Properties

Label 168.2.i.e.125.3
Level $168$
Weight $2$
Character 168.125
Analytic conductor $1.341$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [168,2,Mod(125,168)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(168, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("168.125");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 168.i (of order \(2\), degree \(1\), 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: \(1.34148675396\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.3317760000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 8x^{6} + 13x^{4} + 12x^{2} + 36 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 125.3
Root \(0.578737 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 168.125
Dual form 168.2.i.e.125.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 1.11803i) q^{2} +(-1.58114 - 0.707107i) q^{3} +(-0.500000 - 1.93649i) q^{4} +1.41421i q^{5} +(2.15988 - 1.15539i) q^{6} +(1.00000 - 2.44949i) q^{7} +(2.59808 + 1.11803i) q^{8} +(2.00000 + 2.23607i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 1.11803i) q^{2} +(-1.58114 - 0.707107i) q^{3} +(-0.500000 - 1.93649i) q^{4} +1.41421i q^{5} +(2.15988 - 1.15539i) q^{6} +(1.00000 - 2.44949i) q^{7} +(2.59808 + 1.11803i) q^{8} +(2.00000 + 2.23607i) q^{9} +(-1.58114 - 1.22474i) q^{10} +3.46410 q^{11} +(-0.578737 + 3.41542i) q^{12} +3.16228 q^{13} +(1.87259 + 3.23935i) q^{14} +(1.00000 - 2.23607i) q^{15} +(-3.50000 + 1.93649i) q^{16} +(-4.23205 + 0.299576i) q^{18} +3.16228 q^{19} +(2.73861 - 0.707107i) q^{20} +(-3.31319 + 3.16588i) q^{21} +(-3.00000 + 3.87298i) q^{22} -4.47214i q^{23} +(-3.31735 - 3.60488i) q^{24} +3.00000 q^{25} +(-2.73861 + 3.53553i) q^{26} +(-1.58114 - 4.94975i) q^{27} +(-5.24342 - 0.711747i) q^{28} -6.92820 q^{29} +(1.63397 + 3.05453i) q^{30} +4.89898i q^{31} +(0.866025 - 5.59017i) q^{32} +(-5.47723 - 2.44949i) q^{33} +(3.46410 + 1.41421i) q^{35} +(3.33013 - 4.99102i) q^{36} +(-2.73861 + 3.53553i) q^{38} +(-5.00000 - 2.23607i) q^{39} +(-1.58114 + 3.67423i) q^{40} +10.9545 q^{41} +(-0.670251 - 6.44599i) q^{42} -7.74597i q^{43} +(-1.73205 - 6.70820i) q^{44} +(-3.16228 + 2.82843i) q^{45} +(5.00000 + 3.87298i) q^{46} -10.9545 q^{47} +(6.90329 - 0.586988i) q^{48} +(-5.00000 - 4.89898i) q^{49} +(-2.59808 + 3.35410i) q^{50} +(-1.58114 - 6.12372i) q^{52} +(6.90329 + 2.51884i) q^{54} +4.89898i q^{55} +(5.33669 - 5.24593i) q^{56} +(-5.00000 - 2.23607i) q^{57} +(6.00000 - 7.74597i) q^{58} +9.89949i q^{59} +(-4.83013 - 0.818458i) q^{60} +3.16228 q^{61} +(-5.47723 - 4.24264i) q^{62} +(7.47723 - 2.66291i) q^{63} +(5.50000 + 5.80948i) q^{64} +4.47214i q^{65} +(7.48203 - 4.00240i) q^{66} +7.74597i q^{67} +(-3.16228 + 7.07107i) q^{69} +(-4.58114 + 2.64824i) q^{70} +8.94427i q^{71} +(2.69615 + 8.04554i) q^{72} +14.6969i q^{73} +(-4.74342 - 2.12132i) q^{75} +(-1.58114 - 6.12372i) q^{76} +(3.46410 - 8.48528i) q^{77} +(6.83013 - 3.65368i) q^{78} -10.0000 q^{79} +(-2.73861 - 4.94975i) q^{80} +(-1.00000 + 8.94427i) q^{81} +(-9.48683 + 12.2474i) q^{82} -7.07107i q^{83} +(7.78729 + 4.83303i) q^{84} +(8.66025 + 6.70820i) q^{86} +(10.9545 + 4.89898i) q^{87} +(9.00000 + 3.87298i) q^{88} +(-0.423665 - 5.98502i) q^{90} +(3.16228 - 7.74597i) q^{91} +(-8.66025 + 2.23607i) q^{92} +(3.46410 - 7.74597i) q^{93} +(9.48683 - 12.2474i) q^{94} +4.47214i q^{95} +(-5.32215 + 8.22646i) q^{96} -4.89898i q^{97} +(9.80735 - 1.34753i) q^{98} +(6.92820 + 7.74597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{4} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{4} + 8 q^{7} + 16 q^{9} + 8 q^{15} - 28 q^{16} - 20 q^{18} - 24 q^{22} + 24 q^{25} - 4 q^{28} + 20 q^{30} - 8 q^{36} - 40 q^{39} + 12 q^{42} + 40 q^{46} - 40 q^{49} - 40 q^{57} + 48 q^{58} - 4 q^{60} + 16 q^{63} + 44 q^{64} - 24 q^{70} - 20 q^{72} + 20 q^{78} - 80 q^{79} - 8 q^{81} + 60 q^{84} + 72 q^{88}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(85\) \(113\) \(127\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 1.11803i −0.612372 + 0.790569i
\(3\) −1.58114 0.707107i −0.912871 0.408248i
\(4\) −0.500000 1.93649i −0.250000 0.968246i
\(5\) 1.41421i 0.632456i 0.948683 + 0.316228i \(0.102416\pi\)
−0.948683 + 0.316228i \(0.897584\pi\)
\(6\) 2.15988 1.15539i 0.881766 0.471688i
\(7\) 1.00000 2.44949i 0.377964 0.925820i
\(8\) 2.59808 + 1.11803i 0.918559 + 0.395285i
\(9\) 2.00000 + 2.23607i 0.666667 + 0.745356i
\(10\) −1.58114 1.22474i −0.500000 0.387298i
\(11\) 3.46410 1.04447 0.522233 0.852803i \(-0.325099\pi\)
0.522233 + 0.852803i \(0.325099\pi\)
\(12\) −0.578737 + 3.41542i −0.167067 + 0.985946i
\(13\) 3.16228 0.877058 0.438529 0.898717i \(-0.355500\pi\)
0.438529 + 0.898717i \(0.355500\pi\)
\(14\) 1.87259 + 3.23935i 0.500470 + 0.865754i
\(15\) 1.00000 2.23607i 0.258199 0.577350i
\(16\) −3.50000 + 1.93649i −0.875000 + 0.484123i
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −4.23205 + 0.299576i −0.997504 + 0.0706108i
\(19\) 3.16228 0.725476 0.362738 0.931891i \(-0.381842\pi\)
0.362738 + 0.931891i \(0.381842\pi\)
\(20\) 2.73861 0.707107i 0.612372 0.158114i
\(21\) −3.31319 + 3.16588i −0.722997 + 0.690851i
\(22\) −3.00000 + 3.87298i −0.639602 + 0.825723i
\(23\) 4.47214i 0.932505i −0.884652 0.466252i \(-0.845604\pi\)
0.884652 0.466252i \(-0.154396\pi\)
\(24\) −3.31735 3.60488i −0.677151 0.735844i
\(25\) 3.00000 0.600000
\(26\) −2.73861 + 3.53553i −0.537086 + 0.693375i
\(27\) −1.58114 4.94975i −0.304290 0.952579i
\(28\) −5.24342 0.711747i −0.990913 0.134508i
\(29\) −6.92820 −1.28654 −0.643268 0.765641i \(-0.722422\pi\)
−0.643268 + 0.765641i \(0.722422\pi\)
\(30\) 1.63397 + 3.05453i 0.298322 + 0.557678i
\(31\) 4.89898i 0.879883i 0.898027 + 0.439941i \(0.145001\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) 0.866025 5.59017i 0.153093 0.988212i
\(33\) −5.47723 2.44949i −0.953463 0.426401i
\(34\) 0 0
\(35\) 3.46410 + 1.41421i 0.585540 + 0.239046i
\(36\) 3.33013 4.99102i 0.555021 0.831836i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) −2.73861 + 3.53553i −0.444262 + 0.573539i
\(39\) −5.00000 2.23607i −0.800641 0.358057i
\(40\) −1.58114 + 3.67423i −0.250000 + 0.580948i
\(41\) 10.9545 1.71080 0.855399 0.517970i \(-0.173312\pi\)
0.855399 + 0.517970i \(0.173312\pi\)
\(42\) −0.670251 6.44599i −0.103422 0.994638i
\(43\) 7.74597i 1.18125i −0.806947 0.590624i \(-0.798881\pi\)
0.806947 0.590624i \(-0.201119\pi\)
\(44\) −1.73205 6.70820i −0.261116 1.01130i
\(45\) −3.16228 + 2.82843i −0.471405 + 0.421637i
\(46\) 5.00000 + 3.87298i 0.737210 + 0.571040i
\(47\) −10.9545 −1.59787 −0.798935 0.601417i \(-0.794603\pi\)
−0.798935 + 0.601417i \(0.794603\pi\)
\(48\) 6.90329 0.586988i 0.996404 0.0847245i
\(49\) −5.00000 4.89898i −0.714286 0.699854i
\(50\) −2.59808 + 3.35410i −0.367423 + 0.474342i
\(51\) 0 0
\(52\) −1.58114 6.12372i −0.219265 0.849208i
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 6.90329 + 2.51884i 0.939419 + 0.342771i
\(55\) 4.89898i 0.660578i
\(56\) 5.33669 5.24593i 0.713145 0.701016i
\(57\) −5.00000 2.23607i −0.662266 0.296174i
\(58\) 6.00000 7.74597i 0.787839 1.01710i
\(59\) 9.89949i 1.28880i 0.764687 + 0.644402i \(0.222894\pi\)
−0.764687 + 0.644402i \(0.777106\pi\)
\(60\) −4.83013 0.818458i −0.623567 0.105662i
\(61\) 3.16228 0.404888 0.202444 0.979294i \(-0.435112\pi\)
0.202444 + 0.979294i \(0.435112\pi\)
\(62\) −5.47723 4.24264i −0.695608 0.538816i
\(63\) 7.47723 2.66291i 0.942042 0.335495i
\(64\) 5.50000 + 5.80948i 0.687500 + 0.726184i
\(65\) 4.47214i 0.554700i
\(66\) 7.48203 4.00240i 0.920974 0.492662i
\(67\) 7.74597i 0.946320i 0.880976 + 0.473160i \(0.156887\pi\)
−0.880976 + 0.473160i \(0.843113\pi\)
\(68\) 0 0
\(69\) −3.16228 + 7.07107i −0.380693 + 0.851257i
\(70\) −4.58114 + 2.64824i −0.547551 + 0.316525i
\(71\) 8.94427i 1.06149i 0.847532 + 0.530745i \(0.178088\pi\)
−0.847532 + 0.530745i \(0.821912\pi\)
\(72\) 2.69615 + 8.04554i 0.317745 + 0.948176i
\(73\) 14.6969i 1.72015i 0.510171 + 0.860073i \(0.329582\pi\)
−0.510171 + 0.860073i \(0.670418\pi\)
\(74\) 0 0
\(75\) −4.74342 2.12132i −0.547723 0.244949i
\(76\) −1.58114 6.12372i −0.181369 0.702439i
\(77\) 3.46410 8.48528i 0.394771 0.966988i
\(78\) 6.83013 3.65368i 0.773360 0.413698i
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) −2.73861 4.94975i −0.306186 0.553399i
\(81\) −1.00000 + 8.94427i −0.111111 + 0.993808i
\(82\) −9.48683 + 12.2474i −1.04765 + 1.35250i
\(83\) 7.07107i 0.776151i −0.921628 0.388075i \(-0.873140\pi\)
0.921628 0.388075i \(-0.126860\pi\)
\(84\) 7.78729 + 4.83303i 0.849663 + 0.527326i
\(85\) 0 0
\(86\) 8.66025 + 6.70820i 0.933859 + 0.723364i
\(87\) 10.9545 + 4.89898i 1.17444 + 0.525226i
\(88\) 9.00000 + 3.87298i 0.959403 + 0.412861i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) −0.423665 5.98502i −0.0446582 0.630877i
\(91\) 3.16228 7.74597i 0.331497 0.811998i
\(92\) −8.66025 + 2.23607i −0.902894 + 0.233126i
\(93\) 3.46410 7.74597i 0.359211 0.803219i
\(94\) 9.48683 12.2474i 0.978492 1.26323i
\(95\) 4.47214i 0.458831i
\(96\) −5.32215 + 8.22646i −0.543190 + 0.839610i
\(97\) 4.89898i 0.497416i −0.968579 0.248708i \(-0.919994\pi\)
0.968579 0.248708i \(-0.0800060\pi\)
\(98\) 9.80735 1.34753i 0.990692 0.136121i
\(99\) 6.92820 + 7.74597i 0.696311 + 0.778499i
\(100\) −1.50000 5.80948i −0.150000 0.580948i
\(101\) 15.5563i 1.54791i −0.633238 0.773957i \(-0.718274\pi\)
0.633238 0.773957i \(-0.281726\pi\)
\(102\) 0 0
\(103\) 9.79796i 0.965422i −0.875780 0.482711i \(-0.839652\pi\)
0.875780 0.482711i \(-0.160348\pi\)
\(104\) 8.21584 + 3.53553i 0.805629 + 0.346688i
\(105\) −4.47723 4.68556i −0.436932 0.457264i
\(106\) 0 0
\(107\) −10.3923 −1.00466 −0.502331 0.864675i \(-0.667524\pi\)
−0.502331 + 0.864675i \(0.667524\pi\)
\(108\) −8.79458 + 5.53674i −0.846258 + 0.532773i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) −5.47723 4.24264i −0.522233 0.404520i
\(111\) 0 0
\(112\) 1.24342 + 10.5097i 0.117492 + 0.993074i
\(113\) 4.47214i 0.420703i −0.977626 0.210352i \(-0.932539\pi\)
0.977626 0.210352i \(-0.0674609\pi\)
\(114\) 6.83013 3.65368i 0.639700 0.342198i
\(115\) 6.32456 0.589768
\(116\) 3.46410 + 13.4164i 0.321634 + 1.24568i
\(117\) 6.32456 + 7.07107i 0.584705 + 0.653720i
\(118\) −11.0680 8.57321i −1.01889 0.789228i
\(119\) 0 0
\(120\) 5.09808 4.69144i 0.465389 0.428268i
\(121\) 1.00000 0.0909091
\(122\) −2.73861 + 3.53553i −0.247942 + 0.320092i
\(123\) −17.3205 7.74597i −1.56174 0.698430i
\(124\) 9.48683 2.44949i 0.851943 0.219971i
\(125\) 11.3137i 1.01193i
\(126\) −3.49824 + 10.6659i −0.311648 + 0.950198i
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) −11.2583 + 1.11803i −0.995105 + 0.0988212i
\(129\) −5.47723 + 12.2474i −0.482243 + 1.07833i
\(130\) −5.00000 3.87298i −0.438529 0.339683i
\(131\) 1.41421i 0.123560i 0.998090 + 0.0617802i \(0.0196778\pi\)
−0.998090 + 0.0617802i \(0.980322\pi\)
\(132\) −2.00480 + 11.8313i −0.174496 + 1.02979i
\(133\) 3.16228 7.74597i 0.274204 0.671660i
\(134\) −8.66025 6.70820i −0.748132 0.579501i
\(135\) 7.00000 2.23607i 0.602464 0.192450i
\(136\) 0 0
\(137\) 17.8885i 1.52832i −0.645026 0.764161i \(-0.723153\pi\)
0.645026 0.764161i \(-0.276847\pi\)
\(138\) −5.16708 9.65926i −0.439851 0.822251i
\(139\) −15.8114 −1.34110 −0.670552 0.741862i \(-0.733943\pi\)
−0.670552 + 0.741862i \(0.733943\pi\)
\(140\) 1.00656 7.41531i 0.0850700 0.626708i
\(141\) 17.3205 + 7.74597i 1.45865 + 0.652328i
\(142\) −10.0000 7.74597i −0.839181 0.650027i
\(143\) 10.9545 0.916057
\(144\) −11.3301 3.95325i −0.944177 0.329438i
\(145\) 9.79796i 0.813676i
\(146\) −16.4317 12.7279i −1.35990 1.05337i
\(147\) 4.44159 + 11.2815i 0.366336 + 0.930482i
\(148\) 0 0
\(149\) 6.92820 0.567581 0.283790 0.958886i \(-0.408408\pi\)
0.283790 + 0.958886i \(0.408408\pi\)
\(150\) 6.47963 3.46618i 0.529059 0.283013i
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 8.21584 + 3.53553i 0.666392 + 0.286770i
\(153\) 0 0
\(154\) 6.48683 + 11.2215i 0.522724 + 0.904250i
\(155\) −6.92820 −0.556487
\(156\) −1.83013 + 10.8005i −0.146527 + 0.864731i
\(157\) −15.8114 −1.26189 −0.630943 0.775829i \(-0.717332\pi\)
−0.630943 + 0.775829i \(0.717332\pi\)
\(158\) 8.66025 11.1803i 0.688973 0.889460i
\(159\) 0 0
\(160\) 7.90569 + 1.22474i 0.625000 + 0.0968246i
\(161\) −10.9545 4.47214i −0.863332 0.352454i
\(162\) −9.13397 8.86400i −0.717633 0.696422i
\(163\) 23.2379i 1.82013i 0.414462 + 0.910066i \(0.363970\pi\)
−0.414462 + 0.910066i \(0.636030\pi\)
\(164\) −5.47723 21.2132i −0.427699 1.65647i
\(165\) 3.46410 7.74597i 0.269680 0.603023i
\(166\) 7.90569 + 6.12372i 0.613601 + 0.475293i
\(167\) −21.9089 −1.69536 −0.847681 0.530506i \(-0.822002\pi\)
−0.847681 + 0.530506i \(0.822002\pi\)
\(168\) −12.1475 + 4.52093i −0.937198 + 0.348797i
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) 6.32456 + 7.07107i 0.483651 + 0.540738i
\(172\) −15.0000 + 3.87298i −1.14374 + 0.295312i
\(173\) 7.07107i 0.537603i −0.963196 0.268802i \(-0.913372\pi\)
0.963196 0.268802i \(-0.0866276\pi\)
\(174\) −14.9641 + 8.00481i −1.13442 + 0.606843i
\(175\) 3.00000 7.34847i 0.226779 0.555492i
\(176\) −12.1244 + 6.70820i −0.913908 + 0.505650i
\(177\) 7.00000 15.6525i 0.526152 1.17651i
\(178\) 0 0
\(179\) 10.3923 0.776757 0.388379 0.921500i \(-0.373035\pi\)
0.388379 + 0.921500i \(0.373035\pi\)
\(180\) 7.05836 + 4.70951i 0.526099 + 0.351026i
\(181\) 3.16228 0.235050 0.117525 0.993070i \(-0.462504\pi\)
0.117525 + 0.993070i \(0.462504\pi\)
\(182\) 5.92164 + 10.2437i 0.438941 + 0.759316i
\(183\) −5.00000 2.23607i −0.369611 0.165295i
\(184\) 5.00000 11.6190i 0.368605 0.856560i
\(185\) 0 0
\(186\) 5.66025 + 10.5812i 0.415030 + 0.775850i
\(187\) 0 0
\(188\) 5.47723 + 21.2132i 0.399468 + 1.54713i
\(189\) −13.7055 1.07676i −0.996928 0.0783231i
\(190\) −5.00000 3.87298i −0.362738 0.280976i
\(191\) 8.94427i 0.647185i 0.946197 + 0.323592i \(0.104891\pi\)
−0.946197 + 0.323592i \(0.895109\pi\)
\(192\) −4.58834 13.0747i −0.331135 0.943583i
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 5.47723 + 4.24264i 0.393242 + 0.304604i
\(195\) 3.16228 7.07107i 0.226455 0.506370i
\(196\) −6.98683 + 12.1319i −0.499059 + 0.866568i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) −14.6603 + 1.03776i −1.04186 + 0.0737506i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 7.79423 + 3.35410i 0.551135 + 0.237171i
\(201\) 5.47723 12.2474i 0.386334 0.863868i
\(202\) 17.3925 + 13.4722i 1.22373 + 0.947900i
\(203\) −6.92820 + 16.9706i −0.486265 + 1.19110i
\(204\) 0 0
\(205\) 15.4919i 1.08200i
\(206\) 10.9545 + 8.48528i 0.763233 + 0.591198i
\(207\) 10.0000 8.94427i 0.695048 0.621670i
\(208\) −11.0680 + 6.12372i −0.767426 + 0.424604i
\(209\) 10.9545 0.757735
\(210\) 9.11600 0.947878i 0.629064 0.0654098i
\(211\) 7.74597i 0.533254i 0.963800 + 0.266627i \(0.0859092\pi\)
−0.963800 + 0.266627i \(0.914091\pi\)
\(212\) 0 0
\(213\) 6.32456 14.1421i 0.433351 0.969003i
\(214\) 9.00000 11.6190i 0.615227 0.794255i
\(215\) 10.9545 0.747087
\(216\) 1.42607 14.6276i 0.0970316 0.995281i
\(217\) 12.0000 + 4.89898i 0.814613 + 0.332564i
\(218\) 0 0
\(219\) 10.3923 23.2379i 0.702247 1.57027i
\(220\) 9.48683 2.44949i 0.639602 0.165145i
\(221\) 0 0
\(222\) 0 0
\(223\) 9.79796i 0.656120i 0.944657 + 0.328060i \(0.106395\pi\)
−0.944657 + 0.328060i \(0.893605\pi\)
\(224\) −12.8270 7.71149i −0.857043 0.515246i
\(225\) 6.00000 + 6.70820i 0.400000 + 0.447214i
\(226\) 5.00000 + 3.87298i 0.332595 + 0.257627i
\(227\) 9.89949i 0.657053i 0.944495 + 0.328526i \(0.106552\pi\)
−0.944495 + 0.328526i \(0.893448\pi\)
\(228\) −1.83013 + 10.8005i −0.121203 + 0.715280i
\(229\) −15.8114 −1.04485 −0.522423 0.852686i \(-0.674972\pi\)
−0.522423 + 0.852686i \(0.674972\pi\)
\(230\) −5.47723 + 7.07107i −0.361158 + 0.466252i
\(231\) −11.4772 + 10.9669i −0.755146 + 0.721570i
\(232\) −18.0000 7.74597i −1.18176 0.508548i
\(233\) 8.94427i 0.585959i 0.956119 + 0.292979i \(0.0946467\pi\)
−0.956119 + 0.292979i \(0.905353\pi\)
\(234\) −13.3829 + 0.947343i −0.874869 + 0.0619298i
\(235\) 15.4919i 1.01058i
\(236\) 19.1703 4.94975i 1.24788 0.322201i
\(237\) 15.8114 + 7.07107i 1.02706 + 0.459315i
\(238\) 0 0
\(239\) 4.47214i 0.289278i −0.989484 0.144639i \(-0.953798\pi\)
0.989484 0.144639i \(-0.0462022\pi\)
\(240\) 0.830127 + 9.76273i 0.0535845 + 0.630181i
\(241\) 4.89898i 0.315571i −0.987473 0.157786i \(-0.949565\pi\)
0.987473 0.157786i \(-0.0504355\pi\)
\(242\) −0.866025 + 1.11803i −0.0556702 + 0.0718699i
\(243\) 7.90569 13.4350i 0.507151 0.861858i
\(244\) −1.58114 6.12372i −0.101222 0.392031i
\(245\) 6.92820 7.07107i 0.442627 0.451754i
\(246\) 23.6603 12.6567i 1.50852 0.806963i
\(247\) 10.0000 0.636285
\(248\) −5.47723 + 12.7279i −0.347804 + 0.808224i
\(249\) −5.00000 + 11.1803i −0.316862 + 0.708525i
\(250\) −12.6491 9.79796i −0.800000 0.619677i
\(251\) 15.5563i 0.981908i −0.871185 0.490954i \(-0.836648\pi\)
0.871185 0.490954i \(-0.163352\pi\)
\(252\) −8.89532 13.1481i −0.560352 0.828254i
\(253\) 15.4919i 0.973970i
\(254\) −6.92820 + 8.94427i −0.434714 + 0.561214i
\(255\) 0 0
\(256\) 8.50000 13.5554i 0.531250 0.847215i
\(257\) 10.9545 0.683320 0.341660 0.939824i \(-0.389011\pi\)
0.341660 + 0.939824i \(0.389011\pi\)
\(258\) −8.94965 16.7303i −0.557181 1.04158i
\(259\) 0 0
\(260\) 8.66025 2.23607i 0.537086 0.138675i
\(261\) −13.8564 15.4919i −0.857690 0.958927i
\(262\) −1.58114 1.22474i −0.0976831 0.0756650i
\(263\) 8.94427i 0.551527i 0.961225 + 0.275764i \(0.0889307\pi\)
−0.961225 + 0.275764i \(0.911069\pi\)
\(264\) −11.4916 12.4877i −0.707261 0.768564i
\(265\) 0 0
\(266\) 5.92164 + 10.2437i 0.363079 + 0.628084i
\(267\) 0 0
\(268\) 15.0000 3.87298i 0.916271 0.236580i
\(269\) 9.89949i 0.603583i 0.953374 + 0.301791i \(0.0975846\pi\)
−0.953374 + 0.301791i \(0.902415\pi\)
\(270\) −3.56218 + 9.76273i −0.216787 + 0.594141i
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) −10.4772 + 10.0114i −0.634111 + 0.605916i
\(274\) 20.0000 + 15.4919i 1.20824 + 0.935902i
\(275\) 10.3923 0.626680
\(276\) 15.2742 + 2.58819i 0.919399 + 0.155791i
\(277\) 15.4919i 0.930820i 0.885095 + 0.465410i \(0.154093\pi\)
−0.885095 + 0.465410i \(0.845907\pi\)
\(278\) 13.6931 17.6777i 0.821255 1.06024i
\(279\) −10.9545 + 9.79796i −0.655826 + 0.586588i
\(280\) 7.41886 + 7.54722i 0.443362 + 0.451033i
\(281\) 8.94427i 0.533571i 0.963756 + 0.266785i \(0.0859614\pi\)
−0.963756 + 0.266785i \(0.914039\pi\)
\(282\) −23.6603 + 12.6567i −1.40895 + 0.753696i
\(283\) −15.8114 −0.939889 −0.469945 0.882696i \(-0.655726\pi\)
−0.469945 + 0.882696i \(0.655726\pi\)
\(284\) 17.3205 4.47214i 1.02778 0.265372i
\(285\) 3.16228 7.07107i 0.187317 0.418854i
\(286\) −9.48683 + 12.2474i −0.560968 + 0.724207i
\(287\) 10.9545 26.8328i 0.646621 1.58389i
\(288\) 14.2321 9.24385i 0.838632 0.544699i
\(289\) −17.0000 −1.00000
\(290\) 10.9545 + 8.48528i 0.643268 + 0.498273i
\(291\) −3.46410 + 7.74597i −0.203069 + 0.454077i
\(292\) 28.4605 7.34847i 1.66552 0.430037i
\(293\) 26.8701i 1.56977i 0.619644 + 0.784883i \(0.287277\pi\)
−0.619644 + 0.784883i \(0.712723\pi\)
\(294\) −16.4596 4.80421i −0.959945 0.280187i
\(295\) −14.0000 −0.815112
\(296\) 0 0
\(297\) −5.47723 17.1464i −0.317821 0.994937i
\(298\) −6.00000 + 7.74597i −0.347571 + 0.448712i
\(299\) 14.1421i 0.817861i
\(300\) −1.73621 + 10.2462i −0.100240 + 0.591567i
\(301\) −18.9737 7.74597i −1.09362 0.446470i
\(302\) −6.92820 + 8.94427i −0.398673 + 0.514685i
\(303\) −11.0000 + 24.5967i −0.631933 + 1.41305i
\(304\) −11.0680 + 6.12372i −0.634792 + 0.351220i
\(305\) 4.47214i 0.256074i
\(306\) 0 0
\(307\) 3.16228 0.180481 0.0902404 0.995920i \(-0.471236\pi\)
0.0902404 + 0.995920i \(0.471236\pi\)
\(308\) −18.1637 2.46556i −1.03497 0.140489i
\(309\) −6.92820 + 15.4919i −0.394132 + 0.881305i
\(310\) 6.00000 7.74597i 0.340777 0.439941i
\(311\) 10.9545 0.621170 0.310585 0.950546i \(-0.399475\pi\)
0.310585 + 0.950546i \(0.399475\pi\)
\(312\) −10.4904 11.3996i −0.593901 0.645378i
\(313\) 9.79796i 0.553813i 0.960897 + 0.276907i \(0.0893093\pi\)
−0.960897 + 0.276907i \(0.910691\pi\)
\(314\) 13.6931 17.6777i 0.772744 0.997609i
\(315\) 3.76593 + 10.5744i 0.212186 + 0.595800i
\(316\) 5.00000 + 19.3649i 0.281272 + 1.08936i
\(317\) −6.92820 −0.389127 −0.194563 0.980890i \(-0.562329\pi\)
−0.194563 + 0.980890i \(0.562329\pi\)
\(318\) 0 0
\(319\) −24.0000 −1.34374
\(320\) −8.21584 + 7.77817i −0.459279 + 0.434813i
\(321\) 16.4317 + 7.34847i 0.917127 + 0.410152i
\(322\) 14.4868 8.37447i 0.807320 0.466691i
\(323\) 0 0
\(324\) 17.8205 2.53564i 0.990028 0.140869i
\(325\) 9.48683 0.526235
\(326\) −25.9808 20.1246i −1.43894 1.11460i
\(327\) 0 0
\(328\) 28.4605 + 12.2474i 1.57147 + 0.676252i
\(329\) −10.9545 + 26.8328i −0.603938 + 1.47934i
\(330\) 5.66025 + 10.5812i 0.311587 + 0.582475i
\(331\) 7.74597i 0.425757i −0.977079 0.212878i \(-0.931716\pi\)
0.977079 0.212878i \(-0.0682838\pi\)
\(332\) −13.6931 + 3.53553i −0.751505 + 0.194038i
\(333\) 0 0
\(334\) 18.9737 24.4949i 1.03819 1.34030i
\(335\) −10.9545 −0.598506
\(336\) 5.46547 17.4965i 0.298166 0.954514i
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) 2.59808 3.35410i 0.141317 0.182439i
\(339\) −3.16228 + 7.07107i −0.171751 + 0.384048i
\(340\) 0 0
\(341\) 16.9706i 0.919007i
\(342\) −13.3829 + 0.947343i −0.723665 + 0.0512265i
\(343\) −17.0000 + 7.34847i −0.917914 + 0.396780i
\(344\) 8.66025 20.1246i 0.466930 1.08505i
\(345\) −10.0000 4.47214i −0.538382 0.240772i
\(346\) 7.90569 + 6.12372i 0.425013 + 0.329213i
\(347\) 17.3205 0.929814 0.464907 0.885360i \(-0.346088\pi\)
0.464907 + 0.885360i \(0.346088\pi\)
\(348\) 4.00961 23.6627i 0.214938 1.26845i
\(349\) 22.1359 1.18491 0.592455 0.805604i \(-0.298159\pi\)
0.592455 + 0.805604i \(0.298159\pi\)
\(350\) 5.61776 + 9.71806i 0.300282 + 0.519452i
\(351\) −5.00000 15.6525i −0.266880 0.835467i
\(352\) 3.00000 19.3649i 0.159901 1.03215i
\(353\) −10.9545 −0.583047 −0.291523 0.956564i \(-0.594162\pi\)
−0.291523 + 0.956564i \(0.594162\pi\)
\(354\) 11.4378 + 21.3817i 0.607913 + 1.13642i
\(355\) −12.6491 −0.671345
\(356\) 0 0
\(357\) 0 0
\(358\) −9.00000 + 11.6190i −0.475665 + 0.614081i
\(359\) 31.3050i 1.65221i −0.563515 0.826106i \(-0.690551\pi\)
0.563515 0.826106i \(-0.309449\pi\)
\(360\) −11.3781 + 3.81294i −0.599679 + 0.200959i
\(361\) −9.00000 −0.473684
\(362\) −2.73861 + 3.53553i −0.143938 + 0.185824i
\(363\) −1.58114 0.707107i −0.0829883 0.0371135i
\(364\) −16.5811 2.25074i −0.869088 0.117971i
\(365\) −20.7846 −1.08792
\(366\) 6.83013 3.65368i 0.357016 0.190981i
\(367\) 19.5959i 1.02290i −0.859313 0.511449i \(-0.829109\pi\)
0.859313 0.511449i \(-0.170891\pi\)
\(368\) 8.66025 + 15.6525i 0.451447 + 0.815942i
\(369\) 21.9089 + 24.4949i 1.14053 + 1.27515i
\(370\) 0 0
\(371\) 0 0
\(372\) −16.7321 2.83522i −0.867516 0.146999i
\(373\) 30.9839i 1.60428i 0.597133 + 0.802142i \(0.296306\pi\)
−0.597133 + 0.802142i \(0.703694\pi\)
\(374\) 0 0
\(375\) 8.00000 17.8885i 0.413118 0.923760i
\(376\) −28.4605 12.2474i −1.46774 0.631614i
\(377\) −21.9089 −1.12837
\(378\) 13.0732 14.3907i 0.672411 0.740178i
\(379\) 23.2379i 1.19365i −0.802371 0.596825i \(-0.796429\pi\)
0.802371 0.596825i \(-0.203571\pi\)
\(380\) 8.66025 2.23607i 0.444262 0.114708i
\(381\) −12.6491 5.65685i −0.648034 0.289809i
\(382\) −10.0000 7.74597i −0.511645 0.396318i
\(383\) 10.9545 0.559746 0.279873 0.960037i \(-0.409708\pi\)
0.279873 + 0.960037i \(0.409708\pi\)
\(384\) 18.5916 + 6.19307i 0.948746 + 0.316039i
\(385\) 12.0000 + 4.89898i 0.611577 + 0.249675i
\(386\) 3.46410 4.47214i 0.176318 0.227626i
\(387\) 17.3205 15.4919i 0.880451 0.787499i
\(388\) −9.48683 + 2.44949i −0.481621 + 0.124354i
\(389\) −27.7128 −1.40510 −0.702548 0.711637i \(-0.747954\pi\)
−0.702548 + 0.711637i \(0.747954\pi\)
\(390\) 5.16708 + 9.65926i 0.261645 + 0.489116i
\(391\) 0 0
\(392\) −7.51316 18.3181i −0.379472 0.925203i
\(393\) 1.00000 2.23607i 0.0504433 0.112795i
\(394\) 0 0
\(395\) 14.1421i 0.711568i
\(396\) 11.5359 17.2894i 0.579701 0.868825i
\(397\) 22.1359 1.11097 0.555486 0.831526i \(-0.312532\pi\)
0.555486 + 0.831526i \(0.312532\pi\)
\(398\) 0 0
\(399\) −10.4772 + 10.0114i −0.524517 + 0.501196i
\(400\) −10.5000 + 5.80948i −0.525000 + 0.290474i
\(401\) 4.47214i 0.223328i −0.993746 0.111664i \(-0.964382\pi\)
0.993746 0.111664i \(-0.0356180\pi\)
\(402\) 8.94965 + 16.7303i 0.446368 + 0.834433i
\(403\) 15.4919i 0.771708i
\(404\) −30.1247 + 7.77817i −1.49876 + 0.386979i
\(405\) −12.6491 1.41421i −0.628539 0.0702728i
\(406\) −12.9737 22.4429i −0.643872 1.11382i
\(407\) 0 0
\(408\) 0 0
\(409\) 9.79796i 0.484478i −0.970217 0.242239i \(-0.922118\pi\)
0.970217 0.242239i \(-0.0778818\pi\)
\(410\) −17.3205 13.4164i −0.855399 0.662589i
\(411\) −12.6491 + 28.2843i −0.623935 + 1.39516i
\(412\) −18.9737 + 4.89898i −0.934765 + 0.241355i
\(413\) 24.2487 + 9.89949i 1.19320 + 0.487122i
\(414\) 1.33975 + 18.9263i 0.0658449 + 0.930177i
\(415\) 10.0000 0.490881
\(416\) 2.73861 17.6777i 0.134272 0.866719i
\(417\) 25.0000 + 11.1803i 1.22426 + 0.547504i
\(418\) −9.48683 + 12.2474i −0.464016 + 0.599042i
\(419\) 24.0416i 1.17451i −0.809402 0.587255i \(-0.800208\pi\)
0.809402 0.587255i \(-0.199792\pi\)
\(420\) −6.83493 + 11.0129i −0.333510 + 0.537374i
\(421\) 30.9839i 1.51006i −0.655690 0.755031i \(-0.727622\pi\)
0.655690 0.755031i \(-0.272378\pi\)
\(422\) −8.66025 6.70820i −0.421575 0.326550i
\(423\) −21.9089 24.4949i −1.06525 1.19098i
\(424\) 0 0
\(425\) 0 0
\(426\) 10.3342 + 19.3185i 0.500692 + 0.935985i
\(427\) 3.16228 7.74597i 0.153033 0.374854i
\(428\) 5.19615 + 20.1246i 0.251166 + 0.972760i
\(429\) −17.3205 7.74597i −0.836242 0.373979i
\(430\) −9.48683 + 12.2474i −0.457496 + 0.590624i
\(431\) 22.3607i 1.07708i 0.842601 + 0.538538i \(0.181023\pi\)
−0.842601 + 0.538538i \(0.818977\pi\)
\(432\) 15.1191 + 14.2623i 0.727420 + 0.686193i
\(433\) 14.6969i 0.706290i −0.935569 0.353145i \(-0.885112\pi\)
0.935569 0.353145i \(-0.114888\pi\)
\(434\) −15.8695 + 9.17377i −0.761762 + 0.440355i
\(435\) −6.92820 + 15.4919i −0.332182 + 0.742781i
\(436\) 0 0
\(437\) 14.1421i 0.676510i
\(438\) 16.9808 + 31.7436i 0.811372 + 1.51677i
\(439\) 24.4949i 1.16908i 0.811366 + 0.584539i \(0.198725\pi\)
−0.811366 + 0.584539i \(0.801275\pi\)
\(440\) −5.47723 + 12.7279i −0.261116 + 0.606780i
\(441\) 0.954451 20.9783i 0.0454501 0.998967i
\(442\) 0 0
\(443\) −17.3205 −0.822922 −0.411461 0.911427i \(-0.634981\pi\)
−0.411461 + 0.911427i \(0.634981\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −10.9545 8.48528i −0.518708 0.401790i
\(447\) −10.9545 4.89898i −0.518128 0.231714i
\(448\) 19.7302 7.66272i 0.932167 0.362029i
\(449\) 8.94427i 0.422106i 0.977475 + 0.211053i \(0.0676893\pi\)
−0.977475 + 0.211053i \(0.932311\pi\)
\(450\) −12.6962 + 0.898729i −0.598502 + 0.0423665i
\(451\) 37.9473 1.78687
\(452\) −8.66025 + 2.23607i −0.407344 + 0.105176i
\(453\) −12.6491 5.65685i −0.594307 0.265782i
\(454\) −11.0680 8.57321i −0.519446 0.402361i
\(455\) 10.9545 + 4.47214i 0.513553 + 0.209657i
\(456\) −10.4904 11.3996i −0.491257 0.533837i
\(457\) 8.00000 0.374224 0.187112 0.982339i \(-0.440087\pi\)
0.187112 + 0.982339i \(0.440087\pi\)
\(458\) 13.6931 17.6777i 0.639835 0.826023i
\(459\) 0 0
\(460\) −3.16228 12.2474i −0.147442 0.571040i
\(461\) 15.5563i 0.724531i −0.932075 0.362266i \(-0.882003\pi\)
0.932075 0.362266i \(-0.117997\pi\)
\(462\) −2.32182 22.3296i −0.108021 1.03887i
\(463\) 14.0000 0.650635 0.325318 0.945605i \(-0.394529\pi\)
0.325318 + 0.945605i \(0.394529\pi\)
\(464\) 24.2487 13.4164i 1.12572 0.622841i
\(465\) 10.9545 + 4.89898i 0.508001 + 0.227185i
\(466\) −10.0000 7.74597i −0.463241 0.358825i
\(467\) 7.07107i 0.327210i −0.986526 0.163605i \(-0.947688\pi\)
0.986526 0.163605i \(-0.0523123\pi\)
\(468\) 10.5308 15.7830i 0.486786 0.729569i
\(469\) 18.9737 + 7.74597i 0.876122 + 0.357676i
\(470\) 17.3205 + 13.4164i 0.798935 + 0.618853i
\(471\) 25.0000 + 11.1803i 1.15194 + 0.515163i
\(472\) −11.0680 + 25.7196i −0.509445 + 1.18384i
\(473\) 26.8328i 1.23377i
\(474\) −21.5988 + 11.5539i −0.992064 + 0.530690i
\(475\) 9.48683 0.435286
\(476\) 0 0
\(477\) 0 0
\(478\) 5.00000 + 3.87298i 0.228695 + 0.177146i
\(479\) −10.9545 −0.500522 −0.250261 0.968178i \(-0.580516\pi\)
−0.250261 + 0.968178i \(0.580516\pi\)
\(480\) −11.6340 7.52666i −0.531016 0.343544i
\(481\) 0 0
\(482\) 5.47723 + 4.24264i 0.249481 + 0.193247i
\(483\) 14.1582 + 14.8170i 0.644222 + 0.674198i
\(484\) −0.500000 1.93649i −0.0227273 0.0880223i
\(485\) 6.92820 0.314594
\(486\) 8.17429 + 20.4739i 0.370793 + 0.928715i
\(487\) 8.00000 0.362515 0.181257 0.983436i \(-0.441983\pi\)
0.181257 + 0.983436i \(0.441983\pi\)
\(488\) 8.21584 + 3.53553i 0.371914 + 0.160046i
\(489\) 16.4317 36.7423i 0.743066 1.66155i
\(490\) 1.90569 + 13.8697i 0.0860905 + 0.626569i
\(491\) −3.46410 −0.156333 −0.0781664 0.996940i \(-0.524907\pi\)
−0.0781664 + 0.996940i \(0.524907\pi\)
\(492\) −6.33975 + 37.4140i −0.285818 + 1.68675i
\(493\) 0 0
\(494\) −8.66025 + 11.1803i −0.389643 + 0.503027i
\(495\) −10.9545 + 9.79796i −0.492366 + 0.440386i
\(496\) −9.48683 17.1464i −0.425971 0.769897i
\(497\) 21.9089 + 8.94427i 0.982749 + 0.401205i
\(498\) −8.16987 15.2726i −0.366101 0.684383i
\(499\) 7.74597i 0.346757i 0.984855 + 0.173379i \(0.0554684\pi\)
−0.984855 + 0.173379i \(0.944532\pi\)
\(500\) 21.9089 5.65685i 0.979796 0.252982i
\(501\) 34.6410 + 15.4919i 1.54765 + 0.692129i
\(502\) 17.3925 + 13.4722i 0.776266 + 0.601293i
\(503\) 32.8634 1.46530 0.732652 0.680603i \(-0.238282\pi\)
0.732652 + 0.680603i \(0.238282\pi\)
\(504\) 22.4036 + 1.44135i 0.997937 + 0.0642026i
\(505\) 22.0000 0.978987
\(506\) 17.3205 + 13.4164i 0.769991 + 0.596432i
\(507\) 4.74342 + 2.12132i 0.210663 + 0.0942111i
\(508\) −4.00000 15.4919i −0.177471 0.687343i
\(509\) 9.89949i 0.438787i 0.975636 + 0.219394i \(0.0704079\pi\)
−0.975636 + 0.219394i \(0.929592\pi\)
\(510\) 0 0
\(511\) 36.0000 + 14.6969i 1.59255 + 0.650154i
\(512\) 7.79423 + 21.2426i 0.344459 + 0.938801i
\(513\) −5.00000 15.6525i −0.220755 0.691074i
\(514\) −9.48683 + 12.2474i −0.418446 + 0.540212i
\(515\) 13.8564 0.610586
\(516\) 26.4557 + 4.48288i 1.16465 + 0.197348i
\(517\) −37.9473 −1.66892
\(518\) 0 0
\(519\) −5.00000 + 11.1803i −0.219476 + 0.490762i
\(520\) −5.00000 + 11.6190i −0.219265 + 0.509525i
\(521\) −32.8634 −1.43977 −0.719885 0.694094i \(-0.755805\pi\)
−0.719885 + 0.694094i \(0.755805\pi\)
\(522\) 29.3205 2.07553i 1.28332 0.0908433i
\(523\) 3.16228 0.138277 0.0691384 0.997607i \(-0.477975\pi\)
0.0691384 + 0.997607i \(0.477975\pi\)
\(524\) 2.73861 0.707107i 0.119637 0.0308901i
\(525\) −9.93957 + 9.49763i −0.433798 + 0.414511i
\(526\) −10.0000 7.74597i −0.436021 0.337740i
\(527\) 0 0
\(528\) 23.9137 2.03339i 1.04071 0.0884918i
\(529\) 3.00000 0.130435
\(530\) 0 0
\(531\) −22.1359 + 19.7990i −0.960618 + 0.859203i
\(532\) −16.5811 2.25074i −0.718884 0.0975820i
\(533\) 34.6410 1.50047
\(534\) 0 0
\(535\) 14.6969i 0.635404i
\(536\) −8.66025 + 20.1246i −0.374066 + 0.869251i
\(537\) −16.4317 7.34847i −0.709079 0.317110i
\(538\) −11.0680 8.57321i −0.477174 0.369618i
\(539\) −17.3205 16.9706i −0.746047 0.730974i
\(540\) −7.83013 12.4374i −0.336955 0.535221i
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −5.00000 2.23607i −0.214571 0.0959589i
\(544\) 0 0
\(545\) 0 0
\(546\) −2.11952 20.3840i −0.0907071 0.872355i
\(547\) 7.74597i 0.331194i −0.986194 0.165597i \(-0.947045\pi\)
0.986194 0.165597i \(-0.0529550\pi\)
\(548\) −34.6410 + 8.94427i −1.47979 + 0.382080i
\(549\) 6.32456 + 7.07107i 0.269925 + 0.301786i
\(550\) −9.00000 + 11.6190i −0.383761 + 0.495434i
\(551\) −21.9089 −0.933351
\(552\) −16.1215 + 14.8356i −0.686178 + 0.631447i
\(553\) −10.0000 + 24.4949i −0.425243 + 1.04163i
\(554\) −17.3205 13.4164i −0.735878 0.570009i
\(555\) 0 0
\(556\) 7.90569 + 30.6186i 0.335276 + 1.29852i
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) −1.46762 20.7327i −0.0621292 0.877686i
\(559\) 24.4949i 1.03602i
\(560\) −14.8630 + 1.75846i −0.628075 + 0.0743083i
\(561\) 0 0
\(562\) −10.0000 7.74597i −0.421825 0.326744i
\(563\) 1.41421i 0.0596020i 0.999556 + 0.0298010i \(0.00948736\pi\)
−0.999556 + 0.0298010i \(0.990513\pi\)
\(564\) 6.33975 37.4140i 0.266951 1.57541i
\(565\) 6.32456 0.266076
\(566\) 13.6931 17.6777i 0.575562 0.743048i
\(567\) 20.9089 + 11.3938i 0.878091 + 0.478493i
\(568\) −10.0000 + 23.2379i −0.419591 + 0.975041i
\(569\) 22.3607i 0.937408i 0.883355 + 0.468704i \(0.155279\pi\)
−0.883355 + 0.468704i \(0.844721\pi\)
\(570\) 5.16708 + 9.65926i 0.216425 + 0.404582i
\(571\) 7.74597i 0.324159i 0.986778 + 0.162079i \(0.0518200\pi\)
−0.986778 + 0.162079i \(0.948180\pi\)
\(572\) −5.47723 21.2132i −0.229014 0.886969i
\(573\) 6.32456 14.1421i 0.264212 0.590796i
\(574\) 20.5132 + 35.4853i 0.856203 + 1.48113i
\(575\) 13.4164i 0.559503i
\(576\) −1.99038 + 23.9173i −0.0829325 + 0.996555i
\(577\) 29.3939i 1.22368i −0.790980 0.611842i \(-0.790429\pi\)
0.790980 0.611842i \(-0.209571\pi\)
\(578\) 14.7224 19.0066i 0.612372 0.790569i
\(579\) 6.32456 + 2.82843i 0.262840 + 0.117545i
\(580\) −18.9737 + 4.89898i −0.787839 + 0.203419i
\(581\) −17.3205 7.07107i −0.718576 0.293357i
\(582\) −5.66025 10.5812i −0.234625 0.438604i
\(583\) 0 0
\(584\) −16.4317 + 38.1838i −0.679948 + 1.58006i
\(585\) −10.0000 + 8.94427i −0.413449 + 0.369800i
\(586\) −30.0416 23.2702i −1.24101 0.961281i
\(587\) 35.3553i 1.45927i 0.683836 + 0.729636i \(0.260310\pi\)
−0.683836 + 0.729636i \(0.739690\pi\)
\(588\) 19.6257 14.2419i 0.809352 0.587324i
\(589\) 15.4919i 0.638334i
\(590\) 12.1244 15.6525i 0.499152 0.644402i
\(591\) 0 0
\(592\) 0 0
\(593\) −32.8634 −1.34954 −0.674768 0.738030i \(-0.735756\pi\)
−0.674768 + 0.738030i \(0.735756\pi\)
\(594\) 23.9137 + 8.72552i 0.981191 + 0.358012i
\(595\) 0 0
\(596\) −3.46410 13.4164i −0.141895 0.549557i
\(597\) 0 0
\(598\) 15.8114 + 12.2474i 0.646576 + 0.500835i
\(599\) 8.94427i 0.365453i 0.983164 + 0.182727i \(0.0584923\pi\)
−0.983164 + 0.182727i \(0.941508\pi\)
\(600\) −9.95205 10.8147i −0.406291 0.441506i
\(601\) 24.4949i 0.999168i 0.866266 + 0.499584i \(0.166514\pi\)
−0.866266 + 0.499584i \(0.833486\pi\)
\(602\) 25.0919 14.5050i 1.02267 0.591180i
\(603\) −17.3205 + 15.4919i −0.705346 + 0.630880i
\(604\) −4.00000 15.4919i −0.162758 0.630358i
\(605\) 1.41421i 0.0574960i
\(606\) −17.9737 33.5998i −0.730132 1.36490i
\(607\) 19.5959i 0.795374i 0.917521 + 0.397687i \(0.130187\pi\)
−0.917521 + 0.397687i \(0.869813\pi\)
\(608\) 2.73861 17.6777i 0.111065 0.716924i
\(609\) 22.9545 21.9338i 0.930161 0.888804i
\(610\) −5.00000 3.87298i −0.202444 0.156813i
\(611\) −34.6410 −1.40143
\(612\) 0 0
\(613\) 46.4758i 1.87714i −0.345089 0.938570i \(-0.612151\pi\)
0.345089 0.938570i \(-0.387849\pi\)
\(614\) −2.73861 + 3.53553i −0.110521 + 0.142683i
\(615\) 10.9545 24.4949i 0.441726 0.987730i
\(616\) 18.4868 18.1724i 0.744856 0.732188i
\(617\) 31.3050i 1.26029i −0.776478 0.630145i \(-0.782995\pi\)
0.776478 0.630145i \(-0.217005\pi\)
\(618\) −11.3205 21.1624i −0.455378 0.851276i
\(619\) 3.16228 0.127103 0.0635513 0.997979i \(-0.479757\pi\)
0.0635513 + 0.997979i \(0.479757\pi\)
\(620\) 3.46410 + 13.4164i 0.139122 + 0.538816i
\(621\) −22.1359 + 7.07107i −0.888285 + 0.283752i
\(622\) −9.48683 + 12.2474i −0.380387 + 0.491078i
\(623\) 0 0
\(624\) 21.8301 1.85622i 0.873904 0.0743083i
\(625\) −1.00000 −0.0400000
\(626\) −10.9545 8.48528i −0.437828 0.339140i
\(627\) −17.3205 7.74597i −0.691714 0.309344i
\(628\) 7.90569 + 30.6186i 0.315472 + 1.22182i
\(629\) 0 0
\(630\) −15.0839 4.94726i −0.600958 0.197104i
\(631\) −10.0000 −0.398094 −0.199047 0.979990i \(-0.563785\pi\)
−0.199047 + 0.979990i \(0.563785\pi\)
\(632\) −25.9808 11.1803i −1.03346 0.444730i
\(633\) 5.47723 12.2474i 0.217700 0.486792i
\(634\) 6.00000 7.74597i 0.238290 0.307632i
\(635\) 11.3137i 0.448971i
\(636\) 0 0
\(637\) −15.8114 15.4919i −0.626470 0.613813i
\(638\) 20.7846 26.8328i 0.822871 1.06232i
\(639\) −20.0000 + 17.8885i −0.791188 + 0.707660i
\(640\) −1.58114 15.9217i −0.0625000 0.629360i
\(641\) 31.3050i 1.23647i −0.785993 0.618236i \(-0.787848\pi\)
0.785993 0.618236i \(-0.212152\pi\)
\(642\) −22.4461 + 12.0072i −0.885876 + 0.473887i
\(643\) 3.16228 0.124708 0.0623540 0.998054i \(-0.480139\pi\)
0.0623540 + 0.998054i \(0.480139\pi\)
\(644\) −3.18303 + 23.4493i −0.125429 + 0.924031i
\(645\) −17.3205 7.74597i −0.681994 0.304997i
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) −12.5981 + 22.1199i −0.494899 + 0.868950i
\(649\) 34.2929i 1.34611i
\(650\) −8.21584 + 10.6066i −0.322252 + 0.416025i
\(651\) −15.5096 16.2312i −0.607868 0.636153i
\(652\) 45.0000 11.6190i 1.76234 0.455033i
\(653\) 48.4974 1.89785 0.948925 0.315501i \(-0.102172\pi\)
0.948925 + 0.315501i \(0.102172\pi\)
\(654\) 0 0
\(655\) −2.00000 −0.0781465
\(656\) −38.3406 + 21.2132i −1.49695 + 0.828236i
\(657\) −32.8634 + 29.3939i −1.28212 + 1.14676i
\(658\) −20.5132 35.4853i −0.799687 1.38336i
\(659\) 24.2487 0.944596 0.472298 0.881439i \(-0.343425\pi\)
0.472298 + 0.881439i \(0.343425\pi\)
\(660\) −16.7321 2.83522i −0.651294 0.110361i
\(661\) 41.1096 1.59898 0.799489 0.600680i \(-0.205104\pi\)
0.799489 + 0.600680i \(0.205104\pi\)
\(662\) 8.66025 + 6.70820i 0.336590 + 0.260722i
\(663\) 0 0
\(664\) 7.90569 18.3712i 0.306800 0.712940i
\(665\) 10.9545 + 4.47214i 0.424795 + 0.173422i
\(666\) 0 0
\(667\) 30.9839i 1.19970i
\(668\) 10.9545 + 42.4264i 0.423840 + 1.64153i
\(669\) 6.92820 15.4919i 0.267860 0.598953i
\(670\) 9.48683 12.2474i 0.366508 0.473160i
\(671\) 10.9545 0.422892
\(672\) 14.8285 + 21.2630i 0.572021 + 0.820239i
\(673\) −46.0000 −1.77317 −0.886585 0.462566i \(-0.846929\pi\)
−0.886585 + 0.462566i \(0.846929\pi\)
\(674\) −6.92820 + 8.94427i −0.266864 + 0.344520i
\(675\) −4.74342 14.8492i −0.182574 0.571548i
\(676\) 1.50000 + 5.80948i 0.0576923 + 0.223441i
\(677\) 7.07107i 0.271763i −0.990725 0.135882i \(-0.956613\pi\)
0.990725 0.135882i \(-0.0433867\pi\)
\(678\) −5.16708 9.65926i −0.198441 0.370962i
\(679\) −12.0000 4.89898i −0.460518 0.188006i
\(680\) 0 0
\(681\) 7.00000 15.6525i 0.268241 0.599804i
\(682\) −18.9737 14.6969i −0.726539 0.562775i
\(683\) −31.1769 −1.19295 −0.596476 0.802631i \(-0.703433\pi\)
−0.596476 + 0.802631i \(0.703433\pi\)
\(684\) 10.5308 15.7830i 0.402655 0.603477i
\(685\) 25.2982 0.966595
\(686\) 6.50659 25.3705i 0.248423 0.968652i
\(687\) 25.0000 + 11.1803i 0.953809 + 0.426557i
\(688\) 15.0000 + 27.1109i 0.571870 + 1.03359i
\(689\) 0 0
\(690\) 13.6603 7.30736i 0.520037 0.278186i
\(691\) 3.16228 0.120299 0.0601494 0.998189i \(-0.480842\pi\)
0.0601494 + 0.998189i \(0.480842\pi\)
\(692\) −13.6931 + 3.53553i −0.520532 + 0.134401i
\(693\) 25.9019 9.22460i 0.983931 0.350413i
\(694\) −15.0000 + 19.3649i −0.569392 + 0.735082i
\(695\) 22.3607i 0.848189i
\(696\) 22.9833 + 24.9754i 0.871179 + 0.946689i
\(697\) 0 0
\(698\) −19.1703 + 24.7487i −0.725606 + 0.936754i
\(699\) 6.32456 14.1421i 0.239217 0.534905i
\(700\) −15.7302 2.13524i −0.594548 0.0807045i
\(701\) 20.7846 0.785024 0.392512 0.919747i \(-0.371606\pi\)
0.392512 + 0.919747i \(0.371606\pi\)
\(702\) 21.8301 + 7.96527i 0.823925 + 0.300630i
\(703\) 0 0
\(704\) 19.0526 + 20.1246i 0.718070 + 0.758475i
\(705\) −10.9545 + 24.4949i −0.412568 + 0.922531i
\(706\) 9.48683 12.2474i 0.357042 0.460939i
\(707\) −38.1051 15.5563i −1.43309 0.585057i
\(708\) −33.8109 5.72920i −1.27069 0.215317i
\(709\) 30.9839i 1.16362i −0.813323 0.581812i \(-0.802344\pi\)
0.813323 0.581812i \(-0.197656\pi\)
\(710\) 10.9545 14.1421i 0.411113 0.530745i
\(711\) −20.0000 22.3607i −0.750059 0.838591i
\(712\) 0 0
\(713\) 21.9089 0.820495
\(714\) 0 0
\(715\) 15.4919i 0.579365i
\(716\) −5.19615 20.1246i −0.194189 0.752092i
\(717\) −3.16228 + 7.07107i −0.118097 + 0.264074i
\(718\) 35.0000 + 27.1109i 1.30619 + 1.01177i
\(719\) 32.8634 1.22560 0.612798 0.790239i \(-0.290044\pi\)
0.612798 + 0.790239i \(0.290044\pi\)
\(720\) 5.59075 16.0232i 0.208355 0.597150i
\(721\) −24.0000 9.79796i −0.893807 0.364895i
\(722\) 7.79423 10.0623i 0.290071 0.374480i
\(723\) −3.46410 + 7.74597i −0.128831 + 0.288076i
\(724\) −1.58114 6.12372i −0.0587626 0.227586i
\(725\) −20.7846 −0.771921
\(726\) 2.15988 1.15539i 0.0801605 0.0428807i
\(727\) 19.5959i 0.726772i −0.931639 0.363386i \(-0.881621\pi\)
0.931639 0.363386i \(-0.118379\pi\)
\(728\) 16.8761 16.5891i 0.625470 0.614832i
\(729\) −22.0000 + 15.6525i −0.814815 + 0.579721i
\(730\) 18.0000 23.2379i 0.666210 0.860073i
\(731\) 0 0
\(732\) −1.83013 + 10.8005i −0.0676434 + 0.399198i
\(733\) −15.8114 −0.584007 −0.292003 0.956417i \(-0.594322\pi\)
−0.292003 + 0.956417i \(0.594322\pi\)
\(734\) 21.9089 + 16.9706i 0.808672 + 0.626395i
\(735\) −15.9545 + 6.28136i −0.588489 + 0.231691i
\(736\) −25.0000 3.87298i −0.921512 0.142760i
\(737\) 26.8328i 0.988399i
\(738\) −46.3598 + 3.28169i −1.70653 + 0.120801i
\(739\) 23.2379i 0.854820i −0.904058 0.427410i \(-0.859426\pi\)
0.904058 0.427410i \(-0.140574\pi\)
\(740\) 0 0
\(741\) −15.8114 7.07107i −0.580846 0.259762i
\(742\) 0 0
\(743\) 49.1935i 1.80473i 0.430968 + 0.902367i \(0.358172\pi\)
−0.430968 + 0.902367i \(0.641828\pi\)
\(744\) 17.6603 16.2516i 0.647456 0.595814i
\(745\) 9.79796i 0.358969i
\(746\) −34.6410 26.8328i −1.26830 0.982419i
\(747\) 15.8114 14.1421i 0.578508 0.517434i
\(748\) 0 0
\(749\) −10.3923 + 25.4558i −0.379727 + 0.930136i
\(750\) 13.0718 + 24.4362i 0.477315 + 0.892284i
\(751\) −40.0000 −1.45962 −0.729810 0.683650i \(-0.760392\pi\)
−0.729810 + 0.683650i \(0.760392\pi\)
\(752\) 38.3406 21.2132i 1.39814 0.773566i
\(753\) −11.0000 + 24.5967i −0.400862 + 0.896355i
\(754\) 18.9737 24.4949i 0.690980 0.892052i
\(755\) 11.3137i 0.411748i
\(756\) 4.76760 + 27.0790i 0.173396 + 0.984852i
\(757\) 46.4758i 1.68919i 0.535404 + 0.844596i \(0.320159\pi\)
−0.535404 + 0.844596i \(0.679841\pi\)
\(758\) 25.9808 + 20.1246i 0.943664 + 0.730959i
\(759\) −10.9545 + 24.4949i −0.397621 + 0.889108i
\(760\) −5.00000 + 11.6190i −0.181369 + 0.421464i
\(761\) 10.9545 0.397099 0.198549 0.980091i \(-0.436377\pi\)
0.198549 + 0.980091i \(0.436377\pi\)
\(762\) 17.2790 9.24316i 0.625952 0.334844i
\(763\) 0 0
\(764\) 17.3205 4.47214i 0.626634 0.161796i
\(765\) 0 0
\(766\) −9.48683 + 12.2474i −0.342773 + 0.442518i
\(767\) 31.3050i 1.13036i
\(768\) −23.0248 + 15.4226i −0.830837 + 0.556516i
\(769\) 24.4949i 0.883309i −0.897185 0.441654i \(-0.854392\pi\)
0.897185 0.441654i \(-0.145608\pi\)
\(770\) −15.8695 + 9.17377i −0.571898 + 0.330600i
\(771\) −17.3205 7.74597i −0.623783 0.278964i
\(772\) 2.00000 + 7.74597i 0.0719816 + 0.278783i
\(773\) 35.3553i 1.27164i 0.771836 + 0.635822i \(0.219339\pi\)
−0.771836 + 0.635822i \(0.780661\pi\)
\(774\) 2.32051 + 32.7813i 0.0834089 + 1.17830i
\(775\) 14.6969i 0.527930i
\(776\) 5.47723 12.7279i 0.196621 0.456906i
\(777\) 0 0
\(778\) 24.0000 30.9839i 0.860442 1.11083i
\(779\) 34.6410 1.24114
\(780\) −15.2742 2.58819i −0.546904 0.0926721i
\(781\) 30.9839i 1.10869i
\(782\) 0 0
\(783\) 10.9545 + 34.2929i 0.391480 + 1.22553i
\(784\) 26.9868 + 7.46397i 0.963815 + 0.266570i
\(785\) 22.3607i 0.798087i
\(786\) 1.63397 + 3.05453i 0.0582819 + 0.108951i
\(787\) −53.7587 −1.91629 −0.958146 0.286281i \(-0.907581\pi\)
−0.958146 + 0.286281i \(0.907581\pi\)
\(788\) 0 0
\(789\) 6.32456 14.1421i 0.225160 0.503473i
\(790\) 15.8114 + 12.2474i 0.562544 + 0.435745i
\(791\) −10.9545 4.47214i −0.389495 0.159011i
\(792\) 9.33975 + 27.8706i 0.331873 + 0.990338i
\(793\) 10.0000 0.355110
\(794\) −19.1703 + 24.7487i −0.680328 + 0.878300i
\(795\) 0 0
\(796\) 0 0
\(797\) 49.4975i 1.75329i −0.481137 0.876645i \(-0.659776\pi\)
0.481137 0.876645i \(-0.340224\pi\)
\(798\) −2.11952 20.3840i −0.0750302 0.721586i
\(799\) 0 0
\(800\) 2.59808 16.7705i 0.0918559 0.592927i
\(801\) 0 0
\(802\) 5.00000 + 3.87298i 0.176556 + 0.136760i
\(803\) 50.9117i 1.79663i
\(804\) −26.4557 4.48288i −0.933020 0.158099i
\(805\) 6.32456 15.4919i 0.222911 0.546019i
\(806\) −17.3205 13.4164i −0.610089 0.472573i
\(807\) 7.00000 15.6525i 0.246412 0.550993i
\(808\) 17.3925 40.4166i 0.611867 1.42185i
\(809\) 22.3607i 0.786160i 0.919504 + 0.393080i \(0.128590\pi\)
−0.919504 + 0.393080i \(0.871410\pi\)
\(810\) 12.5356 12.9174i 0.440456 0.453871i
\(811\) 22.1359 0.777298 0.388649 0.921386i \(-0.372942\pi\)
0.388649 + 0.921386i \(0.372942\pi\)
\(812\) 36.3275 + 4.93113i 1.27484 + 0.173049i
\(813\) 0 0
\(814\) 0 0
\(815\) −32.8634 −1.15115
\(816\) 0 0
\(817\) 24.4949i 0.856968i
\(818\) 10.9545 + 8.48528i 0.383013 + 0.296681i
\(819\) 23.6451 8.42087i 0.826225 0.294249i
\(820\) 30.0000 7.74597i 1.04765 0.270501i
\(821\) 13.8564 0.483592 0.241796 0.970327i \(-0.422264\pi\)
0.241796 + 0.970327i \(0.422264\pi\)
\(822\) −20.6683 38.6370i −0.720891 1.34762i
\(823\) 26.0000 0.906303 0.453152 0.891434i \(-0.350300\pi\)
0.453152 + 0.891434i \(0.350300\pi\)
\(824\) 10.9545 25.4558i 0.381616 0.886796i
\(825\) −16.4317 7.34847i −0.572078 0.255841i
\(826\) −32.0680 + 18.5377i −1.11579 + 0.645008i
\(827\) 51.9615 1.80688 0.903440 0.428715i \(-0.141034\pi\)
0.903440 + 0.428715i \(0.141034\pi\)
\(828\) −22.3205 14.8928i −0.775691 0.517560i
\(829\) −34.7851 −1.20813 −0.604067 0.796933i \(-0.706454\pi\)
−0.604067 + 0.796933i \(0.706454\pi\)
\(830\) −8.66025 + 11.1803i −0.300602 + 0.388075i
\(831\) 10.9545 24.4949i 0.380006 0.849719i
\(832\) 17.3925 + 18.3712i 0.602977 + 0.636906i
\(833\) 0 0
\(834\) −34.1506 + 18.2684i −1.18254 + 0.632583i
\(835\) 30.9839i 1.07224i
\(836\) −5.47723 21.2132i −0.189434 0.733674i
\(837\) 24.2487 7.74597i 0.838158 0.267740i
\(838\) 26.8794 + 20.8207i 0.928532 + 0.719238i
\(839\) 21.9089 0.756379 0.378190 0.925728i \(-0.376547\pi\)
0.378190 + 0.925728i \(0.376547\pi\)
\(840\) −6.39356 17.1791i −0.220599 0.592736i
\(841\) 19.0000 0.655172
\(842\) 34.6410 + 26.8328i 1.19381 + 0.924720i
\(843\) 6.32456 14.1421i 0.217829 0.487081i
\(844\) 15.0000 3.87298i 0.516321 0.133314i
\(845\) 4.24264i 0.145951i
\(846\) 46.3598 3.28169i 1.59388 0.112827i
\(847\) 1.00000 2.44949i 0.0343604 0.0841655i
\(848\) 0 0
\(849\) 25.0000 + 11.1803i 0.857998 + 0.383708i
\(850\) 0 0
\(851\) 0 0
\(852\) −30.5484 5.17638i −1.04657 0.177340i
\(853\) −53.7587 −1.84066 −0.920332 0.391139i \(-0.872081\pi\)
−0.920332 + 0.391139i \(0.872081\pi\)
\(854\) 5.92164 + 10.2437i 0.202634 + 0.350533i
\(855\) −10.0000 + 8.94427i −0.341993 + 0.305888i
\(856\) −27.0000 11.6190i −0.922841 0.397128i
\(857\) 54.7723 1.87098 0.935492 0.353347i \(-0.114957\pi\)
0.935492 + 0.353347i \(0.114957\pi\)
\(858\) 23.6603 12.6567i 0.807748 0.432093i
\(859\) 3.16228 0.107896 0.0539478 0.998544i \(-0.482820\pi\)
0.0539478 + 0.998544i \(0.482820\pi\)
\(860\) −5.47723 21.2132i −0.186772 0.723364i
\(861\) −36.2942 + 34.6804i −1.23690 + 1.18191i
\(862\) −25.0000 19.3649i −0.851503 0.659572i
\(863\) 8.94427i 0.304467i 0.988345 + 0.152233i \(0.0486465\pi\)
−0.988345 + 0.152233i \(0.951353\pi\)
\(864\) −29.0392 + 4.55223i −0.987935 + 0.154870i
\(865\) 10.0000 0.340010
\(866\) 16.4317 + 12.7279i 0.558371 + 0.432512i
\(867\) 26.8794 + 12.0208i 0.912871 + 0.408248i
\(868\) 3.48683 25.6874i 0.118351 0.871887i
\(869\) −34.6410 −1.17512
\(870\) −11.3205 21.1624i −0.383801 0.717472i
\(871\) 24.4949i 0.829978i
\(872\) 0 0
\(873\) 10.9545 9.79796i 0.370752 0.331611i
\(874\) 15.8114 + 12.2474i 0.534828 + 0.414276i
\(875\) 27.7128 + 11.3137i 0.936864 + 0.382473i
\(876\) −50.1962 8.50566i −1.69597 0.287380i
\(877\) 15.4919i 0.523125i −0.965186 0.261563i \(-0.915762\pi\)
0.965186 0.261563i \(-0.0842378\pi\)
\(878\) −27.3861 21.2132i −0.924237 0.715911i
\(879\) 19.0000 42.4853i 0.640854 1.43299i
\(880\) −9.48683 17.1464i −0.319801 0.578006i
\(881\) −32.8634 −1.10719 −0.553597 0.832785i \(-0.686745\pi\)
−0.553597 + 0.832785i \(0.686745\pi\)
\(882\) 22.6279 + 19.2348i 0.761920 + 0.647671i
\(883\) 23.2379i 0.782018i −0.920387 0.391009i \(-0.872126\pi\)
0.920387 0.391009i \(-0.127874\pi\)
\(884\) 0 0
\(885\) 22.1359 + 9.89949i 0.744092 + 0.332768i
\(886\) 15.0000 19.3649i 0.503935 0.650577i
\(887\) −21.9089 −0.735629 −0.367814 0.929899i \(-0.619894\pi\)
−0.367814 + 0.929899i \(0.619894\pi\)
\(888\) 0 0
\(889\) 8.00000 19.5959i 0.268311 0.657226i
\(890\) 0 0
\(891\) −3.46410 + 30.9839i −0.116052 + 1.03800i
\(892\) 18.9737 4.89898i 0.635285 0.164030i
\(893\) −34.6410 −1.15922
\(894\) 14.9641 8.00481i 0.500473 0.267721i
\(895\) 14.6969i 0.491264i
\(896\) −8.51972 + 28.6952i −0.284624 + 0.958639i
\(897\) −10.0000 + 22.3607i −0.333890 + 0.746601i
\(898\) −10.0000 7.74597i −0.333704 0.258486i
\(899\) 33.9411i 1.13200i
\(900\) 9.99038 14.9731i 0.333013 0.499102i
\(901\) 0 0
\(902\) −32.8634 + 42.4264i −1.09423 + 1.41264i
\(903\) 24.5228 + 25.6639i 0.816067 + 0.854040i
\(904\) 5.00000 11.6190i 0.166298 0.386441i
\(905\) 4.47214i 0.148659i
\(906\) 17.2790 9.24316i 0.574057 0.307083i
\(907\) 38.7298i 1.28600i 0.765865 + 0.643002i \(0.222311\pi\)
−0.765865 + 0.643002i \(0.777689\pi\)
\(908\) 19.1703 4.94975i 0.636188 0.164263i
\(909\) 34.7851 31.1127i 1.15375 1.03194i
\(910\) −14.4868 + 8.37447i −0.480234 + 0.277611i
\(911\) 31.3050i 1.03718i −0.855023 0.518590i \(-0.826457\pi\)
0.855023 0.518590i \(-0.173543\pi\)
\(912\) 21.8301 1.85622i 0.722868 0.0614656i
\(913\) 24.4949i 0.810663i
\(914\) −6.92820 + 8.94427i −0.229165 + 0.295850i
\(915\) 3.16228 7.07107i 0.104542 0.233762i
\(916\) 7.90569 + 30.6186i 0.261211 + 1.01167i
\(917\) 3.46410 + 1.41421i 0.114395 + 0.0467014i
\(918\) 0 0
\(919\) −10.0000 −0.329870 −0.164935 0.986304i \(-0.552741\pi\)
−0.164935 + 0.986304i \(0.552741\pi\)
\(920\) 16.4317 + 7.07107i 0.541736 + 0.233126i
\(921\) −5.00000 2.23607i −0.164756 0.0736809i
\(922\) 17.3925 + 13.4722i 0.572792 + 0.443683i
\(923\) 28.2843i 0.930988i
\(924\) 26.9760 + 16.7421i 0.887444 + 0.550774i
\(925\) 0 0
\(926\) −12.1244 + 15.6525i −0.398431 + 0.514372i
\(927\) 21.9089 19.5959i 0.719583 0.643614i
\(928\) −6.00000 + 38.7298i −0.196960 + 1.27137i
\(929\) 21.9089 0.718808 0.359404 0.933182i \(-0.382980\pi\)
0.359404 + 0.933182i \(0.382980\pi\)
\(930\) −14.9641 + 8.00481i −0.490691 + 0.262488i
\(931\) −15.8114 15.4919i −0.518197 0.507728i
\(932\) 17.3205 4.47214i 0.567352 0.146490i
\(933\) −17.3205 7.74597i −0.567048 0.253592i
\(934\) 7.90569 + 6.12372i 0.258682 + 0.200374i
\(935\) 0 0
\(936\) 8.52598 + 25.4422i 0.278680 + 0.831606i
\(937\) 44.0908i 1.44038i 0.693775 + 0.720192i \(0.255946\pi\)
−0.693775 + 0.720192i \(0.744054\pi\)
\(938\) −25.0919 + 14.5050i −0.819281 + 0.473605i
\(939\) 6.92820 15.4919i 0.226093 0.505560i
\(940\) −30.0000 + 7.74597i −0.978492 + 0.252646i
\(941\) 1.41421i 0.0461020i 0.999734 + 0.0230510i \(0.00733802\pi\)
−0.999734 + 0.0230510i \(0.992662\pi\)
\(942\) −34.1506 + 18.2684i −1.11269 + 0.595216i
\(943\) 48.9898i 1.59533i
\(944\) −19.1703 34.6482i −0.623940 1.12770i
\(945\) 1.52277 19.3825i 0.0495359 0.630513i
\(946\) 30.0000 + 23.2379i 0.975384 + 0.755529i
\(947\) −17.3205 −0.562841 −0.281420 0.959585i \(-0.590806\pi\)
−0.281420 + 0.959585i \(0.590806\pi\)
\(948\) 5.78737 34.1542i 0.187965 1.10928i
\(949\) 46.4758i 1.50867i
\(950\) −8.21584 + 10.6066i −0.266557 + 0.344124i
\(951\) 10.9545 + 4.89898i 0.355222 + 0.158860i
\(952\) 0 0
\(953\) 17.8885i 0.579467i −0.957107 0.289733i \(-0.906433\pi\)
0.957107 0.289733i \(-0.0935666\pi\)
\(954\) 0 0
\(955\) −12.6491 −0.409316
\(956\) −8.66025 + 2.23607i −0.280093 + 0.0723196i
\(957\) 37.9473 + 16.9706i 1.22666 + 0.548580i
\(958\) 9.48683 12.2474i 0.306506 0.395697i
\(959\) −43.8178 17.8885i −1.41495 0.577651i
\(960\) 18.4904 6.48890i 0.596774 0.209428i
\(961\) 7.00000 0.225806
\(962\) 0 0
\(963\) −20.7846 23.2379i −0.669775 0.748831i
\(964\) −9.48683 + 2.44949i −0.305550 + 0.0788928i
\(965\) 5.65685i 0.182101i
\(966\) −28.8273 + 2.99745i −0.927504 + 0.0964415i
\(967\) 32.0000 1.02905 0.514525 0.857475i \(-0.327968\pi\)
0.514525 + 0.857475i \(0.327968\pi\)
\(968\) 2.59808 + 1.11803i 0.0835053 + 0.0359350i
\(969\) 0 0
\(970\) −6.00000 + 7.74597i −0.192648 + 0.248708i
\(971\) 41.0122i 1.31614i −0.752955 0.658072i \(-0.771372\pi\)
0.752955 0.658072i \(-0.228628\pi\)
\(972\) −29.9697 8.59180i −0.961278 0.275582i
\(973\) −15.8114 + 38.7298i −0.506890 + 1.24162i
\(974\) −6.92820 + 8.94427i −0.221994 + 0.286593i
\(975\) −15.0000 6.70820i −0.480384 0.214834i
\(976\) −11.0680 + 6.12372i −0.354277 + 0.196016i
\(977\) 8.94427i 0.286153i 0.989712 + 0.143076i \(0.0456994\pi\)
−0.989712 + 0.143076i \(0.954301\pi\)
\(978\) 26.8489 + 50.1910i 0.858535 + 1.60493i
\(979\) 0 0
\(980\) −17.1572 9.88087i −0.548066 0.315633i
\(981\) 0 0
\(982\) 3.00000 3.87298i 0.0957338 0.123592i
\(983\) −43.8178 −1.39757 −0.698785 0.715331i \(-0.746276\pi\)
−0.698785 + 0.715331i \(0.746276\pi\)
\(984\) −36.3397 39.4895i −1.15847 1.25888i
\(985\) 0 0
\(986\) 0 0
\(987\) 36.2942 34.6804i 1.15526 1.10389i
\(988\) −5.00000 19.3649i −0.159071 0.616080i
\(989\) −34.6410 −1.10152
\(990\) −1.46762 20.7327i −0.0466440 0.658929i
\(991\) 2.00000 0.0635321 0.0317660 0.999495i \(-0.489887\pi\)
0.0317660 + 0.999495i \(0.489887\pi\)
\(992\) 27.3861 + 4.24264i 0.869510 + 0.134704i
\(993\) −5.47723 + 12.2474i −0.173814 + 0.388661i
\(994\) −28.9737 + 16.7489i −0.918989 + 0.531244i
\(995\) 0 0
\(996\) 24.1506 + 4.09229i 0.765242 + 0.129669i
\(997\) 3.16228 0.100150 0.0500752 0.998745i \(-0.484054\pi\)
0.0500752 + 0.998745i \(0.484054\pi\)
\(998\) −8.66025 6.70820i −0.274136 0.212344i
\(999\) 0 0
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 168.2.i.e.125.3 yes 8
3.2 odd 2 inner 168.2.i.e.125.5 yes 8
4.3 odd 2 672.2.i.d.209.8 8
7.6 odd 2 inner 168.2.i.e.125.4 yes 8
8.3 odd 2 672.2.i.d.209.2 8
8.5 even 2 inner 168.2.i.e.125.8 yes 8
12.11 even 2 672.2.i.d.209.6 8
21.20 even 2 inner 168.2.i.e.125.6 yes 8
24.5 odd 2 inner 168.2.i.e.125.2 yes 8
24.11 even 2 672.2.i.d.209.4 8
28.27 even 2 672.2.i.d.209.1 8
56.13 odd 2 inner 168.2.i.e.125.7 yes 8
56.27 even 2 672.2.i.d.209.7 8
84.83 odd 2 672.2.i.d.209.3 8
168.83 odd 2 672.2.i.d.209.5 8
168.125 even 2 inner 168.2.i.e.125.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.2.i.e.125.1 8 168.125 even 2 inner
168.2.i.e.125.2 yes 8 24.5 odd 2 inner
168.2.i.e.125.3 yes 8 1.1 even 1 trivial
168.2.i.e.125.4 yes 8 7.6 odd 2 inner
168.2.i.e.125.5 yes 8 3.2 odd 2 inner
168.2.i.e.125.6 yes 8 21.20 even 2 inner
168.2.i.e.125.7 yes 8 56.13 odd 2 inner
168.2.i.e.125.8 yes 8 8.5 even 2 inner
672.2.i.d.209.1 8 28.27 even 2
672.2.i.d.209.2 8 8.3 odd 2
672.2.i.d.209.3 8 84.83 odd 2
672.2.i.d.209.4 8 24.11 even 2
672.2.i.d.209.5 8 168.83 odd 2
672.2.i.d.209.6 8 12.11 even 2
672.2.i.d.209.7 8 56.27 even 2
672.2.i.d.209.8 8 4.3 odd 2