Properties

Label 1150.2.e.f.1057.2
Level $1150$
Weight $2$
Character 1150.1057
Analytic conductor $9.183$
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] = [1150,2,Mod(643,1150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1150, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1150.643");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1150.e (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: \(9.18279623245\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: 16.0.12877254853348294656.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4x^{14} + 26x^{12} + 12x^{10} + 35x^{8} + 180x^{6} + 686x^{4} + 632x^{2} + 169 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1057.2
Root \(1.90419 + 1.19709i\) of defining polynomial
Character \(\chi\) \(=\) 1150.1057
Dual form 1150.2.e.f.643.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(-1.22474 + 1.22474i) q^{3} +1.00000i q^{4} +1.73205 q^{6} +(2.39417 - 2.39417i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(-1.22474 + 1.22474i) q^{3} +1.00000i q^{4} +1.73205 q^{6} +(2.39417 - 2.39417i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.14655i q^{11} +(-1.22474 - 1.22474i) q^{12} +(-0.896575 + 0.896575i) q^{13} -3.38587 q^{14} -1.00000 q^{16} +(3.91201 - 3.91201i) q^{17} +2.14655 q^{19} +5.86450i q^{21} +(1.51784 - 1.51784i) q^{22} +(-1.27671 - 4.62277i) q^{23} +1.73205i q^{24} +1.26795 q^{26} +(-3.67423 - 3.67423i) q^{27} +(2.39417 + 2.39417i) q^{28} +1.46410i q^{29} +1.26795 q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.62898 - 2.62898i) q^{33} -5.53242 q^{34} +(-1.75265 + 1.75265i) q^{37} +(-1.51784 - 1.51784i) q^{38} -2.19615i q^{39} +1.92820 q^{41} +(4.14682 - 4.14682i) q^{42} +(6.54099 + 6.54099i) q^{43} -2.14655 q^{44} +(-2.36603 + 4.17156i) q^{46} +(-0.896575 - 0.896575i) q^{47} +(1.22474 - 1.22474i) q^{48} -4.46410i q^{49} +9.58244i q^{51} +(-0.896575 - 0.896575i) q^{52} +(-1.11114 - 1.11114i) q^{53} +5.19615i q^{54} -3.38587i q^{56} +(-2.62898 + 2.62898i) q^{57} +(1.03528 - 1.03528i) q^{58} -7.46410i q^{59} +5.86450i q^{61} +(-0.896575 - 0.896575i) q^{62} -1.00000i q^{64} +3.71794i q^{66} +(0.876327 - 0.876327i) q^{67} +(3.91201 + 3.91201i) q^{68} +(7.22536 + 4.09808i) q^{69} +14.9282 q^{71} +(7.91688 - 7.91688i) q^{73} +2.47863 q^{74} +2.14655i q^{76} +(5.13922 + 5.13922i) q^{77} +(-1.55291 + 1.55291i) q^{78} +16.0221 q^{79} +9.00000 q^{81} +(-1.36345 - 1.36345i) q^{82} +(10.9226 + 10.9226i) q^{83} -5.86450 q^{84} -9.25036i q^{86} +(-1.79315 - 1.79315i) q^{87} +(1.51784 + 1.51784i) q^{88} +9.58244 q^{89} +4.29311i q^{91} +(4.62277 - 1.27671i) q^{92} +(-1.55291 + 1.55291i) q^{93} +1.26795i q^{94} -1.73205 q^{96} +(-6.54099 + 6.54099i) q^{97} +(-3.15660 + 3.15660i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{16} + 48 q^{26} + 48 q^{31} - 80 q^{41} - 24 q^{46} + 128 q^{71} + 144 q^{81}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).

\(n\) \(51\) \(277\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) −1.22474 + 1.22474i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) 1.73205 0.707107
\(7\) 2.39417 2.39417i 0.904911 0.904911i −0.0909447 0.995856i \(-0.528989\pi\)
0.995856 + 0.0909447i \(0.0289886\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 0 0
\(10\) 0 0
\(11\) 2.14655i 0.647210i 0.946192 + 0.323605i \(0.104895\pi\)
−0.946192 + 0.323605i \(0.895105\pi\)
\(12\) −1.22474 1.22474i −0.353553 0.353553i
\(13\) −0.896575 + 0.896575i −0.248665 + 0.248665i −0.820423 0.571757i \(-0.806262\pi\)
0.571757 + 0.820423i \(0.306262\pi\)
\(14\) −3.38587 −0.904911
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 3.91201 3.91201i 0.948803 0.948803i −0.0499492 0.998752i \(-0.515906\pi\)
0.998752 + 0.0499492i \(0.0159059\pi\)
\(18\) 0 0
\(19\) 2.14655 0.492453 0.246227 0.969212i \(-0.420809\pi\)
0.246227 + 0.969212i \(0.420809\pi\)
\(20\) 0 0
\(21\) 5.86450i 1.27974i
\(22\) 1.51784 1.51784i 0.323605 0.323605i
\(23\) −1.27671 4.62277i −0.266212 0.963915i
\(24\) 1.73205i 0.353553i
\(25\) 0 0
\(26\) 1.26795 0.248665
\(27\) −3.67423 3.67423i −0.707107 0.707107i
\(28\) 2.39417 + 2.39417i 0.452456 + 0.452456i
\(29\) 1.46410i 0.271877i 0.990717 + 0.135938i \(0.0434049\pi\)
−0.990717 + 0.135938i \(0.956595\pi\)
\(30\) 0 0
\(31\) 1.26795 0.227730 0.113865 0.993496i \(-0.463677\pi\)
0.113865 + 0.993496i \(0.463677\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) −2.62898 2.62898i −0.457647 0.457647i
\(34\) −5.53242 −0.948803
\(35\) 0 0
\(36\) 0 0
\(37\) −1.75265 + 1.75265i −0.288135 + 0.288135i −0.836342 0.548208i \(-0.815310\pi\)
0.548208 + 0.836342i \(0.315310\pi\)
\(38\) −1.51784 1.51784i −0.246227 0.246227i
\(39\) 2.19615i 0.351666i
\(40\) 0 0
\(41\) 1.92820 0.301135 0.150567 0.988600i \(-0.451890\pi\)
0.150567 + 0.988600i \(0.451890\pi\)
\(42\) 4.14682 4.14682i 0.639869 0.639869i
\(43\) 6.54099 + 6.54099i 0.997492 + 0.997492i 0.999997 0.00250455i \(-0.000797223\pi\)
−0.00250455 + 0.999997i \(0.500797\pi\)
\(44\) −2.14655 −0.323605
\(45\) 0 0
\(46\) −2.36603 + 4.17156i −0.348851 + 0.615063i
\(47\) −0.896575 0.896575i −0.130779 0.130779i 0.638687 0.769466i \(-0.279478\pi\)
−0.769466 + 0.638687i \(0.779478\pi\)
\(48\) 1.22474 1.22474i 0.176777 0.176777i
\(49\) 4.46410i 0.637729i
\(50\) 0 0
\(51\) 9.58244i 1.34181i
\(52\) −0.896575 0.896575i −0.124333 0.124333i
\(53\) −1.11114 1.11114i −0.152627 0.152627i 0.626663 0.779290i \(-0.284420\pi\)
−0.779290 + 0.626663i \(0.784420\pi\)
\(54\) 5.19615i 0.707107i
\(55\) 0 0
\(56\) 3.38587i 0.452456i
\(57\) −2.62898 + 2.62898i −0.348217 + 0.348217i
\(58\) 1.03528 1.03528i 0.135938 0.135938i
\(59\) 7.46410i 0.971743i −0.874030 0.485872i \(-0.838502\pi\)
0.874030 0.485872i \(-0.161498\pi\)
\(60\) 0 0
\(61\) 5.86450i 0.750872i 0.926848 + 0.375436i \(0.122507\pi\)
−0.926848 + 0.375436i \(0.877493\pi\)
\(62\) −0.896575 0.896575i −0.113865 0.113865i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 3.71794i 0.457647i
\(67\) 0.876327 0.876327i 0.107060 0.107060i −0.651547 0.758608i \(-0.725880\pi\)
0.758608 + 0.651547i \(0.225880\pi\)
\(68\) 3.91201 + 3.91201i 0.474401 + 0.474401i
\(69\) 7.22536 + 4.09808i 0.869831 + 0.493350i
\(70\) 0 0
\(71\) 14.9282 1.77165 0.885826 0.464018i \(-0.153593\pi\)
0.885826 + 0.464018i \(0.153593\pi\)
\(72\) 0 0
\(73\) 7.91688 7.91688i 0.926600 0.926600i −0.0708844 0.997485i \(-0.522582\pi\)
0.997485 + 0.0708844i \(0.0225821\pi\)
\(74\) 2.47863 0.288135
\(75\) 0 0
\(76\) 2.14655i 0.246227i
\(77\) 5.13922 + 5.13922i 0.585668 + 0.585668i
\(78\) −1.55291 + 1.55291i −0.175833 + 0.175833i
\(79\) 16.0221 1.80263 0.901313 0.433167i \(-0.142604\pi\)
0.901313 + 0.433167i \(0.142604\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) −1.36345 1.36345i −0.150567 0.150567i
\(83\) 10.9226 + 10.9226i 1.19891 + 1.19891i 0.974492 + 0.224422i \(0.0720495\pi\)
0.224422 + 0.974492i \(0.427950\pi\)
\(84\) −5.86450 −0.639869
\(85\) 0 0
\(86\) 9.25036i 0.997492i
\(87\) −1.79315 1.79315i −0.192246 0.192246i
\(88\) 1.51784 + 1.51784i 0.161803 + 0.161803i
\(89\) 9.58244 1.01574 0.507868 0.861435i \(-0.330434\pi\)
0.507868 + 0.861435i \(0.330434\pi\)
\(90\) 0 0
\(91\) 4.29311i 0.450040i
\(92\) 4.62277 1.27671i 0.481957 0.133106i
\(93\) −1.55291 + 1.55291i −0.161030 + 0.161030i
\(94\) 1.26795i 0.130779i
\(95\) 0 0
\(96\) −1.73205 −0.176777
\(97\) −6.54099 + 6.54099i −0.664137 + 0.664137i −0.956353 0.292215i \(-0.905608\pi\)
0.292215 + 0.956353i \(0.405608\pi\)
\(98\) −3.15660 + 3.15660i −0.318864 + 0.318864i
\(99\) 0 0
\(100\) 0 0
\(101\) −7.12436 −0.708900 −0.354450 0.935075i \(-0.615332\pi\)
−0.354450 + 0.935075i \(0.615332\pi\)
\(102\) 6.77581 6.77581i 0.670905 0.670905i
\(103\) 13.7235 + 13.7235i 1.35222 + 1.35222i 0.883177 + 0.469040i \(0.155400\pi\)
0.469040 + 0.883177i \(0.344600\pi\)
\(104\) 1.26795i 0.124333i
\(105\) 0 0
\(106\) 1.57139i 0.152627i
\(107\) 3.91201 3.91201i 0.378189 0.378189i −0.492260 0.870448i \(-0.663829\pi\)
0.870448 + 0.492260i \(0.163829\pi\)
\(108\) 3.67423 3.67423i 0.353553 0.353553i
\(109\) 4.29311 0.411205 0.205603 0.978636i \(-0.434085\pi\)
0.205603 + 0.978636i \(0.434085\pi\)
\(110\) 0 0
\(111\) 4.29311i 0.407484i
\(112\) −2.39417 + 2.39417i −0.226228 + 0.226228i
\(113\) −8.70035 8.70035i −0.818460 0.818460i 0.167424 0.985885i \(-0.446455\pi\)
−0.985885 + 0.167424i \(0.946455\pi\)
\(114\) 3.71794 0.348217
\(115\) 0 0
\(116\) −1.46410 −0.135938
\(117\) 0 0
\(118\) −5.27792 + 5.27792i −0.485872 + 0.485872i
\(119\) 18.7321i 1.71716i
\(120\) 0 0
\(121\) 6.39230 0.581119
\(122\) 4.14682 4.14682i 0.375436 0.375436i
\(123\) −2.36156 + 2.36156i −0.212934 + 0.212934i
\(124\) 1.26795i 0.113865i
\(125\) 0 0
\(126\) 0 0
\(127\) 1.55291 + 1.55291i 0.137799 + 0.137799i 0.772641 0.634843i \(-0.218935\pi\)
−0.634843 + 0.772641i \(0.718935\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −16.0221 −1.41067
\(130\) 0 0
\(131\) −14.0000 −1.22319 −0.611593 0.791173i \(-0.709471\pi\)
−0.611593 + 0.791173i \(0.709471\pi\)
\(132\) 2.62898 2.62898i 0.228823 0.228823i
\(133\) 5.13922 5.13922i 0.445627 0.445627i
\(134\) −1.23931 −0.107060
\(135\) 0 0
\(136\) 5.53242i 0.474401i
\(137\) −3.91201 + 3.91201i −0.334226 + 0.334226i −0.854189 0.519963i \(-0.825946\pi\)
0.519963 + 0.854189i \(0.325946\pi\)
\(138\) −2.21132 8.00688i −0.188240 0.681591i
\(139\) 2.07180i 0.175728i 0.996133 + 0.0878638i \(0.0280040\pi\)
−0.996133 + 0.0878638i \(0.971996\pi\)
\(140\) 0 0
\(141\) 2.19615 0.184949
\(142\) −10.5558 10.5558i −0.885826 0.885826i
\(143\) −1.92455 1.92455i −0.160939 0.160939i
\(144\) 0 0
\(145\) 0 0
\(146\) −11.1962 −0.926600
\(147\) 5.46739 + 5.46739i 0.450942 + 0.450942i
\(148\) −1.75265 1.75265i −0.144067 0.144067i
\(149\) 1.57139 0.128733 0.0643665 0.997926i \(-0.479497\pi\)
0.0643665 + 0.997926i \(0.479497\pi\)
\(150\) 0 0
\(151\) −8.19615 −0.666993 −0.333497 0.942751i \(-0.608229\pi\)
−0.333497 + 0.942751i \(0.608229\pi\)
\(152\) 1.51784 1.51784i 0.123113 0.123113i
\(153\) 0 0
\(154\) 7.26795i 0.585668i
\(155\) 0 0
\(156\) 2.19615 0.175833
\(157\) −10.0463 + 10.0463i −0.801782 + 0.801782i −0.983374 0.181592i \(-0.941875\pi\)
0.181592 + 0.983374i \(0.441875\pi\)
\(158\) −11.3293 11.3293i −0.901313 0.901313i
\(159\) 2.72172 0.215847
\(160\) 0 0
\(161\) −14.1244 8.01105i −1.11316 0.631359i
\(162\) −6.36396 6.36396i −0.500000 0.500000i
\(163\) 13.9527 13.9527i 1.09286 1.09286i 0.0976349 0.995222i \(-0.468872\pi\)
0.995222 0.0976349i \(-0.0311277\pi\)
\(164\) 1.92820i 0.150567i
\(165\) 0 0
\(166\) 15.4469i 1.19891i
\(167\) −14.2808 14.2808i −1.10508 1.10508i −0.993787 0.111297i \(-0.964499\pi\)
−0.111297 0.993787i \(-0.535501\pi\)
\(168\) 4.14682 + 4.14682i 0.319934 + 0.319934i
\(169\) 11.3923i 0.876331i
\(170\) 0 0
\(171\) 0 0
\(172\) −6.54099 + 6.54099i −0.498746 + 0.498746i
\(173\) −3.58630 + 3.58630i −0.272661 + 0.272661i −0.830171 0.557509i \(-0.811757\pi\)
0.557509 + 0.830171i \(0.311757\pi\)
\(174\) 2.53590i 0.192246i
\(175\) 0 0
\(176\) 2.14655i 0.161803i
\(177\) 9.14162 + 9.14162i 0.687126 + 0.687126i
\(178\) −6.77581 6.77581i −0.507868 0.507868i
\(179\) 1.00000i 0.0747435i 0.999301 + 0.0373718i \(0.0118986\pi\)
−0.999301 + 0.0373718i \(0.988101\pi\)
\(180\) 0 0
\(181\) 7.43588i 0.552705i −0.961056 0.276352i \(-0.910874\pi\)
0.961056 0.276352i \(-0.0891257\pi\)
\(182\) 3.03569 3.03569i 0.225020 0.225020i
\(183\) −7.18251 7.18251i −0.530946 0.530946i
\(184\) −4.17156 2.36603i −0.307532 0.174426i
\(185\) 0 0
\(186\) 2.19615 0.161030
\(187\) 8.39735 + 8.39735i 0.614075 + 0.614075i
\(188\) 0.896575 0.896575i 0.0653895 0.0653895i
\(189\) −17.5935 −1.27974
\(190\) 0 0
\(191\) 17.5935i 1.27302i −0.771268 0.636510i \(-0.780377\pi\)
0.771268 0.636510i \(-0.219623\pi\)
\(192\) 1.22474 + 1.22474i 0.0883883 + 0.0883883i
\(193\) −11.0227 + 11.0227i −0.793432 + 0.793432i −0.982050 0.188619i \(-0.939599\pi\)
0.188619 + 0.982050i \(0.439599\pi\)
\(194\) 9.25036 0.664137
\(195\) 0 0
\(196\) 4.46410 0.318864
\(197\) 16.7303 + 16.7303i 1.19199 + 1.19199i 0.976509 + 0.215478i \(0.0691308\pi\)
0.215478 + 0.976509i \(0.430869\pi\)
\(198\) 0 0
\(199\) −1.57139 −0.111393 −0.0556963 0.998448i \(-0.517738\pi\)
−0.0556963 + 0.998448i \(0.517738\pi\)
\(200\) 0 0
\(201\) 2.14655i 0.151406i
\(202\) 5.03768 + 5.03768i 0.354450 + 0.354450i
\(203\) 3.50531 + 3.50531i 0.246024 + 0.246024i
\(204\) −9.58244 −0.670905
\(205\) 0 0
\(206\) 19.4080i 1.35222i
\(207\) 0 0
\(208\) 0.896575 0.896575i 0.0621663 0.0621663i
\(209\) 4.60770i 0.318721i
\(210\) 0 0
\(211\) −6.46410 −0.445007 −0.222504 0.974932i \(-0.571423\pi\)
−0.222504 + 0.974932i \(0.571423\pi\)
\(212\) 1.11114 1.11114i 0.0763133 0.0763133i
\(213\) −18.2832 + 18.2832i −1.25275 + 1.25275i
\(214\) −5.53242 −0.378189
\(215\) 0 0
\(216\) −5.19615 −0.353553
\(217\) 3.03569 3.03569i 0.206076 0.206076i
\(218\) −3.03569 3.03569i −0.205603 0.205603i
\(219\) 19.3923i 1.31041i
\(220\) 0 0
\(221\) 7.01483i 0.471869i
\(222\) −3.03569 + 3.03569i −0.203742 + 0.203742i
\(223\) 11.5911 11.5911i 0.776198 0.776198i −0.202984 0.979182i \(-0.565064\pi\)
0.979182 + 0.202984i \(0.0650639\pi\)
\(224\) 3.38587 0.226228
\(225\) 0 0
\(226\) 12.3042i 0.818460i
\(227\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(228\) −2.62898 2.62898i −0.174109 0.174109i
\(229\) 10.1576 0.671233 0.335617 0.941999i \(-0.391055\pi\)
0.335617 + 0.941999i \(0.391055\pi\)
\(230\) 0 0
\(231\) −12.5885 −0.828260
\(232\) 1.03528 + 1.03528i 0.0679692 + 0.0679692i
\(233\) −18.2832 + 18.2832i −1.19777 + 1.19777i −0.222944 + 0.974831i \(0.571567\pi\)
−0.974831 + 0.222944i \(0.928433\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 7.46410 0.485872
\(237\) −19.6230 + 19.6230i −1.27465 + 1.27465i
\(238\) −13.2456 + 13.2456i −0.858582 + 0.858582i
\(239\) 3.26795i 0.211386i −0.994399 0.105693i \(-0.966294\pi\)
0.994399 0.105693i \(-0.0337061\pi\)
\(240\) 0 0
\(241\) 9.58244i 0.617259i −0.951182 0.308629i \(-0.900130\pi\)
0.951182 0.308629i \(-0.0998703\pi\)
\(242\) −4.52004 4.52004i −0.290559 0.290559i
\(243\) 0 0
\(244\) −5.86450 −0.375436
\(245\) 0 0
\(246\) 3.33975 0.212934
\(247\) −1.92455 + 1.92455i −0.122456 + 0.122456i
\(248\) 0.896575 0.896575i 0.0569326 0.0569326i
\(249\) −26.7549 −1.69552
\(250\) 0 0
\(251\) 13.8755i 0.875817i −0.899020 0.437908i \(-0.855719\pi\)
0.899020 0.437908i \(-0.144281\pi\)
\(252\) 0 0
\(253\) 9.92303 2.74052i 0.623856 0.172295i
\(254\) 2.19615i 0.137799i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −14.5211 14.5211i −0.905800 0.905800i 0.0901303 0.995930i \(-0.471272\pi\)
−0.995930 + 0.0901303i \(0.971272\pi\)
\(258\) 11.3293 + 11.3293i 0.705334 + 0.705334i
\(259\) 8.39230i 0.521472i
\(260\) 0 0
\(261\) 0 0
\(262\) 9.89949 + 9.89949i 0.611593 + 0.611593i
\(263\) −15.4762 15.4762i −0.954301 0.954301i 0.0446996 0.999000i \(-0.485767\pi\)
−0.999000 + 0.0446996i \(0.985767\pi\)
\(264\) −3.71794 −0.228823
\(265\) 0 0
\(266\) −7.26795 −0.445627
\(267\) −11.7360 + 11.7360i −0.718234 + 0.718234i
\(268\) 0.876327 + 0.876327i 0.0535302 + 0.0535302i
\(269\) 4.33975i 0.264599i 0.991210 + 0.132299i \(0.0422361\pi\)
−0.991210 + 0.132299i \(0.957764\pi\)
\(270\) 0 0
\(271\) 18.7846 1.14108 0.570542 0.821269i \(-0.306733\pi\)
0.570542 + 0.821269i \(0.306733\pi\)
\(272\) −3.91201 + 3.91201i −0.237201 + 0.237201i
\(273\) −5.25796 5.25796i −0.318226 0.318226i
\(274\) 5.53242 0.334226
\(275\) 0 0
\(276\) −4.09808 + 7.22536i −0.246675 + 0.434915i
\(277\) 1.31268 + 1.31268i 0.0788712 + 0.0788712i 0.745442 0.666571i \(-0.232239\pi\)
−0.666571 + 0.745442i \(0.732239\pi\)
\(278\) 1.46498 1.46498i 0.0878638 0.0878638i
\(279\) 0 0
\(280\) 0 0
\(281\) 16.0221i 0.955798i 0.878415 + 0.477899i \(0.158602\pi\)
−0.878415 + 0.477899i \(0.841398\pi\)
\(282\) −1.55291 1.55291i −0.0924747 0.0924747i
\(283\) 9.63960 + 9.63960i 0.573015 + 0.573015i 0.932970 0.359955i \(-0.117208\pi\)
−0.359955 + 0.932970i \(0.617208\pi\)
\(284\) 14.9282i 0.885826i
\(285\) 0 0
\(286\) 2.72172i 0.160939i
\(287\) 4.61645 4.61645i 0.272500 0.272500i
\(288\) 0 0
\(289\) 13.6077i 0.800453i
\(290\) 0 0
\(291\) 16.0221i 0.939232i
\(292\) 7.91688 + 7.91688i 0.463300 + 0.463300i
\(293\) −18.9815 18.9815i −1.10891 1.10891i −0.993294 0.115615i \(-0.963116\pi\)
−0.115615 0.993294i \(-0.536884\pi\)
\(294\) 7.73205i 0.450942i
\(295\) 0 0
\(296\) 2.47863i 0.144067i
\(297\) 7.88694 7.88694i 0.457647 0.457647i
\(298\) −1.11114 1.11114i −0.0643665 0.0643665i
\(299\) 5.28933 + 3.00000i 0.305890 + 0.173494i
\(300\) 0 0
\(301\) 31.3205 1.80528
\(302\) 5.79555 + 5.79555i 0.333497 + 0.333497i
\(303\) 8.72552 8.72552i 0.501268 0.501268i
\(304\) −2.14655 −0.123113
\(305\) 0 0
\(306\) 0 0
\(307\) 21.3011 + 21.3011i 1.21572 + 1.21572i 0.969116 + 0.246604i \(0.0793146\pi\)
0.246604 + 0.969116i \(0.420685\pi\)
\(308\) −5.13922 + 5.13922i −0.292834 + 0.292834i
\(309\) −33.6156 −1.91232
\(310\) 0 0
\(311\) 10.7846 0.611539 0.305770 0.952106i \(-0.401086\pi\)
0.305770 + 0.952106i \(0.401086\pi\)
\(312\) −1.55291 1.55291i −0.0879165 0.0879165i
\(313\) −14.8346 14.8346i −0.838504 0.838504i 0.150158 0.988662i \(-0.452022\pi\)
−0.988662 + 0.150158i \(0.952022\pi\)
\(314\) 14.2076 0.801782
\(315\) 0 0
\(316\) 16.0221i 0.901313i
\(317\) −21.3891 21.3891i −1.20133 1.20133i −0.973762 0.227567i \(-0.926923\pi\)
−0.227567 0.973762i \(-0.573077\pi\)
\(318\) −1.92455 1.92455i −0.107923 0.107923i
\(319\) −3.14277 −0.175962
\(320\) 0 0
\(321\) 9.58244i 0.534839i
\(322\) 4.32276 + 15.6521i 0.240898 + 0.872257i
\(323\) 8.39735 8.39735i 0.467241 0.467241i
\(324\) 9.00000i 0.500000i
\(325\) 0 0
\(326\) −19.7321 −1.09286
\(327\) −5.25796 + 5.25796i −0.290766 + 0.290766i
\(328\) 1.36345 1.36345i 0.0752837 0.0752837i
\(329\) −4.29311 −0.236687
\(330\) 0 0
\(331\) −21.7846 −1.19739 −0.598695 0.800977i \(-0.704314\pi\)
−0.598695 + 0.800977i \(0.704314\pi\)
\(332\) −10.9226 + 10.9226i −0.599457 + 0.599457i
\(333\) 0 0
\(334\) 20.1962i 1.10508i
\(335\) 0 0
\(336\) 5.86450i 0.319934i
\(337\) −18.2770 + 18.2770i −0.995613 + 0.995613i −0.999990 0.00437692i \(-0.998607\pi\)
0.00437692 + 0.999990i \(0.498607\pi\)
\(338\) 8.05558 8.05558i 0.438166 0.438166i
\(339\) 21.3114 1.15748
\(340\) 0 0
\(341\) 2.72172i 0.147389i
\(342\) 0 0
\(343\) 6.07137 + 6.07137i 0.327823 + 0.327823i
\(344\) 9.25036 0.498746
\(345\) 0 0
\(346\) 5.07180 0.272661
\(347\) −8.39735 8.39735i −0.450793 0.450793i 0.444824 0.895618i \(-0.353266\pi\)
−0.895618 + 0.444824i \(0.853266\pi\)
\(348\) 1.79315 1.79315i 0.0961230 0.0961230i
\(349\) 30.7846i 1.64786i −0.566690 0.823931i \(-0.691776\pi\)
0.566690 0.823931i \(-0.308224\pi\)
\(350\) 0 0
\(351\) 6.58846 0.351666
\(352\) −1.51784 + 1.51784i −0.0809013 + 0.0809013i
\(353\) −19.4201 + 19.4201i −1.03363 + 1.03363i −0.0342104 + 0.999415i \(0.510892\pi\)
−0.999415 + 0.0342104i \(0.989108\pi\)
\(354\) 12.9282i 0.687126i
\(355\) 0 0
\(356\) 9.58244i 0.507868i
\(357\) 22.9420 + 22.9420i 1.21422 + 1.21422i
\(358\) 0.707107 0.707107i 0.0373718 0.0373718i
\(359\) 17.5935 0.928549 0.464274 0.885691i \(-0.346315\pi\)
0.464274 + 0.885691i \(0.346315\pi\)
\(360\) 0 0
\(361\) −14.3923 −0.757490
\(362\) −5.25796 + 5.25796i −0.276352 + 0.276352i
\(363\) −7.82894 + 7.82894i −0.410913 + 0.410913i
\(364\) −4.29311 −0.225020
\(365\) 0 0
\(366\) 10.1576i 0.530946i
\(367\) 15.9458 15.9458i 0.832363 0.832363i −0.155477 0.987840i \(-0.549691\pi\)
0.987840 + 0.155477i \(0.0496913\pi\)
\(368\) 1.27671 + 4.62277i 0.0665529 + 0.240979i
\(369\) 0 0
\(370\) 0 0
\(371\) −5.32051 −0.276227
\(372\) −1.55291 1.55291i −0.0805149 0.0805149i
\(373\) −4.61645 4.61645i −0.239031 0.239031i 0.577418 0.816449i \(-0.304060\pi\)
−0.816449 + 0.577418i \(0.804060\pi\)
\(374\) 11.8756i 0.614075i
\(375\) 0 0
\(376\) −1.26795 −0.0653895
\(377\) −1.31268 1.31268i −0.0676063 0.0676063i
\(378\) 12.4405 + 12.4405i 0.639869 + 0.639869i
\(379\) −5.28933 −0.271695 −0.135847 0.990730i \(-0.543376\pi\)
−0.135847 + 0.990730i \(0.543376\pi\)
\(380\) 0 0
\(381\) −3.80385 −0.194877
\(382\) −12.4405 + 12.4405i −0.636510 + 0.636510i
\(383\) −6.54099 6.54099i −0.334229 0.334229i 0.519961 0.854190i \(-0.325947\pi\)
−0.854190 + 0.519961i \(0.825947\pi\)
\(384\) 1.73205i 0.0883883i
\(385\) 0 0
\(386\) 15.5885 0.793432
\(387\) 0 0
\(388\) −6.54099 6.54099i −0.332069 0.332069i
\(389\) 29.3225 1.48671 0.743354 0.668898i \(-0.233234\pi\)
0.743354 + 0.668898i \(0.233234\pi\)
\(390\) 0 0
\(391\) −23.0788 13.0899i −1.16715 0.661982i
\(392\) −3.15660 3.15660i −0.159432 0.159432i
\(393\) 17.1464 17.1464i 0.864923 0.864923i
\(394\) 23.6603i 1.19199i
\(395\) 0 0
\(396\) 0 0
\(397\) −13.3843 13.3843i −0.671737 0.671737i 0.286379 0.958116i \(-0.407548\pi\)
−0.958116 + 0.286379i \(0.907548\pi\)
\(398\) 1.11114 + 1.11114i 0.0556963 + 0.0556963i
\(399\) 12.5885i 0.630211i
\(400\) 0 0
\(401\) 6.43966i 0.321581i −0.986989 0.160791i \(-0.948596\pi\)
0.986989 0.160791i \(-0.0514044\pi\)
\(402\) 1.51784 1.51784i 0.0757031 0.0757031i
\(403\) −1.13681 + 1.13681i −0.0566286 + 0.0566286i
\(404\) 7.12436i 0.354450i
\(405\) 0 0
\(406\) 4.95725i 0.246024i
\(407\) −3.76217 3.76217i −0.186484 0.186484i
\(408\) 6.77581 + 6.77581i 0.335452 + 0.335452i
\(409\) 12.4641i 0.616310i 0.951336 + 0.308155i \(0.0997116\pi\)
−0.951336 + 0.308155i \(0.900288\pi\)
\(410\) 0 0
\(411\) 9.58244i 0.472667i
\(412\) −13.7235 + 13.7235i −0.676109 + 0.676109i
\(413\) −17.8703 17.8703i −0.879341 0.879341i
\(414\) 0 0
\(415\) 0 0
\(416\) −1.26795 −0.0621663
\(417\) −2.53742 2.53742i −0.124258 0.124258i
\(418\) 3.25813 3.25813i 0.159360 0.159360i
\(419\) −10.7328 −0.524330 −0.262165 0.965023i \(-0.584437\pi\)
−0.262165 + 0.965023i \(0.584437\pi\)
\(420\) 0 0
\(421\) 36.7584i 1.79149i 0.444565 + 0.895746i \(0.353358\pi\)
−0.444565 + 0.895746i \(0.646642\pi\)
\(422\) 4.57081 + 4.57081i 0.222504 + 0.222504i
\(423\) 0 0
\(424\) −1.57139 −0.0763133
\(425\) 0 0
\(426\) 25.8564 1.25275
\(427\) 14.0406 + 14.0406i 0.679472 + 0.679472i
\(428\) 3.91201 + 3.91201i 0.189094 + 0.189094i
\(429\) 4.71416 0.227602
\(430\) 0 0
\(431\) 2.72172i 0.131101i −0.997849 0.0655504i \(-0.979120\pi\)
0.997849 0.0655504i \(-0.0208803\pi\)
\(432\) 3.67423 + 3.67423i 0.176777 + 0.176777i
\(433\) 13.4887 + 13.4887i 0.648225 + 0.648225i 0.952564 0.304339i \(-0.0984354\pi\)
−0.304339 + 0.952564i \(0.598435\pi\)
\(434\) −4.29311 −0.206076
\(435\) 0 0
\(436\) 4.29311i 0.205603i
\(437\) −2.74052 9.92303i −0.131097 0.474683i
\(438\) 13.7124 13.7124i 0.655205 0.655205i
\(439\) 34.9808i 1.66954i −0.550598 0.834770i \(-0.685600\pi\)
0.550598 0.834770i \(-0.314400\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 4.96023 4.96023i 0.235934 0.235934i
\(443\) −12.8159 + 12.8159i −0.608900 + 0.608900i −0.942658 0.333759i \(-0.891683\pi\)
0.333759 + 0.942658i \(0.391683\pi\)
\(444\) 4.29311 0.203742
\(445\) 0 0
\(446\) −16.3923 −0.776198
\(447\) −1.92455 + 1.92455i −0.0910280 + 0.0910280i
\(448\) −2.39417 2.39417i −0.113114 0.113114i
\(449\) 18.8564i 0.889889i 0.895558 + 0.444944i \(0.146777\pi\)
−0.895558 + 0.444944i \(0.853223\pi\)
\(450\) 0 0
\(451\) 4.13899i 0.194898i
\(452\) 8.70035 8.70035i 0.409230 0.409230i
\(453\) 10.0382 10.0382i 0.471636 0.471636i
\(454\) 0 0
\(455\) 0 0
\(456\) 3.71794i 0.174109i
\(457\) 20.4993 20.4993i 0.958917 0.958917i −0.0402715 0.999189i \(-0.512822\pi\)
0.999189 + 0.0402715i \(0.0128223\pi\)
\(458\) −7.18251 7.18251i −0.335617 0.335617i
\(459\) −28.7473 −1.34181
\(460\) 0 0
\(461\) −20.3923 −0.949764 −0.474882 0.880049i \(-0.657509\pi\)
−0.474882 + 0.880049i \(0.657509\pi\)
\(462\) 8.90138 + 8.90138i 0.414130 + 0.414130i
\(463\) −28.9778 + 28.9778i −1.34671 + 1.34671i −0.457504 + 0.889208i \(0.651256\pi\)
−0.889208 + 0.457504i \(0.848744\pi\)
\(464\) 1.46410i 0.0679692i
\(465\) 0 0
\(466\) 25.8564 1.19777
\(467\) 20.4364 20.4364i 0.945684 0.945684i −0.0529155 0.998599i \(-0.516851\pi\)
0.998599 + 0.0529155i \(0.0168514\pi\)
\(468\) 0 0
\(469\) 4.19615i 0.193760i
\(470\) 0 0
\(471\) 24.6083i 1.13389i
\(472\) −5.27792 5.27792i −0.242936 0.242936i
\(473\) −14.0406 + 14.0406i −0.645587 + 0.645587i
\(474\) 27.7511 1.27465
\(475\) 0 0
\(476\) 18.7321 0.858582
\(477\) 0 0
\(478\) −2.31079 + 2.31079i −0.105693 + 0.105693i
\(479\) 37.9087 1.73209 0.866046 0.499964i \(-0.166653\pi\)
0.866046 + 0.499964i \(0.166653\pi\)
\(480\) 0 0
\(481\) 3.14277i 0.143298i
\(482\) −6.77581 + 6.77581i −0.308629 + 0.308629i
\(483\) 27.1102 7.48724i 1.23356 0.340681i
\(484\) 6.39230i 0.290559i
\(485\) 0 0
\(486\) 0 0
\(487\) −14.5211 14.5211i −0.658013 0.658013i 0.296897 0.954910i \(-0.404048\pi\)
−0.954910 + 0.296897i \(0.904048\pi\)
\(488\) 4.14682 + 4.14682i 0.187718 + 0.187718i
\(489\) 34.1769i 1.54553i
\(490\) 0 0
\(491\) 11.4641 0.517368 0.258684 0.965962i \(-0.416711\pi\)
0.258684 + 0.965962i \(0.416711\pi\)
\(492\) −2.36156 2.36156i −0.106467 0.106467i
\(493\) 5.72758 + 5.72758i 0.257957 + 0.257957i
\(494\) 2.72172 0.122456
\(495\) 0 0
\(496\) −1.26795 −0.0569326
\(497\) 35.7407 35.7407i 1.60319 1.60319i
\(498\) 18.9186 + 18.9186i 0.847761 + 0.847761i
\(499\) 22.0000i 0.984855i 0.870353 + 0.492428i \(0.163890\pi\)
−0.870353 + 0.492428i \(0.836110\pi\)
\(500\) 0 0
\(501\) 34.9808 1.56283
\(502\) −9.81149 + 9.81149i −0.437908 + 0.437908i
\(503\) 8.29365 + 8.29365i 0.369796 + 0.369796i 0.867403 0.497607i \(-0.165788\pi\)
−0.497607 + 0.867403i \(0.665788\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −8.95448 5.07880i −0.398075 0.225780i
\(507\) −13.9527 13.9527i −0.619660 0.619660i
\(508\) −1.55291 + 1.55291i −0.0688994 + 0.0688994i
\(509\) 11.8038i 0.523196i −0.965177 0.261598i \(-0.915750\pi\)
0.965177 0.261598i \(-0.0842495\pi\)
\(510\) 0 0
\(511\) 37.9087i 1.67698i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −7.88694 7.88694i −0.348217 0.348217i
\(514\) 20.5359i 0.905800i
\(515\) 0 0
\(516\) 16.0221i 0.705334i
\(517\) 1.92455 1.92455i 0.0846415 0.0846415i
\(518\) 5.93426 5.93426i 0.260736 0.260736i
\(519\) 8.78461i 0.385602i
\(520\) 0 0
\(521\) 38.4839i 1.68601i 0.537907 + 0.843004i \(0.319215\pi\)
−0.537907 + 0.843004i \(0.680785\pi\)
\(522\) 0 0
\(523\) 28.7930 + 28.7930i 1.25903 + 1.25903i 0.951558 + 0.307471i \(0.0994826\pi\)
0.307471 + 0.951558i \(0.400517\pi\)
\(524\) 14.0000i 0.611593i
\(525\) 0 0
\(526\) 21.8866i 0.954301i
\(527\) 4.96023 4.96023i 0.216071 0.216071i
\(528\) 2.62898 + 2.62898i 0.114412 + 0.114412i
\(529\) −19.7400 + 11.8038i −0.858263 + 0.513211i
\(530\) 0 0
\(531\) 0 0
\(532\) 5.13922 + 5.13922i 0.222813 + 0.222813i
\(533\) −1.72878 + 1.72878i −0.0748818 + 0.0748818i
\(534\) 16.5973 0.718234
\(535\) 0 0
\(536\) 1.23931i 0.0535302i
\(537\) −1.22474 1.22474i −0.0528516 0.0528516i
\(538\) 3.06866 3.06866i 0.132299 0.132299i
\(539\) 9.58244 0.412745
\(540\) 0 0
\(541\) 4.39230 0.188840 0.0944200 0.995532i \(-0.469900\pi\)
0.0944200 + 0.995532i \(0.469900\pi\)
\(542\) −13.2827 13.2827i −0.570542 0.570542i
\(543\) 9.10706 + 9.10706i 0.390821 + 0.390821i
\(544\) 5.53242 0.237201
\(545\) 0 0
\(546\) 7.43588i 0.318226i
\(547\) −26.8565 26.8565i −1.14830 1.14830i −0.986887 0.161412i \(-0.948395\pi\)
−0.161412 0.986887i \(-0.551605\pi\)
\(548\) −3.91201 3.91201i −0.167113 0.167113i
\(549\) 0 0
\(550\) 0 0
\(551\) 3.14277i 0.133887i
\(552\) 8.00688 2.21132i 0.340795 0.0941201i
\(553\) 38.3596 38.3596i 1.63122 1.63122i
\(554\) 1.85641i 0.0788712i
\(555\) 0 0
\(556\) −2.07180 −0.0878638
\(557\) 24.2394 24.2394i 1.02706 1.02706i 0.0274340 0.999624i \(-0.491266\pi\)
0.999624 0.0274340i \(-0.00873361\pi\)
\(558\) 0 0
\(559\) −11.7290 −0.496083
\(560\) 0 0
\(561\) −20.5692 −0.868433
\(562\) 11.3293 11.3293i 0.477899 0.477899i
\(563\) −15.6481 15.6481i −0.659487 0.659487i 0.295772 0.955259i \(-0.404423\pi\)
−0.955259 + 0.295772i \(0.904423\pi\)
\(564\) 2.19615i 0.0924747i
\(565\) 0 0
\(566\) 13.6325i 0.573015i
\(567\) 21.5475 21.5475i 0.904911 0.904911i
\(568\) 10.5558 10.5558i 0.442913 0.442913i
\(569\) −37.3335 −1.56510 −0.782551 0.622586i \(-0.786082\pi\)
−0.782551 + 0.622586i \(0.786082\pi\)
\(570\) 0 0
\(571\) 24.6083i 1.02983i −0.857242 0.514913i \(-0.827824\pi\)
0.857242 0.514913i \(-0.172176\pi\)
\(572\) 1.92455 1.92455i 0.0804694 0.0804694i
\(573\) 21.5475 + 21.5475i 0.900161 + 0.900161i
\(574\) −6.52864 −0.272500
\(575\) 0 0
\(576\) 0 0
\(577\) −16.4022 16.4022i −0.682831 0.682831i 0.277806 0.960637i \(-0.410393\pi\)
−0.960637 + 0.277806i \(0.910393\pi\)
\(578\) −9.62209 + 9.62209i −0.400226 + 0.400226i
\(579\) 27.0000i 1.12208i
\(580\) 0 0
\(581\) 52.3013 2.16982
\(582\) −11.3293 + 11.3293i −0.469616 + 0.469616i
\(583\) 2.38512 2.38512i 0.0987815 0.0987815i
\(584\) 11.1962i 0.463300i
\(585\) 0 0
\(586\) 26.8438i 1.10891i
\(587\) 20.8207 + 20.8207i 0.859361 + 0.859361i 0.991263 0.131902i \(-0.0421084\pi\)
−0.131902 + 0.991263i \(0.542108\pi\)
\(588\) −5.46739 + 5.46739i −0.225471 + 0.225471i
\(589\) 2.72172 0.112147
\(590\) 0 0
\(591\) −40.9808 −1.68572
\(592\) 1.75265 1.75265i 0.0720336 0.0720336i
\(593\) 2.53742 2.53742i 0.104199 0.104199i −0.653085 0.757285i \(-0.726526\pi\)
0.757285 + 0.653085i \(0.226526\pi\)
\(594\) −11.1538 −0.457647
\(595\) 0 0
\(596\) 1.57139i 0.0643665i
\(597\) 1.92455 1.92455i 0.0787665 0.0787665i
\(598\) −1.61880 5.86144i −0.0661976 0.239692i
\(599\) 4.19615i 0.171450i −0.996319 0.0857251i \(-0.972679\pi\)
0.996319 0.0857251i \(-0.0273207\pi\)
\(600\) 0 0
\(601\) −12.6077 −0.514279 −0.257139 0.966374i \(-0.582780\pi\)
−0.257139 + 0.966374i \(0.582780\pi\)
\(602\) −22.1469 22.1469i −0.902642 0.902642i
\(603\) 0 0
\(604\) 8.19615i 0.333497i
\(605\) 0 0
\(606\) −12.3397 −0.501268
\(607\) −13.8004 13.8004i −0.560139 0.560139i 0.369208 0.929347i \(-0.379629\pi\)
−0.929347 + 0.369208i \(0.879629\pi\)
\(608\) 1.51784 + 1.51784i 0.0615567 + 0.0615567i
\(609\) −8.58622 −0.347931
\(610\) 0 0
\(611\) 1.60770 0.0650404
\(612\) 0 0
\(613\) 5.89948 + 5.89948i 0.238278 + 0.238278i 0.816137 0.577859i \(-0.196112\pi\)
−0.577859 + 0.816137i \(0.696112\pi\)
\(614\) 30.1244i 1.21572i
\(615\) 0 0
\(616\) 7.26795 0.292834
\(617\) 30.9523 30.9523i 1.24609 1.24609i 0.288663 0.957431i \(-0.406789\pi\)
0.957431 0.288663i \(-0.0932106\pi\)
\(618\) 23.7698 + 23.7698i 0.956162 + 0.956162i
\(619\) −33.1945 −1.33420 −0.667100 0.744968i \(-0.732465\pi\)
−0.667100 + 0.744968i \(0.732465\pi\)
\(620\) 0 0
\(621\) −12.2942 + 21.6761i −0.493350 + 0.869831i
\(622\) −7.62587 7.62587i −0.305770 0.305770i
\(623\) 22.9420 22.9420i 0.919151 0.919151i
\(624\) 2.19615i 0.0879165i
\(625\) 0 0
\(626\) 20.9794i 0.838504i
\(627\) −5.64325 5.64325i −0.225370 0.225370i
\(628\) −10.0463 10.0463i −0.400891 0.400891i
\(629\) 13.7128i 0.546766i
\(630\) 0 0
\(631\) 42.6229i 1.69679i 0.529364 + 0.848395i \(0.322430\pi\)
−0.529364 + 0.848395i \(0.677570\pi\)
\(632\) 11.3293 11.3293i 0.450657 0.450657i
\(633\) 7.91688 7.91688i 0.314668 0.314668i
\(634\) 30.2487i 1.20133i
\(635\) 0 0
\(636\) 2.72172i 0.107923i
\(637\) 4.00240 + 4.00240i 0.158581 + 0.158581i
\(638\) 2.22228 + 2.22228i 0.0879808 + 0.0879808i
\(639\) 0 0
\(640\) 0 0
\(641\) 5.44344i 0.215003i −0.994205 0.107502i \(-0.965715\pi\)
0.994205 0.107502i \(-0.0342851\pi\)
\(642\) 6.77581 6.77581i 0.267420 0.267420i
\(643\) 29.6693 + 29.6693i 1.17004 + 1.17004i 0.982199 + 0.187843i \(0.0601498\pi\)
0.187843 + 0.982199i \(0.439850\pi\)
\(644\) 8.01105 14.1244i 0.315680 0.556578i
\(645\) 0 0
\(646\) −11.8756 −0.467241
\(647\) −6.69213 6.69213i −0.263095 0.263095i 0.563215 0.826310i \(-0.309564\pi\)
−0.826310 + 0.563215i \(0.809564\pi\)
\(648\) 6.36396 6.36396i 0.250000 0.250000i
\(649\) 16.0221 0.628922
\(650\) 0 0
\(651\) 7.43588i 0.291435i
\(652\) 13.9527 + 13.9527i 0.546429 + 0.546429i
\(653\) 9.62209 9.62209i 0.376542 0.376542i −0.493311 0.869853i \(-0.664214\pi\)
0.869853 + 0.493311i \(0.164214\pi\)
\(654\) 7.43588 0.290766
\(655\) 0 0
\(656\) −1.92820 −0.0752837
\(657\) 0 0
\(658\) 3.03569 + 3.03569i 0.118343 + 0.118343i
\(659\) −28.7473 −1.11984 −0.559918 0.828548i \(-0.689167\pi\)
−0.559918 + 0.828548i \(0.689167\pi\)
\(660\) 0 0
\(661\) 23.4580i 0.912410i −0.889875 0.456205i \(-0.849208\pi\)
0.889875 0.456205i \(-0.150792\pi\)
\(662\) 15.4040 + 15.4040i 0.598695 + 0.598695i
\(663\) −8.59138 8.59138i −0.333661 0.333661i
\(664\) 15.4469 0.599457
\(665\) 0 0
\(666\) 0 0
\(667\) 6.76821 1.86923i 0.262066 0.0723768i
\(668\) 14.2808 14.2808i 0.552542 0.552542i
\(669\) 28.3923i 1.09771i
\(670\) 0 0
\(671\) −12.5885 −0.485972
\(672\) −4.14682 + 4.14682i −0.159967 + 0.159967i
\(673\) −26.1122 + 26.1122i −1.00655 + 1.00655i −0.00657228 + 0.999978i \(0.502092\pi\)
−0.999978 + 0.00657228i \(0.997908\pi\)
\(674\) 25.8476 0.995613
\(675\) 0 0
\(676\) −11.3923 −0.438166
\(677\) −6.36910 + 6.36910i −0.244784 + 0.244784i −0.818826 0.574042i \(-0.805375\pi\)
0.574042 + 0.818826i \(0.305375\pi\)
\(678\) −15.0695 15.0695i −0.578739 0.578739i
\(679\) 31.3205i 1.20197i
\(680\) 0 0
\(681\) 0 0
\(682\) 1.92455 1.92455i 0.0736947 0.0736947i
\(683\) 10.3664 10.3664i 0.396658 0.396658i −0.480395 0.877052i \(-0.659507\pi\)
0.877052 + 0.480395i \(0.159507\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 8.58622i 0.327823i
\(687\) −12.4405 + 12.4405i −0.474634 + 0.474634i
\(688\) −6.54099 6.54099i −0.249373 0.249373i
\(689\) 1.99244 0.0759059
\(690\) 0 0
\(691\) −40.1769 −1.52840 −0.764201 0.644978i \(-0.776866\pi\)
−0.764201 + 0.644978i \(0.776866\pi\)
\(692\) −3.58630 3.58630i −0.136331 0.136331i
\(693\) 0 0
\(694\) 11.8756i 0.450793i
\(695\) 0 0
\(696\) −2.53590 −0.0961230
\(697\) 7.54316 7.54316i 0.285717 0.285717i
\(698\) −21.7680 + 21.7680i −0.823931 + 0.823931i
\(699\) 44.7846i 1.69391i
\(700\) 0 0
\(701\) 43.7732i 1.65329i 0.562723 + 0.826645i \(0.309754\pi\)
−0.562723 + 0.826645i \(0.690246\pi\)
\(702\) −4.65874 4.65874i −0.175833 0.175833i
\(703\) −3.76217 + 3.76217i −0.141893 + 0.141893i
\(704\) 2.14655 0.0809013
\(705\) 0 0
\(706\) 27.4641 1.03363
\(707\) −17.0569 + 17.0569i −0.641491 + 0.641491i
\(708\) −9.14162 + 9.14162i −0.343563 + 0.343563i
\(709\) 17.1724 0.644924 0.322462 0.946582i \(-0.395489\pi\)
0.322462 + 0.946582i \(0.395489\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 6.77581 6.77581i 0.253934 0.253934i
\(713\) −1.61880 5.86144i −0.0606245 0.219513i
\(714\) 32.4449i 1.21422i
\(715\) 0 0
\(716\) −1.00000 −0.0373718
\(717\) 4.00240 + 4.00240i 0.149473 + 0.149473i
\(718\) −12.4405 12.4405i −0.464274 0.464274i
\(719\) 9.26795i 0.345636i −0.984954 0.172818i \(-0.944713\pi\)
0.984954 0.172818i \(-0.0552873\pi\)
\(720\) 0 0
\(721\) 65.7128 2.44727
\(722\) 10.1769 + 10.1769i 0.378745 + 0.378745i
\(723\) 11.7360 + 11.7360i 0.436468 + 0.436468i
\(724\) 7.43588 0.276352
\(725\) 0 0
\(726\) 11.0718 0.410913
\(727\) −17.8703 + 17.8703i −0.662774 + 0.662774i −0.956033 0.293259i \(-0.905260\pi\)
0.293259 + 0.956033i \(0.405260\pi\)
\(728\) 3.03569 + 3.03569i 0.112510 + 0.112510i
\(729\) 27.0000i 1.00000i
\(730\) 0 0
\(731\) 51.1769 1.89285
\(732\) 7.18251 7.18251i 0.265473 0.265473i
\(733\) 2.86379 + 2.86379i 0.105777 + 0.105777i 0.758014 0.652238i \(-0.226170\pi\)
−0.652238 + 0.758014i \(0.726170\pi\)
\(734\) −22.5507 −0.832363
\(735\) 0 0
\(736\) 2.36603 4.17156i 0.0872129 0.153766i
\(737\) 1.88108 + 1.88108i 0.0692906 + 0.0692906i
\(738\) 0 0
\(739\) 7.85641i 0.289003i 0.989505 + 0.144501i \(0.0461578\pi\)
−0.989505 + 0.144501i \(0.953842\pi\)
\(740\) 0 0
\(741\) 4.71416i 0.173179i
\(742\) 3.76217 + 3.76217i 0.138114 + 0.138114i
\(743\) −22.1890 22.1890i −0.814037 0.814037i 0.171199 0.985236i \(-0.445236\pi\)
−0.985236 + 0.171199i \(0.945236\pi\)
\(744\) 2.19615i 0.0805149i
\(745\) 0 0
\(746\) 6.52864i 0.239031i
\(747\) 0 0
\(748\) −8.39735 + 8.39735i −0.307037 + 0.307037i
\(749\) 18.7321i 0.684454i
\(750\) 0 0
\(751\) 28.9014i 1.05463i −0.849671 0.527314i \(-0.823199\pi\)
0.849671 0.527314i \(-0.176801\pi\)
\(752\) 0.896575 + 0.896575i 0.0326947 + 0.0326947i
\(753\) 16.9940 + 16.9940i 0.619296 + 0.619296i
\(754\) 1.85641i 0.0676063i
\(755\) 0 0
\(756\) 17.5935i 0.639869i
\(757\) −28.3863 + 28.3863i −1.03172 + 1.03172i −0.0322357 + 0.999480i \(0.510263\pi\)
−0.999480 + 0.0322357i \(0.989737\pi\)
\(758\) 3.74012 + 3.74012i 0.135847 + 0.135847i
\(759\) −8.79674 + 15.5096i −0.319302 + 0.562964i
\(760\) 0 0
\(761\) 24.8564 0.901044 0.450522 0.892765i \(-0.351238\pi\)
0.450522 + 0.892765i \(0.351238\pi\)
\(762\) 2.68973 + 2.68973i 0.0974385 + 0.0974385i
\(763\) 10.2784 10.2784i 0.372104 0.372104i
\(764\) 17.5935 0.636510
\(765\) 0 0
\(766\) 9.25036i 0.334229i
\(767\) 6.69213 + 6.69213i 0.241639 + 0.241639i
\(768\) −1.22474 + 1.22474i −0.0441942 + 0.0441942i
\(769\) −18.1687 −0.655178 −0.327589 0.944820i \(-0.606236\pi\)
−0.327589 + 0.944820i \(0.606236\pi\)
\(770\) 0 0
\(771\) 35.5692 1.28099
\(772\) −11.0227 11.0227i −0.396716 0.396716i
\(773\) −15.6481 15.6481i −0.562821 0.562821i 0.367287 0.930108i \(-0.380287\pi\)
−0.930108 + 0.367287i \(0.880287\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 9.25036i 0.332069i
\(777\) −10.2784 10.2784i −0.368737 0.368737i
\(778\) −20.7341 20.7341i −0.743354 0.743354i
\(779\) 4.13899 0.148295
\(780\) 0 0
\(781\) 32.0442i 1.14663i
\(782\) 7.06328 + 25.5751i 0.252582 + 0.914565i
\(783\) 5.37945 5.37945i 0.192246 0.192246i
\(784\) 4.46410i 0.159432i
\(785\) 0 0
\(786\) −24.2487 −0.864923
\(787\) −4.78834 + 4.78834i −0.170686 + 0.170686i −0.787281 0.616595i \(-0.788512\pi\)
0.616595 + 0.787281i \(0.288512\pi\)
\(788\) −16.7303 + 16.7303i −0.595993 + 0.595993i
\(789\) 37.9087 1.34959
\(790\) 0 0
\(791\) −41.6603 −1.48127
\(792\) 0 0
\(793\) −5.25796 5.25796i −0.186716 0.186716i
\(794\) 18.9282i 0.671737i
\(795\) 0 0
\(796\) 1.57139i 0.0556963i
\(797\) −6.54099 + 6.54099i −0.231694 + 0.231694i −0.813399 0.581706i \(-0.802386\pi\)
0.581706 + 0.813399i \(0.302386\pi\)
\(798\) 8.90138 8.90138i 0.315106 0.315106i
\(799\) −7.01483 −0.248167
\(800\) 0 0
\(801\) 0 0
\(802\) −4.55353 + 4.55353i −0.160791 + 0.160791i
\(803\) 16.9940 + 16.9940i 0.599705 + 0.599705i
\(804\) −2.14655 −0.0757031
\(805\) 0 0
\(806\) 1.60770 0.0566286
\(807\) −5.31508 5.31508i −0.187100 0.187100i
\(808\) −5.03768 + 5.03768i −0.177225 + 0.177225i
\(809\) 29.8564i 1.04970i −0.851196 0.524848i \(-0.824122\pi\)
0.851196 0.524848i \(-0.175878\pi\)
\(810\) 0 0
\(811\) −13.2154 −0.464055 −0.232028 0.972709i \(-0.574536\pi\)
−0.232028 + 0.972709i \(0.574536\pi\)
\(812\) −3.50531 + 3.50531i −0.123012 + 0.123012i
\(813\) −23.0064 + 23.0064i −0.806868 + 0.806868i
\(814\) 5.32051i 0.186484i
\(815\) 0 0
\(816\) 9.58244i 0.335452i
\(817\) 14.0406 + 14.0406i 0.491218 + 0.491218i
\(818\) 8.81345 8.81345i 0.308155 0.308155i
\(819\) 0 0
\(820\) 0 0
\(821\) 3.41154 0.119064 0.0595318 0.998226i \(-0.481039\pi\)
0.0595318 + 0.998226i \(0.481039\pi\)
\(822\) −6.77581 + 6.77581i −0.236333 + 0.236333i
\(823\) −10.2141 + 10.2141i −0.356040 + 0.356040i −0.862351 0.506311i \(-0.831009\pi\)
0.506311 + 0.862351i \(0.331009\pi\)
\(824\) 19.4080 0.676109
\(825\) 0 0
\(826\) 25.2725i 0.879341i
\(827\) −24.4742 + 24.4742i −0.851053 + 0.851053i −0.990263 0.139210i \(-0.955544\pi\)
0.139210 + 0.990263i \(0.455544\pi\)
\(828\) 0 0
\(829\) 34.6410i 1.20313i −0.798823 0.601566i \(-0.794544\pi\)
0.798823 0.601566i \(-0.205456\pi\)
\(830\) 0 0
\(831\) −3.21539 −0.111541
\(832\) 0.896575 + 0.896575i 0.0310832 + 0.0310832i
\(833\) −17.4636 17.4636i −0.605079 0.605079i
\(834\) 3.58846i 0.124258i
\(835\) 0 0
\(836\) −4.60770 −0.159360
\(837\) −4.65874 4.65874i −0.161030 0.161030i
\(838\) 7.58922 + 7.58922i 0.262165 + 0.262165i
\(839\) 33.6156 1.16054 0.580269 0.814425i \(-0.302947\pi\)
0.580269 + 0.814425i \(0.302947\pi\)
\(840\) 0 0
\(841\) 26.8564 0.926083
\(842\) 25.9921 25.9921i 0.895746 0.895746i
\(843\) −19.6230 19.6230i −0.675851 0.675851i
\(844\) 6.46410i 0.222504i
\(845\) 0 0
\(846\) 0 0
\(847\) 15.3043 15.3043i 0.525861 0.525861i
\(848\) 1.11114 + 1.11114i 0.0381566 + 0.0381566i
\(849\) −23.6121 −0.810365
\(850\) 0 0
\(851\) 10.3397 + 5.86450i 0.354442 + 0.201032i
\(852\) −18.2832 18.2832i −0.626373 0.626373i
\(853\) 25.2156 25.2156i 0.863366 0.863366i −0.128361 0.991727i \(-0.540972\pi\)
0.991727 + 0.128361i \(0.0409718\pi\)
\(854\) 19.8564i 0.679472i
\(855\) 0 0
\(856\) 5.53242i 0.189094i
\(857\) 2.36156 + 2.36156i 0.0806693 + 0.0806693i 0.746290 0.665621i \(-0.231833\pi\)
−0.665621 + 0.746290i \(0.731833\pi\)
\(858\) −3.33341 3.33341i −0.113801 0.113801i
\(859\) 9.39230i 0.320461i 0.987080 + 0.160231i \(0.0512238\pi\)
−0.987080 + 0.160231i \(0.948776\pi\)
\(860\) 0 0
\(861\) 11.3079i 0.385374i
\(862\) −1.92455 + 1.92455i −0.0655504 + 0.0655504i
\(863\) −33.9411 + 33.9411i −1.15537 + 1.15537i −0.169910 + 0.985460i \(0.554348\pi\)
−0.985460 + 0.169910i \(0.945652\pi\)
\(864\) 5.19615i 0.176777i
\(865\) 0 0
\(866\) 19.0759i 0.648225i
\(867\) 16.6660 + 16.6660i 0.566006 + 0.566006i
\(868\) 3.03569 + 3.03569i 0.103038 + 0.103038i
\(869\) 34.3923i 1.16668i
\(870\) 0 0
\(871\) 1.57139i 0.0532444i
\(872\) 3.03569 3.03569i 0.102801 0.102801i
\(873\) 0 0
\(874\) −5.07880 + 8.95448i −0.171793 + 0.302890i
\(875\) 0 0
\(876\) −19.3923 −0.655205
\(877\) 2.68973 + 2.68973i 0.0908256 + 0.0908256i 0.751060 0.660234i \(-0.229543\pi\)
−0.660234 + 0.751060i \(0.729543\pi\)
\(878\) −24.7351 + 24.7351i −0.834770 + 0.834770i
\(879\) 46.4949 1.56823
\(880\) 0 0
\(881\) 35.1870i 1.18548i −0.805394 0.592740i \(-0.798046\pi\)
0.805394 0.592740i \(-0.201954\pi\)
\(882\) 0 0
\(883\) 32.4118 32.4118i 1.09074 1.09074i 0.0952938 0.995449i \(-0.469621\pi\)
0.995449 0.0952938i \(-0.0303791\pi\)
\(884\) −7.01483 −0.235934
\(885\) 0 0
\(886\) 18.1244 0.608900
\(887\) 28.0812 + 28.0812i 0.942874 + 0.942874i 0.998454 0.0555799i \(-0.0177007\pi\)
−0.0555799 + 0.998454i \(0.517701\pi\)
\(888\) −3.03569 3.03569i −0.101871 0.101871i
\(889\) 7.43588 0.249391
\(890\) 0 0
\(891\) 19.3190i 0.647210i
\(892\) 11.5911 + 11.5911i 0.388099 + 0.388099i
\(893\) −1.92455 1.92455i −0.0644025 0.0644025i
\(894\) 2.72172 0.0910280
\(895\) 0 0
\(896\) 3.38587i 0.113114i
\(897\) −10.1523 + 2.80384i −0.338976 + 0.0936176i
\(898\) 13.3335 13.3335i 0.444944 0.444944i
\(899\) 1.85641i 0.0619146i
\(900\) 0 0
\(901\) −8.69358 −0.289625
\(902\) 2.92671 2.92671i 0.0974488 0.0974488i
\(903\) −38.3596 + 38.3596i −1.27653 + 1.27653i
\(904\) −12.3042 −0.409230
\(905\) 0 0
\(906\) −14.1962 −0.471636
\(907\) −13.4258 + 13.4258i −0.445796 + 0.445796i −0.893954 0.448159i \(-0.852080\pi\)
0.448159 + 0.893954i \(0.352080\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 7.01483i 0.232412i 0.993225 + 0.116206i \(0.0370732\pi\)
−0.993225 + 0.116206i \(0.962927\pi\)
\(912\) 2.62898 2.62898i 0.0870543 0.0870543i
\(913\) −23.4460 + 23.4460i −0.775950 + 0.775950i
\(914\) −28.9904 −0.958917
\(915\) 0 0
\(916\) 10.1576i 0.335617i
\(917\) −33.5184 + 33.5184i −1.10687 + 1.10687i
\(918\) 20.3274 + 20.3274i 0.670905 + 0.670905i
\(919\) −26.1797 −0.863589 −0.431794 0.901972i \(-0.642119\pi\)
−0.431794 + 0.901972i \(0.642119\pi\)
\(920\) 0 0
\(921\) −52.1769 −1.71929
\(922\) 14.4195 + 14.4195i 0.474882 + 0.474882i
\(923\) −13.3843 + 13.3843i −0.440548 + 0.440548i
\(924\) 12.5885i 0.414130i
\(925\) 0 0
\(926\) 40.9808 1.34671
\(927\) 0 0
\(928\) −1.03528 + 1.03528i −0.0339846 + 0.0339846i
\(929\) 28.1051i 0.922099i −0.887374 0.461050i \(-0.847473\pi\)
0.887374 0.461050i \(-0.152527\pi\)
\(930\) 0 0
\(931\) 9.58244i 0.314052i
\(932\) −18.2832 18.2832i −0.598887 0.598887i
\(933\) −13.2084 + 13.2084i −0.432423 + 0.432423i
\(934\) −28.9014 −0.945684
\(935\) 0 0
\(936\) 0 0
\(937\) 30.0760 30.0760i 0.982540 0.982540i −0.0173104 0.999850i \(-0.505510\pi\)
0.999850 + 0.0173104i \(0.00551033\pi\)
\(938\) −2.96713 + 2.96713i −0.0968802 + 0.0968802i
\(939\) 36.3373 1.18582
\(940\) 0 0
\(941\) 20.3152i 0.662257i 0.943586 + 0.331128i \(0.107429\pi\)
−0.943586 + 0.331128i \(0.892571\pi\)
\(942\) −17.4007 + 17.4007i −0.566946 + 0.566946i
\(943\) −2.46175 8.91364i −0.0801656 0.290268i
\(944\) 7.46410i 0.242936i
\(945\) 0 0
\(946\) 19.8564 0.645587
\(947\) 1.79315 + 1.79315i 0.0582696 + 0.0582696i 0.735641 0.677372i \(-0.236881\pi\)
−0.677372 + 0.735641i \(0.736881\pi\)
\(948\) −19.6230 19.6230i −0.637325 0.637325i
\(949\) 14.1962i 0.460827i
\(950\) 0 0
\(951\) 52.3923 1.69894
\(952\) −13.2456 13.2456i −0.429291 0.429291i
\(953\) 2.62898 + 2.62898i 0.0851611 + 0.0851611i 0.748404 0.663243i \(-0.230820\pi\)
−0.663243 + 0.748404i \(0.730820\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 3.26795 0.105693
\(957\) 3.84910 3.84910i 0.124424 0.124424i
\(958\) −26.8055 26.8055i −0.866046 0.866046i
\(959\) 18.7321i 0.604889i
\(960\) 0 0
\(961\) −29.3923 −0.948139
\(962\) −2.22228 + 2.22228i −0.0716491 + 0.0716491i
\(963\) 0 0
\(964\) 9.58244 0.308629
\(965\) 0 0
\(966\) −24.4641 13.8755i −0.787120 0.446438i
\(967\) 14.6969 + 14.6969i 0.472622 + 0.472622i 0.902762 0.430140i \(-0.141536\pi\)
−0.430140 + 0.902762i \(0.641536\pi\)
\(968\) 4.52004 4.52004i 0.145280 0.145280i
\(969\) 20.5692i 0.660779i
\(970\) 0 0
\(971\) 37.3335i 1.19809i 0.800715 + 0.599045i \(0.204453\pi\)
−0.800715 + 0.599045i \(0.795547\pi\)
\(972\) 0 0
\(973\) 4.96023 + 4.96023i 0.159018 + 0.159018i
\(974\) 20.5359i 0.658013i
\(975\) 0 0
\(976\) 5.86450i 0.187718i
\(977\) −18.2770 + 18.2770i −0.584734 + 0.584734i −0.936201 0.351466i \(-0.885683\pi\)
0.351466 + 0.936201i \(0.385683\pi\)
\(978\) 24.1667 24.1667i 0.772767 0.772767i
\(979\) 20.5692i 0.657395i
\(980\) 0 0
\(981\) 0 0
\(982\) −8.10634 8.10634i −0.258684 0.258684i
\(983\) −22.1890 22.1890i −0.707721 0.707721i 0.258335 0.966055i \(-0.416826\pi\)
−0.966055 + 0.258335i \(0.916826\pi\)
\(984\) 3.33975i 0.106467i
\(985\) 0 0
\(986\) 8.10003i 0.257957i
\(987\) 5.25796 5.25796i 0.167363 0.167363i
\(988\) −1.92455 1.92455i −0.0612280 0.0612280i
\(989\) 21.8866 38.5885i 0.695953 1.22704i
\(990\) 0 0
\(991\) −26.1051 −0.829256 −0.414628 0.909991i \(-0.636088\pi\)
−0.414628 + 0.909991i \(0.636088\pi\)
\(992\) 0.896575 + 0.896575i 0.0284663 + 0.0284663i
\(993\) 26.6806 26.6806i 0.846683 0.846683i
\(994\) −50.5449 −1.60319
\(995\) 0 0
\(996\) 26.7549i 0.847761i
\(997\) 6.27603 + 6.27603i 0.198764 + 0.198764i 0.799470 0.600706i \(-0.205114\pi\)
−0.600706 + 0.799470i \(0.705114\pi\)
\(998\) 15.5563 15.5563i 0.492428 0.492428i
\(999\) 12.8793 0.407484
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 1150.2.e.f.1057.2 yes 16
5.2 odd 4 inner 1150.2.e.f.643.8 yes 16
5.3 odd 4 inner 1150.2.e.f.643.1 16
5.4 even 2 inner 1150.2.e.f.1057.7 yes 16
23.22 odd 2 inner 1150.2.e.f.1057.1 yes 16
115.22 even 4 inner 1150.2.e.f.643.7 yes 16
115.68 even 4 inner 1150.2.e.f.643.2 yes 16
115.114 odd 2 inner 1150.2.e.f.1057.8 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1150.2.e.f.643.1 16 5.3 odd 4 inner
1150.2.e.f.643.2 yes 16 115.68 even 4 inner
1150.2.e.f.643.7 yes 16 115.22 even 4 inner
1150.2.e.f.643.8 yes 16 5.2 odd 4 inner
1150.2.e.f.1057.1 yes 16 23.22 odd 2 inner
1150.2.e.f.1057.2 yes 16 1.1 even 1 trivial
1150.2.e.f.1057.7 yes 16 5.4 even 2 inner
1150.2.e.f.1057.8 yes 16 115.114 odd 2 inner