Properties

Label 770.2.l.c.573.12
Level $770$
Weight $2$
Character 770.573
Analytic conductor $6.148$
Analytic rank $0$
Dimension $40$
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] = [770,2,Mod(573,770)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(770, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("770.573");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.l (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: \(6.14848095564\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 573.12
Character \(\chi\) \(=\) 770.573
Dual form 770.2.l.c.727.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.65110 + 1.65110i) q^{3} -1.00000i q^{4} +(2.15340 + 0.602381i) q^{5} +2.33501i q^{6} +(0.00754262 + 2.64574i) q^{7} +(-0.707107 - 0.707107i) q^{8} -2.45228i q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.65110 + 1.65110i) q^{3} -1.00000i q^{4} +(2.15340 + 0.602381i) q^{5} +2.33501i q^{6} +(0.00754262 + 2.64574i) q^{7} +(-0.707107 - 0.707107i) q^{8} -2.45228i q^{9} +(1.94863 - 1.09674i) q^{10} -1.00000 q^{11} +(1.65110 + 1.65110i) q^{12} +(0.174289 - 0.174289i) q^{13} +(1.87615 + 1.86549i) q^{14} +(-4.55008 + 2.56089i) q^{15} -1.00000 q^{16} +(5.60245 + 5.60245i) q^{17} +(-1.73402 - 1.73402i) q^{18} -5.84195 q^{19} +(0.602381 - 2.15340i) q^{20} +(-4.38084 - 4.35594i) q^{21} +(-0.707107 + 0.707107i) q^{22} +(-2.78391 - 2.78391i) q^{23} +2.33501 q^{24} +(4.27428 + 2.59433i) q^{25} -0.246482i q^{26} +(-0.904344 - 0.904344i) q^{27} +(2.64574 - 0.00754262i) q^{28} -1.55340i q^{29} +(-1.40657 + 5.02822i) q^{30} +5.97580i q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.65110 - 1.65110i) q^{33} +7.92306 q^{34} +(-1.57750 + 5.70188i) q^{35} -2.45228 q^{36} +(-3.47188 + 3.47188i) q^{37} +(-4.13088 + 4.13088i) q^{38} +0.575538i q^{39} +(-1.09674 - 1.94863i) q^{40} +5.31279i q^{41} +(-6.17783 + 0.0176121i) q^{42} +(2.57014 + 2.57014i) q^{43} +1.00000i q^{44} +(1.47721 - 5.28074i) q^{45} -3.93704 q^{46} +(3.10826 + 3.10826i) q^{47} +(1.65110 - 1.65110i) q^{48} +(-6.99989 + 0.0399116i) q^{49} +(4.85684 - 1.18790i) q^{50} -18.5004 q^{51} +(-0.174289 - 0.174289i) q^{52} +(6.13111 + 6.13111i) q^{53} -1.27894 q^{54} +(-2.15340 - 0.602381i) q^{55} +(1.86549 - 1.87615i) q^{56} +(9.64566 - 9.64566i) q^{57} +(-1.09842 - 1.09842i) q^{58} -8.26608 q^{59} +(2.56089 + 4.55008i) q^{60} +5.87018i q^{61} +(4.22553 + 4.22553i) q^{62} +(6.48809 - 0.0184966i) q^{63} +1.00000i q^{64} +(0.480302 - 0.270326i) q^{65} -2.33501i q^{66} +(6.82513 - 6.82513i) q^{67} +(5.60245 - 5.60245i) q^{68} +9.19304 q^{69} +(2.91638 + 5.14730i) q^{70} +7.24081 q^{71} +(-1.73402 + 1.73402i) q^{72} +(-0.699312 + 0.699312i) q^{73} +4.90998i q^{74} +(-11.3408 + 2.77375i) q^{75} +5.84195i q^{76} +(-0.00754262 - 2.64574i) q^{77} +(0.406966 + 0.406966i) q^{78} -7.29601i q^{79} +(-2.15340 - 0.602381i) q^{80} +10.3432 q^{81} +(3.75671 + 3.75671i) q^{82} +(8.97769 - 8.97769i) q^{83} +(-4.35594 + 4.38084i) q^{84} +(8.68951 + 15.4391i) q^{85} +3.63473 q^{86} +(2.56483 + 2.56483i) q^{87} +(0.707107 + 0.707107i) q^{88} -4.37218 q^{89} +(-2.68951 - 4.77859i) q^{90} +(0.462438 + 0.459809i) q^{91} +(-2.78391 + 2.78391i) q^{92} +(-9.86666 - 9.86666i) q^{93} +4.39575 q^{94} +(-12.5801 - 3.51908i) q^{95} -2.33501i q^{96} +(0.622902 + 0.622902i) q^{97} +(-4.92145 + 4.97789i) q^{98} +2.45228i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(617\) \(661\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) −1.65110 + 1.65110i −0.953264 + 0.953264i −0.998956 0.0456912i \(-0.985451\pi\)
0.0456912 + 0.998956i \(0.485451\pi\)
\(4\) 1.00000i 0.500000i
\(5\) 2.15340 + 0.602381i 0.963030 + 0.269393i
\(6\) 2.33501i 0.953264i
\(7\) 0.00754262 + 2.64574i 0.00285084 + 0.999996i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 2.45228i 0.817426i
\(10\) 1.94863 1.09674i 0.616212 0.346819i
\(11\) −1.00000 −0.301511
\(12\) 1.65110 + 1.65110i 0.476632 + 0.476632i
\(13\) 0.174289 0.174289i 0.0483390 0.0483390i −0.682524 0.730863i \(-0.739118\pi\)
0.730863 + 0.682524i \(0.239118\pi\)
\(14\) 1.87615 + 1.86549i 0.501423 + 0.498573i
\(15\) −4.55008 + 2.56089i −1.17483 + 0.661220i
\(16\) −1.00000 −0.250000
\(17\) 5.60245 + 5.60245i 1.35879 + 1.35879i 0.875408 + 0.483385i \(0.160593\pi\)
0.483385 + 0.875408i \(0.339407\pi\)
\(18\) −1.73402 1.73402i −0.408713 0.408713i
\(19\) −5.84195 −1.34024 −0.670118 0.742255i \(-0.733756\pi\)
−0.670118 + 0.742255i \(0.733756\pi\)
\(20\) 0.602381 2.15340i 0.134696 0.481515i
\(21\) −4.38084 4.35594i −0.955978 0.950543i
\(22\) −0.707107 + 0.707107i −0.150756 + 0.150756i
\(23\) −2.78391 2.78391i −0.580486 0.580486i 0.354551 0.935037i \(-0.384634\pi\)
−0.935037 + 0.354551i \(0.884634\pi\)
\(24\) 2.33501 0.476632
\(25\) 4.27428 + 2.59433i 0.854855 + 0.518867i
\(26\) 0.246482i 0.0483390i
\(27\) −0.904344 0.904344i −0.174041 0.174041i
\(28\) 2.64574 0.00754262i 0.499998 0.00142542i
\(29\) 1.55340i 0.288460i −0.989544 0.144230i \(-0.953930\pi\)
0.989544 0.144230i \(-0.0460704\pi\)
\(30\) −1.40657 + 5.02822i −0.256803 + 0.918023i
\(31\) 5.97580i 1.07329i 0.843810 + 0.536643i \(0.180308\pi\)
−0.843810 + 0.536643i \(0.819692\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 1.65110 1.65110i 0.287420 0.287420i
\(34\) 7.92306 1.35879
\(35\) −1.57750 + 5.70188i −0.266646 + 0.963794i
\(36\) −2.45228 −0.408713
\(37\) −3.47188 + 3.47188i −0.570773 + 0.570773i −0.932344 0.361571i \(-0.882240\pi\)
0.361571 + 0.932344i \(0.382240\pi\)
\(38\) −4.13088 + 4.13088i −0.670118 + 0.670118i
\(39\) 0.575538i 0.0921598i
\(40\) −1.09674 1.94863i −0.173409 0.308106i
\(41\) 5.31279i 0.829718i 0.909886 + 0.414859i \(0.136169\pi\)
−0.909886 + 0.414859i \(0.863831\pi\)
\(42\) −6.17783 + 0.0176121i −0.953261 + 0.00271761i
\(43\) 2.57014 + 2.57014i 0.391943 + 0.391943i 0.875379 0.483437i \(-0.160612\pi\)
−0.483437 + 0.875379i \(0.660612\pi\)
\(44\) 1.00000i 0.150756i
\(45\) 1.47721 5.28074i 0.220209 0.787206i
\(46\) −3.93704 −0.580486
\(47\) 3.10826 + 3.10826i 0.453387 + 0.453387i 0.896477 0.443090i \(-0.146118\pi\)
−0.443090 + 0.896477i \(0.646118\pi\)
\(48\) 1.65110 1.65110i 0.238316 0.238316i
\(49\) −6.99989 + 0.0399116i −0.999984 + 0.00570166i
\(50\) 4.85684 1.18790i 0.686861 0.167994i
\(51\) −18.5004 −2.59058
\(52\) −0.174289 0.174289i −0.0241695 0.0241695i
\(53\) 6.13111 + 6.13111i 0.842173 + 0.842173i 0.989141 0.146968i \(-0.0469516\pi\)
−0.146968 + 0.989141i \(0.546952\pi\)
\(54\) −1.27894 −0.174041
\(55\) −2.15340 0.602381i −0.290365 0.0812250i
\(56\) 1.86549 1.87615i 0.249286 0.250712i
\(57\) 9.64566 9.64566i 1.27760 1.27760i
\(58\) −1.09842 1.09842i −0.144230 0.144230i
\(59\) −8.26608 −1.07615 −0.538076 0.842896i \(-0.680849\pi\)
−0.538076 + 0.842896i \(0.680849\pi\)
\(60\) 2.56089 + 4.55008i 0.330610 + 0.587413i
\(61\) 5.87018i 0.751600i 0.926701 + 0.375800i \(0.122632\pi\)
−0.926701 + 0.375800i \(0.877368\pi\)
\(62\) 4.22553 + 4.22553i 0.536643 + 0.536643i
\(63\) 6.48809 0.0184966i 0.817423 0.00233035i
\(64\) 1.00000i 0.125000i
\(65\) 0.480302 0.270326i 0.0595741 0.0335298i
\(66\) 2.33501i 0.287420i
\(67\) 6.82513 6.82513i 0.833822 0.833822i −0.154215 0.988037i \(-0.549285\pi\)
0.988037 + 0.154215i \(0.0492848\pi\)
\(68\) 5.60245 5.60245i 0.679397 0.679397i
\(69\) 9.19304 1.10671
\(70\) 2.91638 + 5.14730i 0.348574 + 0.615220i
\(71\) 7.24081 0.859326 0.429663 0.902989i \(-0.358632\pi\)
0.429663 + 0.902989i \(0.358632\pi\)
\(72\) −1.73402 + 1.73402i −0.204357 + 0.204357i
\(73\) −0.699312 + 0.699312i −0.0818483 + 0.0818483i −0.746846 0.664997i \(-0.768433\pi\)
0.664997 + 0.746846i \(0.268433\pi\)
\(74\) 4.90998i 0.570773i
\(75\) −11.3408 + 2.77375i −1.30952 + 0.320286i
\(76\) 5.84195i 0.670118i
\(77\) −0.00754262 2.64574i −0.000859561 0.301510i
\(78\) 0.406966 + 0.406966i 0.0460799 + 0.0460799i
\(79\) 7.29601i 0.820865i −0.911891 0.410433i \(-0.865378\pi\)
0.911891 0.410433i \(-0.134622\pi\)
\(80\) −2.15340 0.602381i −0.240758 0.0673482i
\(81\) 10.3432 1.14924
\(82\) 3.75671 + 3.75671i 0.414859 + 0.414859i
\(83\) 8.97769 8.97769i 0.985430 0.985430i −0.0144656 0.999895i \(-0.504605\pi\)
0.999895 + 0.0144656i \(0.00460470\pi\)
\(84\) −4.35594 + 4.38084i −0.475271 + 0.477989i
\(85\) 8.68951 + 15.4391i 0.942510 + 1.67461i
\(86\) 3.63473 0.391943
\(87\) 2.56483 + 2.56483i 0.274978 + 0.274978i
\(88\) 0.707107 + 0.707107i 0.0753778 + 0.0753778i
\(89\) −4.37218 −0.463450 −0.231725 0.972781i \(-0.574437\pi\)
−0.231725 + 0.972781i \(0.574437\pi\)
\(90\) −2.68951 4.77859i −0.283499 0.503707i
\(91\) 0.462438 + 0.459809i 0.0484766 + 0.0482010i
\(92\) −2.78391 + 2.78391i −0.290243 + 0.290243i
\(93\) −9.86666 9.86666i −1.02312 1.02312i
\(94\) 4.39575 0.453387
\(95\) −12.5801 3.51908i −1.29069 0.361050i
\(96\) 2.33501i 0.238316i
\(97\) 0.622902 + 0.622902i 0.0632461 + 0.0632461i 0.738022 0.674776i \(-0.235760\pi\)
−0.674776 + 0.738022i \(0.735760\pi\)
\(98\) −4.92145 + 4.97789i −0.497141 + 0.502843i
\(99\) 2.45228i 0.246463i
\(100\) 2.59433 4.27428i 0.259433 0.427428i
\(101\) 0.369909i 0.0368073i 0.999831 + 0.0184037i \(0.00585840\pi\)
−0.999831 + 0.0184037i \(0.994142\pi\)
\(102\) −13.0818 + 13.0818i −1.29529 + 1.29529i
\(103\) 8.40496 8.40496i 0.828166 0.828166i −0.159097 0.987263i \(-0.550858\pi\)
0.987263 + 0.159097i \(0.0508584\pi\)
\(104\) −0.246482 −0.0241695
\(105\) −6.80978 12.0190i −0.664567 1.17294i
\(106\) 8.67070 0.842173
\(107\) −3.66759 + 3.66759i −0.354559 + 0.354559i −0.861803 0.507243i \(-0.830665\pi\)
0.507243 + 0.861803i \(0.330665\pi\)
\(108\) −0.904344 + 0.904344i −0.0870206 + 0.0870206i
\(109\) 18.7822i 1.79901i −0.436911 0.899505i \(-0.643928\pi\)
0.436911 0.899505i \(-0.356072\pi\)
\(110\) −1.94863 + 1.09674i −0.185795 + 0.104570i
\(111\) 11.4649i 1.08820i
\(112\) −0.00754262 2.64574i −0.000712710 0.249999i
\(113\) −8.65869 8.65869i −0.814541 0.814541i 0.170770 0.985311i \(-0.445375\pi\)
−0.985311 + 0.170770i \(0.945375\pi\)
\(114\) 13.6410i 1.27760i
\(115\) −4.31790 7.67185i −0.402647 0.715404i
\(116\) −1.55340 −0.144230
\(117\) −0.427405 0.427405i −0.0395136 0.0395136i
\(118\) −5.84500 + 5.84500i −0.538076 + 0.538076i
\(119\) −14.7804 + 14.8649i −1.35491 + 1.36266i
\(120\) 5.02822 + 1.40657i 0.459011 + 0.128401i
\(121\) 1.00000 0.0909091
\(122\) 4.15084 + 4.15084i 0.375800 + 0.375800i
\(123\) −8.77196 8.77196i −0.790941 0.790941i
\(124\) 5.97580 0.536643
\(125\) 7.64145 + 8.16138i 0.683472 + 0.729976i
\(126\) 4.57470 4.60085i 0.407546 0.409877i
\(127\) −6.75899 + 6.75899i −0.599764 + 0.599764i −0.940250 0.340486i \(-0.889408\pi\)
0.340486 + 0.940250i \(0.389408\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −8.48713 −0.747250
\(130\) 0.148476 0.530774i 0.0130222 0.0465520i
\(131\) 4.14114i 0.361813i 0.983500 + 0.180907i \(0.0579032\pi\)
−0.983500 + 0.180907i \(0.942097\pi\)
\(132\) −1.65110 1.65110i −0.143710 0.143710i
\(133\) −0.0440636 15.4563i −0.00382080 1.34023i
\(134\) 9.65219i 0.833822i
\(135\) −1.40266 2.49218i −0.120721 0.214492i
\(136\) 7.92306i 0.679397i
\(137\) 10.1281 10.1281i 0.865301 0.865301i −0.126647 0.991948i \(-0.540422\pi\)
0.991948 + 0.126647i \(0.0404216\pi\)
\(138\) 6.50046 6.50046i 0.553356 0.553356i
\(139\) 12.4510 1.05608 0.528041 0.849219i \(-0.322927\pi\)
0.528041 + 0.849219i \(0.322927\pi\)
\(140\) 5.70188 + 1.57750i 0.481897 + 0.133323i
\(141\) −10.2641 −0.864395
\(142\) 5.12003 5.12003i 0.429663 0.429663i
\(143\) −0.174289 + 0.174289i −0.0145748 + 0.0145748i
\(144\) 2.45228i 0.204357i
\(145\) 0.935739 3.34510i 0.0777089 0.277795i
\(146\) 0.988977i 0.0818483i
\(147\) 11.4916 11.6234i 0.947814 0.958684i
\(148\) 3.47188 + 3.47188i 0.285387 + 0.285387i
\(149\) 9.48708i 0.777212i −0.921404 0.388606i \(-0.872957\pi\)
0.921404 0.388606i \(-0.127043\pi\)
\(150\) −6.05780 + 9.98048i −0.494617 + 0.814903i
\(151\) −0.184085 −0.0149806 −0.00749032 0.999972i \(-0.502384\pi\)
−0.00749032 + 0.999972i \(0.502384\pi\)
\(152\) 4.13088 + 4.13088i 0.335059 + 0.335059i
\(153\) 13.7388 13.7388i 1.11071 1.11071i
\(154\) −1.87615 1.86549i −0.151185 0.150325i
\(155\) −3.59971 + 12.8683i −0.289135 + 1.03361i
\(156\) 0.575538 0.0460799
\(157\) −9.08936 9.08936i −0.725410 0.725410i 0.244292 0.969702i \(-0.421445\pi\)
−0.969702 + 0.244292i \(0.921445\pi\)
\(158\) −5.15906 5.15906i −0.410433 0.410433i
\(159\) −20.2462 −1.60563
\(160\) −1.94863 + 1.09674i −0.154053 + 0.0867047i
\(161\) 7.34451 7.38650i 0.578828 0.582138i
\(162\) 7.31372 7.31372i 0.574620 0.574620i
\(163\) 6.69266 + 6.69266i 0.524210 + 0.524210i 0.918840 0.394630i \(-0.129127\pi\)
−0.394630 + 0.918840i \(0.629127\pi\)
\(164\) 5.31279 0.414859
\(165\) 4.55008 2.56089i 0.354223 0.199365i
\(166\) 12.6964i 0.985430i
\(167\) 5.27402 + 5.27402i 0.408116 + 0.408116i 0.881081 0.472965i \(-0.156816\pi\)
−0.472965 + 0.881081i \(0.656816\pi\)
\(168\) 0.0176121 + 6.17783i 0.00135880 + 0.476630i
\(169\) 12.9392i 0.995327i
\(170\) 17.0615 + 4.77270i 1.30856 + 0.366049i
\(171\) 14.3261i 1.09554i
\(172\) 2.57014 2.57014i 0.195971 0.195971i
\(173\) 9.25971 9.25971i 0.704003 0.704003i −0.261264 0.965267i \(-0.584139\pi\)
0.965267 + 0.261264i \(0.0841395\pi\)
\(174\) 3.62721 0.274978
\(175\) −6.83170 + 11.3282i −0.516428 + 0.856331i
\(176\) 1.00000 0.0753778
\(177\) 13.6481 13.6481i 1.02586 1.02586i
\(178\) −3.09160 + 3.09160i −0.231725 + 0.231725i
\(179\) 12.5815i 0.940384i −0.882564 0.470192i \(-0.844185\pi\)
0.882564 0.470192i \(-0.155815\pi\)
\(180\) −5.28074 1.47721i −0.393603 0.110104i
\(181\) 22.1174i 1.64397i −0.569509 0.821985i \(-0.692867\pi\)
0.569509 0.821985i \(-0.307133\pi\)
\(182\) 0.652127 0.00185912i 0.0483388 0.000137807i
\(183\) −9.69227 9.69227i −0.716473 0.716473i
\(184\) 3.93704i 0.290243i
\(185\) −9.56774 + 5.38496i −0.703434 + 0.395910i
\(186\) −13.9536 −1.02312
\(187\) −5.60245 5.60245i −0.409692 0.409692i
\(188\) 3.10826 3.10826i 0.226694 0.226694i
\(189\) 2.38584 2.39948i 0.173544 0.174537i
\(190\) −11.3838 + 6.40709i −0.825869 + 0.464819i
\(191\) −6.49463 −0.469935 −0.234967 0.972003i \(-0.575498\pi\)
−0.234967 + 0.972003i \(0.575498\pi\)
\(192\) −1.65110 1.65110i −0.119158 0.119158i
\(193\) 9.30134 + 9.30134i 0.669525 + 0.669525i 0.957606 0.288081i \(-0.0930173\pi\)
−0.288081 + 0.957606i \(0.593017\pi\)
\(194\) 0.880916 0.0632461
\(195\) −0.346693 + 1.23936i −0.0248272 + 0.0887527i
\(196\) 0.0399116 + 6.99989i 0.00285083 + 0.499992i
\(197\) 8.69365 8.69365i 0.619397 0.619397i −0.325980 0.945377i \(-0.605694\pi\)
0.945377 + 0.325980i \(0.105694\pi\)
\(198\) 1.73402 + 1.73402i 0.123232 + 0.123232i
\(199\) 16.3032 1.15570 0.577851 0.816142i \(-0.303892\pi\)
0.577851 + 0.816142i \(0.303892\pi\)
\(200\) −1.18790 4.85684i −0.0839970 0.343430i
\(201\) 22.5380i 1.58971i
\(202\) 0.261565 + 0.261565i 0.0184037 + 0.0184037i
\(203\) 4.10990 0.0117167i 0.288458 0.000822353i
\(204\) 18.5004i 1.29529i
\(205\) −3.20032 + 11.4406i −0.223520 + 0.799044i
\(206\) 11.8864i 0.828166i
\(207\) −6.82692 + 6.82692i −0.474504 + 0.474504i
\(208\) −0.174289 + 0.174289i −0.0120848 + 0.0120848i
\(209\) 5.84195 0.404096
\(210\) −13.3140 3.68348i −0.918751 0.254184i
\(211\) 28.5557 1.96586 0.982928 0.183991i \(-0.0589016\pi\)
0.982928 + 0.183991i \(0.0589016\pi\)
\(212\) 6.13111 6.13111i 0.421086 0.421086i
\(213\) −11.9553 + 11.9553i −0.819165 + 0.819165i
\(214\) 5.18676i 0.354559i
\(215\) 3.98634 + 7.08275i 0.271866 + 0.483039i
\(216\) 1.27894i 0.0870206i
\(217\) −15.8104 + 0.0450732i −1.07328 + 0.00305977i
\(218\) −13.2810 13.2810i −0.899505 0.899505i
\(219\) 2.30927i 0.156046i
\(220\) −0.602381 + 2.15340i −0.0406125 + 0.145182i
\(221\) 1.95289 0.131365
\(222\) −8.10688 8.10688i −0.544098 0.544098i
\(223\) −11.1562 + 11.1562i −0.747076 + 0.747076i −0.973929 0.226853i \(-0.927156\pi\)
0.226853 + 0.973929i \(0.427156\pi\)
\(224\) −1.87615 1.86549i −0.125356 0.124643i
\(225\) 6.36203 10.4817i 0.424135 0.698781i
\(226\) −12.2452 −0.814541
\(227\) 17.0882 + 17.0882i 1.13418 + 1.13418i 0.989474 + 0.144708i \(0.0462242\pi\)
0.144708 + 0.989474i \(0.453776\pi\)
\(228\) −9.64566 9.64566i −0.638799 0.638799i
\(229\) −22.2615 −1.47108 −0.735541 0.677480i \(-0.763072\pi\)
−0.735541 + 0.677480i \(0.763072\pi\)
\(230\) −8.47804 2.37160i −0.559025 0.156379i
\(231\) 4.38084 + 4.35594i 0.288238 + 0.286599i
\(232\) −1.09842 + 1.09842i −0.0721149 + 0.0721149i
\(233\) 11.7748 + 11.7748i 0.771395 + 0.771395i 0.978350 0.206955i \(-0.0663554\pi\)
−0.206955 + 0.978350i \(0.566355\pi\)
\(234\) −0.604442 −0.0395136
\(235\) 4.82098 + 8.56570i 0.314486 + 0.558765i
\(236\) 8.26608i 0.538076i
\(237\) 12.0465 + 12.0465i 0.782502 + 0.782502i
\(238\) 0.0597606 + 20.9624i 0.00387370 + 1.35879i
\(239\) 26.4952i 1.71383i 0.515454 + 0.856917i \(0.327623\pi\)
−0.515454 + 0.856917i \(0.672377\pi\)
\(240\) 4.55008 2.56089i 0.293706 0.165305i
\(241\) 15.2640i 0.983239i −0.870810 0.491620i \(-0.836405\pi\)
0.870810 0.491620i \(-0.163595\pi\)
\(242\) 0.707107 0.707107i 0.0454545 0.0454545i
\(243\) −14.3646 + 14.3646i −0.921489 + 0.921489i
\(244\) 5.87018 0.375800
\(245\) −15.0976 4.13065i −0.964551 0.263898i
\(246\) −12.4054 −0.790941
\(247\) −1.01819 + 1.01819i −0.0647857 + 0.0647857i
\(248\) 4.22553 4.22553i 0.268321 0.268321i
\(249\) 29.6462i 1.87875i
\(250\) 11.1743 + 0.367646i 0.706724 + 0.0232520i
\(251\) 5.99446i 0.378367i −0.981942 0.189184i \(-0.939416\pi\)
0.981942 0.189184i \(-0.0605841\pi\)
\(252\) −0.0184966 6.48809i −0.00116518 0.408711i
\(253\) 2.78391 + 2.78391i 0.175023 + 0.175023i
\(254\) 9.55866i 0.599764i
\(255\) −39.8388 11.1443i −2.49481 0.697883i
\(256\) 1.00000 0.0625000
\(257\) −10.1867 10.1867i −0.635427 0.635427i 0.313997 0.949424i \(-0.398332\pi\)
−0.949424 + 0.313997i \(0.898332\pi\)
\(258\) −6.00131 + 6.00131i −0.373625 + 0.373625i
\(259\) −9.21188 9.15950i −0.572398 0.569144i
\(260\) −0.270326 0.480302i −0.0167649 0.0297871i
\(261\) −3.80937 −0.235794
\(262\) 2.92823 + 2.92823i 0.180907 + 0.180907i
\(263\) −1.12520 1.12520i −0.0693827 0.0693827i 0.671564 0.740947i \(-0.265623\pi\)
−0.740947 + 0.671564i \(0.765623\pi\)
\(264\) −2.33501 −0.143710
\(265\) 9.50948 + 16.8960i 0.584163 + 1.03791i
\(266\) −10.9604 10.8981i −0.672025 0.668205i
\(267\) 7.21892 7.21892i 0.441790 0.441790i
\(268\) −6.82513 6.82513i −0.416911 0.416911i
\(269\) −24.9262 −1.51978 −0.759889 0.650053i \(-0.774747\pi\)
−0.759889 + 0.650053i \(0.774747\pi\)
\(270\) −2.75406 0.770406i −0.167607 0.0468854i
\(271\) 19.9841i 1.21395i −0.794722 0.606973i \(-0.792384\pi\)
0.794722 0.606973i \(-0.207616\pi\)
\(272\) −5.60245 5.60245i −0.339698 0.339698i
\(273\) −1.52272 + 0.00434106i −0.0921594 + 0.000262733i
\(274\) 14.3233i 0.865301i
\(275\) −4.27428 2.59433i −0.257748 0.156444i
\(276\) 9.19304i 0.553356i
\(277\) 12.2107 12.2107i 0.733670 0.733670i −0.237674 0.971345i \(-0.576385\pi\)
0.971345 + 0.237674i \(0.0763851\pi\)
\(278\) 8.80421 8.80421i 0.528041 0.528041i
\(279\) 14.6543 0.877332
\(280\) 5.14730 2.91638i 0.307610 0.174287i
\(281\) −12.1194 −0.722984 −0.361492 0.932375i \(-0.617733\pi\)
−0.361492 + 0.932375i \(0.617733\pi\)
\(282\) −7.25783 + 7.25783i −0.432198 + 0.432198i
\(283\) 2.54038 2.54038i 0.151010 0.151010i −0.627559 0.778569i \(-0.715946\pi\)
0.778569 + 0.627559i \(0.215946\pi\)
\(284\) 7.24081i 0.429663i
\(285\) 26.5813 14.9606i 1.57454 0.886191i
\(286\) 0.246482i 0.0145748i
\(287\) −14.0563 + 0.0400723i −0.829715 + 0.00236539i
\(288\) 1.73402 + 1.73402i 0.102178 + 0.102178i
\(289\) 45.7748i 2.69264i
\(290\) −1.70367 3.02701i −0.100043 0.177752i
\(291\) −2.05695 −0.120580
\(292\) 0.699312 + 0.699312i 0.0409241 + 0.0409241i
\(293\) −5.00456 + 5.00456i −0.292370 + 0.292370i −0.838016 0.545646i \(-0.816284\pi\)
0.545646 + 0.838016i \(0.316284\pi\)
\(294\) −0.0931941 16.3448i −0.00543519 0.953249i
\(295\) −17.8002 4.97933i −1.03637 0.289908i
\(296\) 4.90998 0.285387
\(297\) 0.904344 + 0.904344i 0.0524754 + 0.0524754i
\(298\) −6.70838 6.70838i −0.388606 0.388606i
\(299\) −0.970409 −0.0561202
\(300\) 2.77375 + 11.3408i 0.160143 + 0.654760i
\(301\) −6.78054 + 6.81931i −0.390824 + 0.393058i
\(302\) −0.130168 + 0.130168i −0.00749032 + 0.00749032i
\(303\) −0.610758 0.610758i −0.0350871 0.0350871i
\(304\) 5.84195 0.335059
\(305\) −3.53608 + 12.6409i −0.202476 + 0.723813i
\(306\) 19.4295i 1.11071i
\(307\) 23.8030 + 23.8030i 1.35851 + 1.35851i 0.875757 + 0.482753i \(0.160363\pi\)
0.482753 + 0.875757i \(0.339637\pi\)
\(308\) −2.64574 + 0.00754262i −0.150755 + 0.000429781i
\(309\) 27.7549i 1.57892i
\(310\) 6.55388 + 11.6446i 0.372236 + 0.661371i
\(311\) 17.3594i 0.984360i 0.870494 + 0.492180i \(0.163800\pi\)
−0.870494 + 0.492180i \(0.836200\pi\)
\(312\) 0.406966 0.406966i 0.0230399 0.0230399i
\(313\) 8.06269 8.06269i 0.455730 0.455730i −0.441521 0.897251i \(-0.645561\pi\)
0.897251 + 0.441521i \(0.145561\pi\)
\(314\) −12.8543 −0.725410
\(315\) 13.9826 + 3.86847i 0.787831 + 0.217964i
\(316\) −7.29601 −0.410433
\(317\) 0.307140 0.307140i 0.0172507 0.0172507i −0.698429 0.715680i \(-0.746117\pi\)
0.715680 + 0.698429i \(0.246117\pi\)
\(318\) −14.3162 + 14.3162i −0.802813 + 0.802813i
\(319\) 1.55340i 0.0869738i
\(320\) −0.602381 + 2.15340i −0.0336741 + 0.120379i
\(321\) 12.1111i 0.675978i
\(322\) −0.0296956 10.4164i −0.00165487 0.580483i
\(323\) −32.7292 32.7292i −1.82110 1.82110i
\(324\) 10.3432i 0.574620i
\(325\) 1.19712 0.292795i 0.0664044 0.0162413i
\(326\) 9.46485 0.524210
\(327\) 31.0114 + 31.0114i 1.71493 + 1.71493i
\(328\) 3.75671 3.75671i 0.207430 0.207430i
\(329\) −8.20022 + 8.24711i −0.452093 + 0.454678i
\(330\) 1.40657 5.02822i 0.0774289 0.276794i
\(331\) 26.9515 1.48139 0.740695 0.671841i \(-0.234496\pi\)
0.740695 + 0.671841i \(0.234496\pi\)
\(332\) −8.97769 8.97769i −0.492715 0.492715i
\(333\) 8.51401 + 8.51401i 0.466565 + 0.466565i
\(334\) 7.45859 0.408116
\(335\) 18.8086 10.5859i 1.02762 0.578370i
\(336\) 4.38084 + 4.35594i 0.238995 + 0.237636i
\(337\) 23.9680 23.9680i 1.30562 1.30562i 0.381076 0.924544i \(-0.375554\pi\)
0.924544 0.381076i \(-0.124446\pi\)
\(338\) 9.14943 + 9.14943i 0.497663 + 0.497663i
\(339\) 28.5928 1.55295
\(340\) 15.4391 8.68951i 0.837304 0.471255i
\(341\) 5.97580i 0.323608i
\(342\) 10.1301 + 10.1301i 0.547772 + 0.547772i
\(343\) −0.158393 18.5196i −0.00855243 0.999963i
\(344\) 3.63473i 0.195971i
\(345\) 19.7963 + 5.53771i 1.06580 + 0.298140i
\(346\) 13.0952i 0.704003i
\(347\) −17.6258 + 17.6258i −0.946205 + 0.946205i −0.998625 0.0524200i \(-0.983307\pi\)
0.0524200 + 0.998625i \(0.483307\pi\)
\(348\) 2.56483 2.56483i 0.137489 0.137489i
\(349\) 32.5283 1.74120 0.870599 0.491993i \(-0.163731\pi\)
0.870599 + 0.491993i \(0.163731\pi\)
\(350\) 3.17950 + 12.8410i 0.169952 + 0.686379i
\(351\) −0.315234 −0.0168260
\(352\) 0.707107 0.707107i 0.0376889 0.0376889i
\(353\) −19.7589 + 19.7589i −1.05166 + 1.05166i −0.0530679 + 0.998591i \(0.516900\pi\)
−0.998591 + 0.0530679i \(0.983100\pi\)
\(354\) 19.3014i 1.02586i
\(355\) 15.5924 + 4.36172i 0.827557 + 0.231496i
\(356\) 4.37218i 0.231725i
\(357\) −0.139542 48.9473i −0.00738533 2.59057i
\(358\) −8.89645 8.89645i −0.470192 0.470192i
\(359\) 0.613084i 0.0323573i 0.999869 + 0.0161787i \(0.00515005\pi\)
−0.999869 + 0.0161787i \(0.994850\pi\)
\(360\) −4.77859 + 2.68951i −0.251854 + 0.141749i
\(361\) 15.1284 0.796231
\(362\) −15.6393 15.6393i −0.821985 0.821985i
\(363\) −1.65110 + 1.65110i −0.0866604 + 0.0866604i
\(364\) 0.459809 0.462438i 0.0241005 0.0242383i
\(365\) −1.92715 + 1.08465i −0.100872 + 0.0567731i
\(366\) −13.7069 −0.716473
\(367\) 9.21581 + 9.21581i 0.481061 + 0.481061i 0.905470 0.424409i \(-0.139518\pi\)
−0.424409 + 0.905470i \(0.639518\pi\)
\(368\) 2.78391 + 2.78391i 0.145121 + 0.145121i
\(369\) 13.0284 0.678233
\(370\) −2.95768 + 10.5732i −0.153762 + 0.549672i
\(371\) −16.1751 + 16.2676i −0.839768 + 0.844570i
\(372\) −9.86666 + 9.86666i −0.511562 + 0.511562i
\(373\) 23.1619 + 23.1619i 1.19928 + 1.19928i 0.974382 + 0.224898i \(0.0722048\pi\)
0.224898 + 0.974382i \(0.427795\pi\)
\(374\) −7.92306 −0.409692
\(375\) −26.0921 0.858458i −1.34739 0.0443306i
\(376\) 4.39575i 0.226694i
\(377\) −0.270741 0.270741i −0.0139439 0.0139439i
\(378\) −0.00964653 3.38373i −0.000496164 0.174040i
\(379\) 18.6719i 0.959109i −0.877512 0.479554i \(-0.840798\pi\)
0.877512 0.479554i \(-0.159202\pi\)
\(380\) −3.51908 + 12.5801i −0.180525 + 0.645344i
\(381\) 22.3196i 1.14347i
\(382\) −4.59239 + 4.59239i −0.234967 + 0.234967i
\(383\) 4.83162 4.83162i 0.246884 0.246884i −0.572807 0.819691i \(-0.694145\pi\)
0.819691 + 0.572807i \(0.194145\pi\)
\(384\) −2.33501 −0.119158
\(385\) 1.57750 5.70188i 0.0803969 0.290595i
\(386\) 13.1541 0.669525
\(387\) 6.30270 6.30270i 0.320384 0.320384i
\(388\) 0.622902 0.622902i 0.0316230 0.0316230i
\(389\) 32.0514i 1.62507i 0.582911 + 0.812536i \(0.301914\pi\)
−0.582911 + 0.812536i \(0.698086\pi\)
\(390\) 0.631214 + 1.12151i 0.0319627 + 0.0567899i
\(391\) 31.1934i 1.57752i
\(392\) 4.97789 + 4.92145i 0.251421 + 0.248571i
\(393\) −6.83745 6.83745i −0.344904 0.344904i
\(394\) 12.2947i 0.619397i
\(395\) 4.39497 15.7112i 0.221135 0.790518i
\(396\) 2.45228 0.123232
\(397\) −21.1347 21.1347i −1.06072 1.06072i −0.998033 0.0626889i \(-0.980032\pi\)
−0.0626889 0.998033i \(-0.519968\pi\)
\(398\) 11.5281 11.5281i 0.577851 0.577851i
\(399\) 25.5927 + 25.4472i 1.28124 + 1.27395i
\(400\) −4.27428 2.59433i −0.213714 0.129717i
\(401\) −34.0114 −1.69845 −0.849223 0.528034i \(-0.822929\pi\)
−0.849223 + 0.528034i \(0.822929\pi\)
\(402\) 15.9368 + 15.9368i 0.794853 + 0.794853i
\(403\) 1.04152 + 1.04152i 0.0518816 + 0.0518816i
\(404\) 0.369909 0.0184037
\(405\) 22.2730 + 6.23052i 1.10675 + 0.309597i
\(406\) 2.89785 2.91442i 0.143818 0.144640i
\(407\) 3.47188 3.47188i 0.172095 0.172095i
\(408\) 13.0818 + 13.0818i 0.647645 + 0.647645i
\(409\) 4.11314 0.203382 0.101691 0.994816i \(-0.467575\pi\)
0.101691 + 0.994816i \(0.467575\pi\)
\(410\) 5.82673 + 10.3527i 0.287762 + 0.511282i
\(411\) 33.4450i 1.64972i
\(412\) −8.40496 8.40496i −0.414083 0.414083i
\(413\) −0.0623479 21.8699i −0.00306794 1.07615i
\(414\) 9.65473i 0.474504i
\(415\) 24.7406 13.9246i 1.21447 0.683531i
\(416\) 0.246482i 0.0120848i
\(417\) −20.5579 + 20.5579i −1.00673 + 1.00673i
\(418\) 4.13088 4.13088i 0.202048 0.202048i
\(419\) −7.61620 −0.372076 −0.186038 0.982543i \(-0.559565\pi\)
−0.186038 + 0.982543i \(0.559565\pi\)
\(420\) −12.0190 + 6.80978i −0.586468 + 0.332283i
\(421\) −31.1762 −1.51943 −0.759717 0.650254i \(-0.774663\pi\)
−0.759717 + 0.650254i \(0.774663\pi\)
\(422\) 20.1919 20.1919i 0.982928 0.982928i
\(423\) 7.62233 7.62233i 0.370610 0.370610i
\(424\) 8.67070i 0.421086i
\(425\) 9.41178 + 38.4810i 0.456538 + 1.86660i
\(426\) 16.9074i 0.819165i
\(427\) −15.5310 + 0.0442765i −0.751596 + 0.00214269i
\(428\) 3.66759 + 3.66759i 0.177280 + 0.177280i
\(429\) 0.575538i 0.0277872i
\(430\) 7.82703 + 2.18949i 0.377453 + 0.105587i
\(431\) 2.40923 0.116049 0.0580243 0.998315i \(-0.481520\pi\)
0.0580243 + 0.998315i \(0.481520\pi\)
\(432\) 0.904344 + 0.904344i 0.0435103 + 0.0435103i
\(433\) −7.56995 + 7.56995i −0.363788 + 0.363788i −0.865206 0.501417i \(-0.832812\pi\)
0.501417 + 0.865206i \(0.332812\pi\)
\(434\) −11.1478 + 11.2115i −0.535111 + 0.538170i
\(435\) 3.97810 + 7.06810i 0.190735 + 0.338890i
\(436\) −18.7822 −0.899505
\(437\) 16.2635 + 16.2635i 0.777987 + 0.777987i
\(438\) −1.63290 1.63290i −0.0780231 0.0780231i
\(439\) 1.17868 0.0562555 0.0281277 0.999604i \(-0.491045\pi\)
0.0281277 + 0.999604i \(0.491045\pi\)
\(440\) 1.09674 + 1.94863i 0.0522849 + 0.0928974i
\(441\) 0.0978744 + 17.1657i 0.00466069 + 0.817413i
\(442\) 1.38090 1.38090i 0.0656827 0.0656827i
\(443\) −20.5251 20.5251i −0.975175 0.975175i 0.0245246 0.999699i \(-0.492193\pi\)
−0.999699 + 0.0245246i \(0.992193\pi\)
\(444\) −11.4649 −0.544098
\(445\) −9.41506 2.63372i −0.446317 0.124850i
\(446\) 15.7773i 0.747076i
\(447\) 15.6641 + 15.6641i 0.740888 + 0.740888i
\(448\) −2.64574 + 0.00754262i −0.124999 + 0.000356355i
\(449\) 20.3061i 0.958303i −0.877732 0.479151i \(-0.840944\pi\)
0.877732 0.479151i \(-0.159056\pi\)
\(450\) −2.91306 11.9103i −0.137323 0.561458i
\(451\) 5.31279i 0.250169i
\(452\) −8.65869 + 8.65869i −0.407271 + 0.407271i
\(453\) 0.303944 0.303944i 0.0142805 0.0142805i
\(454\) 24.1663 1.13418
\(455\) 0.718834 + 1.26872i 0.0336995 + 0.0594783i
\(456\) −13.6410 −0.638799
\(457\) −12.7759 + 12.7759i −0.597633 + 0.597633i −0.939682 0.342049i \(-0.888879\pi\)
0.342049 + 0.939682i \(0.388879\pi\)
\(458\) −15.7413 + 15.7413i −0.735541 + 0.735541i
\(459\) 10.1331i 0.472972i
\(460\) −7.67185 + 4.31790i −0.357702 + 0.201323i
\(461\) 2.72914i 0.127108i 0.997978 + 0.0635542i \(0.0202436\pi\)
−0.997978 + 0.0635542i \(0.979756\pi\)
\(462\) 6.17783 0.0176121i 0.287419 0.000819389i
\(463\) 20.9039 + 20.9039i 0.971486 + 0.971486i 0.999605 0.0281184i \(-0.00895154\pi\)
−0.0281184 + 0.999605i \(0.508952\pi\)
\(464\) 1.55340i 0.0721149i
\(465\) −15.3034 27.1904i −0.709678 1.26092i
\(466\) 16.6521 0.771395
\(467\) 7.04339 + 7.04339i 0.325929 + 0.325929i 0.851036 0.525107i \(-0.175975\pi\)
−0.525107 + 0.851036i \(0.675975\pi\)
\(468\) −0.427405 + 0.427405i −0.0197568 + 0.0197568i
\(469\) 18.1090 + 18.0060i 0.836196 + 0.831442i
\(470\) 9.46581 + 2.64791i 0.436625 + 0.122139i
\(471\) 30.0149 1.38302
\(472\) 5.84500 + 5.84500i 0.269038 + 0.269038i
\(473\) −2.57014 2.57014i −0.118175 0.118175i
\(474\) 17.0363 0.782502
\(475\) −24.9701 15.1560i −1.14571 0.695404i
\(476\) 14.8649 + 14.7804i 0.681331 + 0.677457i
\(477\) 15.0352 15.0352i 0.688414 0.688414i
\(478\) 18.7350 + 18.7350i 0.856917 + 0.856917i
\(479\) −28.4335 −1.29916 −0.649579 0.760294i \(-0.725055\pi\)
−0.649579 + 0.760294i \(0.725055\pi\)
\(480\) 1.40657 5.02822i 0.0642006 0.229506i
\(481\) 1.21022i 0.0551813i
\(482\) −10.7933 10.7933i −0.491620 0.491620i
\(483\) 0.0693396 + 24.3224i 0.00315506 + 1.10671i
\(484\) 1.00000i 0.0454545i
\(485\) 0.966133 + 1.71658i 0.0438699 + 0.0779459i
\(486\) 20.3146i 0.921489i
\(487\) 2.98613 2.98613i 0.135314 0.135314i −0.636205 0.771520i \(-0.719497\pi\)
0.771520 + 0.636205i \(0.219497\pi\)
\(488\) 4.15084 4.15084i 0.187900 0.187900i
\(489\) −22.1005 −0.999421
\(490\) −13.5964 + 7.75481i −0.614224 + 0.350327i
\(491\) −41.7259 −1.88306 −0.941531 0.336927i \(-0.890612\pi\)
−0.941531 + 0.336927i \(0.890612\pi\)
\(492\) −8.77196 + 8.77196i −0.395470 + 0.395470i
\(493\) 8.70285 8.70285i 0.391957 0.391957i
\(494\) 1.43993i 0.0647857i
\(495\) −1.47721 + 5.28074i −0.0663954 + 0.237352i
\(496\) 5.97580i 0.268321i
\(497\) 0.0546147 + 19.1573i 0.00244980 + 0.859323i
\(498\) 20.9630 + 20.9630i 0.939375 + 0.939375i
\(499\) 22.5409i 1.00907i −0.863392 0.504534i \(-0.831664\pi\)
0.863392 0.504534i \(-0.168336\pi\)
\(500\) 8.16138 7.64145i 0.364988 0.341736i
\(501\) −17.4159 −0.778085
\(502\) −4.23872 4.23872i −0.189184 0.189184i
\(503\) 16.1802 16.1802i 0.721438 0.721438i −0.247460 0.968898i \(-0.579596\pi\)
0.968898 + 0.247460i \(0.0795960\pi\)
\(504\) −4.60085 4.57470i −0.204938 0.203773i
\(505\) −0.222826 + 0.796563i −0.00991563 + 0.0354466i
\(506\) 3.93704 0.175023
\(507\) −21.3640 21.3640i −0.948810 0.948810i
\(508\) 6.75899 + 6.75899i 0.299882 + 0.299882i
\(509\) −23.9927 −1.06346 −0.531729 0.846914i \(-0.678458\pi\)
−0.531729 + 0.846914i \(0.678458\pi\)
\(510\) −36.0505 + 20.2901i −1.59634 + 0.898461i
\(511\) −1.85547 1.84492i −0.0820813 0.0816146i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 5.28313 + 5.28313i 0.233256 + 0.233256i
\(514\) −14.4061 −0.635427
\(515\) 23.1622 13.0363i 1.02065 0.574447i
\(516\) 8.48713i 0.373625i
\(517\) −3.10826 3.10826i −0.136701 0.136701i
\(518\) −12.9905 + 0.0370341i −0.570771 + 0.00162718i
\(519\) 30.5775i 1.34220i
\(520\) −0.530774 0.148476i −0.0232760 0.00651109i
\(521\) 36.3625i 1.59307i −0.604591 0.796536i \(-0.706663\pi\)
0.604591 0.796536i \(-0.293337\pi\)
\(522\) −2.69363 + 2.69363i −0.117897 + 0.117897i
\(523\) −2.72002 + 2.72002i −0.118938 + 0.118938i −0.764071 0.645133i \(-0.776802\pi\)
0.645133 + 0.764071i \(0.276802\pi\)
\(524\) 4.14114 0.180907
\(525\) −7.42417 29.9838i −0.324017 1.30860i
\(526\) −1.59127 −0.0693827
\(527\) −33.4791 + 33.4791i −1.45837 + 1.45837i
\(528\) −1.65110 + 1.65110i −0.0718550 + 0.0718550i
\(529\) 7.49968i 0.326073i
\(530\) 18.6715 + 5.22306i 0.811038 + 0.226875i
\(531\) 20.2707i 0.879675i
\(532\) −15.4563 + 0.0440636i −0.670115 + 0.00191040i
\(533\) 0.925960 + 0.925960i 0.0401078 + 0.0401078i
\(534\) 10.2091i 0.441790i
\(535\) −10.1071 + 5.68851i −0.436967 + 0.245936i
\(536\) −9.65219 −0.416911
\(537\) 20.7733 + 20.7733i 0.896434 + 0.896434i
\(538\) −17.6255 + 17.6255i −0.759889 + 0.759889i
\(539\) 6.99989 0.0399116i 0.301506 0.00171912i
\(540\) −2.49218 + 1.40266i −0.107246 + 0.0603607i
\(541\) −0.196243 −0.00843715 −0.00421857 0.999991i \(-0.501343\pi\)
−0.00421857 + 0.999991i \(0.501343\pi\)
\(542\) −14.1309 14.1309i −0.606973 0.606973i
\(543\) 36.5180 + 36.5180i 1.56714 + 1.56714i
\(544\) −7.92306 −0.339698
\(545\) 11.3140 40.4456i 0.484640 1.73250i
\(546\) −1.07366 + 1.07980i −0.0459483 + 0.0462111i
\(547\) −13.3227 + 13.3227i −0.569639 + 0.569639i −0.932027 0.362388i \(-0.881961\pi\)
0.362388 + 0.932027i \(0.381961\pi\)
\(548\) −10.1281 10.1281i −0.432650 0.432650i
\(549\) 14.3953 0.614377
\(550\) −4.85684 + 1.18790i −0.207096 + 0.0506521i
\(551\) 9.07490i 0.386604i
\(552\) −6.50046 6.50046i −0.276678 0.276678i
\(553\) 19.3033 0.0550310i 0.820862 0.00234016i
\(554\) 17.2686i 0.733670i
\(555\) 6.90621 24.6884i 0.293152 1.04797i
\(556\) 12.4510i 0.528041i
\(557\) 5.60100 5.60100i 0.237322 0.237322i −0.578418 0.815740i \(-0.696330\pi\)
0.815740 + 0.578418i \(0.196330\pi\)
\(558\) 10.3622 10.3622i 0.438666 0.438666i
\(559\) 0.895894 0.0378923
\(560\) 1.57750 5.70188i 0.0666616 0.240949i
\(561\) 18.5004 0.781089
\(562\) −8.56973 + 8.56973i −0.361492 + 0.361492i
\(563\) −15.0915 + 15.0915i −0.636032 + 0.636032i −0.949574 0.313542i \(-0.898484\pi\)
0.313542 + 0.949574i \(0.398484\pi\)
\(564\) 10.2641i 0.432198i
\(565\) −13.4298 23.8615i −0.564997 1.00386i
\(566\) 3.59264i 0.151010i
\(567\) 0.0780146 + 27.3653i 0.00327630 + 1.14924i
\(568\) −5.12003 5.12003i −0.214832 0.214832i
\(569\) 0.116714i 0.00489292i 0.999997 + 0.00244646i \(0.000778734\pi\)
−0.999997 + 0.00244646i \(0.999221\pi\)
\(570\) 8.21709 29.3746i 0.344176 1.23037i
\(571\) 16.3706 0.685090 0.342545 0.939501i \(-0.388711\pi\)
0.342545 + 0.939501i \(0.388711\pi\)
\(572\) 0.174289 + 0.174289i 0.00728738 + 0.00728738i
\(573\) 10.7233 10.7233i 0.447972 0.447972i
\(574\) −9.91094 + 9.96761i −0.413675 + 0.416040i
\(575\) −4.67681 19.1216i −0.195036 0.797426i
\(576\) 2.45228 0.102178
\(577\) 4.06513 + 4.06513i 0.169234 + 0.169234i 0.786642 0.617409i \(-0.211818\pi\)
−0.617409 + 0.786642i \(0.711818\pi\)
\(578\) 32.3677 + 32.3677i 1.34632 + 1.34632i
\(579\) −30.7149 −1.27647
\(580\) −3.34510 0.935739i −0.138898 0.0388545i
\(581\) 23.8204 + 23.6849i 0.988235 + 0.982616i
\(582\) −1.45448 + 1.45448i −0.0602902 + 0.0602902i
\(583\) −6.13111 6.13111i −0.253925 0.253925i
\(584\) 0.988977 0.0409241
\(585\) −0.662914 1.17783i −0.0274081 0.0486975i
\(586\) 7.07752i 0.292370i
\(587\) −5.94212 5.94212i −0.245257 0.245257i 0.573764 0.819021i \(-0.305483\pi\)
−0.819021 + 0.573764i \(0.805483\pi\)
\(588\) −11.6234 11.4916i −0.479342 0.473907i
\(589\) 34.9103i 1.43846i
\(590\) −16.1075 + 9.06572i −0.663137 + 0.373230i
\(591\) 28.7082i 1.18090i
\(592\) 3.47188 3.47188i 0.142693 0.142693i
\(593\) −30.1675 + 30.1675i −1.23883 + 1.23883i −0.278350 + 0.960480i \(0.589787\pi\)
−0.960480 + 0.278350i \(0.910213\pi\)
\(594\) 1.27894 0.0524754
\(595\) −40.7824 + 23.1066i −1.67191 + 0.947280i
\(596\) −9.48708 −0.388606
\(597\) −26.9182 + 26.9182i −1.10169 + 1.10169i
\(598\) −0.686183 + 0.686183i −0.0280601 + 0.0280601i
\(599\) 44.7384i 1.82796i −0.405760 0.913980i \(-0.632993\pi\)
0.405760 0.913980i \(-0.367007\pi\)
\(600\) 9.98048 + 6.05780i 0.407451 + 0.247309i
\(601\) 20.5386i 0.837786i −0.908036 0.418893i \(-0.862418\pi\)
0.908036 0.418893i \(-0.137582\pi\)
\(602\) 0.0274154 + 9.61654i 0.00111737 + 0.391941i
\(603\) −16.7371 16.7371i −0.681588 0.681588i
\(604\) 0.184085i 0.00749032i
\(605\) 2.15340 + 0.602381i 0.0875482 + 0.0244903i
\(606\) −0.863742 −0.0350871
\(607\) 7.82014 + 7.82014i 0.317410 + 0.317410i 0.847771 0.530362i \(-0.177944\pi\)
−0.530362 + 0.847771i \(0.677944\pi\)
\(608\) 4.13088 4.13088i 0.167529 0.167529i
\(609\) −6.76652 + 6.80521i −0.274193 + 0.275761i
\(610\) 6.43805 + 11.4388i 0.260669 + 0.463144i
\(611\) 1.08347 0.0438326
\(612\) −13.7388 13.7388i −0.555356 0.555356i
\(613\) −23.6072 23.6072i −0.953487 0.953487i 0.0454782 0.998965i \(-0.485519\pi\)
−0.998965 + 0.0454782i \(0.985519\pi\)
\(614\) 33.6625 1.35851
\(615\) −13.6055 24.1736i −0.548626 0.974774i
\(616\) −1.86549 + 1.87615i −0.0751626 + 0.0755924i
\(617\) 21.0998 21.0998i 0.849445 0.849445i −0.140619 0.990064i \(-0.544909\pi\)
0.990064 + 0.140619i \(0.0449092\pi\)
\(618\) 19.6257 + 19.6257i 0.789461 + 0.789461i
\(619\) 21.5632 0.866698 0.433349 0.901226i \(-0.357332\pi\)
0.433349 + 0.901226i \(0.357332\pi\)
\(620\) 12.8683 + 3.59971i 0.516803 + 0.144568i
\(621\) 5.03523i 0.202057i
\(622\) 12.2749 + 12.2749i 0.492180 + 0.492180i
\(623\) −0.0329777 11.5677i −0.00132122 0.463448i
\(624\) 0.575538i 0.0230399i
\(625\) 11.5389 + 22.1778i 0.461554 + 0.887112i
\(626\) 11.4024i 0.455730i
\(627\) −9.64566 + 9.64566i −0.385211 + 0.385211i
\(628\) −9.08936 + 9.08936i −0.362705 + 0.362705i
\(629\) −38.9020 −1.55113
\(630\) 12.6226 7.15178i 0.502897 0.284934i
\(631\) −1.20140 −0.0478271 −0.0239135 0.999714i \(-0.507613\pi\)
−0.0239135 + 0.999714i \(0.507613\pi\)
\(632\) −5.15906 + 5.15906i −0.205216 + 0.205216i
\(633\) −47.1484 + 47.1484i −1.87398 + 1.87398i
\(634\) 0.434362i 0.0172507i
\(635\) −18.6263 + 10.4833i −0.739163 + 0.416019i
\(636\) 20.2462i 0.802813i
\(637\) −1.21305 + 1.22696i −0.0480626 + 0.0486139i
\(638\) 1.09842 + 1.09842i 0.0434869 + 0.0434869i
\(639\) 17.7565i 0.702436i
\(640\) 1.09674 + 1.94863i 0.0433523 + 0.0770264i
\(641\) 38.7703 1.53133 0.765667 0.643237i \(-0.222409\pi\)
0.765667 + 0.643237i \(0.222409\pi\)
\(642\) −8.56387 8.56387i −0.337989 0.337989i
\(643\) −23.7814 + 23.7814i −0.937845 + 0.937845i −0.998178 0.0603332i \(-0.980784\pi\)
0.0603332 + 0.998178i \(0.480784\pi\)
\(644\) −7.38650 7.34451i −0.291069 0.289414i
\(645\) −18.2762 5.11248i −0.719624 0.201304i
\(646\) −46.2861 −1.82110
\(647\) 16.5759 + 16.5759i 0.651665 + 0.651665i 0.953394 0.301729i \(-0.0975636\pi\)
−0.301729 + 0.953394i \(0.597564\pi\)
\(648\) −7.31372 7.31372i −0.287310 0.287310i
\(649\) 8.26608 0.324472
\(650\) 0.639456 1.05353i 0.0250815 0.0413229i
\(651\) 26.0302 26.1790i 1.02020 1.02604i
\(652\) 6.69266 6.69266i 0.262105 0.262105i
\(653\) −8.93778 8.93778i −0.349762 0.349762i 0.510259 0.860021i \(-0.329550\pi\)
−0.860021 + 0.510259i \(0.829550\pi\)
\(654\) 43.8567 1.71493
\(655\) −2.49454 + 8.91755i −0.0974699 + 0.348437i
\(656\) 5.31279i 0.207430i
\(657\) 1.71491 + 1.71491i 0.0669049 + 0.0669049i
\(658\) 0.0331555 + 11.6300i 0.00129253 + 0.453385i
\(659\) 39.7412i 1.54810i 0.633126 + 0.774049i \(0.281772\pi\)
−0.633126 + 0.774049i \(0.718228\pi\)
\(660\) −2.56089 4.55008i −0.0996827 0.177112i
\(661\) 4.69774i 0.182721i −0.995818 0.0913605i \(-0.970878\pi\)
0.995818 0.0913605i \(-0.0291216\pi\)
\(662\) 19.0576 19.0576i 0.740695 0.740695i
\(663\) −3.22442 + 3.22442i −0.125226 + 0.125226i
\(664\) −12.6964 −0.492715
\(665\) 9.21568 33.3101i 0.357369 1.29171i
\(666\) 12.0406 0.466565
\(667\) −4.32453 + 4.32453i −0.167447 + 0.167447i
\(668\) 5.27402 5.27402i 0.204058 0.204058i
\(669\) 36.8401i 1.42432i
\(670\) 5.81429 20.7850i 0.224626 0.802996i
\(671\) 5.87018i 0.226616i
\(672\) 6.17783 0.0176121i 0.238315 0.000679402i
\(673\) −0.821891 0.821891i −0.0316816 0.0316816i 0.691089 0.722770i \(-0.257131\pi\)
−0.722770 + 0.691089i \(0.757131\pi\)
\(674\) 33.8959i 1.30562i
\(675\) −1.51924 6.21159i −0.0584758 0.239084i
\(676\) 12.9392 0.497663
\(677\) 22.1594 + 22.1594i 0.851656 + 0.851656i 0.990337 0.138681i \(-0.0442863\pi\)
−0.138681 + 0.990337i \(0.544286\pi\)
\(678\) 20.2181 20.2181i 0.776473 0.776473i
\(679\) −1.64334 + 1.65273i −0.0630655 + 0.0634261i
\(680\) 4.77270 17.0615i 0.183025 0.654279i
\(681\) −56.4287 −2.16235
\(682\) −4.22553 4.22553i −0.161804 0.161804i
\(683\) −13.5920 13.5920i −0.520082 0.520082i 0.397514 0.917596i \(-0.369873\pi\)
−0.917596 + 0.397514i \(0.869873\pi\)
\(684\) 14.3261 0.547772
\(685\) 27.9108 15.7089i 1.06642 0.600205i
\(686\) −13.2073 12.9833i −0.504258 0.495705i
\(687\) 36.7561 36.7561i 1.40233 1.40233i
\(688\) −2.57014 2.57014i −0.0979857 0.0979857i
\(689\) 2.13717 0.0814196
\(690\) 17.9139 10.0824i 0.681969 0.383829i
\(691\) 36.0061i 1.36974i −0.728667 0.684868i \(-0.759860\pi\)
0.728667 0.684868i \(-0.240140\pi\)
\(692\) −9.25971 9.25971i −0.352001 0.352001i
\(693\) −6.48809 + 0.0184966i −0.246462 + 0.000702628i
\(694\) 24.9267i 0.946205i
\(695\) 26.8121 + 7.50026i 1.01704 + 0.284501i
\(696\) 3.62721i 0.137489i
\(697\) −29.7646 + 29.7646i −1.12742 + 1.12742i
\(698\) 23.0010 23.0010i 0.870599 0.870599i
\(699\) −38.8829 −1.47069
\(700\) 11.3282 + 6.83170i 0.428165 + 0.258214i
\(701\) 28.1878 1.06464 0.532319 0.846544i \(-0.321321\pi\)
0.532319 + 0.846544i \(0.321321\pi\)
\(702\) −0.222904 + 0.222904i −0.00841298 + 0.00841298i
\(703\) 20.2825 20.2825i 0.764971 0.764971i
\(704\) 1.00000i 0.0376889i
\(705\) −22.1028 6.18291i −0.832439 0.232862i
\(706\) 27.9433i 1.05166i
\(707\) −0.978683 + 0.00279008i −0.0368072 + 0.000104932i
\(708\) −13.6481 13.6481i −0.512929 0.512929i
\(709\) 13.3379i 0.500916i −0.968127 0.250458i \(-0.919419\pi\)
0.968127 0.250458i \(-0.0805813\pi\)
\(710\) 14.1097 7.94127i 0.529527 0.298030i
\(711\) −17.8918 −0.670997
\(712\) 3.09160 + 3.09160i 0.115863 + 0.115863i
\(713\) 16.6361 16.6361i 0.623027 0.623027i
\(714\) −34.7097 34.5123i −1.29898 1.29159i
\(715\) −0.480302 + 0.270326i −0.0179623 + 0.0101096i
\(716\) −12.5815 −0.470192
\(717\) −43.7463 43.7463i −1.63374 1.63374i
\(718\) 0.433516 + 0.433516i 0.0161787 + 0.0161787i
\(719\) 16.0240 0.597594 0.298797 0.954317i \(-0.403415\pi\)
0.298797 + 0.954317i \(0.403415\pi\)
\(720\) −1.47721 + 5.28074i −0.0550522 + 0.196802i
\(721\) 22.3007 + 22.1740i 0.830523 + 0.825801i
\(722\) 10.6974 10.6974i 0.398115 0.398115i
\(723\) 25.2024 + 25.2024i 0.937287 + 0.937287i
\(724\) −22.1174 −0.821985
\(725\) 4.03004 6.63967i 0.149672 0.246591i
\(726\) 2.33501i 0.0866604i
\(727\) 14.4143 + 14.4143i 0.534595 + 0.534595i 0.921936 0.387341i \(-0.126606\pi\)
−0.387341 + 0.921936i \(0.626606\pi\)
\(728\) −0.00185912 0.652127i −6.89035e−5 0.0241694i
\(729\) 16.4053i 0.607605i
\(730\) −0.595740 + 2.12966i −0.0220493 + 0.0788224i
\(731\) 28.7981i 1.06514i
\(732\) −9.69227 + 9.69227i −0.358237 + 0.358237i
\(733\) 12.1058 12.1058i 0.447138 0.447138i −0.447264 0.894402i \(-0.647601\pi\)
0.894402 + 0.447264i \(0.147601\pi\)
\(734\) 13.0331 0.481061
\(735\) 31.7478 18.1076i 1.17104 0.667908i
\(736\) 3.93704 0.145121
\(737\) −6.82513 + 6.82513i −0.251407 + 0.251407i
\(738\) 9.21249 9.21249i 0.339117 0.339117i
\(739\) 52.7975i 1.94219i −0.238702 0.971093i \(-0.576722\pi\)
0.238702 0.971093i \(-0.423278\pi\)
\(740\) 5.38496 + 9.56774i 0.197955 + 0.351717i
\(741\) 3.36226i 0.123516i
\(742\) 0.0653998 + 22.9404i 0.00240090 + 0.842169i
\(743\) 18.8400 + 18.8400i 0.691172 + 0.691172i 0.962490 0.271318i \(-0.0874594\pi\)
−0.271318 + 0.962490i \(0.587459\pi\)
\(744\) 13.9536i 0.511562i
\(745\) 5.71483 20.4295i 0.209375 0.748478i
\(746\) 32.7559 1.19928
\(747\) −22.0158 22.0158i −0.805516 0.805516i
\(748\) −5.60245 + 5.60245i −0.204846 + 0.204846i
\(749\) −9.73116 9.67583i −0.355569 0.353547i
\(750\) −19.0569 + 17.8429i −0.695861 + 0.651530i
\(751\) 26.1515 0.954281 0.477141 0.878827i \(-0.341673\pi\)
0.477141 + 0.878827i \(0.341673\pi\)
\(752\) −3.10826 3.10826i −0.113347 0.113347i
\(753\) 9.89747 + 9.89747i 0.360684 + 0.360684i
\(754\) −0.382885 −0.0139439
\(755\) −0.396409 0.110889i −0.0144268 0.00403568i
\(756\) −2.39948 2.38584i −0.0872683 0.0867721i
\(757\) −3.83287 + 3.83287i −0.139308 + 0.139308i −0.773322 0.634014i \(-0.781406\pi\)
0.634014 + 0.773322i \(0.281406\pi\)
\(758\) −13.2030 13.2030i −0.479554 0.479554i
\(759\) −9.19304 −0.333686
\(760\) 6.40709 + 11.3838i 0.232409 + 0.412934i
\(761\) 21.4031i 0.775862i 0.921688 + 0.387931i \(0.126810\pi\)
−0.921688 + 0.387931i \(0.873190\pi\)
\(762\) −15.7823 15.7823i −0.571733 0.571733i
\(763\) 49.6929 0.141667i 1.79900 0.00512869i
\(764\) 6.49463i 0.234967i
\(765\) 37.8610 21.3091i 1.36887 0.770432i
\(766\) 6.83294i 0.246884i
\(767\) −1.44069 + 1.44069i −0.0520201 + 0.0520201i
\(768\) −1.65110 + 1.65110i −0.0595790 + 0.0595790i
\(769\) −30.0882 −1.08501 −0.542505 0.840053i \(-0.682524\pi\)
−0.542505 + 0.840053i \(0.682524\pi\)
\(770\) −2.91638 5.14730i −0.105099 0.185496i
\(771\) 33.6385 1.21146
\(772\) 9.30134 9.30134i 0.334762 0.334762i
\(773\) −28.3430 + 28.3430i −1.01943 + 1.01943i −0.0196183 + 0.999808i \(0.506245\pi\)
−0.999808 + 0.0196183i \(0.993755\pi\)
\(774\) 8.91336i 0.320384i
\(775\) −15.5032 + 25.5422i −0.556892 + 0.917503i
\(776\) 0.880916i 0.0316230i
\(777\) 30.3330 0.0864750i 1.08819 0.00310227i
\(778\) 22.6638 + 22.6638i 0.812536 + 0.812536i
\(779\) 31.0370i 1.11202i
\(780\) 1.23936 + 0.346693i 0.0443763 + 0.0124136i
\(781\) −7.24081 −0.259097
\(782\) −22.0571 22.0571i −0.788760 0.788760i
\(783\) −1.40481 + 1.40481i −0.0502038 + 0.0502038i
\(784\) 6.99989 0.0399116i 0.249996 0.00142542i
\(785\) −14.0978 25.0483i −0.503172 0.894012i
\(786\) −9.66962 −0.344904
\(787\) −25.2455 25.2455i −0.899904 0.899904i 0.0955234 0.995427i \(-0.469548\pi\)
−0.995427 + 0.0955234i \(0.969548\pi\)
\(788\) −8.69365 8.69365i −0.309699 0.309699i
\(789\) 3.71564 0.132280
\(790\) −8.00181 14.2172i −0.284691 0.505827i
\(791\) 22.8433 22.9740i 0.812216 0.816860i
\(792\) 1.73402 1.73402i 0.0616158 0.0616158i
\(793\) 1.02311 + 1.02311i 0.0363316 + 0.0363316i
\(794\) −29.8890 −1.06072
\(795\) −43.5982 12.1959i −1.54627 0.432544i
\(796\) 16.3032i 0.577851i
\(797\) 0.829786 + 0.829786i 0.0293925 + 0.0293925i 0.721650 0.692258i \(-0.243384\pi\)
−0.692258 + 0.721650i \(0.743384\pi\)
\(798\) 36.0906 0.102889i 1.27759 0.00364223i
\(799\) 34.8278i 1.23212i
\(800\) −4.85684 + 1.18790i −0.171715 + 0.0419985i
\(801\) 10.7218i 0.378836i
\(802\) −24.0497 + 24.0497i −0.849223 + 0.849223i
\(803\) 0.699312 0.699312i 0.0246782 0.0246782i
\(804\) 22.5380 0.794853
\(805\) 20.2652 11.4819i 0.714253 0.404684i
\(806\) 1.47293 0.0518816
\(807\) 41.1557 41.1557i 1.44875 1.44875i
\(808\) 0.261565 0.261565i 0.00920183 0.00920183i
\(809\) 13.0221i 0.457834i 0.973446 + 0.228917i \(0.0735185\pi\)
−0.973446 + 0.228917i \(0.926482\pi\)
\(810\) 20.1550 11.3437i 0.708175 0.398578i
\(811\) 13.6474i 0.479226i 0.970869 + 0.239613i \(0.0770205\pi\)
−0.970869 + 0.239613i \(0.922979\pi\)
\(812\) −0.0117167 4.10990i −0.000411176 0.144229i
\(813\) 32.9958 + 32.9958i 1.15721 + 1.15721i
\(814\) 4.90998i 0.172095i
\(815\) 10.3805 + 18.4435i 0.363612 + 0.646048i
\(816\) 18.5004 0.647645
\(817\) −15.0146 15.0146i −0.525295 0.525295i
\(818\) 2.90843 2.90843i 0.101691 0.101691i
\(819\) 1.12758 1.13403i 0.0394008 0.0396261i
\(820\) 11.4406 + 3.20032i 0.399522 + 0.111760i
\(821\) 16.9473 0.591463 0.295732 0.955271i \(-0.404437\pi\)
0.295732 + 0.955271i \(0.404437\pi\)
\(822\) 23.6492 + 23.6492i 0.824860 + 0.824860i
\(823\) 9.35366 + 9.35366i 0.326048 + 0.326048i 0.851082 0.525034i \(-0.175947\pi\)
−0.525034 + 0.851082i \(0.675947\pi\)
\(824\) −11.8864 −0.414083
\(825\) 11.3408 2.77375i 0.394835 0.0965697i
\(826\) −15.5084 15.4203i −0.539608 0.536540i
\(827\) −10.2275 + 10.2275i −0.355645 + 0.355645i −0.862205 0.506560i \(-0.830917\pi\)
0.506560 + 0.862205i \(0.330917\pi\)
\(828\) 6.82692 + 6.82692i 0.237252 + 0.237252i
\(829\) 7.06038 0.245217 0.122609 0.992455i \(-0.460874\pi\)
0.122609 + 0.992455i \(0.460874\pi\)
\(830\) 7.64805 27.3404i 0.265468 0.948999i
\(831\) 40.3223i 1.39876i
\(832\) 0.174289 + 0.174289i 0.00604238 + 0.00604238i
\(833\) −39.4401 38.9929i −1.36652 1.35102i
\(834\) 29.0733i 1.00673i
\(835\) 8.18012 + 14.5341i 0.283085 + 0.502972i
\(836\) 5.84195i 0.202048i
\(837\) 5.40418 5.40418i 0.186796 0.186796i
\(838\) −5.38547 + 5.38547i −0.186038 + 0.186038i
\(839\) 8.36005 0.288621 0.144310 0.989532i \(-0.453904\pi\)
0.144310 + 0.989532i \(0.453904\pi\)
\(840\) −3.68348 + 13.3140i −0.127092 + 0.459375i
\(841\) 26.5869 0.916791
\(842\) −22.0449 + 22.0449i −0.759717 + 0.759717i
\(843\) 20.0104 20.0104i 0.689195 0.689195i
\(844\) 28.5557i 0.982928i
\(845\) −7.79435 + 27.8634i −0.268134 + 0.958530i
\(846\) 10.7796i 0.370610i
\(847\) 0.00754262 + 2.64574i 0.000259167 + 0.0909087i
\(848\) −6.13111 6.13111i −0.210543 0.210543i
\(849\) 8.38886i 0.287905i
\(850\) 33.8653 + 20.5551i 1.16157 + 0.705033i
\(851\) 19.3308 0.662651
\(852\) 11.9553 + 11.9553i 0.409583 + 0.409583i
\(853\) −14.5398 + 14.5398i −0.497834 + 0.497834i −0.910763 0.412929i \(-0.864506\pi\)
0.412929 + 0.910763i \(0.364506\pi\)
\(854\) −10.9507 + 11.0134i −0.374727 + 0.376870i
\(855\) −8.62976 + 30.8498i −0.295132 + 1.05504i
\(856\) 5.18676 0.177280
\(857\) −7.95621 7.95621i −0.271779 0.271779i 0.558037 0.829816i \(-0.311555\pi\)
−0.829816 + 0.558037i \(0.811555\pi\)
\(858\) −0.406966 0.406966i −0.0138936 0.0138936i
\(859\) −18.9137 −0.645326 −0.322663 0.946514i \(-0.604578\pi\)
−0.322663 + 0.946514i \(0.604578\pi\)
\(860\) 7.08275 3.98634i 0.241520 0.135933i
\(861\) 23.1422 23.2745i 0.788683 0.793192i
\(862\) 1.70358 1.70358i 0.0580243 0.0580243i
\(863\) −0.296888 0.296888i −0.0101062 0.0101062i 0.702036 0.712142i \(-0.252275\pi\)
−0.712142 + 0.702036i \(0.752275\pi\)
\(864\) 1.27894 0.0435103
\(865\) 25.5177 14.3620i 0.867629 0.488323i
\(866\) 10.7055i 0.363788i
\(867\) −75.5789 75.5789i −2.56679 2.56679i
\(868\) 0.0450732 + 15.8104i 0.00152988 + 0.536641i
\(869\) 7.29601i 0.247500i
\(870\) 7.81084 + 2.18496i 0.264812 + 0.0740772i
\(871\) 2.37909i 0.0806123i
\(872\) −13.2810 + 13.2810i −0.449752 + 0.449752i
\(873\) 1.52753 1.52753i 0.0516990 0.0516990i
\(874\) 23.0000 0.777987
\(875\) −21.5353 + 20.2789i −0.728025 + 0.685551i
\(876\) −2.30927 −0.0780231
\(877\) 15.9103 15.9103i 0.537253 0.537253i −0.385468 0.922721i \(-0.625960\pi\)
0.922721 + 0.385468i \(0.125960\pi\)
\(878\) 0.833455 0.833455i 0.0281277 0.0281277i
\(879\) 16.5261i 0.557411i
\(880\) 2.15340 + 0.602381i 0.0725911 + 0.0203062i
\(881\) 16.7161i 0.563180i 0.959535 + 0.281590i \(0.0908617\pi\)
−0.959535 + 0.281590i \(0.909138\pi\)
\(882\) 12.2072 + 12.0688i 0.411037 + 0.406376i
\(883\) −25.8566 25.8566i −0.870144 0.870144i 0.122344 0.992488i \(-0.460959\pi\)
−0.992488 + 0.122344i \(0.960959\pi\)
\(884\) 1.95289i 0.0656827i
\(885\) 37.6113 21.1686i 1.26429 0.711573i
\(886\) −29.0268 −0.975175
\(887\) −36.7666 36.7666i −1.23450 1.23450i −0.962217 0.272283i \(-0.912221\pi\)
−0.272283 0.962217i \(-0.587779\pi\)
\(888\) −8.10688 + 8.10688i −0.272049 + 0.272049i
\(889\) −17.9335 17.8316i −0.601471 0.598051i
\(890\) −8.51977 + 4.79513i −0.285583 + 0.160733i
\(891\) −10.3432 −0.346509
\(892\) 11.1562 + 11.1562i 0.373538 + 0.373538i
\(893\) −18.1583 18.1583i −0.607645 0.607645i
\(894\) 22.1524 0.740888
\(895\) 7.57884 27.0930i 0.253333 0.905618i
\(896\) −1.86549 + 1.87615i −0.0623216 + 0.0626779i
\(897\) 1.60225 1.60225i 0.0534974 0.0534974i
\(898\) −14.3586 14.3586i −0.479151 0.479151i
\(899\) 9.28282 0.309599
\(900\) −10.4817 6.36203i −0.349390 0.212068i
\(901\) 68.6984i 2.28868i
\(902\) −3.75671 3.75671i −0.125085 0.125085i
\(903\) −0.0640152 22.4547i −0.00213029 0.747247i
\(904\) 12.2452i 0.407271i
\(905\) 13.3231 47.6275i 0.442874 1.58319i
\(906\) 0.429841i 0.0142805i
\(907\) −23.9547 + 23.9547i −0.795403 + 0.795403i −0.982367 0.186963i \(-0.940135\pi\)
0.186963 + 0.982367i \(0.440135\pi\)
\(908\) 17.0882 17.0882i 0.567091 0.567091i
\(909\) 0.907120 0.0300873
\(910\) 1.40541 + 0.388825i 0.0465889 + 0.0128894i
\(911\) −8.04984 −0.266703 −0.133351 0.991069i \(-0.542574\pi\)
−0.133351 + 0.991069i \(0.542574\pi\)
\(912\) −9.64566 + 9.64566i −0.319400 + 0.319400i
\(913\) −8.97769 + 8.97769i −0.297118 + 0.297118i
\(914\) 18.0679i 0.597633i
\(915\) −15.0329 26.7098i −0.496973 0.882998i
\(916\) 22.2615i 0.735541i
\(917\) −10.9564 + 0.0312351i −0.361812 + 0.00103147i
\(918\) −7.16517 7.16517i −0.236486 0.236486i
\(919\) 38.1618i 1.25884i −0.777065 0.629420i \(-0.783292\pi\)
0.777065 0.629420i \(-0.216708\pi\)
\(920\) −2.37160 + 8.47804i −0.0781893 + 0.279513i
\(921\) −78.6024 −2.59004
\(922\) 1.92979 + 1.92979i 0.0635542 + 0.0635542i
\(923\) 1.26199 1.26199i 0.0415390 0.0415390i
\(924\) 4.35594 4.38084i 0.143300 0.144119i
\(925\) −23.8470 + 5.83255i −0.784084 + 0.191773i
\(926\) 29.5626 0.971486
\(927\) −20.6113 20.6113i −0.676964 0.676964i
\(928\) 1.09842 + 1.09842i 0.0360574 + 0.0360574i
\(929\) −44.9165 −1.47366 −0.736831 0.676077i \(-0.763679\pi\)
−0.736831 + 0.676077i \(0.763679\pi\)
\(930\) −30.0476 8.40536i −0.985300 0.275622i
\(931\) 40.8930 0.233162i 1.34021 0.00764157i
\(932\) 11.7748 11.7748i 0.385698 0.385698i
\(933\) −28.6621 28.6621i −0.938355 0.938355i
\(934\) 9.96086 0.325929
\(935\) −8.68951 15.4391i −0.284177 0.504913i
\(936\) 0.604442i 0.0197568i
\(937\) 17.2385 + 17.2385i 0.563158 + 0.563158i 0.930203 0.367045i \(-0.119631\pi\)
−0.367045 + 0.930203i \(0.619631\pi\)
\(938\) 25.5372 0.0728028i 0.833819 0.00237710i
\(939\) 26.6246i 0.868863i
\(940\) 8.56570 4.82098i 0.279382 0.157243i
\(941\) 7.51266i 0.244906i −0.992474 0.122453i \(-0.960924\pi\)
0.992474 0.122453i \(-0.0390761\pi\)
\(942\) 21.2238 21.2238i 0.691508 0.691508i
\(943\) 14.7903 14.7903i 0.481639 0.481639i
\(944\) 8.26608 0.269038
\(945\) 6.58307 3.72986i 0.214147 0.121332i
\(946\) −3.63473 −0.118175
\(947\) −20.7575 + 20.7575i −0.674528 + 0.674528i −0.958757 0.284228i \(-0.908263\pi\)
0.284228 + 0.958757i \(0.408263\pi\)
\(948\) 12.0465 12.0465i 0.391251 0.391251i
\(949\) 0.243765i 0.00791294i
\(950\) −28.3734 + 6.93964i −0.920555 + 0.225152i
\(951\) 1.01424i 0.0328890i
\(952\) 20.9624 0.0597606i 0.679394 0.00193685i
\(953\) −4.37098 4.37098i −0.141590 0.141590i 0.632759 0.774349i \(-0.281922\pi\)
−0.774349 + 0.632759i \(0.781922\pi\)
\(954\) 21.2630i 0.688414i
\(955\) −13.9855 3.91224i −0.452561 0.126597i
\(956\) 26.4952 0.856917
\(957\) −2.56483 2.56483i −0.0829091 0.0829091i
\(958\) −20.1055 + 20.1055i −0.649579 + 0.649579i
\(959\) 26.8727 + 26.7199i 0.867764 + 0.862830i
\(960\) −2.56089 4.55008i −0.0826525 0.146853i
\(961\) −4.71019 −0.151942
\(962\) 0.855754 + 0.855754i 0.0275906 + 0.0275906i
\(963\) 8.99396 + 8.99396i 0.289826 + 0.289826i
\(964\) −15.2640 −0.491620
\(965\) 14.4266 + 25.6325i 0.464408 + 0.825138i
\(966\) 17.2476 + 17.1495i 0.554931 + 0.551776i
\(967\) −2.91714 + 2.91714i −0.0938089 + 0.0938089i −0.752454 0.658645i \(-0.771130\pi\)
0.658645 + 0.752454i \(0.271130\pi\)
\(968\) −0.707107 0.707107i −0.0227273 0.0227273i
\(969\) 108.079 3.47198
\(970\) 1.89697 + 0.530647i 0.0609079 + 0.0170380i
\(971\) 52.8711i 1.69672i −0.529423 0.848358i \(-0.677592\pi\)
0.529423 0.848358i \(-0.322408\pi\)
\(972\) 14.3646 + 14.3646i 0.460745 + 0.460745i
\(973\) 0.0939134 + 32.9422i 0.00301073 + 1.05608i
\(974\) 4.22302i 0.135314i
\(975\) −1.49314 + 2.46001i −0.0478187 + 0.0787832i
\(976\) 5.87018i 0.187900i
\(977\) −1.30914 + 1.30914i −0.0418832 + 0.0418832i −0.727738 0.685855i \(-0.759428\pi\)
0.685855 + 0.727738i \(0.259428\pi\)
\(978\) −15.6274 + 15.6274i −0.499710 + 0.499710i
\(979\) 4.37218 0.139735
\(980\) −4.13065 + 15.0976i −0.131949 + 0.482275i
\(981\) −46.0592 −1.47056
\(982\) −29.5046 + 29.5046i −0.941531 + 0.941531i
\(983\) 6.95163 6.95163i 0.221723 0.221723i −0.587501 0.809224i \(-0.699888\pi\)
0.809224 + 0.587501i \(0.199888\pi\)
\(984\) 12.4054i 0.395470i
\(985\) 23.9578 13.4840i 0.763359 0.429637i
\(986\) 12.3077i 0.391957i
\(987\) −0.0774184 27.1562i −0.00246425 0.864392i
\(988\) 1.01819 + 1.01819i 0.0323928 + 0.0323928i
\(989\) 14.3101i 0.455034i
\(990\) 2.68951 + 4.77859i 0.0854781 + 0.151874i
\(991\) −15.7718 −0.501007 −0.250503 0.968116i \(-0.580596\pi\)
−0.250503 + 0.968116i \(0.580596\pi\)
\(992\) −4.22553 4.22553i −0.134161 0.134161i
\(993\) −44.4998 + 44.4998i −1.41216 + 1.41216i
\(994\) 13.5849 + 13.5076i 0.430886 + 0.428436i
\(995\) 35.1073 + 9.82072i 1.11298 + 0.311338i
\(996\) 29.6462 0.939375
\(997\) −4.36904 4.36904i −0.138369 0.138369i 0.634530 0.772899i \(-0.281194\pi\)
−0.772899 + 0.634530i \(0.781194\pi\)
\(998\) −15.9388 15.9388i −0.504534 0.504534i
\(999\) 6.27955 0.198676
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 770.2.l.c.573.12 40
5.2 odd 4 inner 770.2.l.c.727.19 yes 40
7.6 odd 2 inner 770.2.l.c.573.19 yes 40
35.27 even 4 inner 770.2.l.c.727.12 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
770.2.l.c.573.12 40 1.1 even 1 trivial
770.2.l.c.573.19 yes 40 7.6 odd 2 inner
770.2.l.c.727.12 yes 40 35.27 even 4 inner
770.2.l.c.727.19 yes 40 5.2 odd 4 inner