Properties

Label 1170.2.i.k.991.1
Level $1170$
Weight $2$
Character 1170.991
Analytic conductor $9.342$
Analytic rank $0$
Dimension $2$
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] = [1170,2,Mod(451,1170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1170, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1170.451");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.i (of order \(3\), 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: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1170.991
Dual form 1170.2.i.k.451.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.00000 + 3.46410i) q^{13} -2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-3.00000 + 5.19615i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(-1.50000 - 2.59808i) q^{23} +1.00000 q^{25} +(-3.50000 + 0.866025i) q^{26} +(-1.00000 - 1.73205i) q^{28} +(-0.500000 - 0.866025i) q^{29} -3.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +2.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(2.50000 + 4.33013i) q^{37} -6.00000 q^{38} -1.00000 q^{40} +(5.00000 + 8.66025i) q^{41} +(-2.50000 + 4.33013i) q^{43} -1.00000 q^{44} +(1.50000 - 2.59808i) q^{46} -3.00000 q^{47} +(1.50000 + 2.59808i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-2.50000 - 2.59808i) q^{52} -14.0000 q^{53} +(0.500000 + 0.866025i) q^{55} +(1.00000 - 1.73205i) q^{56} +(0.500000 - 0.866025i) q^{58} +(-2.50000 + 4.33013i) q^{59} +(5.00000 - 8.66025i) q^{61} +(-1.50000 - 2.59808i) q^{62} +1.00000 q^{64} +(-1.00000 + 3.46410i) q^{65} +(1.00000 + 1.73205i) q^{68} -2.00000 q^{70} +(2.00000 - 3.46410i) q^{71} -2.00000 q^{73} +(-2.50000 + 4.33013i) q^{74} +(-3.00000 - 5.19615i) q^{76} -2.00000 q^{77} +5.00000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-5.00000 + 8.66025i) q^{82} +6.00000 q^{83} +(1.00000 - 1.73205i) q^{85} -5.00000 q^{86} +(-0.500000 - 0.866025i) q^{88} +(5.00000 + 8.66025i) q^{89} +(-5.00000 - 5.19615i) q^{91} +3.00000 q^{92} +(-1.50000 - 2.59808i) q^{94} +(-3.00000 + 5.19615i) q^{95} +(5.00000 - 8.66025i) q^{97} +(-1.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} + q^{10} + q^{11} - 2 q^{13} - 4 q^{14} - q^{16} + 2 q^{17} - 6 q^{19} - q^{20} - q^{22} - 3 q^{23} + 2 q^{25} - 7 q^{26} - 2 q^{28} - q^{29} - 6 q^{31} + q^{32} + 4 q^{34} - 2 q^{35} + 5 q^{37} - 12 q^{38} - 2 q^{40} + 10 q^{41} - 5 q^{43} - 2 q^{44} + 3 q^{46} - 6 q^{47} + 3 q^{49} + q^{50} - 5 q^{52} - 28 q^{53} + q^{55} + 2 q^{56} + q^{58} - 5 q^{59} + 10 q^{61} - 3 q^{62} + 2 q^{64} - 2 q^{65} + 2 q^{68} - 4 q^{70} + 4 q^{71} - 4 q^{73} - 5 q^{74} - 6 q^{76} - 4 q^{77} + 10 q^{79} - q^{80} - 10 q^{82} + 12 q^{83} + 2 q^{85} - 10 q^{86} - q^{88} + 10 q^{89} - 10 q^{91} + 6 q^{92} - 3 q^{94} - 6 q^{95} + 10 q^{97} - 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −1.00000 + 1.73205i −0.377964 + 0.654654i −0.990766 0.135583i \(-0.956709\pi\)
0.612801 + 0.790237i \(0.290043\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i 0.931505 0.363727i \(-0.118496\pi\)
−0.780750 + 0.624844i \(0.785163\pi\)
\(12\) 0 0
\(13\) −1.00000 + 3.46410i −0.277350 + 0.960769i
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) 0 0
\(19\) −3.00000 + 5.19615i −0.688247 + 1.19208i 0.284157 + 0.958778i \(0.408286\pi\)
−0.972404 + 0.233301i \(0.925047\pi\)
\(20\) −0.500000 + 0.866025i −0.111803 + 0.193649i
\(21\) 0 0
\(22\) −0.500000 + 0.866025i −0.106600 + 0.184637i
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −3.50000 + 0.866025i −0.686406 + 0.169842i
\(27\) 0 0
\(28\) −1.00000 1.73205i −0.188982 0.327327i
\(29\) −0.500000 0.866025i −0.0928477 0.160817i 0.815861 0.578249i \(-0.196264\pi\)
−0.908708 + 0.417432i \(0.862930\pi\)
\(30\) 0 0
\(31\) −3.00000 −0.538816 −0.269408 0.963026i \(-0.586828\pi\)
−0.269408 + 0.963026i \(0.586828\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) −1.00000 + 1.73205i −0.169031 + 0.292770i
\(36\) 0 0
\(37\) 2.50000 + 4.33013i 0.410997 + 0.711868i 0.994999 0.0998840i \(-0.0318472\pi\)
−0.584002 + 0.811752i \(0.698514\pi\)
\(38\) −6.00000 −0.973329
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) 5.00000 + 8.66025i 0.780869 + 1.35250i 0.931436 + 0.363905i \(0.118557\pi\)
−0.150567 + 0.988600i \(0.548110\pi\)
\(42\) 0 0
\(43\) −2.50000 + 4.33013i −0.381246 + 0.660338i −0.991241 0.132068i \(-0.957838\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) −1.00000 −0.150756
\(45\) 0 0
\(46\) 1.50000 2.59808i 0.221163 0.383065i
\(47\) −3.00000 −0.437595 −0.218797 0.975770i \(-0.570213\pi\)
−0.218797 + 0.975770i \(0.570213\pi\)
\(48\) 0 0
\(49\) 1.50000 + 2.59808i 0.214286 + 0.371154i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) 0 0
\(52\) −2.50000 2.59808i −0.346688 0.360288i
\(53\) −14.0000 −1.92305 −0.961524 0.274721i \(-0.911414\pi\)
−0.961524 + 0.274721i \(0.911414\pi\)
\(54\) 0 0
\(55\) 0.500000 + 0.866025i 0.0674200 + 0.116775i
\(56\) 1.00000 1.73205i 0.133631 0.231455i
\(57\) 0 0
\(58\) 0.500000 0.866025i 0.0656532 0.113715i
\(59\) −2.50000 + 4.33013i −0.325472 + 0.563735i −0.981608 0.190909i \(-0.938857\pi\)
0.656136 + 0.754643i \(0.272190\pi\)
\(60\) 0 0
\(61\) 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) −1.50000 2.59808i −0.190500 0.329956i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.00000 + 3.46410i −0.124035 + 0.429669i
\(66\) 0 0
\(67\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(68\) 1.00000 + 1.73205i 0.121268 + 0.210042i
\(69\) 0 0
\(70\) −2.00000 −0.239046
\(71\) 2.00000 3.46410i 0.237356 0.411113i −0.722599 0.691268i \(-0.757052\pi\)
0.959955 + 0.280155i \(0.0903858\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −2.50000 + 4.33013i −0.290619 + 0.503367i
\(75\) 0 0
\(76\) −3.00000 5.19615i −0.344124 0.596040i
\(77\) −2.00000 −0.227921
\(78\) 0 0
\(79\) 5.00000 0.562544 0.281272 0.959628i \(-0.409244\pi\)
0.281272 + 0.959628i \(0.409244\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) 0 0
\(82\) −5.00000 + 8.66025i −0.552158 + 0.956365i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) 1.00000 1.73205i 0.108465 0.187867i
\(86\) −5.00000 −0.539164
\(87\) 0 0
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) 5.00000 + 8.66025i 0.529999 + 0.917985i 0.999388 + 0.0349934i \(0.0111410\pi\)
−0.469389 + 0.882992i \(0.655526\pi\)
\(90\) 0 0
\(91\) −5.00000 5.19615i −0.524142 0.544705i
\(92\) 3.00000 0.312772
\(93\) 0 0
\(94\) −1.50000 2.59808i −0.154713 0.267971i
\(95\) −3.00000 + 5.19615i −0.307794 + 0.533114i
\(96\) 0 0
\(97\) 5.00000 8.66025i 0.507673 0.879316i −0.492287 0.870433i \(-0.663839\pi\)
0.999961 0.00888289i \(-0.00282755\pi\)
\(98\) −1.50000 + 2.59808i −0.151523 + 0.262445i
\(99\) 0 0
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 7.00000 + 12.1244i 0.696526 + 1.20642i 0.969664 + 0.244443i \(0.0786053\pi\)
−0.273138 + 0.961975i \(0.588061\pi\)
\(102\) 0 0
\(103\) −6.00000 −0.591198 −0.295599 0.955312i \(-0.595519\pi\)
−0.295599 + 0.955312i \(0.595519\pi\)
\(104\) 1.00000 3.46410i 0.0980581 0.339683i
\(105\) 0 0
\(106\) −7.00000 12.1244i −0.679900 1.17762i
\(107\) −3.00000 5.19615i −0.290021 0.502331i 0.683793 0.729676i \(-0.260329\pi\)
−0.973814 + 0.227345i \(0.926996\pi\)
\(108\) 0 0
\(109\) −6.00000 −0.574696 −0.287348 0.957826i \(-0.592774\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(110\) −0.500000 + 0.866025i −0.0476731 + 0.0825723i
\(111\) 0 0
\(112\) 2.00000 0.188982
\(113\) 8.50000 14.7224i 0.799613 1.38497i −0.120256 0.992743i \(-0.538371\pi\)
0.919868 0.392227i \(-0.128295\pi\)
\(114\) 0 0
\(115\) −1.50000 2.59808i −0.139876 0.242272i
\(116\) 1.00000 0.0928477
\(117\) 0 0
\(118\) −5.00000 −0.460287
\(119\) 2.00000 + 3.46410i 0.183340 + 0.317554i
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 10.0000 0.905357
\(123\) 0 0
\(124\) 1.50000 2.59808i 0.134704 0.233314i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 7.00000 + 12.1244i 0.621150 + 1.07586i 0.989272 + 0.146085i \(0.0466674\pi\)
−0.368122 + 0.929777i \(0.619999\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −3.50000 + 0.866025i −0.306970 + 0.0759555i
\(131\) −13.0000 −1.13582 −0.567908 0.823092i \(-0.692247\pi\)
−0.567908 + 0.823092i \(0.692247\pi\)
\(132\) 0 0
\(133\) −6.00000 10.3923i −0.520266 0.901127i
\(134\) 0 0
\(135\) 0 0
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) −4.50000 + 7.79423i −0.384461 + 0.665906i −0.991694 0.128618i \(-0.958946\pi\)
0.607233 + 0.794524i \(0.292279\pi\)
\(138\) 0 0
\(139\) −5.00000 + 8.66025i −0.424094 + 0.734553i −0.996335 0.0855324i \(-0.972741\pi\)
0.572241 + 0.820086i \(0.306074\pi\)
\(140\) −1.00000 1.73205i −0.0845154 0.146385i
\(141\) 0 0
\(142\) 4.00000 0.335673
\(143\) −3.50000 + 0.866025i −0.292685 + 0.0724207i
\(144\) 0 0
\(145\) −0.500000 0.866025i −0.0415227 0.0719195i
\(146\) −1.00000 1.73205i −0.0827606 0.143346i
\(147\) 0 0
\(148\) −5.00000 −0.410997
\(149\) 5.50000 9.52628i 0.450578 0.780423i −0.547844 0.836580i \(-0.684551\pi\)
0.998422 + 0.0561570i \(0.0178847\pi\)
\(150\) 0 0
\(151\) 24.0000 1.95309 0.976546 0.215308i \(-0.0690756\pi\)
0.976546 + 0.215308i \(0.0690756\pi\)
\(152\) 3.00000 5.19615i 0.243332 0.421464i
\(153\) 0 0
\(154\) −1.00000 1.73205i −0.0805823 0.139573i
\(155\) −3.00000 −0.240966
\(156\) 0 0
\(157\) 25.0000 1.99522 0.997609 0.0691164i \(-0.0220180\pi\)
0.997609 + 0.0691164i \(0.0220180\pi\)
\(158\) 2.50000 + 4.33013i 0.198889 + 0.344486i
\(159\) 0 0
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) 6.00000 0.472866
\(162\) 0 0
\(163\) −8.50000 + 14.7224i −0.665771 + 1.15315i 0.313304 + 0.949653i \(0.398564\pi\)
−0.979076 + 0.203497i \(0.934769\pi\)
\(164\) −10.0000 −0.780869
\(165\) 0 0
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) −3.50000 6.06218i −0.270838 0.469105i 0.698239 0.715865i \(-0.253967\pi\)
−0.969077 + 0.246760i \(0.920634\pi\)
\(168\) 0 0
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) 2.00000 0.153393
\(171\) 0 0
\(172\) −2.50000 4.33013i −0.190623 0.330169i
\(173\) 2.00000 3.46410i 0.152057 0.263371i −0.779926 0.625871i \(-0.784744\pi\)
0.931984 + 0.362500i \(0.118077\pi\)
\(174\) 0 0
\(175\) −1.00000 + 1.73205i −0.0755929 + 0.130931i
\(176\) 0.500000 0.866025i 0.0376889 0.0652791i
\(177\) 0 0
\(178\) −5.00000 + 8.66025i −0.374766 + 0.649113i
\(179\) −3.50000 6.06218i −0.261602 0.453108i 0.705066 0.709142i \(-0.250918\pi\)
−0.966668 + 0.256034i \(0.917584\pi\)
\(180\) 0 0
\(181\) 16.0000 1.18927 0.594635 0.803996i \(-0.297296\pi\)
0.594635 + 0.803996i \(0.297296\pi\)
\(182\) 2.00000 6.92820i 0.148250 0.513553i
\(183\) 0 0
\(184\) 1.50000 + 2.59808i 0.110581 + 0.191533i
\(185\) 2.50000 + 4.33013i 0.183804 + 0.318357i
\(186\) 0 0
\(187\) 2.00000 0.146254
\(188\) 1.50000 2.59808i 0.109399 0.189484i
\(189\) 0 0
\(190\) −6.00000 −0.435286
\(191\) 12.0000 20.7846i 0.868290 1.50392i 0.00454614 0.999990i \(-0.498553\pi\)
0.863743 0.503932i \(-0.168114\pi\)
\(192\) 0 0
\(193\) 2.00000 + 3.46410i 0.143963 + 0.249351i 0.928986 0.370116i \(-0.120682\pi\)
−0.785022 + 0.619467i \(0.787349\pi\)
\(194\) 10.0000 0.717958
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −6.00000 10.3923i −0.427482 0.740421i 0.569166 0.822222i \(-0.307266\pi\)
−0.996649 + 0.0818013i \(0.973933\pi\)
\(198\) 0 0
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 0 0
\(202\) −7.00000 + 12.1244i −0.492518 + 0.853067i
\(203\) 2.00000 0.140372
\(204\) 0 0
\(205\) 5.00000 + 8.66025i 0.349215 + 0.604858i
\(206\) −3.00000 5.19615i −0.209020 0.362033i
\(207\) 0 0
\(208\) 3.50000 0.866025i 0.242681 0.0600481i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) 4.00000 + 6.92820i 0.275371 + 0.476957i 0.970229 0.242190i \(-0.0778659\pi\)
−0.694857 + 0.719148i \(0.744533\pi\)
\(212\) 7.00000 12.1244i 0.480762 0.832704i
\(213\) 0 0
\(214\) 3.00000 5.19615i 0.205076 0.355202i
\(215\) −2.50000 + 4.33013i −0.170499 + 0.295312i
\(216\) 0 0
\(217\) 3.00000 5.19615i 0.203653 0.352738i
\(218\) −3.00000 5.19615i −0.203186 0.351928i
\(219\) 0 0
\(220\) −1.00000 −0.0674200
\(221\) 5.00000 + 5.19615i 0.336336 + 0.349531i
\(222\) 0 0
\(223\) −5.00000 8.66025i −0.334825 0.579934i 0.648626 0.761107i \(-0.275344\pi\)
−0.983451 + 0.181173i \(0.942010\pi\)
\(224\) 1.00000 + 1.73205i 0.0668153 + 0.115728i
\(225\) 0 0
\(226\) 17.0000 1.13082
\(227\) 10.0000 17.3205i 0.663723 1.14960i −0.315906 0.948790i \(-0.602309\pi\)
0.979630 0.200812i \(-0.0643581\pi\)
\(228\) 0 0
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 1.50000 2.59808i 0.0989071 0.171312i
\(231\) 0 0
\(232\) 0.500000 + 0.866025i 0.0328266 + 0.0568574i
\(233\) −3.00000 −0.196537 −0.0982683 0.995160i \(-0.531330\pi\)
−0.0982683 + 0.995160i \(0.531330\pi\)
\(234\) 0 0
\(235\) −3.00000 −0.195698
\(236\) −2.50000 4.33013i −0.162736 0.281867i
\(237\) 0 0
\(238\) −2.00000 + 3.46410i −0.129641 + 0.224544i
\(239\) 8.00000 0.517477 0.258738 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) 0 0
\(241\) 3.50000 6.06218i 0.225455 0.390499i −0.731001 0.682376i \(-0.760947\pi\)
0.956456 + 0.291877i \(0.0942799\pi\)
\(242\) 10.0000 0.642824
\(243\) 0 0
\(244\) 5.00000 + 8.66025i 0.320092 + 0.554416i
\(245\) 1.50000 + 2.59808i 0.0958315 + 0.165985i
\(246\) 0 0
\(247\) −15.0000 15.5885i −0.954427 0.991870i
\(248\) 3.00000 0.190500
\(249\) 0 0
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 1.50000 2.59808i 0.0946792 0.163989i −0.814795 0.579748i \(-0.803151\pi\)
0.909475 + 0.415759i \(0.136484\pi\)
\(252\) 0 0
\(253\) 1.50000 2.59808i 0.0943042 0.163340i
\(254\) −7.00000 + 12.1244i −0.439219 + 0.760750i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 10.5000 + 18.1865i 0.654972 + 1.13444i 0.981901 + 0.189396i \(0.0606529\pi\)
−0.326929 + 0.945049i \(0.606014\pi\)
\(258\) 0 0
\(259\) −10.0000 −0.621370
\(260\) −2.50000 2.59808i −0.155043 0.161126i
\(261\) 0 0
\(262\) −6.50000 11.2583i −0.401571 0.695542i
\(263\) 11.5000 + 19.9186i 0.709120 + 1.22823i 0.965184 + 0.261573i \(0.0842411\pi\)
−0.256063 + 0.966660i \(0.582426\pi\)
\(264\) 0 0
\(265\) −14.0000 −0.860013
\(266\) 6.00000 10.3923i 0.367884 0.637193i
\(267\) 0 0
\(268\) 0 0
\(269\) 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i \(-0.648441\pi\)
0.998361 0.0572259i \(-0.0182255\pi\)
\(270\) 0 0
\(271\) 14.5000 + 25.1147i 0.880812 + 1.52561i 0.850439 + 0.526073i \(0.176336\pi\)
0.0303728 + 0.999539i \(0.490331\pi\)
\(272\) −2.00000 −0.121268
\(273\) 0 0
\(274\) −9.00000 −0.543710
\(275\) 0.500000 + 0.866025i 0.0301511 + 0.0522233i
\(276\) 0 0
\(277\) 9.50000 16.4545i 0.570800 0.988654i −0.425684 0.904872i \(-0.639967\pi\)
0.996484 0.0837823i \(-0.0267000\pi\)
\(278\) −10.0000 −0.599760
\(279\) 0 0
\(280\) 1.00000 1.73205i 0.0597614 0.103510i
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 0 0
\(283\) 6.50000 + 11.2583i 0.386385 + 0.669238i 0.991960 0.126550i \(-0.0403903\pi\)
−0.605575 + 0.795788i \(0.707057\pi\)
\(284\) 2.00000 + 3.46410i 0.118678 + 0.205557i
\(285\) 0 0
\(286\) −2.50000 2.59808i −0.147828 0.153627i
\(287\) −20.0000 −1.18056
\(288\) 0 0
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 0.500000 0.866025i 0.0293610 0.0508548i
\(291\) 0 0
\(292\) 1.00000 1.73205i 0.0585206 0.101361i
\(293\) −7.00000 + 12.1244i −0.408944 + 0.708312i −0.994772 0.102123i \(-0.967436\pi\)
0.585827 + 0.810436i \(0.300770\pi\)
\(294\) 0 0
\(295\) −2.50000 + 4.33013i −0.145556 + 0.252110i
\(296\) −2.50000 4.33013i −0.145310 0.251684i
\(297\) 0 0
\(298\) 11.0000 0.637213
\(299\) 10.5000 2.59808i 0.607231 0.150251i
\(300\) 0 0
\(301\) −5.00000 8.66025i −0.288195 0.499169i
\(302\) 12.0000 + 20.7846i 0.690522 + 1.19602i
\(303\) 0 0
\(304\) 6.00000 0.344124
\(305\) 5.00000 8.66025i 0.286299 0.495885i
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 1.00000 1.73205i 0.0569803 0.0986928i
\(309\) 0 0
\(310\) −1.50000 2.59808i −0.0851943 0.147561i
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −12.0000 −0.678280 −0.339140 0.940736i \(-0.610136\pi\)
−0.339140 + 0.940736i \(0.610136\pi\)
\(314\) 12.5000 + 21.6506i 0.705416 + 1.22182i
\(315\) 0 0
\(316\) −2.50000 + 4.33013i −0.140636 + 0.243589i
\(317\) −12.0000 −0.673987 −0.336994 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) 0 0
\(319\) 0.500000 0.866025i 0.0279946 0.0484881i
\(320\) 1.00000 0.0559017
\(321\) 0 0
\(322\) 3.00000 + 5.19615i 0.167183 + 0.289570i
\(323\) 6.00000 + 10.3923i 0.333849 + 0.578243i
\(324\) 0 0
\(325\) −1.00000 + 3.46410i −0.0554700 + 0.192154i
\(326\) −17.0000 −0.941543
\(327\) 0 0
\(328\) −5.00000 8.66025i −0.276079 0.478183i
\(329\) 3.00000 5.19615i 0.165395 0.286473i
\(330\) 0 0
\(331\) −2.00000 + 3.46410i −0.109930 + 0.190404i −0.915742 0.401768i \(-0.868396\pi\)
0.805812 + 0.592172i \(0.201729\pi\)
\(332\) −3.00000 + 5.19615i −0.164646 + 0.285176i
\(333\) 0 0
\(334\) 3.50000 6.06218i 0.191511 0.331708i
\(335\) 0 0
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) 0.500000 12.9904i 0.0271964 0.706584i
\(339\) 0 0
\(340\) 1.00000 + 1.73205i 0.0542326 + 0.0939336i
\(341\) −1.50000 2.59808i −0.0812296 0.140694i
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) 2.50000 4.33013i 0.134791 0.233465i
\(345\) 0 0
\(346\) 4.00000 0.215041
\(347\) −9.00000 + 15.5885i −0.483145 + 0.836832i −0.999813 0.0193540i \(-0.993839\pi\)
0.516667 + 0.856186i \(0.327172\pi\)
\(348\) 0 0
\(349\) −4.00000 6.92820i −0.214115 0.370858i 0.738883 0.673833i \(-0.235353\pi\)
−0.952998 + 0.302975i \(0.902020\pi\)
\(350\) −2.00000 −0.106904
\(351\) 0 0
\(352\) 1.00000 0.0533002
\(353\) −7.00000 12.1244i −0.372572 0.645314i 0.617388 0.786659i \(-0.288191\pi\)
−0.989960 + 0.141344i \(0.954858\pi\)
\(354\) 0 0
\(355\) 2.00000 3.46410i 0.106149 0.183855i
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) 3.50000 6.06218i 0.184981 0.320396i
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) 0 0
\(361\) −8.50000 14.7224i −0.447368 0.774865i
\(362\) 8.00000 + 13.8564i 0.420471 + 0.728277i
\(363\) 0 0
\(364\) 7.00000 1.73205i 0.366900 0.0907841i
\(365\) −2.00000 −0.104685
\(366\) 0 0
\(367\) −18.0000 31.1769i −0.939592 1.62742i −0.766233 0.642563i \(-0.777871\pi\)
−0.173360 0.984859i \(-0.555462\pi\)
\(368\) −1.50000 + 2.59808i −0.0781929 + 0.135434i
\(369\) 0 0
\(370\) −2.50000 + 4.33013i −0.129969 + 0.225113i
\(371\) 14.0000 24.2487i 0.726844 1.25893i
\(372\) 0 0
\(373\) −18.5000 + 32.0429i −0.957894 + 1.65912i −0.230291 + 0.973122i \(0.573968\pi\)
−0.727603 + 0.685999i \(0.759366\pi\)
\(374\) 1.00000 + 1.73205i 0.0517088 + 0.0895622i
\(375\) 0 0
\(376\) 3.00000 0.154713
\(377\) 3.50000 0.866025i 0.180259 0.0446026i
\(378\) 0 0
\(379\) 15.0000 + 25.9808i 0.770498 + 1.33454i 0.937290 + 0.348550i \(0.113326\pi\)
−0.166792 + 0.985992i \(0.553341\pi\)
\(380\) −3.00000 5.19615i −0.153897 0.266557i
\(381\) 0 0
\(382\) 24.0000 1.22795
\(383\) −13.5000 + 23.3827i −0.689818 + 1.19480i 0.282079 + 0.959391i \(0.408976\pi\)
−0.971897 + 0.235408i \(0.924357\pi\)
\(384\) 0 0
\(385\) −2.00000 −0.101929
\(386\) −2.00000 + 3.46410i −0.101797 + 0.176318i
\(387\) 0 0
\(388\) 5.00000 + 8.66025i 0.253837 + 0.439658i
\(389\) 1.00000 0.0507020 0.0253510 0.999679i \(-0.491930\pi\)
0.0253510 + 0.999679i \(0.491930\pi\)
\(390\) 0 0
\(391\) −6.00000 −0.303433
\(392\) −1.50000 2.59808i −0.0757614 0.131223i
\(393\) 0 0
\(394\) 6.00000 10.3923i 0.302276 0.523557i
\(395\) 5.00000 0.251577
\(396\) 0 0
\(397\) 6.50000 11.2583i 0.326226 0.565039i −0.655534 0.755166i \(-0.727556\pi\)
0.981760 + 0.190126i \(0.0608897\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) −6.00000 10.3923i −0.299626 0.518967i 0.676425 0.736512i \(-0.263528\pi\)
−0.976050 + 0.217545i \(0.930195\pi\)
\(402\) 0 0
\(403\) 3.00000 10.3923i 0.149441 0.517678i
\(404\) −14.0000 −0.696526
\(405\) 0 0
\(406\) 1.00000 + 1.73205i 0.0496292 + 0.0859602i
\(407\) −2.50000 + 4.33013i −0.123920 + 0.214636i
\(408\) 0 0
\(409\) 13.0000 22.5167i 0.642809 1.11338i −0.341994 0.939702i \(-0.611102\pi\)
0.984803 0.173675i \(-0.0555643\pi\)
\(410\) −5.00000 + 8.66025i −0.246932 + 0.427699i
\(411\) 0 0
\(412\) 3.00000 5.19615i 0.147799 0.255996i
\(413\) −5.00000 8.66025i −0.246034 0.426143i
\(414\) 0 0
\(415\) 6.00000 0.294528
\(416\) 2.50000 + 2.59808i 0.122573 + 0.127381i
\(417\) 0 0
\(418\) −3.00000 5.19615i −0.146735 0.254152i
\(419\) 2.00000 + 3.46410i 0.0977064 + 0.169232i 0.910735 0.412991i \(-0.135516\pi\)
−0.813029 + 0.582224i \(0.802183\pi\)
\(420\) 0 0
\(421\) 28.0000 1.36464 0.682318 0.731055i \(-0.260972\pi\)
0.682318 + 0.731055i \(0.260972\pi\)
\(422\) −4.00000 + 6.92820i −0.194717 + 0.337260i
\(423\) 0 0
\(424\) 14.0000 0.679900
\(425\) 1.00000 1.73205i 0.0485071 0.0840168i
\(426\) 0 0
\(427\) 10.0000 + 17.3205i 0.483934 + 0.838198i
\(428\) 6.00000 0.290021
\(429\) 0 0
\(430\) −5.00000 −0.241121
\(431\) 6.00000 + 10.3923i 0.289010 + 0.500580i 0.973574 0.228373i \(-0.0733406\pi\)
−0.684564 + 0.728953i \(0.740007\pi\)
\(432\) 0 0
\(433\) −8.00000 + 13.8564i −0.384455 + 0.665896i −0.991693 0.128624i \(-0.958944\pi\)
0.607238 + 0.794520i \(0.292277\pi\)
\(434\) 6.00000 0.288009
\(435\) 0 0
\(436\) 3.00000 5.19615i 0.143674 0.248851i
\(437\) 18.0000 0.861057
\(438\) 0 0
\(439\) −14.0000 24.2487i −0.668184 1.15733i −0.978412 0.206666i \(-0.933739\pi\)
0.310228 0.950662i \(-0.399595\pi\)
\(440\) −0.500000 0.866025i −0.0238366 0.0412861i
\(441\) 0 0
\(442\) −2.00000 + 6.92820i −0.0951303 + 0.329541i
\(443\) −16.0000 −0.760183 −0.380091 0.924949i \(-0.624107\pi\)
−0.380091 + 0.924949i \(0.624107\pi\)
\(444\) 0 0
\(445\) 5.00000 + 8.66025i 0.237023 + 0.410535i
\(446\) 5.00000 8.66025i 0.236757 0.410075i
\(447\) 0 0
\(448\) −1.00000 + 1.73205i −0.0472456 + 0.0818317i
\(449\) −18.0000 + 31.1769i −0.849473 + 1.47133i 0.0322072 + 0.999481i \(0.489746\pi\)
−0.881680 + 0.471848i \(0.843587\pi\)
\(450\) 0 0
\(451\) −5.00000 + 8.66025i −0.235441 + 0.407795i
\(452\) 8.50000 + 14.7224i 0.399806 + 0.692485i
\(453\) 0 0
\(454\) 20.0000 0.938647
\(455\) −5.00000 5.19615i −0.234404 0.243599i
\(456\) 0 0
\(457\) −7.00000 12.1244i −0.327446 0.567153i 0.654558 0.756012i \(-0.272855\pi\)
−0.982004 + 0.188858i \(0.939521\pi\)
\(458\) 11.0000 + 19.0526i 0.513996 + 0.890268i
\(459\) 0 0
\(460\) 3.00000 0.139876
\(461\) 13.5000 23.3827i 0.628758 1.08904i −0.359044 0.933321i \(-0.616897\pi\)
0.987801 0.155719i \(-0.0497696\pi\)
\(462\) 0 0
\(463\) 10.0000 0.464739 0.232370 0.972628i \(-0.425352\pi\)
0.232370 + 0.972628i \(0.425352\pi\)
\(464\) −0.500000 + 0.866025i −0.0232119 + 0.0402042i
\(465\) 0 0
\(466\) −1.50000 2.59808i −0.0694862 0.120354i
\(467\) 2.00000 0.0925490 0.0462745 0.998929i \(-0.485265\pi\)
0.0462745 + 0.998929i \(0.485265\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −1.50000 2.59808i −0.0691898 0.119840i
\(471\) 0 0
\(472\) 2.50000 4.33013i 0.115072 0.199310i
\(473\) −5.00000 −0.229900
\(474\) 0 0
\(475\) −3.00000 + 5.19615i −0.137649 + 0.238416i
\(476\) −4.00000 −0.183340
\(477\) 0 0
\(478\) 4.00000 + 6.92820i 0.182956 + 0.316889i
\(479\) −2.00000 3.46410i −0.0913823 0.158279i 0.816711 0.577047i \(-0.195795\pi\)
−0.908093 + 0.418769i \(0.862462\pi\)
\(480\) 0 0
\(481\) −17.5000 + 4.33013i −0.797931 + 0.197437i
\(482\) 7.00000 0.318841
\(483\) 0 0
\(484\) 5.00000 + 8.66025i 0.227273 + 0.393648i
\(485\) 5.00000 8.66025i 0.227038 0.393242i
\(486\) 0 0
\(487\) −1.00000 + 1.73205i −0.0453143 + 0.0784867i −0.887793 0.460243i \(-0.847762\pi\)
0.842479 + 0.538730i \(0.181096\pi\)
\(488\) −5.00000 + 8.66025i −0.226339 + 0.392031i
\(489\) 0 0
\(490\) −1.50000 + 2.59808i −0.0677631 + 0.117369i
\(491\) 12.0000 + 20.7846i 0.541552 + 0.937996i 0.998815 + 0.0486647i \(0.0154966\pi\)
−0.457263 + 0.889332i \(0.651170\pi\)
\(492\) 0 0
\(493\) −2.00000 −0.0900755
\(494\) 6.00000 20.7846i 0.269953 0.935144i
\(495\) 0 0
\(496\) 1.50000 + 2.59808i 0.0673520 + 0.116657i
\(497\) 4.00000 + 6.92820i 0.179425 + 0.310772i
\(498\) 0 0
\(499\) −40.0000 −1.79065 −0.895323 0.445418i \(-0.853055\pi\)
−0.895323 + 0.445418i \(0.853055\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) 0 0
\(502\) 3.00000 0.133897
\(503\) 20.0000 34.6410i 0.891756 1.54457i 0.0539870 0.998542i \(-0.482807\pi\)
0.837769 0.546025i \(-0.183860\pi\)
\(504\) 0 0
\(505\) 7.00000 + 12.1244i 0.311496 + 0.539527i
\(506\) 3.00000 0.133366
\(507\) 0 0
\(508\) −14.0000 −0.621150
\(509\) −4.50000 7.79423i −0.199459 0.345473i 0.748894 0.662690i \(-0.230585\pi\)
−0.948353 + 0.317217i \(0.897252\pi\)
\(510\) 0 0
\(511\) 2.00000 3.46410i 0.0884748 0.153243i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −10.5000 + 18.1865i −0.463135 + 0.802174i
\(515\) −6.00000 −0.264392
\(516\) 0 0
\(517\) −1.50000 2.59808i −0.0659699 0.114263i
\(518\) −5.00000 8.66025i −0.219687 0.380510i
\(519\) 0 0
\(520\) 1.00000 3.46410i 0.0438529 0.151911i
\(521\) −22.0000 −0.963837 −0.481919 0.876216i \(-0.660060\pi\)
−0.481919 + 0.876216i \(0.660060\pi\)
\(522\) 0 0
\(523\) −16.5000 28.5788i −0.721495 1.24967i −0.960401 0.278623i \(-0.910122\pi\)
0.238906 0.971043i \(-0.423211\pi\)
\(524\) 6.50000 11.2583i 0.283954 0.491822i
\(525\) 0 0
\(526\) −11.5000 + 19.9186i −0.501424 + 0.868492i
\(527\) −3.00000 + 5.19615i −0.130682 + 0.226348i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) −7.00000 12.1244i −0.304061 0.526648i
\(531\) 0 0
\(532\) 12.0000 0.520266
\(533\) −35.0000 + 8.66025i −1.51602 + 0.375117i
\(534\) 0 0
\(535\) −3.00000 5.19615i −0.129701 0.224649i
\(536\) 0 0
\(537\) 0 0
\(538\) 18.0000 0.776035
\(539\) −1.50000 + 2.59808i −0.0646096 + 0.111907i
\(540\) 0 0
\(541\) −8.00000 −0.343947 −0.171973 0.985102i \(-0.555014\pi\)
−0.171973 + 0.985102i \(0.555014\pi\)
\(542\) −14.5000 + 25.1147i −0.622828 + 1.07877i
\(543\) 0 0
\(544\) −1.00000 1.73205i −0.0428746 0.0742611i
\(545\) −6.00000 −0.257012
\(546\) 0 0
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) −4.50000 7.79423i −0.192230 0.332953i
\(549\) 0 0
\(550\) −0.500000 + 0.866025i −0.0213201 + 0.0369274i
\(551\) 6.00000 0.255609
\(552\) 0 0
\(553\) −5.00000 + 8.66025i −0.212622 + 0.368271i
\(554\) 19.0000 0.807233
\(555\) 0 0
\(556\) −5.00000 8.66025i −0.212047 0.367277i
\(557\) −17.0000 29.4449i −0.720313 1.24762i −0.960874 0.276985i \(-0.910665\pi\)
0.240561 0.970634i \(-0.422669\pi\)
\(558\) 0 0
\(559\) −12.5000 12.9904i −0.528694 0.549435i
\(560\) 2.00000 0.0845154
\(561\) 0 0
\(562\) 15.0000 + 25.9808i 0.632737 + 1.09593i
\(563\) −12.0000 + 20.7846i −0.505740 + 0.875967i 0.494238 + 0.869326i \(0.335447\pi\)
−0.999978 + 0.00664037i \(0.997886\pi\)
\(564\) 0 0
\(565\) 8.50000 14.7224i 0.357598 0.619377i
\(566\) −6.50000 + 11.2583i −0.273215 + 0.473223i
\(567\) 0 0
\(568\) −2.00000 + 3.46410i −0.0839181 + 0.145350i
\(569\) −9.00000 15.5885i −0.377300 0.653502i 0.613369 0.789797i \(-0.289814\pi\)
−0.990668 + 0.136295i \(0.956481\pi\)
\(570\) 0 0
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 1.00000 3.46410i 0.0418121 0.144841i
\(573\) 0 0
\(574\) −10.0000 17.3205i −0.417392 0.722944i
\(575\) −1.50000 2.59808i −0.0625543 0.108347i
\(576\) 0 0
\(577\) −18.0000 −0.749350 −0.374675 0.927156i \(-0.622246\pi\)
−0.374675 + 0.927156i \(0.622246\pi\)
\(578\) −6.50000 + 11.2583i −0.270364 + 0.468285i
\(579\) 0 0
\(580\) 1.00000 0.0415227
\(581\) −6.00000 + 10.3923i −0.248922 + 0.431145i
\(582\) 0 0
\(583\) −7.00000 12.1244i −0.289910 0.502140i
\(584\) 2.00000 0.0827606
\(585\) 0 0
\(586\) −14.0000 −0.578335
\(587\) −9.00000 15.5885i −0.371470 0.643404i 0.618322 0.785925i \(-0.287813\pi\)
−0.989792 + 0.142520i \(0.954479\pi\)
\(588\) 0 0
\(589\) 9.00000 15.5885i 0.370839 0.642311i
\(590\) −5.00000 −0.205847
\(591\) 0 0
\(592\) 2.50000 4.33013i 0.102749 0.177967i
\(593\) 35.0000 1.43728 0.718639 0.695383i \(-0.244765\pi\)
0.718639 + 0.695383i \(0.244765\pi\)
\(594\) 0 0
\(595\) 2.00000 + 3.46410i 0.0819920 + 0.142014i
\(596\) 5.50000 + 9.52628i 0.225289 + 0.390212i
\(597\) 0 0
\(598\) 7.50000 + 7.79423i 0.306698 + 0.318730i
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 0 0
\(601\) 5.50000 + 9.52628i 0.224350 + 0.388585i 0.956124 0.292962i \(-0.0946409\pi\)
−0.731774 + 0.681547i \(0.761308\pi\)
\(602\) 5.00000 8.66025i 0.203785 0.352966i
\(603\) 0 0
\(604\) −12.0000 + 20.7846i −0.488273 + 0.845714i
\(605\) 5.00000 8.66025i 0.203279 0.352089i
\(606\) 0 0
\(607\) 5.00000 8.66025i 0.202944 0.351509i −0.746532 0.665350i \(-0.768282\pi\)
0.949476 + 0.313841i \(0.101616\pi\)
\(608\) 3.00000 + 5.19615i 0.121666 + 0.210732i
\(609\) 0 0
\(610\) 10.0000 0.404888
\(611\) 3.00000 10.3923i 0.121367 0.420428i
\(612\) 0 0
\(613\) 18.5000 + 32.0429i 0.747208 + 1.29420i 0.949156 + 0.314806i \(0.101939\pi\)
−0.201948 + 0.979396i \(0.564727\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 2.00000 0.0805823
\(617\) 1.50000 2.59808i 0.0603877 0.104595i −0.834251 0.551385i \(-0.814100\pi\)
0.894639 + 0.446790i \(0.147433\pi\)
\(618\) 0 0
\(619\) −10.0000 −0.401934 −0.200967 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) 1.50000 2.59808i 0.0602414 0.104341i
\(621\) 0 0
\(622\) 0 0
\(623\) −20.0000 −0.801283
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −6.00000 10.3923i −0.239808 0.415360i
\(627\) 0 0
\(628\) −12.5000 + 21.6506i −0.498804 + 0.863954i
\(629\) 10.0000 0.398726
\(630\) 0 0
\(631\) −24.0000 + 41.5692i −0.955425 + 1.65484i −0.222032 + 0.975039i \(0.571269\pi\)
−0.733393 + 0.679805i \(0.762064\pi\)
\(632\) −5.00000 −0.198889
\(633\) 0 0
\(634\) −6.00000 10.3923i −0.238290 0.412731i
\(635\) 7.00000 + 12.1244i 0.277787 + 0.481140i
\(636\) 0 0
\(637\) −10.5000 + 2.59808i −0.416025 + 0.102940i
\(638\) 1.00000 0.0395904
\(639\) 0 0
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) −15.0000 + 25.9808i −0.592464 + 1.02618i 0.401435 + 0.915888i \(0.368512\pi\)
−0.993899 + 0.110291i \(0.964822\pi\)
\(642\) 0 0
\(643\) 20.0000 34.6410i 0.788723 1.36611i −0.138027 0.990429i \(-0.544076\pi\)
0.926750 0.375680i \(-0.122591\pi\)
\(644\) −3.00000 + 5.19615i −0.118217 + 0.204757i
\(645\) 0 0
\(646\) −6.00000 + 10.3923i −0.236067 + 0.408880i
\(647\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) 0 0
\(649\) −5.00000 −0.196267
\(650\) −3.50000 + 0.866025i −0.137281 + 0.0339683i
\(651\) 0 0
\(652\) −8.50000 14.7224i −0.332886 0.576575i
\(653\) −9.00000 15.5885i −0.352197 0.610023i 0.634437 0.772975i \(-0.281232\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(654\) 0 0
\(655\) −13.0000 −0.507952
\(656\) 5.00000 8.66025i 0.195217 0.338126i
\(657\) 0 0
\(658\) 6.00000 0.233904
\(659\) −6.50000 + 11.2583i −0.253204 + 0.438562i −0.964406 0.264425i \(-0.914818\pi\)
0.711202 + 0.702988i \(0.248151\pi\)
\(660\) 0 0
\(661\) 6.00000 + 10.3923i 0.233373 + 0.404214i 0.958799 0.284087i \(-0.0916904\pi\)
−0.725426 + 0.688301i \(0.758357\pi\)
\(662\) −4.00000 −0.155464
\(663\) 0 0
\(664\) −6.00000 −0.232845
\(665\) −6.00000 10.3923i −0.232670 0.402996i
\(666\) 0 0
\(667\) −1.50000 + 2.59808i −0.0580802 + 0.100598i
\(668\) 7.00000 0.270838
\(669\) 0 0
\(670\) 0 0
\(671\) 10.0000 0.386046
\(672\) 0 0
\(673\) 8.00000 + 13.8564i 0.308377 + 0.534125i 0.978008 0.208569i \(-0.0668807\pi\)
−0.669630 + 0.742695i \(0.733547\pi\)
\(674\) −11.0000 19.0526i −0.423704 0.733877i
\(675\) 0 0
\(676\) 11.5000 6.06218i 0.442308 0.233161i
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 10.0000 + 17.3205i 0.383765 + 0.664700i
\(680\) −1.00000 + 1.73205i −0.0383482 + 0.0664211i
\(681\) 0 0
\(682\) 1.50000 2.59808i 0.0574380 0.0994855i
\(683\) −22.0000 + 38.1051i −0.841807 + 1.45805i 0.0465592 + 0.998916i \(0.485174\pi\)
−0.888366 + 0.459136i \(0.848159\pi\)
\(684\) 0 0
\(685\) −4.50000 + 7.79423i −0.171936 + 0.297802i
\(686\) −10.0000 17.3205i −0.381802 0.661300i
\(687\) 0 0
\(688\) 5.00000 0.190623
\(689\) 14.0000 48.4974i 0.533358 1.84760i
\(690\) 0 0
\(691\) 7.00000 + 12.1244i 0.266293 + 0.461232i 0.967901 0.251330i \(-0.0808679\pi\)
−0.701609 + 0.712562i \(0.747535\pi\)
\(692\) 2.00000 + 3.46410i 0.0760286 + 0.131685i
\(693\) 0 0
\(694\) −18.0000 −0.683271
\(695\) −5.00000 + 8.66025i −0.189661 + 0.328502i
\(696\) 0 0
\(697\) 20.0000 0.757554
\(698\) 4.00000 6.92820i 0.151402 0.262236i
\(699\) 0 0
\(700\) −1.00000 1.73205i −0.0377964 0.0654654i
\(701\) −23.0000 −0.868698 −0.434349 0.900745i \(-0.643022\pi\)
−0.434349 + 0.900745i \(0.643022\pi\)
\(702\) 0 0
\(703\) −30.0000 −1.13147
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) 7.00000 12.1244i 0.263448 0.456306i
\(707\) −28.0000 −1.05305
\(708\) 0 0
\(709\) 8.00000 13.8564i 0.300446 0.520388i −0.675791 0.737093i \(-0.736198\pi\)
0.976237 + 0.216705i \(0.0695310\pi\)
\(710\) 4.00000 0.150117
\(711\) 0 0
\(712\) −5.00000 8.66025i −0.187383 0.324557i
\(713\) 4.50000 + 7.79423i 0.168526 + 0.291896i
\(714\) 0 0
\(715\) −3.50000 + 0.866025i −0.130893 + 0.0323875i
\(716\) 7.00000 0.261602
\(717\) 0 0
\(718\) −6.00000 10.3923i −0.223918 0.387837i
\(719\) −24.0000 + 41.5692i −0.895049 + 1.55027i −0.0613050 + 0.998119i \(0.519526\pi\)
−0.833744 + 0.552151i \(0.813807\pi\)
\(720\) 0 0
\(721\) 6.00000 10.3923i 0.223452 0.387030i
\(722\) 8.50000 14.7224i 0.316337 0.547912i
\(723\) 0 0
\(724\) −8.00000 + 13.8564i −0.297318 + 0.514969i
\(725\) −0.500000 0.866025i −0.0185695 0.0321634i
\(726\) 0 0
\(727\) −32.0000 −1.18681 −0.593407 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) 5.00000 + 5.19615i 0.185312 + 0.192582i
\(729\) 0 0
\(730\) −1.00000 1.73205i −0.0370117 0.0641061i
\(731\) 5.00000 + 8.66025i 0.184932 + 0.320311i
\(732\) 0 0
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) 18.0000 31.1769i 0.664392 1.15076i
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) 0 0
\(738\) 0 0
\(739\) −12.0000 20.7846i −0.441427 0.764574i 0.556369 0.830936i \(-0.312194\pi\)
−0.997796 + 0.0663614i \(0.978861\pi\)
\(740\) −5.00000 −0.183804
\(741\) 0 0
\(742\) 28.0000 1.02791
\(743\) −7.50000 12.9904i −0.275148 0.476571i 0.695024 0.718986i \(-0.255394\pi\)
−0.970173 + 0.242415i \(0.922060\pi\)
\(744\) 0 0
\(745\) 5.50000 9.52628i 0.201504 0.349016i
\(746\) −37.0000 −1.35467
\(747\) 0 0
\(748\) −1.00000 + 1.73205i −0.0365636 + 0.0633300i
\(749\) 12.0000 0.438470
\(750\) 0 0
\(751\) −20.5000 35.5070i −0.748056 1.29567i −0.948753 0.316017i \(-0.897654\pi\)
0.200698 0.979653i \(-0.435679\pi\)
\(752\) 1.50000 + 2.59808i 0.0546994 + 0.0947421i
\(753\) 0 0
\(754\) 2.50000 + 2.59808i 0.0910446 + 0.0946164i
\(755\) 24.0000 0.873449
\(756\) 0 0
\(757\) 27.0000 + 46.7654i 0.981332 + 1.69972i 0.657222 + 0.753697i \(0.271731\pi\)
0.324109 + 0.946020i \(0.394935\pi\)
\(758\) −15.0000 + 25.9808i −0.544825 + 0.943664i
\(759\) 0 0
\(760\) 3.00000 5.19615i 0.108821 0.188484i
\(761\) −10.0000 + 17.3205i −0.362500 + 0.627868i −0.988372 0.152058i \(-0.951410\pi\)
0.625872 + 0.779926i \(0.284743\pi\)
\(762\) 0 0
\(763\) 6.00000 10.3923i 0.217215 0.376227i
\(764\) 12.0000 + 20.7846i 0.434145 + 0.751961i
\(765\) 0 0
\(766\) −27.0000 −0.975550
\(767\) −12.5000 12.9904i −0.451349 0.469055i
\(768\) 0 0
\(769\) 14.5000 + 25.1147i 0.522883 + 0.905661i 0.999645 + 0.0266282i \(0.00847701\pi\)
−0.476762 + 0.879032i \(0.658190\pi\)
\(770\) −1.00000 1.73205i −0.0360375 0.0624188i
\(771\) 0 0
\(772\) −4.00000 −0.143963
\(773\) −8.00000 + 13.8564i −0.287740 + 0.498380i −0.973270 0.229664i \(-0.926237\pi\)
0.685530 + 0.728044i \(0.259571\pi\)
\(774\) 0 0
\(775\) −3.00000 −0.107763
\(776\) −5.00000 + 8.66025i −0.179490 + 0.310885i
\(777\) 0 0
\(778\) 0.500000 + 0.866025i 0.0179259 + 0.0310485i
\(779\) −60.0000 −2.14972
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) −3.00000 5.19615i −0.107280 0.185814i
\(783\) 0 0
\(784\) 1.50000 2.59808i 0.0535714 0.0927884i
\(785\) 25.0000 0.892288
\(786\) 0 0
\(787\) −12.5000 + 21.6506i −0.445577 + 0.771762i −0.998092 0.0617409i \(-0.980335\pi\)
0.552515 + 0.833503i \(0.313668\pi\)
\(788\) 12.0000 0.427482
\(789\) 0 0
\(790\) 2.50000 + 4.33013i 0.0889460 + 0.154059i
\(791\) 17.0000 + 29.4449i 0.604450 + 1.04694i
\(792\) 0 0
\(793\) 25.0000 + 25.9808i 0.887776 + 0.922604i
\(794\) 13.0000 0.461353
\(795\) 0 0
\(796\) 0 0
\(797\) −26.0000 + 45.0333i −0.920967 + 1.59516i −0.123045 + 0.992401i \(0.539266\pi\)
−0.797922 + 0.602761i \(0.794067\pi\)
\(798\) 0 0
\(799\) −3.00000 + 5.19615i −0.106132 + 0.183827i
\(800\) 0.500000 0.866025i 0.0176777 0.0306186i
\(801\) 0 0
\(802\) 6.00000 10.3923i 0.211867 0.366965i
\(803\) −1.00000 1.73205i −0.0352892 0.0611227i
\(804\) 0 0
\(805\) 6.00000 0.211472
\(806\) 10.5000 2.59808i 0.369847 0.0915133i
\(807\) 0 0
\(808\) −7.00000 12.1244i −0.246259 0.426533i
\(809\) 1.00000 + 1.73205i 0.0351581 + 0.0608957i 0.883069 0.469243i \(-0.155473\pi\)
−0.847911 + 0.530139i \(0.822140\pi\)
\(810\) 0 0
\(811\) 52.0000 1.82597 0.912983 0.407997i \(-0.133772\pi\)
0.912983 + 0.407997i \(0.133772\pi\)
\(812\) −1.00000 + 1.73205i −0.0350931 + 0.0607831i
\(813\) 0 0
\(814\) −5.00000 −0.175250
\(815\) −8.50000 + 14.7224i −0.297742 + 0.515704i
\(816\) 0 0
\(817\) −15.0000 25.9808i −0.524784 0.908952i
\(818\) 26.0000 0.909069
\(819\) 0 0
\(820\) −10.0000 −0.349215
\(821\) 11.5000 + 19.9186i 0.401353 + 0.695163i 0.993889 0.110380i \(-0.0352068\pi\)
−0.592537 + 0.805543i \(0.701873\pi\)
\(822\) 0 0
\(823\) 11.0000 19.0526i 0.383436 0.664130i −0.608115 0.793849i \(-0.708074\pi\)
0.991551 + 0.129719i \(0.0414074\pi\)
\(824\) 6.00000 0.209020
\(825\) 0 0
\(826\) 5.00000 8.66025i 0.173972 0.301329i
\(827\) 18.0000 0.625921 0.312961 0.949766i \(-0.398679\pi\)
0.312961 + 0.949766i \(0.398679\pi\)
\(828\) 0 0
\(829\) −13.0000 22.5167i −0.451509 0.782036i 0.546971 0.837151i \(-0.315781\pi\)
−0.998480 + 0.0551154i \(0.982447\pi\)
\(830\) 3.00000 + 5.19615i 0.104132 + 0.180361i
\(831\) 0 0
\(832\) −1.00000 + 3.46410i −0.0346688 + 0.120096i
\(833\) 6.00000 0.207888
\(834\) 0 0
\(835\) −3.50000 6.06218i −0.121122 0.209790i
\(836\) 3.00000 5.19615i 0.103757 0.179713i
\(837\) 0 0
\(838\) −2.00000 + 3.46410i −0.0690889 + 0.119665i
\(839\) 19.0000 32.9090i 0.655953 1.13614i −0.325701 0.945473i \(-0.605600\pi\)
0.981654 0.190671i \(-0.0610663\pi\)
\(840\) 0 0
\(841\) 14.0000 24.2487i 0.482759 0.836162i
\(842\) 14.0000 + 24.2487i 0.482472 + 0.835666i
\(843\) 0 0
\(844\) −8.00000 −0.275371
\(845\) −11.0000 6.92820i −0.378412 0.238337i
\(846\) 0 0
\(847\) 10.0000 + 17.3205i 0.343604 + 0.595140i
\(848\) 7.00000 + 12.1244i 0.240381 + 0.416352i
\(849\) 0 0
\(850\) 2.00000 0.0685994
\(851\) 7.50000 12.9904i 0.257097 0.445305i
\(852\) 0 0
\(853\) 7.00000 0.239675 0.119838 0.992793i \(-0.461763\pi\)
0.119838 + 0.992793i \(0.461763\pi\)
\(854\) −10.0000 + 17.3205i −0.342193 + 0.592696i
\(855\) 0 0
\(856\) 3.00000 + 5.19615i 0.102538 + 0.177601i
\(857\) 35.0000 1.19558 0.597789 0.801654i \(-0.296046\pi\)
0.597789 + 0.801654i \(0.296046\pi\)
\(858\) 0 0
\(859\) 18.0000 0.614152 0.307076 0.951685i \(-0.400649\pi\)
0.307076 + 0.951685i \(0.400649\pi\)
\(860\) −2.50000 4.33013i −0.0852493 0.147656i
\(861\) 0 0
\(862\) −6.00000 + 10.3923i −0.204361 + 0.353963i
\(863\) 51.0000 1.73606 0.868030 0.496512i \(-0.165386\pi\)
0.868030 + 0.496512i \(0.165386\pi\)
\(864\) 0 0
\(865\) 2.00000 3.46410i 0.0680020 0.117783i
\(866\) −16.0000 −0.543702
\(867\) 0 0
\(868\) 3.00000 + 5.19615i 0.101827 + 0.176369i
\(869\) 2.50000 + 4.33013i 0.0848067 + 0.146889i
\(870\) 0 0
\(871\) 0 0
\(872\) 6.00000 0.203186
\(873\) 0 0
\(874\) 9.00000 + 15.5885i 0.304430 + 0.527287i
\(875\) −1.00000 + 1.73205i −0.0338062 + 0.0585540i
\(876\) 0 0
\(877\) −6.50000 + 11.2583i −0.219489 + 0.380167i −0.954652 0.297724i \(-0.903772\pi\)
0.735163 + 0.677891i \(0.237106\pi\)
\(878\) 14.0000 24.2487i 0.472477 0.818354i
\(879\) 0 0
\(880\) 0.500000 0.866025i 0.0168550 0.0291937i
\(881\) 27.0000 + 46.7654i 0.909653 + 1.57557i 0.814546 + 0.580098i \(0.196986\pi\)
0.0951067 + 0.995467i \(0.469681\pi\)
\(882\) 0 0
\(883\) −1.00000 −0.0336527 −0.0168263 0.999858i \(-0.505356\pi\)
−0.0168263 + 0.999858i \(0.505356\pi\)
\(884\) −7.00000 + 1.73205i −0.235435 + 0.0582552i
\(885\) 0 0
\(886\) −8.00000 13.8564i −0.268765 0.465515i
\(887\) 0.500000 + 0.866025i 0.0167884 + 0.0290783i 0.874298 0.485390i \(-0.161323\pi\)
−0.857509 + 0.514469i \(0.827989\pi\)
\(888\) 0 0
\(889\) −28.0000 −0.939090
\(890\) −5.00000 + 8.66025i −0.167600 + 0.290292i
\(891\) 0 0
\(892\) 10.0000 0.334825
\(893\) 9.00000 15.5885i 0.301174 0.521648i
\(894\) 0 0
\(895\) −3.50000 6.06218i −0.116992 0.202636i
\(896\) −2.00000 −0.0668153
\(897\) 0 0
\(898\) −36.0000 −1.20134
\(899\) 1.50000 + 2.59808i 0.0500278 + 0.0866507i
\(900\) 0 0
\(901\) −14.0000 + 24.2487i −0.466408 + 0.807842i
\(902\) −10.0000 −0.332964
\(903\) 0 0
\(904\) −8.50000 + 14.7224i −0.282706 + 0.489661i
\(905\) 16.0000 0.531858
\(906\) 0 0
\(907\) 26.5000 + 45.8993i 0.879918 + 1.52406i 0.851430 + 0.524469i \(0.175736\pi\)
0.0284883 + 0.999594i \(0.490931\pi\)
\(908\) 10.0000 + 17.3205i 0.331862 + 0.574801i
\(909\) 0 0
\(910\) 2.00000 6.92820i 0.0662994 0.229668i
\(911\) −34.0000 −1.12647 −0.563235 0.826297i \(-0.690443\pi\)
−0.563235 + 0.826297i \(0.690443\pi\)
\(912\) 0 0
\(913\) 3.00000 + 5.19615i 0.0992855 + 0.171968i
\(914\) 7.00000 12.1244i 0.231539 0.401038i
\(915\) 0 0
\(916\) −11.0000 + 19.0526i −0.363450 + 0.629514i
\(917\) 13.0000 22.5167i 0.429298 0.743566i
\(918\) 0 0
\(919\) 28.0000 48.4974i 0.923635 1.59978i 0.129893 0.991528i \(-0.458537\pi\)
0.793742 0.608254i \(-0.208130\pi\)
\(920\) 1.50000 + 2.59808i 0.0494535 + 0.0856560i
\(921\) 0 0
\(922\) 27.0000 0.889198
\(923\) 10.0000 + 10.3923i 0.329154 + 0.342067i
\(924\) 0 0
\(925\) 2.50000 + 4.33013i 0.0821995 + 0.142374i
\(926\) 5.00000 + 8.66025i 0.164310 + 0.284594i
\(927\) 0 0
\(928\) −1.00000 −0.0328266
\(929\) 12.0000 20.7846i 0.393707 0.681921i −0.599228 0.800578i \(-0.704526\pi\)
0.992935 + 0.118657i \(0.0378590\pi\)
\(930\) 0 0
\(931\) −18.0000 −0.589926
\(932\) 1.50000 2.59808i 0.0491341 0.0851028i
\(933\) 0 0
\(934\) 1.00000 + 1.73205i 0.0327210 + 0.0566744i
\(935\) 2.00000 0.0654070
\(936\) 0 0
\(937\) −18.0000 −0.588034 −0.294017 0.955800i \(-0.594992\pi\)
−0.294017 + 0.955800i \(0.594992\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 1.50000 2.59808i 0.0489246 0.0847399i
\(941\) −26.0000 −0.847576 −0.423788 0.905761i \(-0.639300\pi\)
−0.423788 + 0.905761i \(0.639300\pi\)
\(942\) 0 0
\(943\) 15.0000 25.9808i 0.488467 0.846050i
\(944\) 5.00000 0.162736
\(945\) 0 0
\(946\) −2.50000 4.33013i −0.0812820 0.140785i
\(947\) 26.0000 + 45.0333i 0.844886 + 1.46339i 0.885720 + 0.464220i \(0.153665\pi\)
−0.0408333 + 0.999166i \(0.513001\pi\)
\(948\) 0 0
\(949\) 2.00000 6.92820i 0.0649227 0.224899i
\(950\) −6.00000 −0.194666
\(951\) 0 0
\(952\) −2.00000 3.46410i −0.0648204 0.112272i
\(953\) 7.50000 12.9904i 0.242949 0.420800i −0.718604 0.695419i \(-0.755219\pi\)
0.961553 + 0.274620i \(0.0885520\pi\)
\(954\) 0 0
\(955\) 12.0000 20.7846i 0.388311 0.672574i
\(956\) −4.00000 + 6.92820i −0.129369 + 0.224074i
\(957\) 0 0
\(958\) 2.00000 3.46410i 0.0646171 0.111920i
\(959\) −9.00000 15.5885i −0.290625 0.503378i
\(960\) 0 0
\(961\) −22.0000 −0.709677
\(962\) −12.5000 12.9904i −0.403016 0.418827i
\(963\) 0 0
\(964\) 3.50000 + 6.06218i 0.112727 + 0.195250i
\(965\) 2.00000 + 3.46410i 0.0643823 + 0.111513i
\(966\) 0 0
\(967\) 16.0000 0.514525 0.257263 0.966342i \(-0.417179\pi\)
0.257263 + 0.966342i \(0.417179\pi\)
\(968\) −5.00000 + 8.66025i −0.160706 + 0.278351i
\(969\) 0 0
\(970\) 10.0000 0.321081
\(971\) −20.0000 + 34.6410i −0.641831 + 1.11168i 0.343193 + 0.939265i \(0.388491\pi\)
−0.985024 + 0.172418i \(0.944842\pi\)
\(972\) 0 0
\(973\) −10.0000 17.3205i −0.320585 0.555270i
\(974\) −2.00000 −0.0640841
\(975\) 0 0
\(976\) −10.0000 −0.320092
\(977\) −19.5000 33.7750i −0.623860 1.08056i −0.988760 0.149511i \(-0.952230\pi\)
0.364900 0.931047i \(-0.381103\pi\)
\(978\) 0 0
\(979\) −5.00000 + 8.66025i −0.159801 + 0.276783i
\(980\) −3.00000 −0.0958315
\(981\) 0 0
\(982\) −12.0000 + 20.7846i −0.382935 + 0.663264i
\(983\) 25.0000 0.797376 0.398688 0.917087i \(-0.369466\pi\)
0.398688 + 0.917087i \(0.369466\pi\)
\(984\) 0 0
\(985\) −6.00000 10.3923i −0.191176 0.331126i
\(986\) −1.00000 1.73205i −0.0318465 0.0551597i
\(987\) 0 0
\(988\) 21.0000 5.19615i 0.668099 0.165312i
\(989\) 15.0000 0.476972
\(990\) 0 0
\(991\) −19.5000 33.7750i −0.619438 1.07290i −0.989588 0.143926i \(-0.954027\pi\)
0.370151 0.928972i \(-0.379306\pi\)
\(992\) −1.50000 + 2.59808i −0.0476250 + 0.0824890i
\(993\) 0 0
\(994\) −4.00000 + 6.92820i −0.126872 + 0.219749i
\(995\) 0 0
\(996\) 0 0
\(997\) 1.00000 1.73205i 0.0316703 0.0548546i −0.849756 0.527176i \(-0.823251\pi\)
0.881426 + 0.472322i \(0.156584\pi\)
\(998\) −20.0000 34.6410i −0.633089 1.09654i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1170.2.i.k.991.1 2
3.2 odd 2 390.2.i.a.211.1 yes 2
13.9 even 3 inner 1170.2.i.k.451.1 2
15.2 even 4 1950.2.z.h.1849.2 4
15.8 even 4 1950.2.z.h.1849.1 4
15.14 odd 2 1950.2.i.s.601.1 2
39.2 even 12 5070.2.b.g.1351.1 2
39.11 even 12 5070.2.b.g.1351.2 2
39.23 odd 6 5070.2.a.f.1.1 1
39.29 odd 6 5070.2.a.o.1.1 1
39.35 odd 6 390.2.i.a.61.1 2
195.74 odd 6 1950.2.i.s.451.1 2
195.113 even 12 1950.2.z.h.1699.2 4
195.152 even 12 1950.2.z.h.1699.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.i.a.61.1 2 39.35 odd 6
390.2.i.a.211.1 yes 2 3.2 odd 2
1170.2.i.k.451.1 2 13.9 even 3 inner
1170.2.i.k.991.1 2 1.1 even 1 trivial
1950.2.i.s.451.1 2 195.74 odd 6
1950.2.i.s.601.1 2 15.14 odd 2
1950.2.z.h.1699.1 4 195.152 even 12
1950.2.z.h.1699.2 4 195.113 even 12
1950.2.z.h.1849.1 4 15.8 even 4
1950.2.z.h.1849.2 4 15.2 even 4
5070.2.a.f.1.1 1 39.23 odd 6
5070.2.a.o.1.1 1 39.29 odd 6
5070.2.b.g.1351.1 2 39.2 even 12
5070.2.b.g.1351.2 2 39.11 even 12