Properties

Label 273.2.n.c.8.11
Level $273$
Weight $2$
Character 273.8
Analytic conductor $2.180$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(8,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.8");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.n (of order \(4\), 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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 8.11
Character \(\chi\) \(=\) 273.8
Dual form 273.2.n.c.239.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.150864 + 0.150864i) q^{2} +(-1.22804 - 1.22144i) q^{3} +1.95448i q^{4} +(0.482343 - 0.482343i) q^{5} +(0.369539 - 0.000996021i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.596590 - 0.596590i) q^{8} +(0.0161717 + 2.99996i) q^{9} +O(q^{10})\) \(q+(-0.150864 + 0.150864i) q^{2} +(-1.22804 - 1.22144i) q^{3} +1.95448i q^{4} +(0.482343 - 0.482343i) q^{5} +(0.369539 - 0.000996021i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.596590 - 0.596590i) q^{8} +(0.0161717 + 2.99996i) q^{9} +0.145537i q^{10} +(2.26572 + 2.26572i) q^{11} +(2.38728 - 2.40018i) q^{12} +(-0.580602 + 3.55850i) q^{13} -0.213354i q^{14} +(-1.18149 + 0.00318447i) q^{15} -3.72895 q^{16} +6.99624 q^{17} +(-0.455026 - 0.450147i) q^{18} +(1.76208 + 1.76208i) q^{19} +(0.942729 + 0.942729i) q^{20} +(1.73204 - 0.00466839i) q^{21} -0.683631 q^{22} -5.46061 q^{23} +(0.00393874 + 1.46134i) q^{24} +4.53469i q^{25} +(-0.449258 - 0.624443i) q^{26} +(3.64441 - 3.70382i) q^{27} +(-1.38203 - 1.38203i) q^{28} +2.64935i q^{29} +(0.177764 - 0.178725i) q^{30} +(2.48703 + 2.48703i) q^{31} +(1.75575 - 1.75575i) q^{32} +(-0.0149585 - 5.54983i) q^{33} +(-1.05548 + 1.05548i) q^{34} +0.682135i q^{35} +(-5.86335 + 0.0316073i) q^{36} +(0.194897 - 0.194897i) q^{37} -0.531670 q^{38} +(5.05949 - 3.66081i) q^{39} -0.575522 q^{40} +(2.65812 - 2.65812i) q^{41} +(-0.260600 + 0.262008i) q^{42} -3.03374i q^{43} +(-4.42829 + 4.42829i) q^{44} +(1.45481 + 1.43921i) q^{45} +(0.823811 - 0.823811i) q^{46} +(-7.69758 - 7.69758i) q^{47} +(4.57931 + 4.55469i) q^{48} -1.00000i q^{49} +(-0.684123 - 0.684123i) q^{50} +(-8.59168 - 8.54549i) q^{51} +(-6.95501 - 1.13477i) q^{52} -6.50740i q^{53} +(0.00896410 + 1.10859i) q^{54} +2.18570 q^{55} +0.843706 q^{56} +(-0.0116334 - 4.31618i) q^{57} +(-0.399692 - 0.399692i) q^{58} +(-6.12738 - 6.12738i) q^{59} +(-0.00622399 - 2.30920i) q^{60} -9.34181 q^{61} -0.750407 q^{62} +(-2.13272 - 2.10985i) q^{63} -6.92814i q^{64} +(1.43637 + 1.99646i) q^{65} +(0.839528 + 0.835014i) q^{66} +(5.81479 + 5.81479i) q^{67} +13.6740i q^{68} +(6.70585 + 6.66980i) q^{69} +(-0.102910 - 0.102910i) q^{70} +(-8.10653 + 8.10653i) q^{71} +(1.78010 - 1.79939i) q^{72} +(6.20581 - 6.20581i) q^{73} +0.0588059i q^{74} +(5.53885 - 5.56879i) q^{75} +(-3.44395 + 3.44395i) q^{76} -3.20421 q^{77} +(-0.211011 + 1.31558i) q^{78} +3.96770 q^{79} +(-1.79863 + 1.79863i) q^{80} +(-8.99948 + 0.0970288i) q^{81} +0.802031i q^{82} +(9.36521 - 9.36521i) q^{83} +(0.00912427 + 3.38525i) q^{84} +(3.37459 - 3.37459i) q^{85} +(0.457683 + 0.457683i) q^{86} +(3.23602 - 3.25351i) q^{87} -2.70341i q^{88} +(8.54508 + 8.54508i) q^{89} +(-0.436604 + 0.00235358i) q^{90} +(-2.10569 - 2.92678i) q^{91} -10.6726i q^{92} +(-0.0164196 - 6.09192i) q^{93} +2.32258 q^{94} +1.69985 q^{95} +(-4.30067 + 0.0115916i) q^{96} +(7.88241 + 7.88241i) q^{97} +(0.150864 + 0.150864i) q^{98} +(-6.76041 + 6.83369i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 8 q^{3} + 4 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 8 q^{3} + 4 q^{6} + 8 q^{13} - 16 q^{15} - 72 q^{16} - 12 q^{18} + 40 q^{19} + 16 q^{22} + 8 q^{24} - 16 q^{27} + 44 q^{33} - 32 q^{34} - 8 q^{37} - 4 q^{39} - 48 q^{40} - 8 q^{42} + 44 q^{45} - 32 q^{46} + 80 q^{48} - 72 q^{52} + 44 q^{54} - 80 q^{55} - 52 q^{57} + 16 q^{58} + 44 q^{60} - 64 q^{61} + 24 q^{63} - 152 q^{66} + 56 q^{67} + 16 q^{70} + 16 q^{72} + 32 q^{73} + 104 q^{76} - 44 q^{78} + 8 q^{79} + 12 q^{84} - 96 q^{85} - 72 q^{87} - 8 q^{91} - 8 q^{93} + 160 q^{94} + 8 q^{96} - 32 q^{97} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.150864 + 0.150864i −0.106677 + 0.106677i −0.758431 0.651754i \(-0.774034\pi\)
0.651754 + 0.758431i \(0.274034\pi\)
\(3\) −1.22804 1.22144i −0.709010 0.705198i
\(4\) 1.95448i 0.977240i
\(5\) 0.482343 0.482343i 0.215710 0.215710i −0.590978 0.806688i \(-0.701258\pi\)
0.806688 + 0.590978i \(0.201258\pi\)
\(6\) 0.369539 0.000996021i 0.150864 0.000406624i
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) −0.596590 0.596590i −0.210926 0.210926i
\(9\) 0.0161717 + 2.99996i 0.00539057 + 0.999985i
\(10\) 0.145537i 0.0460227i
\(11\) 2.26572 + 2.26572i 0.683139 + 0.683139i 0.960706 0.277567i \(-0.0895282\pi\)
−0.277567 + 0.960706i \(0.589528\pi\)
\(12\) 2.38728 2.40018i 0.689148 0.692873i
\(13\) −0.580602 + 3.55850i −0.161030 + 0.986950i
\(14\) 0.213354i 0.0570214i
\(15\) −1.18149 + 0.00318447i −0.305059 + 0.000822227i
\(16\) −3.72895 −0.932238
\(17\) 6.99624 1.69684 0.848419 0.529325i \(-0.177555\pi\)
0.848419 + 0.529325i \(0.177555\pi\)
\(18\) −0.455026 0.450147i −0.107251 0.106101i
\(19\) 1.76208 + 1.76208i 0.404248 + 0.404248i 0.879727 0.475479i \(-0.157725\pi\)
−0.475479 + 0.879727i \(0.657725\pi\)
\(20\) 0.942729 + 0.942729i 0.210801 + 0.210801i
\(21\) 1.73204 0.00466839i 0.377963 0.00101873i
\(22\) −0.683631 −0.145751
\(23\) −5.46061 −1.13862 −0.569308 0.822124i \(-0.692789\pi\)
−0.569308 + 0.822124i \(0.692789\pi\)
\(24\) 0.00393874 + 1.46134i 0.000803993 + 0.298294i
\(25\) 4.53469i 0.906938i
\(26\) −0.449258 0.624443i −0.0881068 0.122463i
\(27\) 3.64441 3.70382i 0.701366 0.712801i
\(28\) −1.38203 1.38203i −0.261178 0.261178i
\(29\) 2.64935i 0.491972i 0.969273 + 0.245986i \(0.0791117\pi\)
−0.969273 + 0.245986i \(0.920888\pi\)
\(30\) 0.177764 0.178725i 0.0324552 0.0326306i
\(31\) 2.48703 + 2.48703i 0.446683 + 0.446683i 0.894250 0.447567i \(-0.147709\pi\)
−0.447567 + 0.894250i \(0.647709\pi\)
\(32\) 1.75575 1.75575i 0.310375 0.310375i
\(33\) −0.0149585 5.54983i −0.00260393 0.966101i
\(34\) −1.05548 + 1.05548i −0.181014 + 0.181014i
\(35\) 0.682135i 0.115302i
\(36\) −5.86335 + 0.0316073i −0.977226 + 0.00526788i
\(37\) 0.194897 0.194897i 0.0320408 0.0320408i −0.690905 0.722946i \(-0.742788\pi\)
0.722946 + 0.690905i \(0.242788\pi\)
\(38\) −0.531670 −0.0862482
\(39\) 5.05949 3.66081i 0.810167 0.586199i
\(40\) −0.575522 −0.0909980
\(41\) 2.65812 2.65812i 0.415128 0.415128i −0.468392 0.883521i \(-0.655167\pi\)
0.883521 + 0.468392i \(0.155167\pi\)
\(42\) −0.260600 + 0.262008i −0.0402114 + 0.0404287i
\(43\) 3.03374i 0.462641i −0.972878 0.231320i \(-0.925695\pi\)
0.972878 0.231320i \(-0.0743046\pi\)
\(44\) −4.42829 + 4.42829i −0.667591 + 0.667591i
\(45\) 1.45481 + 1.43921i 0.216870 + 0.214544i
\(46\) 0.823811 0.823811i 0.121464 0.121464i
\(47\) −7.69758 7.69758i −1.12281 1.12281i −0.991318 0.131489i \(-0.958024\pi\)
−0.131489 0.991318i \(-0.541976\pi\)
\(48\) 4.57931 + 4.55469i 0.660966 + 0.657413i
\(49\) 1.00000i 0.142857i
\(50\) −0.684123 0.684123i −0.0967497 0.0967497i
\(51\) −8.59168 8.54549i −1.20308 1.19661i
\(52\) −6.95501 1.13477i −0.964486 0.157365i
\(53\) 6.50740i 0.893860i −0.894569 0.446930i \(-0.852517\pi\)
0.894569 0.446930i \(-0.147483\pi\)
\(54\) 0.00896410 + 1.10859i 0.00121986 + 0.150859i
\(55\) 2.18570 0.294720
\(56\) 0.843706 0.112745
\(57\) −0.0116334 4.31618i −0.00154088 0.571691i
\(58\) −0.399692 0.399692i −0.0524822 0.0524822i
\(59\) −6.12738 6.12738i −0.797717 0.797717i 0.185018 0.982735i \(-0.440766\pi\)
−0.982735 + 0.185018i \(0.940766\pi\)
\(60\) −0.00622399 2.30920i −0.000803513 0.298116i
\(61\) −9.34181 −1.19610 −0.598048 0.801460i \(-0.704057\pi\)
−0.598048 + 0.801460i \(0.704057\pi\)
\(62\) −0.750407 −0.0953018
\(63\) −2.13272 2.10985i −0.268698 0.265817i
\(64\) 6.92814i 0.866018i
\(65\) 1.43637 + 1.99646i 0.178159 + 0.247631i
\(66\) 0.839528 + 0.835014i 0.103339 + 0.102783i
\(67\) 5.81479 + 5.81479i 0.710390 + 0.710390i 0.966617 0.256227i \(-0.0824794\pi\)
−0.256227 + 0.966617i \(0.582479\pi\)
\(68\) 13.6740i 1.65822i
\(69\) 6.70585 + 6.66980i 0.807290 + 0.802950i
\(70\) −0.102910 0.102910i −0.0123001 0.0123001i
\(71\) −8.10653 + 8.10653i −0.962068 + 0.962068i −0.999306 0.0372384i \(-0.988144\pi\)
0.0372384 + 0.999306i \(0.488144\pi\)
\(72\) 1.78010 1.79939i 0.209786 0.212060i
\(73\) 6.20581 6.20581i 0.726335 0.726335i −0.243553 0.969888i \(-0.578313\pi\)
0.969888 + 0.243553i \(0.0783129\pi\)
\(74\) 0.0588059i 0.00683605i
\(75\) 5.53885 5.56879i 0.639571 0.643028i
\(76\) −3.44395 + 3.44395i −0.395048 + 0.395048i
\(77\) −3.20421 −0.365153
\(78\) −0.211011 + 1.31558i −0.0238923 + 0.148960i
\(79\) 3.96770 0.446401 0.223201 0.974773i \(-0.428349\pi\)
0.223201 + 0.974773i \(0.428349\pi\)
\(80\) −1.79863 + 1.79863i −0.201093 + 0.201093i
\(81\) −8.99948 + 0.0970288i −0.999942 + 0.0107810i
\(82\) 0.802031i 0.0885695i
\(83\) 9.36521 9.36521i 1.02796 1.02796i 0.0283674 0.999598i \(-0.490969\pi\)
0.999598 0.0283674i \(-0.00903082\pi\)
\(84\) 0.00912427 + 3.38525i 0.000995539 + 0.369361i
\(85\) 3.37459 3.37459i 0.366025 0.366025i
\(86\) 0.457683 + 0.457683i 0.0493533 + 0.0493533i
\(87\) 3.23602 3.25351i 0.346938 0.348813i
\(88\) 2.70341i 0.288184i
\(89\) 8.54508 + 8.54508i 0.905777 + 0.905777i 0.995928 0.0901515i \(-0.0287351\pi\)
−0.0901515 + 0.995928i \(0.528735\pi\)
\(90\) −0.436604 + 0.00235358i −0.0460221 + 0.000248089i
\(91\) −2.10569 2.92678i −0.220736 0.306810i
\(92\) 10.6726i 1.11270i
\(93\) −0.0164196 6.09192i −0.00170263 0.631703i
\(94\) 2.32258 0.239556
\(95\) 1.69985 0.174401
\(96\) −4.30067 + 0.0115916i −0.438935 + 0.00118306i
\(97\) 7.88241 + 7.88241i 0.800338 + 0.800338i 0.983148 0.182810i \(-0.0585195\pi\)
−0.182810 + 0.983148i \(0.558519\pi\)
\(98\) 0.150864 + 0.150864i 0.0152396 + 0.0152396i
\(99\) −6.76041 + 6.83369i −0.679446 + 0.686811i
\(100\) −8.86296 −0.886296
\(101\) 4.29867 0.427734 0.213867 0.976863i \(-0.431394\pi\)
0.213867 + 0.976863i \(0.431394\pi\)
\(102\) 2.58539 0.00696841i 0.255992 0.000689975i
\(103\) 2.69298i 0.265348i −0.991160 0.132674i \(-0.957644\pi\)
0.991160 0.132674i \(-0.0423563\pi\)
\(104\) 2.46935 1.77658i 0.242139 0.174208i
\(105\) 0.833187 0.837691i 0.0813107 0.0817502i
\(106\) 0.981734 + 0.981734i 0.0953545 + 0.0953545i
\(107\) 14.6863i 1.41978i −0.704313 0.709889i \(-0.748745\pi\)
0.704313 0.709889i \(-0.251255\pi\)
\(108\) 7.23905 + 7.12292i 0.696578 + 0.685403i
\(109\) 14.5346 + 14.5346i 1.39216 + 1.39216i 0.820464 + 0.571699i \(0.193715\pi\)
0.571699 + 0.820464i \(0.306285\pi\)
\(110\) −0.329745 + 0.329745i −0.0314399 + 0.0314399i
\(111\) −0.477396 + 0.00128673i −0.0453124 + 0.000122131i
\(112\) 2.63677 2.63677i 0.249151 0.249151i
\(113\) 12.7034i 1.19503i 0.801856 + 0.597517i \(0.203846\pi\)
−0.801856 + 0.597517i \(0.796154\pi\)
\(114\) 0.652912 + 0.649402i 0.0611508 + 0.0608221i
\(115\) −2.63388 + 2.63388i −0.245611 + 0.245611i
\(116\) −5.17810 −0.480774
\(117\) −10.6847 1.68423i −0.987803 0.155707i
\(118\) 1.84881 0.170197
\(119\) −4.94709 + 4.94709i −0.453499 + 0.453499i
\(120\) 0.706765 + 0.702965i 0.0645185 + 0.0641716i
\(121\) 0.733069i 0.0666427i
\(122\) 1.40935 1.40935i 0.127596 0.127596i
\(123\) −6.51101 + 0.0175492i −0.587078 + 0.00158235i
\(124\) −4.86084 + 4.86084i −0.436517 + 0.436517i
\(125\) 4.59899 + 4.59899i 0.411346 + 0.411346i
\(126\) 0.640054 0.00345031i 0.0570205 0.000307378i
\(127\) 7.09824i 0.629867i −0.949114 0.314934i \(-0.898018\pi\)
0.949114 0.314934i \(-0.101982\pi\)
\(128\) 4.55670 + 4.55670i 0.402759 + 0.402759i
\(129\) −3.70553 + 3.72556i −0.326254 + 0.328017i
\(130\) −0.517892 0.0844988i −0.0454221 0.00741104i
\(131\) 0.537316i 0.0469455i −0.999724 0.0234728i \(-0.992528\pi\)
0.999724 0.0234728i \(-0.00747230\pi\)
\(132\) 10.8470 0.0292360i 0.944112 0.00254467i
\(133\) −2.49195 −0.216080
\(134\) −1.75449 −0.151565
\(135\) −0.0286600 3.54436i −0.00246666 0.305050i
\(136\) −4.17389 4.17389i −0.357908 0.357908i
\(137\) 0.824478 + 0.824478i 0.0704399 + 0.0704399i 0.741449 0.671009i \(-0.234139\pi\)
−0.671009 + 0.741449i \(0.734139\pi\)
\(138\) −2.01791 + 0.00543888i −0.171776 + 0.000462988i
\(139\) −11.0135 −0.934154 −0.467077 0.884217i \(-0.654693\pi\)
−0.467077 + 0.884217i \(0.654693\pi\)
\(140\) −1.33322 −0.112678
\(141\) 0.0508201 + 18.8551i 0.00427983 + 1.58788i
\(142\) 2.44597i 0.205261i
\(143\) −9.37802 + 6.74706i −0.784229 + 0.564218i
\(144\) −0.0603035 11.1867i −0.00502529 0.932224i
\(145\) 1.27789 + 1.27789i 0.106123 + 0.106123i
\(146\) 1.87247i 0.154967i
\(147\) −1.22144 + 1.22804i −0.100743 + 0.101287i
\(148\) 0.380922 + 0.380922i 0.0313116 + 0.0313116i
\(149\) 8.65446 8.65446i 0.709001 0.709001i −0.257324 0.966325i \(-0.582841\pi\)
0.966325 + 0.257324i \(0.0828409\pi\)
\(150\) 0.00451665 + 1.67575i 0.000368783 + 0.136824i
\(151\) −1.97985 + 1.97985i −0.161118 + 0.161118i −0.783062 0.621944i \(-0.786343\pi\)
0.621944 + 0.783062i \(0.286343\pi\)
\(152\) 2.10248i 0.170533i
\(153\) 0.113141 + 20.9884i 0.00914692 + 1.69681i
\(154\) 0.483400 0.483400i 0.0389535 0.0389535i
\(155\) 2.39920 0.192708
\(156\) 7.15498 + 9.88867i 0.572857 + 0.791728i
\(157\) 3.37297 0.269192 0.134596 0.990901i \(-0.457026\pi\)
0.134596 + 0.990901i \(0.457026\pi\)
\(158\) −0.598585 + 0.598585i −0.0476208 + 0.0476208i
\(159\) −7.94839 + 7.99135i −0.630348 + 0.633755i
\(160\) 1.69374i 0.133902i
\(161\) 3.86123 3.86123i 0.304308 0.304308i
\(162\) 1.34306 1.37234i 0.105521 0.107821i
\(163\) 8.94685 8.94685i 0.700772 0.700772i −0.263805 0.964576i \(-0.584977\pi\)
0.964576 + 0.263805i \(0.0849774\pi\)
\(164\) 5.19524 + 5.19524i 0.405680 + 0.405680i
\(165\) −2.68413 2.66970i −0.208959 0.207836i
\(166\) 2.82575i 0.219321i
\(167\) 5.08432 + 5.08432i 0.393436 + 0.393436i 0.875910 0.482474i \(-0.160262\pi\)
−0.482474 + 0.875910i \(0.660262\pi\)
\(168\) −1.03611 1.03054i −0.0799373 0.0795075i
\(169\) −12.3258 4.13214i −0.948139 0.317857i
\(170\) 1.01821i 0.0780931i
\(171\) −5.25766 + 5.31465i −0.402063 + 0.406422i
\(172\) 5.92938 0.452111
\(173\) −17.6050 −1.33849 −0.669243 0.743044i \(-0.733381\pi\)
−0.669243 + 0.743044i \(0.733381\pi\)
\(174\) 0.00263881 + 0.979038i 0.000200047 + 0.0742207i
\(175\) −3.20651 3.20651i −0.242389 0.242389i
\(176\) −8.44874 8.44874i −0.636848 0.636848i
\(177\) 0.0404536 + 15.0089i 0.00304068 + 1.12814i
\(178\) −2.57830 −0.193251
\(179\) 11.2103 0.837895 0.418947 0.908011i \(-0.362399\pi\)
0.418947 + 0.908011i \(0.362399\pi\)
\(180\) −2.81290 + 2.84339i −0.209661 + 0.211934i
\(181\) 23.1248i 1.71885i −0.511258 0.859427i \(-0.670820\pi\)
0.511258 0.859427i \(-0.329180\pi\)
\(182\) 0.759221 + 0.123874i 0.0562772 + 0.00918215i
\(183\) 11.4721 + 11.4105i 0.848045 + 0.843485i
\(184\) 3.25775 + 3.25775i 0.240164 + 0.240164i
\(185\) 0.188014i 0.0138231i
\(186\) 0.921531 + 0.916577i 0.0675700 + 0.0672067i
\(187\) 15.8515 + 15.8515i 1.15918 + 1.15918i
\(188\) 15.0448 15.0448i 1.09725 1.09725i
\(189\) 0.0420151 + 5.19598i 0.00305615 + 0.377952i
\(190\) −0.256447 + 0.256447i −0.0186046 + 0.0186046i
\(191\) 10.1254i 0.732651i 0.930487 + 0.366326i \(0.119384\pi\)
−0.930487 + 0.366326i \(0.880616\pi\)
\(192\) −8.46231 + 8.50805i −0.610714 + 0.614015i
\(193\) −9.40769 + 9.40769i −0.677180 + 0.677180i −0.959361 0.282181i \(-0.908942\pi\)
0.282181 + 0.959361i \(0.408942\pi\)
\(194\) −2.37835 −0.170756
\(195\) 0.674643 4.20617i 0.0483122 0.301210i
\(196\) 1.95448 0.139606
\(197\) 17.9619 17.9619i 1.27973 1.27973i 0.338913 0.940818i \(-0.389941\pi\)
0.940818 0.338913i \(-0.110059\pi\)
\(198\) −0.0110555 2.05086i −0.000785679 0.145749i
\(199\) 16.1933i 1.14792i −0.818885 0.573958i \(-0.805407\pi\)
0.818885 0.573958i \(-0.194593\pi\)
\(200\) 2.70535 2.70535i 0.191297 0.191297i
\(201\) −0.0383898 14.2432i −0.00270781 1.00464i
\(202\) −0.648516 + 0.648516i −0.0456294 + 0.0456294i
\(203\) −1.87337 1.87337i −0.131485 0.131485i
\(204\) 16.7020 16.7923i 1.16937 1.17569i
\(205\) 2.56425i 0.179095i
\(206\) 0.406275 + 0.406275i 0.0283065 + 0.0283065i
\(207\) −0.0883073 16.3816i −0.00613779 1.13860i
\(208\) 2.16504 13.2695i 0.150118 0.920072i
\(209\) 7.98473i 0.552316i
\(210\) 0.000679421 0.252076i 4.68845e−5 0.0173949i
\(211\) −0.155025 −0.0106723 −0.00533617 0.999986i \(-0.501699\pi\)
−0.00533617 + 0.999986i \(0.501699\pi\)
\(212\) 12.7186 0.873515
\(213\) 19.8568 0.0535201i 1.36056 0.00366713i
\(214\) 2.21564 + 2.21564i 0.151458 + 0.151458i
\(215\) −1.46330 1.46330i −0.0997964 0.0997964i
\(216\) −4.38388 + 0.0354484i −0.298285 + 0.00241196i
\(217\) −3.51719 −0.238762
\(218\) −4.38551 −0.297024
\(219\) −15.2010 + 0.0409713i −1.02719 + 0.00276859i
\(220\) 4.27191i 0.288012i
\(221\) −4.06203 + 24.8961i −0.273242 + 1.67469i
\(222\) 0.0718279 0.0722161i 0.00482077 0.00484683i
\(223\) −1.28745 1.28745i −0.0862142 0.0862142i 0.662685 0.748899i \(-0.269417\pi\)
−0.748899 + 0.662685i \(0.769417\pi\)
\(224\) 2.48300i 0.165902i
\(225\) −13.6039 + 0.0733337i −0.906925 + 0.00488891i
\(226\) −1.91649 1.91649i −0.127483 0.127483i
\(227\) −10.2367 + 10.2367i −0.679431 + 0.679431i −0.959871 0.280440i \(-0.909520\pi\)
0.280440 + 0.959871i \(0.409520\pi\)
\(228\) 8.43588 0.0227373i 0.558680 0.00150581i
\(229\) 15.8188 15.8188i 1.04533 1.04533i 0.0464123 0.998922i \(-0.485221\pi\)
0.998922 0.0464123i \(-0.0147788\pi\)
\(230\) 0.794719i 0.0524022i
\(231\) 3.93490 + 3.91374i 0.258897 + 0.257505i
\(232\) 1.58057 1.58057i 0.103770 0.103770i
\(233\) −26.3871 −1.72868 −0.864339 0.502909i \(-0.832263\pi\)
−0.864339 + 0.502909i \(0.832263\pi\)
\(234\) 1.86604 1.35785i 0.121987 0.0887657i
\(235\) −7.42574 −0.484402
\(236\) 11.9758 11.9758i 0.779561 0.779561i
\(237\) −4.87250 4.84631i −0.316503 0.314801i
\(238\) 1.49268i 0.0967561i
\(239\) −1.97439 + 1.97439i −0.127713 + 0.127713i −0.768074 0.640361i \(-0.778785\pi\)
0.640361 + 0.768074i \(0.278785\pi\)
\(240\) 4.40572 0.0118747i 0.284388 0.000766511i
\(241\) 1.72902 1.72902i 0.111376 0.111376i −0.649222 0.760599i \(-0.724906\pi\)
0.760599 + 0.649222i \(0.224906\pi\)
\(242\) 0.110594 + 0.110594i 0.00710925 + 0.00710925i
\(243\) 11.1702 + 10.8732i 0.716572 + 0.697514i
\(244\) 18.2584i 1.16887i
\(245\) −0.482343 0.482343i −0.0308157 0.0308157i
\(246\) 0.979632 0.984927i 0.0624591 0.0627967i
\(247\) −7.29341 + 5.24728i −0.464069 + 0.333877i
\(248\) 2.96747i 0.188435i
\(249\) −22.9399 + 0.0618300i −1.45376 + 0.00391832i
\(250\) −1.38765 −0.0877625
\(251\) −26.0371 −1.64345 −0.821724 0.569885i \(-0.806988\pi\)
−0.821724 + 0.569885i \(0.806988\pi\)
\(252\) 4.12367 4.16837i 0.259767 0.262582i
\(253\) −12.3722 12.3722i −0.777833 0.777833i
\(254\) 1.07087 + 1.07087i 0.0671925 + 0.0671925i
\(255\) −8.26599 + 0.0222793i −0.517636 + 0.00139519i
\(256\) 12.4814 0.780087
\(257\) 2.75007 0.171545 0.0857724 0.996315i \(-0.472664\pi\)
0.0857724 + 0.996315i \(0.472664\pi\)
\(258\) −0.00302167 1.12109i −0.000188121 0.0697958i
\(259\) 0.275626i 0.0171265i
\(260\) −3.90205 + 2.80735i −0.241995 + 0.174104i
\(261\) −7.94793 + 0.0428445i −0.491964 + 0.00265201i
\(262\) 0.0810618 + 0.0810618i 0.00500802 + 0.00500802i
\(263\) 2.53223i 0.156144i −0.996948 0.0780720i \(-0.975124\pi\)
0.996948 0.0780720i \(-0.0248764\pi\)
\(264\) −3.30205 + 3.31990i −0.203227 + 0.204325i
\(265\) −3.13879 3.13879i −0.192815 0.192815i
\(266\) 0.375947 0.375947i 0.0230508 0.0230508i
\(267\) −0.0564154 20.9310i −0.00345257 1.28096i
\(268\) −11.3649 + 11.3649i −0.694221 + 0.694221i
\(269\) 21.4014i 1.30487i −0.757845 0.652435i \(-0.773748\pi\)
0.757845 0.652435i \(-0.226252\pi\)
\(270\) 0.539042 + 0.530395i 0.0328051 + 0.0322788i
\(271\) 1.24920 1.24920i 0.0758836 0.0758836i −0.668146 0.744030i \(-0.732912\pi\)
0.744030 + 0.668146i \(0.232912\pi\)
\(272\) −26.0887 −1.58186
\(273\) −0.989016 + 6.16619i −0.0598580 + 0.373195i
\(274\) −0.248769 −0.0150287
\(275\) −10.2743 + 10.2743i −0.619565 + 0.619565i
\(276\) −13.0360 + 13.1065i −0.784675 + 0.788916i
\(277\) 13.0013i 0.781173i 0.920566 + 0.390586i \(0.127728\pi\)
−0.920566 + 0.390586i \(0.872272\pi\)
\(278\) 1.66155 1.66155i 0.0996530 0.0996530i
\(279\) −7.42075 + 7.50119i −0.444269 + 0.449085i
\(280\) 0.406955 0.406955i 0.0243202 0.0243202i
\(281\) 8.36416 + 8.36416i 0.498964 + 0.498964i 0.911115 0.412151i \(-0.135222\pi\)
−0.412151 + 0.911115i \(0.635222\pi\)
\(282\) −2.85222 2.83689i −0.169848 0.168934i
\(283\) 9.91078i 0.589135i −0.955631 0.294567i \(-0.904824\pi\)
0.955631 0.294567i \(-0.0951755\pi\)
\(284\) −15.8440 15.8440i −0.940171 0.940171i
\(285\) −2.08749 2.07626i −0.123652 0.122987i
\(286\) 0.396918 2.43270i 0.0234702 0.143849i
\(287\) 3.75915i 0.221895i
\(288\) 5.29556 + 5.23877i 0.312044 + 0.308697i
\(289\) 31.9474 1.87926
\(290\) −0.385577 −0.0226419
\(291\) −0.0520404 19.3078i −0.00305066 1.13184i
\(292\) 12.1291 + 12.1291i 0.709804 + 0.709804i
\(293\) −5.43142 5.43142i −0.317307 0.317307i 0.530425 0.847732i \(-0.322032\pi\)
−0.847732 + 0.530425i \(0.822032\pi\)
\(294\) −0.000996021 0.369539i −5.80891e−5 0.0215520i
\(295\) −5.91100 −0.344152
\(296\) −0.232547 −0.0135165
\(297\) 16.6490 0.134625i 0.966073 0.00781173i
\(298\) 2.61130i 0.151268i
\(299\) 3.17044 19.4316i 0.183351 1.12376i
\(300\) 10.8841 + 10.8256i 0.628393 + 0.625015i
\(301\) 2.14518 + 2.14518i 0.123646 + 0.123646i
\(302\) 0.597377i 0.0343752i
\(303\) −5.27895 5.25057i −0.303268 0.301637i
\(304\) −6.57070 6.57070i −0.376856 0.376856i
\(305\) −4.50596 + 4.50596i −0.258010 + 0.258010i
\(306\) −3.18347 3.14934i −0.181987 0.180036i
\(307\) 14.3434 14.3434i 0.818619 0.818619i −0.167289 0.985908i \(-0.553501\pi\)
0.985908 + 0.167289i \(0.0535013\pi\)
\(308\) 6.26255i 0.356842i
\(309\) −3.28932 + 3.30710i −0.187123 + 0.188134i
\(310\) −0.361954 + 0.361954i −0.0205576 + 0.0205576i
\(311\) 11.0703 0.627742 0.313871 0.949466i \(-0.398374\pi\)
0.313871 + 0.949466i \(0.398374\pi\)
\(312\) −5.20245 0.834438i −0.294531 0.0472408i
\(313\) 1.23211 0.0696430 0.0348215 0.999394i \(-0.488914\pi\)
0.0348215 + 0.999394i \(0.488914\pi\)
\(314\) −0.508861 + 0.508861i −0.0287167 + 0.0287167i
\(315\) −2.04638 + 0.0110313i −0.115300 + 0.000621543i
\(316\) 7.75479i 0.436241i
\(317\) 6.47040 6.47040i 0.363414 0.363414i −0.501654 0.865068i \(-0.667275\pi\)
0.865068 + 0.501654i \(0.167275\pi\)
\(318\) −0.00648150 2.40474i −0.000363465 0.134851i
\(319\) −6.00267 + 6.00267i −0.336085 + 0.336085i
\(320\) −3.34174 3.34174i −0.186809 0.186809i
\(321\) −17.9384 + 18.0354i −1.00123 + 1.00664i
\(322\) 1.16505i 0.0649254i
\(323\) 12.3279 + 12.3279i 0.685944 + 0.685944i
\(324\) −0.189641 17.5893i −0.0105356 0.977183i
\(325\) −16.1367 2.63285i −0.895102 0.146044i
\(326\) 2.69952i 0.149513i
\(327\) −0.0959588 35.6022i −0.00530654 1.96881i
\(328\) −3.17161 −0.175123
\(329\) 10.8860 0.600166
\(330\) 0.807703 0.00217700i 0.0444626 0.000119840i
\(331\) 18.7507 + 18.7507i 1.03063 + 1.03063i 0.999516 + 0.0311157i \(0.00990603\pi\)
0.0311157 + 0.999516i \(0.490094\pi\)
\(332\) 18.3041 + 18.3041i 1.00457 + 1.00457i
\(333\) 0.587834 + 0.581530i 0.0322131 + 0.0318676i
\(334\) −1.53409 −0.0839414
\(335\) 5.60944 0.306477
\(336\) −6.45871 + 0.0174082i −0.352352 + 0.000949694i
\(337\) 33.9505i 1.84940i 0.380696 + 0.924700i \(0.375684\pi\)
−0.380696 + 0.924700i \(0.624316\pi\)
\(338\) 2.48292 1.23613i 0.135053 0.0672367i
\(339\) 15.5164 15.6003i 0.842736 0.847291i
\(340\) 6.59556 + 6.59556i 0.357695 + 0.357695i
\(341\) 11.2698i 0.610293i
\(342\) −0.00859800 1.59499i −0.000464927 0.0862469i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) −1.80990 + 1.80990i −0.0975832 + 0.0975832i
\(345\) 6.45165 0.0173892i 0.347345 0.000936201i
\(346\) 2.65597 2.65597i 0.142786 0.142786i
\(347\) 15.9489i 0.856182i −0.903736 0.428091i \(-0.859186\pi\)
0.903736 0.428091i \(-0.140814\pi\)
\(348\) 6.35892 + 6.32473i 0.340874 + 0.339041i
\(349\) 0.619415 0.619415i 0.0331565 0.0331565i −0.690334 0.723491i \(-0.742536\pi\)
0.723491 + 0.690334i \(0.242536\pi\)
\(350\) 0.967497 0.0517149
\(351\) 11.0641 + 15.1191i 0.590558 + 0.806995i
\(352\) 7.95604 0.424058
\(353\) 1.55571 1.55571i 0.0828023 0.0828023i −0.664493 0.747295i \(-0.731352\pi\)
0.747295 + 0.664493i \(0.231352\pi\)
\(354\) −2.27041 2.25821i −0.120671 0.120022i
\(355\) 7.82025i 0.415056i
\(356\) −16.7012 + 16.7012i −0.885161 + 0.885161i
\(357\) 12.1178 0.0326612i 0.641342 0.00172861i
\(358\) −1.69123 + 1.69123i −0.0893843 + 0.0893843i
\(359\) 14.1096 + 14.1096i 0.744678 + 0.744678i 0.973474 0.228796i \(-0.0734790\pi\)
−0.228796 + 0.973474i \(0.573479\pi\)
\(360\) −0.00930717 1.72654i −0.000490531 0.0909966i
\(361\) 12.7902i 0.673166i
\(362\) 3.48871 + 3.48871i 0.183363 + 0.183363i
\(363\) −0.895400 + 0.900240i −0.0469963 + 0.0472503i
\(364\) 5.72034 4.11553i 0.299827 0.215712i
\(365\) 5.98665i 0.313356i
\(366\) −3.45217 + 0.00930464i −0.180448 + 0.000486361i
\(367\) −5.46456 −0.285248 −0.142624 0.989777i \(-0.545554\pi\)
−0.142624 + 0.989777i \(0.545554\pi\)
\(368\) 20.3623 1.06146
\(369\) 8.01723 + 7.93125i 0.417360 + 0.412885i
\(370\) 0.0283646 + 0.0283646i 0.00147461 + 0.00147461i
\(371\) 4.60142 + 4.60142i 0.238894 + 0.238894i
\(372\) 11.9065 0.0320918i 0.617326 0.00166388i
\(373\) −20.5478 −1.06393 −0.531963 0.846767i \(-0.678546\pi\)
−0.531963 + 0.846767i \(0.678546\pi\)
\(374\) −4.78285 −0.247315
\(375\) −0.0303630 11.2651i −0.00156794 0.581729i
\(376\) 9.18460i 0.473659i
\(377\) −9.42770 1.53822i −0.485551 0.0792222i
\(378\) −0.790227 0.777550i −0.0406449 0.0399929i
\(379\) 17.0497 + 17.0497i 0.875786 + 0.875786i 0.993095 0.117309i \(-0.0374269\pi\)
−0.117309 + 0.993095i \(0.537427\pi\)
\(380\) 3.32232i 0.170432i
\(381\) −8.67007 + 8.71694i −0.444181 + 0.446582i
\(382\) −1.52757 1.52757i −0.0781572 0.0781572i
\(383\) 20.0335 20.0335i 1.02366 1.02366i 0.0239518 0.999713i \(-0.492375\pi\)
0.999713 0.0239518i \(-0.00762484\pi\)
\(384\) −0.0300838 11.1616i −0.00153521 0.569586i
\(385\) −1.54552 + 1.54552i −0.0787672 + 0.0787672i
\(386\) 2.83857i 0.144479i
\(387\) 9.10109 0.0490607i 0.462634 0.00249390i
\(388\) −15.4060 + 15.4060i −0.782122 + 0.782122i
\(389\) 4.65272 0.235902 0.117951 0.993019i \(-0.462367\pi\)
0.117951 + 0.993019i \(0.462367\pi\)
\(390\) 0.532782 + 0.736341i 0.0269785 + 0.0372861i
\(391\) −38.2037 −1.93205
\(392\) −0.596590 + 0.596590i −0.0301324 + 0.0301324i
\(393\) −0.656299 + 0.659846i −0.0331059 + 0.0332848i
\(394\) 5.41961i 0.273036i
\(395\) 1.91379 1.91379i 0.0962933 0.0962933i
\(396\) −13.3563 13.2131i −0.671180 0.663982i
\(397\) −18.4669 + 18.4669i −0.926827 + 0.926827i −0.997500 0.0706727i \(-0.977485\pi\)
0.0706727 + 0.997500i \(0.477485\pi\)
\(398\) 2.44300 + 2.44300i 0.122456 + 0.122456i
\(399\) 3.06022 + 3.04377i 0.153203 + 0.152379i
\(400\) 16.9096i 0.845482i
\(401\) −8.87467 8.87467i −0.443180 0.443180i 0.449899 0.893079i \(-0.351460\pi\)
−0.893079 + 0.449899i \(0.851460\pi\)
\(402\) 2.15459 + 2.14300i 0.107461 + 0.106883i
\(403\) −10.2940 + 7.40611i −0.512783 + 0.368924i
\(404\) 8.40167i 0.417998i
\(405\) −4.29403 + 4.38763i −0.213372 + 0.218023i
\(406\) 0.565250 0.0280529
\(407\) 0.883161 0.0437767
\(408\) 0.0275564 + 10.2239i 0.00136425 + 0.506157i
\(409\) −4.25749 4.25749i −0.210519 0.210519i 0.593969 0.804488i \(-0.297560\pi\)
−0.804488 + 0.593969i \(0.797560\pi\)
\(410\) 0.386854 + 0.386854i 0.0191053 + 0.0191053i
\(411\) −0.00544328 2.01954i −0.000268497 0.0996167i
\(412\) 5.26338 0.259308
\(413\) 8.66543 0.426398
\(414\) 2.48472 + 2.45808i 0.122117 + 0.120808i
\(415\) 9.03448i 0.443485i
\(416\) 5.22843 + 7.26721i 0.256345 + 0.356304i
\(417\) 13.5251 + 13.4523i 0.662325 + 0.658764i
\(418\) −1.20461 1.20461i −0.0589195 0.0589195i
\(419\) 20.5965i 1.00620i 0.864227 + 0.503102i \(0.167808\pi\)
−0.864227 + 0.503102i \(0.832192\pi\)
\(420\) 1.63725 + 1.62845i 0.0798896 + 0.0794601i
\(421\) −4.61599 4.61599i −0.224970 0.224970i 0.585618 0.810587i \(-0.300852\pi\)
−0.810587 + 0.585618i \(0.800852\pi\)
\(422\) 0.0233877 0.0233877i 0.00113850 0.00113850i
\(423\) 22.9679 23.2169i 1.11674 1.12884i
\(424\) −3.88225 + 3.88225i −0.188539 + 0.188539i
\(425\) 31.7258i 1.53893i
\(426\) −2.98761 + 3.00376i −0.144750 + 0.145532i
\(427\) 6.60566 6.60566i 0.319670 0.319670i
\(428\) 28.7041 1.38746
\(429\) 19.7577 + 3.16901i 0.953912 + 0.153001i
\(430\) 0.441520 0.0212920
\(431\) −22.9077 + 22.9077i −1.10342 + 1.10342i −0.109430 + 0.993995i \(0.534902\pi\)
−0.993995 + 0.109430i \(0.965098\pi\)
\(432\) −13.5898 + 13.8114i −0.653840 + 0.664500i
\(433\) 14.5183i 0.697703i −0.937178 0.348852i \(-0.886572\pi\)
0.937178 0.348852i \(-0.113428\pi\)
\(434\) 0.530618 0.530618i 0.0254705 0.0254705i
\(435\) −0.00843677 3.13018i −0.000404512 0.150080i
\(436\) −28.4076 + 28.4076i −1.36048 + 1.36048i
\(437\) −9.62202 9.62202i −0.460284 0.460284i
\(438\) 2.28711 2.29947i 0.109282 0.109873i
\(439\) 31.6097i 1.50865i 0.656502 + 0.754324i \(0.272035\pi\)
−0.656502 + 0.754324i \(0.727965\pi\)
\(440\) −1.30397 1.30397i −0.0621642 0.0621642i
\(441\) 2.99996 0.0161717i 0.142855 0.000770081i
\(442\) −3.14312 4.36875i −0.149503 0.207800i
\(443\) 28.5097i 1.35454i −0.735737 0.677268i \(-0.763164\pi\)
0.735737 0.677268i \(-0.236836\pi\)
\(444\) −0.00251488 0.933061i −0.000119351 0.0442811i
\(445\) 8.24331 0.390770
\(446\) 0.388461 0.0183942
\(447\) −21.1989 + 0.0571375i −1.00267 + 0.00270251i
\(448\) 4.89894 + 4.89894i 0.231453 + 0.231453i
\(449\) −23.0757 23.0757i −1.08901 1.08901i −0.995631 0.0933780i \(-0.970233\pi\)
−0.0933780 0.995631i \(-0.529767\pi\)
\(450\) 2.04128 2.06340i 0.0962267 0.0972698i
\(451\) 12.0451 0.567181
\(452\) −24.8285 −1.16783
\(453\) 4.84960 0.0130711i 0.227854 0.000614136i
\(454\) 3.08870i 0.144960i
\(455\) −2.42738 0.396049i −0.113797 0.0185671i
\(456\) −2.56805 + 2.58193i −0.120260 + 0.120910i
\(457\) 27.8568 + 27.8568i 1.30309 + 1.30309i 0.926300 + 0.376787i \(0.122971\pi\)
0.376787 + 0.926300i \(0.377029\pi\)
\(458\) 4.77298i 0.223027i
\(459\) 25.4971 25.9129i 1.19010 1.20951i
\(460\) −5.14787 5.14787i −0.240021 0.240021i
\(461\) 3.24146 3.24146i 0.150970 0.150970i −0.627581 0.778551i \(-0.715955\pi\)
0.778551 + 0.627581i \(0.215955\pi\)
\(462\) −1.18408 + 0.00319146i −0.0550884 + 0.000148480i
\(463\) −20.4120 + 20.4120i −0.948624 + 0.948624i −0.998743 0.0501194i \(-0.984040\pi\)
0.0501194 + 0.998743i \(0.484040\pi\)
\(464\) 9.87929i 0.458635i
\(465\) −2.94631 2.93047i −0.136632 0.135898i
\(466\) 3.98088 3.98088i 0.184411 0.184411i
\(467\) 22.0340 1.01961 0.509806 0.860289i \(-0.329717\pi\)
0.509806 + 0.860289i \(0.329717\pi\)
\(468\) 3.29180 20.8831i 0.152164 0.965321i
\(469\) −8.22336 −0.379719
\(470\) 1.12028 1.12028i 0.0516746 0.0516746i
\(471\) −4.14214 4.11988i −0.190860 0.189834i
\(472\) 7.31107i 0.336519i
\(473\) 6.87359 6.87359i 0.316048 0.316048i
\(474\) 1.46622 0.00395191i 0.0673458 0.000181517i
\(475\) −7.99048 + 7.99048i −0.366628 + 0.366628i
\(476\) −9.66899 9.66899i −0.443177 0.443177i
\(477\) 19.5219 0.105236i 0.893847 0.00481841i
\(478\) 0.595731i 0.0272481i
\(479\) −25.6102 25.6102i −1.17016 1.17016i −0.982171 0.187989i \(-0.939803\pi\)
−0.187989 0.982171i \(-0.560197\pi\)
\(480\) −2.06880 + 2.07999i −0.0944275 + 0.0949379i
\(481\) 0.580382 + 0.806697i 0.0264631 + 0.0367822i
\(482\) 0.521696i 0.0237626i
\(483\) −9.45802 + 0.0254922i −0.430355 + 0.00115994i
\(484\) 1.43277 0.0651259
\(485\) 7.60405 0.345282
\(486\) −3.32556 + 0.0448196i −0.150851 + 0.00203306i
\(487\) −4.86196 4.86196i −0.220317 0.220317i 0.588315 0.808632i \(-0.299791\pi\)
−0.808632 + 0.588315i \(0.799791\pi\)
\(488\) 5.57323 + 5.57323i 0.252288 + 0.252288i
\(489\) −21.9151 + 0.0590680i −0.991037 + 0.00267115i
\(490\) 0.145537 0.00657468
\(491\) 2.14655 0.0968722 0.0484361 0.998826i \(-0.484576\pi\)
0.0484361 + 0.998826i \(0.484576\pi\)
\(492\) −0.0342995 12.7256i −0.00154634 0.573716i
\(493\) 18.5355i 0.834796i
\(494\) 0.308688 1.89194i 0.0138885 0.0851226i
\(495\) 0.0353465 + 6.55701i 0.00158871 + 0.294716i
\(496\) −9.27400 9.27400i −0.416415 0.416415i
\(497\) 11.4644i 0.514247i
\(498\) 3.45148 3.47014i 0.154665 0.155501i
\(499\) −8.53774 8.53774i −0.382202 0.382202i 0.489693 0.871895i \(-0.337109\pi\)
−0.871895 + 0.489693i \(0.837109\pi\)
\(500\) −8.98863 + 8.98863i −0.401984 + 0.401984i
\(501\) −0.0335672 12.4539i −0.00149967 0.556401i
\(502\) 3.92807 3.92807i 0.175319 0.175319i
\(503\) 21.0850i 0.940132i 0.882631 + 0.470066i \(0.155770\pi\)
−0.882631 + 0.470066i \(0.844230\pi\)
\(504\) 0.0136442 + 2.53108i 0.000607759 + 0.112743i
\(505\) 2.07343 2.07343i 0.0922665 0.0922665i
\(506\) 3.73304 0.165954
\(507\) 10.0894 + 20.1297i 0.448088 + 0.893990i
\(508\) 13.8734 0.615531
\(509\) −2.38009 + 2.38009i −0.105496 + 0.105496i −0.757884 0.652389i \(-0.773767\pi\)
0.652389 + 0.757884i \(0.273767\pi\)
\(510\) 1.24368 1.25040i 0.0550711 0.0553688i
\(511\) 8.77634i 0.388242i
\(512\) −10.9964 + 10.9964i −0.485977 + 0.485977i
\(513\) 12.9482 0.104700i 0.571675 0.00462260i
\(514\) −0.414888 + 0.414888i −0.0182999 + 0.0182999i
\(515\) −1.29894 1.29894i −0.0572382 0.0572382i
\(516\) −7.28153 7.24238i −0.320551 0.318828i
\(517\) 34.8810i 1.53407i
\(518\) −0.0415821 0.0415821i −0.00182701 0.00182701i
\(519\) 21.6197 + 21.5035i 0.949000 + 0.943898i
\(520\) 0.334149 2.04799i 0.0146534 0.0898104i
\(521\) 0.110256i 0.00483042i −0.999997 0.00241521i \(-0.999231\pi\)
0.999997 0.00241521i \(-0.000768787\pi\)
\(522\) 1.19260 1.20552i 0.0521985 0.0527643i
\(523\) −0.172813 −0.00755658 −0.00377829 0.999993i \(-0.501203\pi\)
−0.00377829 + 0.999993i \(0.501203\pi\)
\(524\) 1.05017 0.0458770
\(525\) 0.0211697 + 7.85429i 0.000923921 + 0.342789i
\(526\) 0.382023 + 0.382023i 0.0166570 + 0.0166570i
\(527\) 17.3998 + 17.3998i 0.757949 + 0.757949i
\(528\) 0.0557794 + 20.6950i 0.00242749 + 0.900636i
\(529\) 6.81824 0.296445
\(530\) 0.947065 0.0411379
\(531\) 18.2828 18.4810i 0.793406 0.802006i
\(532\) 4.87047i 0.211162i
\(533\) 7.91560 + 11.0022i 0.342863 + 0.476559i
\(534\) 3.16625 + 3.14923i 0.137017 + 0.136281i
\(535\) −7.08383 7.08383i −0.306261 0.306261i
\(536\) 6.93809i 0.299680i
\(537\) −13.7667 13.6927i −0.594076 0.590882i
\(538\) 3.22872 + 3.22872i 0.139200 + 0.139200i
\(539\) 2.26572 2.26572i 0.0975913 0.0975913i
\(540\) 6.92739 0.0560153i 0.298107 0.00241052i
\(541\) 19.0795 19.0795i 0.820292 0.820292i −0.165858 0.986150i \(-0.553039\pi\)
0.986150 + 0.165858i \(0.0530393\pi\)
\(542\) 0.376920i 0.0161901i
\(543\) −28.2456 + 28.3982i −1.21213 + 1.21869i
\(544\) 12.2836 12.2836i 0.526656 0.526656i
\(545\) 14.0213 0.600607
\(546\) −0.781051 1.07947i −0.0334259 0.0461968i
\(547\) 6.64711 0.284210 0.142105 0.989852i \(-0.454613\pi\)
0.142105 + 0.989852i \(0.454613\pi\)
\(548\) −1.61143 + 1.61143i −0.0688367 + 0.0688367i
\(549\) −0.151073 28.0250i −0.00644764 1.19608i
\(550\) 3.10006i 0.132187i
\(551\) −4.66836 + 4.66836i −0.198879 + 0.198879i
\(552\) −0.0215079 7.97978i −0.000915439 0.339642i
\(553\) −2.80559 + 2.80559i −0.119306 + 0.119306i
\(554\) −1.96143 1.96143i −0.0833333 0.0833333i
\(555\) −0.229648 + 0.230889i −0.00974800 + 0.00980069i
\(556\) 21.5257i 0.912893i
\(557\) −0.645771 0.645771i −0.0273622 0.0273622i 0.693293 0.720656i \(-0.256159\pi\)
−0.720656 + 0.693293i \(0.756159\pi\)
\(558\) −0.0121354 2.25119i −0.000513731 0.0953005i
\(559\) 10.7956 + 1.76139i 0.456603 + 0.0744991i
\(560\) 2.54365i 0.107489i
\(561\) −0.104653 38.8279i −0.00441846 1.63932i
\(562\) −2.52371 −0.106456
\(563\) −1.44022 −0.0606979 −0.0303489 0.999539i \(-0.509662\pi\)
−0.0303489 + 0.999539i \(0.509662\pi\)
\(564\) −36.8518 + 0.0993269i −1.55174 + 0.00418242i
\(565\) 6.12738 + 6.12738i 0.257781 + 0.257781i
\(566\) 1.49518 + 1.49518i 0.0628473 + 0.0628473i
\(567\) 6.29498 6.43220i 0.264364 0.270127i
\(568\) 9.67255 0.405851
\(569\) 7.58332 0.317909 0.158955 0.987286i \(-0.449188\pi\)
0.158955 + 0.987286i \(0.449188\pi\)
\(570\) 0.628162 0.00169309i 0.0263108 7.09156e-5i
\(571\) 21.6013i 0.903987i 0.892021 + 0.451993i \(0.149287\pi\)
−0.892021 + 0.451993i \(0.850713\pi\)
\(572\) −13.1870 18.3291i −0.551376 0.766380i
\(573\) 12.3676 12.4345i 0.516664 0.519457i
\(574\) −0.567121 0.567121i −0.0236712 0.0236712i
\(575\) 24.7622i 1.03265i
\(576\) 20.7841 0.112040i 0.866005 0.00466833i
\(577\) −8.06019 8.06019i −0.335550 0.335550i 0.519139 0.854690i \(-0.326253\pi\)
−0.854690 + 0.519139i \(0.826253\pi\)
\(578\) −4.81973 + 4.81973i −0.200474 + 0.200474i
\(579\) 23.0439 0.0621104i 0.957674 0.00258122i
\(580\) −2.49762 + 2.49762i −0.103708 + 0.103708i
\(581\) 13.2444i 0.549470i
\(582\) 2.92071 + 2.90501i 0.121067 + 0.120417i
\(583\) 14.7439 14.7439i 0.610630 0.610630i
\(584\) −7.40465 −0.306407
\(585\) −5.96608 + 4.34132i −0.246667 + 0.179492i
\(586\) 1.63882 0.0676989
\(587\) −9.37281 + 9.37281i −0.386857 + 0.386857i −0.873565 0.486708i \(-0.838198\pi\)
0.486708 + 0.873565i \(0.338198\pi\)
\(588\) −2.40018 2.38728i −0.0989819 0.0984497i
\(589\) 8.76467i 0.361142i
\(590\) 0.891759 0.891759i 0.0367131 0.0367131i
\(591\) −43.9973 + 0.118586i −1.80981 + 0.00487798i
\(592\) −0.726760 + 0.726760i −0.0298697 + 0.0298697i
\(593\) −33.7433 33.7433i −1.38567 1.38567i −0.834183 0.551487i \(-0.814060\pi\)
−0.551487 0.834183i \(-0.685940\pi\)
\(594\) −2.49143 + 2.53205i −0.102225 + 0.103891i
\(595\) 4.77239i 0.195649i
\(596\) 16.9150 + 16.9150i 0.692864 + 0.692864i
\(597\) −19.7792 + 19.8861i −0.809508 + 0.813883i
\(598\) 2.45322 + 3.40984i 0.100320 + 0.139439i
\(599\) 14.5774i 0.595617i 0.954626 + 0.297809i \(0.0962557\pi\)
−0.954626 + 0.297809i \(0.903744\pi\)
\(600\) −6.62671 + 0.0178610i −0.270534 + 0.000729172i
\(601\) −2.77235 −0.113087 −0.0565433 0.998400i \(-0.518008\pi\)
−0.0565433 + 0.998400i \(0.518008\pi\)
\(602\) −0.647262 −0.0263804
\(603\) −17.3501 + 17.5382i −0.706550 + 0.714209i
\(604\) −3.86957 3.86957i −0.157451 0.157451i
\(605\) −0.353591 0.353591i −0.0143755 0.0143755i
\(606\) 1.58853 0.00428157i 0.0645295 0.000173927i
\(607\) −12.2679 −0.497940 −0.248970 0.968511i \(-0.580092\pi\)
−0.248970 + 0.968511i \(0.580092\pi\)
\(608\) 6.18752 0.250937
\(609\) 0.0123682 + 4.58879i 0.000501184 + 0.185947i
\(610\) 1.35958i 0.0550476i
\(611\) 31.8610 22.9226i 1.28896 0.927348i
\(612\) −41.0215 + 0.221132i −1.65819 + 0.00893874i
\(613\) −10.5026 10.5026i −0.424195 0.424195i 0.462450 0.886645i \(-0.346970\pi\)
−0.886645 + 0.462450i \(0.846970\pi\)
\(614\) 4.32781i 0.174656i
\(615\) −3.13207 + 3.14900i −0.126297 + 0.126980i
\(616\) 1.91160 + 1.91160i 0.0770204 + 0.0770204i
\(617\) −27.8456 + 27.8456i −1.12102 + 1.12102i −0.129435 + 0.991588i \(0.541316\pi\)
−0.991588 + 0.129435i \(0.958684\pi\)
\(618\) −0.00268227 0.995163i −0.000107897 0.0400313i
\(619\) 12.4038 12.4038i 0.498549 0.498549i −0.412437 0.910986i \(-0.635322\pi\)
0.910986 + 0.412437i \(0.135322\pi\)
\(620\) 4.68918i 0.188322i
\(621\) −19.9007 + 20.2251i −0.798586 + 0.811607i
\(622\) −1.67012 + 1.67012i −0.0669658 + 0.0669658i
\(623\) −12.0846 −0.484158
\(624\) −18.8666 + 13.6510i −0.755268 + 0.546477i
\(625\) −18.2369 −0.729475
\(626\) −0.185882 + 0.185882i −0.00742932 + 0.00742932i
\(627\) 9.75287 9.80558i 0.389492 0.391597i
\(628\) 6.59240i 0.263065i
\(629\) 1.36355 1.36355i 0.0543681 0.0543681i
\(630\) 0.307061 0.310390i 0.0122336 0.0123662i
\(631\) 18.3687 18.3687i 0.731245 0.731245i −0.239621 0.970867i \(-0.577023\pi\)
0.970867 + 0.239621i \(0.0770232\pi\)
\(632\) −2.36709 2.36709i −0.0941578 0.0941578i
\(633\) 0.190377 + 0.189353i 0.00756680 + 0.00752612i
\(634\) 1.95231i 0.0775360i
\(635\) −3.42379 3.42379i −0.135869 0.135869i
\(636\) −15.6189 15.5350i −0.619331 0.616002i
\(637\) 3.55850 + 0.580602i 0.140993 + 0.0230043i
\(638\) 1.81118i 0.0717052i
\(639\) −24.4503 24.1881i −0.967240 0.956868i
\(640\) 4.39578 0.173759
\(641\) −2.15928 −0.0852865 −0.0426432 0.999090i \(-0.513578\pi\)
−0.0426432 + 0.999090i \(0.513578\pi\)
\(642\) −0.0146279 5.42717i −0.000577316 0.214193i
\(643\) 15.1851 + 15.1851i 0.598841 + 0.598841i 0.940004 0.341163i \(-0.110821\pi\)
−0.341163 + 0.940004i \(0.610821\pi\)
\(644\) 7.54670 + 7.54670i 0.297382 + 0.297382i
\(645\) 0.00966086 + 3.58433i 0.000380396 + 0.141133i
\(646\) −3.71969 −0.146349
\(647\) −4.76357 −0.187275 −0.0936377 0.995606i \(-0.529850\pi\)
−0.0936377 + 0.995606i \(0.529850\pi\)
\(648\) 5.42689 + 5.31111i 0.213188 + 0.208640i
\(649\) 27.7658i 1.08990i
\(650\) 2.83165 2.03725i 0.111067 0.0799074i
\(651\) 4.31925 + 4.29603i 0.169285 + 0.168375i
\(652\) 17.4864 + 17.4864i 0.684822 + 0.684822i
\(653\) 15.2734i 0.597694i −0.954301 0.298847i \(-0.903398\pi\)
0.954301 0.298847i \(-0.0966021\pi\)
\(654\) 5.38558 + 5.35663i 0.210593 + 0.209461i
\(655\) −0.259170 0.259170i −0.0101266 0.0101266i
\(656\) −9.91200 + 9.91200i −0.386998 + 0.386998i
\(657\) 18.7175 + 18.5168i 0.730240 + 0.722409i
\(658\) −1.64231 + 1.64231i −0.0640240 + 0.0640240i
\(659\) 42.9450i 1.67290i −0.548043 0.836450i \(-0.684627\pi\)
0.548043 0.836450i \(-0.315373\pi\)
\(660\) 5.21788 5.24608i 0.203106 0.204204i
\(661\) 15.7811 15.7811i 0.613815 0.613815i −0.330123 0.943938i \(-0.607090\pi\)
0.943938 + 0.330123i \(0.107090\pi\)
\(662\) −5.65762 −0.219890
\(663\) 35.3974 25.6119i 1.37472 0.994685i
\(664\) −11.1744 −0.433650
\(665\) −1.20198 + 1.20198i −0.0466106 + 0.0466106i
\(666\) −0.176415 0.000950992i −0.00683595 3.68502e-5i
\(667\) 14.4671i 0.560166i
\(668\) −9.93720 + 9.93720i −0.384482 + 0.384482i
\(669\) 0.00849988 + 3.15359i 0.000328624 + 0.121925i
\(670\) −0.846265 + 0.846265i −0.0326941 + 0.0326941i
\(671\) −21.1659 21.1659i −0.817100 0.817100i
\(672\) 3.03283 3.04923i 0.116994 0.117626i
\(673\) 50.2096i 1.93544i −0.252032 0.967719i \(-0.581099\pi\)
0.252032 0.967719i \(-0.418901\pi\)
\(674\) −5.12192 5.12192i −0.197289 0.197289i
\(675\) 16.7957 + 16.5263i 0.646467 + 0.636096i
\(676\) 8.07618 24.0905i 0.310622 0.926559i
\(677\) 33.4956i 1.28734i 0.765303 + 0.643671i \(0.222589\pi\)
−0.765303 + 0.643671i \(0.777411\pi\)
\(678\) 0.0126528 + 4.69440i 0.000485929 + 0.180287i
\(679\) −11.1474 −0.427799
\(680\) −4.02649 −0.154409
\(681\) 25.0745 0.0675834i 0.960857 0.00258980i
\(682\) −1.70021 1.70021i −0.0651044 0.0651044i
\(683\) −1.55629 1.55629i −0.0595499 0.0595499i 0.676705 0.736255i \(-0.263407\pi\)
−0.736255 + 0.676705i \(0.763407\pi\)
\(684\) −10.3874 10.2760i −0.397171 0.392912i
\(685\) 0.795361 0.0303892
\(686\) −0.213354 −0.00814591
\(687\) −38.7478 + 0.104437i −1.47832 + 0.00398452i
\(688\) 11.3127i 0.431291i
\(689\) 23.1566 + 3.77821i 0.882194 + 0.143938i
\(690\) −0.970701 + 0.975947i −0.0369539 + 0.0371537i
\(691\) 14.7515 + 14.7515i 0.561172 + 0.561172i 0.929640 0.368469i \(-0.120118\pi\)
−0.368469 + 0.929640i \(0.620118\pi\)
\(692\) 34.4087i 1.30802i
\(693\) −0.0518175 9.61248i −0.00196838 0.365148i
\(694\) 2.40612 + 2.40612i 0.0913351 + 0.0913351i
\(695\) −5.31229 + 5.31229i −0.201507 + 0.201507i
\(696\) −3.87159 + 0.0104351i −0.146752 + 0.000395542i
\(697\) 18.5968 18.5968i 0.704406 0.704406i
\(698\) 0.186895i 0.00707409i
\(699\) 32.4045 + 32.2303i 1.22565 + 1.21906i
\(700\) 6.26706 6.26706i 0.236873 0.236873i
\(701\) 33.6849 1.27226 0.636130 0.771582i \(-0.280534\pi\)
0.636130 + 0.771582i \(0.280534\pi\)
\(702\) −3.95010 0.611748i −0.149087 0.0230890i
\(703\) 0.686846 0.0259049
\(704\) 15.6972 15.6972i 0.591610 0.591610i
\(705\) 9.11912 + 9.07009i 0.343446 + 0.341599i
\(706\) 0.469403i 0.0176662i
\(707\) −3.03962 + 3.03962i −0.114317 + 0.114317i
\(708\) −29.3346 + 0.0790657i −1.10246 + 0.00297147i
\(709\) −8.52119 + 8.52119i −0.320020 + 0.320020i −0.848775 0.528755i \(-0.822659\pi\)
0.528755 + 0.848775i \(0.322659\pi\)
\(710\) −1.17980 1.17980i −0.0442770 0.0442770i
\(711\) 0.0641645 + 11.9029i 0.00240636 + 0.446395i
\(712\) 10.1958i 0.382105i
\(713\) −13.5807 13.5807i −0.508600 0.508600i
\(714\) −1.82322 + 1.83307i −0.0682322 + 0.0686010i
\(715\) −1.26902 + 7.77781i −0.0474588 + 0.290874i
\(716\) 21.9102i 0.818824i
\(717\) 4.83623 0.0130351i 0.180612 0.000486806i
\(718\) −4.25728 −0.158880
\(719\) 6.61231 0.246598 0.123299 0.992370i \(-0.460653\pi\)
0.123299 + 0.992370i \(0.460653\pi\)
\(720\) −5.42491 5.36673i −0.202174 0.200006i
\(721\) 1.90423 + 1.90423i 0.0709171 + 0.0709171i
\(722\) 1.92958 + 1.92958i 0.0718115 + 0.0718115i
\(723\) −4.23521 + 0.0114152i −0.157509 + 0.000424535i
\(724\) 45.1970 1.67973
\(725\) −12.0140 −0.446188
\(726\) −0.000730152 0.270898i −2.70985e−5 0.0100540i
\(727\) 13.3668i 0.495748i 0.968792 + 0.247874i \(0.0797319\pi\)
−0.968792 + 0.247874i \(0.920268\pi\)
\(728\) −0.489857 + 3.00232i −0.0181553 + 0.111274i
\(729\) −0.436619 26.9965i −0.0161711 0.999869i
\(730\) 0.903173 + 0.903173i 0.0334279 + 0.0334279i
\(731\) 21.2248i 0.785027i
\(732\) −22.3015 + 22.4221i −0.824288 + 0.828743i
\(733\) −35.9949 35.9949i −1.32950 1.32950i −0.905802 0.423702i \(-0.860730\pi\)
−0.423702 0.905802i \(-0.639270\pi\)
\(734\) 0.824407 0.824407i 0.0304294 0.0304294i
\(735\) 0.00318447 + 1.18149i 0.000117461 + 0.0435799i
\(736\) −9.58744 + 9.58744i −0.353398 + 0.353398i
\(737\) 26.3493i 0.970590i
\(738\) −2.40606 + 0.0129702i −0.0885682 + 0.000477440i
\(739\) −18.9168 + 18.9168i −0.695865 + 0.695865i −0.963516 0.267651i \(-0.913753\pi\)
0.267651 + 0.963516i \(0.413753\pi\)
\(740\) 0.367470 0.0135085
\(741\) 15.3659 + 2.46458i 0.564479 + 0.0905387i
\(742\) −1.38838 −0.0509691
\(743\) −10.9283 + 10.9283i −0.400922 + 0.400922i −0.878558 0.477636i \(-0.841494\pi\)
0.477636 + 0.878558i \(0.341494\pi\)
\(744\) −3.62459 + 3.64418i −0.132884 + 0.133602i
\(745\) 8.34883i 0.305877i
\(746\) 3.09994 3.09994i 0.113497 0.113497i
\(747\) 28.2467 + 27.9438i 1.03349 + 1.02241i
\(748\) −30.9814 + 30.9814i −1.13279 + 1.13279i
\(749\) 10.3848 + 10.3848i 0.379452 + 0.379452i
\(750\) 1.70409 + 1.69493i 0.0622245 + 0.0618900i
\(751\) 31.7550i 1.15876i 0.815059 + 0.579378i \(0.196704\pi\)
−0.815059 + 0.579378i \(0.803296\pi\)
\(752\) 28.7039 + 28.7039i 1.04672 + 1.04672i
\(753\) 31.9747 + 31.8028i 1.16522 + 1.15896i
\(754\) 1.65437 1.19024i 0.0602484 0.0433460i
\(755\) 1.90993i 0.0695094i
\(756\) −10.1554 + 0.0821176i −0.369350 + 0.00298659i
\(757\) 48.8723 1.77629 0.888147 0.459559i \(-0.151993\pi\)
0.888147 + 0.459559i \(0.151993\pi\)
\(758\) −5.14440 −0.186853
\(759\) 0.0816823 + 30.3054i 0.00296488 + 1.10002i
\(760\) −1.01411 1.01411i −0.0367858 0.0367858i
\(761\) −10.2908 10.2908i −0.373041 0.373041i 0.495543 0.868583i \(-0.334969\pi\)
−0.868583 + 0.495543i \(0.834969\pi\)
\(762\) −0.00707000 2.62308i −0.000256119 0.0950242i
\(763\) −20.5550 −0.744142
\(764\) −19.7900 −0.715976
\(765\) 10.1782 + 10.0690i 0.367993 + 0.364047i
\(766\) 6.04469i 0.218403i
\(767\) 25.3618 18.2467i 0.915763 0.658850i
\(768\) −15.3277 15.2453i −0.553090 0.550116i
\(769\) −8.68174 8.68174i −0.313072 0.313072i 0.533027 0.846098i \(-0.321054\pi\)
−0.846098 + 0.533027i \(0.821054\pi\)
\(770\) 0.466329i 0.0168053i
\(771\) −3.37720 3.35905i −0.121627 0.120973i
\(772\) −18.3871 18.3871i −0.661767 0.661767i
\(773\) −1.81881 + 1.81881i −0.0654181 + 0.0654181i −0.739059 0.673641i \(-0.764729\pi\)
0.673641 + 0.739059i \(0.264729\pi\)
\(774\) −1.36563 + 1.38043i −0.0490865 + 0.0496186i
\(775\) −11.2779 + 11.2779i −0.405114 + 0.405114i
\(776\) 9.40514i 0.337625i
\(777\) 0.336660 0.338480i 0.0120776 0.0121429i
\(778\) −0.701930 + 0.701930i −0.0251654 + 0.0251654i
\(779\) 9.36762 0.335630
\(780\) 8.22088 + 1.31858i 0.294355 + 0.0472126i
\(781\) −36.7342 −1.31445
\(782\) 5.76358 5.76358i 0.206105 0.206105i
\(783\) 9.81272 + 9.65530i 0.350678 + 0.345052i
\(784\) 3.72895i 0.133177i
\(785\) 1.62693 1.62693i 0.0580675 0.0580675i
\(786\) −0.000535178 0.198559i −1.90892e−5 0.00708238i
\(787\) −26.0942 + 26.0942i −0.930158 + 0.930158i −0.997715 0.0675575i \(-0.978479\pi\)
0.0675575 + 0.997715i \(0.478479\pi\)
\(788\) 35.1061 + 35.1061i 1.25060 + 1.25060i
\(789\) −3.09296 + 3.10968i −0.110112 + 0.110708i
\(790\) 0.577446i 0.0205446i
\(791\) −8.98265 8.98265i −0.319386 0.319386i
\(792\) 8.11010 0.0437187i 0.288180 0.00155348i
\(793\) 5.42387 33.2428i 0.192607 1.18049i
\(794\) 5.57199i 0.197743i
\(795\) 0.0207226 + 7.68842i 0.000734956 + 0.272680i
\(796\) 31.6495 1.12179
\(797\) 19.6614 0.696441 0.348220 0.937413i \(-0.386786\pi\)
0.348220 + 0.937413i \(0.386786\pi\)
\(798\) −0.920875 + 0.00248204i −0.0325986 + 8.78632e-5i
\(799\) −53.8541 53.8541i −1.90522 1.90522i
\(800\) 7.96177 + 7.96177i 0.281491 + 0.281491i
\(801\) −25.4967 + 25.7731i −0.900881 + 0.910646i
\(802\) 2.67774 0.0945544
\(803\) 28.1212 0.992375
\(804\) 27.8381 0.0750321i 0.981774 0.00264618i
\(805\) 3.72487i 0.131285i
\(806\) 0.435688 2.67032i 0.0153465 0.0940581i
\(807\) −26.1406 + 26.2819i −0.920192 + 0.925165i
\(808\) −2.56454 2.56454i −0.0902204 0.0902204i
\(809\) 10.3579i 0.364164i 0.983283 + 0.182082i \(0.0582837\pi\)
−0.983283 + 0.182082i \(0.941716\pi\)
\(810\) −0.0141212 1.30975i −0.000496170 0.0460201i
\(811\) 35.4816 + 35.4816i 1.24593 + 1.24593i 0.957503 + 0.288424i \(0.0931313\pi\)
0.288424 + 0.957503i \(0.406869\pi\)
\(812\) 3.66147 3.66147i 0.128492 0.128492i
\(813\) −3.05990 + 0.00824735i −0.107315 + 0.000289247i
\(814\) −0.133238 + 0.133238i −0.00466997 + 0.00466997i
\(815\) 8.63090i 0.302327i
\(816\) 32.0379 + 31.8657i 1.12155 + 1.11552i
\(817\) 5.34569 5.34569i 0.187022 0.187022i
\(818\) 1.28461 0.0449152
\(819\) 8.74617 6.36431i 0.305616 0.222387i
\(820\) 5.01177 0.175019
\(821\) −16.5284 + 16.5284i −0.576846 + 0.576846i −0.934033 0.357187i \(-0.883736\pi\)
0.357187 + 0.934033i \(0.383736\pi\)
\(822\) 0.305498 + 0.303856i 0.0106555 + 0.0105982i
\(823\) 34.7929i 1.21280i −0.795159 0.606401i \(-0.792613\pi\)
0.795159 0.606401i \(-0.207387\pi\)
\(824\) −1.60661 + 1.60661i −0.0559688 + 0.0559688i
\(825\) 25.1667 0.0678320i 0.876194 0.00236161i
\(826\) −1.30730 + 1.30730i −0.0454869 + 0.0454869i
\(827\) 17.9323 + 17.9323i 0.623566 + 0.623566i 0.946441 0.322876i \(-0.104650\pi\)
−0.322876 + 0.946441i \(0.604650\pi\)
\(828\) 32.0175 0.172595i 1.11268 0.00599809i
\(829\) 30.6603i 1.06488i 0.846468 + 0.532439i \(0.178724\pi\)
−0.846468 + 0.532439i \(0.821276\pi\)
\(830\) 1.36298 + 1.36298i 0.0473097 + 0.0473097i
\(831\) 15.8803 15.9661i 0.550882 0.553859i
\(832\) 24.6538 + 4.02249i 0.854716 + 0.139455i
\(833\) 6.99624i 0.242405i
\(834\) −4.06993 + 0.0109697i −0.140930 + 0.000379849i
\(835\) 4.90477 0.169737
\(836\) −15.6060 −0.539745
\(837\) 18.2752 0.147775i 0.631685 0.00510785i
\(838\) −3.10728 3.10728i −0.107339 0.107339i
\(839\) 29.2035 + 29.2035i 1.00822 + 1.00822i 0.999966 + 0.00824984i \(0.00262603\pi\)
0.00824984 + 0.999966i \(0.497374\pi\)
\(840\) −0.996829 + 0.00268676i −0.0343939 + 9.27019e-5i
\(841\) 21.9810 0.757964
\(842\) 1.39278 0.0479982
\(843\) −0.0552210 20.4879i −0.00190191 0.705639i
\(844\) 0.302993i 0.0104294i
\(845\) −7.93837 + 3.95215i −0.273088 + 0.135958i
\(846\) 0.0375601 + 6.96764i 0.00129134 + 0.239552i
\(847\) 0.518358 + 0.518358i 0.0178110 + 0.0178110i
\(848\) 24.2658i 0.833290i
\(849\) −12.1054 + 12.1708i −0.415457 + 0.417702i
\(850\) −4.78629 4.78629i −0.164169 0.164169i
\(851\) −1.06425 + 1.06425i −0.0364822 + 0.0364822i
\(852\) 0.104604 + 38.8097i 0.00358367 + 1.32960i
\(853\) 10.1411 10.1411i 0.347224 0.347224i −0.511851 0.859074i \(-0.671040\pi\)
0.859074 + 0.511851i \(0.171040\pi\)
\(854\) 1.99312i 0.0682031i
\(855\) 0.0274895 + 5.09948i 0.000940120 + 0.174398i
\(856\) −8.76170 + 8.76170i −0.299469 + 0.299469i
\(857\) 21.5730 0.736921 0.368460 0.929643i \(-0.379885\pi\)
0.368460 + 0.929643i \(0.379885\pi\)
\(858\) −3.45883 + 2.50265i −0.118082 + 0.0854389i
\(859\) −25.1184 −0.857030 −0.428515 0.903535i \(-0.640963\pi\)
−0.428515 + 0.903535i \(0.640963\pi\)
\(860\) 2.85999 2.85999i 0.0975250 0.0975250i
\(861\) 4.59157 4.61639i 0.156480 0.157326i
\(862\) 6.91191i 0.235420i
\(863\) −36.9361 + 36.9361i −1.25732 + 1.25732i −0.304950 + 0.952368i \(0.598640\pi\)
−0.952368 + 0.304950i \(0.901360\pi\)
\(864\) −0.104323 12.9016i −0.00354915 0.438922i
\(865\) −8.49166 + 8.49166i −0.288725 + 0.288725i
\(866\) 2.19029 + 2.19029i 0.0744290 + 0.0744290i
\(867\) −39.2328 39.0218i −1.33241 1.32525i
\(868\) 6.87427i 0.233328i
\(869\) 8.98968 + 8.98968i 0.304954 + 0.304954i
\(870\) 0.473505 + 0.470959i 0.0160533 + 0.0159670i
\(871\) −24.0680 + 17.3158i −0.815513 + 0.586725i
\(872\) 17.3424i 0.587288i
\(873\) −23.5194 + 23.7744i −0.796012 + 0.804640i
\(874\) 2.90324 0.0982035
\(875\) −6.50395 −0.219874
\(876\) −0.0800777 29.7101i −0.00270557 1.00381i
\(877\) −9.54564 9.54564i −0.322333 0.322333i 0.527328 0.849662i \(-0.323194\pi\)
−0.849662 + 0.527328i \(0.823194\pi\)
\(878\) −4.76878 4.76878i −0.160938 0.160938i
\(879\) 0.0358588 + 13.3042i 0.00120949 + 0.448738i
\(880\) −8.15038 −0.274749
\(881\) 26.3627 0.888183 0.444092 0.895981i \(-0.353527\pi\)
0.444092 + 0.895981i \(0.353527\pi\)
\(882\) −0.450147 + 0.455026i −0.0151572 + 0.0153215i
\(883\) 41.4709i 1.39561i 0.716289 + 0.697804i \(0.245839\pi\)
−0.716289 + 0.697804i \(0.754161\pi\)
\(884\) −48.6590 7.93916i −1.63658 0.267023i
\(885\) 7.25895 + 7.21992i 0.244007 + 0.242695i
\(886\) 4.30109 + 4.30109i 0.144498 + 0.144498i
\(887\) 0.0464034i 0.00155807i 1.00000 0.000779036i \(0.000247975\pi\)
−1.00000 0.000779036i \(0.999752\pi\)
\(888\) 0.285577 + 0.284042i 0.00958335 + 0.00953183i
\(889\) 5.01922 + 5.01922i 0.168339 + 0.168339i
\(890\) −1.24362 + 1.24362i −0.0416863 + 0.0416863i
\(891\) −20.6101 20.1704i −0.690464 0.675734i
\(892\) 2.51630 2.51630i 0.0842519 0.0842519i
\(893\) 27.1275i 0.907786i
\(894\) 3.18954 3.20678i 0.106674 0.107251i
\(895\) 5.40719 5.40719i 0.180742 0.180742i
\(896\) −6.44415 −0.215284
\(897\) −27.6279 + 19.9903i −0.922469 + 0.667455i
\(898\) 6.96260 0.232345
\(899\) −6.58900 + 6.58900i −0.219755 + 0.219755i
\(900\) −0.143329 26.5885i −0.00477764 0.886283i
\(901\) 45.5273i 1.51674i
\(902\) −1.81717 + 1.81717i −0.0605053 + 0.0605053i
\(903\) −0.0141627 5.25457i −0.000471304 0.174861i
\(904\) 7.57871 7.57871i 0.252064 0.252064i
\(905\) −11.1541 11.1541i −0.370774 0.370774i
\(906\) −0.729659 + 0.733603i −0.0242413 + 0.0243723i
\(907\) 43.4181i 1.44167i −0.693105 0.720836i \(-0.743758\pi\)
0.693105 0.720836i \(-0.256242\pi\)
\(908\) −20.0074 20.0074i −0.663967 0.663967i
\(909\) 0.0695168 + 12.8958i 0.00230573 + 0.427727i
\(910\) 0.425954 0.306455i 0.0141203 0.0101589i
\(911\) 28.1213i 0.931699i 0.884864 + 0.465850i \(0.154251\pi\)
−0.884864 + 0.465850i \(0.845749\pi\)
\(912\) 0.0433804 + 16.0948i 0.00143647 + 0.532952i
\(913\) 42.4378 1.40449
\(914\) −8.40520 −0.278019
\(915\) 11.0373 0.0297487i 0.364880 0.000983463i
\(916\) 30.9175 + 30.9175i 1.02154 + 1.02154i
\(917\) 0.379940 + 0.379940i 0.0125467 + 0.0125467i
\(918\) 0.0627150 + 7.75594i 0.00206990 + 0.255984i
\(919\) −1.38595 −0.0457184 −0.0228592 0.999739i \(-0.507277\pi\)
−0.0228592 + 0.999739i \(0.507277\pi\)
\(920\) 3.14270 0.103612
\(921\) −35.1338 + 0.0946962i −1.15770 + 0.00312035i
\(922\) 0.978041i 0.0322101i
\(923\) −24.1404 33.5537i −0.794591 1.10443i
\(924\) −7.64933 + 7.69068i −0.251645 + 0.253005i
\(925\) 0.883796 + 0.883796i 0.0290590 + 0.0290590i
\(926\) 6.15887i 0.202393i
\(927\) 8.07883 0.0435501i 0.265344 0.00143037i
\(928\) 4.65158 + 4.65158i 0.152696 + 0.152696i
\(929\) 17.0813 17.0813i 0.560420 0.560420i −0.369007 0.929427i \(-0.620302\pi\)
0.929427 + 0.369007i \(0.120302\pi\)
\(930\) 0.886598 0.00238965i 0.0290727 7.83598e-5i
\(931\) 1.76208 1.76208i 0.0577498 0.0577498i
\(932\) 51.5731i 1.68933i
\(933\) −13.5948 13.5218i −0.445075 0.442683i
\(934\) −3.32415 + 3.32415i −0.108769 + 0.108769i
\(935\) 15.2917 0.500092
\(936\) 5.36961 + 7.37920i 0.175511 + 0.241197i
\(937\) −17.1536 −0.560384 −0.280192 0.959944i \(-0.590398\pi\)
−0.280192 + 0.959944i \(0.590398\pi\)
\(938\) 1.24061 1.24061i 0.0405074 0.0405074i
\(939\) −1.51308 1.50495i −0.0493776 0.0491121i
\(940\) 14.5135i 0.473377i
\(941\) 7.59277 7.59277i 0.247517 0.247517i −0.572434 0.819951i \(-0.694001\pi\)
0.819951 + 0.572434i \(0.194001\pi\)
\(942\) 1.24644 0.00335955i 0.0406114 0.000109460i
\(943\) −14.5149 + 14.5149i −0.472672 + 0.472672i
\(944\) 22.8487 + 22.8487i 0.743662 + 0.743662i
\(945\) 2.52651 + 2.48598i 0.0821874 + 0.0808689i
\(946\) 2.07396i 0.0674303i
\(947\) −23.1528 23.1528i −0.752365 0.752365i 0.222555 0.974920i \(-0.428560\pi\)
−0.974920 + 0.222555i \(0.928560\pi\)
\(948\) 9.47201 9.52321i 0.307637 0.309299i
\(949\) 18.4803 + 25.6865i 0.599894 + 0.833818i
\(950\) 2.41096i 0.0782218i
\(951\) −15.8491 + 0.0427182i −0.513943 + 0.00138523i
\(952\) 5.90277 0.191310
\(953\) −39.1269 −1.26744 −0.633722 0.773561i \(-0.718474\pi\)
−0.633722 + 0.773561i \(0.718474\pi\)
\(954\) −2.92928 + 2.96104i −0.0948391 + 0.0958671i
\(955\) 4.88393 + 4.88393i 0.158040 + 0.158040i
\(956\) −3.85891 3.85891i −0.124806 0.124806i
\(957\) 14.7034 0.0396302i 0.475294 0.00128106i
\(958\) 7.72734 0.249659
\(959\) −1.16599 −0.0376517
\(960\) 0.0220625 + 8.18553i 0.000712063 + 0.264187i
\(961\) 18.6294i 0.600948i
\(962\) −0.209261 0.0341428i −0.00674684 0.00110081i
\(963\) 44.0583 0.237503i 1.41976 0.00765341i
\(964\) 3.37934 + 3.37934i 0.108841 + 0.108841i
\(965\) 9.07546i 0.292149i
\(966\) 1.42303 1.43072i 0.0457853 0.0460328i
\(967\) 2.90975 + 2.90975i 0.0935714 + 0.0935714i 0.752343 0.658772i \(-0.228924\pi\)
−0.658772 + 0.752343i \(0.728924\pi\)
\(968\) −0.437342 + 0.437342i −0.0140567 + 0.0140567i
\(969\) −0.0813901 30.1970i −0.00261463 0.970068i
\(970\) −1.14718 + 1.14718i −0.0368337 + 0.0368337i
\(971\) 19.5157i 0.626289i 0.949706 + 0.313144i \(0.101382\pi\)
−0.949706 + 0.313144i \(0.898618\pi\)
\(972\) −21.2514 + 21.8320i −0.681638 + 0.700262i
\(973\) 7.78773 7.78773i 0.249663 0.249663i
\(974\) 1.46699 0.0470055
\(975\) 16.6007 + 22.9432i 0.531646 + 0.734771i
\(976\) 34.8352 1.11505
\(977\) 28.9855 28.9855i 0.927329 0.927329i −0.0702036 0.997533i \(-0.522365\pi\)
0.997533 + 0.0702036i \(0.0223649\pi\)
\(978\) 3.29730 3.31513i 0.105436 0.106006i
\(979\) 38.7214i 1.23754i
\(980\) 0.942729 0.942729i 0.0301144 0.0301144i
\(981\) −43.3681 + 43.8382i −1.38464 + 1.39965i
\(982\) −0.323837 + 0.323837i −0.0103341 + 0.0103341i
\(983\) 36.9089 + 36.9089i 1.17721 + 1.17721i 0.980452 + 0.196759i \(0.0630417\pi\)
0.196759 + 0.980452i \(0.436958\pi\)
\(984\) 3.89487 + 3.87394i 0.124164 + 0.123497i
\(985\) 17.3276i 0.552102i
\(986\) −2.79634 2.79634i −0.0890537 0.0890537i
\(987\) −13.3685 13.2966i −0.425523 0.423236i
\(988\) −10.2557 14.2548i −0.326278 0.453507i
\(989\) 16.5661i 0.526770i
\(990\) −0.994552 0.983887i −0.0316089 0.0312700i
\(991\) 3.59633 0.114241 0.0571206 0.998367i \(-0.481808\pi\)
0.0571206 + 0.998367i \(0.481808\pi\)
\(992\) 8.73318 0.277279
\(993\) −0.123794 45.9295i −0.00392848 1.45753i
\(994\) 1.72956 + 1.72956i 0.0548584 + 0.0548584i
\(995\) −7.81074 7.81074i −0.247617 0.247617i
\(996\) −0.120845 44.8356i −0.00382913 1.42067i
\(997\) −24.3260 −0.770413 −0.385206 0.922830i \(-0.625870\pi\)
−0.385206 + 0.922830i \(0.625870\pi\)
\(998\) 2.57608 0.0815444
\(999\) −0.0115804 1.43215i −0.000366389 0.0453111i
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 273.2.n.c.8.11 48
3.2 odd 2 inner 273.2.n.c.8.14 yes 48
13.5 odd 4 inner 273.2.n.c.239.14 yes 48
39.5 even 4 inner 273.2.n.c.239.11 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.n.c.8.11 48 1.1 even 1 trivial
273.2.n.c.8.14 yes 48 3.2 odd 2 inner
273.2.n.c.239.11 yes 48 39.5 even 4 inner
273.2.n.c.239.14 yes 48 13.5 odd 4 inner