Properties

Label 1710.2.p.c.1063.10
Level $1710$
Weight $2$
Character 1710.1063
Analytic conductor $13.654$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1710,2,Mod(37,1710)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1710, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1710.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.p (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: \(13.6544187456\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 108x^{16} + 1318x^{12} + 4652x^{8} + 5057x^{4} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: no (minimal twist has level 570)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1063.10
Root \(0.339574 + 0.339574i\) of defining polynomial
Character \(\chi\) \(=\) 1710.1063
Dual form 1710.2.p.c.37.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(1.29975 + 1.81952i) q^{5} +(-0.728588 + 0.728588i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(1.29975 + 1.81952i) q^{5} +(-0.728588 + 0.728588i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.367533 + 2.20566i) q^{10} +4.80832 q^{11} +(-0.531491 + 0.531491i) q^{13} -1.03038 q^{14} -1.00000 q^{16} +(3.72984 - 3.72984i) q^{17} +(2.90517 - 3.24961i) q^{19} +(-1.81952 + 1.29975i) q^{20} +(3.39999 + 3.39999i) q^{22} +(4.07973 + 4.07973i) q^{23} +(-1.62130 + 4.72984i) q^{25} -0.751642 q^{26} +(-0.728588 - 0.728588i) q^{28} +0.494819 q^{29} +8.62312i q^{31} +(-0.707107 - 0.707107i) q^{32} +5.27479 q^{34} +(-2.27266 - 0.378698i) q^{35} +(-5.47836 - 5.47836i) q^{37} +(4.35209 - 0.243552i) q^{38} +(-2.20566 - 0.367533i) q^{40} +5.82553i q^{41} +(-3.04079 - 3.04079i) q^{43} +4.80832i q^{44} +5.76961i q^{46} +(-0.910451 + 0.910451i) q^{47} +5.93832i q^{49} +(-4.49094 + 2.19807i) q^{50} +(-0.531491 - 0.531491i) q^{52} +(3.53266 - 3.53266i) q^{53} +(6.24961 + 8.74883i) q^{55} -1.03038i q^{56} +(0.349890 + 0.349890i) q^{58} -12.1307 q^{59} -5.32419 q^{61} +(-6.09747 + 6.09747i) q^{62} -1.00000i q^{64} +(-1.65786 - 0.276253i) q^{65} +(-9.19128 - 9.19128i) q^{67} +(3.72984 + 3.72984i) q^{68} +(-1.33924 - 1.87480i) q^{70} +2.06076i q^{71} +(3.31160 + 3.31160i) q^{73} -7.74758i q^{74} +(3.24961 + 2.90517i) q^{76} +(-3.50328 + 3.50328i) q^{77} -2.77074 q^{79} +(-1.29975 - 1.81952i) q^{80} +(-4.11927 + 4.11927i) q^{82} +(3.57770 + 3.57770i) q^{83} +(11.6344 + 1.93866i) q^{85} -4.30033i q^{86} +(-3.39999 + 3.39999i) q^{88} +1.08630 q^{89} -0.774476i q^{91} +(-4.07973 + 4.07973i) q^{92} -1.28757 q^{94} +(9.68873 + 1.06234i) q^{95} +(-2.81665 - 2.81665i) q^{97} +(-4.19903 + 4.19903i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 12 q^{5} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 12 q^{5} - 4 q^{7} + 8 q^{11} - 20 q^{16} + 12 q^{17} + 4 q^{23} - 28 q^{25} - 24 q^{26} - 4 q^{28} - 4 q^{35} + 12 q^{38} - 12 q^{43} + 44 q^{47} + 64 q^{55} - 8 q^{58} + 24 q^{62} + 12 q^{68} - 4 q^{73} + 4 q^{76} - 88 q^{77} + 12 q^{80} - 8 q^{82} - 76 q^{83} - 12 q^{85} - 4 q^{92} + 24 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(1027\) \(1351\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) 1.29975 + 1.81952i 0.581266 + 0.813714i
\(6\) 0 0
\(7\) −0.728588 + 0.728588i −0.275380 + 0.275380i −0.831262 0.555881i \(-0.812381\pi\)
0.555881 + 0.831262i \(0.312381\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 0 0
\(10\) −0.367533 + 2.20566i −0.116224 + 0.697490i
\(11\) 4.80832 1.44976 0.724881 0.688874i \(-0.241895\pi\)
0.724881 + 0.688874i \(0.241895\pi\)
\(12\) 0 0
\(13\) −0.531491 + 0.531491i −0.147409 + 0.147409i −0.776960 0.629550i \(-0.783239\pi\)
0.629550 + 0.776960i \(0.283239\pi\)
\(14\) −1.03038 −0.275380
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 3.72984 3.72984i 0.904619 0.904619i −0.0912125 0.995831i \(-0.529074\pi\)
0.995831 + 0.0912125i \(0.0290743\pi\)
\(18\) 0 0
\(19\) 2.90517 3.24961i 0.666493 0.745511i
\(20\) −1.81952 + 1.29975i −0.406857 + 0.290633i
\(21\) 0 0
\(22\) 3.39999 + 3.39999i 0.724881 + 0.724881i
\(23\) 4.07973 + 4.07973i 0.850682 + 0.850682i 0.990217 0.139535i \(-0.0445607\pi\)
−0.139535 + 0.990217i \(0.544561\pi\)
\(24\) 0 0
\(25\) −1.62130 + 4.72984i −0.324260 + 0.945968i
\(26\) −0.751642 −0.147409
\(27\) 0 0
\(28\) −0.728588 0.728588i −0.137690 0.137690i
\(29\) 0.494819 0.0918856 0.0459428 0.998944i \(-0.485371\pi\)
0.0459428 + 0.998944i \(0.485371\pi\)
\(30\) 0 0
\(31\) 8.62312i 1.54876i 0.632722 + 0.774379i \(0.281938\pi\)
−0.632722 + 0.774379i \(0.718062\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 0 0
\(34\) 5.27479 0.904619
\(35\) −2.27266 0.378698i −0.384150 0.0640117i
\(36\) 0 0
\(37\) −5.47836 5.47836i −0.900637 0.900637i 0.0948538 0.995491i \(-0.469762\pi\)
−0.995491 + 0.0948538i \(0.969762\pi\)
\(38\) 4.35209 0.243552i 0.706002 0.0395093i
\(39\) 0 0
\(40\) −2.20566 0.367533i −0.348745 0.0581120i
\(41\) 5.82553i 0.909794i 0.890544 + 0.454897i \(0.150324\pi\)
−0.890544 + 0.454897i \(0.849676\pi\)
\(42\) 0 0
\(43\) −3.04079 3.04079i −0.463716 0.463716i 0.436155 0.899871i \(-0.356340\pi\)
−0.899871 + 0.436155i \(0.856340\pi\)
\(44\) 4.80832i 0.724881i
\(45\) 0 0
\(46\) 5.76961i 0.850682i
\(47\) −0.910451 + 0.910451i −0.132803 + 0.132803i −0.770384 0.637581i \(-0.779935\pi\)
0.637581 + 0.770384i \(0.279935\pi\)
\(48\) 0 0
\(49\) 5.93832i 0.848331i
\(50\) −4.49094 + 2.19807i −0.635114 + 0.310854i
\(51\) 0 0
\(52\) −0.531491 0.531491i −0.0737046 0.0737046i
\(53\) 3.53266 3.53266i 0.485248 0.485248i −0.421555 0.906803i \(-0.638516\pi\)
0.906803 + 0.421555i \(0.138516\pi\)
\(54\) 0 0
\(55\) 6.24961 + 8.74883i 0.842697 + 1.17969i
\(56\) 1.03038i 0.137690i
\(57\) 0 0
\(58\) 0.349890 + 0.349890i 0.0459428 + 0.0459428i
\(59\) −12.1307 −1.57928 −0.789641 0.613569i \(-0.789733\pi\)
−0.789641 + 0.613569i \(0.789733\pi\)
\(60\) 0 0
\(61\) −5.32419 −0.681692 −0.340846 0.940119i \(-0.610713\pi\)
−0.340846 + 0.940119i \(0.610713\pi\)
\(62\) −6.09747 + 6.09747i −0.774379 + 0.774379i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −1.65786 0.276253i −0.205633 0.0342650i
\(66\) 0 0
\(67\) −9.19128 9.19128i −1.12289 1.12289i −0.991304 0.131590i \(-0.957992\pi\)
−0.131590 0.991304i \(-0.542008\pi\)
\(68\) 3.72984 + 3.72984i 0.452309 + 0.452309i
\(69\) 0 0
\(70\) −1.33924 1.87480i −0.160069 0.224081i
\(71\) 2.06076i 0.244567i 0.992495 + 0.122284i \(0.0390217\pi\)
−0.992495 + 0.122284i \(0.960978\pi\)
\(72\) 0 0
\(73\) 3.31160 + 3.31160i 0.387594 + 0.387594i 0.873828 0.486235i \(-0.161630\pi\)
−0.486235 + 0.873828i \(0.661630\pi\)
\(74\) 7.74758i 0.900637i
\(75\) 0 0
\(76\) 3.24961 + 2.90517i 0.372756 + 0.333246i
\(77\) −3.50328 + 3.50328i −0.399236 + 0.399236i
\(78\) 0 0
\(79\) −2.77074 −0.311733 −0.155866 0.987778i \(-0.549817\pi\)
−0.155866 + 0.987778i \(0.549817\pi\)
\(80\) −1.29975 1.81952i −0.145316 0.203428i
\(81\) 0 0
\(82\) −4.11927 + 4.11927i −0.454897 + 0.454897i
\(83\) 3.57770 + 3.57770i 0.392703 + 0.392703i 0.875650 0.482947i \(-0.160433\pi\)
−0.482947 + 0.875650i \(0.660433\pi\)
\(84\) 0 0
\(85\) 11.6344 + 1.93866i 1.26192 + 0.210277i
\(86\) 4.30033i 0.463716i
\(87\) 0 0
\(88\) −3.39999 + 3.39999i −0.362441 + 0.362441i
\(89\) 1.08630 0.115147 0.0575736 0.998341i \(-0.481664\pi\)
0.0575736 + 0.998341i \(0.481664\pi\)
\(90\) 0 0
\(91\) 0.774476i 0.0811872i
\(92\) −4.07973 + 4.07973i −0.425341 + 0.425341i
\(93\) 0 0
\(94\) −1.28757 −0.132803
\(95\) 9.68873 + 1.06234i 0.994042 + 0.108994i
\(96\) 0 0
\(97\) −2.81665 2.81665i −0.285988 0.285988i 0.549503 0.835491i \(-0.314817\pi\)
−0.835491 + 0.549503i \(0.814817\pi\)
\(98\) −4.19903 + 4.19903i −0.424166 + 0.424166i
\(99\) 0 0
\(100\) −4.72984 1.62130i −0.472984 0.162130i
\(101\) 14.0592 1.39894 0.699470 0.714662i \(-0.253419\pi\)
0.699470 + 0.714662i \(0.253419\pi\)
\(102\) 0 0
\(103\) 6.63327 6.63327i 0.653596 0.653596i −0.300261 0.953857i \(-0.597074\pi\)
0.953857 + 0.300261i \(0.0970739\pi\)
\(104\) 0.751642i 0.0737046i
\(105\) 0 0
\(106\) 4.99593 0.485248
\(107\) 1.54262 + 1.54262i 0.149131 + 0.149131i 0.777730 0.628599i \(-0.216371\pi\)
−0.628599 + 0.777730i \(0.716371\pi\)
\(108\) 0 0
\(109\) 18.4286 1.76514 0.882569 0.470183i \(-0.155812\pi\)
0.882569 + 0.470183i \(0.155812\pi\)
\(110\) −1.76721 + 10.6055i −0.168497 + 1.01119i
\(111\) 0 0
\(112\) 0.728588 0.728588i 0.0688451 0.0688451i
\(113\) −5.25913 + 5.25913i −0.494738 + 0.494738i −0.909795 0.415058i \(-0.863761\pi\)
0.415058 + 0.909795i \(0.363761\pi\)
\(114\) 0 0
\(115\) −2.12052 + 12.7258i −0.197740 + 1.18668i
\(116\) 0.494819i 0.0459428i
\(117\) 0 0
\(118\) −8.57770 8.57770i −0.789641 0.789641i
\(119\) 5.43503i 0.498229i
\(120\) 0 0
\(121\) 12.1199 1.10181
\(122\) −3.76477 3.76477i −0.340846 0.340846i
\(123\) 0 0
\(124\) −8.62312 −0.774379
\(125\) −10.7133 + 3.19762i −0.958229 + 0.286004i
\(126\) 0 0
\(127\) −9.35800 9.35800i −0.830388 0.830388i 0.157181 0.987570i \(-0.449759\pi\)
−0.987570 + 0.157181i \(0.949759\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 0 0
\(130\) −0.976946 1.36763i −0.0856839 0.119949i
\(131\) −12.6267 −1.10320 −0.551601 0.834108i \(-0.685983\pi\)
−0.551601 + 0.834108i \(0.685983\pi\)
\(132\) 0 0
\(133\) 0.250951 + 4.48430i 0.0217602 + 0.388838i
\(134\) 12.9984i 1.12289i
\(135\) 0 0
\(136\) 5.27479i 0.452309i
\(137\) −0.378698 + 0.378698i −0.0323544 + 0.0323544i −0.723099 0.690745i \(-0.757283\pi\)
0.690745 + 0.723099i \(0.257283\pi\)
\(138\) 0 0
\(139\) 22.7942i 1.93338i −0.255957 0.966688i \(-0.582391\pi\)
0.255957 0.966688i \(-0.417609\pi\)
\(140\) 0.378698 2.27266i 0.0320058 0.192075i
\(141\) 0 0
\(142\) −1.45718 + 1.45718i −0.122284 + 0.122284i
\(143\) −2.55558 + 2.55558i −0.213708 + 0.213708i
\(144\) 0 0
\(145\) 0.643141 + 0.900333i 0.0534100 + 0.0747686i
\(146\) 4.68331i 0.387594i
\(147\) 0 0
\(148\) 5.47836 5.47836i 0.450319 0.450319i
\(149\) 15.8801i 1.30095i 0.759529 + 0.650473i \(0.225429\pi\)
−0.759529 + 0.650473i \(0.774571\pi\)
\(150\) 0 0
\(151\) 13.3507i 1.08646i −0.839583 0.543231i \(-0.817201\pi\)
0.839583 0.543231i \(-0.182799\pi\)
\(152\) 0.243552 + 4.35209i 0.0197547 + 0.353001i
\(153\) 0 0
\(154\) −4.95439 −0.399236
\(155\) −15.6899 + 11.2079i −1.26025 + 0.900240i
\(156\) 0 0
\(157\) 11.7372 11.7372i 0.936727 0.936727i −0.0613870 0.998114i \(-0.519552\pi\)
0.998114 + 0.0613870i \(0.0195524\pi\)
\(158\) −1.95921 1.95921i −0.155866 0.155866i
\(159\) 0 0
\(160\) 0.367533 2.20566i 0.0290560 0.174372i
\(161\) −5.94489 −0.468523
\(162\) 0 0
\(163\) −0.988668 0.988668i −0.0774384 0.0774384i 0.667327 0.744765i \(-0.267438\pi\)
−0.744765 + 0.667327i \(0.767438\pi\)
\(164\) −5.82553 −0.454897
\(165\) 0 0
\(166\) 5.05963i 0.392703i
\(167\) 7.42584 + 7.42584i 0.574629 + 0.574629i 0.933418 0.358790i \(-0.116811\pi\)
−0.358790 + 0.933418i \(0.616811\pi\)
\(168\) 0 0
\(169\) 12.4350i 0.956541i
\(170\) 6.85591 + 9.59758i 0.525824 + 0.736101i
\(171\) 0 0
\(172\) 3.04079 3.04079i 0.231858 0.231858i
\(173\) 11.0462 11.0462i 0.839825 0.839825i −0.149011 0.988836i \(-0.547609\pi\)
0.988836 + 0.149011i \(0.0476090\pi\)
\(174\) 0 0
\(175\) −2.26484 4.62737i −0.171206 0.349796i
\(176\) −4.80832 −0.362441
\(177\) 0 0
\(178\) 0.768128 + 0.768128i 0.0575736 + 0.0575736i
\(179\) −19.0425 −1.42330 −0.711652 0.702532i \(-0.752053\pi\)
−0.711652 + 0.702532i \(0.752053\pi\)
\(180\) 0 0
\(181\) 1.78110i 0.132388i 0.997807 + 0.0661941i \(0.0210857\pi\)
−0.997807 + 0.0661941i \(0.978914\pi\)
\(182\) 0.547637 0.547637i 0.0405936 0.0405936i
\(183\) 0 0
\(184\) −5.76961 −0.425341
\(185\) 2.84749 17.0885i 0.209351 1.25637i
\(186\) 0 0
\(187\) 17.9343 17.9343i 1.31148 1.31148i
\(188\) −0.910451 0.910451i −0.0664014 0.0664014i
\(189\) 0 0
\(190\) 6.09977 + 7.60215i 0.442524 + 0.551518i
\(191\) 14.8650 1.07559 0.537797 0.843075i \(-0.319257\pi\)
0.537797 + 0.843075i \(0.319257\pi\)
\(192\) 0 0
\(193\) −5.04632 + 5.04632i −0.363242 + 0.363242i −0.865005 0.501763i \(-0.832685\pi\)
0.501763 + 0.865005i \(0.332685\pi\)
\(194\) 3.98335i 0.285988i
\(195\) 0 0
\(196\) −5.93832 −0.424166
\(197\) 7.66209 7.66209i 0.545901 0.545901i −0.379351 0.925253i \(-0.623853\pi\)
0.925253 + 0.379351i \(0.123853\pi\)
\(198\) 0 0
\(199\) 20.9302i 1.48370i −0.670565 0.741851i \(-0.733948\pi\)
0.670565 0.741851i \(-0.266052\pi\)
\(200\) −2.19807 4.49094i −0.155427 0.317557i
\(201\) 0 0
\(202\) 9.94134 + 9.94134i 0.699470 + 0.699470i
\(203\) −0.360520 + 0.360520i −0.0253035 + 0.0253035i
\(204\) 0 0
\(205\) −10.5997 + 7.57173i −0.740312 + 0.528832i
\(206\) 9.38086 0.653596
\(207\) 0 0
\(208\) 0.531491 0.531491i 0.0368523 0.0368523i
\(209\) 13.9690 15.6252i 0.966256 1.08081i
\(210\) 0 0
\(211\) 27.6388i 1.90273i 0.308062 + 0.951366i \(0.400319\pi\)
−0.308062 + 0.951366i \(0.599681\pi\)
\(212\) 3.53266 + 3.53266i 0.242624 + 0.242624i
\(213\) 0 0
\(214\) 2.18160i 0.149131i
\(215\) 1.58051 9.48504i 0.107790 0.646875i
\(216\) 0 0
\(217\) −6.28270 6.28270i −0.426498 0.426498i
\(218\) 13.0310 + 13.0310i 0.882569 + 0.882569i
\(219\) 0 0
\(220\) −8.74883 + 6.24961i −0.589846 + 0.421349i
\(221\) 3.96475i 0.266698i
\(222\) 0 0
\(223\) 8.04571 8.04571i 0.538781 0.538781i −0.384390 0.923171i \(-0.625588\pi\)
0.923171 + 0.384390i \(0.125588\pi\)
\(224\) 1.03038 0.0688451
\(225\) 0 0
\(226\) −7.43754 −0.494738
\(227\) −1.98330 1.98330i −0.131636 0.131636i 0.638219 0.769855i \(-0.279671\pi\)
−0.769855 + 0.638219i \(0.779671\pi\)
\(228\) 0 0
\(229\) 19.6443i 1.29813i 0.760732 + 0.649066i \(0.224840\pi\)
−0.760732 + 0.649066i \(0.775160\pi\)
\(230\) −10.4979 + 7.49905i −0.692212 + 0.494473i
\(231\) 0 0
\(232\) −0.349890 + 0.349890i −0.0229714 + 0.0229714i
\(233\) 4.73992 + 4.73992i 0.310523 + 0.310523i 0.845112 0.534589i \(-0.179534\pi\)
−0.534589 + 0.845112i \(0.679534\pi\)
\(234\) 0 0
\(235\) −2.83994 0.473225i −0.185257 0.0308698i
\(236\) 12.1307i 0.789641i
\(237\) 0 0
\(238\) −3.84315 + 3.84315i −0.249114 + 0.249114i
\(239\) 21.1851i 1.37035i −0.728378 0.685176i \(-0.759725\pi\)
0.728378 0.685176i \(-0.240275\pi\)
\(240\) 0 0
\(241\) 16.2784i 1.04859i 0.851538 + 0.524293i \(0.175671\pi\)
−0.851538 + 0.524293i \(0.824329\pi\)
\(242\) 8.57008 + 8.57008i 0.550905 + 0.550905i
\(243\) 0 0
\(244\) 5.32419i 0.340846i
\(245\) −10.8049 + 7.71833i −0.690299 + 0.493106i
\(246\) 0 0
\(247\) 0.183064 + 3.27121i 0.0116481 + 0.208142i
\(248\) −6.09747 6.09747i −0.387190 0.387190i
\(249\) 0 0
\(250\) −9.83652 5.31441i −0.622116 0.336113i
\(251\) −5.24992 −0.331372 −0.165686 0.986179i \(-0.552984\pi\)
−0.165686 + 0.986179i \(0.552984\pi\)
\(252\) 0 0
\(253\) 19.6166 + 19.6166i 1.23329 + 1.23329i
\(254\) 13.2342i 0.830388i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −16.0320 16.0320i −1.00005 1.00005i −1.00000 4.94079e-5i \(-0.999984\pi\)
−4.94079e−5 1.00000i \(-0.500016\pi\)
\(258\) 0 0
\(259\) 7.98294 0.496036
\(260\) 0.276253 1.65786i 0.0171325 0.102816i
\(261\) 0 0
\(262\) −8.92844 8.92844i −0.551601 0.551601i
\(263\) 5.94999 + 5.94999i 0.366892 + 0.366892i 0.866342 0.499450i \(-0.166465\pi\)
−0.499450 + 0.866342i \(0.666465\pi\)
\(264\) 0 0
\(265\) 11.0193 + 1.83617i 0.676911 + 0.112795i
\(266\) −2.99343 + 3.34833i −0.183539 + 0.205299i
\(267\) 0 0
\(268\) 9.19128 9.19128i 0.561447 0.561447i
\(269\) 26.2880 1.60281 0.801404 0.598123i \(-0.204087\pi\)
0.801404 + 0.598123i \(0.204087\pi\)
\(270\) 0 0
\(271\) −11.9318 −0.724802 −0.362401 0.932022i \(-0.618043\pi\)
−0.362401 + 0.932022i \(0.618043\pi\)
\(272\) −3.72984 + 3.72984i −0.226155 + 0.226155i
\(273\) 0 0
\(274\) −0.535560 −0.0323544
\(275\) −7.79573 + 22.7426i −0.470100 + 1.37143i
\(276\) 0 0
\(277\) −13.1943 + 13.1943i −0.792771 + 0.792771i −0.981944 0.189173i \(-0.939419\pi\)
0.189173 + 0.981944i \(0.439419\pi\)
\(278\) 16.1179 16.1179i 0.966688 0.966688i
\(279\) 0 0
\(280\) 1.87480 1.33924i 0.112040 0.0800346i
\(281\) 25.4814i 1.52009i −0.649870 0.760045i \(-0.725177\pi\)
0.649870 0.760045i \(-0.274823\pi\)
\(282\) 0 0
\(283\) −14.9451 14.9451i −0.888392 0.888392i 0.105977 0.994369i \(-0.466203\pi\)
−0.994369 + 0.105977i \(0.966203\pi\)
\(284\) −2.06076 −0.122284
\(285\) 0 0
\(286\) −3.61413 −0.213708
\(287\) −4.24441 4.24441i −0.250540 0.250540i
\(288\) 0 0
\(289\) 10.8234i 0.636671i
\(290\) −0.181862 + 1.09140i −0.0106793 + 0.0640893i
\(291\) 0 0
\(292\) −3.31160 + 3.31160i −0.193797 + 0.193797i
\(293\) 19.3388 19.3388i 1.12978 1.12978i 0.139570 0.990212i \(-0.455428\pi\)
0.990212 0.139570i \(-0.0445719\pi\)
\(294\) 0 0
\(295\) −15.7669 22.0720i −0.917982 1.28508i
\(296\) 7.74758 0.450319
\(297\) 0 0
\(298\) −11.2289 + 11.2289i −0.650473 + 0.650473i
\(299\) −4.33668 −0.250797
\(300\) 0 0
\(301\) 4.43097 0.255397
\(302\) 9.44035 9.44035i 0.543231 0.543231i
\(303\) 0 0
\(304\) −2.90517 + 3.24961i −0.166623 + 0.186378i
\(305\) −6.92011 9.68746i −0.396244 0.554702i
\(306\) 0 0
\(307\) −0.00353863 0.00353863i −0.000201960 0.000201960i 0.707006 0.707208i \(-0.250045\pi\)
−0.707208 + 0.707006i \(0.750045\pi\)
\(308\) −3.50328 3.50328i −0.199618 0.199618i
\(309\) 0 0
\(310\) −19.0196 3.16928i −1.08024 0.180003i
\(311\) 11.6925 0.663019 0.331509 0.943452i \(-0.392442\pi\)
0.331509 + 0.943452i \(0.392442\pi\)
\(312\) 0 0
\(313\) −16.6688 16.6688i −0.942174 0.942174i 0.0562432 0.998417i \(-0.482088\pi\)
−0.998417 + 0.0562432i \(0.982088\pi\)
\(314\) 16.5988 0.936727
\(315\) 0 0
\(316\) 2.77074i 0.155866i
\(317\) −6.96737 6.96737i −0.391327 0.391327i 0.483834 0.875160i \(-0.339244\pi\)
−0.875160 + 0.483834i \(0.839244\pi\)
\(318\) 0 0
\(319\) 2.37925 0.133212
\(320\) 1.81952 1.29975i 0.101714 0.0726582i
\(321\) 0 0
\(322\) −4.20367 4.20367i −0.234261 0.234261i
\(323\) −1.28468 22.9564i −0.0714818 1.27733i
\(324\) 0 0
\(325\) −1.65216 3.37558i −0.0916454 0.187243i
\(326\) 1.39819i 0.0774384i
\(327\) 0 0
\(328\) −4.11927 4.11927i −0.227449 0.227449i
\(329\) 1.32669i 0.0731426i
\(330\) 0 0
\(331\) 12.2381i 0.672669i −0.941743 0.336335i \(-0.890813\pi\)
0.941743 0.336335i \(-0.109187\pi\)
\(332\) −3.57770 + 3.57770i −0.196352 + 0.196352i
\(333\) 0 0
\(334\) 10.5017i 0.574629i
\(335\) 4.77735 28.6701i 0.261015 1.56641i
\(336\) 0 0
\(337\) 18.9918 + 18.9918i 1.03455 + 1.03455i 0.999381 + 0.0351664i \(0.0111961\pi\)
0.0351664 + 0.999381i \(0.488804\pi\)
\(338\) −8.79290 + 8.79290i −0.478271 + 0.478271i
\(339\) 0 0
\(340\) −1.93866 + 11.6344i −0.105138 + 0.630962i
\(341\) 41.4627i 2.24533i
\(342\) 0 0
\(343\) −9.42671 9.42671i −0.508994 0.508994i
\(344\) 4.30033 0.231858
\(345\) 0 0
\(346\) 15.6216 0.839825
\(347\) −1.51527 + 1.51527i −0.0813438 + 0.0813438i −0.746608 0.665264i \(-0.768319\pi\)
0.665264 + 0.746608i \(0.268319\pi\)
\(348\) 0 0
\(349\) 21.3136i 1.14089i −0.821336 0.570444i \(-0.806771\pi\)
0.821336 0.570444i \(-0.193229\pi\)
\(350\) 1.67056 4.87353i 0.0892950 0.260501i
\(351\) 0 0
\(352\) −3.39999 3.39999i −0.181220 0.181220i
\(353\) −9.37463 9.37463i −0.498961 0.498961i 0.412153 0.911115i \(-0.364777\pi\)
−0.911115 + 0.412153i \(0.864777\pi\)
\(354\) 0 0
\(355\) −3.74959 + 2.67847i −0.199008 + 0.142158i
\(356\) 1.08630i 0.0575736i
\(357\) 0 0
\(358\) −13.4651 13.4651i −0.711652 0.711652i
\(359\) 30.1209i 1.58972i −0.606792 0.794861i \(-0.707544\pi\)
0.606792 0.794861i \(-0.292456\pi\)
\(360\) 0 0
\(361\) −2.11992 18.8814i −0.111575 0.993756i
\(362\) −1.25943 + 1.25943i −0.0661941 + 0.0661941i
\(363\) 0 0
\(364\) 0.774476 0.0405936
\(365\) −1.72127 + 10.3298i −0.0900954 + 0.540685i
\(366\) 0 0
\(367\) −10.0986 + 10.0986i −0.527140 + 0.527140i −0.919719 0.392578i \(-0.871583\pi\)
0.392578 + 0.919719i \(0.371583\pi\)
\(368\) −4.07973 4.07973i −0.212671 0.212671i
\(369\) 0 0
\(370\) 14.0969 10.0699i 0.732861 0.523510i
\(371\) 5.14771i 0.267256i
\(372\) 0 0
\(373\) 11.5759 11.5759i 0.599377 0.599377i −0.340770 0.940147i \(-0.610688\pi\)
0.940147 + 0.340770i \(0.110688\pi\)
\(374\) 25.3629 1.31148
\(375\) 0 0
\(376\) 1.28757i 0.0664014i
\(377\) −0.262992 + 0.262992i −0.0135448 + 0.0135448i
\(378\) 0 0
\(379\) 30.6895 1.57641 0.788206 0.615412i \(-0.211010\pi\)
0.788206 + 0.615412i \(0.211010\pi\)
\(380\) −1.06234 + 9.68873i −0.0544971 + 0.497021i
\(381\) 0 0
\(382\) 10.5111 + 10.5111i 0.537797 + 0.537797i
\(383\) 6.71232 6.71232i 0.342983 0.342983i −0.514504 0.857488i \(-0.672024\pi\)
0.857488 + 0.514504i \(0.172024\pi\)
\(384\) 0 0
\(385\) −10.9277 1.82090i −0.556926 0.0928017i
\(386\) −7.13657 −0.363242
\(387\) 0 0
\(388\) 2.81665 2.81665i 0.142994 0.142994i
\(389\) 1.69598i 0.0859894i 0.999075 + 0.0429947i \(0.0136899\pi\)
−0.999075 + 0.0429947i \(0.986310\pi\)
\(390\) 0 0
\(391\) 30.4335 1.53909
\(392\) −4.19903 4.19903i −0.212083 0.212083i
\(393\) 0 0
\(394\) 10.8358 0.545901
\(395\) −3.60127 5.04142i −0.181199 0.253661i
\(396\) 0 0
\(397\) −17.6346 + 17.6346i −0.885057 + 0.885057i −0.994043 0.108986i \(-0.965240\pi\)
0.108986 + 0.994043i \(0.465240\pi\)
\(398\) 14.7999 14.7999i 0.741851 0.741851i
\(399\) 0 0
\(400\) 1.62130 4.72984i 0.0810651 0.236492i
\(401\) 1.30146i 0.0649918i −0.999472 0.0324959i \(-0.989654\pi\)
0.999472 0.0324959i \(-0.0103456\pi\)
\(402\) 0 0
\(403\) −4.58311 4.58311i −0.228301 0.228301i
\(404\) 14.0592i 0.699470i
\(405\) 0 0
\(406\) −0.509852 −0.0253035
\(407\) −26.3417 26.3417i −1.30571 1.30571i
\(408\) 0 0
\(409\) 18.8682 0.932971 0.466485 0.884529i \(-0.345520\pi\)
0.466485 + 0.884529i \(0.345520\pi\)
\(410\) −12.8491 2.14107i −0.634572 0.105740i
\(411\) 0 0
\(412\) 6.63327 + 6.63327i 0.326798 + 0.326798i
\(413\) 8.83828 8.83828i 0.434903 0.434903i
\(414\) 0 0
\(415\) −1.85958 + 11.1598i −0.0912831 + 0.547813i
\(416\) 0.751642 0.0368523
\(417\) 0 0
\(418\) 20.9262 1.17107i 1.02354 0.0572791i
\(419\) 20.1568i 0.984725i 0.870390 + 0.492363i \(0.163867\pi\)
−0.870390 + 0.492363i \(0.836133\pi\)
\(420\) 0 0
\(421\) 8.85286i 0.431462i −0.976453 0.215731i \(-0.930787\pi\)
0.976453 0.215731i \(-0.0692134\pi\)
\(422\) −19.5436 + 19.5436i −0.951366 + 0.951366i
\(423\) 0 0
\(424\) 4.99593i 0.242624i
\(425\) 11.5943 + 23.6887i 0.562408 + 1.14907i
\(426\) 0 0
\(427\) 3.87914 3.87914i 0.187725 0.187725i
\(428\) −1.54262 + 1.54262i −0.0745656 + 0.0745656i
\(429\) 0 0
\(430\) 7.82453 5.58935i 0.377332 0.269542i
\(431\) 25.3047i 1.21889i 0.792830 + 0.609443i \(0.208607\pi\)
−0.792830 + 0.609443i \(0.791393\pi\)
\(432\) 0 0
\(433\) 6.00560 6.00560i 0.288611 0.288611i −0.547920 0.836531i \(-0.684580\pi\)
0.836531 + 0.547920i \(0.184580\pi\)
\(434\) 8.88509i 0.426498i
\(435\) 0 0
\(436\) 18.4286i 0.882569i
\(437\) 25.1099 1.40520i 1.20117 0.0672198i
\(438\) 0 0
\(439\) −38.4260 −1.83397 −0.916986 0.398919i \(-0.869386\pi\)
−0.916986 + 0.398919i \(0.869386\pi\)
\(440\) −10.6055 1.76721i −0.505597 0.0842486i
\(441\) 0 0
\(442\) −2.80350 + 2.80350i −0.133349 + 0.133349i
\(443\) −27.7457 27.7457i −1.31824 1.31824i −0.915171 0.403066i \(-0.867945\pi\)
−0.403066 0.915171i \(-0.632055\pi\)
\(444\) 0 0
\(445\) 1.41191 + 1.97654i 0.0669311 + 0.0936969i
\(446\) 11.3784 0.538781
\(447\) 0 0
\(448\) 0.728588 + 0.728588i 0.0344226 + 0.0344226i
\(449\) −28.1598 −1.32894 −0.664472 0.747313i \(-0.731344\pi\)
−0.664472 + 0.747313i \(0.731344\pi\)
\(450\) 0 0
\(451\) 28.0110i 1.31899i
\(452\) −5.25913 5.25913i −0.247369 0.247369i
\(453\) 0 0
\(454\) 2.80480i 0.131636i
\(455\) 1.40917 1.00663i 0.0660631 0.0471913i
\(456\) 0 0
\(457\) −19.5575 + 19.5575i −0.914859 + 0.914859i −0.996650 0.0817904i \(-0.973936\pi\)
0.0817904 + 0.996650i \(0.473936\pi\)
\(458\) −13.8906 + 13.8906i −0.649066 + 0.649066i
\(459\) 0 0
\(460\) −12.7258 2.12052i −0.593342 0.0988698i
\(461\) −9.61570 −0.447848 −0.223924 0.974607i \(-0.571887\pi\)
−0.223924 + 0.974607i \(0.571887\pi\)
\(462\) 0 0
\(463\) 16.6735 + 16.6735i 0.774882 + 0.774882i 0.978956 0.204074i \(-0.0654182\pi\)
−0.204074 + 0.978956i \(0.565418\pi\)
\(464\) −0.494819 −0.0229714
\(465\) 0 0
\(466\) 6.70326i 0.310523i
\(467\) 17.1190 17.1190i 0.792171 0.792171i −0.189676 0.981847i \(-0.560744\pi\)
0.981847 + 0.189676i \(0.0607437\pi\)
\(468\) 0 0
\(469\) 13.3933 0.618446
\(470\) −1.67352 2.34276i −0.0771938 0.108064i
\(471\) 0 0
\(472\) 8.57770 8.57770i 0.394820 0.394820i
\(473\) −14.6211 14.6211i −0.672278 0.672278i
\(474\) 0 0
\(475\) 10.6600 + 19.0096i 0.489113 + 0.872221i
\(476\) −5.43503 −0.249114
\(477\) 0 0
\(478\) 14.9801 14.9801i 0.685176 0.685176i
\(479\) 14.2801i 0.652474i 0.945288 + 0.326237i \(0.105781\pi\)
−0.945288 + 0.326237i \(0.894219\pi\)
\(480\) 0 0
\(481\) 5.82340 0.265524
\(482\) −11.5106 + 11.5106i −0.524293 + 0.524293i
\(483\) 0 0
\(484\) 12.1199i 0.550905i
\(485\) 1.46401 8.78590i 0.0664774 0.398947i
\(486\) 0 0
\(487\) −13.6790 13.6790i −0.619856 0.619856i 0.325639 0.945494i \(-0.394421\pi\)
−0.945494 + 0.325639i \(0.894421\pi\)
\(488\) 3.76477 3.76477i 0.170423 0.170423i
\(489\) 0 0
\(490\) −13.0979 2.18253i −0.591702 0.0985965i
\(491\) −6.60655 −0.298150 −0.149075 0.988826i \(-0.547630\pi\)
−0.149075 + 0.988826i \(0.547630\pi\)
\(492\) 0 0
\(493\) 1.84560 1.84560i 0.0831215 0.0831215i
\(494\) −2.18365 + 2.44254i −0.0982471 + 0.109895i
\(495\) 0 0
\(496\) 8.62312i 0.387190i
\(497\) −1.50144 1.50144i −0.0673490 0.0673490i
\(498\) 0 0
\(499\) 35.7269i 1.59935i −0.600430 0.799677i \(-0.705004\pi\)
0.600430 0.799677i \(-0.294996\pi\)
\(500\) −3.19762 10.7133i −0.143002 0.479114i
\(501\) 0 0
\(502\) −3.71225 3.71225i −0.165686 0.165686i
\(503\) 8.52003 + 8.52003i 0.379889 + 0.379889i 0.871062 0.491173i \(-0.163432\pi\)
−0.491173 + 0.871062i \(0.663432\pi\)
\(504\) 0 0
\(505\) 18.2734 + 25.5809i 0.813156 + 1.13834i
\(506\) 27.7421i 1.23329i
\(507\) 0 0
\(508\) 9.35800 9.35800i 0.415194 0.415194i
\(509\) 13.4408 0.595753 0.297877 0.954604i \(-0.403722\pi\)
0.297877 + 0.954604i \(0.403722\pi\)
\(510\) 0 0
\(511\) −4.82559 −0.213471
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 22.6727i 1.00005i
\(515\) 20.6910 + 3.44777i 0.911752 + 0.151927i
\(516\) 0 0
\(517\) −4.37774 + 4.37774i −0.192533 + 0.192533i
\(518\) 5.64479 + 5.64479i 0.248018 + 0.248018i
\(519\) 0 0
\(520\) 1.36763 0.976946i 0.0599744 0.0428419i
\(521\) 13.5544i 0.593831i 0.954904 + 0.296916i \(0.0959580\pi\)
−0.954904 + 0.296916i \(0.904042\pi\)
\(522\) 0 0
\(523\) 5.40357 5.40357i 0.236282 0.236282i −0.579027 0.815308i \(-0.696567\pi\)
0.815308 + 0.579027i \(0.196567\pi\)
\(524\) 12.6267i 0.551601i
\(525\) 0 0
\(526\) 8.41456i 0.366892i
\(527\) 32.1629 + 32.1629i 1.40104 + 1.40104i
\(528\) 0 0
\(529\) 10.2884i 0.447321i
\(530\) 6.49346 + 9.09020i 0.282058 + 0.394853i
\(531\) 0 0
\(532\) −4.48430 + 0.250951i −0.194419 + 0.0108801i
\(533\) −3.09622 3.09622i −0.134112 0.134112i
\(534\) 0 0
\(535\) −0.801810 + 4.81186i −0.0346653 + 0.208035i
\(536\) 12.9984 0.561447
\(537\) 0 0
\(538\) 18.5884 + 18.5884i 0.801404 + 0.801404i
\(539\) 28.5533i 1.22988i
\(540\) 0 0
\(541\) 7.68488 0.330399 0.165200 0.986260i \(-0.447173\pi\)
0.165200 + 0.986260i \(0.447173\pi\)
\(542\) −8.43702 8.43702i −0.362401 0.362401i
\(543\) 0 0
\(544\) −5.27479 −0.226155
\(545\) 23.9525 + 33.5312i 1.02601 + 1.43632i
\(546\) 0 0
\(547\) −17.8604 17.8604i −0.763656 0.763656i 0.213325 0.976981i \(-0.431571\pi\)
−0.976981 + 0.213325i \(0.931571\pi\)
\(548\) −0.378698 0.378698i −0.0161772 0.0161772i
\(549\) 0 0
\(550\) −21.5938 + 10.5690i −0.920765 + 0.450664i
\(551\) 1.43754 1.60797i 0.0612411 0.0685018i
\(552\) 0 0
\(553\) 2.01873 2.01873i 0.0858451 0.0858451i
\(554\) −18.6596 −0.792771
\(555\) 0 0
\(556\) 22.7942 0.966688
\(557\) −12.5198 + 12.5198i −0.530480 + 0.530480i −0.920715 0.390235i \(-0.872394\pi\)
0.390235 + 0.920715i \(0.372394\pi\)
\(558\) 0 0
\(559\) 3.23231 0.136712
\(560\) 2.27266 + 0.378698i 0.0960375 + 0.0160029i
\(561\) 0 0
\(562\) 18.0180 18.0180i 0.760045 0.760045i
\(563\) −11.0759 + 11.0759i −0.466791 + 0.466791i −0.900873 0.434082i \(-0.857073\pi\)
0.434082 + 0.900873i \(0.357073\pi\)
\(564\) 0 0
\(565\) −16.4046 2.73354i −0.690149 0.115001i
\(566\) 21.1355i 0.888392i
\(567\) 0 0
\(568\) −1.45718 1.45718i −0.0611418 0.0611418i
\(569\) 43.4414 1.82116 0.910579 0.413336i \(-0.135636\pi\)
0.910579 + 0.413336i \(0.135636\pi\)
\(570\) 0 0
\(571\) 15.6768 0.656052 0.328026 0.944669i \(-0.393617\pi\)
0.328026 + 0.944669i \(0.393617\pi\)
\(572\) −2.55558 2.55558i −0.106854 0.106854i
\(573\) 0 0
\(574\) 6.00250i 0.250540i
\(575\) −25.9109 + 12.6820i −1.08056 + 0.528876i
\(576\) 0 0
\(577\) 6.59569 6.59569i 0.274582 0.274582i −0.556359 0.830942i \(-0.687802\pi\)
0.830942 + 0.556359i \(0.187802\pi\)
\(578\) 7.65330 7.65330i 0.318335 0.318335i
\(579\) 0 0
\(580\) −0.900333 + 0.643141i −0.0373843 + 0.0267050i
\(581\) −5.21334 −0.216286
\(582\) 0 0
\(583\) 16.9861 16.9861i 0.703494 0.703494i
\(584\) −4.68331 −0.193797
\(585\) 0 0
\(586\) 27.3491 1.12978
\(587\) 23.8623 23.8623i 0.984904 0.984904i −0.0149835 0.999888i \(-0.504770\pi\)
0.999888 + 0.0149835i \(0.00476957\pi\)
\(588\) 0 0
\(589\) 28.0218 + 25.0517i 1.15462 + 1.03224i
\(590\) 4.45843 26.7561i 0.183551 1.10153i
\(591\) 0 0
\(592\) 5.47836 + 5.47836i 0.225159 + 0.225159i
\(593\) −22.7988 22.7988i −0.936236 0.936236i 0.0618495 0.998085i \(-0.480300\pi\)
−0.998085 + 0.0618495i \(0.980300\pi\)
\(594\) 0 0
\(595\) −9.88915 + 7.06418i −0.405416 + 0.289603i
\(596\) −15.8801 −0.650473
\(597\) 0 0
\(598\) −3.06650 3.06650i −0.125398 0.125398i
\(599\) 11.4248 0.466805 0.233402 0.972380i \(-0.425014\pi\)
0.233402 + 0.972380i \(0.425014\pi\)
\(600\) 0 0
\(601\) 7.14156i 0.291310i 0.989335 + 0.145655i \(0.0465290\pi\)
−0.989335 + 0.145655i \(0.953471\pi\)
\(602\) 3.13317 + 3.13317i 0.127698 + 0.127698i
\(603\) 0 0
\(604\) 13.3507 0.543231
\(605\) 15.7529 + 22.0524i 0.640445 + 0.896559i
\(606\) 0 0
\(607\) 6.44190 + 6.44190i 0.261469 + 0.261469i 0.825651 0.564182i \(-0.190808\pi\)
−0.564182 + 0.825651i \(0.690808\pi\)
\(608\) −4.35209 + 0.243552i −0.176501 + 0.00987733i
\(609\) 0 0
\(610\) 1.95681 11.7433i 0.0792290 0.475473i
\(611\) 0.967793i 0.0391527i
\(612\) 0 0
\(613\) −21.1379 21.1379i −0.853752 0.853752i 0.136841 0.990593i \(-0.456305\pi\)
−0.990593 + 0.136841i \(0.956305\pi\)
\(614\) 0.00500438i 0.000201960i
\(615\) 0 0
\(616\) 4.95439i 0.199618i
\(617\) 9.52678 9.52678i 0.383534 0.383534i −0.488840 0.872373i \(-0.662580\pi\)
0.872373 + 0.488840i \(0.162580\pi\)
\(618\) 0 0
\(619\) 6.57762i 0.264377i 0.991225 + 0.132188i \(0.0422004\pi\)
−0.991225 + 0.132188i \(0.957800\pi\)
\(620\) −11.2079 15.6899i −0.450120 0.630123i
\(621\) 0 0
\(622\) 8.26782 + 8.26782i 0.331509 + 0.331509i
\(623\) −0.791463 + 0.791463i −0.0317093 + 0.0317093i
\(624\) 0 0
\(625\) −19.7428 15.3370i −0.789710 0.613480i
\(626\) 23.5732i 0.942174i
\(627\) 0 0
\(628\) 11.7372 + 11.7372i 0.468363 + 0.468363i
\(629\) −40.8668 −1.62947
\(630\) 0 0
\(631\) −17.0875 −0.680241 −0.340121 0.940382i \(-0.610468\pi\)
−0.340121 + 0.940382i \(0.610468\pi\)
\(632\) 1.95921 1.95921i 0.0779332 0.0779332i
\(633\) 0 0
\(634\) 9.85335i 0.391327i
\(635\) 4.86401 29.1901i 0.193022 1.15837i
\(636\) 0 0
\(637\) −3.15616 3.15616i −0.125052 0.125052i
\(638\) 1.68238 + 1.68238i 0.0666062 + 0.0666062i
\(639\) 0 0
\(640\) 2.20566 + 0.367533i 0.0871862 + 0.0145280i
\(641\) 46.7376i 1.84602i 0.384773 + 0.923011i \(0.374280\pi\)
−0.384773 + 0.923011i \(0.625720\pi\)
\(642\) 0 0
\(643\) −7.16897 7.16897i −0.282717 0.282717i 0.551475 0.834191i \(-0.314065\pi\)
−0.834191 + 0.551475i \(0.814065\pi\)
\(644\) 5.94489i 0.234261i
\(645\) 0 0
\(646\) 15.3242 17.1410i 0.602922 0.674404i
\(647\) 6.19558 6.19558i 0.243574 0.243574i −0.574753 0.818327i \(-0.694902\pi\)
0.818327 + 0.574753i \(0.194902\pi\)
\(648\) 0 0
\(649\) −58.3282 −2.28958
\(650\) 1.21864 3.55515i 0.0477989 0.139444i
\(651\) 0 0
\(652\) 0.988668 0.988668i 0.0387192 0.0387192i
\(653\) −17.2336 17.2336i −0.674401 0.674401i 0.284326 0.958728i \(-0.408230\pi\)
−0.958728 + 0.284326i \(0.908230\pi\)
\(654\) 0 0
\(655\) −16.4116 22.9746i −0.641253 0.897690i
\(656\) 5.82553i 0.227449i
\(657\) 0 0
\(658\) 0.938110 0.938110i 0.0365713 0.0365713i
\(659\) 21.6005 0.841436 0.420718 0.907191i \(-0.361778\pi\)
0.420718 + 0.907191i \(0.361778\pi\)
\(660\) 0 0
\(661\) 1.49297i 0.0580696i 0.999578 + 0.0290348i \(0.00924337\pi\)
−0.999578 + 0.0290348i \(0.990757\pi\)
\(662\) 8.65367 8.65367i 0.336335 0.336335i
\(663\) 0 0
\(664\) −5.05963 −0.196352
\(665\) −7.83310 + 6.28508i −0.303755 + 0.243725i
\(666\) 0 0
\(667\) 2.01873 + 2.01873i 0.0781655 + 0.0781655i
\(668\) −7.42584 + 7.42584i −0.287314 + 0.287314i
\(669\) 0 0
\(670\) 23.6509 16.8947i 0.913714 0.652700i
\(671\) −25.6004 −0.988291
\(672\) 0 0
\(673\) −8.49705 + 8.49705i −0.327537 + 0.327537i −0.851649 0.524112i \(-0.824397\pi\)
0.524112 + 0.851649i \(0.324397\pi\)
\(674\) 26.8584i 1.03455i
\(675\) 0 0
\(676\) −12.4350 −0.478271
\(677\) 5.92660 + 5.92660i 0.227778 + 0.227778i 0.811764 0.583986i \(-0.198508\pi\)
−0.583986 + 0.811764i \(0.698508\pi\)
\(678\) 0 0
\(679\) 4.10436 0.157511
\(680\) −9.59758 + 6.85591i −0.368050 + 0.262912i
\(681\) 0 0
\(682\) −29.3186 + 29.3186i −1.12267 + 1.12267i
\(683\) −26.3647 + 26.3647i −1.00882 + 1.00882i −0.00885484 + 0.999961i \(0.502819\pi\)
−0.999961 + 0.00885484i \(0.997181\pi\)
\(684\) 0 0
\(685\) −1.18126 0.196836i −0.0451337 0.00752071i
\(686\) 13.3314i 0.508994i
\(687\) 0 0
\(688\) 3.04079 + 3.04079i 0.115929 + 0.115929i
\(689\) 3.75515i 0.143060i
\(690\) 0 0
\(691\) 19.3186 0.734913 0.367456 0.930041i \(-0.380229\pi\)
0.367456 + 0.930041i \(0.380229\pi\)
\(692\) 11.0462 + 11.0462i 0.419912 + 0.419912i
\(693\) 0 0
\(694\) −2.14291 −0.0813438
\(695\) 41.4744 29.6267i 1.57322 1.12381i
\(696\) 0 0
\(697\) 21.7283 + 21.7283i 0.823017 + 0.823017i
\(698\) 15.0710 15.0710i 0.570444 0.570444i
\(699\) 0 0
\(700\) 4.62737 2.26484i 0.174898 0.0856031i
\(701\) −8.82340 −0.333255 −0.166628 0.986020i \(-0.553288\pi\)
−0.166628 + 0.986020i \(0.553288\pi\)
\(702\) 0 0
\(703\) −33.7181 + 1.88694i −1.27170 + 0.0711672i
\(704\) 4.80832i 0.181220i
\(705\) 0 0
\(706\) 13.2577i 0.498961i
\(707\) −10.2434 + 10.2434i −0.385241 + 0.385241i
\(708\) 0 0
\(709\) 1.20583i 0.0452859i −0.999744 0.0226429i \(-0.992792\pi\)
0.999744 0.0226429i \(-0.00720808\pi\)
\(710\) −4.54533 0.757396i −0.170583 0.0284246i
\(711\) 0 0
\(712\) −0.768128 + 0.768128i −0.0287868 + 0.0287868i
\(713\) −35.1800 + 35.1800i −1.31750 + 1.31750i
\(714\) 0 0
\(715\) −7.97154 1.32831i −0.298119 0.0496761i
\(716\) 19.0425i 0.711652i
\(717\) 0 0
\(718\) 21.2987 21.2987i 0.794861 0.794861i
\(719\) 9.38938i 0.350165i 0.984554 + 0.175082i \(0.0560192\pi\)
−0.984554 + 0.175082i \(0.943981\pi\)
\(720\) 0 0
\(721\) 9.66585i 0.359975i
\(722\) 11.8521 14.8502i 0.441091 0.552665i
\(723\) 0 0
\(724\) −1.78110 −0.0661941
\(725\) −0.802251 + 2.34042i −0.0297949 + 0.0869209i
\(726\) 0 0
\(727\) −17.4688 + 17.4688i −0.647884 + 0.647884i −0.952481 0.304597i \(-0.901478\pi\)
0.304597 + 0.952481i \(0.401478\pi\)
\(728\) 0.547637 + 0.547637i 0.0202968 + 0.0202968i
\(729\) 0 0
\(730\) −8.52138 + 6.08713i −0.315390 + 0.225295i
\(731\) −22.6833 −0.838973
\(732\) 0 0
\(733\) 13.1840 + 13.1840i 0.486963 + 0.486963i 0.907347 0.420383i \(-0.138104\pi\)
−0.420383 + 0.907347i \(0.638104\pi\)
\(734\) −14.2815 −0.527140
\(735\) 0 0
\(736\) 5.76961i 0.212671i
\(737\) −44.1946 44.1946i −1.62793 1.62793i
\(738\) 0 0
\(739\) 47.8710i 1.76096i 0.474080 + 0.880482i \(0.342781\pi\)
−0.474080 + 0.880482i \(0.657219\pi\)
\(740\) 17.0885 + 2.84749i 0.628185 + 0.104676i
\(741\) 0 0
\(742\) −3.63998 + 3.63998i −0.133628 + 0.133628i
\(743\) −19.4260 + 19.4260i −0.712670 + 0.712670i −0.967093 0.254423i \(-0.918114\pi\)
0.254423 + 0.967093i \(0.418114\pi\)
\(744\) 0 0
\(745\) −28.8941 + 20.6401i −1.05860 + 0.756196i
\(746\) 16.3708 0.599377
\(747\) 0 0
\(748\) 17.9343 + 17.9343i 0.655741 + 0.655741i
\(749\) −2.24788 −0.0821356
\(750\) 0 0
\(751\) 23.5009i 0.857559i 0.903409 + 0.428779i \(0.141056\pi\)
−0.903409 + 0.428779i \(0.858944\pi\)
\(752\) 0.910451 0.910451i 0.0332007 0.0332007i
\(753\) 0 0
\(754\) −0.371927 −0.0135448
\(755\) 24.2918 17.3525i 0.884069 0.631523i
\(756\) 0 0
\(757\) 19.2062 19.2062i 0.698060 0.698060i −0.265932 0.963992i \(-0.585680\pi\)
0.963992 + 0.265932i \(0.0856796\pi\)
\(758\) 21.7007 + 21.7007i 0.788206 + 0.788206i
\(759\) 0 0
\(760\) −7.60215 + 6.09977i −0.275759 + 0.221262i
\(761\) 23.7982 0.862685 0.431343 0.902188i \(-0.358040\pi\)
0.431343 + 0.902188i \(0.358040\pi\)
\(762\) 0 0
\(763\) −13.4268 + 13.4268i −0.486084 + 0.486084i
\(764\) 14.8650i 0.537797i
\(765\) 0 0
\(766\) 9.49265 0.342983
\(767\) 6.44736 6.44736i 0.232801 0.232801i
\(768\) 0 0
\(769\) 28.9884i 1.04535i −0.852532 0.522675i \(-0.824934\pi\)
0.852532 0.522675i \(-0.175066\pi\)
\(770\) −6.43947 9.01461i −0.232062 0.324864i
\(771\) 0 0
\(772\) −5.04632 5.04632i −0.181621 0.181621i
\(773\) −29.2365 + 29.2365i −1.05156 + 1.05156i −0.0529667 + 0.998596i \(0.516868\pi\)
−0.998596 + 0.0529667i \(0.983132\pi\)
\(774\) 0 0
\(775\) −40.7860 13.9807i −1.46508 0.502201i
\(776\) 3.98335 0.142994
\(777\) 0 0
\(778\) −1.19924 + 1.19924i −0.0429947 + 0.0429947i
\(779\) 18.9307 + 16.9242i 0.678262 + 0.606371i
\(780\) 0 0
\(781\) 9.90878i 0.354564i
\(782\) 21.5197 + 21.5197i 0.769543 + 0.769543i
\(783\) 0 0
\(784\) 5.93832i 0.212083i
\(785\) 36.6113 + 6.10062i 1.30671 + 0.217740i
\(786\) 0 0
\(787\) 12.6866 + 12.6866i 0.452228 + 0.452228i 0.896093 0.443866i \(-0.146393\pi\)
−0.443866 + 0.896093i \(0.646393\pi\)
\(788\) 7.66209 + 7.66209i 0.272951 + 0.272951i
\(789\) 0 0
\(790\) 1.01834 6.11130i 0.0362308 0.217430i
\(791\) 7.66348i 0.272482i
\(792\) 0 0
\(793\) 2.82976 2.82976i 0.100488 0.100488i
\(794\) −24.9391 −0.885057
\(795\) 0 0
\(796\) 20.9302 0.741851
\(797\) −15.7202 15.7202i −0.556838 0.556838i 0.371568 0.928406i \(-0.378820\pi\)
−0.928406 + 0.371568i \(0.878820\pi\)
\(798\) 0 0
\(799\) 6.79167i 0.240272i
\(800\) 4.49094 2.19807i 0.158779 0.0777134i
\(801\) 0 0
\(802\) 0.920271 0.920271i 0.0324959 0.0324959i
\(803\) 15.9232 + 15.9232i 0.561919 + 0.561919i
\(804\) 0 0
\(805\) −7.72686 10.8168i −0.272336 0.381243i
\(806\) 6.48150i 0.228301i
\(807\) 0 0
\(808\) −9.94134 + 9.94134i −0.349735 + 0.349735i
\(809\) 11.4400i 0.402210i 0.979570 + 0.201105i \(0.0644533\pi\)
−0.979570 + 0.201105i \(0.935547\pi\)
\(810\) 0 0
\(811\) 17.5878i 0.617592i 0.951128 + 0.308796i \(0.0999260\pi\)
−0.951128 + 0.308796i \(0.900074\pi\)
\(812\) −0.360520 0.360520i −0.0126518 0.0126518i
\(813\) 0 0
\(814\) 37.2528i 1.30571i
\(815\) 0.513880 3.08392i 0.0180004 0.108025i
\(816\) 0 0
\(817\) −18.7154 + 1.04735i −0.654769 + 0.0366422i
\(818\) 13.3418 + 13.3418i 0.466485 + 0.466485i
\(819\) 0 0
\(820\) −7.57173 10.5997i −0.264416 0.370156i
\(821\) −13.1354 −0.458428 −0.229214 0.973376i \(-0.573616\pi\)
−0.229214 + 0.973376i \(0.573616\pi\)
\(822\) 0 0
\(823\) −23.2779 23.2779i −0.811417 0.811417i 0.173429 0.984846i \(-0.444515\pi\)
−0.984846 + 0.173429i \(0.944515\pi\)
\(824\) 9.38086i 0.326798i
\(825\) 0 0
\(826\) 12.4992 0.434903
\(827\) −33.6240 33.6240i −1.16922 1.16922i −0.982393 0.186828i \(-0.940179\pi\)
−0.186828 0.982393i \(-0.559821\pi\)
\(828\) 0 0
\(829\) −22.3434 −0.776020 −0.388010 0.921655i \(-0.626837\pi\)
−0.388010 + 0.921655i \(0.626837\pi\)
\(830\) −9.20609 + 6.57625i −0.319548 + 0.228265i
\(831\) 0 0
\(832\) 0.531491 + 0.531491i 0.0184261 + 0.0184261i
\(833\) 22.1490 + 22.1490i 0.767416 + 0.767416i
\(834\) 0 0
\(835\) −3.85973 + 23.1632i −0.133571 + 0.801595i
\(836\) 15.6252 + 13.9690i 0.540407 + 0.483128i
\(837\) 0 0
\(838\) −14.2530 + 14.2530i −0.492363 + 0.492363i
\(839\) 31.3884 1.08365 0.541824 0.840492i \(-0.317734\pi\)
0.541824 + 0.840492i \(0.317734\pi\)
\(840\) 0 0
\(841\) −28.7552 −0.991557
\(842\) 6.25992 6.25992i 0.215731 0.215731i
\(843\) 0 0
\(844\) −27.6388 −0.951366
\(845\) −22.6258 + 16.1624i −0.778351 + 0.556005i
\(846\) 0 0
\(847\) −8.83043 + 8.83043i −0.303417 + 0.303417i
\(848\) −3.53266 + 3.53266i −0.121312 + 0.121312i
\(849\) 0 0
\(850\) −8.55203 + 24.9489i −0.293332 + 0.855740i
\(851\) 44.7005i 1.53231i
\(852\) 0 0
\(853\) −16.0193 16.0193i −0.548490 0.548490i 0.377514 0.926004i \(-0.376779\pi\)
−0.926004 + 0.377514i \(0.876779\pi\)
\(854\) 5.48593 0.187725
\(855\) 0 0
\(856\) −2.18160 −0.0745656
\(857\) 14.3582 + 14.3582i 0.490467 + 0.490467i 0.908453 0.417986i \(-0.137264\pi\)
−0.417986 + 0.908453i \(0.637264\pi\)
\(858\) 0 0
\(859\) 23.5232i 0.802602i −0.915946 0.401301i \(-0.868558\pi\)
0.915946 0.401301i \(-0.131442\pi\)
\(860\) 9.48504 + 1.58051i 0.323437 + 0.0538950i
\(861\) 0 0
\(862\) −17.8931 + 17.8931i −0.609443 + 0.609443i
\(863\) −34.2060 + 34.2060i −1.16439 + 1.16439i −0.180881 + 0.983505i \(0.557895\pi\)
−0.983505 + 0.180881i \(0.942105\pi\)
\(864\) 0 0
\(865\) 34.4560 + 5.74146i 1.17154 + 0.195216i
\(866\) 8.49320 0.288611
\(867\) 0 0
\(868\) 6.28270 6.28270i 0.213249 0.213249i
\(869\) −13.3226 −0.451938
\(870\) 0 0
\(871\) 9.77017 0.331050
\(872\) −13.0310 + 13.0310i −0.441284 + 0.441284i
\(873\) 0 0
\(874\) 18.7490 + 16.7617i 0.634193 + 0.566974i
\(875\) 5.47585 10.1353i 0.185118 0.342637i
\(876\) 0 0
\(877\) 34.2759 + 34.2759i 1.15742 + 1.15742i 0.985029 + 0.172387i \(0.0551479\pi\)
0.172387 + 0.985029i \(0.444852\pi\)
\(878\) −27.1713 27.1713i −0.916986 0.916986i
\(879\) 0 0
\(880\) −6.24961 8.74883i −0.210674 0.294923i
\(881\) 16.2818 0.548548 0.274274 0.961652i \(-0.411562\pi\)
0.274274 + 0.961652i \(0.411562\pi\)
\(882\) 0 0
\(883\) −16.4556 16.4556i −0.553774 0.553774i 0.373754 0.927528i \(-0.378070\pi\)
−0.927528 + 0.373754i \(0.878070\pi\)
\(884\) −3.96475 −0.133349
\(885\) 0 0
\(886\) 39.2383i 1.31824i
\(887\) 20.1627 + 20.1627i 0.676997 + 0.676997i 0.959320 0.282322i \(-0.0911047\pi\)
−0.282322 + 0.959320i \(0.591105\pi\)
\(888\) 0 0
\(889\) 13.6363 0.457345
\(890\) −0.399250 + 2.39600i −0.0133829 + 0.0803140i
\(891\) 0 0
\(892\) 8.04571 + 8.04571i 0.269390 + 0.269390i
\(893\) 0.313590 + 5.60363i 0.0104939 + 0.187518i
\(894\) 0 0
\(895\) −24.7505 34.6482i −0.827318 1.15816i
\(896\) 1.03038i 0.0344226i
\(897\) 0 0
\(898\) −19.9120 19.9120i −0.664472 0.664472i
\(899\) 4.26689i 0.142309i
\(900\) 0 0
\(901\) 26.3525i 0.877929i
\(902\) −19.8068 + 19.8068i −0.659493 + 0.659493i
\(903\) 0 0
\(904\) 7.43754i 0.247369i
\(905\) −3.24075 + 2.31499i −0.107726 + 0.0769527i
\(906\) 0 0
\(907\) −36.3346 36.3346i −1.20647 1.20647i −0.972162 0.234309i \(-0.924717\pi\)
−0.234309 0.972162i \(-0.575283\pi\)
\(908\) 1.98330 1.98330i 0.0658180 0.0658180i
\(909\) 0 0
\(910\) 1.70823 + 0.284645i 0.0566272 + 0.00943590i
\(911\) 9.50181i 0.314809i −0.987534 0.157405i \(-0.949687\pi\)
0.987534 0.157405i \(-0.0503127\pi\)
\(912\) 0 0
\(913\) 17.2027 + 17.2027i 0.569326 + 0.569326i
\(914\) −27.6584 −0.914859
\(915\) 0 0
\(916\) −19.6443 −0.649066
\(917\) 9.19968 9.19968i 0.303800 0.303800i
\(918\) 0 0
\(919\) 3.20583i 0.105751i −0.998601 0.0528753i \(-0.983161\pi\)
0.998601 0.0528753i \(-0.0168386\pi\)
\(920\) −7.49905 10.4979i −0.247236 0.346106i
\(921\) 0 0
\(922\) −6.79932 6.79932i −0.223924 0.223924i
\(923\) −1.09527 1.09527i −0.0360514 0.0360514i
\(924\) 0 0
\(925\) 34.7939 17.0297i 1.14402 0.559933i
\(926\) 23.5799i 0.774882i
\(927\) 0 0
\(928\) −0.349890 0.349890i −0.0114857 0.0114857i
\(929\) 0.680198i 0.0223166i −0.999938 0.0111583i \(-0.996448\pi\)
0.999938 0.0111583i \(-0.00355187\pi\)
\(930\) 0 0
\(931\) 19.2972 + 17.2519i 0.632441 + 0.565407i
\(932\) −4.73992 + 4.73992i −0.155261 + 0.155261i
\(933\) 0 0
\(934\) 24.2099 0.792171
\(935\) 55.9418 + 9.32168i 1.82949 + 0.304852i
\(936\) 0 0
\(937\) 20.6037 20.6037i 0.673093 0.673093i −0.285335 0.958428i \(-0.592105\pi\)
0.958428 + 0.285335i \(0.0921048\pi\)
\(938\) 9.47051 + 9.47051i 0.309223 + 0.309223i
\(939\) 0 0
\(940\) 0.473225 2.83994i 0.0154349 0.0926286i
\(941\) 16.5409i 0.539220i 0.962970 + 0.269610i \(0.0868947\pi\)
−0.962970 + 0.269610i \(0.913105\pi\)
\(942\) 0 0
\(943\) −23.7666 + 23.7666i −0.773946 + 0.773946i
\(944\) 12.1307 0.394820
\(945\) 0 0
\(946\) 20.6773i 0.672278i
\(947\) −21.1699 + 21.1699i −0.687929 + 0.687929i −0.961774 0.273845i \(-0.911704\pi\)
0.273845 + 0.961774i \(0.411704\pi\)
\(948\) 0 0
\(949\) −3.52017 −0.114270
\(950\) −5.90409 + 20.9796i −0.191554 + 0.680667i
\(951\) 0 0
\(952\) −3.84315 3.84315i −0.124557 0.124557i
\(953\) 28.1289 28.1289i 0.911186 0.911186i −0.0851800 0.996366i \(-0.527147\pi\)
0.996366 + 0.0851800i \(0.0271465\pi\)
\(954\) 0 0
\(955\) 19.3208 + 27.0471i 0.625205 + 0.875225i
\(956\) 21.1851 0.685176
\(957\) 0 0
\(958\) −10.0976 + 10.0976i −0.326237 + 0.326237i
\(959\) 0.551830i 0.0178195i
\(960\) 0 0
\(961\) −43.3582 −1.39865
\(962\) 4.11777 + 4.11777i 0.132762 + 0.132762i
\(963\) 0 0
\(964\) −16.2784 −0.524293
\(965\) −15.7408 2.62292i −0.506715 0.0844349i
\(966\) 0 0
\(967\) −2.96462 + 2.96462i −0.0953359 + 0.0953359i −0.753166 0.657830i \(-0.771474\pi\)
0.657830 + 0.753166i \(0.271474\pi\)
\(968\) −8.57008 + 8.57008i −0.275453 + 0.275453i
\(969\) 0 0
\(970\) 7.24778 5.17736i 0.232712 0.166235i
\(971\) 4.90480i 0.157403i −0.996898 0.0787013i \(-0.974923\pi\)
0.996898 0.0787013i \(-0.0250773\pi\)
\(972\) 0 0
\(973\) 16.6076 + 16.6076i 0.532414 + 0.532414i
\(974\) 19.3451i 0.619856i
\(975\) 0 0
\(976\) 5.32419 0.170423
\(977\) −11.6920 11.6920i −0.374061 0.374061i 0.494893 0.868954i \(-0.335207\pi\)
−0.868954 + 0.494893i \(0.835207\pi\)
\(978\) 0 0
\(979\) 5.22326 0.166936
\(980\) −7.71833 10.8049i −0.246553 0.345149i
\(981\) 0 0
\(982\) −4.67154 4.67154i −0.149075 0.149075i
\(983\) −24.4836 + 24.4836i −0.780907 + 0.780907i −0.979984 0.199077i \(-0.936206\pi\)
0.199077 + 0.979984i \(0.436206\pi\)
\(984\) 0 0
\(985\) 23.9001 + 3.98252i 0.761521 + 0.126894i
\(986\) 2.61007 0.0831215
\(987\) 0 0
\(988\) −3.27121 + 0.183064i −0.104071 + 0.00582404i
\(989\) 24.8112i 0.788950i
\(990\) 0 0
\(991\) 56.2681i 1.78741i 0.448650 + 0.893707i \(0.351905\pi\)
−0.448650 + 0.893707i \(0.648095\pi\)
\(992\) 6.09747 6.09747i 0.193595 0.193595i
\(993\) 0 0
\(994\) 2.12336i 0.0673490i
\(995\) 38.0829 27.2040i 1.20731 0.862425i
\(996\) 0 0
\(997\) −2.01280 + 2.01280i −0.0637459 + 0.0637459i −0.738261 0.674515i \(-0.764353\pi\)
0.674515 + 0.738261i \(0.264353\pi\)
\(998\) 25.2627 25.2627i 0.799677 0.799677i
\(999\) 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 1710.2.p.c.1063.10 20
3.2 odd 2 570.2.m.b.493.1 yes 20
5.2 odd 4 inner 1710.2.p.c.37.5 20
15.2 even 4 570.2.m.b.37.6 yes 20
19.18 odd 2 inner 1710.2.p.c.1063.5 20
57.56 even 2 570.2.m.b.493.6 yes 20
95.37 even 4 inner 1710.2.p.c.37.10 20
285.227 odd 4 570.2.m.b.37.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.m.b.37.1 20 285.227 odd 4
570.2.m.b.37.6 yes 20 15.2 even 4
570.2.m.b.493.1 yes 20 3.2 odd 2
570.2.m.b.493.6 yes 20 57.56 even 2
1710.2.p.c.37.5 20 5.2 odd 4 inner
1710.2.p.c.37.10 20 95.37 even 4 inner
1710.2.p.c.1063.5 20 19.18 odd 2 inner
1710.2.p.c.1063.10 20 1.1 even 1 trivial