Properties

Label 700.2.g.l.251.5
Level $700$
Weight $2$
Character 700.251
Analytic conductor $5.590$
Analytic rank $0$
Dimension $16$
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] = [700,2,Mod(251,700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(700, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("700.251");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.g (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: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 17x^{12} - 104x^{10} + 713x^{8} + 238x^{6} + 1004x^{4} - 152x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.5
Root \(-0.645096 - 0.854135i\) of defining polynomial
Character \(\chi\) \(=\) 700.251
Dual form 700.2.g.l.251.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.927153 - 1.06789i) q^{2} -0.662153 q^{3} +(-0.280776 + 1.98019i) q^{4} +(0.613917 + 0.707107i) q^{6} +(-2.35829 + 1.19935i) q^{7} +(2.37495 - 1.53610i) q^{8} -2.56155 q^{9} +O(q^{10})\) \(q+(-0.927153 - 1.06789i) q^{2} -0.662153 q^{3} +(-0.280776 + 1.98019i) q^{4} +(0.613917 + 0.707107i) q^{6} +(-2.35829 + 1.19935i) q^{7} +(2.37495 - 1.53610i) q^{8} -2.56155 q^{9} +3.09218i q^{11} +(0.185917 - 1.31119i) q^{12} -4.66988i q^{13} +(3.46728 + 1.40642i) q^{14} +(-3.84233 - 1.11198i) q^{16} -2.04750i q^{17} +(2.37495 + 2.73546i) q^{18} +5.60083 q^{19} +(1.56155 - 0.794156i) q^{21} +(3.30210 - 2.86692i) q^{22} -1.87285i q^{23} +(-1.57258 + 1.01714i) q^{24} +(-4.98691 + 4.32969i) q^{26} +3.68260 q^{27} +(-1.71280 - 5.00663i) q^{28} +3.56155 q^{29} +8.74599 q^{31} +(2.37495 + 5.13416i) q^{32} -2.04750i q^{33} +(-2.18650 + 1.89834i) q^{34} +(0.719224 - 5.07237i) q^{36} +3.70861 q^{37} +(-5.19283 - 5.98107i) q^{38} +3.09218i q^{39} -8.48528i q^{41} +(-2.29587 - 0.931263i) q^{42} +4.27156i q^{43} +(-6.12311 - 0.868210i) q^{44} +(-2.00000 + 1.73642i) q^{46} -0.290319 q^{47} +(2.54421 + 0.736303i) q^{48} +(4.12311 - 5.65685i) q^{49} +1.35576i q^{51} +(9.24726 + 1.31119i) q^{52} +9.49980 q^{53} +(-3.41433 - 3.93261i) q^{54} +(-3.75850 + 6.47099i) q^{56} -3.70861 q^{57} +(-3.30210 - 3.80335i) q^{58} -8.05650 q^{59} -6.45101i q^{61} +(-8.10887 - 9.33976i) q^{62} +(6.04090 - 3.07221i) q^{63} +(3.28078 - 7.29634i) q^{64} +(-2.18650 + 1.89834i) q^{66} -2.39871i q^{67} +(4.05444 + 0.574888i) q^{68} +1.24012i q^{69} -9.65719i q^{71} +(-6.08356 + 3.93481i) q^{72} +4.09499i q^{73} +(-3.43845 - 3.96039i) q^{74} +(-1.57258 + 11.0907i) q^{76} +(-3.70861 - 7.29226i) q^{77} +(3.30210 - 2.86692i) q^{78} +1.35576i q^{79} +5.24621 q^{81} +(-9.06134 + 7.86715i) q^{82} -12.4536 q^{83} +(1.13413 + 3.31516i) q^{84} +(4.56155 - 3.96039i) q^{86} -2.35829 q^{87} +(4.74990 + 7.34376i) q^{88} -2.82843i q^{89} +(5.60083 + 11.0129i) q^{91} +(3.70861 + 0.525853i) q^{92} -5.79119 q^{93} +(0.269170 + 0.310029i) q^{94} +(-1.57258 - 3.39960i) q^{96} +6.14249i q^{97} +(-9.86364 + 0.841745i) q^{98} -7.92077i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 12 q^{4} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 12 q^{4} - 8 q^{9} + 4 q^{14} - 12 q^{16} - 8 q^{21} + 24 q^{29} + 28 q^{36} - 32 q^{44} - 32 q^{46} - 20 q^{56} + 36 q^{64} - 88 q^{74} - 48 q^{81} - 40 q^{84} + 40 q^{86}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.927153 1.06789i −0.655596 0.755112i
\(3\) −0.662153 −0.382294 −0.191147 0.981561i \(-0.561221\pi\)
−0.191147 + 0.981561i \(0.561221\pi\)
\(4\) −0.280776 + 1.98019i −0.140388 + 0.990097i
\(5\) 0 0
\(6\) 0.613917 + 0.707107i 0.250631 + 0.288675i
\(7\) −2.35829 + 1.19935i −0.891352 + 0.453313i
\(8\) 2.37495 1.53610i 0.839672 0.543094i
\(9\) −2.56155 −0.853851
\(10\) 0 0
\(11\) 3.09218i 0.932326i 0.884699 + 0.466163i \(0.154364\pi\)
−0.884699 + 0.466163i \(0.845636\pi\)
\(12\) 0.185917 1.31119i 0.0536696 0.378508i
\(13\) 4.66988i 1.29519i −0.761984 0.647596i \(-0.775775\pi\)
0.761984 0.647596i \(-0.224225\pi\)
\(14\) 3.46728 + 1.40642i 0.926668 + 0.375880i
\(15\) 0 0
\(16\) −3.84233 1.11198i −0.960582 0.277996i
\(17\) 2.04750i 0.496590i −0.968684 0.248295i \(-0.920130\pi\)
0.968684 0.248295i \(-0.0798703\pi\)
\(18\) 2.37495 + 2.73546i 0.559781 + 0.644753i
\(19\) 5.60083 1.28492 0.642459 0.766320i \(-0.277914\pi\)
0.642459 + 0.766320i \(0.277914\pi\)
\(20\) 0 0
\(21\) 1.56155 0.794156i 0.340759 0.173299i
\(22\) 3.30210 2.86692i 0.704011 0.611229i
\(23\) 1.87285i 0.390517i −0.980752 0.195258i \(-0.937445\pi\)
0.980752 0.195258i \(-0.0625545\pi\)
\(24\) −1.57258 + 1.01714i −0.321002 + 0.207622i
\(25\) 0 0
\(26\) −4.98691 + 4.32969i −0.978014 + 0.849122i
\(27\) 3.68260 0.708717
\(28\) −1.71280 5.00663i −0.323688 0.946164i
\(29\) 3.56155 0.661364 0.330682 0.943742i \(-0.392721\pi\)
0.330682 + 0.943742i \(0.392721\pi\)
\(30\) 0 0
\(31\) 8.74599 1.57083 0.785414 0.618971i \(-0.212450\pi\)
0.785414 + 0.618971i \(0.212450\pi\)
\(32\) 2.37495 + 5.13416i 0.419836 + 0.907600i
\(33\) 2.04750i 0.356423i
\(34\) −2.18650 + 1.89834i −0.374981 + 0.325563i
\(35\) 0 0
\(36\) 0.719224 5.07237i 0.119871 0.845395i
\(37\) 3.70861 0.609692 0.304846 0.952402i \(-0.401395\pi\)
0.304846 + 0.952402i \(0.401395\pi\)
\(38\) −5.19283 5.98107i −0.842388 0.970258i
\(39\) 3.09218i 0.495144i
\(40\) 0 0
\(41\) 8.48528i 1.32518i −0.748983 0.662589i \(-0.769458\pi\)
0.748983 0.662589i \(-0.230542\pi\)
\(42\) −2.29587 0.931263i −0.354260 0.143697i
\(43\) 4.27156i 0.651407i 0.945472 + 0.325703i \(0.105601\pi\)
−0.945472 + 0.325703i \(0.894399\pi\)
\(44\) −6.12311 0.868210i −0.923093 0.130888i
\(45\) 0 0
\(46\) −2.00000 + 1.73642i −0.294884 + 0.256021i
\(47\) −0.290319 −0.0423474 −0.0211737 0.999776i \(-0.506740\pi\)
−0.0211737 + 0.999776i \(0.506740\pi\)
\(48\) 2.54421 + 0.736303i 0.367225 + 0.106276i
\(49\) 4.12311 5.65685i 0.589015 0.808122i
\(50\) 0 0
\(51\) 1.35576i 0.189844i
\(52\) 9.24726 + 1.31119i 1.28236 + 0.181830i
\(53\) 9.49980 1.30490 0.652449 0.757833i \(-0.273742\pi\)
0.652449 + 0.757833i \(0.273742\pi\)
\(54\) −3.41433 3.93261i −0.464632 0.535161i
\(55\) 0 0
\(56\) −3.75850 + 6.47099i −0.502251 + 0.864722i
\(57\) −3.70861 −0.491217
\(58\) −3.30210 3.80335i −0.433587 0.499404i
\(59\) −8.05650 −1.04887 −0.524434 0.851451i \(-0.675723\pi\)
−0.524434 + 0.851451i \(0.675723\pi\)
\(60\) 0 0
\(61\) 6.45101i 0.825967i −0.910738 0.412984i \(-0.864487\pi\)
0.910738 0.412984i \(-0.135513\pi\)
\(62\) −8.10887 9.33976i −1.02983 1.18615i
\(63\) 6.04090 3.07221i 0.761081 0.387062i
\(64\) 3.28078 7.29634i 0.410097 0.912042i
\(65\) 0 0
\(66\) −2.18650 + 1.89834i −0.269139 + 0.233670i
\(67\) 2.39871i 0.293049i −0.989207 0.146524i \(-0.953191\pi\)
0.989207 0.146524i \(-0.0468086\pi\)
\(68\) 4.05444 + 0.574888i 0.491673 + 0.0697154i
\(69\) 1.24012i 0.149292i
\(70\) 0 0
\(71\) 9.65719i 1.14610i −0.819521 0.573049i \(-0.805760\pi\)
0.819521 0.573049i \(-0.194240\pi\)
\(72\) −6.08356 + 3.93481i −0.716954 + 0.463722i
\(73\) 4.09499i 0.479282i 0.970862 + 0.239641i \(0.0770298\pi\)
−0.970862 + 0.239641i \(0.922970\pi\)
\(74\) −3.43845 3.96039i −0.399711 0.460386i
\(75\) 0 0
\(76\) −1.57258 + 11.0907i −0.180387 + 1.27219i
\(77\) −3.70861 7.29226i −0.422635 0.831030i
\(78\) 3.30210 2.86692i 0.373890 0.324615i
\(79\) 1.35576i 0.152534i 0.997087 + 0.0762672i \(0.0243002\pi\)
−0.997087 + 0.0762672i \(0.975700\pi\)
\(80\) 0 0
\(81\) 5.24621 0.582912
\(82\) −9.06134 + 7.86715i −1.00066 + 0.868781i
\(83\) −12.4536 −1.36696 −0.683482 0.729968i \(-0.739535\pi\)
−0.683482 + 0.729968i \(0.739535\pi\)
\(84\) 1.13413 + 3.31516i 0.123744 + 0.361713i
\(85\) 0 0
\(86\) 4.56155 3.96039i 0.491885 0.427059i
\(87\) −2.35829 −0.252836
\(88\) 4.74990 + 7.34376i 0.506341 + 0.782848i
\(89\) 2.82843i 0.299813i −0.988700 0.149906i \(-0.952103\pi\)
0.988700 0.149906i \(-0.0478972\pi\)
\(90\) 0 0
\(91\) 5.60083 + 11.0129i 0.587127 + 1.15447i
\(92\) 3.70861 + 0.525853i 0.386649 + 0.0548240i
\(93\) −5.79119 −0.600518
\(94\) 0.269170 + 0.310029i 0.0277628 + 0.0319770i
\(95\) 0 0
\(96\) −1.57258 3.39960i −0.160501 0.346970i
\(97\) 6.14249i 0.623675i 0.950135 + 0.311837i \(0.100944\pi\)
−0.950135 + 0.311837i \(0.899056\pi\)
\(98\) −9.86364 + 0.841745i −0.996378 + 0.0850291i
\(99\) 7.92077i 0.796068i
\(100\) 0 0
\(101\) 2.38247i 0.237064i −0.992950 0.118532i \(-0.962181\pi\)
0.992950 0.118532i \(-0.0378189\pi\)
\(102\) 1.44780 1.25699i 0.143353 0.124461i
\(103\) 1.03399 0.101882 0.0509409 0.998702i \(-0.483778\pi\)
0.0509409 + 0.998702i \(0.483778\pi\)
\(104\) −7.17341 11.0907i −0.703411 1.08754i
\(105\) 0 0
\(106\) −8.80776 10.1447i −0.855486 0.985344i
\(107\) 14.6875i 1.41990i −0.704254 0.709948i \(-0.748718\pi\)
0.704254 0.709948i \(-0.251282\pi\)
\(108\) −1.03399 + 7.29226i −0.0994955 + 0.701698i
\(109\) −0.438447 −0.0419956 −0.0209978 0.999780i \(-0.506684\pi\)
−0.0209978 + 0.999780i \(0.506684\pi\)
\(110\) 0 0
\(111\) −2.45567 −0.233082
\(112\) 10.3950 1.98593i 0.982236 0.187652i
\(113\) −3.70861 −0.348877 −0.174438 0.984668i \(-0.555811\pi\)
−0.174438 + 0.984668i \(0.555811\pi\)
\(114\) 3.43845 + 3.96039i 0.322040 + 0.370924i
\(115\) 0 0
\(116\) −1.00000 + 7.05256i −0.0928477 + 0.654814i
\(117\) 11.9621i 1.10590i
\(118\) 7.46960 + 8.60345i 0.687633 + 0.792012i
\(119\) 2.45567 + 4.82860i 0.225111 + 0.442637i
\(120\) 0 0
\(121\) 1.43845 0.130768
\(122\) −6.88897 + 5.98107i −0.623698 + 0.541501i
\(123\) 5.61856i 0.506608i
\(124\) −2.45567 + 17.3188i −0.220526 + 1.55527i
\(125\) 0 0
\(126\) −8.88161 3.60261i −0.791237 0.320946i
\(127\) 17.0862i 1.51616i 0.652163 + 0.758079i \(0.273862\pi\)
−0.652163 + 0.758079i \(0.726138\pi\)
\(128\) −10.8335 + 3.26131i −0.957552 + 0.288262i
\(129\) 2.82843i 0.249029i
\(130\) 0 0
\(131\) 5.60083 0.489347 0.244673 0.969606i \(-0.421319\pi\)
0.244673 + 0.969606i \(0.421319\pi\)
\(132\) 4.05444 + 0.574888i 0.352893 + 0.0500376i
\(133\) −13.2084 + 6.71737i −1.14531 + 0.582470i
\(134\) −2.56155 + 2.22397i −0.221284 + 0.192121i
\(135\) 0 0
\(136\) −3.14516 4.86270i −0.269695 0.416973i
\(137\) 13.2084 1.12847 0.564235 0.825614i \(-0.309171\pi\)
0.564235 + 0.825614i \(0.309171\pi\)
\(138\) 1.32431 1.14978i 0.112732 0.0978755i
\(139\) 14.3468 1.21688 0.608441 0.793599i \(-0.291795\pi\)
0.608441 + 0.793599i \(0.291795\pi\)
\(140\) 0 0
\(141\) 0.192236 0.0161892
\(142\) −10.3128 + 8.95369i −0.865432 + 0.751377i
\(143\) 14.4401 1.20754
\(144\) 9.84233 + 2.84840i 0.820194 + 0.237367i
\(145\) 0 0
\(146\) 4.37300 3.79668i 0.361912 0.314216i
\(147\) −2.73013 + 3.74571i −0.225177 + 0.308941i
\(148\) −1.04129 + 7.34376i −0.0855935 + 0.603654i
\(149\) 2.00000 0.163846 0.0819232 0.996639i \(-0.473894\pi\)
0.0819232 + 0.996639i \(0.473894\pi\)
\(150\) 0 0
\(151\) 18.9337i 1.54080i 0.637558 + 0.770402i \(0.279945\pi\)
−0.637558 + 0.770402i \(0.720055\pi\)
\(152\) 13.3017 8.60345i 1.07891 0.697832i
\(153\) 5.24477i 0.424014i
\(154\) −4.34888 + 10.7214i −0.350443 + 0.863957i
\(155\) 0 0
\(156\) −6.12311 0.868210i −0.490241 0.0695124i
\(157\) 2.62238i 0.209289i −0.994510 0.104644i \(-0.966630\pi\)
0.994510 0.104644i \(-0.0333705\pi\)
\(158\) 1.44780 1.25699i 0.115181 0.100001i
\(159\) −6.29033 −0.498855
\(160\) 0 0
\(161\) 2.24621 + 4.41674i 0.177026 + 0.348088i
\(162\) −4.86404 5.60237i −0.382155 0.440164i
\(163\) 15.7392i 1.23279i −0.787436 0.616396i \(-0.788592\pi\)
0.787436 0.616396i \(-0.211408\pi\)
\(164\) 16.8025 + 2.38247i 1.31205 + 0.186039i
\(165\) 0 0
\(166\) 11.5464 + 13.2991i 0.896175 + 1.03221i
\(167\) 8.39919 0.649949 0.324974 0.945723i \(-0.394644\pi\)
0.324974 + 0.945723i \(0.394644\pi\)
\(168\) 2.48871 4.28479i 0.192008 0.330578i
\(169\) −8.80776 −0.677520
\(170\) 0 0
\(171\) −14.3468 −1.09713
\(172\) −8.45851 1.19935i −0.644955 0.0914498i
\(173\) 8.76487i 0.666381i 0.942860 + 0.333190i \(0.108125\pi\)
−0.942860 + 0.333190i \(0.891875\pi\)
\(174\) 2.18650 + 2.51840i 0.165758 + 0.190919i
\(175\) 0 0
\(176\) 3.43845 11.8812i 0.259183 0.895576i
\(177\) 5.33464 0.400976
\(178\) −3.02045 + 2.62238i −0.226392 + 0.196556i
\(179\) 1.73642i 0.129786i 0.997892 + 0.0648931i \(0.0206706\pi\)
−0.997892 + 0.0648931i \(0.979329\pi\)
\(180\) 0 0
\(181\) 9.27944i 0.689735i 0.938651 + 0.344868i \(0.112076\pi\)
−0.938651 + 0.344868i \(0.887924\pi\)
\(182\) 6.56779 16.1918i 0.486837 1.20021i
\(183\) 4.27156i 0.315763i
\(184\) −2.87689 4.44793i −0.212087 0.327906i
\(185\) 0 0
\(186\) 5.36932 + 6.18435i 0.393697 + 0.453459i
\(187\) 6.33122 0.462984
\(188\) 0.0815148 0.574888i 0.00594508 0.0419280i
\(189\) −8.68466 + 4.41674i −0.631716 + 0.321270i
\(190\) 0 0
\(191\) 13.7245i 0.993067i −0.868018 0.496534i \(-0.834606\pi\)
0.868018 0.496534i \(-0.165394\pi\)
\(192\) −2.17238 + 4.83129i −0.156778 + 0.348669i
\(193\) 3.70861 0.266952 0.133476 0.991052i \(-0.457386\pi\)
0.133476 + 0.991052i \(0.457386\pi\)
\(194\) 6.55950 5.69502i 0.470944 0.408879i
\(195\) 0 0
\(196\) 10.0440 + 9.75286i 0.717428 + 0.696633i
\(197\) −11.1258 −0.792683 −0.396341 0.918103i \(-0.629720\pi\)
−0.396341 + 0.918103i \(0.629720\pi\)
\(198\) −8.45851 + 7.34376i −0.601120 + 0.521899i
\(199\) 6.29033 0.445909 0.222955 0.974829i \(-0.428430\pi\)
0.222955 + 0.974829i \(0.428430\pi\)
\(200\) 0 0
\(201\) 1.58831i 0.112031i
\(202\) −2.54421 + 2.20891i −0.179010 + 0.155418i
\(203\) −8.39919 + 4.27156i −0.589508 + 0.299805i
\(204\) −2.68466 0.380664i −0.187964 0.0266518i
\(205\) 0 0
\(206\) −0.958664 1.10418i −0.0667933 0.0769322i
\(207\) 4.79741i 0.333443i
\(208\) −5.19283 + 17.9432i −0.360058 + 1.24414i
\(209\) 17.3188i 1.19796i
\(210\) 0 0
\(211\) 25.1181i 1.72920i −0.502461 0.864600i \(-0.667572\pi\)
0.502461 0.864600i \(-0.332428\pi\)
\(212\) −2.66732 + 18.8114i −0.183192 + 1.29197i
\(213\) 6.39454i 0.438147i
\(214\) −15.6847 + 13.6176i −1.07218 + 0.930879i
\(215\) 0 0
\(216\) 8.74599 5.65685i 0.595090 0.384900i
\(217\) −20.6256 + 10.4895i −1.40016 + 0.712076i
\(218\) 0.406507 + 0.468213i 0.0275322 + 0.0317114i
\(219\) 2.71151i 0.183227i
\(220\) 0 0
\(221\) −9.56155 −0.643180
\(222\) 2.27678 + 2.62238i 0.152807 + 0.176003i
\(223\) 19.1567 1.28283 0.641413 0.767196i \(-0.278349\pi\)
0.641413 + 0.767196i \(0.278349\pi\)
\(224\) −11.7585 9.25946i −0.785648 0.618674i
\(225\) 0 0
\(226\) 3.43845 + 3.96039i 0.228722 + 0.263441i
\(227\) −14.0683 −0.933743 −0.466871 0.884325i \(-0.654619\pi\)
−0.466871 + 0.884325i \(0.654619\pi\)
\(228\) 1.04129 7.34376i 0.0689611 0.486353i
\(229\) 8.03932i 0.531253i −0.964076 0.265627i \(-0.914421\pi\)
0.964076 0.265627i \(-0.0855788\pi\)
\(230\) 0 0
\(231\) 2.45567 + 4.82860i 0.161571 + 0.317698i
\(232\) 8.45851 5.47091i 0.555328 0.359183i
\(233\) 7.41722 0.485918 0.242959 0.970037i \(-0.421882\pi\)
0.242959 + 0.970037i \(0.421882\pi\)
\(234\) 12.7742 11.0907i 0.835079 0.725024i
\(235\) 0 0
\(236\) 2.26208 15.9534i 0.147249 1.03848i
\(237\) 0.897718i 0.0583131i
\(238\) 2.87963 7.09923i 0.186659 0.460175i
\(239\) 3.09218i 0.200016i −0.994987 0.100008i \(-0.968113\pi\)
0.994987 0.100008i \(-0.0318869\pi\)
\(240\) 0 0
\(241\) 18.9071i 1.21791i 0.793204 + 0.608956i \(0.208411\pi\)
−0.793204 + 0.608956i \(0.791589\pi\)
\(242\) −1.33366 1.53610i −0.0857309 0.0987444i
\(243\) −14.5216 −0.931561
\(244\) 12.7742 + 1.81129i 0.817787 + 0.115956i
\(245\) 0 0
\(246\) 6.00000 5.20926i 0.382546 0.332130i
\(247\) 26.1552i 1.66422i
\(248\) 20.7713 13.4347i 1.31898 0.853107i
\(249\) 8.24621 0.522582
\(250\) 0 0
\(251\) −3.14516 −0.198521 −0.0992605 0.995061i \(-0.531648\pi\)
−0.0992605 + 0.995061i \(0.531648\pi\)
\(252\) 4.38742 + 12.8247i 0.276381 + 0.807883i
\(253\) 5.79119 0.364089
\(254\) 18.2462 15.8415i 1.14487 0.993987i
\(255\) 0 0
\(256\) 13.5270 + 8.54521i 0.845437 + 0.534076i
\(257\) 28.0193i 1.74779i −0.486111 0.873897i \(-0.661585\pi\)
0.486111 0.873897i \(-0.338415\pi\)
\(258\) −3.02045 + 2.62238i −0.188045 + 0.163262i
\(259\) −8.74599 + 4.44793i −0.543450 + 0.276381i
\(260\) 0 0
\(261\) −9.12311 −0.564706
\(262\) −5.19283 5.98107i −0.320814 0.369512i
\(263\) 11.9935i 0.739553i 0.929121 + 0.369776i \(0.120566\pi\)
−0.929121 + 0.369776i \(0.879434\pi\)
\(264\) −3.14516 4.86270i −0.193571 0.299278i
\(265\) 0 0
\(266\) 19.4196 + 7.87709i 1.19069 + 0.482976i
\(267\) 1.87285i 0.114617i
\(268\) 4.74990 + 0.673500i 0.290146 + 0.0411406i
\(269\) 16.5246i 1.00752i 0.863843 + 0.503761i \(0.168051\pi\)
−0.863843 + 0.503761i \(0.831949\pi\)
\(270\) 0 0
\(271\) −8.74599 −0.531281 −0.265641 0.964072i \(-0.585583\pi\)
−0.265641 + 0.964072i \(0.585583\pi\)
\(272\) −2.27678 + 7.86715i −0.138050 + 0.477016i
\(273\) −3.70861 7.29226i −0.224455 0.441348i
\(274\) −12.2462 14.1051i −0.739821 0.852122i
\(275\) 0 0
\(276\) −2.45567 0.348195i −0.147814 0.0209589i
\(277\) −2.08258 −0.125130 −0.0625651 0.998041i \(-0.519928\pi\)
−0.0625651 + 0.998041i \(0.519928\pi\)
\(278\) −13.3017 15.3208i −0.797783 0.918882i
\(279\) −22.4033 −1.34125
\(280\) 0 0
\(281\) −20.0540 −1.19632 −0.598160 0.801377i \(-0.704101\pi\)
−0.598160 + 0.801377i \(0.704101\pi\)
\(282\) −0.178232 0.205287i −0.0106136 0.0122246i
\(283\) −19.5285 −1.16085 −0.580425 0.814314i \(-0.697113\pi\)
−0.580425 + 0.814314i \(0.697113\pi\)
\(284\) 19.1231 + 2.71151i 1.13475 + 0.160899i
\(285\) 0 0
\(286\) −13.3882 15.4204i −0.791659 0.911828i
\(287\) 10.1768 + 20.0108i 0.600720 + 1.18120i
\(288\) −6.08356 13.1514i −0.358477 0.774955i
\(289\) 12.8078 0.753398
\(290\) 0 0
\(291\) 4.06727i 0.238427i
\(292\) −8.10887 1.14978i −0.474536 0.0672856i
\(293\) 15.1594i 0.885622i −0.896615 0.442811i \(-0.853981\pi\)
0.896615 0.442811i \(-0.146019\pi\)
\(294\) 6.53125 0.557364i 0.380910 0.0325062i
\(295\) 0 0
\(296\) 8.80776 5.69681i 0.511941 0.331120i
\(297\) 11.3873i 0.660755i
\(298\) −1.85431 2.13578i −0.107417 0.123722i
\(299\) −8.74599 −0.505794
\(300\) 0 0
\(301\) −5.12311 10.0736i −0.295291 0.580632i
\(302\) 20.2191 17.5544i 1.16348 1.01014i
\(303\) 1.57756i 0.0906284i
\(304\) −21.5202 6.22803i −1.23427 0.357202i
\(305\) 0 0
\(306\) 5.60083 4.86270i 0.320178 0.277982i
\(307\) −26.1500 −1.49246 −0.746231 0.665687i \(-0.768139\pi\)
−0.746231 + 0.665687i \(0.768139\pi\)
\(308\) 15.4814 5.29627i 0.882133 0.301783i
\(309\) −0.684658 −0.0389489
\(310\) 0 0
\(311\) −19.9477 −1.13113 −0.565564 0.824704i \(-0.691341\pi\)
−0.565564 + 0.824704i \(0.691341\pi\)
\(312\) 4.74990 + 7.34376i 0.268910 + 0.415759i
\(313\) 11.3873i 0.643646i −0.946800 0.321823i \(-0.895704\pi\)
0.946800 0.321823i \(-0.104296\pi\)
\(314\) −2.80042 + 2.43135i −0.158037 + 0.137209i
\(315\) 0 0
\(316\) −2.68466 0.380664i −0.151024 0.0214140i
\(317\) 31.7515 1.78334 0.891670 0.452686i \(-0.149534\pi\)
0.891670 + 0.452686i \(0.149534\pi\)
\(318\) 5.83209 + 6.71737i 0.327047 + 0.376692i
\(319\) 11.0129i 0.616607i
\(320\) 0 0
\(321\) 9.72540i 0.542819i
\(322\) 2.63401 6.49370i 0.146788 0.361880i
\(323\) 11.4677i 0.638079i
\(324\) −1.47301 + 10.3885i −0.0818340 + 0.577140i
\(325\) 0 0
\(326\) −16.8078 + 14.5927i −0.930896 + 0.808213i
\(327\) 0.290319 0.0160547
\(328\) −13.0343 20.1521i −0.719697 1.11271i
\(329\) 0.684658 0.348195i 0.0377464 0.0191966i
\(330\) 0 0
\(331\) 1.73642i 0.0954423i −0.998861 0.0477211i \(-0.984804\pi\)
0.998861 0.0477211i \(-0.0151959\pi\)
\(332\) 3.49668 24.6606i 0.191905 1.35343i
\(333\) −9.49980 −0.520586
\(334\) −7.78733 8.96941i −0.426104 0.490784i
\(335\) 0 0
\(336\) −6.88309 + 1.31499i −0.375503 + 0.0717384i
\(337\) −5.33464 −0.290596 −0.145298 0.989388i \(-0.546414\pi\)
−0.145298 + 0.989388i \(0.546414\pi\)
\(338\) 8.16614 + 9.40572i 0.444179 + 0.511604i
\(339\) 2.45567 0.133374
\(340\) 0 0
\(341\) 27.0442i 1.46452i
\(342\) 13.3017 + 15.3208i 0.719273 + 0.828455i
\(343\) −2.93893 + 18.2856i −0.158687 + 0.987329i
\(344\) 6.56155 + 10.1447i 0.353775 + 0.546968i
\(345\) 0 0
\(346\) 9.35991 8.12637i 0.503192 0.436876i
\(347\) 4.27156i 0.229309i −0.993405 0.114655i \(-0.963424\pi\)
0.993405 0.114655i \(-0.0365761\pi\)
\(348\) 0.662153 4.66988i 0.0354952 0.250332i
\(349\) 36.3236i 1.94436i −0.234241 0.972179i \(-0.575260\pi\)
0.234241 0.972179i \(-0.424740\pi\)
\(350\) 0 0
\(351\) 17.1973i 0.917924i
\(352\) −15.8757 + 7.34376i −0.846179 + 0.391424i
\(353\) 27.1216i 1.44353i −0.692136 0.721767i \(-0.743330\pi\)
0.692136 0.721767i \(-0.256670\pi\)
\(354\) −4.94602 5.69681i −0.262878 0.302782i
\(355\) 0 0
\(356\) 5.60083 + 0.794156i 0.296843 + 0.0420902i
\(357\) −1.62603 3.19727i −0.0860586 0.169218i
\(358\) 1.85431 1.60993i 0.0980031 0.0850873i
\(359\) 26.4738i 1.39724i −0.715495 0.698618i \(-0.753799\pi\)
0.715495 0.698618i \(-0.246201\pi\)
\(360\) 0 0
\(361\) 12.3693 0.651017
\(362\) 9.90941 8.60345i 0.520827 0.452187i
\(363\) −0.952473 −0.0499919
\(364\) −23.3803 + 7.99855i −1.22546 + 0.419238i
\(365\) 0 0
\(366\) 4.56155 3.96039i 0.238436 0.207013i
\(367\) 31.8191 1.66094 0.830472 0.557061i \(-0.188071\pi\)
0.830472 + 0.557061i \(0.188071\pi\)
\(368\) −2.08258 + 7.19612i −0.108562 + 0.375124i
\(369\) 21.7355i 1.13150i
\(370\) 0 0
\(371\) −22.4033 + 11.3936i −1.16312 + 0.591527i
\(372\) 1.62603 11.4677i 0.0843057 0.594571i
\(373\) 22.7082 1.17579 0.587893 0.808938i \(-0.299957\pi\)
0.587893 + 0.808938i \(0.299957\pi\)
\(374\) −5.87000 6.76104i −0.303531 0.349605i
\(375\) 0 0
\(376\) −0.689494 + 0.445960i −0.0355579 + 0.0229986i
\(377\) 16.6320i 0.856593i
\(378\) 12.7686 + 5.17927i 0.656746 + 0.266393i
\(379\) 5.20926i 0.267582i −0.991010 0.133791i \(-0.957285\pi\)
0.991010 0.133791i \(-0.0427150\pi\)
\(380\) 0 0
\(381\) 11.3137i 0.579619i
\(382\) −14.6562 + 12.7247i −0.749877 + 0.651051i
\(383\) 26.9752 1.37837 0.689185 0.724586i \(-0.257969\pi\)
0.689185 + 0.724586i \(0.257969\pi\)
\(384\) 7.17341 2.15949i 0.366067 0.110201i
\(385\) 0 0
\(386\) −3.43845 3.96039i −0.175012 0.201578i
\(387\) 10.9418i 0.556204i
\(388\) −12.1633 1.72466i −0.617498 0.0875566i
\(389\) −16.9309 −0.858429 −0.429215 0.903203i \(-0.641210\pi\)
−0.429215 + 0.903203i \(0.641210\pi\)
\(390\) 0 0
\(391\) −3.83466 −0.193927
\(392\) 1.10266 19.7683i 0.0556928 0.998448i
\(393\) −3.70861 −0.187075
\(394\) 10.3153 + 11.8812i 0.519679 + 0.598564i
\(395\) 0 0
\(396\) 15.6847 + 2.22397i 0.788184 + 0.111758i
\(397\) 12.8599i 0.645418i 0.946498 + 0.322709i \(0.104593\pi\)
−0.946498 + 0.322709i \(0.895407\pi\)
\(398\) −5.83209 6.71737i −0.292336 0.336712i
\(399\) 8.74599 4.44793i 0.437847 0.222675i
\(400\) 0 0
\(401\) 17.5616 0.876982 0.438491 0.898736i \(-0.355513\pi\)
0.438491 + 0.898736i \(0.355513\pi\)
\(402\) 1.69614 1.47261i 0.0845958 0.0734469i
\(403\) 40.8427i 2.03452i
\(404\) 4.71774 + 0.668940i 0.234717 + 0.0332810i
\(405\) 0 0
\(406\) 12.3489 + 5.00902i 0.612865 + 0.248594i
\(407\) 11.4677i 0.568432i
\(408\) 2.08258 + 3.21985i 0.103103 + 0.159406i
\(409\) 4.76493i 0.235611i −0.993037 0.117805i \(-0.962414\pi\)
0.993037 0.117805i \(-0.0375859\pi\)
\(410\) 0 0
\(411\) −8.74599 −0.431408
\(412\) −0.290319 + 2.04750i −0.0143030 + 0.100873i
\(413\) 18.9996 9.66259i 0.934909 0.475465i
\(414\) 5.12311 4.44793i 0.251787 0.218604i
\(415\) 0 0
\(416\) 23.9759 11.0907i 1.17552 0.543768i
\(417\) −9.49980 −0.465207
\(418\) 18.4945 16.0571i 0.904597 0.785380i
\(419\) −20.6372 −1.00819 −0.504095 0.863648i \(-0.668174\pi\)
−0.504095 + 0.863648i \(0.668174\pi\)
\(420\) 0 0
\(421\) 8.43845 0.411265 0.205632 0.978629i \(-0.434075\pi\)
0.205632 + 0.978629i \(0.434075\pi\)
\(422\) −26.8233 + 23.2883i −1.30574 + 1.13366i
\(423\) 0.743668 0.0361584
\(424\) 22.5616 14.5927i 1.09569 0.708683i
\(425\) 0 0
\(426\) 6.82867 5.92872i 0.330850 0.287247i
\(427\) 7.73704 + 15.2134i 0.374421 + 0.736227i
\(428\) 29.0841 + 4.12391i 1.40584 + 0.199337i
\(429\) −9.56155 −0.461636
\(430\) 0 0
\(431\) 15.4609i 0.744724i 0.928087 + 0.372362i \(0.121452\pi\)
−0.928087 + 0.372362i \(0.878548\pi\)
\(432\) −14.1498 4.09499i −0.680781 0.197020i
\(433\) 38.5088i 1.85062i 0.379218 + 0.925308i \(0.376193\pi\)
−0.379218 + 0.925308i \(0.623807\pi\)
\(434\) 30.3248 + 12.3005i 1.45564 + 0.590443i
\(435\) 0 0
\(436\) 0.123106 0.868210i 0.00589569 0.0415797i
\(437\) 10.4895i 0.501782i
\(438\) −2.89560 + 2.51398i −0.138357 + 0.120123i
\(439\) 23.7823 1.13507 0.567534 0.823350i \(-0.307898\pi\)
0.567534 + 0.823350i \(0.307898\pi\)
\(440\) 0 0
\(441\) −10.5616 + 14.4903i −0.502931 + 0.690016i
\(442\) 8.86502 + 10.2107i 0.421666 + 0.485673i
\(443\) 13.8664i 0.658812i −0.944188 0.329406i \(-0.893152\pi\)
0.944188 0.329406i \(-0.106848\pi\)
\(444\) 0.689494 4.86270i 0.0327219 0.230773i
\(445\) 0 0
\(446\) −17.7612 20.4572i −0.841015 0.968677i
\(447\) −1.32431 −0.0626376
\(448\) 1.01384 + 21.1417i 0.0478996 + 0.998852i
\(449\) −18.6847 −0.881784 −0.440892 0.897560i \(-0.645338\pi\)
−0.440892 + 0.897560i \(0.645338\pi\)
\(450\) 0 0
\(451\) 26.2380 1.23550
\(452\) 1.04129 7.34376i 0.0489782 0.345422i
\(453\) 12.5370i 0.589041i
\(454\) 13.0434 + 15.0233i 0.612158 + 0.705080i
\(455\) 0 0
\(456\) −8.80776 + 5.69681i −0.412461 + 0.266777i
\(457\) 37.5427 1.75617 0.878086 0.478504i \(-0.158821\pi\)
0.878086 + 0.478504i \(0.158821\pi\)
\(458\) −8.58511 + 7.45368i −0.401156 + 0.348287i
\(459\) 7.54011i 0.351942i
\(460\) 0 0
\(461\) 19.7012i 0.917578i 0.888545 + 0.458789i \(0.151717\pi\)
−0.888545 + 0.458789i \(0.848283\pi\)
\(462\) 2.87963 7.09923i 0.133972 0.330286i
\(463\) 27.2069i 1.26441i 0.774800 + 0.632206i \(0.217850\pi\)
−0.774800 + 0.632206i \(0.782150\pi\)
\(464\) −13.6847 3.96039i −0.635294 0.183856i
\(465\) 0 0
\(466\) −6.87689 7.92077i −0.318566 0.366923i
\(467\) −31.0297 −1.43588 −0.717941 0.696104i \(-0.754915\pi\)
−0.717941 + 0.696104i \(0.754915\pi\)
\(468\) −23.6873 3.35869i −1.09495 0.155255i
\(469\) 2.87689 + 5.65685i 0.132843 + 0.261209i
\(470\) 0 0
\(471\) 1.73642i 0.0800100i
\(472\) −19.1338 + 12.3756i −0.880704 + 0.569634i
\(473\) −13.2084 −0.607323
\(474\) −0.958664 + 0.832322i −0.0440329 + 0.0382298i
\(475\) 0 0
\(476\) −10.2510 + 3.50694i −0.469856 + 0.160740i
\(477\) −24.3342 −1.11419
\(478\) −3.30210 + 2.86692i −0.151035 + 0.131130i
\(479\) −3.83466 −0.175210 −0.0876050 0.996155i \(-0.527921\pi\)
−0.0876050 + 0.996155i \(0.527921\pi\)
\(480\) 0 0
\(481\) 17.3188i 0.789667i
\(482\) 20.1907 17.5297i 0.919659 0.798458i
\(483\) −1.48734 2.92456i −0.0676762 0.133072i
\(484\) −0.403882 + 2.84840i −0.0183583 + 0.129473i
\(485\) 0 0
\(486\) 13.4637 + 15.5075i 0.610728 + 0.703433i
\(487\) 38.9699i 1.76589i −0.469473 0.882947i \(-0.655556\pi\)
0.469473 0.882947i \(-0.344444\pi\)
\(488\) −9.90941 15.3208i −0.448578 0.693541i
\(489\) 10.4218i 0.471290i
\(490\) 0 0
\(491\) 6.56502i 0.296275i 0.988967 + 0.148138i \(0.0473278\pi\)
−0.988967 + 0.148138i \(0.952672\pi\)
\(492\) −11.1258 1.57756i −0.501591 0.0711218i
\(493\) 7.29226i 0.328427i
\(494\) −27.9309 + 24.2499i −1.25667 + 1.09105i
\(495\) 0 0
\(496\) −33.6050 9.72540i −1.50891 0.436683i
\(497\) 11.5824 + 22.7745i 0.519541 + 1.02158i
\(498\) −7.64550 8.80604i −0.342603 0.394608i
\(499\) 34.0139i 1.52267i 0.648357 + 0.761336i \(0.275456\pi\)
−0.648357 + 0.761336i \(0.724544\pi\)
\(500\) 0 0
\(501\) −5.56155 −0.248472
\(502\) 2.91605 + 3.35869i 0.130149 + 0.149906i
\(503\) 7.81855 0.348612 0.174306 0.984692i \(-0.444232\pi\)
0.174306 + 0.984692i \(0.444232\pi\)
\(504\) 9.62760 16.5758i 0.428848 0.738344i
\(505\) 0 0
\(506\) −5.36932 6.18435i −0.238695 0.274928i
\(507\) 5.83209 0.259012
\(508\) −33.8340 4.79741i −1.50114 0.212851i
\(509\) 1.14235i 0.0506338i 0.999679 + 0.0253169i \(0.00805948\pi\)
−0.999679 + 0.0253169i \(0.991941\pi\)
\(510\) 0 0
\(511\) −4.91134 9.65719i −0.217265 0.427209i
\(512\) −3.41624 22.3680i −0.150978 0.988537i
\(513\) 20.6256 0.910644
\(514\) −29.9215 + 25.9781i −1.31978 + 1.14585i
\(515\) 0 0
\(516\) 5.60083 + 0.794156i 0.246563 + 0.0349608i
\(517\) 0.897718i 0.0394816i
\(518\) 12.8588 + 5.21585i 0.564982 + 0.229171i
\(519\) 5.80369i 0.254754i
\(520\) 0 0
\(521\) 2.82843i 0.123916i −0.998079 0.0619578i \(-0.980266\pi\)
0.998079 0.0619578i \(-0.0197344\pi\)
\(522\) 8.45851 + 9.74247i 0.370219 + 0.426416i
\(523\) −7.15640 −0.312927 −0.156464 0.987684i \(-0.550009\pi\)
−0.156464 + 0.987684i \(0.550009\pi\)
\(524\) −1.57258 + 11.0907i −0.0686985 + 0.484501i
\(525\) 0 0
\(526\) 12.8078 11.1198i 0.558445 0.484848i
\(527\) 17.9074i 0.780058i
\(528\) −2.27678 + 7.86715i −0.0990841 + 0.342374i
\(529\) 19.4924 0.847497
\(530\) 0 0
\(531\) 20.6372 0.895576
\(532\) −9.59309 28.0413i −0.415913 1.21574i
\(533\) −39.6252 −1.71636
\(534\) 2.00000 1.73642i 0.0865485 0.0751422i
\(535\) 0 0
\(536\) −3.68466 5.69681i −0.159153 0.246065i
\(537\) 1.14978i 0.0496165i
\(538\) 17.6465 15.3208i 0.760793 0.660528i
\(539\) 17.4920 + 12.7494i 0.753433 + 0.549154i
\(540\) 0 0
\(541\) −23.5616 −1.01299 −0.506495 0.862243i \(-0.669059\pi\)
−0.506495 + 0.862243i \(0.669059\pi\)
\(542\) 8.10887 + 9.33976i 0.348306 + 0.401177i
\(543\) 6.14441i 0.263682i
\(544\) 10.5122 4.86270i 0.450706 0.208486i
\(545\) 0 0
\(546\) −4.34888 + 10.7214i −0.186115 + 0.458835i
\(547\) 37.3923i 1.59878i 0.600812 + 0.799390i \(0.294844\pi\)
−0.600812 + 0.799390i \(0.705156\pi\)
\(548\) −3.70861 + 26.1552i −0.158424 + 1.11729i
\(549\) 16.5246i 0.705253i
\(550\) 0 0
\(551\) 19.9477 0.849799
\(552\) 1.90495 + 2.94521i 0.0810799 + 0.125357i
\(553\) −1.62603 3.19727i −0.0691458 0.135962i
\(554\) 1.93087 + 2.22397i 0.0820348 + 0.0944873i
\(555\) 0 0
\(556\) −4.02825 + 28.4095i −0.170836 + 1.20483i
\(557\) 9.49980 0.402519 0.201260 0.979538i \(-0.435496\pi\)
0.201260 + 0.979538i \(0.435496\pi\)
\(558\) 20.7713 + 23.9243i 0.879319 + 1.01280i
\(559\) 19.9477 0.843696
\(560\) 0 0
\(561\) −4.19224 −0.176996
\(562\) 18.5931 + 21.4154i 0.784302 + 0.903355i
\(563\) −27.9277 −1.17701 −0.588506 0.808493i \(-0.700284\pi\)
−0.588506 + 0.808493i \(0.700284\pi\)
\(564\) −0.0539753 + 0.380664i −0.00227277 + 0.0160289i
\(565\) 0 0
\(566\) 18.1059 + 20.8543i 0.761048 + 0.876571i
\(567\) −12.3721 + 6.29206i −0.519580 + 0.264242i
\(568\) −14.8344 22.9354i −0.622439 0.962346i
\(569\) −13.8617 −0.581114 −0.290557 0.956858i \(-0.593841\pi\)
−0.290557 + 0.956858i \(0.593841\pi\)
\(570\) 0 0
\(571\) 17.5780i 0.735615i −0.929902 0.367807i \(-0.880109\pi\)
0.929902 0.367807i \(-0.119891\pi\)
\(572\) −4.05444 + 28.5942i −0.169524 + 1.19558i
\(573\) 9.08770i 0.379644i
\(574\) 11.9338 29.4208i 0.498108 1.22800i
\(575\) 0 0
\(576\) −8.40388 + 18.6899i −0.350162 + 0.778748i
\(577\) 18.9316i 0.788132i 0.919082 + 0.394066i \(0.128932\pi\)
−0.919082 + 0.394066i \(0.871068\pi\)
\(578\) −11.8748 13.6773i −0.493925 0.568900i
\(579\) −2.45567 −0.102054
\(580\) 0 0
\(581\) 29.3693 14.9363i 1.21844 0.619662i
\(582\) −4.34339 + 3.77098i −0.180039 + 0.156312i
\(583\) 29.3751i 1.21659i
\(584\) 6.29033 + 9.72540i 0.260296 + 0.402440i
\(585\) 0 0
\(586\) −16.1886 + 14.0551i −0.668744 + 0.580610i
\(587\) 9.06134 0.374002 0.187001 0.982360i \(-0.440123\pi\)
0.187001 + 0.982360i \(0.440123\pi\)
\(588\) −6.65066 6.45789i −0.274269 0.266319i
\(589\) 48.9848 2.01839
\(590\) 0 0
\(591\) 7.36701 0.303038
\(592\) −14.2497 4.12391i −0.585659 0.169492i
\(593\) 31.2165i 1.28191i 0.767579 + 0.640955i \(0.221461\pi\)
−0.767579 + 0.640955i \(0.778539\pi\)
\(594\) 12.1603 10.5577i 0.498944 0.433188i
\(595\) 0 0
\(596\) −0.561553 + 3.96039i −0.0230021 + 0.162224i
\(597\) −4.16516 −0.170469
\(598\) 8.10887 + 9.33976i 0.331596 + 0.381931i
\(599\) 14.4858i 0.591873i −0.955208 0.295937i \(-0.904368\pi\)
0.955208 0.295937i \(-0.0956317\pi\)
\(600\) 0 0
\(601\) 39.4024i 1.60726i −0.595130 0.803630i \(-0.702899\pi\)
0.595130 0.803630i \(-0.297101\pi\)
\(602\) −6.00758 + 14.8107i −0.244851 + 0.603638i
\(603\) 6.14441i 0.250220i
\(604\) −37.4924 5.31614i −1.52555 0.216311i
\(605\) 0 0
\(606\) 1.68466 1.46264i 0.0684346 0.0594156i
\(607\) 10.6302 0.431466 0.215733 0.976452i \(-0.430786\pi\)
0.215733 + 0.976452i \(0.430786\pi\)
\(608\) 13.3017 + 28.7556i 0.539455 + 1.16619i
\(609\) 5.56155 2.82843i 0.225365 0.114614i
\(610\) 0 0
\(611\) 1.35576i 0.0548480i
\(612\) −10.3857 1.47261i −0.419815 0.0595266i
\(613\) −13.6650 −0.551923 −0.275961 0.961169i \(-0.588996\pi\)
−0.275961 + 0.961169i \(0.588996\pi\)
\(614\) 24.2451 + 27.9254i 0.978452 + 1.12698i
\(615\) 0 0
\(616\) −20.0094 11.6220i −0.806203 0.468262i
\(617\) −35.9166 −1.44595 −0.722974 0.690875i \(-0.757226\pi\)
−0.722974 + 0.690875i \(0.757226\pi\)
\(618\) 0.634783 + 0.731140i 0.0255347 + 0.0294107i
\(619\) 10.5122 0.422520 0.211260 0.977430i \(-0.432243\pi\)
0.211260 + 0.977430i \(0.432243\pi\)
\(620\) 0 0
\(621\) 6.89697i 0.276766i
\(622\) 18.4945 + 21.3019i 0.741563 + 0.854128i
\(623\) 3.39228 + 6.67026i 0.135909 + 0.267238i
\(624\) 3.43845 11.8812i 0.137648 0.475627i
\(625\) 0 0
\(626\) −12.1603 + 10.5577i −0.486024 + 0.421971i
\(627\) 11.4677i 0.457975i
\(628\) 5.19283 + 0.736303i 0.207216 + 0.0293817i
\(629\) 7.59336i 0.302767i
\(630\) 0 0
\(631\) 32.2775i 1.28495i 0.766308 + 0.642474i \(0.222092\pi\)
−0.766308 + 0.642474i \(0.777908\pi\)
\(632\) 2.08258 + 3.21985i 0.0828406 + 0.128079i
\(633\) 16.6320i 0.661063i
\(634\) −29.4384 33.9071i −1.16915 1.34662i
\(635\) 0 0
\(636\) 1.76618 12.4561i 0.0700334 0.493915i
\(637\) −26.4168 19.2544i −1.04667 0.762887i
\(638\) 11.7606 10.2107i 0.465607 0.404245i
\(639\) 24.7374i 0.978597i
\(640\) 0 0
\(641\) −17.8617 −0.705496 −0.352748 0.935718i \(-0.614753\pi\)
−0.352748 + 0.935718i \(0.614753\pi\)
\(642\) 10.3857 9.01693i 0.409889 0.355870i
\(643\) 0.499124 0.0196835 0.00984176 0.999952i \(-0.496867\pi\)
0.00984176 + 0.999952i \(0.496867\pi\)
\(644\) −9.37668 + 3.20782i −0.369493 + 0.126406i
\(645\) 0 0
\(646\) −12.2462 + 10.6323i −0.481821 + 0.418322i
\(647\) 5.87787 0.231083 0.115541 0.993303i \(-0.463140\pi\)
0.115541 + 0.993303i \(0.463140\pi\)
\(648\) 12.4595 8.05872i 0.489455 0.316576i
\(649\) 24.9121i 0.977886i
\(650\) 0 0
\(651\) 13.6573 6.94568i 0.535273 0.272223i
\(652\) 31.1667 + 4.41921i 1.22058 + 0.173069i
\(653\) 11.1258 0.435387 0.217694 0.976017i \(-0.430147\pi\)
0.217694 + 0.976017i \(0.430147\pi\)
\(654\) −0.269170 0.310029i −0.0105254 0.0121231i
\(655\) 0 0
\(656\) −9.43549 + 32.6032i −0.368394 + 1.27294i
\(657\) 10.4895i 0.409236i
\(658\) −1.00662 0.408309i −0.0392420 0.0159176i
\(659\) 19.6950i 0.767210i 0.923497 + 0.383605i \(0.125318\pi\)
−0.923497 + 0.383605i \(0.874682\pi\)
\(660\) 0 0
\(661\) 42.3286i 1.64639i −0.567756 0.823197i \(-0.692188\pi\)
0.567756 0.823197i \(-0.307812\pi\)
\(662\) −1.85431 + 1.60993i −0.0720696 + 0.0625716i
\(663\) 6.33122 0.245884
\(664\) −29.5767 + 19.1300i −1.14780 + 0.742390i
\(665\) 0 0
\(666\) 8.80776 + 10.1447i 0.341294 + 0.393101i
\(667\) 6.67026i 0.258274i
\(668\) −2.35829 + 16.6320i −0.0912452 + 0.643512i
\(669\) −12.6847 −0.490417
\(670\) 0 0
\(671\) 19.9477 0.770071
\(672\) 7.78593 + 6.13118i 0.300349 + 0.236516i
\(673\) −5.79119 −0.223234 −0.111617 0.993751i \(-0.535603\pi\)
−0.111617 + 0.993751i \(0.535603\pi\)
\(674\) 4.94602 + 5.69681i 0.190514 + 0.219433i
\(675\) 0 0
\(676\) 2.47301 17.4411i 0.0951159 0.670811i
\(677\) 6.46532i 0.248482i −0.992252 0.124241i \(-0.960350\pi\)
0.992252 0.124241i \(-0.0396496\pi\)
\(678\) −2.27678 2.62238i −0.0874392 0.100712i
\(679\) −7.36701 14.4858i −0.282720 0.555914i
\(680\) 0 0
\(681\) 9.31534 0.356965
\(682\) 28.8802 25.0741i 1.10588 0.960135i
\(683\) 5.32326i 0.203689i −0.994800 0.101845i \(-0.967526\pi\)
0.994800 0.101845i \(-0.0324744\pi\)
\(684\) 4.02825 28.4095i 0.154024 1.08626i
\(685\) 0 0
\(686\) 22.2518 13.8151i 0.849579 0.527462i
\(687\) 5.32326i 0.203095i
\(688\) 4.74990 16.4127i 0.181088 0.625730i
\(689\) 44.3629i 1.69009i
\(690\) 0 0
\(691\) −12.9678 −0.493320 −0.246660 0.969102i \(-0.579333\pi\)
−0.246660 + 0.969102i \(0.579333\pi\)
\(692\) −17.3561 2.46097i −0.659781 0.0935520i
\(693\) 9.49980 + 18.6795i 0.360868 + 0.709576i
\(694\) −4.56155 + 3.96039i −0.173154 + 0.150334i
\(695\) 0 0
\(696\) −5.60083 + 3.62258i −0.212299 + 0.137314i
\(697\) −17.3736 −0.658071
\(698\) −38.7896 + 33.6775i −1.46821 + 1.27471i
\(699\) −4.91134 −0.185764
\(700\) 0 0
\(701\) 47.6695 1.80045 0.900226 0.435423i \(-0.143401\pi\)
0.900226 + 0.435423i \(0.143401\pi\)
\(702\) −18.3648 + 15.9445i −0.693135 + 0.601787i
\(703\) 20.7713 0.783404
\(704\) 22.5616 + 10.1447i 0.850321 + 0.382344i
\(705\) 0 0
\(706\) −28.9628 + 25.1458i −1.09003 + 0.946375i
\(707\) 2.85742 + 5.61856i 0.107464 + 0.211308i
\(708\) −1.49784 + 10.5636i −0.0562923 + 0.397005i
\(709\) −10.1922 −0.382777 −0.191389 0.981514i \(-0.561299\pi\)
−0.191389 + 0.981514i \(0.561299\pi\)
\(710\) 0 0
\(711\) 3.47284i 0.130242i
\(712\) −4.34475 6.71737i −0.162827 0.251744i
\(713\) 16.3800i 0.613434i
\(714\) −1.90676 + 4.70078i −0.0713585 + 0.175922i
\(715\) 0 0
\(716\) −3.43845 0.487546i −0.128501 0.0182204i
\(717\) 2.04750i 0.0764651i
\(718\) −28.2711 + 24.5453i −1.05507 + 0.916022i
\(719\) −36.0607 −1.34484 −0.672418 0.740172i \(-0.734744\pi\)
−0.672418 + 0.740172i \(0.734744\pi\)
\(720\) 0 0
\(721\) −2.43845 + 1.24012i −0.0908125 + 0.0461843i
\(722\) −11.4682 13.2091i −0.426804 0.491590i
\(723\) 12.5194i 0.465601i
\(724\) −18.3751 2.60545i −0.682904 0.0968307i
\(725\) 0 0
\(726\) 0.883088 + 1.01714i 0.0327745 + 0.0377494i
\(727\) −6.20393 −0.230091 −0.115045 0.993360i \(-0.536701\pi\)
−0.115045 + 0.993360i \(0.536701\pi\)
\(728\) 30.2187 + 17.5517i 1.11998 + 0.650511i
\(729\) −6.12311 −0.226782
\(730\) 0 0
\(731\) 8.74599 0.323482
\(732\) −8.45851 1.19935i −0.312636 0.0443294i
\(733\) 11.0644i 0.408674i 0.978901 + 0.204337i \(0.0655038\pi\)
−0.978901 + 0.204337i \(0.934496\pi\)
\(734\) −29.5012 33.9793i −1.08891 1.25420i
\(735\) 0 0
\(736\) 9.61553 4.44793i 0.354433 0.163953i
\(737\) 7.41722 0.273217
\(738\) 23.2111 20.1521i 0.854413 0.741810i
\(739\) 14.6996i 0.540732i 0.962758 + 0.270366i \(0.0871447\pi\)
−0.962758 + 0.270366i \(0.912855\pi\)
\(740\) 0 0
\(741\) 17.3188i 0.636220i
\(742\) 32.9384 + 13.3607i 1.20921 + 0.490485i
\(743\) 4.79741i 0.176000i 0.996120 + 0.0880000i \(0.0280475\pi\)
−0.996120 + 0.0880000i \(0.971952\pi\)
\(744\) −13.7538 + 8.89586i −0.504238 + 0.326138i
\(745\) 0 0
\(746\) −21.0540 24.2499i −0.770841 0.887851i
\(747\) 31.9006 1.16718
\(748\) −1.77766 + 12.5370i −0.0649975 + 0.458399i
\(749\) 17.6155 + 34.6375i 0.643657 + 1.26563i
\(750\) 0 0
\(751\) 24.3567i 0.888790i 0.895831 + 0.444395i \(0.146581\pi\)
−0.895831 + 0.444395i \(0.853419\pi\)
\(752\) 1.11550 + 0.322830i 0.0406782 + 0.0117724i
\(753\) 2.08258 0.0758934
\(754\) −17.7612 + 15.4204i −0.646823 + 0.561578i
\(755\) 0 0
\(756\) −6.30755 18.4374i −0.229403 0.670562i
\(757\) 28.4994 1.03583 0.517914 0.855433i \(-0.326709\pi\)
0.517914 + 0.855433i \(0.326709\pi\)
\(758\) −5.56292 + 4.82978i −0.202054 + 0.175425i
\(759\) −3.83466 −0.139189
\(760\) 0 0
\(761\) 3.52482i 0.127775i −0.997957 0.0638873i \(-0.979650\pi\)
0.997957 0.0638873i \(-0.0203498\pi\)
\(762\) −12.0818 + 10.4895i −0.437677 + 0.379996i
\(763\) 1.03399 0.525853i 0.0374329 0.0190372i
\(764\) 27.1771 + 3.85350i 0.983232 + 0.139415i
\(765\) 0 0
\(766\) −25.0101 28.8066i −0.903653 1.04082i
\(767\) 37.6229i 1.35848i
\(768\) −8.95694 5.65824i −0.323206 0.204174i
\(769\) 8.83348i 0.318543i 0.987235 + 0.159272i \(0.0509146\pi\)
−0.987235 + 0.159272i \(0.949085\pi\)
\(770\) 0 0
\(771\) 18.5531i 0.668172i
\(772\) −1.04129 + 7.34376i −0.0374769 + 0.264308i
\(773\) 48.4234i 1.74167i 0.491575 + 0.870835i \(0.336421\pi\)
−0.491575 + 0.870835i \(0.663579\pi\)
\(774\) −11.6847 + 10.1447i −0.419996 + 0.364645i
\(775\) 0 0
\(776\) 9.43549 + 14.5881i 0.338714 + 0.523682i
\(777\) 5.79119 2.94521i 0.207758 0.105659i
\(778\) 15.6975 + 18.0803i 0.562783 + 0.648210i
\(779\) 47.5246i 1.70275i
\(780\) 0 0
\(781\) 29.8617 1.06854
\(782\) 3.55531 + 4.09499i 0.127138 + 0.146437i
\(783\) 13.1158 0.468720
\(784\) −22.1327 + 17.1507i −0.790452 + 0.612524i
\(785\) 0 0
\(786\) 3.43845 + 3.96039i 0.122645 + 0.141262i
\(787\) −37.4882 −1.33631 −0.668154 0.744023i \(-0.732915\pi\)
−0.668154 + 0.744023i \(0.732915\pi\)
\(788\) 3.12387 22.0313i 0.111283 0.784832i
\(789\) 7.94156i 0.282727i
\(790\) 0 0
\(791\) 8.74599 4.44793i 0.310972 0.158150i
\(792\) −12.1671 18.8114i −0.432340 0.668435i
\(793\) −30.1254 −1.06979
\(794\) 13.7329 11.9231i 0.487363 0.423133i
\(795\) 0 0
\(796\) −1.76618 + 12.4561i −0.0626004 + 0.441493i
\(797\) 47.2737i 1.67452i 0.546805 + 0.837260i \(0.315844\pi\)
−0.546805 + 0.837260i \(0.684156\pi\)
\(798\) −12.8588 5.21585i −0.455196 0.184639i
\(799\) 0.594427i 0.0210293i
\(800\) 0 0
\(801\) 7.24517i 0.255995i
\(802\) −16.2822 18.7538i −0.574946 0.662220i
\(803\) −12.6624 −0.446847
\(804\) −3.14516 0.445960i −0.110921 0.0157278i
\(805\) 0 0
\(806\) −43.6155 + 37.8674i −1.53629 + 1.33382i
\(807\) 10.9418i 0.385170i
\(808\) −3.65971 5.65824i −0.128748 0.199056i
\(809\) −10.0540 −0.353479 −0.176739 0.984258i \(-0.556555\pi\)
−0.176739 + 0.984258i \(0.556555\pi\)
\(810\) 0 0
\(811\) 3.14516 0.110442 0.0552208 0.998474i \(-0.482414\pi\)
0.0552208 + 0.998474i \(0.482414\pi\)
\(812\) −6.10022 17.8314i −0.214076 0.625758i
\(813\) 5.79119 0.203106
\(814\) 12.2462 10.6323i 0.429229 0.372661i
\(815\) 0 0
\(816\) 1.50758 5.20926i 0.0527758 0.182361i
\(817\) 23.9243i 0.837005i
\(818\) −5.08842 + 4.41782i −0.177913 + 0.154465i
\(819\) −14.3468 28.2102i −0.501319 0.985746i
\(820\) 0 0
\(821\) −7.06913 −0.246714 −0.123357 0.992362i \(-0.539366\pi\)
−0.123357 + 0.992362i \(0.539366\pi\)
\(822\) 8.10887 + 9.33976i 0.282829 + 0.325761i
\(823\) 3.21985i 0.112237i −0.998424 0.0561185i \(-0.982128\pi\)
0.998424 0.0561185i \(-0.0178725\pi\)
\(824\) 2.45567 1.58831i 0.0855473 0.0553314i
\(825\) 0 0
\(826\) −27.9341 11.3308i −0.971952 0.394248i
\(827\) 2.39871i 0.0834112i −0.999130 0.0417056i \(-0.986721\pi\)
0.999130 0.0417056i \(-0.0132792\pi\)
\(828\) −9.49980 1.34700i −0.330141 0.0468115i
\(829\) 25.9018i 0.899607i −0.893128 0.449803i \(-0.851494\pi\)
0.893128 0.449803i \(-0.148506\pi\)
\(830\) 0 0
\(831\) 1.37899 0.0478366
\(832\) −34.0730 15.3208i −1.18127 0.531154i
\(833\) −11.5824 8.44204i −0.401306 0.292499i
\(834\) 8.80776 + 10.1447i 0.304988 + 0.351284i
\(835\) 0 0
\(836\) −34.2945 4.86270i −1.18610 0.168180i
\(837\) 32.2080 1.11327
\(838\) 19.1338 + 22.0382i 0.660966 + 0.761297i
\(839\) 47.2623 1.63168 0.815838 0.578280i \(-0.196276\pi\)
0.815838 + 0.578280i \(0.196276\pi\)
\(840\) 0 0
\(841\) −16.3153 −0.562598
\(842\) −7.82373 9.01133i −0.269623 0.310551i
\(843\) 13.2788 0.457346
\(844\) 49.7386 + 7.05256i 1.71207 + 0.242759i
\(845\) 0 0
\(846\) −0.689494 0.794156i −0.0237053 0.0273036i
\(847\) −3.39228 + 1.72521i −0.116560 + 0.0592788i
\(848\) −36.5014 10.5636i −1.25346 0.362756i
\(849\) 12.9309 0.443786
\(850\) 0 0
\(851\) 6.94568i 0.238095i
\(852\) −12.6624 1.79544i −0.433808 0.0615107i
\(853\) 45.2262i 1.54851i −0.632871 0.774257i \(-0.718124\pi\)
0.632871 0.774257i \(-0.281876\pi\)
\(854\) 9.07280 22.3674i 0.310465 0.765398i
\(855\) 0 0
\(856\) −22.5616 34.8821i −0.771138 1.19225i
\(857\) 14.5845i 0.498198i −0.968478 0.249099i \(-0.919866\pi\)
0.968478 0.249099i \(-0.0801344\pi\)
\(858\) 8.86502 + 10.2107i 0.302647 + 0.348587i
\(859\) 3.14516 0.107312 0.0536558 0.998559i \(-0.482913\pi\)
0.0536558 + 0.998559i \(0.482913\pi\)
\(860\) 0 0
\(861\) −6.73863 13.2502i −0.229652 0.451566i
\(862\) 16.5105 14.3346i 0.562350 0.488238i
\(863\) 28.8492i 0.982038i −0.871149 0.491019i \(-0.836625\pi\)
0.871149 0.491019i \(-0.163375\pi\)
\(864\) 8.74599 + 18.9071i 0.297545 + 0.643232i
\(865\) 0 0
\(866\) 41.1232 35.7035i 1.39742 1.21326i
\(867\) −8.48071 −0.288020
\(868\) −14.9801 43.7879i −0.508458 1.48626i
\(869\) −4.19224 −0.142212
\(870\) 0 0
\(871\) −11.2017 −0.379554
\(872\) −1.04129 + 0.673500i −0.0352625 + 0.0228076i
\(873\) 15.7343i 0.532525i
\(874\) −11.2017 + 9.72540i −0.378902 + 0.328966i
\(875\) 0 0
\(876\) 5.36932 + 0.761329i 0.181412 + 0.0257229i
\(877\) −3.70861 −0.125231 −0.0626154 0.998038i \(-0.519944\pi\)
−0.0626154 + 0.998038i \(0.519944\pi\)
\(878\) −22.0498 25.3969i −0.744146 0.857103i
\(879\) 10.0379i 0.338569i
\(880\) 0 0
\(881\) 54.0883i 1.82228i −0.412095 0.911141i \(-0.635203\pi\)
0.412095 0.911141i \(-0.364797\pi\)
\(882\) 25.2662 2.15617i 0.850759 0.0726022i
\(883\) 19.7155i 0.663479i −0.943371 0.331740i \(-0.892364\pi\)
0.943371 0.331740i \(-0.107636\pi\)
\(884\) 2.68466 18.9337i 0.0902948 0.636810i
\(885\) 0 0
\(886\) −14.8078 + 12.8563i −0.497477 + 0.431914i
\(887\) −15.3110 −0.514095 −0.257047 0.966399i \(-0.582750\pi\)
−0.257047 + 0.966399i \(0.582750\pi\)
\(888\) −5.83209 + 3.77216i −0.195712 + 0.126585i
\(889\) −20.4924 40.2944i −0.687294 1.35143i
\(890\) 0 0
\(891\) 16.2222i 0.543464i
\(892\) −5.37874 + 37.9339i −0.180094 + 1.27012i
\(893\) −1.62603 −0.0544130
\(894\) 1.22783 + 1.41421i 0.0410649 + 0.0472984i
\(895\) 0 0
\(896\) 21.6370 20.6843i 0.722842 0.691013i
\(897\) 5.79119 0.193362
\(898\) 17.3235 + 19.9532i 0.578094 + 0.665845i
\(899\) 31.1493 1.03889
\(900\) 0 0
\(901\) 19.4508i 0.648000i
\(902\) −24.3266 28.0193i −0.809988 0.932940i
\(903\) 3.39228 + 6.67026i 0.112888 + 0.221972i
\(904\) −8.80776 + 5.69681i −0.292942 + 0.189473i
\(905\) 0 0
\(906\) −13.3882 + 11.6237i −0.444792 + 0.386173i
\(907\) 2.62926i 0.0873033i 0.999047 + 0.0436516i \(0.0138992\pi\)
−0.999047 + 0.0436516i \(0.986101\pi\)
\(908\) 3.95003 27.8579i 0.131086 0.924495i
\(909\) 6.10281i 0.202418i
\(910\) 0 0
\(911\) 40.3652i 1.33736i 0.743551 + 0.668679i \(0.233140\pi\)
−0.743551 + 0.668679i \(0.766860\pi\)
\(912\) 14.2497 + 4.12391i 0.471855 + 0.136556i
\(913\) 38.5088i 1.27446i
\(914\) −34.8078 40.0914i −1.15134 1.32611i
\(915\) 0 0
\(916\) 15.9194 + 2.25725i 0.525992 + 0.0745817i
\(917\) −13.2084 + 6.71737i −0.436180 + 0.221827i
\(918\) −8.05200 + 6.99083i −0.265756 + 0.230732i
\(919\) 11.7743i 0.388398i 0.980962 + 0.194199i \(0.0622107\pi\)
−0.980962 + 0.194199i \(0.937789\pi\)
\(920\) 0 0
\(921\) 17.3153 0.570560
\(922\) 21.0387 18.2660i 0.692874 0.601560i
\(923\) −45.0979 −1.48442
\(924\) −10.2510 + 3.50694i −0.337235 + 0.115370i
\(925\) 0 0
\(926\) 29.0540 25.2250i 0.954773 0.828943i
\(927\) −2.64861 −0.0869919
\(928\) 8.45851 + 18.2856i 0.277664 + 0.600254i
\(929\) 17.6670i 0.579634i 0.957082 + 0.289817i \(0.0935944\pi\)
−0.957082 + 0.289817i \(0.906406\pi\)
\(930\) 0 0
\(931\) 23.0928 31.6831i 0.756837 1.03837i
\(932\) −2.08258 + 14.6875i −0.0682172 + 0.481106i
\(933\) 13.2084 0.432424
\(934\) 28.7692 + 33.1363i 0.941358 + 1.08425i
\(935\) 0 0
\(936\) 18.3751 + 28.4095i 0.600608 + 0.928593i
\(937\) 38.7609i 1.26626i −0.774045 0.633131i \(-0.781769\pi\)
0.774045 0.633131i \(-0.218231\pi\)
\(938\) 3.37358 8.31697i 0.110151 0.271559i
\(939\) 7.54011i 0.246062i
\(940\) 0 0
\(941\) 37.9119i 1.23589i 0.786220 + 0.617946i \(0.212035\pi\)
−0.786220 + 0.617946i \(0.787965\pi\)
\(942\) 1.85431 1.60993i 0.0604165 0.0524542i
\(943\) −15.8917 −0.517504
\(944\) 30.9557 + 8.95869i 1.00752 + 0.291581i
\(945\) 0 0
\(946\) 12.2462 + 14.1051i 0.398159 + 0.458597i
\(947\) 41.5991i 1.35179i −0.736998 0.675895i \(-0.763757\pi\)
0.736998 0.675895i \(-0.236243\pi\)
\(948\) 1.77766 + 0.252058i 0.0577356 + 0.00818647i
\(949\) 19.1231 0.620762
\(950\) 0 0
\(951\) −21.0243 −0.681761
\(952\) 13.2493 + 7.69552i 0.429413 + 0.249413i
\(953\) 24.7908 0.803053 0.401526 0.915848i \(-0.368480\pi\)
0.401526 + 0.915848i \(0.368480\pi\)
\(954\) 22.5616 + 25.9863i 0.730457 + 0.841337i
\(955\) 0 0
\(956\) 6.12311 + 0.868210i 0.198035 + 0.0280799i
\(957\) 7.29226i 0.235725i
\(958\) 3.55531 + 4.09499i 0.114867 + 0.132303i
\(959\) −31.1493 + 15.8415i −1.00586 + 0.511550i
\(960\) 0 0
\(961\) 45.4924 1.46750
\(962\) −18.4945 + 16.0571i −0.596287 + 0.517703i
\(963\) 37.6229i 1.21238i
\(964\) −37.4396 5.30866i −1.20585 0.170980i
\(965\) 0 0
\(966\) −1.74412 + 4.29982i −0.0561161 + 0.138345i
\(967\) 18.1379i 0.583277i −0.956529 0.291638i \(-0.905800\pi\)
0.956529 0.291638i \(-0.0942004\pi\)
\(968\) 3.41624 2.20960i 0.109802 0.0710193i
\(969\) 7.59336i 0.243934i
\(970\) 0 0
\(971\) 32.9155 1.05631 0.528154 0.849148i \(-0.322884\pi\)
0.528154 + 0.849148i \(0.322884\pi\)
\(972\) 4.07732 28.7556i 0.130780 0.922335i
\(973\) −33.8340 + 17.2069i −1.08467 + 0.551628i
\(974\) −41.6155 + 36.1310i −1.33345 + 1.15771i
\(975\) 0 0
\(976\) −7.17341 + 24.7869i −0.229615 + 0.793409i
\(977\) 5.79119 0.185277 0.0926383 0.995700i \(-0.470470\pi\)
0.0926383 + 0.995700i \(0.470470\pi\)
\(978\) 11.1293 9.66259i 0.355876 0.308975i
\(979\) 8.74599 0.279523
\(980\) 0 0
\(981\) 1.12311 0.0358580
\(982\) 7.01071 6.08677i 0.223721 0.194237i
\(983\) 38.4406 1.22607 0.613033 0.790057i \(-0.289949\pi\)
0.613033 + 0.790057i \(0.289949\pi\)
\(984\) 8.63068 + 13.3438i 0.275136 + 0.425385i
\(985\) 0 0
\(986\) −7.78733 + 6.76104i −0.247999 + 0.215315i
\(987\) −0.453349 + 0.230559i −0.0144303 + 0.00733876i
\(988\) 51.7924 + 7.34376i 1.64773 + 0.233636i
\(989\) 8.00000 0.254385
\(990\) 0 0
\(991\) 50.2361i 1.59580i −0.602787 0.797902i \(-0.705943\pi\)
0.602787 0.797902i \(-0.294057\pi\)
\(992\) 20.7713 + 44.9033i 0.659489 + 1.42568i
\(993\) 1.14978i 0.0364871i
\(994\) 13.5820 33.4841i 0.430796 1.06205i
\(995\) 0 0
\(996\) −2.31534 + 16.3291i −0.0733644 + 0.517407i
\(997\) 26.7987i 0.848724i −0.905493 0.424362i \(-0.860498\pi\)
0.905493 0.424362i \(-0.139502\pi\)
\(998\) 36.3231 31.5361i 1.14979 0.998258i
\(999\) 13.6573 0.432099
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 700.2.g.l.251.5 16
4.3 odd 2 inner 700.2.g.l.251.8 16
5.2 odd 4 140.2.c.b.139.14 yes 16
5.3 odd 4 140.2.c.b.139.3 yes 16
5.4 even 2 inner 700.2.g.l.251.12 16
7.6 odd 2 inner 700.2.g.l.251.6 16
20.3 even 4 140.2.c.b.139.16 yes 16
20.7 even 4 140.2.c.b.139.1 16
20.19 odd 2 inner 700.2.g.l.251.9 16
28.27 even 2 inner 700.2.g.l.251.7 16
35.2 odd 12 980.2.s.f.619.3 32
35.3 even 12 980.2.s.f.19.8 32
35.12 even 12 980.2.s.f.619.4 32
35.13 even 4 140.2.c.b.139.4 yes 16
35.17 even 12 980.2.s.f.19.9 32
35.18 odd 12 980.2.s.f.19.7 32
35.23 odd 12 980.2.s.f.619.14 32
35.27 even 4 140.2.c.b.139.13 yes 16
35.32 odd 12 980.2.s.f.19.10 32
35.33 even 12 980.2.s.f.619.13 32
35.34 odd 2 inner 700.2.g.l.251.11 16
40.3 even 4 2240.2.e.f.2239.7 16
40.13 odd 4 2240.2.e.f.2239.11 16
40.27 even 4 2240.2.e.f.2239.9 16
40.37 odd 4 2240.2.e.f.2239.5 16
140.3 odd 12 980.2.s.f.19.3 32
140.23 even 12 980.2.s.f.619.9 32
140.27 odd 4 140.2.c.b.139.2 yes 16
140.47 odd 12 980.2.s.f.619.7 32
140.67 even 12 980.2.s.f.19.13 32
140.83 odd 4 140.2.c.b.139.15 yes 16
140.87 odd 12 980.2.s.f.19.14 32
140.103 odd 12 980.2.s.f.619.10 32
140.107 even 12 980.2.s.f.619.8 32
140.123 even 12 980.2.s.f.19.4 32
140.139 even 2 inner 700.2.g.l.251.10 16
280.13 even 4 2240.2.e.f.2239.6 16
280.27 odd 4 2240.2.e.f.2239.8 16
280.83 odd 4 2240.2.e.f.2239.10 16
280.237 even 4 2240.2.e.f.2239.12 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.c.b.139.1 16 20.7 even 4
140.2.c.b.139.2 yes 16 140.27 odd 4
140.2.c.b.139.3 yes 16 5.3 odd 4
140.2.c.b.139.4 yes 16 35.13 even 4
140.2.c.b.139.13 yes 16 35.27 even 4
140.2.c.b.139.14 yes 16 5.2 odd 4
140.2.c.b.139.15 yes 16 140.83 odd 4
140.2.c.b.139.16 yes 16 20.3 even 4
700.2.g.l.251.5 16 1.1 even 1 trivial
700.2.g.l.251.6 16 7.6 odd 2 inner
700.2.g.l.251.7 16 28.27 even 2 inner
700.2.g.l.251.8 16 4.3 odd 2 inner
700.2.g.l.251.9 16 20.19 odd 2 inner
700.2.g.l.251.10 16 140.139 even 2 inner
700.2.g.l.251.11 16 35.34 odd 2 inner
700.2.g.l.251.12 16 5.4 even 2 inner
980.2.s.f.19.3 32 140.3 odd 12
980.2.s.f.19.4 32 140.123 even 12
980.2.s.f.19.7 32 35.18 odd 12
980.2.s.f.19.8 32 35.3 even 12
980.2.s.f.19.9 32 35.17 even 12
980.2.s.f.19.10 32 35.32 odd 12
980.2.s.f.19.13 32 140.67 even 12
980.2.s.f.19.14 32 140.87 odd 12
980.2.s.f.619.3 32 35.2 odd 12
980.2.s.f.619.4 32 35.12 even 12
980.2.s.f.619.7 32 140.47 odd 12
980.2.s.f.619.8 32 140.107 even 12
980.2.s.f.619.9 32 140.23 even 12
980.2.s.f.619.10 32 140.103 odd 12
980.2.s.f.619.13 32 35.33 even 12
980.2.s.f.619.14 32 35.23 odd 12
2240.2.e.f.2239.5 16 40.37 odd 4
2240.2.e.f.2239.6 16 280.13 even 4
2240.2.e.f.2239.7 16 40.3 even 4
2240.2.e.f.2239.8 16 280.27 odd 4
2240.2.e.f.2239.9 16 40.27 even 4
2240.2.e.f.2239.10 16 280.83 odd 4
2240.2.e.f.2239.11 16 40.13 odd 4
2240.2.e.f.2239.12 16 280.237 even 4