Properties

Label 129.2.d.a.128.11
Level $129$
Weight $2$
Character 129.128
Analytic conductor $1.030$
Analytic rank $0$
Dimension $12$
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] = [129,2,Mod(128,129)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(129, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("129.128");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 129 = 3 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 129.d (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.03007018607\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 6x^{10} + 29x^{8} + 88x^{6} + 261x^{4} + 486x^{2} + 729 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 128.11
Root \(0.583090 - 1.63095i\) of defining polynomial
Character \(\chi\) \(=\) 129.128
Dual form 129.2.d.a.128.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.26382 q^{2} +(-0.583090 - 1.63095i) q^{3} +3.12489 q^{4} -1.38036 q^{5} +(-1.32001 - 3.69218i) q^{6} +0.790787i q^{7} +2.54654 q^{8} +(-2.32001 + 1.90198i) q^{9} +O(q^{10})\) \(q+2.26382 q^{2} +(-0.583090 - 1.63095i) q^{3} +3.12489 q^{4} -1.38036 q^{5} +(-1.32001 - 3.69218i) q^{6} +0.790787i q^{7} +2.54654 q^{8} +(-2.32001 + 1.90198i) q^{9} -3.12489 q^{10} +4.15328i q^{11} +(-1.82209 - 5.09654i) q^{12} +3.64002 q^{13} +1.79020i q^{14} +(0.804874 + 2.25130i) q^{15} -0.484862 q^{16} +1.44088i q^{17} +(-5.25209 + 4.30575i) q^{18} -6.14039i q^{19} -4.31346 q^{20} +(1.28974 - 0.461100i) q^{21} +9.40229i q^{22} -5.94348i q^{23} +(-1.48486 - 4.15328i) q^{24} -3.09461 q^{25} +8.24036 q^{26} +(4.45482 + 2.67480i) q^{27} +2.47112i q^{28} -4.59618 q^{29} +(1.82209 + 5.09654i) q^{30} -1.15516 q^{31} -6.19072 q^{32} +(6.77381 - 2.42174i) q^{33} +3.26190i q^{34} -1.09157i q^{35} +(-7.24977 + 5.94348i) q^{36} +10.1931i q^{37} -13.9007i q^{38} +(-2.12246 - 5.93671i) q^{39} -3.51514 q^{40} -8.82525i q^{41} +(2.91973 - 1.04385i) q^{42} +(5.15516 - 4.05269i) q^{43} +12.9785i q^{44} +(3.20245 - 2.62542i) q^{45} -13.4550i q^{46} -5.37060i q^{47} +(0.282718 + 0.790787i) q^{48} +6.37466 q^{49} -7.00564 q^{50} +(2.35001 - 0.840166i) q^{51} +11.3747 q^{52} +5.02128i q^{53} +(10.0849 + 6.05527i) q^{54} -5.73302i q^{55} +2.01377i q^{56} +(-10.0147 + 3.58040i) q^{57} -10.4049 q^{58} +3.80397i q^{59} +(2.51514 + 7.03505i) q^{60} +4.84348i q^{61} -2.61508 q^{62} +(-1.50406 - 1.83463i) q^{63} -13.0450 q^{64} -5.02454 q^{65} +(15.3347 - 5.48238i) q^{66} -0.515138 q^{67} +4.50260i q^{68} +(-9.69354 + 3.46559i) q^{69} -2.47112i q^{70} +15.4602 q^{71} +(-5.90800 + 4.84348i) q^{72} +11.8734i q^{73} +23.0753i q^{74} +(1.80444 + 5.04716i) q^{75} -19.1880i q^{76} -3.28436 q^{77} +(-4.80487 - 13.4396i) q^{78} +7.60975 q^{79} +0.669284 q^{80} +(1.76491 - 8.82525i) q^{81} -19.9788i q^{82} -7.95725i q^{83} +(4.03028 - 1.44088i) q^{84} -1.98894i q^{85} +(11.6704 - 9.17457i) q^{86} +(2.67999 + 7.49615i) q^{87} +10.5765i q^{88} +0.419798 q^{89} +(7.24977 - 5.94348i) q^{90} +2.87848i q^{91} -18.5727i q^{92} +(0.673563 + 1.88401i) q^{93} -12.1581i q^{94} +8.47594i q^{95} +(3.60975 + 10.0968i) q^{96} -11.4995 q^{97} +14.4311 q^{98} +(-7.89948 - 9.63567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{4} - 12 q^{9} - 4 q^{10} + 12 q^{13} - 8 q^{15} - 4 q^{16} - 4 q^{21} - 16 q^{24} + 16 q^{31} - 20 q^{36} - 44 q^{40} + 32 q^{43} - 24 q^{49} + 36 q^{52} + 40 q^{54} + 12 q^{57} - 28 q^{58} + 32 q^{60} - 28 q^{64} + 36 q^{66} - 8 q^{67} - 40 q^{78} + 56 q^{79} - 44 q^{81} + 52 q^{84} + 48 q^{87} + 20 q^{90} + 8 q^{96} - 4 q^{97} - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/129\mathbb{Z}\right)^\times\).

\(n\) \(44\) \(46\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.26382 1.60076 0.800382 0.599491i \(-0.204630\pi\)
0.800382 + 0.599491i \(0.204630\pi\)
\(3\) −0.583090 1.63095i −0.336647 0.941631i
\(4\) 3.12489 1.56244
\(5\) −1.38036 −0.617315 −0.308658 0.951173i \(-0.599880\pi\)
−0.308658 + 0.951173i \(0.599880\pi\)
\(6\) −1.32001 3.69218i −0.538893 1.50733i
\(7\) 0.790787i 0.298889i 0.988770 + 0.149445i \(0.0477486\pi\)
−0.988770 + 0.149445i \(0.952251\pi\)
\(8\) 2.54654 0.900338
\(9\) −2.32001 + 1.90198i −0.773337 + 0.633995i
\(10\) −3.12489 −0.988176
\(11\) 4.15328i 1.25226i 0.779718 + 0.626131i \(0.215363\pi\)
−0.779718 + 0.626131i \(0.784637\pi\)
\(12\) −1.82209 5.09654i −0.525992 1.47124i
\(13\) 3.64002 1.00956 0.504780 0.863248i \(-0.331573\pi\)
0.504780 + 0.863248i \(0.331573\pi\)
\(14\) 1.79020i 0.478451i
\(15\) 0.804874 + 2.25130i 0.207817 + 0.581283i
\(16\) −0.484862 −0.121215
\(17\) 1.44088i 0.349466i 0.984616 + 0.174733i \(0.0559062\pi\)
−0.984616 + 0.174733i \(0.944094\pi\)
\(18\) −5.25209 + 4.30575i −1.23793 + 1.01488i
\(19\) 6.14039i 1.40870i −0.709852 0.704351i \(-0.751238\pi\)
0.709852 0.704351i \(-0.248762\pi\)
\(20\) −4.31346 −0.964520
\(21\) 1.28974 0.461100i 0.281443 0.100620i
\(22\) 9.40229i 2.00458i
\(23\) 5.94348i 1.23930i −0.784877 0.619651i \(-0.787274\pi\)
0.784877 0.619651i \(-0.212726\pi\)
\(24\) −1.48486 4.15328i −0.303096 0.847786i
\(25\) −3.09461 −0.618922
\(26\) 8.24036 1.61607
\(27\) 4.45482 + 2.67480i 0.857331 + 0.514766i
\(28\) 2.47112i 0.466997i
\(29\) −4.59618 −0.853489 −0.426745 0.904372i \(-0.640340\pi\)
−0.426745 + 0.904372i \(0.640340\pi\)
\(30\) 1.82209 + 5.09654i 0.332667 + 0.930497i
\(31\) −1.15516 −0.207473 −0.103737 0.994605i \(-0.533080\pi\)
−0.103737 + 0.994605i \(0.533080\pi\)
\(32\) −6.19072 −1.09437
\(33\) 6.77381 2.42174i 1.17917 0.421571i
\(34\) 3.26190i 0.559412i
\(35\) 1.09157i 0.184509i
\(36\) −7.24977 + 5.94348i −1.20830 + 0.990581i
\(37\) 10.1931i 1.67573i 0.545876 + 0.837866i \(0.316197\pi\)
−0.545876 + 0.837866i \(0.683803\pi\)
\(38\) 13.9007i 2.25500i
\(39\) −2.12246 5.93671i −0.339866 0.950634i
\(40\) −3.51514 −0.555792
\(41\) 8.82525i 1.37827i −0.724632 0.689137i \(-0.757990\pi\)
0.724632 0.689137i \(-0.242010\pi\)
\(42\) 2.91973 1.04385i 0.450524 0.161069i
\(43\) 5.15516 4.05269i 0.786155 0.618030i
\(44\) 12.9785i 1.95659i
\(45\) 3.20245 2.62542i 0.477393 0.391375i
\(46\) 13.4550i 1.98383i
\(47\) 5.37060i 0.783382i −0.920097 0.391691i \(-0.871890\pi\)
0.920097 0.391691i \(-0.128110\pi\)
\(48\) 0.282718 + 0.790787i 0.0408069 + 0.114140i
\(49\) 6.37466 0.910665
\(50\) −7.00564 −0.990747
\(51\) 2.35001 0.840166i 0.329068 0.117647i
\(52\) 11.3747 1.57738
\(53\) 5.02128i 0.689726i 0.938653 + 0.344863i \(0.112075\pi\)
−0.938653 + 0.344863i \(0.887925\pi\)
\(54\) 10.0849 + 6.05527i 1.37238 + 0.824018i
\(55\) 5.73302i 0.773041i
\(56\) 2.01377i 0.269101i
\(57\) −10.0147 + 3.58040i −1.32648 + 0.474235i
\(58\) −10.4049 −1.36623
\(59\) 3.80397i 0.495235i 0.968858 + 0.247617i \(0.0796476\pi\)
−0.968858 + 0.247617i \(0.920352\pi\)
\(60\) 2.51514 + 7.03505i 0.324703 + 0.908222i
\(61\) 4.84348i 0.620144i 0.950713 + 0.310072i \(0.100353\pi\)
−0.950713 + 0.310072i \(0.899647\pi\)
\(62\) −2.61508 −0.332115
\(63\) −1.50406 1.83463i −0.189494 0.231142i
\(64\) −13.0450 −1.63062
\(65\) −5.02454 −0.623217
\(66\) 15.3347 5.48238i 1.88757 0.674835i
\(67\) −0.515138 −0.0629341 −0.0314671 0.999505i \(-0.510018\pi\)
−0.0314671 + 0.999505i \(0.510018\pi\)
\(68\) 4.50260i 0.546020i
\(69\) −9.69354 + 3.46559i −1.16697 + 0.417208i
\(70\) 2.47112i 0.295355i
\(71\) 15.4602 1.83479 0.917393 0.397983i \(-0.130290\pi\)
0.917393 + 0.397983i \(0.130290\pi\)
\(72\) −5.90800 + 4.84348i −0.696265 + 0.570809i
\(73\) 11.8734i 1.38968i 0.719166 + 0.694839i \(0.244524\pi\)
−0.719166 + 0.694839i \(0.755476\pi\)
\(74\) 23.0753i 2.68245i
\(75\) 1.80444 + 5.04716i 0.208358 + 0.582796i
\(76\) 19.1880i 2.20102i
\(77\) −3.28436 −0.374288
\(78\) −4.80487 13.4396i −0.544045 1.52174i
\(79\) 7.60975 0.856163 0.428082 0.903740i \(-0.359190\pi\)
0.428082 + 0.903740i \(0.359190\pi\)
\(80\) 0.669284 0.0748282
\(81\) 1.76491 8.82525i 0.196101 0.980584i
\(82\) 19.9788i 2.20629i
\(83\) 7.95725i 0.873422i −0.899602 0.436711i \(-0.856143\pi\)
0.899602 0.436711i \(-0.143857\pi\)
\(84\) 4.03028 1.44088i 0.439739 0.157213i
\(85\) 1.98894i 0.215731i
\(86\) 11.6704 9.17457i 1.25845 0.989319i
\(87\) 2.67999 + 7.49615i 0.287325 + 0.803672i
\(88\) 10.5765i 1.12746i
\(89\) 0.419798 0.0444985 0.0222492 0.999752i \(-0.492917\pi\)
0.0222492 + 0.999752i \(0.492917\pi\)
\(90\) 7.24977 5.94348i 0.764193 0.626498i
\(91\) 2.87848i 0.301747i
\(92\) 18.5727i 1.93634i
\(93\) 0.673563 + 1.88401i 0.0698453 + 0.195363i
\(94\) 12.1581i 1.25401i
\(95\) 8.47594i 0.869613i
\(96\) 3.60975 + 10.0968i 0.368418 + 1.03050i
\(97\) −11.4995 −1.16760 −0.583801 0.811897i \(-0.698435\pi\)
−0.583801 + 0.811897i \(0.698435\pi\)
\(98\) 14.4311 1.45776
\(99\) −7.89948 9.63567i −0.793928 0.968421i
\(100\) −9.67030 −0.967030
\(101\) 6.16705i 0.613645i −0.951767 0.306822i \(-0.900734\pi\)
0.951767 0.306822i \(-0.0992658\pi\)
\(102\) 5.32001 1.90198i 0.526760 0.188325i
\(103\) −1.54541 −0.152274 −0.0761371 0.997097i \(-0.524259\pi\)
−0.0761371 + 0.997097i \(0.524259\pi\)
\(104\) 9.26946 0.908946
\(105\) −1.78030 + 0.636483i −0.173739 + 0.0621144i
\(106\) 11.3673i 1.10409i
\(107\) 16.5589i 1.60081i 0.599458 + 0.800406i \(0.295383\pi\)
−0.599458 + 0.800406i \(0.704617\pi\)
\(108\) 13.9208 + 8.35844i 1.33953 + 0.804292i
\(109\) −5.57947 −0.534416 −0.267208 0.963639i \(-0.586101\pi\)
−0.267208 + 0.963639i \(0.586101\pi\)
\(110\) 12.9785i 1.23746i
\(111\) 16.6244 5.94348i 1.57792 0.564131i
\(112\) 0.383422i 0.0362300i
\(113\) 3.11198 0.292750 0.146375 0.989229i \(-0.453239\pi\)
0.146375 + 0.989229i \(0.453239\pi\)
\(114\) −22.6714 + 8.10538i −2.12338 + 0.759139i
\(115\) 8.20414i 0.765040i
\(116\) −14.3625 −1.33353
\(117\) −8.44490 + 6.92327i −0.780731 + 0.640056i
\(118\) 8.61151i 0.792753i
\(119\) −1.13943 −0.104452
\(120\) 2.04964 + 5.73302i 0.187106 + 0.523351i
\(121\) −6.24977 −0.568161
\(122\) 10.9648i 0.992703i
\(123\) −14.3936 + 5.14592i −1.29782 + 0.463992i
\(124\) −3.60975 −0.324165
\(125\) 11.1735 0.999385
\(126\) −3.40493 4.15328i −0.303335 0.370004i
\(127\) 10.2947 0.913509 0.456755 0.889593i \(-0.349012\pi\)
0.456755 + 0.889593i \(0.349012\pi\)
\(128\) −17.1500 −1.51586
\(129\) −9.61567 6.04474i −0.846613 0.532210i
\(130\) −11.3747 −0.997623
\(131\) −21.1454 −1.84749 −0.923743 0.383013i \(-0.874887\pi\)
−0.923743 + 0.383013i \(0.874887\pi\)
\(132\) 21.1674 7.56766i 1.84238 0.658680i
\(133\) 4.85574 0.421046
\(134\) −1.16618 −0.100743
\(135\) −6.14925 3.69218i −0.529244 0.317773i
\(136\) 3.66927i 0.314637i
\(137\) −11.9198 −1.01838 −0.509191 0.860654i \(-0.670055\pi\)
−0.509191 + 0.860654i \(0.670055\pi\)
\(138\) −21.9444 + 7.84547i −1.86803 + 0.667851i
\(139\) −14.6850 −1.24556 −0.622782 0.782396i \(-0.713998\pi\)
−0.622782 + 0.782396i \(0.713998\pi\)
\(140\) 3.41103i 0.288285i
\(141\) −8.75919 + 3.13154i −0.737657 + 0.263724i
\(142\) 34.9991 2.93706
\(143\) 15.1181i 1.26424i
\(144\) 1.12489 0.922200i 0.0937405 0.0768500i
\(145\) 6.34438 0.526872
\(146\) 26.8793i 2.22454i
\(147\) −3.71700 10.3968i −0.306573 0.857510i
\(148\) 31.8522i 2.61824i
\(149\) 6.08687 0.498656 0.249328 0.968419i \(-0.419790\pi\)
0.249328 + 0.968419i \(0.419790\pi\)
\(150\) 4.08492 + 11.4259i 0.333532 + 0.932918i
\(151\) 13.9611i 1.13614i −0.822981 0.568069i \(-0.807691\pi\)
0.822981 0.568069i \(-0.192309\pi\)
\(152\) 15.6367i 1.26831i
\(153\) −2.74054 3.34287i −0.221560 0.270255i
\(154\) −7.43521 −0.599146
\(155\) 1.59454 0.128076
\(156\) −6.63245 18.5515i −0.531021 1.48531i
\(157\) 2.85454i 0.227817i 0.993491 + 0.113909i \(0.0363371\pi\)
−0.993491 + 0.113909i \(0.963663\pi\)
\(158\) 17.2271 1.37051
\(159\) 8.18948 2.92786i 0.649468 0.232195i
\(160\) 8.54541 0.675574
\(161\) 4.70003 0.370414
\(162\) 3.99544 19.9788i 0.313911 1.56968i
\(163\) 3.64533i 0.285524i 0.989757 + 0.142762i \(0.0455984\pi\)
−0.989757 + 0.142762i \(0.954402\pi\)
\(164\) 27.5779i 2.15347i
\(165\) −9.35029 + 3.34287i −0.727919 + 0.260242i
\(166\) 18.0138i 1.39814i
\(167\) 12.5750i 0.973084i −0.873657 0.486542i \(-0.838258\pi\)
0.873657 0.486542i \(-0.161742\pi\)
\(168\) 3.28436 1.17421i 0.253394 0.0905922i
\(169\) 0.249771 0.0192131
\(170\) 4.50260i 0.345334i
\(171\) 11.6789 + 14.2458i 0.893110 + 1.08940i
\(172\) 16.1093 12.6642i 1.22832 0.965636i
\(173\) 19.4949i 1.48217i 0.671411 + 0.741085i \(0.265689\pi\)
−0.671411 + 0.741085i \(0.734311\pi\)
\(174\) 6.06701 + 16.9699i 0.459939 + 1.28649i
\(175\) 2.44718i 0.184989i
\(176\) 2.01377i 0.151794i
\(177\) 6.20409 2.21806i 0.466328 0.166719i
\(178\) 0.950346 0.0712315
\(179\) −3.67949 −0.275018 −0.137509 0.990501i \(-0.543910\pi\)
−0.137509 + 0.990501i \(0.543910\pi\)
\(180\) 10.0073 8.20414i 0.745899 0.611501i
\(181\) 10.8751 0.808341 0.404170 0.914684i \(-0.367560\pi\)
0.404170 + 0.914684i \(0.367560\pi\)
\(182\) 6.51637i 0.483025i
\(183\) 7.89948 2.82418i 0.583947 0.208770i
\(184\) 15.1353i 1.11579i
\(185\) 14.0701i 1.03445i
\(186\) 1.52483 + 4.26507i 0.111806 + 0.312730i
\(187\) −5.98440 −0.437623
\(188\) 16.7825i 1.22399i
\(189\) −2.11520 + 3.52281i −0.153858 + 0.256247i
\(190\) 19.1880i 1.39204i
\(191\) 4.28023 0.309707 0.154853 0.987937i \(-0.450510\pi\)
0.154853 + 0.987937i \(0.450510\pi\)
\(192\) 7.60639 + 21.2757i 0.548944 + 1.53544i
\(193\) −14.2342 −1.02460 −0.512299 0.858807i \(-0.671206\pi\)
−0.512299 + 0.858807i \(0.671206\pi\)
\(194\) −26.0329 −1.86905
\(195\) 2.92976 + 8.19478i 0.209804 + 0.586841i
\(196\) 19.9201 1.42286
\(197\) 19.9700i 1.42280i −0.702787 0.711401i \(-0.748061\pi\)
0.702787 0.711401i \(-0.251939\pi\)
\(198\) −17.8830 21.8134i −1.27089 1.55021i
\(199\) 9.37835i 0.664814i −0.943136 0.332407i \(-0.892139\pi\)
0.943136 0.332407i \(-0.107861\pi\)
\(200\) −7.88054 −0.557239
\(201\) 0.300372 + 0.840166i 0.0211866 + 0.0592607i
\(202\) 13.9611i 0.982300i
\(203\) 3.63460i 0.255099i
\(204\) 7.34353 2.62542i 0.514150 0.183816i
\(205\) 12.1820i 0.850829i
\(206\) −3.49854 −0.243755
\(207\) 11.3044 + 13.7890i 0.785711 + 0.958398i
\(208\) −1.76491 −0.122374
\(209\) 25.5028 1.76406
\(210\) −4.03028 + 1.44088i −0.278115 + 0.0994305i
\(211\) 8.22808i 0.566445i 0.959054 + 0.283222i \(0.0914034\pi\)
−0.959054 + 0.283222i \(0.908597\pi\)
\(212\) 15.6909i 1.07766i
\(213\) −9.01468 25.2148i −0.617676 1.72769i
\(214\) 37.4865i 2.56252i
\(215\) −7.11597 + 5.59417i −0.485305 + 0.381519i
\(216\) 11.3444 + 6.81148i 0.771887 + 0.463463i
\(217\) 0.913486i 0.0620115i
\(218\) −12.6309 −0.855474
\(219\) 19.3650 6.92327i 1.30856 0.467831i
\(220\) 17.9150i 1.20783i
\(221\) 5.24485i 0.352807i
\(222\) 37.6347 13.4550i 2.52588 0.903039i
\(223\) 4.15145i 0.278002i −0.990292 0.139001i \(-0.955611\pi\)
0.990292 0.139001i \(-0.0443891\pi\)
\(224\) 4.89554i 0.327097i
\(225\) 7.17953 5.88590i 0.478635 0.392393i
\(226\) 7.04496 0.468623
\(227\) 21.4635 1.42458 0.712290 0.701885i \(-0.247658\pi\)
0.712290 + 0.701885i \(0.247658\pi\)
\(228\) −31.2947 + 11.1883i −2.07254 + 0.740966i
\(229\) 15.8439 1.04700 0.523498 0.852027i \(-0.324627\pi\)
0.523498 + 0.852027i \(0.324627\pi\)
\(230\) 18.5727i 1.22465i
\(231\) 1.91508 + 5.35664i 0.126003 + 0.352441i
\(232\) −11.7044 −0.768429
\(233\) 6.05364 0.396587 0.198294 0.980143i \(-0.436460\pi\)
0.198294 + 0.980143i \(0.436460\pi\)
\(234\) −19.1177 + 15.6730i −1.24977 + 1.02458i
\(235\) 7.41335i 0.483594i
\(236\) 11.8870i 0.773776i
\(237\) −4.43717 12.4111i −0.288225 0.806190i
\(238\) −2.57947 −0.167202
\(239\) 10.0968i 0.653106i 0.945179 + 0.326553i \(0.105887\pi\)
−0.945179 + 0.326553i \(0.894113\pi\)
\(240\) −0.390253 1.09157i −0.0251907 0.0704605i
\(241\) 18.8046i 1.21131i −0.795727 0.605655i \(-0.792911\pi\)
0.795727 0.605655i \(-0.207089\pi\)
\(242\) −14.1484 −0.909491
\(243\) −15.4227 + 2.26744i −0.989365 + 0.145456i
\(244\) 15.1353i 0.968939i
\(245\) −8.79931 −0.562168
\(246\) −32.5845 + 11.6494i −2.07751 + 0.742741i
\(247\) 22.3512i 1.42217i
\(248\) −2.94166 −0.186796
\(249\) −12.9779 + 4.63980i −0.822441 + 0.294035i
\(250\) 25.2947 1.59978
\(251\) 8.43231i 0.532243i −0.963940 0.266121i \(-0.914258\pi\)
0.963940 0.266121i \(-0.0857422\pi\)
\(252\) −4.70003 5.73302i −0.296074 0.361147i
\(253\) 24.6850 1.55193
\(254\) 23.3054 1.46231
\(255\) −3.24386 + 1.15973i −0.203139 + 0.0726251i
\(256\) −12.7346 −0.795915
\(257\) −20.0564 −1.25108 −0.625541 0.780191i \(-0.715122\pi\)
−0.625541 + 0.780191i \(0.715122\pi\)
\(258\) −21.7682 13.6842i −1.35523 0.851941i
\(259\) −8.06055 −0.500858
\(260\) −15.7011 −0.973741
\(261\) 10.6632 8.74187i 0.660035 0.541108i
\(262\) −47.8695 −2.95739
\(263\) 9.75780 0.601692 0.300846 0.953673i \(-0.402731\pi\)
0.300846 + 0.953673i \(0.402731\pi\)
\(264\) 17.2498 6.16705i 1.06165 0.379556i
\(265\) 6.93117i 0.425779i
\(266\) 10.9925 0.673995
\(267\) −0.244780 0.684670i −0.0149803 0.0419011i
\(268\) −1.60975 −0.0983310
\(269\) 10.2225i 0.623278i 0.950201 + 0.311639i \(0.100878\pi\)
−0.950201 + 0.311639i \(0.899122\pi\)
\(270\) −13.9208 8.35844i −0.847194 0.508679i
\(271\) −1.73463 −0.105371 −0.0526857 0.998611i \(-0.516778\pi\)
−0.0526857 + 0.998611i \(0.516778\pi\)
\(272\) 0.698630i 0.0423607i
\(273\) 4.69467 1.67841i 0.284134 0.101582i
\(274\) −26.9844 −1.63019
\(275\) 12.8528i 0.775053i
\(276\) −30.2912 + 10.8296i −1.82332 + 0.651863i
\(277\) 26.5026i 1.59239i 0.605042 + 0.796194i \(0.293156\pi\)
−0.605042 + 0.796194i \(0.706844\pi\)
\(278\) −33.2442 −1.99385
\(279\) 2.67999 2.19710i 0.160447 0.131537i
\(280\) 2.77972i 0.166120i
\(281\) 4.79771i 0.286208i 0.989708 + 0.143104i \(0.0457083\pi\)
−0.989708 + 0.143104i \(0.954292\pi\)
\(282\) −19.8292 + 7.08925i −1.18081 + 0.422159i
\(283\) −12.1249 −0.720750 −0.360375 0.932808i \(-0.617351\pi\)
−0.360375 + 0.932808i \(0.617351\pi\)
\(284\) 48.3113 2.86675
\(285\) 13.8239 4.94224i 0.818854 0.292753i
\(286\) 34.2246i 2.02374i
\(287\) 6.97889 0.411951
\(288\) 14.3625 11.7747i 0.846321 0.693828i
\(289\) 14.9239 0.877874
\(290\) 14.3625 0.843397
\(291\) 6.70527 + 18.7552i 0.393070 + 1.09945i
\(292\) 37.1030i 2.17129i
\(293\) 17.8741i 1.04421i 0.852880 + 0.522107i \(0.174854\pi\)
−0.852880 + 0.522107i \(0.825146\pi\)
\(294\) −8.41462 23.5364i −0.490751 1.37267i
\(295\) 5.25084i 0.305716i
\(296\) 25.9571i 1.50872i
\(297\) −11.1092 + 18.5021i −0.644622 + 1.07360i
\(298\) 13.7796 0.798230
\(299\) 21.6344i 1.25115i
\(300\) 5.63866 + 15.7718i 0.325548 + 0.910585i
\(301\) 3.20482 + 4.07663i 0.184722 + 0.234973i
\(302\) 31.6054i 1.81869i
\(303\) −10.0582 + 3.59595i −0.577827 + 0.206582i
\(304\) 2.97724i 0.170756i
\(305\) 6.68574i 0.382824i
\(306\) −6.20409 7.56766i −0.354664 0.432614i
\(307\) −12.1854 −0.695460 −0.347730 0.937595i \(-0.613047\pi\)
−0.347730 + 0.937595i \(0.613047\pi\)
\(308\) −10.2633 −0.584803
\(309\) 0.901116 + 2.52050i 0.0512627 + 0.143386i
\(310\) 3.60975 0.205020
\(311\) 4.15328i 0.235511i 0.993043 + 0.117756i \(0.0375699\pi\)
−0.993043 + 0.117756i \(0.962430\pi\)
\(312\) −5.40493 15.1181i −0.305994 0.855891i
\(313\) 5.61032i 0.317114i −0.987350 0.158557i \(-0.949316\pi\)
0.987350 0.158557i \(-0.0506842\pi\)
\(314\) 6.46217i 0.364681i
\(315\) 2.07615 + 2.53245i 0.116978 + 0.142688i
\(316\) 23.7796 1.33771
\(317\) 20.7122i 1.16331i 0.813434 + 0.581657i \(0.197595\pi\)
−0.813434 + 0.581657i \(0.802405\pi\)
\(318\) 18.5395 6.62815i 1.03964 0.371688i
\(319\) 19.0892i 1.06879i
\(320\) 18.0067 1.00661
\(321\) 27.0068 9.65535i 1.50737 0.538909i
\(322\) 10.6400 0.592945
\(323\) 8.84759 0.492293
\(324\) 5.51514 27.5779i 0.306397 1.53211i
\(325\) −11.2645 −0.624839
\(326\) 8.25237i 0.457056i
\(327\) 3.25333 + 9.09985i 0.179910 + 0.503223i
\(328\) 22.4739i 1.24091i
\(329\) 4.24700 0.234145
\(330\) −21.1674 + 7.56766i −1.16523 + 0.416586i
\(331\) 7.62320i 0.419009i −0.977808 0.209505i \(-0.932815\pi\)
0.977808 0.209505i \(-0.0671851\pi\)
\(332\) 24.8655i 1.36467i
\(333\) −19.3871 23.6481i −1.06241 1.29591i
\(334\) 28.4676i 1.55768i
\(335\) 0.711075 0.0388502
\(336\) −0.625344 + 0.223570i −0.0341153 + 0.0121967i
\(337\) 19.8898 1.08347 0.541733 0.840551i \(-0.317768\pi\)
0.541733 + 0.840551i \(0.317768\pi\)
\(338\) 0.565436 0.0307557
\(339\) −1.81456 5.07548i −0.0985535 0.275662i
\(340\) 6.21520i 0.337067i
\(341\) 4.79771i 0.259811i
\(342\) 26.4390 + 32.2499i 1.42966 + 1.74387i
\(343\) 10.5765i 0.571077i
\(344\) 13.1278 10.3203i 0.707805 0.556435i
\(345\) 13.3806 4.78375i 0.720385 0.257549i
\(346\) 44.1330i 2.37260i
\(347\) −27.8502 −1.49508 −0.747538 0.664219i \(-0.768764\pi\)
−0.747538 + 0.664219i \(0.768764\pi\)
\(348\) 8.37466 + 23.4246i 0.448929 + 1.25569i
\(349\) 23.3395i 1.24933i −0.780892 0.624666i \(-0.785235\pi\)
0.780892 0.624666i \(-0.214765\pi\)
\(350\) 5.53997i 0.296124i
\(351\) 16.2157 + 9.73634i 0.865528 + 0.519687i
\(352\) 25.7118i 1.37044i
\(353\) 27.2828i 1.45212i 0.687633 + 0.726058i \(0.258650\pi\)
−0.687633 + 0.726058i \(0.741350\pi\)
\(354\) 14.0450 5.02128i 0.746481 0.266878i
\(355\) −21.3406 −1.13264
\(356\) 1.31182 0.0695263
\(357\) 0.664392 + 1.85836i 0.0351633 + 0.0983549i
\(358\) −8.32970 −0.440238
\(359\) 0.627085i 0.0330963i 0.999863 + 0.0165481i \(0.00526768\pi\)
−0.999863 + 0.0165481i \(0.994732\pi\)
\(360\) 8.15516 6.68574i 0.429815 0.352369i
\(361\) −18.7044 −0.984440
\(362\) 24.6193 1.29396
\(363\) 3.64418 + 10.1931i 0.191270 + 0.534998i
\(364\) 8.99493i 0.471462i
\(365\) 16.3896i 0.857869i
\(366\) 17.8830 6.39345i 0.934760 0.334191i
\(367\) −16.2909 −0.850380 −0.425190 0.905104i \(-0.639793\pi\)
−0.425190 + 0.905104i \(0.639793\pi\)
\(368\) 2.88177i 0.150223i
\(369\) 16.7855 + 20.4747i 0.873818 + 1.06587i
\(370\) 31.8522i 1.65592i
\(371\) −3.97077 −0.206152
\(372\) 2.10481 + 5.88733i 0.109129 + 0.305244i
\(373\) 7.53605i 0.390202i −0.980783 0.195101i \(-0.937497\pi\)
0.980783 0.195101i \(-0.0625035\pi\)
\(374\) −13.5476 −0.700531
\(375\) −6.51514 18.2234i −0.336440 0.941052i
\(376\) 13.6764i 0.705309i
\(377\) −16.7302 −0.861650
\(378\) −4.78843 + 7.97502i −0.246290 + 0.410191i
\(379\) −29.0440 −1.49189 −0.745946 0.666006i \(-0.768002\pi\)
−0.745946 + 0.666006i \(0.768002\pi\)
\(380\) 26.4863i 1.35872i
\(381\) −6.00275 16.7902i −0.307530 0.860188i
\(382\) 9.68968 0.495767
\(383\) −8.98467 −0.459095 −0.229548 0.973297i \(-0.573725\pi\)
−0.229548 + 0.973297i \(0.573725\pi\)
\(384\) 10.0000 + 27.9708i 0.510310 + 1.42738i
\(385\) 4.53360 0.231054
\(386\) −32.2236 −1.64014
\(387\) −4.25188 + 19.2073i −0.216135 + 0.976363i
\(388\) −35.9348 −1.82431
\(389\) 27.6542 1.40212 0.701062 0.713101i \(-0.252710\pi\)
0.701062 + 0.713101i \(0.252710\pi\)
\(390\) 6.63245 + 18.5515i 0.335847 + 0.939393i
\(391\) 8.56387 0.433094
\(392\) 16.2333 0.819906
\(393\) 12.3297 + 34.4872i 0.621951 + 1.73965i
\(394\) 45.2084i 2.27757i
\(395\) −10.5042 −0.528523
\(396\) −24.6850 30.1104i −1.24047 1.51310i
\(397\) −4.28383 −0.214999 −0.107500 0.994205i \(-0.534284\pi\)
−0.107500 + 0.994205i \(0.534284\pi\)
\(398\) 21.2309i 1.06421i
\(399\) −2.83133 7.91948i −0.141744 0.396470i
\(400\) 1.50046 0.0750229
\(401\) 13.1043i 0.654397i −0.944956 0.327198i \(-0.893895\pi\)
0.944956 0.327198i \(-0.106105\pi\)
\(402\) 0.679988 + 1.90198i 0.0339147 + 0.0948624i
\(403\) −4.20482 −0.209457
\(404\) 19.2713i 0.958785i
\(405\) −2.43621 + 12.1820i −0.121056 + 0.605329i
\(406\) 8.22808i 0.408353i
\(407\) −42.3348 −2.09846
\(408\) 5.98440 2.13951i 0.296272 0.105922i
\(409\) 0.913486i 0.0451690i 0.999745 + 0.0225845i \(0.00718948\pi\)
−0.999745 + 0.0225845i \(0.992811\pi\)
\(410\) 27.5779i 1.36198i
\(411\) 6.95035 + 19.4407i 0.342835 + 0.958939i
\(412\) −4.82924 −0.237920
\(413\) −3.00813 −0.148020
\(414\) 25.5912 + 31.2157i 1.25774 + 1.53417i
\(415\) 10.9839i 0.539177i
\(416\) −22.5344 −1.10484
\(417\) 8.56267 + 23.9505i 0.419316 + 1.17286i
\(418\) 57.7337 2.82385
\(419\) 19.6345 0.959208 0.479604 0.877485i \(-0.340780\pi\)
0.479604 + 0.877485i \(0.340780\pi\)
\(420\) −5.56323 + 1.98894i −0.271458 + 0.0970502i
\(421\) 1.89018i 0.0921217i −0.998939 0.0460609i \(-0.985333\pi\)
0.998939 0.0460609i \(-0.0146668\pi\)
\(422\) 18.6269i 0.906744i
\(423\) 10.2148 + 12.4599i 0.496660 + 0.605819i
\(424\) 12.7869i 0.620987i
\(425\) 4.45898i 0.216292i
\(426\) −20.4076 57.0818i −0.988752 2.76562i
\(427\) −3.83016 −0.185354
\(428\) 51.7448i 2.50118i
\(429\) 24.6568 8.81519i 1.19044 0.425601i
\(430\) −16.1093 + 12.6642i −0.776859 + 0.610722i
\(431\) 38.4169i 1.85048i −0.379384 0.925239i \(-0.623864\pi\)
0.379384 0.925239i \(-0.376136\pi\)
\(432\) −2.15997 1.29691i −0.103922 0.0623976i
\(433\) 23.8456i 1.14595i −0.819574 0.572973i \(-0.805790\pi\)
0.819574 0.572973i \(-0.194210\pi\)
\(434\) 2.06797i 0.0992657i
\(435\) −3.69935 10.3474i −0.177370 0.496119i
\(436\) −17.4352 −0.834995
\(437\) −36.4953 −1.74581
\(438\) 43.8388 15.6730i 2.09470 0.748887i
\(439\) −1.71526 −0.0818647 −0.0409323 0.999162i \(-0.513033\pi\)
−0.0409323 + 0.999162i \(0.513033\pi\)
\(440\) 14.5994i 0.695998i
\(441\) −14.7893 + 12.1245i −0.704251 + 0.577357i
\(442\) 11.8734i 0.564761i
\(443\) 30.7374i 1.46038i −0.683244 0.730190i \(-0.739432\pi\)
0.683244 0.730190i \(-0.260568\pi\)
\(444\) 51.9494 18.5727i 2.46541 0.881422i
\(445\) −0.579471 −0.0274696
\(446\) 9.39814i 0.445015i
\(447\) −3.54920 9.92740i −0.167871 0.469550i
\(448\) 10.3158i 0.487375i
\(449\) −34.7969 −1.64217 −0.821084 0.570808i \(-0.806630\pi\)
−0.821084 + 0.570808i \(0.806630\pi\)
\(450\) 16.2532 13.3246i 0.766182 0.628129i
\(451\) 36.6538 1.72596
\(452\) 9.72457 0.457405
\(453\) −22.7699 + 8.14058i −1.06982 + 0.382478i
\(454\) 48.5895 2.28042
\(455\) 3.97334i 0.186273i
\(456\) −25.5028 + 9.11763i −1.19428 + 0.426972i
\(457\) 4.33736i 0.202893i −0.994841 0.101446i \(-0.967653\pi\)
0.994841 0.101446i \(-0.0323471\pi\)
\(458\) 35.8678 1.67599
\(459\) −3.85408 + 6.41889i −0.179893 + 0.299608i
\(460\) 25.6370i 1.19533i
\(461\) 16.0297i 0.746576i −0.927715 0.373288i \(-0.878230\pi\)
0.927715 0.373288i \(-0.121770\pi\)
\(462\) 4.33540 + 12.1265i 0.201701 + 0.564175i
\(463\) 9.09369i 0.422619i 0.977419 + 0.211310i \(0.0677729\pi\)
−0.977419 + 0.211310i \(0.932227\pi\)
\(464\) 2.22851 0.103456
\(465\) −0.929759 2.60061i −0.0431165 0.120601i
\(466\) 13.7044 0.634842
\(467\) 8.32602 0.385282 0.192641 0.981269i \(-0.438295\pi\)
0.192641 + 0.981269i \(0.438295\pi\)
\(468\) −26.3893 + 21.6344i −1.21985 + 1.00005i
\(469\) 0.407364i 0.0188103i
\(470\) 16.7825i 0.774119i
\(471\) 4.65562 1.66445i 0.214520 0.0766940i
\(472\) 9.68696i 0.445878i
\(473\) 16.8320 + 21.4109i 0.773935 + 0.984472i
\(474\) −10.0450 28.0966i −0.461380 1.29052i
\(475\) 19.0021i 0.871876i
\(476\) −3.56060 −0.163200
\(477\) −9.55041 11.6494i −0.437283 0.533391i
\(478\) 22.8573i 1.04547i
\(479\) 39.2307i 1.79250i 0.443552 + 0.896249i \(0.353718\pi\)
−0.443552 + 0.896249i \(0.646282\pi\)
\(480\) −4.98275 13.9372i −0.227430 0.636142i
\(481\) 37.1030i 1.69175i
\(482\) 42.5702i 1.93902i
\(483\) −2.74054 7.66552i −0.124699 0.348793i
\(484\) −19.5298 −0.887719
\(485\) 15.8735 0.720778
\(486\) −34.9142 + 5.13307i −1.58374 + 0.232841i
\(487\) −19.0984 −0.865431 −0.432715 0.901531i \(-0.642444\pi\)
−0.432715 + 0.901531i \(0.642444\pi\)
\(488\) 12.3341i 0.558339i
\(489\) 5.94536 2.12555i 0.268858 0.0961209i
\(490\) −19.9201 −0.899897
\(491\) −4.49233 −0.202736 −0.101368 0.994849i \(-0.532322\pi\)
−0.101368 + 0.994849i \(0.532322\pi\)
\(492\) −44.9783 + 16.0804i −2.02778 + 0.724961i
\(493\) 6.62257i 0.298265i
\(494\) 50.5990i 2.27656i
\(495\) 10.9041 + 13.3007i 0.490104 + 0.597821i
\(496\) 0.560094 0.0251490
\(497\) 12.2257i 0.548398i
\(498\) −29.3796 + 10.5037i −1.31653 + 0.470681i
\(499\) 41.7606i 1.86946i 0.355356 + 0.934731i \(0.384360\pi\)
−0.355356 + 0.934731i \(0.615640\pi\)
\(500\) 34.9158 1.56148
\(501\) −20.5093 + 7.33237i −0.916286 + 0.327586i
\(502\) 19.0892i 0.851995i
\(503\) 3.35290 0.149499 0.0747493 0.997202i \(-0.476184\pi\)
0.0747493 + 0.997202i \(0.476184\pi\)
\(504\) −3.83016 4.67197i −0.170609 0.208106i
\(505\) 8.51275i 0.378812i
\(506\) 55.8824 2.48427
\(507\) −0.145639 0.407364i −0.00646805 0.0180917i
\(508\) 32.1698 1.42731
\(509\) 30.9784i 1.37309i −0.727087 0.686546i \(-0.759126\pi\)
0.727087 0.686546i \(-0.240874\pi\)
\(510\) −7.34353 + 2.62542i −0.325177 + 0.116256i
\(511\) −9.38934 −0.415360
\(512\) 5.47108 0.241790
\(513\) 16.4243 27.3543i 0.725151 1.20772i
\(514\) −45.4040 −2.00269
\(515\) 2.13323 0.0940012
\(516\) −30.0479 18.8891i −1.32278 0.831547i
\(517\) 22.3056 0.981000
\(518\) −18.2476 −0.801756
\(519\) 31.7953 11.3673i 1.39566 0.498969i
\(520\) −12.7952 −0.561106
\(521\) 13.6912 0.599822 0.299911 0.953967i \(-0.403043\pi\)
0.299911 + 0.953967i \(0.403043\pi\)
\(522\) 24.1396 19.7900i 1.05656 0.866186i
\(523\) 22.4499i 0.981666i 0.871254 + 0.490833i \(0.163308\pi\)
−0.871254 + 0.490833i \(0.836692\pi\)
\(524\) −66.0771 −2.88659
\(525\) −3.99123 + 1.42692i −0.174191 + 0.0622761i
\(526\) 22.0899 0.963166
\(527\) 1.66445i 0.0725048i
\(528\) −3.28436 + 1.17421i −0.142934 + 0.0511009i
\(529\) −12.3250 −0.535870
\(530\) 15.6909i 0.681571i
\(531\) −7.23509 8.82525i −0.313976 0.382983i
\(532\) 15.1736 0.657860
\(533\) 32.1241i 1.39145i
\(534\) −0.554138 1.54997i −0.0239799 0.0670738i
\(535\) 22.8573i 0.988206i
\(536\) −1.31182 −0.0566620
\(537\) 2.14547 + 6.00107i 0.0925840 + 0.258965i
\(538\) 23.1419i 0.997720i
\(539\) 26.4758i 1.14039i
\(540\) −19.2157 11.5377i −0.826913 0.496502i
\(541\) 24.2947 1.04451 0.522256 0.852789i \(-0.325091\pi\)
0.522256 + 0.852789i \(0.325091\pi\)
\(542\) −3.92690 −0.168675
\(543\) −6.34117 17.7368i −0.272126 0.761159i
\(544\) 8.92011i 0.382447i
\(545\) 7.70167 0.329903
\(546\) 10.6279 3.79963i 0.454832 0.162609i
\(547\) −31.9726 −1.36705 −0.683525 0.729927i \(-0.739554\pi\)
−0.683525 + 0.729927i \(0.739554\pi\)
\(548\) −37.2482 −1.59116
\(549\) −9.21222 11.2369i −0.393168 0.479580i
\(550\) 29.0964i 1.24068i
\(551\) 28.2223i 1.20231i
\(552\) −24.6850 + 8.82525i −1.05066 + 0.375628i
\(553\) 6.01769i 0.255898i
\(554\) 59.9971i 2.54903i
\(555\) −22.9477 + 8.20414i −0.974075 + 0.348246i
\(556\) −45.8889 −1.94612
\(557\) 15.6473i 0.662998i 0.943456 + 0.331499i \(0.107554\pi\)
−0.943456 + 0.331499i \(0.892446\pi\)
\(558\) 6.06701 4.97384i 0.256837 0.210559i
\(559\) 18.7649 14.7519i 0.793671 0.623939i
\(560\) 0.529261i 0.0223653i
\(561\) 3.48945 + 9.76028i 0.147325 + 0.412079i
\(562\) 10.8612i 0.458151i
\(563\) 13.0764i 0.551103i 0.961286 + 0.275551i \(0.0888605\pi\)
−0.961286 + 0.275551i \(0.911140\pi\)
\(564\) −27.3715 + 9.78571i −1.15255 + 0.412053i
\(565\) −4.29564 −0.180719
\(566\) −27.4486 −1.15375
\(567\) 6.97889 + 1.39567i 0.293086 + 0.0586125i
\(568\) 39.3700 1.65193
\(569\) 3.28528i 0.137726i 0.997626 + 0.0688631i \(0.0219372\pi\)
−0.997626 + 0.0688631i \(0.978063\pi\)
\(570\) 31.2947 11.1883i 1.31079 0.468628i
\(571\) 9.40229i 0.393474i −0.980456 0.196737i \(-0.936966\pi\)
0.980456 0.196737i \(-0.0630345\pi\)
\(572\) 47.2422i 1.97529i
\(573\) −2.49576 6.98085i −0.104262 0.291629i
\(574\) 15.7990 0.659436
\(575\) 18.3928i 0.767031i
\(576\) 30.2645 24.8113i 1.26102 1.03380i
\(577\) 11.6759i 0.486074i −0.970017 0.243037i \(-0.921856\pi\)
0.970017 0.243037i \(-0.0781436\pi\)
\(578\) 33.7849 1.40527
\(579\) 8.29981 + 23.2153i 0.344928 + 0.964793i
\(580\) 19.8255 0.823207
\(581\) 6.29249 0.261057
\(582\) 15.1795 + 42.4584i 0.629212 + 1.75996i
\(583\) −20.8548 −0.863718
\(584\) 30.2361i 1.25118i
\(585\) 11.6570 9.55660i 0.481957 0.395117i
\(586\) 40.4637i 1.67154i
\(587\) 9.96549 0.411320 0.205660 0.978624i \(-0.434066\pi\)
0.205660 + 0.978624i \(0.434066\pi\)
\(588\) −11.6152 32.4887i −0.479003 1.33981i
\(589\) 7.09314i 0.292268i
\(590\) 11.8870i 0.489379i
\(591\) −32.5701 + 11.6443i −1.33975 + 0.478982i
\(592\) 4.94224i 0.203125i
\(593\) 7.66844 0.314905 0.157453 0.987527i \(-0.449672\pi\)
0.157453 + 0.987527i \(0.449672\pi\)
\(594\) −25.1493 + 41.8855i −1.03189 + 1.71858i
\(595\) 1.57283 0.0644796
\(596\) 19.0208 0.779121
\(597\) −15.2956 + 5.46842i −0.626009 + 0.223808i
\(598\) 48.9765i 2.00280i
\(599\) 31.9548i 1.30564i −0.757515 0.652818i \(-0.773587\pi\)
0.757515 0.652818i \(-0.226413\pi\)
\(600\) 4.59507 + 12.8528i 0.187593 + 0.524713i
\(601\) 21.1530i 0.862849i −0.902149 0.431424i \(-0.858011\pi\)
0.902149 0.431424i \(-0.141989\pi\)
\(602\) 7.25513 + 9.22877i 0.295697 + 0.376137i
\(603\) 1.19513 0.979785i 0.0486693 0.0398999i
\(604\) 43.6269i 1.77515i
\(605\) 8.62693 0.350734
\(606\) −22.7699 + 8.14058i −0.924964 + 0.330689i
\(607\) 9.30353i 0.377619i 0.982014 + 0.188809i \(0.0604628\pi\)
−0.982014 + 0.188809i \(0.939537\pi\)
\(608\) 38.0134i 1.54165i
\(609\) −5.92786 + 2.11930i −0.240209 + 0.0858783i
\(610\) 15.1353i 0.612811i
\(611\) 19.5491i 0.790872i
\(612\) −8.56387 10.4461i −0.346174 0.422258i
\(613\) 20.8898 0.843731 0.421865 0.906658i \(-0.361375\pi\)
0.421865 + 0.906658i \(0.361375\pi\)
\(614\) −27.5856 −1.11327
\(615\) 19.8683 7.10321i 0.801167 0.286429i
\(616\) −8.36376 −0.336985
\(617\) 40.0920i 1.61404i −0.590523 0.807021i \(-0.701079\pi\)
0.590523 0.807021i \(-0.298921\pi\)
\(618\) 2.03996 + 5.70595i 0.0820594 + 0.229527i
\(619\) 28.7181 1.15428 0.577139 0.816646i \(-0.304169\pi\)
0.577139 + 0.816646i \(0.304169\pi\)
\(620\) 4.98275 0.200112
\(621\) 15.8976 26.4772i 0.637950 1.06249i
\(622\) 9.40229i 0.376998i
\(623\) 0.331970i 0.0133001i
\(624\) 1.02910 + 2.87848i 0.0411970 + 0.115232i
\(625\) 0.0496535 0.00198614
\(626\) 12.7008i 0.507625i
\(627\) −14.8704 41.5938i −0.593867 1.66110i
\(628\) 8.92011i 0.355951i
\(629\) −14.6871 −0.585611
\(630\) 4.70003 + 5.73302i 0.187254 + 0.228409i
\(631\) 23.0432i 0.917335i 0.888608 + 0.458667i \(0.151673\pi\)
−0.888608 + 0.458667i \(0.848327\pi\)
\(632\) 19.3785 0.770836
\(633\) 13.4196 4.79771i 0.533382 0.190692i
\(634\) 46.8888i 1.86219i
\(635\) −14.2104 −0.563923
\(636\) 25.5912 9.14923i 1.01476 0.362791i
\(637\) 23.2039 0.919372
\(638\) 43.2146i 1.71088i
\(639\) −35.8678 + 29.4050i −1.41891 + 1.16324i
\(640\) 23.6732 0.935764
\(641\) 11.9349 0.471400 0.235700 0.971826i \(-0.424262\pi\)
0.235700 + 0.971826i \(0.424262\pi\)
\(642\) 61.1386 21.8580i 2.41295 0.862666i
\(643\) −23.3288 −0.919997 −0.459999 0.887920i \(-0.652150\pi\)
−0.459999 + 0.887920i \(0.652150\pi\)
\(644\) 14.6871 0.578751
\(645\) 13.2731 + 8.34391i 0.522627 + 0.328541i
\(646\) 20.0294 0.788045
\(647\) 24.7629 0.973529 0.486765 0.873533i \(-0.338177\pi\)
0.486765 + 0.873533i \(0.338177\pi\)
\(648\) 4.49441 22.4739i 0.176557 0.882856i
\(649\) −15.7990 −0.620164
\(650\) −25.5007 −1.00022
\(651\) −1.48985 + 0.532645i −0.0583919 + 0.0208760i
\(652\) 11.3912i 0.446115i
\(653\) 26.0682 1.02013 0.510064 0.860136i \(-0.329622\pi\)
0.510064 + 0.860136i \(0.329622\pi\)
\(654\) 7.36497 + 20.6004i 0.287993 + 0.805541i
\(655\) 29.1883 1.14048
\(656\) 4.27903i 0.167068i
\(657\) −22.5830 27.5465i −0.881048 1.07469i
\(658\) 9.61445 0.374810
\(659\) 10.5545i 0.411144i 0.978642 + 0.205572i \(0.0659055\pi\)
−0.978642 + 0.205572i \(0.934094\pi\)
\(660\) −29.2186 + 10.4461i −1.13733 + 0.406613i
\(661\) −48.3094 −1.87902 −0.939509 0.342524i \(-0.888718\pi\)
−0.939509 + 0.342524i \(0.888718\pi\)
\(662\) 17.2576i 0.670734i
\(663\) 8.55411 3.05822i 0.332214 0.118772i
\(664\) 20.2635i 0.786375i
\(665\) −6.70266 −0.259918
\(666\) −43.8889 53.5350i −1.70066 2.07444i
\(667\) 27.3173i 1.05773i
\(668\) 39.2955i 1.52039i
\(669\) −6.77082 + 2.42067i −0.261775 + 0.0935885i
\(670\) 1.60975 0.0621900
\(671\) −20.1163 −0.776583
\(672\) −7.98439 + 2.85454i −0.308005 + 0.110116i
\(673\) 20.1763i 0.777740i −0.921293 0.388870i \(-0.872866\pi\)
0.921293 0.388870i \(-0.127134\pi\)
\(674\) 45.0269 1.73437
\(675\) −13.7859 8.27746i −0.530621 0.318600i
\(676\) 0.780505 0.0300194
\(677\) 34.1094 1.31093 0.655466 0.755225i \(-0.272472\pi\)
0.655466 + 0.755225i \(0.272472\pi\)
\(678\) −4.10784 11.4900i −0.157761 0.441270i
\(679\) 9.09369i 0.348984i
\(680\) 5.06491i 0.194230i
\(681\) −12.5151 35.0059i −0.479581 1.34143i
\(682\) 10.8612i 0.415896i
\(683\) 13.5793i 0.519599i 0.965663 + 0.259800i \(0.0836565\pi\)
−0.965663 + 0.259800i \(0.916344\pi\)
\(684\) 36.4953 + 44.5164i 1.39543 + 1.70213i
\(685\) 16.4537 0.628662
\(686\) 23.9433i 0.914160i
\(687\) −9.23843 25.8407i −0.352468 0.985884i
\(688\) −2.49954 + 1.96500i −0.0952941 + 0.0749148i
\(689\) 18.2776i 0.696321i
\(690\) 30.2912 10.8296i 1.15317 0.412274i
\(691\) 43.0220i 1.63663i −0.574768 0.818317i \(-0.694908\pi\)
0.574768 0.818317i \(-0.305092\pi\)
\(692\) 60.9193i 2.31581i
\(693\) 7.61976 6.24681i 0.289451 0.237297i
\(694\) −63.0478 −2.39326
\(695\) 20.2705 0.768905
\(696\) 6.82470 + 19.0892i 0.258689 + 0.723576i
\(697\) 12.7162 0.481659
\(698\) 52.8364i 1.99989i
\(699\) −3.52982 9.87320i −0.133510 0.373439i
\(700\) 7.64715i 0.289035i
\(701\) 22.2615i 0.840806i 0.907338 + 0.420403i \(0.138111\pi\)
−0.907338 + 0.420403i \(0.861889\pi\)
\(702\) 36.7093 + 22.0413i 1.38551 + 0.831896i
\(703\) 62.5895 2.36061
\(704\) 54.1794i 2.04196i
\(705\) 12.0908 4.32265i 0.455367 0.162801i
\(706\) 61.7634i 2.32449i
\(707\) 4.87682 0.183412
\(708\) 19.3871 6.93117i 0.728611 0.260489i
\(709\) −8.11021 −0.304585 −0.152293 0.988335i \(-0.548666\pi\)
−0.152293 + 0.988335i \(0.548666\pi\)
\(710\) −48.3113 −1.81309
\(711\) −17.6547 + 14.4736i −0.662103 + 0.542803i
\(712\) 1.06903 0.0400636
\(713\) 6.86568i 0.257122i
\(714\) 1.50406 + 4.20699i 0.0562882 + 0.157443i
\(715\) 20.8683i 0.780432i
\(716\) −11.4980 −0.429700
\(717\) 16.4673 5.88733i 0.614984 0.219866i
\(718\) 1.41961i 0.0529793i
\(719\) 2.88177i 0.107472i −0.998555 0.0537359i \(-0.982887\pi\)
0.998555 0.0537359i \(-0.0171129\pi\)
\(720\) −1.55275 + 1.27297i −0.0578674 + 0.0474407i
\(721\) 1.22209i 0.0455131i
\(722\) −42.3433 −1.57586
\(723\) −30.6694 + 10.9648i −1.14061 + 0.407784i
\(724\) 33.9835 1.26299
\(725\) 14.2234 0.528243
\(726\) 8.24977 + 23.0753i 0.306178 + 0.856405i
\(727\) 23.1180i 0.857399i 0.903447 + 0.428700i \(0.141028\pi\)
−0.903447 + 0.428700i \(0.858972\pi\)
\(728\) 7.33017i 0.271674i
\(729\) 12.6909 + 23.8315i 0.470033 + 0.882649i
\(730\) 37.1030i 1.37325i
\(731\) 5.83946 + 7.42799i 0.215980 + 0.274734i
\(732\) 24.6850 8.82525i 0.912383 0.326191i
\(733\) 32.3583i 1.19518i −0.801801 0.597591i \(-0.796125\pi\)
0.801801 0.597591i \(-0.203875\pi\)
\(734\) −36.8798 −1.36126
\(735\) 5.13079 + 14.3513i 0.189252 + 0.529354i
\(736\) 36.7944i 1.35626i
\(737\) 2.13951i 0.0788100i
\(738\) 37.9994 + 46.3510i 1.39878 + 1.70621i
\(739\) 7.67408i 0.282295i 0.989989 + 0.141148i \(0.0450793\pi\)
−0.989989 + 0.141148i \(0.954921\pi\)
\(740\) 43.9675i 1.61628i
\(741\) −36.4537 + 13.0327i −1.33916 + 0.478770i
\(742\) −8.98910 −0.330000
\(743\) 34.3439 1.25995 0.629977 0.776613i \(-0.283064\pi\)
0.629977 + 0.776613i \(0.283064\pi\)
\(744\) 1.71526 + 4.79771i 0.0628843 + 0.175893i
\(745\) −8.40207 −0.307828
\(746\) 17.0603i 0.624621i
\(747\) 15.1346 + 18.4609i 0.553745 + 0.675450i
\(748\) −18.7006 −0.683761
\(749\) −13.0946 −0.478466
\(750\) −14.7491 41.2545i −0.538561 1.50640i
\(751\) 36.1147i 1.31785i −0.752211 0.658923i \(-0.771012\pi\)
0.752211 0.658923i \(-0.228988\pi\)
\(752\) 2.60400i 0.0949581i
\(753\) −13.7527 + 4.91680i −0.501176 + 0.179178i
\(754\) −37.8742 −1.37930
\(755\) 19.2713i 0.701356i
\(756\) −6.60975 + 11.0084i −0.240394 + 0.400371i
\(757\) 46.4814i 1.68940i 0.535244 + 0.844698i \(0.320220\pi\)
−0.535244 + 0.844698i \(0.679780\pi\)
\(758\) −65.7505 −2.38817
\(759\) −14.3936 40.2600i −0.522453 1.46135i
\(760\) 21.5843i 0.782945i
\(761\) −41.1600 −1.49205 −0.746025 0.665918i \(-0.768040\pi\)
−0.746025 + 0.665918i \(0.768040\pi\)
\(762\) −13.5892 38.0100i −0.492283 1.37696i
\(763\) 4.41217i 0.159731i
\(764\) 13.3752 0.483899
\(765\) 3.78293 + 4.61436i 0.136772 + 0.166833i
\(766\) −20.3397 −0.734903
\(767\) 13.8465i 0.499969i
\(768\) 7.42544 + 20.7696i 0.267942 + 0.749458i
\(769\) 14.3756 0.518396 0.259198 0.965824i \(-0.416542\pi\)
0.259198 + 0.965824i \(0.416542\pi\)
\(770\) 10.2633 0.369862
\(771\) 11.6947 + 32.7110i 0.421173 + 1.17806i
\(772\) −44.4802 −1.60088
\(773\) −17.9885 −0.647003 −0.323501 0.946228i \(-0.604860\pi\)
−0.323501 + 0.946228i \(0.604860\pi\)
\(774\) −9.62549 + 43.4820i −0.345981 + 1.56293i
\(775\) 3.57477 0.128410
\(776\) −29.2840 −1.05124
\(777\) 4.70003 + 13.1464i 0.168613 + 0.471624i
\(778\) 62.6041 2.24447
\(779\) −54.1905 −1.94158
\(780\) 9.15516 + 25.6078i 0.327807 + 0.916905i
\(781\) 64.2105i 2.29763i
\(782\) 19.3871 0.693281
\(783\) −20.4752 12.2939i −0.731723 0.439347i
\(784\) −3.09083 −0.110387
\(785\) 3.94029i 0.140635i
\(786\) 27.9122 + 78.0729i 0.995596 + 2.78477i
\(787\) −2.57947 −0.0919482 −0.0459741 0.998943i \(-0.514639\pi\)
−0.0459741 + 0.998943i \(0.514639\pi\)
\(788\) 62.4039i 2.22305i
\(789\) −5.68968 15.9145i −0.202558 0.566571i
\(790\) −23.7796 −0.846040
\(791\) 2.46091i 0.0874999i
\(792\) −20.1163 24.5376i −0.714803 0.871906i
\(793\) 17.6304i 0.626073i
\(794\) −9.69782 −0.344163
\(795\) −11.3044 + 4.04150i −0.400926 + 0.143337i
\(796\) 29.3063i 1.03873i
\(797\) 47.7714i 1.69215i 0.533063 + 0.846076i \(0.321041\pi\)
−0.533063 + 0.846076i \(0.678959\pi\)
\(798\) −6.40963 17.9283i −0.226898 0.634654i
\(799\) 7.73841 0.273765
\(800\) 19.1579 0.677333
\(801\) −0.973935 + 0.798448i −0.0344123 + 0.0282118i
\(802\) 29.6658i 1.04753i
\(803\) −49.3136 −1.74024
\(804\) 0.938628 + 2.62542i 0.0331029 + 0.0925915i
\(805\) −6.48773 −0.228662
\(806\) −9.51895 −0.335291
\(807\) 16.6724 5.96065i 0.586897 0.209825i
\(808\) 15.7046i 0.552487i
\(809\) 22.4918i 0.790771i 0.918515 + 0.395386i \(0.129389\pi\)
−0.918515 + 0.395386i \(0.870611\pi\)
\(810\) −5.51514 + 27.5779i −0.193782 + 0.968989i
\(811\) 20.5481i 0.721542i 0.932654 + 0.360771i \(0.117486\pi\)
−0.932654 + 0.360771i \(0.882514\pi\)
\(812\) 11.3577i 0.398577i
\(813\) 1.01145 + 2.82910i 0.0354730 + 0.0992210i
\(814\) −95.8383 −3.35913
\(815\) 5.03186i 0.176258i
\(816\) −1.13943 + 0.407364i −0.0398881 + 0.0142606i
\(817\) −24.8851 31.6547i −0.870619 1.10746i
\(818\) 2.06797i 0.0723049i
\(819\) −5.47483 6.67811i −0.191306 0.233352i
\(820\) 38.0674i 1.32937i
\(821\) 29.4659i 1.02837i −0.857680 0.514184i \(-0.828095\pi\)
0.857680 0.514184i \(-0.171905\pi\)
\(822\) 15.7343 + 44.0103i 0.548798 + 1.53503i
\(823\) −17.9239 −0.624786 −0.312393 0.949953i \(-0.601131\pi\)
−0.312393 + 0.949953i \(0.601131\pi\)
\(824\) −3.93546 −0.137098
\(825\) −20.9623 + 7.49434i −0.729813 + 0.260919i
\(826\) −6.80986 −0.236945
\(827\) 16.0839i 0.559291i −0.960103 0.279646i \(-0.909783\pi\)
0.960103 0.279646i \(-0.0902170\pi\)
\(828\) 35.3250 + 43.0889i 1.22763 + 1.49744i
\(829\) 46.9875i 1.63194i −0.578091 0.815972i \(-0.696202\pi\)
0.578091 0.815972i \(-0.303798\pi\)
\(830\) 24.8655i 0.863094i
\(831\) 43.2245 15.4534i 1.49944 0.536073i
\(832\) −47.4839 −1.64621
\(833\) 9.18514i 0.318246i
\(834\) 19.3843 + 54.2197i 0.671225 + 1.87747i
\(835\) 17.3580i 0.600700i
\(836\) 79.6932 2.75625
\(837\) −5.14604 3.08983i −0.177873 0.106800i
\(838\) 44.4490 1.53546
\(839\) 10.4024 0.359131 0.179566 0.983746i \(-0.442531\pi\)
0.179566 + 0.983746i \(0.442531\pi\)
\(840\) −4.53360 + 1.62083i −0.156424 + 0.0559240i
\(841\) −7.87511 −0.271556
\(842\) 4.27903i 0.147465i
\(843\) 7.82484 2.79750i 0.269502 0.0963510i
\(844\) 25.7118i 0.885037i
\(845\) −0.344773 −0.0118606
\(846\) 23.1245 + 28.2069i 0.795036 + 0.969772i
\(847\) 4.94224i 0.169817i
\(848\) 2.43463i 0.0836055i
\(849\) 7.06990 + 19.7751i 0.242638 + 0.678680i
\(850\) 10.0943i 0.346232i
\(851\) 60.5824 2.07674
\(852\) −28.1698 78.7934i −0.965083 2.69942i
\(853\) −0.280047 −0.00958862 −0.00479431 0.999989i \(-0.501526\pi\)
−0.00479431 + 0.999989i \(0.501526\pi\)
\(854\) −8.67079 −0.296708
\(855\) −16.1211 19.6643i −0.551330 0.672504i
\(856\) 42.1680i 1.44127i
\(857\) 2.54303i 0.0868683i 0.999056 + 0.0434341i \(0.0138299\pi\)
−0.999056 + 0.0434341i \(0.986170\pi\)
\(858\) 55.8186 19.9560i 1.90562 0.681287i
\(859\) 2.47112i 0.0843135i −0.999111 0.0421567i \(-0.986577\pi\)
0.999111 0.0421567i \(-0.0134229\pi\)
\(860\) −22.2366 + 17.4811i −0.758262 + 0.596102i
\(861\) −4.06932 11.3822i −0.138682 0.387906i
\(862\) 86.9690i 2.96218i
\(863\) 33.7475 1.14878 0.574390 0.818582i \(-0.305239\pi\)
0.574390 + 0.818582i \(0.305239\pi\)
\(864\) −27.5786 16.5589i −0.938241 0.563346i
\(865\) 26.9100i 0.914966i
\(866\) 53.9821i 1.83439i
\(867\) −8.70195 24.3401i −0.295534 0.826633i
\(868\) 2.85454i 0.0968894i
\(869\) 31.6054i 1.07214i
\(870\) −8.37466 23.4246i −0.283927 0.794169i
\(871\) −1.87511 −0.0635358
\(872\) −14.2083 −0.481155
\(873\) 26.6791 21.8720i 0.902950 0.740253i
\(874\) −82.6188 −2.79462
\(875\) 8.83583i 0.298706i
\(876\) 60.5133 21.6344i 2.04456 0.730959i
\(877\) 16.1661 0.545889 0.272945 0.962030i \(-0.412002\pi\)
0.272945 + 0.962030i \(0.412002\pi\)
\(878\) −3.88303 −0.131046
\(879\) 29.1518 10.4222i 0.983265 0.351532i
\(880\) 2.77972i 0.0937045i
\(881\) 16.8803i 0.568713i −0.958719 0.284356i \(-0.908220\pi\)
0.958719 0.284356i \(-0.0917799\pi\)
\(882\) −33.4803 + 27.4477i −1.12734 + 0.924212i
\(883\) 44.9229 1.51178 0.755889 0.654700i \(-0.227205\pi\)
0.755889 + 0.654700i \(0.227205\pi\)
\(884\) 16.3896i 0.551241i
\(885\) −8.56387 + 3.06171i −0.287872 + 0.102918i
\(886\) 69.5841i 2.33772i
\(887\) −11.3609 −0.381462 −0.190731 0.981642i \(-0.561086\pi\)
−0.190731 + 0.981642i \(0.561086\pi\)
\(888\) 42.3348 15.1353i 1.42066 0.507908i
\(889\) 8.14093i 0.273038i
\(890\) −1.31182 −0.0439723
\(891\) 36.6538 + 7.33017i 1.22795 + 0.245570i
\(892\) 12.9728i 0.434362i
\(893\) −32.9776 −1.10355
\(894\) −8.03474 22.4739i −0.268722 0.751638i
\(895\) 5.07901 0.169773
\(896\) 13.5620i 0.453075i
\(897\) −35.2847 + 12.6148i −1.17812 + 0.421197i
\(898\) −78.7740 −2.62872
\(899\) 5.30933 0.177076
\(900\) 22.4352 18.3928i 0.747840 0.613092i
\(901\) −7.23509 −0.241036
\(902\) 82.9776 2.76285
\(903\) 4.78010 7.60395i 0.159072 0.253043i
\(904\) 7.92477 0.263574
\(905\) −15.0116 −0.499001
\(906\) −51.5470 + 18.4288i −1.71253 + 0.612257i
\(907\) 38.7825 1.28775 0.643875 0.765131i \(-0.277326\pi\)
0.643875 + 0.765131i \(0.277326\pi\)
\(908\) 67.0709 2.22583
\(909\) 11.7296 + 14.3076i 0.389048 + 0.474554i
\(910\) 8.99493i 0.298179i
\(911\) −23.7070 −0.785449 −0.392724 0.919656i \(-0.628467\pi\)
−0.392724 + 0.919656i \(0.628467\pi\)
\(912\) 4.85574 1.73600i 0.160790 0.0574847i
\(913\) 33.0487 1.09375
\(914\) 9.81900i 0.324784i
\(915\) −10.9041 + 3.89839i −0.360479 + 0.128877i
\(916\) 49.5104 1.63587
\(917\) 16.7215i 0.552194i
\(918\) −8.72494 + 14.5312i −0.287966 + 0.479601i
\(919\) 48.6950 1.60630 0.803149 0.595778i \(-0.203156\pi\)
0.803149 + 0.595778i \(0.203156\pi\)
\(920\) 20.8922i 0.688794i
\(921\) 7.10521 + 19.8739i 0.234125 + 0.654866i
\(922\) 36.2883i 1.19509i
\(923\) 56.2754 1.85233
\(924\) 5.98440 + 16.7389i 0.196872 + 0.550669i
\(925\) 31.5436i 1.03715i
\(926\) 20.5865i 0.676514i
\(927\) 3.58538 2.93935i 0.117759 0.0965411i
\(928\) 28.4537 0.934037
\(929\) 2.58626 0.0848523 0.0424262 0.999100i \(-0.486491\pi\)
0.0424262 + 0.999100i \(0.486491\pi\)
\(930\) −2.10481 5.88733i −0.0690194 0.193053i
\(931\) 39.1429i 1.28286i
\(932\) 18.9169 0.619645
\(933\) 6.77381 2.42174i 0.221765 0.0792842i
\(934\) 18.8486 0.616746
\(935\) 8.26062 0.270151
\(936\) −21.5053 + 17.6304i −0.702921 + 0.576267i
\(937\) 46.6280i 1.52327i 0.648005 + 0.761636i \(0.275603\pi\)
−0.648005 + 0.761636i \(0.724397\pi\)
\(938\) 0.922200i 0.0301109i
\(939\) −9.15017 + 3.27132i −0.298605 + 0.106756i
\(940\) 23.1659i 0.755588i
\(941\) 38.0240i 1.23955i −0.784781 0.619773i \(-0.787225\pi\)
0.784781 0.619773i \(-0.212775\pi\)
\(942\) 10.5395 3.76803i 0.343395 0.122769i
\(943\) −52.4528 −1.70810
\(944\) 1.84440i 0.0600301i
\(945\) 2.91973 4.86275i 0.0949788 0.158185i
\(946\) 38.1046 + 48.4703i 1.23889 + 1.57591i
\(947\) 40.7364i 1.32375i −0.749612 0.661877i \(-0.769760\pi\)
0.749612 0.661877i \(-0.230240\pi\)
\(948\) −13.8656 38.7834i −0.450335 1.25963i
\(949\) 43.2195i 1.40296i
\(950\) 43.0174i 1.39567i
\(951\) 33.7806 12.0771i 1.09541 0.391627i
\(952\) −2.90161 −0.0940417
\(953\) 33.7229 1.09239 0.546196 0.837658i \(-0.316076\pi\)
0.546196 + 0.837658i \(0.316076\pi\)
\(954\) −21.6204 26.3722i −0.699987 0.853833i
\(955\) −5.90826 −0.191187
\(956\) 31.5512i 1.02044i
\(957\) −31.1337 + 11.1308i −1.00641 + 0.359806i
\(958\) 88.8113i 2.86936i
\(959\) 9.42606i 0.304383i
\(960\) −10.4995 29.3681i −0.338871 0.947852i
\(961\) −29.6656 −0.956955
\(962\) 83.9947i 2.70810i
\(963\) −31.4948 38.4169i −1.01491 1.23797i
\(964\) 58.7622i 1.89260i
\(965\) 19.6483 0.632500
\(966\) −6.20409 17.3534i −0.199613 0.558336i
\(967\) −20.3241 −0.653579 −0.326789 0.945097i \(-0.605967\pi\)
−0.326789 + 0.945097i \(0.605967\pi\)
\(968\) −15.9153 −0.511537
\(969\) −5.15894 14.4300i −0.165729 0.463558i
\(970\) 35.9348 1.15380
\(971\) 14.4736i 0.464481i 0.972658 + 0.232240i \(0.0746056\pi\)
−0.972658 + 0.232240i \(0.925394\pi\)
\(972\) −48.1941 + 7.08548i −1.54583 + 0.227267i
\(973\) 11.6127i 0.372286i
\(974\) −43.2353 −1.38535
\(975\) 6.56819 + 18.3718i 0.210350 + 0.588368i
\(976\) 2.34842i 0.0751710i
\(977\) 10.2661i 0.328443i 0.986424 + 0.164221i \(0.0525112\pi\)
−0.986424 + 0.164221i \(0.947489\pi\)
\(978\) 13.4592 4.81187i 0.430378 0.153867i
\(979\) 1.74354i 0.0557237i
\(980\) −27.4968 −0.878355
\(981\) 12.9444 10.6121i 0.413284 0.338817i
\(982\) −10.1698 −0.324533
\(983\) −1.68775 −0.0538309 −0.0269154 0.999638i \(-0.508568\pi\)
−0.0269154 + 0.999638i \(0.508568\pi\)
\(984\) −36.6538 + 13.1043i −1.16848 + 0.417749i
\(985\) 27.5657i 0.878317i
\(986\) 14.9923i 0.477452i
\(987\) −2.47638 6.92665i −0.0788241 0.220478i
\(988\) 69.8448i 2.22206i
\(989\) −24.0871 30.6396i −0.765925 0.974283i
\(990\) 24.6850 + 30.1104i 0.784540 + 0.956970i
\(991\) 45.2324i 1.43685i 0.695603 + 0.718427i \(0.255137\pi\)
−0.695603 + 0.718427i \(0.744863\pi\)
\(992\) 7.15128 0.227053
\(993\) −12.4331 + 4.44501i −0.394552 + 0.141058i
\(994\) 27.6768i 0.877855i
\(995\) 12.9455i 0.410400i
\(996\) −40.5545 + 14.4988i −1.28502 + 0.459413i
\(997\) 19.1641i 0.606932i 0.952842 + 0.303466i \(0.0981439\pi\)
−0.952842 + 0.303466i \(0.901856\pi\)
\(998\) 94.5386i 2.99257i
\(999\) −27.2645 + 45.4084i −0.862609 + 1.43666i
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 129.2.d.a.128.11 yes 12
3.2 odd 2 inner 129.2.d.a.128.1 12
4.3 odd 2 2064.2.l.h.257.8 12
12.11 even 2 2064.2.l.h.257.6 12
43.42 odd 2 inner 129.2.d.a.128.2 yes 12
129.128 even 2 inner 129.2.d.a.128.12 yes 12
172.171 even 2 2064.2.l.h.257.5 12
516.515 odd 2 2064.2.l.h.257.7 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
129.2.d.a.128.1 12 3.2 odd 2 inner
129.2.d.a.128.2 yes 12 43.42 odd 2 inner
129.2.d.a.128.11 yes 12 1.1 even 1 trivial
129.2.d.a.128.12 yes 12 129.128 even 2 inner
2064.2.l.h.257.5 12 172.171 even 2
2064.2.l.h.257.6 12 12.11 even 2
2064.2.l.h.257.7 12 516.515 odd 2
2064.2.l.h.257.8 12 4.3 odd 2