Properties

Label 729.2.g.a.55.8
Level $729$
Weight $2$
Character 729.55
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(28,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([44]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.g (of order \(27\), degree \(18\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 55.8
Character \(\chi\) \(=\) 729.55
Dual form 729.2.g.a.676.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.971435 - 2.25204i) q^{2} +(-2.75551 - 2.92067i) q^{4} +(-0.232513 - 3.99210i) q^{5} +(-1.28109 - 0.303625i) q^{7} +(-4.64483 + 1.69058i) q^{8} +O(q^{10})\) \(q+(0.971435 - 2.25204i) q^{2} +(-2.75551 - 2.92067i) q^{4} +(-0.232513 - 3.99210i) q^{5} +(-1.28109 - 0.303625i) q^{7} +(-4.64483 + 1.69058i) q^{8} +(-9.21624 - 3.35444i) q^{10} +(2.04879 + 1.34751i) q^{11} +(-1.30311 - 0.152312i) q^{13} +(-1.92827 + 2.59012i) q^{14} +(-0.237953 + 4.08549i) q^{16} +(-0.206593 + 0.173352i) q^{17} +(1.02778 + 0.862409i) q^{19} +(-11.0189 + 11.6794i) q^{20} +(5.02492 - 3.30494i) q^{22} +(5.82111 - 1.37963i) q^{23} +(-10.9166 + 1.27597i) q^{25} +(-1.60890 + 2.78670i) q^{26} +(2.64328 + 4.57830i) q^{28} +(3.30965 + 4.44563i) q^{29} +(0.369677 - 1.23481i) q^{31} +(0.135207 + 0.0679036i) q^{32} +(0.189704 + 0.633655i) q^{34} +(-0.914230 + 5.18486i) q^{35} +(-0.00841562 - 0.0477273i) q^{37} +(2.94060 - 1.47682i) q^{38} +(7.82896 + 18.1496i) q^{40} +(-1.64212 - 3.80687i) q^{41} +(5.59352 - 2.80917i) q^{43} +(-1.70983 - 9.69693i) q^{44} +(2.54785 - 14.4496i) q^{46} +(-2.38036 - 7.95094i) q^{47} +(-4.70641 - 2.36365i) q^{49} +(-7.73125 + 25.8242i) q^{50} +(3.14588 + 4.22565i) q^{52} +(5.79529 + 10.0377i) q^{53} +(4.90304 - 8.49231i) q^{55} +(6.46377 - 0.755507i) q^{56} +(13.2268 - 3.13482i) q^{58} +(-8.15031 + 5.36055i) q^{59} +(2.93311 - 3.10891i) q^{61} +(-2.42172 - 2.03206i) q^{62} +(-5.98568 + 5.02258i) q^{64} +(-0.305054 + 5.23757i) q^{65} +(-0.791752 + 1.06351i) q^{67} +(1.07557 + 0.125716i) q^{68} +(10.7884 + 7.09563i) q^{70} +(-7.40721 - 2.69600i) q^{71} +(-8.12155 + 2.95600i) q^{73} +(-0.115659 - 0.0274117i) q^{74} +(-0.313243 - 5.37818i) q^{76} +(-2.21556 - 2.34836i) q^{77} +(2.07109 - 4.80133i) q^{79} +16.3650 q^{80} -10.1684 q^{82} +(2.24944 - 5.21479i) q^{83} +(0.740074 + 0.784433i) q^{85} +(-0.892623 - 15.3257i) q^{86} +(-11.7944 - 2.79532i) q^{88} +(8.61170 - 3.13440i) q^{89} +(1.62316 + 0.590783i) q^{91} +(-20.0696 - 13.2000i) q^{92} +(-20.2182 - 2.36317i) q^{94} +(3.20385 - 4.30352i) q^{95} +(-0.721447 + 12.3868i) q^{97} +(-9.89500 + 8.30289i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.971435 2.25204i 0.686908 1.59243i −0.113887 0.993494i \(-0.536330\pi\)
0.800795 0.598938i \(-0.204410\pi\)
\(3\) 0 0
\(4\) −2.75551 2.92067i −1.37775 1.46033i
\(5\) −0.232513 3.99210i −0.103983 1.78532i −0.498954 0.866629i \(-0.666282\pi\)
0.394971 0.918694i \(-0.370755\pi\)
\(6\) 0 0
\(7\) −1.28109 0.303625i −0.484208 0.114759i −0.0187406 0.999824i \(-0.505966\pi\)
−0.465468 + 0.885065i \(0.654114\pi\)
\(8\) −4.64483 + 1.69058i −1.64220 + 0.597711i
\(9\) 0 0
\(10\) −9.21624 3.35444i −2.91443 1.06077i
\(11\) 2.04879 + 1.34751i 0.617734 + 0.406290i 0.819447 0.573154i \(-0.194280\pi\)
−0.201713 + 0.979445i \(0.564651\pi\)
\(12\) 0 0
\(13\) −1.30311 0.152312i −0.361418 0.0422437i −0.0665537 0.997783i \(-0.521200\pi\)
−0.294864 + 0.955539i \(0.595274\pi\)
\(14\) −1.92827 + 2.59012i −0.515353 + 0.692239i
\(15\) 0 0
\(16\) −0.237953 + 4.08549i −0.0594882 + 1.02137i
\(17\) −0.206593 + 0.173352i −0.0501061 + 0.0420440i −0.667497 0.744613i \(-0.732634\pi\)
0.617391 + 0.786657i \(0.288190\pi\)
\(18\) 0 0
\(19\) 1.02778 + 0.862409i 0.235789 + 0.197850i 0.753024 0.657993i \(-0.228594\pi\)
−0.517235 + 0.855843i \(0.673039\pi\)
\(20\) −11.0189 + 11.6794i −2.46390 + 2.61159i
\(21\) 0 0
\(22\) 5.02492 3.30494i 1.07132 0.704616i
\(23\) 5.82111 1.37963i 1.21379 0.287673i 0.426630 0.904426i \(-0.359701\pi\)
0.787156 + 0.616754i \(0.211553\pi\)
\(24\) 0 0
\(25\) −10.9166 + 1.27597i −2.18333 + 0.255194i
\(26\) −1.60890 + 2.78670i −0.315531 + 0.546516i
\(27\) 0 0
\(28\) 2.64328 + 4.57830i 0.499533 + 0.865216i
\(29\) 3.30965 + 4.44563i 0.614587 + 0.825533i 0.995062 0.0992581i \(-0.0316469\pi\)
−0.380475 + 0.924791i \(0.624240\pi\)
\(30\) 0 0
\(31\) 0.369677 1.23481i 0.0663960 0.221778i −0.918352 0.395764i \(-0.870480\pi\)
0.984748 + 0.173986i \(0.0556649\pi\)
\(32\) 0.135207 + 0.0679036i 0.0239015 + 0.0120038i
\(33\) 0 0
\(34\) 0.189704 + 0.633655i 0.0325339 + 0.108671i
\(35\) −0.914230 + 5.18486i −0.154533 + 0.876401i
\(36\) 0 0
\(37\) −0.00841562 0.0477273i −0.00138352 0.00784632i 0.984108 0.177570i \(-0.0568236\pi\)
−0.985492 + 0.169724i \(0.945712\pi\)
\(38\) 2.94060 1.47682i 0.477028 0.239572i
\(39\) 0 0
\(40\) 7.82896 + 18.1496i 1.23787 + 2.86970i
\(41\) −1.64212 3.80687i −0.256456 0.594533i 0.740537 0.672015i \(-0.234571\pi\)
−0.996994 + 0.0774824i \(0.975312\pi\)
\(42\) 0 0
\(43\) 5.59352 2.80917i 0.853003 0.428394i 0.0321157 0.999484i \(-0.489775\pi\)
0.820888 + 0.571090i \(0.193479\pi\)
\(44\) −1.70983 9.69693i −0.257767 1.46187i
\(45\) 0 0
\(46\) 2.54785 14.4496i 0.375660 2.13048i
\(47\) −2.38036 7.95094i −0.347210 1.15976i −0.936154 0.351590i \(-0.885641\pi\)
0.588944 0.808174i \(-0.299544\pi\)
\(48\) 0 0
\(49\) −4.70641 2.36365i −0.672345 0.337664i
\(50\) −7.73125 + 25.8242i −1.09336 + 3.65209i
\(51\) 0 0
\(52\) 3.14588 + 4.22565i 0.436256 + 0.585993i
\(53\) 5.79529 + 10.0377i 0.796044 + 1.37879i 0.922174 + 0.386775i \(0.126411\pi\)
−0.126130 + 0.992014i \(0.540256\pi\)
\(54\) 0 0
\(55\) 4.90304 8.49231i 0.661125 1.14510i
\(56\) 6.46377 0.755507i 0.863758 0.100959i
\(57\) 0 0
\(58\) 13.2268 3.13482i 1.73677 0.411622i
\(59\) −8.15031 + 5.36055i −1.06108 + 0.697884i −0.955040 0.296478i \(-0.904188\pi\)
−0.106041 + 0.994362i \(0.533817\pi\)
\(60\) 0 0
\(61\) 2.93311 3.10891i 0.375546 0.398055i −0.511842 0.859080i \(-0.671037\pi\)
0.887387 + 0.461025i \(0.152518\pi\)
\(62\) −2.42172 2.03206i −0.307558 0.258072i
\(63\) 0 0
\(64\) −5.98568 + 5.02258i −0.748210 + 0.627823i
\(65\) −0.305054 + 5.23757i −0.0378372 + 0.649640i
\(66\) 0 0
\(67\) −0.791752 + 1.06351i −0.0967278 + 0.129928i −0.847852 0.530233i \(-0.822105\pi\)
0.751124 + 0.660161i \(0.229512\pi\)
\(68\) 1.07557 + 0.125716i 0.130432 + 0.0152453i
\(69\) 0 0
\(70\) 10.7884 + 7.09563i 1.28946 + 0.848090i
\(71\) −7.40721 2.69600i −0.879074 0.319957i −0.137238 0.990538i \(-0.543823\pi\)
−0.741836 + 0.670581i \(0.766045\pi\)
\(72\) 0 0
\(73\) −8.12155 + 2.95600i −0.950556 + 0.345974i −0.770326 0.637650i \(-0.779906\pi\)
−0.180230 + 0.983624i \(0.557684\pi\)
\(74\) −0.115659 0.0274117i −0.0134451 0.00318654i
\(75\) 0 0
\(76\) −0.313243 5.37818i −0.0359315 0.616919i
\(77\) −2.21556 2.34836i −0.252486 0.267620i
\(78\) 0 0
\(79\) 2.07109 4.80133i 0.233016 0.540192i −0.761085 0.648653i \(-0.775333\pi\)
0.994101 + 0.108460i \(0.0345921\pi\)
\(80\) 16.3650 1.82967
\(81\) 0 0
\(82\) −10.1684 −1.12291
\(83\) 2.24944 5.21479i 0.246908 0.572398i −0.749020 0.662548i \(-0.769475\pi\)
0.995928 + 0.0901496i \(0.0287345\pi\)
\(84\) 0 0
\(85\) 0.740074 + 0.784433i 0.0802723 + 0.0850837i
\(86\) −0.892623 15.3257i −0.0962540 1.65262i
\(87\) 0 0
\(88\) −11.7944 2.79532i −1.25729 0.297982i
\(89\) 8.61170 3.13440i 0.912838 0.332246i 0.157453 0.987527i \(-0.449672\pi\)
0.755385 + 0.655281i \(0.227450\pi\)
\(90\) 0 0
\(91\) 1.62316 + 0.590783i 0.170154 + 0.0619309i
\(92\) −20.0696 13.2000i −2.09240 1.37619i
\(93\) 0 0
\(94\) −20.2182 2.36317i −2.08535 0.243742i
\(95\) 3.20385 4.30352i 0.328708 0.441532i
\(96\) 0 0
\(97\) −0.721447 + 12.3868i −0.0732518 + 1.25769i 0.738729 + 0.674002i \(0.235426\pi\)
−0.811981 + 0.583684i \(0.801611\pi\)
\(98\) −9.89500 + 8.30289i −0.999546 + 0.838719i
\(99\) 0 0
\(100\) 33.8076 + 28.3679i 3.38076 + 2.83679i
\(101\) 8.54489 9.05705i 0.850248 0.901211i −0.145864 0.989305i \(-0.546596\pi\)
0.996112 + 0.0880941i \(0.0280776\pi\)
\(102\) 0 0
\(103\) 5.22232 3.43478i 0.514571 0.338439i −0.265519 0.964106i \(-0.585543\pi\)
0.780090 + 0.625667i \(0.215173\pi\)
\(104\) 6.31023 1.49555i 0.618769 0.146651i
\(105\) 0 0
\(106\) 28.2351 3.30021i 2.74244 0.320545i
\(107\) 9.92075 17.1832i 0.959075 1.66117i 0.234320 0.972159i \(-0.424714\pi\)
0.724755 0.689007i \(-0.241953\pi\)
\(108\) 0 0
\(109\) −1.91684 3.32007i −0.183600 0.318005i 0.759504 0.650503i \(-0.225442\pi\)
−0.943104 + 0.332498i \(0.892109\pi\)
\(110\) −14.3620 19.2915i −1.36937 1.83938i
\(111\) 0 0
\(112\) 1.54530 5.16165i 0.146017 0.487730i
\(113\) 3.11864 + 1.56624i 0.293377 + 0.147339i 0.589400 0.807841i \(-0.299364\pi\)
−0.296023 + 0.955181i \(0.595661\pi\)
\(114\) 0 0
\(115\) −6.86111 22.9177i −0.639802 2.13709i
\(116\) 3.86445 21.9164i 0.358805 2.03488i
\(117\) 0 0
\(118\) 4.15466 + 23.5622i 0.382467 + 2.16908i
\(119\) 0.317299 0.159353i 0.0290867 0.0146079i
\(120\) 0 0
\(121\) −1.97511 4.57883i −0.179556 0.416257i
\(122\) −4.15207 9.62557i −0.375910 0.871458i
\(123\) 0 0
\(124\) −4.62511 + 2.32282i −0.415347 + 0.208595i
\(125\) 4.16009 + 23.5930i 0.372090 + 2.11022i
\(126\) 0 0
\(127\) 2.28154 12.9392i 0.202454 1.14817i −0.698943 0.715177i \(-0.746346\pi\)
0.901397 0.432994i \(-0.142543\pi\)
\(128\) 5.58314 + 18.6490i 0.493484 + 1.64835i
\(129\) 0 0
\(130\) 11.4989 + 5.77495i 1.00852 + 0.506496i
\(131\) −1.24215 + 4.14908i −0.108528 + 0.362507i −0.994950 0.100369i \(-0.967998\pi\)
0.886423 + 0.462877i \(0.153183\pi\)
\(132\) 0 0
\(133\) −1.05483 1.41689i −0.0914656 0.122860i
\(134\) 1.62592 + 2.81618i 0.140458 + 0.243281i
\(135\) 0 0
\(136\) 0.666523 1.15445i 0.0571539 0.0989935i
\(137\) 22.2688 2.60285i 1.90255 0.222376i 0.917887 0.396841i \(-0.129894\pi\)
0.984663 + 0.174465i \(0.0558195\pi\)
\(138\) 0 0
\(139\) −9.34045 + 2.21373i −0.792247 + 0.187766i −0.606765 0.794882i \(-0.707533\pi\)
−0.185482 + 0.982648i \(0.559385\pi\)
\(140\) 17.6624 11.6168i 1.49275 0.981795i
\(141\) 0 0
\(142\) −13.2671 + 14.0623i −1.11335 + 1.18008i
\(143\) −2.46456 2.06801i −0.206097 0.172936i
\(144\) 0 0
\(145\) 16.9779 14.2461i 1.40994 1.18308i
\(146\) −1.23252 + 21.1616i −0.102004 + 1.75135i
\(147\) 0 0
\(148\) −0.116206 + 0.156092i −0.00955211 + 0.0128307i
\(149\) 16.5311 + 1.93221i 1.35428 + 0.158293i 0.762071 0.647493i \(-0.224182\pi\)
0.592208 + 0.805785i \(0.298257\pi\)
\(150\) 0 0
\(151\) 1.53093 + 1.00691i 0.124585 + 0.0819412i 0.610272 0.792192i \(-0.291060\pi\)
−0.485687 + 0.874133i \(0.661430\pi\)
\(152\) −6.23183 2.26820i −0.505468 0.183975i
\(153\) 0 0
\(154\) −7.44086 + 2.70825i −0.599601 + 0.218237i
\(155\) −5.01543 1.18868i −0.402849 0.0954770i
\(156\) 0 0
\(157\) 0.628412 + 10.7894i 0.0501528 + 0.861090i 0.925771 + 0.378085i \(0.123417\pi\)
−0.875618 + 0.483004i \(0.839546\pi\)
\(158\) −8.80086 9.32836i −0.700159 0.742125i
\(159\) 0 0
\(160\) 0.239641 0.555549i 0.0189453 0.0439200i
\(161\) −7.87629 −0.620738
\(162\) 0 0
\(163\) 3.76716 0.295067 0.147533 0.989057i \(-0.452867\pi\)
0.147533 + 0.989057i \(0.452867\pi\)
\(164\) −6.59372 + 15.2860i −0.514883 + 1.19363i
\(165\) 0 0
\(166\) −9.55873 10.1317i −0.741901 0.786369i
\(167\) 0.688138 + 11.8149i 0.0532498 + 0.914263i 0.914121 + 0.405441i \(0.132882\pi\)
−0.860872 + 0.508822i \(0.830081\pi\)
\(168\) 0 0
\(169\) −10.9747 2.60105i −0.844206 0.200081i
\(170\) 2.48551 0.904650i 0.190630 0.0693835i
\(171\) 0 0
\(172\) −23.6176 8.59612i −1.80083 0.655448i
\(173\) −7.99384 5.25763i −0.607761 0.399730i 0.207993 0.978130i \(-0.433307\pi\)
−0.815753 + 0.578400i \(0.803677\pi\)
\(174\) 0 0
\(175\) 14.3726 + 1.67992i 1.08647 + 0.126990i
\(176\) −5.99277 + 8.04968i −0.451722 + 0.606768i
\(177\) 0 0
\(178\) 1.30691 22.4387i 0.0979569 1.68185i
\(179\) 1.08723 0.912294i 0.0812633 0.0681880i −0.601251 0.799060i \(-0.705331\pi\)
0.682514 + 0.730872i \(0.260886\pi\)
\(180\) 0 0
\(181\) −7.58350 6.36331i −0.563677 0.472981i 0.315864 0.948804i \(-0.397706\pi\)
−0.879541 + 0.475823i \(0.842150\pi\)
\(182\) 2.90726 3.08152i 0.215501 0.228417i
\(183\) 0 0
\(184\) −24.7057 + 16.2492i −1.82133 + 1.19791i
\(185\) −0.188576 + 0.0446932i −0.0138644 + 0.00328591i
\(186\) 0 0
\(187\) −0.656860 + 0.0767759i −0.0480343 + 0.00561441i
\(188\) −16.6630 + 28.8611i −1.21527 + 2.10491i
\(189\) 0 0
\(190\) −6.57936 11.3958i −0.477317 0.826737i
\(191\) 10.6439 + 14.2973i 0.770166 + 1.03451i 0.998147 + 0.0608474i \(0.0193803\pi\)
−0.227981 + 0.973666i \(0.573212\pi\)
\(192\) 0 0
\(193\) −7.92466 + 26.4702i −0.570430 + 1.90537i −0.184533 + 0.982826i \(0.559077\pi\)
−0.385897 + 0.922542i \(0.626108\pi\)
\(194\) 27.1946 + 13.6577i 1.95246 + 0.980563i
\(195\) 0 0
\(196\) 6.06513 + 20.2589i 0.433223 + 1.44707i
\(197\) 1.04040 5.90042i 0.0741256 0.420387i −0.925052 0.379840i \(-0.875979\pi\)
0.999178 0.0405468i \(-0.0129100\pi\)
\(198\) 0 0
\(199\) 2.78863 + 15.8151i 0.197681 + 1.12110i 0.908549 + 0.417779i \(0.137191\pi\)
−0.710868 + 0.703326i \(0.751698\pi\)
\(200\) 48.5488 24.3821i 3.43292 1.72408i
\(201\) 0 0
\(202\) −12.0960 28.0418i −0.851074 1.97301i
\(203\) −2.89017 6.70017i −0.202850 0.470260i
\(204\) 0 0
\(205\) −14.8156 + 7.44067i −1.03477 + 0.519679i
\(206\) −2.66210 15.0975i −0.185478 1.05190i
\(207\) 0 0
\(208\) 0.932348 5.28761i 0.0646467 0.366630i
\(209\) 0.943600 + 3.15184i 0.0652701 + 0.218017i
\(210\) 0 0
\(211\) −9.00002 4.51998i −0.619587 0.311168i 0.111175 0.993801i \(-0.464539\pi\)
−0.730762 + 0.682633i \(0.760835\pi\)
\(212\) 13.3479 44.5852i 0.916740 3.06212i
\(213\) 0 0
\(214\) −29.0600 39.0343i −1.98650 2.66833i
\(215\) −12.5151 21.6767i −0.853520 1.47834i
\(216\) 0 0
\(217\) −0.848510 + 1.46966i −0.0576006 + 0.0997672i
\(218\) −9.33901 + 1.09157i −0.632518 + 0.0739307i
\(219\) 0 0
\(220\) −38.3136 + 9.08049i −2.58310 + 0.612206i
\(221\) 0.295617 0.194430i 0.0198853 0.0130788i
\(222\) 0 0
\(223\) 8.95026 9.48672i 0.599354 0.635278i −0.354676 0.934989i \(-0.615409\pi\)
0.954030 + 0.299711i \(0.0968903\pi\)
\(224\) −0.152596 0.128043i −0.0101957 0.00855525i
\(225\) 0 0
\(226\) 6.55678 5.50179i 0.436151 0.365974i
\(227\) 0.947304 16.2646i 0.0628748 1.07952i −0.808372 0.588673i \(-0.799651\pi\)
0.871246 0.490846i \(-0.163312\pi\)
\(228\) 0 0
\(229\) −4.02339 + 5.40434i −0.265873 + 0.357129i −0.914931 0.403609i \(-0.867756\pi\)
0.649059 + 0.760738i \(0.275163\pi\)
\(230\) −58.2767 6.81156i −3.84265 0.449141i
\(231\) 0 0
\(232\) −22.8885 15.0540i −1.50270 0.988343i
\(233\) 12.9692 + 4.72040i 0.849641 + 0.309244i 0.729894 0.683560i \(-0.239569\pi\)
0.119747 + 0.992804i \(0.461792\pi\)
\(234\) 0 0
\(235\) −31.1875 + 11.3513i −2.03445 + 0.740479i
\(236\) 38.1147 + 9.03334i 2.48105 + 0.588020i
\(237\) 0 0
\(238\) −0.0506351 0.869371i −0.00328218 0.0563529i
\(239\) 8.60415 + 9.11986i 0.556556 + 0.589915i 0.943163 0.332330i \(-0.107835\pi\)
−0.386607 + 0.922244i \(0.626353\pi\)
\(240\) 0 0
\(241\) 5.42266 12.5711i 0.349304 0.809778i −0.649475 0.760383i \(-0.725011\pi\)
0.998779 0.0493949i \(-0.0157293\pi\)
\(242\) −12.2304 −0.786199
\(243\) 0 0
\(244\) −17.1623 −1.09870
\(245\) −8.34163 + 19.3381i −0.532927 + 1.23546i
\(246\) 0 0
\(247\) −1.20796 1.28036i −0.0768604 0.0814672i
\(248\) 0.370454 + 6.36044i 0.0235238 + 0.403889i
\(249\) 0 0
\(250\) 57.1737 + 13.5504i 3.61598 + 0.857003i
\(251\) 12.4879 4.54521i 0.788226 0.286891i 0.0836277 0.996497i \(-0.473349\pi\)
0.704599 + 0.709606i \(0.251127\pi\)
\(252\) 0 0
\(253\) 13.7853 + 5.01745i 0.866676 + 0.315444i
\(254\) −26.9233 17.7077i −1.68932 1.11108i
\(255\) 0 0
\(256\) 31.9000 + 3.72858i 1.99375 + 0.233036i
\(257\) 2.00787 2.69704i 0.125248 0.168237i −0.735076 0.677984i \(-0.762854\pi\)
0.860324 + 0.509747i \(0.170261\pi\)
\(258\) 0 0
\(259\) −0.00371001 + 0.0636984i −0.000230529 + 0.00395803i
\(260\) 16.1378 13.5412i 1.00082 0.839790i
\(261\) 0 0
\(262\) 8.13723 + 6.82794i 0.502720 + 0.421832i
\(263\) −16.7605 + 17.7651i −1.03350 + 1.09544i −0.0381328 + 0.999273i \(0.512141\pi\)
−0.995365 + 0.0961708i \(0.969340\pi\)
\(264\) 0 0
\(265\) 38.7242 25.4693i 2.37881 1.56457i
\(266\) −4.21558 + 0.999112i −0.258474 + 0.0612595i
\(267\) 0 0
\(268\) 5.28783 0.618059i 0.323006 0.0377539i
\(269\) −0.417322 + 0.722824i −0.0254446 + 0.0440713i −0.878467 0.477802i \(-0.841433\pi\)
0.853023 + 0.521874i \(0.174767\pi\)
\(270\) 0 0
\(271\) 14.1085 + 24.4366i 0.857029 + 1.48442i 0.874750 + 0.484575i \(0.161026\pi\)
−0.0177208 + 0.999843i \(0.505641\pi\)
\(272\) −0.659069 0.885283i −0.0399619 0.0536782i
\(273\) 0 0
\(274\) 15.7710 52.6787i 0.952758 3.18243i
\(275\) −24.0853 12.0961i −1.45240 0.729422i
\(276\) 0 0
\(277\) 7.69228 + 25.6940i 0.462185 + 1.54380i 0.798465 + 0.602042i \(0.205646\pi\)
−0.336280 + 0.941762i \(0.609169\pi\)
\(278\) −4.08824 + 23.1856i −0.245196 + 1.39058i
\(279\) 0 0
\(280\) −4.51897 25.6284i −0.270060 1.53159i
\(281\) −13.0781 + 6.56809i −0.780177 + 0.391819i −0.793871 0.608087i \(-0.791937\pi\)
0.0136939 + 0.999906i \(0.495641\pi\)
\(282\) 0 0
\(283\) 0.462413 + 1.07199i 0.0274876 + 0.0637234i 0.931407 0.363980i \(-0.118582\pi\)
−0.903919 + 0.427703i \(0.859323\pi\)
\(284\) 12.5365 + 29.0629i 0.743905 + 1.72456i
\(285\) 0 0
\(286\) −7.05141 + 3.54135i −0.416959 + 0.209405i
\(287\) 0.947854 + 5.37555i 0.0559500 + 0.317308i
\(288\) 0 0
\(289\) −2.93939 + 16.6701i −0.172905 + 0.980594i
\(290\) −15.5899 52.0740i −0.915473 3.05789i
\(291\) 0 0
\(292\) 31.0125 + 15.5751i 1.81487 + 0.911463i
\(293\) 4.79954 16.0316i 0.280392 0.936575i −0.695538 0.718490i \(-0.744834\pi\)
0.975930 0.218085i \(-0.0699811\pi\)
\(294\) 0 0
\(295\) 23.2949 + 31.2905i 1.35628 + 1.82180i
\(296\) 0.119776 + 0.207458i 0.00696184 + 0.0120583i
\(297\) 0 0
\(298\) 20.4103 35.3516i 1.18234 2.04786i
\(299\) −7.79569 + 0.911186i −0.450837 + 0.0526952i
\(300\) 0 0
\(301\) −8.01876 + 1.90048i −0.462194 + 0.109542i
\(302\) 3.75480 2.46957i 0.216064 0.142108i
\(303\) 0 0
\(304\) −3.76793 + 3.99377i −0.216105 + 0.229058i
\(305\) −13.0931 10.9864i −0.749707 0.629079i
\(306\) 0 0
\(307\) −15.6362 + 13.1204i −0.892407 + 0.748818i −0.968691 0.248268i \(-0.920139\pi\)
0.0762844 + 0.997086i \(0.475694\pi\)
\(308\) −0.753776 + 12.9418i −0.0429504 + 0.737429i
\(309\) 0 0
\(310\) −7.54912 + 10.1402i −0.428761 + 0.575926i
\(311\) 6.59097 + 0.770374i 0.373740 + 0.0436839i 0.300889 0.953659i \(-0.402716\pi\)
0.0728501 + 0.997343i \(0.476791\pi\)
\(312\) 0 0
\(313\) 7.66936 + 5.04422i 0.433498 + 0.285116i 0.747444 0.664325i \(-0.231281\pi\)
−0.313946 + 0.949441i \(0.601651\pi\)
\(314\) 24.9087 + 9.06601i 1.40568 + 0.511625i
\(315\) 0 0
\(316\) −19.7300 + 7.18114i −1.10990 + 0.403971i
\(317\) −0.0487426 0.0115522i −0.00273766 0.000648836i 0.229247 0.973368i \(-0.426374\pi\)
−0.231984 + 0.972719i \(0.574522\pi\)
\(318\) 0 0
\(319\) 0.790245 + 13.5680i 0.0442452 + 0.759661i
\(320\) 21.4424 + 22.7276i 1.19867 + 1.27051i
\(321\) 0 0
\(322\) −7.65130 + 17.7377i −0.426390 + 0.988483i
\(323\) −0.361832 −0.0201329
\(324\) 0 0
\(325\) 14.4199 0.799874
\(326\) 3.65955 8.48379i 0.202684 0.469874i
\(327\) 0 0
\(328\) 14.0632 + 14.9061i 0.776510 + 0.823053i
\(329\) 0.635356 + 10.9086i 0.0350283 + 0.601413i
\(330\) 0 0
\(331\) −18.0022 4.26660i −0.989491 0.234514i −0.296164 0.955137i \(-0.595708\pi\)
−0.693327 + 0.720623i \(0.743856\pi\)
\(332\) −21.4290 + 7.79954i −1.17607 + 0.428055i
\(333\) 0 0
\(334\) 27.2761 + 9.92767i 1.49248 + 0.543218i
\(335\) 4.42972 + 2.91347i 0.242022 + 0.159180i
\(336\) 0 0
\(337\) 3.62501 + 0.423702i 0.197467 + 0.0230805i 0.214251 0.976779i \(-0.431269\pi\)
−0.0167846 + 0.999859i \(0.505343\pi\)
\(338\) −16.5188 + 22.1887i −0.898507 + 1.20690i
\(339\) 0 0
\(340\) 0.251787 4.32302i 0.0136551 0.234449i
\(341\) 2.42131 2.03172i 0.131121 0.110024i
\(342\) 0 0
\(343\) 12.3716 + 10.3810i 0.668005 + 0.560523i
\(344\) −21.2318 + 22.5044i −1.14474 + 1.21336i
\(345\) 0 0
\(346\) −19.6059 + 12.8950i −1.05402 + 0.693239i
\(347\) −3.98981 + 0.945603i −0.214184 + 0.0507626i −0.336307 0.941752i \(-0.609178\pi\)
0.122123 + 0.992515i \(0.461030\pi\)
\(348\) 0 0
\(349\) −7.51393 + 0.878252i −0.402211 + 0.0470118i −0.314794 0.949160i \(-0.601935\pi\)
−0.0874174 + 0.996172i \(0.527861\pi\)
\(350\) 17.7453 30.7358i 0.948528 1.64290i
\(351\) 0 0
\(352\) 0.185511 + 0.321314i 0.00988775 + 0.0171261i
\(353\) −1.22443 1.64470i −0.0651699 0.0875384i 0.768343 0.640038i \(-0.221081\pi\)
−0.833513 + 0.552500i \(0.813674\pi\)
\(354\) 0 0
\(355\) −9.04045 + 30.1972i −0.479817 + 1.60270i
\(356\) −32.8842 16.5150i −1.74286 0.875296i
\(357\) 0 0
\(358\) −0.998349 3.33472i −0.0527644 0.176245i
\(359\) 1.74531 9.89817i 0.0921141 0.522405i −0.903479 0.428631i \(-0.858996\pi\)
0.995594 0.0937737i \(-0.0298930\pi\)
\(360\) 0 0
\(361\) −2.98674 16.9386i −0.157197 0.891506i
\(362\) −21.6973 + 10.8968i −1.14038 + 0.572722i
\(363\) 0 0
\(364\) −2.74716 6.36863i −0.143990 0.333807i
\(365\) 13.6890 + 31.7348i 0.716517 + 1.66107i
\(366\) 0 0
\(367\) 29.0225 14.5756i 1.51496 0.760842i 0.519363 0.854554i \(-0.326169\pi\)
0.995599 + 0.0937115i \(0.0298731\pi\)
\(368\) 4.25131 + 24.1104i 0.221615 + 1.25684i
\(369\) 0 0
\(370\) −0.0825380 + 0.468096i −0.00429095 + 0.0243352i
\(371\) −4.37661 14.6189i −0.227222 0.758975i
\(372\) 0 0
\(373\) 13.4959 + 6.77789i 0.698791 + 0.350946i 0.762469 0.647024i \(-0.223987\pi\)
−0.0636783 + 0.997970i \(0.520283\pi\)
\(374\) −0.465194 + 1.55386i −0.0240546 + 0.0803480i
\(375\) 0 0
\(376\) 24.4981 + 32.9066i 1.26339 + 1.69703i
\(377\) −3.63572 6.29725i −0.187249 0.324325i
\(378\) 0 0
\(379\) 1.32973 2.30316i 0.0683037 0.118305i −0.829851 0.557985i \(-0.811575\pi\)
0.898155 + 0.439680i \(0.144908\pi\)
\(380\) −21.3974 + 2.50100i −1.09766 + 0.128298i
\(381\) 0 0
\(382\) 42.5378 10.0817i 2.17643 0.515822i
\(383\) −1.29846 + 0.854009i −0.0663481 + 0.0436378i −0.582250 0.813010i \(-0.697827\pi\)
0.515902 + 0.856648i \(0.327457\pi\)
\(384\) 0 0
\(385\) −8.85973 + 9.39076i −0.451534 + 0.478598i
\(386\) 51.9137 + 43.5607i 2.64234 + 2.21718i
\(387\) 0 0
\(388\) 38.1656 32.0247i 1.93757 1.62581i
\(389\) −0.213782 + 3.67050i −0.0108392 + 0.186102i 0.988543 + 0.150943i \(0.0482308\pi\)
−0.999382 + 0.0351591i \(0.988806\pi\)
\(390\) 0 0
\(391\) −0.963439 + 1.29412i −0.0487232 + 0.0654466i
\(392\) 25.8564 + 3.02218i 1.30595 + 0.152643i
\(393\) 0 0
\(394\) −12.2773 8.07490i −0.618521 0.406807i
\(395\) −19.6490 7.15164i −0.988647 0.359838i
\(396\) 0 0
\(397\) 36.1674 13.1638i 1.81519 0.660674i 0.818965 0.573844i \(-0.194548\pi\)
0.996223 0.0868301i \(-0.0276737\pi\)
\(398\) 38.3252 + 9.08325i 1.92107 + 0.455302i
\(399\) 0 0
\(400\) −2.61533 44.9034i −0.130766 2.24517i
\(401\) 12.2187 + 12.9510i 0.610171 + 0.646743i 0.956625 0.291324i \(-0.0940957\pi\)
−0.346454 + 0.938067i \(0.612614\pi\)
\(402\) 0 0
\(403\) −0.669806 + 1.55279i −0.0333654 + 0.0773498i
\(404\) −49.9982 −2.48750
\(405\) 0 0
\(406\) −17.8966 −0.888196
\(407\) 0.0470713 0.109124i 0.00233324 0.00540905i
\(408\) 0 0
\(409\) 12.5796 + 13.3336i 0.622022 + 0.659305i 0.959395 0.282066i \(-0.0910198\pi\)
−0.337373 + 0.941371i \(0.609538\pi\)
\(410\) 2.36430 + 40.5934i 0.116764 + 2.00477i
\(411\) 0 0
\(412\) −24.4220 5.78812i −1.20319 0.285160i
\(413\) 12.0689 4.39273i 0.593873 0.216152i
\(414\) 0 0
\(415\) −21.3410 7.76749i −1.04759 0.381291i
\(416\) −0.165848 0.109080i −0.00813134 0.00534807i
\(417\) 0 0
\(418\) 8.01472 + 0.936786i 0.392013 + 0.0458197i
\(419\) 7.45896 10.0191i 0.364394 0.489466i −0.581680 0.813418i \(-0.697604\pi\)
0.946074 + 0.323952i \(0.105012\pi\)
\(420\) 0 0
\(421\) −1.25709 + 21.5834i −0.0612668 + 1.05191i 0.817889 + 0.575376i \(0.195144\pi\)
−0.879156 + 0.476534i \(0.841893\pi\)
\(422\) −18.9221 + 15.8775i −0.921114 + 0.772906i
\(423\) 0 0
\(424\) −43.8878 36.8262i −2.13138 1.78844i
\(425\) 2.03410 2.15602i 0.0986685 0.104583i
\(426\) 0 0
\(427\) −4.70153 + 3.09224i −0.227523 + 0.149644i
\(428\) −77.5233 + 18.3734i −3.74723 + 0.888110i
\(429\) 0 0
\(430\) −60.9744 + 7.12688i −2.94045 + 0.343689i
\(431\) −15.5400 + 26.9162i −0.748538 + 1.29651i 0.199986 + 0.979799i \(0.435910\pi\)
−0.948524 + 0.316707i \(0.897423\pi\)
\(432\) 0 0
\(433\) −6.64480 11.5091i −0.319329 0.553093i 0.661019 0.750369i \(-0.270124\pi\)
−0.980348 + 0.197275i \(0.936791\pi\)
\(434\) 2.48546 + 3.33856i 0.119306 + 0.160256i
\(435\) 0 0
\(436\) −4.41495 + 14.7469i −0.211438 + 0.706251i
\(437\) 7.17262 + 3.60223i 0.343113 + 0.172318i
\(438\) 0 0
\(439\) 0.367842 + 1.22868i 0.0175562 + 0.0586417i 0.966319 0.257348i \(-0.0828487\pi\)
−0.948763 + 0.315990i \(0.897663\pi\)
\(440\) −8.41685 + 47.7343i −0.401258 + 2.27564i
\(441\) 0 0
\(442\) −0.150692 0.854617i −0.00716769 0.0406500i
\(443\) 34.9439 17.5495i 1.66023 0.833800i 0.663939 0.747787i \(-0.268884\pi\)
0.996294 0.0860134i \(-0.0274128\pi\)
\(444\) 0 0
\(445\) −14.5152 33.6500i −0.688086 1.59516i
\(446\) −12.6699 29.3721i −0.599936 1.39081i
\(447\) 0 0
\(448\) 9.19320 4.61700i 0.434338 0.218133i
\(449\) 2.78437 + 15.7909i 0.131403 + 0.745221i 0.977298 + 0.211871i \(0.0679558\pi\)
−0.845895 + 0.533349i \(0.820933\pi\)
\(450\) 0 0
\(451\) 1.76543 10.0123i 0.0831310 0.471459i
\(452\) −4.01897 13.4243i −0.189036 0.631426i
\(453\) 0 0
\(454\) −35.7082 17.9333i −1.67587 0.841654i
\(455\) 1.98106 6.61720i 0.0928735 0.310219i
\(456\) 0 0
\(457\) −2.30852 3.10088i −0.107988 0.145053i 0.744844 0.667239i \(-0.232524\pi\)
−0.852832 + 0.522186i \(0.825117\pi\)
\(458\) 8.26234 + 14.3108i 0.386074 + 0.668699i
\(459\) 0 0
\(460\) −48.0292 + 83.1890i −2.23937 + 3.87871i
\(461\) −21.0874 + 2.46477i −0.982140 + 0.114796i −0.591981 0.805952i \(-0.701654\pi\)
−0.390159 + 0.920748i \(0.627580\pi\)
\(462\) 0 0
\(463\) 18.7929 4.45400i 0.873381 0.206995i 0.230603 0.973048i \(-0.425930\pi\)
0.642778 + 0.766053i \(0.277782\pi\)
\(464\) −18.9501 + 12.4637i −0.879738 + 0.578613i
\(465\) 0 0
\(466\) 23.2293 24.6216i 1.07607 1.14057i
\(467\) 3.15564 + 2.64790i 0.146026 + 0.122530i 0.712874 0.701292i \(-0.247393\pi\)
−0.566848 + 0.823822i \(0.691838\pi\)
\(468\) 0 0
\(469\) 1.33722 1.12206i 0.0617469 0.0518118i
\(470\) −4.73300 + 81.2625i −0.218317 + 3.74836i
\(471\) 0 0
\(472\) 28.7944 38.6776i 1.32537 1.78028i
\(473\) 15.2453 + 1.78193i 0.700982 + 0.0819330i
\(474\) 0 0
\(475\) −12.3203 8.10318i −0.565293 0.371799i
\(476\) −1.33974 0.487625i −0.0614068 0.0223503i
\(477\) 0 0
\(478\) 28.8966 10.5175i 1.32170 0.481060i
\(479\) −27.9772 6.63072i −1.27831 0.302966i −0.465269 0.885169i \(-0.654042\pi\)
−0.813043 + 0.582204i \(0.802191\pi\)
\(480\) 0 0
\(481\) 0.00369705 + 0.0634758i 0.000168571 + 0.00289425i
\(482\) −23.0429 24.4241i −1.04958 1.11249i
\(483\) 0 0
\(484\) −7.93080 + 18.3857i −0.360491 + 0.835712i
\(485\) 49.6170 2.25299
\(486\) 0 0
\(487\) 8.88765 0.402738 0.201369 0.979515i \(-0.435461\pi\)
0.201369 + 0.979515i \(0.435461\pi\)
\(488\) −8.36792 + 19.3990i −0.378798 + 0.878153i
\(489\) 0 0
\(490\) 35.4467 + 37.5713i 1.60132 + 1.69730i
\(491\) −1.63971 28.1528i −0.0739991 1.27052i −0.807108 0.590404i \(-0.798968\pi\)
0.733108 0.680112i \(-0.238069\pi\)
\(492\) 0 0
\(493\) −1.45441 0.344701i −0.0655033 0.0155246i
\(494\) −4.05686 + 1.47658i −0.182527 + 0.0664344i
\(495\) 0 0
\(496\) 4.95683 + 1.80414i 0.222568 + 0.0810082i
\(497\) 8.67076 + 5.70285i 0.388937 + 0.255808i
\(498\) 0 0
\(499\) −1.18198 0.138153i −0.0529126 0.00618460i 0.0895954 0.995978i \(-0.471443\pi\)
−0.142508 + 0.989794i \(0.545517\pi\)
\(500\) 57.4443 77.1611i 2.56899 3.45075i
\(501\) 0 0
\(502\) 1.89515 32.5385i 0.0845848 1.45226i
\(503\) −4.59276 + 3.85379i −0.204781 + 0.171832i −0.739411 0.673255i \(-0.764896\pi\)
0.534629 + 0.845087i \(0.320451\pi\)
\(504\) 0 0
\(505\) −38.1435 32.0062i −1.69736 1.42426i
\(506\) 24.6910 26.1710i 1.09765 1.16344i
\(507\) 0 0
\(508\) −44.0780 + 28.9906i −1.95565 + 1.28625i
\(509\) −24.4578 + 5.79659i −1.08407 + 0.256929i −0.733557 0.679628i \(-0.762141\pi\)
−0.350514 + 0.936558i \(0.613993\pi\)
\(510\) 0 0
\(511\) 11.3020 1.32101i 0.499971 0.0584382i
\(512\) 19.9189 34.5006i 0.880300 1.52473i
\(513\) 0 0
\(514\) −4.12333 7.14181i −0.181872 0.315012i
\(515\) −14.9262 20.0494i −0.657729 0.883483i
\(516\) 0 0
\(517\) 5.83713 19.4974i 0.256717 0.857494i
\(518\) 0.139847 + 0.0702339i 0.00614454 + 0.00308590i
\(519\) 0 0
\(520\) −7.43761 24.8433i −0.326161 1.08945i
\(521\) 5.84968 33.1752i 0.256279 1.45343i −0.536488 0.843908i \(-0.680250\pi\)
0.792768 0.609524i \(-0.208639\pi\)
\(522\) 0 0
\(523\) 4.18478 + 23.7331i 0.182988 + 1.03778i 0.928513 + 0.371299i \(0.121087\pi\)
−0.745526 + 0.666477i \(0.767801\pi\)
\(524\) 15.5409 7.80492i 0.678906 0.340960i
\(525\) 0 0
\(526\) 23.7260 + 55.0030i 1.03450 + 2.39824i
\(527\) 0.137684 + 0.319187i 0.00599759 + 0.0139040i
\(528\) 0 0
\(529\) 11.4284 5.73957i 0.496888 0.249547i
\(530\) −19.7398 111.950i −0.857443 4.86280i
\(531\) 0 0
\(532\) −1.23166 + 6.98506i −0.0533990 + 0.302841i
\(533\) 1.56004 + 5.21089i 0.0675727 + 0.225709i
\(534\) 0 0
\(535\) −70.9040 35.6093i −3.06545 1.53952i
\(536\) 1.87961 6.27833i 0.0811867 0.271183i
\(537\) 0 0
\(538\) 1.22243 + 1.64200i 0.0527025 + 0.0707918i
\(539\) −6.45742 11.1846i −0.278141 0.481754i
\(540\) 0 0
\(541\) −11.3703 + 19.6940i −0.488849 + 0.846712i −0.999918 0.0128282i \(-0.995917\pi\)
0.511068 + 0.859540i \(0.329250\pi\)
\(542\) 68.7376 8.03428i 2.95253 0.345102i
\(543\) 0 0
\(544\) −0.0397040 + 0.00941003i −0.00170230 + 0.000403452i
\(545\) −12.8084 + 8.42419i −0.548650 + 0.360853i
\(546\) 0 0
\(547\) −0.267245 + 0.283263i −0.0114266 + 0.0121115i −0.733062 0.680162i \(-0.761909\pi\)
0.721635 + 0.692274i \(0.243391\pi\)
\(548\) −68.9639 57.8676i −2.94599 2.47198i
\(549\) 0 0
\(550\) −50.6382 + 42.4905i −2.15922 + 1.81180i
\(551\) −0.432364 + 7.42340i −0.0184193 + 0.316247i
\(552\) 0 0
\(553\) −4.11107 + 5.52213i −0.174821 + 0.234825i
\(554\) 65.3365 + 7.63674i 2.77588 + 0.324454i
\(555\) 0 0
\(556\) 32.2033 + 21.1804i 1.36572 + 0.898250i
\(557\) −19.6611 7.15607i −0.833069 0.303212i −0.109951 0.993937i \(-0.535069\pi\)
−0.723118 + 0.690725i \(0.757292\pi\)
\(558\) 0 0
\(559\) −7.71685 + 2.80870i −0.326388 + 0.118795i
\(560\) −20.9652 4.96883i −0.885939 0.209971i
\(561\) 0 0
\(562\) 2.08703 + 35.8330i 0.0880361 + 1.51152i
\(563\) −9.51661 10.0870i −0.401077 0.425117i 0.495084 0.868845i \(-0.335137\pi\)
−0.896162 + 0.443728i \(0.853656\pi\)
\(564\) 0 0
\(565\) 5.52746 12.8141i 0.232542 0.539093i
\(566\) 2.86338 0.120357
\(567\) 0 0
\(568\) 38.9631 1.63485
\(569\) 3.68383 8.54007i 0.154434 0.358019i −0.823381 0.567489i \(-0.807915\pi\)
0.977815 + 0.209471i \(0.0671741\pi\)
\(570\) 0 0
\(571\) −24.7267 26.2088i −1.03478 1.09680i −0.995227 0.0975862i \(-0.968888\pi\)
−0.0395538 0.999217i \(-0.512594\pi\)
\(572\) 0.751142 + 12.8966i 0.0314068 + 0.539234i
\(573\) 0 0
\(574\) 13.0267 + 3.08739i 0.543725 + 0.128865i
\(575\) −61.7866 + 22.4885i −2.57668 + 0.937834i
\(576\) 0 0
\(577\) 8.15363 + 2.96768i 0.339440 + 0.123546i 0.506115 0.862466i \(-0.331081\pi\)
−0.166675 + 0.986012i \(0.553303\pi\)
\(578\) 34.6863 + 22.8135i 1.44276 + 0.948918i
\(579\) 0 0
\(580\) −88.3909 10.3314i −3.67023 0.428989i
\(581\) −4.46509 + 5.99766i −0.185243 + 0.248825i
\(582\) 0 0
\(583\) −1.65262 + 28.3745i −0.0684447 + 1.17515i
\(584\) 32.7259 27.4603i 1.35421 1.13631i
\(585\) 0 0
\(586\) −31.4413 26.3824i −1.29883 1.08985i
\(587\) 6.35311 6.73390i 0.262221 0.277938i −0.582864 0.812569i \(-0.698068\pi\)
0.845085 + 0.534632i \(0.179550\pi\)
\(588\) 0 0
\(589\) 1.44486 0.950296i 0.0595342 0.0391563i
\(590\) 93.0969 22.0644i 3.83274 0.908375i
\(591\) 0 0
\(592\) 0.196992 0.0230251i 0.00809633 0.000946325i
\(593\) −18.3119 + 31.7171i −0.751979 + 1.30247i 0.194884 + 0.980826i \(0.437567\pi\)
−0.946862 + 0.321639i \(0.895766\pi\)
\(594\) 0 0
\(595\) −0.709932 1.22964i −0.0291044 0.0504102i
\(596\) −39.9082 53.6060i −1.63470 2.19579i
\(597\) 0 0
\(598\) −5.52098 + 18.4414i −0.225770 + 0.754123i
\(599\) −22.1250 11.1116i −0.904001 0.454007i −0.0648441 0.997895i \(-0.520655\pi\)
−0.839157 + 0.543889i \(0.816951\pi\)
\(600\) 0 0
\(601\) −6.33556 21.1622i −0.258433 0.863226i −0.984467 0.175568i \(-0.943824\pi\)
0.726034 0.687658i \(-0.241361\pi\)
\(602\) −3.50974 + 19.9047i −0.143046 + 0.811257i
\(603\) 0 0
\(604\) −1.27765 7.24590i −0.0519867 0.294831i
\(605\) −17.8199 + 8.94950i −0.724482 + 0.363849i
\(606\) 0 0
\(607\) −3.79033 8.78698i −0.153845 0.356653i 0.823811 0.566865i \(-0.191844\pi\)
−0.977656 + 0.210212i \(0.932585\pi\)
\(608\) 0.0804024 + 0.186394i 0.00326075 + 0.00755927i
\(609\) 0 0
\(610\) −37.4609 + 18.8135i −1.51675 + 0.761738i
\(611\) 1.89085 + 10.7235i 0.0764954 + 0.433827i
\(612\) 0 0
\(613\) −2.38544 + 13.5285i −0.0963469 + 0.546410i 0.897979 + 0.440037i \(0.145035\pi\)
−0.994326 + 0.106373i \(0.966076\pi\)
\(614\) 14.3580 + 47.9590i 0.579441 + 1.93547i
\(615\) 0 0
\(616\) 14.2610 + 7.16214i 0.574592 + 0.288571i
\(617\) −3.90172 + 13.0327i −0.157077 + 0.524675i −0.999909 0.0135025i \(-0.995702\pi\)
0.842831 + 0.538178i \(0.180887\pi\)
\(618\) 0 0
\(619\) −8.51625 11.4393i −0.342297 0.459785i 0.597325 0.801999i \(-0.296230\pi\)
−0.939622 + 0.342215i \(0.888823\pi\)
\(620\) 10.3483 + 17.9238i 0.415599 + 0.719839i
\(621\) 0 0
\(622\) 8.13761 14.0947i 0.326288 0.565148i
\(623\) −11.9841 + 1.40074i −0.480132 + 0.0561194i
\(624\) 0 0
\(625\) 39.7451 9.41976i 1.58980 0.376790i
\(626\) 18.8101 12.3716i 0.751801 0.494467i
\(627\) 0 0
\(628\) 29.7807 31.5657i 1.18838 1.25961i
\(629\) 0.0100122 + 0.00840126i 0.000399214 + 0.000334980i
\(630\) 0 0
\(631\) −6.09157 + 5.11144i −0.242502 + 0.203483i −0.755935 0.654646i \(-0.772818\pi\)
0.513434 + 0.858129i \(0.328373\pi\)
\(632\) −1.50284 + 25.8027i −0.0597797 + 1.02638i
\(633\) 0 0
\(634\) −0.0733662 + 0.0985479i −0.00291374 + 0.00391384i
\(635\) −52.1852 6.09958i −2.07091 0.242054i
\(636\) 0 0
\(637\) 5.77297 + 3.79694i 0.228733 + 0.150440i
\(638\) 31.3233 + 11.4007i 1.24010 + 0.451360i
\(639\) 0 0
\(640\) 73.1505 26.6246i 2.89153 1.05243i
\(641\) −4.09023 0.969403i −0.161555 0.0382891i 0.149043 0.988831i \(-0.452381\pi\)
−0.310597 + 0.950542i \(0.600529\pi\)
\(642\) 0 0
\(643\) −1.11571 19.1561i −0.0439995 0.755442i −0.946092 0.323899i \(-0.895006\pi\)
0.902092 0.431543i \(-0.142031\pi\)
\(644\) 21.7032 + 23.0040i 0.855225 + 0.906486i
\(645\) 0 0
\(646\) −0.351496 + 0.814859i −0.0138294 + 0.0320602i
\(647\) 33.3755 1.31213 0.656063 0.754706i \(-0.272221\pi\)
0.656063 + 0.754706i \(0.272221\pi\)
\(648\) 0 0
\(649\) −23.9217 −0.939009
\(650\) 14.0080 32.4742i 0.549440 1.27374i
\(651\) 0 0
\(652\) −10.3804 11.0026i −0.406530 0.430896i
\(653\) 0.709166 + 12.1759i 0.0277518 + 0.476480i 0.983340 + 0.181775i \(0.0581844\pi\)
−0.955588 + 0.294705i \(0.904779\pi\)
\(654\) 0 0
\(655\) 16.8524 + 3.99409i 0.658477 + 0.156062i
\(656\) 15.9437 5.80302i 0.622496 0.226570i
\(657\) 0 0
\(658\) 25.1839 + 9.16619i 0.981770 + 0.357335i
\(659\) −19.5651 12.8682i −0.762148 0.501272i 0.107947 0.994157i \(-0.465572\pi\)
−0.870095 + 0.492884i \(0.835943\pi\)
\(660\) 0 0
\(661\) 33.4396 + 3.90853i 1.30065 + 0.152024i 0.738073 0.674721i \(-0.235736\pi\)
0.562577 + 0.826745i \(0.309810\pi\)
\(662\) −27.0965 + 36.3969i −1.05314 + 1.41461i
\(663\) 0 0
\(664\) −1.63225 + 28.0247i −0.0633437 + 1.08757i
\(665\) −5.41109 + 4.54045i −0.209833 + 0.176071i
\(666\) 0 0
\(667\) 25.3992 + 21.3124i 0.983460 + 0.825221i
\(668\) 32.6112 34.5658i 1.26176 1.33739i
\(669\) 0 0
\(670\) 10.8644 7.14565i 0.419730 0.276061i
\(671\) 10.1986 2.41712i 0.393713 0.0933118i
\(672\) 0 0
\(673\) 12.3262 1.44072i 0.475140 0.0555358i 0.124847 0.992176i \(-0.460156\pi\)
0.350293 + 0.936640i \(0.386082\pi\)
\(674\) 4.47565 7.75205i 0.172396 0.298598i
\(675\) 0 0
\(676\) 22.6440 + 39.2206i 0.870925 + 1.50849i
\(677\) 8.84021 + 11.8745i 0.339757 + 0.456373i 0.938860 0.344299i \(-0.111883\pi\)
−0.599103 + 0.800672i \(0.704476\pi\)
\(678\) 0 0
\(679\) 4.68517 15.6496i 0.179800 0.600575i
\(680\) −4.76367 2.39240i −0.182678 0.0917445i
\(681\) 0 0
\(682\) −2.22337 7.42657i −0.0851372 0.284378i
\(683\) −6.94875 + 39.4083i −0.265887 + 1.50792i 0.500612 + 0.865672i \(0.333108\pi\)
−0.766499 + 0.642246i \(0.778003\pi\)
\(684\) 0 0
\(685\) −15.5686 88.2941i −0.594847 3.37354i
\(686\) 35.3967 17.7769i 1.35145 0.678725i
\(687\) 0 0
\(688\) 10.1458 + 23.5207i 0.386807 + 0.896719i
\(689\) −6.02304 13.9630i −0.229460 0.531947i
\(690\) 0 0
\(691\) −35.1761 + 17.6661i −1.33816 + 0.672050i −0.966584 0.256351i \(-0.917480\pi\)
−0.371578 + 0.928402i \(0.621183\pi\)
\(692\) 6.67130 + 37.8348i 0.253605 + 1.43826i
\(693\) 0 0
\(694\) −1.74631 + 9.90380i −0.0662889 + 0.375943i
\(695\) 11.0092 + 36.7733i 0.417603 + 1.39489i
\(696\) 0 0
\(697\) 0.999178 + 0.501806i 0.0378466 + 0.0190073i
\(698\) −5.32143 + 17.7748i −0.201419 + 0.672787i
\(699\) 0 0
\(700\) −34.6975 46.6068i −1.31144 1.76157i
\(701\) 2.37301 + 4.11018i 0.0896274 + 0.155239i 0.907354 0.420368i \(-0.138099\pi\)
−0.817726 + 0.575607i \(0.804766\pi\)
\(702\) 0 0
\(703\) 0.0325111 0.0563108i 0.00122618 0.00212380i
\(704\) −19.0314 + 2.22445i −0.717273 + 0.0838372i
\(705\) 0 0
\(706\) −4.89337 + 1.15975i −0.184165 + 0.0436478i
\(707\) −13.6968 + 9.00850i −0.515120 + 0.338800i
\(708\) 0 0
\(709\) −0.249769 + 0.264740i −0.00938029 + 0.00994253i −0.732047 0.681254i \(-0.761435\pi\)
0.722667 + 0.691197i \(0.242916\pi\)
\(710\) 59.2231 + 49.6940i 2.22260 + 1.86498i
\(711\) 0 0
\(712\) −34.7009 + 29.1175i −1.30047 + 1.09123i
\(713\) 0.448356 7.69797i 0.0167911 0.288291i
\(714\) 0 0
\(715\) −7.68268 + 10.3196i −0.287316 + 0.385932i
\(716\) −5.66038 0.661604i −0.211538 0.0247253i
\(717\) 0 0
\(718\) −20.5956 13.5459i −0.768621 0.505530i
\(719\) 15.2471 + 5.54950i 0.568622 + 0.206961i 0.610301 0.792170i \(-0.291049\pi\)
−0.0416792 + 0.999131i \(0.513271\pi\)
\(720\) 0 0
\(721\) −7.73318 + 2.81465i −0.287998 + 0.104823i
\(722\) −41.0478 9.72852i −1.52764 0.362058i
\(723\) 0 0
\(724\) 2.31127 + 39.6830i 0.0858978 + 1.47481i
\(725\) −41.8027 44.3083i −1.55251 1.64557i
\(726\) 0 0
\(727\) −6.27054 + 14.5368i −0.232562 + 0.539138i −0.994035 0.109057i \(-0.965217\pi\)
0.761474 + 0.648196i \(0.224476\pi\)
\(728\) −8.53809 −0.316443
\(729\) 0 0
\(730\) 84.7659 3.13733
\(731\) −0.668605 + 1.55000i −0.0247293 + 0.0573289i
\(732\) 0 0
\(733\) −31.3546 33.2339i −1.15811 1.22752i −0.969399 0.245491i \(-0.921051\pi\)
−0.188710 0.982033i \(-0.560431\pi\)
\(734\) −4.63146 79.5191i −0.170950 2.93510i
\(735\) 0 0
\(736\) 0.880738 + 0.208739i 0.0324644 + 0.00769421i
\(737\) −3.05522 + 1.11201i −0.112541 + 0.0409614i
\(738\) 0 0
\(739\) −2.12852 0.774717i −0.0782987 0.0284984i 0.302574 0.953126i \(-0.402154\pi\)
−0.380873 + 0.924628i \(0.624376\pi\)
\(740\) 0.650156 + 0.427614i 0.0239002 + 0.0157194i
\(741\) 0 0
\(742\) −37.1739 4.34500i −1.36470 0.159510i
\(743\) 1.63022 2.18977i 0.0598071 0.0803349i −0.771213 0.636577i \(-0.780350\pi\)
0.831020 + 0.556242i \(0.187757\pi\)
\(744\) 0 0
\(745\) 3.86987 66.4430i 0.141781 2.43428i
\(746\) 28.3745 23.8090i 1.03886 0.871709i
\(747\) 0 0
\(748\) 2.03422 + 1.70691i 0.0743785 + 0.0624109i
\(749\) −17.9267 + 19.0012i −0.655027 + 0.694288i
\(750\) 0 0
\(751\) 36.0238 23.6932i 1.31453 0.864579i 0.318021 0.948084i \(-0.396982\pi\)
0.996507 + 0.0835052i \(0.0266115\pi\)
\(752\) 33.0499 7.83297i 1.20521 0.285639i
\(753\) 0 0
\(754\) −17.7135 + 2.07041i −0.645088 + 0.0754000i
\(755\) 3.66372 6.34576i 0.133337 0.230946i
\(756\) 0 0
\(757\) 19.3916 + 33.5873i 0.704800 + 1.22075i 0.966764 + 0.255672i \(0.0822968\pi\)
−0.261963 + 0.965078i \(0.584370\pi\)
\(758\) −3.89506 5.23198i −0.141475 0.190034i
\(759\) 0 0
\(760\) −7.60591 + 25.4055i −0.275895 + 0.921554i
\(761\) 38.7081 + 19.4400i 1.40317 + 0.704698i 0.979561 0.201147i \(-0.0644670\pi\)
0.423608 + 0.905845i \(0.360763\pi\)
\(762\) 0 0
\(763\) 1.44760 + 4.83532i 0.0524067 + 0.175050i
\(764\) 12.4282 70.4836i 0.449635 2.55001i
\(765\) 0 0
\(766\) 0.661895 + 3.75379i 0.0239152 + 0.135630i
\(767\) 11.4372 5.74400i 0.412975 0.207404i
\(768\) 0 0
\(769\) 19.7676 + 45.8265i 0.712839 + 1.65255i 0.756912 + 0.653517i \(0.226707\pi\)
−0.0440729 + 0.999028i \(0.514033\pi\)
\(770\) 12.5417 + 29.0750i 0.451972 + 1.04779i
\(771\) 0 0
\(772\) 99.1473 49.7936i 3.56839 1.79211i
\(773\) −1.64610 9.33547i −0.0592059 0.335774i 0.940789 0.338993i \(-0.110086\pi\)
−0.999995 + 0.00321947i \(0.998975\pi\)
\(774\) 0 0
\(775\) −2.46005 + 13.9516i −0.0883676 + 0.501157i
\(776\) −17.5898 58.7541i −0.631438 2.10915i
\(777\) 0 0
\(778\) 8.05843 + 4.04710i 0.288909 + 0.145095i
\(779\) 1.59534 5.32880i 0.0571589 0.190924i
\(780\) 0 0
\(781\) −11.5429 15.5049i −0.413039 0.554808i
\(782\) 1.97850 + 3.42686i 0.0707509 + 0.122544i
\(783\) 0 0
\(784\) 10.7766 18.6656i 0.384878 0.666628i
\(785\) 42.9264 5.01737i 1.53211 0.179078i
\(786\) 0 0
\(787\) −45.6778 + 10.8258i −1.62824 + 0.385899i −0.940428 0.339993i \(-0.889575\pi\)
−0.687809 + 0.725892i \(0.741427\pi\)
\(788\) −20.1000 + 13.2200i −0.716033 + 0.470942i
\(789\) 0 0
\(790\) −35.1935 + 37.3029i −1.25213 + 1.32718i
\(791\) −3.51972 2.95340i −0.125147 0.105011i
\(792\) 0 0
\(793\) −4.29569 + 3.60451i −0.152544 + 0.128000i
\(794\) 5.48874 94.2381i 0.194788 3.34439i
\(795\) 0 0
\(796\) 38.5066 51.7234i 1.36483 1.83329i
\(797\) 29.2751 + 3.42177i 1.03698 + 0.121205i 0.617509 0.786564i \(-0.288142\pi\)
0.419469 + 0.907769i \(0.362216\pi\)
\(798\) 0 0
\(799\) 1.87007 + 1.22997i 0.0661585 + 0.0435131i
\(800\) −1.56265 0.568758i −0.0552480 0.0201086i
\(801\) 0 0
\(802\) 41.0358 14.9358i 1.44903 0.527402i
\(803\) −20.6226 4.88765i −0.727757 0.172482i
\(804\) 0 0
\(805\) 1.83134 + 31.4429i 0.0645463 + 1.10822i
\(806\) 2.84626 + 3.01686i 0.100255 + 0.106264i
\(807\) 0 0
\(808\) −24.3779 + 56.5143i −0.857612 + 1.98817i
\(809\) 10.6073 0.372933 0.186467 0.982461i \(-0.440296\pi\)
0.186467 + 0.982461i \(0.440296\pi\)
\(810\) 0 0
\(811\) −6.86583 −0.241092 −0.120546 0.992708i \(-0.538465\pi\)
−0.120546 + 0.992708i \(0.538465\pi\)
\(812\) −11.6051 + 26.9036i −0.407259 + 0.944131i
\(813\) 0 0
\(814\) −0.200024 0.212013i −0.00701083 0.00743105i
\(815\) −0.875916 15.0389i −0.0306820 0.526789i
\(816\) 0 0
\(817\) 8.17155 + 1.93669i 0.285886 + 0.0677563i
\(818\) 42.2481 15.3771i 1.47717 0.537646i
\(819\) 0 0
\(820\) 62.5562 + 22.7686i 2.18456 + 0.795114i
\(821\) 16.8063 + 11.0537i 0.586546 + 0.385777i 0.807815 0.589436i \(-0.200650\pi\)
−0.221270 + 0.975213i \(0.571020\pi\)
\(822\) 0 0
\(823\) 53.7250 + 6.27955i 1.87274 + 0.218891i 0.975087 0.221821i \(-0.0712000\pi\)
0.897648 + 0.440712i \(0.145274\pi\)
\(824\) −18.4501 + 24.7827i −0.642738 + 0.863347i
\(825\) 0 0
\(826\) 1.83157 31.4469i 0.0637286 1.09418i
\(827\) 28.7038 24.0854i 0.998129 0.837530i 0.0114051 0.999935i \(-0.496370\pi\)
0.986724 + 0.162405i \(0.0519251\pi\)
\(828\) 0 0
\(829\) −35.2264 29.5585i −1.22346 1.02661i −0.998636 0.0522095i \(-0.983374\pi\)
−0.224828 0.974399i \(-0.572182\pi\)
\(830\) −38.2241 + 40.5152i −1.32678 + 1.40630i
\(831\) 0 0
\(832\) 8.56500 5.63329i 0.296938 0.195299i
\(833\) 1.38205 0.327553i 0.0478853 0.0113490i
\(834\) 0 0
\(835\) 47.0062 5.49424i 1.62672 0.190136i
\(836\) 6.60539 11.4409i 0.228452 0.395691i
\(837\) 0 0
\(838\) −15.3176 26.5308i −0.529136 0.916491i
\(839\) 10.5477 + 14.1680i 0.364146 + 0.489133i 0.946003 0.324158i \(-0.105081\pi\)
−0.581857 + 0.813291i \(0.697674\pi\)
\(840\) 0 0
\(841\) −0.492563 + 1.64527i −0.0169849 + 0.0567336i
\(842\) 47.3855 + 23.7979i 1.63301 + 0.820129i
\(843\) 0 0
\(844\) 11.5983 + 38.7409i 0.399229 + 1.33352i
\(845\) −7.83189 + 44.4168i −0.269425 + 1.52799i
\(846\) 0 0
\(847\) 1.14006 + 6.46561i 0.0391730 + 0.222161i
\(848\) −42.3881 + 21.2881i −1.45561 + 0.731036i
\(849\) 0 0
\(850\) −2.87945 6.67532i −0.0987644 0.228962i
\(851\) −0.114834 0.266216i −0.00393647 0.00912576i
\(852\) 0 0
\(853\) −32.8756 + 16.5107i −1.12564 + 0.565317i −0.911424 0.411469i \(-0.865016\pi\)
−0.214215 + 0.976786i \(0.568719\pi\)
\(854\) 2.39663 + 13.5919i 0.0820108 + 0.465107i
\(855\) 0 0
\(856\) −17.0306 + 96.5851i −0.582093 + 3.30121i
\(857\) −7.36638 24.6054i −0.251631 0.840505i −0.986705 0.162519i \(-0.948038\pi\)
0.735075 0.677986i \(-0.237147\pi\)
\(858\) 0 0
\(859\) −26.9510 13.5353i −0.919555 0.461818i −0.0749379 0.997188i \(-0.523876\pi\)
−0.844618 + 0.535370i \(0.820172\pi\)
\(860\) −28.8252 + 96.2828i −0.982930 + 3.28322i
\(861\) 0 0
\(862\) 45.5201 + 61.1441i 1.55042 + 2.08258i
\(863\) −23.2433 40.2586i −0.791212 1.37042i −0.925217 0.379438i \(-0.876117\pi\)
0.134006 0.990981i \(-0.457216\pi\)
\(864\) 0 0
\(865\) −19.1303 + 33.1347i −0.650451 + 1.12661i
\(866\) −32.3740 + 3.78398i −1.10011 + 0.128585i
\(867\) 0 0
\(868\) 6.63047 1.57145i 0.225053 0.0533385i
\(869\) 10.7131 7.04612i 0.363417 0.239023i
\(870\) 0 0
\(871\) 1.19373 1.26527i 0.0404478 0.0428722i
\(872\) 14.5163 + 12.1806i 0.491583 + 0.412487i
\(873\) 0 0
\(874\) 15.0801 12.6537i 0.510091 0.428018i
\(875\) 1.83397 31.4880i 0.0619994 1.06449i
\(876\) 0 0
\(877\) −5.56004 + 7.46843i −0.187749 + 0.252191i −0.886025 0.463638i \(-0.846544\pi\)
0.698275 + 0.715829i \(0.253951\pi\)
\(878\) 3.12437 + 0.365186i 0.105442 + 0.0123244i
\(879\) 0 0
\(880\) 33.5286 + 22.0521i 1.13025 + 0.743376i
\(881\) −36.4164 13.2545i −1.22690 0.446555i −0.354366 0.935107i \(-0.615303\pi\)
−0.872535 + 0.488551i \(0.837526\pi\)
\(882\) 0 0
\(883\) 16.7575 6.09921i 0.563933 0.205255i −0.0442931 0.999019i \(-0.514104\pi\)
0.608226 + 0.793764i \(0.291881\pi\)
\(884\) −1.38244 0.327645i −0.0464966 0.0110199i
\(885\) 0 0
\(886\) −5.57640 95.7431i −0.187343 3.21655i
\(887\) −30.4660 32.2921i −1.02295 1.08426i −0.996414 0.0846130i \(-0.973035\pi\)
−0.0265335 0.999648i \(-0.508447\pi\)
\(888\) 0 0
\(889\) −6.85154 + 15.8837i −0.229793 + 0.532721i
\(890\) −89.8816 −3.01284
\(891\) 0 0
\(892\) −52.3701 −1.75348
\(893\) 4.41048 10.2246i 0.147591 0.342155i
\(894\) 0 0
\(895\) −3.89477 4.12821i −0.130188 0.137991i
\(896\) −1.49023 25.5863i −0.0497851 0.854778i
\(897\) 0 0
\(898\) 38.2667 + 9.06937i 1.27698 + 0.302649i
\(899\) 6.71300 2.44333i 0.223891 0.0814897i
\(900\) 0 0
\(901\) −2.93733 1.06910i −0.0978565 0.0356169i
\(902\) −20.8330 13.7021i −0.693663 0.456229i
\(903\) 0 0
\(904\) −17.1334 2.00261i −0.569849 0.0666058i
\(905\) −23.6397 + 31.7536i −0.785811 + 1.05553i
\(906\) 0 0
\(907\) 0.530141 9.10217i 0.0176030 0.302232i −0.978003 0.208591i \(-0.933112\pi\)
0.995606 0.0936414i \(-0.0298507\pi\)
\(908\) −50.1138 + 42.0505i −1.66308 + 1.39549i
\(909\) 0 0
\(910\) −12.9777 10.8896i −0.430207 0.360987i
\(911\) 1.16229 1.23196i 0.0385084 0.0408166i −0.707833 0.706380i \(-0.750327\pi\)
0.746342 + 0.665563i \(0.231809\pi\)
\(912\) 0 0
\(913\) 11.6356 7.65288i 0.385084 0.253273i
\(914\) −9.22588 + 2.18657i −0.305165 + 0.0723254i
\(915\) 0 0
\(916\) 26.8708 3.14074i 0.887836 0.103773i
\(917\) 2.85108 4.93822i 0.0941511 0.163074i
\(918\) 0 0
\(919\) −20.4302 35.3862i −0.673931 1.16728i −0.976780 0.214245i \(-0.931271\pi\)
0.302849 0.953039i \(-0.402062\pi\)
\(920\) 70.6129 + 94.8496i 2.32804 + 3.12710i
\(921\) 0 0
\(922\) −14.9343 + 49.8841i −0.491835 + 1.64284i
\(923\) 9.24179 + 4.64140i 0.304197 + 0.152774i
\(924\) 0 0
\(925\) 0.152769 + 0.510283i 0.00502301 + 0.0167780i
\(926\) 8.22550 46.6491i 0.270307 1.53299i
\(927\) 0 0
\(928\) 0.145614 + 0.825819i 0.00478002 + 0.0271088i
\(929\) 23.2913 11.6973i 0.764163 0.383777i −0.0236274 0.999721i \(-0.507522\pi\)
0.787790 + 0.615944i \(0.211225\pi\)
\(930\) 0 0
\(931\) −2.79872 6.48816i −0.0917243 0.212641i
\(932\) −21.9500 50.8859i −0.718997 1.66682i
\(933\) 0 0
\(934\) 9.02867 4.53437i 0.295427 0.148369i
\(935\) 0.459226 + 2.60440i 0.0150183 + 0.0851730i
\(936\) 0 0
\(937\) −6.10524 + 34.6246i −0.199450 + 1.13114i 0.706488 + 0.707725i \(0.250278\pi\)
−0.905938 + 0.423410i \(0.860833\pi\)
\(938\) −1.22790 4.10147i −0.0400923 0.133918i
\(939\) 0 0
\(940\) 119.091 + 59.8097i 3.88432 + 1.95078i
\(941\) 2.73376 9.13140i 0.0891180 0.297675i −0.901798 0.432158i \(-0.857752\pi\)
0.990916 + 0.134483i \(0.0429374\pi\)
\(942\) 0 0
\(943\) −14.8110 19.8947i −0.482314 0.647860i
\(944\) −19.9611 34.5736i −0.649678 1.12527i
\(945\) 0 0
\(946\) 18.8228 32.6021i 0.611983 1.05999i
\(947\) −5.29637 + 0.619057i −0.172109 + 0.0201167i −0.201711 0.979445i \(-0.564650\pi\)
0.0296019 + 0.999562i \(0.490576\pi\)
\(948\) 0 0
\(949\) 11.0335 2.61499i 0.358163 0.0848863i
\(950\) −30.2170 + 19.8740i −0.980370 + 0.644799i
\(951\) 0 0
\(952\) −1.20440 + 1.27659i −0.0390348 + 0.0413745i
\(953\) −18.6871 15.6804i −0.605335 0.507937i 0.287820 0.957684i \(-0.407069\pi\)
−0.893156 + 0.449748i \(0.851514\pi\)
\(954\) 0 0
\(955\) 54.6013 45.8159i 1.76686 1.48257i
\(956\) 2.92730 50.2597i 0.0946755 1.62552i
\(957\) 0 0
\(958\) −42.1107 + 56.5645i −1.36053 + 1.82752i
\(959\) −29.3187 3.42687i −0.946750 0.110659i
\(960\) 0 0
\(961\) 24.5120 + 16.1218i 0.790711 + 0.520059i
\(962\) 0.146541 + 0.0533367i 0.00472469 + 0.00171965i
\(963\) 0 0
\(964\) −51.6583 + 18.8021i −1.66380 + 0.605574i
\(965\) 107.514 + 25.4814i 3.46101 + 0.820275i
\(966\) 0 0
\(967\) 1.26458 + 21.7120i 0.0406662 + 0.698211i 0.955611 + 0.294632i \(0.0951970\pi\)
−0.914945 + 0.403579i \(0.867766\pi\)
\(968\) 16.9150 + 17.9288i 0.543667 + 0.576254i
\(969\) 0 0
\(970\) 48.1997 111.739i 1.54760 3.58773i
\(971\) −29.3878 −0.943100 −0.471550 0.881839i \(-0.656305\pi\)
−0.471550 + 0.881839i \(0.656305\pi\)
\(972\) 0 0
\(973\) 12.6381 0.405160
\(974\) 8.63377 20.0153i 0.276644 0.641332i
\(975\) 0 0
\(976\) 12.0035 + 12.7230i 0.384222 + 0.407252i
\(977\) 3.48814 + 59.8890i 0.111595 + 1.91602i 0.336577 + 0.941656i \(0.390731\pi\)
−0.224982 + 0.974363i \(0.572232\pi\)
\(978\) 0 0
\(979\) 21.8672 + 5.18263i 0.698880 + 0.165638i
\(980\) 79.4655 28.9231i 2.53843 0.923914i
\(981\) 0 0
\(982\) −64.9940 23.6559i −2.07404 0.754889i
\(983\) −23.2878 15.3166i −0.742766 0.488525i 0.120852 0.992670i \(-0.461437\pi\)
−0.863619 + 0.504145i \(0.831808\pi\)
\(984\) 0 0
\(985\) −23.7970 2.78147i −0.758235 0.0886249i
\(986\) −2.18914 + 2.94053i −0.0697165 + 0.0936455i
\(987\) 0 0
\(988\) −0.410970 + 7.05608i −0.0130747 + 0.224484i
\(989\) 28.6849 24.0695i 0.912126 0.765365i
\(990\) 0 0
\(991\) 12.6278 + 10.5959i 0.401134 + 0.336591i 0.820932 0.571026i \(-0.193455\pi\)
−0.419798 + 0.907618i \(0.637899\pi\)
\(992\) 0.133831 0.141852i 0.00424913 0.00450382i
\(993\) 0 0
\(994\) 21.2661 13.9869i 0.674520 0.443639i
\(995\) 62.4872 14.8097i 1.98098 0.469500i
\(996\) 0 0
\(997\) 22.5720 2.63829i 0.714864 0.0835556i 0.249117 0.968473i \(-0.419860\pi\)
0.465747 + 0.884918i \(0.345786\pi\)
\(998\) −1.45934 + 2.52765i −0.0461947 + 0.0800115i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 729.2.g.a.55.8 144
3.2 odd 2 729.2.g.d.55.1 144
9.2 odd 6 81.2.g.a.61.8 yes 144
9.4 even 3 729.2.g.b.541.8 144
9.5 odd 6 729.2.g.c.541.1 144
9.7 even 3 243.2.g.a.19.1 144
81.4 even 27 729.2.g.b.190.8 144
81.23 odd 54 81.2.g.a.4.8 144
81.29 odd 54 6561.2.a.c.1.7 72
81.31 even 27 inner 729.2.g.a.676.8 144
81.50 odd 54 729.2.g.d.676.1 144
81.52 even 27 6561.2.a.d.1.66 72
81.58 even 27 243.2.g.a.64.1 144
81.77 odd 54 729.2.g.c.190.1 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.4.8 144 81.23 odd 54
81.2.g.a.61.8 yes 144 9.2 odd 6
243.2.g.a.19.1 144 9.7 even 3
243.2.g.a.64.1 144 81.58 even 27
729.2.g.a.55.8 144 1.1 even 1 trivial
729.2.g.a.676.8 144 81.31 even 27 inner
729.2.g.b.190.8 144 81.4 even 27
729.2.g.b.541.8 144 9.4 even 3
729.2.g.c.190.1 144 81.77 odd 54
729.2.g.c.541.1 144 9.5 odd 6
729.2.g.d.55.1 144 3.2 odd 2
729.2.g.d.676.1 144 81.50 odd 54
6561.2.a.c.1.7 72 81.29 odd 54
6561.2.a.d.1.66 72 81.52 even 27