Properties

Label 731.2.f.c.259.5
Level $731$
Weight $2$
Character 731.259
Analytic conductor $5.837$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [731,2,Mod(259,731)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(731, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("731.259");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.f (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: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 259.5
Character \(\chi\) \(=\) 731.259
Dual form 731.2.f.c.302.24

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.18921i q^{2} +(0.566370 - 0.566370i) q^{3} -2.79262 q^{4} +(2.16421 - 2.16421i) q^{5} +(-1.23990 - 1.23990i) q^{6} +(0.402819 + 0.402819i) q^{7} +1.73522i q^{8} +2.35845i q^{9} +O(q^{10})\) \(q-2.18921i q^{2} +(0.566370 - 0.566370i) q^{3} -2.79262 q^{4} +(2.16421 - 2.16421i) q^{5} +(-1.23990 - 1.23990i) q^{6} +(0.402819 + 0.402819i) q^{7} +1.73522i q^{8} +2.35845i q^{9} +(-4.73791 - 4.73791i) q^{10} +(-0.753153 - 0.753153i) q^{11} +(-1.58166 + 1.58166i) q^{12} -1.40800 q^{13} +(0.881854 - 0.881854i) q^{14} -2.45149i q^{15} -1.78650 q^{16} +(-2.51684 - 3.26581i) q^{17} +5.16313 q^{18} -3.93447i q^{19} +(-6.04383 + 6.04383i) q^{20} +0.456289 q^{21} +(-1.64881 + 1.64881i) q^{22} +(-4.48958 - 4.48958i) q^{23} +(0.982775 + 0.982775i) q^{24} -4.36762i q^{25} +3.08240i q^{26} +(3.03486 + 3.03486i) q^{27} +(-1.12492 - 1.12492i) q^{28} +(-1.51852 + 1.51852i) q^{29} -5.36681 q^{30} +(7.25769 - 7.25769i) q^{31} +7.38145i q^{32} -0.853127 q^{33} +(-7.14954 + 5.50987i) q^{34} +1.74357 q^{35} -6.58627i q^{36} +(3.66111 - 3.66111i) q^{37} -8.61336 q^{38} +(-0.797448 + 0.797448i) q^{39} +(3.75538 + 3.75538i) q^{40} +(6.57620 + 6.57620i) q^{41} -0.998911i q^{42} +1.00000i q^{43} +(2.10327 + 2.10327i) q^{44} +(5.10419 + 5.10419i) q^{45} +(-9.82862 + 9.82862i) q^{46} +3.13213 q^{47} +(-1.01182 + 1.01182i) q^{48} -6.67547i q^{49} -9.56163 q^{50} +(-3.27512 - 0.424198i) q^{51} +3.93201 q^{52} +12.8477i q^{53} +(6.64394 - 6.64394i) q^{54} -3.25997 q^{55} +(-0.698978 + 0.698978i) q^{56} +(-2.22836 - 2.22836i) q^{57} +(3.32436 + 3.32436i) q^{58} +10.6980i q^{59} +6.84609i q^{60} +(-7.86213 - 7.86213i) q^{61} +(-15.8886 - 15.8886i) q^{62} +(-0.950028 + 0.950028i) q^{63} +12.5865 q^{64} +(-3.04721 + 3.04721i) q^{65} +1.86767i q^{66} +10.4169 q^{67} +(7.02858 + 9.12019i) q^{68} -5.08553 q^{69} -3.81704i q^{70} +(1.76577 - 1.76577i) q^{71} -4.09243 q^{72} +(-1.14439 + 1.14439i) q^{73} +(-8.01492 - 8.01492i) q^{74} +(-2.47369 - 2.47369i) q^{75} +10.9875i q^{76} -0.606769i q^{77} +(1.74578 + 1.74578i) q^{78} +(2.93031 + 2.93031i) q^{79} +(-3.86636 + 3.86636i) q^{80} -3.63764 q^{81} +(14.3967 - 14.3967i) q^{82} +15.9295i q^{83} -1.27424 q^{84} +(-12.5149 - 1.62095i) q^{85} +2.18921 q^{86} +1.72009i q^{87} +(1.30688 - 1.30688i) q^{88} +12.2961 q^{89} +(11.1741 - 11.1741i) q^{90} +(-0.567169 - 0.567169i) q^{91} +(12.5377 + 12.5377i) q^{92} -8.22107i q^{93} -6.85688i q^{94} +(-8.51502 - 8.51502i) q^{95} +(4.18063 + 4.18063i) q^{96} +(-2.65003 + 2.65003i) q^{97} -14.6140 q^{98} +(1.77627 - 1.77627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.18921i 1.54800i −0.633184 0.774001i \(-0.718252\pi\)
0.633184 0.774001i \(-0.281748\pi\)
\(3\) 0.566370 0.566370i 0.326994 0.326994i −0.524448 0.851442i \(-0.675728\pi\)
0.851442 + 0.524448i \(0.175728\pi\)
\(4\) −2.79262 −1.39631
\(5\) 2.16421 2.16421i 0.967865 0.967865i −0.0316346 0.999500i \(-0.510071\pi\)
0.999500 + 0.0316346i \(0.0100713\pi\)
\(6\) −1.23990 1.23990i −0.506187 0.506187i
\(7\) 0.402819 + 0.402819i 0.152251 + 0.152251i 0.779123 0.626871i \(-0.215665\pi\)
−0.626871 + 0.779123i \(0.715665\pi\)
\(8\) 1.73522i 0.613492i
\(9\) 2.35845i 0.786150i
\(10\) −4.73791 4.73791i −1.49826 1.49826i
\(11\) −0.753153 0.753153i −0.227084 0.227084i 0.584389 0.811473i \(-0.301334\pi\)
−0.811473 + 0.584389i \(0.801334\pi\)
\(12\) −1.58166 + 1.58166i −0.456585 + 0.456585i
\(13\) −1.40800 −0.390509 −0.195254 0.980753i \(-0.562553\pi\)
−0.195254 + 0.980753i \(0.562553\pi\)
\(14\) 0.881854 0.881854i 0.235685 0.235685i
\(15\) 2.45149i 0.632972i
\(16\) −1.78650 −0.446625
\(17\) −2.51684 3.26581i −0.610422 0.792076i
\(18\) 5.16313 1.21696
\(19\) 3.93447i 0.902629i −0.892365 0.451315i \(-0.850955\pi\)
0.892365 0.451315i \(-0.149045\pi\)
\(20\) −6.04383 + 6.04383i −1.35144 + 1.35144i
\(21\) 0.456289 0.0995704
\(22\) −1.64881 + 1.64881i −0.351527 + 0.351527i
\(23\) −4.48958 4.48958i −0.936143 0.936143i 0.0619375 0.998080i \(-0.480272\pi\)
−0.998080 + 0.0619375i \(0.980272\pi\)
\(24\) 0.982775 + 0.982775i 0.200608 + 0.200608i
\(25\) 4.36762i 0.873525i
\(26\) 3.08240i 0.604508i
\(27\) 3.03486 + 3.03486i 0.584060 + 0.584060i
\(28\) −1.12492 1.12492i −0.212590 0.212590i
\(29\) −1.51852 + 1.51852i −0.281983 + 0.281983i −0.833899 0.551916i \(-0.813897\pi\)
0.551916 + 0.833899i \(0.313897\pi\)
\(30\) −5.36681 −0.979842
\(31\) 7.25769 7.25769i 1.30352 1.30352i 0.377516 0.926003i \(-0.376778\pi\)
0.926003 0.377516i \(-0.123222\pi\)
\(32\) 7.38145i 1.30487i
\(33\) −0.853127 −0.148510
\(34\) −7.14954 + 5.50987i −1.22614 + 0.944935i
\(35\) 1.74357 0.294717
\(36\) 6.58627i 1.09771i
\(37\) 3.66111 3.66111i 0.601883 0.601883i −0.338929 0.940812i \(-0.610065\pi\)
0.940812 + 0.338929i \(0.110065\pi\)
\(38\) −8.61336 −1.39727
\(39\) −0.797448 + 0.797448i −0.127694 + 0.127694i
\(40\) 3.75538 + 3.75538i 0.593778 + 0.593778i
\(41\) 6.57620 + 6.57620i 1.02703 + 1.02703i 0.999624 + 0.0274060i \(0.00872469\pi\)
0.0274060 + 0.999624i \(0.491275\pi\)
\(42\) 0.998911i 0.154135i
\(43\) 1.00000i 0.152499i
\(44\) 2.10327 + 2.10327i 0.317080 + 0.317080i
\(45\) 5.10419 + 5.10419i 0.760887 + 0.760887i
\(46\) −9.82862 + 9.82862i −1.44915 + 1.44915i
\(47\) 3.13213 0.456868 0.228434 0.973559i \(-0.426639\pi\)
0.228434 + 0.973559i \(0.426639\pi\)
\(48\) −1.01182 + 1.01182i −0.146043 + 0.146043i
\(49\) 6.67547i 0.953639i
\(50\) −9.56163 −1.35222
\(51\) −3.27512 0.424198i −0.458608 0.0593997i
\(52\) 3.93201 0.545272
\(53\) 12.8477i 1.76477i 0.470530 + 0.882384i \(0.344063\pi\)
−0.470530 + 0.882384i \(0.655937\pi\)
\(54\) 6.64394 6.64394i 0.904126 0.904126i
\(55\) −3.25997 −0.439574
\(56\) −0.698978 + 0.698978i −0.0934049 + 0.0934049i
\(57\) −2.22836 2.22836i −0.295154 0.295154i
\(58\) 3.32436 + 3.32436i 0.436510 + 0.436510i
\(59\) 10.6980i 1.39276i 0.717674 + 0.696379i \(0.245207\pi\)
−0.717674 + 0.696379i \(0.754793\pi\)
\(60\) 6.84609i 0.883826i
\(61\) −7.86213 7.86213i −1.00664 1.00664i −0.999978 0.00666445i \(-0.997879\pi\)
−0.00666445 0.999978i \(-0.502121\pi\)
\(62\) −15.8886 15.8886i −2.01785 2.01785i
\(63\) −0.950028 + 0.950028i −0.119692 + 0.119692i
\(64\) 12.5865 1.57331
\(65\) −3.04721 + 3.04721i −0.377960 + 0.377960i
\(66\) 1.86767i 0.229894i
\(67\) 10.4169 1.27263 0.636316 0.771429i \(-0.280458\pi\)
0.636316 + 0.771429i \(0.280458\pi\)
\(68\) 7.02858 + 9.12019i 0.852340 + 1.10599i
\(69\) −5.08553 −0.612226
\(70\) 3.81704i 0.456223i
\(71\) 1.76577 1.76577i 0.209559 0.209559i −0.594521 0.804080i \(-0.702658\pi\)
0.804080 + 0.594521i \(0.202658\pi\)
\(72\) −4.09243 −0.482297
\(73\) −1.14439 + 1.14439i −0.133941 + 0.133941i −0.770899 0.636958i \(-0.780193\pi\)
0.636958 + 0.770899i \(0.280193\pi\)
\(74\) −8.01492 8.01492i −0.931716 0.931716i
\(75\) −2.47369 2.47369i −0.285637 0.285637i
\(76\) 10.9875i 1.26035i
\(77\) 0.606769i 0.0691477i
\(78\) 1.74578 + 1.74578i 0.197670 + 0.197670i
\(79\) 2.93031 + 2.93031i 0.329685 + 0.329685i 0.852467 0.522781i \(-0.175106\pi\)
−0.522781 + 0.852467i \(0.675106\pi\)
\(80\) −3.86636 + 3.86636i −0.432272 + 0.432272i
\(81\) −3.63764 −0.404182
\(82\) 14.3967 14.3967i 1.58985 1.58985i
\(83\) 15.9295i 1.74848i 0.485490 + 0.874242i \(0.338641\pi\)
−0.485490 + 0.874242i \(0.661359\pi\)
\(84\) −1.27424 −0.139031
\(85\) −12.5149 1.62095i −1.35743 0.175816i
\(86\) 2.18921 0.236068
\(87\) 1.72009i 0.184413i
\(88\) 1.30688 1.30688i 0.139314 0.139314i
\(89\) 12.2961 1.30338 0.651689 0.758486i \(-0.274061\pi\)
0.651689 + 0.758486i \(0.274061\pi\)
\(90\) 11.1741 11.1741i 1.17786 1.17786i
\(91\) −0.567169 0.567169i −0.0594554 0.0594554i
\(92\) 12.5377 + 12.5377i 1.30715 + 1.30715i
\(93\) 8.22107i 0.852485i
\(94\) 6.85688i 0.707233i
\(95\) −8.51502 8.51502i −0.873623 0.873623i
\(96\) 4.18063 + 4.18063i 0.426684 + 0.426684i
\(97\) −2.65003 + 2.65003i −0.269069 + 0.269069i −0.828725 0.559656i \(-0.810933\pi\)
0.559656 + 0.828725i \(0.310933\pi\)
\(98\) −14.6140 −1.47624
\(99\) 1.77627 1.77627i 0.178522 0.178522i
\(100\) 12.1971i 1.21971i
\(101\) 14.0256 1.39560 0.697799 0.716293i \(-0.254163\pi\)
0.697799 + 0.716293i \(0.254163\pi\)
\(102\) −0.928658 + 7.16991i −0.0919508 + 0.709927i
\(103\) 16.7382 1.64926 0.824632 0.565669i \(-0.191382\pi\)
0.824632 + 0.565669i \(0.191382\pi\)
\(104\) 2.44318i 0.239574i
\(105\) 0.987506 0.987506i 0.0963707 0.0963707i
\(106\) 28.1263 2.73187
\(107\) 9.78511 9.78511i 0.945963 0.945963i −0.0526504 0.998613i \(-0.516767\pi\)
0.998613 + 0.0526504i \(0.0167669\pi\)
\(108\) −8.47524 8.47524i −0.815530 0.815530i
\(109\) 0.619197 + 0.619197i 0.0593083 + 0.0593083i 0.736139 0.676831i \(-0.236647\pi\)
−0.676831 + 0.736139i \(0.736647\pi\)
\(110\) 7.13674i 0.680461i
\(111\) 4.14708i 0.393624i
\(112\) −0.719635 0.719635i −0.0679991 0.0679991i
\(113\) 2.18074 + 2.18074i 0.205147 + 0.205147i 0.802201 0.597054i \(-0.203662\pi\)
−0.597054 + 0.802201i \(0.703662\pi\)
\(114\) −4.87835 + 4.87835i −0.456899 + 0.456899i
\(115\) −19.4328 −1.81212
\(116\) 4.24067 4.24067i 0.393736 0.393736i
\(117\) 3.32070i 0.306998i
\(118\) 23.4201 2.15599
\(119\) 0.301702 2.32936i 0.0276570 0.213532i
\(120\) 4.25387 0.388323
\(121\) 9.86552i 0.896865i
\(122\) −17.2118 + 17.2118i −1.55828 + 1.55828i
\(123\) 7.44913 0.671665
\(124\) −20.2680 + 20.2680i −1.82012 + 1.82012i
\(125\) 1.36859 + 1.36859i 0.122411 + 0.122411i
\(126\) 2.07981 + 2.07981i 0.185284 + 0.185284i
\(127\) 17.0234i 1.51058i 0.655389 + 0.755292i \(0.272505\pi\)
−0.655389 + 0.755292i \(0.727495\pi\)
\(128\) 12.7916i 1.13063i
\(129\) 0.566370 + 0.566370i 0.0498661 + 0.0498661i
\(130\) 6.67097 + 6.67097i 0.585082 + 0.585082i
\(131\) 1.97390 1.97390i 0.172460 0.172460i −0.615599 0.788059i \(-0.711086\pi\)
0.788059 + 0.615599i \(0.211086\pi\)
\(132\) 2.38246 0.207367
\(133\) 1.58488 1.58488i 0.137426 0.137426i
\(134\) 22.8048i 1.97004i
\(135\) 13.1362 1.13058
\(136\) 5.66690 4.36726i 0.485932 0.374489i
\(137\) −20.4491 −1.74708 −0.873542 0.486748i \(-0.838183\pi\)
−0.873542 + 0.486748i \(0.838183\pi\)
\(138\) 11.1333i 0.947727i
\(139\) 5.86712 5.86712i 0.497643 0.497643i −0.413061 0.910703i \(-0.635540\pi\)
0.910703 + 0.413061i \(0.135540\pi\)
\(140\) −4.86914 −0.411517
\(141\) 1.77394 1.77394i 0.149393 0.149393i
\(142\) −3.86564 3.86564i −0.324398 0.324398i
\(143\) 1.06044 + 1.06044i 0.0886784 + 0.0886784i
\(144\) 4.21337i 0.351114i
\(145\) 6.57282i 0.545843i
\(146\) 2.50531 + 2.50531i 0.207341 + 0.207341i
\(147\) −3.78079 3.78079i −0.311834 0.311834i
\(148\) −10.2241 + 10.2241i −0.840416 + 0.840416i
\(149\) −18.3940 −1.50690 −0.753449 0.657507i \(-0.771611\pi\)
−0.753449 + 0.657507i \(0.771611\pi\)
\(150\) −5.41542 + 5.41542i −0.442167 + 0.442167i
\(151\) 12.8981i 1.04963i −0.851217 0.524814i \(-0.824135\pi\)
0.851217 0.524814i \(-0.175865\pi\)
\(152\) 6.82716 0.553756
\(153\) 7.70226 5.93583i 0.622691 0.479884i
\(154\) −1.32834 −0.107041
\(155\) 31.4143i 2.52326i
\(156\) 2.22697 2.22697i 0.178301 0.178301i
\(157\) −8.95308 −0.714533 −0.357267 0.934002i \(-0.616291\pi\)
−0.357267 + 0.934002i \(0.616291\pi\)
\(158\) 6.41505 6.41505i 0.510354 0.510354i
\(159\) 7.27655 + 7.27655i 0.577068 + 0.577068i
\(160\) 15.9750 + 15.9750i 1.26294 + 1.26294i
\(161\) 3.61698i 0.285058i
\(162\) 7.96354i 0.625675i
\(163\) 9.85582 + 9.85582i 0.771967 + 0.771967i 0.978450 0.206483i \(-0.0662018\pi\)
−0.206483 + 0.978450i \(0.566202\pi\)
\(164\) −18.3649 18.3649i −1.43405 1.43405i
\(165\) −1.84635 + 1.84635i −0.143738 + 0.143738i
\(166\) 34.8729 2.70666
\(167\) −0.761123 + 0.761123i −0.0588975 + 0.0588975i −0.735942 0.677045i \(-0.763260\pi\)
0.677045 + 0.735942i \(0.263260\pi\)
\(168\) 0.791761i 0.0610857i
\(169\) −11.0175 −0.847503
\(170\) −3.54859 + 27.3976i −0.272164 + 2.10130i
\(171\) 9.27925 0.709602
\(172\) 2.79262i 0.212936i
\(173\) −4.10707 + 4.10707i −0.312255 + 0.312255i −0.845783 0.533528i \(-0.820866\pi\)
0.533528 + 0.845783i \(0.320866\pi\)
\(174\) 3.76564 0.285472
\(175\) 1.75936 1.75936i 0.132995 0.132995i
\(176\) 1.34551 + 1.34551i 0.101421 + 0.101421i
\(177\) 6.05901 + 6.05901i 0.455423 + 0.455423i
\(178\) 26.9186i 2.01763i
\(179\) 8.18519i 0.611789i −0.952065 0.305895i \(-0.901044\pi\)
0.952065 0.305895i \(-0.0989556\pi\)
\(180\) −14.2541 14.2541i −1.06244 1.06244i
\(181\) −7.18141 7.18141i −0.533790 0.533790i 0.387908 0.921698i \(-0.373198\pi\)
−0.921698 + 0.387908i \(0.873198\pi\)
\(182\) −1.24165 + 1.24165i −0.0920371 + 0.0920371i
\(183\) −8.90574 −0.658332
\(184\) 7.79040 7.79040i 0.574316 0.574316i
\(185\) 15.8468i 1.16508i
\(186\) −17.9976 −1.31965
\(187\) −0.564095 + 4.35522i −0.0412507 + 0.318485i
\(188\) −8.74687 −0.637931
\(189\) 2.44500i 0.177848i
\(190\) −18.6411 + 18.6411i −1.35237 + 1.35237i
\(191\) 5.79320 0.419182 0.209591 0.977789i \(-0.432787\pi\)
0.209591 + 0.977789i \(0.432787\pi\)
\(192\) 7.12862 7.12862i 0.514464 0.514464i
\(193\) 6.13949 + 6.13949i 0.441930 + 0.441930i 0.892660 0.450730i \(-0.148836\pi\)
−0.450730 + 0.892660i \(0.648836\pi\)
\(194\) 5.80145 + 5.80145i 0.416520 + 0.416520i
\(195\) 3.45169i 0.247181i
\(196\) 18.6421i 1.33158i
\(197\) −17.4206 17.4206i −1.24116 1.24116i −0.959518 0.281647i \(-0.909119\pi\)
−0.281647 0.959518i \(-0.590881\pi\)
\(198\) −3.88863 3.88863i −0.276353 0.276353i
\(199\) −6.61092 + 6.61092i −0.468635 + 0.468635i −0.901472 0.432837i \(-0.857513\pi\)
0.432837 + 0.901472i \(0.357513\pi\)
\(200\) 7.57878 0.535901
\(201\) 5.89984 5.89984i 0.416142 0.416142i
\(202\) 30.7049i 2.16039i
\(203\) −1.22338 −0.0858645
\(204\) 9.14617 + 1.18463i 0.640360 + 0.0829405i
\(205\) 28.4646 1.98805
\(206\) 36.6434i 2.55307i
\(207\) 10.5885 10.5885i 0.735949 0.735949i
\(208\) 2.51539 0.174411
\(209\) −2.96326 + 2.96326i −0.204973 + 0.204973i
\(210\) −2.16185 2.16185i −0.149182 0.149182i
\(211\) −12.1401 12.1401i −0.835757 0.835757i 0.152540 0.988297i \(-0.451255\pi\)
−0.988297 + 0.152540i \(0.951255\pi\)
\(212\) 35.8788i 2.46417i
\(213\) 2.00016i 0.137049i
\(214\) −21.4216 21.4216i −1.46435 1.46435i
\(215\) 2.16421 + 2.16421i 0.147598 + 0.147598i
\(216\) −5.26615 + 5.26615i −0.358316 + 0.358316i
\(217\) 5.84707 0.396925
\(218\) 1.35555 1.35555i 0.0918095 0.0918095i
\(219\) 1.29630i 0.0875958i
\(220\) 9.10386 0.613782
\(221\) 3.54370 + 4.59826i 0.238375 + 0.309313i
\(222\) −9.07882 −0.609331
\(223\) 0.454104i 0.0304090i 0.999884 + 0.0152045i \(0.00483993\pi\)
−0.999884 + 0.0152045i \(0.995160\pi\)
\(224\) −2.97339 + 2.97339i −0.198668 + 0.198668i
\(225\) 10.3008 0.686722
\(226\) 4.77409 4.77409i 0.317568 0.317568i
\(227\) 12.2925 + 12.2925i 0.815882 + 0.815882i 0.985508 0.169627i \(-0.0542562\pi\)
−0.169627 + 0.985508i \(0.554256\pi\)
\(228\) 6.22299 + 6.22299i 0.412127 + 0.412127i
\(229\) 12.0555i 0.796651i −0.917244 0.398325i \(-0.869591\pi\)
0.917244 0.398325i \(-0.130409\pi\)
\(230\) 42.5424i 2.80516i
\(231\) −0.343655 0.343655i −0.0226109 0.0226109i
\(232\) −2.63497 2.63497i −0.172994 0.172994i
\(233\) −12.6358 + 12.6358i −0.827801 + 0.827801i −0.987212 0.159411i \(-0.949040\pi\)
0.159411 + 0.987212i \(0.449040\pi\)
\(234\) −7.26969 −0.475234
\(235\) 6.77860 6.77860i 0.442187 0.442187i
\(236\) 29.8754i 1.94473i
\(237\) 3.31928 0.215610
\(238\) −5.09945 0.660489i −0.330548 0.0428131i
\(239\) −13.8055 −0.893004 −0.446502 0.894783i \(-0.647330\pi\)
−0.446502 + 0.894783i \(0.647330\pi\)
\(240\) 4.37958i 0.282701i
\(241\) 2.87314 2.87314i 0.185075 0.185075i −0.608488 0.793563i \(-0.708224\pi\)
0.793563 + 0.608488i \(0.208224\pi\)
\(242\) −21.5977 −1.38835
\(243\) −11.1648 + 11.1648i −0.716225 + 0.716225i
\(244\) 21.9560 + 21.9560i 1.40559 + 1.40559i
\(245\) −14.4471 14.4471i −0.922994 0.922994i
\(246\) 16.3077i 1.03974i
\(247\) 5.53973i 0.352484i
\(248\) 12.5937 + 12.5937i 0.799699 + 0.799699i
\(249\) 9.02196 + 9.02196i 0.571744 + 0.571744i
\(250\) 2.99613 2.99613i 0.189492 0.189492i
\(251\) −4.69906 −0.296602 −0.148301 0.988942i \(-0.547380\pi\)
−0.148301 + 0.988942i \(0.547380\pi\)
\(252\) 2.65307 2.65307i 0.167128 0.167128i
\(253\) 6.76269i 0.425166i
\(254\) 37.2678 2.33839
\(255\) −8.00610 + 6.16999i −0.501362 + 0.386380i
\(256\) −2.83039 −0.176899
\(257\) 7.77325i 0.484882i 0.970166 + 0.242441i \(0.0779480\pi\)
−0.970166 + 0.242441i \(0.922052\pi\)
\(258\) 1.23990 1.23990i 0.0771928 0.0771928i
\(259\) 2.94953 0.183275
\(260\) 8.50971 8.50971i 0.527750 0.527750i
\(261\) −3.58136 3.58136i −0.221681 0.221681i
\(262\) −4.32127 4.32127i −0.266969 0.266969i
\(263\) 20.3181i 1.25287i 0.779474 + 0.626434i \(0.215486\pi\)
−0.779474 + 0.626434i \(0.784514\pi\)
\(264\) 1.48036i 0.0911099i
\(265\) 27.8052 + 27.8052i 1.70806 + 1.70806i
\(266\) −3.46963 3.46963i −0.212736 0.212736i
\(267\) 6.96411 6.96411i 0.426197 0.426197i
\(268\) −29.0906 −1.77699
\(269\) 6.60334 6.60334i 0.402613 0.402613i −0.476540 0.879153i \(-0.658109\pi\)
0.879153 + 0.476540i \(0.158109\pi\)
\(270\) 28.7578i 1.75014i
\(271\) −2.28337 −0.138705 −0.0693525 0.997592i \(-0.522093\pi\)
−0.0693525 + 0.997592i \(0.522093\pi\)
\(272\) 4.49632 + 5.83437i 0.272630 + 0.353761i
\(273\) −0.642454 −0.0388831
\(274\) 44.7673i 2.70449i
\(275\) −3.28949 + 3.28949i −0.198364 + 0.198364i
\(276\) 14.2020 0.854858
\(277\) −1.79201 + 1.79201i −0.107672 + 0.107672i −0.758890 0.651219i \(-0.774258\pi\)
0.651219 + 0.758890i \(0.274258\pi\)
\(278\) −12.8443 12.8443i −0.770352 0.770352i
\(279\) 17.1169 + 17.1169i 1.02476 + 1.02476i
\(280\) 3.02547i 0.180807i
\(281\) 13.4498i 0.802347i 0.916002 + 0.401173i \(0.131398\pi\)
−0.916002 + 0.401173i \(0.868602\pi\)
\(282\) −3.88353 3.88353i −0.231261 0.231261i
\(283\) 5.96084 + 5.96084i 0.354335 + 0.354335i 0.861720 0.507385i \(-0.169388\pi\)
−0.507385 + 0.861720i \(0.669388\pi\)
\(284\) −4.93114 + 4.93114i −0.292610 + 0.292610i
\(285\) −9.64531 −0.571339
\(286\) 2.32152 2.32152i 0.137274 0.137274i
\(287\) 5.29804i 0.312733i
\(288\) −17.4088 −1.02582
\(289\) −4.33108 + 16.4390i −0.254769 + 0.967002i
\(290\) 14.3893 0.844966
\(291\) 3.00179i 0.175968i
\(292\) 3.19586 3.19586i 0.187024 0.187024i
\(293\) 12.2219 0.714012 0.357006 0.934102i \(-0.383797\pi\)
0.357006 + 0.934102i \(0.383797\pi\)
\(294\) −8.27692 + 8.27692i −0.482720 + 0.482720i
\(295\) 23.1527 + 23.1527i 1.34800 + 1.34800i
\(296\) 6.35282 + 6.35282i 0.369250 + 0.369250i
\(297\) 4.57144i 0.265262i
\(298\) 40.2683i 2.33268i
\(299\) 6.32133 + 6.32133i 0.365572 + 0.365572i
\(300\) 6.90809 + 6.90809i 0.398839 + 0.398839i
\(301\) −0.402819 + 0.402819i −0.0232181 + 0.0232181i
\(302\) −28.2365 −1.62483
\(303\) 7.94367 7.94367i 0.456352 0.456352i
\(304\) 7.02892i 0.403136i
\(305\) −34.0306 −1.94859
\(306\) −12.9948 16.8618i −0.742861 0.963927i
\(307\) 3.79679 0.216694 0.108347 0.994113i \(-0.465444\pi\)
0.108347 + 0.994113i \(0.465444\pi\)
\(308\) 1.69448i 0.0965518i
\(309\) 9.48002 9.48002i 0.539299 0.539299i
\(310\) −68.7725 −3.90601
\(311\) −3.32062 + 3.32062i −0.188295 + 0.188295i −0.794959 0.606664i \(-0.792508\pi\)
0.606664 + 0.794959i \(0.292508\pi\)
\(312\) −1.38375 1.38375i −0.0783392 0.0783392i
\(313\) 9.03199 + 9.03199i 0.510518 + 0.510518i 0.914685 0.404167i \(-0.132439\pi\)
−0.404167 + 0.914685i \(0.632439\pi\)
\(314\) 19.6001i 1.10610i
\(315\) 4.11212i 0.231692i
\(316\) −8.18325 8.18325i −0.460344 0.460344i
\(317\) 7.26784 + 7.26784i 0.408203 + 0.408203i 0.881111 0.472909i \(-0.156796\pi\)
−0.472909 + 0.881111i \(0.656796\pi\)
\(318\) 15.9299 15.9299i 0.893303 0.893303i
\(319\) 2.28736 0.128068
\(320\) 27.2399 27.2399i 1.52276 1.52276i
\(321\) 11.0840i 0.618648i
\(322\) −7.91831 −0.441270
\(323\) −12.8492 + 9.90241i −0.714951 + 0.550985i
\(324\) 10.1586 0.564364
\(325\) 6.14961i 0.341119i
\(326\) 21.5764 21.5764i 1.19501 1.19501i
\(327\) 0.701389 0.0387869
\(328\) −11.4111 + 11.4111i −0.630075 + 0.630075i
\(329\) 1.26168 + 1.26168i 0.0695588 + 0.0695588i
\(330\) 4.04203 + 4.04203i 0.222507 + 0.222507i
\(331\) 16.4087i 0.901903i −0.892549 0.450951i \(-0.851085\pi\)
0.892549 0.450951i \(-0.148915\pi\)
\(332\) 44.4850i 2.44143i
\(333\) 8.63455 + 8.63455i 0.473170 + 0.473170i
\(334\) 1.66626 + 1.66626i 0.0911734 + 0.0911734i
\(335\) 22.5445 22.5445i 1.23174 1.23174i
\(336\) −0.815159 −0.0444706
\(337\) −17.9541 + 17.9541i −0.978020 + 0.978020i −0.999764 0.0217436i \(-0.993078\pi\)
0.0217436 + 0.999764i \(0.493078\pi\)
\(338\) 24.1197i 1.31194i
\(339\) 2.47021 0.134164
\(340\) 34.9493 + 4.52669i 1.89539 + 0.245494i
\(341\) −10.9323 −0.592017
\(342\) 20.3142i 1.09847i
\(343\) 5.50874 5.50874i 0.297444 0.297444i
\(344\) −1.73522 −0.0935567
\(345\) −11.0062 + 11.0062i −0.592552 + 0.592552i
\(346\) 8.99123 + 8.99123i 0.483372 + 0.483372i
\(347\) 11.9552 + 11.9552i 0.641786 + 0.641786i 0.950994 0.309208i \(-0.100064\pi\)
−0.309208 + 0.950994i \(0.600064\pi\)
\(348\) 4.80357i 0.257499i
\(349\) 9.90470i 0.530186i 0.964223 + 0.265093i \(0.0854027\pi\)
−0.964223 + 0.265093i \(0.914597\pi\)
\(350\) −3.85161 3.85161i −0.205877 0.205877i
\(351\) −4.27309 4.27309i −0.228080 0.228080i
\(352\) 5.55936 5.55936i 0.296315 0.296315i
\(353\) 5.79827 0.308611 0.154305 0.988023i \(-0.450686\pi\)
0.154305 + 0.988023i \(0.450686\pi\)
\(354\) 13.2644 13.2644i 0.704997 0.704997i
\(355\) 7.64302i 0.405649i
\(356\) −34.3382 −1.81992
\(357\) −1.14840 1.49015i −0.0607800 0.0788673i
\(358\) −17.9191 −0.947052
\(359\) 6.20024i 0.327236i −0.986524 0.163618i \(-0.947684\pi\)
0.986524 0.163618i \(-0.0523164\pi\)
\(360\) −8.85687 + 8.85687i −0.466798 + 0.466798i
\(361\) 3.51995 0.185261
\(362\) −15.7216 + 15.7216i −0.826308 + 0.826308i
\(363\) −5.58753 5.58753i −0.293269 0.293269i
\(364\) 1.58389 + 1.58389i 0.0830183 + 0.0830183i
\(365\) 4.95342i 0.259274i
\(366\) 19.4965i 1.01910i
\(367\) −25.5070 25.5070i −1.33146 1.33146i −0.904069 0.427387i \(-0.859434\pi\)
−0.427387 0.904069i \(-0.640566\pi\)
\(368\) 8.02063 + 8.02063i 0.418104 + 0.418104i
\(369\) −15.5096 + 15.5096i −0.807400 + 0.807400i
\(370\) −34.6920 −1.80355
\(371\) −5.17530 + 5.17530i −0.268688 + 0.268688i
\(372\) 22.9584i 1.19034i
\(373\) −32.0065 −1.65723 −0.828616 0.559817i \(-0.810871\pi\)
−0.828616 + 0.559817i \(0.810871\pi\)
\(374\) 9.53448 + 1.23492i 0.493016 + 0.0638562i
\(375\) 1.55026 0.0800551
\(376\) 5.43493i 0.280285i
\(377\) 2.13808 2.13808i 0.110117 0.110117i
\(378\) 5.35261 0.275309
\(379\) 6.47290 6.47290i 0.332491 0.332491i −0.521041 0.853532i \(-0.674456\pi\)
0.853532 + 0.521041i \(0.174456\pi\)
\(380\) 23.7793 + 23.7793i 1.21985 + 1.21985i
\(381\) 9.64155 + 9.64155i 0.493951 + 0.493951i
\(382\) 12.6825i 0.648894i
\(383\) 20.9481i 1.07040i −0.844727 0.535198i \(-0.820237\pi\)
0.844727 0.535198i \(-0.179763\pi\)
\(384\) −7.24477 7.24477i −0.369708 0.369708i
\(385\) −1.31318 1.31318i −0.0669256 0.0669256i
\(386\) 13.4406 13.4406i 0.684109 0.684109i
\(387\) −2.35845 −0.119887
\(388\) 7.40052 7.40052i 0.375705 0.375705i
\(389\) 29.4850i 1.49495i −0.664291 0.747474i \(-0.731267\pi\)
0.664291 0.747474i \(-0.268733\pi\)
\(390\) 7.55647 0.382637
\(391\) −3.36260 + 25.9617i −0.170054 + 1.31294i
\(392\) 11.5834 0.585050
\(393\) 2.23591i 0.112787i
\(394\) −38.1372 + 38.1372i −1.92133 + 1.92133i
\(395\) 12.6836 0.638182
\(396\) −4.96047 + 4.96047i −0.249273 + 0.249273i
\(397\) 4.78562 + 4.78562i 0.240183 + 0.240183i 0.816926 0.576743i \(-0.195676\pi\)
−0.576743 + 0.816926i \(0.695676\pi\)
\(398\) 14.4727 + 14.4727i 0.725449 + 0.725449i
\(399\) 1.79525i 0.0898752i
\(400\) 7.80276i 0.390138i
\(401\) 20.4973 + 20.4973i 1.02359 + 1.02359i 0.999715 + 0.0238704i \(0.00759891\pi\)
0.0238704 + 0.999715i \(0.492401\pi\)
\(402\) −12.9160 12.9160i −0.644190 0.644190i
\(403\) −10.2188 + 10.2188i −0.509035 + 0.509035i
\(404\) −39.1682 −1.94869
\(405\) −7.87262 + 7.87262i −0.391194 + 0.391194i
\(406\) 2.67823i 0.132918i
\(407\) −5.51475 −0.273356
\(408\) 0.736077 5.68304i 0.0364412 0.281353i
\(409\) −32.8607 −1.62485 −0.812427 0.583062i \(-0.801854\pi\)
−0.812427 + 0.583062i \(0.801854\pi\)
\(410\) 62.3149i 3.07751i
\(411\) −11.5818 + 11.5818i −0.571286 + 0.571286i
\(412\) −46.7435 −2.30289
\(413\) −4.30935 + 4.30935i −0.212049 + 0.212049i
\(414\) −23.1803 23.1803i −1.13925 1.13925i
\(415\) 34.4747 + 34.4747i 1.69230 + 1.69230i
\(416\) 10.3931i 0.509562i
\(417\) 6.64592i 0.325452i
\(418\) 6.48718 + 6.48718i 0.317299 + 0.317299i
\(419\) −11.5121 11.5121i −0.562401 0.562401i 0.367588 0.929989i \(-0.380184\pi\)
−0.929989 + 0.367588i \(0.880184\pi\)
\(420\) −2.75773 + 2.75773i −0.134564 + 0.134564i
\(421\) 0.581655 0.0283481 0.0141741 0.999900i \(-0.495488\pi\)
0.0141741 + 0.999900i \(0.495488\pi\)
\(422\) −26.5771 + 26.5771i −1.29375 + 1.29375i
\(423\) 7.38698i 0.359167i
\(424\) −22.2936 −1.08267
\(425\) −14.2638 + 10.9926i −0.691898 + 0.533219i
\(426\) −4.37877 −0.212152
\(427\) 6.33403i 0.306525i
\(428\) −27.3261 + 27.3261i −1.32086 + 1.32086i
\(429\) 1.20120 0.0579945
\(430\) 4.73791 4.73791i 0.228482 0.228482i
\(431\) −1.19245 1.19245i −0.0574384 0.0574384i 0.677804 0.735243i \(-0.262932\pi\)
−0.735243 + 0.677804i \(0.762932\pi\)
\(432\) −5.42178 5.42178i −0.260856 0.260856i
\(433\) 15.2894i 0.734760i 0.930071 + 0.367380i \(0.119745\pi\)
−0.930071 + 0.367380i \(0.880255\pi\)
\(434\) 12.8004i 0.614440i
\(435\) 3.72265 + 3.72265i 0.178487 + 0.178487i
\(436\) −1.72918 1.72918i −0.0828129 0.0828129i
\(437\) −17.6641 + 17.6641i −0.844990 + 0.844990i
\(438\) 2.83787 0.135599
\(439\) 0.321400 0.321400i 0.0153396 0.0153396i −0.699395 0.714735i \(-0.746547\pi\)
0.714735 + 0.699395i \(0.246547\pi\)
\(440\) 5.65675i 0.269675i
\(441\) 15.7438 0.749704
\(442\) 10.0665 7.75789i 0.478817 0.369005i
\(443\) 17.0265 0.808955 0.404477 0.914548i \(-0.367453\pi\)
0.404477 + 0.914548i \(0.367453\pi\)
\(444\) 11.5812i 0.549622i
\(445\) 26.6113 26.6113i 1.26149 1.26149i
\(446\) 0.994126 0.0470732
\(447\) −10.4178 + 10.4178i −0.492746 + 0.492746i
\(448\) 5.07009 + 5.07009i 0.239539 + 0.239539i
\(449\) 9.54373 + 9.54373i 0.450396 + 0.450396i 0.895486 0.445090i \(-0.146828\pi\)
−0.445090 + 0.895486i \(0.646828\pi\)
\(450\) 22.5506i 1.06305i
\(451\) 9.90578i 0.466445i
\(452\) −6.08999 6.08999i −0.286449 0.286449i
\(453\) −7.30507 7.30507i −0.343222 0.343222i
\(454\) 26.9108 26.9108i 1.26299 1.26299i
\(455\) −2.45495 −0.115090
\(456\) 3.86670 3.86670i 0.181075 0.181075i
\(457\) 7.73666i 0.361906i −0.983492 0.180953i \(-0.942082\pi\)
0.983492 0.180953i \(-0.0579181\pi\)
\(458\) −26.3920 −1.23322
\(459\) 2.27305 17.5496i 0.106097 0.819143i
\(460\) 54.2685 2.53028
\(461\) 22.8933i 1.06625i 0.846038 + 0.533123i \(0.178982\pi\)
−0.846038 + 0.533123i \(0.821018\pi\)
\(462\) −0.752333 + 0.752333i −0.0350017 + 0.0350017i
\(463\) −36.2641 −1.68534 −0.842668 0.538433i \(-0.819016\pi\)
−0.842668 + 0.538433i \(0.819016\pi\)
\(464\) 2.71284 2.71284i 0.125941 0.125941i
\(465\) −17.7921 17.7921i −0.825090 0.825090i
\(466\) 27.6624 + 27.6624i 1.28144 + 1.28144i
\(467\) 23.4262i 1.08403i −0.840368 0.542017i \(-0.817661\pi\)
0.840368 0.542017i \(-0.182339\pi\)
\(468\) 9.27345i 0.428666i
\(469\) 4.19614 + 4.19614i 0.193760 + 0.193760i
\(470\) −14.8397 14.8397i −0.684506 0.684506i
\(471\) −5.07075 + 5.07075i −0.233648 + 0.233648i
\(472\) −18.5633 −0.854446
\(473\) 0.753153 0.753153i 0.0346300 0.0346300i
\(474\) 7.26658i 0.333765i
\(475\) −17.1843 −0.788469
\(476\) −0.842541 + 6.50503i −0.0386178 + 0.298157i
\(477\) −30.3007 −1.38737
\(478\) 30.2231i 1.38237i
\(479\) 10.3219 10.3219i 0.471620 0.471620i −0.430818 0.902439i \(-0.641775\pi\)
0.902439 + 0.430818i \(0.141775\pi\)
\(480\) 18.0955 0.825945
\(481\) −5.15484 + 5.15484i −0.235040 + 0.235040i
\(482\) −6.28989 6.28989i −0.286497 0.286497i
\(483\) −2.04855 2.04855i −0.0932121 0.0932121i
\(484\) 27.5507i 1.25230i
\(485\) 11.4704i 0.520845i
\(486\) 24.4421 + 24.4421i 1.10872 + 1.10872i
\(487\) 24.4506 + 24.4506i 1.10796 + 1.10796i 0.993418 + 0.114545i \(0.0365409\pi\)
0.114545 + 0.993418i \(0.463459\pi\)
\(488\) 13.6425 13.6425i 0.617567 0.617567i
\(489\) 11.1641 0.504857
\(490\) −31.6278 + 31.6278i −1.42880 + 1.42880i
\(491\) 2.59418i 0.117074i −0.998285 0.0585370i \(-0.981356\pi\)
0.998285 0.0585370i \(-0.0186435\pi\)
\(492\) −20.8026 −0.937854
\(493\) 8.78109 + 1.13734i 0.395481 + 0.0512233i
\(494\) 12.1276 0.545647
\(495\) 7.68847i 0.345571i
\(496\) −12.9658 + 12.9658i −0.582184 + 0.582184i
\(497\) 1.42257 0.0638112
\(498\) 19.7509 19.7509i 0.885061 0.885061i
\(499\) 4.90042 + 4.90042i 0.219373 + 0.219373i 0.808234 0.588861i \(-0.200424\pi\)
−0.588861 + 0.808234i \(0.700424\pi\)
\(500\) −3.82197 3.82197i −0.170924 0.170924i
\(501\) 0.862154i 0.0385182i
\(502\) 10.2872i 0.459141i
\(503\) 11.1720 + 11.1720i 0.498137 + 0.498137i 0.910858 0.412721i \(-0.135421\pi\)
−0.412721 + 0.910858i \(0.635421\pi\)
\(504\) −1.64851 1.64851i −0.0734303 0.0734303i
\(505\) 30.3544 30.3544i 1.35075 1.35075i
\(506\) 14.8049 0.658159
\(507\) −6.24000 + 6.24000i −0.277128 + 0.277128i
\(508\) 47.5400i 2.10925i
\(509\) 11.5197 0.510601 0.255301 0.966862i \(-0.417826\pi\)
0.255301 + 0.966862i \(0.417826\pi\)
\(510\) 13.5074 + 17.5270i 0.598117 + 0.776109i
\(511\) −0.921967 −0.0407854
\(512\) 19.3869i 0.856787i
\(513\) 11.9406 11.9406i 0.527190 0.527190i
\(514\) 17.0172 0.750598
\(515\) 36.2250 36.2250i 1.59627 1.59627i
\(516\) −1.58166 1.58166i −0.0696286 0.0696286i
\(517\) −2.35897 2.35897i −0.103748 0.103748i
\(518\) 6.45713i 0.283710i
\(519\) 4.65225i 0.204211i
\(520\) −5.28757 5.28757i −0.231875 0.231875i
\(521\) −27.6504 27.6504i −1.21138 1.21138i −0.970572 0.240813i \(-0.922586\pi\)
−0.240813 0.970572i \(-0.577414\pi\)
\(522\) −7.84035 + 7.84035i −0.343163 + 0.343163i
\(523\) −38.3290 −1.67601 −0.838006 0.545661i \(-0.816279\pi\)
−0.838006 + 0.545661i \(0.816279\pi\)
\(524\) −5.51236 + 5.51236i −0.240808 + 0.240808i
\(525\) 1.99290i 0.0869772i
\(526\) 44.4805 1.93944
\(527\) −41.9687 5.43584i −1.82818 0.236789i
\(528\) 1.52411 0.0663283
\(529\) 17.3127i 0.752726i
\(530\) 60.8712 60.8712i 2.64408 2.64408i
\(531\) −25.2307 −1.09492
\(532\) −4.42597 + 4.42597i −0.191890 + 0.191890i
\(533\) −9.25929 9.25929i −0.401064 0.401064i
\(534\) −15.2459 15.2459i −0.659754 0.659754i
\(535\) 42.3541i 1.83113i
\(536\) 18.0757i 0.780749i
\(537\) −4.63584 4.63584i −0.200051 0.200051i
\(538\) −14.4561 14.4561i −0.623246 0.623246i
\(539\) −5.02765 + 5.02765i −0.216556 + 0.216556i
\(540\) −36.6844 −1.57865
\(541\) 15.0818 15.0818i 0.648417 0.648417i −0.304194 0.952610i \(-0.598387\pi\)
0.952610 + 0.304194i \(0.0983870\pi\)
\(542\) 4.99878i 0.214716i
\(543\) −8.13466 −0.349092
\(544\) 24.1064 18.5779i 1.03355 0.796521i
\(545\) 2.68015 0.114805
\(546\) 1.40646i 0.0601911i
\(547\) 11.6749 11.6749i 0.499181 0.499181i −0.412002 0.911183i \(-0.635170\pi\)
0.911183 + 0.412002i \(0.135170\pi\)
\(548\) 57.1067 2.43948
\(549\) 18.5424 18.5424i 0.791372 0.791372i
\(550\) 7.20137 + 7.20137i 0.307068 + 0.307068i
\(551\) 5.97459 + 5.97459i 0.254526 + 0.254526i
\(552\) 8.82450i 0.375596i
\(553\) 2.36077i 0.100390i
\(554\) 3.92309 + 3.92309i 0.166676 + 0.166676i
\(555\) −8.97517 8.97517i −0.380975 0.380975i
\(556\) −16.3847 + 16.3847i −0.694865 + 0.694865i
\(557\) −2.57463 −0.109091 −0.0545453 0.998511i \(-0.517371\pi\)
−0.0545453 + 0.998511i \(0.517371\pi\)
\(558\) 37.4724 37.4724i 1.58633 1.58633i
\(559\) 1.40800i 0.0595520i
\(560\) −3.11489 −0.131628
\(561\) 2.14718 + 2.78615i 0.0906540 + 0.117631i
\(562\) 29.4444 1.24204
\(563\) 44.9006i 1.89233i −0.323681 0.946166i \(-0.604920\pi\)
0.323681 0.946166i \(-0.395080\pi\)
\(564\) −4.95396 + 4.95396i −0.208599 + 0.208599i
\(565\) 9.43917 0.397109
\(566\) 13.0495 13.0495i 0.548512 0.548512i
\(567\) −1.46531 1.46531i −0.0615372 0.0615372i
\(568\) 3.06400 + 3.06400i 0.128563 + 0.128563i
\(569\) 44.0724i 1.84761i 0.382864 + 0.923805i \(0.374938\pi\)
−0.382864 + 0.923805i \(0.625062\pi\)
\(570\) 21.1156i 0.884434i
\(571\) −13.3101 13.3101i −0.557011 0.557011i 0.371444 0.928455i \(-0.378863\pi\)
−0.928455 + 0.371444i \(0.878863\pi\)
\(572\) −2.96141 2.96141i −0.123823 0.123823i
\(573\) 3.28110 3.28110i 0.137070 0.137070i
\(574\) 11.5985 0.484112
\(575\) −19.6088 + 19.6088i −0.817744 + 0.817744i
\(576\) 29.6847i 1.23686i
\(577\) −23.7653 −0.989364 −0.494682 0.869074i \(-0.664716\pi\)
−0.494682 + 0.869074i \(0.664716\pi\)
\(578\) 35.9884 + 9.48162i 1.49692 + 0.394383i
\(579\) 6.95444 0.289017
\(580\) 18.3554i 0.762167i
\(581\) −6.41668 + 6.41668i −0.266209 + 0.266209i
\(582\) 6.57153 0.272399
\(583\) 9.67629 9.67629i 0.400751 0.400751i
\(584\) −1.98577 1.98577i −0.0821718 0.0821718i
\(585\) −7.18669 7.18669i −0.297133 0.297133i
\(586\) 26.7563i 1.10529i
\(587\) 12.5894i 0.519622i −0.965660 0.259811i \(-0.916340\pi\)
0.965660 0.259811i \(-0.0836602\pi\)
\(588\) 10.5583 + 10.5583i 0.435418 + 0.435418i
\(589\) −28.5551 28.5551i −1.17659 1.17659i
\(590\) 50.6860 50.6860i 2.08671 2.08671i
\(591\) −19.7330 −0.811706
\(592\) −6.54057 + 6.54057i −0.268816 + 0.268816i
\(593\) 34.3974i 1.41253i 0.707947 + 0.706265i \(0.249621\pi\)
−0.707947 + 0.706265i \(0.750379\pi\)
\(594\) −10.0078 −0.410626
\(595\) −4.38828 5.69418i −0.179902 0.233438i
\(596\) 51.3676 2.10410
\(597\) 7.48845i 0.306482i
\(598\) 13.8387 13.8387i 0.565906 0.565906i
\(599\) −7.08031 −0.289294 −0.144647 0.989483i \(-0.546205\pi\)
−0.144647 + 0.989483i \(0.546205\pi\)
\(600\) 4.29239 4.29239i 0.175236 0.175236i
\(601\) 31.6600 + 31.6600i 1.29144 + 1.29144i 0.933898 + 0.357540i \(0.116384\pi\)
0.357540 + 0.933898i \(0.383616\pi\)
\(602\) 0.881854 + 0.881854i 0.0359417 + 0.0359417i
\(603\) 24.5678i 1.00048i
\(604\) 36.0194i 1.46561i
\(605\) −21.3511 21.3511i −0.868045 0.868045i
\(606\) −17.3903 17.3903i −0.706434 0.706434i
\(607\) 17.1134 17.1134i 0.694611 0.694611i −0.268632 0.963243i \(-0.586572\pi\)
0.963243 + 0.268632i \(0.0865716\pi\)
\(608\) 29.0421 1.17781
\(609\) −0.692886 + 0.692886i −0.0280772 + 0.0280772i
\(610\) 74.5000i 3.01642i
\(611\) −4.41004 −0.178411
\(612\) −21.5095 + 16.5765i −0.869471 + 0.670067i
\(613\) 10.4587 0.422422 0.211211 0.977440i \(-0.432259\pi\)
0.211211 + 0.977440i \(0.432259\pi\)
\(614\) 8.31195i 0.335443i
\(615\) 16.1215 16.1215i 0.650081 0.650081i
\(616\) 1.05288 0.0424216
\(617\) 1.70626 1.70626i 0.0686912 0.0686912i −0.671927 0.740618i \(-0.734533\pi\)
0.740618 + 0.671927i \(0.234533\pi\)
\(618\) −20.7537 20.7537i −0.834837 0.834837i
\(619\) 15.1477 + 15.1477i 0.608836 + 0.608836i 0.942642 0.333806i \(-0.108333\pi\)
−0.333806 + 0.942642i \(0.608333\pi\)
\(620\) 87.7284i 3.52326i
\(621\) 27.2505i 1.09353i
\(622\) 7.26953 + 7.26953i 0.291481 + 0.291481i
\(623\) 4.95308 + 4.95308i 0.198441 + 0.198441i
\(624\) 1.42464 1.42464i 0.0570312 0.0570312i
\(625\) 27.7620 1.11048
\(626\) 19.7729 19.7729i 0.790284 0.790284i
\(627\) 3.35660i 0.134050i
\(628\) 25.0026 0.997712
\(629\) −21.1709 2.74209i −0.844140 0.109334i
\(630\) 9.00229 0.358660
\(631\) 19.5922i 0.779952i 0.920825 + 0.389976i \(0.127517\pi\)
−0.920825 + 0.389976i \(0.872483\pi\)
\(632\) −5.08472 + 5.08472i −0.202259 + 0.202259i
\(633\) −13.7515 −0.546575
\(634\) 15.9108 15.9108i 0.631899 0.631899i
\(635\) 36.8423 + 36.8423i 1.46204 + 1.46204i
\(636\) −20.3207 20.3207i −0.805767 0.805767i
\(637\) 9.39906i 0.372404i
\(638\) 5.00751i 0.198249i
\(639\) 4.16449 + 4.16449i 0.164745 + 0.164745i
\(640\) −27.6837 27.6837i −1.09429 1.09429i
\(641\) −5.04657 + 5.04657i −0.199327 + 0.199327i −0.799712 0.600384i \(-0.795014\pi\)
0.600384 + 0.799712i \(0.295014\pi\)
\(642\) −24.2651 −0.957668
\(643\) −22.8572 + 22.8572i −0.901399 + 0.901399i −0.995557 0.0941582i \(-0.969984\pi\)
0.0941582 + 0.995557i \(0.469984\pi\)
\(644\) 10.1009i 0.398029i
\(645\) 2.45149 0.0965273
\(646\) 21.6784 + 28.1296i 0.852926 + 1.10675i
\(647\) −22.1459 −0.870644 −0.435322 0.900275i \(-0.643366\pi\)
−0.435322 + 0.900275i \(0.643366\pi\)
\(648\) 6.31210i 0.247963i
\(649\) 8.05722 8.05722i 0.316274 0.316274i
\(650\) 13.4628 0.528053
\(651\) 3.31160 3.31160i 0.129792 0.129792i
\(652\) −27.5236 27.5236i −1.07791 1.07791i
\(653\) 15.9665 + 15.9665i 0.624816 + 0.624816i 0.946759 0.321943i \(-0.104336\pi\)
−0.321943 + 0.946759i \(0.604336\pi\)
\(654\) 1.53549i 0.0600422i
\(655\) 8.54387i 0.333837i
\(656\) −11.7484 11.7484i −0.458697 0.458697i
\(657\) −2.69900 2.69900i −0.105298 0.105298i
\(658\) 2.76208 2.76208i 0.107677 0.107677i
\(659\) 20.6444 0.804192 0.402096 0.915598i \(-0.368282\pi\)
0.402096 + 0.915598i \(0.368282\pi\)
\(660\) 5.15615 5.15615i 0.200703 0.200703i
\(661\) 5.09042i 0.197994i −0.995088 0.0989972i \(-0.968437\pi\)
0.995088 0.0989972i \(-0.0315635\pi\)
\(662\) −35.9220 −1.39615
\(663\) 4.61136 + 0.597271i 0.179090 + 0.0231961i
\(664\) −27.6411 −1.07268
\(665\) 6.86003i 0.266020i
\(666\) 18.9028 18.9028i 0.732469 0.732469i
\(667\) 13.6351 0.527952
\(668\) 2.12553 2.12553i 0.0822393 0.0822393i
\(669\) 0.257191 + 0.257191i 0.00994356 + 0.00994356i
\(670\) −49.3545 49.3545i −1.90673 1.90673i
\(671\) 11.8428i 0.457185i
\(672\) 3.36807i 0.129926i
\(673\) −27.5902 27.5902i −1.06352 1.06352i −0.997841 0.0656819i \(-0.979078\pi\)
−0.0656819 0.997841i \(-0.520922\pi\)
\(674\) 39.3051 + 39.3051i 1.51398 + 1.51398i
\(675\) 13.2552 13.2552i 0.510191 0.510191i
\(676\) 30.7678 1.18338
\(677\) −35.8947 + 35.8947i −1.37955 + 1.37955i −0.534167 + 0.845379i \(0.679375\pi\)
−0.845379 + 0.534167i \(0.820625\pi\)
\(678\) 5.40780i 0.207685i
\(679\) −2.13496 −0.0819323
\(680\) 2.81269 21.7160i 0.107862 0.832772i
\(681\) 13.9242 0.533577
\(682\) 23.9331i 0.916444i
\(683\) −20.0605 + 20.0605i −0.767595 + 0.767595i −0.977683 0.210088i \(-0.932625\pi\)
0.210088 + 0.977683i \(0.432625\pi\)
\(684\) −25.9135 −0.990826
\(685\) −44.2562 + 44.2562i −1.69094 + 1.69094i
\(686\) −12.0598 12.0598i −0.460444 0.460444i
\(687\) −6.82788 6.82788i −0.260500 0.260500i
\(688\) 1.78650i 0.0681096i
\(689\) 18.0896i 0.689157i
\(690\) 24.0948 + 24.0948i 0.917271 + 0.917271i
\(691\) 4.15865 + 4.15865i 0.158203 + 0.158203i 0.781770 0.623567i \(-0.214317\pi\)
−0.623567 + 0.781770i \(0.714317\pi\)
\(692\) 11.4695 11.4695i 0.436006 0.436006i
\(693\) 1.43103 0.0543605
\(694\) 26.1723 26.1723i 0.993487 0.993487i
\(695\) 25.3954i 0.963302i
\(696\) −2.98474 −0.113136
\(697\) 4.92543 38.0279i 0.186564 1.44041i
\(698\) 21.6834 0.820730
\(699\) 14.3131i 0.541371i
\(700\) −4.91324 + 4.91324i −0.185703 + 0.185703i
\(701\) −10.8175 −0.408570 −0.204285 0.978911i \(-0.565487\pi\)
−0.204285 + 0.978911i \(0.565487\pi\)
\(702\) −9.35467 + 9.35467i −0.353069 + 0.353069i
\(703\) −14.4045 14.4045i −0.543277 0.543277i
\(704\) −9.47958 9.47958i −0.357275 0.357275i
\(705\) 7.67838i 0.289185i
\(706\) 12.6936i 0.477730i
\(707\) 5.64977 + 5.64977i 0.212482 + 0.212482i
\(708\) −16.9205 16.9205i −0.635913 0.635913i
\(709\) 20.1983 20.1983i 0.758563 0.758563i −0.217498 0.976061i \(-0.569789\pi\)
0.976061 + 0.217498i \(0.0697895\pi\)
\(710\) −16.7321 −0.627946
\(711\) −6.91099 + 6.91099i −0.259182 + 0.259182i
\(712\) 21.3363i 0.799613i
\(713\) −65.1679 −2.44056
\(714\) −3.26226 + 2.51409i −0.122087 + 0.0940876i
\(715\) 4.59003 0.171657
\(716\) 22.8581i 0.854249i
\(717\) −7.81902 + 7.81902i −0.292007 + 0.292007i
\(718\) −13.5736 −0.506562
\(719\) −18.6242 + 18.6242i −0.694567 + 0.694567i −0.963233 0.268667i \(-0.913417\pi\)
0.268667 + 0.963233i \(0.413417\pi\)
\(720\) −9.11862 9.11862i −0.339831 0.339831i
\(721\) 6.74247 + 6.74247i 0.251103 + 0.251103i
\(722\) 7.70590i 0.286784i
\(723\) 3.25452i 0.121037i
\(724\) 20.0550 + 20.0550i 0.745337 + 0.745337i
\(725\) 6.63235 + 6.63235i 0.246319 + 0.246319i
\(726\) −12.2323 + 12.2323i −0.453982 + 0.453982i
\(727\) 47.9013 1.77656 0.888281 0.459301i \(-0.151900\pi\)
0.888281 + 0.459301i \(0.151900\pi\)
\(728\) 0.984161 0.984161i 0.0364754 0.0364754i
\(729\) 1.73394i 0.0642201i
\(730\) 10.8441 0.401357
\(731\) 3.26581 2.51684i 0.120790 0.0930885i
\(732\) 24.8704 0.919236
\(733\) 4.79484i 0.177101i −0.996072 0.0885506i \(-0.971776\pi\)
0.996072 0.0885506i \(-0.0282235\pi\)
\(734\) −55.8401 + 55.8401i −2.06110 + 2.06110i
\(735\) −16.3648 −0.603627
\(736\) 33.1396 33.1396i 1.22154 1.22154i
\(737\) −7.84555 7.84555i −0.288994 0.288994i
\(738\) 33.9538 + 33.9538i 1.24986 + 1.24986i
\(739\) 8.81694i 0.324336i 0.986763 + 0.162168i \(0.0518487\pi\)
−0.986763 + 0.162168i \(0.948151\pi\)
\(740\) 44.2542i 1.62682i
\(741\) 3.13754 + 3.13754i 0.115260 + 0.115260i
\(742\) 11.3298 + 11.3298i 0.415930 + 0.415930i
\(743\) 27.7101 27.7101i 1.01659 1.01659i 0.0167249 0.999860i \(-0.494676\pi\)
0.999860 0.0167249i \(-0.00532395\pi\)
\(744\) 14.2653 0.522993
\(745\) −39.8086 + 39.8086i −1.45847 + 1.45847i
\(746\) 70.0688i 2.56540i
\(747\) −37.5688 −1.37457
\(748\) 1.57531 12.1625i 0.0575989 0.444705i
\(749\) 7.88326 0.288048
\(750\) 3.39384i 0.123925i
\(751\) 17.0242 17.0242i 0.621220 0.621220i −0.324623 0.945843i \(-0.605237\pi\)
0.945843 + 0.324623i \(0.105237\pi\)
\(752\) −5.59555 −0.204049
\(753\) −2.66141 + 2.66141i −0.0969871 + 0.0969871i
\(754\) −4.68070 4.68070i −0.170461 0.170461i
\(755\) −27.9141 27.9141i −1.01590 1.01590i
\(756\) 6.82797i 0.248331i
\(757\) 34.1715i 1.24199i −0.783816 0.620993i \(-0.786730\pi\)
0.783816 0.620993i \(-0.213270\pi\)
\(758\) −14.1705 14.1705i −0.514696 0.514696i
\(759\) 3.83018 + 3.83018i 0.139027 + 0.139027i
\(760\) 14.7754 14.7754i 0.535961 0.535961i
\(761\) 15.6184 0.566165 0.283083 0.959096i \(-0.408643\pi\)
0.283083 + 0.959096i \(0.408643\pi\)
\(762\) 21.1073 21.1073i 0.764638 0.764638i
\(763\) 0.498849i 0.0180595i
\(764\) −16.1782 −0.585308
\(765\) 3.82292 29.5157i 0.138218 1.06714i
\(766\) −45.8596 −1.65698
\(767\) 15.0627i 0.543884i
\(768\) −1.60305 + 1.60305i −0.0578449 + 0.0578449i
\(769\) −44.3669 −1.59991 −0.799956 0.600059i \(-0.795144\pi\)
−0.799956 + 0.600059i \(0.795144\pi\)
\(770\) −2.87481 + 2.87481i −0.103601 + 0.103601i
\(771\) 4.40253 + 4.40253i 0.158553 + 0.158553i
\(772\) −17.1453 17.1453i −0.617072 0.617072i
\(773\) 29.4703i 1.05997i 0.848006 + 0.529986i \(0.177803\pi\)
−0.848006 + 0.529986i \(0.822197\pi\)
\(774\) 5.16313i 0.185585i
\(775\) −31.6988 31.6988i −1.13866 1.13866i
\(776\) −4.59837 4.59837i −0.165072 0.165072i
\(777\) 1.67052 1.67052i 0.0599297 0.0599297i
\(778\) −64.5487 −2.31418
\(779\) 25.8739 25.8739i 0.927028 0.927028i
\(780\) 9.63928i 0.345142i
\(781\) −2.65980 −0.0951750
\(782\) 56.8355 + 7.36142i 2.03243 + 0.263244i
\(783\) −9.21703 −0.329390
\(784\) 11.9257i 0.425919i
\(785\) −19.3764 + 19.3764i −0.691572 + 0.691572i
\(786\) −4.89488 −0.174594
\(787\) 23.8435 23.8435i 0.849927 0.849927i −0.140196 0.990124i \(-0.544773\pi\)
0.990124 + 0.140196i \(0.0447734\pi\)
\(788\) 48.6491 + 48.6491i 1.73305 + 1.73305i
\(789\) 11.5076 + 11.5076i 0.409680 + 0.409680i
\(790\) 27.7670i 0.987907i
\(791\) 1.75689i 0.0624677i
\(792\) 3.08222 + 3.08222i 0.109522 + 0.109522i
\(793\) 11.0699 + 11.0699i 0.393102 + 0.393102i
\(794\) 10.4767 10.4767i 0.371804 0.371804i
\(795\) 31.4960 1.11705
\(796\) 18.4618 18.4618i 0.654361 0.654361i
\(797\) 47.3675i 1.67784i −0.544252 0.838922i \(-0.683186\pi\)
0.544252 0.838922i \(-0.316814\pi\)
\(798\) −3.93018 −0.139127
\(799\) −7.88306 10.2290i −0.278883 0.361874i
\(800\) 32.2394 1.13984
\(801\) 28.9996i 1.02465i
\(802\) 44.8728 44.8728i 1.58451 1.58451i
\(803\) 1.72381 0.0608318
\(804\) −16.4760 + 16.4760i −0.581065 + 0.581065i
\(805\) −7.82790 7.82790i −0.275897 0.275897i
\(806\) 22.3711 + 22.3711i 0.787988 + 0.787988i
\(807\) 7.47987i 0.263304i
\(808\) 24.3375i 0.856189i
\(809\) 20.9683 + 20.9683i 0.737205 + 0.737205i 0.972036 0.234831i \(-0.0754536\pi\)
−0.234831 + 0.972036i \(0.575454\pi\)
\(810\) 17.2348 + 17.2348i 0.605569 + 0.605569i
\(811\) 8.12732 8.12732i 0.285389 0.285389i −0.549865 0.835254i \(-0.685321\pi\)
0.835254 + 0.549865i \(0.185321\pi\)
\(812\) 3.41644 0.119894
\(813\) −1.29323 + 1.29323i −0.0453557 + 0.0453557i
\(814\) 12.0729i 0.423156i
\(815\) 42.6602 1.49432
\(816\) 5.85099 + 0.757830i 0.204826 + 0.0265293i
\(817\) 3.93447 0.137650
\(818\) 71.9387i 2.51528i
\(819\) 1.33764 1.33764i 0.0467409 0.0467409i
\(820\) −79.4909 −2.77594
\(821\) −10.0028 + 10.0028i −0.349101 + 0.349101i −0.859775 0.510673i \(-0.829396\pi\)
0.510673 + 0.859775i \(0.329396\pi\)
\(822\) 25.3549 + 25.3549i 0.884352 + 0.884352i
\(823\) 31.6115 + 31.6115i 1.10191 + 1.10191i 0.994181 + 0.107727i \(0.0343571\pi\)
0.107727 + 0.994181i \(0.465643\pi\)
\(824\) 29.0444i 1.01181i
\(825\) 3.72614i 0.129727i
\(826\) 9.43405 + 9.43405i 0.328253 + 0.328253i
\(827\) −1.23920 1.23920i −0.0430913 0.0430913i 0.685233 0.728324i \(-0.259700\pi\)
−0.728324 + 0.685233i \(0.759700\pi\)
\(828\) −29.5696 + 29.5696i −1.02761 + 1.02761i
\(829\) −19.0371 −0.661187 −0.330594 0.943773i \(-0.607249\pi\)
−0.330594 + 0.943773i \(0.607249\pi\)
\(830\) 75.4722 75.4722i 2.61968 2.61968i
\(831\) 2.02989i 0.0704160i
\(832\) −17.7218 −0.614393
\(833\) −21.8009 + 16.8011i −0.755355 + 0.582123i
\(834\) −14.5493 −0.503801
\(835\) 3.29446i 0.114010i
\(836\) 8.27527 8.27527i 0.286206 0.286206i
\(837\) 44.0522 1.52267
\(838\) −25.2023 + 25.2023i −0.870599 + 0.870599i
\(839\) 34.0266 + 34.0266i 1.17473 + 1.17473i 0.981069 + 0.193660i \(0.0620357\pi\)
0.193660 + 0.981069i \(0.437964\pi\)
\(840\) 1.71354 + 1.71354i 0.0591227 + 0.0591227i
\(841\) 24.3882i 0.840971i
\(842\) 1.27336i 0.0438830i
\(843\) 7.61755 + 7.61755i 0.262362 + 0.262362i
\(844\) 33.9027 + 33.9027i 1.16698 + 1.16698i
\(845\) −23.8443 + 23.8443i −0.820268 + 0.820268i
\(846\) 16.1716 0.555992
\(847\) 3.97402 3.97402i 0.136549 0.136549i
\(848\) 22.9524i 0.788189i
\(849\) 6.75208 0.231731
\(850\) 24.0651 + 31.2265i 0.825425 + 1.07106i
\(851\) −32.8737 −1.12690
\(852\) 5.58570i 0.191363i
\(853\) 23.9534 23.9534i 0.820148 0.820148i −0.165981 0.986129i \(-0.553079\pi\)
0.986129 + 0.165981i \(0.0530790\pi\)
\(854\) −13.8665 −0.474502
\(855\) 20.0823 20.0823i 0.686799 0.686799i
\(856\) 16.9793 + 16.9793i 0.580341 + 0.580341i
\(857\) −13.7646 13.7646i −0.470189 0.470189i 0.431787 0.901976i \(-0.357883\pi\)
−0.901976 + 0.431787i \(0.857883\pi\)
\(858\) 2.62968i 0.0897757i
\(859\) 5.32329i 0.181628i 0.995868 + 0.0908141i \(0.0289469\pi\)
−0.995868 + 0.0908141i \(0.971053\pi\)
\(860\) −6.04383 6.04383i −0.206093 0.206093i
\(861\) 3.00065 + 3.00065i 0.102262 + 0.102262i
\(862\) −2.61052 + 2.61052i −0.0889147 + 0.0889147i
\(863\) 22.4195 0.763169 0.381584 0.924334i \(-0.375379\pi\)
0.381584 + 0.924334i \(0.375379\pi\)
\(864\) −22.4017 + 22.4017i −0.762121 + 0.762121i
\(865\) 17.7772i 0.604441i
\(866\) 33.4716 1.13741
\(867\) 6.85758 + 11.7636i 0.232896 + 0.399512i
\(868\) −16.3287 −0.554231
\(869\) 4.41394i 0.149733i
\(870\) 8.14964 8.14964i 0.276299 0.276299i
\(871\) −14.6670 −0.496973
\(872\) −1.07444 + 1.07444i −0.0363852 + 0.0363852i
\(873\) −6.24995 6.24995i −0.211529 0.211529i
\(874\) 38.6704 + 38.6704i 1.30805 + 1.30805i
\(875\) 1.10259i 0.0372744i
\(876\) 3.62008i 0.122311i
\(877\) −18.1654 18.1654i −0.613403 0.613403i 0.330428 0.943831i \(-0.392807\pi\)
−0.943831 + 0.330428i \(0.892807\pi\)
\(878\) −0.703611 0.703611i −0.0237457 0.0237457i
\(879\) 6.92213 6.92213i 0.233478 0.233478i
\(880\) 5.82392 0.196324
\(881\) 12.3483 12.3483i 0.416024 0.416024i −0.467807 0.883831i \(-0.654956\pi\)
0.883831 + 0.467807i \(0.154956\pi\)
\(882\) 34.4664i 1.16054i
\(883\) −1.19226 −0.0401227 −0.0200613 0.999799i \(-0.506386\pi\)
−0.0200613 + 0.999799i \(0.506386\pi\)
\(884\) −9.89623 12.8412i −0.332846 0.431897i
\(885\) 26.2260 0.881577
\(886\) 37.2746i 1.25226i
\(887\) −11.7737 + 11.7737i −0.395322 + 0.395322i −0.876579 0.481257i \(-0.840180\pi\)
0.481257 + 0.876579i \(0.340180\pi\)
\(888\) 7.19609 0.241485
\(889\) −6.85735 + 6.85735i −0.229988 + 0.229988i
\(890\) −58.2575 58.2575i −1.95280 1.95280i
\(891\) 2.73970 + 2.73970i 0.0917834 + 0.0917834i
\(892\) 1.26814i 0.0424605i
\(893\) 12.3233i 0.412383i
\(894\) 22.8068 + 22.8068i 0.762772 + 0.762772i
\(895\) −17.7145 17.7145i −0.592130 0.592130i
\(896\) 5.15269 5.15269i 0.172139 0.172139i
\(897\) 7.16042 0.239079
\(898\) 20.8932 20.8932i 0.697215 0.697215i
\(899\) 22.0419i 0.735140i
\(900\) −28.7663 −0.958878
\(901\) 41.9582 32.3356i 1.39783 1.07725i
\(902\) −21.6858 −0.722058
\(903\) 0.456289i 0.0151843i
\(904\) −3.78406 + 3.78406i −0.125856 + 0.125856i
\(905\) −31.0842 −1.03327
\(906\) −15.9923 + 15.9923i −0.531309 + 0.531309i
\(907\) −4.25135 4.25135i −0.141164 0.141164i 0.632993 0.774157i \(-0.281826\pi\)
−0.774157 + 0.632993i \(0.781826\pi\)
\(908\) −34.3283 34.3283i −1.13923 1.13923i
\(909\) 33.0787i 1.09715i
\(910\) 5.37438i 0.178159i
\(911\) 13.4127 + 13.4127i 0.444382 + 0.444382i 0.893482 0.449099i \(-0.148255\pi\)
−0.449099 + 0.893482i \(0.648255\pi\)
\(912\) 3.98097 + 3.98097i 0.131823 + 0.131823i
\(913\) 11.9973 11.9973i 0.397053 0.397053i
\(914\) −16.9371 −0.560231
\(915\) −19.2739 + 19.2739i −0.637176 + 0.637176i
\(916\) 33.6665i 1.11237i
\(917\) 1.59025 0.0525146
\(918\) −38.4196 4.97617i −1.26804 0.164238i
\(919\) 15.3942 0.507809 0.253905 0.967229i \(-0.418285\pi\)
0.253905 + 0.967229i \(0.418285\pi\)
\(920\) 33.7202i 1.11172i
\(921\) 2.15039 2.15039i 0.0708576 0.0708576i
\(922\) 50.1180 1.65055
\(923\) −2.48621 + 2.48621i −0.0818345 + 0.0818345i
\(924\) 0.959701 + 0.959701i 0.0315718 + 0.0315718i
\(925\) −15.9904 15.9904i −0.525760 0.525760i
\(926\) 79.3896i 2.60890i
\(927\) 39.4762i 1.29657i
\(928\) −11.2089 11.2089i −0.367951 0.367951i
\(929\) −2.84903 2.84903i −0.0934738 0.0934738i 0.658824 0.752297i \(-0.271054\pi\)
−0.752297 + 0.658824i \(0.771054\pi\)
\(930\) −38.9507 + 38.9507i −1.27724 + 1.27724i
\(931\) −26.2644 −0.860782
\(932\) 35.2871 35.2871i 1.15587 1.15587i
\(933\) 3.76140i 0.123143i
\(934\) −51.2847 −1.67809
\(935\) 8.20480 + 10.6464i 0.268326 + 0.348176i
\(936\) 5.76213 0.188341
\(937\) 3.41787i 0.111657i −0.998440 0.0558284i \(-0.982220\pi\)
0.998440 0.0558284i \(-0.0177800\pi\)
\(938\) 9.18621 9.18621i 0.299940 0.299940i
\(939\) 10.2309 0.333873
\(940\) −18.9301 + 18.9301i −0.617431 + 0.617431i
\(941\) 15.2387 + 15.2387i 0.496768 + 0.496768i 0.910430 0.413662i \(-0.135751\pi\)
−0.413662 + 0.910430i \(0.635751\pi\)
\(942\) 11.1009 + 11.1009i 0.361688 + 0.361688i
\(943\) 59.0488i 1.92289i
\(944\) 19.1119i 0.622040i
\(945\) 5.29150 + 5.29150i 0.172133 + 0.172133i
\(946\) −1.64881 1.64881i −0.0536074 0.0536074i
\(947\) −12.1567 + 12.1567i −0.395041 + 0.395041i −0.876480 0.481439i \(-0.840114\pi\)
0.481439 + 0.876480i \(0.340114\pi\)
\(948\) −9.26949 −0.301059
\(949\) 1.61130 1.61130i 0.0523052 0.0523052i
\(950\) 37.6199i 1.22055i
\(951\) 8.23257 0.266960
\(952\) 4.04195 + 0.523519i 0.131000 + 0.0169674i
\(953\) −36.9520 −1.19699 −0.598496 0.801125i \(-0.704235\pi\)
−0.598496 + 0.801125i \(0.704235\pi\)
\(954\) 66.3344i 2.14766i
\(955\) 12.5377 12.5377i 0.405711 0.405711i
\(956\) 38.5536 1.24691
\(957\) 1.29549 1.29549i 0.0418774 0.0418774i
\(958\) −22.5968 22.5968i −0.730070 0.730070i
\(959\) −8.23728 8.23728i −0.265996 0.265996i
\(960\) 30.8557i 0.995864i
\(961\) 74.3480i 2.39832i
\(962\) 11.2850 + 11.2850i 0.363843 + 0.363843i
\(963\) 23.0777 + 23.0777i 0.743669 + 0.743669i
\(964\) −8.02360 + 8.02360i −0.258423 + 0.258423i
\(965\) 26.5743 0.855457
\(966\) −4.48469 + 4.48469i −0.144293 + 0.144293i
\(967\) 6.51055i 0.209365i −0.994506 0.104683i \(-0.966617\pi\)
0.994506 0.104683i \(-0.0333827\pi\)
\(968\) 17.1188 0.550220
\(969\) −1.66900 + 12.8859i −0.0536159 + 0.413953i
\(970\) 25.1111 0.806270
\(971\) 28.3045i 0.908336i 0.890916 + 0.454168i \(0.150063\pi\)
−0.890916 + 0.454168i \(0.849937\pi\)
\(972\) 31.1792 31.1792i 1.00007 1.00007i
\(973\) 4.72677 0.151533
\(974\) 53.5274 53.5274i 1.71513 1.71513i
\(975\) 3.48295 + 3.48295i 0.111544 + 0.111544i
\(976\) 14.0457 + 14.0457i 0.449591 + 0.449591i
\(977\) 35.9561i 1.15034i −0.818035 0.575169i \(-0.804936\pi\)
0.818035 0.575169i \(-0.195064\pi\)
\(978\) 24.4405i 0.781520i
\(979\) −9.26081 9.26081i −0.295977 0.295977i
\(980\) 40.3454 + 40.3454i 1.28879 + 1.28879i
\(981\) −1.46035 + 1.46035i −0.0466253 + 0.0466253i
\(982\) −5.67921 −0.181231
\(983\) 39.8828 39.8828i 1.27206 1.27206i 0.327058 0.945004i \(-0.393943\pi\)
0.945004 0.327058i \(-0.106057\pi\)
\(984\) 12.9259i 0.412061i
\(985\) −75.4036 −2.40256
\(986\) 2.48987 19.2236i 0.0792937 0.612205i
\(987\) 1.42916 0.0454906
\(988\) 15.4704i 0.492178i
\(989\) 4.48958 4.48958i 0.142760 0.142760i
\(990\) −16.8316 −0.534945
\(991\) −29.1811 + 29.1811i −0.926970 + 0.926970i −0.997509 0.0705393i \(-0.977528\pi\)
0.0705393 + 0.997509i \(0.477528\pi\)
\(992\) 53.5722 + 53.5722i 1.70092 + 1.70092i
\(993\) −9.29338 9.29338i −0.294917 0.294917i
\(994\) 3.11431i 0.0987799i
\(995\) 28.6148i 0.907152i
\(996\) −25.1949 25.1949i −0.798333 0.798333i
\(997\) −0.200109 0.200109i −0.00633750 0.00633750i 0.703931 0.710268i \(-0.251426\pi\)
−0.710268 + 0.703931i \(0.751426\pi\)
\(998\) 10.7280 10.7280i 0.339590 0.339590i
\(999\) 22.2219 0.703071
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 731.2.f.c.259.5 56
17.13 even 4 inner 731.2.f.c.302.24 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.f.c.259.5 56 1.1 even 1 trivial
731.2.f.c.302.24 yes 56 17.13 even 4 inner