Properties

Label 1274.2.o.e.569.3
Level $1274$
Weight $2$
Character 1274.569
Analytic conductor $10.173$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1274,2,Mod(459,1274)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1274, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1274.459");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1274.o (of order \(6\), degree \(2\), not 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: \(10.1729412175\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + 3842 x^{4} - 3394 x^{3} + 2141 x^{2} - 832 x + 169 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 182)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 569.3
Root \(0.500000 - 2.47866i\) of defining polynomial
Character \(\chi\) \(=\) 1274.569
Dual form 1274.2.o.e.459.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +(1.67234 - 2.89658i) q^{3} -1.00000 q^{4} +(-1.35408 - 0.781779i) q^{5} +(-2.89658 - 1.67234i) q^{6} +1.00000i q^{8} +(-4.09347 - 7.09010i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(1.67234 - 2.89658i) q^{3} -1.00000 q^{4} +(-1.35408 - 0.781779i) q^{5} +(-2.89658 - 1.67234i) q^{6} +1.00000i q^{8} +(-4.09347 - 7.09010i) q^{9} +(-0.781779 + 1.35408i) q^{10} +(2.48215 + 1.43307i) q^{11} +(-1.67234 + 2.89658i) q^{12} +(-2.99598 + 2.00602i) q^{13} +(-4.52898 + 2.61481i) q^{15} +1.00000 q^{16} -2.22961 q^{17} +(-7.09010 + 4.09347i) q^{18} +(-6.26657 + 3.61801i) q^{19} +(1.35408 + 0.781779i) q^{20} +(1.43307 - 2.48215i) q^{22} +1.66735 q^{23} +(2.89658 + 1.67234i) q^{24} +(-1.27764 - 2.21294i) q^{25} +(2.00602 + 2.99598i) q^{26} -17.3487 q^{27} +(-2.41379 - 4.18080i) q^{29} +(2.61481 + 4.52898i) q^{30} +(-0.517851 + 0.298982i) q^{31} -1.00000i q^{32} +(8.30201 - 4.79317i) q^{33} +2.22961i q^{34} +(4.09347 + 7.09010i) q^{36} +0.0385636i q^{37} +(3.61801 + 6.26657i) q^{38} +(0.800299 + 12.0329i) q^{39} +(0.781779 - 1.35408i) q^{40} +(6.88896 - 3.97734i) q^{41} +(5.04571 - 8.73942i) q^{43} +(-2.48215 - 1.43307i) q^{44} +12.8007i q^{45} -1.66735i q^{46} +(-6.08501 - 3.51318i) q^{47} +(1.67234 - 2.89658i) q^{48} +(-2.21294 + 1.27764i) q^{50} +(-3.72868 + 6.45826i) q^{51} +(2.99598 - 2.00602i) q^{52} +(2.99202 + 5.18233i) q^{53} +17.3487i q^{54} +(-2.24069 - 3.88098i) q^{55} +24.2022i q^{57} +(-4.18080 + 2.41379i) q^{58} +0.896206i q^{59} +(4.52898 - 2.61481i) q^{60} +(-7.12846 - 12.3469i) q^{61} +(0.298982 + 0.517851i) q^{62} -1.00000 q^{64} +(5.62506 - 0.374120i) q^{65} +(-4.79317 - 8.30201i) q^{66} +(1.42103 + 0.820432i) q^{67} +2.22961 q^{68} +(2.78838 - 4.82962i) q^{69} +(-1.98724 - 1.14733i) q^{71} +(7.09010 - 4.09347i) q^{72} +(9.72351 - 5.61387i) q^{73} +0.0385636 q^{74} -8.54664 q^{75} +(6.26657 - 3.61801i) q^{76} +(12.0329 - 0.800299i) q^{78} +(-2.13049 + 3.69011i) q^{79} +(-1.35408 - 0.781779i) q^{80} +(-16.7326 + 28.9816i) q^{81} +(-3.97734 - 6.88896i) q^{82} -4.94829i q^{83} +(3.01907 + 1.74306i) q^{85} +(-8.73942 - 5.04571i) q^{86} -16.1467 q^{87} +(-1.43307 + 2.48215i) q^{88} -2.42120i q^{89} +12.8007 q^{90} -1.66735 q^{92} +2.00000i q^{93} +(-3.51318 + 6.08501i) q^{94} +11.3139 q^{95} +(-2.89658 - 1.67234i) q^{96} +(4.23338 + 2.44414i) q^{97} -23.4649i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{3} - 12 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{3} - 12 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 18 q^{11} - 2 q^{12} + 8 q^{13} - 6 q^{15} + 12 q^{16} + 8 q^{17} + 12 q^{19} - 2 q^{22} + 12 q^{23} + 6 q^{24} + 12 q^{25} + 2 q^{26} - 40 q^{27} - 10 q^{29} + 14 q^{30} - 18 q^{31} + 12 q^{33} + 6 q^{36} + 4 q^{38} + 24 q^{39} - 2 q^{40} + 24 q^{41} + 26 q^{43} - 18 q^{44} - 48 q^{47} + 2 q^{48} - 12 q^{50} + 18 q^{51} - 8 q^{52} - 18 q^{53} + 6 q^{55} - 24 q^{58} + 6 q^{60} + 28 q^{61} + 2 q^{62} - 12 q^{64} - 4 q^{65} + 42 q^{67} - 8 q^{68} - 32 q^{69} + 48 q^{71} + 48 q^{73} - 96 q^{75} - 12 q^{76} - 8 q^{78} - 22 q^{79} - 34 q^{81} - 6 q^{82} + 54 q^{85} + 6 q^{86} + 4 q^{87} + 2 q^{88} - 12 q^{90} - 12 q^{92} - 8 q^{94} - 64 q^{95} - 6 q^{96} - 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(885\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.67234 2.89658i 0.965528 1.67234i 0.257339 0.966321i \(-0.417154\pi\)
0.708189 0.706023i \(-0.249512\pi\)
\(4\) −1.00000 −0.500000
\(5\) −1.35408 0.781779i −0.605563 0.349622i 0.165664 0.986182i \(-0.447023\pi\)
−0.771227 + 0.636560i \(0.780357\pi\)
\(6\) −2.89658 1.67234i −1.18253 0.682732i
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −4.09347 7.09010i −1.36449 2.36337i
\(10\) −0.781779 + 1.35408i −0.247220 + 0.428198i
\(11\) 2.48215 + 1.43307i 0.748396 + 0.432087i 0.825114 0.564966i \(-0.191111\pi\)
−0.0767180 + 0.997053i \(0.524444\pi\)
\(12\) −1.67234 + 2.89658i −0.482764 + 0.836172i
\(13\) −2.99598 + 2.00602i −0.830935 + 0.556370i
\(14\) 0 0
\(15\) −4.52898 + 2.61481i −1.16938 + 0.675140i
\(16\) 1.00000 0.250000
\(17\) −2.22961 −0.540760 −0.270380 0.962754i \(-0.587149\pi\)
−0.270380 + 0.962754i \(0.587149\pi\)
\(18\) −7.09010 + 4.09347i −1.67115 + 0.964840i
\(19\) −6.26657 + 3.61801i −1.43765 + 0.830028i −0.997686 0.0679872i \(-0.978342\pi\)
−0.439964 + 0.898015i \(0.645009\pi\)
\(20\) 1.35408 + 0.781779i 0.302782 + 0.174811i
\(21\) 0 0
\(22\) 1.43307 2.48215i 0.305531 0.529196i
\(23\) 1.66735 0.347667 0.173833 0.984775i \(-0.444385\pi\)
0.173833 + 0.984775i \(0.444385\pi\)
\(24\) 2.89658 + 1.67234i 0.591263 + 0.341366i
\(25\) −1.27764 2.21294i −0.255529 0.442589i
\(26\) 2.00602 + 2.99598i 0.393413 + 0.587560i
\(27\) −17.3487 −3.33876
\(28\) 0 0
\(29\) −2.41379 4.18080i −0.448229 0.776356i 0.550042 0.835137i \(-0.314612\pi\)
−0.998271 + 0.0587816i \(0.981278\pi\)
\(30\) 2.61481 + 4.52898i 0.477396 + 0.826874i
\(31\) −0.517851 + 0.298982i −0.0930088 + 0.0536987i −0.545783 0.837927i \(-0.683768\pi\)
0.452774 + 0.891625i \(0.350434\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 8.30201 4.79317i 1.44519 0.834384i
\(34\) 2.22961i 0.382375i
\(35\) 0 0
\(36\) 4.09347 + 7.09010i 0.682245 + 1.18168i
\(37\) 0.0385636i 0.00633982i 0.999995 + 0.00316991i \(0.00100902\pi\)
−0.999995 + 0.00316991i \(0.998991\pi\)
\(38\) 3.61801 + 6.26657i 0.586918 + 1.01657i
\(39\) 0.800299 + 12.0329i 0.128150 + 1.92680i
\(40\) 0.781779 1.35408i 0.123610 0.214099i
\(41\) 6.88896 3.97734i 1.07588 0.621157i 0.146095 0.989271i \(-0.453330\pi\)
0.929781 + 0.368114i \(0.119996\pi\)
\(42\) 0 0
\(43\) 5.04571 8.73942i 0.769463 1.33275i −0.168391 0.985720i \(-0.553857\pi\)
0.937854 0.347029i \(-0.112809\pi\)
\(44\) −2.48215 1.43307i −0.374198 0.216043i
\(45\) 12.8007i 1.90822i
\(46\) 1.66735i 0.245838i
\(47\) −6.08501 3.51318i −0.887590 0.512450i −0.0144363 0.999896i \(-0.504595\pi\)
−0.873153 + 0.487446i \(0.837929\pi\)
\(48\) 1.67234 2.89658i 0.241382 0.418086i
\(49\) 0 0
\(50\) −2.21294 + 1.27764i −0.312958 + 0.180686i
\(51\) −3.72868 + 6.45826i −0.522119 + 0.904337i
\(52\) 2.99598 2.00602i 0.415467 0.278185i
\(53\) 2.99202 + 5.18233i 0.410985 + 0.711848i 0.994998 0.0998972i \(-0.0318514\pi\)
−0.584012 + 0.811745i \(0.698518\pi\)
\(54\) 17.3487i 2.36086i
\(55\) −2.24069 3.88098i −0.302134 0.523312i
\(56\) 0 0
\(57\) 24.2022i 3.20566i
\(58\) −4.18080 + 2.41379i −0.548966 + 0.316946i
\(59\) 0.896206i 0.116676i 0.998297 + 0.0583381i \(0.0185801\pi\)
−0.998297 + 0.0583381i \(0.981420\pi\)
\(60\) 4.52898 2.61481i 0.584688 0.337570i
\(61\) −7.12846 12.3469i −0.912706 1.58085i −0.810225 0.586119i \(-0.800655\pi\)
−0.102481 0.994735i \(-0.532678\pi\)
\(62\) 0.298982 + 0.517851i 0.0379707 + 0.0657672i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 5.62506 0.374120i 0.697703 0.0464038i
\(66\) −4.79317 8.30201i −0.589998 1.02191i
\(67\) 1.42103 + 0.820432i 0.173606 + 0.100232i 0.584285 0.811548i \(-0.301375\pi\)
−0.410679 + 0.911780i \(0.634708\pi\)
\(68\) 2.22961 0.270380
\(69\) 2.78838 4.82962i 0.335682 0.581418i
\(70\) 0 0
\(71\) −1.98724 1.14733i −0.235841 0.136163i 0.377422 0.926041i \(-0.376810\pi\)
−0.613264 + 0.789878i \(0.710144\pi\)
\(72\) 7.09010 4.09347i 0.835576 0.482420i
\(73\) 9.72351 5.61387i 1.13805 0.657054i 0.192104 0.981375i \(-0.438469\pi\)
0.945947 + 0.324321i \(0.105136\pi\)
\(74\) 0.0385636 0.00448293
\(75\) −8.54664 −0.986881
\(76\) 6.26657 3.61801i 0.718825 0.415014i
\(77\) 0 0
\(78\) 12.0329 0.800299i 1.36245 0.0906160i
\(79\) −2.13049 + 3.69011i −0.239699 + 0.415170i −0.960628 0.277839i \(-0.910382\pi\)
0.720929 + 0.693009i \(0.243715\pi\)
\(80\) −1.35408 0.781779i −0.151391 0.0874055i
\(81\) −16.7326 + 28.9816i −1.85917 + 3.22018i
\(82\) −3.97734 6.88896i −0.439224 0.760759i
\(83\) 4.94829i 0.543145i −0.962418 0.271572i \(-0.912456\pi\)
0.962418 0.271572i \(-0.0875437\pi\)
\(84\) 0 0
\(85\) 3.01907 + 1.74306i 0.327465 + 0.189062i
\(86\) −8.73942 5.04571i −0.942396 0.544092i
\(87\) −16.1467 −1.73111
\(88\) −1.43307 + 2.48215i −0.152766 + 0.264598i
\(89\) 2.42120i 0.256647i −0.991732 0.128323i \(-0.959040\pi\)
0.991732 0.128323i \(-0.0409595\pi\)
\(90\) 12.8007 1.34932
\(91\) 0 0
\(92\) −1.66735 −0.173833
\(93\) 2.00000i 0.207390i
\(94\) −3.51318 + 6.08501i −0.362357 + 0.627621i
\(95\) 11.3139 1.16078
\(96\) −2.89658 1.67234i −0.295631 0.170683i
\(97\) 4.23338 + 2.44414i 0.429835 + 0.248165i 0.699276 0.714852i \(-0.253506\pi\)
−0.269442 + 0.963017i \(0.586839\pi\)
\(98\) 0 0
\(99\) 23.4649i 2.35831i
\(100\) 1.27764 + 2.21294i 0.127764 + 0.221294i
\(101\) −3.68373 + 6.38042i −0.366545 + 0.634875i −0.989023 0.147763i \(-0.952793\pi\)
0.622478 + 0.782638i \(0.286126\pi\)
\(102\) 6.45826 + 3.72868i 0.639463 + 0.369194i
\(103\) −2.89263 + 5.01017i −0.285019 + 0.493667i −0.972614 0.232427i \(-0.925333\pi\)
0.687595 + 0.726094i \(0.258667\pi\)
\(104\) −2.00602 2.99598i −0.196706 0.293780i
\(105\) 0 0
\(106\) 5.18233 2.99202i 0.503352 0.290611i
\(107\) −1.02896 −0.0994729 −0.0497365 0.998762i \(-0.515838\pi\)
−0.0497365 + 0.998762i \(0.515838\pi\)
\(108\) 17.3487 1.66938
\(109\) 12.2573 7.07674i 1.17403 0.677829i 0.219407 0.975633i \(-0.429588\pi\)
0.954627 + 0.297805i \(0.0962545\pi\)
\(110\) −3.88098 + 2.24069i −0.370037 + 0.213641i
\(111\) 0.111703 + 0.0644917i 0.0106024 + 0.00612128i
\(112\) 0 0
\(113\) 6.77051 11.7269i 0.636916 1.10317i −0.349189 0.937052i \(-0.613543\pi\)
0.986106 0.166119i \(-0.0531237\pi\)
\(114\) 24.2022 2.26675
\(115\) −2.25773 1.30350i −0.210534 0.121552i
\(116\) 2.41379 + 4.18080i 0.224115 + 0.388178i
\(117\) 26.4868 + 13.0302i 2.44871 + 1.20464i
\(118\) 0.896206 0.0825025
\(119\) 0 0
\(120\) −2.61481 4.52898i −0.238698 0.413437i
\(121\) −1.39263 2.41210i −0.126602 0.219282i
\(122\) −12.3469 + 7.12846i −1.11783 + 0.645381i
\(123\) 26.6060i 2.39898i
\(124\) 0.517851 0.298982i 0.0465044 0.0268493i
\(125\) 11.8131i 1.05660i
\(126\) 0 0
\(127\) 4.92583 + 8.53178i 0.437096 + 0.757073i 0.997464 0.0711707i \(-0.0226735\pi\)
−0.560368 + 0.828244i \(0.689340\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −16.8763 29.2306i −1.48588 2.57361i
\(130\) −0.374120 5.62506i −0.0328125 0.493350i
\(131\) 7.39614 12.8105i 0.646204 1.11926i −0.337818 0.941211i \(-0.609689\pi\)
0.984022 0.178047i \(-0.0569778\pi\)
\(132\) −8.30201 + 4.79317i −0.722597 + 0.417192i
\(133\) 0 0
\(134\) 0.820432 1.42103i 0.0708746 0.122758i
\(135\) 23.4915 + 13.5628i 2.02183 + 1.16730i
\(136\) 2.22961i 0.191188i
\(137\) 0.458997i 0.0392148i −0.999808 0.0196074i \(-0.993758\pi\)
0.999808 0.0196074i \(-0.00624163\pi\)
\(138\) −4.82962 2.78838i −0.411125 0.237363i
\(139\) 7.65731 13.2628i 0.649485 1.12494i −0.333762 0.942658i \(-0.608318\pi\)
0.983246 0.182283i \(-0.0583486\pi\)
\(140\) 0 0
\(141\) −20.3525 + 11.7505i −1.71399 + 0.989570i
\(142\) −1.14733 + 1.98724i −0.0962819 + 0.166765i
\(143\) −10.3112 + 0.685794i −0.862268 + 0.0573490i
\(144\) −4.09347 7.09010i −0.341122 0.590841i
\(145\) 7.54819i 0.626843i
\(146\) −5.61387 9.72351i −0.464607 0.804723i
\(147\) 0 0
\(148\) 0.0385636i 0.00316991i
\(149\) −8.86563 + 5.11858i −0.726301 + 0.419330i −0.817067 0.576542i \(-0.804402\pi\)
0.0907665 + 0.995872i \(0.471068\pi\)
\(150\) 8.54664i 0.697830i
\(151\) 13.1731 7.60551i 1.07201 0.618927i 0.143283 0.989682i \(-0.454234\pi\)
0.928731 + 0.370754i \(0.120901\pi\)
\(152\) −3.61801 6.26657i −0.293459 0.508286i
\(153\) 9.12684 + 15.8082i 0.737862 + 1.27801i
\(154\) 0 0
\(155\) 0.934950 0.0750970
\(156\) −0.800299 12.0329i −0.0640752 0.963400i
\(157\) −1.13709 1.96950i −0.0907500 0.157184i 0.817077 0.576529i \(-0.195593\pi\)
−0.907827 + 0.419345i \(0.862260\pi\)
\(158\) 3.69011 + 2.13049i 0.293570 + 0.169493i
\(159\) 20.0147 1.58727
\(160\) −0.781779 + 1.35408i −0.0618050 + 0.107049i
\(161\) 0 0
\(162\) 28.9816 + 16.7326i 2.27701 + 1.31463i
\(163\) −0.00848066 + 0.00489631i −0.000664256 + 0.000383509i −0.500332 0.865834i \(-0.666789\pi\)
0.499668 + 0.866217i \(0.333455\pi\)
\(164\) −6.88896 + 3.97734i −0.537938 + 0.310578i
\(165\) −14.9888 −1.16688
\(166\) −4.94829 −0.384061
\(167\) −21.6080 + 12.4754i −1.67208 + 0.965376i −0.705608 + 0.708603i \(0.749326\pi\)
−0.966472 + 0.256773i \(0.917341\pi\)
\(168\) 0 0
\(169\) 4.95177 12.0200i 0.380906 0.924614i
\(170\) 1.74306 3.01907i 0.133687 0.231552i
\(171\) 51.3040 + 29.6204i 3.92332 + 2.26513i
\(172\) −5.04571 + 8.73942i −0.384731 + 0.666374i
\(173\) 1.60275 + 2.77604i 0.121855 + 0.211058i 0.920499 0.390745i \(-0.127782\pi\)
−0.798644 + 0.601803i \(0.794449\pi\)
\(174\) 16.1467i 1.22408i
\(175\) 0 0
\(176\) 2.48215 + 1.43307i 0.187099 + 0.108022i
\(177\) 2.59594 + 1.49877i 0.195123 + 0.112654i
\(178\) −2.42120 −0.181477
\(179\) −7.89998 + 13.6832i −0.590472 + 1.02273i 0.403697 + 0.914893i \(0.367725\pi\)
−0.994169 + 0.107835i \(0.965608\pi\)
\(180\) 12.8007i 0.954111i
\(181\) −9.11907 −0.677815 −0.338908 0.940820i \(-0.610057\pi\)
−0.338908 + 0.940820i \(0.610057\pi\)
\(182\) 0 0
\(183\) −47.6850 −3.52497
\(184\) 1.66735i 0.122919i
\(185\) 0.0301482 0.0522183i 0.00221654 0.00383916i
\(186\) 2.00000 0.146647
\(187\) −5.53423 3.19519i −0.404703 0.233655i
\(188\) 6.08501 + 3.51318i 0.443795 + 0.256225i
\(189\) 0 0
\(190\) 11.3139i 0.820799i
\(191\) 1.63068 + 2.82443i 0.117992 + 0.204368i 0.918972 0.394323i \(-0.129021\pi\)
−0.800980 + 0.598691i \(0.795688\pi\)
\(192\) −1.67234 + 2.89658i −0.120691 + 0.209043i
\(193\) −19.1158 11.0365i −1.37599 0.794426i −0.384313 0.923203i \(-0.625562\pi\)
−0.991674 + 0.128777i \(0.958895\pi\)
\(194\) 2.44414 4.23338i 0.175479 0.303939i
\(195\) 8.32336 16.9191i 0.596048 1.21160i
\(196\) 0 0
\(197\) −4.56660 + 2.63653i −0.325357 + 0.187845i −0.653778 0.756687i \(-0.726817\pi\)
0.328421 + 0.944531i \(0.393484\pi\)
\(198\) −23.4649 −1.66758
\(199\) 8.86762 0.628609 0.314304 0.949322i \(-0.398229\pi\)
0.314304 + 0.949322i \(0.398229\pi\)
\(200\) 2.21294 1.27764i 0.156479 0.0903431i
\(201\) 4.75290 2.74409i 0.335244 0.193553i
\(202\) 6.38042 + 3.68373i 0.448924 + 0.259187i
\(203\) 0 0
\(204\) 3.72868 6.45826i 0.261060 0.452169i
\(205\) −12.4376 −0.868681
\(206\) 5.01017 + 2.89263i 0.349075 + 0.201539i
\(207\) −6.82525 11.8217i −0.474388 0.821663i
\(208\) −2.99598 + 2.00602i −0.207734 + 0.139092i
\(209\) −20.7394 −1.43458
\(210\) 0 0
\(211\) −3.28453 5.68898i −0.226117 0.391646i 0.730537 0.682873i \(-0.239270\pi\)
−0.956654 + 0.291227i \(0.905936\pi\)
\(212\) −2.99202 5.18233i −0.205493 0.355924i
\(213\) −6.64668 + 3.83746i −0.455423 + 0.262939i
\(214\) 1.02896i 0.0703380i
\(215\) −13.6646 + 7.88925i −0.931917 + 0.538043i
\(216\) 17.3487i 1.18043i
\(217\) 0 0
\(218\) −7.07674 12.2573i −0.479297 0.830167i
\(219\) 37.5533i 2.53762i
\(220\) 2.24069 + 3.88098i 0.151067 + 0.261656i
\(221\) 6.67987 4.47264i 0.449337 0.300863i
\(222\) 0.0644917 0.111703i 0.00432840 0.00749700i
\(223\) 14.6463 8.45606i 0.980790 0.566260i 0.0782817 0.996931i \(-0.475057\pi\)
0.902509 + 0.430672i \(0.141723\pi\)
\(224\) 0 0
\(225\) −10.4600 + 18.1172i −0.697333 + 1.20782i
\(226\) −11.7269 6.77051i −0.780060 0.450368i
\(227\) 16.1322i 1.07073i −0.844620 0.535367i \(-0.820173\pi\)
0.844620 0.535367i \(-0.179827\pi\)
\(228\) 24.2022i 1.60283i
\(229\) 5.98583 + 3.45592i 0.395555 + 0.228374i 0.684564 0.728953i \(-0.259993\pi\)
−0.289009 + 0.957326i \(0.593326\pi\)
\(230\) −1.30350 + 2.25773i −0.0859502 + 0.148870i
\(231\) 0 0
\(232\) 4.18080 2.41379i 0.274483 0.158473i
\(233\) −3.73702 + 6.47272i −0.244821 + 0.424042i −0.962081 0.272763i \(-0.912062\pi\)
0.717261 + 0.696805i \(0.245396\pi\)
\(234\) 13.0302 26.4868i 0.851810 1.73150i
\(235\) 5.49306 + 9.51426i 0.358328 + 0.620642i
\(236\) 0.896206i 0.0583381i
\(237\) 7.12582 + 12.3423i 0.462872 + 0.801717i
\(238\) 0 0
\(239\) 19.8696i 1.28526i 0.766179 + 0.642628i \(0.222156\pi\)
−0.766179 + 0.642628i \(0.777844\pi\)
\(240\) −4.52898 + 2.61481i −0.292344 + 0.168785i
\(241\) 10.6445i 0.685674i −0.939395 0.342837i \(-0.888612\pi\)
0.939395 0.342837i \(-0.111388\pi\)
\(242\) −2.41210 + 1.39263i −0.155055 + 0.0895213i
\(243\) 29.9422 + 51.8613i 1.92079 + 3.32691i
\(244\) 7.12846 + 12.3469i 0.456353 + 0.790427i
\(245\) 0 0
\(246\) −26.6060 −1.69633
\(247\) 11.5167 23.4103i 0.732792 1.48956i
\(248\) −0.298982 0.517851i −0.0189853 0.0328836i
\(249\) −14.3331 8.27524i −0.908325 0.524422i
\(250\) 11.8131 0.747128
\(251\) −7.95696 + 13.7819i −0.502239 + 0.869904i 0.497757 + 0.867316i \(0.334157\pi\)
−0.999997 + 0.00258749i \(0.999176\pi\)
\(252\) 0 0
\(253\) 4.13861 + 2.38943i 0.260192 + 0.150222i
\(254\) 8.53178 4.92583i 0.535332 0.309074i
\(255\) 10.0979 5.83000i 0.632352 0.365089i
\(256\) 1.00000 0.0625000
\(257\) −31.1018 −1.94008 −0.970039 0.242950i \(-0.921885\pi\)
−0.970039 + 0.242950i \(0.921885\pi\)
\(258\) −29.2306 + 16.8763i −1.81982 + 1.05067i
\(259\) 0 0
\(260\) −5.62506 + 0.374120i −0.348851 + 0.0232019i
\(261\) −19.7615 + 34.2280i −1.22321 + 2.11866i
\(262\) −12.8105 7.39614i −0.791435 0.456935i
\(263\) 14.1873 24.5732i 0.874829 1.51525i 0.0178837 0.999840i \(-0.494307\pi\)
0.856945 0.515408i \(-0.172360\pi\)
\(264\) 4.79317 + 8.30201i 0.294999 + 0.510954i
\(265\) 9.35639i 0.574758i
\(266\) 0 0
\(267\) −7.01321 4.04908i −0.429202 0.247800i
\(268\) −1.42103 0.820432i −0.0868032 0.0501159i
\(269\) 21.4017 1.30488 0.652441 0.757840i \(-0.273745\pi\)
0.652441 + 0.757840i \(0.273745\pi\)
\(270\) 13.5628 23.4915i 0.825408 1.42965i
\(271\) 5.74656i 0.349079i −0.984650 0.174539i \(-0.944156\pi\)
0.984650 0.174539i \(-0.0558436\pi\)
\(272\) −2.22961 −0.135190
\(273\) 0 0
\(274\) −0.458997 −0.0277290
\(275\) 7.32381i 0.441642i
\(276\) −2.78838 + 4.82962i −0.167841 + 0.290709i
\(277\) −26.6020 −1.59836 −0.799180 0.601092i \(-0.794733\pi\)
−0.799180 + 0.601092i \(0.794733\pi\)
\(278\) −13.2628 7.65731i −0.795453 0.459255i
\(279\) 4.23962 + 2.44774i 0.253819 + 0.146543i
\(280\) 0 0
\(281\) 6.69143i 0.399177i 0.979880 + 0.199589i \(0.0639606\pi\)
−0.979880 + 0.199589i \(0.936039\pi\)
\(282\) 11.7505 + 20.3525i 0.699732 + 1.21197i
\(283\) −9.96692 + 17.2632i −0.592472 + 1.02619i 0.401426 + 0.915891i \(0.368515\pi\)
−0.993898 + 0.110300i \(0.964819\pi\)
\(284\) 1.98724 + 1.14733i 0.117921 + 0.0680816i
\(285\) 18.9208 32.7717i 1.12077 1.94123i
\(286\) 0.685794 + 10.3112i 0.0405519 + 0.609716i
\(287\) 0 0
\(288\) −7.09010 + 4.09347i −0.417788 + 0.241210i
\(289\) −12.0288 −0.707578
\(290\) 7.54819 0.443245
\(291\) 14.1593 8.17490i 0.830035 0.479221i
\(292\) −9.72351 + 5.61387i −0.569025 + 0.328527i
\(293\) 7.67375 + 4.43044i 0.448305 + 0.258829i 0.707114 0.707099i \(-0.249997\pi\)
−0.258809 + 0.965929i \(0.583330\pi\)
\(294\) 0 0
\(295\) 0.700635 1.21354i 0.0407926 0.0706548i
\(296\) −0.0385636 −0.00224147
\(297\) −43.0620 24.8619i −2.49871 1.44263i
\(298\) 5.11858 + 8.86563i 0.296511 + 0.513572i
\(299\) −4.99535 + 3.34474i −0.288888 + 0.193431i
\(300\) 8.54664 0.493441
\(301\) 0 0
\(302\) −7.60551 13.1731i −0.437648 0.758028i
\(303\) 12.3209 + 21.3405i 0.707820 + 1.22598i
\(304\) −6.26657 + 3.61801i −0.359413 + 0.207507i
\(305\) 22.2915i 1.27641i
\(306\) 15.8082 9.12684i 0.903692 0.521747i
\(307\) 8.34636i 0.476352i 0.971222 + 0.238176i \(0.0765495\pi\)
−0.971222 + 0.238176i \(0.923450\pi\)
\(308\) 0 0
\(309\) 9.67493 + 16.7575i 0.550387 + 0.953299i
\(310\) 0.934950i 0.0531016i
\(311\) −3.34448 5.79281i −0.189648 0.328480i 0.755485 0.655166i \(-0.227401\pi\)
−0.945133 + 0.326686i \(0.894068\pi\)
\(312\) −12.0329 + 0.800299i −0.681226 + 0.0453080i
\(313\) −10.6894 + 18.5145i −0.604199 + 1.04650i 0.387978 + 0.921669i \(0.373174\pi\)
−0.992177 + 0.124835i \(0.960160\pi\)
\(314\) −1.96950 + 1.13709i −0.111146 + 0.0641699i
\(315\) 0 0
\(316\) 2.13049 3.69011i 0.119849 0.207585i
\(317\) 27.4336 + 15.8388i 1.54083 + 0.889596i 0.998787 + 0.0492433i \(0.0156810\pi\)
0.542039 + 0.840353i \(0.317652\pi\)
\(318\) 20.0147i 1.12237i
\(319\) 13.8365i 0.774695i
\(320\) 1.35408 + 0.781779i 0.0756954 + 0.0437028i
\(321\) −1.72077 + 2.98046i −0.0960439 + 0.166353i
\(322\) 0 0
\(323\) 13.9720 8.06675i 0.777424 0.448846i
\(324\) 16.7326 28.9816i 0.929587 1.61009i
\(325\) 8.26700 + 4.06695i 0.458571 + 0.225594i
\(326\) 0.00489631 + 0.00848066i 0.000271182 + 0.000469700i
\(327\) 47.3390i 2.61785i
\(328\) 3.97734 + 6.88896i 0.219612 + 0.380379i
\(329\) 0 0
\(330\) 14.9888i 0.825106i
\(331\) 21.3644 12.3347i 1.17429 0.677979i 0.219606 0.975589i \(-0.429523\pi\)
0.954688 + 0.297609i \(0.0961893\pi\)
\(332\) 4.94829i 0.271572i
\(333\) 0.273420 0.157859i 0.0149833 0.00865062i
\(334\) 12.4754 + 21.6080i 0.682624 + 1.18234i
\(335\) −1.28279 2.22186i −0.0700865 0.121393i
\(336\) 0 0
\(337\) 28.0871 1.53000 0.765002 0.644028i \(-0.222738\pi\)
0.765002 + 0.644028i \(0.222738\pi\)
\(338\) −12.0200 4.95177i −0.653801 0.269341i
\(339\) −22.6453 39.2227i −1.22992 2.13029i
\(340\) −3.01907 1.74306i −0.163732 0.0945309i
\(341\) −1.71385 −0.0928099
\(342\) 29.6204 51.3040i 1.60169 2.77420i
\(343\) 0 0
\(344\) 8.73942 + 5.04571i 0.471198 + 0.272046i
\(345\) −7.55139 + 4.35980i −0.406553 + 0.234724i
\(346\) 2.77604 1.60275i 0.149241 0.0861643i
\(347\) −10.1080 −0.542623 −0.271312 0.962492i \(-0.587457\pi\)
−0.271312 + 0.962492i \(0.587457\pi\)
\(348\) 16.1467 0.865556
\(349\) 15.0596 8.69465i 0.806121 0.465414i −0.0394863 0.999220i \(-0.512572\pi\)
0.845607 + 0.533806i \(0.179239\pi\)
\(350\) 0 0
\(351\) 51.9763 34.8018i 2.77429 1.85758i
\(352\) 1.43307 2.48215i 0.0763828 0.132299i
\(353\) 2.88091 + 1.66329i 0.153335 + 0.0885282i 0.574704 0.818361i \(-0.305117\pi\)
−0.421369 + 0.906889i \(0.638450\pi\)
\(354\) 1.49877 2.59594i 0.0796585 0.137973i
\(355\) 1.79392 + 3.10716i 0.0952113 + 0.164911i
\(356\) 2.42120i 0.128323i
\(357\) 0 0
\(358\) 13.6832 + 7.89998i 0.723177 + 0.417527i
\(359\) −6.94911 4.01207i −0.366760 0.211749i 0.305282 0.952262i \(-0.401249\pi\)
−0.672042 + 0.740513i \(0.734583\pi\)
\(360\) −12.8007 −0.674659
\(361\) 16.6800 28.8905i 0.877893 1.52055i
\(362\) 9.11907i 0.479288i
\(363\) −9.31579 −0.488952
\(364\) 0 0
\(365\) −17.5552 −0.918882
\(366\) 47.6850i 2.49253i
\(367\) 0.519540 0.899869i 0.0271198 0.0469728i −0.852147 0.523302i \(-0.824700\pi\)
0.879267 + 0.476330i \(0.158033\pi\)
\(368\) 1.66735 0.0869167
\(369\) −56.3995 32.5623i −2.93604 1.69512i
\(370\) −0.0522183 0.0301482i −0.00271470 0.00156733i
\(371\) 0 0
\(372\) 2.00000i 0.103695i
\(373\) −13.6562 23.6532i −0.707092 1.22472i −0.965931 0.258798i \(-0.916673\pi\)
0.258840 0.965920i \(-0.416660\pi\)
\(374\) −3.19519 + 5.53423i −0.165219 + 0.286168i
\(375\) 34.2177 + 19.7556i 1.76700 + 1.02018i
\(376\) 3.51318 6.08501i 0.181178 0.313810i
\(377\) 15.6184 + 7.68349i 0.804390 + 0.395720i
\(378\) 0 0
\(379\) −1.91535 + 1.10583i −0.0983850 + 0.0568026i −0.548385 0.836226i \(-0.684757\pi\)
0.450000 + 0.893028i \(0.351424\pi\)
\(380\) −11.3139 −0.580392
\(381\) 32.9507 1.68812
\(382\) 2.82443 1.63068i 0.144510 0.0834331i
\(383\) 19.3458 11.1693i 0.988522 0.570724i 0.0836900 0.996492i \(-0.473329\pi\)
0.904832 + 0.425768i \(0.139996\pi\)
\(384\) 2.89658 + 1.67234i 0.147816 + 0.0853414i
\(385\) 0 0
\(386\) −11.0365 + 19.1158i −0.561744 + 0.972969i
\(387\) −82.6178 −4.19970
\(388\) −4.23338 2.44414i −0.214917 0.124083i
\(389\) 6.13022 + 10.6178i 0.310814 + 0.538346i 0.978539 0.206062i \(-0.0660649\pi\)
−0.667725 + 0.744408i \(0.732732\pi\)
\(390\) −16.9191 8.32336i −0.856733 0.421470i
\(391\) −3.71755 −0.188004
\(392\) 0 0
\(393\) −24.7378 42.8471i −1.24786 2.16135i
\(394\) 2.63653 + 4.56660i 0.132826 + 0.230062i
\(395\) 5.76971 3.33114i 0.290305 0.167608i
\(396\) 23.4649i 1.17916i
\(397\) 2.54193 1.46759i 0.127576 0.0736561i −0.434854 0.900501i \(-0.643200\pi\)
0.562430 + 0.826845i \(0.309867\pi\)
\(398\) 8.86762i 0.444493i
\(399\) 0 0
\(400\) −1.27764 2.21294i −0.0638822 0.110647i
\(401\) 21.8502i 1.09115i 0.838062 + 0.545575i \(0.183689\pi\)
−0.838062 + 0.545575i \(0.816311\pi\)
\(402\) −2.74409 4.75290i −0.136863 0.237053i
\(403\) 0.951708 1.93456i 0.0474080 0.0963674i
\(404\) 3.68373 6.38042i 0.183273 0.317438i
\(405\) 45.3145 26.1623i 2.25169 1.30002i
\(406\) 0 0
\(407\) −0.0552644 + 0.0957207i −0.00273935 + 0.00474470i
\(408\) −6.45826 3.72868i −0.319731 0.184597i
\(409\) 7.38191i 0.365012i −0.983205 0.182506i \(-0.941579\pi\)
0.983205 0.182506i \(-0.0584208\pi\)
\(410\) 12.4376i 0.614250i
\(411\) −1.32952 0.767601i −0.0655806 0.0378630i
\(412\) 2.89263 5.01017i 0.142509 0.246834i
\(413\) 0 0
\(414\) −11.8217 + 6.82525i −0.581004 + 0.335443i
\(415\) −3.86846 + 6.70038i −0.189895 + 0.328909i
\(416\) 2.00602 + 2.99598i 0.0983532 + 0.146890i
\(417\) −25.6113 44.3601i −1.25419 2.17232i
\(418\) 20.7394i 1.01440i
\(419\) −4.29137 7.43287i −0.209647 0.363119i 0.741956 0.670448i \(-0.233898\pi\)
−0.951603 + 0.307329i \(0.900565\pi\)
\(420\) 0 0
\(421\) 7.49525i 0.365296i −0.983178 0.182648i \(-0.941533\pi\)
0.983178 0.182648i \(-0.0584669\pi\)
\(422\) −5.68898 + 3.28453i −0.276935 + 0.159889i
\(423\) 57.5244i 2.79693i
\(424\) −5.18233 + 2.99202i −0.251676 + 0.145305i
\(425\) 2.84865 + 4.93401i 0.138180 + 0.239334i
\(426\) 3.83746 + 6.64668i 0.185926 + 0.322033i
\(427\) 0 0
\(428\) 1.02896 0.0497365
\(429\) −15.2575 + 31.0142i −0.736637 + 1.49738i
\(430\) 7.88925 + 13.6646i 0.380454 + 0.658965i
\(431\) 14.2713 + 8.23956i 0.687426 + 0.396886i 0.802647 0.596454i \(-0.203424\pi\)
−0.115221 + 0.993340i \(0.536758\pi\)
\(432\) −17.3487 −0.834689
\(433\) 12.7805 22.1365i 0.614192 1.06381i −0.376333 0.926484i \(-0.622815\pi\)
0.990526 0.137328i \(-0.0438515\pi\)
\(434\) 0 0
\(435\) 21.8640 + 12.6232i 1.04830 + 0.605235i
\(436\) −12.2573 + 7.07674i −0.587017 + 0.338914i
\(437\) −10.4486 + 6.03249i −0.499823 + 0.288573i
\(438\) −37.5533 −1.79437
\(439\) 9.20839 0.439493 0.219746 0.975557i \(-0.429477\pi\)
0.219746 + 0.975557i \(0.429477\pi\)
\(440\) 3.88098 2.24069i 0.185019 0.106821i
\(441\) 0 0
\(442\) −4.47264 6.67987i −0.212742 0.317729i
\(443\) 3.10379 5.37593i 0.147466 0.255418i −0.782824 0.622243i \(-0.786222\pi\)
0.930290 + 0.366825i \(0.119555\pi\)
\(444\) −0.111703 0.0644917i −0.00530118 0.00306064i
\(445\) −1.89284 + 3.27850i −0.0897294 + 0.155416i
\(446\) −8.45606 14.6463i −0.400406 0.693523i
\(447\) 34.2401i 1.61950i
\(448\) 0 0
\(449\) 4.51968 + 2.60944i 0.213297 + 0.123147i 0.602843 0.797860i \(-0.294035\pi\)
−0.389546 + 0.921007i \(0.627368\pi\)
\(450\) 18.1172 + 10.4600i 0.854055 + 0.493089i
\(451\) 22.7992 1.07357
\(452\) −6.77051 + 11.7269i −0.318458 + 0.551586i
\(453\) 50.8761i 2.39037i
\(454\) −16.1322 −0.757123
\(455\) 0 0
\(456\) −24.2022 −1.13337
\(457\) 33.9332i 1.58733i −0.608357 0.793664i \(-0.708171\pi\)
0.608357 0.793664i \(-0.291829\pi\)
\(458\) 3.45592 5.98583i 0.161484 0.279699i
\(459\) 38.6808 1.80547
\(460\) 2.25773 + 1.30350i 0.105267 + 0.0607760i
\(461\) −0.731583 0.422380i −0.0340732 0.0196722i 0.482867 0.875694i \(-0.339596\pi\)
−0.516940 + 0.856022i \(0.672929\pi\)
\(462\) 0 0
\(463\) 6.50221i 0.302183i 0.988520 + 0.151092i \(0.0482789\pi\)
−0.988520 + 0.151092i \(0.951721\pi\)
\(464\) −2.41379 4.18080i −0.112057 0.194089i
\(465\) 1.56356 2.70816i 0.0725082 0.125588i
\(466\) 6.47272 + 3.73702i 0.299843 + 0.173114i
\(467\) 4.76379 8.25113i 0.220442 0.381817i −0.734500 0.678608i \(-0.762583\pi\)
0.954942 + 0.296792i \(0.0959167\pi\)
\(468\) −26.4868 13.0302i −1.22435 0.602321i
\(469\) 0 0
\(470\) 9.51426 5.49306i 0.438860 0.253376i
\(471\) −7.60645 −0.350487
\(472\) −0.896206 −0.0412512
\(473\) 25.0484 14.4617i 1.15173 0.664949i
\(474\) 12.3423 7.12582i 0.566900 0.327300i
\(475\) 16.0129 + 9.24505i 0.734722 + 0.424192i
\(476\) 0 0
\(477\) 24.4955 42.4274i 1.12157 1.94262i
\(478\) 19.8696 0.908813
\(479\) −2.46123 1.42099i −0.112457 0.0649268i 0.442717 0.896662i \(-0.354015\pi\)
−0.555173 + 0.831735i \(0.687348\pi\)
\(480\) 2.61481 + 4.52898i 0.119349 + 0.206719i
\(481\) −0.0773594 0.115536i −0.00352729 0.00526798i
\(482\) −10.6445 −0.484844
\(483\) 0 0
\(484\) 1.39263 + 2.41210i 0.0633011 + 0.109641i
\(485\) −3.82156 6.61913i −0.173528 0.300559i
\(486\) 51.8613 29.9422i 2.35248 1.35820i
\(487\) 5.26374i 0.238523i 0.992863 + 0.119261i \(0.0380526\pi\)
−0.992863 + 0.119261i \(0.961947\pi\)
\(488\) 12.3469 7.12846i 0.558916 0.322690i
\(489\) 0.0327533i 0.00148115i
\(490\) 0 0
\(491\) 11.4457 + 19.8245i 0.516536 + 0.894666i 0.999816 + 0.0192004i \(0.00611205\pi\)
−0.483280 + 0.875466i \(0.660555\pi\)
\(492\) 26.6060i 1.19949i
\(493\) 5.38181 + 9.32157i 0.242384 + 0.419822i
\(494\) −23.4103 11.5167i −1.05328 0.518162i
\(495\) −18.3444 + 31.7734i −0.824517 + 1.42811i
\(496\) −0.517851 + 0.298982i −0.0232522 + 0.0134247i
\(497\) 0 0
\(498\) −8.27524 + 14.3331i −0.370822 + 0.642283i
\(499\) 5.88791 + 3.39938i 0.263579 + 0.152177i 0.625966 0.779850i \(-0.284705\pi\)
−0.362387 + 0.932028i \(0.618038\pi\)
\(500\) 11.8131i 0.528299i
\(501\) 83.4527i 3.72839i
\(502\) 13.7819 + 7.95696i 0.615115 + 0.355137i
\(503\) 5.40300 9.35827i 0.240908 0.417265i −0.720065 0.693906i \(-0.755888\pi\)
0.960973 + 0.276642i \(0.0892215\pi\)
\(504\) 0 0
\(505\) 9.97615 5.75973i 0.443933 0.256305i
\(506\) 2.38943 4.13861i 0.106223 0.183984i
\(507\) −26.5358 34.4448i −1.17850 1.52975i
\(508\) −4.92583 8.53178i −0.218548 0.378537i
\(509\) 27.3194i 1.21091i 0.795879 + 0.605455i \(0.207009\pi\)
−0.795879 + 0.605455i \(0.792991\pi\)
\(510\) −5.83000 10.0979i −0.258157 0.447141i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 108.717 62.7677i 4.79996 2.77126i
\(514\) 31.1018i 1.37184i
\(515\) 7.83369 4.52279i 0.345194 0.199298i
\(516\) 16.8763 + 29.2306i 0.742938 + 1.28681i
\(517\) −10.0693 17.4405i −0.442846 0.767031i
\(518\) 0 0
\(519\) 10.7214 0.470616
\(520\) 0.374120 + 5.62506i 0.0164062 + 0.246675i
\(521\) −1.81790 3.14870i −0.0796437 0.137947i 0.823453 0.567385i \(-0.192045\pi\)
−0.903096 + 0.429438i \(0.858712\pi\)
\(522\) 34.2280 + 19.7615i 1.49812 + 0.864938i
\(523\) 7.18446 0.314155 0.157077 0.987586i \(-0.449793\pi\)
0.157077 + 0.987586i \(0.449793\pi\)
\(524\) −7.39614 + 12.8105i −0.323102 + 0.559629i
\(525\) 0 0
\(526\) −24.5732 14.1873i −1.07144 0.618597i
\(527\) 1.15461 0.666613i 0.0502955 0.0290381i
\(528\) 8.30201 4.79317i 0.361299 0.208596i
\(529\) −20.2199 −0.879128
\(530\) −9.35639 −0.406415
\(531\) 6.35419 3.66859i 0.275748 0.159203i
\(532\) 0 0
\(533\) −12.6606 + 25.7354i −0.548389 + 1.11473i
\(534\) −4.04908 + 7.01321i −0.175221 + 0.303491i
\(535\) 1.39329 + 0.804416i 0.0602371 + 0.0347779i
\(536\) −0.820432 + 1.42103i −0.0354373 + 0.0613792i
\(537\) 26.4230 + 45.7659i 1.14023 + 1.97494i
\(538\) 21.4017i 0.922691i
\(539\) 0 0
\(540\) −23.4915 13.5628i −1.01091 0.583651i
\(541\) 0.385436 + 0.222531i 0.0165712 + 0.00956737i 0.508263 0.861202i \(-0.330288\pi\)
−0.491692 + 0.870769i \(0.663621\pi\)
\(542\) −5.74656 −0.246836
\(543\) −15.2502 + 26.4142i −0.654450 + 1.13354i
\(544\) 2.22961i 0.0955938i
\(545\) −22.1298 −0.947935
\(546\) 0 0
\(547\) −5.67129 −0.242487 −0.121243 0.992623i \(-0.538688\pi\)
−0.121243 + 0.992623i \(0.538688\pi\)
\(548\) 0.458997i 0.0196074i
\(549\) −58.3603 + 101.083i −2.49076 + 4.31412i
\(550\) −7.32381 −0.312288
\(551\) 30.2524 + 17.4662i 1.28879 + 0.744085i
\(552\) 4.82962 + 2.78838i 0.205562 + 0.118682i
\(553\) 0 0
\(554\) 26.6020i 1.13021i
\(555\) −0.100836 0.174654i −0.00428027 0.00741364i
\(556\) −7.65731 + 13.2628i −0.324742 + 0.562470i
\(557\) −22.9561 13.2537i −0.972683 0.561579i −0.0726298 0.997359i \(-0.523139\pi\)
−0.900053 + 0.435780i \(0.856472\pi\)
\(558\) 2.44774 4.23962i 0.103621 0.179477i
\(559\) 2.41462 + 36.3049i 0.102128 + 1.53553i
\(560\) 0 0
\(561\) −18.5103 + 10.6869i −0.781504 + 0.451202i
\(562\) 6.69143 0.282261
\(563\) −11.5376 −0.486252 −0.243126 0.969995i \(-0.578173\pi\)
−0.243126 + 0.969995i \(0.578173\pi\)
\(564\) 20.3525 11.7505i 0.856993 0.494785i
\(565\) −18.3356 + 10.5861i −0.771386 + 0.445360i
\(566\) 17.2632 + 9.96692i 0.725627 + 0.418941i
\(567\) 0 0
\(568\) 1.14733 1.98724i 0.0481409 0.0833826i
\(569\) 32.1581 1.34814 0.674069 0.738668i \(-0.264545\pi\)
0.674069 + 0.738668i \(0.264545\pi\)
\(570\) −32.7717 18.9208i −1.37266 0.792504i
\(571\) 5.77702 + 10.0061i 0.241761 + 0.418742i 0.961216 0.275797i \(-0.0889418\pi\)
−0.719455 + 0.694539i \(0.755608\pi\)
\(572\) 10.3112 0.685794i 0.431134 0.0286745i
\(573\) 10.9083 0.455699
\(574\) 0 0
\(575\) −2.13028 3.68976i −0.0888389 0.153873i
\(576\) 4.09347 + 7.09010i 0.170561 + 0.295421i
\(577\) −7.91591 + 4.57025i −0.329543 + 0.190262i −0.655638 0.755075i \(-0.727600\pi\)
0.326095 + 0.945337i \(0.394267\pi\)
\(578\) 12.0288i 0.500333i
\(579\) −63.9364 + 36.9137i −2.65711 + 1.53408i
\(580\) 7.54819i 0.313422i
\(581\) 0 0
\(582\) −8.17490 14.1593i −0.338860 0.586923i
\(583\) 17.1511i 0.710325i
\(584\) 5.61387 + 9.72351i 0.232304 + 0.402362i
\(585\) −25.6785 38.3508i −1.06168 1.58561i
\(586\) 4.43044 7.67375i 0.183020 0.317000i
\(587\) −37.0629 + 21.3983i −1.52975 + 0.883201i −0.530378 + 0.847761i \(0.677950\pi\)
−0.999372 + 0.0354398i \(0.988717\pi\)
\(588\) 0 0
\(589\) 2.16344 3.74718i 0.0891428 0.154400i
\(590\) −1.21354 0.700635i −0.0499605 0.0288447i
\(591\) 17.6367i 0.725478i
\(592\) 0.0385636i 0.00158496i
\(593\) −12.3356 7.12195i −0.506561 0.292463i 0.224858 0.974392i \(-0.427808\pi\)
−0.731419 + 0.681928i \(0.761142\pi\)
\(594\) −24.8619 + 43.0620i −1.02009 + 1.76686i
\(595\) 0 0
\(596\) 8.86563 5.11858i 0.363150 0.209665i
\(597\) 14.8297 25.6858i 0.606939 1.05125i
\(598\) 3.34474 + 4.99535i 0.136777 + 0.204275i
\(599\) −1.87367 3.24530i −0.0765563 0.132599i 0.825206 0.564832i \(-0.191059\pi\)
−0.901762 + 0.432233i \(0.857726\pi\)
\(600\) 8.54664i 0.348915i
\(601\) 5.33462 + 9.23984i 0.217604 + 0.376901i 0.954075 0.299568i \(-0.0968426\pi\)
−0.736471 + 0.676469i \(0.763509\pi\)
\(602\) 0 0
\(603\) 13.4337i 0.547061i
\(604\) −13.1731 + 7.60551i −0.536007 + 0.309464i
\(605\) 4.35490i 0.177052i
\(606\) 21.3405 12.3209i 0.866898 0.500504i
\(607\) 4.82628 + 8.35936i 0.195893 + 0.339296i 0.947193 0.320665i \(-0.103906\pi\)
−0.751300 + 0.659961i \(0.770573\pi\)
\(608\) 3.61801 + 6.26657i 0.146730 + 0.254143i
\(609\) 0 0
\(610\) 22.2915 0.902558
\(611\) 25.2781 1.68123i 1.02264 0.0680153i
\(612\) −9.12684 15.8082i −0.368931 0.639007i
\(613\) 3.45968 + 1.99745i 0.139735 + 0.0806761i 0.568238 0.822864i \(-0.307625\pi\)
−0.428503 + 0.903541i \(0.640959\pi\)
\(614\) 8.34636 0.336832
\(615\) −20.8000 + 36.0266i −0.838736 + 1.45273i
\(616\) 0 0
\(617\) 2.80199 + 1.61773i 0.112804 + 0.0651273i 0.555340 0.831623i \(-0.312588\pi\)
−0.442537 + 0.896750i \(0.645921\pi\)
\(618\) 16.7575 9.67493i 0.674084 0.389183i
\(619\) 34.0070 19.6340i 1.36686 0.789156i 0.376333 0.926485i \(-0.377185\pi\)
0.990526 + 0.137329i \(0.0438517\pi\)
\(620\) −0.934950 −0.0375485
\(621\) −28.9263 −1.16077
\(622\) −5.79281 + 3.34448i −0.232270 + 0.134101i
\(623\) 0 0
\(624\) 0.800299 + 12.0329i 0.0320376 + 0.481700i
\(625\) 2.84703 4.93120i 0.113881 0.197248i
\(626\) 18.5145 + 10.6894i 0.739990 + 0.427233i
\(627\) −34.6834 + 60.0735i −1.38512 + 2.39910i
\(628\) 1.13709 + 1.96950i 0.0453750 + 0.0785918i
\(629\) 0.0859819i 0.00342832i
\(630\) 0 0
\(631\) 25.4983 + 14.7215i 1.01507 + 0.586052i 0.912673 0.408691i \(-0.134015\pi\)
0.102400 + 0.994743i \(0.467348\pi\)
\(632\) −3.69011 2.13049i −0.146785 0.0847463i
\(633\) −21.9715 −0.873288
\(634\) 15.8388 27.4336i 0.629040 1.08953i
\(635\) 15.4036i 0.611274i
\(636\) −20.0147 −0.793636
\(637\) 0 0
\(638\) −13.8365 −0.547792
\(639\) 18.7863i 0.743173i
\(640\) 0.781779 1.35408i 0.0309025 0.0535247i
\(641\) −4.09119 −0.161592 −0.0807961 0.996731i \(-0.525746\pi\)
−0.0807961 + 0.996731i \(0.525746\pi\)
\(642\) 2.98046 + 1.72077i 0.117629 + 0.0679133i
\(643\) −19.2672 11.1239i −0.759825 0.438685i 0.0694080 0.997588i \(-0.477889\pi\)
−0.829233 + 0.558903i \(0.811222\pi\)
\(644\) 0 0
\(645\) 52.7742i 2.07798i
\(646\) −8.06675 13.9720i −0.317382 0.549722i
\(647\) 24.9292 43.1786i 0.980066 1.69752i 0.317980 0.948097i \(-0.396996\pi\)
0.662086 0.749427i \(-0.269671\pi\)
\(648\) −28.9816 16.7326i −1.13851 0.657317i
\(649\) −1.28433 + 2.22452i −0.0504142 + 0.0873200i
\(650\) 4.06695 8.26700i 0.159519 0.324259i
\(651\) 0 0
\(652\) 0.00848066 0.00489631i 0.000332128 0.000191754i
\(653\) 7.40353 0.289723 0.144861 0.989452i \(-0.453726\pi\)
0.144861 + 0.989452i \(0.453726\pi\)
\(654\) −47.3390 −1.85110
\(655\) −20.0299 + 11.5643i −0.782635 + 0.451854i
\(656\) 6.88896 3.97734i 0.268969 0.155289i
\(657\) −79.6058 45.9604i −3.10572 1.79309i
\(658\) 0 0
\(659\) −15.0410 + 26.0518i −0.585914 + 1.01483i 0.408847 + 0.912603i \(0.365931\pi\)
−0.994761 + 0.102230i \(0.967402\pi\)
\(660\) 14.9888 0.583438
\(661\) 23.0639 + 13.3160i 0.897082 + 0.517931i 0.876252 0.481852i \(-0.160036\pi\)
0.0208300 + 0.999783i \(0.493369\pi\)
\(662\) −12.3347 21.3644i −0.479404 0.830351i
\(663\) −1.78436 26.8286i −0.0692986 1.04194i
\(664\) 4.94829 0.192031
\(665\) 0 0
\(666\) −0.157859 0.273420i −0.00611691 0.0105948i
\(667\) −4.02463 6.97087i −0.155834 0.269913i
\(668\) 21.6080 12.4754i 0.836040 0.482688i
\(669\) 56.5657i 2.18696i
\(670\) −2.22186 + 1.28279i −0.0858380 + 0.0495586i
\(671\) 40.8623i 1.57747i
\(672\) 0 0
\(673\) −1.84652 3.19827i −0.0711783 0.123284i 0.828240 0.560374i \(-0.189343\pi\)
−0.899418 + 0.437090i \(0.856009\pi\)
\(674\) 28.0871i 1.08188i
\(675\) 22.1654 + 38.3917i 0.853148 + 1.47770i
\(676\) −4.95177 + 12.0200i −0.190453 + 0.462307i
\(677\) −17.8266 + 30.8767i −0.685134 + 1.18669i 0.288261 + 0.957552i \(0.406923\pi\)
−0.973395 + 0.229134i \(0.926410\pi\)
\(678\) −39.2227 + 22.6453i −1.50634 + 0.869686i
\(679\) 0 0
\(680\) −1.74306 + 3.01907i −0.0668434 + 0.115776i
\(681\) −46.7283 26.9786i −1.79063 1.03382i
\(682\) 1.71385i 0.0656265i
\(683\) 30.2653i 1.15807i 0.815304 + 0.579034i \(0.196570\pi\)
−0.815304 + 0.579034i \(0.803430\pi\)
\(684\) −51.3040 29.6204i −1.96166 1.13256i
\(685\) −0.358834 + 0.621519i −0.0137104 + 0.0237470i
\(686\) 0 0
\(687\) 20.0207 11.5590i 0.763838 0.441002i
\(688\) 5.04571 8.73942i 0.192366 0.333187i
\(689\) −19.3599 9.52410i −0.737553 0.362839i
\(690\) 4.35980 + 7.55139i 0.165975 + 0.287477i
\(691\) 3.50309i 0.133264i −0.997778 0.0666320i \(-0.978775\pi\)
0.997778 0.0666320i \(-0.0212253\pi\)
\(692\) −1.60275 2.77604i −0.0609273 0.105529i
\(693\) 0 0
\(694\) 10.1080i 0.383693i
\(695\) −20.7372 + 11.9726i −0.786608 + 0.454148i
\(696\) 16.1467i 0.612040i
\(697\) −15.3597 + 8.86793i −0.581791 + 0.335897i
\(698\) −8.69465 15.0596i −0.329097 0.570013i
\(699\) 12.4992 + 21.6492i 0.472762 + 0.818849i
\(700\) 0 0
\(701\) −45.2243 −1.70810 −0.854048 0.520194i \(-0.825860\pi\)
−0.854048 + 0.520194i \(0.825860\pi\)
\(702\) −34.8018 51.9763i −1.31351 1.96172i
\(703\) −0.139524 0.241662i −0.00526223 0.00911445i
\(704\) −2.48215 1.43307i −0.0935495 0.0540108i
\(705\) 36.7451 1.38390
\(706\) 1.66329 2.88091i 0.0625989 0.108424i
\(707\) 0 0
\(708\) −2.59594 1.49877i −0.0975613 0.0563270i
\(709\) −2.59657 + 1.49913i −0.0975161 + 0.0563009i −0.547965 0.836501i \(-0.684597\pi\)
0.450449 + 0.892802i \(0.351264\pi\)
\(710\) 3.10716 1.79392i 0.116610 0.0673245i
\(711\) 34.8843 1.30827
\(712\) 2.42120 0.0907383
\(713\) −0.863440 + 0.498507i −0.0323361 + 0.0186692i
\(714\) 0 0
\(715\) 14.4984 + 7.13248i 0.542208 + 0.266740i
\(716\) 7.89998 13.6832i 0.295236 0.511364i
\(717\) 57.5539 + 33.2287i 2.14939 + 1.24095i
\(718\) −4.01207 + 6.94911i −0.149729 + 0.259339i
\(719\) 10.0397 + 17.3892i 0.374417 + 0.648509i 0.990240 0.139376i \(-0.0445096\pi\)
−0.615823 + 0.787885i \(0.711176\pi\)
\(720\) 12.8007i 0.477056i
\(721\) 0 0
\(722\) −28.8905 16.6800i −1.07519 0.620764i
\(723\) −30.8327 17.8013i −1.14668 0.662037i
\(724\) 9.11907 0.338908
\(725\) −6.16792 + 10.6832i −0.229071 + 0.396762i
\(726\) 9.31579i 0.345741i
\(727\) 32.5895 1.20868 0.604338 0.796728i \(-0.293438\pi\)
0.604338 + 0.796728i \(0.293438\pi\)
\(728\) 0 0
\(729\) 99.8990 3.69996
\(730\) 17.5552i 0.649748i
\(731\) −11.2500 + 19.4855i −0.416095 + 0.720698i
\(732\) 47.6850 1.76249
\(733\) 16.0380 + 9.25952i 0.592376 + 0.342008i 0.766036 0.642797i \(-0.222226\pi\)
−0.173661 + 0.984806i \(0.555560\pi\)
\(734\) −0.899869 0.519540i −0.0332148 0.0191766i
\(735\) 0 0
\(736\) 1.66735i 0.0614594i
\(737\) 2.35147 + 4.07287i 0.0866176 + 0.150026i
\(738\) −32.5623 + 56.3995i −1.19863 + 2.07609i
\(739\) −13.7968 7.96559i −0.507524 0.293019i 0.224291 0.974522i \(-0.427993\pi\)
−0.731815 + 0.681503i \(0.761327\pi\)
\(740\) −0.0301482 + 0.0522183i −0.00110827 + 0.00191958i
\(741\) −48.5501 72.5093i −1.78353 2.66370i
\(742\) 0 0
\(743\) 10.5962 6.11773i 0.388738 0.224438i −0.292875 0.956151i \(-0.594612\pi\)
0.681613 + 0.731713i \(0.261279\pi\)
\(744\) −2.00000 −0.0733236
\(745\) 16.0064 0.586428
\(746\) −23.6532 + 13.6562i −0.866007 + 0.499989i
\(747\) −35.0838 + 20.2556i −1.28365 + 0.741115i
\(748\) 5.53423 + 3.19519i 0.202351 + 0.116828i
\(749\) 0 0
\(750\) 19.7556 34.2177i 0.721373 1.24945i
\(751\) 20.8213 0.759782 0.379891 0.925031i \(-0.375962\pi\)
0.379891 + 0.925031i \(0.375962\pi\)
\(752\) −6.08501 3.51318i −0.221897 0.128113i
\(753\) 26.6136 + 46.0960i 0.969852 + 1.67983i
\(754\) 7.68349 15.6184i 0.279816 0.568790i
\(755\) −23.7833 −0.865563
\(756\) 0 0
\(757\) −13.5575 23.4823i −0.492757 0.853480i 0.507208 0.861824i \(-0.330678\pi\)
−0.999965 + 0.00834344i \(0.997344\pi\)
\(758\) 1.10583 + 1.91535i 0.0401655 + 0.0695687i
\(759\) 13.8424 7.99190i 0.502446 0.290087i
\(760\) 11.3139i 0.410399i
\(761\) 41.8920 24.1864i 1.51858 0.876755i 0.518824 0.854881i \(-0.326370\pi\)
0.999761 0.0218739i \(-0.00696324\pi\)
\(762\) 32.9507i 1.19368i
\(763\) 0 0
\(764\) −1.63068 2.82443i −0.0589961 0.102184i
\(765\) 28.5407i 1.03189i
\(766\) −11.1693 19.3458i −0.403563 0.698991i
\(767\) −1.79781 2.68501i −0.0649151 0.0969503i
\(768\) 1.67234 2.89658i 0.0603455 0.104521i
\(769\) 15.0214 8.67264i 0.541687 0.312743i −0.204075 0.978955i \(-0.565419\pi\)
0.745762 + 0.666212i \(0.232085\pi\)
\(770\) 0 0
\(771\) −52.0129 + 90.0890i −1.87320 + 3.24448i
\(772\) 19.1158 + 11.0365i 0.687993 + 0.397213i
\(773\) 14.0480i 0.505270i −0.967562 0.252635i \(-0.918703\pi\)
0.967562 0.252635i \(-0.0812971\pi\)
\(774\) 82.6178i 2.96963i
\(775\) 1.32326 + 0.763984i 0.0475329 + 0.0274431i
\(776\) −2.44414 + 4.23338i −0.0877396 + 0.151970i
\(777\) 0 0
\(778\) 10.6178 6.13022i 0.380668 0.219779i
\(779\) −28.7801 + 49.8487i −1.03116 + 1.78601i
\(780\) −8.32336 + 16.9191i −0.298024 + 0.605802i
\(781\) −3.28841 5.69569i −0.117669 0.203808i
\(782\) 3.71755i 0.132939i
\(783\) 41.8760 + 72.5314i 1.49653 + 2.59206i
\(784\) 0 0
\(785\) 3.55582i 0.126913i
\(786\) −42.8471 + 24.7378i −1.52831 + 0.882368i
\(787\) 7.75577i 0.276463i −0.990400 0.138232i \(-0.955858\pi\)
0.990400 0.138232i \(-0.0441419\pi\)
\(788\) 4.56660 2.63653i 0.162678 0.0939224i
\(789\) −47.4522 82.1896i −1.68934 2.92603i
\(790\) −3.33114 5.76971i −0.118517 0.205277i
\(791\) 0 0
\(792\) 23.4649 0.833789
\(793\) 46.1248 + 22.6911i 1.63794 + 0.805784i
\(794\) −1.46759 2.54193i −0.0520827 0.0902099i
\(795\) −27.1016 15.6471i −0.961193 0.554945i
\(796\) −8.86762 −0.314304
\(797\) 16.9246 29.3143i 0.599500 1.03836i −0.393395 0.919370i \(-0.628699\pi\)
0.992895 0.118995i \(-0.0379673\pi\)
\(798\) 0 0
\(799\) 13.5672 + 7.83303i 0.479973 + 0.277113i
\(800\) −2.21294 + 1.27764i −0.0782394 + 0.0451715i
\(801\) −17.1665 + 9.91111i −0.606550 + 0.350192i
\(802\) 21.8502 0.771559
\(803\) 32.1803 1.13562
\(804\) −4.75290 + 2.74409i −0.167622 + 0.0967766i
\(805\) 0 0
\(806\) −1.93456 0.951708i −0.0681420 0.0335225i
\(807\) 35.7909 61.9917i 1.25990 2.18221i
\(808\) −6.38042 3.68373i −0.224462 0.129593i
\(809\) 16.4170 28.4351i 0.577191 0.999723i −0.418609 0.908166i \(-0.637482\pi\)
0.995800 0.0915570i \(-0.0291844\pi\)
\(810\) −26.1623 45.3145i −0.919250 1.59219i
\(811\) 12.2083i 0.428690i 0.976758 + 0.214345i \(0.0687617\pi\)
−0.976758 + 0.214345i \(0.931238\pi\)
\(812\) 0 0
\(813\) −16.6454 9.61023i −0.583780 0.337045i
\(814\) 0.0957207 + 0.0552644i 0.00335501 + 0.00193701i
\(815\) 0.0153113 0.000536332
\(816\) −3.72868 + 6.45826i −0.130530 + 0.226084i
\(817\) 73.0216i 2.55470i
\(818\) −7.38191 −0.258102
\(819\) 0 0
\(820\) 12.4376 0.434340
\(821\) 47.4868i 1.65730i 0.559767 + 0.828650i \(0.310891\pi\)
−0.559767 + 0.828650i \(0.689109\pi\)
\(822\) −0.767601 + 1.32952i −0.0267732 + 0.0463725i
\(823\) −22.0459 −0.768471 −0.384235 0.923235i \(-0.625535\pi\)
−0.384235 + 0.923235i \(0.625535\pi\)
\(824\) −5.01017 2.89263i −0.174538 0.100769i
\(825\) −21.2140 12.2479i −0.738578 0.426418i
\(826\) 0 0
\(827\) 45.9092i 1.59642i −0.602380 0.798209i \(-0.705781\pi\)
0.602380 0.798209i \(-0.294219\pi\)
\(828\) 6.82525 + 11.8217i 0.237194 + 0.410832i
\(829\) −13.3883 + 23.1893i −0.464996 + 0.805396i −0.999201 0.0399584i \(-0.987277\pi\)
0.534206 + 0.845355i \(0.320611\pi\)
\(830\) 6.70038 + 3.86846i 0.232573 + 0.134276i
\(831\) −44.4877 + 77.0550i −1.54326 + 2.67301i
\(832\) 2.99598 2.00602i 0.103867 0.0695462i
\(833\) 0 0
\(834\) −44.3601 + 25.6113i −1.53606 + 0.886847i
\(835\) 39.0120 1.35007
\(836\) 20.7394 0.717288
\(837\) 8.98404 5.18694i 0.310534 0.179287i
\(838\) −7.43287 + 4.29137i −0.256764 + 0.148243i
\(839\) 24.5960 + 14.2005i 0.849147 + 0.490255i 0.860363 0.509682i \(-0.170237\pi\)
−0.0112158 + 0.999937i \(0.503570\pi\)
\(840\) 0 0
\(841\) 2.84726 4.93160i 0.0981814 0.170055i
\(842\) −7.49525 −0.258304
\(843\) 19.3823 + 11.1904i 0.667562 + 0.385417i
\(844\) 3.28453 + 5.68898i 0.113058 + 0.195823i
\(845\) −16.1021 + 12.4048i −0.553928 + 0.426739i
\(846\) 57.5244 1.97773
\(847\) 0 0
\(848\) 2.99202 + 5.18233i 0.102746 + 0.177962i
\(849\) 33.3362 + 57.7400i 1.14410 + 1.98163i
\(850\) 4.93401 2.84865i 0.169235 0.0977079i
\(851\) 0.0642991i 0.00220415i
\(852\) 6.64668 3.83746i 0.227712 0.131469i
\(853\) 21.3316i 0.730379i 0.930933 + 0.365189i \(0.118996\pi\)
−0.930933 + 0.365189i \(0.881004\pi\)
\(854\) 0 0
\(855\) −46.3132 80.2168i −1.58388 2.74336i
\(856\) 1.02896i 0.0351690i
\(857\) −20.5412 35.5784i −0.701673 1.21533i −0.967879 0.251417i \(-0.919103\pi\)
0.266206 0.963916i \(-0.414230\pi\)
\(858\) 31.0142 + 15.2575i 1.05881 + 0.520881i
\(859\) 14.4309 24.9951i 0.492376 0.852820i −0.507586 0.861601i \(-0.669462\pi\)
0.999961 + 0.00878126i \(0.00279520\pi\)
\(860\) 13.6646 7.88925i 0.465958 0.269021i
\(861\) 0 0
\(862\) 8.23956 14.2713i 0.280641 0.486084i
\(863\) 19.6875 + 11.3666i 0.670171 + 0.386923i 0.796141 0.605111i \(-0.206871\pi\)
−0.125970 + 0.992034i \(0.540204\pi\)
\(864\) 17.3487i 0.590214i
\(865\) 5.01198i 0.170412i
\(866\) −22.1365 12.7805i −0.752229 0.434300i
\(867\) −20.1163 + 34.8425i −0.683187 + 1.18331i
\(868\) 0 0
\(869\) −10.5764 + 6.10627i −0.358779 + 0.207141i
\(870\) 12.6232 21.8640i 0.427966 0.741258i
\(871\) −5.90318 + 0.392617i −0.200022 + 0.0133033i
\(872\) 7.07674 + 12.2573i 0.239649 + 0.415084i
\(873\) 40.0201i 1.35448i
\(874\) 6.03249 + 10.4486i 0.204052 + 0.353428i
\(875\) 0 0
\(876\) 37.5533i 1.26881i
\(877\) −25.4765 + 14.7089i −0.860282 + 0.496684i −0.864107 0.503309i \(-0.832116\pi\)
0.00382498 + 0.999993i \(0.498782\pi\)
\(878\) 9.20839i 0.310768i
\(879\) 25.6663 14.8184i 0.865703 0.499814i
\(880\) −2.24069 3.88098i −0.0755335 0.130828i
\(881\) −2.11104 3.65644i −0.0711229 0.123188i 0.828271 0.560328i \(-0.189325\pi\)
−0.899394 + 0.437140i \(0.855992\pi\)
\(882\) 0 0
\(883\) 37.1982 1.25182 0.625910 0.779895i \(-0.284728\pi\)
0.625910 + 0.779895i \(0.284728\pi\)
\(884\) −6.67987 + 4.47264i −0.224668 + 0.150431i
\(885\) −2.34341 4.05890i −0.0787727 0.136438i
\(886\) −5.37593 3.10379i −0.180608 0.104274i
\(887\) 56.1894 1.88665 0.943327 0.331865i \(-0.107678\pi\)
0.943327 + 0.331865i \(0.107678\pi\)
\(888\) −0.0644917 + 0.111703i −0.00216420 + 0.00374850i
\(889\) 0 0
\(890\) 3.27850 + 1.89284i 0.109896 + 0.0634482i
\(891\) −83.0654 + 47.9578i −2.78280 + 1.60665i
\(892\) −14.6463 + 8.45606i −0.490395 + 0.283130i
\(893\) 50.8429 1.70139
\(894\) 34.2401 1.14516
\(895\) 21.3944 12.3521i 0.715136 0.412884i
\(896\) 0 0
\(897\) 1.33438 + 20.0630i 0.0445536 + 0.669884i
\(898\) 2.60944 4.51968i 0.0870781 0.150824i
\(899\) 2.49997 + 1.44336i 0.0833785 + 0.0481386i
\(900\) 10.4600 18.1172i 0.348666 0.603908i
\(901\) −6.67104 11.5546i −0.222245 0.384939i
\(902\) 22.7992i 0.759132i
\(903\) 0 0
\(904\) 11.7269 + 6.77051i 0.390030 + 0.225184i
\(905\) 12.3480 + 7.12910i 0.410460 + 0.236979i
\(906\) −50.8761 −1.69025
\(907\) −0.326806 + 0.566045i −0.0108514 + 0.0187952i −0.871400 0.490573i \(-0.836788\pi\)
0.860549 + 0.509368i \(0.170121\pi\)
\(908\) 16.1322i 0.535367i
\(909\) 60.3170 2.00059
\(910\) 0 0
\(911\) 39.7806 1.31799 0.658995 0.752147i \(-0.270982\pi\)
0.658995 + 0.752147i \(0.270982\pi\)
\(912\) 24.2022i 0.801415i
\(913\) 7.09124 12.2824i 0.234686 0.406487i
\(914\) −33.9332 −1.12241
\(915\) 64.5693 + 37.2791i 2.13460 + 1.23241i
\(916\) −5.98583 3.45592i −0.197777 0.114187i
\(917\) 0 0
\(918\) 38.6808i 1.27666i
\(919\) −17.3028 29.9693i −0.570767 0.988597i −0.996487 0.0837423i \(-0.973313\pi\)
0.425721 0.904855i \(-0.360021\pi\)
\(920\) 1.30350 2.25773i 0.0429751 0.0744351i
\(921\) 24.1759 + 13.9580i 0.796624 + 0.459931i
\(922\) −0.422380 + 0.731583i −0.0139103 + 0.0240934i
\(923\) 8.25528 0.549054i 0.271726 0.0180723i
\(924\) 0 0
\(925\) 0.0853392 0.0492706i 0.00280593 0.00162001i
\(926\) 6.50221 0.213676
\(927\) 47.3635 1.55562
\(928\) −4.18080 + 2.41379i −0.137242 + 0.0792365i
\(929\) 16.6889 9.63536i 0.547546 0.316126i −0.200586 0.979676i \(-0.564285\pi\)
0.748132 + 0.663550i \(0.230951\pi\)
\(930\) −2.70816 1.56356i −0.0888041 0.0512711i
\(931\) 0 0
\(932\) 3.73702 6.47272i 0.122410 0.212021i
\(933\) −22.3725 −0.732442
\(934\) −8.25113 4.76379i −0.269985 0.155876i
\(935\) 4.99586 + 8.65308i 0.163382 + 0.282986i
\(936\) −13.0302 + 26.4868i −0.425905 + 0.865748i
\(937\) 50.9507 1.66449 0.832244 0.554410i \(-0.187056\pi\)
0.832244 + 0.554410i \(0.187056\pi\)
\(938\) 0 0
\(939\) 35.7526 + 61.9254i 1.16674 + 2.02086i
\(940\) −5.49306 9.51426i −0.179164 0.310321i
\(941\) −21.0456 + 12.1507i −0.686068 + 0.396102i −0.802138 0.597139i \(-0.796304\pi\)
0.116069 + 0.993241i \(0.462971\pi\)
\(942\) 7.60645i 0.247831i
\(943\) 11.4863 6.63163i 0.374046 0.215956i
\(944\) 0.896206i 0.0291690i
\(945\) 0 0
\(946\) −14.4617 25.0484i −0.470190 0.814393i
\(947\) 25.6665i 0.834049i 0.908895 + 0.417024i \(0.136927\pi\)
−0.908895 + 0.417024i \(0.863073\pi\)
\(948\) −7.12582 12.3423i −0.231436 0.400859i
\(949\) −17.8699 + 36.3246i −0.580081 + 1.17915i
\(950\) 9.24505 16.0129i 0.299949 0.519527i
\(951\) 91.7569 52.9759i 2.97542 1.71786i
\(952\) 0 0
\(953\) 2.40492 4.16544i 0.0779029 0.134932i −0.824442 0.565946i \(-0.808511\pi\)
0.902345 + 0.431015i \(0.141844\pi\)
\(954\) −42.4274 24.4955i −1.37364 0.793070i
\(955\) 5.09934i 0.165011i
\(956\) 19.8696i 0.642628i
\(957\) −40.0786 23.1394i −1.29556 0.747990i
\(958\) −1.42099 + 2.46123i −0.0459102 + 0.0795188i
\(959\) 0 0
\(960\) 4.52898 2.61481i 0.146172 0.0843925i
\(961\) −15.3212 + 26.5371i −0.494233 + 0.856037i
\(962\) −0.115536 + 0.0773594i −0.00372502 + 0.00249417i
\(963\) 4.21200 + 7.29540i 0.135730 + 0.235091i
\(964\) 10.6445i 0.342837i
\(965\) 17.2562 + 29.8887i 0.555498 + 0.962150i
\(966\) 0 0
\(967\) 58.2044i 1.87173i −0.352362 0.935864i \(-0.614622\pi\)
0.352362 0.935864i \(-0.385378\pi\)
\(968\) 2.41210 1.39263i 0.0775277 0.0447607i
\(969\) 53.9615i 1.73349i
\(970\) −6.61913 + 3.82156i −0.212528 + 0.122703i
\(971\) −18.0669 31.2927i −0.579793 1.00423i −0.995503 0.0947336i \(-0.969800\pi\)
0.415710 0.909497i \(-0.363533\pi\)
\(972\) −29.9422 51.8613i −0.960395 1.66345i
\(973\) 0 0
\(974\) 5.26374 0.168661
\(975\) 25.6055 17.1447i 0.820034 0.549071i
\(976\) −7.12846 12.3469i −0.228177 0.395213i
\(977\) −14.4794 8.35970i −0.463238 0.267451i 0.250167 0.968203i \(-0.419515\pi\)
−0.713405 + 0.700752i \(0.752848\pi\)
\(978\) 0.0327533 0.00104733
\(979\) 3.46975 6.00978i 0.110894 0.192073i
\(980\) 0 0
\(981\) −100.349 57.9368i −3.20391 1.84978i
\(982\) 19.8245 11.4457i 0.632625 0.365246i
\(983\) −40.2497 + 23.2382i −1.28377 + 0.741183i −0.977535 0.210774i \(-0.932402\pi\)
−0.306232 + 0.951957i \(0.599068\pi\)
\(984\) 26.6060 0.848167
\(985\) 8.24472 0.262699
\(986\) 9.32157 5.38181i 0.296859 0.171392i
\(987\) 0 0
\(988\) −11.5167 + 23.4103i −0.366396 + 0.744782i
\(989\) 8.41296 14.5717i 0.267517 0.463352i
\(990\) 31.7734 + 18.3444i 1.00982 + 0.583022i
\(991\) −17.6755 + 30.6148i −0.561480 + 0.972512i 0.435887 + 0.900001i \(0.356435\pi\)
−0.997368 + 0.0725110i \(0.976899\pi\)
\(992\) 0.298982 + 0.517851i 0.00949267 + 0.0164418i
\(993\) 82.5118i 2.61843i
\(994\) 0 0
\(995\) −12.0075 6.93251i −0.380662 0.219775i
\(996\) 14.3331 + 8.27524i 0.454163 + 0.262211i
\(997\) −1.48780 −0.0471190 −0.0235595 0.999722i \(-0.507500\pi\)
−0.0235595 + 0.999722i \(0.507500\pi\)
\(998\) 3.39938 5.88791i 0.107606 0.186378i
\(999\) 0.669028i 0.0211671i
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 1274.2.o.e.569.3 12
7.2 even 3 1274.2.m.c.491.3 12
7.3 odd 6 1274.2.v.e.361.6 12
7.4 even 3 1274.2.v.d.361.4 12
7.5 odd 6 182.2.m.b.127.1 yes 12
7.6 odd 2 1274.2.o.d.569.1 12
13.4 even 6 1274.2.v.d.667.4 12
21.5 even 6 1638.2.bj.g.127.6 12
28.19 even 6 1456.2.cc.d.673.6 12
91.4 even 6 inner 1274.2.o.e.459.6 12
91.17 odd 6 1274.2.o.d.459.4 12
91.30 even 6 1274.2.m.c.589.3 12
91.54 even 12 2366.2.a.bf.1.6 6
91.68 odd 6 2366.2.d.r.337.6 12
91.69 odd 6 1274.2.v.e.667.6 12
91.75 odd 6 2366.2.d.r.337.12 12
91.82 odd 6 182.2.m.b.43.1 12
91.89 even 12 2366.2.a.bh.1.6 6
273.173 even 6 1638.2.bj.g.1135.4 12
364.355 even 6 1456.2.cc.d.225.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
182.2.m.b.43.1 12 91.82 odd 6
182.2.m.b.127.1 yes 12 7.5 odd 6
1274.2.m.c.491.3 12 7.2 even 3
1274.2.m.c.589.3 12 91.30 even 6
1274.2.o.d.459.4 12 91.17 odd 6
1274.2.o.d.569.1 12 7.6 odd 2
1274.2.o.e.459.6 12 91.4 even 6 inner
1274.2.o.e.569.3 12 1.1 even 1 trivial
1274.2.v.d.361.4 12 7.4 even 3
1274.2.v.d.667.4 12 13.4 even 6
1274.2.v.e.361.6 12 7.3 odd 6
1274.2.v.e.667.6 12 91.69 odd 6
1456.2.cc.d.225.6 12 364.355 even 6
1456.2.cc.d.673.6 12 28.19 even 6
1638.2.bj.g.127.6 12 21.5 even 6
1638.2.bj.g.1135.4 12 273.173 even 6
2366.2.a.bf.1.6 6 91.54 even 12
2366.2.a.bh.1.6 6 91.89 even 12
2366.2.d.r.337.6 12 91.68 odd 6
2366.2.d.r.337.12 12 91.75 odd 6