Properties

Label 1386.2.r.a.1277.1
Level $1386$
Weight $2$
Character 1386.1277
Analytic conductor $11.067$
Analytic rank $0$
Dimension $8$
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] = [1386,2,Mod(89,1386)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1386.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.r (of order \(6\), 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: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1277.1
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1386.1277
Dual form 1386.2.r.a.89.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.25882 - 2.18034i) q^{5} +(1.48356 + 2.19067i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.25882 - 2.18034i) q^{5} +(1.48356 + 2.19067i) q^{7} +1.00000i q^{8} +(2.18034 + 1.25882i) q^{10} +(-0.866025 - 0.500000i) q^{11} -2.44949i q^{13} +(-2.38014 - 1.15539i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.64626 + 4.58346i) q^{17} +(-4.52761 + 2.61401i) q^{19} -2.51764 q^{20} +1.00000 q^{22} +(-4.28376 + 2.47323i) q^{23} +(-0.669251 + 1.15918i) q^{25} +(1.22474 + 2.12132i) q^{26} +(2.63896 - 0.189469i) q^{28} -8.05986i q^{29} +(7.44414 + 4.29788i) q^{31} +(0.866025 + 0.500000i) q^{32} -5.29253i q^{34} +(2.90887 - 5.99233i) q^{35} +(5.91189 + 10.2397i) q^{37} +(2.61401 - 4.52761i) q^{38} +(2.18034 - 1.25882i) q^{40} +1.92480 q^{41} -11.9841 q^{43} +(-0.866025 + 0.500000i) q^{44} +(2.47323 - 4.28376i) q^{46} +(-0.637756 - 1.10463i) q^{47} +(-2.59808 + 6.50000i) q^{49} -1.33850i q^{50} +(-2.12132 - 1.22474i) q^{52} +(-0.414578 - 0.239357i) q^{53} +2.51764i q^{55} +(-2.19067 + 1.48356i) q^{56} +(4.02993 + 6.98004i) q^{58} +(-3.02494 + 5.23936i) q^{59} +(10.7536 - 6.20857i) q^{61} -8.59575 q^{62} -1.00000 q^{64} +(-5.34072 + 3.08346i) q^{65} +(-6.11571 + 10.5927i) q^{67} +(2.64626 + 4.58346i) q^{68} +(0.477014 + 6.64394i) q^{70} +14.7055i q^{71} +(-8.52432 - 4.92152i) q^{73} +(-10.2397 - 5.91189i) q^{74} +5.22803i q^{76} +(-0.189469 - 2.63896i) q^{77} +(3.52677 + 6.10854i) q^{79} +(-1.25882 + 2.18034i) q^{80} +(-1.66693 + 0.962402i) q^{82} -9.35827 q^{83} +13.3247 q^{85} +(10.3786 - 5.99207i) q^{86} +(0.500000 - 0.866025i) q^{88} +(7.92392 + 13.7246i) q^{89} +(5.36603 - 3.63397i) q^{91} +4.94646i q^{92} +(1.10463 + 0.637756i) q^{94} +(11.3989 + 6.58114i) q^{95} -13.6556i q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} - 8 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} - 8 q^{5} - 4 q^{16} + 4 q^{17} + 24 q^{19} - 16 q^{20} + 8 q^{22} - 24 q^{23} - 4 q^{25} + 12 q^{31} - 16 q^{35} + 12 q^{37} + 8 q^{38} - 16 q^{41} - 32 q^{43} + 8 q^{46} - 48 q^{53} - 4 q^{58} - 16 q^{59} - 24 q^{62} - 8 q^{64} + 12 q^{65} - 24 q^{67} - 4 q^{68} - 20 q^{70} - 24 q^{73} + 12 q^{74} + 40 q^{79} - 8 q^{80} + 12 q^{82} - 72 q^{83} - 32 q^{85} + 24 q^{86} + 4 q^{88} + 16 q^{89} + 36 q^{91} - 24 q^{95} - 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −1.25882 2.18034i −0.562961 0.975077i −0.997236 0.0742968i \(-0.976329\pi\)
0.434275 0.900780i \(-0.357005\pi\)
\(6\) 0 0
\(7\) 1.48356 + 2.19067i 0.560734 + 0.827996i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.18034 + 1.25882i 0.689484 + 0.398074i
\(11\) −0.866025 0.500000i −0.261116 0.150756i
\(12\) 0 0
\(13\) 2.44949i 0.679366i −0.940540 0.339683i \(-0.889680\pi\)
0.940540 0.339683i \(-0.110320\pi\)
\(14\) −2.38014 1.15539i −0.636119 0.308792i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.64626 + 4.58346i −0.641813 + 1.11165i 0.343214 + 0.939257i \(0.388484\pi\)
−0.985028 + 0.172396i \(0.944849\pi\)
\(18\) 0 0
\(19\) −4.52761 + 2.61401i −1.03870 + 0.599696i −0.919466 0.393170i \(-0.871379\pi\)
−0.119238 + 0.992866i \(0.538045\pi\)
\(20\) −2.51764 −0.562961
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −4.28376 + 2.47323i −0.893226 + 0.515704i −0.874996 0.484129i \(-0.839136\pi\)
−0.0182299 + 0.999834i \(0.505803\pi\)
\(24\) 0 0
\(25\) −0.669251 + 1.15918i −0.133850 + 0.231835i
\(26\) 1.22474 + 2.12132i 0.240192 + 0.416025i
\(27\) 0 0
\(28\) 2.63896 0.189469i 0.498716 0.0358062i
\(29\) 8.05986i 1.49668i −0.663317 0.748339i \(-0.730852\pi\)
0.663317 0.748339i \(-0.269148\pi\)
\(30\) 0 0
\(31\) 7.44414 + 4.29788i 1.33701 + 0.771922i 0.986363 0.164587i \(-0.0526291\pi\)
0.350645 + 0.936509i \(0.385962\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 5.29253i 0.907661i
\(35\) 2.90887 5.99233i 0.491688 1.01289i
\(36\) 0 0
\(37\) 5.91189 + 10.2397i 0.971909 + 1.68340i 0.689780 + 0.724019i \(0.257707\pi\)
0.282129 + 0.959376i \(0.408959\pi\)
\(38\) 2.61401 4.52761i 0.424049 0.734475i
\(39\) 0 0
\(40\) 2.18034 1.25882i 0.344742 0.199037i
\(41\) 1.92480 0.300604 0.150302 0.988640i \(-0.451975\pi\)
0.150302 + 0.988640i \(0.451975\pi\)
\(42\) 0 0
\(43\) −11.9841 −1.82756 −0.913782 0.406204i \(-0.866852\pi\)
−0.913782 + 0.406204i \(0.866852\pi\)
\(44\) −0.866025 + 0.500000i −0.130558 + 0.0753778i
\(45\) 0 0
\(46\) 2.47323 4.28376i 0.364658 0.631606i
\(47\) −0.637756 1.10463i −0.0930263 0.161126i 0.815757 0.578395i \(-0.196321\pi\)
−0.908783 + 0.417269i \(0.862987\pi\)
\(48\) 0 0
\(49\) −2.59808 + 6.50000i −0.371154 + 0.928571i
\(50\) 1.33850i 0.189293i
\(51\) 0 0
\(52\) −2.12132 1.22474i −0.294174 0.169842i
\(53\) −0.414578 0.239357i −0.0569467 0.0328782i 0.471256 0.881996i \(-0.343801\pi\)
−0.528203 + 0.849118i \(0.677134\pi\)
\(54\) 0 0
\(55\) 2.51764i 0.339478i
\(56\) −2.19067 + 1.48356i −0.292741 + 0.198250i
\(57\) 0 0
\(58\) 4.02993 + 6.98004i 0.529155 + 0.916524i
\(59\) −3.02494 + 5.23936i −0.393814 + 0.682106i −0.992949 0.118542i \(-0.962178\pi\)
0.599135 + 0.800648i \(0.295511\pi\)
\(60\) 0 0
\(61\) 10.7536 6.20857i 1.37685 0.794925i 0.385072 0.922886i \(-0.374177\pi\)
0.991779 + 0.127961i \(0.0408432\pi\)
\(62\) −8.59575 −1.09166
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −5.34072 + 3.08346i −0.662434 + 0.382457i
\(66\) 0 0
\(67\) −6.11571 + 10.5927i −0.747153 + 1.29411i 0.202028 + 0.979380i \(0.435247\pi\)
−0.949182 + 0.314728i \(0.898087\pi\)
\(68\) 2.64626 + 4.58346i 0.320907 + 0.555827i
\(69\) 0 0
\(70\) 0.477014 + 6.64394i 0.0570140 + 0.794103i
\(71\) 14.7055i 1.74522i 0.488416 + 0.872611i \(0.337575\pi\)
−0.488416 + 0.872611i \(0.662425\pi\)
\(72\) 0 0
\(73\) −8.52432 4.92152i −0.997696 0.576020i −0.0901305 0.995930i \(-0.528728\pi\)
−0.907566 + 0.419910i \(0.862062\pi\)
\(74\) −10.2397 5.91189i −1.19034 0.687243i
\(75\) 0 0
\(76\) 5.22803i 0.599696i
\(77\) −0.189469 2.63896i −0.0215920 0.300737i
\(78\) 0 0
\(79\) 3.52677 + 6.10854i 0.396792 + 0.687265i 0.993328 0.115322i \(-0.0367899\pi\)
−0.596536 + 0.802587i \(0.703457\pi\)
\(80\) −1.25882 + 2.18034i −0.140740 + 0.243769i
\(81\) 0 0
\(82\) −1.66693 + 0.962402i −0.184081 + 0.106279i
\(83\) −9.35827 −1.02720 −0.513602 0.858029i \(-0.671689\pi\)
−0.513602 + 0.858029i \(0.671689\pi\)
\(84\) 0 0
\(85\) 13.3247 1.44526
\(86\) 10.3786 5.99207i 1.11915 0.646142i
\(87\) 0 0
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) 7.92392 + 13.7246i 0.839934 + 1.45481i 0.889949 + 0.456060i \(0.150740\pi\)
−0.0500147 + 0.998748i \(0.515927\pi\)
\(90\) 0 0
\(91\) 5.36603 3.63397i 0.562512 0.380944i
\(92\) 4.94646i 0.515704i
\(93\) 0 0
\(94\) 1.10463 + 0.637756i 0.113934 + 0.0657796i
\(95\) 11.3989 + 6.58114i 1.16950 + 0.675211i
\(96\) 0 0
\(97\) 13.6556i 1.38652i −0.720689 0.693259i \(-0.756174\pi\)
0.720689 0.693259i \(-0.243826\pi\)
\(98\) −1.00000 6.92820i −0.101015 0.699854i
\(99\) 0 0
\(100\) 0.669251 + 1.15918i 0.0669251 + 0.115918i
\(101\) 0.689211 1.19375i 0.0685791 0.118782i −0.829697 0.558214i \(-0.811487\pi\)
0.898276 + 0.439432i \(0.144820\pi\)
\(102\) 0 0
\(103\) −9.08978 + 5.24799i −0.895643 + 0.517100i −0.875784 0.482703i \(-0.839655\pi\)
−0.0198589 + 0.999803i \(0.506322\pi\)
\(104\) 2.44949 0.240192
\(105\) 0 0
\(106\) 0.478713 0.0464968
\(107\) 2.50535 1.44646i 0.242201 0.139835i −0.373987 0.927434i \(-0.622009\pi\)
0.616188 + 0.787599i \(0.288676\pi\)
\(108\) 0 0
\(109\) −6.76941 + 11.7250i −0.648392 + 1.12305i 0.335115 + 0.942177i \(0.391225\pi\)
−0.983507 + 0.180870i \(0.942109\pi\)
\(110\) −1.25882 2.18034i −0.120024 0.207887i
\(111\) 0 0
\(112\) 1.15539 2.38014i 0.109175 0.224902i
\(113\) 14.5699i 1.37062i 0.728250 + 0.685312i \(0.240334\pi\)
−0.728250 + 0.685312i \(0.759666\pi\)
\(114\) 0 0
\(115\) 10.7850 + 6.22670i 1.00570 + 0.580643i
\(116\) −6.98004 4.02993i −0.648080 0.374169i
\(117\) 0 0
\(118\) 6.04989i 0.556937i
\(119\) −13.9668 + 1.00277i −1.28033 + 0.0919236i
\(120\) 0 0
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) −6.20857 + 10.7536i −0.562097 + 0.973581i
\(123\) 0 0
\(124\) 7.44414 4.29788i 0.668504 0.385961i
\(125\) −9.21833 −0.824512
\(126\) 0 0
\(127\) −6.59675 −0.585367 −0.292683 0.956209i \(-0.594548\pi\)
−0.292683 + 0.956209i \(0.594548\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 3.08346 5.34072i 0.270438 0.468412i
\(131\) −0.757359 1.31178i −0.0661708 0.114611i 0.831042 0.556210i \(-0.187745\pi\)
−0.897213 + 0.441599i \(0.854412\pi\)
\(132\) 0 0
\(133\) −12.4434 6.04044i −1.07898 0.523772i
\(134\) 12.2314i 1.05663i
\(135\) 0 0
\(136\) −4.58346 2.64626i −0.393029 0.226915i
\(137\) 12.0316 + 6.94646i 1.02793 + 0.593476i 0.916391 0.400284i \(-0.131088\pi\)
0.111540 + 0.993760i \(0.464422\pi\)
\(138\) 0 0
\(139\) 13.5911i 1.15278i −0.817174 0.576391i \(-0.804460\pi\)
0.817174 0.576391i \(-0.195540\pi\)
\(140\) −3.73508 5.51532i −0.315672 0.466129i
\(141\) 0 0
\(142\) −7.35275 12.7353i −0.617029 1.06873i
\(143\) −1.22474 + 2.12132i −0.102418 + 0.177394i
\(144\) 0 0
\(145\) −17.5732 + 10.1459i −1.45938 + 0.842571i
\(146\) 9.84304 0.814616
\(147\) 0 0
\(148\) 11.8238 0.971909
\(149\) −5.76098 + 3.32611i −0.471958 + 0.272485i −0.717059 0.697012i \(-0.754512\pi\)
0.245101 + 0.969498i \(0.421179\pi\)
\(150\) 0 0
\(151\) −4.00877 + 6.94339i −0.326229 + 0.565045i −0.981760 0.190123i \(-0.939111\pi\)
0.655532 + 0.755168i \(0.272445\pi\)
\(152\) −2.61401 4.52761i −0.212025 0.367237i
\(153\) 0 0
\(154\) 1.48356 + 2.19067i 0.119549 + 0.176529i
\(155\) 21.6410i 1.73825i
\(156\) 0 0
\(157\) −19.0820 11.0170i −1.52291 0.879254i −0.999633 0.0270921i \(-0.991375\pi\)
−0.523279 0.852161i \(-0.675291\pi\)
\(158\) −6.10854 3.52677i −0.485969 0.280575i
\(159\) 0 0
\(160\) 2.51764i 0.199037i
\(161\) −11.7733 5.71512i −0.927864 0.450414i
\(162\) 0 0
\(163\) 5.03225 + 8.71611i 0.394156 + 0.682699i 0.992993 0.118172i \(-0.0377035\pi\)
−0.598837 + 0.800871i \(0.704370\pi\)
\(164\) 0.962402 1.66693i 0.0751509 0.130165i
\(165\) 0 0
\(166\) 8.10450 4.67914i 0.629031 0.363171i
\(167\) 4.76268 0.368547 0.184274 0.982875i \(-0.441007\pi\)
0.184274 + 0.982875i \(0.441007\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) −11.5395 + 6.66234i −0.885040 + 0.510978i
\(171\) 0 0
\(172\) −5.99207 + 10.3786i −0.456891 + 0.791359i
\(173\) 7.36843 + 12.7625i 0.560211 + 0.970314i 0.997478 + 0.0709824i \(0.0226134\pi\)
−0.437266 + 0.899332i \(0.644053\pi\)
\(174\) 0 0
\(175\) −3.53225 + 0.253604i −0.267013 + 0.0191707i
\(176\) 1.00000i 0.0753778i
\(177\) 0 0
\(178\) −13.7246 7.92392i −1.02871 0.593923i
\(179\) −2.03491 1.17486i −0.152096 0.0878129i 0.422020 0.906586i \(-0.361321\pi\)
−0.574117 + 0.818773i \(0.694654\pi\)
\(180\) 0 0
\(181\) 11.9236i 0.886271i −0.896455 0.443136i \(-0.853866\pi\)
0.896455 0.443136i \(-0.146134\pi\)
\(182\) −2.83013 + 5.83013i −0.209783 + 0.432158i
\(183\) 0 0
\(184\) −2.47323 4.28376i −0.182329 0.315803i
\(185\) 14.8840 25.7798i 1.09429 1.89537i
\(186\) 0 0
\(187\) 4.58346 2.64626i 0.335176 0.193514i
\(188\) −1.27551 −0.0930263
\(189\) 0 0
\(190\) −13.1623 −0.954892
\(191\) −21.2839 + 12.2882i −1.54005 + 0.889146i −0.541212 + 0.840886i \(0.682034\pi\)
−0.998835 + 0.0482604i \(0.984632\pi\)
\(192\) 0 0
\(193\) 7.05657 12.2223i 0.507943 0.879783i −0.492015 0.870587i \(-0.663739\pi\)
0.999958 0.00919638i \(-0.00292734\pi\)
\(194\) 6.82780 + 11.8261i 0.490208 + 0.849065i
\(195\) 0 0
\(196\) 4.33013 + 5.50000i 0.309295 + 0.392857i
\(197\) 0.579219i 0.0412676i −0.999787 0.0206338i \(-0.993432\pi\)
0.999787 0.0206338i \(-0.00656841\pi\)
\(198\) 0 0
\(199\) 2.08228 + 1.20220i 0.147609 + 0.0852220i 0.571985 0.820264i \(-0.306173\pi\)
−0.424377 + 0.905486i \(0.639507\pi\)
\(200\) −1.15918 0.669251i −0.0819661 0.0473232i
\(201\) 0 0
\(202\) 1.37842i 0.0969854i
\(203\) 17.6565 11.9573i 1.23924 0.839239i
\(204\) 0 0
\(205\) −2.42298 4.19672i −0.169228 0.293112i
\(206\) 5.24799 9.08978i 0.365645 0.633315i
\(207\) 0 0
\(208\) −2.12132 + 1.22474i −0.147087 + 0.0849208i
\(209\) 5.22803 0.361630
\(210\) 0 0
\(211\) −5.99343 −0.412605 −0.206302 0.978488i \(-0.566143\pi\)
−0.206302 + 0.978488i \(0.566143\pi\)
\(212\) −0.414578 + 0.239357i −0.0284733 + 0.0164391i
\(213\) 0 0
\(214\) −1.44646 + 2.50535i −0.0988782 + 0.171262i
\(215\) 15.0859 + 26.1295i 1.02885 + 1.78202i
\(216\) 0 0
\(217\) 1.62863 + 22.6838i 0.110558 + 1.53988i
\(218\) 13.5388i 0.916964i
\(219\) 0 0
\(220\) 2.18034 + 1.25882i 0.146998 + 0.0848696i
\(221\) 11.2271 + 6.48200i 0.755220 + 0.436026i
\(222\) 0 0
\(223\) 7.48993i 0.501563i 0.968044 + 0.250781i \(0.0806875\pi\)
−0.968044 + 0.250781i \(0.919313\pi\)
\(224\) 0.189469 + 2.63896i 0.0126594 + 0.176323i
\(225\) 0 0
\(226\) −7.28497 12.6179i −0.484589 0.839332i
\(227\) 4.88304 8.45768i 0.324099 0.561356i −0.657231 0.753689i \(-0.728272\pi\)
0.981330 + 0.192334i \(0.0616056\pi\)
\(228\) 0 0
\(229\) 0.195181 0.112688i 0.0128980 0.00744664i −0.493537 0.869725i \(-0.664296\pi\)
0.506435 + 0.862278i \(0.330963\pi\)
\(230\) −12.4534 −0.821153
\(231\) 0 0
\(232\) 8.05986 0.529155
\(233\) 0.445759 0.257359i 0.0292027 0.0168602i −0.485328 0.874332i \(-0.661300\pi\)
0.514530 + 0.857472i \(0.327966\pi\)
\(234\) 0 0
\(235\) −1.60564 + 2.78105i −0.104740 + 0.181416i
\(236\) 3.02494 + 5.23936i 0.196907 + 0.341053i
\(237\) 0 0
\(238\) 11.5942 7.85180i 0.751540 0.508957i
\(239\) 15.4899i 1.00196i −0.865459 0.500980i \(-0.832973\pi\)
0.865459 0.500980i \(-0.167027\pi\)
\(240\) 0 0
\(241\) −14.2882 8.24932i −0.920387 0.531386i −0.0366285 0.999329i \(-0.511662\pi\)
−0.883759 + 0.467943i \(0.844995\pi\)
\(242\) −0.866025 0.500000i −0.0556702 0.0321412i
\(243\) 0 0
\(244\) 12.4171i 0.794925i
\(245\) 17.4427 2.51764i 1.11437 0.160846i
\(246\) 0 0
\(247\) 6.40300 + 11.0903i 0.407413 + 0.705660i
\(248\) −4.29788 + 7.44414i −0.272915 + 0.472703i
\(249\) 0 0
\(250\) 7.98331 4.60916i 0.504909 0.291509i
\(251\) 18.6367 1.17634 0.588169 0.808738i \(-0.299849\pi\)
0.588169 + 0.808738i \(0.299849\pi\)
\(252\) 0 0
\(253\) 4.94646 0.310981
\(254\) 5.71295 3.29837i 0.358463 0.206958i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −0.575454 0.996716i −0.0358959 0.0621734i 0.847519 0.530764i \(-0.178095\pi\)
−0.883415 + 0.468591i \(0.844762\pi\)
\(258\) 0 0
\(259\) −13.6611 + 28.1423i −0.848862 + 1.74867i
\(260\) 6.16693i 0.382457i
\(261\) 0 0
\(262\) 1.31178 + 0.757359i 0.0810423 + 0.0467898i
\(263\) 6.18929 + 3.57339i 0.381648 + 0.220345i 0.678535 0.734568i \(-0.262615\pi\)
−0.296887 + 0.954913i \(0.595948\pi\)
\(264\) 0 0
\(265\) 1.20523i 0.0740365i
\(266\) 13.7966 0.990548i 0.845921 0.0607344i
\(267\) 0 0
\(268\) 6.11571 + 10.5927i 0.373577 + 0.647054i
\(269\) 6.68968 11.5869i 0.407877 0.706464i −0.586774 0.809750i \(-0.699602\pi\)
0.994652 + 0.103286i \(0.0329358\pi\)
\(270\) 0 0
\(271\) 5.92100 3.41849i 0.359675 0.207659i −0.309263 0.950977i \(-0.600082\pi\)
0.668938 + 0.743318i \(0.266749\pi\)
\(272\) 5.29253 0.320907
\(273\) 0 0
\(274\) −13.8929 −0.839302
\(275\) 1.15918 0.669251i 0.0699010 0.0403573i
\(276\) 0 0
\(277\) 2.87404 4.97798i 0.172684 0.299098i −0.766673 0.642037i \(-0.778089\pi\)
0.939357 + 0.342940i \(0.111423\pi\)
\(278\) 6.79555 + 11.7702i 0.407570 + 0.705932i
\(279\) 0 0
\(280\) 5.99233 + 2.90887i 0.358110 + 0.173838i
\(281\) 6.45821i 0.385265i 0.981271 + 0.192632i \(0.0617025\pi\)
−0.981271 + 0.192632i \(0.938298\pi\)
\(282\) 0 0
\(283\) 5.87843 + 3.39391i 0.349436 + 0.201747i 0.664437 0.747344i \(-0.268671\pi\)
−0.315001 + 0.949091i \(0.602005\pi\)
\(284\) 12.7353 + 7.35275i 0.755703 + 0.436305i
\(285\) 0 0
\(286\) 2.44949i 0.144841i
\(287\) 2.85557 + 4.21661i 0.168559 + 0.248899i
\(288\) 0 0
\(289\) −5.50543 9.53568i −0.323849 0.560923i
\(290\) 10.1459 17.5732i 0.595788 1.03193i
\(291\) 0 0
\(292\) −8.52432 + 4.92152i −0.498848 + 0.288010i
\(293\) −3.15159 −0.184118 −0.0920589 0.995754i \(-0.529345\pi\)
−0.0920589 + 0.995754i \(0.529345\pi\)
\(294\) 0 0
\(295\) 15.2314 0.886808
\(296\) −10.2397 + 5.91189i −0.595170 + 0.343622i
\(297\) 0 0
\(298\) 3.32611 5.76098i 0.192676 0.333725i
\(299\) 6.05816 + 10.4930i 0.350352 + 0.606828i
\(300\) 0 0
\(301\) −17.7792 26.2533i −1.02478 1.51322i
\(302\) 8.01753i 0.461357i
\(303\) 0 0
\(304\) 4.52761 + 2.61401i 0.259676 + 0.149924i
\(305\) −27.0736 15.6309i −1.55023 0.895024i
\(306\) 0 0
\(307\) 15.0711i 0.860151i −0.902793 0.430076i \(-0.858487\pi\)
0.902793 0.430076i \(-0.141513\pi\)
\(308\) −2.38014 1.15539i −0.135621 0.0658347i
\(309\) 0 0
\(310\) 10.8205 + 18.7417i 0.614563 + 1.06445i
\(311\) 15.9573 27.6388i 0.904854 1.56725i 0.0837402 0.996488i \(-0.473313\pi\)
0.821113 0.570765i \(-0.193353\pi\)
\(312\) 0 0
\(313\) 13.8126 7.97469i 0.780733 0.450756i −0.0559572 0.998433i \(-0.517821\pi\)
0.836690 + 0.547677i \(0.184488\pi\)
\(314\) 22.0340 1.24345
\(315\) 0 0
\(316\) 7.05354 0.396792
\(317\) −21.9318 + 12.6623i −1.23181 + 0.711188i −0.967408 0.253224i \(-0.918509\pi\)
−0.264405 + 0.964412i \(0.585176\pi\)
\(318\) 0 0
\(319\) −4.02993 + 6.98004i −0.225633 + 0.390807i
\(320\) 1.25882 + 2.18034i 0.0703701 + 0.121885i
\(321\) 0 0
\(322\) 13.0535 0.937200i 0.727444 0.0522281i
\(323\) 27.6695i 1.53957i
\(324\) 0 0
\(325\) 2.83939 + 1.63932i 0.157501 + 0.0909333i
\(326\) −8.71611 5.03225i −0.482741 0.278711i
\(327\) 0 0
\(328\) 1.92480i 0.106279i
\(329\) 1.47372 3.03590i 0.0812488 0.167374i
\(330\) 0 0
\(331\) −7.03882 12.1916i −0.386888 0.670110i 0.605141 0.796118i \(-0.293117\pi\)
−0.992029 + 0.126008i \(0.959783\pi\)
\(332\) −4.67914 + 8.10450i −0.256801 + 0.444792i
\(333\) 0 0
\(334\) −4.12460 + 2.38134i −0.225688 + 0.130301i
\(335\) 30.7943 1.68247
\(336\) 0 0
\(337\) −8.15142 −0.444036 −0.222018 0.975043i \(-0.571264\pi\)
−0.222018 + 0.975043i \(0.571264\pi\)
\(338\) −6.06218 + 3.50000i −0.329739 + 0.190375i
\(339\) 0 0
\(340\) 6.66234 11.5395i 0.361316 0.625817i
\(341\) −4.29788 7.44414i −0.232743 0.403123i
\(342\) 0 0
\(343\) −18.0938 + 3.95164i −0.976972 + 0.213368i
\(344\) 11.9841i 0.646142i
\(345\) 0 0
\(346\) −12.7625 7.36843i −0.686116 0.396129i
\(347\) 19.5502 + 11.2873i 1.04951 + 0.605933i 0.922511 0.385970i \(-0.126133\pi\)
0.126996 + 0.991903i \(0.459466\pi\)
\(348\) 0 0
\(349\) 22.9498i 1.22848i −0.789121 0.614238i \(-0.789464\pi\)
0.789121 0.614238i \(-0.210536\pi\)
\(350\) 2.93222 1.98575i 0.156734 0.106143i
\(351\) 0 0
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) −12.5990 + 21.8222i −0.670579 + 1.16148i 0.307161 + 0.951658i \(0.400621\pi\)
−0.977740 + 0.209820i \(0.932712\pi\)
\(354\) 0 0
\(355\) 32.0630 18.5116i 1.70173 0.982492i
\(356\) 15.8478 0.839934
\(357\) 0 0
\(358\) 2.34971 0.124186
\(359\) 17.0558 9.84714i 0.900168 0.519712i 0.0229134 0.999737i \(-0.492706\pi\)
0.877255 + 0.480025i \(0.159372\pi\)
\(360\) 0 0
\(361\) 4.16614 7.21597i 0.219271 0.379788i
\(362\) 5.96178 + 10.3261i 0.313344 + 0.542728i
\(363\) 0 0
\(364\) −0.464102 6.46410i −0.0243255 0.338811i
\(365\) 24.7812i 1.29711i
\(366\) 0 0
\(367\) 2.81282 + 1.62398i 0.146828 + 0.0847712i 0.571614 0.820523i \(-0.306317\pi\)
−0.424786 + 0.905294i \(0.639651\pi\)
\(368\) 4.28376 + 2.47323i 0.223307 + 0.128926i
\(369\) 0 0
\(370\) 29.7680i 1.54756i
\(371\) −0.0907012 1.26330i −0.00470897 0.0655875i
\(372\) 0 0
\(373\) −3.41177 5.90935i −0.176655 0.305975i 0.764078 0.645124i \(-0.223194\pi\)
−0.940733 + 0.339149i \(0.889861\pi\)
\(374\) −2.64626 + 4.58346i −0.136835 + 0.237005i
\(375\) 0 0
\(376\) 1.10463 0.637756i 0.0569668 0.0328898i
\(377\) −19.7425 −1.01679
\(378\) 0 0
\(379\) 18.8929 0.970464 0.485232 0.874385i \(-0.338735\pi\)
0.485232 + 0.874385i \(0.338735\pi\)
\(380\) 11.3989 6.58114i 0.584750 0.337605i
\(381\) 0 0
\(382\) 12.2882 21.2839i 0.628722 1.08898i
\(383\) −13.2165 22.8916i −0.675329 1.16970i −0.976373 0.216094i \(-0.930668\pi\)
0.301043 0.953610i \(-0.402665\pi\)
\(384\) 0 0
\(385\) −5.51532 + 3.73508i −0.281087 + 0.190357i
\(386\) 14.1131i 0.718340i
\(387\) 0 0
\(388\) −11.8261 6.82780i −0.600380 0.346629i
\(389\) −10.1046 5.83391i −0.512325 0.295791i 0.221464 0.975169i \(-0.428917\pi\)
−0.733789 + 0.679378i \(0.762250\pi\)
\(390\) 0 0
\(391\) 26.1793i 1.32394i
\(392\) −6.50000 2.59808i −0.328300 0.131223i
\(393\) 0 0
\(394\) 0.289609 + 0.501618i 0.0145903 + 0.0252711i
\(395\) 8.87913 15.3791i 0.446757 0.773806i
\(396\) 0 0
\(397\) −8.68678 + 5.01532i −0.435977 + 0.251711i −0.701890 0.712286i \(-0.747660\pi\)
0.265913 + 0.963997i \(0.414327\pi\)
\(398\) −2.40441 −0.120522
\(399\) 0 0
\(400\) 1.33850 0.0669251
\(401\) −4.52281 + 2.61125i −0.225858 + 0.130399i −0.608660 0.793431i \(-0.708293\pi\)
0.382802 + 0.923831i \(0.374959\pi\)
\(402\) 0 0
\(403\) 10.5276 18.2343i 0.524417 0.908318i
\(404\) −0.689211 1.19375i −0.0342895 0.0593912i
\(405\) 0 0
\(406\) −9.31231 + 19.1836i −0.462162 + 0.952065i
\(407\) 11.8238i 0.586083i
\(408\) 0 0
\(409\) −16.6456 9.61037i −0.823074 0.475202i 0.0284013 0.999597i \(-0.490958\pi\)
−0.851475 + 0.524395i \(0.824292\pi\)
\(410\) 4.19672 + 2.42298i 0.207261 + 0.119662i
\(411\) 0 0
\(412\) 10.4960i 0.517100i
\(413\) −15.9654 + 1.14626i −0.785606 + 0.0564040i
\(414\) 0 0
\(415\) 11.7804 + 20.4042i 0.578276 + 1.00160i
\(416\) 1.22474 2.12132i 0.0600481 0.104006i
\(417\) 0 0
\(418\) −4.52761 + 2.61401i −0.221452 + 0.127856i
\(419\) 17.4755 0.853733 0.426866 0.904315i \(-0.359617\pi\)
0.426866 + 0.904315i \(0.359617\pi\)
\(420\) 0 0
\(421\) 27.8519 1.35742 0.678710 0.734406i \(-0.262539\pi\)
0.678710 + 0.734406i \(0.262539\pi\)
\(422\) 5.19046 2.99672i 0.252668 0.145878i
\(423\) 0 0
\(424\) 0.239357 0.414578i 0.0116242 0.0201337i
\(425\) −3.54203 6.13497i −0.171814 0.297590i
\(426\) 0 0
\(427\) 29.5545 + 14.3467i 1.43024 + 0.694285i
\(428\) 2.89293i 0.139835i
\(429\) 0 0
\(430\) −26.1295 15.0859i −1.26008 0.727505i
\(431\) 30.1846 + 17.4271i 1.45394 + 0.839434i 0.998702 0.0509348i \(-0.0162201\pi\)
0.455240 + 0.890369i \(0.349553\pi\)
\(432\) 0 0
\(433\) 27.2068i 1.30748i 0.756721 + 0.653738i \(0.226800\pi\)
−0.756721 + 0.653738i \(0.773200\pi\)
\(434\) −12.7524 18.8305i −0.612132 0.903891i
\(435\) 0 0
\(436\) 6.76941 + 11.7250i 0.324196 + 0.561524i
\(437\) 12.9301 22.3956i 0.618532 1.07133i
\(438\) 0 0
\(439\) −20.0987 + 11.6040i −0.959260 + 0.553829i −0.895945 0.444165i \(-0.853501\pi\)
−0.0633147 + 0.997994i \(0.520167\pi\)
\(440\) −2.51764 −0.120024
\(441\) 0 0
\(442\) −12.9640 −0.616634
\(443\) −15.7172 + 9.07435i −0.746749 + 0.431135i −0.824518 0.565836i \(-0.808554\pi\)
0.0777693 + 0.996971i \(0.475220\pi\)
\(444\) 0 0
\(445\) 19.9496 34.5537i 0.945700 1.63800i
\(446\) −3.74496 6.48647i −0.177329 0.307143i
\(447\) 0 0
\(448\) −1.48356 2.19067i −0.0700918 0.103499i
\(449\) 31.9656i 1.50855i −0.656560 0.754274i \(-0.727989\pi\)
0.656560 0.754274i \(-0.272011\pi\)
\(450\) 0 0
\(451\) −1.66693 0.962402i −0.0784926 0.0453177i
\(452\) 12.6179 + 7.28497i 0.593497 + 0.342656i
\(453\) 0 0
\(454\) 9.76608i 0.458345i
\(455\) −14.6781 7.12524i −0.688122 0.334036i
\(456\) 0 0
\(457\) −12.9607 22.4486i −0.606276 1.05010i −0.991848 0.127424i \(-0.959329\pi\)
0.385572 0.922678i \(-0.374004\pi\)
\(458\) −0.112688 + 0.195181i −0.00526557 + 0.00912023i
\(459\) 0 0
\(460\) 10.7850 6.22670i 0.502852 0.290322i
\(461\) −21.8282 −1.01664 −0.508321 0.861168i \(-0.669734\pi\)
−0.508321 + 0.861168i \(0.669734\pi\)
\(462\) 0 0
\(463\) 4.92621 0.228940 0.114470 0.993427i \(-0.463483\pi\)
0.114470 + 0.993427i \(0.463483\pi\)
\(464\) −6.98004 + 4.02993i −0.324040 + 0.187085i
\(465\) 0 0
\(466\) −0.257359 + 0.445759i −0.0119219 + 0.0206494i
\(467\) −1.87404 3.24592i −0.0867200 0.150203i 0.819403 0.573218i \(-0.194305\pi\)
−0.906123 + 0.423015i \(0.860972\pi\)
\(468\) 0 0
\(469\) −32.2782 + 2.31747i −1.49047 + 0.107011i
\(470\) 3.21128i 0.148125i
\(471\) 0 0
\(472\) −5.23936 3.02494i −0.241161 0.139234i
\(473\) 10.3786 + 5.99207i 0.477207 + 0.275516i
\(474\) 0 0
\(475\) 6.99772i 0.321078i
\(476\) −6.11496 + 12.5970i −0.280279 + 0.577381i
\(477\) 0 0
\(478\) 7.74496 + 13.4147i 0.354246 + 0.613573i
\(479\) 1.93134 3.34517i 0.0882450 0.152845i −0.818524 0.574472i \(-0.805207\pi\)
0.906769 + 0.421627i \(0.138541\pi\)
\(480\) 0 0
\(481\) 25.0820 14.4811i 1.14364 0.660282i
\(482\) 16.4986 0.751493
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −29.7739 + 17.1899i −1.35196 + 0.780555i
\(486\) 0 0
\(487\) −5.80946 + 10.0623i −0.263252 + 0.455966i −0.967104 0.254381i \(-0.918128\pi\)
0.703852 + 0.710346i \(0.251462\pi\)
\(488\) 6.20857 + 10.7536i 0.281049 + 0.486790i
\(489\) 0 0
\(490\) −13.8470 + 10.9017i −0.625544 + 0.492488i
\(491\) 25.7345i 1.16138i −0.814124 0.580691i \(-0.802783\pi\)
0.814124 0.580691i \(-0.197217\pi\)
\(492\) 0 0
\(493\) 36.9421 + 21.3285i 1.66379 + 0.960588i
\(494\) −11.0903 6.40300i −0.498977 0.288085i
\(495\) 0 0
\(496\) 8.59575i 0.385961i
\(497\) −32.2149 + 21.8165i −1.44504 + 0.978606i
\(498\) 0 0
\(499\) −11.3984 19.7425i −0.510261 0.883797i −0.999929 0.0118887i \(-0.996216\pi\)
0.489669 0.871909i \(-0.337118\pi\)
\(500\) −4.60916 + 7.98331i −0.206128 + 0.357024i
\(501\) 0 0
\(502\) −16.1399 + 9.31835i −0.720357 + 0.415898i
\(503\) −20.4955 −0.913848 −0.456924 0.889506i \(-0.651049\pi\)
−0.456924 + 0.889506i \(0.651049\pi\)
\(504\) 0 0
\(505\) −3.47037 −0.154429
\(506\) −4.28376 + 2.47323i −0.190436 + 0.109949i
\(507\) 0 0
\(508\) −3.29837 + 5.71295i −0.146342 + 0.253471i
\(509\) 5.99259 + 10.3795i 0.265617 + 0.460062i 0.967725 0.252008i \(-0.0810911\pi\)
−0.702108 + 0.712070i \(0.747758\pi\)
\(510\) 0 0
\(511\) −1.86495 25.9754i −0.0825004 1.14908i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 0.996716 + 0.575454i 0.0439633 + 0.0253822i
\(515\) 22.8848 + 13.2125i 1.00842 + 0.582214i
\(516\) 0 0
\(517\) 1.27551i 0.0560970i
\(518\) −2.24024 31.2025i −0.0984303 1.37096i
\(519\) 0 0
\(520\) −3.08346 5.34072i −0.135219 0.234206i
\(521\) 2.33369 4.04208i 0.102241 0.177087i −0.810367 0.585923i \(-0.800732\pi\)
0.912608 + 0.408837i \(0.134065\pi\)
\(522\) 0 0
\(523\) −17.5494 + 10.1322i −0.767383 + 0.443049i −0.831940 0.554865i \(-0.812770\pi\)
0.0645573 + 0.997914i \(0.479436\pi\)
\(524\) −1.51472 −0.0661708
\(525\) 0 0
\(526\) −7.14678 −0.311614
\(527\) −39.3983 + 22.7466i −1.71622 + 0.990859i
\(528\) 0 0
\(529\) 0.733751 1.27089i 0.0319022 0.0552562i
\(530\) −0.602614 1.04376i −0.0261759 0.0453379i
\(531\) 0 0
\(532\) −11.4529 + 7.75611i −0.496546 + 0.336270i
\(533\) 4.71479i 0.204220i
\(534\) 0 0
\(535\) −6.30756 3.64167i −0.272700 0.157443i
\(536\) −10.5927 6.11571i −0.457536 0.264159i
\(537\) 0 0
\(538\) 13.3794i 0.576826i
\(539\) 5.50000 4.33013i 0.236902 0.186512i
\(540\) 0 0
\(541\) 6.53334 + 11.3161i 0.280890 + 0.486516i 0.971604 0.236612i \(-0.0760370\pi\)
−0.690714 + 0.723128i \(0.742704\pi\)
\(542\) −3.41849 + 5.92100i −0.146837 + 0.254329i
\(543\) 0 0
\(544\) −4.58346 + 2.64626i −0.196514 + 0.113458i
\(545\) 34.0858 1.46008
\(546\) 0 0
\(547\) 24.2492 1.03682 0.518411 0.855132i \(-0.326524\pi\)
0.518411 + 0.855132i \(0.326524\pi\)
\(548\) 12.0316 6.94646i 0.513966 0.296738i
\(549\) 0 0
\(550\) −0.669251 + 1.15918i −0.0285369 + 0.0494274i
\(551\) 21.0686 + 36.4918i 0.897552 + 1.55461i
\(552\) 0 0
\(553\) −8.14962 + 16.7884i −0.346557 + 0.713915i
\(554\) 5.74807i 0.244212i
\(555\) 0 0
\(556\) −11.7702 6.79555i −0.499170 0.288196i
\(557\) 20.6838 + 11.9418i 0.876402 + 0.505991i 0.869471 0.493985i \(-0.164460\pi\)
0.00693183 + 0.999976i \(0.497794\pi\)
\(558\) 0 0
\(559\) 29.3550i 1.24159i
\(560\) −6.64394 + 0.477014i −0.280758 + 0.0201575i
\(561\) 0 0
\(562\) −3.22911 5.59298i −0.136212 0.235925i
\(563\) −1.15091 + 1.99343i −0.0485050 + 0.0840131i −0.889259 0.457405i \(-0.848779\pi\)
0.840754 + 0.541418i \(0.182112\pi\)
\(564\) 0 0
\(565\) 31.7674 18.3409i 1.33646 0.771608i
\(566\) −6.78783 −0.285314
\(567\) 0 0
\(568\) −14.7055 −0.617029
\(569\) 21.7718 12.5699i 0.912720 0.526959i 0.0314144 0.999506i \(-0.489999\pi\)
0.881305 + 0.472548i \(0.156666\pi\)
\(570\) 0 0
\(571\) −17.9626 + 31.1122i −0.751713 + 1.30200i 0.195279 + 0.980748i \(0.437439\pi\)
−0.946992 + 0.321257i \(0.895895\pi\)
\(572\) 1.22474 + 2.12132i 0.0512092 + 0.0886969i
\(573\) 0 0
\(574\) −4.58130 2.22391i −0.191220 0.0928241i
\(575\) 6.62085i 0.276108i
\(576\) 0 0
\(577\) −2.60396 1.50340i −0.108404 0.0625874i 0.444818 0.895621i \(-0.353269\pi\)
−0.553222 + 0.833034i \(0.686602\pi\)
\(578\) 9.53568 + 5.50543i 0.396632 + 0.228996i
\(579\) 0 0
\(580\) 20.2918i 0.842571i
\(581\) −13.8836 20.5009i −0.575989 0.850520i
\(582\) 0 0
\(583\) 0.239357 + 0.414578i 0.00991314 + 0.0171701i
\(584\) 4.92152 8.52432i 0.203654 0.352739i
\(585\) 0 0
\(586\) 2.72936 1.57579i 0.112749 0.0650954i
\(587\) 30.2752 1.24959 0.624796 0.780788i \(-0.285182\pi\)
0.624796 + 0.780788i \(0.285182\pi\)
\(588\) 0 0
\(589\) −44.9389 −1.85167
\(590\) −13.1908 + 7.61571i −0.543057 + 0.313534i
\(591\) 0 0
\(592\) 5.91189 10.2397i 0.242977 0.420849i
\(593\) 2.54071 + 4.40063i 0.104334 + 0.180712i 0.913466 0.406915i \(-0.133395\pi\)
−0.809132 + 0.587627i \(0.800062\pi\)
\(594\) 0 0
\(595\) 19.7680 + 29.1900i 0.810409 + 1.19667i
\(596\) 6.65221i 0.272485i
\(597\) 0 0
\(598\) −10.4930 6.05816i −0.429092 0.247736i
\(599\) −34.0097 19.6355i −1.38960 0.802285i −0.396329 0.918108i \(-0.629716\pi\)
−0.993270 + 0.115823i \(0.963049\pi\)
\(600\) 0 0
\(601\) 8.04133i 0.328013i 0.986459 + 0.164006i \(0.0524417\pi\)
−0.986459 + 0.164006i \(0.947558\pi\)
\(602\) 28.5239 + 13.8464i 1.16255 + 0.564338i
\(603\) 0 0
\(604\) 4.00877 + 6.94339i 0.163114 + 0.282522i
\(605\) 1.25882 2.18034i 0.0511783 0.0886434i
\(606\) 0 0
\(607\) 29.6848 17.1385i 1.20487 0.695632i 0.243236 0.969967i \(-0.421791\pi\)
0.961634 + 0.274335i \(0.0884578\pi\)
\(608\) −5.22803 −0.212025
\(609\) 0 0
\(610\) 31.2618 1.26576
\(611\) −2.70577 + 1.56218i −0.109464 + 0.0631990i
\(612\) 0 0
\(613\) −18.8924 + 32.7226i −0.763057 + 1.32165i 0.178211 + 0.983992i \(0.442969\pi\)
−0.941268 + 0.337661i \(0.890364\pi\)
\(614\) 7.53553 + 13.0519i 0.304109 + 0.526733i
\(615\) 0 0
\(616\) 2.63896 0.189469i 0.106327 0.00763391i
\(617\) 0.0377832i 0.00152109i −1.00000 0.000760547i \(-0.999758\pi\)
1.00000 0.000760547i \(-0.000242090\pi\)
\(618\) 0 0
\(619\) 5.61028 + 3.23910i 0.225496 + 0.130190i 0.608493 0.793559i \(-0.291774\pi\)
−0.382996 + 0.923750i \(0.625108\pi\)
\(620\) −18.7417 10.8205i −0.752683 0.434562i
\(621\) 0 0
\(622\) 31.9145i 1.27966i
\(623\) −18.3105 + 37.7201i −0.733595 + 1.51122i
\(624\) 0 0
\(625\) 14.9505 + 25.8950i 0.598018 + 1.03580i
\(626\) −7.97469 + 13.8126i −0.318733 + 0.552061i
\(627\) 0 0
\(628\) −19.0820 + 11.0170i −0.761456 + 0.439627i
\(629\) −62.5777 −2.49514
\(630\) 0 0
\(631\) −17.8145 −0.709184 −0.354592 0.935021i \(-0.615380\pi\)
−0.354592 + 0.935021i \(0.615380\pi\)
\(632\) −6.10854 + 3.52677i −0.242985 + 0.140287i
\(633\) 0 0
\(634\) 12.6623 21.9318i 0.502886 0.871023i
\(635\) 8.30411 + 14.3831i 0.329539 + 0.570778i
\(636\) 0 0
\(637\) 15.9217 + 6.36396i 0.630840 + 0.252149i
\(638\) 8.05986i 0.319093i
\(639\) 0 0
\(640\) −2.18034 1.25882i −0.0861854 0.0497592i
\(641\) −16.1473 9.32265i −0.637780 0.368222i 0.145979 0.989288i \(-0.453367\pi\)
−0.783759 + 0.621065i \(0.786700\pi\)
\(642\) 0 0
\(643\) 7.04112i 0.277674i −0.990315 0.138837i \(-0.955664\pi\)
0.990315 0.138837i \(-0.0443365\pi\)
\(644\) −10.8361 + 7.33839i −0.427001 + 0.289173i
\(645\) 0 0
\(646\) 13.8347 + 23.9625i 0.544321 + 0.942791i
\(647\) −25.0127 + 43.3232i −0.983350 + 1.70321i −0.334299 + 0.942467i \(0.608500\pi\)
−0.649051 + 0.760745i \(0.724834\pi\)
\(648\) 0 0
\(649\) 5.23936 3.02494i 0.205663 0.118739i
\(650\) −3.27865 −0.128599
\(651\) 0 0
\(652\) 10.0645 0.394156
\(653\) −2.68285 + 1.54894i −0.104988 + 0.0606149i −0.551575 0.834126i \(-0.685973\pi\)
0.446587 + 0.894740i \(0.352639\pi\)
\(654\) 0 0
\(655\) −1.90676 + 3.30260i −0.0745031 + 0.129043i
\(656\) −0.962402 1.66693i −0.0375755 0.0650826i
\(657\) 0 0
\(658\) 0.241670 + 3.36603i 0.00942127 + 0.131221i
\(659\) 41.9739i 1.63507i 0.575878 + 0.817536i \(0.304660\pi\)
−0.575878 + 0.817536i \(0.695340\pi\)
\(660\) 0 0
\(661\) −22.8408 13.1872i −0.888405 0.512921i −0.0149846 0.999888i \(-0.504770\pi\)
−0.873420 + 0.486967i \(0.838103\pi\)
\(662\) 12.1916 + 7.03882i 0.473840 + 0.273571i
\(663\) 0 0
\(664\) 9.35827i 0.363171i
\(665\) 2.49384 + 34.7347i 0.0967070 + 1.34695i
\(666\) 0 0
\(667\) 19.9339 + 34.5265i 0.771843 + 1.33687i
\(668\) 2.38134 4.12460i 0.0921369 0.159586i
\(669\) 0 0
\(670\) −26.6687 + 15.3972i −1.03030 + 0.594844i
\(671\) −12.4171 −0.479358
\(672\) 0 0
\(673\) −6.60164 −0.254475 −0.127237 0.991872i \(-0.540611\pi\)
−0.127237 + 0.991872i \(0.540611\pi\)
\(674\) 7.05934 4.07571i 0.271916 0.156991i
\(675\) 0 0
\(676\) 3.50000 6.06218i 0.134615 0.233161i
\(677\) −4.52228 7.83282i −0.173805 0.301040i 0.765942 0.642910i \(-0.222273\pi\)
−0.939747 + 0.341870i \(0.888940\pi\)
\(678\) 0 0
\(679\) 29.9149 20.2590i 1.14803 0.777468i
\(680\) 13.3247i 0.510978i
\(681\) 0 0
\(682\) 7.44414 + 4.29788i 0.285051 + 0.164574i
\(683\) −27.2954 15.7590i −1.04443 0.603003i −0.123346 0.992364i \(-0.539363\pi\)
−0.921085 + 0.389361i \(0.872696\pi\)
\(684\) 0 0
\(685\) 34.9774i 1.33642i
\(686\) 13.6938 12.4691i 0.522834 0.476073i
\(687\) 0 0
\(688\) 5.99207 + 10.3786i 0.228446 + 0.395679i
\(689\) −0.586302 + 1.01550i −0.0223363 + 0.0386876i
\(690\) 0 0
\(691\) 26.3742 15.2272i 1.00332 0.579268i 0.0940927 0.995563i \(-0.470005\pi\)
0.909230 + 0.416295i \(0.136672\pi\)
\(692\) 14.7369 0.560211
\(693\) 0 0
\(694\) −22.5746 −0.856919
\(695\) −29.6332 + 17.1087i −1.12405 + 0.648972i
\(696\) 0 0
\(697\) −5.09354 + 8.82227i −0.192932 + 0.334167i
\(698\) 11.4749 + 19.8751i 0.434332 + 0.752284i
\(699\) 0 0
\(700\) −1.54650 + 3.18582i −0.0584521 + 0.120413i
\(701\) 26.3465i 0.995093i −0.867437 0.497547i \(-0.834234\pi\)
0.867437 0.497547i \(-0.165766\pi\)
\(702\) 0 0
\(703\) −53.5334 30.9075i −2.01905 1.16570i
\(704\) 0.866025 + 0.500000i 0.0326396 + 0.0188445i
\(705\) 0 0
\(706\) 25.1981i 0.948342i
\(707\) 3.63760 0.261168i 0.136806 0.00982223i
\(708\) 0 0
\(709\) −5.35292 9.27154i −0.201033 0.348200i 0.747828 0.663892i \(-0.231097\pi\)
−0.948862 + 0.315692i \(0.897763\pi\)
\(710\) −18.5116 + 32.0630i −0.694726 + 1.20330i
\(711\) 0 0
\(712\) −13.7246 + 7.92392i −0.514353 + 0.296962i
\(713\) −42.5186 −1.59233
\(714\) 0 0
\(715\) 6.16693 0.230630
\(716\) −2.03491 + 1.17486i −0.0760482 + 0.0439065i
\(717\) 0 0
\(718\) −9.84714 + 17.0558i −0.367492 + 0.636515i
\(719\) −15.3059 26.5107i −0.570815 0.988681i −0.996482 0.0838012i \(-0.973294\pi\)
0.425667 0.904880i \(-0.360039\pi\)
\(720\) 0 0
\(721\) −24.9819 12.1270i −0.930374 0.451633i
\(722\) 8.33229i 0.310096i
\(723\) 0 0
\(724\) −10.3261 5.96178i −0.383767 0.221568i
\(725\) 9.34279 + 5.39406i 0.346983 + 0.200331i
\(726\) 0 0
\(727\) 7.03188i 0.260798i −0.991462 0.130399i \(-0.958374\pi\)
0.991462 0.130399i \(-0.0416258\pi\)
\(728\) 3.63397 + 5.36603i 0.134684 + 0.198878i
\(729\) 0 0
\(730\) −12.3906 21.4612i −0.458597 0.794313i
\(731\) 31.7132 54.9289i 1.17296 2.03162i
\(732\) 0 0
\(733\) 19.5539 11.2895i 0.722240 0.416985i −0.0933367 0.995635i \(-0.529753\pi\)
0.815577 + 0.578649i \(0.196420\pi\)
\(734\) −3.24796 −0.119885
\(735\) 0 0
\(736\) −4.94646 −0.182329
\(737\) 10.5927 6.11571i 0.390188 0.225275i
\(738\) 0 0
\(739\) −9.24921 + 16.0201i −0.340238 + 0.589309i −0.984477 0.175515i \(-0.943841\pi\)
0.644239 + 0.764824i \(0.277174\pi\)
\(740\) −14.8840 25.7798i −0.547147 0.947686i
\(741\) 0 0
\(742\) 0.710202 + 1.04870i 0.0260723 + 0.0384991i
\(743\) 22.8029i 0.836558i −0.908319 0.418279i \(-0.862633\pi\)
0.908319 0.418279i \(-0.137367\pi\)
\(744\) 0 0
\(745\) 14.5041 + 8.37393i 0.531388 + 0.306797i
\(746\) 5.90935 + 3.41177i 0.216357 + 0.124914i
\(747\) 0 0
\(748\) 5.29253i 0.193514i
\(749\) 6.88557 + 3.34247i 0.251593 + 0.122131i
\(750\) 0 0
\(751\) 15.6992 + 27.1918i 0.572871 + 0.992242i 0.996269 + 0.0862983i \(0.0275038\pi\)
−0.423398 + 0.905944i \(0.639163\pi\)
\(752\) −0.637756 + 1.10463i −0.0232566 + 0.0402816i
\(753\) 0 0
\(754\) 17.0975 9.87127i 0.622656 0.359490i
\(755\) 20.1852 0.734616
\(756\) 0 0
\(757\) −15.6251 −0.567905 −0.283953 0.958838i \(-0.591646\pi\)
−0.283953 + 0.958838i \(0.591646\pi\)
\(758\) −16.3618 + 9.44646i −0.594286 + 0.343111i
\(759\) 0 0
\(760\) −6.58114 + 11.3989i −0.238723 + 0.413481i
\(761\) −20.4241 35.3755i −0.740372 1.28236i −0.952326 0.305082i \(-0.901316\pi\)
0.211954 0.977280i \(-0.432017\pi\)
\(762\) 0 0
\(763\) −35.7284 + 2.56518i −1.29345 + 0.0928658i
\(764\) 24.5765i 0.889146i
\(765\) 0 0
\(766\) 22.8916 + 13.2165i 0.827106 + 0.477530i
\(767\) 12.8338 + 7.40957i 0.463400 + 0.267544i
\(768\) 0 0
\(769\) 1.71477i 0.0618361i −0.999522 0.0309181i \(-0.990157\pi\)
0.999522 0.0309181i \(-0.00984309\pi\)
\(770\) 2.90887 5.99233i 0.104828 0.215949i
\(771\) 0 0
\(772\) −7.05657 12.2223i −0.253972 0.439892i
\(773\) 8.25433 14.2969i 0.296887 0.514224i −0.678535 0.734568i \(-0.737385\pi\)
0.975422 + 0.220344i \(0.0707180\pi\)
\(774\) 0 0
\(775\) −9.96399 + 5.75272i −0.357917 + 0.206644i
\(776\) 13.6556 0.490208
\(777\) 0 0
\(778\) 11.6678 0.418312
\(779\) −8.71475 + 5.03146i −0.312238 + 0.180271i
\(780\) 0 0
\(781\) 7.35275 12.7353i 0.263102 0.455706i
\(782\) 13.0897 + 22.6719i 0.468085 + 0.810747i
\(783\) 0 0
\(784\) 6.92820 1.00000i 0.247436 0.0357143i
\(785\) 55.4737i 1.97994i
\(786\) 0 0
\(787\) 37.9077 + 21.8860i 1.35126 + 0.780153i 0.988427 0.151699i \(-0.0484744\pi\)
0.362838 + 0.931852i \(0.381808\pi\)
\(788\) −0.501618 0.289609i −0.0178694 0.0103169i
\(789\) 0 0
\(790\) 17.7583i 0.631810i
\(791\) −31.9179 + 21.6154i −1.13487 + 0.768556i
\(792\) 0 0
\(793\) −15.2078 26.3407i −0.540046 0.935386i
\(794\) 5.01532 8.68678i 0.177987 0.308282i
\(795\) 0 0
\(796\) 2.08228 1.20220i 0.0738045 0.0426110i
\(797\) −27.8981 −0.988203 −0.494102 0.869404i \(-0.664503\pi\)
−0.494102 + 0.869404i \(0.664503\pi\)
\(798\) 0 0
\(799\) 6.75069 0.238822
\(800\) −1.15918 + 0.669251i −0.0409831 + 0.0236616i
\(801\) 0 0
\(802\) 2.61125 4.52281i 0.0922063 0.159706i
\(803\) 4.92152 + 8.52432i 0.173677 + 0.300817i
\(804\) 0 0
\(805\) 2.35953 + 32.8640i 0.0831625 + 1.15830i
\(806\) 21.0552i 0.741638i
\(807\) 0 0
\(808\) 1.19375 + 0.689211i 0.0419959 + 0.0242464i
\(809\) 9.97340 + 5.75815i 0.350646 + 0.202446i 0.664970 0.746870i \(-0.268444\pi\)
−0.314324 + 0.949316i \(0.601778\pi\)
\(810\) 0 0
\(811\) 7.86619i 0.276219i 0.990417 + 0.138110i \(0.0441026\pi\)
−0.990417 + 0.138110i \(0.955897\pi\)
\(812\) −1.52709 21.2696i −0.0535904 0.746417i
\(813\) 0 0
\(814\) 5.91189 + 10.2397i 0.207212 + 0.358901i
\(815\) 12.6694 21.9440i 0.443789 0.768665i
\(816\) 0 0
\(817\) 54.2595 31.3267i 1.89830 1.09598i
\(818\) 19.2207 0.672037
\(819\) 0 0
\(820\) −4.84596 −0.169228
\(821\) −7.40031 + 4.27257i −0.258272 + 0.149114i −0.623546 0.781786i \(-0.714309\pi\)
0.365274 + 0.930900i \(0.380975\pi\)
\(822\) 0 0
\(823\) 4.71503 8.16668i 0.164356 0.284673i −0.772071 0.635537i \(-0.780779\pi\)
0.936426 + 0.350864i \(0.114112\pi\)
\(824\) −5.24799 9.08978i −0.182822 0.316658i
\(825\) 0 0
\(826\) 13.2533 8.97540i 0.461142 0.312294i
\(827\) 10.9084i 0.379323i 0.981850 + 0.189662i \(0.0607391\pi\)
−0.981850 + 0.189662i \(0.939261\pi\)
\(828\) 0 0
\(829\) −9.54168 5.50889i −0.331396 0.191332i 0.325065 0.945692i \(-0.394614\pi\)
−0.656461 + 0.754360i \(0.727947\pi\)
\(830\) −20.4042 11.7804i −0.708240 0.408903i
\(831\) 0 0
\(832\) 2.44949i 0.0849208i
\(833\) −22.9173 29.1089i −0.794038 1.00856i
\(834\) 0 0
\(835\) −5.99536 10.3843i −0.207478 0.359362i
\(836\) 2.61401 4.52761i 0.0904076 0.156591i
\(837\) 0 0
\(838\) −15.1342 + 8.73774i −0.522803 + 0.301840i
\(839\) 19.2163 0.663422 0.331711 0.943381i \(-0.392374\pi\)
0.331711 + 0.943381i \(0.392374\pi\)
\(840\) 0 0
\(841\) −35.9613 −1.24004
\(842\) −24.1205 + 13.9260i −0.831246 + 0.479920i
\(843\) 0 0
\(844\) −2.99672 + 5.19046i −0.103151 + 0.178663i
\(845\) −8.81173 15.2624i −0.303133 0.525041i
\(846\) 0 0
\(847\) −1.15539 + 2.38014i −0.0396998 + 0.0817826i
\(848\) 0.478713i 0.0164391i
\(849\) 0 0
\(850\) 6.13497 + 3.54203i 0.210428 + 0.121491i
\(851\) −50.6503 29.2430i −1.73627 1.00244i
\(852\) 0 0
\(853\) 50.2570i 1.72077i −0.509649 0.860383i \(-0.670225\pi\)
0.509649 0.860383i \(-0.329775\pi\)
\(854\) −32.7683 + 2.35266i −1.12131 + 0.0805063i
\(855\) 0 0
\(856\) 1.44646 + 2.50535i 0.0494391 + 0.0856310i
\(857\) −6.92321 + 11.9914i −0.236492 + 0.409617i −0.959705 0.281008i \(-0.909331\pi\)
0.723213 + 0.690625i \(0.242664\pi\)
\(858\) 0 0
\(859\) −11.3460 + 6.55059i −0.387119 + 0.223503i −0.680911 0.732366i \(-0.738416\pi\)
0.293792 + 0.955869i \(0.405083\pi\)
\(860\) 30.1717 1.02885
\(861\) 0 0
\(862\) −34.8542 −1.18714
\(863\) 29.1086 16.8058i 0.990867 0.572077i 0.0853335 0.996352i \(-0.472804\pi\)
0.905533 + 0.424275i \(0.139471\pi\)
\(864\) 0 0
\(865\) 18.5510 32.1313i 0.630754 1.09250i
\(866\) −13.6034 23.5618i −0.462262 0.800662i
\(867\) 0 0
\(868\) 20.4591 + 9.93149i 0.694427 + 0.337097i
\(869\) 7.05354i 0.239275i
\(870\) 0 0
\(871\) 25.9468 + 14.9804i 0.879173 + 0.507591i
\(872\) −11.7250 6.76941i −0.397057 0.229241i
\(873\) 0 0
\(874\) 25.8603i 0.874736i
\(875\) −13.6760 20.1943i −0.462332 0.682693i
\(876\) 0 0
\(877\) 14.0399 + 24.3178i 0.474093 + 0.821153i 0.999560 0.0296608i \(-0.00944271\pi\)
−0.525467 + 0.850814i \(0.676109\pi\)
\(878\) 11.6040 20.0987i 0.391616 0.678299i
\(879\) 0 0
\(880\) 2.18034 1.25882i 0.0734992 0.0424348i
\(881\) −20.4395 −0.688623 −0.344312 0.938855i \(-0.611888\pi\)
−0.344312 + 0.938855i \(0.611888\pi\)
\(882\) 0 0
\(883\) −28.7609 −0.967880 −0.483940 0.875101i \(-0.660795\pi\)
−0.483940 + 0.875101i \(0.660795\pi\)
\(884\) 11.2271 6.48200i 0.377610 0.218013i
\(885\) 0 0
\(886\) 9.07435 15.7172i 0.304859 0.528031i
\(887\) 24.6498 + 42.6947i 0.827659 + 1.43355i 0.899870 + 0.436158i \(0.143661\pi\)
−0.0722117 + 0.997389i \(0.523006\pi\)
\(888\) 0 0
\(889\) −9.78670 14.4513i −0.328235 0.484681i
\(890\) 39.8991i 1.33742i
\(891\) 0 0
\(892\) 6.48647 + 3.74496i 0.217183 + 0.125391i
\(893\) 5.77502 + 3.33421i 0.193254 + 0.111575i
\(894\) 0 0
\(895\) 5.91573i 0.197741i
\(896\) 2.38014 + 1.15539i 0.0795149 + 0.0385990i
\(897\) 0 0
\(898\) 15.9828 + 27.6830i 0.533352 + 0.923793i
\(899\) 34.6403 59.9987i 1.15532 2.00107i
\(900\) 0 0
\(901\) 2.19417 1.26680i 0.0730983 0.0422033i
\(902\) 1.92480 0.0640889
\(903\) 0 0
\(904\) −14.5699 −0.484589
\(905\) −25.9974 + 15.0096i −0.864183 + 0.498936i
\(906\) 0 0
\(907\) −18.2780 + 31.6584i −0.606911 + 1.05120i 0.384835 + 0.922985i \(0.374258\pi\)
−0.991746 + 0.128215i \(0.959075\pi\)
\(908\) −4.88304 8.45768i −0.162049 0.280678i
\(909\) 0 0
\(910\) 16.2743 1.16844i 0.539487 0.0387334i
\(911\) 33.3749i 1.10576i −0.833261 0.552880i \(-0.813529\pi\)
0.833261 0.552880i \(-0.186471\pi\)
\(912\) 0 0
\(913\) 8.10450 + 4.67914i 0.268220 + 0.154857i
\(914\) 22.4486 + 12.9607i 0.742534 + 0.428702i
\(915\) 0 0
\(916\) 0.225376i 0.00744664i
\(917\) 1.75010 3.60524i 0.0577933 0.119056i
\(918\) 0 0
\(919\) 4.34095 + 7.51874i 0.143195 + 0.248020i 0.928698 0.370837i \(-0.120929\pi\)
−0.785503 + 0.618857i \(0.787596\pi\)
\(920\) −6.22670 + 10.7850i −0.205288 + 0.355570i
\(921\) 0 0
\(922\) 18.9038 10.9141i 0.622563 0.359437i
\(923\) 36.0210 1.18564
\(924\) 0 0
\(925\) −15.8262 −0.520361
\(926\) −4.26622 + 2.46311i −0.140197 + 0.0809427i
\(927\) 0 0
\(928\) 4.02993 6.98004i 0.132289 0.229131i
\(929\) 18.8642 + 32.6738i 0.618915 + 1.07199i 0.989684 + 0.143267i \(0.0457608\pi\)
−0.370769 + 0.928725i \(0.620906\pi\)
\(930\) 0 0
\(931\) −5.22803 36.2208i −0.171342 1.18709i
\(932\) 0.514719i 0.0168602i
\(933\) 0 0
\(934\) 3.24592 + 1.87404i 0.106210 + 0.0613203i
\(935\) −11.5395 6.66234i −0.377382 0.217882i
\(936\) 0 0
\(937\) 2.55832i 0.0835768i −0.999126 0.0417884i \(-0.986694\pi\)
0.999126 0.0417884i \(-0.0133055\pi\)
\(938\) 26.7950 18.1461i 0.874889 0.592491i
\(939\) 0 0
\(940\) 1.60564 + 2.78105i 0.0523702 + 0.0907078i
\(941\) −24.3638 + 42.1993i −0.794236 + 1.37566i 0.129087 + 0.991633i \(0.458795\pi\)
−0.923323 + 0.384024i \(0.874538\pi\)
\(942\) 0 0
\(943\) −8.24540 + 4.76049i −0.268507 + 0.155023i
\(944\) 6.04989 0.196907
\(945\) 0 0
\(946\) −11.9841 −0.389638
\(947\) −30.4320 + 17.5699i −0.988908 + 0.570946i −0.904948 0.425523i \(-0.860090\pi\)
−0.0839599 + 0.996469i \(0.526757\pi\)
\(948\) 0 0
\(949\) −12.0552 + 20.8802i −0.391329 + 0.677801i
\(950\) 3.49886 + 6.06021i 0.113518 + 0.196619i
\(951\) 0 0
\(952\) −1.00277 13.9668i −0.0324999 0.452665i
\(953\) 1.34315i 0.0435088i −0.999763 0.0217544i \(-0.993075\pi\)
0.999763 0.0217544i \(-0.00692518\pi\)
\(954\) 0 0
\(955\) 53.5851 + 30.9374i 1.73397 + 1.00111i
\(956\) −13.4147 7.74496i −0.433861 0.250490i
\(957\) 0 0
\(958\) 3.86267i 0.124797i
\(959\) 2.63227 + 36.6629i 0.0850006 + 1.18391i
\(960\) 0 0
\(961\) 21.4435 + 37.1412i 0.691726 + 1.19810i
\(962\) −14.4811 + 25.0820i −0.466890 + 0.808677i
\(963\) 0 0
\(964\) −14.2882 + 8.24932i −0.460194 + 0.265693i
\(965\) −35.5318 −1.14381
\(966\) 0 0
\(967\) −34.3045 −1.10316 −0.551580 0.834122i \(-0.685975\pi\)
−0.551580 + 0.834122i \(0.685975\pi\)
\(968\) −0.866025 + 0.500000i −0.0278351 + 0.0160706i
\(969\) 0 0
\(970\) 17.1899 29.7739i 0.551936 0.955981i
\(971\) −2.71114 4.69583i −0.0870046 0.150696i 0.819239 0.573452i \(-0.194396\pi\)
−0.906244 + 0.422756i \(0.861063\pi\)
\(972\) 0 0
\(973\) 29.7736 20.1633i 0.954499 0.646405i
\(974\) 11.6189i 0.372294i
\(975\) 0 0
\(976\) −10.7536 6.20857i −0.344213 0.198731i
\(977\) 3.04148 + 1.75600i 0.0973056 + 0.0561794i 0.547863 0.836568i \(-0.315441\pi\)
−0.450558 + 0.892747i \(0.648775\pi\)
\(978\) 0 0
\(979\) 15.8478i 0.506499i
\(980\) 6.54102 16.3646i 0.208945 0.522749i
\(981\) 0 0
\(982\) 12.8672 + 22.2867i 0.410610 + 0.711198i
\(983\) −0.0659506 + 0.114230i −0.00210350 + 0.00364336i −0.867075 0.498177i \(-0.834003\pi\)
0.864972 + 0.501821i \(0.167336\pi\)
\(984\) 0 0
\(985\) −1.26289 + 0.729131i −0.0402391 + 0.0232321i
\(986\) −42.6570 −1.35848
\(987\) 0 0
\(988\) 12.8060 0.407413
\(989\) 51.3372 29.6396i 1.63243 0.942483i
\(990\) 0 0
\(991\) −13.6398 + 23.6249i −0.433283 + 0.750468i −0.997154 0.0753949i \(-0.975978\pi\)
0.563871 + 0.825863i \(0.309312\pi\)
\(992\) 4.29788 + 7.44414i 0.136458 + 0.236352i
\(993\) 0 0
\(994\) 16.9907 35.0011i 0.538911 1.11017i
\(995\) 6.05343i 0.191907i
\(996\) 0 0
\(997\) 39.6642 + 22.9001i 1.25618 + 0.725254i 0.972329 0.233615i \(-0.0750555\pi\)
0.283848 + 0.958869i \(0.408389\pi\)
\(998\) 19.7425 + 11.3984i 0.624939 + 0.360809i
\(999\) 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 1386.2.r.a.1277.1 yes 8
3.2 odd 2 1386.2.r.c.1277.4 yes 8
7.5 odd 6 1386.2.r.c.89.4 yes 8
21.5 even 6 inner 1386.2.r.a.89.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1386.2.r.a.89.1 8 21.5 even 6 inner
1386.2.r.a.1277.1 yes 8 1.1 even 1 trivial
1386.2.r.c.89.4 yes 8 7.5 odd 6
1386.2.r.c.1277.4 yes 8 3.2 odd 2