Properties

Label 729.2.g.c.55.5
Level $729$
Weight $2$
Character 729.55
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(28,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([44]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.g (of order \(27\), degree \(18\), not 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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 55.5
Character \(\chi\) \(=\) 729.55
Dual form 729.2.g.c.676.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0800459 + 0.185567i) q^{2} +(1.34446 + 1.42504i) q^{4} +(-0.0529885 - 0.909778i) q^{5} +(0.159621 + 0.0378310i) q^{7} +(-0.751874 + 0.273660i) q^{8} +O(q^{10})\) \(q+(-0.0800459 + 0.185567i) q^{2} +(1.34446 + 1.42504i) q^{4} +(-0.0529885 - 0.909778i) q^{5} +(0.159621 + 0.0378310i) q^{7} +(-0.751874 + 0.273660i) q^{8} +(0.173067 + 0.0629911i) q^{10} +(0.626618 + 0.412133i) q^{11} +(3.50987 + 0.410245i) q^{13} +(-0.0197972 + 0.0265923i) q^{14} +(-0.218428 + 3.75026i) q^{16} +(-3.09332 + 2.59561i) q^{17} +(1.63194 + 1.36936i) q^{19} +(1.22523 - 1.29867i) q^{20} +(-0.126637 + 0.0832903i) q^{22} +(7.98355 - 1.89214i) q^{23} +(4.14130 - 0.484049i) q^{25} +(-0.357079 + 0.618479i) q^{26} +(0.160693 + 0.278329i) q^{28} +(-3.92999 - 5.27889i) q^{29} +(-1.60483 + 5.36050i) q^{31} +(-2.10848 - 1.05892i) q^{32} +(-0.234052 - 0.781788i) q^{34} +(0.0259597 - 0.147225i) q^{35} +(0.783915 + 4.44580i) q^{37} +(-0.384740 + 0.193224i) q^{38} +(0.288810 + 0.669538i) q^{40} +(4.33453 + 10.0486i) q^{41} +(-3.09218 + 1.55295i) q^{43} +(0.255154 + 1.44705i) q^{44} +(-0.287932 + 1.63294i) q^{46} +(-2.56133 - 8.55545i) q^{47} +(-6.23138 - 3.12952i) q^{49} +(-0.241671 + 0.807237i) q^{50} +(4.13425 + 5.55326i) q^{52} +(3.06986 + 5.31715i) q^{53} +(0.341746 - 0.591922i) q^{55} +(-0.130368 + 0.0152378i) q^{56} +(1.29417 - 0.306724i) q^{58} +(2.43628 - 1.60237i) q^{59} +(4.84595 - 5.13641i) q^{61} +(-0.866274 - 0.726890i) q^{62} +(-5.39019 + 4.52290i) q^{64} +(0.187249 - 3.21494i) q^{65} +(5.30383 - 7.12428i) q^{67} +(-7.85768 - 0.918431i) q^{68} +(0.0252421 + 0.0166020i) q^{70} +(-8.94644 - 3.25624i) q^{71} +(8.28233 - 3.01452i) q^{73} +(-0.887745 - 0.210399i) q^{74} +(0.242679 + 4.16663i) q^{76} +(0.0844303 + 0.0894909i) q^{77} +(-1.27718 + 2.96084i) q^{79} +3.42347 q^{80} -2.21165 q^{82} +(-6.66541 + 15.4521i) q^{83} +(2.52534 + 2.67670i) q^{85} +(-0.0406606 - 0.698115i) q^{86} +(-0.583922 - 0.138392i) q^{88} +(10.7409 - 3.90935i) q^{89} +(0.544730 + 0.198266i) q^{91} +(13.4299 + 8.83298i) q^{92} +(1.79264 + 0.209529i) q^{94} +(1.15934 - 1.55727i) q^{95} +(0.263420 - 4.52275i) q^{97} +(1.07953 - 0.905836i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{17}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0800459 + 0.185567i −0.0566010 + 0.131216i −0.944170 0.329459i \(-0.893134\pi\)
0.887569 + 0.460675i \(0.152393\pi\)
\(3\) 0 0
\(4\) 1.34446 + 1.42504i 0.672228 + 0.712520i
\(5\) −0.0529885 0.909778i −0.0236972 0.406865i −0.989210 0.146508i \(-0.953197\pi\)
0.965512 0.260357i \(-0.0838403\pi\)
\(6\) 0 0
\(7\) 0.159621 + 0.0378310i 0.0603312 + 0.0142988i 0.260671 0.965428i \(-0.416056\pi\)
−0.200339 + 0.979727i \(0.564204\pi\)
\(8\) −0.751874 + 0.273660i −0.265828 + 0.0967534i
\(9\) 0 0
\(10\) 0.173067 + 0.0629911i 0.0547284 + 0.0199195i
\(11\) 0.626618 + 0.412133i 0.188932 + 0.124263i 0.640451 0.767999i \(-0.278747\pi\)
−0.451519 + 0.892262i \(0.649118\pi\)
\(12\) 0 0
\(13\) 3.50987 + 0.410245i 0.973463 + 0.113781i 0.587929 0.808912i \(-0.299943\pi\)
0.385533 + 0.922694i \(0.374017\pi\)
\(14\) −0.0197972 + 0.0265923i −0.00529104 + 0.00710710i
\(15\) 0 0
\(16\) −0.218428 + 3.75026i −0.0546069 + 0.937564i
\(17\) −3.09332 + 2.59561i −0.750241 + 0.629527i −0.935567 0.353150i \(-0.885110\pi\)
0.185326 + 0.982677i \(0.440666\pi\)
\(18\) 0 0
\(19\) 1.63194 + 1.36936i 0.374394 + 0.314154i 0.810497 0.585743i \(-0.199197\pi\)
−0.436103 + 0.899897i \(0.643642\pi\)
\(20\) 1.22523 1.29867i 0.273969 0.290391i
\(21\) 0 0
\(22\) −0.126637 + 0.0832903i −0.0269990 + 0.0177575i
\(23\) 7.98355 1.89214i 1.66469 0.394538i 0.712891 0.701275i \(-0.247385\pi\)
0.951794 + 0.306737i \(0.0992372\pi\)
\(24\) 0 0
\(25\) 4.14130 0.484049i 0.828261 0.0968098i
\(26\) −0.357079 + 0.618479i −0.0700289 + 0.121294i
\(27\) 0 0
\(28\) 0.160693 + 0.278329i 0.0303682 + 0.0525992i
\(29\) −3.92999 5.27889i −0.729780 0.980265i −0.999848 0.0174234i \(-0.994454\pi\)
0.270068 0.962841i \(-0.412954\pi\)
\(30\) 0 0
\(31\) −1.60483 + 5.36050i −0.288236 + 0.962774i 0.684140 + 0.729351i \(0.260178\pi\)
−0.972375 + 0.233423i \(0.925007\pi\)
\(32\) −2.10848 1.05892i −0.372730 0.187192i
\(33\) 0 0
\(34\) −0.234052 0.781788i −0.0401396 0.134075i
\(35\) 0.0259597 0.147225i 0.00438799 0.0248855i
\(36\) 0 0
\(37\) 0.783915 + 4.44580i 0.128875 + 0.730885i 0.978931 + 0.204193i \(0.0654569\pi\)
−0.850056 + 0.526692i \(0.823432\pi\)
\(38\) −0.384740 + 0.193224i −0.0624130 + 0.0313450i
\(39\) 0 0
\(40\) 0.288810 + 0.669538i 0.0456649 + 0.105863i
\(41\) 4.33453 + 10.0486i 0.676940 + 1.56932i 0.815363 + 0.578950i \(0.196537\pi\)
−0.138423 + 0.990373i \(0.544203\pi\)
\(42\) 0 0
\(43\) −3.09218 + 1.55295i −0.471553 + 0.236823i −0.668673 0.743557i \(-0.733137\pi\)
0.197120 + 0.980379i \(0.436841\pi\)
\(44\) 0.255154 + 1.44705i 0.0384659 + 0.218151i
\(45\) 0 0
\(46\) −0.287932 + 1.63294i −0.0424533 + 0.240764i
\(47\) −2.56133 8.55545i −0.373609 1.24794i −0.913719 0.406346i \(-0.866803\pi\)
0.540110 0.841594i \(-0.318383\pi\)
\(48\) 0 0
\(49\) −6.23138 3.12952i −0.890197 0.447074i
\(50\) −0.241671 + 0.807237i −0.0341774 + 0.114161i
\(51\) 0 0
\(52\) 4.13425 + 5.55326i 0.573317 + 0.770098i
\(53\) 3.06986 + 5.31715i 0.421677 + 0.730366i 0.996104 0.0881898i \(-0.0281082\pi\)
−0.574426 + 0.818556i \(0.694775\pi\)
\(54\) 0 0
\(55\) 0.341746 0.591922i 0.0460810 0.0798147i
\(56\) −0.130368 + 0.0152378i −0.0174212 + 0.00203624i
\(57\) 0 0
\(58\) 1.29417 0.306724i 0.169933 0.0402748i
\(59\) 2.43628 1.60237i 0.317177 0.208611i −0.380930 0.924604i \(-0.624396\pi\)
0.698107 + 0.715993i \(0.254026\pi\)
\(60\) 0 0
\(61\) 4.84595 5.13641i 0.620461 0.657650i −0.338573 0.940940i \(-0.609944\pi\)
0.959034 + 0.283290i \(0.0914258\pi\)
\(62\) −0.866274 0.726890i −0.110017 0.0923151i
\(63\) 0 0
\(64\) −5.39019 + 4.52290i −0.673774 + 0.565363i
\(65\) 0.187249 3.21494i 0.0232254 0.398764i
\(66\) 0 0
\(67\) 5.30383 7.12428i 0.647966 0.870370i −0.349824 0.936816i \(-0.613759\pi\)
0.997790 + 0.0664457i \(0.0211659\pi\)
\(68\) −7.85768 0.918431i −0.952883 0.111376i
\(69\) 0 0
\(70\) 0.0252421 + 0.0166020i 0.00301701 + 0.00198432i
\(71\) −8.94644 3.25624i −1.06175 0.386444i −0.248663 0.968590i \(-0.579991\pi\)
−0.813084 + 0.582146i \(0.802213\pi\)
\(72\) 0 0
\(73\) 8.28233 3.01452i 0.969373 0.352823i 0.191673 0.981459i \(-0.438609\pi\)
0.777700 + 0.628636i \(0.216386\pi\)
\(74\) −0.887745 0.210399i −0.103198 0.0244584i
\(75\) 0 0
\(76\) 0.242679 + 4.16663i 0.0278372 + 0.477946i
\(77\) 0.0844303 + 0.0894909i 0.00962173 + 0.0101984i
\(78\) 0 0
\(79\) −1.27718 + 2.96084i −0.143694 + 0.333121i −0.974830 0.222948i \(-0.928432\pi\)
0.831136 + 0.556069i \(0.187691\pi\)
\(80\) 3.42347 0.382756
\(81\) 0 0
\(82\) −2.21165 −0.244236
\(83\) −6.66541 + 15.4521i −0.731623 + 1.69609i −0.0137642 + 0.999905i \(0.504381\pi\)
−0.717859 + 0.696188i \(0.754878\pi\)
\(84\) 0 0
\(85\) 2.52534 + 2.67670i 0.273911 + 0.290329i
\(86\) −0.0406606 0.698115i −0.00438454 0.0752797i
\(87\) 0 0
\(88\) −0.583922 0.138392i −0.0622463 0.0147527i
\(89\) 10.7409 3.90935i 1.13853 0.414390i 0.297146 0.954832i \(-0.403965\pi\)
0.841382 + 0.540442i \(0.181743\pi\)
\(90\) 0 0
\(91\) 0.544730 + 0.198266i 0.0571033 + 0.0207839i
\(92\) 13.4299 + 8.83298i 1.40016 + 0.920902i
\(93\) 0 0
\(94\) 1.79264 + 0.209529i 0.184896 + 0.0216113i
\(95\) 1.15934 1.55727i 0.118946 0.159772i
\(96\) 0 0
\(97\) 0.263420 4.52275i 0.0267463 0.459216i −0.958172 0.286194i \(-0.907610\pi\)
0.984918 0.173022i \(-0.0553531\pi\)
\(98\) 1.07953 0.905836i 0.109049 0.0915032i
\(99\) 0 0
\(100\) 6.25759 + 5.25074i 0.625759 + 0.525074i
\(101\) −1.57950 + 1.67417i −0.157166 + 0.166586i −0.801172 0.598435i \(-0.795790\pi\)
0.644006 + 0.765020i \(0.277271\pi\)
\(102\) 0 0
\(103\) −2.17433 + 1.43008i −0.214243 + 0.140910i −0.652095 0.758137i \(-0.726110\pi\)
0.437852 + 0.899047i \(0.355739\pi\)
\(104\) −2.75125 + 0.652058i −0.269782 + 0.0639395i
\(105\) 0 0
\(106\) −1.23242 + 0.144049i −0.119703 + 0.0139913i
\(107\) −5.97720 + 10.3528i −0.577837 + 1.00084i 0.417890 + 0.908498i \(0.362770\pi\)
−0.995727 + 0.0923460i \(0.970563\pi\)
\(108\) 0 0
\(109\) −9.06553 15.7020i −0.868320 1.50397i −0.863712 0.503985i \(-0.831867\pi\)
−0.00460743 0.999989i \(-0.501467\pi\)
\(110\) 0.0824859 + 0.110798i 0.00786472 + 0.0105642i
\(111\) 0 0
\(112\) −0.176742 + 0.590358i −0.0167005 + 0.0557836i
\(113\) −10.6343 5.34075i −1.00039 0.502416i −0.128288 0.991737i \(-0.540948\pi\)
−0.872104 + 0.489321i \(0.837244\pi\)
\(114\) 0 0
\(115\) −2.14446 7.16299i −0.199972 0.667953i
\(116\) 2.23893 12.6976i 0.207880 1.17894i
\(117\) 0 0
\(118\) 0.102333 + 0.580358i 0.00942050 + 0.0534263i
\(119\) −0.591955 + 0.297291i −0.0542644 + 0.0272526i
\(120\) 0 0
\(121\) −4.13408 9.58388i −0.375826 0.871262i
\(122\) 0.565251 + 1.31040i 0.0511754 + 0.118638i
\(123\) 0 0
\(124\) −9.79654 + 4.92001i −0.879756 + 0.441830i
\(125\) −1.45106 8.22939i −0.129787 0.736059i
\(126\) 0 0
\(127\) 2.53378 14.3698i 0.224837 1.27511i −0.638160 0.769903i \(-0.720304\pi\)
0.862997 0.505209i \(-0.168585\pi\)
\(128\) −1.76124 5.88294i −0.155673 0.519983i
\(129\) 0 0
\(130\) 0.581599 + 0.292090i 0.0510096 + 0.0256180i
\(131\) 1.91215 6.38704i 0.167066 0.558038i −0.832923 0.553388i \(-0.813335\pi\)
0.999989 0.00465022i \(-0.00148022\pi\)
\(132\) 0 0
\(133\) 0.208689 + 0.280318i 0.0180956 + 0.0243066i
\(134\) 0.897484 + 1.55449i 0.0775308 + 0.134287i
\(135\) 0 0
\(136\) 1.61548 2.79809i 0.138526 0.239934i
\(137\) 14.5286 1.69815i 1.24126 0.145082i 0.529991 0.848003i \(-0.322195\pi\)
0.711268 + 0.702921i \(0.248121\pi\)
\(138\) 0 0
\(139\) −3.22602 + 0.764581i −0.273628 + 0.0648509i −0.365139 0.930953i \(-0.618978\pi\)
0.0915111 + 0.995804i \(0.470830\pi\)
\(140\) 0.244703 0.160943i 0.0206811 0.0136022i
\(141\) 0 0
\(142\) 1.32038 1.39952i 0.110804 0.117445i
\(143\) 2.03027 + 1.70360i 0.169780 + 0.142462i
\(144\) 0 0
\(145\) −4.59437 + 3.85513i −0.381542 + 0.320151i
\(146\) −0.103570 + 1.77823i −0.00857152 + 0.147167i
\(147\) 0 0
\(148\) −5.28150 + 7.09429i −0.434137 + 0.583147i
\(149\) −4.86894 0.569097i −0.398879 0.0466223i −0.0857110 0.996320i \(-0.527316\pi\)
−0.313168 + 0.949698i \(0.601390\pi\)
\(150\) 0 0
\(151\) −13.4990 8.87841i −1.09853 0.722515i −0.135196 0.990819i \(-0.543166\pi\)
−0.963334 + 0.268304i \(0.913537\pi\)
\(152\) −1.60176 0.582992i −0.129920 0.0472869i
\(153\) 0 0
\(154\) −0.0233649 + 0.00850413i −0.00188280 + 0.000685282i
\(155\) 4.96190 + 1.17599i 0.398549 + 0.0944580i
\(156\) 0 0
\(157\) −0.718876 12.3426i −0.0573726 0.985049i −0.897040 0.441949i \(-0.854287\pi\)
0.839668 0.543100i \(-0.182750\pi\)
\(158\) −0.447203 0.474007i −0.0355775 0.0377100i
\(159\) 0 0
\(160\) −0.851656 + 1.97436i −0.0673293 + 0.156087i
\(161\) 1.34593 0.106074
\(162\) 0 0
\(163\) −12.1435 −0.951151 −0.475576 0.879675i \(-0.657760\pi\)
−0.475576 + 0.879675i \(0.657760\pi\)
\(164\) −8.49203 + 19.6867i −0.663116 + 1.53728i
\(165\) 0 0
\(166\) −2.33388 2.47376i −0.181144 0.192001i
\(167\) −0.147754 2.53683i −0.0114335 0.196306i −0.999188 0.0402900i \(-0.987172\pi\)
0.987754 0.156016i \(-0.0498652\pi\)
\(168\) 0 0
\(169\) −0.498703 0.118195i −0.0383618 0.00909191i
\(170\) −0.698851 + 0.254361i −0.0535994 + 0.0195086i
\(171\) 0 0
\(172\) −6.37031 2.31860i −0.485732 0.176792i
\(173\) 8.13490 + 5.35041i 0.618485 + 0.406784i 0.819724 0.572758i \(-0.194127\pi\)
−0.201240 + 0.979542i \(0.564497\pi\)
\(174\) 0 0
\(175\) 0.679353 + 0.0794050i 0.0513543 + 0.00600245i
\(176\) −1.68248 + 2.25996i −0.126821 + 0.170351i
\(177\) 0 0
\(178\) −0.134314 + 2.30608i −0.0100672 + 0.172848i
\(179\) −2.85196 + 2.39308i −0.213165 + 0.178867i −0.743118 0.669160i \(-0.766654\pi\)
0.529953 + 0.848027i \(0.322210\pi\)
\(180\) 0 0
\(181\) −5.59668 4.69618i −0.415998 0.349064i 0.410640 0.911798i \(-0.365305\pi\)
−0.826638 + 0.562734i \(0.809750\pi\)
\(182\) −0.0803951 + 0.0852138i −0.00595928 + 0.00631647i
\(183\) 0 0
\(184\) −5.48482 + 3.60743i −0.404347 + 0.265943i
\(185\) 4.00315 0.948764i 0.294318 0.0697545i
\(186\) 0 0
\(187\) −3.00807 + 0.351593i −0.219972 + 0.0257110i
\(188\) 8.74825 15.1524i 0.638032 1.10510i
\(189\) 0 0
\(190\) 0.196177 + 0.339789i 0.0142322 + 0.0246509i
\(191\) −12.4068 16.6652i −0.897724 1.20585i −0.977900 0.209072i \(-0.932956\pi\)
0.0801764 0.996781i \(-0.474452\pi\)
\(192\) 0 0
\(193\) 1.00178 3.34618i 0.0721097 0.240863i −0.914335 0.404960i \(-0.867286\pi\)
0.986444 + 0.164096i \(0.0524708\pi\)
\(194\) 0.818189 + 0.410910i 0.0587426 + 0.0295016i
\(195\) 0 0
\(196\) −3.91813 13.0875i −0.279866 0.934819i
\(197\) −0.205736 + 1.16678i −0.0146580 + 0.0831299i −0.991259 0.131928i \(-0.957883\pi\)
0.976601 + 0.215058i \(0.0689942\pi\)
\(198\) 0 0
\(199\) −0.191285 1.08483i −0.0135599 0.0769018i 0.977277 0.211967i \(-0.0679868\pi\)
−0.990837 + 0.135065i \(0.956876\pi\)
\(200\) −2.98128 + 1.49725i −0.210808 + 0.105872i
\(201\) 0 0
\(202\) −0.184239 0.427113i −0.0129630 0.0300516i
\(203\) −0.427605 0.991299i −0.0300120 0.0695755i
\(204\) 0 0
\(205\) 8.91228 4.47592i 0.622461 0.312612i
\(206\) −0.0913296 0.517956i −0.00636324 0.0360877i
\(207\) 0 0
\(208\) −2.30518 + 13.0733i −0.159835 + 0.906470i
\(209\) 0.458245 + 1.53065i 0.0316975 + 0.105877i
\(210\) 0 0
\(211\) −13.3899 6.72464i −0.921795 0.462943i −0.0763959 0.997078i \(-0.524341\pi\)
−0.845400 + 0.534134i \(0.820638\pi\)
\(212\) −3.44986 + 11.5233i −0.236937 + 0.791426i
\(213\) 0 0
\(214\) −1.44269 1.93787i −0.0986205 0.132470i
\(215\) 1.57669 + 2.73091i 0.107529 + 0.186246i
\(216\) 0 0
\(217\) −0.458958 + 0.794939i −0.0311561 + 0.0539640i
\(218\) 3.63943 0.425388i 0.246493 0.0288109i
\(219\) 0 0
\(220\) 1.30297 0.308810i 0.0878465 0.0208200i
\(221\) −11.9220 + 7.84122i −0.801960 + 0.527457i
\(222\) 0 0
\(223\) −3.50053 + 3.71034i −0.234413 + 0.248463i −0.833892 0.551927i \(-0.813893\pi\)
0.599480 + 0.800390i \(0.295374\pi\)
\(224\) −0.296499 0.248792i −0.0198107 0.0166231i
\(225\) 0 0
\(226\) 1.84230 1.54588i 0.122548 0.102830i
\(227\) 0.974692 16.7348i 0.0646926 1.11073i −0.797226 0.603681i \(-0.793700\pi\)
0.861918 0.507047i \(-0.169263\pi\)
\(228\) 0 0
\(229\) 9.62801 12.9327i 0.636237 0.854614i −0.360712 0.932677i \(-0.617466\pi\)
0.996948 + 0.0780631i \(0.0248736\pi\)
\(230\) 1.50087 + 0.175427i 0.0989646 + 0.0115673i
\(231\) 0 0
\(232\) 4.39947 + 2.89358i 0.288840 + 0.189973i
\(233\) 9.85526 + 3.58702i 0.645639 + 0.234993i 0.644024 0.765005i \(-0.277264\pi\)
0.00161517 + 0.999999i \(0.499486\pi\)
\(234\) 0 0
\(235\) −7.64784 + 2.78358i −0.498890 + 0.181581i
\(236\) 5.55892 + 1.31749i 0.361855 + 0.0857611i
\(237\) 0 0
\(238\) −0.00778390 0.133644i −0.000504556 0.00866289i
\(239\) −0.0373051 0.0395411i −0.00241307 0.00255770i 0.726166 0.687519i \(-0.241300\pi\)
−0.728579 + 0.684962i \(0.759819\pi\)
\(240\) 0 0
\(241\) 4.71185 10.9233i 0.303517 0.703631i −0.696385 0.717669i \(-0.745209\pi\)
0.999901 + 0.0140375i \(0.00446842\pi\)
\(242\) 2.10937 0.135596
\(243\) 0 0
\(244\) 13.8348 0.885680
\(245\) −2.51697 + 5.83500i −0.160804 + 0.372784i
\(246\) 0 0
\(247\) 5.16613 + 5.47578i 0.328713 + 0.348416i
\(248\) −0.260325 4.46960i −0.0165306 0.283820i
\(249\) 0 0
\(250\) 1.64326 + 0.389459i 0.103929 + 0.0246316i
\(251\) 4.18194 1.52210i 0.263961 0.0960741i −0.206649 0.978415i \(-0.566256\pi\)
0.470611 + 0.882341i \(0.344034\pi\)
\(252\) 0 0
\(253\) 5.78245 + 2.10464i 0.363540 + 0.132318i
\(254\) 2.46374 + 1.62043i 0.154589 + 0.101675i
\(255\) 0 0
\(256\) −12.7450 1.48967i −0.796560 0.0931045i
\(257\) −9.24063 + 12.4123i −0.576415 + 0.774259i −0.990726 0.135876i \(-0.956615\pi\)
0.414311 + 0.910135i \(0.364023\pi\)
\(258\) 0 0
\(259\) −0.0430594 + 0.739301i −0.00267558 + 0.0459380i
\(260\) 4.83316 4.05550i 0.299740 0.251512i
\(261\) 0 0
\(262\) 1.03217 + 0.866090i 0.0637674 + 0.0535072i
\(263\) −9.83748 + 10.4271i −0.606605 + 0.642964i −0.955776 0.294095i \(-0.904982\pi\)
0.349171 + 0.937059i \(0.386463\pi\)
\(264\) 0 0
\(265\) 4.67476 3.07463i 0.287168 0.188873i
\(266\) −0.0687225 + 0.0162875i −0.00421365 + 0.000998653i
\(267\) 0 0
\(268\) 17.2832 2.02011i 1.05574 0.123398i
\(269\) −0.910225 + 1.57656i −0.0554974 + 0.0961243i −0.892439 0.451167i \(-0.851008\pi\)
0.836942 + 0.547292i \(0.184341\pi\)
\(270\) 0 0
\(271\) 6.79318 + 11.7661i 0.412656 + 0.714742i 0.995179 0.0980726i \(-0.0312677\pi\)
−0.582523 + 0.812814i \(0.697934\pi\)
\(272\) −9.05852 12.1677i −0.549254 0.737776i
\(273\) 0 0
\(274\) −0.847832 + 2.83196i −0.0512194 + 0.171085i
\(275\) 2.79451 + 1.40346i 0.168515 + 0.0846315i
\(276\) 0 0
\(277\) 6.27704 + 20.9668i 0.377150 + 1.25977i 0.910371 + 0.413794i \(0.135797\pi\)
−0.533220 + 0.845977i \(0.679018\pi\)
\(278\) 0.116349 0.659846i 0.00697813 0.0395749i
\(279\) 0 0
\(280\) 0.0207711 + 0.117799i 0.00124131 + 0.00703981i
\(281\) −22.5755 + 11.3379i −1.34674 + 0.676360i −0.968422 0.249315i \(-0.919795\pi\)
−0.378321 + 0.925675i \(0.623498\pi\)
\(282\) 0 0
\(283\) 8.86520 + 20.5519i 0.526982 + 1.22168i 0.949053 + 0.315118i \(0.102044\pi\)
−0.422071 + 0.906563i \(0.638697\pi\)
\(284\) −7.38782 17.1269i −0.438387 1.01629i
\(285\) 0 0
\(286\) −0.478648 + 0.240386i −0.0283030 + 0.0142143i
\(287\) 0.311737 + 1.76795i 0.0184012 + 0.104359i
\(288\) 0 0
\(289\) −0.120543 + 0.683633i −0.00709076 + 0.0402137i
\(290\) −0.347626 1.16115i −0.0204133 0.0681852i
\(291\) 0 0
\(292\) 15.4310 + 7.74975i 0.903033 + 0.453520i
\(293\) 3.75533 12.5437i 0.219389 0.732809i −0.775456 0.631401i \(-0.782480\pi\)
0.994845 0.101408i \(-0.0323347\pi\)
\(294\) 0 0
\(295\) −1.58690 2.13157i −0.0923926 0.124105i
\(296\) −1.80604 3.12816i −0.104974 0.181820i
\(297\) 0 0
\(298\) 0.495345 0.857962i 0.0286945 0.0497004i
\(299\) 28.7975 3.36594i 1.66540 0.194657i
\(300\) 0 0
\(301\) −0.552328 + 0.130904i −0.0318357 + 0.00754519i
\(302\) 2.72808 1.79429i 0.156983 0.103250i
\(303\) 0 0
\(304\) −5.49193 + 5.82110i −0.314984 + 0.333863i
\(305\) −4.92977 4.13657i −0.282278 0.236859i
\(306\) 0 0
\(307\) 11.2563 9.44513i 0.642429 0.539062i −0.262334 0.964977i \(-0.584492\pi\)
0.904763 + 0.425915i \(0.140048\pi\)
\(308\) −0.0140153 + 0.240633i −0.000798595 + 0.0137113i
\(309\) 0 0
\(310\) −0.615406 + 0.826633i −0.0349527 + 0.0469496i
\(311\) 33.1562 + 3.87540i 1.88011 + 0.219754i 0.977535 0.210772i \(-0.0675976\pi\)
0.902578 + 0.430525i \(0.141672\pi\)
\(312\) 0 0
\(313\) 19.0991 + 12.5617i 1.07954 + 0.710027i 0.959207 0.282706i \(-0.0912321\pi\)
0.120337 + 0.992733i \(0.461602\pi\)
\(314\) 2.34793 + 0.854577i 0.132501 + 0.0482266i
\(315\) 0 0
\(316\) −5.93643 + 2.16069i −0.333950 + 0.121548i
\(317\) 18.2788 + 4.33215i 1.02664 + 0.243318i 0.709235 0.704972i \(-0.249041\pi\)
0.317404 + 0.948290i \(0.397189\pi\)
\(318\) 0 0
\(319\) −0.286996 4.92752i −0.0160687 0.275888i
\(320\) 4.40046 + 4.66421i 0.245993 + 0.260737i
\(321\) 0 0
\(322\) −0.107736 + 0.249760i −0.00600389 + 0.0139186i
\(323\) −8.60246 −0.478654
\(324\) 0 0
\(325\) 14.7340 0.817296
\(326\) 0.972037 2.25343i 0.0538361 0.124806i
\(327\) 0 0
\(328\) −6.00891 6.36907i −0.331787 0.351673i
\(329\) −0.0851827 1.46253i −0.00469628 0.0806320i
\(330\) 0 0
\(331\) −5.75969 1.36507i −0.316581 0.0750312i 0.0692533 0.997599i \(-0.477938\pi\)
−0.385835 + 0.922568i \(0.626086\pi\)
\(332\) −30.9813 + 11.2763i −1.70032 + 0.618865i
\(333\) 0 0
\(334\) 0.482581 + 0.175645i 0.0264056 + 0.00961087i
\(335\) −6.76256 4.44780i −0.369478 0.243009i
\(336\) 0 0
\(337\) 12.0532 + 1.40882i 0.656579 + 0.0767431i 0.437858 0.899044i \(-0.355737\pi\)
0.218721 + 0.975787i \(0.429811\pi\)
\(338\) 0.0618523 0.0830821i 0.00336432 0.00451907i
\(339\) 0 0
\(340\) −0.419201 + 7.19740i −0.0227344 + 0.390334i
\(341\) −3.21485 + 2.69758i −0.174094 + 0.146082i
\(342\) 0 0
\(343\) −1.75592 1.47339i −0.0948108 0.0795557i
\(344\) 1.89995 2.01383i 0.102438 0.108578i
\(345\) 0 0
\(346\) −1.64403 + 1.08129i −0.0883834 + 0.0581307i
\(347\) −2.37343 + 0.562512i −0.127412 + 0.0301972i −0.293827 0.955859i \(-0.594929\pi\)
0.166415 + 0.986056i \(0.446781\pi\)
\(348\) 0 0
\(349\) −22.8259 + 2.66797i −1.22184 + 0.142813i −0.702456 0.711727i \(-0.747913\pi\)
−0.519386 + 0.854540i \(0.673839\pi\)
\(350\) −0.0691144 + 0.119710i −0.00369432 + 0.00639875i
\(351\) 0 0
\(352\) −0.884797 1.53251i −0.0471598 0.0816833i
\(353\) −13.8275 18.5736i −0.735965 0.988573i −0.999712 0.0239812i \(-0.992366\pi\)
0.263747 0.964592i \(-0.415042\pi\)
\(354\) 0 0
\(355\) −2.48839 + 8.31181i −0.132070 + 0.441145i
\(356\) 20.0116 + 10.0502i 1.06061 + 0.532659i
\(357\) 0 0
\(358\) −0.215789 0.720786i −0.0114048 0.0380947i
\(359\) −5.43706 + 30.8351i −0.286957 + 1.62741i 0.411254 + 0.911521i \(0.365091\pi\)
−0.698211 + 0.715892i \(0.746020\pi\)
\(360\) 0 0
\(361\) −2.51123 14.2419i −0.132170 0.749574i
\(362\) 1.31945 0.662652i 0.0693487 0.0348282i
\(363\) 0 0
\(364\) 0.449829 + 1.04282i 0.0235775 + 0.0546587i
\(365\) −3.18141 7.37534i −0.166523 0.386043i
\(366\) 0 0
\(367\) 6.85833 3.44438i 0.358002 0.179795i −0.260702 0.965419i \(-0.583954\pi\)
0.618704 + 0.785624i \(0.287658\pi\)
\(368\) 5.35217 + 30.3537i 0.279001 + 1.58229i
\(369\) 0 0
\(370\) −0.144376 + 0.818799i −0.00750577 + 0.0425673i
\(371\) 0.288862 + 0.964867i 0.0149970 + 0.0500934i
\(372\) 0 0
\(373\) 23.1933 + 11.6481i 1.20090 + 0.603116i 0.932842 0.360286i \(-0.117321\pi\)
0.268061 + 0.963402i \(0.413617\pi\)
\(374\) 0.175540 0.586343i 0.00907693 0.0303191i
\(375\) 0 0
\(376\) 4.26708 + 5.73169i 0.220058 + 0.295589i
\(377\) −11.6281 20.1405i −0.598878 1.03729i
\(378\) 0 0
\(379\) −13.2851 + 23.0104i −0.682408 + 1.18197i 0.291835 + 0.956469i \(0.405734\pi\)
−0.974244 + 0.225497i \(0.927599\pi\)
\(380\) 3.77785 0.441567i 0.193800 0.0226519i
\(381\) 0 0
\(382\) 4.08563 0.968313i 0.209039 0.0495432i
\(383\) 2.25216 1.48127i 0.115080 0.0756892i −0.490664 0.871349i \(-0.663246\pi\)
0.605744 + 0.795659i \(0.292875\pi\)
\(384\) 0 0
\(385\) 0.0769430 0.0815548i 0.00392138 0.00415642i
\(386\) 0.540753 + 0.453746i 0.0275236 + 0.0230951i
\(387\) 0 0
\(388\) 6.79926 5.70525i 0.345180 0.289640i
\(389\) 1.37770 23.6542i 0.0698522 1.19932i −0.763215 0.646144i \(-0.776380\pi\)
0.833067 0.553172i \(-0.186583\pi\)
\(390\) 0 0
\(391\) −19.7845 + 26.5751i −1.00054 + 1.34396i
\(392\) 5.54164 + 0.647725i 0.279895 + 0.0327150i
\(393\) 0 0
\(394\) −0.200049 0.131574i −0.0100783 0.00662861i
\(395\) 2.76138 + 1.00506i 0.138940 + 0.0505702i
\(396\) 0 0
\(397\) −0.102939 + 0.0374669i −0.00516638 + 0.00188041i −0.344602 0.938749i \(-0.611986\pi\)
0.339436 + 0.940629i \(0.389764\pi\)
\(398\) 0.216621 + 0.0513402i 0.0108582 + 0.00257345i
\(399\) 0 0
\(400\) 0.910733 + 15.6367i 0.0455367 + 0.781834i
\(401\) 5.79656 + 6.14400i 0.289467 + 0.306817i 0.855745 0.517397i \(-0.173099\pi\)
−0.566279 + 0.824214i \(0.691617\pi\)
\(402\) 0 0
\(403\) −7.83185 + 18.1563i −0.390132 + 0.904429i
\(404\) −4.50932 −0.224347
\(405\) 0 0
\(406\) 0.218181 0.0108281
\(407\) −1.34105 + 3.10890i −0.0664732 + 0.154102i
\(408\) 0 0
\(409\) 3.46931 + 3.67725i 0.171546 + 0.181828i 0.807443 0.589946i \(-0.200851\pi\)
−0.635896 + 0.771774i \(0.719369\pi\)
\(410\) 0.117192 + 2.01211i 0.00578770 + 0.0993709i
\(411\) 0 0
\(412\) −4.96120 1.17583i −0.244421 0.0579288i
\(413\) 0.449503 0.163606i 0.0221186 0.00805050i
\(414\) 0 0
\(415\) 14.4112 + 5.24525i 0.707418 + 0.257479i
\(416\) −6.96608 4.58166i −0.341540 0.224634i
\(417\) 0 0
\(418\) −0.320719 0.0374866i −0.0156869 0.00183353i
\(419\) 7.62869 10.2471i 0.372686 0.500604i −0.575727 0.817642i \(-0.695281\pi\)
0.948413 + 0.317038i \(0.102688\pi\)
\(420\) 0 0
\(421\) 1.05866 18.1765i 0.0515960 0.885870i −0.868868 0.495043i \(-0.835152\pi\)
0.920464 0.390826i \(-0.127811\pi\)
\(422\) 2.31968 1.94644i 0.112920 0.0947512i
\(423\) 0 0
\(424\) −3.76324 3.15773i −0.182759 0.153353i
\(425\) −11.5540 + 12.2465i −0.560451 + 0.594043i
\(426\) 0 0
\(427\) 0.967834 0.636554i 0.0468368 0.0308050i
\(428\) −22.7892 + 5.40115i −1.10156 + 0.261074i
\(429\) 0 0
\(430\) −0.632975 + 0.0739842i −0.0305248 + 0.00356783i
\(431\) −11.5675 + 20.0355i −0.557188 + 0.965077i 0.440542 + 0.897732i \(0.354786\pi\)
−0.997730 + 0.0673455i \(0.978547\pi\)
\(432\) 0 0
\(433\) 16.7531 + 29.0173i 0.805104 + 1.39448i 0.916221 + 0.400674i \(0.131224\pi\)
−0.111116 + 0.993807i \(0.535443\pi\)
\(434\) −0.110777 0.148799i −0.00531746 0.00714259i
\(435\) 0 0
\(436\) 10.1877 34.0293i 0.487903 1.62971i
\(437\) 15.6197 + 7.84452i 0.747193 + 0.375254i
\(438\) 0 0
\(439\) 9.07834 + 30.3238i 0.433286 + 1.44727i 0.844411 + 0.535696i \(0.179951\pi\)
−0.411125 + 0.911579i \(0.634864\pi\)
\(440\) −0.0949649 + 0.538573i −0.00452727 + 0.0256755i
\(441\) 0 0
\(442\) −0.500767 2.83999i −0.0238191 0.135085i
\(443\) −20.2054 + 10.1475i −0.959988 + 0.482124i −0.858557 0.512718i \(-0.828638\pi\)
−0.101431 + 0.994843i \(0.532342\pi\)
\(444\) 0 0
\(445\) −4.12578 9.56464i −0.195581 0.453407i
\(446\) −0.408316 0.946582i −0.0193343 0.0448219i
\(447\) 0 0
\(448\) −1.03150 + 0.518037i −0.0487336 + 0.0244749i
\(449\) −3.12921 17.7466i −0.147677 0.837515i −0.965179 0.261590i \(-0.915753\pi\)
0.817503 0.575925i \(-0.195358\pi\)
\(450\) 0 0
\(451\) −1.42525 + 8.08302i −0.0671126 + 0.380615i
\(452\) −6.68657 22.3347i −0.314510 1.05054i
\(453\) 0 0
\(454\) 3.02742 + 1.52042i 0.142084 + 0.0713571i
\(455\) 0.151513 0.506089i 0.00710305 0.0237258i
\(456\) 0 0
\(457\) −14.0687 18.8975i −0.658104 0.883987i 0.340309 0.940314i \(-0.389468\pi\)
−0.998412 + 0.0563271i \(0.982061\pi\)
\(458\) 1.62920 + 2.82185i 0.0761274 + 0.131856i
\(459\) 0 0
\(460\) 7.32442 12.6863i 0.341503 0.591500i
\(461\) 39.9000 4.66364i 1.85833 0.217207i 0.888141 0.459570i \(-0.151997\pi\)
0.970186 + 0.242363i \(0.0779226\pi\)
\(462\) 0 0
\(463\) −10.6863 + 2.53271i −0.496636 + 0.117705i −0.471298 0.881974i \(-0.656214\pi\)
−0.0253382 + 0.999679i \(0.508066\pi\)
\(464\) 20.6556 13.5854i 0.958912 0.630686i
\(465\) 0 0
\(466\) −1.45451 + 1.54169i −0.0673787 + 0.0714173i
\(467\) −1.29116 1.08341i −0.0597479 0.0501344i 0.612425 0.790529i \(-0.290194\pi\)
−0.672173 + 0.740395i \(0.734639\pi\)
\(468\) 0 0
\(469\) 1.11612 0.936540i 0.0515378 0.0432454i
\(470\) 0.0956358 1.64200i 0.00441135 0.0757400i
\(471\) 0 0
\(472\) −1.39328 + 1.87149i −0.0641307 + 0.0861425i
\(473\) −2.57764 0.301283i −0.118520 0.0138530i
\(474\) 0 0
\(475\) 7.42121 + 4.88101i 0.340509 + 0.223956i
\(476\) −1.21951 0.443865i −0.0558961 0.0203445i
\(477\) 0 0
\(478\) 0.0103237 0.00375751i 0.000472194 0.000171864i
\(479\) −19.3534 4.58684i −0.884280 0.209578i −0.236706 0.971581i \(-0.576068\pi\)
−0.647573 + 0.762003i \(0.724216\pi\)
\(480\) 0 0
\(481\) 0.927571 + 15.9258i 0.0422936 + 0.726153i
\(482\) 1.64984 + 1.74873i 0.0751483 + 0.0796525i
\(483\) 0 0
\(484\) 8.09932 18.7763i 0.368151 0.853469i
\(485\) −4.12866 −0.187473
\(486\) 0 0
\(487\) −16.9386 −0.767563 −0.383782 0.923424i \(-0.625378\pi\)
−0.383782 + 0.923424i \(0.625378\pi\)
\(488\) −2.23792 + 5.18808i −0.101306 + 0.234853i
\(489\) 0 0
\(490\) −0.881312 0.934136i −0.0398136 0.0422000i
\(491\) 1.99994 + 34.3376i 0.0902558 + 1.54963i 0.674635 + 0.738152i \(0.264301\pi\)
−0.584379 + 0.811481i \(0.698662\pi\)
\(492\) 0 0
\(493\) 25.8586 + 6.12861i 1.16461 + 0.276019i
\(494\) −1.42965 + 0.520352i −0.0643232 + 0.0234117i
\(495\) 0 0
\(496\) −19.7527 7.18940i −0.886923 0.322814i
\(497\) −1.30486 0.858218i −0.0585308 0.0384963i
\(498\) 0 0
\(499\) −17.4742 2.04244i −0.782251 0.0914320i −0.284413 0.958702i \(-0.591799\pi\)
−0.497838 + 0.867270i \(0.665873\pi\)
\(500\) 9.77631 13.1319i 0.437210 0.587275i
\(501\) 0 0
\(502\) −0.0522949 + 0.897869i −0.00233404 + 0.0400738i
\(503\) 17.6438 14.8049i 0.786697 0.660117i −0.158229 0.987402i \(-0.550578\pi\)
0.944925 + 0.327286i \(0.106134\pi\)
\(504\) 0 0
\(505\) 1.60682 + 1.34828i 0.0715023 + 0.0599976i
\(506\) −0.853414 + 0.904566i −0.0379389 + 0.0402129i
\(507\) 0 0
\(508\) 23.8841 15.7088i 1.05968 0.696965i
\(509\) −31.1626 + 7.38567i −1.38126 + 0.327364i −0.853085 0.521773i \(-0.825271\pi\)
−0.528173 + 0.849137i \(0.677123\pi\)
\(510\) 0 0
\(511\) 1.43608 0.167854i 0.0635284 0.00742541i
\(512\) 7.43754 12.8822i 0.328696 0.569318i
\(513\) 0 0
\(514\) −1.56365 2.70831i −0.0689695 0.119459i
\(515\) 1.41627 + 1.90238i 0.0624082 + 0.0838287i
\(516\) 0 0
\(517\) 1.92101 6.41661i 0.0844858 0.282202i
\(518\) −0.133743 0.0671685i −0.00587635 0.00295121i
\(519\) 0 0
\(520\) 0.739012 + 2.46847i 0.0324078 + 0.108250i
\(521\) 0.436835 2.47742i 0.0191381 0.108538i −0.973742 0.227653i \(-0.926895\pi\)
0.992880 + 0.119116i \(0.0380059\pi\)
\(522\) 0 0
\(523\) 4.83329 + 27.4110i 0.211345 + 1.19860i 0.887137 + 0.461506i \(0.152691\pi\)
−0.675792 + 0.737092i \(0.736198\pi\)
\(524\) 11.6726 5.86220i 0.509920 0.256091i
\(525\) 0 0
\(526\) −1.14748 2.66016i −0.0500326 0.115989i
\(527\) −8.94950 20.7473i −0.389846 0.903765i
\(528\) 0 0
\(529\) 39.6034 19.8896i 1.72188 0.864763i
\(530\) 0.196357 + 1.11359i 0.00852919 + 0.0483714i
\(531\) 0 0
\(532\) −0.118891 + 0.674265i −0.00515458 + 0.0292331i
\(533\) 11.0913 + 37.0474i 0.480416 + 1.60470i
\(534\) 0 0
\(535\) 9.73548 + 4.88934i 0.420901 + 0.211385i
\(536\) −2.03819 + 6.80801i −0.0880362 + 0.294061i
\(537\) 0 0
\(538\) −0.219698 0.295105i −0.00947184 0.0127229i
\(539\) −2.61492 4.52917i −0.112633 0.195085i
\(540\) 0 0
\(541\) 3.23851 5.60926i 0.139234 0.241161i −0.787973 0.615710i \(-0.788869\pi\)
0.927207 + 0.374549i \(0.122203\pi\)
\(542\) −2.72718 + 0.318761i −0.117142 + 0.0136920i
\(543\) 0 0
\(544\) 9.27075 2.19721i 0.397480 0.0942046i
\(545\) −13.8049 + 9.07964i −0.591338 + 0.388929i
\(546\) 0 0
\(547\) −10.5678 + 11.2012i −0.451847 + 0.478930i −0.912749 0.408521i \(-0.866045\pi\)
0.460902 + 0.887451i \(0.347526\pi\)
\(548\) 21.9529 + 18.4207i 0.937783 + 0.786893i
\(549\) 0 0
\(550\) −0.484125 + 0.406229i −0.0206431 + 0.0173217i
\(551\) 0.815199 13.9964i 0.0347286 0.596268i
\(552\) 0 0
\(553\) −0.315877 + 0.424297i −0.0134325 + 0.0180429i
\(554\) −4.39320 0.513491i −0.186649 0.0218161i
\(555\) 0 0
\(556\) −5.42680 3.56926i −0.230148 0.151370i
\(557\) 21.2492 + 7.73409i 0.900359 + 0.327704i 0.750397 0.660988i \(-0.229862\pi\)
0.149963 + 0.988692i \(0.452085\pi\)
\(558\) 0 0
\(559\) −11.4902 + 4.18210i −0.485985 + 0.176884i
\(560\) 0.546460 + 0.129513i 0.0230921 + 0.00547294i
\(561\) 0 0
\(562\) −0.296857 5.09683i −0.0125221 0.214997i
\(563\) −16.2816 17.2575i −0.686189 0.727318i 0.286846 0.957977i \(-0.407393\pi\)
−0.973035 + 0.230659i \(0.925912\pi\)
\(564\) 0 0
\(565\) −4.29540 + 9.95785i −0.180709 + 0.418930i
\(566\) −4.52338 −0.190132
\(567\) 0 0
\(568\) 7.61770 0.319632
\(569\) −0.250584 + 0.580919i −0.0105050 + 0.0243534i −0.923388 0.383868i \(-0.874592\pi\)
0.912883 + 0.408222i \(0.133851\pi\)
\(570\) 0 0
\(571\) −27.5133 29.1624i −1.15140 1.22041i −0.971581 0.236708i \(-0.923932\pi\)
−0.179815 0.983700i \(-0.557550\pi\)
\(572\) 0.301912 + 5.18363i 0.0126236 + 0.216739i
\(573\) 0 0
\(574\) −0.353026 0.0836688i −0.0147350 0.00349227i
\(575\) 32.1464 11.7003i 1.34060 0.487938i
\(576\) 0 0
\(577\) 15.7332 + 5.72640i 0.654980 + 0.238393i 0.648068 0.761583i \(-0.275577\pi\)
0.00691246 + 0.999976i \(0.497800\pi\)
\(578\) −0.117211 0.0770909i −0.00487533 0.00320656i
\(579\) 0 0
\(580\) −11.6706 1.36410i −0.484597 0.0566413i
\(581\) −1.64851 + 2.21434i −0.0683918 + 0.0918661i
\(582\) 0 0
\(583\) −0.267745 + 4.59701i −0.0110889 + 0.190389i
\(584\) −5.40231 + 4.53308i −0.223549 + 0.187580i
\(585\) 0 0
\(586\) 2.02710 + 1.70094i 0.0837386 + 0.0702650i
\(587\) −11.3031 + 11.9806i −0.466531 + 0.494494i −0.917328 0.398133i \(-0.869658\pi\)
0.450797 + 0.892626i \(0.351140\pi\)
\(588\) 0 0
\(589\) −9.95946 + 6.55044i −0.410372 + 0.269906i
\(590\) 0.522574 0.123852i 0.0215140 0.00509892i
\(591\) 0 0
\(592\) −16.8441 + 1.96880i −0.692289 + 0.0809170i
\(593\) 20.1750 34.9441i 0.828487 1.43498i −0.0707373 0.997495i \(-0.522535\pi\)
0.899225 0.437487i \(-0.144131\pi\)
\(594\) 0 0
\(595\) 0.301836 + 0.522795i 0.0123741 + 0.0214325i
\(596\) −5.73508 7.70355i −0.234918 0.315550i
\(597\) 0 0
\(598\) −1.68051 + 5.61330i −0.0687212 + 0.229545i
\(599\) 5.03341 + 2.52787i 0.205660 + 0.103286i 0.548648 0.836054i \(-0.315143\pi\)
−0.342988 + 0.939340i \(0.611439\pi\)
\(600\) 0 0
\(601\) −4.90209 16.3741i −0.199960 0.667914i −0.997876 0.0651446i \(-0.979249\pi\)
0.797916 0.602769i \(-0.205936\pi\)
\(602\) 0.0199201 0.112972i 0.000811882 0.00460441i
\(603\) 0 0
\(604\) −5.49667 31.1732i −0.223656 1.26842i
\(605\) −8.50014 + 4.26893i −0.345580 + 0.173557i
\(606\) 0 0
\(607\) 7.17870 + 16.6421i 0.291374 + 0.675482i 0.999533 0.0305719i \(-0.00973286\pi\)
−0.708158 + 0.706054i \(0.750474\pi\)
\(608\) −1.99088 4.61537i −0.0807408 0.187178i
\(609\) 0 0
\(610\) 1.16222 0.583689i 0.0470569 0.0236329i
\(611\) −5.48012 31.0793i −0.221702 1.25733i
\(612\) 0 0
\(613\) 3.85172 21.8442i 0.155570 0.882279i −0.802694 0.596392i \(-0.796601\pi\)
0.958263 0.285887i \(-0.0922883\pi\)
\(614\) 0.851690 + 2.84484i 0.0343714 + 0.114808i
\(615\) 0 0
\(616\) −0.0879710 0.0441807i −0.00354445 0.00178009i
\(617\) −2.87922 + 9.61726i −0.115913 + 0.387176i −0.996182 0.0872982i \(-0.972177\pi\)
0.880269 + 0.474474i \(0.157362\pi\)
\(618\) 0 0
\(619\) −11.9054 15.9918i −0.478520 0.642764i 0.495665 0.868514i \(-0.334924\pi\)
−0.974185 + 0.225750i \(0.927517\pi\)
\(620\) 4.99522 + 8.65197i 0.200613 + 0.347472i
\(621\) 0 0
\(622\) −3.37316 + 5.84249i −0.135252 + 0.234263i
\(623\) 1.86236 0.217679i 0.0746141 0.00872113i
\(624\) 0 0
\(625\) 12.8755 3.05155i 0.515021 0.122062i
\(626\) −3.85984 + 2.53866i −0.154270 + 0.101465i
\(627\) 0 0
\(628\) 16.6222 17.6185i 0.663299 0.703056i
\(629\) −13.9644 11.7176i −0.556799 0.467210i
\(630\) 0 0
\(631\) 1.55588 1.30554i 0.0619385 0.0519726i −0.611293 0.791404i \(-0.709350\pi\)
0.673231 + 0.739432i \(0.264906\pi\)
\(632\) 0.150017 2.57570i 0.00596736 0.102456i
\(633\) 0 0
\(634\) −2.26705 + 3.04518i −0.0900360 + 0.120939i
\(635\) −13.2076 1.54374i −0.524127 0.0612616i
\(636\) 0 0
\(637\) −20.5875 13.5406i −0.815705 0.536498i
\(638\) 0.937360 + 0.341171i 0.0371105 + 0.0135071i
\(639\) 0 0
\(640\) −5.25884 + 1.91406i −0.207874 + 0.0756599i
\(641\) 26.0313 + 6.16954i 1.02818 + 0.243682i 0.709890 0.704312i \(-0.248745\pi\)
0.318286 + 0.947995i \(0.396893\pi\)
\(642\) 0 0
\(643\) 0.509005 + 8.73928i 0.0200732 + 0.344643i 0.993360 + 0.115050i \(0.0367027\pi\)
−0.973287 + 0.229594i \(0.926260\pi\)
\(644\) 1.80954 + 1.91800i 0.0713058 + 0.0755798i
\(645\) 0 0
\(646\) 0.688592 1.59634i 0.0270923 0.0628070i
\(647\) 1.73387 0.0681653 0.0340827 0.999419i \(-0.489149\pi\)
0.0340827 + 0.999419i \(0.489149\pi\)
\(648\) 0 0
\(649\) 2.18701 0.0858477
\(650\) −1.17940 + 2.73415i −0.0462598 + 0.107242i
\(651\) 0 0
\(652\) −16.3264 17.3049i −0.639390 0.677714i
\(653\) −1.50395 25.8218i −0.0588540 1.01048i −0.890444 0.455094i \(-0.849606\pi\)
0.831590 0.555391i \(-0.187431\pi\)
\(654\) 0 0
\(655\) −5.91211 1.40120i −0.231005 0.0547493i
\(656\) −38.6315 + 14.0607i −1.50831 + 0.548979i
\(657\) 0 0
\(658\) 0.278217 + 0.101263i 0.0108460 + 0.00394763i
\(659\) 6.50297 + 4.27707i 0.253320 + 0.166611i 0.669818 0.742526i \(-0.266372\pi\)
−0.416498 + 0.909137i \(0.636743\pi\)
\(660\) 0 0
\(661\) −7.77288 0.908519i −0.302330 0.0353373i −0.0364244 0.999336i \(-0.511597\pi\)
−0.265905 + 0.963999i \(0.585671\pi\)
\(662\) 0.714353 0.959543i 0.0277641 0.0372937i
\(663\) 0 0
\(664\) 0.782915 13.4421i 0.0303830 0.521656i
\(665\) 0.243969 0.204714i 0.00946070 0.00793847i
\(666\) 0 0
\(667\) −41.3636 34.7082i −1.60161 1.34391i
\(668\) 3.41644 3.62122i 0.132186 0.140109i
\(669\) 0 0
\(670\) 1.36668 0.898881i 0.0527995 0.0347268i
\(671\) 5.15345 1.22139i 0.198947 0.0471512i
\(672\) 0 0
\(673\) −6.28264 + 0.734335i −0.242178 + 0.0283066i −0.236316 0.971676i \(-0.575940\pi\)
−0.00586206 + 0.999983i \(0.501866\pi\)
\(674\) −1.22624 + 2.12391i −0.0472330 + 0.0818099i
\(675\) 0 0
\(676\) −0.502052 0.869580i −0.0193097 0.0334454i
\(677\) 14.7295 + 19.7852i 0.566102 + 0.760407i 0.989342 0.145610i \(-0.0465146\pi\)
−0.423240 + 0.906018i \(0.639107\pi\)
\(678\) 0 0
\(679\) 0.213148 0.711963i 0.00817986 0.0273226i
\(680\) −2.63124 1.32146i −0.100903 0.0506756i
\(681\) 0 0
\(682\) −0.243247 0.812503i −0.00931442 0.0311123i
\(683\) −3.77494 + 21.4087i −0.144444 + 0.819183i 0.823368 + 0.567508i \(0.192092\pi\)
−0.967812 + 0.251675i \(0.919019\pi\)
\(684\) 0 0
\(685\) −2.31478 13.1278i −0.0884433 0.501587i
\(686\) 0.413968 0.207902i 0.0158054 0.00793775i
\(687\) 0 0
\(688\) −5.14855 11.9357i −0.196287 0.455043i
\(689\) 8.59346 + 19.9219i 0.327385 + 0.758963i
\(690\) 0 0
\(691\) −43.4188 + 21.8058i −1.65173 + 0.829530i −0.654428 + 0.756125i \(0.727090\pi\)
−0.997302 + 0.0734052i \(0.976613\pi\)
\(692\) 3.31247 + 18.7859i 0.125921 + 0.714134i
\(693\) 0 0
\(694\) 0.0855992 0.485457i 0.00324930 0.0184277i
\(695\) 0.866541 + 2.89445i 0.0328698 + 0.109793i
\(696\) 0 0
\(697\) −39.4902 19.8327i −1.49580 0.751219i
\(698\) 1.33203 4.44930i 0.0504182 0.168409i
\(699\) 0 0
\(700\) 0.800205 + 1.07486i 0.0302449 + 0.0406259i
\(701\) −12.9938 22.5060i −0.490770 0.850039i 0.509174 0.860664i \(-0.329951\pi\)
−0.999944 + 0.0106253i \(0.996618\pi\)
\(702\) 0 0
\(703\) −4.80861 + 8.32876i −0.181360 + 0.314125i
\(704\) −5.24163 + 0.612659i −0.197551 + 0.0230904i
\(705\) 0 0
\(706\) 4.55349 1.07920i 0.171373 0.0406161i
\(707\) −0.315457 + 0.207479i −0.0118640 + 0.00780306i
\(708\) 0 0
\(709\) −24.8863 + 26.3779i −0.934624 + 0.990643i −0.999974 0.00721930i \(-0.997702\pi\)
0.0653504 + 0.997862i \(0.479183\pi\)
\(710\) −1.34322 1.12709i −0.0504100 0.0422990i
\(711\) 0 0
\(712\) −7.00594 + 5.87868i −0.262559 + 0.220313i
\(713\) −2.66943 + 45.8324i −0.0999710 + 1.71644i
\(714\) 0 0
\(715\) 1.44232 1.93737i 0.0539396 0.0724534i
\(716\) −7.24456 0.846768i −0.270742 0.0316452i
\(717\) 0 0
\(718\) −5.28677 3.47716i −0.197301 0.129767i
\(719\) 0.547249 + 0.199183i 0.0204090 + 0.00742825i 0.352204 0.935923i \(-0.385432\pi\)
−0.331795 + 0.943351i \(0.607654\pi\)
\(720\) 0 0
\(721\) −0.401170 + 0.146014i −0.0149404 + 0.00543785i
\(722\) 2.84385 + 0.674004i 0.105837 + 0.0250838i
\(723\) 0 0
\(724\) −0.832257 14.2893i −0.0309306 0.531057i
\(725\) −18.8305 19.9592i −0.699347 0.741265i
\(726\) 0 0
\(727\) 7.92165 18.3644i 0.293798 0.681100i −0.705830 0.708381i \(-0.749426\pi\)
0.999628 + 0.0272815i \(0.00868504\pi\)
\(728\) −0.463826 −0.0171905
\(729\) 0 0
\(730\) 1.62328 0.0600803
\(731\) 5.53426 12.8299i 0.204692 0.474530i
\(732\) 0 0
\(733\) 29.4243 + 31.1879i 1.08681 + 1.15195i 0.987617 + 0.156883i \(0.0501447\pi\)
0.0991931 + 0.995068i \(0.468374\pi\)
\(734\) 0.0901836 + 1.54839i 0.00332874 + 0.0571522i
\(735\) 0 0
\(736\) −18.8368 4.46440i −0.694333 0.164560i
\(737\) 6.25963 2.27832i 0.230577 0.0839230i
\(738\) 0 0
\(739\) −30.4321 11.0764i −1.11946 0.407452i −0.285008 0.958525i \(-0.591996\pi\)
−0.834457 + 0.551074i \(0.814218\pi\)
\(740\) 6.73408 + 4.42908i 0.247550 + 0.162816i
\(741\) 0 0
\(742\) −0.202170 0.0236303i −0.00742189 0.000867495i
\(743\) 7.48588 10.0553i 0.274630 0.368893i −0.643313 0.765603i \(-0.722441\pi\)
0.917944 + 0.396710i \(0.129848\pi\)
\(744\) 0 0
\(745\) −0.259754 + 4.45981i −0.00951666 + 0.163395i
\(746\) −4.01804 + 3.37153i −0.147111 + 0.123441i
\(747\) 0 0
\(748\) −4.54525 3.81392i −0.166191 0.139451i
\(749\) −1.34575 + 1.42641i −0.0491725 + 0.0521198i
\(750\) 0 0
\(751\) 20.4708 13.4639i 0.746991 0.491304i −0.118048 0.993008i \(-0.537664\pi\)
0.865039 + 0.501704i \(0.167293\pi\)
\(752\) 32.6446 7.73691i 1.19043 0.282136i
\(753\) 0 0
\(754\) 4.66819 0.545634i 0.170006 0.0198708i
\(755\) −7.36209 + 12.7515i −0.267934 + 0.464075i
\(756\) 0 0
\(757\) −10.7313 18.5872i −0.390037 0.675564i 0.602417 0.798182i \(-0.294205\pi\)
−0.992454 + 0.122617i \(0.960871\pi\)
\(758\) −3.20657 4.30717i −0.116468 0.156443i
\(759\) 0 0
\(760\) −0.445518 + 1.48813i −0.0161606 + 0.0539803i
\(761\) −31.8202 15.9807i −1.15348 0.579301i −0.233925 0.972255i \(-0.575157\pi\)
−0.919558 + 0.392954i \(0.871453\pi\)
\(762\) 0 0
\(763\) −0.853032 2.84933i −0.0308818 0.103153i
\(764\) 7.06821 40.0858i 0.255719 1.45025i
\(765\) 0 0
\(766\) 0.0945988 + 0.536496i 0.00341799 + 0.0193844i
\(767\) 9.20840 4.62463i 0.332496 0.166986i
\(768\) 0 0
\(769\) −6.57150 15.2344i −0.236974 0.549368i 0.757680 0.652626i \(-0.226333\pi\)
−0.994655 + 0.103258i \(0.967073\pi\)
\(770\) 0.00897493 + 0.0208062i 0.000323434 + 0.000749805i
\(771\) 0 0
\(772\) 6.11529 3.07121i 0.220094 0.110535i
\(773\) 1.97712 + 11.2128i 0.0711121 + 0.403297i 0.999498 + 0.0316795i \(0.0100856\pi\)
−0.928386 + 0.371617i \(0.878803\pi\)
\(774\) 0 0
\(775\) −4.05134 + 22.9763i −0.145528 + 0.825332i
\(776\) 1.03964 + 3.47263i 0.0373208 + 0.124660i
\(777\) 0 0
\(778\) 4.27917 + 2.14908i 0.153416 + 0.0770482i
\(779\) −6.68643 + 22.3342i −0.239566 + 0.800207i
\(780\) 0 0
\(781\) −4.26400 5.72754i −0.152578 0.204948i
\(782\) −3.34781 5.79858i −0.119718 0.207357i
\(783\) 0 0
\(784\) 13.0976 22.6857i 0.467771 0.810204i
\(785\) −11.1910 + 1.30804i −0.399422 + 0.0466858i
\(786\) 0 0
\(787\) −41.8993 + 9.93032i −1.49355 + 0.353978i −0.894621 0.446826i \(-0.852554\pi\)
−0.598928 + 0.800803i \(0.704406\pi\)
\(788\) −1.93932 + 1.27551i −0.0690853 + 0.0454381i
\(789\) 0 0
\(790\) −0.407544 + 0.431972i −0.0144998 + 0.0153689i
\(791\) −1.49542 1.25480i −0.0531709 0.0446157i
\(792\) 0 0
\(793\) 19.1159 16.0401i 0.678824 0.569601i
\(794\) 0.00128725 0.0221013i 4.56829e−5 0.000784345i
\(795\) 0 0
\(796\) 1.28876 1.73110i 0.0456787 0.0613572i
\(797\) −32.4769 3.79600i −1.15039 0.134461i −0.480550 0.876967i \(-0.659563\pi\)
−0.669839 + 0.742506i \(0.733637\pi\)
\(798\) 0 0
\(799\) 30.1296 + 19.8166i 1.06591 + 0.701059i
\(800\) −9.24443 3.36470i −0.326840 0.118960i
\(801\) 0 0
\(802\) −1.60412 + 0.583851i −0.0566433 + 0.0206165i
\(803\) 6.43224 + 1.52447i 0.226989 + 0.0537973i
\(804\) 0 0
\(805\) −0.0713187 1.22449i −0.00251365 0.0431578i
\(806\) −2.74230 2.90667i −0.0965936 0.102383i
\(807\) 0 0
\(808\) 0.729430 1.69101i 0.0256612 0.0594895i
\(809\) 25.5159 0.897092 0.448546 0.893760i \(-0.351942\pi\)
0.448546 + 0.893760i \(0.351942\pi\)
\(810\) 0 0
\(811\) −8.80464 −0.309173 −0.154586 0.987979i \(-0.549404\pi\)
−0.154586 + 0.987979i \(0.549404\pi\)
\(812\) 0.837745 1.94211i 0.0293991 0.0681547i
\(813\) 0 0
\(814\) −0.469564 0.497709i −0.0164582 0.0174447i
\(815\) 0.643465 + 11.0479i 0.0225396 + 0.386990i
\(816\) 0 0
\(817\) −7.17282 1.69999i −0.250945 0.0594751i
\(818\) −0.960082 + 0.349441i −0.0335685 + 0.0122179i
\(819\) 0 0
\(820\) 18.3605 + 6.68268i 0.641177 + 0.233369i
\(821\) −4.92307 3.23796i −0.171816 0.113005i 0.460688 0.887562i \(-0.347603\pi\)
−0.632505 + 0.774557i \(0.717973\pi\)
\(822\) 0 0
\(823\) 44.9011 + 5.24818i 1.56515 + 0.182940i 0.854066 0.520164i \(-0.174129\pi\)
0.711087 + 0.703104i \(0.248203\pi\)
\(824\) 1.24347 1.67026i 0.0433182 0.0581864i
\(825\) 0 0
\(826\) −0.00562101 + 0.0965090i −0.000195580 + 0.00335798i
\(827\) −3.29612 + 2.76578i −0.114617 + 0.0961755i −0.698295 0.715810i \(-0.746058\pi\)
0.583678 + 0.811986i \(0.301613\pi\)
\(828\) 0 0
\(829\) 39.1908 + 32.8850i 1.36115 + 1.14214i 0.975624 + 0.219448i \(0.0704255\pi\)
0.385529 + 0.922696i \(0.374019\pi\)
\(830\) −2.12691 + 2.25439i −0.0738260 + 0.0782510i
\(831\) 0 0
\(832\) −20.7744 + 13.6635i −0.720221 + 0.473697i
\(833\) 27.3987 6.49360i 0.949308 0.224990i
\(834\) 0 0
\(835\) −2.30013 + 0.268846i −0.0795992 + 0.00930381i
\(836\) −1.56514 + 2.71090i −0.0541315 + 0.0937586i
\(837\) 0 0
\(838\) 1.29088 + 2.23588i 0.0445928 + 0.0772370i
\(839\) 13.2967 + 17.8606i 0.459054 + 0.616616i 0.970032 0.242978i \(-0.0781242\pi\)
−0.510978 + 0.859594i \(0.670717\pi\)
\(840\) 0 0
\(841\) −4.10456 + 13.7102i −0.141537 + 0.472765i
\(842\) 3.28823 + 1.65141i 0.113320 + 0.0569114i
\(843\) 0 0
\(844\) −8.41919 28.1220i −0.289800 0.968001i
\(845\) −0.0811055 + 0.459972i −0.00279011 + 0.0158235i
\(846\) 0 0
\(847\) −0.297321 1.68619i −0.0102161 0.0579381i
\(848\) −20.6112 + 10.3513i −0.707792 + 0.355466i
\(849\) 0 0
\(850\) −1.34770 3.12433i −0.0462258 0.107164i
\(851\) 14.6705 + 34.0100i 0.502898 + 1.16585i
\(852\) 0 0
\(853\) −5.96502 + 2.99574i −0.204238 + 0.102572i −0.547978 0.836493i \(-0.684602\pi\)
0.343740 + 0.939065i \(0.388306\pi\)
\(854\) 0.0406525 + 0.230552i 0.00139110 + 0.00788933i
\(855\) 0 0
\(856\) 1.66095 9.41973i 0.0567702 0.321960i
\(857\) 0.928156 + 3.10026i 0.0317052 + 0.105903i 0.972378 0.233413i \(-0.0749895\pi\)
−0.940672 + 0.339316i \(0.889804\pi\)
\(858\) 0 0
\(859\) −7.99921 4.01735i −0.272930 0.137070i 0.307071 0.951687i \(-0.400651\pi\)
−0.580000 + 0.814616i \(0.696948\pi\)
\(860\) −1.77186 + 5.91843i −0.0604200 + 0.201817i
\(861\) 0 0
\(862\) −2.79201 3.75032i −0.0950961 0.127736i
\(863\) 8.30305 + 14.3813i 0.282639 + 0.489546i 0.972034 0.234840i \(-0.0754567\pi\)
−0.689395 + 0.724386i \(0.742123\pi\)
\(864\) 0 0
\(865\) 4.43662 7.68446i 0.150850 0.261279i
\(866\) −6.72568 + 0.786119i −0.228548 + 0.0267134i
\(867\) 0 0
\(868\) −1.74987 + 0.414726i −0.0593944 + 0.0140767i
\(869\) −2.02057 + 1.32895i −0.0685431 + 0.0450815i
\(870\) 0 0
\(871\) 21.5385 22.8294i 0.729803 0.773546i
\(872\) 11.1131 + 9.32502i 0.376338 + 0.315785i
\(873\) 0 0
\(874\) −2.70598 + 2.27059i −0.0915312 + 0.0768038i
\(875\) 0.0797050 1.36848i 0.00269452 0.0462631i
\(876\) 0 0
\(877\) 3.34093 4.48765i 0.112815 0.151537i −0.742129 0.670257i \(-0.766184\pi\)
0.854944 + 0.518720i \(0.173591\pi\)
\(878\) −6.35379 0.742651i −0.214430 0.0250633i
\(879\) 0 0
\(880\) 2.14521 + 1.41093i 0.0723151 + 0.0475624i
\(881\) −8.40136 3.05784i −0.283049 0.103021i 0.196595 0.980485i \(-0.437012\pi\)
−0.479643 + 0.877464i \(0.659234\pi\)
\(882\) 0 0
\(883\) 13.8259 5.03222i 0.465279 0.169348i −0.0987335 0.995114i \(-0.531479\pi\)
0.564013 + 0.825766i \(0.309257\pi\)
\(884\) −27.2026 6.44714i −0.914924 0.216841i
\(885\) 0 0
\(886\) −0.265691 4.56173i −0.00892605 0.153254i
\(887\) −3.02558 3.20693i −0.101589 0.107678i 0.674584 0.738198i \(-0.264323\pi\)
−0.776173 + 0.630520i \(0.782842\pi\)
\(888\) 0 0
\(889\) 0.948069 2.19787i 0.0317972 0.0737142i
\(890\) 2.10514 0.0705643
\(891\) 0 0
\(892\) −9.99369 −0.334614
\(893\) 7.53557 17.4694i 0.252168 0.584591i
\(894\) 0 0
\(895\) 2.32829 + 2.46784i 0.0778261 + 0.0824909i
\(896\) −0.0585738 1.00567i −0.00195681 0.0335972i
\(897\) 0 0
\(898\) 3.54367 + 0.839866i 0.118254 + 0.0280267i
\(899\) 34.6044 12.5950i 1.15412 0.420066i
\(900\) 0 0
\(901\) −23.2973 8.47952i −0.776145 0.282494i
\(902\) −1.38586 0.911494i −0.0461441 0.0303494i
\(903\) 0 0
\(904\) 9.45721 + 1.10539i 0.314542 + 0.0367647i
\(905\) −3.97592 + 5.34058i −0.132164 + 0.177527i
\(906\) 0 0
\(907\) −0.190545 + 3.27154i −0.00632696 + 0.108630i −0.999993 0.00374388i \(-0.998808\pi\)
0.993666 + 0.112374i \(0.0358453\pi\)
\(908\) 25.1582 21.1102i 0.834904 0.700568i
\(909\) 0 0
\(910\) 0.0817857 + 0.0686263i 0.00271117 + 0.00227494i
\(911\) 28.8869 30.6183i 0.957064 1.01443i −0.0428181 0.999083i \(-0.513634\pi\)
0.999882 0.0153459i \(-0.00488493\pi\)
\(912\) 0 0
\(913\) −10.5450 + 6.93556i −0.348989 + 0.229534i
\(914\) 4.63289 1.09802i 0.153242 0.0363191i
\(915\) 0 0
\(916\) 31.3740 3.66709i 1.03663 0.121164i
\(917\) 0.546849 0.947170i 0.0180585 0.0312783i
\(918\) 0 0
\(919\) 15.0654 + 26.0940i 0.496962 + 0.860763i 0.999994 0.00350463i \(-0.00111556\pi\)
−0.503032 + 0.864268i \(0.667782\pi\)
\(920\) 3.57259 + 4.79882i 0.117785 + 0.158212i
\(921\) 0 0
\(922\) −2.32841 + 7.77744i −0.0766822 + 0.256136i
\(923\) −30.0650 15.0992i −0.989601 0.496996i
\(924\) 0 0
\(925\) 5.39841 + 18.0320i 0.177499 + 0.592887i
\(926\) 0.385410 2.18577i 0.0126654 0.0718288i
\(927\) 0 0
\(928\) 2.69639 + 15.2920i 0.0885133 + 0.501984i
\(929\) 31.8711 16.0063i 1.04566 0.525149i 0.158857 0.987302i \(-0.449219\pi\)
0.886800 + 0.462153i \(0.152923\pi\)
\(930\) 0 0
\(931\) −5.88382 13.6402i −0.192834 0.447040i
\(932\) 8.13831 + 18.8667i 0.266579 + 0.618000i
\(933\) 0 0
\(934\) 0.304399 0.152875i 0.00996022 0.00500221i
\(935\) 0.479264 + 2.71804i 0.0156736 + 0.0888895i
\(936\) 0 0
\(937\) −2.81383 + 15.9580i −0.0919239 + 0.521326i 0.903723 + 0.428118i \(0.140823\pi\)
−0.995647 + 0.0932080i \(0.970288\pi\)
\(938\) 0.0844499 + 0.282082i 0.00275739 + 0.00921032i
\(939\) 0 0
\(940\) −14.2489 7.15606i −0.464748 0.233405i
\(941\) 4.48119 14.9682i 0.146083 0.487950i −0.853360 0.521322i \(-0.825439\pi\)
0.999443 + 0.0333712i \(0.0106244\pi\)
\(942\) 0 0
\(943\) 53.6182 + 72.0217i 1.74605 + 2.34535i
\(944\) 5.47715 + 9.48670i 0.178266 + 0.308766i
\(945\) 0 0
\(946\) 0.262238 0.454209i 0.00852609 0.0147676i
\(947\) −50.6399 + 5.91895i −1.64558 + 0.192340i −0.887817 0.460196i \(-0.847779\pi\)
−0.757758 + 0.652536i \(0.773705\pi\)
\(948\) 0 0
\(949\) 30.3066 7.18279i 0.983793 0.233163i
\(950\) −1.49979 + 0.986430i −0.0486597 + 0.0320040i
\(951\) 0 0
\(952\) 0.363719 0.385520i 0.0117882 0.0124948i
\(953\) −30.4826 25.5779i −0.987428 0.828550i −0.00223469 0.999998i \(-0.500711\pi\)
−0.985193 + 0.171447i \(0.945156\pi\)
\(954\) 0 0
\(955\) −14.5042 + 12.1705i −0.469346 + 0.393828i
\(956\) 0.00619258 0.106323i 0.000200282 0.00343872i
\(957\) 0 0
\(958\) 2.40033 3.22420i 0.0775511 0.104169i
\(959\) 2.38331 + 0.278569i 0.0769612 + 0.00899547i
\(960\) 0 0
\(961\) −0.259364 0.170587i −0.00836659 0.00550279i
\(962\) −3.02955 1.10267i −0.0976767 0.0355514i
\(963\) 0 0
\(964\) 21.9010 7.97131i 0.705384 0.256739i
\(965\) −3.09736 0.734088i −0.0997076 0.0236311i
\(966\) 0 0
\(967\) −1.31277 22.5395i −0.0422160 0.724820i −0.951311 0.308232i \(-0.900263\pi\)
0.909095 0.416588i \(-0.136774\pi\)
\(968\) 5.73103 + 6.07454i 0.184202 + 0.195243i
\(969\) 0 0
\(970\) 0.330482 0.766144i 0.0106111 0.0245994i
\(971\) 7.94868 0.255085 0.127543 0.991833i \(-0.459291\pi\)
0.127543 + 0.991833i \(0.459291\pi\)
\(972\) 0 0
\(973\) −0.543867 −0.0174356
\(974\) 1.35587 3.14326i 0.0434449 0.100717i
\(975\) 0 0
\(976\) 18.2044 + 19.2955i 0.582708 + 0.617634i
\(977\) −2.25420 38.7032i −0.0721184 1.23822i −0.819206 0.573499i \(-0.805585\pi\)
0.747088 0.664726i \(-0.231452\pi\)
\(978\) 0 0
\(979\) 8.34159 + 1.97699i 0.266598 + 0.0631849i
\(980\) −11.6991 + 4.25811i −0.373713 + 0.136020i
\(981\) 0 0
\(982\) −6.53202 2.37746i −0.208445 0.0758678i
\(983\) −14.0749 9.25721i −0.448920 0.295259i 0.304847 0.952401i \(-0.401395\pi\)
−0.753767 + 0.657142i \(0.771765\pi\)
\(984\) 0 0
\(985\) 1.07242 + 0.125347i 0.0341700 + 0.00399390i
\(986\) −3.20715 + 4.30795i −0.102136 + 0.137193i
\(987\) 0 0
\(988\) −0.857569 + 14.7239i −0.0272829 + 0.468429i
\(989\) −21.7482 + 18.2489i −0.691552 + 0.580281i
\(990\) 0 0
\(991\) −5.22377 4.38327i −0.165939 0.139239i 0.556037 0.831158i \(-0.312321\pi\)
−0.721976 + 0.691919i \(0.756766\pi\)
\(992\) 9.06009 9.60313i 0.287658 0.304900i
\(993\) 0 0
\(994\) 0.263706 0.173442i 0.00836424 0.00550125i
\(995\) −0.976821 + 0.231511i −0.0309673 + 0.00733939i
\(996\) 0 0
\(997\) 11.7447 1.37276i 0.371960 0.0434758i 0.0719402 0.997409i \(-0.477081\pi\)
0.300019 + 0.953933i \(0.403007\pi\)
\(998\) 1.77775 3.07914i 0.0562735 0.0974686i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 729.2.g.c.55.5 144
3.2 odd 2 729.2.g.b.55.4 144
9.2 odd 6 729.2.g.a.298.5 144
9.4 even 3 81.2.g.a.7.5 144
9.5 odd 6 243.2.g.a.100.4 144
9.7 even 3 729.2.g.d.298.4 144
81.4 even 27 81.2.g.a.58.5 yes 144
81.23 odd 54 729.2.g.a.433.5 144
81.29 odd 54 6561.2.a.d.1.37 72
81.31 even 27 inner 729.2.g.c.676.5 144
81.50 odd 54 729.2.g.b.676.4 144
81.52 even 27 6561.2.a.c.1.36 72
81.58 even 27 729.2.g.d.433.4 144
81.77 odd 54 243.2.g.a.226.4 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.7.5 144 9.4 even 3
81.2.g.a.58.5 yes 144 81.4 even 27
243.2.g.a.100.4 144 9.5 odd 6
243.2.g.a.226.4 144 81.77 odd 54
729.2.g.a.298.5 144 9.2 odd 6
729.2.g.a.433.5 144 81.23 odd 54
729.2.g.b.55.4 144 3.2 odd 2
729.2.g.b.676.4 144 81.50 odd 54
729.2.g.c.55.5 144 1.1 even 1 trivial
729.2.g.c.676.5 144 81.31 even 27 inner
729.2.g.d.298.4 144 9.7 even 3
729.2.g.d.433.4 144 81.58 even 27
6561.2.a.c.1.36 72 81.52 even 27
6561.2.a.d.1.37 72 81.29 odd 54