Properties

Label 1560.2.w.d.781.3
Level $1560$
Weight $2$
Character 1560.781
Analytic conductor $12.457$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1560,2,Mod(781,1560)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1560, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1560.781");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1560.w (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: \(12.4566627153\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 781.3
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1560.781
Dual form 1560.2.w.d.781.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.36603 - 0.366025i) q^{2} +1.00000i q^{3} +(1.73205 - 1.00000i) q^{4} -1.00000i q^{5} +(0.366025 + 1.36603i) q^{6} +4.73205 q^{7} +(2.00000 - 2.00000i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(1.36603 - 0.366025i) q^{2} +1.00000i q^{3} +(1.73205 - 1.00000i) q^{4} -1.00000i q^{5} +(0.366025 + 1.36603i) q^{6} +4.73205 q^{7} +(2.00000 - 2.00000i) q^{8} -1.00000 q^{9} +(-0.366025 - 1.36603i) q^{10} -4.73205i q^{11} +(1.00000 + 1.73205i) q^{12} -1.00000i q^{13} +(6.46410 - 1.73205i) q^{14} +1.00000 q^{15} +(2.00000 - 3.46410i) q^{16} -4.00000 q^{17} +(-1.36603 + 0.366025i) q^{18} -0.732051i q^{19} +(-1.00000 - 1.73205i) q^{20} +4.73205i q^{21} +(-1.73205 - 6.46410i) q^{22} -2.00000 q^{23} +(2.00000 + 2.00000i) q^{24} -1.00000 q^{25} +(-0.366025 - 1.36603i) q^{26} -1.00000i q^{27} +(8.19615 - 4.73205i) q^{28} +4.92820i q^{29} +(1.36603 - 0.366025i) q^{30} +0.196152 q^{31} +(1.46410 - 5.46410i) q^{32} +4.73205 q^{33} +(-5.46410 + 1.46410i) q^{34} -4.73205i q^{35} +(-1.73205 + 1.00000i) q^{36} -0.535898i q^{37} +(-0.267949 - 1.00000i) q^{38} +1.00000 q^{39} +(-2.00000 - 2.00000i) q^{40} -4.92820 q^{41} +(1.73205 + 6.46410i) q^{42} +1.46410i q^{43} +(-4.73205 - 8.19615i) q^{44} +1.00000i q^{45} +(-2.73205 + 0.732051i) q^{46} -8.73205 q^{47} +(3.46410 + 2.00000i) q^{48} +15.3923 q^{49} +(-1.36603 + 0.366025i) q^{50} -4.00000i q^{51} +(-1.00000 - 1.73205i) q^{52} +12.3923i q^{53} +(-0.366025 - 1.36603i) q^{54} -4.73205 q^{55} +(9.46410 - 9.46410i) q^{56} +0.732051 q^{57} +(1.80385 + 6.73205i) q^{58} +7.66025i q^{59} +(1.73205 - 1.00000i) q^{60} -2.92820i q^{61} +(0.267949 - 0.0717968i) q^{62} -4.73205 q^{63} -8.00000i q^{64} -1.00000 q^{65} +(6.46410 - 1.73205i) q^{66} +12.1962i q^{67} +(-6.92820 + 4.00000i) q^{68} -2.00000i q^{69} +(-1.73205 - 6.46410i) q^{70} +13.2679 q^{71} +(-2.00000 + 2.00000i) q^{72} +15.8564 q^{73} +(-0.196152 - 0.732051i) q^{74} -1.00000i q^{75} +(-0.732051 - 1.26795i) q^{76} -22.3923i q^{77} +(1.36603 - 0.366025i) q^{78} +17.4641 q^{79} +(-3.46410 - 2.00000i) q^{80} +1.00000 q^{81} +(-6.73205 + 1.80385i) q^{82} +5.26795i q^{83} +(4.73205 + 8.19615i) q^{84} +4.00000i q^{85} +(0.535898 + 2.00000i) q^{86} -4.92820 q^{87} +(-9.46410 - 9.46410i) q^{88} +0.928203 q^{89} +(0.366025 + 1.36603i) q^{90} -4.73205i q^{91} +(-3.46410 + 2.00000i) q^{92} +0.196152i q^{93} +(-11.9282 + 3.19615i) q^{94} -0.732051 q^{95} +(5.46410 + 1.46410i) q^{96} -0.535898 q^{97} +(21.0263 - 5.63397i) q^{98} +4.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{6} + 12 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{6} + 12 q^{7} + 8 q^{8} - 4 q^{9} + 2 q^{10} + 4 q^{12} + 12 q^{14} + 4 q^{15} + 8 q^{16} - 16 q^{17} - 2 q^{18} - 4 q^{20} - 8 q^{23} + 8 q^{24} - 4 q^{25} + 2 q^{26} + 12 q^{28} + 2 q^{30} - 20 q^{31} - 8 q^{32} + 12 q^{33} - 8 q^{34} - 8 q^{38} + 4 q^{39} - 8 q^{40} + 8 q^{41} - 12 q^{44} - 4 q^{46} - 28 q^{47} + 20 q^{49} - 2 q^{50} - 4 q^{52} + 2 q^{54} - 12 q^{55} + 24 q^{56} - 4 q^{57} + 28 q^{58} + 8 q^{62} - 12 q^{63} - 4 q^{65} + 12 q^{66} + 60 q^{71} - 8 q^{72} + 8 q^{73} + 20 q^{74} + 4 q^{76} + 2 q^{78} + 56 q^{79} + 4 q^{81} - 20 q^{82} + 12 q^{84} + 16 q^{86} + 8 q^{87} - 24 q^{88} - 24 q^{89} - 2 q^{90} - 20 q^{94} + 4 q^{95} + 8 q^{96} - 16 q^{97} + 46 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times\).

\(n\) \(391\) \(521\) \(781\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 0.366025i 0.965926 0.258819i
\(3\) 1.00000i 0.577350i
\(4\) 1.73205 1.00000i 0.866025 0.500000i
\(5\) 1.00000i 0.447214i
\(6\) 0.366025 + 1.36603i 0.149429 + 0.557678i
\(7\) 4.73205 1.78855 0.894274 0.447521i \(-0.147693\pi\)
0.894274 + 0.447521i \(0.147693\pi\)
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) −1.00000 −0.333333
\(10\) −0.366025 1.36603i −0.115747 0.431975i
\(11\) 4.73205i 1.42677i −0.700774 0.713384i \(-0.747162\pi\)
0.700774 0.713384i \(-0.252838\pi\)
\(12\) 1.00000 + 1.73205i 0.288675 + 0.500000i
\(13\) 1.00000i 0.277350i
\(14\) 6.46410 1.73205i 1.72760 0.462910i
\(15\) 1.00000 0.258199
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) −4.00000 −0.970143 −0.485071 0.874475i \(-0.661206\pi\)
−0.485071 + 0.874475i \(0.661206\pi\)
\(18\) −1.36603 + 0.366025i −0.321975 + 0.0862730i
\(19\) 0.732051i 0.167944i −0.996468 0.0839720i \(-0.973239\pi\)
0.996468 0.0839720i \(-0.0267606\pi\)
\(20\) −1.00000 1.73205i −0.223607 0.387298i
\(21\) 4.73205i 1.03262i
\(22\) −1.73205 6.46410i −0.369274 1.37815i
\(23\) −2.00000 −0.417029 −0.208514 0.978019i \(-0.566863\pi\)
−0.208514 + 0.978019i \(0.566863\pi\)
\(24\) 2.00000 + 2.00000i 0.408248 + 0.408248i
\(25\) −1.00000 −0.200000
\(26\) −0.366025 1.36603i −0.0717835 0.267900i
\(27\) 1.00000i 0.192450i
\(28\) 8.19615 4.73205i 1.54893 0.894274i
\(29\) 4.92820i 0.915144i 0.889172 + 0.457572i \(0.151281\pi\)
−0.889172 + 0.457572i \(0.848719\pi\)
\(30\) 1.36603 0.366025i 0.249401 0.0668268i
\(31\) 0.196152 0.0352300 0.0176150 0.999845i \(-0.494393\pi\)
0.0176150 + 0.999845i \(0.494393\pi\)
\(32\) 1.46410 5.46410i 0.258819 0.965926i
\(33\) 4.73205 0.823744
\(34\) −5.46410 + 1.46410i −0.937086 + 0.251091i
\(35\) 4.73205i 0.799863i
\(36\) −1.73205 + 1.00000i −0.288675 + 0.166667i
\(37\) 0.535898i 0.0881012i −0.999029 0.0440506i \(-0.985974\pi\)
0.999029 0.0440506i \(-0.0140263\pi\)
\(38\) −0.267949 1.00000i −0.0434671 0.162221i
\(39\) 1.00000 0.160128
\(40\) −2.00000 2.00000i −0.316228 0.316228i
\(41\) −4.92820 −0.769656 −0.384828 0.922988i \(-0.625739\pi\)
−0.384828 + 0.922988i \(0.625739\pi\)
\(42\) 1.73205 + 6.46410i 0.267261 + 0.997433i
\(43\) 1.46410i 0.223273i 0.993749 + 0.111637i \(0.0356093\pi\)
−0.993749 + 0.111637i \(0.964391\pi\)
\(44\) −4.73205 8.19615i −0.713384 1.23562i
\(45\) 1.00000i 0.149071i
\(46\) −2.73205 + 0.732051i −0.402819 + 0.107935i
\(47\) −8.73205 −1.27370 −0.636850 0.770988i \(-0.719763\pi\)
−0.636850 + 0.770988i \(0.719763\pi\)
\(48\) 3.46410 + 2.00000i 0.500000 + 0.288675i
\(49\) 15.3923 2.19890
\(50\) −1.36603 + 0.366025i −0.193185 + 0.0517638i
\(51\) 4.00000i 0.560112i
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) 12.3923i 1.70221i 0.524992 + 0.851107i \(0.324068\pi\)
−0.524992 + 0.851107i \(0.675932\pi\)
\(54\) −0.366025 1.36603i −0.0498097 0.185893i
\(55\) −4.73205 −0.638070
\(56\) 9.46410 9.46410i 1.26469 1.26469i
\(57\) 0.732051 0.0969625
\(58\) 1.80385 + 6.73205i 0.236857 + 0.883962i
\(59\) 7.66025i 0.997280i 0.866809 + 0.498640i \(0.166167\pi\)
−0.866809 + 0.498640i \(0.833833\pi\)
\(60\) 1.73205 1.00000i 0.223607 0.129099i
\(61\) 2.92820i 0.374918i −0.982272 0.187459i \(-0.939975\pi\)
0.982272 0.187459i \(-0.0600252\pi\)
\(62\) 0.267949 0.0717968i 0.0340296 0.00911820i
\(63\) −4.73205 −0.596182
\(64\) 8.00000i 1.00000i
\(65\) −1.00000 −0.124035
\(66\) 6.46410 1.73205i 0.795676 0.213201i
\(67\) 12.1962i 1.49000i 0.667066 + 0.744999i \(0.267550\pi\)
−0.667066 + 0.744999i \(0.732450\pi\)
\(68\) −6.92820 + 4.00000i −0.840168 + 0.485071i
\(69\) 2.00000i 0.240772i
\(70\) −1.73205 6.46410i −0.207020 0.772608i
\(71\) 13.2679 1.57462 0.787308 0.616560i \(-0.211474\pi\)
0.787308 + 0.616560i \(0.211474\pi\)
\(72\) −2.00000 + 2.00000i −0.235702 + 0.235702i
\(73\) 15.8564 1.85585 0.927926 0.372764i \(-0.121590\pi\)
0.927926 + 0.372764i \(0.121590\pi\)
\(74\) −0.196152 0.732051i −0.0228023 0.0850992i
\(75\) 1.00000i 0.115470i
\(76\) −0.732051 1.26795i −0.0839720 0.145444i
\(77\) 22.3923i 2.55184i
\(78\) 1.36603 0.366025i 0.154672 0.0414442i
\(79\) 17.4641 1.96486 0.982432 0.186618i \(-0.0597528\pi\)
0.982432 + 0.186618i \(0.0597528\pi\)
\(80\) −3.46410 2.00000i −0.387298 0.223607i
\(81\) 1.00000 0.111111
\(82\) −6.73205 + 1.80385i −0.743431 + 0.199202i
\(83\) 5.26795i 0.578233i 0.957294 + 0.289116i \(0.0933614\pi\)
−0.957294 + 0.289116i \(0.906639\pi\)
\(84\) 4.73205 + 8.19615i 0.516309 + 0.894274i
\(85\) 4.00000i 0.433861i
\(86\) 0.535898 + 2.00000i 0.0577874 + 0.215666i
\(87\) −4.92820 −0.528359
\(88\) −9.46410 9.46410i −1.00888 1.00888i
\(89\) 0.928203 0.0983893 0.0491947 0.998789i \(-0.484335\pi\)
0.0491947 + 0.998789i \(0.484335\pi\)
\(90\) 0.366025 + 1.36603i 0.0385825 + 0.143992i
\(91\) 4.73205i 0.496054i
\(92\) −3.46410 + 2.00000i −0.361158 + 0.208514i
\(93\) 0.196152i 0.0203401i
\(94\) −11.9282 + 3.19615i −1.23030 + 0.329658i
\(95\) −0.732051 −0.0751068
\(96\) 5.46410 + 1.46410i 0.557678 + 0.149429i
\(97\) −0.535898 −0.0544122 −0.0272061 0.999630i \(-0.508661\pi\)
−0.0272061 + 0.999630i \(0.508661\pi\)
\(98\) 21.0263 5.63397i 2.12397 0.569117i
\(99\) 4.73205i 0.475589i
\(100\) −1.73205 + 1.00000i −0.173205 + 0.100000i
\(101\) 12.0000i 1.19404i −0.802225 0.597022i \(-0.796350\pi\)
0.802225 0.597022i \(-0.203650\pi\)
\(102\) −1.46410 5.46410i −0.144968 0.541027i
\(103\) −12.9282 −1.27385 −0.636927 0.770924i \(-0.719795\pi\)
−0.636927 + 0.770924i \(0.719795\pi\)
\(104\) −2.00000 2.00000i −0.196116 0.196116i
\(105\) 4.73205 0.461801
\(106\) 4.53590 + 16.9282i 0.440565 + 1.64421i
\(107\) 4.00000i 0.386695i −0.981130 0.193347i \(-0.938066\pi\)
0.981130 0.193347i \(-0.0619344\pi\)
\(108\) −1.00000 1.73205i −0.0962250 0.166667i
\(109\) 15.8564i 1.51877i 0.650643 + 0.759384i \(0.274500\pi\)
−0.650643 + 0.759384i \(0.725500\pi\)
\(110\) −6.46410 + 1.73205i −0.616328 + 0.165145i
\(111\) 0.535898 0.0508652
\(112\) 9.46410 16.3923i 0.894274 1.54893i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 1.00000 0.267949i 0.0936586 0.0250957i
\(115\) 2.00000i 0.186501i
\(116\) 4.92820 + 8.53590i 0.457572 + 0.792538i
\(117\) 1.00000i 0.0924500i
\(118\) 2.80385 + 10.4641i 0.258115 + 0.963299i
\(119\) −18.9282 −1.73515
\(120\) 2.00000 2.00000i 0.182574 0.182574i
\(121\) −11.3923 −1.03566
\(122\) −1.07180 4.00000i −0.0970359 0.362143i
\(123\) 4.92820i 0.444361i
\(124\) 0.339746 0.196152i 0.0305101 0.0176150i
\(125\) 1.00000i 0.0894427i
\(126\) −6.46410 + 1.73205i −0.575868 + 0.154303i
\(127\) −16.9282 −1.50214 −0.751068 0.660225i \(-0.770461\pi\)
−0.751068 + 0.660225i \(0.770461\pi\)
\(128\) −2.92820 10.9282i −0.258819 0.965926i
\(129\) −1.46410 −0.128907
\(130\) −1.36603 + 0.366025i −0.119808 + 0.0321026i
\(131\) 7.85641i 0.686417i 0.939259 + 0.343209i \(0.111514\pi\)
−0.939259 + 0.343209i \(0.888486\pi\)
\(132\) 8.19615 4.73205i 0.713384 0.411872i
\(133\) 3.46410i 0.300376i
\(134\) 4.46410 + 16.6603i 0.385640 + 1.43923i
\(135\) −1.00000 −0.0860663
\(136\) −8.00000 + 8.00000i −0.685994 + 0.685994i
\(137\) 10.3923 0.887875 0.443937 0.896058i \(-0.353581\pi\)
0.443937 + 0.896058i \(0.353581\pi\)
\(138\) −0.732051 2.73205i −0.0623163 0.232568i
\(139\) 2.00000i 0.169638i −0.996396 0.0848189i \(-0.972969\pi\)
0.996396 0.0848189i \(-0.0270312\pi\)
\(140\) −4.73205 8.19615i −0.399931 0.692701i
\(141\) 8.73205i 0.735371i
\(142\) 18.1244 4.85641i 1.52096 0.407541i
\(143\) −4.73205 −0.395714
\(144\) −2.00000 + 3.46410i −0.166667 + 0.288675i
\(145\) 4.92820 0.409265
\(146\) 21.6603 5.80385i 1.79262 0.480330i
\(147\) 15.3923i 1.26954i
\(148\) −0.535898 0.928203i −0.0440506 0.0762978i
\(149\) 3.46410i 0.283790i −0.989882 0.141895i \(-0.954680\pi\)
0.989882 0.141895i \(-0.0453196\pi\)
\(150\) −0.366025 1.36603i −0.0298858 0.111536i
\(151\) 18.7321 1.52439 0.762196 0.647346i \(-0.224121\pi\)
0.762196 + 0.647346i \(0.224121\pi\)
\(152\) −1.46410 1.46410i −0.118754 0.118754i
\(153\) 4.00000 0.323381
\(154\) −8.19615 30.5885i −0.660465 2.46489i
\(155\) 0.196152i 0.0157553i
\(156\) 1.73205 1.00000i 0.138675 0.0800641i
\(157\) 22.7846i 1.81841i −0.416349 0.909205i \(-0.636691\pi\)
0.416349 0.909205i \(-0.363309\pi\)
\(158\) 23.8564 6.39230i 1.89791 0.508544i
\(159\) −12.3923 −0.982774
\(160\) −5.46410 1.46410i −0.431975 0.115747i
\(161\) −9.46410 −0.745876
\(162\) 1.36603 0.366025i 0.107325 0.0287577i
\(163\) 20.1962i 1.58188i 0.611891 + 0.790942i \(0.290409\pi\)
−0.611891 + 0.790942i \(0.709591\pi\)
\(164\) −8.53590 + 4.92820i −0.666542 + 0.384828i
\(165\) 4.73205i 0.368390i
\(166\) 1.92820 + 7.19615i 0.149658 + 0.558530i
\(167\) 9.80385 0.758645 0.379322 0.925265i \(-0.376157\pi\)
0.379322 + 0.925265i \(0.376157\pi\)
\(168\) 9.46410 + 9.46410i 0.730171 + 0.730171i
\(169\) −1.00000 −0.0769231
\(170\) 1.46410 + 5.46410i 0.112291 + 0.419077i
\(171\) 0.732051i 0.0559813i
\(172\) 1.46410 + 2.53590i 0.111637 + 0.193360i
\(173\) 9.46410i 0.719542i 0.933041 + 0.359771i \(0.117145\pi\)
−0.933041 + 0.359771i \(0.882855\pi\)
\(174\) −6.73205 + 1.80385i −0.510355 + 0.136749i
\(175\) −4.73205 −0.357709
\(176\) −16.3923 9.46410i −1.23562 0.713384i
\(177\) −7.66025 −0.575780
\(178\) 1.26795 0.339746i 0.0950368 0.0254650i
\(179\) 10.3923i 0.776757i 0.921500 + 0.388379i \(0.126965\pi\)
−0.921500 + 0.388379i \(0.873035\pi\)
\(180\) 1.00000 + 1.73205i 0.0745356 + 0.129099i
\(181\) 4.92820i 0.366310i −0.983084 0.183155i \(-0.941369\pi\)
0.983084 0.183155i \(-0.0586311\pi\)
\(182\) −1.73205 6.46410i −0.128388 0.479151i
\(183\) 2.92820 0.216459
\(184\) −4.00000 + 4.00000i −0.294884 + 0.294884i
\(185\) −0.535898 −0.0394000
\(186\) 0.0717968 + 0.267949i 0.00526439 + 0.0196470i
\(187\) 18.9282i 1.38417i
\(188\) −15.1244 + 8.73205i −1.10306 + 0.636850i
\(189\) 4.73205i 0.344206i
\(190\) −1.00000 + 0.267949i −0.0725476 + 0.0194391i
\(191\) −16.3923 −1.18611 −0.593053 0.805164i \(-0.702077\pi\)
−0.593053 + 0.805164i \(0.702077\pi\)
\(192\) 8.00000 0.577350
\(193\) −3.46410 −0.249351 −0.124676 0.992198i \(-0.539789\pi\)
−0.124676 + 0.992198i \(0.539789\pi\)
\(194\) −0.732051 + 0.196152i −0.0525582 + 0.0140829i
\(195\) 1.00000i 0.0716115i
\(196\) 26.6603 15.3923i 1.90430 1.09945i
\(197\) 2.39230i 0.170445i 0.996362 + 0.0852223i \(0.0271601\pi\)
−0.996362 + 0.0852223i \(0.972840\pi\)
\(198\) 1.73205 + 6.46410i 0.123091 + 0.459384i
\(199\) −9.07180 −0.643083 −0.321541 0.946896i \(-0.604201\pi\)
−0.321541 + 0.946896i \(0.604201\pi\)
\(200\) −2.00000 + 2.00000i −0.141421 + 0.141421i
\(201\) −12.1962 −0.860250
\(202\) −4.39230 16.3923i −0.309041 1.15336i
\(203\) 23.3205i 1.63678i
\(204\) −4.00000 6.92820i −0.280056 0.485071i
\(205\) 4.92820i 0.344201i
\(206\) −17.6603 + 4.73205i −1.23045 + 0.329698i
\(207\) 2.00000 0.139010
\(208\) −3.46410 2.00000i −0.240192 0.138675i
\(209\) −3.46410 −0.239617
\(210\) 6.46410 1.73205i 0.446065 0.119523i
\(211\) 0.928203i 0.0639001i −0.999489 0.0319501i \(-0.989828\pi\)
0.999489 0.0319501i \(-0.0101718\pi\)
\(212\) 12.3923 + 21.4641i 0.851107 + 1.47416i
\(213\) 13.2679i 0.909105i
\(214\) −1.46410 5.46410i −0.100084 0.373518i
\(215\) 1.46410 0.0998509
\(216\) −2.00000 2.00000i −0.136083 0.136083i
\(217\) 0.928203 0.0630105
\(218\) 5.80385 + 21.6603i 0.393086 + 1.46702i
\(219\) 15.8564i 1.07148i
\(220\) −8.19615 + 4.73205i −0.552584 + 0.319035i
\(221\) 4.00000i 0.269069i
\(222\) 0.732051 0.196152i 0.0491320 0.0131649i
\(223\) −26.9808 −1.80677 −0.903383 0.428835i \(-0.858924\pi\)
−0.903383 + 0.428835i \(0.858924\pi\)
\(224\) 6.92820 25.8564i 0.462910 1.72760i
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 5.66025i 0.375684i 0.982199 + 0.187842i \(0.0601493\pi\)
−0.982199 + 0.187842i \(0.939851\pi\)
\(228\) 1.26795 0.732051i 0.0839720 0.0484812i
\(229\) 6.00000i 0.396491i −0.980152 0.198246i \(-0.936476\pi\)
0.980152 0.198246i \(-0.0635244\pi\)
\(230\) 0.732051 + 2.73205i 0.0482700 + 0.180146i
\(231\) 22.3923 1.47331
\(232\) 9.85641 + 9.85641i 0.647105 + 0.647105i
\(233\) 11.8564 0.776739 0.388370 0.921504i \(-0.373038\pi\)
0.388370 + 0.921504i \(0.373038\pi\)
\(234\) 0.366025 + 1.36603i 0.0239278 + 0.0892999i
\(235\) 8.73205i 0.569616i
\(236\) 7.66025 + 13.2679i 0.498640 + 0.863670i
\(237\) 17.4641i 1.13442i
\(238\) −25.8564 + 6.92820i −1.67602 + 0.449089i
\(239\) −19.8038 −1.28100 −0.640502 0.767956i \(-0.721274\pi\)
−0.640502 + 0.767956i \(0.721274\pi\)
\(240\) 2.00000 3.46410i 0.129099 0.223607i
\(241\) −20.9282 −1.34810 −0.674052 0.738684i \(-0.735448\pi\)
−0.674052 + 0.738684i \(0.735448\pi\)
\(242\) −15.5622 + 4.16987i −1.00037 + 0.268050i
\(243\) 1.00000i 0.0641500i
\(244\) −2.92820 5.07180i −0.187459 0.324689i
\(245\) 15.3923i 0.983378i
\(246\) −1.80385 6.73205i −0.115009 0.429220i
\(247\) −0.732051 −0.0465793
\(248\) 0.392305 0.392305i 0.0249114 0.0249114i
\(249\) −5.26795 −0.333843
\(250\) 0.366025 + 1.36603i 0.0231495 + 0.0863950i
\(251\) 6.39230i 0.403479i −0.979439 0.201739i \(-0.935341\pi\)
0.979439 0.201739i \(-0.0646594\pi\)
\(252\) −8.19615 + 4.73205i −0.516309 + 0.298091i
\(253\) 9.46410i 0.595003i
\(254\) −23.1244 + 6.19615i −1.45095 + 0.388781i
\(255\) −4.00000 −0.250490
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −3.07180 −0.191613 −0.0958067 0.995400i \(-0.530543\pi\)
−0.0958067 + 0.995400i \(0.530543\pi\)
\(258\) −2.00000 + 0.535898i −0.124515 + 0.0333636i
\(259\) 2.53590i 0.157573i
\(260\) −1.73205 + 1.00000i −0.107417 + 0.0620174i
\(261\) 4.92820i 0.305048i
\(262\) 2.87564 + 10.7321i 0.177658 + 0.663028i
\(263\) 16.5359 1.01965 0.509824 0.860279i \(-0.329711\pi\)
0.509824 + 0.860279i \(0.329711\pi\)
\(264\) 9.46410 9.46410i 0.582475 0.582475i
\(265\) 12.3923 0.761253
\(266\) −1.26795 4.73205i −0.0777430 0.290141i
\(267\) 0.928203i 0.0568051i
\(268\) 12.1962 + 21.1244i 0.744999 + 1.29038i
\(269\) 4.14359i 0.252639i −0.991990 0.126320i \(-0.959683\pi\)
0.991990 0.126320i \(-0.0403165\pi\)
\(270\) −1.36603 + 0.366025i −0.0831337 + 0.0222756i
\(271\) 5.66025 0.343836 0.171918 0.985111i \(-0.445004\pi\)
0.171918 + 0.985111i \(0.445004\pi\)
\(272\) −8.00000 + 13.8564i −0.485071 + 0.840168i
\(273\) 4.73205 0.286397
\(274\) 14.1962 3.80385i 0.857621 0.229799i
\(275\) 4.73205i 0.285353i
\(276\) −2.00000 3.46410i −0.120386 0.208514i
\(277\) 21.4641i 1.28965i 0.764329 + 0.644826i \(0.223070\pi\)
−0.764329 + 0.644826i \(0.776930\pi\)
\(278\) −0.732051 2.73205i −0.0439055 0.163858i
\(279\) −0.196152 −0.0117433
\(280\) −9.46410 9.46410i −0.565588 0.565588i
\(281\) −18.3923 −1.09719 −0.548596 0.836087i \(-0.684838\pi\)
−0.548596 + 0.836087i \(0.684838\pi\)
\(282\) −3.19615 11.9282i −0.190328 0.710314i
\(283\) 5.46410i 0.324807i 0.986724 + 0.162404i \(0.0519246\pi\)
−0.986724 + 0.162404i \(0.948075\pi\)
\(284\) 22.9808 13.2679i 1.36366 0.787308i
\(285\) 0.732051i 0.0433629i
\(286\) −6.46410 + 1.73205i −0.382230 + 0.102418i
\(287\) −23.3205 −1.37657
\(288\) −1.46410 + 5.46410i −0.0862730 + 0.321975i
\(289\) −1.00000 −0.0588235
\(290\) 6.73205 1.80385i 0.395320 0.105926i
\(291\) 0.535898i 0.0314149i
\(292\) 27.4641 15.8564i 1.60721 0.927926i
\(293\) 22.7846i 1.33109i −0.746357 0.665546i \(-0.768199\pi\)
0.746357 0.665546i \(-0.231801\pi\)
\(294\) 5.63397 + 21.0263i 0.328580 + 1.22628i
\(295\) 7.66025 0.445997
\(296\) −1.07180 1.07180i −0.0622969 0.0622969i
\(297\) −4.73205 −0.274581
\(298\) −1.26795 4.73205i −0.0734503 0.274120i
\(299\) 2.00000i 0.115663i
\(300\) −1.00000 1.73205i −0.0577350 0.100000i
\(301\) 6.92820i 0.399335i
\(302\) 25.5885 6.85641i 1.47245 0.394542i
\(303\) 12.0000 0.689382
\(304\) −2.53590 1.46410i −0.145444 0.0839720i
\(305\) −2.92820 −0.167668
\(306\) 5.46410 1.46410i 0.312362 0.0836971i
\(307\) 19.1244i 1.09148i 0.837953 + 0.545742i \(0.183752\pi\)
−0.837953 + 0.545742i \(0.816248\pi\)
\(308\) −22.3923 38.7846i −1.27592 2.20996i
\(309\) 12.9282i 0.735460i
\(310\) −0.0717968 0.267949i −0.00407778 0.0152185i
\(311\) −31.7128 −1.79827 −0.899134 0.437673i \(-0.855803\pi\)
−0.899134 + 0.437673i \(0.855803\pi\)
\(312\) 2.00000 2.00000i 0.113228 0.113228i
\(313\) 8.00000 0.452187 0.226093 0.974106i \(-0.427405\pi\)
0.226093 + 0.974106i \(0.427405\pi\)
\(314\) −8.33975 31.1244i −0.470639 1.75645i
\(315\) 4.73205i 0.266621i
\(316\) 30.2487 17.4641i 1.70162 0.982432i
\(317\) 20.5359i 1.15341i −0.816952 0.576705i \(-0.804338\pi\)
0.816952 0.576705i \(-0.195662\pi\)
\(318\) −16.9282 + 4.53590i −0.949286 + 0.254361i
\(319\) 23.3205 1.30570
\(320\) −8.00000 −0.447214
\(321\) 4.00000 0.223258
\(322\) −12.9282 + 3.46410i −0.720461 + 0.193047i
\(323\) 2.92820i 0.162930i
\(324\) 1.73205 1.00000i 0.0962250 0.0555556i
\(325\) 1.00000i 0.0554700i
\(326\) 7.39230 + 27.5885i 0.409422 + 1.52798i
\(327\) −15.8564 −0.876861
\(328\) −9.85641 + 9.85641i −0.544229 + 0.544229i
\(329\) −41.3205 −2.27807
\(330\) −1.73205 6.46410i −0.0953463 0.355837i
\(331\) 12.0526i 0.662469i 0.943549 + 0.331234i \(0.107465\pi\)
−0.943549 + 0.331234i \(0.892535\pi\)
\(332\) 5.26795 + 9.12436i 0.289116 + 0.500764i
\(333\) 0.535898i 0.0293671i
\(334\) 13.3923 3.58846i 0.732794 0.196352i
\(335\) 12.1962 0.666347
\(336\) 16.3923 + 9.46410i 0.894274 + 0.516309i
\(337\) −20.0000 −1.08947 −0.544735 0.838608i \(-0.683370\pi\)
−0.544735 + 0.838608i \(0.683370\pi\)
\(338\) −1.36603 + 0.366025i −0.0743020 + 0.0199092i
\(339\) 0 0
\(340\) 4.00000 + 6.92820i 0.216930 + 0.375735i
\(341\) 0.928203i 0.0502650i
\(342\) 0.267949 + 1.00000i 0.0144890 + 0.0540738i
\(343\) 39.7128 2.14429
\(344\) 2.92820 + 2.92820i 0.157878 + 0.157878i
\(345\) −2.00000 −0.107676
\(346\) 3.46410 + 12.9282i 0.186231 + 0.695025i
\(347\) 31.7128i 1.70243i −0.524815 0.851216i \(-0.675865\pi\)
0.524815 0.851216i \(-0.324135\pi\)
\(348\) −8.53590 + 4.92820i −0.457572 + 0.264179i
\(349\) 34.7846i 1.86198i −0.365048 0.930989i \(-0.618947\pi\)
0.365048 0.930989i \(-0.381053\pi\)
\(350\) −6.46410 + 1.73205i −0.345521 + 0.0925820i
\(351\) −1.00000 −0.0533761
\(352\) −25.8564 6.92820i −1.37815 0.369274i
\(353\) 21.7128 1.15566 0.577828 0.816158i \(-0.303900\pi\)
0.577828 + 0.816158i \(0.303900\pi\)
\(354\) −10.4641 + 2.80385i −0.556161 + 0.149023i
\(355\) 13.2679i 0.704190i
\(356\) 1.60770 0.928203i 0.0852077 0.0491947i
\(357\) 18.9282i 1.00179i
\(358\) 3.80385 + 14.1962i 0.201040 + 0.750290i
\(359\) 13.2679 0.700256 0.350128 0.936702i \(-0.386138\pi\)
0.350128 + 0.936702i \(0.386138\pi\)
\(360\) 2.00000 + 2.00000i 0.105409 + 0.105409i
\(361\) 18.4641 0.971795
\(362\) −1.80385 6.73205i −0.0948081 0.353829i
\(363\) 11.3923i 0.597941i
\(364\) −4.73205 8.19615i −0.248027 0.429595i
\(365\) 15.8564i 0.829962i
\(366\) 4.00000 1.07180i 0.209083 0.0560237i
\(367\) −0.535898 −0.0279737 −0.0139868 0.999902i \(-0.504452\pi\)
−0.0139868 + 0.999902i \(0.504452\pi\)
\(368\) −4.00000 + 6.92820i −0.208514 + 0.361158i
\(369\) 4.92820 0.256552
\(370\) −0.732051 + 0.196152i −0.0380575 + 0.0101975i
\(371\) 58.6410i 3.04449i
\(372\) 0.196152 + 0.339746i 0.0101700 + 0.0176150i
\(373\) 0.928203i 0.0480605i −0.999711 0.0240303i \(-0.992350\pi\)
0.999711 0.0240303i \(-0.00764981\pi\)
\(374\) 6.92820 + 25.8564i 0.358249 + 1.33700i
\(375\) −1.00000 −0.0516398
\(376\) −17.4641 + 17.4641i −0.900642 + 0.900642i
\(377\) 4.92820 0.253815
\(378\) −1.73205 6.46410i −0.0890871 0.332478i
\(379\) 24.7321i 1.27040i −0.772348 0.635200i \(-0.780918\pi\)
0.772348 0.635200i \(-0.219082\pi\)
\(380\) −1.26795 + 0.732051i −0.0650444 + 0.0375534i
\(381\) 16.9282i 0.867258i
\(382\) −22.3923 + 6.00000i −1.14569 + 0.306987i
\(383\) −6.87564 −0.351329 −0.175665 0.984450i \(-0.556207\pi\)
−0.175665 + 0.984450i \(0.556207\pi\)
\(384\) 10.9282 2.92820i 0.557678 0.149429i
\(385\) −22.3923 −1.14122
\(386\) −4.73205 + 1.26795i −0.240855 + 0.0645369i
\(387\) 1.46410i 0.0744245i
\(388\) −0.928203 + 0.535898i −0.0471224 + 0.0272061i
\(389\) 8.92820i 0.452678i −0.974049 0.226339i \(-0.927324\pi\)
0.974049 0.226339i \(-0.0726757\pi\)
\(390\) −0.366025 1.36603i −0.0185344 0.0691714i
\(391\) 8.00000 0.404577
\(392\) 30.7846 30.7846i 1.55486 1.55486i
\(393\) −7.85641 −0.396303
\(394\) 0.875644 + 3.26795i 0.0441143 + 0.164637i
\(395\) 17.4641i 0.878714i
\(396\) 4.73205 + 8.19615i 0.237795 + 0.411872i
\(397\) 15.8564i 0.795810i 0.917427 + 0.397905i \(0.130263\pi\)
−0.917427 + 0.397905i \(0.869737\pi\)
\(398\) −12.3923 + 3.32051i −0.621170 + 0.166442i
\(399\) 3.46410 0.173422
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) −10.0000 −0.499376 −0.249688 0.968326i \(-0.580328\pi\)
−0.249688 + 0.968326i \(0.580328\pi\)
\(402\) −16.6603 + 4.46410i −0.830938 + 0.222649i
\(403\) 0.196152i 0.00977105i
\(404\) −12.0000 20.7846i −0.597022 1.03407i
\(405\) 1.00000i 0.0496904i
\(406\) 8.53590 + 31.8564i 0.423630 + 1.58101i
\(407\) −2.53590 −0.125700
\(408\) −8.00000 8.00000i −0.396059 0.396059i
\(409\) −24.2487 −1.19902 −0.599511 0.800367i \(-0.704638\pi\)
−0.599511 + 0.800367i \(0.704638\pi\)
\(410\) 1.80385 + 6.73205i 0.0890857 + 0.332472i
\(411\) 10.3923i 0.512615i
\(412\) −22.3923 + 12.9282i −1.10319 + 0.636927i
\(413\) 36.2487i 1.78368i
\(414\) 2.73205 0.732051i 0.134273 0.0359783i
\(415\) 5.26795 0.258593
\(416\) −5.46410 1.46410i −0.267900 0.0717835i
\(417\) 2.00000 0.0979404
\(418\) −4.73205 + 1.26795i −0.231452 + 0.0620174i
\(419\) 36.6410i 1.79003i −0.446035 0.895015i \(-0.647164\pi\)
0.446035 0.895015i \(-0.352836\pi\)
\(420\) 8.19615 4.73205i 0.399931 0.230900i
\(421\) 5.32051i 0.259306i −0.991559 0.129653i \(-0.958614\pi\)
0.991559 0.129653i \(-0.0413863\pi\)
\(422\) −0.339746 1.26795i −0.0165386 0.0617228i
\(423\) 8.73205 0.424567
\(424\) 24.7846 + 24.7846i 1.20365 + 1.20365i
\(425\) 4.00000 0.194029
\(426\) 4.85641 + 18.1244i 0.235294 + 0.878128i
\(427\) 13.8564i 0.670559i
\(428\) −4.00000 6.92820i −0.193347 0.334887i
\(429\) 4.73205i 0.228466i
\(430\) 2.00000 0.535898i 0.0964486 0.0258433i
\(431\) −39.1244 −1.88455 −0.942277 0.334835i \(-0.891320\pi\)
−0.942277 + 0.334835i \(0.891320\pi\)
\(432\) −3.46410 2.00000i −0.166667 0.0962250i
\(433\) 17.7128 0.851223 0.425612 0.904906i \(-0.360059\pi\)
0.425612 + 0.904906i \(0.360059\pi\)
\(434\) 1.26795 0.339746i 0.0608635 0.0163083i
\(435\) 4.92820i 0.236289i
\(436\) 15.8564 + 27.4641i 0.759384 + 1.31529i
\(437\) 1.46410i 0.0700375i
\(438\) 5.80385 + 21.6603i 0.277319 + 1.03497i
\(439\) −17.8564 −0.852240 −0.426120 0.904667i \(-0.640120\pi\)
−0.426120 + 0.904667i \(0.640120\pi\)
\(440\) −9.46410 + 9.46410i −0.451183 + 0.451183i
\(441\) −15.3923 −0.732967
\(442\) 1.46410 + 5.46410i 0.0696402 + 0.259901i
\(443\) 6.92820i 0.329169i −0.986363 0.164584i \(-0.947372\pi\)
0.986363 0.164584i \(-0.0526283\pi\)
\(444\) 0.928203 0.535898i 0.0440506 0.0254326i
\(445\) 0.928203i 0.0440011i
\(446\) −36.8564 + 9.87564i −1.74520 + 0.467625i
\(447\) 3.46410 0.163846
\(448\) 37.8564i 1.78855i
\(449\) 26.3923 1.24553 0.622765 0.782409i \(-0.286009\pi\)
0.622765 + 0.782409i \(0.286009\pi\)
\(450\) 1.36603 0.366025i 0.0643951 0.0172546i
\(451\) 23.3205i 1.09812i
\(452\) 0 0
\(453\) 18.7321i 0.880109i
\(454\) 2.07180 + 7.73205i 0.0972342 + 0.362883i
\(455\) −4.73205 −0.221842
\(456\) 1.46410 1.46410i 0.0685628 0.0685628i
\(457\) 15.0718 0.705029 0.352514 0.935806i \(-0.385327\pi\)
0.352514 + 0.935806i \(0.385327\pi\)
\(458\) −2.19615 8.19615i −0.102619 0.382981i
\(459\) 4.00000i 0.186704i
\(460\) 2.00000 + 3.46410i 0.0932505 + 0.161515i
\(461\) 3.07180i 0.143068i 0.997438 + 0.0715339i \(0.0227894\pi\)
−0.997438 + 0.0715339i \(0.977211\pi\)
\(462\) 30.5885 8.19615i 1.42310 0.381320i
\(463\) 19.6603 0.913689 0.456845 0.889546i \(-0.348979\pi\)
0.456845 + 0.889546i \(0.348979\pi\)
\(464\) 17.0718 + 9.85641i 0.792538 + 0.457572i
\(465\) 0.196152 0.00909635
\(466\) 16.1962 4.33975i 0.750272 0.201035i
\(467\) 19.6077i 0.907336i 0.891171 + 0.453668i \(0.149885\pi\)
−0.891171 + 0.453668i \(0.850115\pi\)
\(468\) 1.00000 + 1.73205i 0.0462250 + 0.0800641i
\(469\) 57.7128i 2.66493i
\(470\) 3.19615 + 11.9282i 0.147428 + 0.550207i
\(471\) 22.7846 1.04986
\(472\) 15.3205 + 15.3205i 0.705184 + 0.705184i
\(473\) 6.92820 0.318559
\(474\) 6.39230 + 23.8564i 0.293608 + 1.09576i
\(475\) 0.732051i 0.0335888i
\(476\) −32.7846 + 18.9282i −1.50268 + 0.867573i
\(477\) 12.3923i 0.567405i
\(478\) −27.0526 + 7.24871i −1.23736 + 0.331548i
\(479\) −39.9090 −1.82349 −0.911744 0.410760i \(-0.865263\pi\)
−0.911744 + 0.410760i \(0.865263\pi\)
\(480\) 1.46410 5.46410i 0.0668268 0.249401i
\(481\) −0.535898 −0.0244349
\(482\) −28.5885 + 7.66025i −1.30217 + 0.348915i
\(483\) 9.46410i 0.430632i
\(484\) −19.7321 + 11.3923i −0.896911 + 0.517832i
\(485\) 0.535898i 0.0243339i
\(486\) 0.366025 + 1.36603i 0.0166032 + 0.0619642i
\(487\) −8.73205 −0.395687 −0.197843 0.980234i \(-0.563394\pi\)
−0.197843 + 0.980234i \(0.563394\pi\)
\(488\) −5.85641 5.85641i −0.265107 0.265107i
\(489\) −20.1962 −0.913302
\(490\) −5.63397 21.0263i −0.254517 0.949870i
\(491\) 41.3205i 1.86477i −0.361469 0.932384i \(-0.617725\pi\)
0.361469 0.932384i \(-0.382275\pi\)
\(492\) −4.92820 8.53590i −0.222181 0.384828i
\(493\) 19.7128i 0.887820i
\(494\) −1.00000 + 0.267949i −0.0449921 + 0.0120556i
\(495\) 4.73205 0.212690
\(496\) 0.392305 0.679492i 0.0176150 0.0305101i
\(497\) 62.7846 2.81627
\(498\) −7.19615 + 1.92820i −0.322467 + 0.0864049i
\(499\) 2.19615i 0.0983133i 0.998791 + 0.0491566i \(0.0156534\pi\)
−0.998791 + 0.0491566i \(0.984347\pi\)
\(500\) 1.00000 + 1.73205i 0.0447214 + 0.0774597i
\(501\) 9.80385i 0.438004i
\(502\) −2.33975 8.73205i −0.104428 0.389731i
\(503\) 35.1769 1.56846 0.784231 0.620470i \(-0.213058\pi\)
0.784231 + 0.620470i \(0.213058\pi\)
\(504\) −9.46410 + 9.46410i −0.421565 + 0.421565i
\(505\) −12.0000 −0.533993
\(506\) 3.46410 + 12.9282i 0.153998 + 0.574729i
\(507\) 1.00000i 0.0444116i
\(508\) −29.3205 + 16.9282i −1.30089 + 0.751068i
\(509\) 5.60770i 0.248557i −0.992247 0.124278i \(-0.960338\pi\)
0.992247 0.124278i \(-0.0396616\pi\)
\(510\) −5.46410 + 1.46410i −0.241954 + 0.0648315i
\(511\) 75.0333 3.31928
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) −0.732051 −0.0323208
\(514\) −4.19615 + 1.12436i −0.185084 + 0.0495932i
\(515\) 12.9282i 0.569685i
\(516\) −2.53590 + 1.46410i −0.111637 + 0.0644535i
\(517\) 41.3205i 1.81727i
\(518\) −0.928203 3.46410i −0.0407829 0.152204i
\(519\) −9.46410 −0.415428
\(520\) −2.00000 + 2.00000i −0.0877058 + 0.0877058i
\(521\) 9.46410 0.414630 0.207315 0.978274i \(-0.433528\pi\)
0.207315 + 0.978274i \(0.433528\pi\)
\(522\) −1.80385 6.73205i −0.0789523 0.294654i
\(523\) 16.0000i 0.699631i 0.936819 + 0.349816i \(0.113756\pi\)
−0.936819 + 0.349816i \(0.886244\pi\)
\(524\) 7.85641 + 13.6077i 0.343209 + 0.594455i
\(525\) 4.73205i 0.206524i
\(526\) 22.5885 6.05256i 0.984904 0.263904i
\(527\) −0.784610 −0.0341781
\(528\) 9.46410 16.3923i 0.411872 0.713384i
\(529\) −19.0000 −0.826087
\(530\) 16.9282 4.53590i 0.735314 0.197027i
\(531\) 7.66025i 0.332427i
\(532\) −3.46410 6.00000i −0.150188 0.260133i
\(533\) 4.92820i 0.213464i
\(534\) 0.339746 + 1.26795i 0.0147022 + 0.0548695i
\(535\) −4.00000 −0.172935
\(536\) 24.3923 + 24.3923i 1.05359 + 1.05359i
\(537\) −10.3923 −0.448461
\(538\) −1.51666 5.66025i −0.0653879 0.244031i
\(539\) 72.8372i 3.13732i
\(540\) −1.73205 + 1.00000i −0.0745356 + 0.0430331i
\(541\) 32.2487i 1.38648i −0.720707 0.693240i \(-0.756183\pi\)
0.720707 0.693240i \(-0.243817\pi\)
\(542\) 7.73205 2.07180i 0.332120 0.0889913i
\(543\) 4.92820 0.211489
\(544\) −5.85641 + 21.8564i −0.251091 + 0.937086i
\(545\) 15.8564 0.679214
\(546\) 6.46410 1.73205i 0.276638 0.0741249i
\(547\) 16.7846i 0.717658i −0.933403 0.358829i \(-0.883176\pi\)
0.933403 0.358829i \(-0.116824\pi\)
\(548\) 18.0000 10.3923i 0.768922 0.443937i
\(549\) 2.92820i 0.124973i
\(550\) 1.73205 + 6.46410i 0.0738549 + 0.275630i
\(551\) 3.60770 0.153693
\(552\) −4.00000 4.00000i −0.170251 0.170251i
\(553\) 82.6410 3.51425
\(554\) 7.85641 + 29.3205i 0.333787 + 1.24571i
\(555\) 0.535898i 0.0227476i
\(556\) −2.00000 3.46410i −0.0848189 0.146911i
\(557\) 34.7846i 1.47387i −0.675963 0.736936i \(-0.736272\pi\)
0.675963 0.736936i \(-0.263728\pi\)
\(558\) −0.267949 + 0.0717968i −0.0113432 + 0.00303940i
\(559\) 1.46410 0.0619249
\(560\) −16.3923 9.46410i −0.692701 0.399931i
\(561\) −18.9282 −0.799149
\(562\) −25.1244 + 6.73205i −1.05981 + 0.283974i
\(563\) 4.67949i 0.197217i 0.995126 + 0.0986085i \(0.0314392\pi\)
−0.995126 + 0.0986085i \(0.968561\pi\)
\(564\) −8.73205 15.1244i −0.367686 0.636850i
\(565\) 0 0
\(566\) 2.00000 + 7.46410i 0.0840663 + 0.313740i
\(567\) 4.73205 0.198727
\(568\) 26.5359 26.5359i 1.11342 1.11342i
\(569\) 35.8564 1.50318 0.751589 0.659631i \(-0.229288\pi\)
0.751589 + 0.659631i \(0.229288\pi\)
\(570\) −0.267949 1.00000i −0.0112232 0.0418854i
\(571\) 26.3923i 1.10448i 0.833684 + 0.552242i \(0.186227\pi\)
−0.833684 + 0.552242i \(0.813773\pi\)
\(572\) −8.19615 + 4.73205i −0.342698 + 0.197857i
\(573\) 16.3923i 0.684798i
\(574\) −31.8564 + 8.53590i −1.32966 + 0.356282i
\(575\) 2.00000 0.0834058
\(576\) 8.00000i 0.333333i
\(577\) −42.3923 −1.76481 −0.882407 0.470486i \(-0.844079\pi\)
−0.882407 + 0.470486i \(0.844079\pi\)
\(578\) −1.36603 + 0.366025i −0.0568192 + 0.0152246i
\(579\) 3.46410i 0.143963i
\(580\) 8.53590 4.92820i 0.354434 0.204633i
\(581\) 24.9282i 1.03420i
\(582\) −0.196152 0.732051i −0.00813078 0.0303445i
\(583\) 58.6410 2.42866
\(584\) 31.7128 31.7128i 1.31229 1.31229i
\(585\) 1.00000 0.0413449
\(586\) −8.33975 31.1244i −0.344512 1.28574i
\(587\) 2.33975i 0.0965717i −0.998834 0.0482858i \(-0.984624\pi\)
0.998834 0.0482858i \(-0.0153758\pi\)
\(588\) 15.3923 + 26.6603i 0.634768 + 1.09945i
\(589\) 0.143594i 0.00591667i
\(590\) 10.4641 2.80385i 0.430800 0.115433i
\(591\) −2.39230 −0.0984063
\(592\) −1.85641 1.07180i −0.0762978 0.0440506i
\(593\) −5.32051 −0.218487 −0.109244 0.994015i \(-0.534843\pi\)
−0.109244 + 0.994015i \(0.534843\pi\)
\(594\) −6.46410 + 1.73205i −0.265225 + 0.0710669i
\(595\) 18.9282i 0.775981i
\(596\) −3.46410 6.00000i −0.141895 0.245770i
\(597\) 9.07180i 0.371284i
\(598\) 0.732051 + 2.73205i 0.0299358 + 0.111722i
\(599\) −38.2487 −1.56280 −0.781400 0.624030i \(-0.785494\pi\)
−0.781400 + 0.624030i \(0.785494\pi\)
\(600\) −2.00000 2.00000i −0.0816497 0.0816497i
\(601\) 40.3923 1.64764 0.823818 0.566854i \(-0.191840\pi\)
0.823818 + 0.566854i \(0.191840\pi\)
\(602\) 2.53590 + 9.46410i 0.103356 + 0.385728i
\(603\) 12.1962i 0.496666i
\(604\) 32.4449 18.7321i 1.32016 0.762196i
\(605\) 11.3923i 0.463163i
\(606\) 16.3923 4.39230i 0.665892 0.178425i
\(607\) 16.5359 0.671171 0.335586 0.942010i \(-0.391066\pi\)
0.335586 + 0.942010i \(0.391066\pi\)
\(608\) −4.00000 1.07180i −0.162221 0.0434671i
\(609\) −23.3205 −0.944995
\(610\) −4.00000 + 1.07180i −0.161955 + 0.0433958i
\(611\) 8.73205i 0.353261i
\(612\) 6.92820 4.00000i 0.280056 0.161690i
\(613\) 26.0000i 1.05013i −0.851062 0.525065i \(-0.824041\pi\)
0.851062 0.525065i \(-0.175959\pi\)
\(614\) 7.00000 + 26.1244i 0.282497 + 1.05429i
\(615\) −4.92820 −0.198724
\(616\) −44.7846 44.7846i −1.80442 1.80442i
\(617\) −0.928203 −0.0373681 −0.0186840 0.999825i \(-0.505948\pi\)
−0.0186840 + 0.999825i \(0.505948\pi\)
\(618\) −4.73205 17.6603i −0.190351 0.710400i
\(619\) 28.0526i 1.12753i −0.825936 0.563764i \(-0.809353\pi\)
0.825936 0.563764i \(-0.190647\pi\)
\(620\) −0.196152 0.339746i −0.00787767 0.0136445i
\(621\) 2.00000i 0.0802572i
\(622\) −43.3205 + 11.6077i −1.73699 + 0.465426i
\(623\) 4.39230 0.175974
\(624\) 2.00000 3.46410i 0.0800641 0.138675i
\(625\) 1.00000 0.0400000
\(626\) 10.9282 2.92820i 0.436779 0.117035i
\(627\) 3.46410i 0.138343i
\(628\) −22.7846 39.4641i −0.909205 1.57479i
\(629\) 2.14359i 0.0854707i
\(630\) 1.73205 + 6.46410i 0.0690066 + 0.257536i
\(631\) 7.80385 0.310666 0.155333 0.987862i \(-0.450355\pi\)
0.155333 + 0.987862i \(0.450355\pi\)
\(632\) 34.9282 34.9282i 1.38937 1.38937i
\(633\) 0.928203 0.0368928
\(634\) −7.51666 28.0526i −0.298525 1.11411i
\(635\) 16.9282i 0.671775i
\(636\) −21.4641 + 12.3923i −0.851107 + 0.491387i
\(637\) 15.3923i 0.609865i
\(638\) 31.8564 8.53590i 1.26121 0.337939i
\(639\) −13.2679 −0.524872
\(640\) −10.9282 + 2.92820i −0.431975 + 0.115747i
\(641\) 29.4641 1.16376 0.581881 0.813274i \(-0.302317\pi\)
0.581881 + 0.813274i \(0.302317\pi\)
\(642\) 5.46410 1.46410i 0.215651 0.0577835i
\(643\) 34.4449i 1.35837i 0.733966 + 0.679186i \(0.237667\pi\)
−0.733966 + 0.679186i \(0.762333\pi\)
\(644\) −16.3923 + 9.46410i −0.645947 + 0.372938i
\(645\) 1.46410i 0.0576489i
\(646\) 1.07180 + 4.00000i 0.0421693 + 0.157378i
\(647\) −38.7846 −1.52478 −0.762390 0.647118i \(-0.775974\pi\)
−0.762390 + 0.647118i \(0.775974\pi\)
\(648\) 2.00000 2.00000i 0.0785674 0.0785674i
\(649\) 36.2487 1.42289
\(650\) 0.366025 + 1.36603i 0.0143567 + 0.0535799i
\(651\) 0.928203i 0.0363792i
\(652\) 20.1962 + 34.9808i 0.790942 + 1.36995i
\(653\) 16.9282i 0.662452i 0.943551 + 0.331226i \(0.107462\pi\)
−0.943551 + 0.331226i \(0.892538\pi\)
\(654\) −21.6603 + 5.80385i −0.846983 + 0.226948i
\(655\) 7.85641 0.306975
\(656\) −9.85641 + 17.0718i −0.384828 + 0.666542i
\(657\) −15.8564 −0.618617
\(658\) −56.4449 + 15.1244i −2.20045 + 0.589609i
\(659\) 34.0000i 1.32445i 0.749304 + 0.662226i \(0.230388\pi\)
−0.749304 + 0.662226i \(0.769612\pi\)
\(660\) −4.73205 8.19615i −0.184195 0.319035i
\(661\) 10.3923i 0.404214i 0.979363 + 0.202107i \(0.0647788\pi\)
−0.979363 + 0.202107i \(0.935221\pi\)
\(662\) 4.41154 + 16.4641i 0.171459 + 0.639895i
\(663\) −4.00000 −0.155347
\(664\) 10.5359 + 10.5359i 0.408872 + 0.408872i
\(665\) −3.46410 −0.134332
\(666\) 0.196152 + 0.732051i 0.00760075 + 0.0283664i
\(667\) 9.85641i 0.381642i
\(668\) 16.9808 9.80385i 0.657005 0.379322i
\(669\) 26.9808i 1.04314i
\(670\) 16.6603 4.46410i 0.643642 0.172463i
\(671\) −13.8564 −0.534921
\(672\) 25.8564 + 6.92820i 0.997433 + 0.267261i
\(673\) −9.07180 −0.349692 −0.174846 0.984596i \(-0.555943\pi\)
−0.174846 + 0.984596i \(0.555943\pi\)
\(674\) −27.3205 + 7.32051i −1.05235 + 0.281975i
\(675\) 1.00000i 0.0384900i
\(676\) −1.73205 + 1.00000i −0.0666173 + 0.0384615i
\(677\) 6.53590i 0.251195i −0.992081 0.125597i \(-0.959915\pi\)
0.992081 0.125597i \(-0.0400848\pi\)
\(678\) 0 0
\(679\) −2.53590 −0.0973188
\(680\) 8.00000 + 8.00000i 0.306786 + 0.306786i
\(681\) −5.66025 −0.216901
\(682\) −0.339746 1.26795i −0.0130095 0.0485523i
\(683\) 33.2679i 1.27296i 0.771292 + 0.636481i \(0.219611\pi\)
−0.771292 + 0.636481i \(0.780389\pi\)
\(684\) 0.732051 + 1.26795i 0.0279907 + 0.0484812i
\(685\) 10.3923i 0.397070i
\(686\) 54.2487 14.5359i 2.07123 0.554983i
\(687\) 6.00000 0.228914
\(688\) 5.07180 + 2.92820i 0.193360 + 0.111637i
\(689\) 12.3923 0.472109
\(690\) −2.73205 + 0.732051i −0.104007 + 0.0278687i
\(691\) 34.5885i 1.31581i −0.753102 0.657903i \(-0.771443\pi\)
0.753102 0.657903i \(-0.228557\pi\)
\(692\) 9.46410 + 16.3923i 0.359771 + 0.623142i
\(693\) 22.3923i 0.850613i
\(694\) −11.6077 43.3205i −0.440622 1.64442i
\(695\) −2.00000 −0.0758643
\(696\) −9.85641 + 9.85641i −0.373606 + 0.373606i
\(697\) 19.7128 0.746676
\(698\) −12.7321 47.5167i −0.481915 1.79853i
\(699\) 11.8564i 0.448450i
\(700\) −8.19615 + 4.73205i −0.309785 + 0.178855i
\(701\) 18.0000i 0.679851i −0.940452 0.339925i \(-0.889598\pi\)
0.940452 0.339925i \(-0.110402\pi\)
\(702\) −1.36603 + 0.366025i −0.0515573 + 0.0138147i
\(703\) −0.392305 −0.0147961
\(704\) −37.8564 −1.42677
\(705\) −8.73205 −0.328868
\(706\) 29.6603 7.94744i 1.11628 0.299106i
\(707\) 56.7846i 2.13561i
\(708\) −13.2679 + 7.66025i −0.498640 + 0.287890i
\(709\) 35.0718i 1.31715i 0.752516 + 0.658574i \(0.228840\pi\)
−0.752516 + 0.658574i \(0.771160\pi\)
\(710\) −4.85641 18.1244i −0.182258 0.680195i
\(711\) −17.4641 −0.654955
\(712\) 1.85641 1.85641i 0.0695718 0.0695718i
\(713\) −0.392305 −0.0146919
\(714\) −6.92820 25.8564i −0.259281 0.967652i
\(715\) 4.73205i 0.176969i
\(716\) 10.3923 + 18.0000i 0.388379 + 0.672692i
\(717\) 19.8038i 0.739588i
\(718\) 18.1244 4.85641i 0.676395 0.181239i
\(719\) −1.85641 −0.0692323 −0.0346161 0.999401i \(-0.511021\pi\)
−0.0346161 + 0.999401i \(0.511021\pi\)
\(720\) 3.46410 + 2.00000i 0.129099 + 0.0745356i
\(721\) −61.1769 −2.27835
\(722\) 25.2224 6.75833i 0.938682 0.251519i
\(723\) 20.9282i 0.778328i
\(724\) −4.92820 8.53590i −0.183155 0.317234i
\(725\) 4.92820i 0.183029i
\(726\) −4.16987 15.5622i −0.154759 0.577567i
\(727\) −4.92820 −0.182777 −0.0913885 0.995815i \(-0.529130\pi\)
−0.0913885 + 0.995815i \(0.529130\pi\)
\(728\) −9.46410 9.46410i −0.350763 0.350763i
\(729\) −1.00000 −0.0370370
\(730\) −5.80385 21.6603i −0.214810 0.801682i
\(731\) 5.85641i 0.216607i
\(732\) 5.07180 2.92820i 0.187459 0.108230i
\(733\) 6.39230i 0.236105i −0.993007 0.118053i \(-0.962335\pi\)
0.993007 0.118053i \(-0.0376651\pi\)
\(734\) −0.732051 + 0.196152i −0.0270205 + 0.00724012i
\(735\) 15.3923 0.567754
\(736\) −2.92820 + 10.9282i −0.107935 + 0.402819i
\(737\) 57.7128 2.12588
\(738\) 6.73205 1.80385i 0.247810 0.0664005i
\(739\) 13.4115i 0.493352i −0.969098 0.246676i \(-0.920662\pi\)
0.969098 0.246676i \(-0.0793383\pi\)
\(740\) −0.928203 + 0.535898i −0.0341214 + 0.0197000i
\(741\) 0.732051i 0.0268926i
\(742\) 21.4641 + 80.1051i 0.787972 + 2.94075i
\(743\) −32.4449 −1.19029 −0.595143 0.803620i \(-0.702905\pi\)
−0.595143 + 0.803620i \(0.702905\pi\)
\(744\) 0.392305 + 0.392305i 0.0143826 + 0.0143826i
\(745\) −3.46410 −0.126915
\(746\) −0.339746 1.26795i −0.0124390 0.0464229i
\(747\) 5.26795i 0.192744i
\(748\) 18.9282 + 32.7846i 0.692084 + 1.19872i
\(749\) 18.9282i 0.691621i
\(750\) −1.36603 + 0.366025i −0.0498802 + 0.0133654i
\(751\) −16.0000 −0.583848 −0.291924 0.956441i \(-0.594295\pi\)
−0.291924 + 0.956441i \(0.594295\pi\)
\(752\) −17.4641 + 30.2487i −0.636850 + 1.10306i
\(753\) 6.39230 0.232949
\(754\) 6.73205 1.80385i 0.245167 0.0656923i
\(755\) 18.7321i 0.681729i
\(756\) −4.73205 8.19615i −0.172103 0.298091i
\(757\) 11.6077i 0.421889i 0.977498 + 0.210944i \(0.0676539\pi\)
−0.977498 + 0.210944i \(0.932346\pi\)
\(758\) −9.05256 33.7846i −0.328804 1.22711i
\(759\) −9.46410 −0.343525
\(760\) −1.46410 + 1.46410i −0.0531085 + 0.0531085i
\(761\) −18.3923 −0.666721 −0.333360 0.942800i \(-0.608183\pi\)
−0.333360 + 0.942800i \(0.608183\pi\)
\(762\) −6.19615 23.1244i −0.224463 0.837707i
\(763\) 75.0333i 2.71639i
\(764\) −28.3923 + 16.3923i −1.02720 + 0.593053i
\(765\) 4.00000i 0.144620i
\(766\) −9.39230 + 2.51666i −0.339358 + 0.0909306i
\(767\) 7.66025 0.276596
\(768\) 13.8564 8.00000i 0.500000 0.288675i
\(769\) −1.32051 −0.0476187 −0.0238094 0.999717i \(-0.507579\pi\)
−0.0238094 + 0.999717i \(0.507579\pi\)
\(770\) −30.5885 + 8.19615i −1.10233 + 0.295369i
\(771\) 3.07180i 0.110628i
\(772\) −6.00000 + 3.46410i −0.215945 + 0.124676i
\(773\) 31.1769i 1.12136i 0.828034 + 0.560678i \(0.189459\pi\)
−0.828034 + 0.560678i \(0.810541\pi\)
\(774\) −0.535898 2.00000i −0.0192625 0.0718885i
\(775\) −0.196152 −0.00704600
\(776\) −1.07180 + 1.07180i −0.0384753 + 0.0384753i
\(777\) 2.53590 0.0909748
\(778\) −3.26795 12.1962i −0.117162 0.437253i
\(779\) 3.60770i 0.129259i
\(780\) −1.00000 1.73205i −0.0358057 0.0620174i
\(781\) 62.7846i 2.24661i
\(782\) 10.9282 2.92820i 0.390792 0.104712i
\(783\) 4.92820 0.176120
\(784\) 30.7846 53.3205i 1.09945 1.90430i
\(785\) −22.7846 −0.813218
\(786\) −10.7321 + 2.87564i −0.382800 + 0.102571i
\(787\) 48.9808i 1.74598i 0.487742 + 0.872988i \(0.337821\pi\)
−0.487742 + 0.872988i \(0.662179\pi\)
\(788\) 2.39230 + 4.14359i 0.0852223 + 0.147609i
\(789\) 16.5359i 0.588694i
\(790\) −6.39230 23.8564i −0.227428 0.848773i
\(791\) 0 0
\(792\) 9.46410 + 9.46410i 0.336292 + 0.336292i
\(793\) −2.92820 −0.103984
\(794\) 5.80385 + 21.6603i 0.205971 + 0.768694i
\(795\) 12.3923i 0.439510i
\(796\) −15.7128 + 9.07180i −0.556926 + 0.321541i
\(797\) 33.7128i 1.19417i 0.802178 + 0.597085i \(0.203674\pi\)
−0.802178 + 0.597085i \(0.796326\pi\)
\(798\) 4.73205 1.26795i 0.167513 0.0448849i
\(799\) 34.9282 1.23567
\(800\) −1.46410 + 5.46410i −0.0517638 + 0.193185i
\(801\) −0.928203 −0.0327964
\(802\) −13.6603 + 3.66025i −0.482360 + 0.129248i
\(803\) 75.0333i 2.64787i
\(804\) −21.1244 + 12.1962i −0.744999 + 0.430125i
\(805\) 9.46410i 0.333566i
\(806\) −0.0717968 0.267949i −0.00252893 0.00943811i
\(807\) 4.14359 0.145861
\(808\) −24.0000 24.0000i −0.844317 0.844317i
\(809\) 20.3923 0.716955 0.358478 0.933538i \(-0.383296\pi\)
0.358478 + 0.933538i \(0.383296\pi\)
\(810\) −0.366025 1.36603i −0.0128608 0.0479972i
\(811\) 23.2679i 0.817048i −0.912748 0.408524i \(-0.866044\pi\)
0.912748 0.408524i \(-0.133956\pi\)
\(812\) 23.3205 + 40.3923i 0.818389 + 1.41749i
\(813\) 5.66025i 0.198514i
\(814\) −3.46410 + 0.928203i −0.121417 + 0.0325335i
\(815\) 20.1962 0.707440
\(816\) −13.8564 8.00000i −0.485071 0.280056i
\(817\) 1.07180 0.0374974
\(818\) −33.1244 + 8.87564i −1.15817 + 0.310330i
\(819\) 4.73205i 0.165351i
\(820\) 4.92820 + 8.53590i 0.172100 + 0.298087i
\(821\) 24.9282i 0.870000i −0.900430 0.435000i \(-0.856748\pi\)
0.900430 0.435000i \(-0.143252\pi\)
\(822\) 3.80385 + 14.1962i 0.132674 + 0.495148i
\(823\) 14.0000 0.488009 0.244005 0.969774i \(-0.421539\pi\)
0.244005 + 0.969774i \(0.421539\pi\)
\(824\) −25.8564 + 25.8564i −0.900751 + 0.900751i
\(825\) −4.73205 −0.164749
\(826\) 13.2679 + 49.5167i 0.461651 + 1.72290i
\(827\) 22.3397i 0.776829i −0.921485 0.388415i \(-0.873023\pi\)
0.921485 0.388415i \(-0.126977\pi\)
\(828\) 3.46410 2.00000i 0.120386 0.0695048i
\(829\) 28.0000i 0.972480i −0.873825 0.486240i \(-0.838368\pi\)
0.873825 0.486240i \(-0.161632\pi\)
\(830\) 7.19615 1.92820i 0.249782 0.0669289i
\(831\) −21.4641 −0.744581
\(832\) −8.00000 −0.277350
\(833\) −61.5692 −2.13325
\(834\) 2.73205 0.732051i 0.0946032 0.0253488i
\(835\) 9.80385i 0.339276i
\(836\) −6.00000 + 3.46410i −0.207514 + 0.119808i
\(837\) 0.196152i 0.00678002i
\(838\) −13.4115 50.0526i −0.463294 1.72904i
\(839\) 30.0526 1.03753 0.518765 0.854917i \(-0.326392\pi\)
0.518765 + 0.854917i \(0.326392\pi\)
\(840\) 9.46410 9.46410i 0.326543 0.326543i
\(841\) 4.71281 0.162511
\(842\) −1.94744 7.26795i −0.0671133 0.250470i
\(843\) 18.3923i 0.633465i
\(844\) −0.928203 1.60770i −0.0319501 0.0553391i
\(845\) 1.00000i 0.0344010i
\(846\) 11.9282 3.19615i 0.410100 0.109886i
\(847\) −53.9090 −1.85233
\(848\) 42.9282 + 24.7846i 1.47416 + 0.851107i
\(849\) −5.46410 −0.187527
\(850\) 5.46410 1.46410i 0.187417 0.0502183i
\(851\) 1.07180i 0.0367407i
\(852\) 13.2679 + 22.9808i 0.454552 + 0.787308i
\(853\) 26.7846i 0.917088i −0.888672 0.458544i \(-0.848371\pi\)
0.888672 0.458544i \(-0.151629\pi\)
\(854\) −5.07180 18.9282i −0.173553 0.647710i
\(855\) 0.732051 0.0250356
\(856\) −8.00000 8.00000i −0.273434 0.273434i
\(857\) 45.7128 1.56152 0.780760 0.624831i \(-0.214832\pi\)
0.780760 + 0.624831i \(0.214832\pi\)
\(858\) −1.73205 6.46410i −0.0591312 0.220681i
\(859\) 0.928203i 0.0316699i −0.999875 0.0158349i \(-0.994959\pi\)
0.999875 0.0158349i \(-0.00504063\pi\)
\(860\) 2.53590 1.46410i 0.0864734 0.0499255i
\(861\) 23.3205i 0.794761i
\(862\) −53.4449 + 14.3205i −1.82034 + 0.487758i
\(863\) −45.1244 −1.53605 −0.768025 0.640419i \(-0.778761\pi\)
−0.768025 + 0.640419i \(0.778761\pi\)
\(864\) −5.46410 1.46410i −0.185893 0.0498097i
\(865\) 9.46410 0.321789
\(866\) 24.1962 6.48334i 0.822219 0.220313i
\(867\) 1.00000i 0.0339618i
\(868\) 1.60770 0.928203i 0.0545687 0.0315053i
\(869\) 82.6410i 2.80340i
\(870\) 1.80385 + 6.73205i 0.0611562 + 0.228238i
\(871\) 12.1962 0.413251
\(872\) 31.7128 + 31.7128i 1.07393 + 1.07393i
\(873\) 0.535898 0.0181374
\(874\) 0.535898 + 2.00000i 0.0181270 + 0.0676510i
\(875\) 4.73205i 0.159973i
\(876\) 15.8564 + 27.4641i 0.535738 + 0.927926i
\(877\) 17.6077i 0.594570i −0.954789 0.297285i \(-0.903919\pi\)
0.954789 0.297285i \(-0.0960811\pi\)
\(878\) −24.3923 + 6.53590i −0.823200 + 0.220576i
\(879\) 22.7846 0.768506
\(880\) −9.46410 + 16.3923i −0.319035 + 0.552584i
\(881\) −35.5692 −1.19836 −0.599179 0.800615i \(-0.704506\pi\)
−0.599179 + 0.800615i \(0.704506\pi\)
\(882\) −21.0263 + 5.63397i −0.707992 + 0.189706i
\(883\) 3.32051i 0.111744i −0.998438 0.0558720i \(-0.982206\pi\)
0.998438 0.0558720i \(-0.0177939\pi\)
\(884\) 4.00000 + 6.92820i 0.134535 + 0.233021i
\(885\) 7.66025i 0.257497i
\(886\) −2.53590 9.46410i −0.0851952 0.317953i
\(887\) −43.1769 −1.44974 −0.724869 0.688886i \(-0.758100\pi\)
−0.724869 + 0.688886i \(0.758100\pi\)
\(888\) 1.07180 1.07180i 0.0359671 0.0359671i
\(889\) −80.1051 −2.68664
\(890\) −0.339746 1.26795i −0.0113883 0.0425018i
\(891\) 4.73205i 0.158530i
\(892\) −46.7321 + 26.9808i −1.56470 + 0.903383i
\(893\) 6.39230i 0.213910i
\(894\) 4.73205 1.26795i 0.158263 0.0424066i
\(895\) 10.3923 0.347376
\(896\) −13.8564 51.7128i −0.462910 1.72760i
\(897\) −2.00000 −0.0667781
\(898\) 36.0526 9.66025i 1.20309 0.322367i
\(899\) 0.966679i 0.0322405i
\(900\) 1.73205 1.00000i 0.0577350 0.0333333i
\(901\) 49.5692i 1.65139i
\(902\) 8.53590 + 31.8564i 0.284214 + 1.06070i
\(903\) −6.92820 −0.230556
\(904\) 0 0
\(905\) −4.92820 −0.163819
\(906\) 6.85641 + 25.5885i 0.227789 + 0.850120i
\(907\) 39.3205i 1.30562i 0.757523 + 0.652808i \(0.226409\pi\)
−0.757523 + 0.652808i \(0.773591\pi\)
\(908\) 5.66025 + 9.80385i 0.187842 + 0.325352i
\(909\) 12.0000i 0.398015i
\(910\) −6.46410 + 1.73205i −0.214283 + 0.0574169i
\(911\) −28.1051 −0.931164 −0.465582 0.885005i \(-0.654155\pi\)
−0.465582 + 0.885005i \(0.654155\pi\)
\(912\) 1.46410 2.53590i 0.0484812 0.0839720i
\(913\) 24.9282 0.825003
\(914\) 20.5885 5.51666i 0.681006 0.182475i
\(915\) 2.92820i 0.0968034i
\(916\) −6.00000 10.3923i −0.198246 0.343371i
\(917\) 37.1769i 1.22769i
\(918\) 1.46410 + 5.46410i 0.0483226 + 0.180342i
\(919\) −33.4641 −1.10388 −0.551939 0.833884i \(-0.686112\pi\)
−0.551939 + 0.833884i \(0.686112\pi\)
\(920\) 4.00000 + 4.00000i 0.131876 + 0.131876i
\(921\) −19.1244 −0.630169
\(922\) 1.12436 + 4.19615i 0.0370287 + 0.138193i
\(923\) 13.2679i 0.436720i
\(924\) 38.7846 22.3923i 1.27592 0.736653i
\(925\) 0.535898i 0.0176202i
\(926\) 26.8564 7.19615i 0.882556 0.236480i
\(927\) 12.9282 0.424618
\(928\) 26.9282 + 7.21539i 0.883962 + 0.236857i
\(929\) 10.3923 0.340960 0.170480 0.985361i \(-0.445468\pi\)
0.170480 + 0.985361i \(0.445468\pi\)
\(930\) 0.267949 0.0717968i 0.00878640 0.00235431i
\(931\) 11.2679i 0.369292i
\(932\) 20.5359 11.8564i 0.672676 0.388370i
\(933\) 31.7128i 1.03823i
\(934\) 7.17691 + 26.7846i 0.234836 + 0.876419i
\(935\) 18.9282 0.619018
\(936\) 2.00000 + 2.00000i 0.0653720 + 0.0653720i
\(937\) −20.6410 −0.674313 −0.337156 0.941449i \(-0.609465\pi\)
−0.337156 + 0.941449i \(0.609465\pi\)
\(938\) 21.1244 + 78.8372i 0.689735 + 2.57412i
\(939\) 8.00000i 0.261070i
\(940\) 8.73205 + 15.1244i 0.284808 + 0.493302i
\(941\) 4.53590i 0.147866i −0.997263 0.0739330i \(-0.976445\pi\)
0.997263 0.0739330i \(-0.0235551\pi\)
\(942\) 31.1244 8.33975i 1.01409 0.271724i
\(943\) 9.85641 0.320969
\(944\) 26.5359 + 15.3205i 0.863670 + 0.498640i
\(945\) −4.73205 −0.153934
\(946\) 9.46410 2.53590i 0.307704 0.0824492i
\(947\) 24.1962i 0.786269i 0.919481 + 0.393135i \(0.128609\pi\)
−0.919481 + 0.393135i \(0.871391\pi\)
\(948\) 17.4641 + 30.2487i 0.567208 + 0.982432i
\(949\) 15.8564i 0.514721i
\(950\) 0.267949 + 1.00000i 0.00869342 + 0.0324443i
\(951\) 20.5359 0.665922
\(952\) −37.8564 + 37.8564i −1.22693 + 1.22693i
\(953\) 12.9282 0.418786 0.209393 0.977832i \(-0.432851\pi\)
0.209393 + 0.977832i \(0.432851\pi\)
\(954\) −4.53590 16.9282i −0.146855 0.548071i
\(955\) 16.3923i 0.530443i
\(956\) −34.3013 + 19.8038i −1.10938 + 0.640502i
\(957\) 23.3205i 0.753845i
\(958\) −54.5167 + 14.6077i −1.76135 + 0.471953i
\(959\) 49.1769 1.58801
\(960\) 8.00000i 0.258199i
\(961\) −30.9615 −0.998759
\(962\) −0.732051 + 0.196152i −0.0236023 + 0.00632421i
\(963\) 4.00000i 0.128898i
\(964\) −36.2487 + 20.9282i −1.16749 + 0.674052i
\(965\) 3.46410i 0.111513i
\(966\) −3.46410 12.9282i −0.111456 0.415958i
\(967\) 12.7321 0.409435 0.204718 0.978821i \(-0.434372\pi\)
0.204718 + 0.978821i \(0.434372\pi\)
\(968\) −22.7846 + 22.7846i −0.732325 + 0.732325i
\(969\) −2.92820 −0.0940674
\(970\) 0.196152 + 0.732051i 0.00629807 + 0.0235047i
\(971\) 30.0000i 0.962746i −0.876516 0.481373i \(-0.840138\pi\)
0.876516 0.481373i \(-0.159862\pi\)
\(972\) 1.00000 + 1.73205i 0.0320750 + 0.0555556i
\(973\) 9.46410i 0.303405i
\(974\) −11.9282 + 3.19615i −0.382204 + 0.102411i
\(975\) −1.00000 −0.0320256
\(976\) −10.1436 5.85641i −0.324689 0.187459i
\(977\) 38.1051 1.21909 0.609545 0.792751i \(-0.291352\pi\)
0.609545 + 0.792751i \(0.291352\pi\)
\(978\) −27.5885 + 7.39230i −0.882182 + 0.236380i
\(979\) 4.39230i 0.140379i
\(980\) −15.3923 26.6603i −0.491689 0.851631i
\(981\) 15.8564i 0.506256i
\(982\) −15.1244 56.4449i −0.482638 1.80123i
\(983\) 57.5167 1.83450 0.917248 0.398316i \(-0.130405\pi\)
0.917248 + 0.398316i \(0.130405\pi\)
\(984\) −9.85641 9.85641i −0.314211 0.314211i
\(985\) 2.39230 0.0762252
\(986\) −7.21539 26.9282i −0.229785 0.857569i
\(987\) 41.3205i 1.31525i
\(988\) −1.26795 + 0.732051i −0.0403388 + 0.0232896i
\(989\) 2.92820i 0.0931114i
\(990\) 6.46410 1.73205i 0.205443 0.0550482i
\(991\) −33.1769 −1.05390 −0.526950 0.849896i \(-0.676664\pi\)
−0.526950 + 0.849896i \(0.676664\pi\)
\(992\) 0.287187 1.07180i 0.00911820 0.0340296i
\(993\) −12.0526 −0.382476
\(994\) 85.7654 22.9808i 2.72031 0.728906i
\(995\) 9.07180i 0.287595i
\(996\) −9.12436 + 5.26795i −0.289116 + 0.166921i
\(997\) 60.1051i 1.90355i −0.306800 0.951774i \(-0.599258\pi\)
0.306800 0.951774i \(-0.400742\pi\)
\(998\) 0.803848 + 3.00000i 0.0254454 + 0.0949633i
\(999\) −0.535898 −0.0169551
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 1560.2.w.d.781.3 4
4.3 odd 2 6240.2.w.c.3121.1 4
8.3 odd 2 6240.2.w.c.3121.3 4
8.5 even 2 inner 1560.2.w.d.781.4 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1560.2.w.d.781.3 4 1.1 even 1 trivial
1560.2.w.d.781.4 yes 4 8.5 even 2 inner
6240.2.w.c.3121.1 4 4.3 odd 2
6240.2.w.c.3121.3 4 8.3 odd 2