Properties

Label 729.2.c.b.244.1
Level $729$
Weight $2$
Character 729.244
Analytic conductor $5.821$
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] = [729,2,Mod(244,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.244");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.c (of order \(3\), degree \(2\), 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: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
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: \( 3^{3} \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 244.1
Root \(0.500000 + 1.00210i\) of defining polynomial
Character \(\chi\) \(=\) 729.244
Dual form 729.2.c.b.487.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.20081 - 2.07986i) q^{2} +(-1.88389 + 3.26300i) q^{4} +(0.0465417 - 0.0806126i) q^{5} +(0.289931 + 0.502175i) q^{7} +4.24555 q^{8} +O(q^{10})\) \(q+(-1.20081 - 2.07986i) q^{2} +(-1.88389 + 3.26300i) q^{4} +(0.0465417 - 0.0806126i) q^{5} +(0.289931 + 0.502175i) q^{7} +4.24555 q^{8} -0.223551 q^{10} +(-1.54654 - 2.67869i) q^{11} +(-2.10087 + 3.63881i) q^{13} +(0.696304 - 1.20603i) q^{14} +(-1.33032 - 2.30417i) q^{16} +1.99099 q^{17} -3.84542 q^{19} +(0.175359 + 0.303731i) q^{20} +(-3.71421 + 6.43320i) q^{22} +(-2.22641 + 3.85625i) q^{23} +(2.49567 + 4.32262i) q^{25} +10.0910 q^{26} -2.18479 q^{28} +(3.19975 + 5.54214i) q^{29} +(-0.828750 + 1.43544i) q^{31} +(1.05064 - 1.81975i) q^{32} +(-2.39080 - 4.14098i) q^{34} +0.0539755 q^{35} +4.03009 q^{37} +(4.61762 + 7.99796i) q^{38} +(0.197595 - 0.342245i) q^{40} +(-0.548078 + 0.949299i) q^{41} +(3.45056 + 5.97655i) q^{43} +11.6541 q^{44} +10.6940 q^{46} +(1.79660 + 3.11180i) q^{47} +(3.33188 - 5.77099i) q^{49} +(5.99365 - 10.3813i) q^{50} +(-7.91561 - 13.7102i) q^{52} -5.40034 q^{53} -0.287915 q^{55} +(1.23091 + 2.13201i) q^{56} +(7.68460 - 13.3101i) q^{58} +(-5.14233 + 8.90677i) q^{59} +(6.59816 + 11.4283i) q^{61} +3.98069 q^{62} -10.3677 q^{64} +(0.195556 + 0.338713i) q^{65} +(4.41865 - 7.65332i) q^{67} +(-3.75080 + 6.49658i) q^{68} +(-0.0648143 - 0.112262i) q^{70} -1.14495 q^{71} +0.195472 q^{73} +(-4.83938 - 8.38205i) q^{74} +(7.24436 - 12.5476i) q^{76} +(0.896780 - 1.55327i) q^{77} +(3.60400 + 6.24231i) q^{79} -0.247661 q^{80} +2.63255 q^{82} +(-7.45022 - 12.9042i) q^{83} +(0.0926639 - 0.160499i) q^{85} +(8.28694 - 14.3534i) q^{86} +(-6.56592 - 11.3725i) q^{88} +1.55313 q^{89} -2.43642 q^{91} +(-8.38862 - 14.5295i) q^{92} +(4.31475 - 7.47336i) q^{94} +(-0.178973 + 0.309990i) q^{95} +(-2.64777 - 4.58607i) q^{97} -16.0038 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{8} + 6 q^{10} - 12 q^{11} - 6 q^{14} + 3 q^{16} + 18 q^{17} + 6 q^{19} - 6 q^{20} - 6 q^{22} - 15 q^{23} + 6 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{29} + 24 q^{35} + 6 q^{37} + 3 q^{38} - 6 q^{40} - 15 q^{41} + 6 q^{44} + 6 q^{46} - 21 q^{47} + 12 q^{49} - 3 q^{50} - 12 q^{52} + 18 q^{53} - 12 q^{55} + 6 q^{56} + 12 q^{58} - 24 q^{59} + 9 q^{61} - 24 q^{62} - 24 q^{64} + 6 q^{65} + 9 q^{67} + 9 q^{68} - 15 q^{70} + 54 q^{71} - 12 q^{73} + 12 q^{74} - 6 q^{76} + 12 q^{77} - 42 q^{80} - 12 q^{82} - 12 q^{83} + 21 q^{86} - 12 q^{88} + 18 q^{89} - 12 q^{91} - 6 q^{92} - 6 q^{94} - 12 q^{95} - 90 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20081 2.07986i −0.849101 1.47069i −0.882011 0.471228i \(-0.843811\pi\)
0.0329100 0.999458i \(-0.489523\pi\)
\(3\) 0 0
\(4\) −1.88389 + 3.26300i −0.941946 + 1.63150i
\(5\) 0.0465417 0.0806126i 0.0208141 0.0360511i −0.855431 0.517917i \(-0.826708\pi\)
0.876245 + 0.481866i \(0.160041\pi\)
\(6\) 0 0
\(7\) 0.289931 + 0.502175i 0.109583 + 0.189804i 0.915602 0.402087i \(-0.131715\pi\)
−0.806018 + 0.591891i \(0.798382\pi\)
\(8\) 4.24555 1.50103
\(9\) 0 0
\(10\) −0.223551 −0.0706931
\(11\) −1.54654 2.67869i −0.466300 0.807655i 0.532959 0.846141i \(-0.321080\pi\)
−0.999259 + 0.0384858i \(0.987747\pi\)
\(12\) 0 0
\(13\) −2.10087 + 3.63881i −0.582676 + 1.00922i 0.412485 + 0.910964i \(0.364661\pi\)
−0.995161 + 0.0982594i \(0.968673\pi\)
\(14\) 0.696304 1.20603i 0.186095 0.322326i
\(15\) 0 0
\(16\) −1.33032 2.30417i −0.332579 0.576043i
\(17\) 1.99099 0.482885 0.241443 0.970415i \(-0.422379\pi\)
0.241443 + 0.970415i \(0.422379\pi\)
\(18\) 0 0
\(19\) −3.84542 −0.882201 −0.441100 0.897458i \(-0.645412\pi\)
−0.441100 + 0.897458i \(0.645412\pi\)
\(20\) 0.175359 + 0.303731i 0.0392115 + 0.0679163i
\(21\) 0 0
\(22\) −3.71421 + 6.43320i −0.791872 + 1.37156i
\(23\) −2.22641 + 3.85625i −0.464238 + 0.804084i −0.999167 0.0408132i \(-0.987005\pi\)
0.534929 + 0.844897i \(0.320338\pi\)
\(24\) 0 0
\(25\) 2.49567 + 4.32262i 0.499134 + 0.864525i
\(26\) 10.0910 1.97900
\(27\) 0 0
\(28\) −2.18479 −0.412887
\(29\) 3.19975 + 5.54214i 0.594179 + 1.02915i 0.993662 + 0.112408i \(0.0358565\pi\)
−0.399483 + 0.916741i \(0.630810\pi\)
\(30\) 0 0
\(31\) −0.828750 + 1.43544i −0.148848 + 0.257812i −0.930802 0.365524i \(-0.880890\pi\)
0.781954 + 0.623336i \(0.214223\pi\)
\(32\) 1.05064 1.81975i 0.185728 0.321690i
\(33\) 0 0
\(34\) −2.39080 4.14098i −0.410018 0.710173i
\(35\) 0.0539755 0.00912352
\(36\) 0 0
\(37\) 4.03009 0.662543 0.331272 0.943535i \(-0.392522\pi\)
0.331272 + 0.943535i \(0.392522\pi\)
\(38\) 4.61762 + 7.99796i 0.749078 + 1.29744i
\(39\) 0 0
\(40\) 0.197595 0.342245i 0.0312425 0.0541136i
\(41\) −0.548078 + 0.949299i −0.0855954 + 0.148256i −0.905645 0.424037i \(-0.860613\pi\)
0.820049 + 0.572293i \(0.193946\pi\)
\(42\) 0 0
\(43\) 3.45056 + 5.97655i 0.526206 + 0.911415i 0.999534 + 0.0305288i \(0.00971911\pi\)
−0.473328 + 0.880886i \(0.656948\pi\)
\(44\) 11.6541 1.75692
\(45\) 0 0
\(46\) 10.6940 1.57674
\(47\) 1.79660 + 3.11180i 0.262061 + 0.453902i 0.966789 0.255575i \(-0.0822646\pi\)
−0.704729 + 0.709477i \(0.748931\pi\)
\(48\) 0 0
\(49\) 3.33188 5.77099i 0.475983 0.824427i
\(50\) 5.99365 10.3813i 0.847630 1.46814i
\(51\) 0 0
\(52\) −7.91561 13.7102i −1.09770 1.90127i
\(53\) −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
\(56\) 1.23091 + 2.13201i 0.164488 + 0.284901i
\(57\) 0 0
\(58\) 7.68460 13.3101i 1.00904 1.74770i
\(59\) −5.14233 + 8.90677i −0.669474 + 1.15956i 0.308577 + 0.951199i \(0.400147\pi\)
−0.978051 + 0.208364i \(0.933186\pi\)
\(60\) 0 0
\(61\) 6.59816 + 11.4283i 0.844808 + 1.46325i 0.885788 + 0.464090i \(0.153619\pi\)
−0.0409801 + 0.999160i \(0.513048\pi\)
\(62\) 3.98069 0.505548
\(63\) 0 0
\(64\) −10.3677 −1.29596
\(65\) 0.195556 + 0.338713i 0.0242557 + 0.0420121i
\(66\) 0 0
\(67\) 4.41865 7.65332i 0.539824 0.935002i −0.459089 0.888390i \(-0.651824\pi\)
0.998913 0.0466119i \(-0.0148424\pi\)
\(68\) −3.75080 + 6.49658i −0.454852 + 0.787826i
\(69\) 0 0
\(70\) −0.0648143 0.112262i −0.00774679 0.0134178i
\(71\) −1.14495 −0.135880 −0.0679401 0.997689i \(-0.521643\pi\)
−0.0679401 + 0.997689i \(0.521643\pi\)
\(72\) 0 0
\(73\) 0.195472 0.0228783 0.0114391 0.999935i \(-0.496359\pi\)
0.0114391 + 0.999935i \(0.496359\pi\)
\(74\) −4.83938 8.38205i −0.562566 0.974394i
\(75\) 0 0
\(76\) 7.24436 12.5476i 0.830985 1.43931i
\(77\) 0.896780 1.55327i 0.102198 0.177011i
\(78\) 0 0
\(79\) 3.60400 + 6.24231i 0.405481 + 0.702314i 0.994377 0.105895i \(-0.0337706\pi\)
−0.588896 + 0.808209i \(0.700437\pi\)
\(80\) −0.247661 −0.0276893
\(81\) 0 0
\(82\) 2.63255 0.290717
\(83\) −7.45022 12.9042i −0.817768 1.41642i −0.907323 0.420434i \(-0.861878\pi\)
0.0895548 0.995982i \(-0.471456\pi\)
\(84\) 0 0
\(85\) 0.0926639 0.160499i 0.0100508 0.0174085i
\(86\) 8.28694 14.3534i 0.893604 1.54777i
\(87\) 0 0
\(88\) −6.56592 11.3725i −0.699929 1.21231i
\(89\) 1.55313 0.164631 0.0823155 0.996606i \(-0.473768\pi\)
0.0823155 + 0.996606i \(0.473768\pi\)
\(90\) 0 0
\(91\) −2.43642 −0.255406
\(92\) −8.38862 14.5295i −0.874575 1.51481i
\(93\) 0 0
\(94\) 4.31475 7.47336i 0.445032 0.770818i
\(95\) −0.178973 + 0.309990i −0.0183622 + 0.0318043i
\(96\) 0 0
\(97\) −2.64777 4.58607i −0.268840 0.465645i 0.699723 0.714415i \(-0.253307\pi\)
−0.968563 + 0.248770i \(0.919974\pi\)
\(98\) −16.0038 −1.61663
\(99\) 0 0
\(100\) −18.8063 −1.88063
\(101\) −3.63449 6.29512i −0.361645 0.626388i 0.626586 0.779352i \(-0.284452\pi\)
−0.988232 + 0.152964i \(0.951118\pi\)
\(102\) 0 0
\(103\) −3.20069 + 5.54375i −0.315373 + 0.546242i −0.979517 0.201363i \(-0.935463\pi\)
0.664144 + 0.747605i \(0.268796\pi\)
\(104\) −8.91933 + 15.4487i −0.874612 + 1.51487i
\(105\) 0 0
\(106\) 6.48478 + 11.2320i 0.629858 + 1.09095i
\(107\) 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 \(0.596462\pi\)
\(110\) 0.345731 + 0.598824i 0.0329642 + 0.0570956i
\(111\) 0 0
\(112\) 0.771398 1.33610i 0.0728903 0.126250i
\(113\) −5.92199 + 10.2572i −0.557094 + 0.964915i 0.440643 + 0.897682i \(0.354750\pi\)
−0.997737 + 0.0672328i \(0.978583\pi\)
\(114\) 0 0
\(115\) 0.207242 + 0.358953i 0.0193254 + 0.0334725i
\(116\) −24.1120 −2.23874
\(117\) 0 0
\(118\) 24.6998 2.27381
\(119\) 0.577248 + 0.999823i 0.0529162 + 0.0916536i
\(120\) 0 0
\(121\) 0.716417 1.24087i 0.0651289 0.112806i
\(122\) 15.8463 27.4466i 1.43465 2.48490i
\(123\) 0 0
\(124\) −3.12255 5.40842i −0.280413 0.485690i
\(125\) 0.930028 0.0831842
\(126\) 0 0
\(127\) 11.5294 1.02307 0.511533 0.859263i \(-0.329078\pi\)
0.511533 + 0.859263i \(0.329078\pi\)
\(128\) 10.3484 + 17.9239i 0.914677 + 1.58427i
\(129\) 0 0
\(130\) 0.469651 0.813459i 0.0411911 0.0713451i
\(131\) −4.50589 + 7.80443i −0.393681 + 0.681876i −0.992932 0.118686i \(-0.962132\pi\)
0.599251 + 0.800561i \(0.295465\pi\)
\(132\) 0 0
\(133\) −1.11491 1.93107i −0.0966746 0.167445i
\(134\) −21.2238 −1.83346
\(135\) 0 0
\(136\) 8.45283 0.724824
\(137\) 5.76012 + 9.97681i 0.492120 + 0.852377i 0.999959 0.00907543i \(-0.00288884\pi\)
−0.507839 + 0.861452i \(0.669556\pi\)
\(138\) 0 0
\(139\) −0.851917 + 1.47556i −0.0722587 + 0.125156i −0.899891 0.436115i \(-0.856354\pi\)
0.827632 + 0.561271i \(0.189687\pi\)
\(140\) −0.101684 + 0.176122i −0.00859386 + 0.0148850i
\(141\) 0 0
\(142\) 1.37486 + 2.38133i 0.115376 + 0.199837i
\(143\) 12.9963 1.08681
\(144\) 0 0
\(145\) 0.595688 0.0494692
\(146\) −0.234725 0.406556i −0.0194260 0.0336468i
\(147\) 0 0
\(148\) −7.59226 + 13.1502i −0.624080 + 1.08094i
\(149\) −10.8264 + 18.7518i −0.886932 + 1.53621i −0.0434485 + 0.999056i \(0.513834\pi\)
−0.843483 + 0.537155i \(0.819499\pi\)
\(150\) 0 0
\(151\) 2.37076 + 4.10628i 0.192930 + 0.334164i 0.946220 0.323524i \(-0.104868\pi\)
−0.753290 + 0.657688i \(0.771534\pi\)
\(152\) −16.3259 −1.32421
\(153\) 0 0
\(154\) −4.30745 −0.347104
\(155\) 0.0771429 + 0.133615i 0.00619626 + 0.0107322i
\(156\) 0 0
\(157\) 0.104603 0.181178i 0.00834822 0.0144595i −0.861821 0.507212i \(-0.830676\pi\)
0.870169 + 0.492753i \(0.164009\pi\)
\(158\) 8.65544 14.9917i 0.688589 1.19267i
\(159\) 0 0
\(160\) −0.0977967 0.169389i −0.00773151 0.0133914i
\(161\) −2.58202 −0.203491
\(162\) 0 0
\(163\) 5.62384 0.440493 0.220247 0.975444i \(-0.429314\pi\)
0.220247 + 0.975444i \(0.429314\pi\)
\(164\) −2.06504 3.57675i −0.161253 0.279298i
\(165\) 0 0
\(166\) −17.8926 + 30.9909i −1.38874 + 2.40536i
\(167\) 8.34025 14.4457i 0.645388 1.11784i −0.338824 0.940850i \(-0.610029\pi\)
0.984212 0.176995i \(-0.0566375\pi\)
\(168\) 0 0
\(169\) −2.32728 4.03097i −0.179022 0.310074i
\(170\) −0.445087 −0.0341366
\(171\) 0 0
\(172\) −26.0019 −1.98263
\(173\) 9.50107 + 16.4563i 0.722353 + 1.25115i 0.960054 + 0.279814i \(0.0902728\pi\)
−0.237701 + 0.971338i \(0.576394\pi\)
\(174\) 0 0
\(175\) −1.44714 + 2.50652i −0.109394 + 0.189475i
\(176\) −4.11478 + 7.12700i −0.310163 + 0.537218i
\(177\) 0 0
\(178\) −1.86501 3.23029i −0.139788 0.242121i
\(179\) −16.2352 −1.21348 −0.606739 0.794901i \(-0.707523\pi\)
−0.606739 + 0.794901i \(0.707523\pi\)
\(180\) 0 0
\(181\) −2.99158 −0.222362 −0.111181 0.993800i \(-0.535463\pi\)
−0.111181 + 0.993800i \(0.535463\pi\)
\(182\) 2.92568 + 5.06743i 0.216866 + 0.375623i
\(183\) 0 0
\(184\) −9.45232 + 16.3719i −0.696834 + 1.20695i
\(185\) 0.187567 0.324876i 0.0137902 0.0238854i
\(186\) 0 0
\(187\) −3.07914 5.33323i −0.225169 0.390005i
\(188\) −13.5384 −0.987388
\(189\) 0 0
\(190\) 0.859649 0.0623655
\(191\) −1.12691 1.95186i −0.0815402 0.141232i 0.822371 0.568951i \(-0.192651\pi\)
−0.903912 + 0.427719i \(0.859317\pi\)
\(192\) 0 0
\(193\) 0.440137 0.762339i 0.0316817 0.0548743i −0.849750 0.527186i \(-0.823247\pi\)
0.881432 + 0.472312i \(0.156580\pi\)
\(194\) −6.35893 + 11.0140i −0.456545 + 0.790759i
\(195\) 0 0
\(196\) 12.5538 + 21.7438i 0.896700 + 1.55313i
\(197\) −20.2766 −1.44464 −0.722322 0.691557i \(-0.756925\pi\)
−0.722322 + 0.691557i \(0.756925\pi\)
\(198\) 0 0
\(199\) −19.0094 −1.34754 −0.673772 0.738939i \(-0.735327\pi\)
−0.673772 + 0.738939i \(0.735327\pi\)
\(200\) 10.5955 + 18.3519i 0.749213 + 1.29768i
\(201\) 0 0
\(202\) −8.72867 + 15.1185i −0.614147 + 1.06373i
\(203\) −1.85541 + 3.21367i −0.130225 + 0.225556i
\(204\) 0 0
\(205\) 0.0510170 + 0.0883640i 0.00356318 + 0.00617161i
\(206\) 15.3737 1.07113
\(207\) 0 0
\(208\) 11.1793 0.775142
\(209\) 5.94711 + 10.3007i 0.411370 + 0.712514i
\(210\) 0 0
\(211\) −8.09203 + 14.0158i −0.557079 + 0.964888i 0.440660 + 0.897674i \(0.354744\pi\)
−0.997739 + 0.0672143i \(0.978589\pi\)
\(212\) 10.1737 17.6213i 0.698729 1.21023i
\(213\) 0 0
\(214\) −6.65688 11.5300i −0.455055 0.788178i
\(215\) 0.642380 0.0438100
\(216\) 0 0
\(217\) −0.961120 −0.0652451
\(218\) 7.48270 + 12.9604i 0.506792 + 0.877790i
\(219\) 0 0
\(220\) 0.542400 0.939465i 0.0365686 0.0633387i
\(221\) −4.18280 + 7.24482i −0.281365 + 0.487339i
\(222\) 0 0
\(223\) −10.7286 18.5826i −0.718443 1.24438i −0.961616 0.274398i \(-0.911522\pi\)
0.243173 0.969983i \(-0.421812\pi\)
\(224\) 1.21845 0.0814108
\(225\) 0 0
\(226\) 28.4448 1.89212
\(227\) −9.55712 16.5534i −0.634329 1.09869i −0.986657 0.162813i \(-0.947943\pi\)
0.352328 0.935876i \(-0.385390\pi\)
\(228\) 0 0
\(229\) −11.2351 + 19.4597i −0.742435 + 1.28594i 0.208949 + 0.977927i \(0.432996\pi\)
−0.951384 + 0.308008i \(0.900337\pi\)
\(230\) 0.497716 0.862069i 0.0328184 0.0568432i
\(231\) 0 0
\(232\) 13.5847 + 23.5294i 0.891880 + 1.54478i
\(233\) 17.6815 1.15835 0.579176 0.815203i \(-0.303374\pi\)
0.579176 + 0.815203i \(0.303374\pi\)
\(234\) 0 0
\(235\) 0.334467 0.0218182
\(236\) −19.3752 33.5588i −1.26122 2.18449i
\(237\) 0 0
\(238\) 1.38633 2.40120i 0.0898625 0.155646i
\(239\) −7.71016 + 13.3544i −0.498729 + 0.863823i −0.999999 0.00146732i \(-0.999533\pi\)
0.501270 + 0.865291i \(0.332866\pi\)
\(240\) 0 0
\(241\) −6.57572 11.3895i −0.423580 0.733661i 0.572707 0.819760i \(-0.305893\pi\)
−0.996287 + 0.0860987i \(0.972560\pi\)
\(242\) −3.44113 −0.221204
\(243\) 0 0
\(244\) −49.7209 −3.18305
\(245\) −0.310143 0.537183i −0.0198143 0.0343194i
\(246\) 0 0
\(247\) 8.07872 13.9928i 0.514037 0.890338i
\(248\) −3.51850 + 6.09422i −0.223425 + 0.386983i
\(249\) 0 0
\(250\) −1.11679 1.93433i −0.0706318 0.122338i
\(251\) −17.4166 −1.09933 −0.549663 0.835386i \(-0.685244\pi\)
−0.549663 + 0.835386i \(0.685244\pi\)
\(252\) 0 0
\(253\) 13.7729 0.865897
\(254\) −13.8446 23.9795i −0.868687 1.50461i
\(255\) 0 0
\(256\) 14.4852 25.0891i 0.905325 1.56807i
\(257\) 5.59379 9.68873i 0.348931 0.604366i −0.637129 0.770757i \(-0.719878\pi\)
0.986060 + 0.166391i \(0.0532114\pi\)
\(258\) 0 0
\(259\) 1.16845 + 2.02381i 0.0726038 + 0.125754i
\(260\) −1.47362 −0.0913903
\(261\) 0 0
\(262\) 21.6429 1.33710
\(263\) −10.3554 17.9362i −0.638544 1.10599i −0.985752 0.168203i \(-0.946204\pi\)
0.347209 0.937788i \(-0.387130\pi\)
\(264\) 0 0
\(265\) −0.251341 + 0.435335i −0.0154397 + 0.0267424i
\(266\) −2.67758 + 4.63771i −0.164173 + 0.284356i
\(267\) 0 0
\(268\) 16.6485 + 28.8361i 1.01697 + 1.76144i
\(269\) 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 \(0.324321\pi\)
\(272\) −2.64864 4.58758i −0.160597 0.278163i
\(273\) 0 0
\(274\) 13.8336 23.9605i 0.835719 1.44751i
\(275\) 7.71931 13.3702i 0.465492 0.806255i
\(276\) 0 0
\(277\) −2.58449 4.47647i −0.155287 0.268965i 0.777877 0.628417i \(-0.216297\pi\)
−0.933163 + 0.359452i \(0.882964\pi\)
\(278\) 4.09197 0.245420
\(279\) 0 0
\(280\) 0.229155 0.0136947
\(281\) −1.64822 2.85480i −0.0983246 0.170303i 0.812667 0.582729i \(-0.198015\pi\)
−0.910991 + 0.412426i \(0.864682\pi\)
\(282\) 0 0
\(283\) 4.56536 7.90744i 0.271382 0.470048i −0.697834 0.716260i \(-0.745853\pi\)
0.969216 + 0.246212i \(0.0791858\pi\)
\(284\) 2.15696 3.73596i 0.127992 0.221688i
\(285\) 0 0
\(286\) −15.6061 27.0306i −0.922809 1.59835i
\(287\) −0.635618 −0.0375194
\(288\) 0 0
\(289\) −13.0360 −0.766822
\(290\) −0.715309 1.23895i −0.0420044 0.0727537i
\(291\) 0 0
\(292\) −0.368248 + 0.637825i −0.0215501 + 0.0373259i
\(293\) −1.41322 + 2.44776i −0.0825610 + 0.143000i −0.904349 0.426793i \(-0.859643\pi\)
0.821788 + 0.569793i \(0.192977\pi\)
\(294\) 0 0
\(295\) 0.478665 + 0.829073i 0.0278690 + 0.0482705i
\(296\) 17.1100 0.994496
\(297\) 0 0
\(298\) 52.0017 3.01238
\(299\) −9.35477 16.2029i −0.541000 0.937040i
\(300\) 0 0
\(301\) −2.00085 + 3.46557i −0.115327 + 0.199752i
\(302\) 5.69367 9.86173i 0.327634 0.567479i
\(303\) 0 0
\(304\) 5.11562 + 8.86052i 0.293401 + 0.508186i
\(305\) 1.22836 0.0703356
\(306\) 0 0
\(307\) 6.29446 0.359244 0.179622 0.983736i \(-0.442513\pi\)
0.179622 + 0.983736i \(0.442513\pi\)
\(308\) 3.37887 + 5.85238i 0.192529 + 0.333470i
\(309\) 0 0
\(310\) 0.185268 0.320894i 0.0105225 0.0182255i
\(311\) −3.68644 + 6.38511i −0.209039 + 0.362066i −0.951412 0.307920i \(-0.900367\pi\)
0.742373 + 0.669987i \(0.233700\pi\)
\(312\) 0 0
\(313\) 2.13538 + 3.69858i 0.120699 + 0.209056i 0.920043 0.391817i \(-0.128153\pi\)
−0.799345 + 0.600873i \(0.794820\pi\)
\(314\) −0.502433 −0.0283539
\(315\) 0 0
\(316\) −27.1582 −1.52777
\(317\) 8.07379 + 13.9842i 0.453469 + 0.785431i 0.998599 0.0529204i \(-0.0168529\pi\)
−0.545130 + 0.838352i \(0.683520\pi\)
\(318\) 0 0
\(319\) 9.89711 17.1423i 0.554132 0.959784i
\(320\) −0.482531 + 0.835769i −0.0269743 + 0.0467209i
\(321\) 0 0
\(322\) 3.10051 + 5.37024i 0.172785 + 0.299272i
\(323\) −7.65618 −0.426001
\(324\) 0 0
\(325\) −20.9723 −1.16333
\(326\) −6.75317 11.6968i −0.374024 0.647828i
\(327\) 0 0
\(328\) −2.32689 + 4.03029i −0.128481 + 0.222536i
\(329\) −1.04178 + 1.80441i −0.0574350 + 0.0994804i
\(330\) 0 0
\(331\) −9.61412 16.6521i −0.528440 0.915284i −0.999450 0.0331567i \(-0.989444\pi\)
0.471011 0.882128i \(-0.343889\pi\)
\(332\) 56.1417 3.08117
\(333\) 0 0
\(334\) −40.0602 −2.19200
\(335\) −0.411303 0.712397i −0.0224719 0.0389224i
\(336\) 0 0
\(337\) 14.7314 25.5155i 0.802469 1.38992i −0.115517 0.993306i \(-0.536852\pi\)
0.917986 0.396612i \(-0.129814\pi\)
\(338\) −5.58925 + 9.68086i −0.304015 + 0.526569i
\(339\) 0 0
\(340\) 0.349138 + 0.604724i 0.0189346 + 0.0327958i
\(341\) 5.12679 0.277631
\(342\) 0 0
\(343\) 7.92309 0.427806
\(344\) 14.6495 + 25.3737i 0.789849 + 1.36806i
\(345\) 0 0
\(346\) 22.8180 39.5219i 1.22670 2.12471i
\(347\) 5.69852 9.87012i 0.305912 0.529856i −0.671552 0.740958i \(-0.734372\pi\)
0.977464 + 0.211102i \(0.0677052\pi\)
\(348\) 0 0
\(349\) −14.0808 24.3887i −0.753728 1.30550i −0.946004 0.324155i \(-0.894920\pi\)
0.192276 0.981341i \(-0.438413\pi\)
\(350\) 6.95097 0.371545
\(351\) 0 0
\(352\) −6.49941 −0.346419
\(353\) 14.3270 + 24.8152i 0.762552 + 1.32078i 0.941531 + 0.336926i \(0.109387\pi\)
−0.178979 + 0.983853i \(0.557280\pi\)
\(354\) 0 0
\(355\) −0.0532878 + 0.0922971i −0.00282822 + 0.00489862i
\(356\) −2.92592 + 5.06784i −0.155074 + 0.268595i
\(357\) 0 0
\(358\) 19.4954 + 33.7671i 1.03037 + 1.78465i
\(359\) 31.0322 1.63782 0.818909 0.573923i \(-0.194579\pi\)
0.818909 + 0.573923i \(0.194579\pi\)
\(360\) 0 0
\(361\) −4.21272 −0.221722
\(362\) 3.59232 + 6.22208i 0.188808 + 0.327025i
\(363\) 0 0
\(364\) 4.58996 7.95004i 0.240579 0.416695i
\(365\) 0.00909761 0.0157575i 0.000476190 0.000824786i
\(366\) 0 0
\(367\) −12.0621 20.8922i −0.629637 1.09056i −0.987625 0.156837i \(-0.949870\pi\)
0.357988 0.933726i \(-0.383463\pi\)
\(368\) 11.8473 0.617583
\(369\) 0 0
\(370\) −0.900932 −0.0468372
\(371\) −1.56572 2.71191i −0.0812883 0.140795i
\(372\) 0 0
\(373\) 6.29281 10.8995i 0.325829 0.564353i −0.655851 0.754891i \(-0.727690\pi\)
0.981680 + 0.190538i \(0.0610232\pi\)
\(374\) −7.39494 + 12.8084i −0.382383 + 0.662307i
\(375\) 0 0
\(376\) 7.62754 + 13.2113i 0.393360 + 0.681320i
\(377\) −26.8890 −1.38486
\(378\) 0 0
\(379\) −7.70522 −0.395790 −0.197895 0.980223i \(-0.563411\pi\)
−0.197895 + 0.980223i \(0.563411\pi\)
\(380\) −0.674330 1.16797i −0.0345924 0.0599158i
\(381\) 0 0
\(382\) −2.70641 + 4.68763i −0.138472 + 0.239840i
\(383\) −8.93081 + 15.4686i −0.456343 + 0.790410i −0.998764 0.0496970i \(-0.984174\pi\)
0.542421 + 0.840107i \(0.317508\pi\)
\(384\) 0 0
\(385\) −0.0834753 0.144584i −0.00425430 0.00736866i
\(386\) −2.11408 −0.107604
\(387\) 0 0
\(388\) 19.9524 1.01293
\(389\) 13.6942 + 23.7191i 0.694325 + 1.20261i 0.970408 + 0.241472i \(0.0776303\pi\)
−0.276083 + 0.961134i \(0.589036\pi\)
\(390\) 0 0
\(391\) −4.43275 + 7.67774i −0.224174 + 0.388280i
\(392\) 14.1457 24.5010i 0.714464 1.23749i
\(393\) 0 0
\(394\) 24.3483 + 42.1725i 1.22665 + 2.12462i
\(395\) 0.670945 0.0337589
\(396\) 0 0
\(397\) 4.21599 0.211594 0.105797 0.994388i \(-0.466261\pi\)
0.105797 + 0.994388i \(0.466261\pi\)
\(398\) 22.8267 + 39.5371i 1.14420 + 1.98181i
\(399\) 0 0
\(400\) 6.64005 11.5009i 0.332002 0.575045i
\(401\) 7.58625 13.1398i 0.378839 0.656169i −0.612054 0.790816i \(-0.709657\pi\)
0.990894 + 0.134647i \(0.0429900\pi\)
\(402\) 0 0
\(403\) −3.48219 6.03132i −0.173460 0.300442i
\(404\) 27.3880 1.36260
\(405\) 0 0
\(406\) 8.91200 0.442295
\(407\) −6.23271 10.7954i −0.308944 0.535107i
\(408\) 0 0
\(409\) −2.35481 + 4.07864i −0.116438 + 0.201676i −0.918354 0.395761i \(-0.870481\pi\)
0.801916 + 0.597437i \(0.203814\pi\)
\(410\) 0.122523 0.212217i 0.00605100 0.0104806i
\(411\) 0 0
\(412\) −12.0595 20.8877i −0.594129 1.02906i
\(413\) −5.96367 −0.293453
\(414\) 0 0
\(415\) −1.38698 −0.0680844
\(416\) 4.41449 + 7.64612i 0.216438 + 0.374882i
\(417\) 0 0
\(418\) 14.2827 24.7384i 0.698590 1.20999i
\(419\) 9.89557 17.1396i 0.483430 0.837325i −0.516389 0.856354i \(-0.672724\pi\)
0.999819 + 0.0190288i \(0.00605741\pi\)
\(420\) 0 0
\(421\) −14.0929 24.4095i −0.686844 1.18965i −0.972854 0.231422i \(-0.925662\pi\)
0.286010 0.958227i \(-0.407671\pi\)
\(422\) 38.8680 1.89206
\(423\) 0 0
\(424\) −22.9274 −1.11345
\(425\) 4.96884 + 8.60628i 0.241024 + 0.417466i
\(426\) 0 0
\(427\) −3.82602 + 6.62686i −0.185154 + 0.320696i
\(428\) −10.4436 + 18.0889i −0.504813 + 0.874361i
\(429\) 0 0
\(430\) −0.771377 1.33606i −0.0371991 0.0644307i
\(431\) 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 \(0.291730\pi\)
\(434\) 1.15412 + 1.99900i 0.0553997 + 0.0959551i
\(435\) 0 0
\(436\) 11.7392 20.3329i 0.562207 0.973771i
\(437\) 8.56148 14.8289i 0.409551 0.709363i
\(438\) 0 0
\(439\) 7.83062 + 13.5630i 0.373735 + 0.647328i 0.990137 0.140104i \(-0.0447436\pi\)
−0.616402 + 0.787432i \(0.711410\pi\)
\(440\) −1.22236 −0.0582735
\(441\) 0 0
\(442\) 20.0910 0.955631
\(443\) −9.12692 15.8083i −0.433633 0.751075i 0.563550 0.826082i \(-0.309435\pi\)
−0.997183 + 0.0750074i \(0.976102\pi\)
\(444\) 0 0
\(445\) 0.0722851 0.125202i 0.00342664 0.00593512i
\(446\) −25.7661 + 44.6283i −1.22006 + 2.11321i
\(447\) 0 0
\(448\) −3.00592 5.20640i −0.142016 0.245979i
\(449\) −28.7216 −1.35546 −0.677729 0.735312i \(-0.737036\pi\)
−0.677729 + 0.735312i \(0.737036\pi\)
\(450\) 0 0
\(451\) 3.39050 0.159652
\(452\) −22.3128 38.6469i −1.04950 1.81780i
\(453\) 0 0
\(454\) −22.9526 + 39.7551i −1.07722 + 1.86580i
\(455\) −0.113395 + 0.196406i −0.00531605 + 0.00920767i
\(456\) 0 0
\(457\) 17.6940 + 30.6468i 0.827688 + 1.43360i 0.899847 + 0.436205i \(0.143678\pi\)
−0.0721589 + 0.997393i \(0.522989\pi\)
\(458\) 53.9648 2.52161
\(459\) 0 0
\(460\) −1.56168 −0.0728139
\(461\) 1.13836 + 1.97171i 0.0530189 + 0.0918315i 0.891317 0.453381i \(-0.149782\pi\)
−0.838298 + 0.545212i \(0.816449\pi\)
\(462\) 0 0
\(463\) −9.18726 + 15.9128i −0.426968 + 0.739531i −0.996602 0.0823678i \(-0.973752\pi\)
0.569634 + 0.821899i \(0.307085\pi\)
\(464\) 8.51336 14.7456i 0.395223 0.684546i
\(465\) 0 0
\(466\) −21.2321 36.7751i −0.983558 1.70357i
\(467\) −4.65870 −0.215579 −0.107789 0.994174i \(-0.534377\pi\)
−0.107789 + 0.994174i \(0.534377\pi\)
\(468\) 0 0
\(469\) 5.12440 0.236623
\(470\) −0.401631 0.695646i −0.0185259 0.0320877i
\(471\) 0 0
\(472\) −21.8320 + 37.8141i −1.00490 + 1.74054i
\(473\) 10.6729 18.4860i 0.490739 0.849985i
\(474\) 0 0
\(475\) −9.59690 16.6223i −0.440336 0.762684i
\(476\) −4.34989 −0.199377
\(477\) 0 0
\(478\) 37.0338 1.69388
\(479\) −7.08795 12.2767i −0.323857 0.560936i 0.657424 0.753521i \(-0.271646\pi\)
−0.981280 + 0.192585i \(0.938313\pi\)
\(480\) 0 0
\(481\) −8.46669 + 14.6647i −0.386048 + 0.668654i
\(482\) −15.7924 + 27.3532i −0.719324 + 1.24591i
\(483\) 0 0
\(484\) 2.69931 + 4.67534i 0.122696 + 0.212515i
\(485\) −0.492926 −0.0223826
\(486\) 0 0
\(487\) −21.4338 −0.971258 −0.485629 0.874165i \(-0.661409\pi\)
−0.485629 + 0.874165i \(0.661409\pi\)
\(488\) 28.0128 + 48.5196i 1.26808 + 2.19638i
\(489\) 0 0
\(490\) −0.744846 + 1.29011i −0.0336487 + 0.0582812i
\(491\) −7.04393 + 12.2004i −0.317888 + 0.550598i −0.980047 0.198765i \(-0.936307\pi\)
0.662159 + 0.749363i \(0.269640\pi\)
\(492\) 0 0
\(493\) 6.37067 + 11.0343i 0.286920 + 0.496961i
\(494\) −38.8041 −1.74588
\(495\) 0 0
\(496\) 4.40999 0.198015
\(497\) −0.331955 0.574963i −0.0148902 0.0257906i
\(498\) 0 0
\(499\) −7.45467 + 12.9119i −0.333717 + 0.578014i −0.983237 0.182330i \(-0.941636\pi\)
0.649521 + 0.760344i \(0.274970\pi\)
\(500\) −1.75207 + 3.03468i −0.0783550 + 0.135715i
\(501\) 0 0
\(502\) 20.9140 + 36.2242i 0.933440 + 1.61676i
\(503\) 15.8631 0.707299 0.353650 0.935378i \(-0.384941\pi\)
0.353650 + 0.935378i \(0.384941\pi\)
\(504\) 0 0
\(505\) −0.676622 −0.0301093
\(506\) −16.5387 28.6458i −0.735234 1.27346i
\(507\) 0 0
\(508\) −21.7201 + 37.6203i −0.963674 + 1.66913i
\(509\) 16.9633 29.3814i 0.751887 1.30231i −0.195020 0.980799i \(-0.562477\pi\)
0.946907 0.321508i \(-0.104190\pi\)
\(510\) 0 0
\(511\) 0.0566734 + 0.0981611i 0.00250708 + 0.00434239i
\(512\) −28.1824 −1.24550
\(513\) 0 0
\(514\) −26.8683 −1.18511
\(515\) 0.297931 + 0.516031i 0.0131284 + 0.0227391i
\(516\) 0 0
\(517\) 5.55702 9.62505i 0.244398 0.423309i
\(518\) 2.80617 4.86043i 0.123296 0.213555i
\(519\) 0 0
\(520\) 0.830242 + 1.43802i 0.0364085 + 0.0630614i
\(521\) 42.7798 1.87422 0.937108 0.349039i \(-0.113492\pi\)
0.937108 + 0.349039i \(0.113492\pi\)
\(522\) 0 0
\(523\) −2.77785 −0.121467 −0.0607335 0.998154i \(-0.519344\pi\)
−0.0607335 + 0.998154i \(0.519344\pi\)
\(524\) −16.9772 29.4054i −0.741653 1.28458i
\(525\) 0 0
\(526\) −24.8698 + 43.0758i −1.08438 + 1.87820i
\(527\) −1.65003 + 2.85794i −0.0718764 + 0.124494i
\(528\) 0 0
\(529\) 1.58622 + 2.74741i 0.0689660 + 0.119453i
\(530\) 1.20725 0.0524396
\(531\) 0 0
\(532\) 8.40145 0.364249
\(533\) −2.30288 3.98870i −0.0997487 0.172770i
\(534\) 0 0
\(535\) 0.258011 0.446888i 0.0111548 0.0193207i
\(536\) 18.7596 32.4925i 0.810290 1.40346i
\(537\) 0 0
\(538\) −33.9167 58.7455i −1.46225 2.53270i
\(539\) −20.6116 −0.887803
\(540\) 0 0
\(541\) −3.59390 −0.154514 −0.0772570 0.997011i \(-0.524616\pi\)
−0.0772570 + 0.997011i \(0.524616\pi\)
\(542\) −20.7292 35.9040i −0.890394 1.54221i
\(543\) 0 0
\(544\) 2.09180 3.62310i 0.0896852 0.155339i
\(545\) −0.290019 + 0.502327i −0.0124230 + 0.0215173i
\(546\) 0 0
\(547\) 19.7929 + 34.2823i 0.846284 + 1.46581i 0.884501 + 0.466537i \(0.154499\pi\)
−0.0382175 + 0.999269i \(0.512168\pi\)
\(548\) −43.4057 −1.85420
\(549\) 0 0
\(550\) −37.0777 −1.58100
\(551\) −12.3044 21.3119i −0.524185 0.907916i
\(552\) 0 0
\(553\) −2.08982 + 3.61967i −0.0888681 + 0.153924i
\(554\) −6.20696 + 10.7508i −0.263709 + 0.456757i
\(555\) 0 0
\(556\) −3.20984 5.55961i −0.136128 0.235780i
\(557\) 11.4346 0.484501 0.242250 0.970214i \(-0.422114\pi\)
0.242250 + 0.970214i \(0.422114\pi\)
\(558\) 0 0
\(559\) −28.9967 −1.22643
\(560\) −0.0718044 0.124369i −0.00303429 0.00525554i
\(561\) 0 0
\(562\) −3.95840 + 6.85615i −0.166975 + 0.289209i
\(563\) 7.25540 12.5667i 0.305778 0.529624i −0.671656 0.740863i \(-0.734417\pi\)
0.977434 + 0.211239i \(0.0677500\pi\)
\(564\) 0 0
\(565\) 0.551239 + 0.954774i 0.0231908 + 0.0401676i
\(566\) −21.9285 −0.921725
\(567\) 0 0
\(568\) −4.86093 −0.203960
\(569\) −0.649591 1.12513i −0.0272323 0.0471677i 0.852088 0.523398i \(-0.175336\pi\)
−0.879320 + 0.476231i \(0.842003\pi\)
\(570\) 0 0
\(571\) −8.02866 + 13.9061i −0.335989 + 0.581950i −0.983674 0.179958i \(-0.942404\pi\)
0.647685 + 0.761908i \(0.275737\pi\)
\(572\) −24.4836 + 42.4069i −1.02371 + 1.77312i
\(573\) 0 0
\(574\) 0.763257 + 1.32200i 0.0318577 + 0.0551792i
\(575\) −22.2255 −0.926867
\(576\) 0 0
\(577\) −8.46033 −0.352208 −0.176104 0.984372i \(-0.556350\pi\)
−0.176104 + 0.984372i \(0.556350\pi\)
\(578\) 15.6537 + 27.1131i 0.651110 + 1.12775i
\(579\) 0 0
\(580\) −1.12221 + 1.94373i −0.0465973 + 0.0807089i
\(581\) 4.32010 7.48263i 0.179228 0.310432i
\(582\) 0 0
\(583\) 8.35184 + 14.4658i 0.345898 + 0.599113i
\(584\) 0.829886 0.0343409
\(585\) 0 0
\(586\) 6.78802 0.280411
\(587\) −9.19260 15.9221i −0.379419 0.657173i 0.611559 0.791199i \(-0.290543\pi\)
−0.990978 + 0.134026i \(0.957210\pi\)
\(588\) 0 0
\(589\) 3.18689 5.51986i 0.131314 0.227442i
\(590\) 1.14957 1.99112i 0.0473272 0.0819731i
\(591\) 0 0
\(592\) −5.36130 9.28604i −0.220348 0.381654i
\(593\) −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
\(596\) −40.7915 70.6529i −1.67088 2.89406i
\(597\) 0 0
\(598\) −22.4666 + 38.9133i −0.918728 + 1.59128i
\(599\) 5.51386 9.55028i 0.225290 0.390214i −0.731116 0.682253i \(-0.761000\pi\)
0.956406 + 0.292039i \(0.0943337\pi\)
\(600\) 0 0
\(601\) −12.8990 22.3417i −0.526160 0.911335i −0.999536 0.0304746i \(-0.990298\pi\)
0.473376 0.880860i \(-0.343035\pi\)
\(602\) 9.61055 0.391697
\(603\) 0 0
\(604\) −17.8650 −0.726918
\(605\) −0.0666866 0.115505i −0.00271120 0.00469593i
\(606\) 0 0
\(607\) 7.39494 12.8084i 0.300151 0.519877i −0.676019 0.736884i \(-0.736296\pi\)
0.976170 + 0.217007i \(0.0696295\pi\)
\(608\) −4.04014 + 6.99772i −0.163849 + 0.283795i
\(609\) 0 0
\(610\) −1.47503 2.55482i −0.0597221 0.103442i
\(611\) −15.0976 −0.610785
\(612\) 0 0
\(613\) 36.2739 1.46509 0.732545 0.680719i \(-0.238332\pi\)
0.732545 + 0.680719i \(0.238332\pi\)
\(614\) −7.55846 13.0916i −0.305034 0.528335i
\(615\) 0 0
\(616\) 3.80732 6.59447i 0.153401 0.265699i
\(617\) −20.1868 + 34.9645i −0.812689 + 1.40762i 0.0982868 + 0.995158i \(0.468664\pi\)
−0.910976 + 0.412460i \(0.864670\pi\)
\(618\) 0 0
\(619\) 3.44665 + 5.96978i 0.138533 + 0.239946i 0.926941 0.375206i \(-0.122428\pi\)
−0.788409 + 0.615152i \(0.789095\pi\)
\(620\) −0.581315 −0.0233462
\(621\) 0 0
\(622\) 17.7069 0.709981
\(623\) 0.450299 + 0.779940i 0.0180408 + 0.0312477i
\(624\) 0 0
\(625\) −12.4351 + 21.5381i −0.497402 + 0.861526i
\(626\) 5.12836 8.88259i 0.204971 0.355020i
\(627\) 0 0
\(628\) 0.394121 + 0.682638i 0.0157271 + 0.0272402i
\(629\) 8.02386 0.319932
\(630\) 0 0
\(631\) 29.8191 1.18708 0.593539 0.804805i \(-0.297730\pi\)
0.593539 + 0.804805i \(0.297730\pi\)
\(632\) 15.3009 + 26.5020i 0.608639 + 1.05419i
\(633\) 0 0
\(634\) 19.3902 33.5848i 0.770082 1.33382i
\(635\) 0.536597 0.929413i 0.0212942 0.0368826i
\(636\) 0 0
\(637\) 13.9997 + 24.2481i 0.554687 + 0.960746i
\(638\) −47.5382 −1.88206
\(639\) 0 0
\(640\) 1.92653 0.0761527
\(641\) 21.4404 + 37.1358i 0.846844 + 1.46678i 0.884011 + 0.467467i \(0.154833\pi\)
−0.0371670 + 0.999309i \(0.511833\pi\)
\(642\) 0 0
\(643\) 13.7066 23.7406i 0.540537 0.936237i −0.458336 0.888779i \(-0.651554\pi\)
0.998873 0.0474584i \(-0.0151122\pi\)
\(644\) 4.86424 8.42511i 0.191678 0.331996i
\(645\) 0 0
\(646\) 9.19363 + 15.9238i 0.361718 + 0.626515i
\(647\) 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
\(650\) 25.1837 + 43.6195i 0.987786 + 1.71090i
\(651\) 0 0
\(652\) −10.5947 + 18.3506i −0.414921 + 0.718664i
\(653\) 16.1231 27.9261i 0.630947 1.09283i −0.356411 0.934329i \(-0.616000\pi\)
0.987358 0.158504i \(-0.0506670\pi\)
\(654\) 0 0
\(655\) 0.419423 + 0.726463i 0.0163882 + 0.0283852i
\(656\) 2.91647 0.113869
\(657\) 0 0
\(658\) 5.00391 0.195073
\(659\) 13.9093 + 24.0916i 0.541829 + 0.938475i 0.998799 + 0.0489934i \(0.0156013\pi\)
−0.456970 + 0.889482i \(0.651065\pi\)
\(660\) 0 0
\(661\) −15.3943 + 26.6637i −0.598769 + 1.03710i 0.394234 + 0.919010i \(0.371010\pi\)
−0.993003 + 0.118088i \(0.962323\pi\)
\(662\) −23.0895 + 39.9921i −0.897398 + 1.55434i
\(663\) 0 0
\(664\) −31.6303 54.7853i −1.22749 2.12608i
\(665\) −0.207559 −0.00804877
\(666\) 0 0
\(667\) −28.4958 −1.10336
\(668\) 31.4243 + 54.4284i 1.21584 + 2.10590i
\(669\) 0 0
\(670\) −0.987793 + 1.71091i −0.0381618 + 0.0660982i
\(671\) 20.4087 35.3488i 0.787868 1.36463i
\(672\) 0 0
\(673\) 13.0653 + 22.6298i 0.503631 + 0.872314i 0.999991 + 0.00419727i \(0.00133604\pi\)
−0.496361 + 0.868116i \(0.665331\pi\)
\(674\) −70.7584 −2.72551
\(675\) 0 0
\(676\) 17.5374 0.674515
\(677\) 9.09725 + 15.7569i 0.349636 + 0.605587i 0.986185 0.165650i \(-0.0529720\pi\)
−0.636549 + 0.771236i \(0.719639\pi\)
\(678\) 0 0
\(679\) 1.53534 2.65928i 0.0589209 0.102054i
\(680\) 0.393409 0.681404i 0.0150865 0.0261307i
\(681\) 0 0
\(682\) −6.15630 10.6630i −0.235737 0.408308i
\(683\) −23.4971 −0.899092 −0.449546 0.893257i \(-0.648414\pi\)
−0.449546 + 0.893257i \(0.648414\pi\)
\(684\) 0 0
\(685\) 1.07234 0.0409721
\(686\) −9.51413 16.4790i −0.363251 0.629169i
\(687\) 0 0
\(688\) 9.18067 15.9014i 0.350010 0.606235i
\(689\) 11.3454 19.6508i 0.432225 0.748635i
\(690\) 0 0
\(691\) 22.2690 + 38.5710i 0.847151 + 1.46731i 0.883740 + 0.467979i \(0.155018\pi\)
−0.0365885 + 0.999330i \(0.511649\pi\)
\(692\) −71.5960 −2.72167
\(693\) 0 0
\(694\) −27.3714 −1.03900
\(695\) 0.0792994 + 0.137351i 0.00300800 + 0.00521000i
\(696\) 0 0
\(697\) −1.09122 + 1.89004i −0.0413327 + 0.0715904i
\(698\) −33.8168 + 58.5724i −1.27998 + 2.21700i
\(699\) 0 0
\(700\) −5.45252 9.44404i −0.206086 0.356951i
\(701\) 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
\(704\) 16.0341 + 27.7719i 0.604308 + 1.04669i
\(705\) 0 0
\(706\) 34.4081 59.5967i 1.29497 2.24295i
\(707\) 2.10750 3.65030i 0.0792607 0.137284i
\(708\) 0 0
\(709\) 7.84201 + 13.5828i 0.294513 + 0.510111i 0.974871 0.222768i \(-0.0715093\pi\)
−0.680359 + 0.732879i \(0.738176\pi\)
\(710\) 0.255954 0.00960579
\(711\) 0 0
\(712\) 6.59387 0.247116
\(713\) −3.69027 6.39174i −0.138202 0.239372i
\(714\) 0 0
\(715\) 0.604871 1.04767i 0.0226209 0.0391805i
\(716\) 30.5854 52.9755i 1.14303 1.97979i
\(717\) 0 0
\(718\) −37.2638 64.5429i −1.39067 2.40872i
\(719\) 53.1607 1.98256 0.991280 0.131771i \(-0.0420664\pi\)
0.991280 + 0.131771i \(0.0420664\pi\)
\(720\) 0 0
\(721\) −3.71191 −0.138239
\(722\) 5.05868 + 8.76190i 0.188265 + 0.326084i
\(723\) 0 0
\(724\) 5.63581 9.76152i 0.209453 0.362784i
\(725\) −15.9710 + 27.6627i −0.593150 + 1.02737i
\(726\) 0 0
\(727\) −0.234586 0.406315i −0.00870032 0.0150694i 0.861642 0.507516i \(-0.169436\pi\)
−0.870343 + 0.492446i \(0.836103\pi\)
\(728\) −10.3440 −0.383372
\(729\) 0 0
\(730\) −0.0436980 −0.00161734
\(731\) 6.87002 + 11.8992i 0.254097 + 0.440109i
\(732\) 0 0
\(733\) 23.2031 40.1890i 0.857028 1.48442i −0.0177237 0.999843i \(-0.505642\pi\)
0.874751 0.484572i \(-0.161025\pi\)
\(734\) −28.9686 + 50.1751i −1.06925 + 1.85200i
\(735\) 0 0
\(736\) 4.67829 + 8.10303i 0.172444 + 0.298682i
\(737\) −27.3345 −1.00688
\(738\) 0 0
\(739\) 25.8093 0.949411 0.474706 0.880145i \(-0.342555\pi\)
0.474706 + 0.880145i \(0.342555\pi\)
\(740\) 0.706714 + 1.22406i 0.0259793 + 0.0449975i
\(741\) 0 0
\(742\) −3.76027 + 6.51298i −0.138044 + 0.239099i
\(743\) 17.3548 30.0594i 0.636687 1.10277i −0.349469 0.936948i \(-0.613638\pi\)
0.986155 0.165825i \(-0.0530288\pi\)
\(744\) 0 0
\(745\) 1.00776 + 1.74549i 0.0369213 + 0.0639497i
\(746\) −30.2259 −1.10665
\(747\) 0 0
\(748\) 23.2031 0.848389
\(749\) 1.60728 + 2.78388i 0.0587286 + 0.101721i
\(750\) 0 0
\(751\) −11.9929 + 20.7724i −0.437628 + 0.757994i −0.997506 0.0705811i \(-0.977515\pi\)
0.559878 + 0.828575i \(0.310848\pi\)
\(752\) 4.78008 8.27934i 0.174312 0.301917i
\(753\) 0 0
\(754\) 32.2886 + 55.9255i 1.17588 + 2.03669i
\(755\) 0.441357 0.0160626
\(756\) 0 0
\(757\) −8.78780 −0.319398 −0.159699 0.987166i \(-0.551052\pi\)
−0.159699 + 0.987166i \(0.551052\pi\)
\(758\) 9.25251 + 16.0258i 0.336066 + 0.582084i
\(759\) 0 0
\(760\) −0.759837 + 1.31608i −0.0275622 + 0.0477391i
\(761\) 6.87694 11.9112i 0.249289 0.431781i −0.714040 0.700105i \(-0.753137\pi\)
0.963329 + 0.268324i \(0.0864698\pi\)
\(762\) 0 0
\(763\) −1.80667 3.12924i −0.0654057 0.113286i
\(764\) 8.49190 0.307226
\(765\) 0 0
\(766\) 42.8969 1.54993
\(767\) −21.6067 37.4239i −0.780172 1.35130i
\(768\) 0 0
\(769\) 15.6790 27.1568i 0.565398 0.979298i −0.431615 0.902058i \(-0.642056\pi\)
0.997013 0.0772399i \(-0.0246107\pi\)
\(770\) −0.200476 + 0.347235i −0.00722466 + 0.0125135i
\(771\) 0 0
\(772\) 1.65834 + 2.87233i 0.0596849 + 0.103377i
\(773\) −28.1214 −1.01146 −0.505729 0.862693i \(-0.668776\pi\)
−0.505729 + 0.862693i \(0.668776\pi\)
\(774\) 0 0
\(775\) −8.27314 −0.297180
\(776\) −11.2412 19.4704i −0.403536 0.698946i
\(777\) 0 0
\(778\) 32.8883 56.9643i 1.17910 2.04227i
\(779\) 2.10759 3.65046i 0.0755123 0.130791i
\(780\) 0 0
\(781\) 1.77071 + 3.06696i 0.0633609 + 0.109744i
\(782\) 21.2916 0.761385
\(783\) 0 0
\(784\) −17.7298 −0.633207
\(785\) −0.00973679 0.0168646i −0.000347521 0.000601924i
\(786\) 0 0
\(787\) 18.1001 31.3503i 0.645198 1.11752i −0.339058 0.940766i \(-0.610108\pi\)
0.984256 0.176750i \(-0.0565585\pi\)
\(788\) 38.1988 66.1623i 1.36078 2.35694i
\(789\) 0 0
\(790\) −0.805678 1.39547i −0.0286647 0.0496488i
\(791\) −6.86787 −0.244193
\(792\) 0 0
\(793\) −55.4474 −1.96900
\(794\) −5.06260 8.76868i −0.179665 0.311189i
\(795\) 0 0
\(796\) 35.8117 62.0278i 1.26931 2.19852i
\(797\) −14.8001 + 25.6344i −0.524245 + 0.908018i 0.475357 + 0.879793i \(0.342319\pi\)
−0.999602 + 0.0282254i \(0.991014\pi\)
\(798\) 0 0
\(799\) 3.57700 + 6.19555i 0.126545 + 0.219183i
\(800\) 10.4881 0.370812
\(801\) 0 0
\(802\) −36.4386 −1.28669
\(803\) −0.302306 0.523609i −0.0106681 0.0184778i
\(804\) 0 0
\(805\) −0.120171 + 0.208143i −0.00423549 + 0.00733608i
\(806\) −8.36289 + 14.4850i −0.294570 + 0.510211i
\(807\) 0 0
\(808\) −15.4304 26.7263i −0.542840 0.940226i
\(809\) 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 \(0.429628\pi\)
\(812\) −6.99080 12.1084i −0.245329 0.424922i
\(813\) 0 0
\(814\) −14.9686 + 25.9264i −0.524649 + 0.908719i
\(815\) 0.261743 0.453353i 0.00916847 0.0158803i
\(816\) 0 0
\(817\) −13.2689 22.9824i −0.464219 0.804051i
\(818\) 11.3107 0.395470
\(819\) 0 0
\(820\) −0.384442 −0.0134253
\(821\) 21.5334 + 37.2969i 0.751520 + 1.30167i 0.947086 + 0.320980i \(0.104012\pi\)
−0.195566 + 0.980691i \(0.562654\pi\)
\(822\) 0 0
\(823\) −5.14205 + 8.90629i −0.179240 + 0.310454i −0.941621 0.336676i \(-0.890697\pi\)
0.762380 + 0.647129i \(0.224031\pi\)
\(824\) −13.5887 + 23.5363i −0.473384 + 0.819925i
\(825\) 0 0
\(826\) 7.16124 + 12.4036i 0.249172 + 0.431578i
\(827\) −6.09463 −0.211931 −0.105965 0.994370i \(-0.533793\pi\)
−0.105965 + 0.994370i \(0.533793\pi\)
\(828\) 0 0
\(829\) −33.6979 −1.17038 −0.585188 0.810898i \(-0.698979\pi\)
−0.585188 + 0.810898i \(0.698979\pi\)
\(830\) 1.66551 + 2.88474i 0.0578105 + 0.100131i
\(831\) 0 0
\(832\) 21.7812 37.7261i 0.755127 1.30792i
\(833\) 6.63373 11.4900i 0.229845 0.398103i
\(834\) 0 0
\(835\) −0.776339 1.34466i −0.0268663 0.0465338i
\(836\) −44.8148 −1.54995
\(837\) 0 0
\(838\) −47.5308 −1.64192
\(839\) −21.1131 36.5690i −0.728905 1.26250i −0.957346 0.288943i \(-0.906696\pi\)
0.228441 0.973558i \(-0.426637\pi\)
\(840\) 0 0
\(841\) −5.97686 + 10.3522i −0.206099 + 0.356973i
\(842\) −33.8457 + 58.6225i −1.16640 + 2.02026i
\(843\) 0 0
\(844\) −30.4890 52.8086i −1.04948 1.81775i
\(845\) −0.433262 −0.0149047
\(846\) 0 0
\(847\) 0.830846 0.0285482
\(848\) 7.18415 + 12.4433i 0.246705 + 0.427305i
\(849\) 0 0
\(850\) 11.9333 20.6690i 0.409308 0.708942i
\(851\) −8.97263 + 15.5411i −0.307578 + 0.532741i
\(852\) 0 0
\(853\) 17.8648 + 30.9427i 0.611679 + 1.05946i 0.990957 + 0.134177i \(0.0428389\pi\)
−0.379278 + 0.925283i \(0.623828\pi\)
\(854\) 18.3773 0.628858
\(855\) 0 0
\(856\) 23.5358 0.804439
\(857\) 3.95433 + 6.84909i 0.135077 + 0.233961i 0.925627 0.378437i \(-0.123538\pi\)
−0.790550 + 0.612398i \(0.790205\pi\)
\(858\) 0 0
\(859\) 22.3596 38.7279i 0.762899 1.32138i −0.178452 0.983949i \(-0.557109\pi\)
0.941350 0.337431i \(-0.109558\pi\)
\(860\) −1.21017 + 2.09608i −0.0412666 + 0.0714759i
\(861\) 0 0
\(862\) −6.24038 10.8087i −0.212548 0.368144i
\(863\) 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
\(866\) −30.4147 52.6798i −1.03353 1.79013i
\(867\) 0 0
\(868\) 1.81065 3.13613i 0.0614574 0.106447i
\(869\) 11.1475 19.3080i 0.378152 0.654978i
\(870\) 0 0
\(871\) 18.5660 + 32.1572i 0.629084 + 1.08961i
\(872\) −26.4556 −0.895899
\(873\) 0 0
\(874\) −41.1229 −1.39100
\(875\) 0.269644 + 0.467036i 0.00911562 + 0.0157887i
\(876\) 0 0
\(877\) 11.0688 19.1718i 0.373767 0.647384i −0.616374 0.787453i \(-0.711399\pi\)
0.990142 + 0.140069i \(0.0447325\pi\)
\(878\) 18.8062 32.5733i 0.634678 1.09929i
\(879\) 0 0
\(880\) 0.383017 + 0.663406i 0.0129115 + 0.0223634i
\(881\) −9.86404 −0.332328 −0.166164 0.986098i \(-0.553138\pi\)
−0.166164 + 0.986098i \(0.553138\pi\)
\(882\) 0 0
\(883\) 47.5731 1.60096 0.800481 0.599358i \(-0.204578\pi\)
0.800481 + 0.599358i \(0.204578\pi\)
\(884\) −15.7599 27.2969i −0.530062 0.918094i
\(885\) 0 0
\(886\) −21.9194 + 37.9655i −0.736397 + 1.27548i
\(887\) 6.67864 11.5678i 0.224247 0.388407i −0.731846 0.681470i \(-0.761341\pi\)
0.956093 + 0.293063i \(0.0946745\pi\)
\(888\) 0 0
\(889\) 3.34272 + 5.78976i 0.112111 + 0.194182i
\(890\) −0.347203 −0.0116383
\(891\) 0 0
\(892\) 80.8465 2.70694
\(893\) −6.90868 11.9662i −0.231190 0.400433i
\(894\) 0 0
\(895\) −0.755615 + 1.30876i −0.0252574 + 0.0437472i
\(896\) −6.00063 + 10.3934i −0.200467 + 0.347219i
\(897\) 0 0
\(898\) 34.4892 + 59.7371i 1.15092 + 1.99345i
\(899\) −10.6072 −0.353769
\(900\) 0 0
\(901\) −10.7520 −0.358201
\(902\) −4.07135 7.05179i −0.135561 0.234799i
\(903\) 0 0
\(904\) −25.1421 + 43.5474i −0.836214 + 1.44836i
\(905\) −0.139233 + 0.241159i −0.00462827 + 0.00801640i
\(906\) 0 0
\(907\) −18.4803 32.0089i −0.613629 1.06284i −0.990623 0.136621i \(-0.956376\pi\)
0.376994 0.926215i \(-0.376958\pi\)
\(908\) 72.0184 2.39001
\(909\) 0 0
\(910\) 0.544665 0.0180555
\(911\) −24.2055 41.9252i −0.801966 1.38905i −0.918321 0.395837i \(-0.870454\pi\)
0.116355 0.993208i \(-0.462879\pi\)
\(912\) 0 0
\(913\) −23.0442 + 39.9137i −0.762650 + 1.32095i
\(914\) 42.4942 73.6021i 1.40558 2.43454i
\(915\) 0 0
\(916\) −42.3314 73.3201i −1.39867 2.42256i
\(917\) −5.22558 −0.172564
\(918\) 0 0
\(919\) 8.93459 0.294725 0.147363 0.989083i \(-0.452922\pi\)
0.147363 + 0.989083i \(0.452922\pi\)
\(920\) 0.879854 + 1.52395i 0.0290079 + 0.0502432i
\(921\) 0 0
\(922\) 2.73392 4.73529i 0.0900369 0.155948i
\(923\) 2.40538 4.16624i 0.0791741 0.137133i
\(924\) 0 0
\(925\) 10.0578 + 17.4206i 0.330698 + 0.572785i
\(926\) 44.1287 1.45016
\(927\) 0 0
\(928\) 13.4471 0.441423
\(929\) −3.12207 5.40759i −0.102432 0.177417i 0.810254 0.586079i \(-0.199329\pi\)
−0.912686 + 0.408661i \(0.865996\pi\)
\(930\) 0 0
\(931\) −12.8125 + 22.1919i −0.419912 + 0.727310i
\(932\) −33.3100 + 57.6946i −1.09110 + 1.88985i
\(933\) 0 0
\(934\) 5.59422 + 9.68947i 0.183048 + 0.317049i
\(935\) −0.573234 −0.0187468
\(936\) 0 0
\(937\) 45.8424 1.49760 0.748802 0.662794i \(-0.230629\pi\)
0.748802 + 0.662794i \(0.230629\pi\)
\(938\) −6.15344 10.6581i −0.200917 0.347998i
\(939\) 0 0
\(940\) −0.630099 + 1.09136i −0.0205516 + 0.0355964i
\(941\) −2.17632 + 3.76949i −0.0709459 + 0.122882i −0.899316 0.437299i \(-0.855935\pi\)
0.828370 + 0.560181i \(0.189268\pi\)
\(942\) 0 0
\(943\) −2.44049 4.22705i −0.0794733 0.137652i
\(944\) 27.3637 0.890612
\(945\) 0 0
\(946\) −51.2644 −1.66675
\(947\) 1.00837 + 1.74654i 0.0327675 + 0.0567550i 0.881944 0.471354i \(-0.156235\pi\)
−0.849177 + 0.528109i \(0.822901\pi\)
\(948\) 0 0
\(949\) −0.410661 + 0.711285i −0.0133306 + 0.0230893i
\(950\) −23.0481 + 39.9205i −0.747780 + 1.29519i
\(951\) 0 0
\(952\) 2.45073 + 4.24480i 0.0794287 + 0.137575i
\(953\) 35.7287 1.15737 0.578684 0.815552i \(-0.303567\pi\)
0.578684 + 0.815552i \(0.303567\pi\)
\(954\) 0 0
\(955\) −0.209793 −0.00678874
\(956\) −29.0502 50.3165i −0.939551 1.62735i
\(957\) 0 0
\(958\) −17.0226 + 29.4840i −0.549974 + 0.952583i
\(959\) −3.34007 + 5.78517i −0.107856 + 0.186813i
\(960\) 0 0
\(961\) 14.1263 + 24.4676i 0.455689 + 0.789276i
\(962\) 40.6676 1.31117
\(963\) 0 0
\(964\) 49.5518 1.59596
\(965\) −0.0409694 0.0709611i −0.00131885 0.00228432i
\(966\) 0 0
\(967\) 0.346658 0.600430i 0.0111478 0.0193085i −0.860398 0.509623i \(-0.829785\pi\)
0.871545 + 0.490315i \(0.163118\pi\)
\(968\) 3.04159 5.26818i 0.0977602 0.169326i
\(969\) 0 0
\(970\) 0.591911 + 1.02522i 0.0190051 + 0.0329178i
\(971\) −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
\(974\) 25.7379 + 44.5794i 0.824697 + 1.42842i
\(975\) 0 0
\(976\) 17.5553 30.4066i 0.561930 0.973292i
\(977\) −6.30166 + 10.9148i −0.201608 + 0.349195i −0.949047 0.315136i \(-0.897950\pi\)
0.747439 + 0.664331i \(0.231283\pi\)
\(978\) 0 0
\(979\) −2.40197 4.16034i −0.0767674 0.132965i
\(980\) 2.33710 0.0746560
\(981\) 0 0
\(982\) 33.8337 1.07968
\(983\) 5.77251 + 9.99828i 0.184115 + 0.318896i 0.943278 0.332005i \(-0.107725\pi\)
−0.759163 + 0.650900i \(0.774392\pi\)
\(984\) 0 0
\(985\) −0.943705 + 1.63455i −0.0300690 + 0.0520810i
\(986\) 15.2999 26.5003i 0.487249 0.843940i
\(987\) 0 0
\(988\) 30.4389 + 52.7217i 0.968390 + 1.67730i
\(989\) −30.7294 −0.977139
\(990\) 0 0
\(991\) 18.6935 0.593819 0.296910 0.954906i \(-0.404044\pi\)
0.296910 + 0.954906i \(0.404044\pi\)
\(992\) 1.74143 + 3.01624i 0.0552904 + 0.0957658i
\(993\) 0 0
\(994\) −0.797231 + 1.38084i −0.0252866 + 0.0437977i
\(995\) −0.884732 + 1.53240i −0.0280479 + 0.0485804i
\(996\) 0 0
\(997\) −1.67940 2.90881i −0.0531872 0.0921230i 0.838206 0.545354i \(-0.183605\pi\)
−0.891393 + 0.453231i \(0.850271\pi\)
\(998\) 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 729.2.c.b.244.1 12
3.2 odd 2 729.2.c.e.244.6 12
9.2 odd 6 729.2.c.e.487.6 12
9.4 even 3 729.2.a.d.1.6 6
9.5 odd 6 729.2.a.a.1.1 6
9.7 even 3 inner 729.2.c.b.487.1 12
27.2 odd 18 27.2.e.a.13.1 12
27.4 even 9 81.2.e.a.73.2 12
27.5 odd 18 243.2.e.d.55.2 12
27.7 even 9 243.2.e.a.190.1 12
27.11 odd 18 243.2.e.c.109.1 12
27.13 even 9 243.2.e.b.136.2 12
27.14 odd 18 243.2.e.c.136.1 12
27.16 even 9 243.2.e.b.109.2 12
27.20 odd 18 243.2.e.d.190.2 12
27.22 even 9 243.2.e.a.55.1 12
27.23 odd 18 27.2.e.a.25.1 yes 12
27.25 even 9 81.2.e.a.10.2 12
108.23 even 18 432.2.u.c.241.1 12
108.83 even 18 432.2.u.c.337.1 12
135.2 even 36 675.2.u.b.499.4 24
135.23 even 36 675.2.u.b.349.4 24
135.29 odd 18 675.2.l.c.526.2 12
135.77 even 36 675.2.u.b.349.1 24
135.83 even 36 675.2.u.b.499.1 24
135.104 odd 18 675.2.l.c.376.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.13.1 12 27.2 odd 18
27.2.e.a.25.1 yes 12 27.23 odd 18
81.2.e.a.10.2 12 27.25 even 9
81.2.e.a.73.2 12 27.4 even 9
243.2.e.a.55.1 12 27.22 even 9
243.2.e.a.190.1 12 27.7 even 9
243.2.e.b.109.2 12 27.16 even 9
243.2.e.b.136.2 12 27.13 even 9
243.2.e.c.109.1 12 27.11 odd 18
243.2.e.c.136.1 12 27.14 odd 18
243.2.e.d.55.2 12 27.5 odd 18
243.2.e.d.190.2 12 27.20 odd 18
432.2.u.c.241.1 12 108.23 even 18
432.2.u.c.337.1 12 108.83 even 18
675.2.l.c.376.2 12 135.104 odd 18
675.2.l.c.526.2 12 135.29 odd 18
675.2.u.b.349.1 24 135.77 even 36
675.2.u.b.349.4 24 135.23 even 36
675.2.u.b.499.1 24 135.83 even 36
675.2.u.b.499.4 24 135.2 even 36
729.2.a.a.1.1 6 9.5 odd 6
729.2.a.d.1.6 6 9.4 even 3
729.2.c.b.244.1 12 1.1 even 1 trivial
729.2.c.b.487.1 12 9.7 even 3 inner
729.2.c.e.244.6 12 3.2 odd 2
729.2.c.e.487.6 12 9.2 odd 6