Properties

Label 729.2.e.g.325.1
Level $729$
Weight $2$
Character 729.325
Analytic conductor $5.821$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.e (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 325.1
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 729.325
Dual form 729.2.e.g.406.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.673648 - 0.565258i) q^{2} +(-0.213011 + 1.20805i) q^{4} +(3.64543 - 1.32683i) q^{5} +(-0.379385 - 2.15160i) q^{7} +(1.41875 + 2.45734i) q^{8} +O(q^{10})\) \(q+(0.673648 - 0.565258i) q^{2} +(-0.213011 + 1.20805i) q^{4} +(3.64543 - 1.32683i) q^{5} +(-0.379385 - 2.15160i) q^{7} +(1.41875 + 2.45734i) q^{8} +(1.70574 - 2.95442i) q^{10} +(0.152704 + 0.0555796i) q^{11} +(1.84730 + 1.55007i) q^{13} +(-1.47178 - 1.23497i) q^{14} +(0.0393628 + 0.0143269i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-1.79813 - 3.11446i) q^{19} +(0.826352 + 4.68647i) q^{20} +(0.134285 - 0.0488759i) q^{22} +(-0.492726 + 2.79439i) q^{23} +(7.69846 - 6.45978i) q^{25} +2.12061 q^{26} +2.68004 q^{28} +(-5.14543 + 4.31753i) q^{29} +(-0.900330 + 5.10602i) q^{31} +(-5.29813 + 1.92836i) q^{32} +(-0.458111 - 2.59808i) q^{34} +(-4.23783 - 7.34013i) q^{35} +(3.31908 - 5.74881i) q^{37} +(-2.97178 - 1.08164i) q^{38} +(8.43242 + 7.07564i) q^{40} +(4.44356 + 3.72859i) q^{41} +(5.85117 + 2.12965i) q^{43} +(-0.0996702 + 0.172634i) q^{44} +(1.24763 + 2.16095i) q^{46} +(-1.28446 - 7.28455i) q^{47} +(2.09240 - 0.761570i) q^{49} +(1.53462 - 8.70323i) q^{50} +(-2.26604 + 1.90144i) q^{52} -1.40373 q^{53} +0.630415 q^{55} +(4.74897 - 3.98486i) q^{56} +(-1.02569 + 5.81699i) q^{58} +(-4.81180 + 1.75135i) q^{59} +(-0.656574 - 3.72362i) q^{61} +(2.27972 + 3.94858i) q^{62} +(-2.52094 + 4.36640i) q^{64} +(8.79086 + 3.19961i) q^{65} +(-4.49273 - 3.76984i) q^{67} +(2.81908 + 2.36549i) q^{68} +(-7.00387 - 2.54920i) q^{70} +(-7.65910 + 13.2660i) q^{71} +(-4.34002 - 7.51714i) q^{73} +(-1.01367 - 5.74881i) q^{74} +(4.14543 - 1.50881i) q^{76} +(0.0616516 - 0.349643i) q^{77} +(-0.971782 + 0.815422i) q^{79} +0.162504 q^{80} +5.10101 q^{82} +(6.49273 - 5.44804i) q^{83} +(2.02094 - 11.4613i) q^{85} +(5.14543 - 1.87278i) q^{86} +(0.0800699 + 0.454099i) q^{88} +(3.86097 + 6.68739i) q^{89} +(2.63429 - 4.56272i) q^{91} +(-3.27079 - 1.19047i) q^{92} +(-4.98293 - 4.18117i) q^{94} +(-10.6873 - 8.96773i) q^{95} +(3.67112 + 1.33618i) q^{97} +(0.979055 - 1.69577i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 9 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 9 q^{7} + 6 q^{8} + 3 q^{11} + 9 q^{13} + 6 q^{14} + 9 q^{16} + 9 q^{17} + 3 q^{19} + 6 q^{20} - 9 q^{22} + 15 q^{23} + 18 q^{25} + 24 q^{26} - 24 q^{28} - 15 q^{29} + 9 q^{31} - 18 q^{32} - 9 q^{34} - 6 q^{35} + 3 q^{37} - 3 q^{38} + 27 q^{40} - 3 q^{41} + 9 q^{43} - 15 q^{44} - 9 q^{46} - 15 q^{47} + 9 q^{49} - 15 q^{50} - 9 q^{52} - 36 q^{53} + 18 q^{55} + 3 q^{56} - 36 q^{58} + 6 q^{59} + 18 q^{61} - 12 q^{62} - 12 q^{64} + 21 q^{65} - 9 q^{67} - 18 q^{70} - 9 q^{71} - 6 q^{73} + 15 q^{74} + 9 q^{76} - 3 q^{77} + 9 q^{79} + 6 q^{80} + 36 q^{82} + 21 q^{83} + 9 q^{85} + 15 q^{86} + 9 q^{88} + 6 q^{91} - 48 q^{92} - 9 q^{94} - 42 q^{95} + 36 q^{97} + 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.673648 0.565258i 0.476341 0.399698i −0.372760 0.927928i \(-0.621589\pi\)
0.849101 + 0.528230i \(0.177144\pi\)
\(3\) 0 0
\(4\) −0.213011 + 1.20805i −0.106506 + 0.604023i
\(5\) 3.64543 1.32683i 1.63029 0.593375i 0.644984 0.764196i \(-0.276864\pi\)
0.985302 + 0.170821i \(0.0546420\pi\)
\(6\) 0 0
\(7\) −0.379385 2.15160i −0.143394 0.813229i −0.968643 0.248459i \(-0.920076\pi\)
0.825248 0.564770i \(-0.191035\pi\)
\(8\) 1.41875 + 2.45734i 0.501603 + 0.868802i
\(9\) 0 0
\(10\) 1.70574 2.95442i 0.539401 0.934271i
\(11\) 0.152704 + 0.0555796i 0.0460419 + 0.0167579i 0.364938 0.931032i \(-0.381090\pi\)
−0.318897 + 0.947790i \(0.603312\pi\)
\(12\) 0 0
\(13\) 1.84730 + 1.55007i 0.512348 + 0.429911i 0.861954 0.506986i \(-0.169240\pi\)
−0.349607 + 0.936897i \(0.613685\pi\)
\(14\) −1.47178 1.23497i −0.393350 0.330060i
\(15\) 0 0
\(16\) 0.0393628 + 0.0143269i 0.00984071 + 0.00358173i
\(17\) 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) 0 0
\(19\) −1.79813 3.11446i −0.412520 0.714506i 0.582645 0.812727i \(-0.302018\pi\)
−0.995165 + 0.0982214i \(0.968685\pi\)
\(20\) 0.826352 + 4.68647i 0.184778 + 1.04793i
\(21\) 0 0
\(22\) 0.134285 0.0488759i 0.0286297 0.0104204i
\(23\) −0.492726 + 2.79439i −0.102740 + 0.582670i 0.889358 + 0.457211i \(0.151152\pi\)
−0.992099 + 0.125459i \(0.959960\pi\)
\(24\) 0 0
\(25\) 7.69846 6.45978i 1.53969 1.29196i
\(26\) 2.12061 0.415887
\(27\) 0 0
\(28\) 2.68004 0.506481
\(29\) −5.14543 + 4.31753i −0.955482 + 0.801745i −0.980212 0.197949i \(-0.936572\pi\)
0.0247300 + 0.999694i \(0.492127\pi\)
\(30\) 0 0
\(31\) −0.900330 + 5.10602i −0.161704 + 0.917069i 0.790694 + 0.612212i \(0.209720\pi\)
−0.952398 + 0.304857i \(0.901391\pi\)
\(32\) −5.29813 + 1.92836i −0.936587 + 0.340890i
\(33\) 0 0
\(34\) −0.458111 2.59808i −0.0785654 0.445566i
\(35\) −4.23783 7.34013i −0.716323 1.24071i
\(36\) 0 0
\(37\) 3.31908 5.74881i 0.545653 0.945099i −0.452912 0.891555i \(-0.649615\pi\)
0.998566 0.0535438i \(-0.0170517\pi\)
\(38\) −2.97178 1.08164i −0.482087 0.175465i
\(39\) 0 0
\(40\) 8.43242 + 7.07564i 1.33328 + 1.11876i
\(41\) 4.44356 + 3.72859i 0.693968 + 0.582308i 0.920050 0.391800i \(-0.128147\pi\)
−0.226082 + 0.974108i \(0.572592\pi\)
\(42\) 0 0
\(43\) 5.85117 + 2.12965i 0.892295 + 0.324769i 0.747161 0.664643i \(-0.231417\pi\)
0.145134 + 0.989412i \(0.453639\pi\)
\(44\) −0.0996702 + 0.172634i −0.0150259 + 0.0260255i
\(45\) 0 0
\(46\) 1.24763 + 2.16095i 0.183952 + 0.318615i
\(47\) −1.28446 7.28455i −0.187358 1.06256i −0.922888 0.385069i \(-0.874178\pi\)
0.735530 0.677492i \(-0.236933\pi\)
\(48\) 0 0
\(49\) 2.09240 0.761570i 0.298914 0.108796i
\(50\) 1.53462 8.70323i 0.217027 1.23082i
\(51\) 0 0
\(52\) −2.26604 + 1.90144i −0.314244 + 0.263682i
\(53\) −1.40373 −0.192818 −0.0964088 0.995342i \(-0.530736\pi\)
−0.0964088 + 0.995342i \(0.530736\pi\)
\(54\) 0 0
\(55\) 0.630415 0.0850051
\(56\) 4.74897 3.98486i 0.634608 0.532499i
\(57\) 0 0
\(58\) −1.02569 + 5.81699i −0.134680 + 0.763808i
\(59\) −4.81180 + 1.75135i −0.626444 + 0.228007i −0.635683 0.771951i \(-0.719281\pi\)
0.00923910 + 0.999957i \(0.497059\pi\)
\(60\) 0 0
\(61\) −0.656574 3.72362i −0.0840657 0.476760i −0.997554 0.0698959i \(-0.977733\pi\)
0.913489 0.406864i \(-0.133378\pi\)
\(62\) 2.27972 + 3.94858i 0.289524 + 0.501470i
\(63\) 0 0
\(64\) −2.52094 + 4.36640i −0.315118 + 0.545801i
\(65\) 8.79086 + 3.19961i 1.09037 + 0.396863i
\(66\) 0 0
\(67\) −4.49273 3.76984i −0.548874 0.460560i 0.325686 0.945478i \(-0.394405\pi\)
−0.874559 + 0.484918i \(0.838849\pi\)
\(68\) 2.81908 + 2.36549i 0.341863 + 0.286857i
\(69\) 0 0
\(70\) −7.00387 2.54920i −0.837123 0.304688i
\(71\) −7.65910 + 13.2660i −0.908968 + 1.57438i −0.0934675 + 0.995622i \(0.529795\pi\)
−0.815500 + 0.578756i \(0.803538\pi\)
\(72\) 0 0
\(73\) −4.34002 7.51714i −0.507961 0.879815i −0.999958 0.00921733i \(-0.997066\pi\)
0.491996 0.870597i \(-0.336267\pi\)
\(74\) −1.01367 5.74881i −0.117837 0.668286i
\(75\) 0 0
\(76\) 4.14543 1.50881i 0.475513 0.173073i
\(77\) 0.0616516 0.349643i 0.00702585 0.0398456i
\(78\) 0 0
\(79\) −0.971782 + 0.815422i −0.109334 + 0.0917421i −0.695816 0.718220i \(-0.744957\pi\)
0.586482 + 0.809962i \(0.300513\pi\)
\(80\) 0.162504 0.0181685
\(81\) 0 0
\(82\) 5.10101 0.563313
\(83\) 6.49273 5.44804i 0.712669 0.598001i −0.212677 0.977122i \(-0.568218\pi\)
0.925347 + 0.379122i \(0.123774\pi\)
\(84\) 0 0
\(85\) 2.02094 11.4613i 0.219202 1.24316i
\(86\) 5.14543 1.87278i 0.554846 0.201947i
\(87\) 0 0
\(88\) 0.0800699 + 0.454099i 0.00853548 + 0.0484071i
\(89\) 3.86097 + 6.68739i 0.409262 + 0.708862i 0.994807 0.101778i \(-0.0324530\pi\)
−0.585546 + 0.810640i \(0.699120\pi\)
\(90\) 0 0
\(91\) 2.63429 4.56272i 0.276148 0.478303i
\(92\) −3.27079 1.19047i −0.341004 0.124115i
\(93\) 0 0
\(94\) −4.98293 4.18117i −0.513950 0.431255i
\(95\) −10.6873 8.96773i −1.09650 0.920069i
\(96\) 0 0
\(97\) 3.67112 + 1.33618i 0.372746 + 0.135668i 0.521599 0.853191i \(-0.325336\pi\)
−0.148853 + 0.988859i \(0.547558\pi\)
\(98\) 0.979055 1.69577i 0.0988995 0.171299i
\(99\) 0 0
\(100\) 6.16385 + 10.6761i 0.616385 + 1.06761i
\(101\) 1.40895 + 7.99054i 0.140196 + 0.795089i 0.971100 + 0.238673i \(0.0767125\pi\)
−0.830904 + 0.556415i \(0.812176\pi\)
\(102\) 0 0
\(103\) −17.5214 + 6.37727i −1.72644 + 0.628371i −0.998367 0.0571322i \(-0.981804\pi\)
−0.728069 + 0.685503i \(0.759582\pi\)
\(104\) −1.18820 + 6.73859i −0.116512 + 0.660774i
\(105\) 0 0
\(106\) −0.945622 + 0.793471i −0.0918470 + 0.0770688i
\(107\) −7.59627 −0.734359 −0.367179 0.930150i \(-0.619676\pi\)
−0.367179 + 0.930150i \(0.619676\pi\)
\(108\) 0 0
\(109\) −15.6382 −1.49786 −0.748932 0.662647i \(-0.769433\pi\)
−0.748932 + 0.662647i \(0.769433\pi\)
\(110\) 0.424678 0.356347i 0.0404914 0.0339764i
\(111\) 0 0
\(112\) 0.0158921 0.0901285i 0.00150166 0.00851635i
\(113\) −2.17365 + 0.791143i −0.204480 + 0.0744245i −0.442230 0.896902i \(-0.645812\pi\)
0.237750 + 0.971326i \(0.423590\pi\)
\(114\) 0 0
\(115\) 1.91147 + 10.8405i 0.178246 + 1.01088i
\(116\) −4.11974 7.13559i −0.382508 0.662523i
\(117\) 0 0
\(118\) −2.25150 + 3.89971i −0.207267 + 0.358997i
\(119\) −6.15910 2.24173i −0.564604 0.205499i
\(120\) 0 0
\(121\) −8.40626 7.05369i −0.764205 0.641244i
\(122\) −2.54710 2.13727i −0.230604 0.193500i
\(123\) 0 0
\(124\) −5.97653 2.17528i −0.536708 0.195346i
\(125\) 9.79473 16.9650i 0.876067 1.51739i
\(126\) 0 0
\(127\) −0.0209445 0.0362770i −0.00185853 0.00321906i 0.865095 0.501609i \(-0.167258\pi\)
−0.866953 + 0.498390i \(0.833925\pi\)
\(128\) −1.18820 6.73859i −0.105023 0.595613i
\(129\) 0 0
\(130\) 7.73055 2.81369i 0.678014 0.246777i
\(131\) −3.18614 + 18.0695i −0.278374 + 1.57874i 0.449662 + 0.893199i \(0.351544\pi\)
−0.728036 + 0.685539i \(0.759567\pi\)
\(132\) 0 0
\(133\) −6.01889 + 5.05044i −0.521904 + 0.437929i
\(134\) −5.15745 −0.445536
\(135\) 0 0
\(136\) 8.51249 0.729940
\(137\) −10.9645 + 9.20031i −0.936761 + 0.786036i −0.977019 0.213153i \(-0.931627\pi\)
0.0402576 + 0.999189i \(0.487182\pi\)
\(138\) 0 0
\(139\) 1.82248 10.3358i 0.154581 0.876672i −0.804587 0.593835i \(-0.797613\pi\)
0.959168 0.282837i \(-0.0912755\pi\)
\(140\) 9.76991 3.55596i 0.825709 0.300533i
\(141\) 0 0
\(142\) 2.33915 + 13.2660i 0.196297 + 1.11325i
\(143\) 0.195937 + 0.339373i 0.0163851 + 0.0283798i
\(144\) 0 0
\(145\) −13.0287 + 22.5663i −1.08197 + 1.87403i
\(146\) −7.17277 2.61068i −0.593623 0.216061i
\(147\) 0 0
\(148\) 6.23783 + 5.23416i 0.512746 + 0.430245i
\(149\) 0.973841 + 0.817150i 0.0797802 + 0.0669435i 0.681806 0.731533i \(-0.261195\pi\)
−0.602025 + 0.798477i \(0.705639\pi\)
\(150\) 0 0
\(151\) −7.38326 2.68729i −0.600841 0.218688i 0.0236500 0.999720i \(-0.492471\pi\)
−0.624491 + 0.781032i \(0.714693\pi\)
\(152\) 5.10220 8.83726i 0.413843 0.716797i
\(153\) 0 0
\(154\) −0.156107 0.270386i −0.0125795 0.0217883i
\(155\) 3.49273 + 19.8082i 0.280543 + 1.59104i
\(156\) 0 0
\(157\) 11.6074 4.22475i 0.926372 0.337172i 0.165602 0.986193i \(-0.447043\pi\)
0.760771 + 0.649021i \(0.224821\pi\)
\(158\) −0.193715 + 1.09861i −0.0154112 + 0.0874011i
\(159\) 0 0
\(160\) −16.7554 + 14.0594i −1.32463 + 1.11149i
\(161\) 6.19934 0.488576
\(162\) 0 0
\(163\) −13.7469 −1.07674 −0.538371 0.842708i \(-0.680960\pi\)
−0.538371 + 0.842708i \(0.680960\pi\)
\(164\) −5.45084 + 4.57380i −0.425639 + 0.357153i
\(165\) 0 0
\(166\) 1.29426 7.34013i 0.100454 0.569705i
\(167\) −3.49273 + 1.27125i −0.270275 + 0.0983721i −0.473603 0.880739i \(-0.657047\pi\)
0.203327 + 0.979111i \(0.434824\pi\)
\(168\) 0 0
\(169\) −1.24763 7.07564i −0.0959712 0.544280i
\(170\) −5.11721 8.86327i −0.392472 0.679782i
\(171\) 0 0
\(172\) −3.81908 + 6.61484i −0.291202 + 0.504377i
\(173\) −1.46538 0.533356i −0.111411 0.0405503i 0.285713 0.958315i \(-0.407770\pi\)
−0.397124 + 0.917765i \(0.629992\pi\)
\(174\) 0 0
\(175\) −16.8195 14.1133i −1.27144 1.06686i
\(176\) 0.00521457 + 0.00437554i 0.000393063 + 0.000329819i
\(177\) 0 0
\(178\) 6.38103 + 2.32251i 0.478279 + 0.174079i
\(179\) −6.09627 + 10.5590i −0.455656 + 0.789220i −0.998726 0.0504679i \(-0.983929\pi\)
0.543069 + 0.839688i \(0.317262\pi\)
\(180\) 0 0
\(181\) 8.43629 + 14.6121i 0.627064 + 1.08611i 0.988138 + 0.153570i \(0.0490771\pi\)
−0.361073 + 0.932537i \(0.617590\pi\)
\(182\) −0.804530 4.56272i −0.0596357 0.338211i
\(183\) 0 0
\(184\) −7.56583 + 2.75374i −0.557760 + 0.203008i
\(185\) 4.47178 25.3607i 0.328772 1.86456i
\(186\) 0 0
\(187\) 0.373455 0.313366i 0.0273098 0.0229156i
\(188\) 9.07367 0.661766
\(189\) 0 0
\(190\) −12.2686 −0.890056
\(191\) 13.3871 11.2331i 0.968658 0.812801i −0.0136814 0.999906i \(-0.504355\pi\)
0.982340 + 0.187105i \(0.0599106\pi\)
\(192\) 0 0
\(193\) −0.345952 + 1.96199i −0.0249022 + 0.141227i −0.994724 0.102588i \(-0.967288\pi\)
0.969822 + 0.243815i \(0.0783989\pi\)
\(194\) 3.22833 1.17502i 0.231781 0.0843612i
\(195\) 0 0
\(196\) 0.474308 + 2.68993i 0.0338791 + 0.192138i
\(197\) 10.5963 + 18.3533i 0.754953 + 1.30762i 0.945398 + 0.325919i \(0.105674\pi\)
−0.190445 + 0.981698i \(0.560993\pi\)
\(198\) 0 0
\(199\) 1.54189 2.67063i 0.109302 0.189316i −0.806186 0.591662i \(-0.798472\pi\)
0.915488 + 0.402346i \(0.131805\pi\)
\(200\) 26.7961 + 9.75297i 1.89477 + 0.689639i
\(201\) 0 0
\(202\) 5.46585 + 4.58639i 0.384576 + 0.322698i
\(203\) 11.2417 + 9.43290i 0.789012 + 0.662060i
\(204\) 0 0
\(205\) 21.1459 + 7.69648i 1.47689 + 0.537545i
\(206\) −8.19846 + 14.2002i −0.571214 + 0.989372i
\(207\) 0 0
\(208\) 0.0505072 + 0.0874810i 0.00350204 + 0.00606572i
\(209\) −0.101481 0.575529i −0.00701960 0.0398101i
\(210\) 0 0
\(211\) −0.946967 + 0.344668i −0.0651919 + 0.0237279i −0.374410 0.927263i \(-0.622155\pi\)
0.309218 + 0.950991i \(0.399933\pi\)
\(212\) 0.299011 1.69577i 0.0205361 0.116466i
\(213\) 0 0
\(214\) −5.11721 + 4.29385i −0.349805 + 0.293522i
\(215\) 24.1557 1.64740
\(216\) 0 0
\(217\) 11.3277 0.768974
\(218\) −10.5346 + 8.83959i −0.713494 + 0.598693i
\(219\) 0 0
\(220\) −0.134285 + 0.761570i −0.00905352 + 0.0513450i
\(221\) 6.79813 2.47432i 0.457292 0.166441i
\(222\) 0 0
\(223\) 3.17499 + 18.0063i 0.212613 + 1.20579i 0.885001 + 0.465590i \(0.154158\pi\)
−0.672387 + 0.740199i \(0.734731\pi\)
\(224\) 6.15910 + 10.6679i 0.411522 + 0.712777i
\(225\) 0 0
\(226\) −1.01707 + 1.76162i −0.0676548 + 0.117181i
\(227\) −2.48545 0.904631i −0.164965 0.0600424i 0.258217 0.966087i \(-0.416865\pi\)
−0.423183 + 0.906044i \(0.639087\pi\)
\(228\) 0 0
\(229\) −2.65270 2.22588i −0.175296 0.147090i 0.550919 0.834559i \(-0.314277\pi\)
−0.726214 + 0.687469i \(0.758722\pi\)
\(230\) 7.41534 + 6.22221i 0.488953 + 0.410281i
\(231\) 0 0
\(232\) −17.9097 6.51860i −1.17583 0.427967i
\(233\) 3.06283 5.30498i 0.200653 0.347541i −0.748086 0.663602i \(-0.769027\pi\)
0.948739 + 0.316061i \(0.102360\pi\)
\(234\) 0 0
\(235\) −14.3478 24.8511i −0.935945 1.62110i
\(236\) −1.09075 6.18594i −0.0710016 0.402670i
\(237\) 0 0
\(238\) −5.41622 + 1.97134i −0.351082 + 0.127783i
\(239\) 5.02734 28.5115i 0.325192 1.84425i −0.183133 0.983088i \(-0.558624\pi\)
0.508325 0.861165i \(-0.330265\pi\)
\(240\) 0 0
\(241\) 17.1027 14.3508i 1.10168 0.924419i 0.104142 0.994562i \(-0.466790\pi\)
0.997537 + 0.0701436i \(0.0223458\pi\)
\(242\) −9.65002 −0.620326
\(243\) 0 0
\(244\) 4.63816 0.296927
\(245\) 6.61721 5.55250i 0.422758 0.354736i
\(246\) 0 0
\(247\) 1.50593 8.54055i 0.0958200 0.543422i
\(248\) −13.8246 + 5.03174i −0.877863 + 0.319516i
\(249\) 0 0
\(250\) −2.99138 16.9650i −0.189192 1.07296i
\(251\) −11.3610 19.6778i −0.717098 1.24205i −0.962145 0.272539i \(-0.912137\pi\)
0.245047 0.969511i \(-0.421197\pi\)
\(252\) 0 0
\(253\) −0.230552 + 0.399328i −0.0144947 + 0.0251055i
\(254\) −0.0346151 0.0125989i −0.00217194 0.000790523i
\(255\) 0 0
\(256\) −12.3341 10.3495i −0.770881 0.646846i
\(257\) 15.0064 + 12.5919i 0.936073 + 0.785459i 0.976898 0.213708i \(-0.0685540\pi\)
−0.0408244 + 0.999166i \(0.512998\pi\)
\(258\) 0 0
\(259\) −13.6284 4.96032i −0.846825 0.308219i
\(260\) −5.73783 + 9.93821i −0.355845 + 0.616341i
\(261\) 0 0
\(262\) 8.06758 + 13.9735i 0.498417 + 0.863283i
\(263\) −3.09105 17.5302i −0.190602 1.08096i −0.918543 0.395320i \(-0.870634\pi\)
0.727941 0.685640i \(-0.240477\pi\)
\(264\) 0 0
\(265\) −5.11721 + 1.86251i −0.314348 + 0.114413i
\(266\) −1.19981 + 6.80445i −0.0735649 + 0.417207i
\(267\) 0 0
\(268\) 5.51114 4.62440i 0.336647 0.282480i
\(269\) −22.7888 −1.38946 −0.694729 0.719272i \(-0.744476\pi\)
−0.694729 + 0.719272i \(0.744476\pi\)
\(270\) 0 0
\(271\) −3.44562 −0.209307 −0.104653 0.994509i \(-0.533373\pi\)
−0.104653 + 0.994509i \(0.533373\pi\)
\(272\) 0.0962667 0.0807773i 0.00583702 0.00489784i
\(273\) 0 0
\(274\) −2.18567 + 12.3955i −0.132041 + 0.748843i
\(275\) 1.53462 0.558554i 0.0925408 0.0336821i
\(276\) 0 0
\(277\) −0.453830 2.57380i −0.0272680 0.154645i 0.968134 0.250434i \(-0.0805734\pi\)
−0.995402 + 0.0957898i \(0.969462\pi\)
\(278\) −4.61468 7.99287i −0.276770 0.479380i
\(279\) 0 0
\(280\) 12.0248 20.8276i 0.718620 1.24469i
\(281\) −12.8598 4.68058i −0.767150 0.279220i −0.0713464 0.997452i \(-0.522730\pi\)
−0.695804 + 0.718232i \(0.744952\pi\)
\(282\) 0 0
\(283\) 17.5273 + 14.7072i 1.04189 + 0.874251i 0.992218 0.124514i \(-0.0397372\pi\)
0.0496744 + 0.998765i \(0.484182\pi\)
\(284\) −14.3944 12.0783i −0.854150 0.716717i
\(285\) 0 0
\(286\) 0.323826 + 0.117863i 0.0191482 + 0.00696938i
\(287\) 6.33662 10.9753i 0.374039 0.647854i
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 3.97906 + 22.5663i 0.233658 + 1.32514i
\(291\) 0 0
\(292\) 10.0055 3.64171i 0.585529 0.213115i
\(293\) −4.21641 + 23.9125i −0.246326 + 1.39698i 0.571068 + 0.820903i \(0.306529\pi\)
−0.817394 + 0.576079i \(0.804582\pi\)
\(294\) 0 0
\(295\) −15.2173 + 12.7689i −0.885988 + 0.743432i
\(296\) 18.8357 1.09481
\(297\) 0 0
\(298\) 1.11793 0.0647597
\(299\) −5.24170 + 4.39831i −0.303135 + 0.254361i
\(300\) 0 0
\(301\) 2.36231 13.3973i 0.136161 0.772209i
\(302\) −6.49273 + 2.36316i −0.373614 + 0.135985i
\(303\) 0 0
\(304\) −0.0261591 0.148356i −0.00150033 0.00850878i
\(305\) −7.33409 12.7030i −0.419949 0.727373i
\(306\) 0 0
\(307\) 8.07444 13.9853i 0.460833 0.798186i −0.538170 0.842836i \(-0.680884\pi\)
0.999003 + 0.0446505i \(0.0142174\pi\)
\(308\) 0.409253 + 0.148956i 0.0233193 + 0.00848754i
\(309\) 0 0
\(310\) 13.5496 + 11.3695i 0.769567 + 0.645744i
\(311\) −14.3327 12.0266i −0.812736 0.681966i 0.138523 0.990359i \(-0.455764\pi\)
−0.951259 + 0.308393i \(0.900209\pi\)
\(312\) 0 0
\(313\) −2.60607 0.948531i −0.147304 0.0536141i 0.267316 0.963609i \(-0.413863\pi\)
−0.414620 + 0.909995i \(0.636085\pi\)
\(314\) 5.43124 9.40718i 0.306502 0.530878i
\(315\) 0 0
\(316\) −0.778066 1.34765i −0.0437696 0.0758112i
\(317\) −3.03580 17.2169i −0.170507 0.966995i −0.943203 0.332218i \(-0.892203\pi\)
0.772695 0.634777i \(-0.218908\pi\)
\(318\) 0 0
\(319\) −1.02569 + 0.373321i −0.0574277 + 0.0209020i
\(320\) −3.39646 + 19.2623i −0.189868 + 1.07679i
\(321\) 0 0
\(322\) 4.17617 3.50423i 0.232729 0.195283i
\(323\) −10.7888 −0.600305
\(324\) 0 0
\(325\) 24.2344 1.34428
\(326\) −9.26058 + 7.77055i −0.512896 + 0.430371i
\(327\) 0 0
\(328\) −2.85814 + 16.2093i −0.157814 + 0.895009i
\(329\) −15.1861 + 5.52730i −0.837239 + 0.304730i
\(330\) 0 0
\(331\) −5.63651 31.9662i −0.309810 1.75702i −0.599950 0.800038i \(-0.704813\pi\)
0.290139 0.956984i \(-0.406298\pi\)
\(332\) 5.19846 + 9.00400i 0.285303 + 0.494159i
\(333\) 0 0
\(334\) −1.63429 + 2.83067i −0.0894241 + 0.154887i
\(335\) −21.3799 7.78163i −1.16811 0.425156i
\(336\) 0 0
\(337\) 6.34730 + 5.32601i 0.345759 + 0.290126i 0.799085 0.601219i \(-0.205318\pi\)
−0.453325 + 0.891345i \(0.649762\pi\)
\(338\) −4.84002 4.06126i −0.263263 0.220903i
\(339\) 0 0
\(340\) 13.4153 + 4.88279i 0.727549 + 0.264806i
\(341\) −0.421274 + 0.729669i −0.0228133 + 0.0395138i
\(342\) 0 0
\(343\) −10.0792 17.4577i −0.544225 0.942626i
\(344\) 3.06805 + 17.3998i 0.165418 + 0.938132i
\(345\) 0 0
\(346\) −1.28864 + 0.469026i −0.0692776 + 0.0252150i
\(347\) −2.59833 + 14.7358i −0.139485 + 0.791061i 0.832145 + 0.554558i \(0.187113\pi\)
−0.971631 + 0.236503i \(0.923999\pi\)
\(348\) 0 0
\(349\) 25.7743 21.6272i 1.37966 1.15768i 0.410328 0.911938i \(-0.365414\pi\)
0.969336 0.245737i \(-0.0790301\pi\)
\(350\) −19.3081 −1.03206
\(351\) 0 0
\(352\) −0.916222 −0.0488348
\(353\) 12.0680 10.1263i 0.642317 0.538968i −0.262412 0.964956i \(-0.584518\pi\)
0.904729 + 0.425988i \(0.140073\pi\)
\(354\) 0 0
\(355\) −10.3191 + 58.5224i −0.547680 + 3.10605i
\(356\) −8.90110 + 3.23974i −0.471757 + 0.171706i
\(357\) 0 0
\(358\) 1.86184 + 10.5590i 0.0984015 + 0.558063i
\(359\) 9.06283 + 15.6973i 0.478318 + 0.828471i 0.999691 0.0248577i \(-0.00791328\pi\)
−0.521373 + 0.853329i \(0.674580\pi\)
\(360\) 0 0
\(361\) 3.03343 5.25406i 0.159654 0.276529i
\(362\) 13.9427 + 5.07472i 0.732811 + 0.266721i
\(363\) 0 0
\(364\) 4.95084 + 4.15425i 0.259494 + 0.217742i
\(365\) −25.7952 21.6447i −1.35018 1.13294i
\(366\) 0 0
\(367\) 17.9884 + 6.54726i 0.938989 + 0.341764i 0.765767 0.643119i \(-0.222360\pi\)
0.173223 + 0.984883i \(0.444582\pi\)
\(368\) −0.0594300 + 0.102936i −0.00309800 + 0.00536590i
\(369\) 0 0
\(370\) −11.3229 19.6119i −0.588652 1.01958i
\(371\) 0.532556 + 3.02027i 0.0276489 + 0.156805i
\(372\) 0 0
\(373\) 14.3302 5.21577i 0.741991 0.270063i 0.0567593 0.998388i \(-0.481923\pi\)
0.685231 + 0.728325i \(0.259701\pi\)
\(374\) 0.0744448 0.422197i 0.00384945 0.0218313i
\(375\) 0 0
\(376\) 16.0783 13.4913i 0.829176 0.695761i
\(377\) −16.1976 −0.834218
\(378\) 0 0
\(379\) 9.84760 0.505837 0.252919 0.967488i \(-0.418610\pi\)
0.252919 + 0.967488i \(0.418610\pi\)
\(380\) 13.1099 11.0005i 0.672526 0.564316i
\(381\) 0 0
\(382\) 2.66860 15.1344i 0.136537 0.774341i
\(383\) 26.6780 9.70999i 1.36318 0.496157i 0.446145 0.894961i \(-0.352797\pi\)
0.917036 + 0.398803i \(0.130574\pi\)
\(384\) 0 0
\(385\) −0.239170 1.35640i −0.0121892 0.0691286i
\(386\) 0.875982 + 1.51724i 0.0445863 + 0.0772257i
\(387\) 0 0
\(388\) −2.39615 + 4.15026i −0.121646 + 0.210698i
\(389\) 10.2280 + 3.72270i 0.518581 + 0.188748i 0.588033 0.808837i \(-0.299903\pi\)
−0.0694513 + 0.997585i \(0.522125\pi\)
\(390\) 0 0
\(391\) 6.52094 + 5.47172i 0.329778 + 0.276717i
\(392\) 4.84002 + 4.06126i 0.244458 + 0.205125i
\(393\) 0 0
\(394\) 17.5125 + 6.37402i 0.882266 + 0.321119i
\(395\) −2.46064 + 4.26195i −0.123808 + 0.214442i
\(396\) 0 0
\(397\) 9.05350 + 15.6811i 0.454382 + 0.787013i 0.998652 0.0518969i \(-0.0165267\pi\)
−0.544270 + 0.838910i \(0.683193\pi\)
\(398\) −0.470904 2.67063i −0.0236043 0.133867i
\(399\) 0 0
\(400\) 0.395582 0.143980i 0.0197791 0.00719900i
\(401\) −0.248970 + 1.41198i −0.0124330 + 0.0705110i −0.990393 0.138281i \(-0.955842\pi\)
0.977960 + 0.208792i \(0.0669533\pi\)
\(402\) 0 0
\(403\) −9.57785 + 8.03677i −0.477107 + 0.400340i
\(404\) −9.95306 −0.495183
\(405\) 0 0
\(406\) 12.9050 0.640463
\(407\) 0.826352 0.693392i 0.0409607 0.0343701i
\(408\) 0 0
\(409\) 1.49407 8.47329i 0.0738770 0.418977i −0.925330 0.379163i \(-0.876212\pi\)
0.999207 0.0398148i \(-0.0126768\pi\)
\(410\) 18.5954 6.76817i 0.918361 0.334256i
\(411\) 0 0
\(412\) −3.97178 22.5251i −0.195676 1.10973i
\(413\) 5.59374 + 9.68864i 0.275250 + 0.476747i
\(414\) 0 0
\(415\) 16.4402 28.4752i 0.807016 1.39779i
\(416\) −12.7763 4.65020i −0.626410 0.227995i
\(417\) 0 0
\(418\) −0.393685 0.330341i −0.0192558 0.0161575i
\(419\) 9.43107 + 7.91361i 0.460738 + 0.386605i 0.843403 0.537282i \(-0.180549\pi\)
−0.382664 + 0.923887i \(0.624993\pi\)
\(420\) 0 0
\(421\) −10.4461 3.80207i −0.509111 0.185301i 0.0746763 0.997208i \(-0.476208\pi\)
−0.583788 + 0.811906i \(0.698430\pi\)
\(422\) −0.443096 + 0.767465i −0.0215696 + 0.0373596i
\(423\) 0 0
\(424\) −1.99154 3.44946i −0.0967179 0.167520i
\(425\) −5.23530 29.6909i −0.253949 1.44022i
\(426\) 0 0
\(427\) −7.76264 + 2.82537i −0.375661 + 0.136729i
\(428\) 1.61809 9.17664i 0.0782133 0.443569i
\(429\) 0 0
\(430\) 16.2724 13.6542i 0.784727 0.658464i
\(431\) 36.8958 1.77721 0.888604 0.458675i \(-0.151676\pi\)
0.888604 + 0.458675i \(0.151676\pi\)
\(432\) 0 0
\(433\) −37.9982 −1.82608 −0.913040 0.407871i \(-0.866271\pi\)
−0.913040 + 0.407871i \(0.866271\pi\)
\(434\) 7.63088 6.40307i 0.366294 0.307357i
\(435\) 0 0
\(436\) 3.33110 18.8916i 0.159531 0.904744i
\(437\) 9.58899 3.49011i 0.458704 0.166955i
\(438\) 0 0
\(439\) 0.0350819 + 0.198960i 0.00167437 + 0.00949582i 0.985633 0.168898i \(-0.0540209\pi\)
−0.983959 + 0.178394i \(0.942910\pi\)
\(440\) 0.894400 + 1.54915i 0.0426388 + 0.0738526i
\(441\) 0 0
\(442\) 3.18092 5.50952i 0.151301 0.262061i
\(443\) 19.9491 + 7.26087i 0.947810 + 0.344974i 0.769245 0.638954i \(-0.220632\pi\)
0.178564 + 0.983928i \(0.442855\pi\)
\(444\) 0 0
\(445\) 22.9479 + 19.2556i 1.08783 + 0.912802i
\(446\) 12.3170 + 10.3352i 0.583228 + 0.489386i
\(447\) 0 0
\(448\) 10.3512 + 3.76752i 0.489047 + 0.177998i
\(449\) −16.6297 + 28.8035i −0.784804 + 1.35932i 0.144312 + 0.989532i \(0.453903\pi\)
−0.929116 + 0.369788i \(0.879430\pi\)
\(450\) 0 0
\(451\) 0.471315 + 0.816341i 0.0221933 + 0.0384400i
\(452\) −0.492726 2.79439i −0.0231759 0.131437i
\(453\) 0 0
\(454\) −2.18567 + 0.795519i −0.102579 + 0.0373355i
\(455\) 3.54916 20.1283i 0.166387 0.943629i
\(456\) 0 0
\(457\) −0.0261591 + 0.0219501i −0.00122367 + 0.00102678i −0.643399 0.765531i \(-0.722476\pi\)
0.642176 + 0.766558i \(0.278032\pi\)
\(458\) −3.04519 −0.142292
\(459\) 0 0
\(460\) −13.5030 −0.629580
\(461\) 11.4802 9.63306i 0.534688 0.448656i −0.335029 0.942208i \(-0.608746\pi\)
0.869717 + 0.493551i \(0.164302\pi\)
\(462\) 0 0
\(463\) −5.28627 + 29.9799i −0.245674 + 1.39329i 0.573248 + 0.819382i \(0.305683\pi\)
−0.818922 + 0.573905i \(0.805428\pi\)
\(464\) −0.264396 + 0.0962321i −0.0122743 + 0.00446746i
\(465\) 0 0
\(466\) −0.935412 5.30498i −0.0433321 0.245749i
\(467\) −0.255367 0.442308i −0.0118170 0.0204676i 0.860056 0.510199i \(-0.170428\pi\)
−0.871873 + 0.489731i \(0.837095\pi\)
\(468\) 0 0
\(469\) −6.40673 + 11.0968i −0.295835 + 0.512401i
\(470\) −23.7126 8.63068i −1.09378 0.398104i
\(471\) 0 0
\(472\) −11.1304 9.33953i −0.512319 0.429887i
\(473\) 0.775129 + 0.650411i 0.0356405 + 0.0299059i
\(474\) 0 0
\(475\) −33.9616 12.3610i −1.55826 0.567162i
\(476\) 4.02007 6.96296i 0.184259 0.319147i
\(477\) 0 0
\(478\) −12.7297 22.0484i −0.582242 1.00847i
\(479\) 2.68298 + 15.2159i 0.122589 + 0.695234i 0.982711 + 0.185147i \(0.0592760\pi\)
−0.860122 + 0.510088i \(0.829613\pi\)
\(480\) 0 0
\(481\) 15.0424 5.47497i 0.685872 0.249637i
\(482\) 3.40925 19.3348i 0.155287 0.880677i
\(483\) 0 0
\(484\) 10.3118 8.65263i 0.468718 0.393301i
\(485\) 15.1557 0.688185
\(486\) 0 0
\(487\) 29.5107 1.33726 0.668629 0.743596i \(-0.266881\pi\)
0.668629 + 0.743596i \(0.266881\pi\)
\(488\) 8.21869 6.89630i 0.372043 0.312181i
\(489\) 0 0
\(490\) 1.31908 7.48086i 0.0595899 0.337951i
\(491\) 2.02734 0.737892i 0.0914926 0.0333006i −0.295868 0.955229i \(-0.595609\pi\)
0.387361 + 0.921928i \(0.373387\pi\)
\(492\) 0 0
\(493\) 3.49912 + 19.8445i 0.157593 + 0.893752i
\(494\) −3.81315 6.60457i −0.171562 0.297153i
\(495\) 0 0
\(496\) −0.108593 + 0.188089i −0.00487597 + 0.00844543i
\(497\) 31.4488 + 11.4464i 1.41067 + 0.513442i
\(498\) 0 0
\(499\) 5.74170 + 4.81786i 0.257034 + 0.215677i 0.762194 0.647349i \(-0.224122\pi\)
−0.505160 + 0.863025i \(0.668567\pi\)
\(500\) 18.4081 + 15.4462i 0.823234 + 0.690775i
\(501\) 0 0
\(502\) −18.7763 6.83402i −0.838028 0.305017i
\(503\) 14.2981 24.7651i 0.637522 1.10422i −0.348453 0.937326i \(-0.613293\pi\)
0.985975 0.166894i \(-0.0533739\pi\)
\(504\) 0 0
\(505\) 15.7383 + 27.2595i 0.700345 + 1.21303i
\(506\) 0.0704123 + 0.399328i 0.00313021 + 0.0177523i
\(507\) 0 0
\(508\) 0.0482857 0.0175745i 0.00214233 0.000779745i
\(509\) 0.293796 1.66620i 0.0130223 0.0738530i −0.977604 0.210453i \(-0.932506\pi\)
0.990626 + 0.136600i \(0.0436174\pi\)
\(510\) 0 0
\(511\) −14.5273 + 12.1899i −0.642652 + 0.539249i
\(512\) −0.473897 −0.0209435
\(513\) 0 0
\(514\) 17.2267 0.759836
\(515\) −55.4115 + 46.4958i −2.44172 + 2.04885i
\(516\) 0 0
\(517\) 0.208730 1.18377i 0.00917994 0.0520620i
\(518\) −11.9846 + 4.36203i −0.526572 + 0.191657i
\(519\) 0 0
\(520\) 4.60947 + 26.1416i 0.202139 + 1.14639i
\(521\) −11.2019 19.4022i −0.490763 0.850026i 0.509181 0.860660i \(-0.329948\pi\)
−0.999943 + 0.0106337i \(0.996615\pi\)
\(522\) 0 0
\(523\) −1.21436 + 2.10332i −0.0531000 + 0.0919720i −0.891354 0.453309i \(-0.850244\pi\)
0.838254 + 0.545281i \(0.183577\pi\)
\(524\) −21.1501 7.69800i −0.923945 0.336289i
\(525\) 0 0
\(526\) −11.9914 10.0620i −0.522849 0.438722i
\(527\) 11.9153 + 9.99816i 0.519041 + 0.435527i
\(528\) 0 0
\(529\) 14.0471 + 5.11273i 0.610744 + 0.222293i
\(530\) −2.39440 + 4.14722i −0.104006 + 0.180144i
\(531\) 0 0
\(532\) −4.81908 8.34689i −0.208934 0.361883i
\(533\) 2.42902 + 13.7756i 0.105212 + 0.596689i
\(534\) 0 0
\(535\) −27.6917 + 10.0789i −1.19721 + 0.435751i
\(536\) 2.88976 16.3886i 0.124819 0.707881i
\(537\) 0 0
\(538\) −15.3516 + 12.8816i −0.661856 + 0.555363i
\(539\) 0.361844 0.0155857
\(540\) 0 0
\(541\) 38.9394 1.67414 0.837069 0.547098i \(-0.184267\pi\)
0.837069 + 0.547098i \(0.184267\pi\)
\(542\) −2.32114 + 1.94767i −0.0997014 + 0.0836594i
\(543\) 0 0
\(544\) −2.93717 + 16.6575i −0.125930 + 0.714184i
\(545\) −57.0078 + 20.7491i −2.44195 + 0.888796i
\(546\) 0 0
\(547\) −2.54782 14.4494i −0.108937 0.617812i −0.989575 0.144021i \(-0.953997\pi\)
0.880638 0.473790i \(-0.157115\pi\)
\(548\) −8.77884 15.2054i −0.375013 0.649542i
\(549\) 0 0
\(550\) 0.718063 1.24372i 0.0306183 0.0530325i
\(551\) 22.6989 + 8.26173i 0.967007 + 0.351962i
\(552\) 0 0
\(553\) 2.12314 + 1.78153i 0.0902851 + 0.0757582i
\(554\) −1.76058 1.47730i −0.0747999 0.0627646i
\(555\) 0 0
\(556\) 12.0979 + 4.40328i 0.513066 + 0.186741i
\(557\) −5.55350 + 9.61894i −0.235309 + 0.407568i −0.959363 0.282176i \(-0.908944\pi\)
0.724053 + 0.689744i \(0.242277\pi\)
\(558\) 0 0
\(559\) 7.50774 + 13.0038i 0.317544 + 0.550002i
\(560\) −0.0616516 0.349643i −0.00260525 0.0147751i
\(561\) 0 0
\(562\) −11.3087 + 4.11603i −0.477029 + 0.173624i
\(563\) −2.83187 + 16.0603i −0.119349 + 0.676863i 0.865155 + 0.501504i \(0.167220\pi\)
−0.984505 + 0.175359i \(0.943891\pi\)
\(564\) 0 0
\(565\) −6.87417 + 5.76811i −0.289199 + 0.242666i
\(566\) 20.1206 0.845733
\(567\) 0 0
\(568\) −43.4653 −1.82376
\(569\) −27.5902 + 23.1509i −1.15664 + 0.970536i −0.999854 0.0170961i \(-0.994558\pi\)
−0.156786 + 0.987633i \(0.550113\pi\)
\(570\) 0 0
\(571\) 6.79978 38.5635i 0.284562 1.61383i −0.422284 0.906464i \(-0.638771\pi\)
0.706846 0.707368i \(-0.250117\pi\)
\(572\) −0.451714 + 0.164411i −0.0188871 + 0.00687435i
\(573\) 0 0
\(574\) −1.93525 10.9753i −0.0807758 0.458102i
\(575\) 14.2579 + 24.6954i 0.594595 + 1.02987i
\(576\) 0 0
\(577\) −5.90286 + 10.2240i −0.245739 + 0.425633i −0.962339 0.271852i \(-0.912364\pi\)
0.716600 + 0.697484i \(0.245697\pi\)
\(578\) 6.61081 + 2.40614i 0.274974 + 0.100082i
\(579\) 0 0
\(580\) −24.4859 20.5461i −1.01672 0.853131i
\(581\) −14.1853 11.9028i −0.588504 0.493813i
\(582\) 0 0
\(583\) −0.214355 0.0780189i −0.00887769 0.00323121i
\(584\) 12.3148 21.3299i 0.509590 0.882636i
\(585\) 0 0
\(586\) 10.6763 + 18.4920i 0.441035 + 0.763896i
\(587\) 6.93923 + 39.3543i 0.286413 + 1.62433i 0.700196 + 0.713951i \(0.253096\pi\)
−0.413783 + 0.910375i \(0.635793\pi\)
\(588\) 0 0
\(589\) 17.5214 6.37727i 0.721957 0.262771i
\(590\) −3.03343 + 17.2035i −0.124884 + 0.708255i
\(591\) 0 0
\(592\) 0.213011 0.178737i 0.00875470 0.00734606i
\(593\) 29.2995 1.20319 0.601594 0.798802i \(-0.294533\pi\)
0.601594 + 0.798802i \(0.294533\pi\)
\(594\) 0 0
\(595\) −25.4270 −1.04240
\(596\) −1.19459 + 1.00238i −0.0489324 + 0.0410592i
\(597\) 0 0
\(598\) −1.04488 + 5.92582i −0.0427284 + 0.242325i
\(599\) 9.46451 3.44480i 0.386709 0.140751i −0.141347 0.989960i \(-0.545143\pi\)
0.528056 + 0.849209i \(0.322921\pi\)
\(600\) 0 0
\(601\) −5.28224 29.9571i −0.215467 1.22197i −0.880094 0.474799i \(-0.842521\pi\)
0.664627 0.747175i \(-0.268590\pi\)
\(602\) −5.98158 10.3604i −0.243791 0.422259i
\(603\) 0 0
\(604\) 4.81908 8.34689i 0.196085 0.339630i
\(605\) −40.0035 14.5601i −1.62637 0.591951i
\(606\) 0 0
\(607\) −17.6759 14.8319i −0.717444 0.602007i 0.209233 0.977866i \(-0.432903\pi\)
−0.926677 + 0.375859i \(0.877348\pi\)
\(608\) 15.5326 + 13.0334i 0.629928 + 0.528573i
\(609\) 0 0
\(610\) −12.1211 4.41171i −0.490768 0.178625i
\(611\) 8.91875 15.4477i 0.360814 0.624948i
\(612\) 0 0
\(613\) −0.382789 0.663010i −0.0154607 0.0267787i 0.858192 0.513330i \(-0.171588\pi\)
−0.873652 + 0.486551i \(0.838255\pi\)
\(614\) −2.46599 13.9853i −0.0995194 0.564403i
\(615\) 0 0
\(616\) 0.946662 0.344557i 0.0381421 0.0138826i
\(617\) 1.61287 9.14706i 0.0649319 0.368247i −0.934977 0.354710i \(-0.884580\pi\)
0.999908 0.0135372i \(-0.00430917\pi\)
\(618\) 0 0
\(619\) −26.8746 + 22.5505i −1.08018 + 0.906381i −0.995936 0.0900639i \(-0.971293\pi\)
−0.0842469 + 0.996445i \(0.526848\pi\)
\(620\) −24.6732 −0.990901
\(621\) 0 0
\(622\) −16.4534 −0.659720
\(623\) 12.9238 10.8444i 0.517781 0.434470i
\(624\) 0 0
\(625\) 4.47090 25.3558i 0.178836 1.01423i
\(626\) −2.29174 + 0.834124i −0.0915962 + 0.0333383i
\(627\) 0 0
\(628\) 2.63119 + 14.9222i 0.104996 + 0.595461i
\(629\) −9.95723 17.2464i −0.397021 0.687660i
\(630\) 0 0
\(631\) −17.8810 + 30.9709i −0.711833 + 1.23293i 0.252336 + 0.967640i \(0.418801\pi\)
−0.964168 + 0.265291i \(0.914532\pi\)
\(632\) −3.38248 1.23112i −0.134548 0.0489715i
\(633\) 0 0
\(634\) −11.7770 9.88210i −0.467725 0.392468i
\(635\) −0.124485 0.104455i −0.00494004 0.00414519i
\(636\) 0 0
\(637\) 5.04576 + 1.83651i 0.199920 + 0.0727650i
\(638\) −0.479933 + 0.831268i −0.0190007 + 0.0329102i
\(639\) 0 0
\(640\) −13.2724 22.9885i −0.524639 0.908702i
\(641\) −0.508151 2.88187i −0.0200708 0.113827i 0.973126 0.230271i \(-0.0739614\pi\)
−0.993197 + 0.116444i \(0.962850\pi\)
\(642\) 0 0
\(643\) 19.0303 6.92648i 0.750483 0.273154i 0.0616741 0.998096i \(-0.480356\pi\)
0.688809 + 0.724943i \(0.258134\pi\)
\(644\) −1.32053 + 7.48909i −0.0520361 + 0.295111i
\(645\) 0 0
\(646\) −7.26786 + 6.09845i −0.285950 + 0.239940i
\(647\) −10.7219 −0.421523 −0.210761 0.977538i \(-0.567594\pi\)
−0.210761 + 0.977538i \(0.567594\pi\)
\(648\) 0 0
\(649\) −0.832119 −0.0326635
\(650\) 16.3255 13.6987i 0.640338 0.537307i
\(651\) 0 0
\(652\) 2.92824 16.6069i 0.114679 0.650376i
\(653\) 33.5724 12.2193i 1.31379 0.478180i 0.412326 0.911036i \(-0.364716\pi\)
0.901463 + 0.432856i \(0.142494\pi\)
\(654\) 0 0
\(655\) 12.3603 + 70.0985i 0.482955 + 2.73897i
\(656\) 0.121492 + 0.210430i 0.00474347 + 0.00821593i
\(657\) 0 0
\(658\) −7.10576 + 12.3075i −0.277011 + 0.479798i
\(659\) 29.0043 + 10.5567i 1.12985 + 0.411231i 0.838237 0.545306i \(-0.183586\pi\)
0.291611 + 0.956537i \(0.405809\pi\)
\(660\) 0 0
\(661\) −7.54395 6.33012i −0.293426 0.246213i 0.484176 0.874971i \(-0.339119\pi\)
−0.777602 + 0.628757i \(0.783564\pi\)
\(662\) −21.8662 18.3479i −0.849853 0.713112i
\(663\) 0 0
\(664\) 22.5993 + 8.22546i 0.877021 + 0.319210i
\(665\) −15.2404 + 26.3971i −0.590996 + 1.02363i
\(666\) 0 0
\(667\) −9.52956 16.5057i −0.368986 0.639103i
\(668\) −0.791737 4.49016i −0.0306332 0.173730i
\(669\) 0 0
\(670\) −18.8011 + 6.84305i −0.726351 + 0.264370i
\(671\) 0.106696 0.605102i 0.00411895 0.0233597i
\(672\) 0 0
\(673\) −15.0890 + 12.6612i −0.581638 + 0.488052i −0.885485 0.464669i \(-0.846173\pi\)
0.303847 + 0.952721i \(0.401729\pi\)
\(674\) 7.28642 0.280662
\(675\) 0 0
\(676\) 8.81345 0.338979
\(677\) 21.7993 18.2918i 0.837816 0.703011i −0.119256 0.992864i \(-0.538051\pi\)
0.957071 + 0.289853i \(0.0936063\pi\)
\(678\) 0 0
\(679\) 1.48215 8.40571i 0.0568799 0.322582i
\(680\) 31.0317 11.2946i 1.19001 0.433128i
\(681\) 0 0
\(682\) 0.128660 + 0.729669i 0.00492666 + 0.0279405i
\(683\) 6.25537 + 10.8346i 0.239355 + 0.414575i 0.960529 0.278179i \(-0.0897307\pi\)
−0.721174 + 0.692754i \(0.756397\pi\)
\(684\) 0 0
\(685\) −27.7631 + 48.0871i −1.06077 + 1.83731i
\(686\) −16.6579 6.06299i −0.636002 0.231486i
\(687\) 0 0
\(688\) 0.199807 + 0.167658i 0.00761758 + 0.00639191i
\(689\) −2.59311 2.17588i −0.0987897 0.0828944i
\(690\) 0 0
\(691\) −40.0548 14.5788i −1.52376 0.554603i −0.561675 0.827358i \(-0.689843\pi\)
−0.962083 + 0.272756i \(0.912065\pi\)
\(692\) 0.956462 1.65664i 0.0363592 0.0629760i
\(693\) 0 0
\(694\) 6.57919 + 11.3955i 0.249743 + 0.432567i
\(695\) −7.07011 40.0966i −0.268184 1.52095i
\(696\) 0 0
\(697\) 16.3525 5.95183i 0.619396 0.225442i
\(698\) 5.13785 29.1382i 0.194471 1.10290i
\(699\) 0 0
\(700\) 20.6322 17.3125i 0.779825 0.654351i
\(701\) −51.7701 −1.95533 −0.977665 0.210167i \(-0.932599\pi\)
−0.977665 + 0.210167i \(0.932599\pi\)
\(702\) 0 0
\(703\) −23.8726 −0.900371
\(704\) −0.627640 + 0.526653i −0.0236551 + 0.0198490i
\(705\) 0 0
\(706\) 2.40565 13.6431i 0.0905378 0.513466i
\(707\) 16.6579 6.06299i 0.626485 0.228022i
\(708\) 0 0
\(709\) 2.63223 + 14.9281i 0.0988553 + 0.560636i 0.993498 + 0.113853i \(0.0363194\pi\)
−0.894642 + 0.446783i \(0.852570\pi\)
\(710\) 26.1288 + 45.2564i 0.980597 + 1.69844i
\(711\) 0 0
\(712\) −10.9555 + 18.9754i −0.410574 + 0.711135i
\(713\) −13.8246 5.03174i −0.517735 0.188440i
\(714\) 0 0
\(715\) 1.16456 + 0.977185i 0.0435522 + 0.0365446i
\(716\) −11.4572 9.61376i −0.428177 0.359283i
\(717\) 0 0
\(718\) 14.9782 + 5.45161i 0.558981 + 0.203452i
\(719\) −1.30747 + 2.26460i −0.0487603 + 0.0844553i −0.889375 0.457178i \(-0.848860\pi\)
0.840615 + 0.541633i \(0.182194\pi\)
\(720\) 0 0
\(721\) 20.3687 + 35.2796i 0.758570 + 1.31388i
\(722\) −0.926433 5.25406i −0.0344783 0.195536i
\(723\) 0 0
\(724\) −19.4491 + 7.07889i −0.722819 + 0.263085i
\(725\) −11.7216 + 66.4767i −0.435330 + 2.46888i
\(726\) 0 0
\(727\) −3.14022 + 2.63495i −0.116464 + 0.0977250i −0.699160 0.714965i \(-0.746442\pi\)
0.582696 + 0.812690i \(0.301998\pi\)
\(728\) 14.9495 0.554067
\(729\) 0 0
\(730\) −29.6117 −1.09598
\(731\) 14.3097 12.0073i 0.529265 0.444106i
\(732\) 0 0
\(733\) −6.63475 + 37.6275i −0.245060 + 1.38981i 0.575293 + 0.817948i \(0.304888\pi\)
−0.820353 + 0.571858i \(0.806223\pi\)
\(734\) 15.8188 5.75756i 0.583882 0.212516i
\(735\) 0 0
\(736\) −2.77807 15.7552i −0.102401 0.580744i
\(737\) −0.476529 0.825373i −0.0175532 0.0304030i
\(738\) 0 0
\(739\) 12.1047 20.9660i 0.445279 0.771247i −0.552792 0.833319i \(-0.686438\pi\)
0.998072 + 0.0620725i \(0.0197710\pi\)
\(740\) 29.6844 + 10.8042i 1.09122 + 0.397171i
\(741\) 0 0
\(742\) 2.06599 + 1.73357i 0.0758448 + 0.0636414i
\(743\) 2.53667 + 2.12852i 0.0930616 + 0.0780879i 0.688131 0.725586i \(-0.258431\pi\)
−0.595070 + 0.803674i \(0.702876\pi\)
\(744\) 0 0
\(745\) 4.63429 + 1.68674i 0.169787 + 0.0617974i
\(746\) 6.70527 11.6139i 0.245497 0.425214i
\(747\) 0 0
\(748\) 0.299011 + 0.517902i 0.0109329 + 0.0189364i
\(749\) 2.88191 + 16.3441i 0.105303 + 0.597202i
\(750\) 0 0
\(751\) −12.8841 + 4.68944i −0.470149 + 0.171120i −0.566220 0.824254i \(-0.691595\pi\)
0.0960710 + 0.995374i \(0.469372\pi\)
\(752\) 0.0538049 0.305143i 0.00196206 0.0111274i
\(753\) 0 0
\(754\) −10.9115 + 9.15581i −0.397372 + 0.333435i
\(755\) −30.4807 −1.10931
\(756\) 0 0
\(757\) 12.3833 0.450079 0.225040 0.974350i \(-0.427749\pi\)
0.225040 + 0.974350i \(0.427749\pi\)
\(758\) 6.63382 5.56643i 0.240951 0.202182i
\(759\) 0 0
\(760\) 6.87417 38.9854i 0.249352 1.41415i
\(761\) 7.12536 2.59342i 0.258294 0.0940114i −0.209628 0.977781i \(-0.567225\pi\)
0.467922 + 0.883770i \(0.345003\pi\)
\(762\) 0 0
\(763\) 5.93289 + 33.6471i 0.214785 + 1.21811i
\(764\) 10.7185 + 18.5650i 0.387783 + 0.671660i
\(765\) 0 0
\(766\) 12.4829 21.6211i 0.451026 0.781201i
\(767\) −11.6035 4.22334i −0.418980 0.152496i
\(768\) 0 0
\(769\) 2.46451 + 2.06797i 0.0888724 + 0.0745728i 0.686141 0.727468i \(-0.259303\pi\)
−0.597269 + 0.802041i \(0.703748\pi\)
\(770\) −0.927833 0.778544i −0.0334368 0.0280568i
\(771\) 0 0
\(772\) −2.29648 0.835852i −0.0826523 0.0300830i
\(773\) −0.0922341 + 0.159754i −0.00331743 + 0.00574596i −0.867679 0.497124i \(-0.834389\pi\)
0.864362 + 0.502870i \(0.167723\pi\)
\(774\) 0 0
\(775\) 26.0526 + 45.1245i 0.935838 + 1.62092i
\(776\) 1.92495 + 10.9169i 0.0691015 + 0.391894i
\(777\) 0 0
\(778\) 8.99437 3.27368i 0.322464 0.117367i
\(779\) 3.62243 20.5438i 0.129787 0.736058i
\(780\) 0 0
\(781\) −1.90689 + 1.60007i −0.0682338 + 0.0572550i
\(782\) 7.48576 0.267690
\(783\) 0 0
\(784\) 0.0932736 0.00333120
\(785\) 36.7085 30.8021i 1.31018 1.09937i
\(786\) 0 0
\(787\) −0.0830066 + 0.470754i −0.00295887 + 0.0167806i −0.986251 0.165252i \(-0.947156\pi\)
0.983293 + 0.182032i \(0.0582675\pi\)
\(788\) −24.4287 + 8.89132i −0.870237 + 0.316740i
\(789\) 0 0
\(790\) 0.751497 + 4.26195i 0.0267370 + 0.151633i
\(791\) 2.52687 + 4.37667i 0.0898453 + 0.155617i
\(792\) 0 0
\(793\) 4.55896 7.89636i 0.161894 0.280408i
\(794\) 14.9628 + 5.44600i 0.531008 + 0.193271i
\(795\) 0 0
\(796\) 2.89780 + 2.43155i 0.102710 + 0.0861839i
\(797\) −11.1068 9.31970i −0.393422 0.330121i 0.424522 0.905418i \(-0.360442\pi\)
−0.817945 + 0.575297i \(0.804887\pi\)
\(798\) 0 0
\(799\) −20.8525 7.58969i −0.737709 0.268504i
\(800\) −28.3307 + 49.0702i −1.00164 + 1.73489i
\(801\) 0 0
\(802\) 0.630415 + 1.09191i 0.0222607 + 0.0385567i
\(803\) −0.244938 1.38911i −0.00864367 0.0490207i
\(804\) 0 0
\(805\) 22.5993 8.22546i 0.796519 0.289909i
\(806\) −1.90925 + 10.8279i −0.0672506 + 0.381397i
\(807\) 0 0
\(808\) −17.6366 + 14.7988i −0.620452 + 0.520621i
\(809\) 14.8743 0.522954 0.261477 0.965210i \(-0.415790\pi\)
0.261477 + 0.965210i \(0.415790\pi\)
\(810\) 0 0
\(811\) 21.5963 0.758347 0.379174 0.925325i \(-0.376208\pi\)
0.379174 + 0.925325i \(0.376208\pi\)
\(812\) −13.7900 + 11.5712i −0.483933 + 0.406068i
\(813\) 0 0
\(814\) 0.164725 0.934204i 0.00577362 0.0327438i
\(815\) −50.1134 + 18.2398i −1.75540 + 0.638912i
\(816\) 0 0
\(817\) −3.88847 22.0526i −0.136040 0.771523i
\(818\) −3.78312 6.55255i −0.132274 0.229105i
\(819\) 0 0
\(820\) −13.8020 + 23.9058i −0.481987 + 0.834826i
\(821\) −3.08347 1.12229i −0.107614 0.0391683i 0.287652 0.957735i \(-0.407125\pi\)
−0.395266 + 0.918567i \(0.629348\pi\)
\(822\) 0 0
\(823\) 10.5189 + 8.82639i 0.366665 + 0.307669i 0.807441 0.589949i \(-0.200852\pi\)
−0.440775 + 0.897617i \(0.645296\pi\)
\(824\) −40.5296 34.0084i −1.41192 1.18474i
\(825\) 0 0
\(826\) 9.24480 + 3.36483i 0.321668 + 0.117077i
\(827\) 10.1163 17.5220i 0.351779 0.609300i −0.634782 0.772691i \(-0.718910\pi\)
0.986561 + 0.163392i \(0.0522434\pi\)
\(828\) 0 0
\(829\) −12.7638 22.1076i −0.443306 0.767828i 0.554627 0.832099i \(-0.312861\pi\)
−0.997932 + 0.0642710i \(0.979528\pi\)
\(830\) −5.02094 28.4752i −0.174280 0.988388i
\(831\) 0 0
\(832\) −11.4251 + 4.15841i −0.396096 + 0.144167i
\(833\) 1.15998 6.57856i 0.0401908 0.227934i
\(834\) 0 0
\(835\) −11.0458 + 9.26849i −0.382254 + 0.320749i
\(836\) 0.716881 0.0247939
\(837\) 0 0
\(838\) 10.8265 0.373994
\(839\) −13.3139 + 11.1717i −0.459646 + 0.385688i −0.843001 0.537913i \(-0.819213\pi\)
0.383355 + 0.923601i \(0.374769\pi\)
\(840\) 0 0
\(841\) 2.79860 15.8717i 0.0965035 0.547298i
\(842\) −9.18614 + 3.34348i −0.316575 + 0.115224i
\(843\) 0 0
\(844\) −0.214660 1.21740i −0.00738890 0.0419045i
\(845\) −13.9363 24.1384i −0.479423 0.830385i
\(846\) 0 0
\(847\) −11.9875 + 20.7630i −0.411896 + 0.713424i
\(848\) −0.0552549 0.0201112i −0.00189746 0.000690620i
\(849\) 0 0
\(850\) −20.3097 17.0419i −0.696618 0.584532i
\(851\) 14.4290 + 12.1074i 0.494620 + 0.415036i
\(852\) 0 0
\(853\) −12.5005 4.54980i −0.428008 0.155782i 0.119029 0.992891i \(-0.462022\pi\)
−0.547037 + 0.837109i \(0.684244\pi\)
\(854\) −3.63223 + 6.29120i −0.124292 + 0.215280i
\(855\) 0 0
\(856\) −10.7772 18.6666i −0.368357 0.638013i
\(857\) 3.45929 + 19.6186i 0.118167 + 0.670159i 0.985133 + 0.171792i \(0.0549558\pi\)
−0.866966 + 0.498367i \(0.833933\pi\)
\(858\) 0 0
\(859\) −24.7558 + 9.01039i −0.844658 + 0.307430i −0.727860 0.685725i \(-0.759485\pi\)
−0.116798 + 0.993156i \(0.537263\pi\)
\(860\) −5.14543 + 29.1812i −0.175458 + 0.995070i
\(861\) 0 0
\(862\) 24.8548 20.8556i 0.846557 0.710346i
\(863\) −38.2995 −1.30373 −0.651866 0.758334i \(-0.726013\pi\)
−0.651866 + 0.758334i \(0.726013\pi\)
\(864\) 0 0
\(865\) −6.04963 −0.205694
\(866\) −25.5974 + 21.4788i −0.869837 + 0.729880i
\(867\) 0 0
\(868\) −2.41292 + 13.6844i −0.0819000 + 0.464478i
\(869\) −0.193715 + 0.0705066i −0.00657134 + 0.00239177i
\(870\) 0 0
\(871\) −2.45589 13.9280i −0.0832146 0.471934i
\(872\) −22.1866 38.4283i −0.751333 1.30135i
\(873\) 0 0
\(874\) 4.48680 7.77136i 0.151768 0.262870i
\(875\) −40.2178 14.6381i −1.35961 0.494858i
\(876\) 0 0
\(877\) −20.7271 17.3921i −0.699906 0.587291i 0.221841 0.975083i \(-0.428793\pi\)
−0.921747 + 0.387792i \(0.873238\pi\)
\(878\) 0.136096 + 0.114198i 0.00459303 + 0.00385401i
\(879\) 0 0
\(880\) 0.0248149 + 0.00903189i 0.000836511 + 0.000304465i
\(881\) 15.2888 26.4810i 0.515093 0.892167i −0.484754 0.874651i \(-0.661091\pi\)
0.999847 0.0175162i \(-0.00557586\pi\)
\(882\) 0 0
\(883\) −22.0526 38.1963i −0.742130 1.28541i −0.951524 0.307575i \(-0.900482\pi\)
0.209394 0.977831i \(-0.432851\pi\)
\(884\) 1.54101 + 8.73951i 0.0518298 + 0.293942i
\(885\) 0 0
\(886\) 17.5429 6.38510i 0.589366 0.214512i
\(887\) 1.36912 7.76466i 0.0459705 0.260712i −0.953157 0.302476i \(-0.902187\pi\)
0.999127 + 0.0417644i \(0.0132979\pi\)
\(888\) 0 0
\(889\) −0.0701076 + 0.0588272i −0.00235133 + 0.00197300i
\(890\) 26.3432 0.883025
\(891\) 0 0
\(892\) −22.4287 −0.750969
\(893\) −20.3778 + 17.0990i −0.681917 + 0.572196i
\(894\) 0 0
\(895\) −8.21348 + 46.5809i −0.274546 + 1.55703i
\(896\) −14.0480 + 5.11305i −0.469310 + 0.170815i
\(897\) 0 0
\(898\) 5.07883 + 28.8035i 0.169483 + 0.961185i
\(899\) −17.4128 30.1599i −0.580750 1.00589i
\(900\) 0 0
\(901\) −2.10560 + 3.64701i −0.0701477 + 0.121499i
\(902\) 0.778943 + 0.283512i 0.0259360 + 0.00943993i
\(903\) 0 0
\(904\) −5.02797 4.21897i −0.167228 0.140321i
\(905\) 50.1416 + 42.0738i 1.66676 + 1.39858i
\(906\) 0 0
\(907\) 12.1284 + 4.41436i 0.402715 + 0.146576i 0.535433 0.844577i \(-0.320148\pi\)
−0.132718 + 0.991154i \(0.542370\pi\)
\(908\) 1.62226 2.80984i 0.0538367 0.0932479i
\(909\) 0 0
\(910\) −8.98680 15.5656i −0.297909 0.515994i
\(911\) −3.67886 20.8639i −0.121886 0.691251i −0.983109 0.183023i \(-0.941412\pi\)
0.861223 0.508228i \(-0.169699\pi\)
\(912\) 0 0
\(913\) 1.29426 0.471073i 0.0428339 0.0155902i
\(914\) −0.00521457 + 0.0295733i −0.000172483 + 0.000978197i
\(915\) 0 0
\(916\) 3.25402 2.73045i 0.107516 0.0902166i
\(917\) 40.0871 1.32379
\(918\) 0 0
\(919\) 31.4688 1.03806 0.519031 0.854756i \(-0.326293\pi\)
0.519031 + 0.854756i \(0.326293\pi\)
\(920\) −23.9270 + 20.0771i −0.788848 + 0.661922i
\(921\) 0 0
\(922\) 2.28848 12.9786i 0.0753669 0.427427i
\(923\) −34.7117 + 12.6340i −1.14255 + 0.415854i
\(924\) 0 0
\(925\) −11.5842 65.6975i −0.380888 2.16012i
\(926\) 13.3853 + 23.1840i 0.439869 + 0.761875i
\(927\) 0 0
\(928\) 18.9354 32.7971i 0.621585 1.07662i
\(929\) −2.18644 0.795800i −0.0717348 0.0261093i 0.305904 0.952063i \(-0.401042\pi\)
−0.377638 + 0.925953i \(0.623264\pi\)
\(930\) 0 0
\(931\) −6.13429 5.14728i −0.201043 0.168695i
\(932\) 5.75624 + 4.83006i 0.188552 + 0.158214i
\(933\) 0 0
\(934\) −0.422046 0.153612i −0.0138098 0.00502634i
\(935\) 0.945622 1.63787i 0.0309252 0.0535639i
\(936\) 0 0
\(937\) 5.49912 + 9.52476i 0.179649 + 0.311160i 0.941760 0.336285i \(-0.109171\pi\)
−0.762112 + 0.647446i \(0.775837\pi\)
\(938\) 1.95666 + 11.0968i 0.0638872 + 0.362323i
\(939\) 0 0
\(940\) 33.0774 12.0392i 1.07887 0.392675i
\(941\) 4.18556 23.7375i 0.136445 0.773821i −0.837397 0.546596i \(-0.815924\pi\)
0.973842 0.227225i \(-0.0729654\pi\)
\(942\) 0 0
\(943\) −12.6086 + 10.5799i −0.410592 + 0.344528i
\(944\) −0.214498 −0.00698131
\(945\) 0 0
\(946\) 0.889814 0.0289304
\(947\) 9.13088 7.66172i 0.296714 0.248972i −0.482261 0.876028i \(-0.660184\pi\)
0.778975 + 0.627055i \(0.215740\pi\)
\(948\) 0 0
\(949\) 3.63475 20.6137i 0.117989 0.669149i
\(950\) −29.8653 + 10.8701i −0.968958 + 0.352672i
\(951\) 0 0
\(952\) −3.22951 18.3155i −0.104669 0.593608i
\(953\) −18.4145 31.8948i −0.596503 1.03317i −0.993333 0.115281i \(-0.963223\pi\)
0.396830 0.917892i \(-0.370110\pi\)
\(954\) 0 0
\(955\) 33.8974 58.7120i 1.09689 1.89988i
\(956\) 33.3723 + 12.1465i 1.07934 + 0.392846i
\(957\) 0 0
\(958\) 10.4083 + 8.73362i 0.336278 + 0.282170i
\(959\) 23.9552 + 20.1008i 0.773553 + 0.649088i
\(960\) 0 0
\(961\) 3.86959 + 1.40841i 0.124825 + 0.0454327i
\(962\) 7.03849 12.1910i 0.226930 0.393054i
\(963\) 0 0
\(964\) 13.6934 + 23.7177i 0.441035 + 0.763895i
\(965\) 1.34208 + 7.61132i 0.0432031 + 0.245017i
\(966\) 0 0
\(967\) −50.3303 + 18.3187i −1.61851 + 0.589090i −0.983098 0.183081i \(-0.941393\pi\)
−0.635415 + 0.772171i \(0.719171\pi\)
\(968\) 5.40697 30.6645i 0.173787 0.985594i
\(969\) 0 0
\(970\) 10.2096 8.56688i 0.327811 0.275066i
\(971\) −53.2327 −1.70832 −0.854159 0.520012i \(-0.825927\pi\)
−0.854159 + 0.520012i \(0.825927\pi\)
\(972\) 0 0
\(973\) −22.9299 −0.735100
\(974\) 19.8799 16.6812i 0.636992 0.534499i
\(975\) 0 0
\(976\) 0.0275033 0.155979i 0.000880358 0.00499276i
\(977\) 12.6454 4.60256i 0.404563 0.147249i −0.131720 0.991287i \(-0.542050\pi\)
0.536283 + 0.844038i \(0.319828\pi\)
\(978\) 0 0
\(979\) 0.217901 + 1.23578i 0.00696416 + 0.0394957i
\(980\) 5.29813 + 9.17664i 0.169243 + 0.293137i
\(981\) 0 0
\(982\) 0.948615 1.64305i 0.0302715 0.0524318i
\(983\) −9.62361 3.50271i −0.306945 0.111719i 0.183955 0.982935i \(-0.441110\pi\)
−0.490900 + 0.871216i \(0.663332\pi\)
\(984\) 0 0
\(985\) 62.9796 + 52.8461i 2.00670 + 1.68382i
\(986\) 13.5744 + 11.3903i 0.432298 + 0.362741i
\(987\) 0 0
\(988\) 9.99660 + 3.63846i 0.318034 + 0.115755i
\(989\) −8.83409 + 15.3011i −0.280908 + 0.486547i
\(990\) 0 0
\(991\) −1.00000 1.73205i −0.0317660 0.0550204i 0.849705 0.527258i \(-0.176780\pi\)
−0.881471 + 0.472237i \(0.843446\pi\)
\(992\) −5.07620 28.7886i −0.161169 0.914038i
\(993\) 0 0
\(994\) 27.6556 10.0658i 0.877182 0.319268i
\(995\) 2.07738 11.7814i 0.0658574 0.373496i
\(996\) 0 0
\(997\) 29.4939 24.7483i 0.934081 0.783787i −0.0424642 0.999098i \(-0.513521\pi\)
0.976546 + 0.215311i \(0.0690764\pi\)
\(998\) 6.59121 0.208641
\(999\) 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.e.g.325.1 6
3.2 odd 2 729.2.e.b.325.1 6
9.2 odd 6 729.2.e.i.568.1 6
9.4 even 3 729.2.e.h.82.1 6
9.5 odd 6 729.2.e.c.82.1 6
9.7 even 3 729.2.e.a.568.1 6
27.2 odd 18 729.2.e.i.163.1 6
27.4 even 9 243.2.a.e.1.3 3
27.5 odd 18 243.2.c.e.82.3 6
27.7 even 9 729.2.e.h.649.1 6
27.11 odd 18 729.2.e.b.406.1 6
27.13 even 9 243.2.c.f.163.1 6
27.14 odd 18 243.2.c.e.163.3 6
27.16 even 9 inner 729.2.e.g.406.1 6
27.20 odd 18 729.2.e.c.649.1 6
27.22 even 9 243.2.c.f.82.1 6
27.23 odd 18 243.2.a.f.1.1 yes 3
27.25 even 9 729.2.e.a.163.1 6
108.23 even 18 3888.2.a.bk.1.3 3
108.31 odd 18 3888.2.a.bd.1.1 3
135.4 even 18 6075.2.a.bv.1.1 3
135.104 odd 18 6075.2.a.bq.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
243.2.a.e.1.3 3 27.4 even 9
243.2.a.f.1.1 yes 3 27.23 odd 18
243.2.c.e.82.3 6 27.5 odd 18
243.2.c.e.163.3 6 27.14 odd 18
243.2.c.f.82.1 6 27.22 even 9
243.2.c.f.163.1 6 27.13 even 9
729.2.e.a.163.1 6 27.25 even 9
729.2.e.a.568.1 6 9.7 even 3
729.2.e.b.325.1 6 3.2 odd 2
729.2.e.b.406.1 6 27.11 odd 18
729.2.e.c.82.1 6 9.5 odd 6
729.2.e.c.649.1 6 27.20 odd 18
729.2.e.g.325.1 6 1.1 even 1 trivial
729.2.e.g.406.1 6 27.16 even 9 inner
729.2.e.h.82.1 6 9.4 even 3
729.2.e.h.649.1 6 27.7 even 9
729.2.e.i.163.1 6 27.2 odd 18
729.2.e.i.568.1 6 9.2 odd 6
3888.2.a.bd.1.1 3 108.31 odd 18
3888.2.a.bk.1.3 3 108.23 even 18
6075.2.a.bq.1.3 3 135.104 odd 18
6075.2.a.bv.1.1 3 135.4 even 18