Properties

Label 108.2.h.a.35.1
Level $108$
Weight $2$
Character 108.35
Analytic conductor $0.862$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [108,2,Mod(35,108)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(108, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("108.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.862384341830\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.170772624.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 35.1
Root \(-1.02187 + 0.977642i\) of defining polynomial
Character \(\chi\) \(=\) 108.35
Dual form 108.2.h.a.71.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.02187 + 0.977642i) q^{2} +(0.0884324 - 1.99804i) q^{4} +(2.18614 - 1.26217i) q^{5} +(1.10489 + 0.637910i) q^{7} +(1.86301 + 2.12819i) q^{8} +O(q^{10})\) \(q+(-1.02187 + 0.977642i) q^{2} +(0.0884324 - 1.99804i) q^{4} +(2.18614 - 1.26217i) q^{5} +(1.10489 + 0.637910i) q^{7} +(1.86301 + 2.12819i) q^{8} +(-1.00000 + 3.42703i) q^{10} +(-0.252704 + 0.437696i) q^{11} +(1.18614 + 2.05446i) q^{13} +(-1.75270 + 0.428329i) q^{14} +(-3.98436 - 0.353383i) q^{16} +0.792287i q^{17} -4.70285i q^{19} +(-2.32854 - 4.47962i) q^{20} +(-0.169680 - 0.694322i) q^{22} +(-1.61030 - 2.78912i) q^{23} +(0.686141 - 1.18843i) q^{25} +(-3.22060 - 0.939764i) q^{26} +(1.37228 - 2.15121i) q^{28} +(-2.18614 - 1.26217i) q^{29} +(-7.04069 + 4.06494i) q^{31} +(4.41698 - 3.53417i) q^{32} +(-0.774573 - 0.809613i) q^{34} +3.22060 q^{35} -6.74456 q^{37} +(4.59771 + 4.80570i) q^{38} +(6.75893 + 2.30110i) q^{40} +(-5.87228 + 3.39036i) q^{41} +(6.69391 + 3.86473i) q^{43} +(0.852189 + 0.543620i) q^{44} +(4.37228 + 1.27582i) q^{46} +(-0.599485 + 1.03834i) q^{47} +(-2.68614 - 4.65253i) q^{49} +(0.460714 + 1.88522i) q^{50} +(4.20979 - 2.18828i) q^{52} +1.87953i q^{53} +1.27582i q^{55} +(0.700825 + 3.53986i) q^{56} +(3.46790 - 0.847492i) q^{58} +(6.18850 + 10.7188i) q^{59} +(1.18614 - 2.05446i) q^{61} +(3.22060 - 11.0371i) q^{62} +(-1.05842 + 7.92967i) q^{64} +(5.18614 + 2.99422i) q^{65} +(6.69391 - 3.86473i) q^{67} +(1.58302 + 0.0700638i) q^{68} +(-3.29103 + 3.14860i) q^{70} -11.8716 q^{71} +3.37228 q^{73} +(6.89206 - 6.59377i) q^{74} +(-9.39651 - 0.415885i) q^{76} +(-0.558422 + 0.322405i) q^{77} +(-8.55691 - 4.94034i) q^{79} +(-9.15640 + 4.25639i) q^{80} +(2.68614 - 9.20550i) q^{82} +(3.82009 - 6.61659i) q^{83} +(1.00000 + 1.73205i) q^{85} +(-10.6186 + 2.59500i) q^{86} +(-1.40229 + 0.277627i) q^{88} -11.9769i q^{89} +3.02661i q^{91} +(-5.71519 + 2.97080i) q^{92} +(-0.402528 - 1.64713i) q^{94} +(-5.93580 - 10.2811i) q^{95} +(-5.24456 + 9.08385i) q^{97} +(7.29339 + 2.12819i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 3 q^{2} - q^{4} + 6 q^{5} - 8 q^{10} - 2 q^{13} - 12 q^{14} - q^{16} - 18 q^{20} + 3 q^{22} - 6 q^{25} - 12 q^{28} - 6 q^{29} + 33 q^{32} + 7 q^{34} - 8 q^{37} + 27 q^{38} + 10 q^{40} - 24 q^{41} + 12 q^{46} - 10 q^{49} - 21 q^{50} + 16 q^{52} - 18 q^{56} + 4 q^{58} - 2 q^{61} + 26 q^{64} + 30 q^{65} + 15 q^{68} - 6 q^{70} + 4 q^{73} + 30 q^{74} - 3 q^{76} + 30 q^{77} + 10 q^{82} + 8 q^{85} - 21 q^{86} - 21 q^{88} - 24 q^{92} - 18 q^{94} + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.02187 + 0.977642i −0.722570 + 0.691297i
\(3\) 0 0
\(4\) 0.0884324 1.99804i 0.0442162 0.999022i
\(5\) 2.18614 1.26217i 0.977672 0.564459i 0.0761054 0.997100i \(-0.475751\pi\)
0.901566 + 0.432641i \(0.142418\pi\)
\(6\) 0 0
\(7\) 1.10489 + 0.637910i 0.417610 + 0.241107i 0.694054 0.719923i \(-0.255823\pi\)
−0.276444 + 0.961030i \(0.589156\pi\)
\(8\) 1.86301 + 2.12819i 0.658672 + 0.752430i
\(9\) 0 0
\(10\) −1.00000 + 3.42703i −0.316228 + 1.08372i
\(11\) −0.252704 + 0.437696i −0.0761931 + 0.131970i −0.901605 0.432561i \(-0.857610\pi\)
0.825411 + 0.564532i \(0.190943\pi\)
\(12\) 0 0
\(13\) 1.18614 + 2.05446i 0.328976 + 0.569804i 0.982309 0.187267i \(-0.0599631\pi\)
−0.653333 + 0.757071i \(0.726630\pi\)
\(14\) −1.75270 + 0.428329i −0.468430 + 0.114476i
\(15\) 0 0
\(16\) −3.98436 0.353383i −0.996090 0.0883459i
\(17\) 0.792287i 0.192158i 0.995374 + 0.0960789i \(0.0306301\pi\)
−0.995374 + 0.0960789i \(0.969370\pi\)
\(18\) 0 0
\(19\) 4.70285i 1.07891i −0.842015 0.539454i \(-0.818631\pi\)
0.842015 0.539454i \(-0.181369\pi\)
\(20\) −2.32854 4.47962i −0.520678 1.00167i
\(21\) 0 0
\(22\) −0.169680 0.694322i −0.0361759 0.148030i
\(23\) −1.61030 2.78912i −0.335771 0.581572i 0.647862 0.761758i \(-0.275664\pi\)
−0.983633 + 0.180186i \(0.942330\pi\)
\(24\) 0 0
\(25\) 0.686141 1.18843i 0.137228 0.237686i
\(26\) −3.22060 0.939764i −0.631612 0.184303i
\(27\) 0 0
\(28\) 1.37228 2.15121i 0.259337 0.406541i
\(29\) −2.18614 1.26217i −0.405956 0.234379i 0.283095 0.959092i \(-0.408639\pi\)
−0.689051 + 0.724713i \(0.741972\pi\)
\(30\) 0 0
\(31\) −7.04069 + 4.06494i −1.26455 + 0.730086i −0.973951 0.226761i \(-0.927186\pi\)
−0.290595 + 0.956846i \(0.593853\pi\)
\(32\) 4.41698 3.53417i 0.780818 0.624758i
\(33\) 0 0
\(34\) −0.774573 0.809613i −0.132838 0.138848i
\(35\) 3.22060 0.544381
\(36\) 0 0
\(37\) −6.74456 −1.10880 −0.554400 0.832251i \(-0.687052\pi\)
−0.554400 + 0.832251i \(0.687052\pi\)
\(38\) 4.59771 + 4.80570i 0.745847 + 0.779588i
\(39\) 0 0
\(40\) 6.75893 + 2.30110i 1.06868 + 0.363837i
\(41\) −5.87228 + 3.39036i −0.917096 + 0.529486i −0.882708 0.469923i \(-0.844282\pi\)
−0.0343887 + 0.999409i \(0.510948\pi\)
\(42\) 0 0
\(43\) 6.69391 + 3.86473i 1.02081 + 0.589366i 0.914339 0.404950i \(-0.132711\pi\)
0.106473 + 0.994316i \(0.466044\pi\)
\(44\) 0.852189 + 0.543620i 0.128472 + 0.0819538i
\(45\) 0 0
\(46\) 4.37228 + 1.27582i 0.644658 + 0.188110i
\(47\) −0.599485 + 1.03834i −0.0874439 + 0.151457i −0.906430 0.422356i \(-0.861203\pi\)
0.818986 + 0.573813i \(0.194537\pi\)
\(48\) 0 0
\(49\) −2.68614 4.65253i −0.383734 0.664647i
\(50\) 0.460714 + 1.88522i 0.0651548 + 0.266610i
\(51\) 0 0
\(52\) 4.20979 2.18828i 0.583792 0.303460i
\(53\) 1.87953i 0.258173i 0.991633 + 0.129086i \(0.0412045\pi\)
−0.991633 + 0.129086i \(0.958796\pi\)
\(54\) 0 0
\(55\) 1.27582i 0.172032i
\(56\) 0.700825 + 3.53986i 0.0936516 + 0.473033i
\(57\) 0 0
\(58\) 3.46790 0.847492i 0.455357 0.111281i
\(59\) 6.18850 + 10.7188i 0.805674 + 1.39547i 0.915835 + 0.401555i \(0.131530\pi\)
−0.110161 + 0.993914i \(0.535137\pi\)
\(60\) 0 0
\(61\) 1.18614 2.05446i 0.151870 0.263046i −0.780045 0.625723i \(-0.784804\pi\)
0.931915 + 0.362677i \(0.118137\pi\)
\(62\) 3.22060 11.0371i 0.409017 1.40172i
\(63\) 0 0
\(64\) −1.05842 + 7.92967i −0.132303 + 0.991209i
\(65\) 5.18614 + 2.99422i 0.643262 + 0.371387i
\(66\) 0 0
\(67\) 6.69391 3.86473i 0.817791 0.472152i −0.0318630 0.999492i \(-0.510144\pi\)
0.849654 + 0.527340i \(0.176811\pi\)
\(68\) 1.58302 + 0.0700638i 0.191970 + 0.00849648i
\(69\) 0 0
\(70\) −3.29103 + 3.14860i −0.393354 + 0.376329i
\(71\) −11.8716 −1.40890 −0.704450 0.709754i \(-0.748806\pi\)
−0.704450 + 0.709754i \(0.748806\pi\)
\(72\) 0 0
\(73\) 3.37228 0.394696 0.197348 0.980334i \(-0.436767\pi\)
0.197348 + 0.980334i \(0.436767\pi\)
\(74\) 6.89206 6.59377i 0.801186 0.766510i
\(75\) 0 0
\(76\) −9.39651 0.415885i −1.07785 0.0477052i
\(77\) −0.558422 + 0.322405i −0.0636381 + 0.0367415i
\(78\) 0 0
\(79\) −8.55691 4.94034i −0.962728 0.555831i −0.0657165 0.997838i \(-0.520933\pi\)
−0.897012 + 0.442007i \(0.854267\pi\)
\(80\) −9.15640 + 4.25639i −1.02372 + 0.475879i
\(81\) 0 0
\(82\) 2.68614 9.20550i 0.296635 1.01658i
\(83\) 3.82009 6.61659i 0.419309 0.726265i −0.576561 0.817054i \(-0.695606\pi\)
0.995870 + 0.0907894i \(0.0289390\pi\)
\(84\) 0 0
\(85\) 1.00000 + 1.73205i 0.108465 + 0.187867i
\(86\) −10.6186 + 2.59500i −1.14504 + 0.279826i
\(87\) 0 0
\(88\) −1.40229 + 0.277627i −0.149485 + 0.0295952i
\(89\) 11.9769i 1.26955i −0.772698 0.634773i \(-0.781093\pi\)
0.772698 0.634773i \(-0.218907\pi\)
\(90\) 0 0
\(91\) 3.02661i 0.317274i
\(92\) −5.71519 + 2.97080i −0.595850 + 0.309728i
\(93\) 0 0
\(94\) −0.402528 1.64713i −0.0415176 0.169888i
\(95\) −5.93580 10.2811i −0.609000 1.05482i
\(96\) 0 0
\(97\) −5.24456 + 9.08385i −0.532505 + 0.922325i 0.466775 + 0.884376i \(0.345416\pi\)
−0.999280 + 0.0379490i \(0.987918\pi\)
\(98\) 7.29339 + 2.12819i 0.736744 + 0.214980i
\(99\) 0 0
\(100\) −2.31386 1.47603i −0.231386 0.147603i
\(101\) −1.06930 0.617359i −0.106399 0.0614295i 0.445856 0.895105i \(-0.352899\pi\)
−0.552255 + 0.833675i \(0.686233\pi\)
\(102\) 0 0
\(103\) −0.411331 + 0.237482i −0.0405297 + 0.0233998i −0.520128 0.854088i \(-0.674116\pi\)
0.479598 + 0.877488i \(0.340782\pi\)
\(104\) −2.16249 + 6.35180i −0.212050 + 0.622845i
\(105\) 0 0
\(106\) −1.83751 1.92063i −0.178474 0.186548i
\(107\) 12.5652 1.21472 0.607360 0.794427i \(-0.292229\pi\)
0.607360 + 0.794427i \(0.292229\pi\)
\(108\) 0 0
\(109\) 13.4891 1.29202 0.646012 0.763327i \(-0.276436\pi\)
0.646012 + 0.763327i \(0.276436\pi\)
\(110\) −1.24730 1.30372i −0.118925 0.124305i
\(111\) 0 0
\(112\) −4.17686 2.93212i −0.394677 0.277059i
\(113\) 6.30298 3.63903i 0.592935 0.342331i −0.173322 0.984865i \(-0.555450\pi\)
0.766257 + 0.642534i \(0.222117\pi\)
\(114\) 0 0
\(115\) −7.04069 4.06494i −0.656548 0.379058i
\(116\) −2.71519 + 4.25639i −0.252099 + 0.395196i
\(117\) 0 0
\(118\) −16.8030 4.90307i −1.54684 0.451364i
\(119\) −0.505408 + 0.875393i −0.0463307 + 0.0802471i
\(120\) 0 0
\(121\) 5.37228 + 9.30506i 0.488389 + 0.845915i
\(122\) 0.796442 + 3.25901i 0.0721065 + 0.295057i
\(123\) 0 0
\(124\) 7.49931 + 14.4271i 0.673458 + 1.29559i
\(125\) 9.15759i 0.819080i
\(126\) 0 0
\(127\) 7.65492i 0.679265i 0.940558 + 0.339632i \(0.110303\pi\)
−0.940558 + 0.339632i \(0.889697\pi\)
\(128\) −6.67081 9.13785i −0.589622 0.807679i
\(129\) 0 0
\(130\) −8.22683 + 2.01049i −0.721541 + 0.176332i
\(131\) −3.82009 6.61659i −0.333763 0.578094i 0.649484 0.760375i \(-0.274985\pi\)
−0.983246 + 0.182282i \(0.941652\pi\)
\(132\) 0 0
\(133\) 3.00000 5.19615i 0.260133 0.450564i
\(134\) −3.06198 + 10.4935i −0.264514 + 0.906500i
\(135\) 0 0
\(136\) −1.68614 + 1.47603i −0.144585 + 0.126569i
\(137\) 4.75544 + 2.74555i 0.406284 + 0.234568i 0.689192 0.724579i \(-0.257966\pi\)
−0.282908 + 0.959147i \(0.591299\pi\)
\(138\) 0 0
\(139\) 13.3233 7.69219i 1.13006 0.652443i 0.186114 0.982528i \(-0.440411\pi\)
0.943951 + 0.330085i \(0.107077\pi\)
\(140\) 0.284805 6.43491i 0.0240705 0.543849i
\(141\) 0 0
\(142\) 12.1312 11.6062i 1.01803 0.973968i
\(143\) −1.19897 −0.100263
\(144\) 0 0
\(145\) −6.37228 −0.529189
\(146\) −3.44603 + 3.29688i −0.285195 + 0.272852i
\(147\) 0 0
\(148\) −0.596438 + 13.4759i −0.0490269 + 1.10771i
\(149\) 11.1861 6.45832i 0.916404 0.529086i 0.0339182 0.999425i \(-0.489201\pi\)
0.882486 + 0.470338i \(0.155868\pi\)
\(150\) 0 0
\(151\) 2.62112 + 1.51330i 0.213304 + 0.123151i 0.602846 0.797858i \(-0.294033\pi\)
−0.389542 + 0.921009i \(0.627367\pi\)
\(152\) 10.0086 8.76144i 0.811804 0.710647i
\(153\) 0 0
\(154\) 0.255437 0.875393i 0.0205837 0.0705411i
\(155\) −10.2613 + 17.7731i −0.824207 + 1.42757i
\(156\) 0 0
\(157\) −5.93070 10.2723i −0.473322 0.819817i 0.526212 0.850353i \(-0.323612\pi\)
−0.999534 + 0.0305363i \(0.990278\pi\)
\(158\) 13.5739 3.31722i 1.07988 0.263904i
\(159\) 0 0
\(160\) 5.19542 13.3012i 0.410734 1.05155i
\(161\) 4.10891i 0.323828i
\(162\) 0 0
\(163\) 1.75079i 0.137132i −0.997647 0.0685660i \(-0.978158\pi\)
0.997647 0.0685660i \(-0.0218424\pi\)
\(164\) 6.25480 + 12.0329i 0.488417 + 0.939611i
\(165\) 0 0
\(166\) 2.56502 + 10.4960i 0.199084 + 0.814645i
\(167\) 8.74507 + 15.1469i 0.676714 + 1.17210i 0.975965 + 0.217928i \(0.0699299\pi\)
−0.299251 + 0.954174i \(0.596737\pi\)
\(168\) 0 0
\(169\) 3.68614 6.38458i 0.283549 0.491122i
\(170\) −2.71519 0.792287i −0.208246 0.0607656i
\(171\) 0 0
\(172\) 8.31386 13.0330i 0.633926 0.993754i
\(173\) −15.3030 8.83518i −1.16346 0.671726i −0.211333 0.977414i \(-0.567780\pi\)
−0.952132 + 0.305688i \(0.901114\pi\)
\(174\) 0 0
\(175\) 1.51622 0.875393i 0.114616 0.0661735i
\(176\) 1.16154 1.65464i 0.0875543 0.124723i
\(177\) 0 0
\(178\) 11.7091 + 12.2388i 0.877634 + 0.917337i
\(179\) −8.83915 −0.660669 −0.330334 0.943864i \(-0.607162\pi\)
−0.330334 + 0.943864i \(0.607162\pi\)
\(180\) 0 0
\(181\) −4.00000 −0.297318 −0.148659 0.988889i \(-0.547496\pi\)
−0.148659 + 0.988889i \(0.547496\pi\)
\(182\) −2.95894 3.09279i −0.219331 0.229253i
\(183\) 0 0
\(184\) 2.93580 8.62319i 0.216430 0.635710i
\(185\) −14.7446 + 8.51278i −1.08404 + 0.625872i
\(186\) 0 0
\(187\) −0.346781 0.200214i −0.0253591 0.0146411i
\(188\) 2.02163 + 1.28962i 0.147443 + 0.0940552i
\(189\) 0 0
\(190\) 16.1168 + 4.70285i 1.16924 + 0.341181i
\(191\) 7.54610 13.0702i 0.546017 0.945728i −0.452526 0.891751i \(-0.649477\pi\)
0.998542 0.0539770i \(-0.0171898\pi\)
\(192\) 0 0
\(193\) −3.87228 6.70699i −0.278733 0.482780i 0.692337 0.721574i \(-0.256581\pi\)
−0.971070 + 0.238795i \(0.923248\pi\)
\(194\) −3.52150 14.4098i −0.252829 1.03456i
\(195\) 0 0
\(196\) −9.53351 + 4.95559i −0.680965 + 0.353971i
\(197\) 23.9538i 1.70663i 0.521392 + 0.853317i \(0.325413\pi\)
−0.521392 + 0.853317i \(0.674587\pi\)
\(198\) 0 0
\(199\) 12.9073i 0.914973i 0.889217 + 0.457486i \(0.151250\pi\)
−0.889217 + 0.457486i \(0.848750\pi\)
\(200\) 3.80749 0.753812i 0.269231 0.0533025i
\(201\) 0 0
\(202\) 1.69624 0.414530i 0.119347 0.0291662i
\(203\) −1.61030 2.78912i −0.113021 0.195758i
\(204\) 0 0
\(205\) −8.55842 + 14.8236i −0.597746 + 1.03533i
\(206\) 0.188154 0.644810i 0.0131093 0.0449261i
\(207\) 0 0
\(208\) −4.00000 8.60485i −0.277350 0.596639i
\(209\) 2.05842 + 1.18843i 0.142384 + 0.0822055i
\(210\) 0 0
\(211\) −15.1863 + 8.76780i −1.04547 + 0.603600i −0.921377 0.388671i \(-0.872934\pi\)
−0.124090 + 0.992271i \(0.539601\pi\)
\(212\) 3.75538 + 0.166211i 0.257920 + 0.0114154i
\(213\) 0 0
\(214\) −12.8399 + 12.2842i −0.877720 + 0.839732i
\(215\) 19.5118 1.33069
\(216\) 0 0
\(217\) −10.3723 −0.704116
\(218\) −13.7841 + 13.1875i −0.933578 + 0.893173i
\(219\) 0 0
\(220\) 2.54915 + 0.112824i 0.171863 + 0.00760658i
\(221\) −1.62772 + 0.939764i −0.109492 + 0.0632154i
\(222\) 0 0
\(223\) −7.04069 4.06494i −0.471479 0.272209i 0.245379 0.969427i \(-0.421087\pi\)
−0.716859 + 0.697218i \(0.754421\pi\)
\(224\) 7.13477 1.08724i 0.476712 0.0726443i
\(225\) 0 0
\(226\) −2.88316 + 9.88067i −0.191785 + 0.657253i
\(227\) 7.19932 12.4696i 0.477835 0.827635i −0.521842 0.853042i \(-0.674755\pi\)
0.999677 + 0.0254070i \(0.00808817\pi\)
\(228\) 0 0
\(229\) −1.81386 3.14170i −0.119863 0.207609i 0.799850 0.600200i \(-0.204912\pi\)
−0.919713 + 0.392591i \(0.871579\pi\)
\(230\) 11.1687 2.72943i 0.736444 0.179974i
\(231\) 0 0
\(232\) −1.38665 7.00396i −0.0910381 0.459832i
\(233\) 4.84630i 0.317491i −0.987320 0.158746i \(-0.949255\pi\)
0.987320 0.158746i \(-0.0507450\pi\)
\(234\) 0 0
\(235\) 3.02661i 0.197434i
\(236\) 21.9639 11.4170i 1.42973 0.743184i
\(237\) 0 0
\(238\) −0.339360 1.38864i −0.0219974 0.0900125i
\(239\) −6.02987 10.4440i −0.390040 0.675569i 0.602414 0.798184i \(-0.294206\pi\)
−0.992454 + 0.122614i \(0.960872\pi\)
\(240\) 0 0
\(241\) 3.24456 5.61975i 0.209001 0.362000i −0.742399 0.669958i \(-0.766312\pi\)
0.951400 + 0.307958i \(0.0996456\pi\)
\(242\) −14.5868 4.25639i −0.937674 0.273611i
\(243\) 0 0
\(244\) −4.00000 2.55164i −0.256074 0.163352i
\(245\) −11.7446 6.78073i −0.750333 0.433205i
\(246\) 0 0
\(247\) 9.66181 5.57825i 0.614766 0.354935i
\(248\) −21.7678 7.41094i −1.38226 0.470595i
\(249\) 0 0
\(250\) −8.95284 9.35785i −0.566227 0.591843i
\(251\) −11.1780 −0.705551 −0.352776 0.935708i \(-0.614762\pi\)
−0.352776 + 0.935708i \(0.614762\pi\)
\(252\) 0 0
\(253\) 1.62772 0.102334
\(254\) −7.48378 7.82233i −0.469574 0.490817i
\(255\) 0 0
\(256\) 15.7502 + 2.81601i 0.984390 + 0.176001i
\(257\) −12.9891 + 7.49927i −0.810239 + 0.467792i −0.847039 0.531531i \(-0.821617\pi\)
0.0367996 + 0.999323i \(0.488284\pi\)
\(258\) 0 0
\(259\) −7.45202 4.30243i −0.463046 0.267340i
\(260\) 6.44121 10.0974i 0.399467 0.626211i
\(261\) 0 0
\(262\) 10.3723 + 3.02661i 0.640802 + 0.186984i
\(263\) −13.9873 + 24.2267i −0.862494 + 1.49388i 0.00701993 + 0.999975i \(0.497765\pi\)
−0.869514 + 0.493908i \(0.835568\pi\)
\(264\) 0 0
\(265\) 2.37228 + 4.10891i 0.145728 + 0.252408i
\(266\) 2.01437 + 8.24271i 0.123509 + 0.505393i
\(267\) 0 0
\(268\) −7.12994 13.7165i −0.435531 0.837868i
\(269\) 21.4843i 1.30992i −0.755663 0.654961i \(-0.772685\pi\)
0.755663 0.654961i \(-0.227315\pi\)
\(270\) 0 0
\(271\) 29.9679i 1.82042i −0.414146 0.910211i \(-0.635920\pi\)
0.414146 0.910211i \(-0.364080\pi\)
\(272\) 0.279981 3.15676i 0.0169763 0.191406i
\(273\) 0 0
\(274\) −7.54360 + 1.84352i −0.455726 + 0.111371i
\(275\) 0.346781 + 0.600642i 0.0209117 + 0.0362201i
\(276\) 0 0
\(277\) −3.18614 + 5.51856i −0.191437 + 0.331578i −0.945727 0.324963i \(-0.894648\pi\)
0.754290 + 0.656541i \(0.227981\pi\)
\(278\) −6.09442 + 20.8858i −0.365519 + 1.25265i
\(279\) 0 0
\(280\) 6.00000 + 6.85407i 0.358569 + 0.409609i
\(281\) 19.9307 + 11.5070i 1.18897 + 0.686450i 0.958072 0.286529i \(-0.0925014\pi\)
0.230894 + 0.972979i \(0.425835\pi\)
\(282\) 0 0
\(283\) −8.55691 + 4.94034i −0.508656 + 0.293673i −0.732281 0.681003i \(-0.761544\pi\)
0.223625 + 0.974675i \(0.428211\pi\)
\(284\) −1.04983 + 23.7200i −0.0622961 + 1.40752i
\(285\) 0 0
\(286\) 1.22519 1.17216i 0.0724470 0.0693115i
\(287\) −8.65099 −0.510652
\(288\) 0 0
\(289\) 16.3723 0.963075
\(290\) 6.51164 6.22981i 0.382376 0.365827i
\(291\) 0 0
\(292\) 0.298219 6.73797i 0.0174519 0.394310i
\(293\) 20.1861 11.6545i 1.17929 0.680862i 0.223437 0.974718i \(-0.428272\pi\)
0.955850 + 0.293857i \(0.0949388\pi\)
\(294\) 0 0
\(295\) 27.0579 + 15.6219i 1.57537 + 0.909540i
\(296\) −12.5652 14.3537i −0.730335 0.834294i
\(297\) 0 0
\(298\) −5.11684 + 17.5356i −0.296411 + 1.01581i
\(299\) 3.82009 6.61659i 0.220921 0.382647i
\(300\) 0 0
\(301\) 4.93070 + 8.54023i 0.284201 + 0.492251i
\(302\) −4.15791 + 1.01612i −0.239261 + 0.0584710i
\(303\) 0 0
\(304\) −1.66191 + 18.7379i −0.0953171 + 1.07469i
\(305\) 5.98844i 0.342897i
\(306\) 0 0
\(307\) 1.20128i 0.0685609i 0.999412 + 0.0342805i \(0.0109140\pi\)
−0.999412 + 0.0342805i \(0.989086\pi\)
\(308\) 0.594797 + 1.14426i 0.0338917 + 0.0652004i
\(309\) 0 0
\(310\) −6.89001 28.1936i −0.391326 1.60129i
\(311\) 9.56773 + 16.5718i 0.542536 + 0.939700i 0.998758 + 0.0498340i \(0.0158692\pi\)
−0.456221 + 0.889866i \(0.650797\pi\)
\(312\) 0 0
\(313\) 9.24456 16.0121i 0.522534 0.905055i −0.477123 0.878837i \(-0.658320\pi\)
0.999656 0.0262180i \(-0.00834640\pi\)
\(314\) 16.1030 + 4.69882i 0.908746 + 0.265170i
\(315\) 0 0
\(316\) −10.6277 + 16.6602i −0.597856 + 0.937210i
\(317\) 28.1644 + 16.2607i 1.58187 + 0.913293i 0.994587 + 0.103911i \(0.0331359\pi\)
0.587283 + 0.809381i \(0.300197\pi\)
\(318\) 0 0
\(319\) 1.10489 0.637910i 0.0618621 0.0357161i
\(320\) 7.69473 + 18.6713i 0.430148 + 1.04376i
\(321\) 0 0
\(322\) 4.01704 + 4.19877i 0.223861 + 0.233988i
\(323\) 3.72601 0.207321
\(324\) 0 0
\(325\) 3.25544 0.180579
\(326\) 1.71164 + 1.78907i 0.0947990 + 0.0990876i
\(327\) 0 0
\(328\) −18.1554 6.18109i −1.00247 0.341294i
\(329\) −1.32473 + 0.764836i −0.0730350 + 0.0421667i
\(330\) 0 0
\(331\) 24.0254 + 13.8711i 1.32056 + 0.762424i 0.983817 0.179174i \(-0.0573426\pi\)
0.336739 + 0.941598i \(0.390676\pi\)
\(332\) −12.8824 8.21782i −0.707014 0.451012i
\(333\) 0 0
\(334\) −23.7446 6.92860i −1.29924 0.379116i
\(335\) 9.75588 16.8977i 0.533021 0.923219i
\(336\) 0 0
\(337\) 7.87228 + 13.6352i 0.428830 + 0.742756i 0.996770 0.0803144i \(-0.0255924\pi\)
−0.567939 + 0.823071i \(0.692259\pi\)
\(338\) 2.47508 + 10.1279i 0.134627 + 0.550887i
\(339\) 0 0
\(340\) 3.54915 1.84487i 0.192479 0.100052i
\(341\) 4.10891i 0.222510i
\(342\) 0 0
\(343\) 15.7848i 0.852300i
\(344\) 4.24589 + 21.4460i 0.228923 + 1.15629i
\(345\) 0 0
\(346\) 24.2753 5.93244i 1.30505 0.318930i
\(347\) −3.47331 6.01594i −0.186457 0.322953i 0.757610 0.652708i \(-0.226367\pi\)
−0.944066 + 0.329755i \(0.893034\pi\)
\(348\) 0 0
\(349\) 2.81386 4.87375i 0.150622 0.260886i −0.780834 0.624739i \(-0.785206\pi\)
0.931456 + 0.363853i \(0.118539\pi\)
\(350\) −0.693562 + 2.37686i −0.0370725 + 0.127049i
\(351\) 0 0
\(352\) 0.430703 + 2.82639i 0.0229566 + 0.150647i
\(353\) −7.24456 4.18265i −0.385589 0.222620i 0.294658 0.955603i \(-0.404794\pi\)
−0.680247 + 0.732983i \(0.738128\pi\)
\(354\) 0 0
\(355\) −25.9530 + 14.9840i −1.37744 + 0.795266i
\(356\) −23.9303 1.05914i −1.26830 0.0561345i
\(357\) 0 0
\(358\) 9.03245 8.64152i 0.477380 0.456719i
\(359\) 1.38712 0.0732096 0.0366048 0.999330i \(-0.488346\pi\)
0.0366048 + 0.999330i \(0.488346\pi\)
\(360\) 0 0
\(361\) −3.11684 −0.164044
\(362\) 4.08748 3.91057i 0.214833 0.205535i
\(363\) 0 0
\(364\) 6.04729 + 0.267650i 0.316964 + 0.0140287i
\(365\) 7.37228 4.25639i 0.385883 0.222790i
\(366\) 0 0
\(367\) −5.52447 3.18955i −0.288375 0.166493i 0.348834 0.937185i \(-0.386578\pi\)
−0.637209 + 0.770691i \(0.719911\pi\)
\(368\) 5.43039 + 11.6819i 0.283079 + 0.608962i
\(369\) 0 0
\(370\) 6.74456 23.1138i 0.350633 1.20163i
\(371\) −1.19897 + 2.07668i −0.0622474 + 0.107816i
\(372\) 0 0
\(373\) 9.93070 + 17.2005i 0.514192 + 0.890607i 0.999864 + 0.0164662i \(0.00524158\pi\)
−0.485672 + 0.874141i \(0.661425\pi\)
\(374\) 0.550103 0.134435i 0.0284451 0.00695147i
\(375\) 0 0
\(376\) −3.32663 + 0.658610i −0.171558 + 0.0339652i
\(377\) 5.98844i 0.308420i
\(378\) 0 0
\(379\) 6.45364i 0.331501i 0.986168 + 0.165751i \(0.0530047\pi\)
−0.986168 + 0.165751i \(0.946995\pi\)
\(380\) −21.0670 + 10.9508i −1.08071 + 0.561764i
\(381\) 0 0
\(382\) 5.06688 + 20.7334i 0.259244 + 1.06082i
\(383\) 4.32550 + 7.49198i 0.221023 + 0.382822i 0.955119 0.296223i \(-0.0957272\pi\)
−0.734096 + 0.679045i \(0.762394\pi\)
\(384\) 0 0
\(385\) −0.813859 + 1.40965i −0.0414781 + 0.0718422i
\(386\) 10.5140 + 3.06796i 0.535148 + 0.156155i
\(387\) 0 0
\(388\) 17.6861 + 11.2822i 0.897878 + 0.572766i
\(389\) −27.3030 15.7634i −1.38432 0.799235i −0.391649 0.920115i \(-0.628095\pi\)
−0.992667 + 0.120879i \(0.961429\pi\)
\(390\) 0 0
\(391\) 2.20979 1.27582i 0.111754 0.0645210i
\(392\) 4.89720 14.3843i 0.247346 0.726518i
\(393\) 0 0
\(394\) −23.4182 24.4776i −1.17979 1.23316i
\(395\) −24.9422 −1.25498
\(396\) 0 0
\(397\) −18.7446 −0.940763 −0.470381 0.882463i \(-0.655884\pi\)
−0.470381 + 0.882463i \(0.655884\pi\)
\(398\) −12.6187 13.1895i −0.632518 0.661132i
\(399\) 0 0
\(400\) −3.15380 + 4.49266i −0.157690 + 0.224633i
\(401\) −3.98913 + 2.30312i −0.199207 + 0.115012i −0.596286 0.802772i \(-0.703357\pi\)
0.397078 + 0.917785i \(0.370024\pi\)
\(402\) 0 0
\(403\) −16.7025 9.64319i −0.832011 0.480362i
\(404\) −1.32807 + 2.08191i −0.0660740 + 0.103579i
\(405\) 0 0
\(406\) 4.37228 + 1.27582i 0.216993 + 0.0633179i
\(407\) 1.70438 2.95207i 0.0844829 0.146329i
\(408\) 0 0
\(409\) −6.87228 11.9031i −0.339812 0.588572i 0.644585 0.764533i \(-0.277030\pi\)
−0.984397 + 0.175960i \(0.943697\pi\)
\(410\) −5.74661 23.5149i −0.283805 1.16132i
\(411\) 0 0
\(412\) 0.438125 + 0.842859i 0.0215849 + 0.0415247i
\(413\) 15.7908i 0.777016i
\(414\) 0 0
\(415\) 19.2864i 0.946731i
\(416\) 12.4999 + 4.88246i 0.612860 + 0.239383i
\(417\) 0 0
\(418\) −3.26530 + 0.797979i −0.159711 + 0.0390305i
\(419\) −13.4819 23.3513i −0.658634 1.14079i −0.980970 0.194162i \(-0.937801\pi\)
0.322336 0.946625i \(-0.395532\pi\)
\(420\) 0 0
\(421\) 5.30298 9.18504i 0.258452 0.447651i −0.707376 0.706838i \(-0.750121\pi\)
0.965827 + 0.259186i \(0.0834544\pi\)
\(422\) 6.94661 23.8063i 0.338156 1.15887i
\(423\) 0 0
\(424\) −4.00000 + 3.50157i −0.194257 + 0.170051i
\(425\) 0.941578 + 0.543620i 0.0456732 + 0.0263695i
\(426\) 0 0
\(427\) 2.62112 1.51330i 0.126845 0.0732339i
\(428\) 1.11117 25.1057i 0.0537103 1.21353i
\(429\) 0 0
\(430\) −19.9385 + 19.0755i −0.961518 + 0.919904i
\(431\) 31.1952 1.50262 0.751310 0.659949i \(-0.229422\pi\)
0.751310 + 0.659949i \(0.229422\pi\)
\(432\) 0 0
\(433\) −8.62772 −0.414622 −0.207311 0.978275i \(-0.566471\pi\)
−0.207311 + 0.978275i \(0.566471\pi\)
\(434\) 10.5991 10.1404i 0.508774 0.486754i
\(435\) 0 0
\(436\) 1.19288 26.9519i 0.0571284 1.29076i
\(437\) −13.1168 + 7.57301i −0.627464 + 0.362266i
\(438\) 0 0
\(439\) 5.65357 + 3.26409i 0.269830 + 0.155786i 0.628810 0.777559i \(-0.283542\pi\)
−0.358980 + 0.933345i \(0.616876\pi\)
\(440\) −2.71519 + 2.37686i −0.129442 + 0.113312i
\(441\) 0 0
\(442\) 0.744563 2.55164i 0.0354152 0.121369i
\(443\) −6.18850 + 10.7188i −0.294025 + 0.509265i −0.974758 0.223266i \(-0.928328\pi\)
0.680733 + 0.732532i \(0.261661\pi\)
\(444\) 0 0
\(445\) −15.1168 26.1831i −0.716607 1.24120i
\(446\) 11.1687 2.72943i 0.528854 0.129242i
\(447\) 0 0
\(448\) −6.22787 + 8.08627i −0.294239 + 0.382040i
\(449\) 19.4024i 0.915657i 0.889041 + 0.457828i \(0.151373\pi\)
−0.889041 + 0.457828i \(0.848627\pi\)
\(450\) 0 0
\(451\) 3.42703i 0.161373i
\(452\) −6.71355 12.9154i −0.315779 0.607492i
\(453\) 0 0
\(454\) 4.83403 + 19.7806i 0.226872 + 0.928351i
\(455\) 3.82009 + 6.61659i 0.179088 + 0.310190i
\(456\) 0 0
\(457\) −19.9891 + 34.6222i −0.935052 + 1.61956i −0.160510 + 0.987034i \(0.551314\pi\)
−0.774541 + 0.632523i \(0.782019\pi\)
\(458\) 4.92498 + 1.43710i 0.230129 + 0.0671511i
\(459\) 0 0
\(460\) −8.74456 + 13.7081i −0.407717 + 0.639145i
\(461\) −0.302985 0.174928i −0.0141114 0.00814722i 0.492928 0.870070i \(-0.335927\pi\)
−0.507039 + 0.861923i \(0.669260\pi\)
\(462\) 0 0
\(463\) 4.13734 2.38870i 0.192279 0.111012i −0.400770 0.916179i \(-0.631257\pi\)
0.593049 + 0.805167i \(0.297924\pi\)
\(464\) 8.26434 + 5.80148i 0.383662 + 0.269327i
\(465\) 0 0
\(466\) 4.73794 + 4.95228i 0.219481 + 0.229410i
\(467\) −5.11313 −0.236608 −0.118304 0.992977i \(-0.537746\pi\)
−0.118304 + 0.992977i \(0.537746\pi\)
\(468\) 0 0
\(469\) 9.86141 0.455357
\(470\) −2.95894 3.09279i −0.136486 0.142660i
\(471\) 0 0
\(472\) −11.2825 + 33.1395i −0.519318 + 1.52537i
\(473\) −3.38316 + 1.95327i −0.155558 + 0.0898113i
\(474\) 0 0
\(475\) −5.58902 3.22682i −0.256442 0.148057i
\(476\) 1.70438 + 1.08724i 0.0781201 + 0.0498336i
\(477\) 0 0
\(478\) 16.3723 + 4.77739i 0.748851 + 0.218513i
\(479\) −6.53528 + 11.3194i −0.298605 + 0.517198i −0.975817 0.218589i \(-0.929855\pi\)
0.677212 + 0.735788i \(0.263188\pi\)
\(480\) 0 0
\(481\) −8.00000 13.8564i −0.364769 0.631798i
\(482\) 2.17858 + 8.91467i 0.0992317 + 0.406052i
\(483\) 0 0
\(484\) 19.0670 9.91119i 0.866682 0.450508i
\(485\) 26.4781i 1.20231i
\(486\) 0 0
\(487\) 42.8752i 1.94286i 0.237325 + 0.971430i \(0.423729\pi\)
−0.237325 + 0.971430i \(0.576271\pi\)
\(488\) 6.58207 1.30312i 0.297956 0.0589897i
\(489\) 0 0
\(490\) 18.6305 4.55296i 0.841641 0.205682i
\(491\) 6.88206 + 11.9201i 0.310583 + 0.537946i 0.978489 0.206300i \(-0.0661423\pi\)
−0.667906 + 0.744246i \(0.732809\pi\)
\(492\) 0 0
\(493\) 1.00000 1.73205i 0.0450377 0.0780076i
\(494\) −4.41957 + 15.1460i −0.198846 + 0.681452i
\(495\) 0 0
\(496\) 29.4891 13.7081i 1.32410 0.615513i
\(497\) −13.1168 7.57301i −0.588371 0.339696i
\(498\) 0 0
\(499\) −2.96790 + 1.71352i −0.132861 + 0.0767076i −0.564958 0.825120i \(-0.691107\pi\)
0.432096 + 0.901828i \(0.357774\pi\)
\(500\) 18.2973 + 0.809827i 0.818278 + 0.0362166i
\(501\) 0 0
\(502\) 11.4225 10.9281i 0.509810 0.487746i
\(503\) 19.3236 0.861597 0.430799 0.902448i \(-0.358232\pi\)
0.430799 + 0.902448i \(0.358232\pi\)
\(504\) 0 0
\(505\) −3.11684 −0.138698
\(506\) −1.66332 + 1.59133i −0.0739434 + 0.0707431i
\(507\) 0 0
\(508\) 15.2949 + 0.676943i 0.678600 + 0.0300345i
\(509\) −12.8139 + 7.39809i −0.567964 + 0.327914i −0.756336 0.654183i \(-0.773012\pi\)
0.188372 + 0.982098i \(0.439679\pi\)
\(510\) 0 0
\(511\) 3.72601 + 2.15121i 0.164829 + 0.0951641i
\(512\) −18.8477 + 12.5205i −0.832960 + 0.553333i
\(513\) 0 0
\(514\) 5.94158 20.3620i 0.262072 0.898129i
\(515\) −0.599485 + 1.03834i −0.0264165 + 0.0457547i
\(516\) 0 0
\(517\) −0.302985 0.524785i −0.0133252 0.0230800i
\(518\) 11.8212 2.88889i 0.519395 0.126931i
\(519\) 0 0
\(520\) 3.28953 + 16.6154i 0.144255 + 0.728632i
\(521\) 26.0357i 1.14064i −0.821421 0.570322i \(-0.806819\pi\)
0.821421 0.570322i \(-0.193181\pi\)
\(522\) 0 0
\(523\) 9.40571i 0.411283i 0.978627 + 0.205641i \(0.0659281\pi\)
−0.978627 + 0.205641i \(0.934072\pi\)
\(524\) −13.5580 + 7.04758i −0.592286 + 0.307875i
\(525\) 0 0
\(526\) −9.39187 38.4311i −0.409505 1.67568i
\(527\) −3.22060 5.57825i −0.140292 0.242992i
\(528\) 0 0
\(529\) 6.31386 10.9359i 0.274516 0.475475i
\(530\) −6.44121 1.87953i −0.279788 0.0816415i
\(531\) 0 0
\(532\) −10.1168 6.45364i −0.438621 0.279801i
\(533\) −13.9307 8.04290i −0.603406 0.348376i
\(534\) 0 0
\(535\) 27.4692 15.8593i 1.18760 0.685659i
\(536\) 20.6957 + 7.04593i 0.893917 + 0.304338i
\(537\) 0 0
\(538\) 21.0040 + 21.9542i 0.905546 + 0.946511i
\(539\) 2.71519 0.116952
\(540\) 0 0
\(541\) −8.97825 −0.386005 −0.193003 0.981198i \(-0.561823\pi\)
−0.193003 + 0.981198i \(0.561823\pi\)
\(542\) 29.2979 + 30.6233i 1.25845 + 1.31538i
\(543\) 0 0
\(544\) 2.80007 + 3.49951i 0.120052 + 0.150040i
\(545\) 29.4891 17.0256i 1.26318 0.729295i
\(546\) 0 0
\(547\) −19.2591 11.1192i −0.823458 0.475424i 0.0281494 0.999604i \(-0.491039\pi\)
−0.851608 + 0.524180i \(0.824372\pi\)
\(548\) 5.90627 9.25878i 0.252303 0.395515i
\(549\) 0 0
\(550\) −0.941578 0.274750i −0.0401490 0.0117154i
\(551\) −5.93580 + 10.2811i −0.252873 + 0.437990i
\(552\) 0 0
\(553\) −6.30298 10.9171i −0.268030 0.464242i
\(554\) −2.13936 8.75415i −0.0908925 0.371928i
\(555\) 0 0
\(556\) −14.1911 27.3007i −0.601838 1.15781i
\(557\) 7.22316i 0.306055i −0.988222 0.153027i \(-0.951098\pi\)
0.988222 0.153027i \(-0.0489023\pi\)
\(558\) 0 0
\(559\) 18.3365i 0.775549i
\(560\) −12.8320 1.13811i −0.542253 0.0480938i
\(561\) 0 0
\(562\) −31.6163 + 7.72645i −1.33365 + 0.325921i
\(563\) −7.89288 13.6709i −0.332645 0.576158i 0.650384 0.759605i \(-0.274608\pi\)
−0.983030 + 0.183447i \(0.941274\pi\)
\(564\) 0 0
\(565\) 9.18614 15.9109i 0.386464 0.669375i
\(566\) 3.91416 13.4140i 0.164525 0.563831i
\(567\) 0 0
\(568\) −22.1168 25.2651i −0.928002 1.06010i
\(569\) 21.9891 + 12.6954i 0.921832 + 0.532220i 0.884219 0.467072i \(-0.154691\pi\)
0.0376130 + 0.999292i \(0.488025\pi\)
\(570\) 0 0
\(571\) 3.66146 2.11395i 0.153227 0.0884659i −0.421426 0.906863i \(-0.638470\pi\)
0.574653 + 0.818397i \(0.305137\pi\)
\(572\) −0.106028 + 2.39560i −0.00443324 + 0.100165i
\(573\) 0 0
\(574\) 8.84018 8.45757i 0.368982 0.353012i
\(575\) −4.41957 −0.184309
\(576\) 0 0
\(577\) 31.8397 1.32550 0.662751 0.748840i \(-0.269389\pi\)
0.662751 + 0.748840i \(0.269389\pi\)
\(578\) −16.7303 + 16.0062i −0.695890 + 0.665771i
\(579\) 0 0
\(580\) −0.563516 + 12.7321i −0.0233987 + 0.528672i
\(581\) 8.44158 4.87375i 0.350216 0.202197i
\(582\) 0 0
\(583\) −0.822662 0.474964i −0.0340712 0.0196710i
\(584\) 6.28258 + 7.17687i 0.259975 + 0.296981i
\(585\) 0 0
\(586\) −9.23369 + 31.6442i −0.381440 + 1.30721i
\(587\) 1.95708 3.38977i 0.0807774 0.139911i −0.822807 0.568321i \(-0.807593\pi\)
0.903584 + 0.428411i \(0.140926\pi\)
\(588\) 0 0
\(589\) 19.1168 + 33.1113i 0.787696 + 1.36433i
\(590\) −42.9222 + 10.4894i −1.76708 + 0.431842i
\(591\) 0 0
\(592\) 26.8728 + 2.38342i 1.10446 + 0.0979578i
\(593\) 8.80773i 0.361690i 0.983512 + 0.180845i \(0.0578833\pi\)
−0.983512 + 0.180845i \(0.942117\pi\)
\(594\) 0 0
\(595\) 2.55164i 0.104607i
\(596\) −11.9148 22.9215i −0.488049 0.938902i
\(597\) 0 0
\(598\) 2.56502 + 10.4960i 0.104892 + 0.429212i
\(599\) −0.0940770 0.162946i −0.00384388 0.00665780i 0.864097 0.503325i \(-0.167890\pi\)
−0.867941 + 0.496667i \(0.834557\pi\)
\(600\) 0 0
\(601\) −7.98913 + 13.8376i −0.325883 + 0.564446i −0.981691 0.190482i \(-0.938995\pi\)
0.655807 + 0.754928i \(0.272328\pi\)
\(602\) −13.3878 3.90653i −0.545647 0.159218i
\(603\) 0 0
\(604\) 3.25544 5.10328i 0.132462 0.207650i
\(605\) 23.4891 + 13.5615i 0.954969 + 0.551351i
\(606\) 0 0
\(607\) −3.44378 + 1.98827i −0.139779 + 0.0807013i −0.568259 0.822850i \(-0.692383\pi\)
0.428480 + 0.903551i \(0.359049\pi\)
\(608\) −16.6207 20.7724i −0.674057 0.842432i
\(609\) 0 0
\(610\) 5.85455 + 6.11940i 0.237044 + 0.247767i
\(611\) −2.84429 −0.115068
\(612\) 0 0
\(613\) 4.23369 0.170997 0.0854985 0.996338i \(-0.472752\pi\)
0.0854985 + 0.996338i \(0.472752\pi\)
\(614\) −1.17443 1.22756i −0.0473960 0.0495401i
\(615\) 0 0
\(616\) −1.72648 0.587788i −0.0695620 0.0236827i
\(617\) 4.24456 2.45060i 0.170880 0.0986574i −0.412121 0.911129i \(-0.635212\pi\)
0.583001 + 0.812472i \(0.301879\pi\)
\(618\) 0 0
\(619\) −8.08103 4.66559i −0.324804 0.187526i 0.328728 0.944425i \(-0.393380\pi\)
−0.653532 + 0.756899i \(0.726713\pi\)
\(620\) 34.6040 + 22.0742i 1.38973 + 0.886522i
\(621\) 0 0
\(622\) −25.9783 7.58039i −1.04163 0.303946i
\(623\) 7.64018 13.2332i 0.306097 0.530176i
\(624\) 0 0
\(625\) 14.9891 + 25.9619i 0.599565 + 1.03848i
\(626\) 6.20732 + 25.4001i 0.248095 + 1.01519i
\(627\) 0 0
\(628\) −21.0489 + 10.9414i −0.839944 + 0.436610i
\(629\) 5.34363i 0.213064i
\(630\) 0 0
\(631\) 42.8752i 1.70683i −0.521228 0.853417i \(-0.674526\pi\)
0.521228 0.853417i \(-0.325474\pi\)
\(632\) −5.42758 27.4147i −0.215898 1.09050i
\(633\) 0 0
\(634\) −44.6775 + 10.9184i −1.77437 + 0.433624i
\(635\) 9.66181 + 16.7347i 0.383417 + 0.664098i
\(636\) 0 0
\(637\) 6.37228 11.0371i 0.252479 0.437306i
\(638\) −0.505408 + 1.73205i −0.0200093 + 0.0685725i
\(639\) 0 0
\(640\) −26.1168 11.5569i −1.03236 0.456827i
\(641\) −18.1277 10.4660i −0.716002 0.413384i 0.0972775 0.995257i \(-0.468987\pi\)
−0.813279 + 0.581873i \(0.802320\pi\)
\(642\) 0 0
\(643\) 31.1307 17.9733i 1.22767 0.708798i 0.261131 0.965303i \(-0.415905\pi\)
0.966543 + 0.256506i \(0.0825713\pi\)
\(644\) −8.20979 0.363361i −0.323511 0.0143184i
\(645\) 0 0
\(646\) −3.80749 + 3.64270i −0.149804 + 0.143320i
\(647\) −46.0993 −1.81235 −0.906174 0.422904i \(-0.861011\pi\)
−0.906174 + 0.422904i \(0.861011\pi\)
\(648\) 0 0
\(649\) −6.25544 −0.245547
\(650\) −3.32663 + 3.18265i −0.130481 + 0.124834i
\(651\) 0 0
\(652\) −3.49815 0.154826i −0.136998 0.00606346i
\(653\) −3.81386 + 2.20193i −0.149248 + 0.0861683i −0.572764 0.819720i \(-0.694129\pi\)
0.423516 + 0.905888i \(0.360796\pi\)
\(654\) 0 0
\(655\) −16.7025 9.64319i −0.652621 0.376791i
\(656\) 24.5954 11.4333i 0.960288 0.446394i
\(657\) 0 0
\(658\) 0.605969 2.07668i 0.0236231 0.0809573i
\(659\) 6.02987 10.4440i 0.234891 0.406842i −0.724350 0.689432i \(-0.757860\pi\)
0.959241 + 0.282590i \(0.0911935\pi\)
\(660\) 0 0
\(661\) −7.81386 13.5340i −0.303924 0.526412i 0.673097 0.739554i \(-0.264964\pi\)
−0.977021 + 0.213142i \(0.931630\pi\)
\(662\) −38.1118 + 9.31383i −1.48126 + 0.361992i
\(663\) 0 0
\(664\) 21.1982 4.19685i 0.822651 0.162869i
\(665\) 15.1460i 0.587338i
\(666\) 0 0
\(667\) 8.12989i 0.314791i
\(668\) 31.0375 16.1336i 1.20088 0.624226i
\(669\) 0 0
\(670\) 6.55065 + 26.8050i 0.253074 + 1.03557i
\(671\) 0.599485 + 1.03834i 0.0231429 + 0.0400846i
\(672\) 0 0
\(673\) −14.9307 + 25.8607i −0.575536 + 0.996858i 0.420447 + 0.907317i \(0.361873\pi\)
−0.995983 + 0.0895410i \(0.971460\pi\)
\(674\) −21.3748 6.23711i −0.823326 0.240244i
\(675\) 0 0
\(676\) −12.4307 7.92967i −0.478104 0.304987i
\(677\) 3.04755 + 1.75950i 0.117127 + 0.0676232i 0.557419 0.830231i \(-0.311792\pi\)
−0.440292 + 0.897855i \(0.645125\pi\)
\(678\) 0 0
\(679\) −11.5894 + 6.69112i −0.444759 + 0.256782i
\(680\) −1.82314 + 5.35501i −0.0699140 + 0.205355i
\(681\) 0 0
\(682\) 4.01704 + 4.19877i 0.153821 + 0.160779i
\(683\) 20.0172 0.765936 0.382968 0.923762i \(-0.374902\pi\)
0.382968 + 0.923762i \(0.374902\pi\)
\(684\) 0 0
\(685\) 13.8614 0.529617
\(686\) 15.4319 + 16.1300i 0.589193 + 0.615847i
\(687\) 0 0
\(688\) −25.3052 17.7640i −0.964752 0.677246i
\(689\) −3.86141 + 2.22938i −0.147108 + 0.0849328i
\(690\) 0 0
\(691\) 17.3961 + 10.0436i 0.661777 + 0.382077i 0.792954 0.609282i \(-0.208542\pi\)
−0.131177 + 0.991359i \(0.541875\pi\)
\(692\) −19.0064 + 29.7947i −0.722513 + 1.13263i
\(693\) 0 0
\(694\) 9.43070 + 2.75186i 0.357985 + 0.104459i
\(695\) 19.4177 33.6324i 0.736555 1.27575i
\(696\) 0 0
\(697\) −2.68614 4.65253i −0.101745 0.176227i
\(698\) 1.88938 + 7.73128i 0.0715143 + 0.292633i
\(699\) 0 0
\(700\) −1.61499 3.10690i −0.0610409 0.117430i
\(701\) 32.7615i 1.23738i −0.785634 0.618692i \(-0.787663\pi\)
0.785634 0.618692i \(-0.212337\pi\)
\(702\) 0 0
\(703\) 31.7187i 1.19629i
\(704\) −3.20332 2.46713i −0.120730 0.0929834i
\(705\) 0 0
\(706\) 11.4921 2.80847i 0.432512 0.105698i
\(707\) −0.787639 1.36423i −0.0296222 0.0513072i
\(708\) 0 0
\(709\) −11.9307 + 20.6646i −0.448067 + 0.776075i −0.998260 0.0589626i \(-0.981221\pi\)
0.550193 + 0.835037i \(0.314554\pi\)
\(710\) 11.8716 40.6844i 0.445533 1.52686i
\(711\) 0 0
\(712\) 25.4891 22.3130i 0.955245 0.836215i
\(713\) 22.6753 + 13.0916i 0.849195 + 0.490283i
\(714\) 0 0
\(715\) −2.62112 + 1.51330i −0.0980242 + 0.0565943i
\(716\) −0.781666 + 17.6610i −0.0292122 + 0.660023i
\(717\) 0 0
\(718\) −1.41746 + 1.35611i −0.0528991 + 0.0506096i
\(719\) −16.2912 −0.607558 −0.303779 0.952743i \(-0.598248\pi\)
−0.303779 + 0.952743i \(0.598248\pi\)
\(720\) 0 0
\(721\) −0.605969 −0.0225675
\(722\) 3.18501 3.04716i 0.118534 0.113403i
\(723\) 0 0
\(724\) −0.353729 + 7.99218i −0.0131463 + 0.297027i
\(725\) −3.00000 + 1.73205i −0.111417 + 0.0643268i
\(726\) 0 0
\(727\) −32.9937 19.0489i −1.22367 0.706485i −0.257969 0.966153i \(-0.583053\pi\)
−0.965698 + 0.259668i \(0.916387\pi\)
\(728\) −6.44121 + 5.63858i −0.238727 + 0.208980i
\(729\) 0 0
\(730\) −3.37228 + 11.5569i −0.124814 + 0.427741i
\(731\) −3.06198 + 5.30350i −0.113251 + 0.196157i
\(732\) 0 0
\(733\) −0.186141 0.322405i −0.00687526 0.0119083i 0.862567 0.505942i \(-0.168855\pi\)
−0.869443 + 0.494034i \(0.835522\pi\)
\(734\) 8.76352 2.14165i 0.323467 0.0790496i
\(735\) 0 0
\(736\) −16.9699 6.62842i −0.625518 0.244327i
\(737\) 3.90653i 0.143899i
\(738\) 0 0
\(739\) 6.45364i 0.237401i −0.992930 0.118700i \(-0.962127\pi\)
0.992930 0.118700i \(-0.0378728\pi\)
\(740\) 15.7050 + 30.2131i 0.577328 + 1.11066i
\(741\) 0 0
\(742\) −0.805056 3.29426i −0.0295546 0.120936i
\(743\) −10.5785 18.3226i −0.388089 0.672190i 0.604103 0.796906i \(-0.293531\pi\)
−0.992193 + 0.124716i \(0.960198\pi\)
\(744\) 0 0
\(745\) 16.3030 28.2376i 0.597295 1.03455i
\(746\) −26.9638 7.86797i −0.987215 0.288067i
\(747\) 0 0
\(748\) −0.430703 + 0.675178i −0.0157481 + 0.0246870i
\(749\) 13.8832 + 8.01544i 0.507279 + 0.292878i
\(750\) 0 0
\(751\) −18.7832 + 10.8445i −0.685408 + 0.395721i −0.801890 0.597472i \(-0.796172\pi\)
0.116481 + 0.993193i \(0.462838\pi\)
\(752\) 2.75550 3.92527i 0.100483 0.143140i
\(753\) 0 0
\(754\) 5.85455 + 6.11940i 0.213210 + 0.222855i
\(755\) 7.64018 0.278054
\(756\) 0 0
\(757\) 14.0000 0.508839 0.254419 0.967094i \(-0.418116\pi\)
0.254419 + 0.967094i \(0.418116\pi\)
\(758\) −6.30935 6.59477i −0.229166 0.239533i
\(759\) 0 0
\(760\) 10.8218 31.7863i 0.392547 1.15301i
\(761\) −15.0475 + 8.68771i −0.545473 + 0.314929i −0.747294 0.664493i \(-0.768647\pi\)
0.201821 + 0.979422i \(0.435314\pi\)
\(762\) 0 0
\(763\) 14.9040 + 8.60485i 0.539563 + 0.311517i
\(764\) −25.4476 16.2333i −0.920661 0.587299i
\(765\) 0 0
\(766\) −11.7446 3.42703i −0.424348 0.123824i
\(767\) −14.6809 + 25.4280i −0.530095 + 0.918152i
\(768\) 0 0
\(769\) −4.04755 7.01056i −0.145958 0.252807i 0.783772 0.621049i \(-0.213293\pi\)
−0.929730 + 0.368242i \(0.879960\pi\)
\(770\) −0.546471 2.23614i −0.0196935 0.0805848i
\(771\) 0 0
\(772\) −13.7433 + 7.14387i −0.494632 + 0.257114i
\(773\) 0.699713i 0.0251669i −0.999921 0.0125835i \(-0.995994\pi\)
0.999921 0.0125835i \(-0.00400555\pi\)
\(774\) 0 0
\(775\) 11.1565i 0.400753i
\(776\) −29.1028 + 5.76181i −1.04473 + 0.206837i
\(777\) 0 0
\(778\) 43.3110 10.5844i 1.55278 0.379470i
\(779\) 15.9444 + 27.6165i 0.571267 + 0.989463i
\(780\) 0 0
\(781\) 3.00000 5.19615i 0.107348 0.185933i
\(782\) −1.01082 + 3.46410i −0.0361467 + 0.123876i
\(783\) 0 0
\(784\) 9.05842 + 19.4866i 0.323515 + 0.695950i
\(785\) −25.9307 14.9711i −0.925506 0.534341i
\(786\) 0 0
\(787\) 30.0903 17.3727i 1.07260 0.619268i 0.143712 0.989620i \(-0.454096\pi\)
0.928892 + 0.370351i \(0.120763\pi\)
\(788\) 47.8607 + 2.11829i 1.70497 + 0.0754609i
\(789\) 0 0
\(790\) 25.4876 24.3845i 0.906809 0.867562i
\(791\) 9.28550 0.330154
\(792\) 0 0
\(793\) 5.62772 0.199846
\(794\) 19.1545 18.3255i 0.679767 0.650347i
\(795\) 0 0
\(796\) 25.7893 + 1.14142i 0.914078 + 0.0404566i
\(797\) −20.6970 + 11.9494i −0.733126 + 0.423270i −0.819565 0.572987i \(-0.805785\pi\)
0.0864387 + 0.996257i \(0.472451\pi\)
\(798\) 0 0
\(799\) −0.822662 0.474964i −0.0291037 0.0168030i
\(800\) −1.16944 7.67420i −0.0413461 0.271324i
\(801\) 0 0
\(802\) 1.82473 6.25343i 0.0644336 0.220816i
\(803\) −0.852189 + 1.47603i −0.0300731 + 0.0520881i
\(804\) 0 0
\(805\) −5.18614 8.98266i −0.182787 0.316597i
\(806\) 26.4954 6.47498i 0.933259 0.228072i
\(807\) 0 0
\(808\) −0.678246 3.42581i −0.0238606 0.120520i
\(809\) 35.8381i 1.26000i 0.776595 + 0.630000i \(0.216945\pi\)
−0.776595 + 0.630000i \(0.783055\pi\)
\(810\) 0 0
\(811\) 1.20128i 0.0421828i −0.999778 0.0210914i \(-0.993286\pi\)
0.999778 0.0210914i \(-0.00671410\pi\)
\(812\) −5.71519 + 2.97080i −0.200564 + 0.104255i
\(813\) 0 0
\(814\) 1.14442 + 4.68290i 0.0401118 + 0.164136i
\(815\) −2.20979 3.82746i −0.0774054 0.134070i
\(816\) 0 0
\(817\) 18.1753 31.4805i 0.635872 1.10136i
\(818\) 18.6596 + 5.44482i 0.652417 + 0.190374i
\(819\) 0 0
\(820\) 28.8614 + 18.4110i 1.00788 + 0.642940i
\(821\) 15.8139 + 9.13014i 0.551907 + 0.318644i 0.749891 0.661561i \(-0.230106\pi\)
−0.197983 + 0.980205i \(0.563439\pi\)
\(822\) 0 0
\(823\) −12.1538 + 7.01701i −0.423656 + 0.244598i −0.696640 0.717421i \(-0.745323\pi\)
0.272984 + 0.962018i \(0.411989\pi\)
\(824\) −1.27172 0.432962i −0.0443025 0.0150829i
\(825\) 0 0
\(826\) −15.4378 16.1362i −0.537149 0.561449i
\(827\) 47.4864 1.65126 0.825632 0.564210i \(-0.190819\pi\)
0.825632 + 0.564210i \(0.190819\pi\)
\(828\) 0 0
\(829\) −48.2337 −1.67523 −0.837613 0.546265i \(-0.816049\pi\)
−0.837613 + 0.546265i \(0.816049\pi\)
\(830\) 18.8552 + 19.7082i 0.654473 + 0.684080i
\(831\) 0 0
\(832\) −17.5466 + 7.23123i −0.608319 + 0.250698i
\(833\) 3.68614 2.12819i 0.127717 0.0737376i
\(834\) 0 0
\(835\) 38.2359 + 22.0755i 1.32321 + 0.763954i
\(836\) 2.55657 4.00772i 0.0884207 0.138610i
\(837\) 0 0
\(838\) 36.6060 + 10.6815i 1.26453 + 0.368987i
\(839\) −21.3102 + 36.9104i −0.735711 + 1.27429i 0.218700 + 0.975792i \(0.429818\pi\)
−0.954411 + 0.298496i \(0.903515\pi\)
\(840\) 0 0
\(841\) −11.3139 19.5962i −0.390133 0.675730i
\(842\) 3.56072 + 14.5703i 0.122711 + 0.502127i
\(843\) 0 0
\(844\) 16.1755 + 31.1182i 0.556783 + 1.07113i
\(845\) 18.6101i 0.640208i
\(846\) 0 0
\(847\) 13.7081i 0.471017i
\(848\) 0.664194 7.48871i 0.0228085 0.257163i
\(849\) 0 0
\(850\) −1.49364 + 0.365017i −0.0512313 + 0.0125200i
\(851\) 10.8608 + 18.8114i 0.372303 + 0.644847i
\(852\) 0 0
\(853\) −22.3030 + 38.6299i −0.763640 + 1.32266i 0.177323 + 0.984153i \(0.443256\pi\)
−0.940963 + 0.338510i \(0.890077\pi\)
\(854\) −1.19897 + 4.10891i −0.0410279 + 0.140604i
\(855\) 0 0
\(856\) 23.4090 + 26.7411i 0.800102 + 0.913992i
\(857\) −32.5367 18.7851i −1.11143 0.641685i −0.172232 0.985056i \(-0.555098\pi\)
−0.939200 + 0.343371i \(0.888431\pi\)
\(858\) 0 0
\(859\) 1.58077 0.912661i 0.0539353 0.0311396i −0.472790 0.881175i \(-0.656753\pi\)
0.526725 + 0.850036i \(0.323420\pi\)
\(860\) 1.72547 38.9854i 0.0588381 1.32939i
\(861\) 0 0
\(862\) −31.8774 + 30.4977i −1.08575 + 1.03876i
\(863\) −40.0344 −1.36279 −0.681393 0.731918i \(-0.738625\pi\)
−0.681393 + 0.731918i \(0.738625\pi\)
\(864\) 0 0
\(865\) −44.6060 −1.51665
\(866\) 8.81640 8.43482i 0.299593 0.286627i
\(867\) 0 0
\(868\) −0.917245 + 20.7243i −0.0311333 + 0.703428i
\(869\) 4.32473 2.49689i 0.146707 0.0847011i
\(870\) 0 0
\(871\) 15.8798 + 9.16823i 0.538068 + 0.310654i
\(872\) 25.1303 + 28.7075i 0.851020 + 0.972158i
\(873\) 0 0
\(874\) 6.00000 20.5622i 0.202953 0.695527i
\(875\) −5.84172 + 10.1182i −0.197486 + 0.342056i
\(876\) 0 0
\(877\) −10.8139 18.7302i −0.365158 0.632472i 0.623643 0.781709i \(-0.285652\pi\)
−0.988802 + 0.149237i \(0.952318\pi\)
\(878\) −8.96831 + 2.19169i −0.302666 + 0.0739661i
\(879\) 0 0
\(880\) 0.450854 5.08333i 0.0151983 0.171359i
\(881\) 52.9562i 1.78414i 0.451898 + 0.892070i \(0.350747\pi\)
−0.451898 + 0.892070i \(0.649253\pi\)
\(882\) 0 0
\(883\) 20.0127i 0.673481i −0.941597 0.336741i \(-0.890675\pi\)
0.941597 0.336741i \(-0.109325\pi\)
\(884\) 1.73375 + 3.33536i 0.0583122 + 0.112180i
\(885\) 0 0
\(886\) −4.15531 17.0033i −0.139600 0.571239i
\(887\) −9.75588 16.8977i −0.327571 0.567369i 0.654459 0.756098i \(-0.272897\pi\)
−0.982029 + 0.188729i \(0.939563\pi\)
\(888\) 0 0
\(889\) −4.88316 + 8.45787i −0.163776 + 0.283668i
\(890\) 41.0452 + 11.9769i 1.37584 + 0.401466i
\(891\) 0 0
\(892\) −8.74456 + 13.7081i −0.292790 + 0.458982i
\(893\) 4.88316 + 2.81929i 0.163409 + 0.0943440i
\(894\) 0 0
\(895\) −19.3236 + 11.1565i −0.645917 + 0.372920i
\(896\) −1.54141 14.3517i −0.0514949 0.479458i
\(897\) 0 0
\(898\) −18.9686 19.8267i −0.632991 0.661626i
\(899\) 20.5226 0.684467
\(900\) 0 0
\(901\) −1.48913 −0.0496100
\(902\) 3.35041 + 3.50198i 0.111557 + 0.116603i
\(903\) 0 0
\(904\) 19.4871 + 6.63444i 0.648130 + 0.220658i
\(905\) −8.74456 + 5.04868i −0.290679 + 0.167824i
\(906\) 0 0
\(907\) −25.8884 14.9467i −0.859611 0.496297i 0.00427097 0.999991i \(-0.498641\pi\)
−0.863882 + 0.503694i \(0.831974\pi\)
\(908\) −24.2781 15.4873i −0.805698 0.513963i
\(909\) 0 0
\(910\) −10.3723 3.02661i −0.343838 0.100331i
\(911\) 17.9015 31.0063i 0.593102 1.02728i −0.400710 0.916205i \(-0.631236\pi\)
0.993812 0.111078i \(-0.0354303\pi\)
\(912\) 0 0
\(913\) 1.93070 + 3.34408i 0.0638970 + 0.110673i
\(914\) −13.4218 54.9215i −0.443955 1.81664i
\(915\) 0 0
\(916\) −6.43765 + 3.34634i −0.212706 + 0.110566i
\(917\) 9.74749i 0.321891i
\(918\) 0 0
\(919\) 36.9711i 1.21956i −0.792570 0.609781i \(-0.791257\pi\)
0.792570 0.609781i \(-0.208743\pi\)
\(920\) −4.46585 22.5570i −0.147235 0.743681i
\(921\) 0 0
\(922\) 0.480628 0.117457i 0.0158286 0.00386823i
\(923\) −14.0814 24.3897i −0.463494 0.802796i
\(924\) 0 0
\(925\) −4.62772 + 8.01544i −0.152158 + 0.263546i
\(926\) −1.89253 + 6.48577i −0.0621925 + 0.213136i
\(927\) 0 0
\(928\) −14.1168 + 2.15121i −0.463408 + 0.0706170i
\(929\) −16.0693 9.27761i −0.527217 0.304389i 0.212666 0.977125i \(-0.431785\pi\)
−0.739882 + 0.672736i \(0.765119\pi\)
\(930\) 0 0
\(931\) −21.8802 + 12.6325i −0.717094 + 0.414014i
\(932\) −9.68311 0.428569i −0.317181 0.0140383i
\(933\) 0 0
\(934\) 5.22495 4.99882i 0.170966 0.163566i
\(935\) −1.01082 −0.0330572
\(936\) 0 0
\(937\) 45.7228 1.49370 0.746850 0.664993i \(-0.231565\pi\)
0.746850 + 0.664993i \(0.231565\pi\)
\(938\) −10.0771 + 9.64092i −0.329028 + 0.314787i
\(939\) 0 0
\(940\) 6.04729 + 0.267650i 0.197241 + 0.00872978i
\(941\) −11.6970 + 6.75327i −0.381312 + 0.220150i −0.678389 0.734703i \(-0.737322\pi\)
0.297077 + 0.954854i \(0.403988\pi\)
\(942\) 0 0
\(943\) 18.9123 + 10.9190i 0.615869 + 0.355572i
\(944\) −20.8694 44.8945i −0.679240 1.46119i
\(945\) 0 0
\(946\) 1.54755 5.30350i 0.0503151 0.172432i
\(947\) −3.28515 + 5.69005i −0.106753 + 0.184902i −0.914453 0.404692i \(-0.867379\pi\)
0.807700 + 0.589594i \(0.200712\pi\)
\(948\) 0 0
\(949\) 4.00000 + 6.92820i 0.129845 + 0.224899i
\(950\) 8.86592 2.16667i 0.287648 0.0702960i
\(951\) 0 0
\(952\) −2.80458 + 0.555254i −0.0908971 + 0.0179959i
\(953\) 10.2997i 0.333641i 0.985987 + 0.166821i \(0.0533500\pi\)
−0.985987 + 0.166821i \(0.946650\pi\)
\(954\) 0 0
\(955\) 38.0978i 1.23282i
\(956\) −21.4009 + 11.1244i −0.692155 + 0.359788i
\(957\) 0 0
\(958\) −4.38816 17.9562i −0.141775 0.580137i
\(959\) 3.50283 + 6.06709i 0.113112 + 0.195916i
\(960\) 0 0
\(961\) 17.5475 30.3932i 0.566050 0.980427i
\(962\) 21.7216 + 6.33830i 0.700331 + 0.204355i
\(963\) 0 0
\(964\) −10.9416 6.97975i −0.352404 0.224802i
\(965\) −16.9307 9.77495i −0.545019 0.314667i
\(966\) 0 0
\(967\) −40.5748 + 23.4259i −1.30480 + 0.753325i −0.981223 0.192878i \(-0.938218\pi\)
−0.323574 + 0.946203i \(0.604885\pi\)
\(968\) −9.79440 + 28.7686i −0.314804 + 0.924659i
\(969\) 0 0
\(970\) −25.8861 27.0571i −0.831152 0.868753i
\(971\) −37.0019 −1.18745 −0.593724 0.804669i \(-0.702343\pi\)
−0.593724 + 0.804669i \(0.702343\pi\)
\(972\) 0 0
\(973\) 19.6277 0.629236
\(974\) −41.9166 43.8128i −1.34309 1.40385i
\(975\) 0 0
\(976\) −5.45202 + 7.76653i −0.174515 + 0.248601i
\(977\) 47.3614 27.3441i 1.51523 0.874816i 0.515385 0.856959i \(-0.327649\pi\)
0.999841 0.0178572i \(-0.00568444\pi\)
\(978\) 0 0
\(979\) 5.24224 + 3.02661i 0.167543 + 0.0967307i
\(980\) −14.5868 + 22.8665i −0.465958 + 0.730444i
\(981\) 0 0
\(982\) −18.6861 5.45257i −0.596299 0.173998i
\(983\) 17.2079 29.8050i 0.548847 0.950631i −0.449507 0.893277i \(-0.648400\pi\)
0.998354 0.0573540i \(-0.0182664\pi\)
\(984\) 0 0
\(985\) 30.2337 + 52.3663i 0.963325 + 1.66853i
\(986\) 0.671457 + 2.74757i 0.0213835 + 0.0875005i
\(987\) 0 0
\(988\) −10.2912 19.7980i −0.327406 0.629859i
\(989\) 24.8935i 0.791568i
\(990\) 0 0
\(991\) 7.65492i 0.243167i −0.992581 0.121583i \(-0.961203\pi\)
0.992581 0.121583i \(-0.0387972\pi\)
\(992\) −16.7324 + 42.8377i −0.531253 + 1.36010i
\(993\) 0 0
\(994\) 20.8074 5.08495i 0.659970 0.161285i
\(995\) 16.2912 + 28.2171i 0.516465 + 0.894543i
\(996\) 0 0
\(997\) 12.0693 20.9046i 0.382238 0.662056i −0.609143 0.793060i \(-0.708487\pi\)
0.991382 + 0.131004i \(0.0418200\pi\)
\(998\) 1.35760 4.65253i 0.0429740 0.147273i
\(999\) 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 108.2.h.a.35.1 8
3.2 odd 2 36.2.h.a.11.4 yes 8
4.3 odd 2 inner 108.2.h.a.35.2 8
8.3 odd 2 1728.2.s.f.575.1 8
8.5 even 2 1728.2.s.f.575.2 8
9.2 odd 6 324.2.b.b.323.1 8
9.4 even 3 36.2.h.a.23.3 yes 8
9.5 odd 6 inner 108.2.h.a.71.2 8
9.7 even 3 324.2.b.b.323.8 8
12.11 even 2 36.2.h.a.11.3 8
15.2 even 4 900.2.o.a.299.6 16
15.8 even 4 900.2.o.a.299.3 16
15.14 odd 2 900.2.r.c.551.1 8
24.5 odd 2 576.2.s.f.191.4 8
24.11 even 2 576.2.s.f.191.1 8
36.7 odd 6 324.2.b.b.323.2 8
36.11 even 6 324.2.b.b.323.7 8
36.23 even 6 inner 108.2.h.a.71.1 8
36.31 odd 6 36.2.h.a.23.4 yes 8
45.4 even 6 900.2.r.c.851.2 8
45.13 odd 12 900.2.o.a.599.1 16
45.22 odd 12 900.2.o.a.599.8 16
60.23 odd 4 900.2.o.a.299.8 16
60.47 odd 4 900.2.o.a.299.1 16
60.59 even 2 900.2.r.c.551.2 8
72.5 odd 6 1728.2.s.f.1151.1 8
72.11 even 6 5184.2.c.j.5183.8 8
72.13 even 6 576.2.s.f.383.1 8
72.29 odd 6 5184.2.c.j.5183.7 8
72.43 odd 6 5184.2.c.j.5183.2 8
72.59 even 6 1728.2.s.f.1151.2 8
72.61 even 6 5184.2.c.j.5183.1 8
72.67 odd 6 576.2.s.f.383.4 8
180.67 even 12 900.2.o.a.599.3 16
180.103 even 12 900.2.o.a.599.6 16
180.139 odd 6 900.2.r.c.851.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.2.h.a.11.3 8 12.11 even 2
36.2.h.a.11.4 yes 8 3.2 odd 2
36.2.h.a.23.3 yes 8 9.4 even 3
36.2.h.a.23.4 yes 8 36.31 odd 6
108.2.h.a.35.1 8 1.1 even 1 trivial
108.2.h.a.35.2 8 4.3 odd 2 inner
108.2.h.a.71.1 8 36.23 even 6 inner
108.2.h.a.71.2 8 9.5 odd 6 inner
324.2.b.b.323.1 8 9.2 odd 6
324.2.b.b.323.2 8 36.7 odd 6
324.2.b.b.323.7 8 36.11 even 6
324.2.b.b.323.8 8 9.7 even 3
576.2.s.f.191.1 8 24.11 even 2
576.2.s.f.191.4 8 24.5 odd 2
576.2.s.f.383.1 8 72.13 even 6
576.2.s.f.383.4 8 72.67 odd 6
900.2.o.a.299.1 16 60.47 odd 4
900.2.o.a.299.3 16 15.8 even 4
900.2.o.a.299.6 16 15.2 even 4
900.2.o.a.299.8 16 60.23 odd 4
900.2.o.a.599.1 16 45.13 odd 12
900.2.o.a.599.3 16 180.67 even 12
900.2.o.a.599.6 16 180.103 even 12
900.2.o.a.599.8 16 45.22 odd 12
900.2.r.c.551.1 8 15.14 odd 2
900.2.r.c.551.2 8 60.59 even 2
900.2.r.c.851.1 8 180.139 odd 6
900.2.r.c.851.2 8 45.4 even 6
1728.2.s.f.575.1 8 8.3 odd 2
1728.2.s.f.575.2 8 8.5 even 2
1728.2.s.f.1151.1 8 72.5 odd 6
1728.2.s.f.1151.2 8 72.59 even 6
5184.2.c.j.5183.1 8 72.61 even 6
5184.2.c.j.5183.2 8 72.43 odd 6
5184.2.c.j.5183.7 8 72.29 odd 6
5184.2.c.j.5183.8 8 72.11 even 6