Properties

Label 432.2.l.a.107.7
Level $432$
Weight $2$
Character 432.107
Analytic conductor $3.450$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [432,2,Mod(107,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.l (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 107.7
Character \(\chi\) \(=\) 432.107
Dual form 432.2.l.a.323.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.604480 - 1.27852i) q^{2} +(-1.26921 + 1.54568i) q^{4} +(0.217410 - 0.217410i) q^{5} -3.81401 q^{7} +(2.74338 + 0.688372i) q^{8} +O(q^{10})\) \(q+(-0.604480 - 1.27852i) q^{2} +(-1.26921 + 1.54568i) q^{4} +(0.217410 - 0.217410i) q^{5} -3.81401 q^{7} +(2.74338 + 0.688372i) q^{8} +(-0.409383 - 0.146542i) q^{10} +(3.83163 + 3.83163i) q^{11} +(-2.88926 + 2.88926i) q^{13} +(2.30549 + 4.87627i) q^{14} +(-0.778226 - 3.92357i) q^{16} -4.71852i q^{17} +(4.77663 + 4.77663i) q^{19} +(0.0601071 + 0.611985i) q^{20} +(2.58266 - 7.21495i) q^{22} +6.18488i q^{23} +4.90547i q^{25} +(5.44047 + 1.94747i) q^{26} +(4.84076 - 5.89522i) q^{28} +(0.322843 + 0.322843i) q^{29} +5.20520i q^{31} +(-4.54592 + 3.36669i) q^{32} +(-6.03271 + 2.85225i) q^{34} +(-0.829205 + 0.829205i) q^{35} +(-2.92710 - 2.92710i) q^{37} +(3.21962 - 8.99438i) q^{38} +(0.746099 - 0.446781i) q^{40} +1.31513 q^{41} +(0.505290 - 0.505290i) q^{43} +(-10.7856 + 1.05932i) q^{44} +(7.90747 - 3.73864i) q^{46} +5.41806 q^{47} +7.54664 q^{49} +(6.27172 - 2.96526i) q^{50} +(-0.798789 - 8.13294i) q^{52} +(1.85772 - 1.85772i) q^{53} +1.66607 q^{55} +(-10.4633 - 2.62545i) q^{56} +(0.217608 - 0.607913i) q^{58} +(-4.77662 - 4.77662i) q^{59} +(-0.832278 + 0.832278i) q^{61} +(6.65493 - 3.14644i) q^{62} +(7.05229 + 3.77693i) q^{64} +1.25631i q^{65} +(-6.48244 - 6.48244i) q^{67} +(7.29331 + 5.98879i) q^{68} +(1.56139 + 0.558914i) q^{70} -2.47601i q^{71} +6.68986i q^{73} +(-1.97297 + 5.51171i) q^{74} +(-13.4457 + 1.32059i) q^{76} +(-14.6139 - 14.6139i) q^{77} +9.28617i q^{79} +(-1.02222 - 0.683830i) q^{80} +(-0.794971 - 1.68142i) q^{82} +(-8.24616 + 8.24616i) q^{83} +(-1.02586 - 1.02586i) q^{85} +(-0.951459 - 0.340583i) q^{86} +(7.87404 + 13.1492i) q^{88} -12.3741 q^{89} +(11.0197 - 11.0197i) q^{91} +(-9.55982 - 7.84989i) q^{92} +(-3.27511 - 6.92708i) q^{94} +2.07698 q^{95} -2.81552 q^{97} +(-4.56179 - 9.64850i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 4 q^{10} - 20 q^{16} + 8 q^{19} + 4 q^{22} - 12 q^{28} - 36 q^{34} - 12 q^{40} + 32 q^{43} - 16 q^{46} + 32 q^{49} - 60 q^{52} + 64 q^{55} - 48 q^{58} - 16 q^{61} + 48 q^{64} - 32 q^{67} - 72 q^{70} - 96 q^{76} + 40 q^{82} - 16 q^{85} + 36 q^{88} + 24 q^{91} - 36 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.604480 1.27852i −0.427432 0.904047i
\(3\) 0 0
\(4\) −1.26921 + 1.54568i −0.634604 + 0.772838i
\(5\) 0.217410 0.217410i 0.0972289 0.0972289i −0.656819 0.754048i \(-0.728099\pi\)
0.754048 + 0.656819i \(0.228099\pi\)
\(6\) 0 0
\(7\) −3.81401 −1.44156 −0.720779 0.693165i \(-0.756216\pi\)
−0.720779 + 0.693165i \(0.756216\pi\)
\(8\) 2.74338 + 0.688372i 0.969932 + 0.243376i
\(9\) 0 0
\(10\) −0.409383 0.146542i −0.129458 0.0463408i
\(11\) 3.83163 + 3.83163i 1.15528 + 1.15528i 0.985478 + 0.169803i \(0.0543130\pi\)
0.169803 + 0.985478i \(0.445687\pi\)
\(12\) 0 0
\(13\) −2.88926 + 2.88926i −0.801337 + 0.801337i −0.983305 0.181967i \(-0.941754\pi\)
0.181967 + 0.983305i \(0.441754\pi\)
\(14\) 2.30549 + 4.87627i 0.616168 + 1.30324i
\(15\) 0 0
\(16\) −0.778226 3.92357i −0.194556 0.980891i
\(17\) 4.71852i 1.14441i −0.820111 0.572205i \(-0.806088\pi\)
0.820111 0.572205i \(-0.193912\pi\)
\(18\) 0 0
\(19\) 4.77663 + 4.77663i 1.09583 + 1.09583i 0.994892 + 0.100943i \(0.0321859\pi\)
0.100943 + 0.994892i \(0.467814\pi\)
\(20\) 0.0601071 + 0.611985i 0.0134404 + 0.136844i
\(21\) 0 0
\(22\) 2.58266 7.21495i 0.550625 1.53823i
\(23\) 6.18488i 1.28964i 0.764336 + 0.644818i \(0.223067\pi\)
−0.764336 + 0.644818i \(0.776933\pi\)
\(24\) 0 0
\(25\) 4.90547i 0.981093i
\(26\) 5.44047 + 1.94747i 1.06696 + 0.381930i
\(27\) 0 0
\(28\) 4.84076 5.89522i 0.914818 1.11409i
\(29\) 0.322843 + 0.322843i 0.0599505 + 0.0599505i 0.736446 0.676496i \(-0.236502\pi\)
−0.676496 + 0.736446i \(0.736502\pi\)
\(30\) 0 0
\(31\) 5.20520i 0.934881i 0.884024 + 0.467441i \(0.154824\pi\)
−0.884024 + 0.467441i \(0.845176\pi\)
\(32\) −4.54592 + 3.36669i −0.803613 + 0.595153i
\(33\) 0 0
\(34\) −6.03271 + 2.85225i −1.03460 + 0.489158i
\(35\) −0.829205 + 0.829205i −0.140161 + 0.140161i
\(36\) 0 0
\(37\) −2.92710 2.92710i −0.481212 0.481212i 0.424307 0.905519i \(-0.360518\pi\)
−0.905519 + 0.424307i \(0.860518\pi\)
\(38\) 3.21962 8.99438i 0.522292 1.45908i
\(39\) 0 0
\(40\) 0.746099 0.446781i 0.117969 0.0706422i
\(41\) 1.31513 0.205389 0.102694 0.994713i \(-0.467254\pi\)
0.102694 + 0.994713i \(0.467254\pi\)
\(42\) 0 0
\(43\) 0.505290 0.505290i 0.0770560 0.0770560i −0.667528 0.744584i \(-0.732648\pi\)
0.744584 + 0.667528i \(0.232648\pi\)
\(44\) −10.7856 + 1.05932i −1.62599 + 0.159699i
\(45\) 0 0
\(46\) 7.90747 3.73864i 1.16589 0.551232i
\(47\) 5.41806 0.790306 0.395153 0.918615i \(-0.370692\pi\)
0.395153 + 0.918615i \(0.370692\pi\)
\(48\) 0 0
\(49\) 7.54664 1.07809
\(50\) 6.27172 2.96526i 0.886955 0.419351i
\(51\) 0 0
\(52\) −0.798789 8.13294i −0.110772 1.12784i
\(53\) 1.85772 1.85772i 0.255178 0.255178i −0.567912 0.823090i \(-0.692248\pi\)
0.823090 + 0.567912i \(0.192248\pi\)
\(54\) 0 0
\(55\) 1.66607 0.224653
\(56\) −10.4633 2.62545i −1.39821 0.350841i
\(57\) 0 0
\(58\) 0.217608 0.607913i 0.0285733 0.0798229i
\(59\) −4.77662 4.77662i −0.621863 0.621863i 0.324145 0.946007i \(-0.394923\pi\)
−0.946007 + 0.324145i \(0.894923\pi\)
\(60\) 0 0
\(61\) −0.832278 + 0.832278i −0.106562 + 0.106562i −0.758378 0.651815i \(-0.774008\pi\)
0.651815 + 0.758378i \(0.274008\pi\)
\(62\) 6.65493 3.14644i 0.845177 0.399598i
\(63\) 0 0
\(64\) 7.05229 + 3.77693i 0.881536 + 0.472117i
\(65\) 1.25631i 0.155826i
\(66\) 0 0
\(67\) −6.48244 6.48244i −0.791956 0.791956i 0.189856 0.981812i \(-0.439198\pi\)
−0.981812 + 0.189856i \(0.939198\pi\)
\(68\) 7.29331 + 5.98879i 0.884444 + 0.726247i
\(69\) 0 0
\(70\) 1.56139 + 0.558914i 0.186622 + 0.0668030i
\(71\) 2.47601i 0.293849i −0.989148 0.146924i \(-0.953063\pi\)
0.989148 0.146924i \(-0.0469374\pi\)
\(72\) 0 0
\(73\) 6.68986i 0.782989i 0.920180 + 0.391494i \(0.128042\pi\)
−0.920180 + 0.391494i \(0.871958\pi\)
\(74\) −1.97297 + 5.51171i −0.229353 + 0.640724i
\(75\) 0 0
\(76\) −13.4457 + 1.32059i −1.54232 + 0.151482i
\(77\) −14.6139 14.6139i −1.66541 1.66541i
\(78\) 0 0
\(79\) 9.28617i 1.04478i 0.852708 + 0.522388i \(0.174959\pi\)
−0.852708 + 0.522388i \(0.825041\pi\)
\(80\) −1.02222 0.683830i −0.114288 0.0764545i
\(81\) 0 0
\(82\) −0.794971 1.68142i −0.0877898 0.185681i
\(83\) −8.24616 + 8.24616i −0.905134 + 0.905134i −0.995875 0.0907409i \(-0.971076\pi\)
0.0907409 + 0.995875i \(0.471076\pi\)
\(84\) 0 0
\(85\) −1.02586 1.02586i −0.111270 0.111270i
\(86\) −0.951459 0.340583i −0.102598 0.0367261i
\(87\) 0 0
\(88\) 7.87404 + 13.1492i 0.839376 + 1.40171i
\(89\) −12.3741 −1.31165 −0.655825 0.754913i \(-0.727679\pi\)
−0.655825 + 0.754913i \(0.727679\pi\)
\(90\) 0 0
\(91\) 11.0197 11.0197i 1.15517 1.15517i
\(92\) −9.55982 7.84989i −0.996680 0.818408i
\(93\) 0 0
\(94\) −3.27511 6.92708i −0.337802 0.714474i
\(95\) 2.07698 0.213094
\(96\) 0 0
\(97\) −2.81552 −0.285873 −0.142937 0.989732i \(-0.545654\pi\)
−0.142937 + 0.989732i \(0.545654\pi\)
\(98\) −4.56179 9.64850i −0.460811 0.974646i
\(99\) 0 0
\(100\) −7.58226 6.22605i −0.758226 0.622605i
\(101\) 6.38111 6.38111i 0.634944 0.634944i −0.314360 0.949304i \(-0.601790\pi\)
0.949304 + 0.314360i \(0.101790\pi\)
\(102\) 0 0
\(103\) −18.5734 −1.83009 −0.915046 0.403350i \(-0.867846\pi\)
−0.915046 + 0.403350i \(0.867846\pi\)
\(104\) −9.91524 + 5.93747i −0.972269 + 0.582216i
\(105\) 0 0
\(106\) −3.49809 1.25217i −0.339764 0.121622i
\(107\) 12.4921 + 12.4921i 1.20766 + 1.20766i 0.971783 + 0.235876i \(0.0757958\pi\)
0.235876 + 0.971783i \(0.424204\pi\)
\(108\) 0 0
\(109\) 4.93373 4.93373i 0.472565 0.472565i −0.430179 0.902744i \(-0.641549\pi\)
0.902744 + 0.430179i \(0.141549\pi\)
\(110\) −1.00711 2.13010i −0.0960241 0.203097i
\(111\) 0 0
\(112\) 2.96816 + 14.9645i 0.280464 + 1.41401i
\(113\) 11.7427i 1.10466i −0.833626 0.552329i \(-0.813739\pi\)
0.833626 0.552329i \(-0.186261\pi\)
\(114\) 0 0
\(115\) 1.34466 + 1.34466i 0.125390 + 0.125390i
\(116\) −0.908766 + 0.0892559i −0.0843768 + 0.00828721i
\(117\) 0 0
\(118\) −3.21961 + 8.99435i −0.296389 + 0.827997i
\(119\) 17.9965i 1.64973i
\(120\) 0 0
\(121\) 18.3628i 1.66935i
\(122\) 1.56718 + 0.560985i 0.141885 + 0.0507892i
\(123\) 0 0
\(124\) −8.04555 6.60648i −0.722512 0.593279i
\(125\) 2.15355 + 2.15355i 0.192620 + 0.192620i
\(126\) 0 0
\(127\) 15.2988i 1.35755i 0.734347 + 0.678774i \(0.237489\pi\)
−0.734347 + 0.678774i \(0.762511\pi\)
\(128\) 0.565902 11.2995i 0.0500192 0.998748i
\(129\) 0 0
\(130\) 1.60622 0.759416i 0.140874 0.0666052i
\(131\) 3.55187 3.55187i 0.310329 0.310329i −0.534708 0.845037i \(-0.679578\pi\)
0.845037 + 0.534708i \(0.179578\pi\)
\(132\) 0 0
\(133\) −18.2181 18.2181i −1.57971 1.57971i
\(134\) −4.36939 + 12.2064i −0.377458 + 1.05447i
\(135\) 0 0
\(136\) 3.24810 12.9447i 0.278522 1.11000i
\(137\) 4.11222 0.351331 0.175665 0.984450i \(-0.443792\pi\)
0.175665 + 0.984450i \(0.443792\pi\)
\(138\) 0 0
\(139\) 6.64500 6.64500i 0.563621 0.563621i −0.366713 0.930334i \(-0.619517\pi\)
0.930334 + 0.366713i \(0.119517\pi\)
\(140\) −0.229249 2.33411i −0.0193751 0.197269i
\(141\) 0 0
\(142\) −3.16562 + 1.49670i −0.265653 + 0.125600i
\(143\) −22.1412 −1.85154
\(144\) 0 0
\(145\) 0.140379 0.0116578
\(146\) 8.55310 4.04389i 0.707859 0.334675i
\(147\) 0 0
\(148\) 8.23944 0.809249i 0.677278 0.0665199i
\(149\) −0.723047 + 0.723047i −0.0592343 + 0.0592343i −0.736103 0.676869i \(-0.763336\pi\)
0.676869 + 0.736103i \(0.263336\pi\)
\(150\) 0 0
\(151\) 5.94167 0.483526 0.241763 0.970335i \(-0.422274\pi\)
0.241763 + 0.970335i \(0.422274\pi\)
\(152\) 9.81603 + 16.3922i 0.796185 + 1.32959i
\(153\) 0 0
\(154\) −9.85027 + 27.5179i −0.793758 + 2.21745i
\(155\) 1.13166 + 1.13166i 0.0908975 + 0.0908975i
\(156\) 0 0
\(157\) 14.0754 14.0754i 1.12334 1.12334i 0.132104 0.991236i \(-0.457827\pi\)
0.991236 0.132104i \(-0.0421732\pi\)
\(158\) 11.8725 5.61331i 0.944527 0.446571i
\(159\) 0 0
\(160\) −0.256377 + 1.72028i −0.0202683 + 0.136000i
\(161\) 23.5892i 1.85909i
\(162\) 0 0
\(163\) −3.39073 3.39073i −0.265583 0.265583i 0.561735 0.827317i \(-0.310134\pi\)
−0.827317 + 0.561735i \(0.810134\pi\)
\(164\) −1.66917 + 2.03277i −0.130341 + 0.158732i
\(165\) 0 0
\(166\) 15.5275 + 5.55821i 1.20517 + 0.431401i
\(167\) 9.15420i 0.708373i −0.935175 0.354187i \(-0.884758\pi\)
0.935175 0.354187i \(-0.115242\pi\)
\(168\) 0 0
\(169\) 3.69568i 0.284283i
\(170\) −0.691464 + 1.93168i −0.0530329 + 0.148153i
\(171\) 0 0
\(172\) 0.139697 + 1.42233i 0.0106518 + 0.108452i
\(173\) 2.30022 + 2.30022i 0.174883 + 0.174883i 0.789121 0.614238i \(-0.210537\pi\)
−0.614238 + 0.789121i \(0.710537\pi\)
\(174\) 0 0
\(175\) 18.7095i 1.41430i
\(176\) 12.0518 18.0155i 0.908438 1.35797i
\(177\) 0 0
\(178\) 7.47989 + 15.8205i 0.560641 + 1.18579i
\(179\) 7.17306 7.17306i 0.536140 0.536140i −0.386253 0.922393i \(-0.626231\pi\)
0.922393 + 0.386253i \(0.126231\pi\)
\(180\) 0 0
\(181\) −17.0999 17.0999i −1.27103 1.27103i −0.945550 0.325476i \(-0.894476\pi\)
−0.325476 0.945550i \(-0.605524\pi\)
\(182\) −20.7500 7.42765i −1.53809 0.550574i
\(183\) 0 0
\(184\) −4.25750 + 16.9675i −0.313867 + 1.25086i
\(185\) −1.27276 −0.0935754
\(186\) 0 0
\(187\) 18.0797 18.0797i 1.32212 1.32212i
\(188\) −6.87664 + 8.37457i −0.501531 + 0.610778i
\(189\) 0 0
\(190\) −1.25549 2.65545i −0.0910831 0.192647i
\(191\) 23.6865 1.71390 0.856949 0.515401i \(-0.172357\pi\)
0.856949 + 0.515401i \(0.172357\pi\)
\(192\) 0 0
\(193\) 26.5740 1.91284 0.956420 0.291995i \(-0.0943191\pi\)
0.956420 + 0.291995i \(0.0943191\pi\)
\(194\) 1.70193 + 3.59969i 0.122191 + 0.258443i
\(195\) 0 0
\(196\) −9.57825 + 11.6647i −0.684161 + 0.833190i
\(197\) −14.5507 + 14.5507i −1.03670 + 1.03670i −0.0373962 + 0.999301i \(0.511906\pi\)
−0.999301 + 0.0373962i \(0.988094\pi\)
\(198\) 0 0
\(199\) −0.329215 −0.0233375 −0.0116687 0.999932i \(-0.503714\pi\)
−0.0116687 + 0.999932i \(0.503714\pi\)
\(200\) −3.37678 + 13.4576i −0.238775 + 0.951594i
\(201\) 0 0
\(202\) −12.0156 4.30110i −0.845415 0.302624i
\(203\) −1.23133 1.23133i −0.0864222 0.0864222i
\(204\) 0 0
\(205\) 0.285923 0.285923i 0.0199697 0.0199697i
\(206\) 11.2273 + 23.7464i 0.782240 + 1.65449i
\(207\) 0 0
\(208\) 13.5847 + 9.08771i 0.941930 + 0.630120i
\(209\) 36.6046i 2.53199i
\(210\) 0 0
\(211\) −5.20144 5.20144i −0.358082 0.358082i 0.505024 0.863105i \(-0.331484\pi\)
−0.863105 + 0.505024i \(0.831484\pi\)
\(212\) 0.513601 + 5.22927i 0.0352743 + 0.359148i
\(213\) 0 0
\(214\) 8.42014 23.5226i 0.575589 1.60797i
\(215\) 0.219711i 0.0149841i
\(216\) 0 0
\(217\) 19.8527i 1.34769i
\(218\) −9.29019 3.32551i −0.629211 0.225232i
\(219\) 0 0
\(220\) −2.11459 + 2.57521i −0.142566 + 0.173621i
\(221\) 13.6331 + 13.6331i 0.917059 + 0.917059i
\(222\) 0 0
\(223\) 0.790802i 0.0529560i −0.999649 0.0264780i \(-0.991571\pi\)
0.999649 0.0264780i \(-0.00842919\pi\)
\(224\) 17.3382 12.8406i 1.15845 0.857947i
\(225\) 0 0
\(226\) −15.0132 + 7.09822i −0.998664 + 0.472167i
\(227\) 4.35838 4.35838i 0.289276 0.289276i −0.547518 0.836794i \(-0.684427\pi\)
0.836794 + 0.547518i \(0.184427\pi\)
\(228\) 0 0
\(229\) 11.9442 + 11.9442i 0.789298 + 0.789298i 0.981379 0.192081i \(-0.0615237\pi\)
−0.192081 + 0.981379i \(0.561524\pi\)
\(230\) 0.906348 2.53199i 0.0597628 0.166954i
\(231\) 0 0
\(232\) 0.663446 + 1.10792i 0.0435574 + 0.0727385i
\(233\) 26.4938 1.73567 0.867833 0.496855i \(-0.165512\pi\)
0.867833 + 0.496855i \(0.165512\pi\)
\(234\) 0 0
\(235\) 1.17794 1.17794i 0.0768406 0.0768406i
\(236\) 13.4456 1.32058i 0.875235 0.0859626i
\(237\) 0 0
\(238\) 23.0088 10.8785i 1.49144 0.705149i
\(239\) −1.09196 −0.0706333 −0.0353167 0.999376i \(-0.511244\pi\)
−0.0353167 + 0.999376i \(0.511244\pi\)
\(240\) 0 0
\(241\) 14.3414 0.923814 0.461907 0.886928i \(-0.347165\pi\)
0.461907 + 0.886928i \(0.347165\pi\)
\(242\) 23.4772 11.1000i 1.50917 0.713533i
\(243\) 0 0
\(244\) −0.230098 2.34276i −0.0147305 0.149980i
\(245\) 1.64072 1.64072i 0.104822 0.104822i
\(246\) 0 0
\(247\) −27.6019 −1.75627
\(248\) −3.58311 + 14.2798i −0.227528 + 0.906771i
\(249\) 0 0
\(250\) 1.45157 4.05513i 0.0918054 0.256469i
\(251\) −5.97677 5.97677i −0.377250 0.377250i 0.492859 0.870109i \(-0.335952\pi\)
−0.870109 + 0.492859i \(0.835952\pi\)
\(252\) 0 0
\(253\) −23.6982 + 23.6982i −1.48989 + 1.48989i
\(254\) 19.5598 9.24782i 1.22729 0.580260i
\(255\) 0 0
\(256\) −14.7887 + 6.10684i −0.924296 + 0.381677i
\(257\) 23.4079i 1.46015i 0.683369 + 0.730073i \(0.260514\pi\)
−0.683369 + 0.730073i \(0.739486\pi\)
\(258\) 0 0
\(259\) 11.1640 + 11.1640i 0.693695 + 0.693695i
\(260\) −1.94185 1.59452i −0.120428 0.0988880i
\(261\) 0 0
\(262\) −6.68816 2.39409i −0.413196 0.147907i
\(263\) 13.3165i 0.821128i −0.911832 0.410564i \(-0.865332\pi\)
0.911832 0.410564i \(-0.134668\pi\)
\(264\) 0 0
\(265\) 0.807777i 0.0496213i
\(266\) −12.2797 + 34.3046i −0.752914 + 2.10335i
\(267\) 0 0
\(268\) 18.2473 1.79219i 1.11463 0.109475i
\(269\) 8.78530 + 8.78530i 0.535649 + 0.535649i 0.922248 0.386599i \(-0.126350\pi\)
−0.386599 + 0.922248i \(0.626350\pi\)
\(270\) 0 0
\(271\) 1.46274i 0.0888554i −0.999013 0.0444277i \(-0.985854\pi\)
0.999013 0.0444277i \(-0.0141464\pi\)
\(272\) −18.5134 + 3.67208i −1.12254 + 0.222652i
\(273\) 0 0
\(274\) −2.48575 5.25754i −0.150170 0.317619i
\(275\) −18.7959 + 18.7959i −1.13344 + 1.13344i
\(276\) 0 0
\(277\) 2.83891 + 2.83891i 0.170573 + 0.170573i 0.787231 0.616658i \(-0.211514\pi\)
−0.616658 + 0.787231i \(0.711514\pi\)
\(278\) −12.5125 4.47897i −0.750450 0.268631i
\(279\) 0 0
\(280\) −2.84563 + 1.70402i −0.170059 + 0.101835i
\(281\) −6.53163 −0.389644 −0.194822 0.980839i \(-0.562413\pi\)
−0.194822 + 0.980839i \(0.562413\pi\)
\(282\) 0 0
\(283\) −1.82128 + 1.82128i −0.108264 + 0.108264i −0.759164 0.650900i \(-0.774392\pi\)
0.650900 + 0.759164i \(0.274392\pi\)
\(284\) 3.82711 + 3.14257i 0.227097 + 0.186477i
\(285\) 0 0
\(286\) 13.3839 + 28.3079i 0.791407 + 1.67388i
\(287\) −5.01592 −0.296080
\(288\) 0 0
\(289\) −5.26448 −0.309675
\(290\) −0.0848564 0.179477i −0.00498294 0.0105392i
\(291\) 0 0
\(292\) −10.3404 8.49082i −0.605123 0.496888i
\(293\) 22.9270 22.9270i 1.33941 1.33941i 0.442778 0.896631i \(-0.353993\pi\)
0.896631 0.442778i \(-0.146007\pi\)
\(294\) 0 0
\(295\) −2.07697 −0.120926
\(296\) −6.01522 10.0451i −0.349627 0.583858i
\(297\) 0 0
\(298\) 1.36149 + 0.487360i 0.0788693 + 0.0282320i
\(299\) −17.8697 17.8697i −1.03343 1.03343i
\(300\) 0 0
\(301\) −1.92718 + 1.92718i −0.111081 + 0.111081i
\(302\) −3.59162 7.59652i −0.206674 0.437130i
\(303\) 0 0
\(304\) 15.0241 22.4587i 0.861693 1.28810i
\(305\) 0.361892i 0.0207219i
\(306\) 0 0
\(307\) 10.8441 + 10.8441i 0.618904 + 0.618904i 0.945250 0.326346i \(-0.105817\pi\)
−0.326346 + 0.945250i \(0.605817\pi\)
\(308\) 41.1363 4.04027i 2.34396 0.230216i
\(309\) 0 0
\(310\) 0.762783 2.13092i 0.0433231 0.121028i
\(311\) 16.4393i 0.932189i −0.884735 0.466095i \(-0.845661\pi\)
0.884735 0.466095i \(-0.154339\pi\)
\(312\) 0 0
\(313\) 0.171508i 0.00969419i −0.999988 0.00484710i \(-0.998457\pi\)
0.999988 0.00484710i \(-0.00154288\pi\)
\(314\) −26.5039 9.48733i −1.49570 0.535401i
\(315\) 0 0
\(316\) −14.3534 11.7861i −0.807442 0.663019i
\(317\) −11.9635 11.9635i −0.671937 0.671937i 0.286226 0.958162i \(-0.407599\pi\)
−0.958162 + 0.286226i \(0.907599\pi\)
\(318\) 0 0
\(319\) 2.47403i 0.138519i
\(320\) 2.35439 0.712096i 0.131614 0.0398074i
\(321\) 0 0
\(322\) −30.1591 + 14.2592i −1.68070 + 0.794633i
\(323\) 22.5387 22.5387i 1.25408 1.25408i
\(324\) 0 0
\(325\) −14.1732 14.1732i −0.786187 0.786187i
\(326\) −2.28547 + 6.38473i −0.126581 + 0.353618i
\(327\) 0 0
\(328\) 3.60791 + 0.905299i 0.199213 + 0.0499868i
\(329\) −20.6645 −1.13927
\(330\) 0 0
\(331\) −2.32460 + 2.32460i −0.127772 + 0.127772i −0.768101 0.640329i \(-0.778798\pi\)
0.640329 + 0.768101i \(0.278798\pi\)
\(332\) −2.27980 23.2120i −0.125120 1.27392i
\(333\) 0 0
\(334\) −11.7038 + 5.53353i −0.640403 + 0.302781i
\(335\) −2.81870 −0.154002
\(336\) 0 0
\(337\) −10.9566 −0.596842 −0.298421 0.954434i \(-0.596460\pi\)
−0.298421 + 0.954434i \(0.596460\pi\)
\(338\) −4.72499 + 2.23397i −0.257006 + 0.121512i
\(339\) 0 0
\(340\) 2.88767 0.283617i 0.156606 0.0153813i
\(341\) −19.9444 + 19.9444i −1.08005 + 1.08005i
\(342\) 0 0
\(343\) −2.08489 −0.112573
\(344\) 1.73403 1.03838i 0.0934926 0.0559854i
\(345\) 0 0
\(346\) 1.55043 4.33131i 0.0833517 0.232853i
\(347\) 1.35986 + 1.35986i 0.0730012 + 0.0730012i 0.742665 0.669663i \(-0.233562\pi\)
−0.669663 + 0.742665i \(0.733562\pi\)
\(348\) 0 0
\(349\) 2.55298 2.55298i 0.136658 0.136658i −0.635469 0.772127i \(-0.719193\pi\)
0.772127 + 0.635469i \(0.219193\pi\)
\(350\) −23.9204 + 11.3095i −1.27860 + 0.604519i
\(351\) 0 0
\(352\) −30.3182 4.51837i −1.61597 0.240830i
\(353\) 12.5253i 0.666656i −0.942811 0.333328i \(-0.891828\pi\)
0.942811 0.333328i \(-0.108172\pi\)
\(354\) 0 0
\(355\) −0.538311 0.538311i −0.0285706 0.0285706i
\(356\) 15.7053 19.1263i 0.832378 1.01369i
\(357\) 0 0
\(358\) −13.5068 4.83490i −0.713859 0.255532i
\(359\) 11.1836i 0.590248i 0.955459 + 0.295124i \(0.0953610\pi\)
−0.955459 + 0.295124i \(0.904639\pi\)
\(360\) 0 0
\(361\) 26.6325i 1.40171i
\(362\) −11.5260 + 32.1991i −0.605791 + 1.69235i
\(363\) 0 0
\(364\) 3.04659 + 31.0191i 0.159685 + 1.62584i
\(365\) 1.45445 + 1.45445i 0.0761292 + 0.0761292i
\(366\) 0 0
\(367\) 13.0743i 0.682473i 0.939977 + 0.341237i \(0.110846\pi\)
−0.939977 + 0.341237i \(0.889154\pi\)
\(368\) 24.2668 4.81323i 1.26499 0.250907i
\(369\) 0 0
\(370\) 0.769360 + 1.62725i 0.0399971 + 0.0845966i
\(371\) −7.08537 + 7.08537i −0.367854 + 0.367854i
\(372\) 0 0
\(373\) −5.64329 5.64329i −0.292198 0.292198i 0.545750 0.837948i \(-0.316245\pi\)
−0.837948 + 0.545750i \(0.816245\pi\)
\(374\) −34.0439 12.1863i −1.76037 0.630141i
\(375\) 0 0
\(376\) 14.8638 + 3.72964i 0.766543 + 0.192342i
\(377\) −1.86556 −0.0960812
\(378\) 0 0
\(379\) −9.86282 + 9.86282i −0.506619 + 0.506619i −0.913487 0.406868i \(-0.866621\pi\)
0.406868 + 0.913487i \(0.366621\pi\)
\(380\) −2.63612 + 3.21034i −0.135230 + 0.164687i
\(381\) 0 0
\(382\) −14.3180 30.2836i −0.732575 1.54945i
\(383\) 14.8365 0.758111 0.379055 0.925374i \(-0.376249\pi\)
0.379055 + 0.925374i \(0.376249\pi\)
\(384\) 0 0
\(385\) −6.35442 −0.323851
\(386\) −16.0635 33.9753i −0.817609 1.72930i
\(387\) 0 0
\(388\) 3.57348 4.35189i 0.181416 0.220934i
\(389\) 3.64954 3.64954i 0.185039 0.185039i −0.608508 0.793548i \(-0.708232\pi\)
0.793548 + 0.608508i \(0.208232\pi\)
\(390\) 0 0
\(391\) 29.1835 1.47587
\(392\) 20.7033 + 5.19489i 1.04568 + 0.262382i
\(393\) 0 0
\(394\) 27.3990 + 9.80772i 1.38034 + 0.494106i
\(395\) 2.01891 + 2.01891i 0.101582 + 0.101582i
\(396\) 0 0
\(397\) 13.3913 13.3913i 0.672088 0.672088i −0.286109 0.958197i \(-0.592362\pi\)
0.958197 + 0.286109i \(0.0923619\pi\)
\(398\) 0.199004 + 0.420907i 0.00997518 + 0.0210982i
\(399\) 0 0
\(400\) 19.2469 3.81756i 0.962346 0.190878i
\(401\) 27.5346i 1.37501i 0.726179 + 0.687505i \(0.241294\pi\)
−0.726179 + 0.687505i \(0.758706\pi\)
\(402\) 0 0
\(403\) −15.0392 15.0392i −0.749155 0.749155i
\(404\) 1.76417 + 17.9621i 0.0877709 + 0.893646i
\(405\) 0 0
\(406\) −0.829958 + 2.31858i −0.0411901 + 0.115069i
\(407\) 22.4311i 1.11187i
\(408\) 0 0
\(409\) 16.2349i 0.802762i 0.915911 + 0.401381i \(0.131470\pi\)
−0.915911 + 0.401381i \(0.868530\pi\)
\(410\) −0.538392 0.192723i −0.0265893 0.00951789i
\(411\) 0 0
\(412\) 23.5735 28.7084i 1.16138 1.41436i
\(413\) 18.2180 + 18.2180i 0.896451 + 0.896451i
\(414\) 0 0
\(415\) 3.58560i 0.176010i
\(416\) 3.40710 22.8616i 0.167047 1.12088i
\(417\) 0 0
\(418\) 46.7996 22.1268i 2.28904 1.08226i
\(419\) −2.15752 + 2.15752i −0.105402 + 0.105402i −0.757841 0.652439i \(-0.773746\pi\)
0.652439 + 0.757841i \(0.273746\pi\)
\(420\) 0 0
\(421\) 17.2411 + 17.2411i 0.840281 + 0.840281i 0.988895 0.148615i \(-0.0474814\pi\)
−0.148615 + 0.988895i \(0.547481\pi\)
\(422\) −3.50596 + 9.79429i −0.170667 + 0.476778i
\(423\) 0 0
\(424\) 6.37525 3.81764i 0.309609 0.185401i
\(425\) 23.1466 1.12277
\(426\) 0 0
\(427\) 3.17431 3.17431i 0.153616 0.153616i
\(428\) −35.1639 + 3.45367i −1.69971 + 0.166940i
\(429\) 0 0
\(430\) −0.280903 + 0.132811i −0.0135464 + 0.00640470i
\(431\) −33.3451 −1.60618 −0.803089 0.595860i \(-0.796811\pi\)
−0.803089 + 0.595860i \(0.796811\pi\)
\(432\) 0 0
\(433\) −22.2248 −1.06805 −0.534027 0.845467i \(-0.679322\pi\)
−0.534027 + 0.845467i \(0.679322\pi\)
\(434\) −25.3819 + 12.0005i −1.21837 + 0.576044i
\(435\) 0 0
\(436\) 1.36402 + 13.8879i 0.0653246 + 0.665108i
\(437\) −29.5429 + 29.5429i −1.41323 + 1.41323i
\(438\) 0 0
\(439\) −0.240504 −0.0114786 −0.00573932 0.999984i \(-0.501827\pi\)
−0.00573932 + 0.999984i \(0.501827\pi\)
\(440\) 4.57068 + 1.14688i 0.217899 + 0.0546753i
\(441\) 0 0
\(442\) 9.18917 25.6710i 0.437084 1.22105i
\(443\) −26.5432 26.5432i −1.26110 1.26110i −0.950559 0.310546i \(-0.899488\pi\)
−0.310546 0.950559i \(-0.600512\pi\)
\(444\) 0 0
\(445\) −2.69025 + 2.69025i −0.127530 + 0.127530i
\(446\) −1.01105 + 0.478024i −0.0478747 + 0.0226351i
\(447\) 0 0
\(448\) −26.8975 14.4052i −1.27079 0.680584i
\(449\) 31.9534i 1.50797i −0.656890 0.753987i \(-0.728128\pi\)
0.656890 0.753987i \(-0.271872\pi\)
\(450\) 0 0
\(451\) 5.03910 + 5.03910i 0.237282 + 0.237282i
\(452\) 18.1504 + 14.9039i 0.853722 + 0.701020i
\(453\) 0 0
\(454\) −8.20681 2.93770i −0.385165 0.137873i
\(455\) 4.79158i 0.224633i
\(456\) 0 0
\(457\) 13.0060i 0.608395i 0.952609 + 0.304198i \(0.0983883\pi\)
−0.952609 + 0.304198i \(0.901612\pi\)
\(458\) 8.05085 22.4910i 0.376191 1.05093i
\(459\) 0 0
\(460\) −3.78505 + 0.371755i −0.176479 + 0.0173332i
\(461\) −14.0979 14.0979i −0.656603 0.656603i 0.297972 0.954575i \(-0.403690\pi\)
−0.954575 + 0.297972i \(0.903690\pi\)
\(462\) 0 0
\(463\) 35.7903i 1.66331i 0.555289 + 0.831657i \(0.312607\pi\)
−0.555289 + 0.831657i \(0.687393\pi\)
\(464\) 1.01545 1.51794i 0.0471412 0.0704687i
\(465\) 0 0
\(466\) −16.0150 33.8728i −0.741880 1.56912i
\(467\) 15.2548 15.2548i 0.705909 0.705909i −0.259763 0.965672i \(-0.583645\pi\)
0.965672 + 0.259763i \(0.0836446\pi\)
\(468\) 0 0
\(469\) 24.7240 + 24.7240i 1.14165 + 1.14165i
\(470\) −2.21806 0.793976i −0.102312 0.0366234i
\(471\) 0 0
\(472\) −9.81600 16.3922i −0.451818 0.754511i
\(473\) 3.87217 0.178043
\(474\) 0 0
\(475\) −23.4316 + 23.4316i −1.07512 + 1.07512i
\(476\) −27.8167 22.8413i −1.27498 1.04693i
\(477\) 0 0
\(478\) 0.660071 + 1.39609i 0.0301909 + 0.0638559i
\(479\) −23.2925 −1.06426 −0.532131 0.846662i \(-0.678609\pi\)
−0.532131 + 0.846662i \(0.678609\pi\)
\(480\) 0 0
\(481\) 16.9143 0.771226
\(482\) −8.66912 18.3358i −0.394868 0.835172i
\(483\) 0 0
\(484\) −28.3830 23.3062i −1.29013 1.05937i
\(485\) −0.612124 + 0.612124i −0.0277951 + 0.0277951i
\(486\) 0 0
\(487\) 6.49302 0.294227 0.147113 0.989120i \(-0.453002\pi\)
0.147113 + 0.989120i \(0.453002\pi\)
\(488\) −2.85617 + 1.71034i −0.129293 + 0.0774234i
\(489\) 0 0
\(490\) −3.08947 1.10590i −0.139568 0.0499596i
\(491\) −9.99765 9.99765i −0.451188 0.451188i 0.444561 0.895749i \(-0.353360\pi\)
−0.895749 + 0.444561i \(0.853360\pi\)
\(492\) 0 0
\(493\) 1.52334 1.52334i 0.0686080 0.0686080i
\(494\) 16.6848 + 35.2895i 0.750685 + 1.58775i
\(495\) 0 0
\(496\) 20.4229 4.05082i 0.917017 0.181887i
\(497\) 9.44353i 0.423600i
\(498\) 0 0
\(499\) −16.6215 16.6215i −0.744080 0.744080i 0.229281 0.973360i \(-0.426363\pi\)
−0.973360 + 0.229281i \(0.926363\pi\)
\(500\) −6.06200 + 0.595389i −0.271101 + 0.0266266i
\(501\) 0 0
\(502\) −4.02856 + 11.2542i −0.179803 + 0.502301i
\(503\) 22.3009i 0.994348i −0.867651 0.497174i \(-0.834371\pi\)
0.867651 0.497174i \(-0.165629\pi\)
\(504\) 0 0
\(505\) 2.77464i 0.123470i
\(506\) 44.6236 + 15.9734i 1.98376 + 0.710106i
\(507\) 0 0
\(508\) −23.6470 19.4173i −1.04916 0.861505i
\(509\) 19.1255 + 19.1255i 0.847721 + 0.847721i 0.989848 0.142128i \(-0.0453943\pi\)
−0.142128 + 0.989848i \(0.545394\pi\)
\(510\) 0 0
\(511\) 25.5152i 1.12872i
\(512\) 16.7472 + 15.2162i 0.740128 + 0.672466i
\(513\) 0 0
\(514\) 29.9274 14.1496i 1.32004 0.624114i
\(515\) −4.03805 + 4.03805i −0.177938 + 0.177938i
\(516\) 0 0
\(517\) 20.7600 + 20.7600i 0.913025 + 0.913025i
\(518\) 7.52492 21.0217i 0.330626 0.923641i
\(519\) 0 0
\(520\) −0.864810 + 3.44654i −0.0379244 + 0.151141i
\(521\) −5.15019 −0.225634 −0.112817 0.993616i \(-0.535987\pi\)
−0.112817 + 0.993616i \(0.535987\pi\)
\(522\) 0 0
\(523\) −0.348495 + 0.348495i −0.0152386 + 0.0152386i −0.714685 0.699446i \(-0.753430\pi\)
0.699446 + 0.714685i \(0.253430\pi\)
\(524\) 0.981980 + 9.99810i 0.0428980 + 0.436769i
\(525\) 0 0
\(526\) −17.0253 + 8.04953i −0.742338 + 0.350976i
\(527\) 24.5609 1.06989
\(528\) 0 0
\(529\) −15.2527 −0.663163
\(530\) −1.03276 + 0.488285i −0.0448600 + 0.0212098i
\(531\) 0 0
\(532\) 51.2818 5.03673i 2.22335 0.218370i
\(533\) −3.79976 + 3.79976i −0.164586 + 0.164586i
\(534\) 0 0
\(535\) 5.43184 0.234839
\(536\) −13.3215 22.2461i −0.575400 0.960886i
\(537\) 0 0
\(538\) 5.92161 16.5427i 0.255299 0.713206i
\(539\) 28.9160 + 28.9160i 1.24550 + 1.24550i
\(540\) 0 0
\(541\) 13.2936 13.2936i 0.571536 0.571536i −0.361021 0.932558i \(-0.617572\pi\)
0.932558 + 0.361021i \(0.117572\pi\)
\(542\) −1.87014 + 0.884200i −0.0803295 + 0.0379797i
\(543\) 0 0
\(544\) 15.8858 + 21.4500i 0.681099 + 0.919663i
\(545\) 2.14529i 0.0918940i
\(546\) 0 0
\(547\) 17.0584 + 17.0584i 0.729366 + 0.729366i 0.970494 0.241127i \(-0.0775171\pi\)
−0.241127 + 0.970494i \(0.577517\pi\)
\(548\) −5.21926 + 6.35615i −0.222956 + 0.271521i
\(549\) 0 0
\(550\) 35.3927 + 12.6691i 1.50915 + 0.540214i
\(551\) 3.08421i 0.131392i
\(552\) 0 0
\(553\) 35.4175i 1.50611i
\(554\) 1.91352 5.34565i 0.0812979 0.227115i
\(555\) 0 0
\(556\) 1.83713 + 18.7049i 0.0779117 + 0.793264i
\(557\) 14.5673 + 14.5673i 0.617236 + 0.617236i 0.944822 0.327586i \(-0.106235\pi\)
−0.327586 + 0.944822i \(0.606235\pi\)
\(558\) 0 0
\(559\) 2.91983i 0.123496i
\(560\) 3.89875 + 2.60813i 0.164752 + 0.110214i
\(561\) 0 0
\(562\) 3.94824 + 8.35079i 0.166546 + 0.352257i
\(563\) 21.3310 21.3310i 0.898994 0.898994i −0.0963535 0.995347i \(-0.530718\pi\)
0.995347 + 0.0963535i \(0.0307179\pi\)
\(564\) 0 0
\(565\) −2.55298 2.55298i −0.107405 0.107405i
\(566\) 3.42946 + 1.22761i 0.144151 + 0.0516001i
\(567\) 0 0
\(568\) 1.70442 6.79265i 0.0715158 0.285013i
\(569\) −21.5582 −0.903765 −0.451882 0.892077i \(-0.649247\pi\)
−0.451882 + 0.892077i \(0.649247\pi\)
\(570\) 0 0
\(571\) −31.5802 + 31.5802i −1.32159 + 1.32159i −0.409100 + 0.912490i \(0.634157\pi\)
−0.912490 + 0.409100i \(0.865843\pi\)
\(572\) 28.1018 34.2231i 1.17499 1.43094i
\(573\) 0 0
\(574\) 3.03202 + 6.41293i 0.126554 + 0.267671i
\(575\) −30.3397 −1.26525
\(576\) 0 0
\(577\) −26.0498 −1.08447 −0.542235 0.840227i \(-0.682422\pi\)
−0.542235 + 0.840227i \(0.682422\pi\)
\(578\) 3.18227 + 6.73072i 0.132365 + 0.279961i
\(579\) 0 0
\(580\) −0.178170 + 0.216981i −0.00739811 + 0.00900963i
\(581\) 31.4509 31.4509i 1.30480 1.30480i
\(582\) 0 0
\(583\) 14.2362 0.589604
\(584\) −4.60511 + 18.3528i −0.190561 + 0.759446i
\(585\) 0 0
\(586\) −43.1714 15.4536i −1.78340 0.638383i
\(587\) −0.757628 0.757628i −0.0312707 0.0312707i 0.691299 0.722569i \(-0.257039\pi\)
−0.722569 + 0.691299i \(0.757039\pi\)
\(588\) 0 0
\(589\) −24.8633 + 24.8633i −1.02448 + 1.02448i
\(590\) 1.25549 + 2.65544i 0.0516877 + 0.109323i
\(591\) 0 0
\(592\) −9.20672 + 13.7626i −0.378394 + 0.565639i
\(593\) 32.5463i 1.33652i 0.743929 + 0.668259i \(0.232960\pi\)
−0.743929 + 0.668259i \(0.767040\pi\)
\(594\) 0 0
\(595\) 3.91262 + 3.91262i 0.160402 + 0.160402i
\(596\) −0.199899 2.03529i −0.00818820 0.0833688i
\(597\) 0 0
\(598\) −12.0449 + 33.6487i −0.492551 + 1.37600i
\(599\) 30.0578i 1.22813i 0.789256 + 0.614065i \(0.210467\pi\)
−0.789256 + 0.614065i \(0.789533\pi\)
\(600\) 0 0
\(601\) 23.7148i 0.967348i −0.875248 0.483674i \(-0.839302\pi\)
0.875248 0.483674i \(-0.160698\pi\)
\(602\) 3.62887 + 1.29899i 0.147902 + 0.0529428i
\(603\) 0 0
\(604\) −7.54121 + 9.18389i −0.306847 + 0.373687i
\(605\) 3.99227 + 3.99227i 0.162309 + 0.162309i
\(606\) 0 0
\(607\) 36.9838i 1.50113i −0.660799 0.750563i \(-0.729782\pi\)
0.660799 0.750563i \(-0.270218\pi\)
\(608\) −37.7956 5.63274i −1.53282 0.228438i
\(609\) 0 0
\(610\) 0.462685 0.218756i 0.0187336 0.00885719i
\(611\) −15.6542 + 15.6542i −0.633302 + 0.633302i
\(612\) 0 0
\(613\) 9.51791 + 9.51791i 0.384425 + 0.384425i 0.872693 0.488269i \(-0.162371\pi\)
−0.488269 + 0.872693i \(0.662371\pi\)
\(614\) 7.30930 20.4194i 0.294979 0.824058i
\(615\) 0 0
\(616\) −30.0316 50.1512i −1.21001 2.02065i
\(617\) 37.4296 1.50686 0.753430 0.657528i \(-0.228398\pi\)
0.753430 + 0.657528i \(0.228398\pi\)
\(618\) 0 0
\(619\) −0.0391337 + 0.0391337i −0.00157291 + 0.00157291i −0.707893 0.706320i \(-0.750354\pi\)
0.706320 + 0.707893i \(0.250354\pi\)
\(620\) −3.18550 + 0.312869i −0.127933 + 0.0125651i
\(621\) 0 0
\(622\) −21.0180 + 9.93725i −0.842743 + 0.398448i
\(623\) 47.1948 1.89082
\(624\) 0 0
\(625\) −23.5909 −0.943637
\(626\) −0.219275 + 0.103673i −0.00876401 + 0.00414361i
\(627\) 0 0
\(628\) 3.89140 + 39.6206i 0.155284 + 1.58103i
\(629\) −13.8116 + 13.8116i −0.550704 + 0.550704i
\(630\) 0 0
\(631\) 36.6535 1.45915 0.729576 0.683900i \(-0.239717\pi\)
0.729576 + 0.683900i \(0.239717\pi\)
\(632\) −6.39234 + 25.4755i −0.254274 + 1.01336i
\(633\) 0 0
\(634\) −8.06382 + 22.5272i −0.320255 + 0.894670i
\(635\) 3.32612 + 3.32612i 0.131993 + 0.131993i
\(636\) 0 0
\(637\) −21.8042 + 21.8042i −0.863915 + 0.863915i
\(638\) 3.16309 1.49551i 0.125228 0.0592076i
\(639\) 0 0
\(640\) −2.33361 2.57967i −0.0922439 0.101971i
\(641\) 12.4650i 0.492339i 0.969227 + 0.246169i \(0.0791719\pi\)
−0.969227 + 0.246169i \(0.920828\pi\)
\(642\) 0 0
\(643\) −5.95415 5.95415i −0.234809 0.234809i 0.579888 0.814696i \(-0.303096\pi\)
−0.814696 + 0.579888i \(0.803096\pi\)
\(644\) 36.4612 + 29.9395i 1.43677 + 1.17978i
\(645\) 0 0
\(646\) −42.4402 15.1919i −1.66979 0.597716i
\(647\) 8.17712i 0.321476i −0.986997 0.160738i \(-0.948613\pi\)
0.986997 0.160738i \(-0.0513874\pi\)
\(648\) 0 0
\(649\) 36.6045i 1.43685i
\(650\) −9.55323 + 26.6880i −0.374709 + 1.04679i
\(651\) 0 0
\(652\) 9.54451 0.937429i 0.373792 0.0367126i
\(653\) −26.9263 26.9263i −1.05371 1.05371i −0.998473 0.0552346i \(-0.982409\pi\)
−0.0552346 0.998473i \(-0.517591\pi\)
\(654\) 0 0
\(655\) 1.54443i 0.0603458i
\(656\) −1.02347 5.16000i −0.0399597 0.201464i
\(657\) 0 0
\(658\) 12.4913 + 26.4199i 0.486961 + 1.02996i
\(659\) −1.76198 + 1.76198i −0.0686372 + 0.0686372i −0.740592 0.671955i \(-0.765455\pi\)
0.671955 + 0.740592i \(0.265455\pi\)
\(660\) 0 0
\(661\) −0.153923 0.153923i −0.00598692 0.00598692i 0.704107 0.710094i \(-0.251348\pi\)
−0.710094 + 0.704107i \(0.751348\pi\)
\(662\) 4.37721 + 1.56686i 0.170125 + 0.0608979i
\(663\) 0 0
\(664\) −28.2988 + 16.9459i −1.09821 + 0.657630i
\(665\) −7.92162 −0.307187
\(666\) 0 0
\(667\) −1.99675 + 1.99675i −0.0773144 + 0.0773144i
\(668\) 14.1494 + 11.6186i 0.547458 + 0.449536i
\(669\) 0 0
\(670\) 1.70385 + 3.60375i 0.0658254 + 0.139225i
\(671\) −6.37797 −0.246219
\(672\) 0 0
\(673\) −23.0014 −0.886639 −0.443320 0.896364i \(-0.646199\pi\)
−0.443320 + 0.896364i \(0.646199\pi\)
\(674\) 6.62302 + 14.0081i 0.255109 + 0.539573i
\(675\) 0 0
\(676\) 5.71233 + 4.69059i 0.219705 + 0.180407i
\(677\) 25.8728 25.8728i 0.994374 0.994374i −0.00561069 0.999984i \(-0.501786\pi\)
0.999984 + 0.00561069i \(0.00178595\pi\)
\(678\) 0 0
\(679\) 10.7384 0.412103
\(680\) −2.10815 3.52049i −0.0808437 0.135005i
\(681\) 0 0
\(682\) 37.5553 + 13.4432i 1.43806 + 0.514769i
\(683\) 16.4249 + 16.4249i 0.628480 + 0.628480i 0.947686 0.319205i \(-0.103416\pi\)
−0.319205 + 0.947686i \(0.603416\pi\)
\(684\) 0 0
\(685\) 0.894039 0.894039i 0.0341595 0.0341595i
\(686\) 1.26027 + 2.66556i 0.0481175 + 0.101772i
\(687\) 0 0
\(688\) −2.37577 1.58931i −0.0905752 0.0605918i
\(689\) 10.7349i 0.408967i
\(690\) 0 0
\(691\) 0.0989768 + 0.0989768i 0.00376526 + 0.00376526i 0.708987 0.705222i \(-0.249153\pi\)
−0.705222 + 0.708987i \(0.749153\pi\)
\(692\) −6.47485 + 0.635938i −0.246137 + 0.0241747i
\(693\) 0 0
\(694\) 0.916595 2.56061i 0.0347935 0.0971996i
\(695\) 2.88938i 0.109601i
\(696\) 0 0
\(697\) 6.20548i 0.235049i
\(698\) −4.80726 1.72080i −0.181957 0.0651333i
\(699\) 0 0
\(700\) 28.9188 + 23.7462i 1.09303 + 0.897522i
\(701\) 9.89571 + 9.89571i 0.373756 + 0.373756i 0.868843 0.495087i \(-0.164864\pi\)
−0.495087 + 0.868843i \(0.664864\pi\)
\(702\) 0 0
\(703\) 27.9633i 1.05466i
\(704\) 12.5500 + 41.4936i 0.472994 + 1.56385i
\(705\) 0 0
\(706\) −16.0138 + 7.57131i −0.602688 + 0.284950i
\(707\) −24.3376 + 24.3376i −0.915309 + 0.915309i
\(708\) 0 0
\(709\) −8.60454 8.60454i −0.323150 0.323150i 0.526824 0.849974i \(-0.323383\pi\)
−0.849974 + 0.526824i \(0.823383\pi\)
\(710\) −0.362841 + 1.01364i −0.0136172 + 0.0380412i
\(711\) 0 0
\(712\) −33.9468 8.51797i −1.27221 0.319224i
\(713\) −32.1935 −1.20566
\(714\) 0 0
\(715\) −4.81373 + 4.81373i −0.180023 + 0.180023i
\(716\) 1.98312 + 20.1913i 0.0741128 + 0.754585i
\(717\) 0 0
\(718\) 14.2984 6.76027i 0.533612 0.252291i
\(719\) 39.6092 1.47717 0.738586 0.674159i \(-0.235494\pi\)
0.738586 + 0.674159i \(0.235494\pi\)
\(720\) 0 0
\(721\) 70.8390 2.63818
\(722\) 34.0500 16.0988i 1.26721 0.599135i
\(723\) 0 0
\(724\) 48.1342 4.72758i 1.78889 0.175699i
\(725\) −1.58370 + 1.58370i −0.0588170 + 0.0588170i
\(726\) 0 0
\(727\) −17.9378 −0.665278 −0.332639 0.943054i \(-0.607939\pi\)
−0.332639 + 0.943054i \(0.607939\pi\)
\(728\) 37.8168 22.6455i 1.40158 0.839299i
\(729\) 0 0
\(730\) 0.980349 2.73872i 0.0362843 0.101364i
\(731\) −2.38422 2.38422i −0.0881836 0.0881836i
\(732\) 0 0
\(733\) 17.8729 17.8729i 0.660152 0.660152i −0.295264 0.955416i \(-0.595408\pi\)
0.955416 + 0.295264i \(0.0954075\pi\)
\(734\) 16.7157 7.90316i 0.616988 0.291711i
\(735\) 0 0
\(736\) −20.8226 28.1160i −0.767531 1.03637i
\(737\) 49.6766i 1.82986i
\(738\) 0 0
\(739\) −17.9555 17.9555i −0.660504 0.660504i 0.294995 0.955499i \(-0.404682\pi\)
−0.955499 + 0.294995i \(0.904682\pi\)
\(740\) 1.61540 1.96728i 0.0593833 0.0723186i
\(741\) 0 0
\(742\) 13.3417 + 4.77579i 0.489790 + 0.175325i
\(743\) 48.9933i 1.79739i 0.438576 + 0.898694i \(0.355483\pi\)
−0.438576 + 0.898694i \(0.644517\pi\)
\(744\) 0 0
\(745\) 0.314396i 0.0115186i
\(746\) −3.80378 + 10.6263i −0.139266 + 0.389056i
\(747\) 0 0
\(748\) 4.99845 + 50.8921i 0.182761 + 1.86080i
\(749\) −47.6450 47.6450i −1.74091 1.74091i
\(750\) 0 0
\(751\) 28.5197i 1.04070i −0.853954 0.520349i \(-0.825802\pi\)
0.853954 0.520349i \(-0.174198\pi\)
\(752\) −4.21647 21.2581i −0.153759 0.775204i
\(753\) 0 0
\(754\) 1.12769 + 2.38515i 0.0410682 + 0.0868620i
\(755\) 1.29178 1.29178i 0.0470127 0.0470127i
\(756\) 0 0
\(757\) 34.5077 + 34.5077i 1.25420 + 1.25420i 0.953817 + 0.300388i \(0.0971161\pi\)
0.300388 + 0.953817i \(0.402884\pi\)
\(758\) 18.5717 + 6.64790i 0.674553 + 0.241462i
\(759\) 0 0
\(760\) 5.69795 + 1.42973i 0.206686 + 0.0518619i
\(761\) 25.2483 0.915248 0.457624 0.889146i \(-0.348701\pi\)
0.457624 + 0.889146i \(0.348701\pi\)
\(762\) 0 0
\(763\) −18.8173 + 18.8173i −0.681230 + 0.681230i
\(764\) −30.0631 + 36.6117i −1.08765 + 1.32456i
\(765\) 0 0
\(766\) −8.96838 18.9687i −0.324041 0.685368i
\(767\) 27.6018 0.996644
\(768\) 0 0
\(769\) −19.4742 −0.702259 −0.351129 0.936327i \(-0.614202\pi\)
−0.351129 + 0.936327i \(0.614202\pi\)
\(770\) 3.84112 + 8.12422i 0.138424 + 0.292777i
\(771\) 0 0
\(772\) −33.7279 + 41.0748i −1.21389 + 1.47831i
\(773\) 10.2401 10.2401i 0.368309 0.368309i −0.498551 0.866860i \(-0.666134\pi\)
0.866860 + 0.498551i \(0.166134\pi\)
\(774\) 0 0
\(775\) −25.5339 −0.917206
\(776\) −7.72406 1.93813i −0.277278 0.0695747i
\(777\) 0 0
\(778\) −6.87208 2.45992i −0.246376 0.0881925i
\(779\) 6.28190 + 6.28190i 0.225072 + 0.225072i
\(780\) 0 0
\(781\) 9.48717 9.48717i 0.339478 0.339478i
\(782\) −17.6409 37.3116i −0.630836 1.33426i
\(783\) 0 0
\(784\) −5.87299 29.6097i −0.209750 1.05749i
\(785\) 6.12028i 0.218442i
\(786\) 0 0
\(787\) 32.7690 + 32.7690i 1.16809 + 1.16809i 0.982657 + 0.185432i \(0.0593683\pi\)
0.185432 + 0.982657i \(0.440632\pi\)
\(788\) −4.02281 40.9586i −0.143307 1.45909i
\(789\) 0 0
\(790\) 1.36082 3.80160i 0.0484158 0.135255i
\(791\) 44.7867i 1.59243i
\(792\) 0 0
\(793\) 4.80934i 0.170785i
\(794\) −25.2157 9.02619i −0.894872 0.320328i
\(795\) 0 0
\(796\) 0.417842 0.508860i 0.0148100 0.0180361i
\(797\) −18.9380 18.9380i −0.670817 0.670817i 0.287087 0.957904i \(-0.407313\pi\)
−0.957904 + 0.287087i \(0.907313\pi\)
\(798\) 0 0
\(799\) 25.5653i 0.904434i
\(800\) −16.5152 22.2999i −0.583900 0.788419i
\(801\) 0 0
\(802\) 35.2034 16.6441i 1.24307 0.587723i
\(803\) −25.6331 + 25.6331i −0.904572 + 0.904572i
\(804\) 0 0
\(805\) −5.12853 5.12853i −0.180757 0.180757i
\(806\) −10.1370 + 28.3187i −0.357059 + 0.997485i
\(807\) 0 0
\(808\) 21.8984 13.1132i 0.770383 0.461322i
\(809\) 29.2888 1.02974 0.514870 0.857268i \(-0.327840\pi\)
0.514870 + 0.857268i \(0.327840\pi\)
\(810\) 0 0
\(811\) −12.8548 + 12.8548i −0.451393 + 0.451393i −0.895817 0.444424i \(-0.853408\pi\)
0.444424 + 0.895817i \(0.353408\pi\)
\(812\) 3.46604 0.340423i 0.121634 0.0119465i
\(813\) 0 0
\(814\) −28.6786 + 13.5592i −1.00518 + 0.475249i
\(815\) −1.47436 −0.0516446
\(816\) 0 0
\(817\) 4.82717 0.168881
\(818\) 20.7565 9.81365i 0.725735 0.343126i
\(819\) 0 0
\(820\) 0.0790487 + 0.804840i 0.00276050 + 0.0281062i
\(821\) 18.6497 18.6497i 0.650880 0.650880i −0.302325 0.953205i \(-0.597763\pi\)
0.953205 + 0.302325i \(0.0977627\pi\)
\(822\) 0 0
\(823\) −2.21917 −0.0773554 −0.0386777 0.999252i \(-0.512315\pi\)
−0.0386777 + 0.999252i \(0.512315\pi\)
\(824\) −50.9539 12.7854i −1.77506 0.445401i
\(825\) 0 0
\(826\) 12.2796 34.3045i 0.427263 1.19361i
\(827\) 21.7284 + 21.7284i 0.755570 + 0.755570i 0.975513 0.219943i \(-0.0705871\pi\)
−0.219943 + 0.975513i \(0.570587\pi\)
\(828\) 0 0
\(829\) 1.37469 1.37469i 0.0477451 0.0477451i −0.682831 0.730576i \(-0.739252\pi\)
0.730576 + 0.682831i \(0.239252\pi\)
\(830\) 4.58425 2.16743i 0.159122 0.0752325i
\(831\) 0 0
\(832\) −31.2885 + 9.46336i −1.08473 + 0.328083i
\(833\) 35.6090i 1.23378i
\(834\) 0 0
\(835\) −1.99022 1.99022i −0.0688744 0.0688744i
\(836\) −56.5789 46.4588i −1.95682 1.60681i
\(837\) 0 0
\(838\) 4.06261 + 1.45425i 0.140340 + 0.0502362i
\(839\) 2.77829i 0.0959171i 0.998849 + 0.0479585i \(0.0152715\pi\)
−0.998849 + 0.0479585i \(0.984728\pi\)
\(840\) 0 0
\(841\) 28.7915i 0.992812i
\(842\) 11.6211 32.4650i 0.400491 1.11882i
\(843\) 0 0
\(844\) 14.6414 1.43803i 0.503979 0.0494991i
\(845\) −0.803481 0.803481i −0.0276406 0.0276406i
\(846\) 0 0
\(847\) 70.0359i 2.40646i
\(848\) −8.73463 5.84317i −0.299948 0.200655i
\(849\) 0 0
\(850\) −13.9916 29.5933i −0.479909 1.01504i
\(851\) 18.1037 18.1037i 0.620588 0.620588i
\(852\) 0 0
\(853\) 17.0961 + 17.0961i 0.585360 + 0.585360i 0.936371 0.351011i \(-0.114162\pi\)
−0.351011 + 0.936371i \(0.614162\pi\)
\(854\) −5.97722 2.13960i −0.204536 0.0732156i
\(855\) 0 0
\(856\) 25.6714 + 42.8699i 0.877432 + 1.46526i
\(857\) −49.4967 −1.69078 −0.845388 0.534153i \(-0.820631\pi\)
−0.845388 + 0.534153i \(0.820631\pi\)
\(858\) 0 0
\(859\) 25.5374 25.5374i 0.871324 0.871324i −0.121293 0.992617i \(-0.538704\pi\)
0.992617 + 0.121293i \(0.0387040\pi\)
\(860\) 0.339601 + 0.278858i 0.0115803 + 0.00950899i
\(861\) 0 0
\(862\) 20.1565 + 42.6323i 0.686532 + 1.45206i
\(863\) −45.8222 −1.55981 −0.779904 0.625900i \(-0.784732\pi\)
−0.779904 + 0.625900i \(0.784732\pi\)
\(864\) 0 0
\(865\) 1.00018 0.0340073
\(866\) 13.4344 + 28.4147i 0.456520 + 0.965571i
\(867\) 0 0
\(868\) 30.6858 + 25.1971i 1.04154 + 0.855247i
\(869\) −35.5812 + 35.5812i −1.20701 + 1.20701i
\(870\) 0 0
\(871\) 37.4589 1.26925
\(872\) 16.9313 10.1389i 0.573367 0.343345i
\(873\) 0 0
\(874\) 55.6292 + 19.9130i 1.88169 + 0.673567i
\(875\) −8.21366 8.21366i −0.277672 0.277672i
\(876\) 0 0
\(877\) 9.65581 9.65581i 0.326054 0.326054i −0.525030 0.851084i \(-0.675946\pi\)
0.851084 + 0.525030i \(0.175946\pi\)
\(878\) 0.145380 + 0.307489i 0.00490634 + 0.0103772i
\(879\) 0 0
\(880\) −1.29658 6.53695i −0.0437078 0.220361i
\(881\) 54.5487i 1.83779i −0.394499 0.918896i \(-0.629082\pi\)
0.394499 0.918896i \(-0.370918\pi\)
\(882\) 0 0
\(883\) −12.7878 12.7878i −0.430344 0.430344i 0.458401 0.888745i \(-0.348422\pi\)
−0.888745 + 0.458401i \(0.848422\pi\)
\(884\) −38.3755 + 3.76911i −1.29071 + 0.126769i
\(885\) 0 0
\(886\) −17.8911 + 49.9807i −0.601062 + 1.67913i
\(887\) 29.3515i 0.985527i −0.870163 0.492763i \(-0.835987\pi\)
0.870163 0.492763i \(-0.164013\pi\)
\(888\) 0 0
\(889\) 58.3497i 1.95699i
\(890\) 5.06574 + 1.81333i 0.169804 + 0.0607829i
\(891\) 0 0
\(892\) 1.22232 + 1.00369i 0.0409264 + 0.0336061i
\(893\) 25.8801 + 25.8801i 0.866045 + 0.866045i
\(894\) 0 0
\(895\) 3.11900i 0.104257i
\(896\) −2.15835 + 43.0965i −0.0721055 + 1.43975i
\(897\) 0 0
\(898\) −40.8529 + 19.3152i −1.36328 + 0.644556i
\(899\) −1.68046 + 1.68046i −0.0560466 + 0.0560466i
\(900\) 0 0
\(901\) −8.76571 8.76571i −0.292028 0.292028i
\(902\) 3.39653 9.48861i 0.113092 0.315936i
\(903\) 0 0
\(904\) 8.08333 32.2147i 0.268848 1.07144i
\(905\) −7.43540 −0.247161
\(906\) 0 0
\(907\) 22.0905 22.0905i 0.733505 0.733505i −0.237808 0.971312i \(-0.576429\pi\)
0.971312 + 0.237808i \(0.0764288\pi\)
\(908\) 1.20495 + 12.2683i 0.0399878 + 0.407139i
\(909\) 0 0
\(910\) −6.12612 + 2.89642i −0.203079 + 0.0960153i
\(911\) −48.9197 −1.62078 −0.810391 0.585889i \(-0.800745\pi\)
−0.810391 + 0.585889i \(0.800745\pi\)
\(912\) 0 0
\(913\) −63.1925 −2.09137
\(914\) 16.6284 7.86187i 0.550018 0.260048i
\(915\) 0 0
\(916\) −33.6216 + 3.30220i −1.11089 + 0.109108i
\(917\) −13.5469 + 13.5469i −0.447357 + 0.447357i
\(918\) 0 0
\(919\) 21.4269 0.706810 0.353405 0.935470i \(-0.385024\pi\)
0.353405 + 0.935470i \(0.385024\pi\)
\(920\) 2.76328 + 4.61453i 0.0911028 + 0.152137i
\(921\) 0 0
\(922\) −9.50247 + 26.5462i −0.312947 + 0.874254i
\(923\) 7.15385 + 7.15385i 0.235472 + 0.235472i
\(924\) 0 0
\(925\) 14.3588 14.3588i 0.472114 0.472114i
\(926\) 45.7584 21.6345i 1.50372 0.710954i
\(927\) 0 0
\(928\) −2.55453 0.380706i −0.0838567 0.0124973i
\(929\) 15.5610i 0.510539i −0.966870 0.255269i \(-0.917836\pi\)
0.966870 0.255269i \(-0.0821642\pi\)
\(930\) 0 0
\(931\) 36.0475 + 36.0475i 1.18141 + 1.18141i
\(932\) −33.6261 + 40.9508i −1.10146 + 1.34139i
\(933\) 0 0
\(934\) −28.7248 10.2823i −0.939903 0.336447i
\(935\) 7.86141i 0.257096i
\(936\) 0 0
\(937\) 19.4793i 0.636360i −0.948030 0.318180i \(-0.896928\pi\)
0.948030 0.318180i \(-0.103072\pi\)
\(938\) 16.6649 46.5553i 0.544128 1.52008i
\(939\) 0 0
\(940\) 0.325664 + 3.31577i 0.0106220 + 0.108149i
\(941\) −5.26841 5.26841i −0.171745 0.171745i 0.616001 0.787746i \(-0.288752\pi\)
−0.787746 + 0.616001i \(0.788752\pi\)
\(942\) 0 0
\(943\) 8.13393i 0.264877i
\(944\) −15.0241 + 22.4587i −0.488992 + 0.730967i
\(945\) 0 0
\(946\) −2.34065 4.95063i −0.0761011 0.160959i
\(947\) 23.4075 23.4075i 0.760641 0.760641i −0.215797 0.976438i \(-0.569235\pi\)
0.976438 + 0.215797i \(0.0692350\pi\)
\(948\) 0 0
\(949\) −19.3288 19.3288i −0.627438 0.627438i
\(950\) 44.1216 + 15.7937i 1.43150 + 0.512417i
\(951\) 0 0
\(952\) −12.3883 + 49.3712i −0.401506 + 1.60013i
\(953\) −61.1868 −1.98204 −0.991018 0.133731i \(-0.957304\pi\)
−0.991018 + 0.133731i \(0.957304\pi\)
\(954\) 0 0
\(955\) 5.14970 5.14970i 0.166640 0.166640i
\(956\) 1.38593 1.68782i 0.0448242 0.0545881i
\(957\) 0 0
\(958\) 14.0799 + 29.7799i 0.454900 + 0.962144i
\(959\) −15.6840 −0.506464
\(960\) 0 0
\(961\) 3.90591 0.125997
\(962\) −10.2244 21.6252i −0.329647 0.697225i
\(963\) 0 0
\(964\) −18.2023 + 22.1672i −0.586256 + 0.713958i
\(965\) 5.77747 5.77747i 0.185983 0.185983i
\(966\) 0 0
\(967\) 34.4866 1.10902 0.554508 0.832178i \(-0.312907\pi\)
0.554508 + 0.832178i \(0.312907\pi\)
\(968\) −12.6404 + 50.3762i −0.406279 + 1.61915i
\(969\) 0 0
\(970\) 1.15263 + 0.412594i 0.0370087 + 0.0132476i
\(971\) −17.8898 17.8898i −0.574110 0.574110i 0.359165 0.933274i \(-0.383062\pi\)
−0.933274 + 0.359165i \(0.883062\pi\)
\(972\) 0 0
\(973\) −25.3441 + 25.3441i −0.812493 + 0.812493i
\(974\) −3.92490 8.30143i −0.125762 0.265995i
\(975\) 0 0
\(976\) 3.91320 + 2.61780i 0.125258 + 0.0837936i
\(977\) 33.3136i 1.06580i 0.846180 + 0.532898i \(0.178897\pi\)
−0.846180 + 0.532898i \(0.821103\pi\)
\(978\) 0 0
\(979\) −47.4129 47.4129i −1.51532 1.51532i
\(980\) 0.453606 + 4.61843i 0.0144899 + 0.147530i
\(981\) 0 0
\(982\) −6.73878 + 18.8255i −0.215043 + 0.600747i
\(983\) 2.60454i 0.0830720i 0.999137 + 0.0415360i \(0.0132251\pi\)
−0.999137 + 0.0415360i \(0.986775\pi\)
\(984\) 0 0
\(985\) 6.32696i 0.201594i
\(986\) −2.86845 1.02679i −0.0913501 0.0326996i
\(987\) 0 0
\(988\) 35.0325 42.6636i 1.11453 1.35731i
\(989\) 3.12516 + 3.12516i 0.0993742 + 0.0993742i
\(990\) 0 0
\(991\) 53.4871i 1.69907i 0.527530 + 0.849537i \(0.323118\pi\)
−0.527530 + 0.849537i \(0.676882\pi\)
\(992\) −17.5243 23.6624i −0.556397 0.751282i
\(993\) 0 0
\(994\) 12.0737 5.70843i 0.382955 0.181060i
\(995\) −0.0715749 + 0.0715749i −0.00226908 + 0.00226908i
\(996\) 0 0
\(997\) 33.9323 + 33.9323i 1.07465 + 1.07465i 0.996979 + 0.0776671i \(0.0247471\pi\)
0.0776671 + 0.996979i \(0.475253\pi\)
\(998\) −11.2035 + 31.2982i −0.354640 + 0.990727i
\(999\) 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 432.2.l.a.107.7 32
3.2 odd 2 inner 432.2.l.a.107.10 yes 32
4.3 odd 2 1728.2.l.a.1295.9 32
12.11 even 2 1728.2.l.a.1295.8 32
16.3 odd 4 inner 432.2.l.a.323.10 yes 32
16.13 even 4 1728.2.l.a.431.8 32
48.29 odd 4 1728.2.l.a.431.9 32
48.35 even 4 inner 432.2.l.a.323.7 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
432.2.l.a.107.7 32 1.1 even 1 trivial
432.2.l.a.107.10 yes 32 3.2 odd 2 inner
432.2.l.a.323.7 yes 32 48.35 even 4 inner
432.2.l.a.323.10 yes 32 16.3 odd 4 inner
1728.2.l.a.431.8 32 16.13 even 4
1728.2.l.a.431.9 32 48.29 odd 4
1728.2.l.a.1295.8 32 12.11 even 2
1728.2.l.a.1295.9 32 4.3 odd 2