Properties

Label 1089.2.e.p.364.11
Level $1089$
Weight $2$
Character 1089.364
Analytic conductor $8.696$
Analytic rank $0$
Dimension $36$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1089,2,Mod(364,1089)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1089, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1089.364");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1089.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.69570878012\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 364.11
Character \(\chi\) \(=\) 1089.364
Dual form 1089.2.e.p.727.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.332160 + 0.575318i) q^{2} +(1.61109 - 0.635904i) q^{3} +(0.779339 - 1.34985i) q^{4} +(-0.558312 + 0.967024i) q^{5} +(0.900989 + 0.715670i) q^{6} +(1.95227 + 3.38143i) q^{7} +2.36410 q^{8} +(2.19125 - 2.04900i) q^{9} -0.741796 q^{10} +(0.397211 - 2.67033i) q^{12} +(-1.33900 + 2.31922i) q^{13} +(-1.29693 + 2.24635i) q^{14} +(-0.284558 + 1.91300i) q^{15} +(-0.773417 - 1.33960i) q^{16} +5.54657 q^{17} +(1.90668 + 0.580070i) q^{18} -5.13234 q^{19} +(0.870228 + 1.50728i) q^{20} +(5.29556 + 4.20635i) q^{21} +(-1.05719 + 1.83110i) q^{23} +(3.80879 - 1.50334i) q^{24} +(1.87658 + 3.25033i) q^{25} -1.77905 q^{26} +(2.22734 - 4.69457i) q^{27} +6.08592 q^{28} +(-0.541520 - 0.937941i) q^{29} +(-1.19510 + 0.471711i) q^{30} +(0.215081 - 0.372532i) q^{31} +(2.87790 - 4.98467i) q^{32} +(1.84235 + 3.19104i) q^{34} -4.35990 q^{35} +(-1.05813 - 4.55474i) q^{36} -8.70580 q^{37} +(-1.70476 - 2.95273i) q^{38} +(-0.682457 + 4.58796i) q^{39} +(-1.31991 + 2.28614i) q^{40} +(1.45954 - 2.52799i) q^{41} +(-0.661016 + 4.44382i) q^{42} +(1.11628 + 1.93346i) q^{43} +(0.758035 + 3.26298i) q^{45} -1.40462 q^{46} +(-6.41773 - 11.1158i) q^{47} +(-2.09790 - 1.66640i) q^{48} +(-4.12272 + 7.14077i) q^{49} +(-1.24665 + 2.15926i) q^{50} +(8.93605 - 3.52709i) q^{51} +(2.08707 + 3.61492i) q^{52} +5.64118 q^{53} +(3.44070 - 0.277916i) q^{54} +(4.61537 + 7.99405i) q^{56} +(-8.26869 + 3.26368i) q^{57} +(0.359743 - 0.623093i) q^{58} +(1.18769 - 2.05713i) q^{59} +(2.36051 + 1.87499i) q^{60} +(2.04223 + 3.53724i) q^{61} +0.285766 q^{62} +(11.2065 + 3.40936i) q^{63} +0.730027 q^{64} +(-1.49516 - 2.58969i) q^{65} +(4.87584 - 8.44521i) q^{67} +(4.32266 - 7.48706i) q^{68} +(-0.538824 + 3.62235i) q^{69} +(-1.44819 - 2.50833i) q^{70} +6.31707 q^{71} +(5.18034 - 4.84406i) q^{72} -11.6727 q^{73} +(-2.89172 - 5.00861i) q^{74} +(5.09024 + 4.04326i) q^{75} +(-3.99983 + 6.92792i) q^{76} +(-2.86622 + 1.13131i) q^{78} +(-2.25735 - 3.90985i) q^{79} +1.72723 q^{80} +(0.603167 - 8.97977i) q^{81} +1.93920 q^{82} +(-0.241002 - 0.417427i) q^{83} +(9.80500 - 3.87007i) q^{84} +(-3.09671 + 5.36367i) q^{85} +(-0.741570 + 1.28444i) q^{86} +(-1.46888 - 1.16676i) q^{87} +16.0830 q^{89} +(-1.62546 + 1.51994i) q^{90} -10.4564 q^{91} +(1.64782 + 2.85410i) q^{92} +(0.109622 - 0.736955i) q^{93} +(4.26343 - 7.38448i) q^{94} +(2.86545 - 4.96310i) q^{95} +(1.46680 - 9.86084i) q^{96} +(-4.00783 - 6.94176i) q^{97} -5.47762 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} - q^{6} - q^{7} - 12 q^{8} - q^{9} - 4 q^{10} - 8 q^{12} - 3 q^{13} - 5 q^{15} + 8 q^{16} - 40 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20} - 8 q^{21} + 10 q^{23}+ \cdots - 164 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(848\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.332160 + 0.575318i 0.234873 + 0.406812i 0.959236 0.282607i \(-0.0911993\pi\)
−0.724363 + 0.689419i \(0.757866\pi\)
\(3\) 1.61109 0.635904i 0.930166 0.367139i
\(4\) 0.779339 1.34985i 0.389670 0.674927i
\(5\) −0.558312 + 0.967024i −0.249685 + 0.432466i −0.963438 0.267930i \(-0.913660\pi\)
0.713754 + 0.700397i \(0.246994\pi\)
\(6\) 0.900989 + 0.715670i 0.367827 + 0.292171i
\(7\) 1.95227 + 3.38143i 0.737889 + 1.27806i 0.953444 + 0.301570i \(0.0975106\pi\)
−0.215555 + 0.976492i \(0.569156\pi\)
\(8\) 2.36410 0.835837
\(9\) 2.19125 2.04900i 0.730417 0.683001i
\(10\) −0.741796 −0.234576
\(11\) 0 0
\(12\) 0.397211 2.67033i 0.114665 0.770858i
\(13\) −1.33900 + 2.31922i −0.371372 + 0.643236i −0.989777 0.142624i \(-0.954446\pi\)
0.618405 + 0.785860i \(0.287779\pi\)
\(14\) −1.29693 + 2.24635i −0.346620 + 0.600364i
\(15\) −0.284558 + 1.91300i −0.0734726 + 0.493934i
\(16\) −0.773417 1.33960i −0.193354 0.334900i
\(17\) 5.54657 1.34524 0.672620 0.739988i \(-0.265169\pi\)
0.672620 + 0.739988i \(0.265169\pi\)
\(18\) 1.90668 + 0.580070i 0.449408 + 0.136724i
\(19\) −5.13234 −1.17744 −0.588720 0.808337i \(-0.700368\pi\)
−0.588720 + 0.808337i \(0.700368\pi\)
\(20\) 0.870228 + 1.50728i 0.194589 + 0.337038i
\(21\) 5.29556 + 4.20635i 1.15559 + 0.917901i
\(22\) 0 0
\(23\) −1.05719 + 1.83110i −0.220439 + 0.381812i −0.954941 0.296795i \(-0.904082\pi\)
0.734502 + 0.678606i \(0.237416\pi\)
\(24\) 3.80879 1.50334i 0.777467 0.306869i
\(25\) 1.87658 + 3.25033i 0.375315 + 0.650065i
\(26\) −1.77905 −0.348901
\(27\) 2.22734 4.69457i 0.428652 0.903469i
\(28\) 6.08592 1.15013
\(29\) −0.541520 0.937941i −0.100558 0.174171i 0.811357 0.584551i \(-0.198729\pi\)
−0.911915 + 0.410380i \(0.865396\pi\)
\(30\) −1.19510 + 0.471711i −0.218195 + 0.0861223i
\(31\) 0.215081 0.372532i 0.0386297 0.0669087i −0.846064 0.533081i \(-0.821034\pi\)
0.884694 + 0.466172i \(0.154367\pi\)
\(32\) 2.87790 4.98467i 0.508746 0.881173i
\(33\) 0 0
\(34\) 1.84235 + 3.19104i 0.315960 + 0.547259i
\(35\) −4.35990 −0.736958
\(36\) −1.05813 4.55474i −0.176355 0.759123i
\(37\) −8.70580 −1.43122 −0.715612 0.698498i \(-0.753852\pi\)
−0.715612 + 0.698498i \(0.753852\pi\)
\(38\) −1.70476 2.95273i −0.276549 0.478996i
\(39\) −0.682457 + 4.58796i −0.109281 + 0.734661i
\(40\) −1.31991 + 2.28614i −0.208695 + 0.361471i
\(41\) 1.45954 2.52799i 0.227942 0.394806i −0.729256 0.684241i \(-0.760134\pi\)
0.957198 + 0.289434i \(0.0934672\pi\)
\(42\) −0.661016 + 4.44382i −0.101997 + 0.685696i
\(43\) 1.11628 + 1.93346i 0.170232 + 0.294850i 0.938501 0.345277i \(-0.112215\pi\)
−0.768269 + 0.640127i \(0.778882\pi\)
\(44\) 0 0
\(45\) 0.758035 + 3.26298i 0.113001 + 0.486416i
\(46\) −1.40462 −0.207101
\(47\) −6.41773 11.1158i −0.936123 1.62141i −0.772619 0.634870i \(-0.781054\pi\)
−0.163503 0.986543i \(-0.552279\pi\)
\(48\) −2.09790 1.66640i −0.302806 0.240524i
\(49\) −4.12272 + 7.14077i −0.588961 + 1.02011i
\(50\) −1.24665 + 2.15926i −0.176303 + 0.305365i
\(51\) 8.93605 3.52709i 1.25130 0.493891i
\(52\) 2.08707 + 3.61492i 0.289425 + 0.501299i
\(53\) 5.64118 0.774876 0.387438 0.921896i \(-0.373360\pi\)
0.387438 + 0.921896i \(0.373360\pi\)
\(54\) 3.44070 0.277916i 0.468221 0.0378196i
\(55\) 0 0
\(56\) 4.61537 + 7.99405i 0.616755 + 1.06825i
\(57\) −8.26869 + 3.26368i −1.09521 + 0.432285i
\(58\) 0.359743 0.623093i 0.0472366 0.0818162i
\(59\) 1.18769 2.05713i 0.154623 0.267816i −0.778298 0.627895i \(-0.783917\pi\)
0.932922 + 0.360079i \(0.117250\pi\)
\(60\) 2.36051 + 1.87499i 0.304740 + 0.242060i
\(61\) 2.04223 + 3.53724i 0.261480 + 0.452897i 0.966636 0.256156i \(-0.0824560\pi\)
−0.705155 + 0.709053i \(0.749123\pi\)
\(62\) 0.285766 0.0362923
\(63\) 11.2065 + 3.40936i 1.41188 + 0.429539i
\(64\) 0.730027 0.0912533
\(65\) −1.49516 2.58969i −0.185452 0.321212i
\(66\) 0 0
\(67\) 4.87584 8.44521i 0.595679 1.03175i −0.397772 0.917484i \(-0.630216\pi\)
0.993451 0.114262i \(-0.0364503\pi\)
\(68\) 4.32266 7.48706i 0.524199 0.907940i
\(69\) −0.538824 + 3.62235i −0.0648668 + 0.436080i
\(70\) −1.44819 2.50833i −0.173091 0.299803i
\(71\) 6.31707 0.749699 0.374849 0.927086i \(-0.377694\pi\)
0.374849 + 0.927086i \(0.377694\pi\)
\(72\) 5.18034 4.84406i 0.610509 0.570877i
\(73\) −11.6727 −1.36618 −0.683091 0.730333i \(-0.739365\pi\)
−0.683091 + 0.730333i \(0.739365\pi\)
\(74\) −2.89172 5.00861i −0.336156 0.582239i
\(75\) 5.09024 + 4.04326i 0.587770 + 0.466875i
\(76\) −3.99983 + 6.92792i −0.458812 + 0.794686i
\(77\) 0 0
\(78\) −2.86622 + 1.13131i −0.324536 + 0.128095i
\(79\) −2.25735 3.90985i −0.253972 0.439893i 0.710644 0.703552i \(-0.248404\pi\)
−0.964616 + 0.263659i \(0.915071\pi\)
\(80\) 1.72723 0.193110
\(81\) 0.603167 8.97977i 0.0670185 0.997752i
\(82\) 1.93920 0.214149
\(83\) −0.241002 0.417427i −0.0264534 0.0458186i 0.852496 0.522734i \(-0.175088\pi\)
−0.878949 + 0.476916i \(0.841755\pi\)
\(84\) 9.80500 3.87007i 1.06981 0.422259i
\(85\) −3.09671 + 5.36367i −0.335886 + 0.581771i
\(86\) −0.741570 + 1.28444i −0.0799656 + 0.138504i
\(87\) −1.46888 1.16676i −0.157481 0.125089i
\(88\) 0 0
\(89\) 16.0830 1.70480 0.852399 0.522891i \(-0.175147\pi\)
0.852399 + 0.522891i \(0.175147\pi\)
\(90\) −1.62546 + 1.51994i −0.171339 + 0.160216i
\(91\) −10.4564 −1.09613
\(92\) 1.64782 + 2.85410i 0.171797 + 0.297561i
\(93\) 0.109622 0.736955i 0.0113672 0.0764187i
\(94\) 4.26343 7.38448i 0.439739 0.761651i
\(95\) 2.86545 4.96310i 0.293989 0.509203i
\(96\) 1.46680 9.86084i 0.149704 1.00642i
\(97\) −4.00783 6.94176i −0.406933 0.704829i 0.587611 0.809143i \(-0.300068\pi\)
−0.994544 + 0.104315i \(0.966735\pi\)
\(98\) −5.47762 −0.553323
\(99\) 0 0
\(100\) 5.84996 0.584996
\(101\) −0.880657 1.52534i −0.0876287 0.151777i 0.818880 0.573965i \(-0.194596\pi\)
−0.906508 + 0.422188i \(0.861262\pi\)
\(102\) 4.99740 + 3.96951i 0.494816 + 0.393040i
\(103\) −1.34383 + 2.32759i −0.132412 + 0.229344i −0.924606 0.380925i \(-0.875605\pi\)
0.792194 + 0.610269i \(0.208939\pi\)
\(104\) −3.16554 + 5.48287i −0.310407 + 0.537640i
\(105\) −7.02422 + 2.77248i −0.685493 + 0.270566i
\(106\) 1.87378 + 3.24548i 0.181997 + 0.315229i
\(107\) −10.2764 −0.993456 −0.496728 0.867906i \(-0.665465\pi\)
−0.496728 + 0.867906i \(0.665465\pi\)
\(108\) −4.60113 6.66525i −0.442744 0.641364i
\(109\) 2.36284 0.226319 0.113160 0.993577i \(-0.463903\pi\)
0.113160 + 0.993577i \(0.463903\pi\)
\(110\) 0 0
\(111\) −14.0259 + 5.53605i −1.33128 + 0.525459i
\(112\) 3.01984 5.23052i 0.285348 0.494237i
\(113\) −0.766216 + 1.32713i −0.0720796 + 0.124845i −0.899813 0.436277i \(-0.856297\pi\)
0.827733 + 0.561122i \(0.189630\pi\)
\(114\) −4.62418 3.67306i −0.433094 0.344014i
\(115\) −1.18048 2.04465i −0.110080 0.190665i
\(116\) −1.68811 −0.156737
\(117\) 1.81800 + 7.82561i 0.168074 + 0.723478i
\(118\) 1.57801 0.145267
\(119\) 10.8284 + 18.7553i 0.992638 + 1.71930i
\(120\) −0.672725 + 4.52253i −0.0614111 + 0.412849i
\(121\) 0 0
\(122\) −1.35669 + 2.34986i −0.122829 + 0.212746i
\(123\) 0.743892 5.00096i 0.0670745 0.450922i
\(124\) −0.335242 0.580657i −0.0301057 0.0521445i
\(125\) −9.77397 −0.874211
\(126\) 1.76088 + 7.57975i 0.156872 + 0.675258i
\(127\) −7.65133 −0.678946 −0.339473 0.940616i \(-0.610249\pi\)
−0.339473 + 0.940616i \(0.610249\pi\)
\(128\) −5.51331 9.54934i −0.487313 0.844050i
\(129\) 3.02793 + 2.40514i 0.266595 + 0.211761i
\(130\) 0.993266 1.72039i 0.0871152 0.150888i
\(131\) 2.67956 4.64113i 0.234114 0.405498i −0.724901 0.688853i \(-0.758114\pi\)
0.959015 + 0.283356i \(0.0914477\pi\)
\(132\) 0 0
\(133\) −10.0197 17.3547i −0.868820 1.50484i
\(134\) 6.47825 0.559635
\(135\) 3.29621 + 4.77493i 0.283692 + 0.410960i
\(136\) 13.1127 1.12440
\(137\) −8.36560 14.4896i −0.714721 1.23793i −0.963067 0.269262i \(-0.913220\pi\)
0.248346 0.968672i \(-0.420113\pi\)
\(138\) −2.26298 + 0.893207i −0.192638 + 0.0760348i
\(139\) −6.87006 + 11.8993i −0.582711 + 1.00928i 0.412446 + 0.910982i \(0.364675\pi\)
−0.995157 + 0.0983023i \(0.968659\pi\)
\(140\) −3.39784 + 5.88524i −0.287170 + 0.497393i
\(141\) −17.4082 13.8276i −1.46603 1.16449i
\(142\) 2.09828 + 3.63433i 0.176084 + 0.304986i
\(143\) 0 0
\(144\) −4.43959 1.35066i −0.369966 0.112555i
\(145\) 1.20935 0.100431
\(146\) −3.87720 6.71550i −0.320879 0.555779i
\(147\) −2.10125 + 14.1261i −0.173309 + 1.16510i
\(148\) −6.78477 + 11.7516i −0.557704 + 0.965973i
\(149\) −2.77983 + 4.81480i −0.227732 + 0.394444i −0.957136 0.289640i \(-0.906464\pi\)
0.729403 + 0.684084i \(0.239798\pi\)
\(150\) −0.635387 + 4.27152i −0.0518791 + 0.348768i
\(151\) 0.0819538 + 0.141948i 0.00666930 + 0.0115516i 0.869341 0.494213i \(-0.164544\pi\)
−0.862671 + 0.505765i \(0.831210\pi\)
\(152\) −12.1334 −0.984147
\(153\) 12.1539 11.3649i 0.982587 0.918801i
\(154\) 0 0
\(155\) 0.240165 + 0.415978i 0.0192905 + 0.0334121i
\(156\) 5.66121 + 4.49679i 0.453260 + 0.360032i
\(157\) −11.9265 + 20.6573i −0.951839 + 1.64863i −0.210397 + 0.977616i \(0.567476\pi\)
−0.741442 + 0.671018i \(0.765858\pi\)
\(158\) 1.49961 2.59739i 0.119302 0.206638i
\(159\) 9.08848 3.58725i 0.720763 0.284488i
\(160\) 3.21353 + 5.56600i 0.254052 + 0.440031i
\(161\) −8.25568 −0.650638
\(162\) 5.36657 2.63571i 0.421638 0.207081i
\(163\) −4.19602 −0.328658 −0.164329 0.986406i \(-0.552546\pi\)
−0.164329 + 0.986406i \(0.552546\pi\)
\(164\) −2.27495 3.94033i −0.177644 0.307688i
\(165\) 0 0
\(166\) 0.160102 0.277306i 0.0124264 0.0215231i
\(167\) −7.92020 + 13.7182i −0.612883 + 1.06155i 0.377869 + 0.925859i \(0.376657\pi\)
−0.990752 + 0.135686i \(0.956676\pi\)
\(168\) 12.5193 + 9.94425i 0.965881 + 0.767215i
\(169\) 2.91415 + 5.04745i 0.224165 + 0.388265i
\(170\) −4.11442 −0.315562
\(171\) −11.2462 + 10.5162i −0.860022 + 0.804193i
\(172\) 3.47985 0.265336
\(173\) 1.30144 + 2.25417i 0.0989470 + 0.171381i 0.911249 0.411856i \(-0.135119\pi\)
−0.812302 + 0.583237i \(0.801786\pi\)
\(174\) 0.183352 1.23262i 0.0138999 0.0934450i
\(175\) −7.32717 + 12.6910i −0.553882 + 0.959352i
\(176\) 0 0
\(177\) 0.605335 4.06949i 0.0454997 0.305881i
\(178\) 5.34215 + 9.25287i 0.400411 + 0.693532i
\(179\) 7.58802 0.567155 0.283578 0.958949i \(-0.408479\pi\)
0.283578 + 0.958949i \(0.408479\pi\)
\(180\) 4.99531 + 1.51973i 0.372328 + 0.113274i
\(181\) −2.40019 −0.178405 −0.0892023 0.996014i \(-0.528432\pi\)
−0.0892023 + 0.996014i \(0.528432\pi\)
\(182\) −3.47319 6.01575i −0.257450 0.445917i
\(183\) 5.53957 + 4.40017i 0.409497 + 0.325270i
\(184\) −2.49930 + 4.32892i −0.184251 + 0.319132i
\(185\) 4.86055 8.41872i 0.357355 0.618956i
\(186\) 0.460396 0.181720i 0.0337579 0.0133243i
\(187\) 0 0
\(188\) −20.0064 −1.45911
\(189\) 20.2227 1.63345i 1.47099 0.118816i
\(190\) 3.80715 0.276200
\(191\) 8.25912 + 14.3052i 0.597609 + 1.03509i 0.993173 + 0.116650i \(0.0372157\pi\)
−0.395564 + 0.918438i \(0.629451\pi\)
\(192\) 1.17614 0.464227i 0.0848807 0.0335027i
\(193\) 4.06748 7.04508i 0.292784 0.507116i −0.681683 0.731647i \(-0.738752\pi\)
0.974467 + 0.224531i \(0.0720851\pi\)
\(194\) 2.66248 4.61155i 0.191155 0.331090i
\(195\) −4.05564 3.22146i −0.290431 0.230694i
\(196\) 6.42600 + 11.1302i 0.459000 + 0.795011i
\(197\) −22.9072 −1.63207 −0.816035 0.578003i \(-0.803832\pi\)
−0.816035 + 0.578003i \(0.803832\pi\)
\(198\) 0 0
\(199\) 9.27177 0.657259 0.328629 0.944459i \(-0.393413\pi\)
0.328629 + 0.944459i \(0.393413\pi\)
\(200\) 4.43642 + 7.68410i 0.313702 + 0.543348i
\(201\) 2.48510 16.7066i 0.175286 1.17839i
\(202\) 0.585039 1.01332i 0.0411632 0.0712967i
\(203\) 2.11439 3.66223i 0.148401 0.257038i
\(204\) 2.20316 14.8112i 0.154252 1.03699i
\(205\) 1.62975 + 2.82282i 0.113827 + 0.197154i
\(206\) −1.78547 −0.124400
\(207\) 1.43537 + 6.17860i 0.0997654 + 0.429442i
\(208\) 4.14243 0.287226
\(209\) 0 0
\(210\) −3.92822 3.12025i −0.271073 0.215318i
\(211\) −2.10529 + 3.64647i −0.144934 + 0.251033i −0.929348 0.369204i \(-0.879630\pi\)
0.784414 + 0.620237i \(0.212964\pi\)
\(212\) 4.39640 7.61478i 0.301946 0.522985i
\(213\) 10.1774 4.01705i 0.697344 0.275244i
\(214\) −3.41341 5.91219i −0.233336 0.404149i
\(215\) −2.49294 −0.170017
\(216\) 5.26567 11.0984i 0.358283 0.755153i
\(217\) 1.67959 0.114018
\(218\) 0.784842 + 1.35939i 0.0531562 + 0.0920693i
\(219\) −18.8058 + 7.42270i −1.27078 + 0.501580i
\(220\) 0 0
\(221\) −7.42687 + 12.8637i −0.499585 + 0.865307i
\(222\) −7.84383 6.23048i −0.526443 0.418162i
\(223\) 3.42953 + 5.94012i 0.229658 + 0.397780i 0.957707 0.287746i \(-0.0929058\pi\)
−0.728049 + 0.685526i \(0.759572\pi\)
\(224\) 22.4738 1.50159
\(225\) 10.7720 + 3.27717i 0.718132 + 0.218478i
\(226\) −1.01803 −0.0677181
\(227\) −14.0650 24.3612i −0.933524 1.61691i −0.777245 0.629198i \(-0.783383\pi\)
−0.156279 0.987713i \(-0.549950\pi\)
\(228\) −2.03862 + 13.7050i −0.135011 + 0.907638i
\(229\) 7.01735 12.1544i 0.463719 0.803186i −0.535423 0.844584i \(-0.679848\pi\)
0.999143 + 0.0413982i \(0.0131812\pi\)
\(230\) 0.784218 1.35831i 0.0517098 0.0895640i
\(231\) 0 0
\(232\) −1.28021 2.21739i −0.0840499 0.145579i
\(233\) −14.5096 −0.950557 −0.475278 0.879835i \(-0.657653\pi\)
−0.475278 + 0.879835i \(0.657653\pi\)
\(234\) −3.89835 + 3.64529i −0.254843 + 0.238300i
\(235\) 14.3324 0.934942
\(236\) −1.85122 3.20641i −0.120504 0.208719i
\(237\) −6.12310 4.86368i −0.397738 0.315930i
\(238\) −7.19353 + 12.4596i −0.466287 + 0.807633i
\(239\) 12.5741 21.7789i 0.813349 1.40876i −0.0971591 0.995269i \(-0.530976\pi\)
0.910508 0.413492i \(-0.135691\pi\)
\(240\) 2.78273 1.09835i 0.179625 0.0708984i
\(241\) −8.87110 15.3652i −0.571438 0.989759i −0.996419 0.0845570i \(-0.973053\pi\)
0.424981 0.905202i \(-0.360281\pi\)
\(242\) 0 0
\(243\) −4.73851 14.8508i −0.303976 0.952680i
\(244\) 6.36635 0.407564
\(245\) −4.60353 7.97355i −0.294109 0.509411i
\(246\) 3.12424 1.23315i 0.199194 0.0786226i
\(247\) 6.87222 11.9030i 0.437269 0.757371i
\(248\) 0.508474 0.880703i 0.0322881 0.0559247i
\(249\) −0.653721 0.519261i −0.0414279 0.0329068i
\(250\) −3.24653 5.62315i −0.205328 0.355639i
\(251\) −21.8775 −1.38090 −0.690448 0.723382i \(-0.742586\pi\)
−0.690448 + 0.723382i \(0.742586\pi\)
\(252\) 13.3358 12.4701i 0.840076 0.785541i
\(253\) 0 0
\(254\) −2.54147 4.40195i −0.159466 0.276203i
\(255\) −1.57832 + 10.6106i −0.0988383 + 0.664461i
\(256\) 4.39263 7.60827i 0.274540 0.475517i
\(257\) −2.58186 + 4.47191i −0.161052 + 0.278950i −0.935246 0.353998i \(-0.884822\pi\)
0.774194 + 0.632948i \(0.218155\pi\)
\(258\) −0.377961 + 2.54092i −0.0235308 + 0.158191i
\(259\) −16.9961 29.4381i −1.05608 1.82919i
\(260\) −4.66095 −0.289060
\(261\) −3.10845 0.945687i −0.192408 0.0585366i
\(262\) 3.56017 0.219948
\(263\) 13.9491 + 24.1605i 0.860135 + 1.48980i 0.871798 + 0.489866i \(0.162954\pi\)
−0.0116625 + 0.999932i \(0.503712\pi\)
\(264\) 0 0
\(265\) −3.14954 + 5.45516i −0.193475 + 0.335108i
\(266\) 6.65631 11.5291i 0.408124 0.706892i
\(267\) 25.9113 10.2273i 1.58575 0.625899i
\(268\) −7.59987 13.1634i −0.464236 0.804080i
\(269\) 3.01959 0.184108 0.0920538 0.995754i \(-0.470657\pi\)
0.0920538 + 0.995754i \(0.470657\pi\)
\(270\) −1.65223 + 3.48241i −0.100552 + 0.211933i
\(271\) −25.3748 −1.54141 −0.770705 0.637192i \(-0.780096\pi\)
−0.770705 + 0.637192i \(0.780096\pi\)
\(272\) −4.28981 7.43017i −0.260108 0.450520i
\(273\) −16.8462 + 6.64926i −1.01958 + 0.402431i
\(274\) 5.55744 9.62577i 0.335737 0.581514i
\(275\) 0 0
\(276\) 4.46973 + 3.55038i 0.269046 + 0.213708i
\(277\) 5.28219 + 9.14903i 0.317376 + 0.549712i 0.979940 0.199294i \(-0.0638649\pi\)
−0.662564 + 0.749006i \(0.730532\pi\)
\(278\) −9.12784 −0.547451
\(279\) −0.292022 1.25701i −0.0174829 0.0752554i
\(280\) −10.3073 −0.615976
\(281\) 11.2853 + 19.5466i 0.673222 + 1.16605i 0.976985 + 0.213307i \(0.0684235\pi\)
−0.303763 + 0.952748i \(0.598243\pi\)
\(282\) 2.17297 14.6082i 0.129398 0.869908i
\(283\) 2.93862 5.08983i 0.174683 0.302559i −0.765369 0.643592i \(-0.777443\pi\)
0.940051 + 0.341033i \(0.110777\pi\)
\(284\) 4.92314 8.52713i 0.292135 0.505992i
\(285\) 1.46045 9.81817i 0.0865095 0.581578i
\(286\) 0 0
\(287\) 11.3977 0.672782
\(288\) −3.90740 16.8195i −0.230246 0.991098i
\(289\) 13.7644 0.809672
\(290\) 0.401698 + 0.695761i 0.0235885 + 0.0408565i
\(291\) −10.8713 8.63524i −0.637286 0.506207i
\(292\) −9.09697 + 15.7564i −0.532360 + 0.922074i
\(293\) −3.54705 + 6.14368i −0.207221 + 0.358918i −0.950838 0.309688i \(-0.899775\pi\)
0.743617 + 0.668606i \(0.233109\pi\)
\(294\) −8.82496 + 3.48324i −0.514682 + 0.203147i
\(295\) 1.32620 + 2.29704i 0.0772142 + 0.133739i
\(296\) −20.5814 −1.19627
\(297\) 0 0
\(298\) −3.69339 −0.213953
\(299\) −2.83116 4.90371i −0.163730 0.283589i
\(300\) 9.42483 3.72001i 0.544143 0.214775i
\(301\) −4.35858 + 7.54928i −0.251224 + 0.435133i
\(302\) −0.0544436 + 0.0942990i −0.00313287 + 0.00542630i
\(303\) −2.38879 1.89746i −0.137233 0.109006i
\(304\) 3.96944 + 6.87527i 0.227663 + 0.394324i
\(305\) −4.56080 −0.261150
\(306\) 10.5755 + 3.21740i 0.604562 + 0.183926i
\(307\) −18.5370 −1.05796 −0.528981 0.848633i \(-0.677426\pi\)
−0.528981 + 0.848633i \(0.677426\pi\)
\(308\) 0 0
\(309\) −0.684919 + 4.60451i −0.0389637 + 0.261941i
\(310\) −0.159546 + 0.276342i −0.00906162 + 0.0156952i
\(311\) −3.43812 + 5.95500i −0.194958 + 0.337677i −0.946887 0.321567i \(-0.895790\pi\)
0.751929 + 0.659244i \(0.229124\pi\)
\(312\) −1.61340 + 10.8464i −0.0913408 + 0.614057i
\(313\) 12.6629 + 21.9328i 0.715749 + 1.23971i 0.962670 + 0.270679i \(0.0872480\pi\)
−0.246920 + 0.969036i \(0.579419\pi\)
\(314\) −15.8460 −0.894244
\(315\) −9.55364 + 8.93346i −0.538287 + 0.503343i
\(316\) −7.03698 −0.395861
\(317\) −5.48963 9.50832i −0.308328 0.534041i 0.669668 0.742660i \(-0.266436\pi\)
−0.977997 + 0.208620i \(0.933103\pi\)
\(318\) 5.08265 + 4.03723i 0.285021 + 0.226397i
\(319\) 0 0
\(320\) −0.407582 + 0.705953i −0.0227845 + 0.0394640i
\(321\) −16.5562 + 6.53480i −0.924079 + 0.364737i
\(322\) −2.74221 4.74964i −0.152817 0.264687i
\(323\) −28.4669 −1.58394
\(324\) −11.6513 7.81247i −0.647295 0.434026i
\(325\) −10.0510 −0.557527
\(326\) −1.39375 2.41405i −0.0771928 0.133702i
\(327\) 3.80676 1.50254i 0.210514 0.0830907i
\(328\) 3.45050 5.97644i 0.190522 0.329994i
\(329\) 25.0583 43.4023i 1.38151 2.39284i
\(330\) 0 0
\(331\) 1.85513 + 3.21317i 0.101967 + 0.176612i 0.912495 0.409088i \(-0.134153\pi\)
−0.810528 + 0.585700i \(0.800820\pi\)
\(332\) −0.751289 −0.0412323
\(333\) −19.0766 + 17.8382i −1.04539 + 0.977528i
\(334\) −10.5231 −0.575798
\(335\) 5.44448 + 9.43012i 0.297464 + 0.515222i
\(336\) 1.53914 10.3472i 0.0839670 0.564485i
\(337\) 16.0976 27.8818i 0.876891 1.51882i 0.0221561 0.999755i \(-0.492947\pi\)
0.854735 0.519065i \(-0.173720\pi\)
\(338\) −1.93593 + 3.35312i −0.105301 + 0.182386i
\(339\) −0.390522 + 2.62536i −0.0212102 + 0.142590i
\(340\) 4.82678 + 8.36023i 0.261769 + 0.453397i
\(341\) 0 0
\(342\) −9.78571 2.97712i −0.529151 0.160984i
\(343\) −4.86291 −0.262572
\(344\) 2.63901 + 4.57090i 0.142286 + 0.246446i
\(345\) −3.20207 2.54346i −0.172394 0.136935i
\(346\) −0.864576 + 1.49749i −0.0464799 + 0.0805055i
\(347\) 10.7612 18.6390i 0.577694 1.00060i −0.418049 0.908424i \(-0.637286\pi\)
0.995743 0.0921708i \(-0.0293806\pi\)
\(348\) −2.71971 + 1.07348i −0.145792 + 0.0575444i
\(349\) 8.40998 + 14.5665i 0.450176 + 0.779727i 0.998397 0.0566062i \(-0.0180280\pi\)
−0.548221 + 0.836334i \(0.684695\pi\)
\(350\) −9.73518 −0.520367
\(351\) 7.90531 + 11.4517i 0.421954 + 0.611248i
\(352\) 0 0
\(353\) −1.56543 2.71140i −0.0833193 0.144313i 0.821355 0.570418i \(-0.193219\pi\)
−0.904674 + 0.426105i \(0.859885\pi\)
\(354\) 2.54232 1.00346i 0.135123 0.0533334i
\(355\) −3.52690 + 6.10876i −0.187188 + 0.324219i
\(356\) 12.5341 21.7098i 0.664308 1.15062i
\(357\) 29.3722 + 23.3308i 1.55454 + 1.23480i
\(358\) 2.52044 + 4.36553i 0.133209 + 0.230725i
\(359\) 8.48869 0.448016 0.224008 0.974587i \(-0.428086\pi\)
0.224008 + 0.974587i \(0.428086\pi\)
\(360\) 1.79207 + 7.71401i 0.0944505 + 0.406564i
\(361\) 7.34092 0.386364
\(362\) −0.797247 1.38087i −0.0419024 0.0725770i
\(363\) 0 0
\(364\) −8.14907 + 14.1146i −0.427127 + 0.739806i
\(365\) 6.51699 11.2878i 0.341115 0.590828i
\(366\) −0.691474 + 4.64858i −0.0361439 + 0.242985i
\(367\) 5.50548 + 9.53578i 0.287384 + 0.497763i 0.973184 0.230026i \(-0.0738811\pi\)
−0.685801 + 0.727789i \(0.740548\pi\)
\(368\) 3.27059 0.170491
\(369\) −1.98165 8.53007i −0.103161 0.444058i
\(370\) 6.45792 0.335731
\(371\) 11.0131 + 19.0753i 0.571773 + 0.990339i
\(372\) −0.909350 0.722311i −0.0471476 0.0374501i
\(373\) −5.50342 + 9.53220i −0.284956 + 0.493558i −0.972599 0.232491i \(-0.925312\pi\)
0.687642 + 0.726050i \(0.258646\pi\)
\(374\) 0 0
\(375\) −15.7468 + 6.21531i −0.813161 + 0.320957i
\(376\) −15.1722 26.2790i −0.782446 1.35524i
\(377\) 2.90039 0.149378
\(378\) 7.65694 + 11.0919i 0.393831 + 0.570508i
\(379\) 25.3868 1.30403 0.652017 0.758204i \(-0.273923\pi\)
0.652017 + 0.758204i \(0.273923\pi\)
\(380\) −4.46631 7.73587i −0.229117 0.396842i
\(381\) −12.3270 + 4.86551i −0.631532 + 0.249268i
\(382\) −5.48670 + 9.50324i −0.280724 + 0.486228i
\(383\) 6.05737 10.4917i 0.309517 0.536099i −0.668740 0.743497i \(-0.733166\pi\)
0.978257 + 0.207397i \(0.0664993\pi\)
\(384\) −14.9549 11.8789i −0.763166 0.606195i
\(385\) 0 0
\(386\) 5.40422 0.275068
\(387\) 6.40773 + 1.94943i 0.325723 + 0.0990950i
\(388\) −12.4938 −0.634278
\(389\) −7.17554 12.4284i −0.363814 0.630145i 0.624771 0.780808i \(-0.285192\pi\)
−0.988585 + 0.150663i \(0.951859\pi\)
\(390\) 0.506244 3.40333i 0.0256347 0.172334i
\(391\) −5.86377 + 10.1563i −0.296544 + 0.513629i
\(392\) −9.74654 + 16.8815i −0.492275 + 0.852645i
\(393\) 1.36571 9.18125i 0.0688908 0.463133i
\(394\) −7.60886 13.1789i −0.383329 0.663945i
\(395\) 5.04123 0.253652
\(396\) 0 0
\(397\) −5.03882 −0.252891 −0.126446 0.991974i \(-0.540357\pi\)
−0.126446 + 0.991974i \(0.540357\pi\)
\(398\) 3.07971 + 5.33422i 0.154372 + 0.267380i
\(399\) −27.1786 21.5884i −1.36063 1.08077i
\(400\) 2.90275 5.02772i 0.145138 0.251386i
\(401\) 9.10009 15.7618i 0.454437 0.787108i −0.544219 0.838943i \(-0.683174\pi\)
0.998656 + 0.0518357i \(0.0165072\pi\)
\(402\) 10.4371 4.11954i 0.520554 0.205464i
\(403\) 0.575989 + 0.997641i 0.0286920 + 0.0496961i
\(404\) −2.74532 −0.136585
\(405\) 8.34689 + 5.59678i 0.414761 + 0.278106i
\(406\) 2.80926 0.139421
\(407\) 0 0
\(408\) 21.1257 8.33840i 1.04588 0.412812i
\(409\) −8.21523 + 14.2292i −0.406217 + 0.703588i −0.994462 0.105094i \(-0.966486\pi\)
0.588245 + 0.808682i \(0.299819\pi\)
\(410\) −1.08268 + 1.87526i −0.0534697 + 0.0926123i
\(411\) −22.6918 18.0245i −1.11930 0.889081i
\(412\) 2.09460 + 3.62796i 0.103194 + 0.178737i
\(413\) 9.27473 0.456380
\(414\) −3.07789 + 2.87808i −0.151270 + 0.141450i
\(415\) 0.538216 0.0264200
\(416\) 7.70703 + 13.3490i 0.377868 + 0.654487i
\(417\) −3.50150 + 23.5396i −0.171469 + 1.15274i
\(418\) 0 0
\(419\) 8.70324 15.0745i 0.425181 0.736435i −0.571256 0.820772i \(-0.693544\pi\)
0.996437 + 0.0843365i \(0.0268771\pi\)
\(420\) −1.73180 + 11.6424i −0.0845032 + 0.568090i
\(421\) −2.27432 3.93924i −0.110844 0.191987i 0.805267 0.592912i \(-0.202022\pi\)
−0.916111 + 0.400925i \(0.868689\pi\)
\(422\) −2.79717 −0.136164
\(423\) −36.8393 11.2076i −1.79119 0.544934i
\(424\) 13.3363 0.647670
\(425\) 10.4086 + 18.0282i 0.504889 + 0.874494i
\(426\) 5.69161 + 4.52094i 0.275760 + 0.219040i
\(427\) −7.97396 + 13.8113i −0.385887 + 0.668376i
\(428\) −8.00879 + 13.8716i −0.387120 + 0.670511i
\(429\) 0 0
\(430\) −0.828055 1.43423i −0.0399323 0.0691648i
\(431\) 12.4848 0.601372 0.300686 0.953723i \(-0.402784\pi\)
0.300686 + 0.953723i \(0.402784\pi\)
\(432\) −8.01150 + 0.647113i −0.385453 + 0.0311342i
\(433\) 28.6862 1.37857 0.689284 0.724491i \(-0.257925\pi\)
0.689284 + 0.724491i \(0.257925\pi\)
\(434\) 0.557892 + 0.966298i 0.0267797 + 0.0463838i
\(435\) 1.94837 0.769030i 0.0934174 0.0368722i
\(436\) 1.84146 3.18949i 0.0881897 0.152749i
\(437\) 5.42585 9.39785i 0.259554 0.449560i
\(438\) −10.5169 8.35378i −0.502519 0.399159i
\(439\) 2.05404 + 3.55769i 0.0980338 + 0.169799i 0.910871 0.412692i \(-0.135411\pi\)
−0.812837 + 0.582491i \(0.802078\pi\)
\(440\) 0 0
\(441\) 5.59753 + 24.0947i 0.266549 + 1.14737i
\(442\) −9.86764 −0.469356
\(443\) 10.6149 + 18.3855i 0.504327 + 0.873520i 0.999987 + 0.00500337i \(0.00159263\pi\)
−0.495661 + 0.868516i \(0.665074\pi\)
\(444\) −3.45803 + 23.2473i −0.164111 + 1.10327i
\(445\) −8.97935 + 15.5527i −0.425662 + 0.737268i
\(446\) −2.27831 + 3.94614i −0.107881 + 0.186855i
\(447\) −1.41681 + 9.52481i −0.0670129 + 0.450508i
\(448\) 1.42521 + 2.46854i 0.0673348 + 0.116627i
\(449\) 25.8949 1.22205 0.611027 0.791610i \(-0.290757\pi\)
0.611027 + 0.791610i \(0.290757\pi\)
\(450\) 1.69261 + 7.28586i 0.0797903 + 0.343459i
\(451\) 0 0
\(452\) 1.19428 + 2.06856i 0.0561744 + 0.0972970i
\(453\) 0.222301 + 0.176577i 0.0104446 + 0.00829631i
\(454\) 9.34364 16.1837i 0.438519 0.759537i
\(455\) 5.83792 10.1116i 0.273686 0.474038i
\(456\) −19.5480 + 7.71567i −0.915420 + 0.361319i
\(457\) 5.15193 + 8.92340i 0.240997 + 0.417419i 0.960999 0.276553i \(-0.0891923\pi\)
−0.720002 + 0.693972i \(0.755859\pi\)
\(458\) 9.32354 0.435660
\(459\) 12.3541 26.0387i 0.576641 1.21538i
\(460\) −3.67998 −0.171580
\(461\) 12.7266 + 22.0432i 0.592738 + 1.02665i 0.993862 + 0.110628i \(0.0352863\pi\)
−0.401124 + 0.916024i \(0.631380\pi\)
\(462\) 0 0
\(463\) 19.9277 34.5158i 0.926119 1.60409i 0.136368 0.990658i \(-0.456457\pi\)
0.789751 0.613427i \(-0.210210\pi\)
\(464\) −0.837642 + 1.45084i −0.0388866 + 0.0673535i
\(465\) 0.651450 + 0.517457i 0.0302103 + 0.0239965i
\(466\) −4.81952 8.34765i −0.223260 0.386697i
\(467\) −17.3769 −0.804108 −0.402054 0.915616i \(-0.631704\pi\)
−0.402054 + 0.915616i \(0.631704\pi\)
\(468\) 11.9803 + 3.64477i 0.553789 + 0.168480i
\(469\) 38.0759 1.75818
\(470\) 4.76065 + 8.24568i 0.219592 + 0.380345i
\(471\) −6.07866 + 40.8650i −0.280090 + 1.88296i
\(472\) 2.80781 4.86327i 0.129240 0.223850i
\(473\) 0 0
\(474\) 0.764314 5.13826i 0.0351061 0.236008i
\(475\) −9.63123 16.6818i −0.441911 0.765412i
\(476\) 33.7560 1.54720
\(477\) 12.3613 11.5588i 0.565983 0.529241i
\(478\) 16.7064 0.764134
\(479\) 10.9480 + 18.9625i 0.500226 + 0.866417i 1.00000 0.000261184i \(8.31374e-5\pi\)
−0.499774 + 0.866156i \(0.666584\pi\)
\(480\) 8.71674 + 6.92385i 0.397863 + 0.316029i
\(481\) 11.6571 20.1907i 0.531517 0.920615i
\(482\) 5.89325 10.2074i 0.268430 0.464935i
\(483\) −13.3007 + 5.24982i −0.605202 + 0.238875i
\(484\) 0 0
\(485\) 8.95046 0.406420
\(486\) 6.97000 7.65900i 0.316166 0.347419i
\(487\) 3.27116 0.148230 0.0741152 0.997250i \(-0.476387\pi\)
0.0741152 + 0.997250i \(0.476387\pi\)
\(488\) 4.82803 + 8.36240i 0.218555 + 0.378548i
\(489\) −6.76019 + 2.66827i −0.305706 + 0.120663i
\(490\) 3.05822 5.29699i 0.138156 0.239294i
\(491\) 3.61195 6.25608i 0.163005 0.282333i −0.772940 0.634479i \(-0.781215\pi\)
0.935945 + 0.352146i \(0.114548\pi\)
\(492\) −6.17083 4.90159i −0.278203 0.220981i
\(493\) −3.00358 5.20235i −0.135274 0.234302i
\(494\) 9.13071 0.410810
\(495\) 0 0
\(496\) −0.665390 −0.0298769
\(497\) 12.3326 + 21.3608i 0.553194 + 0.958161i
\(498\) 0.0816004 0.548575i 0.00365660 0.0245822i
\(499\) −7.41726 + 12.8471i −0.332042 + 0.575114i −0.982912 0.184076i \(-0.941071\pi\)
0.650870 + 0.759189i \(0.274404\pi\)
\(500\) −7.61724 + 13.1934i −0.340653 + 0.590029i
\(501\) −4.03674 + 27.1378i −0.180348 + 1.21243i
\(502\) −7.26683 12.5865i −0.324335 0.561764i
\(503\) −32.9813 −1.47057 −0.735283 0.677760i \(-0.762951\pi\)
−0.735283 + 0.677760i \(0.762951\pi\)
\(504\) 26.4933 + 8.06007i 1.18010 + 0.359024i
\(505\) 1.96673 0.0875181
\(506\) 0 0
\(507\) 7.90466 + 6.27880i 0.351058 + 0.278851i
\(508\) −5.96298 + 10.3282i −0.264565 + 0.458239i
\(509\) −19.3347 + 33.4887i −0.856995 + 1.48436i 0.0177866 + 0.999842i \(0.494338\pi\)
−0.874782 + 0.484517i \(0.838995\pi\)
\(510\) −6.62872 + 2.61638i −0.293525 + 0.115855i
\(511\) −22.7882 39.4704i −1.00809 1.74607i
\(512\) −16.2170 −0.716698
\(513\) −11.4315 + 24.0941i −0.504712 + 1.06378i
\(514\) −3.43036 −0.151307
\(515\) −1.50055 2.59904i −0.0661223 0.114527i
\(516\) 5.60638 2.21285i 0.246807 0.0974155i
\(517\) 0 0
\(518\) 11.2908 19.5563i 0.496091 0.859255i
\(519\) 3.53018 + 2.80408i 0.154958 + 0.123086i
\(520\) −3.53471 6.12230i −0.155007 0.268481i
\(521\) −17.4844 −0.766005 −0.383002 0.923747i \(-0.625110\pi\)
−0.383002 + 0.923747i \(0.625110\pi\)
\(522\) −0.488433 2.10247i −0.0213781 0.0920226i
\(523\) 14.4881 0.633522 0.316761 0.948505i \(-0.397405\pi\)
0.316761 + 0.948505i \(0.397405\pi\)
\(524\) −4.17657 7.23404i −0.182454 0.316020i
\(525\) −3.73448 + 25.1058i −0.162986 + 1.09571i
\(526\) −9.26664 + 16.0503i −0.404045 + 0.699826i
\(527\) 1.19296 2.06627i 0.0519663 0.0900082i
\(528\) 0 0
\(529\) 9.26470 + 16.0469i 0.402813 + 0.697693i
\(530\) −4.18461 −0.181768
\(531\) −1.61255 6.94126i −0.0699788 0.301225i
\(532\) −31.2350 −1.35421
\(533\) 3.90865 + 6.76998i 0.169302 + 0.293240i
\(534\) 14.4906 + 11.5102i 0.627071 + 0.498093i
\(535\) 5.73743 9.93751i 0.248051 0.429636i
\(536\) 11.5270 19.9653i 0.497890 0.862371i
\(537\) 12.2250 4.82525i 0.527548 0.208225i
\(538\) 1.00299 + 1.73722i 0.0432418 + 0.0748971i
\(539\) 0 0
\(540\) 9.01432 0.728114i 0.387915 0.0313330i
\(541\) 33.0983 1.42301 0.711503 0.702683i \(-0.248015\pi\)
0.711503 + 0.702683i \(0.248015\pi\)
\(542\) −8.42851 14.5986i −0.362035 0.627064i
\(543\) −3.86693 + 1.52629i −0.165946 + 0.0654994i
\(544\) 15.9625 27.6478i 0.684385 1.18539i
\(545\) −1.31920 + 2.28493i −0.0565084 + 0.0978754i
\(546\) −9.42108 7.48332i −0.403185 0.320257i
\(547\) −4.60707 7.97968i −0.196984 0.341186i 0.750565 0.660796i \(-0.229781\pi\)
−0.947549 + 0.319610i \(0.896448\pi\)
\(548\) −26.0786 −1.11402
\(549\) 11.7229 + 3.56645i 0.500319 + 0.152213i
\(550\) 0 0
\(551\) 2.77927 + 4.81383i 0.118401 + 0.205076i
\(552\) −1.27384 + 8.56362i −0.0542180 + 0.364492i
\(553\) 8.81393 15.2662i 0.374807 0.649184i
\(554\) −3.50907 + 6.07788i −0.149086 + 0.258225i
\(555\) 2.47730 16.6542i 0.105156 0.706931i
\(556\) 10.7082 + 18.5472i 0.454129 + 0.786575i
\(557\) 37.0518 1.56994 0.784968 0.619536i \(-0.212679\pi\)
0.784968 + 0.619536i \(0.212679\pi\)
\(558\) 0.626185 0.585535i 0.0265085 0.0247877i
\(559\) −5.97883 −0.252877
\(560\) 3.37202 + 5.84052i 0.142494 + 0.246807i
\(561\) 0 0
\(562\) −7.49703 + 12.9852i −0.316243 + 0.547749i
\(563\) 13.4970 23.3775i 0.568832 0.985246i −0.427850 0.903850i \(-0.640729\pi\)
0.996682 0.0813962i \(-0.0259379\pi\)
\(564\) −32.2322 + 12.7221i −1.35722 + 0.535698i
\(565\) −0.855575 1.48190i −0.0359943 0.0623440i
\(566\) 3.90436 0.164113
\(567\) 31.5420 15.4914i 1.32464 0.650576i
\(568\) 14.9342 0.626625
\(569\) 13.7379 + 23.7947i 0.575921 + 0.997524i 0.995941 + 0.0900095i \(0.0286898\pi\)
−0.420020 + 0.907515i \(0.637977\pi\)
\(570\) 6.13368 2.42098i 0.256911 0.101404i
\(571\) 19.5052 33.7840i 0.816266 1.41381i −0.0921492 0.995745i \(-0.529374\pi\)
0.908415 0.418069i \(-0.137293\pi\)
\(572\) 0 0
\(573\) 22.4030 + 17.7950i 0.935897 + 0.743398i
\(574\) 3.78585 + 6.55728i 0.158018 + 0.273696i
\(575\) −7.93558 −0.330937
\(576\) 1.59967 1.49583i 0.0666530 0.0623261i
\(577\) −29.1659 −1.21419 −0.607096 0.794629i \(-0.707666\pi\)
−0.607096 + 0.794629i \(0.707666\pi\)
\(578\) 4.57199 + 7.91893i 0.190170 + 0.329384i
\(579\) 2.07310 13.9368i 0.0861550 0.579195i
\(580\) 0.942493 1.63245i 0.0391349 0.0677836i
\(581\) 0.941002 1.62986i 0.0390393 0.0676181i
\(582\) 1.35700 9.12273i 0.0562496 0.378149i
\(583\) 0 0
\(584\) −27.5954 −1.14191
\(585\) −8.58257 2.61108i −0.354846 0.107955i
\(586\) −4.71276 −0.194682
\(587\) 2.54397 + 4.40628i 0.105001 + 0.181867i 0.913739 0.406303i \(-0.133182\pi\)
−0.808738 + 0.588169i \(0.799849\pi\)
\(588\) 17.4306 + 13.8454i 0.718826 + 0.570975i
\(589\) −1.10387 + 1.91196i −0.0454842 + 0.0787809i
\(590\) −0.881020 + 1.52597i −0.0362710 + 0.0628232i
\(591\) −36.9057 + 14.5668i −1.51810 + 0.599197i
\(592\) 6.73321 + 11.6623i 0.276733 + 0.479316i
\(593\) 3.46422 0.142258 0.0711292 0.997467i \(-0.477340\pi\)
0.0711292 + 0.997467i \(0.477340\pi\)
\(594\) 0 0
\(595\) −24.1825 −0.991386
\(596\) 4.33286 + 7.50473i 0.177481 + 0.307406i
\(597\) 14.9377 5.89596i 0.611360 0.241306i
\(598\) 1.88080 3.25763i 0.0769114 0.133215i
\(599\) −12.4374 + 21.5422i −0.508179 + 0.880192i 0.491776 + 0.870722i \(0.336348\pi\)
−0.999955 + 0.00947029i \(0.996985\pi\)
\(600\) 12.0338 + 9.55868i 0.491280 + 0.390231i
\(601\) −5.53406 9.58527i −0.225739 0.390991i 0.730802 0.682590i \(-0.239146\pi\)
−0.956541 + 0.291598i \(0.905813\pi\)
\(602\) −5.79098 −0.236023
\(603\) −6.62007 28.4962i −0.269590 1.16045i
\(604\) 0.255479 0.0103953
\(605\) 0 0
\(606\) 0.298180 2.00458i 0.0121127 0.0814304i
\(607\) 13.9805 24.2149i 0.567451 0.982854i −0.429366 0.903131i \(-0.641263\pi\)
0.996817 0.0797235i \(-0.0254037\pi\)
\(608\) −14.7704 + 25.5830i −0.599017 + 1.03753i
\(609\) 1.07765 7.24475i 0.0436687 0.293572i
\(610\) −1.51492 2.62391i −0.0613371 0.106239i
\(611\) 34.3734 1.39060
\(612\) −5.86899 25.2632i −0.237240 1.02120i
\(613\) 10.9923 0.443974 0.221987 0.975050i \(-0.428746\pi\)
0.221987 + 0.975050i \(0.428746\pi\)
\(614\) −6.15726 10.6647i −0.248487 0.430391i
\(615\) 4.42073 + 3.51146i 0.178261 + 0.141596i
\(616\) 0 0
\(617\) −9.31311 + 16.1308i −0.374932 + 0.649401i −0.990317 0.138826i \(-0.955667\pi\)
0.615385 + 0.788227i \(0.289001\pi\)
\(618\) −2.87656 + 1.13539i −0.115712 + 0.0456720i
\(619\) −1.34424 2.32829i −0.0540296 0.0935820i 0.837746 0.546061i \(-0.183873\pi\)
−0.891775 + 0.452479i \(0.850540\pi\)
\(620\) 0.748679 0.0300677
\(621\) 6.24152 + 9.04154i 0.250463 + 0.362825i
\(622\) −4.56803 −0.183161
\(623\) 31.3985 + 54.3837i 1.25795 + 2.17884i
\(624\) 6.67385 2.63419i 0.267168 0.105452i
\(625\) −3.92596 + 6.79996i −0.157038 + 0.271998i
\(626\) −8.41222 + 14.5704i −0.336220 + 0.582350i
\(627\) 0 0
\(628\) 18.5896 + 32.1981i 0.741805 + 1.28484i
\(629\) −48.2873 −1.92534
\(630\) −8.31292 2.52905i −0.331195 0.100760i
\(631\) −39.2289 −1.56168 −0.780839 0.624732i \(-0.785208\pi\)
−0.780839 + 0.624732i \(0.785208\pi\)
\(632\) −5.33662 9.24329i −0.212279 0.367678i
\(633\) −1.07302 + 7.21356i −0.0426485 + 0.286713i
\(634\) 3.64688 6.31657i 0.144836 0.250863i
\(635\) 4.27183 7.39902i 0.169522 0.293621i
\(636\) 2.24074 15.0638i 0.0888510 0.597319i
\(637\) −11.0407 19.1230i −0.437447 0.757681i
\(638\) 0 0
\(639\) 13.8423 12.9437i 0.547593 0.512045i
\(640\) 12.3126 0.486698
\(641\) −12.8745 22.2993i −0.508511 0.880768i −0.999951 0.00985628i \(-0.996863\pi\)
0.491440 0.870911i \(-0.336471\pi\)
\(642\) −9.25891 7.35450i −0.365420 0.290259i
\(643\) 6.66603 11.5459i 0.262883 0.455326i −0.704124 0.710077i \(-0.748660\pi\)
0.967007 + 0.254751i \(0.0819935\pi\)
\(644\) −6.43397 + 11.1440i −0.253534 + 0.439134i
\(645\) −4.01636 + 1.58527i −0.158144 + 0.0624199i
\(646\) −9.45557 16.3775i −0.372024 0.644365i
\(647\) 23.8506 0.937663 0.468832 0.883288i \(-0.344675\pi\)
0.468832 + 0.883288i \(0.344675\pi\)
\(648\) 1.42595 21.2291i 0.0560165 0.833957i
\(649\) 0 0
\(650\) −3.33853 5.78250i −0.130948 0.226808i
\(651\) 2.70597 1.06806i 0.106056 0.0418605i
\(652\) −3.27013 + 5.66402i −0.128068 + 0.221820i
\(653\) −6.36247 + 11.0201i −0.248983 + 0.431251i −0.963244 0.268629i \(-0.913430\pi\)
0.714261 + 0.699879i \(0.246763\pi\)
\(654\) 2.12889 + 1.69102i 0.0832464 + 0.0661239i
\(655\) 2.99206 + 5.18240i 0.116909 + 0.202493i
\(656\) −4.51533 −0.176294
\(657\) −25.5778 + 23.9173i −0.997883 + 0.933105i
\(658\) 33.2935 1.29792
\(659\) 13.6263 + 23.6015i 0.530806 + 0.919383i 0.999354 + 0.0359452i \(0.0114442\pi\)
−0.468547 + 0.883438i \(0.655223\pi\)
\(660\) 0 0
\(661\) −21.8220 + 37.7968i −0.848777 + 1.47012i 0.0335234 + 0.999438i \(0.489327\pi\)
−0.882300 + 0.470687i \(0.844006\pi\)
\(662\) −1.23240 + 2.13458i −0.0478985 + 0.0829627i
\(663\) −3.78530 + 25.4474i −0.147009 + 0.988296i
\(664\) −0.569753 0.986841i −0.0221107 0.0382969i
\(665\) 22.3765 0.867724
\(666\) −16.5991 5.04997i −0.643203 0.195682i
\(667\) 2.28996 0.0886675
\(668\) 12.3450 + 21.3822i 0.477644 + 0.827304i
\(669\) 9.30265 + 7.38924i 0.359661 + 0.285685i
\(670\) −3.61688 + 6.26462i −0.139732 + 0.242023i
\(671\) 0 0
\(672\) 36.2074 14.2912i 1.39673 0.551294i
\(673\) 13.3433 + 23.1113i 0.514348 + 0.890877i 0.999861 + 0.0166477i \(0.00529938\pi\)
−0.485513 + 0.874229i \(0.661367\pi\)
\(674\) 21.3879 0.823831
\(675\) 19.4386 1.57012i 0.748194 0.0604339i
\(676\) 9.08443 0.349401
\(677\) −13.5415 23.4546i −0.520443 0.901434i −0.999717 0.0237689i \(-0.992433\pi\)
0.479274 0.877665i \(-0.340900\pi\)
\(678\) −1.64014 + 0.647367i −0.0629891 + 0.0248620i
\(679\) 15.6487 27.1044i 0.600543 1.04017i
\(680\) −7.32095 + 12.6803i −0.280746 + 0.486266i
\(681\) −38.1514 30.3043i −1.46196 1.16126i
\(682\) 0 0
\(683\) −16.7343 −0.640322 −0.320161 0.947363i \(-0.603737\pi\)
−0.320161 + 0.947363i \(0.603737\pi\)
\(684\) 5.43068 + 23.3765i 0.207647 + 0.893822i
\(685\) 18.6824 0.713820
\(686\) −1.61526 2.79772i −0.0616711 0.106817i
\(687\) 3.57657 24.0443i 0.136455 0.917346i
\(688\) 1.72671 2.99074i 0.0658301 0.114021i
\(689\) −7.55356 + 13.0831i −0.287768 + 0.498428i
\(690\) 0.399697 2.68705i 0.0152162 0.102294i
\(691\) 18.7598 + 32.4929i 0.713656 + 1.23609i 0.963476 + 0.267796i \(0.0862953\pi\)
−0.249820 + 0.968292i \(0.580371\pi\)
\(692\) 4.05707 0.154226
\(693\) 0 0
\(694\) 14.2978 0.542738
\(695\) −7.67127 13.2870i −0.290988 0.504005i
\(696\) −3.47259 2.75833i −0.131628 0.104554i
\(697\) 8.09543 14.0217i 0.306636 0.531109i
\(698\) −5.58692 + 9.67683i −0.211468 + 0.366273i
\(699\) −23.3764 + 9.22673i −0.884175 + 0.348987i
\(700\) 11.4207 + 19.7812i 0.431662 + 0.747660i
\(701\) 10.2007 0.385275 0.192637 0.981270i \(-0.438296\pi\)
0.192637 + 0.981270i \(0.438296\pi\)
\(702\) −3.96256 + 8.35188i −0.149557 + 0.315221i
\(703\) 44.6811 1.68518
\(704\) 0 0
\(705\) 23.0908 9.11402i 0.869651 0.343254i
\(706\) 1.03995 1.80124i 0.0391388 0.0677905i
\(707\) 3.43856 5.95577i 0.129321 0.223990i
\(708\) −5.02146 3.98862i −0.188718 0.149902i
\(709\) 7.24884 + 12.5554i 0.272236 + 0.471526i 0.969434 0.245352i \(-0.0789036\pi\)
−0.697198 + 0.716878i \(0.745570\pi\)
\(710\) −4.68598 −0.175862
\(711\) −12.9577 3.94214i −0.485953 0.147842i
\(712\) 38.0220 1.42493
\(713\) 0.454763 + 0.787673i 0.0170310 + 0.0294986i
\(714\) −3.66637 + 24.6479i −0.137210 + 0.922426i
\(715\) 0 0
\(716\) 5.91364 10.2427i 0.221003 0.382789i
\(717\) 6.40870 43.0838i 0.239337 1.60899i
\(718\) 2.81961 + 4.88370i 0.105227 + 0.182258i
\(719\) 19.2266 0.717032 0.358516 0.933524i \(-0.383283\pi\)
0.358516 + 0.933524i \(0.383283\pi\)
\(720\) 3.78480 3.53910i 0.141051 0.131895i
\(721\) −10.4941 −0.390821
\(722\) 2.43836 + 4.22337i 0.0907464 + 0.157177i
\(723\) −24.0630 19.1136i −0.894912 0.710843i
\(724\) −1.87056 + 3.23991i −0.0695188 + 0.120410i
\(725\) 2.03241 3.52023i 0.0754818 0.130738i
\(726\) 0 0
\(727\) −0.363414 0.629451i −0.0134783 0.0233450i 0.859208 0.511627i \(-0.170957\pi\)
−0.872686 + 0.488282i \(0.837624\pi\)
\(728\) −24.7200 −0.916183
\(729\) −17.0779 20.9128i −0.632514 0.774549i
\(730\) 8.65874 0.320474
\(731\) 6.19154 + 10.7241i 0.229003 + 0.396644i
\(732\) 10.2568 4.04839i 0.379102 0.149633i
\(733\) 0.937944 1.62457i 0.0346438 0.0600048i −0.848184 0.529702i \(-0.822304\pi\)
0.882827 + 0.469697i \(0.155637\pi\)
\(734\) −3.65740 + 6.33481i −0.134997 + 0.233822i
\(735\) −12.4871 9.91874i −0.460595 0.365858i
\(736\) 6.08497 + 10.5395i 0.224295 + 0.388490i
\(737\) 0 0
\(738\) 4.24928 3.97343i 0.156418 0.146264i
\(739\) −52.5826 −1.93428 −0.967140 0.254243i \(-0.918174\pi\)
−0.967140 + 0.254243i \(0.918174\pi\)
\(740\) −7.57603 13.1221i −0.278500 0.482377i
\(741\) 3.50260 23.5470i 0.128671 0.865020i
\(742\) −7.31624 + 12.6721i −0.268588 + 0.465208i
\(743\) 16.6664 28.8671i 0.611431 1.05903i −0.379568 0.925164i \(-0.623928\pi\)
0.990999 0.133866i \(-0.0427392\pi\)
\(744\) 0.259157 1.74224i 0.00950116 0.0638735i
\(745\) −3.10402 5.37632i −0.113723 0.196973i
\(746\) −7.31206 −0.267714
\(747\) −1.38341 0.420875i −0.0506162 0.0153990i
\(748\) 0 0
\(749\) −20.0623 34.7489i −0.733060 1.26970i
\(750\) −8.80624 6.99494i −0.321559 0.255419i
\(751\) 11.6820 20.2339i 0.426284 0.738345i −0.570256 0.821467i \(-0.693156\pi\)
0.996539 + 0.0831223i \(0.0264892\pi\)
\(752\) −9.92717 + 17.1944i −0.362007 + 0.627014i
\(753\) −35.2467 + 13.9120i −1.28446 + 0.506981i
\(754\) 0.963394 + 1.66865i 0.0350847 + 0.0607685i
\(755\) −0.183023 −0.00666089
\(756\) 13.5554 28.5708i 0.493007 1.03911i
\(757\) −33.8030 −1.22859 −0.614296 0.789076i \(-0.710560\pi\)
−0.614296 + 0.789076i \(0.710560\pi\)
\(758\) 8.43250 + 14.6055i 0.306282 + 0.530496i
\(759\) 0 0
\(760\) 6.77421 11.7333i 0.245726 0.425611i
\(761\) −10.0560 + 17.4174i −0.364528 + 0.631381i −0.988700 0.149906i \(-0.952103\pi\)
0.624172 + 0.781287i \(0.285436\pi\)
\(762\) −6.89376 5.47583i −0.249735 0.198368i
\(763\) 4.61291 + 7.98979i 0.166998 + 0.289250i
\(764\) 25.7466 0.931480
\(765\) 4.20449 + 18.0983i 0.152014 + 0.654346i
\(766\) 8.04807 0.290788
\(767\) 3.18063 + 5.50901i 0.114846 + 0.198919i
\(768\) 2.23882 15.0509i 0.0807865 0.543104i
\(769\) −0.313500 + 0.542997i −0.0113051 + 0.0195810i −0.871623 0.490178i \(-0.836932\pi\)
0.860318 + 0.509759i \(0.170265\pi\)
\(770\) 0 0
\(771\) −1.31591 + 8.84649i −0.0473914 + 0.318598i
\(772\) −6.33989 10.9810i −0.228178 0.395215i
\(773\) 28.7378 1.03363 0.516813 0.856098i \(-0.327118\pi\)
0.516813 + 0.856098i \(0.327118\pi\)
\(774\) 1.00685 + 4.33401i 0.0361905 + 0.155783i
\(775\) 1.61447 0.0579933
\(776\) −9.47491 16.4110i −0.340130 0.589122i
\(777\) −46.1021 36.6196i −1.65390 1.31372i
\(778\) 4.76686 8.25644i 0.170900 0.296008i
\(779\) −7.49085 + 12.9745i −0.268387 + 0.464861i
\(780\) −7.50923 + 2.96392i −0.268874 + 0.106125i
\(781\) 0 0
\(782\) −7.79085 −0.278600
\(783\) −5.60938 + 0.453087i −0.200463 + 0.0161920i
\(784\) 12.7543 0.455512
\(785\) −13.3174 23.0664i −0.475319 0.823277i
\(786\) 5.73578 2.26393i 0.204588 0.0807517i
\(787\) 7.05147 12.2135i 0.251358 0.435364i −0.712542 0.701629i \(-0.752456\pi\)
0.963900 + 0.266265i \(0.0857896\pi\)
\(788\) −17.8525 + 30.9214i −0.635968 + 1.10153i
\(789\) 37.8370 + 30.0545i 1.34703 + 1.06997i
\(790\) 1.67450 + 2.90031i 0.0595759 + 0.103188i
\(791\) −5.98345 −0.212747
\(792\) 0 0
\(793\) −10.9382 −0.388426
\(794\) −1.67370 2.89893i −0.0593973 0.102879i
\(795\) −1.60524 + 10.7916i −0.0569322 + 0.382738i
\(796\) 7.22586 12.5156i 0.256114 0.443602i
\(797\) −13.0773 + 22.6506i −0.463223 + 0.802326i −0.999119 0.0419576i \(-0.986641\pi\)
0.535896 + 0.844284i \(0.319974\pi\)
\(798\) 3.39256 22.8072i 0.120095 0.807365i
\(799\) −35.5964 61.6548i −1.25931 2.18119i
\(800\) 21.6024 0.763760
\(801\) 35.2420 32.9542i 1.24521 1.16438i
\(802\) 12.0908 0.426939
\(803\) 0 0
\(804\) −20.6148 16.3746i −0.727026 0.577489i
\(805\) 4.60924 7.98344i 0.162454 0.281379i
\(806\) −0.382641 + 0.662754i −0.0134780 + 0.0233445i
\(807\) 4.86484 1.92017i 0.171251 0.0675932i
\(808\) −2.08196 3.60607i −0.0732433 0.126861i
\(809\) 15.8533 0.557374 0.278687 0.960382i \(-0.410101\pi\)
0.278687 + 0.960382i \(0.410101\pi\)
\(810\) −0.447427 + 6.66115i −0.0157210 + 0.234049i
\(811\) −36.3264 −1.27559 −0.637796 0.770206i \(-0.720154\pi\)
−0.637796 + 0.770206i \(0.720154\pi\)
\(812\) −3.29565 5.70824i −0.115655 0.200320i
\(813\) −40.8812 + 16.1360i −1.43377 + 0.565913i
\(814\) 0 0
\(815\) 2.34269 4.05766i 0.0820608 0.142134i
\(816\) −11.6362 9.24280i −0.407347 0.323563i
\(817\) −5.72915 9.92318i −0.200438 0.347168i
\(818\) −10.9151 −0.381637
\(819\) −22.9126 + 21.4252i −0.800630 + 0.748656i
\(820\) 5.08053 0.177420
\(821\) 8.17837 + 14.1653i 0.285427 + 0.494374i 0.972713 0.232013i \(-0.0745313\pi\)
−0.687286 + 0.726387i \(0.741198\pi\)
\(822\) 2.83249 19.0420i 0.0987946 0.664167i
\(823\) 13.0873 22.6678i 0.456193 0.790150i −0.542563 0.840015i \(-0.682546\pi\)
0.998756 + 0.0498656i \(0.0158793\pi\)
\(824\) −3.17696 + 5.50265i −0.110675 + 0.191694i
\(825\) 0 0
\(826\) 3.08070 + 5.33592i 0.107191 + 0.185661i
\(827\) 5.53930 0.192620 0.0963101 0.995351i \(-0.469296\pi\)
0.0963101 + 0.995351i \(0.469296\pi\)
\(828\) 9.45885 + 2.87767i 0.328718 + 0.100006i
\(829\) 18.5033 0.642647 0.321324 0.946969i \(-0.395872\pi\)
0.321324 + 0.946969i \(0.395872\pi\)
\(830\) 0.178774 + 0.309646i 0.00620534 + 0.0107480i
\(831\) 14.3280 + 11.3810i 0.497033 + 0.394802i
\(832\) −0.977507 + 1.69309i −0.0338890 + 0.0586974i
\(833\) −22.8670 + 39.6068i −0.792294 + 1.37229i
\(834\) −14.7058 + 5.80443i −0.509221 + 0.200991i
\(835\) −8.84388 15.3180i −0.306055 0.530103i
\(836\) 0 0
\(837\) −1.26981 1.83947i −0.0438912 0.0635813i
\(838\) 11.5635 0.399454
\(839\) 8.98265 + 15.5584i 0.310115 + 0.537136i 0.978387 0.206782i \(-0.0662990\pi\)
−0.668272 + 0.743917i \(0.732966\pi\)
\(840\) −16.6060 + 6.55443i −0.572960 + 0.226149i
\(841\) 13.9135 24.0989i 0.479776 0.830997i
\(842\) 1.51088 2.61692i 0.0520683 0.0901850i
\(843\) 30.6114 + 24.3151i 1.05431 + 0.837458i
\(844\) 3.28147 + 5.68367i 0.112953 + 0.195640i
\(845\) −6.50801 −0.223882
\(846\) −5.78858 24.9170i −0.199015 0.856666i
\(847\) 0 0
\(848\) −4.36299 7.55692i −0.149826 0.259506i
\(849\) 1.49774 10.0689i 0.0514024 0.345563i
\(850\) −6.91462 + 11.9765i −0.237169 + 0.410790i
\(851\) 9.20367 15.9412i 0.315498 0.546458i
\(852\) 2.50921 16.8687i 0.0859640 0.577911i
\(853\) −13.9565 24.1734i −0.477863 0.827683i 0.521815 0.853059i \(-0.325255\pi\)
−0.999678 + 0.0253757i \(0.991922\pi\)
\(854\) −10.5945 −0.362537
\(855\) −3.89049 16.7467i −0.133052 0.572725i
\(856\) −24.2944 −0.830367
\(857\) 4.24983 + 7.36093i 0.145172 + 0.251445i 0.929437 0.368981i \(-0.120293\pi\)
−0.784265 + 0.620426i \(0.786960\pi\)
\(858\) 0 0
\(859\) −13.9259 + 24.1203i −0.475145 + 0.822974i −0.999595 0.0284667i \(-0.990938\pi\)
0.524450 + 0.851441i \(0.324271\pi\)
\(860\) −1.94284 + 3.36510i −0.0662504 + 0.114749i
\(861\) 18.3627 7.24782i 0.625799 0.247005i
\(862\) 4.14695 + 7.18273i 0.141246 + 0.244645i
\(863\) 13.5940 0.462745 0.231372 0.972865i \(-0.425678\pi\)
0.231372 + 0.972865i \(0.425678\pi\)
\(864\) −16.9908 24.6131i −0.578038 0.837353i
\(865\) −2.90645 −0.0988221
\(866\) 9.52840 + 16.5037i 0.323788 + 0.560818i
\(867\) 22.1758 8.75286i 0.753129 0.297263i
\(868\) 1.30897 2.26720i 0.0444293 0.0769538i
\(869\) 0 0
\(870\) 1.08961 + 0.865495i 0.0369412 + 0.0293430i
\(871\) 13.0575 + 22.6163i 0.442438 + 0.766324i
\(872\) 5.58600 0.189166
\(873\) −23.0058 6.99909i −0.778630 0.236883i
\(874\) 7.20901 0.243848
\(875\) −19.0814 33.0500i −0.645071 1.11730i
\(876\) −4.63651 + 31.1699i −0.156653 + 1.05313i
\(877\) −18.0890 + 31.3310i −0.610822 + 1.05797i 0.380281 + 0.924871i \(0.375827\pi\)
−0.991102 + 0.133103i \(0.957506\pi\)
\(878\) −1.36454 + 2.36345i −0.0460509 + 0.0797625i
\(879\) −1.80785 + 12.1536i −0.0609772 + 0.409932i
\(880\) 0 0
\(881\) 26.6423 0.897601 0.448800 0.893632i \(-0.351851\pi\)
0.448800 + 0.893632i \(0.351851\pi\)
\(882\) −12.0028 + 11.2237i −0.404157 + 0.377920i
\(883\) −20.4764 −0.689087 −0.344544 0.938770i \(-0.611966\pi\)
−0.344544 + 0.938770i \(0.611966\pi\)
\(884\) 11.5761 + 20.0504i 0.389346 + 0.674367i
\(885\) 3.59733 + 2.85741i 0.120923 + 0.0960510i
\(886\) −7.05166 + 12.2138i −0.236905 + 0.410332i
\(887\) 16.0006 27.7138i 0.537247 0.930539i −0.461804 0.886982i \(-0.652798\pi\)
0.999051 0.0435570i \(-0.0138690\pi\)
\(888\) −33.1586 + 13.0878i −1.11273 + 0.439198i
\(889\) −14.9375 25.8725i −0.500987 0.867734i
\(890\) −11.9303 −0.399906
\(891\) 0 0
\(892\) 10.6911 0.357963
\(893\) 32.9380 + 57.0503i 1.10223 + 1.90912i
\(894\) −5.95041 + 2.34865i −0.199011 + 0.0785504i
\(895\) −4.23648 + 7.33780i −0.141610 + 0.245275i
\(896\) 21.5270 37.2858i 0.719165 1.24563i
\(897\) −7.67955 6.09999i −0.256413 0.203673i
\(898\) 8.60125 + 14.8978i 0.287027 + 0.497146i
\(899\) −0.465884 −0.0155381
\(900\) 12.8187 11.9866i 0.427291 0.399553i
\(901\) 31.2892 1.04239
\(902\) 0 0
\(903\) −2.22146 + 14.9342i −0.0739256 + 0.496980i
\(904\) −1.81141 + 3.13746i −0.0602467 + 0.104350i
\(905\) 1.34005 2.32104i 0.0445449 0.0771540i
\(906\) −0.0277486 + 0.186546i −0.000921885 + 0.00619756i
\(907\) 24.5251 + 42.4788i 0.814344 + 1.41048i 0.909798 + 0.415051i \(0.136236\pi\)
−0.0954547 + 0.995434i \(0.530431\pi\)
\(908\) −43.8455 −1.45506
\(909\) −5.05518 1.53794i −0.167670 0.0510103i
\(910\) 7.75650 0.257125
\(911\) 11.6906 + 20.2488i 0.387328 + 0.670872i 0.992089 0.125535i \(-0.0400647\pi\)
−0.604761 + 0.796407i \(0.706731\pi\)
\(912\) 10.7672 + 8.55253i 0.356536 + 0.283203i
\(913\) 0 0
\(914\) −3.42253 + 5.92800i −0.113207 + 0.196081i
\(915\) −7.34787 + 2.90023i −0.242913 + 0.0958786i
\(916\) −10.9378 18.9448i −0.361395 0.625954i
\(917\) 20.9249 0.691001
\(918\) 19.0841 1.54148i 0.629869 0.0508765i
\(919\) −7.59931 −0.250678 −0.125339 0.992114i \(-0.540002\pi\)
−0.125339 + 0.992114i \(0.540002\pi\)
\(920\) −2.79078 4.83377i −0.0920093 0.159365i
\(921\) −29.8649 + 11.7878i −0.984081 + 0.388420i
\(922\) −8.45456 + 14.6437i −0.278436 + 0.482265i
\(923\) −8.45857 + 14.6507i −0.278417 + 0.482233i
\(924\) 0 0
\(925\) −16.3371 28.2967i −0.537160 0.930389i
\(926\) 26.4768 0.870081
\(927\) 1.82456 + 7.85384i 0.0599263 + 0.257954i
\(928\) −6.23377 −0.204633
\(929\) 7.43837 + 12.8836i 0.244045 + 0.422699i 0.961863 0.273533i \(-0.0881922\pi\)
−0.717818 + 0.696231i \(0.754859\pi\)
\(930\) −0.0813170 + 0.546670i −0.00266649 + 0.0179260i
\(931\) 21.1592 36.6489i 0.693466 1.20112i
\(932\) −11.3079 + 19.5859i −0.370403 + 0.641557i
\(933\) −1.75233 + 11.7804i −0.0573686 + 0.385672i
\(934\) −5.77192 9.99727i −0.188863 0.327121i
\(935\) 0 0
\(936\) 4.29794 + 18.5006i 0.140482 + 0.604710i
\(937\) 17.8231 0.582257 0.291128 0.956684i \(-0.405969\pi\)
0.291128 + 0.956684i \(0.405969\pi\)
\(938\) 12.6473 + 21.9058i 0.412949 + 0.715248i
\(939\) 34.3483 + 27.2834i 1.12091 + 0.890360i
\(940\) 11.1698 19.3466i 0.364318 0.631018i
\(941\) −21.3296 + 36.9439i −0.695324 + 1.20434i 0.274748 + 0.961516i \(0.411406\pi\)
−0.970071 + 0.242820i \(0.921928\pi\)
\(942\) −25.5295 + 10.0766i −0.831795 + 0.328312i
\(943\) 3.08601 + 5.34513i 0.100494 + 0.174062i
\(944\) −3.67430 −0.119588
\(945\) −9.71100 + 20.4678i −0.315899 + 0.665819i
\(946\) 0 0
\(947\) −3.44670 5.96986i −0.112003 0.193994i 0.804575 0.593851i \(-0.202393\pi\)
−0.916578 + 0.399857i \(0.869060\pi\)
\(948\) −11.3372 + 4.47484i −0.368216 + 0.145336i
\(949\) 15.6297 27.0715i 0.507363 0.878778i
\(950\) 6.39822 11.0820i 0.207586 0.359549i
\(951\) −14.8907 11.8279i −0.482864 0.383547i
\(952\) 25.5995 + 44.3396i 0.829683 + 1.43705i
\(953\) −23.6805 −0.767085 −0.383543 0.923523i \(-0.625296\pi\)
−0.383543 + 0.923523i \(0.625296\pi\)
\(954\) 10.7559 + 3.27228i 0.348236 + 0.105944i
\(955\) −18.4446 −0.596855
\(956\) −19.5989 33.9463i −0.633874 1.09790i
\(957\) 0 0
\(958\) −7.27297 + 12.5972i −0.234979 + 0.406996i
\(959\) 32.6638 56.5754i 1.05477 1.82692i
\(960\) −0.207735 + 1.39654i −0.00670462 + 0.0450732i
\(961\) 15.4075 + 26.6865i 0.497015 + 0.860856i
\(962\) 15.4881 0.499356
\(963\) −22.5181 + 21.0564i −0.725637 + 0.678532i
\(964\) −27.6544 −0.890688
\(965\) 4.54184 + 7.86670i 0.146207 + 0.253238i
\(966\) −7.43827 5.90834i −0.239323 0.190098i
\(967\) 15.5700 26.9680i 0.500696 0.867231i −0.499303 0.866427i \(-0.666411\pi\)
1.00000 0.000804082i \(-0.000255947\pi\)
\(968\) 0 0
\(969\) −45.8628 + 18.1022i −1.47333 + 0.581527i
\(970\) 2.97299 + 5.14937i 0.0954569 + 0.165336i
\(971\) 13.3548 0.428577 0.214288 0.976770i \(-0.431257\pi\)
0.214288 + 0.976770i \(0.431257\pi\)
\(972\) −23.7393 5.17751i −0.761440 0.166069i
\(973\) −53.6488 −1.71990
\(974\) 1.08655 + 1.88196i 0.0348153 + 0.0603018i
\(975\) −16.1930 + 6.39145i −0.518592 + 0.204690i
\(976\) 3.15899 5.47153i 0.101117 0.175139i
\(977\) 4.45796 7.72142i 0.142623 0.247030i −0.785861 0.618404i \(-0.787780\pi\)
0.928484 + 0.371373i \(0.121113\pi\)
\(978\) −3.78057 3.00297i −0.120889 0.0960244i
\(979\) 0 0
\(980\) −14.3508 −0.458421
\(981\) 5.17758 4.84147i 0.165307 0.154576i
\(982\) 4.79899 0.153142
\(983\) 8.42927 + 14.5999i 0.268852 + 0.465665i 0.968566 0.248758i \(-0.0800224\pi\)
−0.699714 + 0.714423i \(0.746689\pi\)
\(984\) 1.75864 11.8228i 0.0560633 0.376897i
\(985\) 12.7894 22.1518i 0.407503 0.705815i
\(986\) 1.99534 3.45603i 0.0635446 0.110062i
\(987\) 12.7716 85.8599i 0.406525 2.73295i
\(988\) −10.7116 18.5530i −0.340781 0.590249i
\(989\) −4.72049 −0.150103
\(990\) 0 0
\(991\) −33.5356 −1.06529 −0.532647 0.846338i \(-0.678803\pi\)
−0.532647 + 0.846338i \(0.678803\pi\)
\(992\) −1.23796 2.14422i −0.0393054 0.0680790i
\(993\) 5.03205 + 3.99704i 0.159687 + 0.126842i
\(994\) −8.19282 + 14.1904i −0.259861 + 0.450092i
\(995\) −5.17654 + 8.96603i −0.164107 + 0.284242i
\(996\) −1.21040 + 0.477748i −0.0383529 + 0.0151380i
\(997\) 1.62184 + 2.80910i 0.0513641 + 0.0889652i 0.890564 0.454857i \(-0.150310\pi\)
−0.839200 + 0.543823i \(0.816976\pi\)
\(998\) −9.85487 −0.311950
\(999\) −19.3908 + 40.8699i −0.613498 + 1.29307i
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 1089.2.e.p.364.11 36
9.4 even 3 9801.2.a.cm.1.8 18
9.5 odd 6 9801.2.a.cp.1.11 18
9.7 even 3 inner 1089.2.e.p.727.11 36
11.5 even 5 99.2.m.b.58.4 yes 72
11.9 even 5 99.2.m.b.4.6 72
11.10 odd 2 1089.2.e.o.364.8 36
33.5 odd 10 297.2.n.b.91.6 72
33.20 odd 10 297.2.n.b.37.4 72
99.5 odd 30 891.2.f.e.487.4 36
99.16 even 15 99.2.m.b.25.6 yes 72
99.20 odd 30 297.2.n.b.235.6 72
99.31 even 15 891.2.f.f.730.6 36
99.32 even 6 9801.2.a.cn.1.8 18
99.38 odd 30 297.2.n.b.289.4 72
99.43 odd 6 1089.2.e.o.727.8 36
99.49 even 15 891.2.f.f.487.6 36
99.76 odd 6 9801.2.a.co.1.11 18
99.86 odd 30 891.2.f.e.730.4 36
99.97 even 15 99.2.m.b.70.4 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.6 72 11.9 even 5
99.2.m.b.25.6 yes 72 99.16 even 15
99.2.m.b.58.4 yes 72 11.5 even 5
99.2.m.b.70.4 yes 72 99.97 even 15
297.2.n.b.37.4 72 33.20 odd 10
297.2.n.b.91.6 72 33.5 odd 10
297.2.n.b.235.6 72 99.20 odd 30
297.2.n.b.289.4 72 99.38 odd 30
891.2.f.e.487.4 36 99.5 odd 30
891.2.f.e.730.4 36 99.86 odd 30
891.2.f.f.487.6 36 99.49 even 15
891.2.f.f.730.6 36 99.31 even 15
1089.2.e.o.364.8 36 11.10 odd 2
1089.2.e.o.727.8 36 99.43 odd 6
1089.2.e.p.364.11 36 1.1 even 1 trivial
1089.2.e.p.727.11 36 9.7 even 3 inner
9801.2.a.cm.1.8 18 9.4 even 3
9801.2.a.cn.1.8 18 99.32 even 6
9801.2.a.co.1.11 18 99.76 odd 6
9801.2.a.cp.1.11 18 9.5 odd 6