Properties

Label 243.2.e.a.55.1
Level $243$
Weight $2$
Character 243.55
Analytic conductor $1.940$
Analytic rank $0$
Dimension $12$
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] = [243,2,Mod(28,243)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(243, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("243.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 243 = 3^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 243.e (of order \(9\), degree \(6\), 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: \(1.94036476912\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 55.1
Root \(0.500000 + 1.00210i\) of defining polynomial
Character \(\chi\) \(=\) 243.55
Dual form 243.2.e.a.190.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.25679 + 0.821403i) q^{2} +(2.88629 - 2.42189i) q^{4} +(-0.0161638 - 0.0916693i) q^{5} +(-0.444200 - 0.372728i) q^{7} +(-2.12277 + 3.67675i) q^{8} +O(q^{10})\) \(q+(-2.25679 + 0.821403i) q^{2} +(2.88629 - 2.42189i) q^{4} +(-0.0161638 - 0.0916693i) q^{5} +(-0.444200 - 0.372728i) q^{7} +(-2.12277 + 3.67675i) q^{8} +(0.111776 + 0.193601i) q^{10} +(0.537108 - 3.04609i) q^{11} +(-3.94834 - 1.43708i) q^{13} +(1.30862 + 0.476300i) q^{14} +(0.462014 - 2.62021i) q^{16} +(-0.995493 - 1.72424i) q^{17} +(1.92271 - 3.33023i) q^{19} +(-0.268666 - 0.225437i) q^{20} +(1.28993 + 7.31556i) q^{22} +(3.41105 - 2.86221i) q^{23} +(4.69032 - 1.70714i) q^{25} +10.0910 q^{26} -2.18479 q^{28} +(6.01357 - 2.18876i) q^{29} +(1.26972 - 1.06542i) q^{31} +(-0.364882 - 2.06935i) q^{32} +(3.66291 + 3.07355i) q^{34} +(-0.0269877 + 0.0467441i) q^{35} +(-2.01505 - 3.49016i) q^{37} +(-1.60368 + 9.09494i) q^{38} +(0.371357 + 0.135163i) q^{40} +(-1.03005 - 0.374907i) q^{41} +(-1.19837 + 6.79628i) q^{43} +(-5.82704 - 10.0927i) q^{44} +(-5.34699 + 9.26126i) q^{46} +(-2.75255 - 2.30966i) q^{47} +(-1.15715 - 6.56252i) q^{49} +(-9.18280 + 7.70529i) q^{50} +(-14.8765 + 5.41460i) q^{52} -5.40034 q^{53} -0.287915 q^{55} +(2.31336 - 0.841995i) q^{56} +(-11.7735 + 9.87913i) q^{58} +(1.78591 + 10.1284i) q^{59} +(-10.1090 - 8.48243i) q^{61} +(-1.99034 + 3.44738i) q^{62} +(5.18386 + 8.97871i) q^{64} +(-0.0679158 + 0.385170i) q^{65} +(8.30434 + 3.02253i) q^{67} +(-7.04920 - 2.56570i) q^{68} +(0.0225098 - 0.127659i) q^{70} +(0.572473 + 0.991553i) q^{71} +(-0.0977361 + 0.169284i) q^{73} +(7.41436 + 6.22139i) q^{74} +(-2.51594 - 14.2686i) q^{76} +(-1.37395 + 1.15288i) q^{77} +(6.77330 - 2.46528i) q^{79} -0.247661 q^{80} +2.63255 q^{82} +(-14.0018 + 5.09625i) q^{83} +(-0.141969 + 0.119126i) q^{85} +(-2.87802 - 16.3221i) q^{86} +(10.0596 + 8.44098i) q^{88} +(-0.776563 + 1.34505i) q^{89} +(1.21821 + 2.11000i) q^{91} +(2.91334 - 16.5224i) q^{92} +(8.10907 + 2.95146i) q^{94} +(-0.336358 - 0.122424i) q^{95} +(0.919560 - 5.21508i) q^{97} +(8.00191 + 13.8597i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} + 6 q^{11} + 3 q^{13} + 21 q^{14} + 9 q^{16} - 9 q^{17} - 3 q^{19} - 24 q^{20} + 12 q^{22} + 12 q^{23} + 12 q^{25} + 30 q^{26} - 12 q^{28} + 24 q^{29} + 12 q^{31} - 27 q^{32} - 12 q^{35} - 3 q^{37} + 30 q^{38} - 15 q^{40} - 6 q^{41} - 15 q^{43} - 3 q^{44} - 3 q^{46} - 12 q^{47} - 33 q^{49} - 21 q^{50} - 45 q^{52} + 18 q^{53} - 12 q^{55} - 30 q^{56} - 51 q^{58} + 3 q^{59} - 33 q^{61} + 12 q^{62} + 12 q^{64} - 21 q^{65} - 6 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} + 21 q^{74} + 6 q^{76} + 12 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 6 q^{83} + 36 q^{85} + 21 q^{86} + 42 q^{88} - 9 q^{89} + 6 q^{91} + 3 q^{92} + 48 q^{94} - 3 q^{95} + 39 q^{97} + 45 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.25679 + 0.821403i −1.59579 + 0.580820i −0.978560 0.205964i \(-0.933967\pi\)
−0.617229 + 0.786784i \(0.711745\pi\)
\(3\) 0 0
\(4\) 2.88629 2.42189i 1.44315 1.21094i
\(5\) −0.0161638 0.0916693i −0.00722866 0.0409957i 0.980980 0.194108i \(-0.0621814\pi\)
−0.988209 + 0.153113i \(0.951070\pi\)
\(6\) 0 0
\(7\) −0.444200 0.372728i −0.167892 0.140878i 0.554971 0.831870i \(-0.312729\pi\)
−0.722862 + 0.690992i \(0.757174\pi\)
\(8\) −2.12277 + 3.67675i −0.750514 + 1.29993i
\(9\) 0 0
\(10\) 0.111776 + 0.193601i 0.0353465 + 0.0612220i
\(11\) 0.537108 3.04609i 0.161944 0.918431i −0.790215 0.612830i \(-0.790031\pi\)
0.952159 0.305602i \(-0.0988577\pi\)
\(12\) 0 0
\(13\) −3.94834 1.43708i −1.09507 0.398574i −0.269574 0.962980i \(-0.586883\pi\)
−0.825497 + 0.564406i \(0.809105\pi\)
\(14\) 1.30862 + 0.476300i 0.349744 + 0.127296i
\(15\) 0 0
\(16\) 0.462014 2.62021i 0.115503 0.655052i
\(17\) −0.995493 1.72424i −0.241443 0.418191i 0.719683 0.694303i \(-0.244287\pi\)
−0.961125 + 0.276112i \(0.910954\pi\)
\(18\) 0 0
\(19\) 1.92271 3.33023i 0.441100 0.764008i −0.556671 0.830733i \(-0.687922\pi\)
0.997771 + 0.0667249i \(0.0212550\pi\)
\(20\) −0.268666 0.225437i −0.0600755 0.0504093i
\(21\) 0 0
\(22\) 1.28993 + 7.31556i 0.275014 + 1.55968i
\(23\) 3.41105 2.86221i 0.711254 0.596813i −0.213697 0.976900i \(-0.568550\pi\)
0.924951 + 0.380087i \(0.124106\pi\)
\(24\) 0 0
\(25\) 4.69032 1.70714i 0.938064 0.341427i
\(26\) 10.0910 1.97900
\(27\) 0 0
\(28\) −2.18479 −0.412887
\(29\) 6.01357 2.18876i 1.11669 0.406443i 0.283248 0.959047i \(-0.408588\pi\)
0.833444 + 0.552604i \(0.186366\pi\)
\(30\) 0 0
\(31\) 1.26972 1.06542i 0.228048 0.191355i −0.521603 0.853188i \(-0.674666\pi\)
0.749651 + 0.661833i \(0.230221\pi\)
\(32\) −0.364882 2.06935i −0.0645026 0.365812i
\(33\) 0 0
\(34\) 3.66291 + 3.07355i 0.628185 + 0.527109i
\(35\) −0.0269877 + 0.0467441i −0.00456176 + 0.00790120i
\(36\) 0 0
\(37\) −2.01505 3.49016i −0.331272 0.573779i 0.651490 0.758657i \(-0.274144\pi\)
−0.982761 + 0.184878i \(0.940811\pi\)
\(38\) −1.60368 + 9.09494i −0.260152 + 1.47539i
\(39\) 0 0
\(40\) 0.371357 + 0.135163i 0.0587167 + 0.0213711i
\(41\) −1.03005 0.374907i −0.160867 0.0585507i 0.260332 0.965519i \(-0.416168\pi\)
−0.421198 + 0.906969i \(0.638390\pi\)
\(42\) 0 0
\(43\) −1.19837 + 6.79628i −0.182749 + 1.03642i 0.746064 + 0.665874i \(0.231941\pi\)
−0.928813 + 0.370548i \(0.879170\pi\)
\(44\) −5.82704 10.0927i −0.878459 1.52154i
\(45\) 0 0
\(46\) −5.34699 + 9.26126i −0.788370 + 1.36550i
\(47\) −2.75255 2.30966i −0.401500 0.336899i 0.419573 0.907722i \(-0.362180\pi\)
−0.821073 + 0.570823i \(0.806624\pi\)
\(48\) 0 0
\(49\) −1.15715 6.56252i −0.165307 0.937503i
\(50\) −9.18280 + 7.70529i −1.29864 + 1.08969i
\(51\) 0 0
\(52\) −14.8765 + 5.41460i −2.06300 + 0.750870i
\(53\) −5.40034 −0.741793 −0.370897 0.928674i \(-0.620950\pi\)
−0.370897 + 0.928674i \(0.620950\pi\)
\(54\) 0 0
\(55\) −0.287915 −0.0388224
\(56\) 2.31336 0.841995i 0.309136 0.112516i
\(57\) 0 0
\(58\) −11.7735 + 9.87913i −1.54593 + 1.29719i
\(59\) 1.78591 + 10.1284i 0.232506 + 1.31861i 0.847803 + 0.530311i \(0.177925\pi\)
−0.615297 + 0.788295i \(0.710964\pi\)
\(60\) 0 0
\(61\) −10.1090 8.48243i −1.29432 1.08606i −0.991097 0.133145i \(-0.957492\pi\)
−0.303224 0.952919i \(-0.598063\pi\)
\(62\) −1.99034 + 3.44738i −0.252774 + 0.437817i
\(63\) 0 0
\(64\) 5.18386 + 8.97871i 0.647982 + 1.12234i
\(65\) −0.0679158 + 0.385170i −0.00842392 + 0.0477744i
\(66\) 0 0
\(67\) 8.30434 + 3.02253i 1.01454 + 0.369261i 0.795173 0.606382i \(-0.207380\pi\)
0.219363 + 0.975643i \(0.429602\pi\)
\(68\) −7.04920 2.56570i −0.854842 0.311137i
\(69\) 0 0
\(70\) 0.0225098 0.127659i 0.00269043 0.0152582i
\(71\) 0.572473 + 0.991553i 0.0679401 + 0.117676i 0.897994 0.440007i \(-0.145024\pi\)
−0.830054 + 0.557683i \(0.811691\pi\)
\(72\) 0 0
\(73\) −0.0977361 + 0.169284i −0.0114391 + 0.0198132i −0.871688 0.490061i \(-0.836975\pi\)
0.860249 + 0.509874i \(0.170308\pi\)
\(74\) 7.41436 + 6.22139i 0.861902 + 0.723221i
\(75\) 0 0
\(76\) −2.51594 14.2686i −0.288598 1.63672i
\(77\) −1.37395 + 1.15288i −0.156576 + 0.131383i
\(78\) 0 0
\(79\) 6.77330 2.46528i 0.762056 0.277366i 0.0683861 0.997659i \(-0.478215\pi\)
0.693670 + 0.720293i \(0.255993\pi\)
\(80\) −0.247661 −0.0276893
\(81\) 0 0
\(82\) 2.63255 0.290717
\(83\) −14.0018 + 5.09625i −1.53690 + 0.559386i −0.965300 0.261145i \(-0.915900\pi\)
−0.571602 + 0.820531i \(0.693678\pi\)
\(84\) 0 0
\(85\) −0.141969 + 0.119126i −0.0153987 + 0.0129211i
\(86\) −2.87802 16.3221i −0.310345 1.76006i
\(87\) 0 0
\(88\) 10.0596 + 8.44098i 1.07235 + 0.899812i
\(89\) −0.776563 + 1.34505i −0.0823155 + 0.142575i −0.904244 0.427016i \(-0.859565\pi\)
0.821929 + 0.569590i \(0.192898\pi\)
\(90\) 0 0
\(91\) 1.21821 + 2.11000i 0.127703 + 0.221189i
\(92\) 2.91334 16.5224i 0.303737 1.72258i
\(93\) 0 0
\(94\) 8.10907 + 2.95146i 0.836387 + 0.304420i
\(95\) −0.336358 0.122424i −0.0345096 0.0125605i
\(96\) 0 0
\(97\) 0.919560 5.21508i 0.0933672 0.529511i −0.901868 0.432011i \(-0.857804\pi\)
0.995235 0.0975004i \(-0.0310847\pi\)
\(98\) 8.00191 + 13.8597i 0.808315 + 1.40004i
\(99\) 0 0
\(100\) 9.40314 16.2867i 0.940314 1.62867i
\(101\) 5.56836 + 4.67241i 0.554073 + 0.464922i 0.876317 0.481734i \(-0.159993\pi\)
−0.322245 + 0.946656i \(0.604437\pi\)
\(102\) 0 0
\(103\) 1.11159 + 6.30412i 0.109528 + 0.621164i 0.989315 + 0.145795i \(0.0465741\pi\)
−0.879787 + 0.475368i \(0.842315\pi\)
\(104\) 13.6652 11.4665i 1.33998 1.12438i
\(105\) 0 0
\(106\) 12.1874 4.43585i 1.18374 0.430848i
\(107\) 5.54365 0.535925 0.267963 0.963429i \(-0.413650\pi\)
0.267963 + 0.963429i \(0.413650\pi\)
\(108\) 0 0
\(109\) −6.23137 −0.596857 −0.298428 0.954432i \(-0.596462\pi\)
−0.298428 + 0.954432i \(0.596462\pi\)
\(110\) 0.649762 0.236494i 0.0619524 0.0225488i
\(111\) 0 0
\(112\) −1.18185 + 0.991691i −0.111674 + 0.0937060i
\(113\) 2.05669 + 11.6640i 0.193477 + 1.09726i 0.914571 + 0.404424i \(0.132528\pi\)
−0.721095 + 0.692836i \(0.756361\pi\)
\(114\) 0 0
\(115\) −0.317513 0.266425i −0.0296082 0.0248442i
\(116\) 12.0560 20.8816i 1.11937 1.93881i
\(117\) 0 0
\(118\) −12.3499 21.3907i −1.13690 1.96917i
\(119\) −0.200476 + 1.13696i −0.0183776 + 0.104225i
\(120\) 0 0
\(121\) 1.34642 + 0.490058i 0.122402 + 0.0445508i
\(122\) 29.7813 + 10.8395i 2.69627 + 0.981362i
\(123\) 0 0
\(124\) 1.08445 6.15022i 0.0973865 0.552306i
\(125\) −0.465014 0.805428i −0.0415921 0.0720396i
\(126\) 0 0
\(127\) −5.76469 + 9.98473i −0.511533 + 0.886002i 0.488377 + 0.872633i \(0.337589\pi\)
−0.999911 + 0.0133693i \(0.995744\pi\)
\(128\) −15.8547 13.3036i −1.40137 1.17589i
\(129\) 0 0
\(130\) −0.163108 0.925032i −0.0143055 0.0811307i
\(131\) 6.90342 5.79266i 0.603155 0.506107i −0.289303 0.957237i \(-0.593424\pi\)
0.892458 + 0.451131i \(0.148979\pi\)
\(132\) 0 0
\(133\) −2.09534 + 0.762641i −0.181689 + 0.0661293i
\(134\) −21.2238 −1.83346
\(135\) 0 0
\(136\) 8.45283 0.724824
\(137\) 10.8255 3.94015i 0.924883 0.336630i 0.164703 0.986343i \(-0.447333\pi\)
0.760179 + 0.649713i \(0.225111\pi\)
\(138\) 0 0
\(139\) 1.30521 1.09520i 0.110707 0.0928940i −0.585754 0.810489i \(-0.699202\pi\)
0.696461 + 0.717595i \(0.254757\pi\)
\(140\) 0.0353145 + 0.200278i 0.00298462 + 0.0169266i
\(141\) 0 0
\(142\) −2.10641 1.76749i −0.176766 0.148325i
\(143\) −6.49816 + 11.2551i −0.543403 + 0.941202i
\(144\) 0 0
\(145\) −0.297844 0.515881i −0.0247346 0.0428416i
\(146\) 0.0815191 0.462318i 0.00674657 0.0382617i
\(147\) 0 0
\(148\) −14.2688 5.19341i −1.17289 0.426896i
\(149\) −20.3469 7.40568i −1.66689 0.606697i −0.675464 0.737393i \(-0.736057\pi\)
−0.991423 + 0.130696i \(0.958279\pi\)
\(150\) 0 0
\(151\) −0.823357 + 4.66949i −0.0670038 + 0.379998i 0.932804 + 0.360385i \(0.117355\pi\)
−0.999808 + 0.0196130i \(0.993757\pi\)
\(152\) 8.16296 + 14.1387i 0.662104 + 1.14680i
\(153\) 0 0
\(154\) 2.15373 3.73036i 0.173552 0.300601i
\(155\) −0.118190 0.0991730i −0.00949323 0.00796576i
\(156\) 0 0
\(157\) −0.0363282 0.206027i −0.00289931 0.0164428i 0.983324 0.181864i \(-0.0582129\pi\)
−0.986223 + 0.165421i \(0.947102\pi\)
\(158\) −13.2609 + 11.1272i −1.05498 + 0.885234i
\(159\) 0 0
\(160\) −0.183798 + 0.0668969i −0.0145305 + 0.00528866i
\(161\) −2.58202 −0.203491
\(162\) 0 0
\(163\) 5.62384 0.440493 0.220247 0.975444i \(-0.429314\pi\)
0.220247 + 0.975444i \(0.429314\pi\)
\(164\) −3.88100 + 1.41257i −0.303056 + 0.110303i
\(165\) 0 0
\(166\) 27.4131 23.0023i 2.12767 1.78532i
\(167\) −2.89654 16.4271i −0.224141 1.27117i −0.864321 0.502941i \(-0.832251\pi\)
0.640180 0.768225i \(-0.278860\pi\)
\(168\) 0 0
\(169\) 3.56560 + 2.99189i 0.274277 + 0.230146i
\(170\) 0.222544 0.385457i 0.0170683 0.0295632i
\(171\) 0 0
\(172\) 13.0010 + 22.5183i 0.991315 + 1.71701i
\(173\) −3.29969 + 18.7135i −0.250871 + 1.42276i 0.555583 + 0.831461i \(0.312495\pi\)
−0.806454 + 0.591297i \(0.798616\pi\)
\(174\) 0 0
\(175\) −2.71974 0.989903i −0.205593 0.0748296i
\(176\) −7.73325 2.81467i −0.582916 0.212164i
\(177\) 0 0
\(178\) 0.647711 3.67335i 0.0485480 0.275329i
\(179\) 8.11761 + 14.0601i 0.606739 + 1.05090i 0.991774 + 0.128001i \(0.0408560\pi\)
−0.385035 + 0.922902i \(0.625811\pi\)
\(180\) 0 0
\(181\) 1.49579 2.59078i 0.111181 0.192571i −0.805066 0.593186i \(-0.797870\pi\)
0.916247 + 0.400614i \(0.131203\pi\)
\(182\) −4.48241 3.76118i −0.332258 0.278798i
\(183\) 0 0
\(184\) 3.28276 + 18.6174i 0.242008 + 1.37250i
\(185\) −0.287370 + 0.241132i −0.0211279 + 0.0177284i
\(186\) 0 0
\(187\) −5.78690 + 2.10626i −0.423180 + 0.154025i
\(188\) −13.5384 −0.987388
\(189\) 0 0
\(190\) 0.859649 0.0623655
\(191\) −2.11790 + 0.770851i −0.153246 + 0.0557768i −0.417504 0.908675i \(-0.637095\pi\)
0.264258 + 0.964452i \(0.414873\pi\)
\(192\) 0 0
\(193\) −0.674328 + 0.565829i −0.0485392 + 0.0407292i −0.666735 0.745295i \(-0.732309\pi\)
0.618195 + 0.786025i \(0.287864\pi\)
\(194\) 2.20843 + 12.5247i 0.158556 + 0.899218i
\(195\) 0 0
\(196\) −19.2335 16.1389i −1.37382 1.15278i
\(197\) 10.1383 17.5600i 0.722322 1.25110i −0.237744 0.971328i \(-0.576408\pi\)
0.960067 0.279771i \(-0.0902586\pi\)
\(198\) 0 0
\(199\) 9.50472 + 16.4627i 0.673772 + 1.16701i 0.976826 + 0.214034i \(0.0686603\pi\)
−0.303054 + 0.952973i \(0.598006\pi\)
\(200\) −3.67977 + 20.8690i −0.260199 + 1.47566i
\(201\) 0 0
\(202\) −16.4045 5.97076i −1.15422 0.420101i
\(203\) −3.48704 1.26918i −0.244742 0.0890788i
\(204\) 0 0
\(205\) −0.0177180 + 0.100484i −0.00123748 + 0.00701809i
\(206\) −7.68684 13.3140i −0.535567 0.927630i
\(207\) 0 0
\(208\) −5.58963 + 9.68152i −0.387571 + 0.671293i
\(209\) −9.11150 7.64545i −0.630255 0.528847i
\(210\) 0 0
\(211\) 2.81033 + 15.9382i 0.193471 + 1.09723i 0.914579 + 0.404408i \(0.132522\pi\)
−0.721108 + 0.692823i \(0.756367\pi\)
\(212\) −15.5869 + 13.0790i −1.07052 + 0.898269i
\(213\) 0 0
\(214\) −12.5108 + 4.55357i −0.855223 + 0.311276i
\(215\) 0.642380 0.0438100
\(216\) 0 0
\(217\) −0.961120 −0.0652451
\(218\) 14.0629 5.11846i 0.952458 0.346666i
\(219\) 0 0
\(220\) −0.831006 + 0.697297i −0.0560264 + 0.0470117i
\(221\) 1.45267 + 8.23850i 0.0977171 + 0.554181i
\(222\) 0 0
\(223\) 16.4372 + 13.7925i 1.10072 + 0.923613i 0.997473 0.0710428i \(-0.0226327\pi\)
0.103246 + 0.994656i \(0.467077\pi\)
\(224\) −0.609223 + 1.05520i −0.0407054 + 0.0705038i
\(225\) 0 0
\(226\) −14.2224 24.6339i −0.946058 1.63862i
\(227\) 3.31915 18.8239i 0.220300 1.24938i −0.651169 0.758933i \(-0.725721\pi\)
0.871469 0.490451i \(-0.163168\pi\)
\(228\) 0 0
\(229\) −21.1150 7.68525i −1.39532 0.507855i −0.468535 0.883445i \(-0.655218\pi\)
−0.926786 + 0.375589i \(0.877440\pi\)
\(230\) 0.935400 + 0.340458i 0.0616784 + 0.0224491i
\(231\) 0 0
\(232\) −4.71792 + 26.7567i −0.309747 + 1.75666i
\(233\) −8.84074 15.3126i −0.579176 1.00316i −0.995574 0.0939796i \(-0.970041\pi\)
0.416398 0.909182i \(-0.363292\pi\)
\(234\) 0 0
\(235\) −0.167233 + 0.289657i −0.0109091 + 0.0188951i
\(236\) 29.6845 + 24.9083i 1.93230 + 1.62139i
\(237\) 0 0
\(238\) −0.481468 2.73054i −0.0312089 0.176995i
\(239\) 11.8126 9.91199i 0.764097 0.641153i −0.175093 0.984552i \(-0.556023\pi\)
0.939190 + 0.343399i \(0.111578\pi\)
\(240\) 0 0
\(241\) −12.3583 + 4.49806i −0.796069 + 0.289746i −0.707857 0.706356i \(-0.750338\pi\)
−0.0882127 + 0.996102i \(0.528116\pi\)
\(242\) −3.44113 −0.221204
\(243\) 0 0
\(244\) −49.7209 −3.18305
\(245\) −0.582878 + 0.212150i −0.0372387 + 0.0135538i
\(246\) 0 0
\(247\) −12.3773 + 10.3858i −0.787550 + 0.660833i
\(248\) 1.22196 + 6.93009i 0.0775946 + 0.440061i
\(249\) 0 0
\(250\) 1.71102 + 1.43571i 0.108214 + 0.0908025i
\(251\) 8.70830 15.0832i 0.549663 0.952045i −0.448634 0.893716i \(-0.648089\pi\)
0.998297 0.0583292i \(-0.0185773\pi\)
\(252\) 0 0
\(253\) −6.88646 11.9277i −0.432948 0.749889i
\(254\) 4.80818 27.2685i 0.301692 1.71098i
\(255\) 0 0
\(256\) 27.2233 + 9.90846i 1.70145 + 0.619279i
\(257\) 10.5129 + 3.82638i 0.655776 + 0.238683i 0.648412 0.761290i \(-0.275434\pi\)
0.00736433 + 0.999973i \(0.497656\pi\)
\(258\) 0 0
\(259\) −0.405798 + 2.30139i −0.0252150 + 0.143002i
\(260\) 0.736812 + 1.27620i 0.0456952 + 0.0791463i
\(261\) 0 0
\(262\) −10.8214 + 18.7433i −0.668550 + 1.15796i
\(263\) 15.8655 + 13.3127i 0.978306 + 0.820896i 0.983833 0.179088i \(-0.0573148\pi\)
−0.00552693 + 0.999985i \(0.501759\pi\)
\(264\) 0 0
\(265\) 0.0872898 + 0.495045i 0.00536217 + 0.0304104i
\(266\) 4.10229 3.44223i 0.251528 0.211057i
\(267\) 0 0
\(268\) 31.2890 11.3883i 1.91128 0.695648i
\(269\) 28.2449 1.72212 0.861060 0.508504i \(-0.169801\pi\)
0.861060 + 0.508504i \(0.169801\pi\)
\(270\) 0 0
\(271\) 17.2626 1.04863 0.524316 0.851524i \(-0.324321\pi\)
0.524316 + 0.851524i \(0.324321\pi\)
\(272\) −4.97781 + 1.81178i −0.301824 + 0.109855i
\(273\) 0 0
\(274\) −21.1943 + 17.7842i −1.28040 + 1.07438i
\(275\) −2.68089 15.2041i −0.161664 0.916840i
\(276\) 0 0
\(277\) 3.95967 + 3.32256i 0.237913 + 0.199633i 0.753947 0.656935i \(-0.228148\pi\)
−0.516034 + 0.856568i \(0.672592\pi\)
\(278\) −2.04598 + 3.54375i −0.122710 + 0.212540i
\(279\) 0 0
\(280\) −0.114578 0.198454i −0.00684733 0.0118599i
\(281\) 0.572421 3.24636i 0.0341478 0.193662i −0.962962 0.269638i \(-0.913096\pi\)
0.997110 + 0.0759760i \(0.0242072\pi\)
\(282\) 0 0
\(283\) 8.58007 + 3.12289i 0.510032 + 0.185637i 0.584201 0.811609i \(-0.301408\pi\)
−0.0741686 + 0.997246i \(0.523630\pi\)
\(284\) 4.05375 + 1.47544i 0.240546 + 0.0875516i
\(285\) 0 0
\(286\) 5.41994 30.7380i 0.320488 1.81758i
\(287\) 0.317809 + 0.550462i 0.0187597 + 0.0324927i
\(288\) 0 0
\(289\) 6.51799 11.2895i 0.383411 0.664087i
\(290\) 1.09592 + 0.919583i 0.0643544 + 0.0539998i
\(291\) 0 0
\(292\) 0.127891 + 0.725308i 0.00748427 + 0.0424454i
\(293\) 2.16517 1.81680i 0.126491 0.106138i −0.577348 0.816498i \(-0.695912\pi\)
0.703839 + 0.710360i \(0.251468\pi\)
\(294\) 0 0
\(295\) 0.899597 0.327426i 0.0523766 0.0190635i
\(296\) 17.1100 0.994496
\(297\) 0 0
\(298\) 52.0017 3.01238
\(299\) −17.5812 + 6.39904i −1.01675 + 0.370066i
\(300\) 0 0
\(301\) 3.06548 2.57224i 0.176691 0.148261i
\(302\) −1.97739 11.2143i −0.113786 0.645313i
\(303\) 0 0
\(304\) −7.83759 6.57652i −0.449517 0.377189i
\(305\) −0.614179 + 1.06379i −0.0351678 + 0.0609124i
\(306\) 0 0
\(307\) −3.14723 5.45116i −0.179622 0.311114i 0.762129 0.647425i \(-0.224154\pi\)
−0.941751 + 0.336311i \(0.890821\pi\)
\(308\) −1.17347 + 6.65508i −0.0668647 + 0.379208i
\(309\) 0 0
\(310\) 0.348190 + 0.126731i 0.0197759 + 0.00719782i
\(311\) −6.92825 2.52168i −0.392865 0.142991i 0.138031 0.990428i \(-0.455922\pi\)
−0.530896 + 0.847437i \(0.678145\pi\)
\(312\) 0 0
\(313\) −0.741608 + 4.20587i −0.0419182 + 0.237730i −0.998567 0.0535138i \(-0.982958\pi\)
0.956649 + 0.291244i \(0.0940690\pi\)
\(314\) 0.251217 + 0.435120i 0.0141770 + 0.0245552i
\(315\) 0 0
\(316\) 13.5791 23.5197i 0.763883 1.32308i
\(317\) −12.3698 10.3795i −0.694755 0.582968i 0.225521 0.974238i \(-0.427591\pi\)
−0.920276 + 0.391270i \(0.872036\pi\)
\(318\) 0 0
\(319\) −3.43723 19.4935i −0.192448 1.09143i
\(320\) 0.739281 0.620330i 0.0413271 0.0346775i
\(321\) 0 0
\(322\) 5.82706 2.12087i 0.324729 0.118192i
\(323\) −7.65618 −0.426001
\(324\) 0 0
\(325\) −20.9723 −1.16333
\(326\) −12.6918 + 4.61944i −0.702934 + 0.255847i
\(327\) 0 0
\(328\) 3.56500 2.99139i 0.196844 0.165172i
\(329\) 0.361805 + 2.05190i 0.0199470 + 0.113125i
\(330\) 0 0
\(331\) 14.7297 + 12.3597i 0.809616 + 0.679349i 0.950516 0.310675i \(-0.100555\pi\)
−0.140900 + 0.990024i \(0.545000\pi\)
\(332\) −28.0708 + 48.6201i −1.54059 + 2.66838i
\(333\) 0 0
\(334\) 20.0301 + 34.6932i 1.09600 + 1.89833i
\(335\) 0.142844 0.810108i 0.00780440 0.0442609i
\(336\) 0 0
\(337\) 27.6859 + 10.0769i 1.50815 + 0.548921i 0.958156 0.286248i \(-0.0924080\pi\)
0.549993 + 0.835169i \(0.314630\pi\)
\(338\) −10.5043 3.82327i −0.571361 0.207958i
\(339\) 0 0
\(340\) −0.121254 + 0.687667i −0.00657593 + 0.0372940i
\(341\) −2.56339 4.43993i −0.138815 0.240435i
\(342\) 0 0
\(343\) −3.96154 + 6.86159i −0.213903 + 0.370491i
\(344\) −22.4444 18.8331i −1.21012 1.01541i
\(345\) 0 0
\(346\) −7.92460 44.9426i −0.426029 2.41613i
\(347\) −8.73063 + 7.32587i −0.468685 + 0.393273i −0.846315 0.532683i \(-0.821184\pi\)
0.377630 + 0.925957i \(0.376739\pi\)
\(348\) 0 0
\(349\) −26.4633 + 9.63184i −1.41655 + 0.515581i −0.933044 0.359763i \(-0.882858\pi\)
−0.483502 + 0.875343i \(0.660635\pi\)
\(350\) 6.95097 0.371545
\(351\) 0 0
\(352\) −6.49941 −0.346419
\(353\) 26.9260 9.80028i 1.43313 0.521616i 0.495302 0.868721i \(-0.335057\pi\)
0.937826 + 0.347104i \(0.112835\pi\)
\(354\) 0 0
\(355\) 0.0816416 0.0685054i 0.00433309 0.00363589i
\(356\) 1.01616 + 5.76294i 0.0538565 + 0.305435i
\(357\) 0 0
\(358\) −29.8687 25.0628i −1.57861 1.32461i
\(359\) −15.5161 + 26.8747i −0.818909 + 1.41839i 0.0875770 + 0.996158i \(0.472088\pi\)
−0.906486 + 0.422235i \(0.861246\pi\)
\(360\) 0 0
\(361\) 2.10636 + 3.64833i 0.110861 + 0.192017i
\(362\) −1.24760 + 7.07549i −0.0655724 + 0.371880i
\(363\) 0 0
\(364\) 8.62630 + 3.13972i 0.452141 + 0.164566i
\(365\) 0.0170979 + 0.00622313i 0.000894945 + 0.000325733i
\(366\) 0 0
\(367\) 4.18913 23.7577i 0.218671 1.24014i −0.655751 0.754977i \(-0.727648\pi\)
0.874422 0.485166i \(-0.161241\pi\)
\(368\) −5.92365 10.2601i −0.308791 0.534843i
\(369\) 0 0
\(370\) 0.450466 0.780230i 0.0234186 0.0405622i
\(371\) 2.39883 + 2.01285i 0.124541 + 0.104502i
\(372\) 0 0
\(373\) −2.18547 12.3944i −0.113159 0.641758i −0.987645 0.156707i \(-0.949912\pi\)
0.874486 0.485051i \(-0.161199\pi\)
\(374\) 11.3297 9.50675i 0.585845 0.491582i
\(375\) 0 0
\(376\) 14.3351 5.21754i 0.739276 0.269074i
\(377\) −26.8890 −1.38486
\(378\) 0 0
\(379\) −7.70522 −0.395790 −0.197895 0.980223i \(-0.563411\pi\)
−0.197895 + 0.980223i \(0.563411\pi\)
\(380\) −1.26733 + 0.461269i −0.0650124 + 0.0236626i
\(381\) 0 0
\(382\) 4.14646 3.47929i 0.212151 0.178016i
\(383\) 3.10164 + 17.5903i 0.158486 + 0.898821i 0.955529 + 0.294898i \(0.0952856\pi\)
−0.797042 + 0.603923i \(0.793603\pi\)
\(384\) 0 0
\(385\) 0.127892 + 0.107314i 0.00651796 + 0.00546922i
\(386\) 1.05704 1.83085i 0.0538020 0.0931878i
\(387\) 0 0
\(388\) −9.97622 17.2793i −0.506466 0.877224i
\(389\) −4.75596 + 26.9724i −0.241137 + 1.36755i 0.588160 + 0.808744i \(0.299852\pi\)
−0.829297 + 0.558809i \(0.811259\pi\)
\(390\) 0 0
\(391\) −8.33084 3.03218i −0.421309 0.153344i
\(392\) 26.5851 + 9.67620i 1.34275 + 0.488722i
\(393\) 0 0
\(394\) −8.45608 + 47.9568i −0.426011 + 2.41603i
\(395\) −0.335472 0.581055i −0.0168794 0.0292361i
\(396\) 0 0
\(397\) −2.10799 + 3.65115i −0.105797 + 0.183246i −0.914064 0.405571i \(-0.867073\pi\)
0.808266 + 0.588817i \(0.200406\pi\)
\(398\) −34.9726 29.3455i −1.75302 1.47096i
\(399\) 0 0
\(400\) −2.30606 13.0783i −0.115303 0.653917i
\(401\) −11.6228 + 9.75269i −0.580415 + 0.487026i −0.885084 0.465432i \(-0.845899\pi\)
0.304668 + 0.952459i \(0.401454\pi\)
\(402\) 0 0
\(403\) −6.54437 + 2.38196i −0.325998 + 0.118654i
\(404\) 27.3880 1.36260
\(405\) 0 0
\(406\) 8.91200 0.442295
\(407\) −11.7137 + 4.26342i −0.580625 + 0.211330i
\(408\) 0 0
\(409\) 3.60777 3.02728i 0.178393 0.149689i −0.549219 0.835679i \(-0.685075\pi\)
0.727612 + 0.685989i \(0.240630\pi\)
\(410\) −0.0425519 0.241324i −0.00210149 0.0119181i
\(411\) 0 0
\(412\) 18.4762 + 15.5034i 0.910258 + 0.763797i
\(413\) 2.98184 5.16469i 0.146727 0.254138i
\(414\) 0 0
\(415\) 0.693492 + 1.20116i 0.0340422 + 0.0589628i
\(416\) −1.53314 + 8.69485i −0.0751682 + 0.426300i
\(417\) 0 0
\(418\) 26.8427 + 9.76994i 1.31292 + 0.477863i
\(419\) 18.5976 + 6.76897i 0.908551 + 0.330686i 0.753674 0.657248i \(-0.228280\pi\)
0.154877 + 0.987934i \(0.450502\pi\)
\(420\) 0 0
\(421\) 4.89440 27.7575i 0.238538 1.35282i −0.596494 0.802617i \(-0.703440\pi\)
0.835032 0.550201i \(-0.185449\pi\)
\(422\) −19.4340 33.6607i −0.946032 1.63858i
\(423\) 0 0
\(424\) 11.4637 19.8557i 0.556726 0.964278i
\(425\) −7.61270 6.38782i −0.369270 0.309855i
\(426\) 0 0
\(427\) 1.32876 + 7.53578i 0.0643033 + 0.364682i
\(428\) 16.0006 13.4261i 0.773418 0.648975i
\(429\) 0 0
\(430\) −1.44971 + 0.527653i −0.0699114 + 0.0254457i
\(431\) 5.19681 0.250321 0.125161 0.992136i \(-0.460055\pi\)
0.125161 + 0.992136i \(0.460055\pi\)
\(432\) 0 0
\(433\) 25.3285 1.21721 0.608605 0.793473i \(-0.291730\pi\)
0.608605 + 0.793473i \(0.291730\pi\)
\(434\) 2.16904 0.789467i 0.104117 0.0378956i
\(435\) 0 0
\(436\) −17.9855 + 15.0917i −0.861351 + 0.722760i
\(437\) −2.97337 16.8628i −0.142236 0.806658i
\(438\) 0 0
\(439\) −11.9972 10.0668i −0.572595 0.480464i 0.309911 0.950766i \(-0.399701\pi\)
−0.882506 + 0.470301i \(0.844145\pi\)
\(440\) 0.611178 1.05859i 0.0291368 0.0504664i
\(441\) 0 0
\(442\) −10.0455 17.3993i −0.477815 0.827600i
\(443\) 3.16975 17.9765i 0.150599 0.854091i −0.812100 0.583518i \(-0.801676\pi\)
0.962700 0.270573i \(-0.0872131\pi\)
\(444\) 0 0
\(445\) 0.135852 + 0.0494459i 0.00643998 + 0.00234396i
\(446\) −48.4245 17.6251i −2.29297 0.834572i
\(447\) 0 0
\(448\) 1.04394 5.92050i 0.0493218 0.279718i
\(449\) 14.3608 + 24.8737i 0.677729 + 1.17386i 0.975663 + 0.219274i \(0.0703690\pi\)
−0.297934 + 0.954586i \(0.596298\pi\)
\(450\) 0 0
\(451\) −1.69525 + 2.93626i −0.0798262 + 0.138263i
\(452\) 34.1852 + 28.6848i 1.60793 + 1.34922i
\(453\) 0 0
\(454\) 7.97135 + 45.2078i 0.374114 + 2.12171i
\(455\) 0.173732 0.145778i 0.00814466 0.00683419i
\(456\) 0 0
\(457\) 33.2538 12.1034i 1.55555 0.566172i 0.585835 0.810430i \(-0.300767\pi\)
0.969710 + 0.244258i \(0.0785444\pi\)
\(458\) 53.9648 2.52161
\(459\) 0 0
\(460\) −1.56168 −0.0728139
\(461\) 2.13943 0.778687i 0.0996430 0.0362671i −0.291718 0.956504i \(-0.594227\pi\)
0.391361 + 0.920237i \(0.372005\pi\)
\(462\) 0 0
\(463\) 14.0757 11.8109i 0.654154 0.548900i −0.254175 0.967158i \(-0.581804\pi\)
0.908328 + 0.418258i \(0.137359\pi\)
\(464\) −2.95666 16.7681i −0.137260 0.778437i
\(465\) 0 0
\(466\) 32.5295 + 27.2955i 1.50690 + 1.26444i
\(467\) 2.32935 4.03455i 0.107789 0.186697i −0.807085 0.590435i \(-0.798956\pi\)
0.914874 + 0.403738i \(0.132289\pi\)
\(468\) 0 0
\(469\) −2.56220 4.43786i −0.118312 0.204922i
\(470\) 0.139485 0.791059i 0.00643397 0.0364888i
\(471\) 0 0
\(472\) −41.0307 14.9340i −1.88859 0.687392i
\(473\) 20.0584 + 7.30068i 0.922288 + 0.335685i
\(474\) 0 0
\(475\) 3.33297 18.9022i 0.152927 0.867292i
\(476\) 2.17495 + 3.76712i 0.0996885 + 0.172666i
\(477\) 0 0
\(478\) −18.5169 + 32.0722i −0.846942 + 1.46695i
\(479\) 10.8594 + 9.11209i 0.496177 + 0.416342i 0.856234 0.516588i \(-0.172798\pi\)
−0.360057 + 0.932930i \(0.617243\pi\)
\(480\) 0 0
\(481\) 2.94045 + 16.6761i 0.134073 + 0.760366i
\(482\) 24.1954 20.3023i 1.10207 0.924745i
\(483\) 0 0
\(484\) 5.07304 1.84643i 0.230593 0.0839288i
\(485\) −0.492926 −0.0223826
\(486\) 0 0
\(487\) −21.4338 −0.971258 −0.485629 0.874165i \(-0.661409\pi\)
−0.485629 + 0.874165i \(0.661409\pi\)
\(488\) 52.6469 19.1619i 2.38321 0.867418i
\(489\) 0 0
\(490\) 1.14117 0.957555i 0.0515528 0.0432579i
\(491\) 2.44633 + 13.8738i 0.110401 + 0.626117i 0.988925 + 0.148418i \(0.0474180\pi\)
−0.878523 + 0.477699i \(0.841471\pi\)
\(492\) 0 0
\(493\) −9.76043 8.18997i −0.439588 0.368858i
\(494\) 19.4020 33.6053i 0.872938 1.51197i
\(495\) 0 0
\(496\) −2.20500 3.81917i −0.0990073 0.171486i
\(497\) 0.115287 0.653824i 0.00517132 0.0293280i
\(498\) 0 0
\(499\) −14.0102 5.09929i −0.627182 0.228276i 0.00882219 0.999961i \(-0.497192\pi\)
−0.636004 + 0.771685i \(0.719414\pi\)
\(500\) −3.29282 1.19849i −0.147259 0.0535980i
\(501\) 0 0
\(502\) −7.26337 + 41.1926i −0.324180 + 1.83852i
\(503\) −7.93153 13.7378i −0.353650 0.612539i 0.633236 0.773958i \(-0.281726\pi\)
−0.986886 + 0.161420i \(0.948393\pi\)
\(504\) 0 0
\(505\) 0.338311 0.585972i 0.0150546 0.0260754i
\(506\) 25.3387 + 21.2617i 1.12644 + 0.945199i
\(507\) 0 0
\(508\) 7.54331 + 42.7803i 0.334680 + 1.89807i
\(509\) −25.9894 + 21.8077i −1.15196 + 0.966608i −0.999764 0.0217430i \(-0.993078\pi\)
−0.152194 + 0.988351i \(0.548634\pi\)
\(510\) 0 0
\(511\) 0.106511 0.0387669i 0.00471177 0.00171495i
\(512\) −28.1824 −1.24550
\(513\) 0 0
\(514\) −26.8683 −1.18511
\(515\) 0.559927 0.203797i 0.0246733 0.00898036i
\(516\) 0 0
\(517\) −8.51386 + 7.14397i −0.374439 + 0.314192i
\(518\) −0.974572 5.52707i −0.0428203 0.242846i
\(519\) 0 0
\(520\) −1.27200 1.06734i −0.0557811 0.0468059i
\(521\) −21.3899 + 37.0484i −0.937108 + 1.62312i −0.166277 + 0.986079i \(0.553175\pi\)
−0.770831 + 0.637040i \(0.780159\pi\)
\(522\) 0 0
\(523\) 1.38893 + 2.40569i 0.0607335 + 0.105193i 0.894793 0.446480i \(-0.147323\pi\)
−0.834060 + 0.551674i \(0.813989\pi\)
\(524\) 5.89612 33.4386i 0.257573 1.46077i
\(525\) 0 0
\(526\) −46.7400 17.0120i −2.03796 0.741758i
\(527\) −3.10104 1.12869i −0.135083 0.0491664i
\(528\) 0 0
\(529\) −0.550887 + 3.12424i −0.0239516 + 0.135836i
\(530\) −0.603626 1.04551i −0.0262198 0.0454141i
\(531\) 0 0
\(532\) −4.20073 + 7.27587i −0.182125 + 0.315449i
\(533\) 3.52821 + 2.96052i 0.152824 + 0.128234i
\(534\) 0 0
\(535\) −0.0896063 0.508183i −0.00387402 0.0219707i
\(536\) −28.7413 + 24.1168i −1.24144 + 1.04169i
\(537\) 0 0
\(538\) −63.7426 + 23.2004i −2.74814 + 1.00024i
\(539\) −20.6116 −0.887803
\(540\) 0 0
\(541\) −3.59390 −0.154514 −0.0772570 0.997011i \(-0.524616\pi\)
−0.0772570 + 0.997011i \(0.524616\pi\)
\(542\) −38.9581 + 14.1796i −1.67339 + 0.609065i
\(543\) 0 0
\(544\) −3.20482 + 2.68917i −0.137406 + 0.115297i
\(545\) 0.100722 + 0.571225i 0.00431447 + 0.0244686i
\(546\) 0 0
\(547\) −30.3245 25.4453i −1.29658 1.08796i −0.990725 0.135884i \(-0.956612\pi\)
−0.305858 0.952077i \(-0.598943\pi\)
\(548\) 21.7029 37.5905i 0.927101 1.60579i
\(549\) 0 0
\(550\) 18.5389 + 32.1102i 0.790499 + 1.36919i
\(551\) 4.27328 24.2350i 0.182048 1.03244i
\(552\) 0 0
\(553\) −3.92757 1.42952i −0.167017 0.0607894i
\(554\) −11.6653 4.24581i −0.495610 0.180387i
\(555\) 0 0
\(556\) 1.11477 6.32215i 0.0472766 0.268119i
\(557\) −5.71731 9.90267i −0.242250 0.419590i 0.719105 0.694902i \(-0.244552\pi\)
−0.961355 + 0.275312i \(0.911219\pi\)
\(558\) 0 0
\(559\) 14.4983 25.1119i 0.613214 1.06212i
\(560\) 0.110011 + 0.0923099i 0.00464880 + 0.00390081i
\(561\) 0 0
\(562\) 1.37474 + 7.79653i 0.0579898 + 0.328877i
\(563\) −11.1159 + 9.32736i −0.468480 + 0.393101i −0.846240 0.532802i \(-0.821139\pi\)
0.377760 + 0.925904i \(0.376694\pi\)
\(564\) 0 0
\(565\) 1.03599 0.377070i 0.0435844 0.0158634i
\(566\) −21.9285 −0.921725
\(567\) 0 0
\(568\) −4.86093 −0.203960
\(569\) −1.22083 + 0.444347i −0.0511800 + 0.0186280i −0.367483 0.930030i \(-0.619780\pi\)
0.316303 + 0.948658i \(0.397558\pi\)
\(570\) 0 0
\(571\) 12.3006 10.3214i 0.514765 0.431939i −0.348037 0.937481i \(-0.613152\pi\)
0.862802 + 0.505542i \(0.168707\pi\)
\(572\) 8.50308 + 48.2234i 0.355532 + 2.01632i
\(573\) 0 0
\(574\) −1.16938 0.981225i −0.0488089 0.0409555i
\(575\) 11.1127 19.2478i 0.463434 0.802691i
\(576\) 0 0
\(577\) 4.23017 + 7.32686i 0.176104 + 0.305021i 0.940543 0.339675i \(-0.110317\pi\)
−0.764439 + 0.644696i \(0.776984\pi\)
\(578\) −5.43649 + 30.8318i −0.226128 + 1.28244i
\(579\) 0 0
\(580\) −2.10907 0.767638i −0.0875743 0.0318745i
\(581\) 8.11913 + 2.95512i 0.336838 + 0.122599i
\(582\) 0 0
\(583\) −2.90057 + 16.4499i −0.120129 + 0.681286i
\(584\) −0.414943 0.718703i −0.0171705 0.0297401i
\(585\) 0 0
\(586\) −3.39401 + 5.87860i −0.140205 + 0.242843i
\(587\) 14.0839 + 11.8178i 0.581304 + 0.487772i 0.885375 0.464877i \(-0.153902\pi\)
−0.304071 + 0.952649i \(0.598346\pi\)
\(588\) 0 0
\(589\) −1.10680 6.27696i −0.0456048 0.258637i
\(590\) −1.76125 + 1.47786i −0.0725094 + 0.0608426i
\(591\) 0 0
\(592\) −10.0759 + 3.66734i −0.414119 + 0.150727i
\(593\) −13.5128 −0.554905 −0.277452 0.960739i \(-0.589490\pi\)
−0.277452 + 0.960739i \(0.589490\pi\)
\(594\) 0 0
\(595\) 0.107464 0.00440561
\(596\) −76.6629 + 27.9030i −3.14023 + 1.14295i
\(597\) 0 0
\(598\) 34.4209 28.8825i 1.40757 1.18109i
\(599\) −1.91494 10.8602i −0.0782425 0.443735i −0.998611 0.0526835i \(-0.983223\pi\)
0.920369 0.391051i \(-0.127889\pi\)
\(600\) 0 0
\(601\) 19.7624 + 16.5826i 0.806123 + 0.676418i 0.949679 0.313225i \(-0.101409\pi\)
−0.143556 + 0.989642i \(0.545854\pi\)
\(602\) −4.80528 + 8.32298i −0.195848 + 0.339219i
\(603\) 0 0
\(604\) 8.93252 + 15.4716i 0.363459 + 0.629529i
\(605\) 0.0231600 0.131347i 0.000941588 0.00534001i
\(606\) 0 0
\(607\) 13.8979 + 5.05843i 0.564100 + 0.205316i 0.608300 0.793707i \(-0.291852\pi\)
−0.0442003 + 0.999023i \(0.514074\pi\)
\(608\) −7.59297 2.76362i −0.307936 0.112079i
\(609\) 0 0
\(610\) 0.512271 2.90523i 0.0207413 0.117629i
\(611\) 7.54882 + 13.0749i 0.305393 + 0.528956i
\(612\) 0 0
\(613\) −18.1370 + 31.4141i −0.732545 + 1.26880i 0.223248 + 0.974762i \(0.428334\pi\)
−0.955792 + 0.294043i \(0.904999\pi\)
\(614\) 11.5802 + 9.71696i 0.467340 + 0.392145i
\(615\) 0 0
\(616\) −1.32227 7.49896i −0.0532757 0.302142i
\(617\) 30.9279 25.9516i 1.24511 1.04477i 0.248005 0.968759i \(-0.420225\pi\)
0.997107 0.0760138i \(-0.0242193\pi\)
\(618\) 0 0
\(619\) 6.47759 2.35765i 0.260356 0.0947619i −0.208544 0.978013i \(-0.566873\pi\)
0.468900 + 0.883251i \(0.344650\pi\)
\(620\) −0.581315 −0.0233462
\(621\) 0 0
\(622\) 17.7069 0.709981
\(623\) 0.846285 0.308023i 0.0339057 0.0123407i
\(624\) 0 0
\(625\) 19.0516 15.9862i 0.762064 0.639448i
\(626\) −1.78106 10.1009i −0.0711856 0.403713i
\(627\) 0 0
\(628\) −0.603829 0.506672i −0.0240954 0.0202184i
\(629\) −4.01193 + 6.94887i −0.159966 + 0.277070i
\(630\) 0 0
\(631\) −14.9095 25.8241i −0.593539 1.02804i −0.993751 0.111617i \(-0.964397\pi\)
0.400212 0.916423i \(-0.368936\pi\)
\(632\) −5.31396 + 30.1370i −0.211378 + 1.19878i
\(633\) 0 0
\(634\) 36.4416 + 13.2637i 1.44728 + 0.526767i
\(635\) 1.00847 + 0.367054i 0.0400200 + 0.0145661i
\(636\) 0 0
\(637\) −4.86204 + 27.5740i −0.192641 + 1.09252i
\(638\) 23.7691 + 41.1693i 0.941028 + 1.62991i
\(639\) 0 0
\(640\) −0.963264 + 1.66842i −0.0380763 + 0.0659502i
\(641\) −32.8485 27.5632i −1.29744 1.08868i −0.990581 0.136926i \(-0.956278\pi\)
−0.306858 0.951755i \(-0.599278\pi\)
\(642\) 0 0
\(643\) −4.76026 26.9968i −0.187726 1.06465i −0.922402 0.386231i \(-0.873777\pi\)
0.734676 0.678419i \(-0.237334\pi\)
\(644\) −7.45245 + 6.25335i −0.293668 + 0.246416i
\(645\) 0 0
\(646\) 17.2784 6.28881i 0.679808 0.247430i
\(647\) 16.1623 0.635407 0.317703 0.948190i \(-0.397088\pi\)
0.317703 + 0.948190i \(0.397088\pi\)
\(648\) 0 0
\(649\) 31.8113 1.24870
\(650\) 47.3299 17.2267i 1.85643 0.675686i
\(651\) 0 0
\(652\) 16.2320 13.6203i 0.635696 0.533412i
\(653\) −5.59951 31.7564i −0.219126 1.24272i −0.873602 0.486641i \(-0.838222\pi\)
0.654476 0.756083i \(-0.272889\pi\)
\(654\) 0 0
\(655\) −0.642594 0.539200i −0.0251082 0.0210683i
\(656\) −1.45823 + 2.52573i −0.0569344 + 0.0986133i
\(657\) 0 0
\(658\) −2.50195 4.33351i −0.0975363 0.168938i
\(659\) −4.83065 + 27.3960i −0.188175 + 1.06719i 0.733632 + 0.679547i \(0.237824\pi\)
−0.921807 + 0.387648i \(0.873288\pi\)
\(660\) 0 0
\(661\) −28.9318 10.5303i −1.12532 0.409582i −0.288728 0.957411i \(-0.593232\pi\)
−0.836590 + 0.547829i \(0.815454\pi\)
\(662\) −43.3940 15.7941i −1.68656 0.613856i
\(663\) 0 0
\(664\) 10.9851 62.2995i 0.426304 2.41769i
\(665\) 0.103779 + 0.179751i 0.00402439 + 0.00697044i
\(666\) 0 0
\(667\) 14.2479 24.6781i 0.551682 0.955540i
\(668\) −48.1448 40.3982i −1.86278 1.56306i
\(669\) 0 0
\(670\) 0.343057 + 1.94557i 0.0132534 + 0.0751640i
\(671\) −31.2679 + 26.2369i −1.20708 + 1.01286i
\(672\) 0 0
\(673\) 24.5547 8.93720i 0.946516 0.344504i 0.177780 0.984070i \(-0.443108\pi\)
0.768736 + 0.639567i \(0.220886\pi\)
\(674\) −70.7584 −2.72551
\(675\) 0 0
\(676\) 17.5374 0.674515
\(677\) 17.0972 6.22288i 0.657100 0.239165i 0.00811624 0.999967i \(-0.497416\pi\)
0.648984 + 0.760802i \(0.275194\pi\)
\(678\) 0 0
\(679\) −2.35227 + 1.97379i −0.0902720 + 0.0757472i
\(680\) −0.136630 0.774865i −0.00523950 0.0297147i
\(681\) 0 0
\(682\) 9.43200 + 7.91438i 0.361170 + 0.303057i
\(683\) 11.7486 20.3491i 0.449546 0.778636i −0.548811 0.835947i \(-0.684919\pi\)
0.998356 + 0.0573104i \(0.0182525\pi\)
\(684\) 0 0
\(685\) −0.536171 0.928676i −0.0204860 0.0354829i
\(686\) 3.30422 18.7392i 0.126156 0.715465i
\(687\) 0 0
\(688\) 17.2540 + 6.27995i 0.657803 + 0.239421i
\(689\) 21.3223 + 7.76070i 0.812317 + 0.295659i
\(690\) 0 0
\(691\) −7.73393 + 43.8613i −0.294213 + 1.66856i 0.376173 + 0.926549i \(0.377240\pi\)
−0.670386 + 0.742013i \(0.733871\pi\)
\(692\) 35.7980 + 62.0039i 1.36084 + 2.35704i
\(693\) 0 0
\(694\) 13.6857 23.7043i 0.519501 0.899802i
\(695\) −0.121494 0.101945i −0.00460852 0.00386701i
\(696\) 0 0
\(697\) 0.378975 + 2.14928i 0.0143547 + 0.0814096i
\(698\) 51.8103 43.4740i 1.96105 1.64552i
\(699\) 0 0
\(700\) −10.2474 + 3.72974i −0.387315 + 0.140971i
\(701\) 25.2567 0.953934 0.476967 0.878921i \(-0.341736\pi\)
0.476967 + 0.878921i \(0.341736\pi\)
\(702\) 0 0
\(703\) −15.4974 −0.584496
\(704\) 30.1343 10.9680i 1.13573 0.413371i
\(705\) 0 0
\(706\) −52.7163 + 44.2343i −1.98401 + 1.66478i
\(707\) −0.731927 4.15097i −0.0275270 0.156113i
\(708\) 0 0
\(709\) −12.0147 10.0815i −0.451220 0.378618i 0.388668 0.921378i \(-0.372935\pi\)
−0.839888 + 0.542759i \(0.817380\pi\)
\(710\) −0.127977 + 0.221663i −0.00480289 + 0.00831886i
\(711\) 0 0
\(712\) −3.29694 5.71046i −0.123558 0.214009i
\(713\) 1.28162 7.26841i 0.0479970 0.272204i
\(714\) 0 0
\(715\) 1.13678 + 0.413756i 0.0425133 + 0.0154736i
\(716\) 57.4818 + 20.9217i 2.14820 + 0.781879i
\(717\) 0 0
\(718\) 12.9416 73.3954i 0.482976 2.73909i
\(719\) −26.5804 46.0385i −0.991280 1.71695i −0.609757 0.792588i \(-0.708733\pi\)
−0.381523 0.924359i \(-0.624600\pi\)
\(720\) 0 0
\(721\) 1.85595 3.21461i 0.0691194 0.119718i
\(722\) −7.75035 6.50332i −0.288438 0.242028i
\(723\) 0 0
\(724\) −1.95730 11.1004i −0.0727424 0.412543i
\(725\) 24.4691 20.5320i 0.908758 0.762539i
\(726\) 0 0
\(727\) −0.440878 + 0.160466i −0.0163512 + 0.00595137i −0.350183 0.936681i \(-0.613881\pi\)
0.333832 + 0.942633i \(0.391658\pi\)
\(728\) −10.3440 −0.383372
\(729\) 0 0
\(730\) −0.0436980 −0.00161734
\(731\) 12.9114 4.69937i 0.477546 0.173812i
\(732\) 0 0
\(733\) −35.5493 + 29.8294i −1.31304 + 1.10177i −0.325312 + 0.945607i \(0.605469\pi\)
−0.987731 + 0.156166i \(0.950086\pi\)
\(734\) 10.0607 + 57.0570i 0.371347 + 2.10601i
\(735\) 0 0
\(736\) −7.16755 6.01429i −0.264199 0.221690i
\(737\) 13.6672 23.6724i 0.503439 0.871983i
\(738\) 0 0
\(739\) −12.9047 22.3515i −0.474706 0.822214i 0.524875 0.851179i \(-0.324112\pi\)
−0.999580 + 0.0289653i \(0.990779\pi\)
\(740\) −0.245439 + 1.39195i −0.00902252 + 0.0511693i
\(741\) 0 0
\(742\) −7.06700 2.57218i −0.259438 0.0944276i
\(743\) 32.6164 + 11.8714i 1.19658 + 0.435519i 0.862029 0.506859i \(-0.169193\pi\)
0.334550 + 0.942378i \(0.391416\pi\)
\(744\) 0 0
\(745\) −0.349990 + 1.98489i −0.0128226 + 0.0727209i
\(746\) 15.1129 + 26.1764i 0.553324 + 0.958385i
\(747\) 0 0
\(748\) −11.6015 + 20.0945i −0.424195 + 0.734727i
\(749\) −2.46249 2.06627i −0.0899774 0.0755000i
\(750\) 0 0
\(751\) 4.16510 + 23.6214i 0.151987 + 0.861959i 0.961489 + 0.274843i \(0.0886257\pi\)
−0.809503 + 0.587116i \(0.800263\pi\)
\(752\) −7.32351 + 6.14515i −0.267061 + 0.224091i
\(753\) 0 0
\(754\) 60.6828 22.0867i 2.20994 0.804351i
\(755\) 0.441357 0.0160626
\(756\) 0 0
\(757\) −8.78780 −0.319398 −0.159699 0.987166i \(-0.551052\pi\)
−0.159699 + 0.987166i \(0.551052\pi\)
\(758\) 17.3890 6.32909i 0.631598 0.229883i
\(759\) 0 0
\(760\) 1.16414 0.976827i 0.0422277 0.0354332i
\(761\) −2.38833 13.5449i −0.0865771 0.491003i −0.997005 0.0773355i \(-0.975359\pi\)
0.910428 0.413667i \(-0.135752\pi\)
\(762\) 0 0
\(763\) 2.76797 + 2.32260i 0.100207 + 0.0840839i
\(764\) −4.24595 + 7.35420i −0.153613 + 0.266066i
\(765\) 0 0
\(766\) −21.4484 37.1498i −0.774963 1.34228i
\(767\) 7.50392 42.5569i 0.270951 1.53664i
\(768\) 0 0
\(769\) 29.4668 + 10.7250i 1.06260 + 0.386755i 0.813405 0.581698i \(-0.197611\pi\)
0.249196 + 0.968453i \(0.419834\pi\)
\(770\) −0.376772 0.137134i −0.0135779 0.00494196i
\(771\) 0 0
\(772\) −0.575935 + 3.26629i −0.0207284 + 0.117556i
\(773\) 14.0607 + 24.3539i 0.505729 + 0.875948i 0.999978 + 0.00662776i \(0.00210970\pi\)
−0.494249 + 0.869320i \(0.664557\pi\)
\(774\) 0 0
\(775\) 4.13657 7.16475i 0.148590 0.257365i
\(776\) 17.2226 + 14.4514i 0.618254 + 0.518776i
\(777\) 0 0
\(778\) −11.4220 64.7774i −0.409499 2.32238i
\(779\) −3.22902 + 2.70947i −0.115692 + 0.0970767i
\(780\) 0 0
\(781\) 3.32784 1.21124i 0.119080 0.0433414i
\(782\) 21.2916 0.761385
\(783\) 0 0
\(784\) −17.7298 −0.633207
\(785\) −0.0182992 + 0.00666036i −0.000653126 + 0.000237718i
\(786\) 0 0
\(787\) −27.7309 + 23.2690i −0.988501 + 0.829451i −0.985350 0.170544i \(-0.945447\pi\)
−0.00315089 + 0.999995i \(0.501003\pi\)
\(788\) −13.2663 75.2370i −0.472593 2.68021i
\(789\) 0 0
\(790\) 1.23437 + 1.03576i 0.0439169 + 0.0368507i
\(791\) 3.43393 5.94775i 0.122097 0.211478i
\(792\) 0 0
\(793\) 27.7237 + 48.0189i 0.984498 + 1.70520i
\(794\) 1.75822 9.97138i 0.0623970 0.353871i
\(795\) 0 0
\(796\) 67.3041 + 24.4967i 2.38553 + 0.868262i
\(797\) −27.8150 10.1238i −0.985258 0.358604i −0.201376 0.979514i \(-0.564541\pi\)
−0.783882 + 0.620910i \(0.786763\pi\)
\(798\) 0 0
\(799\) −1.24228 + 7.04531i −0.0439487 + 0.249245i
\(800\) −5.24407 9.08300i −0.185406 0.321133i
\(801\) 0 0
\(802\) 18.2193 31.5568i 0.643346 1.11431i
\(803\) 0.463159 + 0.388637i 0.0163445 + 0.0137147i
\(804\) 0 0
\(805\) 0.0417351 + 0.236691i 0.00147097 + 0.00834228i
\(806\) 12.8127 10.7511i 0.451308 0.378692i
\(807\) 0 0
\(808\) −28.9997 + 10.5550i −1.02021 + 0.371324i
\(809\) 5.75943 0.202491 0.101245 0.994861i \(-0.467717\pi\)
0.101245 + 0.994861i \(0.467717\pi\)
\(810\) 0 0
\(811\) 12.4896 0.438569 0.219284 0.975661i \(-0.429628\pi\)
0.219284 + 0.975661i \(0.429628\pi\)
\(812\) −13.1384 + 4.78199i −0.461068 + 0.167815i
\(813\) 0 0
\(814\) 22.9332 19.2433i 0.803809 0.674476i
\(815\) −0.0909025 0.515534i −0.00318418 0.0180584i
\(816\) 0 0
\(817\) 20.3291 + 17.0581i 0.711225 + 0.596788i
\(818\) −5.65535 + 9.79536i −0.197735 + 0.342487i
\(819\) 0 0
\(820\) 0.192221 + 0.332936i 0.00671265 + 0.0116266i
\(821\) −7.47846 + 42.4125i −0.261000 + 1.48021i 0.519188 + 0.854660i \(0.326235\pi\)
−0.780188 + 0.625545i \(0.784877\pi\)
\(822\) 0 0
\(823\) −9.66389 3.51737i −0.336862 0.122608i 0.168050 0.985778i \(-0.446253\pi\)
−0.504912 + 0.863171i \(0.668475\pi\)
\(824\) −25.5383 9.29520i −0.889670 0.323814i
\(825\) 0 0
\(826\) −2.48707 + 14.1049i −0.0865364 + 0.490772i
\(827\) 3.04731 + 5.27810i 0.105965 + 0.183538i 0.914132 0.405416i \(-0.132873\pi\)
−0.808167 + 0.588954i \(0.799540\pi\)
\(828\) 0 0
\(829\) 16.8489 29.1832i 0.585188 1.01358i −0.409664 0.912236i \(-0.634354\pi\)
0.994852 0.101339i \(-0.0323126\pi\)
\(830\) −2.55170 2.14113i −0.0885709 0.0743198i
\(831\) 0 0
\(832\) −7.56453 42.9006i −0.262253 1.48731i
\(833\) −10.1635 + 8.52816i −0.352143 + 0.295483i
\(834\) 0 0
\(835\) −1.45904 + 0.531047i −0.0504922 + 0.0183776i
\(836\) −44.8148 −1.54995
\(837\) 0 0
\(838\) −47.5308 −1.64192
\(839\) −39.6797 + 14.4422i −1.36989 + 0.498601i −0.919099 0.394027i \(-0.871082\pi\)
−0.450795 + 0.892628i \(0.648859\pi\)
\(840\) 0 0
\(841\) 9.15708 7.68370i 0.315761 0.264955i
\(842\) 11.7545 + 66.6630i 0.405086 + 2.29736i
\(843\) 0 0
\(844\) 46.7119 + 39.1960i 1.60789 + 1.34918i
\(845\) 0.216631 0.375216i 0.00745234 0.0129078i
\(846\) 0 0
\(847\) −0.415423 0.719533i −0.0142741 0.0247235i
\(848\) −2.49503 + 14.1500i −0.0856796 + 0.485913i
\(849\) 0 0
\(850\) 22.4272 + 8.16284i 0.769247 + 0.279983i
\(851\) −16.8630 6.13764i −0.578057 0.210396i
\(852\) 0 0
\(853\) −6.20438 + 35.1868i −0.212434 + 1.20477i 0.672870 + 0.739760i \(0.265061\pi\)
−0.885304 + 0.465012i \(0.846050\pi\)
\(854\) −9.18865 15.9152i −0.314429 0.544607i
\(855\) 0 0
\(856\) −11.7679 + 20.3826i −0.402219 + 0.696664i
\(857\) −6.05838 5.08358i −0.206950 0.173652i 0.533421 0.845850i \(-0.320906\pi\)
−0.740372 + 0.672198i \(0.765350\pi\)
\(858\) 0 0
\(859\) −7.76540 44.0398i −0.264952 1.50262i −0.769172 0.639042i \(-0.779331\pi\)
0.504220 0.863575i \(-0.331780\pi\)
\(860\) 1.85410 1.55577i 0.0632241 0.0530513i
\(861\) 0 0
\(862\) −11.7281 + 4.26867i −0.399460 + 0.145391i
\(863\) 22.9170 0.780103 0.390052 0.920793i \(-0.372457\pi\)
0.390052 + 0.920793i \(0.372457\pi\)
\(864\) 0 0
\(865\) 1.76878 0.0601405
\(866\) −57.1610 + 20.8049i −1.94241 + 0.706979i
\(867\) 0 0
\(868\) −2.77407 + 2.32772i −0.0941581 + 0.0790080i
\(869\) −3.87147 21.9562i −0.131331 0.744814i
\(870\) 0 0
\(871\) −28.4447 23.8680i −0.963813 0.808735i
\(872\) 13.2278 22.9112i 0.447950 0.775871i
\(873\) 0 0
\(874\) 20.5614 + 35.6134i 0.695501 + 1.20464i
\(875\) −0.0936462 + 0.531094i −0.00316582 + 0.0179543i
\(876\) 0 0
\(877\) 20.8026 + 7.57152i 0.702453 + 0.255672i 0.668458 0.743750i \(-0.266955\pi\)
0.0339951 + 0.999422i \(0.489177\pi\)
\(878\) 35.3441 + 12.8642i 1.19280 + 0.434145i
\(879\) 0 0
\(880\) −0.133021 + 0.754397i −0.00448412 + 0.0254307i
\(881\) 4.93202 + 8.54251i 0.166164 + 0.287804i 0.937068 0.349147i \(-0.113529\pi\)
−0.770904 + 0.636951i \(0.780195\pi\)
\(882\) 0 0
\(883\) −23.7865 + 41.1995i −0.800481 + 1.38647i 0.118819 + 0.992916i \(0.462089\pi\)
−0.919300 + 0.393558i \(0.871244\pi\)
\(884\) 24.1455 + 20.2605i 0.812102 + 0.681434i
\(885\) 0 0
\(886\) 7.61253 + 43.1728i 0.255748 + 1.45042i
\(887\) −10.2323 + 8.58590i −0.343566 + 0.288286i −0.798200 0.602392i \(-0.794214\pi\)
0.454634 + 0.890678i \(0.349770\pi\)
\(888\) 0 0
\(889\) 6.28226 2.28656i 0.210700 0.0766886i
\(890\) −0.347203 −0.0116383
\(891\) 0 0
\(892\) 80.8465 2.70694
\(893\) −12.9841 + 4.72581i −0.434495 + 0.158143i
\(894\) 0 0
\(895\) 1.15767 0.971400i 0.0386966 0.0324703i
\(896\) 2.08400 + 11.8189i 0.0696215 + 0.394843i
\(897\) 0 0
\(898\) −52.8406 44.3385i −1.76331 1.47960i
\(899\) 5.30359 9.18609i 0.176885 0.306373i
\(900\) 0 0
\(901\) 5.37600 + 9.31150i 0.179100 + 0.310211i
\(902\) 1.41397 8.01899i 0.0470799 0.267003i
\(903\) 0 0
\(904\) −47.2517 17.1982i −1.57157 0.572004i
\(905\) −0.261673 0.0952412i −0.00869830 0.00316592i
\(906\) 0 0
\(907\) 6.41815 36.3991i 0.213111 1.20861i −0.671043 0.741418i \(-0.734154\pi\)
0.884154 0.467195i \(-0.154735\pi\)
\(908\) −36.0092 62.3697i −1.19501 2.06981i
\(909\) 0 0
\(910\) −0.272332 + 0.471694i −0.00902773 + 0.0156365i
\(911\) 37.0851 + 31.1181i 1.22868 + 1.03099i 0.998323 + 0.0578814i \(0.0184345\pi\)
0.230359 + 0.973106i \(0.426010\pi\)
\(912\) 0 0
\(913\) 8.00315 + 45.3881i 0.264866 + 1.50213i
\(914\) −65.1049 + 54.6295i −2.15348 + 1.80698i
\(915\) 0 0
\(916\) −79.5569 + 28.9564i −2.62863 + 0.956745i
\(917\) −5.22558 −0.172564
\(918\) 0 0
\(919\) 8.93459 0.294725 0.147363 0.989083i \(-0.452922\pi\)
0.147363 + 0.989083i \(0.452922\pi\)
\(920\) 1.65359 0.601856i 0.0545171 0.0198426i
\(921\) 0 0
\(922\) −4.18861 + 3.51466i −0.137945 + 0.115749i
\(923\) −0.835380 4.73767i −0.0274969 0.155942i
\(924\) 0 0
\(925\) −15.4094 12.9300i −0.506658 0.425137i
\(926\) −22.0643 + 38.2165i −0.725079 + 1.25587i
\(927\) 0 0
\(928\) −6.72355 11.6455i −0.220711 0.382283i
\(929\) 1.08429 6.14929i 0.0355742 0.201752i −0.961841 0.273611i \(-0.911782\pi\)
0.997415 + 0.0718590i \(0.0228932\pi\)
\(930\) 0 0
\(931\) −24.0796 8.76426i −0.789177 0.287237i
\(932\) −62.6023 22.7854i −2.05061 0.746360i
\(933\) 0 0
\(934\) −1.94285 + 11.0185i −0.0635720 + 0.360535i
\(935\) 0.286617 + 0.496435i 0.00937338 + 0.0162352i
\(936\) 0 0
\(937\) −22.9212 + 39.7006i −0.748802 + 1.29696i 0.199595 + 0.979878i \(0.436037\pi\)
−0.948397 + 0.317085i \(0.897296\pi\)
\(938\) 9.42762 + 7.91071i 0.307823 + 0.258294i
\(939\) 0 0
\(940\) 0.218831 + 1.24105i 0.00713749 + 0.0404787i
\(941\) 3.33431 2.79782i 0.108695 0.0912063i −0.586820 0.809717i \(-0.699620\pi\)
0.695516 + 0.718511i \(0.255176\pi\)
\(942\) 0 0
\(943\) −4.58662 + 1.66939i −0.149361 + 0.0543629i
\(944\) 27.3637 0.890612
\(945\) 0 0
\(946\) −51.2644 −1.66675
\(947\) 1.89511 0.689764i 0.0615828 0.0224143i −0.311045 0.950395i \(-0.600679\pi\)
0.372628 + 0.927981i \(0.378457\pi\)
\(948\) 0 0
\(949\) 0.629169 0.527935i 0.0204237 0.0171375i
\(950\) 8.00453 + 45.3959i 0.259701 + 1.47284i
\(951\) 0 0
\(952\) −3.75474 3.15060i −0.121692 0.102112i
\(953\) −17.8644 + 30.9420i −0.578684 + 1.00231i 0.416947 + 0.908931i \(0.363100\pi\)
−0.995631 + 0.0933786i \(0.970233\pi\)
\(954\) 0 0
\(955\) 0.104896 + 0.181686i 0.00339437 + 0.00587922i
\(956\) 10.0890 57.2178i 0.326303 1.85055i
\(957\) 0 0
\(958\) −31.9920 11.6441i −1.03361 0.376205i
\(959\) −6.27727 2.28474i −0.202704 0.0737781i
\(960\) 0 0
\(961\) −4.90603 + 27.8235i −0.158259 + 0.897531i
\(962\) −20.3338 35.2191i −0.655587 1.13551i
\(963\) 0 0
\(964\) −24.7759 + 42.9131i −0.797978 + 1.38214i
\(965\) 0.0627688 + 0.0526693i 0.00202060 + 0.00169548i
\(966\) 0 0
\(967\) −0.120393 0.682784i −0.00387159 0.0219569i 0.982811 0.184616i \(-0.0591041\pi\)
−0.986682 + 0.162659i \(0.947993\pi\)
\(968\) −4.65998 + 3.91019i −0.149777 + 0.125678i
\(969\) 0 0
\(970\) 1.11243 0.404891i 0.0357180 0.0130003i
\(971\) −47.4942 −1.52416 −0.762081 0.647482i \(-0.775822\pi\)
−0.762081 + 0.647482i \(0.775822\pi\)
\(972\) 0 0
\(973\) −0.987988 −0.0316734
\(974\) 48.3715 17.6058i 1.54992 0.564126i
\(975\) 0 0
\(976\) −26.8962 + 22.5686i −0.860927 + 0.722404i
\(977\) 2.18854 + 12.4118i 0.0700177 + 0.397090i 0.999595 + 0.0284625i \(0.00906113\pi\)
−0.929577 + 0.368628i \(0.879828\pi\)
\(978\) 0 0
\(979\) 3.68004 + 3.08792i 0.117615 + 0.0986903i
\(980\) −1.16855 + 2.02399i −0.0373280 + 0.0646540i
\(981\) 0 0
\(982\) −16.9168 29.3008i −0.539838 0.935027i
\(983\) −2.00477 + 11.3696i −0.0639423 + 0.362635i 0.936001 + 0.351997i \(0.114497\pi\)
−0.999943 + 0.0106378i \(0.996614\pi\)
\(984\) 0 0
\(985\) −1.77359 0.645533i −0.0565111 0.0205684i
\(986\) 28.7545 + 10.4658i 0.915729 + 0.333298i
\(987\) 0 0
\(988\) −10.5713 + 59.9529i −0.336318 + 1.90736i
\(989\) 15.3647 + 26.6125i 0.488569 + 0.846227i
\(990\) 0 0
\(991\) −9.34676 + 16.1891i −0.296910 + 0.514263i −0.975427 0.220322i \(-0.929289\pi\)
0.678518 + 0.734584i \(0.262623\pi\)
\(992\) −2.66802 2.23874i −0.0847098 0.0710800i
\(993\) 0 0
\(994\) 0.276875 + 1.57024i 0.00878195 + 0.0498049i
\(995\) 1.35549 1.13739i 0.0429719 0.0360577i
\(996\) 0 0
\(997\) −3.15624 + 1.14878i −0.0999593 + 0.0363822i −0.391516 0.920171i \(-0.628049\pi\)
0.291556 + 0.956554i \(0.405827\pi\)
\(998\) 35.8066 1.13344
\(999\) 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 243.2.e.a.55.1 12
3.2 odd 2 243.2.e.d.55.2 12
9.2 odd 6 243.2.e.c.136.1 12
9.4 even 3 81.2.e.a.73.2 12
9.5 odd 6 27.2.e.a.25.1 yes 12
9.7 even 3 243.2.e.b.136.2 12
27.2 odd 18 729.2.a.a.1.1 6
27.4 even 9 inner 243.2.e.a.190.1 12
27.5 odd 18 27.2.e.a.13.1 12
27.7 even 9 729.2.c.b.487.1 12
27.11 odd 18 729.2.c.e.244.6 12
27.13 even 9 243.2.e.b.109.2 12
27.14 odd 18 243.2.e.c.109.1 12
27.16 even 9 729.2.c.b.244.1 12
27.20 odd 18 729.2.c.e.487.6 12
27.22 even 9 81.2.e.a.10.2 12
27.23 odd 18 243.2.e.d.190.2 12
27.25 even 9 729.2.a.d.1.6 6
36.23 even 6 432.2.u.c.241.1 12
45.14 odd 6 675.2.l.c.376.2 12
45.23 even 12 675.2.u.b.349.4 24
45.32 even 12 675.2.u.b.349.1 24
108.59 even 18 432.2.u.c.337.1 12
135.32 even 36 675.2.u.b.499.4 24
135.59 odd 18 675.2.l.c.526.2 12
135.113 even 36 675.2.u.b.499.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.13.1 12 27.5 odd 18
27.2.e.a.25.1 yes 12 9.5 odd 6
81.2.e.a.10.2 12 27.22 even 9
81.2.e.a.73.2 12 9.4 even 3
243.2.e.a.55.1 12 1.1 even 1 trivial
243.2.e.a.190.1 12 27.4 even 9 inner
243.2.e.b.109.2 12 27.13 even 9
243.2.e.b.136.2 12 9.7 even 3
243.2.e.c.109.1 12 27.14 odd 18
243.2.e.c.136.1 12 9.2 odd 6
243.2.e.d.55.2 12 3.2 odd 2
243.2.e.d.190.2 12 27.23 odd 18
432.2.u.c.241.1 12 36.23 even 6
432.2.u.c.337.1 12 108.59 even 18
675.2.l.c.376.2 12 45.14 odd 6
675.2.l.c.526.2 12 135.59 odd 18
675.2.u.b.349.1 24 45.32 even 12
675.2.u.b.349.4 24 45.23 even 12
675.2.u.b.499.1 24 135.113 even 36
675.2.u.b.499.4 24 135.32 even 36
729.2.a.a.1.1 6 27.2 odd 18
729.2.a.d.1.6 6 27.25 even 9
729.2.c.b.244.1 12 27.16 even 9
729.2.c.b.487.1 12 27.7 even 9
729.2.c.e.244.6 12 27.11 odd 18
729.2.c.e.487.6 12 27.20 odd 18