215 + 0.814463i \(0.697031\pi\)
\(390\) 0 0
\(391\) −6.24561 −0.315854
\(392\) −6.62722 3.23030i −0.334725 0.163155i
\(393\) 7.30486 0.368482
\(394\) −1.56972 + 2.71884i −0.0790816 + 0.136973i
\(395\) −7.93227 13.7391i −0.399116 0.691289i
\(396\) 6.44246 + 11.1587i 0.323746 + 0.560744i
\(397\) −7.94133 + 13.7548i −0.398564 + 0.690333i −0.993549 0.113404i \(-0.963825\pi\)
0.594985 + 0.803737i \(0.297158\pi\)
\(398\) 0.937591 0.0469972
\(399\) −22.0863 5.09616i −1.10570 0.255127i
\(400\) 5.58441 0.279221
\(401\) 3.31787 5.74671i 0.165686 0.286977i −0.771212 0.636578i \(-0.780349\pi\)
0.936899 + 0.349601i \(0.113683\pi\)
\(402\) 0.207259 + 0.358984i 0.0103372 + 0.0179045i
\(403\) 0 0
\(404\) −0.768670 + 1.33137i −0.0382427 + 0.0662384i
\(405\) −2.69334 −0.133833
\(406\) −1.13763 + 1.22026i −0.0564595 + 0.0605603i
\(407\) 26.6637 1.32167
\(408\) −0.472570 + 0.818515i −0.0233957 + 0.0405225i
\(409\) 2.93617 + 5.08560i 0.145184 + 0.251467i 0.929442 0.368969i \(-0.120289\pi\)
−0.784257 + 0.620436i \(0.786956\pi\)
\(410\) −0.837115 1.44992i −0.0413421 0.0716067i
\(411\) −5.73593 + 9.93492i −0.282933 + 0.490053i
\(412\) −4.17663 −0.205768
\(413\) −6.93892 22.6862i −0.341442 1.11632i
\(414\) 3.61227 0.177533
\(415\) −1.37428 + 2.38032i −0.0674607 + 0.116845i
\(416\) 0 0
\(417\) −3.16932 5.48942i −0.155202 0.268818i
\(418\) 3.96508 6.86773i 0.193939 0.335911i
\(419\) −30.1423 −1.47255 −0.736274 0.676683i \(-0.763417\pi\)
−0.736274 + 0.676683i \(0.763417\pi\)
\(420\) −4.36896 14.2839i −0.213183 0.696985i
\(421\) −40.0580 −1.95231 −0.976153 0.217083i \(-0.930346\pi\)
−0.976153 + 0.217083i \(0.930346\pi\)
\(422\) −2.54788 + 4.41306i −0.124029 + 0.214824i
\(423\) −1.11481 1.93091i −0.0542040 0.0938840i
\(424\) 4.88672 + 8.46405i 0.237320 + 0.411051i
\(425\) −0.613394 + 1.06243i −0.0297540 + 0.0515354i
\(426\) 3.77453 0.182876
\(427\) −17.0411 + 18.2789i −0.824679 + 0.884577i
\(428\) 22.2238 1.07423
\(429\) 0 0
\(430\) 0.772544 + 1.33809i 0.0372554 + 0.0645282i
\(431\) −1.95793 3.39124i −0.0943104 0.163350i 0.815010 0.579447i \(-0.196731\pi\)
−0.909321 + 0.416096i \(0.863398\pi\)
\(432\) −9.58632 + 16.6040i −0.461222 + 0.798860i
\(433\) −40.7925 −1.96036 −0.980182 0.198100i \(-0.936523\pi\)
−0.980182 + 0.198100i \(0.936523\pi\)
\(434\) 1.76566 + 0.407405i 0.0847542 + 0.0195561i
\(435\) −6.88612 −0.330164
\(436\) −7.78785 + 13.4890i −0.372971 + 0.646004i
\(437\) 29.8131 + 51.6378i 1.42615 + 2.47017i
\(438\) −0.117775 0.203992i −0.00562750 0.00974711i
\(439\) 12.7811 22.1376i 0.610010 1.05657i −0.381228 0.924481i \(-0.624499\pi\)
0.991238 0.132087i \(-0.0421680\pi\)
\(440\) 10.6467 0.507563
\(441\) 9.82637 6.63149i 0.467923 0.315785i
\(442\) 0 0
\(443\) 13.7282 23.7779i 0.652247 1.12972i −0.330330 0.943866i \(-0.607160\pi\)
0.982576 0.185859i \(-0.0595067\pi\)
\(444\) 7.44586 + 12.8966i 0.353365 + 0.612046i
\(445\) 9.81535 + 17.0007i 0.465292 + 0.805910i
\(446\) −1.60422 + 2.77859i −0.0759621 + 0.131570i
\(447\) 21.1057 0.998267
\(448\) −16.3083 3.76296i −0.770496 0.177783i
\(449\) 14.8036 0.698626 0.349313 0.937006i \(-0.386415\pi\)
0.349313 + 0.937006i \(0.386415\pi\)
\(450\) 0.354769 0.614477i 0.0167240 0.0289667i
\(451\) 4.80913 + 8.32966i 0.226453 + 0.392229i
\(452\) 7.75230 + 13.4274i 0.364637 + 0.631571i
\(453\) −0.918611 + 1.59108i −0.0431601 + 0.0747555i
\(454\) −4.12489 −0.193590
\(455\) 0 0
\(456\) 9.02315 0.422548
\(457\) −0.325975 + 0.564606i −0.0152485 + 0.0264112i −0.873549 0.486736i \(-0.838187\pi\)
0.858300 + 0.513147i \(0.171521\pi\)
\(458\) 1.16121 + 2.01127i 0.0542596 + 0.0939805i
\(459\) −2.10593 3.64758i −0.0982965 0.170254i
\(460\) −19.6467 + 34.0290i −0.916031 + 1.58661i
\(461\) −12.4955 −0.581972 −0.290986 0.956727i \(-0.593983\pi\)
−0.290986 + 0.956727i \(0.593983\pi\)
\(462\) −0.935844 3.05966i −0.0435394 0.142348i
\(463\) 0.309503 0.0143838 0.00719190 0.999974i \(-0.497711\pi\)
0.00719190 + 0.999974i \(0.497711\pi\)
\(464\) −4.20233 + 7.27865i −0.195088 + 0.337903i
\(465\) 3.73973 + 6.47741i 0.173426 + 0.300382i
\(466\) −2.71486 4.70227i −0.125763 0.217829i
\(467\) −12.2387 + 21.1980i −0.566338 + 0.980926i 0.430586 + 0.902549i \(0.358307\pi\)
−0.996924 + 0.0783762i \(0.975026\pi\)
\(468\) 0 0
\(469\) −1.04668 3.42205i −0.0483314 0.158016i
\(470\) −0.904302 −0.0417123
\(471\) −0.940659 + 1.62927i −0.0433433 + 0.0750727i
\(472\) 4.72198 + 8.17871i 0.217347 + 0.376456i
\(473\) −4.43818 7.68716i −0.204068 0.353456i
\(474\) 0.948959 1.64364i 0.0435871 0.0754951i
\(475\) 11.7120 0.537384
\(476\) 2.73106 2.92943i 0.125178 0.134270i
\(477\) −15.7152 −0.719549
\(478\) 2.21909 3.84357i 0.101499 0.175801i
\(479\) 4.06925 + 7.04815i 0.185929 + 0.322038i 0.943889 0.330262i \(-0.107137\pi\)
−0.757960 + 0.652301i \(0.773804\pi\)
\(480\) 4.48686 + 7.77147i 0.204796 + 0.354718i
\(481\) 0 0
\(482\) 4.39746 0.200299
\(483\) 23.4415 + 5.40885i 1.06662 + 0.246111i
\(484\) −8.81325 −0.400602
\(485\) −3.03826 + 5.26243i −0.137960 + 0.238954i
\(486\) 1.99653 + 3.45809i 0.0905645 + 0.156862i
\(487\) 2.30480 + 3.99203i 0.104440 + 0.180896i 0.913509 0.406817i \(-0.133362\pi\)
−0.809069 + 0.587714i \(0.800028\pi\)
\(488\) 4.97410 8.61540i 0.225167 0.390001i
\(489\) −7.48464 −0.338467
\(490\) −0.336574 4.79630i −0.0152049 0.216675i
\(491\) 13.0189 0.587537 0.293768 0.955877i \(-0.405091\pi\)
0.293768 + 0.955877i \(0.405091\pi\)
\(492\) −2.68591 + 4.65213i −0.121090 + 0.209734i
\(493\) −0.923171 1.59898i −0.0415775 0.0720144i
\(494\) 0 0
\(495\) −8.55969 + 14.8258i −0.384729 + 0.666371i
\(496\) 9.12885 0.409897
\(497\) −31.7512 7.32624i −1.42424 0.328627i
\(498\) −0.328817 −0.0147347
\(499\) −16.1603 + 27.9905i −0.723436 + 1.25303i 0.236178 + 0.971710i \(0.424105\pi\)
−0.959614 + 0.281319i \(0.909228\pi\)
\(500\) −8.48928 14.7039i −0.379652 0.657577i
\(501\) −5.45718 9.45211i −0.243809 0.422289i
\(502\) 2.73900 4.74408i 0.122247 0.211739i
\(503\) −31.8253 −1.41902 −0.709509 0.704696i \(-0.751083\pi\)
−0.709509 + 0.704696i \(0.751083\pi\)
\(504\) −3.21802 + 3.45176i −0.143342 + 0.153754i
\(505\) −2.04256 −0.0908929
\(506\) −4.20838 + 7.28912i −0.187085 + 0.324041i
\(507\) 0 0
\(508\) 1.72377 + 2.98566i 0.0764801 + 0.132467i
\(509\) 1.12788 1.95354i 0.0499922 0.0865891i −0.839946 0.542669i \(-0.817414\pi\)
0.889939 + 0.456080i \(0.150747\pi\)
\(510\) −0.616382 −0.0272938
\(511\) 0.594776 + 1.94457i 0.0263114 + 0.0860228i
\(512\) 18.4807 0.816739
\(513\) −20.1051 + 34.8231i −0.887663 + 1.53748i
\(514\) −1.84710 3.19927i −0.0814722 0.141114i
\(515\) −2.77461 4.80576i −0.122264 0.211767i
\(516\) 2.47873 4.29329i 0.109120 0.189001i
\(517\) 5.19512 0.228481
\(518\) 1.40204 + 4.58385i 0.0616021 + 0.201403i
\(519\) −12.7236 −0.558502
\(520\) 0 0
\(521\) −5.38562 9.32817i −0.235948 0.408675i 0.723600 0.690220i \(-0.242486\pi\)
−0.959548 + 0.281546i \(0.909153\pi\)
\(522\) 0.533934 + 0.924801i 0.0233697 + 0.0404775i
\(523\) −3.70397 + 6.41546i −0.161963 + 0.280528i −0.935573 0.353134i \(-0.885116\pi\)
0.773610 + 0.633663i \(0.218449\pi\)
\(524\) 12.3224 0.538305
\(525\) 3.22232 3.45637i 0.140634 0.150848i
\(526\) 6.94909 0.302995
\(527\) −1.00272 + 1.73676i −0.0436790 + 0.0756543i
\(528\) −8.05953 13.9595i −0.350746 0.607510i
\(529\) −20.1424 34.8877i −0.875757 1.51686i
\(530\) −3.18692 + 5.51991i −0.138431 + 0.239770i
\(531\) −15.1854 −0.658990
\(532\) −37.2567 8.59656i −1.61528 0.372708i
\(533\) 0 0
\(534\) −1.17424 + 2.03384i −0.0508142 + 0.0880127i
\(535\) 14.7637 + 25.5715i 0.638290 + 1.10555i
\(536\) 0.712276 + 1.23370i 0.0307656 + 0.0532876i
\(537\) −7.22580 + 12.5154i −0.311816 + 0.540081i
\(538\) −8.06161 −0.347561
\(539\) 1.93358 + 27.5543i 0.0832854 + 1.18685i
\(540\) −26.4983 −1.14031
\(541\) 16.2741 28.1875i 0.699676 1.21188i −0.268902 0.963168i \(-0.586661\pi\)
0.968579 0.248708i \(-0.0800058\pi\)
\(542\) 1.93728 + 3.35546i 0.0832132 + 0.144129i
\(543\) 8.52445 + 14.7648i 0.365819 + 0.633617i
\(544\) −1.20304 + 2.08373i −0.0515799 + 0.0893391i
\(545\) −20.6944 −0.886453
\(546\) 0 0
\(547\) −13.4997 −0.577206 −0.288603 0.957449i \(-0.593191\pi\)
−0.288603 + 0.957449i \(0.593191\pi\)
\(548\) −9.67577 + 16.7589i −0.413329 + 0.715906i
\(549\) 7.99810 + 13.8531i 0.341350 + 0.591236i
\(550\) 0.826627 + 1.43176i 0.0352475 + 0.0610504i
\(551\) −8.81342 + 15.2653i −0.375464 + 0.650323i
\(552\) −9.57680 −0.407616
\(553\) −11.1729 + 11.9844i −0.475119 + 0.509628i
\(554\) −4.10915 −0.174581
\(555\) −9.89284 + 17.1349i −0.419928 + 0.727336i
\(556\) −5.34623 9.25994i −0.226731 0.392709i
\(557\) −14.8851 25.7818i −0.630703 1.09241i −0.987408 0.158193i \(-0.949433\pi\)
0.356705 0.934217i \(-0.383900\pi\)
\(558\) 0.579941 1.00449i 0.0245509 0.0425233i
\(559\) 0 0
\(560\) −7.08483 23.1632i −0.299389 0.978826i
\(561\) 3.54105 0.149503
\(562\) 0.709566 1.22900i 0.0299312 0.0518424i
\(563\) −7.06629 12.2392i −0.297809 0.515819i 0.677826 0.735223i \(-0.262922\pi\)
−0.975634 + 0.219403i \(0.929589\pi\)
\(564\) 1.45074 + 2.51275i 0.0610872 + 0.105806i
\(565\) −10.3000 + 17.8401i −0.433324 + 0.750538i
\(566\) −8.25410 −0.346946
\(567\) 0.813601 + 2.66000i 0.0341680 + 0.111710i
\(568\) 12.9717 0.544280
\(569\) 12.1270 21.0046i 0.508391 0.880558i −0.491562 0.870842i \(-0.663574\pi\)
0.999953 0.00971585i \(-0.00309270\pi\)
\(570\) 2.94227 + 5.09616i 0.123238 + 0.213455i
\(571\) −0.604159 1.04643i −0.0252832 0.0437919i 0.853107 0.521736i \(-0.174715\pi\)
−0.878390 + 0.477944i \(0.841382\pi\)
\(572\) 0 0
\(573\) 16.1514 0.674732
\(574\) −1.17910 + 1.26475i −0.0492149 + 0.0527895i
\(575\) −12.4307 −0.518394
\(576\) −5.35657 + 9.27786i −0.223191 + 0.386577i
\(577\) −7.30518 12.6529i −0.304119 0.526749i 0.672946 0.739692i \(-0.265029\pi\)
−0.977065 + 0.212943i \(0.931695\pi\)
\(578\) 2.19643 + 3.80433i 0.0913595 + 0.158239i
\(579\) −2.22575 + 3.85510i −0.0924988 + 0.160213i
\(580\) −11.6160 −0.482328
\(581\) 2.76600 + 0.638224i 0.114753 + 0.0264780i
\(582\) −0.726951 −0.0301331
\(583\) 18.3085 31.7113i 0.758262 1.31335i
\(584\) −0.404749 0.701046i −0.0167486 0.0290095i
\(585\) 0 0
\(586\) −2.34841 + 4.06757i −0.0970120 + 0.168030i
\(587\) −21.5095 −0.887793 −0.443897 0.896078i \(-0.646404\pi\)
−0.443897 + 0.896078i \(0.646404\pi\)
\(588\) −12.7874 + 8.62977i −0.527343 + 0.355886i
\(589\) 19.1457 0.788884
\(590\) −3.07949 + 5.33383i −0.126780 + 0.219590i
\(591\) 6.69168 + 11.5903i 0.275259 + 0.476763i
\(592\) 12.0744 + 20.9135i 0.496256 + 0.859541i
\(593\) −1.32429 + 2.29373i −0.0543820 + 0.0941923i −0.891935 0.452164i \(-0.850652\pi\)
0.837553 + 0.546356i \(0.183986\pi\)
\(594\) −5.67602 −0.232890
\(595\) 5.18499 + 1.19638i 0.212564 + 0.0490467i
\(596\) 35.6027 1.45834
\(597\) 1.99846 3.46143i 0.0817915 0.141667i
\(598\) 0 0
\(599\) 20.1250 + 34.8576i 0.822287 + 1.42424i 0.903975 + 0.427584i \(0.140635\pi\)
−0.0816889 + 0.996658i \(0.526031\pi\)
\(600\) −0.940558 + 1.62909i −0.0383981 + 0.0665075i
\(601\) 38.3449 1.56412 0.782061 0.623202i \(-0.214169\pi\)
0.782061 + 0.623202i \(0.214169\pi\)
\(602\) 1.08816 1.16719i 0.0443499 0.0475712i
\(603\) −2.29060 −0.0932806
\(604\) −1.54958 + 2.68395i −0.0630515 + 0.109208i
\(605\) −5.85480 10.1408i −0.238031 0.412283i
\(606\) −0.122179 0.211620i −0.00496317 0.00859646i
\(607\) −21.2773 + 36.8534i −0.863620 + 1.49583i 0.00479063 + 0.999989i \(0.498475\pi\)
−0.868411 + 0.495845i \(0.834858\pi\)
\(608\) 22.9706 0.931582
\(609\) 2.08015 + 6.80089i 0.0842921 + 0.275586i
\(610\) 6.48782 0.262684
\(611\) 0 0
\(612\) −1.28180 2.22014i −0.0518136 0.0897438i
\(613\) 7.63261 + 13.2201i 0.308278 + 0.533953i 0.977986 0.208672i \(-0.0669140\pi\)
−0.669708 + 0.742625i \(0.733581\pi\)
\(614\) −1.15773 + 2.00524i −0.0467221 + 0.0809251i
\(615\) −7.13718 −0.287799
\(616\) −3.21616 10.5150i −0.129583 0.423660i
\(617\) −13.9812 −0.562863 −0.281431 0.959581i \(-0.590809\pi\)
−0.281431 + 0.959581i \(0.590809\pi\)
\(618\) 0.331934 0.574926i 0.0133523 0.0231269i
\(619\) −4.25792 7.37494i −0.171140 0.296424i 0.767678 0.640835i \(-0.221412\pi\)
−0.938819 + 0.344411i \(0.888079\pi\)
\(620\) 6.30845 + 10.9265i 0.253353 + 0.438821i
\(621\) 21.3388 36.9598i 0.856295 1.48315i
\(622\) −4.40331 −0.176557
\(623\) 13.8253 14.8294i 0.553897 0.594129i
\(624\) 0 0
\(625\) 15.1856 26.3023i 0.607425 1.05209i
\(626\) −1.34682 2.33275i −0.0538296 0.0932356i
\(627\) −16.9030 29.2769i −0.675042 1.16921i
\(628\) −1.58677 + 2.74837i −0.0633190 + 0.109672i
\(629\) −5.30504 −0.211526
\(630\) −2.99884 0.691949i −0.119477 0.0275679i
\(631\) −36.8292 −1.46615 −0.733074 0.680149i \(-0.761915\pi\)
−0.733074 + 0.680149i \(0.761915\pi\)
\(632\) 3.26123 5.64861i 0.129725 0.224690i
\(633\) 10.8615 + 18.8127i 0.431707 + 0.747739i
\(634\) 1.36006 + 2.35570i 0.0540150 + 0.0935567i
\(635\) −2.29027 + 3.96686i −0.0908865 + 0.157420i
\(636\) 20.4507 0.810922
\(637\) 0 0
\(638\) −2.48818 −0.0985081
\(639\) −10.4289 + 18.0634i −0.412561 + 0.714576i
\(640\) 10.0235 + 17.3612i 0.396214 + 0.686263i
\(641\) −12.9374 22.4082i −0.510996 0.885070i −0.999919 0.0127435i \(-0.995944\pi\)
0.488923 0.872327i \(-0.337390\pi\)
\(642\) −1.76622 + 3.05918i −0.0697071 + 0.120736i
\(643\) −40.5252 −1.59816 −0.799078 0.601227i \(-0.794679\pi\)
−0.799078 + 0.601227i \(0.794679\pi\)
\(644\) 39.5427 + 9.12404i 1.55820 + 0.359538i
\(645\) 6.58666 0.259350
\(646\) −0.788896 + 1.36641i −0.0310387 + 0.0537606i
\(647\) −0.892002 1.54499i −0.0350682 0.0607399i 0.847959 0.530062i \(-0.177832\pi\)
−0.883027 + 0.469322i \(0.844498\pi\)
\(648\) −0.553661 0.958969i −0.0217499 0.0376719i
\(649\) 17.6913 30.6423i 0.694445 1.20281i
\(650\) 0 0
\(651\) 5.26754 5.65014i 0.206451 0.221446i
\(652\) −12.6256 −0.494457
\(653\) −6.20210 + 10.7424i −0.242707 + 0.420381i −0.961484 0.274860i \(-0.911369\pi\)
0.718778 + 0.695240i \(0.244702\pi\)
\(654\) −1.23787 2.14405i −0.0484044 0.0838389i
\(655\) 8.18597 + 14.1785i 0.319852 + 0.554000i
\(656\) −4.35554 + 7.54402i −0.170055 + 0.294545i
\(657\) 1.30163 0.0507815
\(658\) 0.273171 + 0.893110i 0.0106493 + 0.0348171i
\(659\) −1.12867 −0.0439668 −0.0219834 0.999758i \(-0.506998\pi\)
−0.0219834 + 0.999758i \(0.506998\pi\)
\(660\) 11.1390 19.2933i 0.433585 0.750991i
\(661\) −14.4627 25.0502i −0.562534 0.974338i −0.997274 0.0737821i \(-0.976493\pi\)
0.434740 0.900556i \(-0.356840\pi\)
\(662\) 0.310913 + 0.538517i 0.0120840 + 0.0209301i
\(663\) 0 0
\(664\) −1.13003 −0.0438535
\(665\) −14.8588 48.5796i −0.576200 1.88384i
\(666\) 3.06828 0.118893
\(667\) 9.35421 16.2020i 0.362196 0.627342i
\(668\) −9.20556 15.9445i −0.356174 0.616911i
\(669\) 6.83874 + 11.8451i 0.264401 + 0.457956i
\(670\) −0.464518 + 0.804568i −0.0179459 + 0.0310832i
\(671\) −37.2718 −1.43886
\(672\) 6.31990 6.77893i 0.243795 0.261503i
\(673\) −7.09960 −0.273669 −0.136835 0.990594i \(-0.543693\pi\)
−0.136835 + 0.990594i \(0.543693\pi\)
\(674\) 2.14498 3.71521i 0.0826214 0.143104i
\(675\) −4.19145 7.25980i −0.161329 0.279430i
\(676\) 0 0
\(677\) 25.2010 43.6494i 0.968552 1.67758i 0.268800 0.963196i \(-0.413373\pi\)
0.699752 0.714386i \(-0.253294\pi\)
\(678\) −2.46443 −0.0946458
\(679\) 6.11509 + 1.41099i 0.234676 + 0.0541488i
\(680\) −2.11828 −0.0812324
\(681\) −8.79213 + 15.2284i −0.336915 + 0.583554i
\(682\) 1.35129 + 2.34050i 0.0517435 + 0.0896224i
\(683\) 13.7641 + 23.8401i 0.526669 + 0.912217i 0.999517 + 0.0310735i \(0.00989259\pi\)
−0.472848 + 0.881144i \(0.656774\pi\)
\(684\) −12.2372 + 21.1954i −0.467901 + 0.810428i
\(685\) −25.7112 −0.982373
\(686\) −4.63527 + 1.78127i −0.176975 + 0.0680093i
\(687\) 9.90037 0.377723
\(688\) 4.01958 6.96212i 0.153245 0.265428i
\(689\) 0 0
\(690\) −3.12280 5.40885i −0.118883 0.205912i
\(691\) −12.1669 + 21.0737i −0.462851 + 0.801682i −0.999102 0.0423772i \(-0.986507\pi\)
0.536251 + 0.844059i \(0.319840\pi\)
\(692\) −21.4630 −0.815901
\(693\) 17.2280 + 3.97517i 0.654439 + 0.151004i
\(694\) −6.11884 −0.232268
\(695\) 7.10319 12.3031i 0.269439 0.466683i
\(696\) −1.41556 2.45182i −0.0536566 0.0929360i
\(697\) −0.956829 1.65728i −0.0362425 0.0627738i
\(698\) −3.04352 + 5.27153i −0.115199 + 0.199531i
\(699\) −23.1467 −0.875488
\(700\) 5.43565 5.83045i 0.205448 0.220370i
\(701\) −20.5588 −0.776495 −0.388248 0.921555i \(-0.626919\pi\)
−0.388248 + 0.921555i \(0.626919\pi\)
\(702\) 0 0
\(703\) 25.3234 + 43.8613i 0.955088 + 1.65426i
\(704\) −12.4811 21.6178i −0.470397 0.814752i
\(705\) −1.92751 + 3.33854i −0.0725940 + 0.125737i
\(706\) 7.31027 0.275126
\(707\) 0.617017 + 2.01728i 0.0232053 + 0.0758678i
\(708\) 19.7612 0.742673
\(709\) 20.4544 35.4281i 0.768183 1.33053i −0.170364 0.985381i \(-0.554494\pi\)
0.938547 0.345151i \(-0.112172\pi\)
\(710\) 4.22981 + 7.32624i 0.158742 + 0.274949i
\(711\) 5.24388 + 9.08267i 0.196661 + 0.340627i
\(712\) −4.03543 + 6.98956i −0.151234 + 0.261945i
\(713\) −20.3204 −0.761006
\(714\) 0.186196 + 0.608753i 0.00696822 + 0.0227820i
\(715\) 0 0
\(716\) −12.1890 + 21.1119i −0.455524 + 0.788990i
\(717\) −9.45989 16.3850i −0.353286 0.611910i
\(718\) −1.93401 3.34981i −0.0721767 0.125014i
\(719\) 0.599734 1.03877i 0.0223663 0.0387396i −0.854626 0.519245i \(-0.826213\pi\)
0.876992 + 0.480505i \(0.159547\pi\)
\(720\) −15.5047 −0.577826
\(721\) −3.90813 + 4.19199i −0.145546 + 0.156118i
\(722\) 9.96865 0.370995
\(723\) 9.37311 16.2347i 0.348590 0.603775i
\(724\) 14.3796 + 24.9063i 0.534415 + 0.925634i
\(725\) −1.83739 3.18246i −0.0682390 0.118193i
\(726\) 0.700425 1.21317i 0.0259952 0.0450250i
\(727\) −2.06230 −0.0764865 −0.0382433 0.999268i \(-0.512176\pi\)
−0.0382433 + 0.999268i \(0.512176\pi\)
\(728\) 0 0
\(729\) 20.1764 0.747273
\(730\) 0.263961 0.457194i 0.00976964 0.0169215i
\(731\) 0.883025 + 1.52944i 0.0326599 + 0.0565685i
\(732\) −10.4082 18.0275i −0.384697 0.666315i
\(733\) 15.0310 26.0345i 0.555184 0.961606i −0.442706 0.896667i \(-0.645981\pi\)
0.997889 0.0649392i \(-0.0206853\pi\)
\(734\) −3.05441 −0.112740
\(735\) −18.4246 8.98066i −0.679601 0.331257i
\(736\) −24.3801 −0.898662
\(737\) 2.66861 4.62216i 0.0982993 0.170259i
\(738\) 0.553401 + 0.958519i 0.0203710 + 0.0352836i
\(739\) 22.1274 + 38.3257i 0.813969 + 1.40984i 0.910066 + 0.414464i \(0.136031\pi\)
−0.0960970 + 0.995372i \(0.530636\pi\)
\(740\) −16.6880 + 28.9044i −0.613461 + 1.06255i
\(741\) 0 0
\(742\) 6.41430 + 1.48003i 0.235476 + 0.0543335i
\(743\) 8.62651 0.316476 0.158238 0.987401i \(-0.449419\pi\)
0.158238 + 0.987401i \(0.449419\pi\)
\(744\) −1.53753 + 2.66308i −0.0563686 + 0.0976334i
\(745\) 23.6515 + 40.9656i 0.866524 + 1.50086i
\(746\) 4.15097 + 7.18969i 0.151978 + 0.263233i
\(747\) 0.908511 1.57359i 0.0332407 0.0575746i
\(748\) 5.97329 0.218405
\(749\) 20.7952 22.3056i 0.759839 0.815028i
\(750\) 2.69871 0.0985430
\(751\) −2.86105 + 4.95549i −0.104401 + 0.180828i −0.913493 0.406853i \(-0.866626\pi\)
0.809092 + 0.587682i \(0.199959\pi\)
\(752\) 2.35256 + 4.07476i 0.0857891 + 0.148591i
\(753\) −11.6763 20.2239i −0.425506 0.736998i
\(754\) 0 0
\(755\) −4.11765 −0.149857
\(756\) 8.00460 + 26.1704i 0.291125 + 0.951807i
\(757\) −34.7222 −1.26200 −0.631000 0.775783i \(-0.717355\pi\)
−0.631000 + 0.775783i \(0.717355\pi\)
\(758\) 1.41927 2.45824i 0.0515501 0.0892873i
\(759\) 17.9402 + 31.0733i 0.651187 + 1.12789i
\(760\) 10.1115 + 17.5137i 0.366783 + 0.635287i
\(761\) −26.5867 + 46.0496i −0.963768 + 1.66930i −0.250880 + 0.968018i \(0.580720\pi\)
−0.712888 + 0.701278i \(0.752613\pi\)
\(762\) −0.547981 −0.0198513
\(763\) 6.25137 + 20.4383i 0.226315 + 0.739917i
\(764\) 27.2452 0.985699
\(765\) 1.70304 2.94976i 0.0615736 0.106649i
\(766\) 4.12265 + 7.14063i 0.148957 + 0.258002i
\(767\) 0 0
\(768\) 6.03145 10.4468i 0.217641 0.376966i
\(769\) −4.91157 −0.177116 −0.0885578 0.996071i \(-0.528226\pi\)
−0.0885578 + 0.996071i \(0.528226\pi\)
\(770\) 4.88999 5.24516i 0.176223 0.189022i
\(771\) −15.7483 −0.567160
\(772\) −3.75455 + 6.50306i −0.135129 + 0.234050i
\(773\) −11.4903 19.9018i −0.413279 0.715819i 0.581967 0.813212i \(-0.302283\pi\)
−0.995246 + 0.0973926i \(0.968950\pi\)
\(774\) −0.510715 0.884585i −0.0183573 0.0317957i
\(775\) −1.99571 + 3.45667i −0.0716881 + 0.124167i
\(776\) −2.49827 −0.0896826
\(777\) 19.9113 + 4.59430i 0.714313 + 0.164820i
\(778\) −4.39178 −0.157453
\(779\) −9.13476 + 15.8219i −0.327287 + 0.566877i
\(780\) 0 0
\(781\) −24.2998 42.0885i −0.869515 1.50604i
\(782\) 0.837302 1.45025i 0.0299419 0.0518608i
\(783\) 12.6164 0.450874
\(784\) −20.7364 + 13.9943i −0.740585 + 0.499796i
\(785\) −4.21648 −0.150493
\(786\) −0.979309 + 1.69621i −0.0349308 + 0.0605019i
\(787\) −1.59387 2.76067i −0.0568154 0.0984071i 0.836219 0.548396i \(-0.184761\pi\)
−0.893034 + 0.449989i \(0.851428\pi\)
\(788\) 11.2880 + 19.5514i 0.402119 + 0.696490i
\(789\) 14.8119 25.6549i 0.527316 0.913339i
\(790\) 4.25368 0.151339
\(791\) 20.7307 + 4.78338i 0.737099 + 0.170077i
\(792\) −7.03836 −0.250097
\(793\) 0 0
\(794\) −2.12927 3.68800i −0.0755650 0.130882i
\(795\) 13.5857 + 23.5312i 0.481837 + 0.834566i
\(796\) 3.37114 5.83899i 0.119487 0.206958i
\(797\) 54.6509 1.93584 0.967918 0.251267i \(-0.0808472\pi\)
0.967918 + 0.251267i \(0.0808472\pi\)
\(798\) 4.14429 4.44530i 0.146706 0.157362i
\(799\) −1.03363 −0.0365670
\(800\) −2.39442 + 4.14725i −0.0846554 + 0.146628i
\(801\) −6.48875 11.2388i −0.229269 0.397105i
\(802\) 0.889604 + 1.54084i 0.0314130 + 0.0544089i
\(803\) −1.51643 + 2.62653i −0.0535136 + 0.0926883i
\(804\) 2.98084 0.105126
\(805\) 15.7705 + 51.5604i 0.555838 + 1.81727i
\(806\) 0 0
\(807\) −17.1832 + 29.7622i −0.604877 + 1.04768i
\(808\) −0.419884 0.727260i −0.0147715 0.0255849i
\(809\) 10.1498 + 17.5799i 0.356847 + 0.618077i 0.987432 0.158043i \(-0.0505185\pi\)
−0.630585 + 0.776120i \(0.717185\pi\)
\(810\) 0.361076 0.625401i 0.0126869 0.0219744i
\(811\) −2.43587 −0.0855350 −0.0427675 0.999085i \(-0.513617\pi\)
−0.0427675 + 0.999085i \(0.513617\pi\)
\(812\) 3.50895 + 11.4722i 0.123140 + 0.402596i
\(813\) 16.5171 0.579280
\(814\) −3.57461 + 6.19141i −0.125290 + 0.217009i
\(815\) −8.38742 14.5274i −0.293799 0.508874i
\(816\) 1.60353 + 2.77740i 0.0561348 + 0.0972284i
\(817\) 8.43015 14.6015i 0.294934 0.510840i
\(818\) −1.57452 −0.0550519
\(819\) 0 0
\(820\) −12.0395 −0.420438
\(821\) 22.6762 39.2763i 0.791405 1.37075i −0.133692 0.991023i \(-0.542683\pi\)
0.925097 0.379731i \(-0.123983\pi\)
\(822\) −1.53795 2.66380i −0.0536421 0.0929108i
\(823\) 1.37871 + 2.38800i 0.0480588 + 0.0832403i 0.889054 0.457802i \(-0.151363\pi\)
−0.840995 + 0.541042i \(0.818030\pi\)
\(824\) 1.14074 1.97581i 0.0397394 0.0688307i
\(825\) 7.04776 0.245372
\(826\) 6.19806 + 1.43013i 0.215658 + 0.0497607i
\(827\) 8.64504 0.300618 0.150309 0.988639i \(-0.451973\pi\)
0.150309 + 0.988639i \(0.451973\pi\)
\(828\) 12.9881 22.4960i 0.451366 0.781789i
\(829\) 14.7871 + 25.6119i 0.513576 + 0.889540i 0.999876 + 0.0157478i \(0.00501289\pi\)
−0.486300 + 0.873792i \(0.661654\pi\)
\(830\) −0.368479 0.638224i −0.0127901 0.0221531i
\(831\) −8.75858 + 15.1703i −0.303832 + 0.526252i
\(832\) 0 0
\(833\) −0.384708 5.48222i −0.0133293 0.189948i
\(834\) 1.69955 0.0588505
\(835\) 12.2308 21.1844i 0.423266 0.733117i
\(836\) −28.5132 49.3863i −0.986150 1.70806i
\(837\) −6.85177 11.8676i −0.236832 0.410204i
\(838\) 4.04096 6.99914i 0.139593 0.241781i
\(839\) −25.2473 −0.871633 −0.435817 0.900035i \(-0.643540\pi\)
−0.435817 + 0.900035i \(0.643540\pi\)
\(840\) 7.95049 + 1.83449i 0.274318 + 0.0632958i
\(841\) −23.4694 −0.809289
\(842\) 5.37028 9.30159i 0.185072 0.320554i
\(843\) −3.02485 5.23920i −0.104182 0.180448i
\(844\) 18.3220 + 31.7346i 0.630669 + 1.09235i
\(845\) 0 0
\(846\) 0.597818 0.0205534
\(847\) −8.24669 + 8.84567i −0.283360 + 0.303941i
\(848\) 33.1634 1.13884
\(849\) −17.5935 + 30.4728i −0.603807 + 1.04582i
\(850\) −0.164466 0.284864i −0.00564115 0.00977076i
\(851\) −26.8772 46.5526i −0.921338 1.59580i
\(852\) 13.5715 23.5064i 0.464950 0.805318i
\(853\) 35.1368 1.20306 0.601531 0.798850i \(-0.294558\pi\)
0.601531 + 0.798850i \(0.294558\pi\)
\(854\) −1.95984 6.40752i −0.0670643 0.219261i
\(855\) −32.5176 −1.11208
\(856\) −6.06986 + 10.5133i −0.207463 + 0.359337i
\(857\) 0.671345 + 1.16280i 0.0229327 + 0.0397206i 0.877264 0.480008i \(-0.159366\pi\)
−0.854331 + 0.519729i \(0.826033\pi\)
\(858\) 0 0
\(859\) −2.38386 + 4.12897i −0.0813363 + 0.140879i −0.903824 0.427904i \(-0.859252\pi\)
0.822488 + 0.568783i \(0.192585\pi\)
\(860\) 11.1108 0.378877
\(861\) 2.15600 + 7.04885i 0.0734762 + 0.240224i
\(862\) 1.04994 0.0357612
\(863\) −13.3052 + 23.0453i −0.452915 + 0.784472i −0.998566 0.0535407i \(-0.982949\pi\)
0.545650 + 0.838013i \(0.316283\pi\)
\(864\) −8.22062 14.2385i −0.279671 0.484405i
\(865\) −14.2583 24.6960i −0.484795 0.839690i
\(866\) 5.46875 9.47216i 0.185836 0.321877i
\(867\) 18.7266 0.635989
\(868\) 8.88566 9.53106i 0.301599 0.323505i
\(869\) −24.4370 −0.828967
\(870\) 0.923171 1.59898i 0.0312984 0.0542105i
\(871\) 0 0
\(872\) −4.25410 7.36831i −0.144062 0.249523i
\(873\) 2.00854 3.47890i 0.0679788 0.117743i
\(874\) −15.9873 −0.540778
\(875\) −22.7015 5.23812i −0.767451 0.177081i
\(876\) −1.69385 −0.0572300
\(877\) 4.01848 6.96022i 0.135695 0.235030i −0.790168 0.612890i \(-0.790007\pi\)
0.925863 + 0.377860i \(0.123340\pi\)
\(878\) 3.42694 + 5.93564i 0.115654 + 0.200318i
\(879\) 10.0112 + 17.3399i 0.337670 + 0.584861i
\(880\) 18.0633 31.2866i 0.608915 1.05467i
\(881\) −54.6697 −1.84187 −0.920935 0.389716i \(-0.872573\pi\)
−0.920935 + 0.389716i \(0.872573\pi\)
\(882\) 0.222503 + 3.17075i 0.00749208 + 0.106765i
\(883\) −8.45085 −0.284394 −0.142197 0.989838i \(-0.545417\pi\)
−0.142197 + 0.989838i \(0.545417\pi\)
\(884\) 0 0
\(885\) 13.1277 + 22.7379i 0.441284 + 0.764327i
\(886\) 3.68088 + 6.37547i 0.123662 + 0.214188i
\(887\) 5.17784 8.96829i 0.173855 0.301126i −0.765909 0.642948i \(-0.777711\pi\)
0.939764 + 0.341823i \(0.111044\pi\)
\(888\) −8.13457 −0.272978
\(889\) 4.60961 + 1.06361i 0.154601 + 0.0356725i
\(890\) −5.26349 −0.176432
\(891\) −2.07434 + 3.59286i −0.0694930 + 0.120365i
\(892\) 11.5361 + 19.9811i 0.386256 + 0.669016i
\(893\) 4.93396 + 8.54587i 0.165109 + 0.285977i
\(894\) −2.82949 + 4.90082i −0.0946323 + 0.163908i
\(895\) −32.3895 −1.08266
\(896\) 14.1185 15.1439i 0.471665 0.505923i
\(897\) 0 0
\(898\) −1.98461 + 3.43745i −0.0662274 + 0.114709i
\(899\) −3.00359 5.20237i −0.100175 0.173509i
\(900\) −2.55117 4.41875i −0.0850389 0.147292i
\(901\) −3.64268 + 6.30931i −0.121355 + 0.210194i
\(902\) −2.57890 −0.0858680
\(903\) −1.98970 6.50514i −0.0662129 0.216478i
\(904\) −8.46935 −0.281686
\(905\) −19.1053 + 33.0914i −0.635082 + 1.09999i
\(906\) −0.246303 0.426609i −0.00818287 0.0141731i
\(907\) −9.24019 16.0045i −0.306815 0.531420i 0.670849 0.741594i \(-0.265930\pi\)
−0.977664 + 0.210175i \(0.932597\pi\)
\(908\) −14.8312 + 25.6884i −0.492190 + 0.852498i
\(909\) 1.35030 0.0447867
\(910\) 0 0
\(911\) −26.6282 −0.882230 −0.441115 0.897451i \(-0.645417\pi\)
−0.441115 + 0.897451i \(0.645417\pi\)
\(912\) 15.3088 26.5155i 0.506924 0.878017i
\(913\) 2.11687 + 3.66653i 0.0700582 + 0.121344i
\(914\) −0.0874022 0.151385i −0.00289101 0.00500737i
\(915\) 13.8287 23.9520i 0.457162 0.791828i
\(916\) 16.7007 0.551805
\(917\) 11.5302 12.3677i 0.380761 0.408417i
\(918\) 1.12931 0.0372727
\(919\) 5.57467 9.65561i 0.183891 0.318509i −0.759311 0.650728i \(-0.774464\pi\)
0.943202 + 0.332219i \(0.107797\pi\)
\(920\) −10.7319 18.5883i −0.353822 0.612837i
\(921\) 4.93536 + 8.54829i 0.162626 + 0.281676i
\(922\) 1.67518 2.90149i 0.0551690 0.0955555i
\(923\) 0 0
\(924\) −22.4194 5.17302i −0.737544 0.170180i
\(925\) −10.5587 −0.347166
\(926\) −0.0414927 + 0.0718675i −0.00136354 + 0.00236171i
\(927\) 1.83424 + 3.17700i 0.0602445 + 0.104347i
\(928\) −3.60365 6.24170i −0.118296 0.204894i
\(929\) 3.87255 6.70745i 0.127054 0.220064i −0.795480 0.605980i \(-0.792781\pi\)
0.922534 + 0.385916i \(0.126114\pi\)
\(930\) −2.00543 −0.0657607
\(931\) −43.4898 + 29.3498i −1.42532 + 0.961901i
\(932\) −39.0455 −1.27898
\(933\) −9.38559 + 16.2563i −0.307270 + 0.532208i
\(934\) −3.28149 5.68371i −0.107374 0.185977i
\(935\) 3.96817 + 6.87306i 0.129773 + 0.224773i
\(936\) 0 0
\(937\) 36.4239 1.18992 0.594959 0.803756i \(-0.297168\pi\)
0.594959 + 0.803756i \(0.297168\pi\)
\(938\) 0.934932 + 0.215725i 0.0305266 + 0.00704367i
\(939\) −11.4829 −0.374729
\(940\) −3.25145 + 5.63168i −0.106051 + 0.183685i
\(941\) −9.89466 17.1381i −0.322557 0.558685i 0.658458 0.752617i \(-0.271209\pi\)
−0.981015 + 0.193933i \(0.937876\pi\)
\(942\) −0.252214 0.436848i −0.00821759 0.0142333i
\(943\) 9.69526 16.7927i 0.315721 0.546845i
\(944\) 32.0454 1.04299
\(945\) −24.7949 + 26.5958i −0.806577 + 0.865161i
\(946\) 2.37998 0.0773798
\(947\) 4.97398 8.61519i 0.161633 0.279956i −0.773822 0.633403i \(-0.781657\pi\)
0.935454 + 0.353448i \(0.114991\pi\)
\(948\) −6.82403 11.8196i −0.221634 0.383882i
\(949\) 0 0
\(950\) −1.57014 + 2.71957i −0.0509422 + 0.0882345i
\(951\) 11.5958 0.376020
\(952\) 0.639889 + 2.09206i 0.0207389 + 0.0678042i
\(953\) 0.0211134 0.000683929 0.000341965 1.00000i \(-0.499891\pi\)
0.000341965 1.00000i \(0.499891\pi\)
\(954\) 2.10682 3.64912i 0.0682108 0.118144i
\(955\) 18.0995 + 31.3493i 0.585686 + 1.01444i
\(956\) −15.9576 27.6394i −0.516106 0.893922i
\(957\) −5.30352 + 9.18596i −0.171438 + 0.296940i
\(958\) −2.18214 −0.0705017
\(959\) 7.76681 + 25.3929i 0.250804 + 0.819981i
\(960\) 18.5230 0.597827
\(961\) 12.2376 21.1962i 0.394761 0.683747i
\(962\) 0 0
\(963\) −9.76001 16.9048i −0.314512 0.544751i
\(964\) 15.8112 27.3858i 0.509245 0.882039i
\(965\) −9.97685 −0.321166
\(966\) −4.39858 + 4.71806i −0.141522 + 0.151801i
\(967\) 19.8102 0.637053 0.318526 0.947914i \(-0.396812\pi\)
0.318526 + 0.947914i \(0.396812\pi\)
\(968\) 2.40711 4.16923i 0.0773674 0.134004i
\(969\) 3.36304 + 5.82495i 0.108036 + 0.187124i
\(970\) −0.814635 1.41099i −0.0261563 0.0453041i
\(971\) 1.80887 3.13305i 0.0580493 0.100544i −0.835540 0.549429i \(-0.814845\pi\)
0.893590 + 0.448885i \(0.148179\pi\)
\(972\) 28.7144 0.921015
\(973\) −14.2966 3.29877i −0.458326 0.105754i
\(974\) −1.23595 −0.0396024
\(975\) 0 0
\(976\) −16.8782 29.2339i −0.540258 0.935755i
\(977\) 1.08085 + 1.87208i 0.0345793 + 0.0598931i 0.882797 0.469754i \(-0.155658\pi\)
−0.848218 + 0.529648i \(0.822324\pi\)
\(978\) 1.00341 1.73796i 0.0320855 0.0555737i
\(979\) 30.2382 0.966416
\(980\) −31.0799 15.1492i −0.992810 0.483924i
\(981\) 13.6807 0.436792
\(982\) −1.74535 + 3.02304i −0.0556965 + 0.0964692i
\(983\) −15.0545 26.0752i −0.480165 0.831671i 0.519576 0.854424i \(-0.326090\pi\)
−0.999741 + 0.0227535i \(0.992757\pi\)
\(984\) −1.46717 2.54121i −0.0467717 0.0810109i
\(985\) −14.9977 + 25.9767i −0.477865 + 0.827687i
\(986\) 0.495051 0.0157656
\(987\) 3.87948 + 0.895146i 0.123485 + 0.0284928i
\(988\) 0 0
\(989\) −8.94742 + 15.4974i −0.284511 + 0.492788i
\(990\) −2.29507 3.97517i −0.0729420 0.126339i
\(991\) 13.5730 + 23.5092i 0.431161 + 0.746793i 0.996974 0.0777408i \(-0.0247706\pi\)
−0.565812 + 0.824534i \(0.691437\pi\)
\(992\) −3.91416 + 6.77953i −0.124275 + 0.215250i
\(993\) 2.65082 0.0841213
\(994\) 5.95783 6.39056i 0.188971 0.202696i
\(995\) 8.95805 0.283989
\(996\) −1.18227 + 2.04776i −0.0374618 + 0.0648858i
\(997\) −25.4005 43.9949i −0.804441 1.39333i −0.916668 0.399650i \(-0.869132\pi\)
0.112227 0.993683i \(-0.464202\pi\)
\(998\) −4.33300 7.50497i −0.137159 0.237566i
\(999\) 18.1252 31.3938i 0.573456 0.993256i
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 1183.2.e.g.170.4 12
7.2 even 3 8281.2.a.ce.1.3 6
7.4 even 3 inner 1183.2.e.g.508.4 12
7.5 odd 6 8281.2.a.cf.1.3 6
13.4 even 6 91.2.h.b.16.4 yes 12
13.10 even 6 91.2.g.b.9.3 12
13.12 even 2 1183.2.e.h.170.3 12
39.17 odd 6 819.2.s.d.289.3 12
39.23 odd 6 819.2.n.d.100.4 12
91.4 even 6 91.2.g.b.81.3 yes 12
91.10 odd 6 637.2.h.l.165.4 12
91.12 odd 6 8281.2.a.ca.1.4 6
91.17 odd 6 637.2.g.l.263.3 12
91.23 even 6 637.2.f.k.295.3 12
91.25 even 6 1183.2.e.h.508.3 12
91.30 even 6 637.2.f.k.393.3 12
91.51 even 6 8281.2.a.bz.1.4 6
91.62 odd 6 637.2.g.l.373.3 12
91.69 odd 6 637.2.h.l.471.4 12
91.75 odd 6 637.2.f.j.295.3 12
91.82 odd 6 637.2.f.j.393.3 12
91.88 even 6 91.2.h.b.74.4 yes 12
273.95 odd 6 819.2.n.d.172.4 12
273.179 odd 6 819.2.s.d.802.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.g.b.9.3 12 13.10 even 6
91.2.g.b.81.3 yes 12 91.4 even 6
91.2.h.b.16.4 yes 12 13.4 even 6
91.2.h.b.74.4 yes 12 91.88 even 6
637.2.f.j.295.3 12 91.75 odd 6
637.2.f.j.393.3 12 91.82 odd 6
637.2.f.k.295.3 12 91.23 even 6
637.2.f.k.393.3 12 91.30 even 6
637.2.g.l.263.3 12 91.17 odd 6
637.2.g.l.373.3 12 91.62 odd 6
637.2.h.l.165.4 12 91.10 odd 6
637.2.h.l.471.4 12 91.69 odd 6
819.2.n.d.100.4 12 39.23 odd 6
819.2.n.d.172.4 12 273.95 odd 6
819.2.s.d.289.3 12 39.17 odd 6
819.2.s.d.802.3 12 273.179 odd 6
1183.2.e.g.170.4 12 1.1 even 1 trivial
1183.2.e.g.508.4 12 7.4 even 3 inner
1183.2.e.h.170.3 12 13.12 even 2
1183.2.e.h.508.3 12 91.25 even 6
8281.2.a.bz.1.4 6 91.51 even 6
8281.2.a.ca.1.4 6 91.12 odd 6
8281.2.a.ce.1.3 6 7.2 even 3
8281.2.a.cf.1.3 6 7.5 odd 6