Properties

Label 1134.2.l.e.215.1
Level $1134$
Weight $2$
Character 1134.215
Analytic conductor $9.055$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1134,2,Mod(215,1134)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1134.215");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.l (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: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 378)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 215.1
Root \(0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1134.215
Dual form 1134.2.l.e.269.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-1.22474 - 2.12132i) q^{5} +(2.62132 - 0.358719i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-1.22474 - 2.12132i) q^{5} +(2.62132 - 0.358719i) q^{7} +1.00000i q^{8} +(-2.12132 + 1.22474i) q^{10} +(3.67423 + 2.12132i) q^{11} +(3.62132 + 2.09077i) q^{13} +(-0.358719 - 2.62132i) q^{14} +1.00000 q^{16} +(-1.22474 - 2.12132i) q^{17} +(4.24264 + 2.44949i) q^{19} +(1.22474 + 2.12132i) q^{20} +(2.12132 - 3.67423i) q^{22} +(-5.19615 + 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(2.09077 - 3.62132i) q^{26} +(-2.62132 + 0.358719i) q^{28} +(8.87039 - 5.12132i) q^{29} +5.61642i q^{31} -1.00000i q^{32} +(-2.12132 + 1.22474i) q^{34} +(-3.97141 - 5.12132i) q^{35} +(1.62132 - 2.80821i) q^{37} +(2.44949 - 4.24264i) q^{38} +(2.12132 - 1.22474i) q^{40} +(1.22474 - 2.12132i) q^{41} +(-3.50000 - 6.06218i) q^{43} +(-3.67423 - 2.12132i) q^{44} +(3.00000 + 5.19615i) q^{46} -7.94282 q^{47} +(6.74264 - 1.88064i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-3.62132 - 2.09077i) q^{52} +(2.15232 - 1.24264i) q^{53} -10.3923i q^{55} +(0.358719 + 2.62132i) q^{56} +(-5.12132 - 8.87039i) q^{58} -2.44949 q^{59} +0.717439i q^{61} +5.61642 q^{62} -1.00000 q^{64} -10.2426i q^{65} -3.48528 q^{67} +(1.22474 + 2.12132i) q^{68} +(-5.12132 + 3.97141i) q^{70} -12.7279i q^{71} +(-13.2426 + 7.64564i) q^{73} +(-2.80821 - 1.62132i) q^{74} +(-4.24264 - 2.44949i) q^{76} +(10.3923 + 4.24264i) q^{77} +9.24264 q^{79} +(-1.22474 - 2.12132i) q^{80} +(-2.12132 - 1.22474i) q^{82} +(2.74666 + 4.75736i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(-6.06218 + 3.50000i) q^{86} +(-2.12132 + 3.67423i) q^{88} +(8.87039 - 15.3640i) q^{89} +(10.2426 + 4.18154i) q^{91} +(5.19615 - 3.00000i) q^{92} +7.94282i q^{94} -12.0000i q^{95} +(5.74264 - 3.31552i) q^{97} +(-1.88064 - 6.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{4} + 4 q^{7} + 12 q^{13} + 8 q^{16} - 4 q^{25} - 4 q^{28} - 4 q^{37} - 28 q^{43} + 24 q^{46} + 20 q^{49} - 12 q^{52} - 24 q^{58} - 8 q^{64} + 40 q^{67} - 24 q^{70} - 72 q^{73} + 40 q^{79} - 24 q^{85} + 48 q^{91} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) −1.22474 2.12132i −0.547723 0.948683i −0.998430 0.0560116i \(-0.982162\pi\)
0.450708 0.892672i \(-0.351172\pi\)
\(6\) 0 0
\(7\) 2.62132 0.358719i 0.990766 0.135583i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −2.12132 + 1.22474i −0.670820 + 0.387298i
\(11\) 3.67423 + 2.12132i 1.10782 + 0.639602i 0.938265 0.345918i \(-0.112432\pi\)
0.169559 + 0.985520i \(0.445766\pi\)
\(12\) 0 0
\(13\) 3.62132 + 2.09077i 1.00437 + 0.579875i 0.909539 0.415618i \(-0.136435\pi\)
0.0948342 + 0.995493i \(0.469768\pi\)
\(14\) −0.358719 2.62132i −0.0958718 0.700577i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −1.22474 2.12132i −0.297044 0.514496i 0.678414 0.734680i \(-0.262668\pi\)
−0.975458 + 0.220184i \(0.929334\pi\)
\(18\) 0 0
\(19\) 4.24264 + 2.44949i 0.973329 + 0.561951i 0.900249 0.435375i \(-0.143384\pi\)
0.0730792 + 0.997326i \(0.476717\pi\)
\(20\) 1.22474 + 2.12132i 0.273861 + 0.474342i
\(21\) 0 0
\(22\) 2.12132 3.67423i 0.452267 0.783349i
\(23\) −5.19615 + 3.00000i −1.08347 + 0.625543i −0.931831 0.362892i \(-0.881789\pi\)
−0.151642 + 0.988436i \(0.548456\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 2.09077 3.62132i 0.410034 0.710199i
\(27\) 0 0
\(28\) −2.62132 + 0.358719i −0.495383 + 0.0677916i
\(29\) 8.87039 5.12132i 1.64719 0.951005i 0.669007 0.743256i \(-0.266719\pi\)
0.978182 0.207750i \(-0.0666139\pi\)
\(30\) 0 0
\(31\) 5.61642i 1.00874i 0.863488 + 0.504369i \(0.168275\pi\)
−0.863488 + 0.504369i \(0.831725\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −2.12132 + 1.22474i −0.363803 + 0.210042i
\(35\) −3.97141 5.12132i −0.671290 0.865661i
\(36\) 0 0
\(37\) 1.62132 2.80821i 0.266543 0.461667i −0.701423 0.712745i \(-0.747452\pi\)
0.967967 + 0.251078i \(0.0807851\pi\)
\(38\) 2.44949 4.24264i 0.397360 0.688247i
\(39\) 0 0
\(40\) 2.12132 1.22474i 0.335410 0.193649i
\(41\) 1.22474 2.12132i 0.191273 0.331295i −0.754399 0.656416i \(-0.772072\pi\)
0.945672 + 0.325121i \(0.105405\pi\)
\(42\) 0 0
\(43\) −3.50000 6.06218i −0.533745 0.924473i −0.999223 0.0394140i \(-0.987451\pi\)
0.465478 0.885059i \(-0.345882\pi\)
\(44\) −3.67423 2.12132i −0.553912 0.319801i
\(45\) 0 0
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) −7.94282 −1.15858 −0.579289 0.815122i \(-0.696670\pi\)
−0.579289 + 0.815122i \(0.696670\pi\)
\(48\) 0 0
\(49\) 6.74264 1.88064i 0.963234 0.268662i
\(50\) 0.866025 + 0.500000i 0.122474 + 0.0707107i
\(51\) 0 0
\(52\) −3.62132 2.09077i −0.502187 0.289938i
\(53\) 2.15232 1.24264i 0.295643 0.170690i −0.344841 0.938661i \(-0.612067\pi\)
0.640484 + 0.767971i \(0.278734\pi\)
\(54\) 0 0
\(55\) 10.3923i 1.40130i
\(56\) 0.358719 + 2.62132i 0.0479359 + 0.350289i
\(57\) 0 0
\(58\) −5.12132 8.87039i −0.672462 1.16474i
\(59\) −2.44949 −0.318896 −0.159448 0.987206i \(-0.550971\pi\)
−0.159448 + 0.987206i \(0.550971\pi\)
\(60\) 0 0
\(61\) 0.717439i 0.0918586i 0.998945 + 0.0459293i \(0.0146249\pi\)
−0.998945 + 0.0459293i \(0.985375\pi\)
\(62\) 5.61642 0.713286
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 10.2426i 1.27044i
\(66\) 0 0
\(67\) −3.48528 −0.425795 −0.212897 0.977075i \(-0.568290\pi\)
−0.212897 + 0.977075i \(0.568290\pi\)
\(68\) 1.22474 + 2.12132i 0.148522 + 0.257248i
\(69\) 0 0
\(70\) −5.12132 + 3.97141i −0.612115 + 0.474674i
\(71\) 12.7279i 1.51053i −0.655422 0.755263i \(-0.727509\pi\)
0.655422 0.755263i \(-0.272491\pi\)
\(72\) 0 0
\(73\) −13.2426 + 7.64564i −1.54993 + 0.894855i −0.551788 + 0.833984i \(0.686054\pi\)
−0.998146 + 0.0608704i \(0.980612\pi\)
\(74\) −2.80821 1.62132i −0.326448 0.188475i
\(75\) 0 0
\(76\) −4.24264 2.44949i −0.486664 0.280976i
\(77\) 10.3923 + 4.24264i 1.18431 + 0.483494i
\(78\) 0 0
\(79\) 9.24264 1.03988 0.519939 0.854203i \(-0.325955\pi\)
0.519939 + 0.854203i \(0.325955\pi\)
\(80\) −1.22474 2.12132i −0.136931 0.237171i
\(81\) 0 0
\(82\) −2.12132 1.22474i −0.234261 0.135250i
\(83\) 2.74666 + 4.75736i 0.301485 + 0.522188i 0.976473 0.215641i \(-0.0691842\pi\)
−0.674987 + 0.737829i \(0.735851\pi\)
\(84\) 0 0
\(85\) −3.00000 + 5.19615i −0.325396 + 0.563602i
\(86\) −6.06218 + 3.50000i −0.653701 + 0.377415i
\(87\) 0 0
\(88\) −2.12132 + 3.67423i −0.226134 + 0.391675i
\(89\) 8.87039 15.3640i 0.940259 1.62858i 0.175283 0.984518i \(-0.443916\pi\)
0.764976 0.644059i \(-0.222751\pi\)
\(90\) 0 0
\(91\) 10.2426 + 4.18154i 1.07372 + 0.438345i
\(92\) 5.19615 3.00000i 0.541736 0.312772i
\(93\) 0 0
\(94\) 7.94282i 0.819239i
\(95\) 12.0000i 1.23117i
\(96\) 0 0
\(97\) 5.74264 3.31552i 0.583077 0.336640i −0.179278 0.983798i \(-0.557376\pi\)
0.762355 + 0.647159i \(0.224043\pi\)
\(98\) −1.88064 6.74264i −0.189973 0.681110i
\(99\) 0 0
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) −3.67423 + 6.36396i −0.365600 + 0.633238i −0.988872 0.148767i \(-0.952470\pi\)
0.623272 + 0.782005i \(0.285803\pi\)
\(102\) 0 0
\(103\) −5.37868 + 3.10538i −0.529977 + 0.305982i −0.741007 0.671497i \(-0.765652\pi\)
0.211030 + 0.977480i \(0.432318\pi\)
\(104\) −2.09077 + 3.62132i −0.205017 + 0.355100i
\(105\) 0 0
\(106\) −1.24264 2.15232i −0.120696 0.209051i
\(107\) 12.5446 + 7.24264i 1.21273 + 0.700173i 0.963354 0.268233i \(-0.0864397\pi\)
0.249380 + 0.968406i \(0.419773\pi\)
\(108\) 0 0
\(109\) −3.86396 6.69258i −0.370100 0.641033i 0.619480 0.785012i \(-0.287343\pi\)
−0.989581 + 0.143980i \(0.954010\pi\)
\(110\) −10.3923 −0.990867
\(111\) 0 0
\(112\) 2.62132 0.358719i 0.247691 0.0338958i
\(113\) 1.52192 + 0.878680i 0.143170 + 0.0826592i 0.569874 0.821732i \(-0.306992\pi\)
−0.426704 + 0.904391i \(0.640325\pi\)
\(114\) 0 0
\(115\) 12.7279 + 7.34847i 1.18688 + 0.685248i
\(116\) −8.87039 + 5.12132i −0.823595 + 0.475503i
\(117\) 0 0
\(118\) 2.44949i 0.225494i
\(119\) −3.97141 5.12132i −0.364058 0.469471i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 0.717439 0.0649539
\(123\) 0 0
\(124\) 5.61642i 0.504369i
\(125\) −9.79796 −0.876356
\(126\) 0 0
\(127\) 17.7279 1.57310 0.786549 0.617527i \(-0.211866\pi\)
0.786549 + 0.617527i \(0.211866\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −10.2426 −0.898339
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) 12.0000 + 4.89898i 1.04053 + 0.424795i
\(134\) 3.48528i 0.301082i
\(135\) 0 0
\(136\) 2.12132 1.22474i 0.181902 0.105021i
\(137\) 5.19615 + 3.00000i 0.443937 + 0.256307i 0.705266 0.708942i \(-0.250827\pi\)
−0.261329 + 0.965250i \(0.584161\pi\)
\(138\) 0 0
\(139\) −9.98528 5.76500i −0.846941 0.488981i 0.0126769 0.999920i \(-0.495965\pi\)
−0.859617 + 0.510938i \(0.829298\pi\)
\(140\) 3.97141 + 5.12132i 0.335645 + 0.432831i
\(141\) 0 0
\(142\) −12.7279 −1.06810
\(143\) 8.87039 + 15.3640i 0.741779 + 1.28480i
\(144\) 0 0
\(145\) −21.7279 12.5446i −1.80441 1.04177i
\(146\) 7.64564 + 13.2426i 0.632758 + 1.09597i
\(147\) 0 0
\(148\) −1.62132 + 2.80821i −0.133272 + 0.230833i
\(149\) −6.71807 + 3.87868i −0.550366 + 0.317754i −0.749270 0.662265i \(-0.769595\pi\)
0.198904 + 0.980019i \(0.436262\pi\)
\(150\) 0 0
\(151\) −8.62132 + 14.9326i −0.701593 + 1.21519i 0.266314 + 0.963886i \(0.414194\pi\)
−0.967907 + 0.251309i \(0.919139\pi\)
\(152\) −2.44949 + 4.24264i −0.198680 + 0.344124i
\(153\) 0 0
\(154\) 4.24264 10.3923i 0.341882 0.837436i
\(155\) 11.9142 6.87868i 0.956973 0.552509i
\(156\) 0 0
\(157\) 10.3923i 0.829396i −0.909959 0.414698i \(-0.863887\pi\)
0.909959 0.414698i \(-0.136113\pi\)
\(158\) 9.24264i 0.735305i
\(159\) 0 0
\(160\) −2.12132 + 1.22474i −0.167705 + 0.0968246i
\(161\) −12.5446 + 9.72792i −0.988655 + 0.766668i
\(162\) 0 0
\(163\) −3.74264 + 6.48244i −0.293146 + 0.507744i −0.974552 0.224162i \(-0.928036\pi\)
0.681406 + 0.731906i \(0.261369\pi\)
\(164\) −1.22474 + 2.12132i −0.0956365 + 0.165647i
\(165\) 0 0
\(166\) 4.75736 2.74666i 0.369243 0.213182i
\(167\) −10.0951 + 17.4853i −0.781185 + 1.35305i 0.150067 + 0.988676i \(0.452051\pi\)
−0.931252 + 0.364376i \(0.881282\pi\)
\(168\) 0 0
\(169\) 2.24264 + 3.88437i 0.172511 + 0.298798i
\(170\) 5.19615 + 3.00000i 0.398527 + 0.230089i
\(171\) 0 0
\(172\) 3.50000 + 6.06218i 0.266872 + 0.462237i
\(173\) −20.7846 −1.58022 −0.790112 0.612962i \(-0.789978\pi\)
−0.790112 + 0.612962i \(0.789978\pi\)
\(174\) 0 0
\(175\) −1.00000 + 2.44949i −0.0755929 + 0.185164i
\(176\) 3.67423 + 2.12132i 0.276956 + 0.159901i
\(177\) 0 0
\(178\) −15.3640 8.87039i −1.15158 0.664864i
\(179\) −16.2189 + 9.36396i −1.21225 + 0.699895i −0.963250 0.268607i \(-0.913437\pi\)
−0.249004 + 0.968502i \(0.580103\pi\)
\(180\) 0 0
\(181\) 9.79796i 0.728277i −0.931345 0.364138i \(-0.881364\pi\)
0.931345 0.364138i \(-0.118636\pi\)
\(182\) 4.18154 10.2426i 0.309956 0.759235i
\(183\) 0 0
\(184\) −3.00000 5.19615i −0.221163 0.383065i
\(185\) −7.94282 −0.583967
\(186\) 0 0
\(187\) 10.3923i 0.759961i
\(188\) 7.94282 0.579289
\(189\) 0 0
\(190\) −12.0000 −0.870572
\(191\) 21.2132i 1.53493i 0.641089 + 0.767467i \(0.278483\pi\)
−0.641089 + 0.767467i \(0.721517\pi\)
\(192\) 0 0
\(193\) 15.4853 1.11465 0.557327 0.830293i \(-0.311827\pi\)
0.557327 + 0.830293i \(0.311827\pi\)
\(194\) −3.31552 5.74264i −0.238040 0.412298i
\(195\) 0 0
\(196\) −6.74264 + 1.88064i −0.481617 + 0.134331i
\(197\) 16.9706i 1.20910i 0.796566 + 0.604551i \(0.206648\pi\)
−0.796566 + 0.604551i \(0.793352\pi\)
\(198\) 0 0
\(199\) 3.10660 1.79360i 0.220221 0.127145i −0.385832 0.922569i \(-0.626085\pi\)
0.606053 + 0.795425i \(0.292752\pi\)
\(200\) −0.866025 0.500000i −0.0612372 0.0353553i
\(201\) 0 0
\(202\) 6.36396 + 3.67423i 0.447767 + 0.258518i
\(203\) 21.4150 16.6066i 1.50304 1.16555i
\(204\) 0 0
\(205\) −6.00000 −0.419058
\(206\) 3.10538 + 5.37868i 0.216362 + 0.374750i
\(207\) 0 0
\(208\) 3.62132 + 2.09077i 0.251093 + 0.144969i
\(209\) 10.3923 + 18.0000i 0.718851 + 1.24509i
\(210\) 0 0
\(211\) 6.74264 11.6786i 0.464183 0.803988i −0.534982 0.844864i \(-0.679682\pi\)
0.999164 + 0.0408759i \(0.0130148\pi\)
\(212\) −2.15232 + 1.24264i −0.147822 + 0.0853449i
\(213\) 0 0
\(214\) 7.24264 12.5446i 0.495097 0.857533i
\(215\) −8.57321 + 14.8492i −0.584688 + 1.01271i
\(216\) 0 0
\(217\) 2.01472 + 14.7224i 0.136768 + 0.999424i
\(218\) −6.69258 + 3.86396i −0.453278 + 0.261700i
\(219\) 0 0
\(220\) 10.3923i 0.700649i
\(221\) 10.2426i 0.688995i
\(222\) 0 0
\(223\) 9.00000 5.19615i 0.602685 0.347960i −0.167412 0.985887i \(-0.553541\pi\)
0.770097 + 0.637927i \(0.220208\pi\)
\(224\) −0.358719 2.62132i −0.0239680 0.175144i
\(225\) 0 0
\(226\) 0.878680 1.52192i 0.0584489 0.101236i
\(227\) 2.15232 3.72792i 0.142854 0.247431i −0.785716 0.618587i \(-0.787705\pi\)
0.928570 + 0.371156i \(0.121039\pi\)
\(228\) 0 0
\(229\) −7.86396 + 4.54026i −0.519665 + 0.300029i −0.736798 0.676113i \(-0.763663\pi\)
0.217132 + 0.976142i \(0.430330\pi\)
\(230\) 7.34847 12.7279i 0.484544 0.839254i
\(231\) 0 0
\(232\) 5.12132 + 8.87039i 0.336231 + 0.582369i
\(233\) 3.04384 + 1.75736i 0.199408 + 0.115128i 0.596379 0.802703i \(-0.296605\pi\)
−0.396971 + 0.917831i \(0.629939\pi\)
\(234\) 0 0
\(235\) 9.72792 + 16.8493i 0.634580 + 1.09912i
\(236\) 2.44949 0.159448
\(237\) 0 0
\(238\) −5.12132 + 3.97141i −0.331966 + 0.257428i
\(239\) 6.71807 + 3.87868i 0.434556 + 0.250891i 0.701286 0.712880i \(-0.252610\pi\)
−0.266730 + 0.963771i \(0.585943\pi\)
\(240\) 0 0
\(241\) −15.9853 9.22911i −1.02970 0.594499i −0.112803 0.993617i \(-0.535983\pi\)
−0.916899 + 0.399118i \(0.869316\pi\)
\(242\) 6.06218 3.50000i 0.389692 0.224989i
\(243\) 0 0
\(244\) 0.717439i 0.0459293i
\(245\) −12.2474 12.0000i −0.782461 0.766652i
\(246\) 0 0
\(247\) 10.2426 + 17.7408i 0.651724 + 1.12882i
\(248\) −5.61642 −0.356643
\(249\) 0 0
\(250\) 9.79796i 0.619677i
\(251\) 5.49333 0.346736 0.173368 0.984857i \(-0.444535\pi\)
0.173368 + 0.984857i \(0.444535\pi\)
\(252\) 0 0
\(253\) −25.4558 −1.60040
\(254\) 17.7279i 1.11235i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 2.15232 + 3.72792i 0.134258 + 0.232541i 0.925314 0.379203i \(-0.123802\pi\)
−0.791056 + 0.611744i \(0.790468\pi\)
\(258\) 0 0
\(259\) 3.24264 7.94282i 0.201488 0.493543i
\(260\) 10.2426i 0.635222i
\(261\) 0 0
\(262\) 0 0
\(263\) −16.2189 9.36396i −1.00010 0.577407i −0.0918204 0.995776i \(-0.529269\pi\)
−0.908277 + 0.418369i \(0.862602\pi\)
\(264\) 0 0
\(265\) −5.27208 3.04384i −0.323861 0.186981i
\(266\) 4.89898 12.0000i 0.300376 0.735767i
\(267\) 0 0
\(268\) 3.48528 0.212897
\(269\) 4.89898 + 8.48528i 0.298696 + 0.517357i 0.975838 0.218496i \(-0.0701150\pi\)
−0.677142 + 0.735853i \(0.736782\pi\)
\(270\) 0 0
\(271\) 13.3492 + 7.70719i 0.810909 + 0.468178i 0.847271 0.531160i \(-0.178244\pi\)
−0.0363626 + 0.999339i \(0.511577\pi\)
\(272\) −1.22474 2.12132i −0.0742611 0.128624i
\(273\) 0 0
\(274\) 3.00000 5.19615i 0.181237 0.313911i
\(275\) −3.67423 + 2.12132i −0.221565 + 0.127920i
\(276\) 0 0
\(277\) 0.863961 1.49642i 0.0519104 0.0899114i −0.838903 0.544282i \(-0.816802\pi\)
0.890813 + 0.454370i \(0.150136\pi\)
\(278\) −5.76500 + 9.98528i −0.345762 + 0.598877i
\(279\) 0 0
\(280\) 5.12132 3.97141i 0.306057 0.237337i
\(281\) 19.2627 11.1213i 1.14912 0.663442i 0.200444 0.979705i \(-0.435761\pi\)
0.948672 + 0.316263i \(0.102428\pi\)
\(282\) 0 0
\(283\) 23.3572i 1.38844i −0.719762 0.694220i \(-0.755749\pi\)
0.719762 0.694220i \(-0.244251\pi\)
\(284\) 12.7279i 0.755263i
\(285\) 0 0
\(286\) 15.3640 8.87039i 0.908490 0.524517i
\(287\) 2.44949 6.00000i 0.144589 0.354169i
\(288\) 0 0
\(289\) 5.50000 9.52628i 0.323529 0.560369i
\(290\) −12.5446 + 21.7279i −0.736646 + 1.27591i
\(291\) 0 0
\(292\) 13.2426 7.64564i 0.774967 0.447427i
\(293\) −3.97141 + 6.87868i −0.232012 + 0.401857i −0.958400 0.285428i \(-0.907864\pi\)
0.726388 + 0.687285i \(0.241198\pi\)
\(294\) 0 0
\(295\) 3.00000 + 5.19615i 0.174667 + 0.302532i
\(296\) 2.80821 + 1.62132i 0.163224 + 0.0942373i
\(297\) 0 0
\(298\) 3.87868 + 6.71807i 0.224686 + 0.389167i
\(299\) −25.0892 −1.45095
\(300\) 0 0
\(301\) −11.3492 14.6354i −0.654159 0.843570i
\(302\) 14.9326 + 8.62132i 0.859273 + 0.496101i
\(303\) 0 0
\(304\) 4.24264 + 2.44949i 0.243332 + 0.140488i
\(305\) 1.52192 0.878680i 0.0871448 0.0503131i
\(306\) 0 0
\(307\) 2.57258i 0.146825i 0.997302 + 0.0734125i \(0.0233890\pi\)
−0.997302 + 0.0734125i \(0.976611\pi\)
\(308\) −10.3923 4.24264i −0.592157 0.241747i
\(309\) 0 0
\(310\) −6.87868 11.9142i −0.390683 0.676682i
\(311\) 17.1464 0.972285 0.486142 0.873880i \(-0.338404\pi\)
0.486142 + 0.873880i \(0.338404\pi\)
\(312\) 0 0
\(313\) 0.594346i 0.0335944i 0.999859 + 0.0167972i \(0.00534697\pi\)
−0.999859 + 0.0167972i \(0.994653\pi\)
\(314\) −10.3923 −0.586472
\(315\) 0 0
\(316\) −9.24264 −0.519939
\(317\) 13.7574i 0.772690i 0.922354 + 0.386345i \(0.126263\pi\)
−0.922354 + 0.386345i \(0.873737\pi\)
\(318\) 0 0
\(319\) 43.4558 2.43306
\(320\) 1.22474 + 2.12132i 0.0684653 + 0.118585i
\(321\) 0 0
\(322\) 9.72792 + 12.5446i 0.542116 + 0.699084i
\(323\) 12.0000i 0.667698i
\(324\) 0 0
\(325\) −3.62132 + 2.09077i −0.200875 + 0.115975i
\(326\) 6.48244 + 3.74264i 0.359029 + 0.207286i
\(327\) 0 0
\(328\) 2.12132 + 1.22474i 0.117130 + 0.0676252i
\(329\) −20.8207 + 2.84924i −1.14788 + 0.157084i
\(330\) 0 0
\(331\) 10.0000 0.549650 0.274825 0.961494i \(-0.411380\pi\)
0.274825 + 0.961494i \(0.411380\pi\)
\(332\) −2.74666 4.75736i −0.150743 0.261094i
\(333\) 0 0
\(334\) 17.4853 + 10.0951i 0.956752 + 0.552381i
\(335\) 4.26858 + 7.39340i 0.233217 + 0.403944i
\(336\) 0 0
\(337\) −14.7279 + 25.5095i −0.802281 + 1.38959i 0.115830 + 0.993269i \(0.463047\pi\)
−0.918111 + 0.396323i \(0.870286\pi\)
\(338\) 3.88437 2.24264i 0.211282 0.121984i
\(339\) 0 0
\(340\) 3.00000 5.19615i 0.162698 0.281801i
\(341\) −11.9142 + 20.6360i −0.645191 + 1.11750i
\(342\) 0 0
\(343\) 17.0000 7.34847i 0.917914 0.396780i
\(344\) 6.06218 3.50000i 0.326851 0.188707i
\(345\) 0 0
\(346\) 20.7846i 1.11739i
\(347\) 28.9706i 1.55522i 0.628746 + 0.777611i \(0.283568\pi\)
−0.628746 + 0.777611i \(0.716432\pi\)
\(348\) 0 0
\(349\) −21.1066 + 12.1859i −1.12981 + 0.652296i −0.943887 0.330268i \(-0.892861\pi\)
−0.185923 + 0.982564i \(0.559528\pi\)
\(350\) 2.44949 + 1.00000i 0.130931 + 0.0534522i
\(351\) 0 0
\(352\) 2.12132 3.67423i 0.113067 0.195837i
\(353\) −15.2913 + 26.4853i −0.813873 + 1.40967i 0.0962614 + 0.995356i \(0.469312\pi\)
−0.910134 + 0.414313i \(0.864022\pi\)
\(354\) 0 0
\(355\) −27.0000 + 15.5885i −1.43301 + 0.827349i
\(356\) −8.87039 + 15.3640i −0.470130 + 0.814288i
\(357\) 0 0
\(358\) 9.36396 + 16.2189i 0.494901 + 0.857193i
\(359\) 2.15232 + 1.24264i 0.113595 + 0.0655841i 0.555721 0.831369i \(-0.312442\pi\)
−0.442126 + 0.896953i \(0.645776\pi\)
\(360\) 0 0
\(361\) 2.50000 + 4.33013i 0.131579 + 0.227901i
\(362\) −9.79796 −0.514969
\(363\) 0 0
\(364\) −10.2426 4.18154i −0.536860 0.219172i
\(365\) 32.4377 + 18.7279i 1.69787 + 0.980264i
\(366\) 0 0
\(367\) −7.97056 4.60181i −0.416060 0.240212i 0.277330 0.960775i \(-0.410550\pi\)
−0.693390 + 0.720562i \(0.743884\pi\)
\(368\) −5.19615 + 3.00000i −0.270868 + 0.156386i
\(369\) 0 0
\(370\) 7.94282i 0.412927i
\(371\) 5.19615 4.02944i 0.269771 0.209198i
\(372\) 0 0
\(373\) 11.0000 + 19.0526i 0.569558 + 0.986504i 0.996610 + 0.0822766i \(0.0262191\pi\)
−0.427051 + 0.904227i \(0.640448\pi\)
\(374\) −10.3923 −0.537373
\(375\) 0 0
\(376\) 7.94282i 0.409619i
\(377\) 42.8300 2.20586
\(378\) 0 0
\(379\) 9.48528 0.487226 0.243613 0.969872i \(-0.421667\pi\)
0.243613 + 0.969872i \(0.421667\pi\)
\(380\) 12.0000i 0.615587i
\(381\) 0 0
\(382\) 21.2132 1.08536
\(383\) −7.64564 13.2426i −0.390674 0.676667i 0.601865 0.798598i \(-0.294425\pi\)
−0.992539 + 0.121931i \(0.961091\pi\)
\(384\) 0 0
\(385\) −3.72792 27.2416i −0.189993 1.38836i
\(386\) 15.4853i 0.788180i
\(387\) 0 0
\(388\) −5.74264 + 3.31552i −0.291538 + 0.168320i
\(389\) −28.1331 16.2426i −1.42640 0.823535i −0.429569 0.903034i \(-0.641334\pi\)
−0.996835 + 0.0794995i \(0.974668\pi\)
\(390\) 0 0
\(391\) 12.7279 + 7.34847i 0.643679 + 0.371628i
\(392\) 1.88064 + 6.74264i 0.0949865 + 0.340555i
\(393\) 0 0
\(394\) 16.9706 0.854965
\(395\) −11.3199 19.6066i −0.569565 0.986515i
\(396\) 0 0
\(397\) −25.8640 14.9326i −1.29807 0.749444i −0.318004 0.948090i \(-0.603012\pi\)
−0.980071 + 0.198646i \(0.936346\pi\)
\(398\) −1.79360 3.10660i −0.0899049 0.155720i
\(399\) 0 0
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) 24.4588 14.1213i 1.22142 0.705185i 0.256197 0.966625i \(-0.417531\pi\)
0.965220 + 0.261440i \(0.0841972\pi\)
\(402\) 0 0
\(403\) −11.7426 + 20.3389i −0.584943 + 1.01315i
\(404\) 3.67423 6.36396i 0.182800 0.316619i
\(405\) 0 0
\(406\) −16.6066 21.4150i −0.824172 1.06281i
\(407\) 11.9142 6.87868i 0.590566 0.340963i
\(408\) 0 0
\(409\) 13.5592i 0.670461i −0.942136 0.335230i \(-0.891186\pi\)
0.942136 0.335230i \(-0.108814\pi\)
\(410\) 6.00000i 0.296319i
\(411\) 0 0
\(412\) 5.37868 3.10538i 0.264989 0.152991i
\(413\) −6.42090 + 0.878680i −0.315952 + 0.0432370i
\(414\) 0 0
\(415\) 6.72792 11.6531i 0.330261 0.572028i
\(416\) 2.09077 3.62132i 0.102508 0.177550i
\(417\) 0 0
\(418\) 18.0000 10.3923i 0.880409 0.508304i
\(419\) −6.42090 + 11.1213i −0.313681 + 0.543312i −0.979156 0.203108i \(-0.934896\pi\)
0.665475 + 0.746420i \(0.268229\pi\)
\(420\) 0 0
\(421\) −13.7279 23.7775i −0.669058 1.15884i −0.978168 0.207816i \(-0.933364\pi\)
0.309110 0.951026i \(-0.399969\pi\)
\(422\) −11.6786 6.74264i −0.568505 0.328227i
\(423\) 0 0
\(424\) 1.24264 + 2.15232i 0.0603480 + 0.104526i
\(425\) 2.44949 0.118818
\(426\) 0 0
\(427\) 0.257359 + 1.88064i 0.0124545 + 0.0910104i
\(428\) −12.5446 7.24264i −0.606367 0.350086i
\(429\) 0 0
\(430\) 14.8492 + 8.57321i 0.716094 + 0.413437i
\(431\) 8.87039 5.12132i 0.427272 0.246685i −0.270912 0.962604i \(-0.587325\pi\)
0.698184 + 0.715919i \(0.253992\pi\)
\(432\) 0 0
\(433\) 26.8213i 1.28895i 0.764626 + 0.644475i \(0.222924\pi\)
−0.764626 + 0.644475i \(0.777076\pi\)
\(434\) 14.7224 2.01472i 0.706699 0.0967096i
\(435\) 0 0
\(436\) 3.86396 + 6.69258i 0.185050 + 0.320516i
\(437\) −29.3939 −1.40610
\(438\) 0 0
\(439\) 25.0892i 1.19744i 0.800957 + 0.598722i \(0.204325\pi\)
−0.800957 + 0.598722i \(0.795675\pi\)
\(440\) 10.3923 0.495434
\(441\) 0 0
\(442\) −10.2426 −0.487193
\(443\) 25.4558i 1.20944i −0.796437 0.604722i \(-0.793284\pi\)
0.796437 0.604722i \(-0.206716\pi\)
\(444\) 0 0
\(445\) −43.4558 −2.06000
\(446\) −5.19615 9.00000i −0.246045 0.426162i
\(447\) 0 0
\(448\) −2.62132 + 0.358719i −0.123846 + 0.0169479i
\(449\) 30.7279i 1.45014i −0.688675 0.725070i \(-0.741807\pi\)
0.688675 0.725070i \(-0.258193\pi\)
\(450\) 0 0
\(451\) 9.00000 5.19615i 0.423793 0.244677i
\(452\) −1.52192 0.878680i −0.0715850 0.0413296i
\(453\) 0 0
\(454\) −3.72792 2.15232i −0.174960 0.101013i
\(455\) −3.67423 26.8492i −0.172251 1.25871i
\(456\) 0 0
\(457\) −23.0000 −1.07589 −0.537947 0.842978i \(-0.680800\pi\)
−0.537947 + 0.842978i \(0.680800\pi\)
\(458\) 4.54026 + 7.86396i 0.212152 + 0.367459i
\(459\) 0 0
\(460\) −12.7279 7.34847i −0.593442 0.342624i
\(461\) 21.1178 + 36.5772i 0.983556 + 1.70357i 0.648187 + 0.761482i \(0.275528\pi\)
0.335369 + 0.942087i \(0.391139\pi\)
\(462\) 0 0
\(463\) 11.0000 19.0526i 0.511213 0.885448i −0.488702 0.872451i \(-0.662530\pi\)
0.999916 0.0129968i \(-0.00413714\pi\)
\(464\) 8.87039 5.12132i 0.411797 0.237751i
\(465\) 0 0
\(466\) 1.75736 3.04384i 0.0814081 0.141003i
\(467\) −1.52192 + 2.63604i −0.0704260 + 0.121981i −0.899088 0.437768i \(-0.855769\pi\)
0.828662 + 0.559749i \(0.189103\pi\)
\(468\) 0 0
\(469\) −9.13604 + 1.25024i −0.421863 + 0.0577306i
\(470\) 16.8493 9.72792i 0.777198 0.448716i
\(471\) 0 0
\(472\) 2.44949i 0.112747i
\(473\) 29.6985i 1.36554i
\(474\) 0 0
\(475\) −4.24264 + 2.44949i −0.194666 + 0.112390i
\(476\) 3.97141 + 5.12132i 0.182029 + 0.234735i
\(477\) 0 0
\(478\) 3.87868 6.71807i 0.177407 0.307277i
\(479\) 1.22474 2.12132i 0.0559600 0.0969256i −0.836688 0.547679i \(-0.815511\pi\)
0.892648 + 0.450754i \(0.148845\pi\)
\(480\) 0 0
\(481\) 11.7426 6.77962i 0.535418 0.309124i
\(482\) −9.22911 + 15.9853i −0.420374 + 0.728110i
\(483\) 0 0
\(484\) −3.50000 6.06218i −0.159091 0.275554i
\(485\) −14.0665 8.12132i −0.638729 0.368770i
\(486\) 0 0
\(487\) −11.0000 19.0526i −0.498458 0.863354i 0.501541 0.865134i \(-0.332767\pi\)
−0.999998 + 0.00178012i \(0.999433\pi\)
\(488\) −0.717439 −0.0324769
\(489\) 0 0
\(490\) −12.0000 + 12.2474i −0.542105 + 0.553283i
\(491\) 0.891519 + 0.514719i 0.0402337 + 0.0232289i 0.519982 0.854177i \(-0.325939\pi\)
−0.479748 + 0.877406i \(0.659272\pi\)
\(492\) 0 0
\(493\) −21.7279 12.5446i −0.978576 0.564981i
\(494\) 17.7408 10.2426i 0.798195 0.460838i
\(495\) 0 0
\(496\) 5.61642i 0.252185i
\(497\) −4.56575 33.3640i −0.204802 1.49658i
\(498\) 0 0
\(499\) −13.2279 22.9114i −0.592163 1.02566i −0.993941 0.109919i \(-0.964941\pi\)
0.401777 0.915737i \(-0.368393\pi\)
\(500\) 9.79796 0.438178
\(501\) 0 0
\(502\) 5.49333i 0.245179i
\(503\) −20.1903 −0.900239 −0.450120 0.892968i \(-0.648619\pi\)
−0.450120 + 0.892968i \(0.648619\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 25.4558i 1.13165i
\(507\) 0 0
\(508\) −17.7279 −0.786549
\(509\) −14.9941 25.9706i −0.664602 1.15112i −0.979393 0.201964i \(-0.935268\pi\)
0.314791 0.949161i \(-0.398066\pi\)
\(510\) 0 0
\(511\) −31.9706 + 24.7921i −1.41429 + 1.09674i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 3.72792 2.15232i 0.164432 0.0949346i
\(515\) 13.1750 + 7.60660i 0.580561 + 0.335187i
\(516\) 0 0
\(517\) −29.1838 16.8493i −1.28350 0.741029i
\(518\) −7.94282 3.24264i −0.348987 0.142473i
\(519\) 0 0
\(520\) 10.2426 0.449170
\(521\) −4.60181 7.97056i −0.201609 0.349197i 0.747438 0.664331i \(-0.231284\pi\)
−0.949047 + 0.315135i \(0.897950\pi\)
\(522\) 0 0
\(523\) 15.2574 + 8.80884i 0.667158 + 0.385184i 0.794999 0.606611i \(-0.207471\pi\)
−0.127841 + 0.991795i \(0.540805\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −9.36396 + 16.2189i −0.408288 + 0.707176i
\(527\) 11.9142 6.87868i 0.518992 0.299640i
\(528\) 0 0
\(529\) 6.50000 11.2583i 0.282609 0.489493i
\(530\) −3.04384 + 5.27208i −0.132216 + 0.229004i
\(531\) 0 0
\(532\) −12.0000 4.89898i −0.520266 0.212398i
\(533\) 8.87039 5.12132i 0.384219 0.221829i
\(534\) 0 0
\(535\) 35.4815i 1.53400i
\(536\) 3.48528i 0.150541i
\(537\) 0 0
\(538\) 8.48528 4.89898i 0.365826 0.211210i
\(539\) 28.7635 + 7.39340i 1.23893 + 0.318456i
\(540\) 0 0
\(541\) −22.7279 + 39.3659i −0.977150 + 1.69247i −0.304499 + 0.952513i \(0.598489\pi\)
−0.672651 + 0.739960i \(0.734844\pi\)
\(542\) 7.70719 13.3492i 0.331052 0.573399i
\(543\) 0 0
\(544\) −2.12132 + 1.22474i −0.0909509 + 0.0525105i
\(545\) −9.46473 + 16.3934i −0.405425 + 0.702216i
\(546\) 0 0
\(547\) −3.01472 5.22165i −0.128900 0.223261i 0.794351 0.607460i \(-0.207811\pi\)
−0.923251 + 0.384198i \(0.874478\pi\)
\(548\) −5.19615 3.00000i −0.221969 0.128154i
\(549\) 0 0
\(550\) 2.12132 + 3.67423i 0.0904534 + 0.156670i
\(551\) 50.1785 2.13768
\(552\) 0 0
\(553\) 24.2279 3.31552i 1.03028 0.140990i
\(554\) −1.49642 0.863961i −0.0635770 0.0367062i
\(555\) 0 0
\(556\) 9.98528 + 5.76500i 0.423470 + 0.244491i
\(557\) 18.3712 10.6066i 0.778412 0.449416i −0.0574555 0.998348i \(-0.518299\pi\)
0.835867 + 0.548932i \(0.184965\pi\)
\(558\) 0 0
\(559\) 29.2708i 1.23802i
\(560\) −3.97141 5.12132i −0.167823 0.216415i
\(561\) 0 0
\(562\) −11.1213 19.2627i −0.469125 0.812548i
\(563\) −16.4800 −0.694548 −0.347274 0.937764i \(-0.612893\pi\)
−0.347274 + 0.937764i \(0.612893\pi\)
\(564\) 0 0
\(565\) 4.30463i 0.181097i
\(566\) −23.3572 −0.981776
\(567\) 0 0
\(568\) 12.7279 0.534052
\(569\) 1.75736i 0.0736723i 0.999321 + 0.0368362i \(0.0117280\pi\)
−0.999321 + 0.0368362i \(0.988272\pi\)
\(570\) 0 0
\(571\) −22.0000 −0.920671 −0.460336 0.887745i \(-0.652271\pi\)
−0.460336 + 0.887745i \(0.652271\pi\)
\(572\) −8.87039 15.3640i −0.370890 0.642399i
\(573\) 0 0
\(574\) −6.00000 2.44949i −0.250435 0.102240i
\(575\) 6.00000i 0.250217i
\(576\) 0 0
\(577\) 15.2574 8.80884i 0.635172 0.366717i −0.147580 0.989050i \(-0.547148\pi\)
0.782752 + 0.622333i \(0.213815\pi\)
\(578\) −9.52628 5.50000i −0.396241 0.228770i
\(579\) 0 0
\(580\) 21.7279 + 12.5446i 0.902203 + 0.520887i
\(581\) 8.90644 + 11.4853i 0.369501 + 0.476490i
\(582\) 0 0
\(583\) 10.5442 0.436694
\(584\) −7.64564 13.2426i −0.316379 0.547984i
\(585\) 0 0
\(586\) 6.87868 + 3.97141i 0.284156 + 0.164057i
\(587\) 5.82655 + 10.0919i 0.240488 + 0.416537i 0.960853 0.277058i \(-0.0893594\pi\)
−0.720366 + 0.693594i \(0.756026\pi\)
\(588\) 0 0
\(589\) −13.7574 + 23.8284i −0.566862 + 0.981834i
\(590\) 5.19615 3.00000i 0.213922 0.123508i
\(591\) 0 0
\(592\) 1.62132 2.80821i 0.0666359 0.115417i
\(593\) −11.3199 + 19.6066i −0.464852 + 0.805147i −0.999195 0.0401210i \(-0.987226\pi\)
0.534343 + 0.845268i \(0.320559\pi\)
\(594\) 0 0
\(595\) −6.00000 + 14.6969i −0.245976 + 0.602516i
\(596\) 6.71807 3.87868i 0.275183 0.158877i
\(597\) 0 0
\(598\) 25.0892i 1.02598i
\(599\) 20.4853i 0.837006i 0.908215 + 0.418503i \(0.137445\pi\)
−0.908215 + 0.418503i \(0.862555\pi\)
\(600\) 0 0
\(601\) 14.9558 8.63476i 0.610062 0.352219i −0.162928 0.986638i \(-0.552094\pi\)
0.772990 + 0.634419i \(0.218760\pi\)
\(602\) −14.6354 + 11.3492i −0.596494 + 0.462561i
\(603\) 0 0
\(604\) 8.62132 14.9326i 0.350797 0.607597i
\(605\) 8.57321 14.8492i 0.348551 0.603708i
\(606\) 0 0
\(607\) −22.7574 + 13.1390i −0.923693 + 0.533294i −0.884811 0.465950i \(-0.845713\pi\)
−0.0388815 + 0.999244i \(0.512379\pi\)
\(608\) 2.44949 4.24264i 0.0993399 0.172062i
\(609\) 0 0
\(610\) −0.878680 1.52192i −0.0355767 0.0616207i
\(611\) −28.7635 16.6066i −1.16365 0.671831i
\(612\) 0 0
\(613\) −7.10660 12.3090i −0.287033 0.497156i 0.686067 0.727538i \(-0.259336\pi\)
−0.973100 + 0.230383i \(0.926002\pi\)
\(614\) 2.57258 0.103821
\(615\) 0 0
\(616\) −4.24264 + 10.3923i −0.170941 + 0.418718i
\(617\) −3.67423 2.12132i −0.147919 0.0854011i 0.424214 0.905562i \(-0.360551\pi\)
−0.572133 + 0.820161i \(0.693884\pi\)
\(618\) 0 0
\(619\) 27.9853 + 16.1573i 1.12482 + 0.649417i 0.942628 0.333845i \(-0.108346\pi\)
0.182196 + 0.983262i \(0.441680\pi\)
\(620\) −11.9142 + 6.87868i −0.478487 + 0.276254i
\(621\) 0 0
\(622\) 17.1464i 0.687509i
\(623\) 17.7408 43.4558i 0.710769 1.74102i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 0.594346 0.0237548
\(627\) 0 0
\(628\) 10.3923i 0.414698i
\(629\) −7.94282 −0.316701
\(630\) 0 0
\(631\) −23.2426 −0.925275 −0.462637 0.886548i \(-0.653097\pi\)
−0.462637 + 0.886548i \(0.653097\pi\)
\(632\) 9.24264i 0.367653i
\(633\) 0 0
\(634\) 13.7574 0.546375
\(635\) −21.7122 37.6066i −0.861622 1.49237i
\(636\) 0 0
\(637\) 28.3492 + 7.28692i 1.12324 + 0.288718i
\(638\) 43.4558i 1.72043i
\(639\) 0 0
\(640\) 2.12132 1.22474i 0.0838525 0.0484123i
\(641\) 7.97887 + 4.60660i 0.315146 + 0.181950i 0.649227 0.760595i \(-0.275092\pi\)
−0.334081 + 0.942544i \(0.608426\pi\)
\(642\) 0 0
\(643\) −1.50000 0.866025i −0.0591542 0.0341527i 0.470131 0.882597i \(-0.344207\pi\)
−0.529285 + 0.848444i \(0.677540\pi\)
\(644\) 12.5446 9.72792i 0.494327 0.383334i
\(645\) 0 0
\(646\) −12.0000 −0.472134
\(647\) −10.3923 18.0000i −0.408564 0.707653i 0.586165 0.810191i \(-0.300637\pi\)
−0.994729 + 0.102538i \(0.967304\pi\)
\(648\) 0 0
\(649\) −9.00000 5.19615i −0.353281 0.203967i
\(650\) 2.09077 + 3.62132i 0.0820068 + 0.142040i
\(651\) 0 0
\(652\) 3.74264 6.48244i 0.146573 0.253872i
\(653\) −12.5446 + 7.24264i −0.490909 + 0.283426i −0.724951 0.688800i \(-0.758138\pi\)
0.234043 + 0.972226i \(0.424805\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.22474 2.12132i 0.0478183 0.0828236i
\(657\) 0 0
\(658\) 2.84924 + 20.8207i 0.111075 + 0.811674i
\(659\) −11.9142 + 6.87868i −0.464112 + 0.267955i −0.713772 0.700378i \(-0.753015\pi\)
0.249660 + 0.968334i \(0.419681\pi\)
\(660\) 0 0
\(661\) 4.89898i 0.190548i 0.995451 + 0.0952741i \(0.0303728\pi\)
−0.995451 + 0.0952741i \(0.969627\pi\)
\(662\) 10.0000i 0.388661i
\(663\) 0 0
\(664\) −4.75736 + 2.74666i −0.184621 + 0.106591i
\(665\) −4.30463 31.4558i −0.166927 1.21981i
\(666\) 0 0
\(667\) −30.7279 + 53.2223i −1.18979 + 2.06078i
\(668\) 10.0951 17.4853i 0.390592 0.676526i
\(669\) 0 0
\(670\) 7.39340 4.26858i 0.285632 0.164910i
\(671\) −1.52192 + 2.63604i −0.0587530 + 0.101763i
\(672\) 0 0
\(673\) −2.72792 4.72490i −0.105154 0.182131i 0.808647 0.588294i \(-0.200200\pi\)
−0.913801 + 0.406162i \(0.866867\pi\)
\(674\) 25.5095 + 14.7279i 0.982590 + 0.567298i
\(675\) 0 0
\(676\) −2.24264 3.88437i −0.0862554 0.149399i
\(677\) 14.6969 0.564849 0.282425 0.959289i \(-0.408861\pi\)
0.282425 + 0.959289i \(0.408861\pi\)
\(678\) 0 0
\(679\) 13.8640 10.7510i 0.532050 0.412586i
\(680\) −5.19615 3.00000i −0.199263 0.115045i
\(681\) 0 0
\(682\) 20.6360 + 11.9142i 0.790195 + 0.456219i
\(683\) 1.52192 0.878680i 0.0582346 0.0336217i −0.470600 0.882347i \(-0.655963\pi\)
0.528835 + 0.848725i \(0.322629\pi\)
\(684\) 0 0
\(685\) 14.6969i 0.561541i
\(686\) −7.34847 17.0000i −0.280566 0.649063i
\(687\) 0 0
\(688\) −3.50000 6.06218i −0.133436 0.231118i
\(689\) 10.3923 0.395915
\(690\) 0 0
\(691\) 26.8213i 1.02033i 0.860077 + 0.510165i \(0.170416\pi\)
−0.860077 + 0.510165i \(0.829584\pi\)
\(692\) 20.7846 0.790112
\(693\) 0 0
\(694\) 28.9706 1.09971
\(695\) 28.2426i 1.07130i
\(696\) 0 0
\(697\) −6.00000 −0.227266
\(698\) 12.1859 + 21.1066i 0.461243 + 0.798897i
\(699\) 0 0
\(700\) 1.00000 2.44949i 0.0377964 0.0925820i
\(701\) 3.51472i 0.132749i −0.997795 0.0663745i \(-0.978857\pi\)
0.997795 0.0663745i \(-0.0211432\pi\)
\(702\) 0 0
\(703\) 13.7574 7.94282i 0.518869 0.299569i
\(704\) −3.67423 2.12132i −0.138478 0.0799503i
\(705\) 0 0
\(706\) 26.4853 + 15.2913i 0.996787 + 0.575495i
\(707\) −7.34847 + 18.0000i −0.276368 + 0.676960i
\(708\) 0 0
\(709\) −26.2132 −0.984458 −0.492229 0.870466i \(-0.663818\pi\)
−0.492229 + 0.870466i \(0.663818\pi\)
\(710\) 15.5885 + 27.0000i 0.585024 + 1.01329i
\(711\) 0 0
\(712\) 15.3640 + 8.87039i 0.575789 + 0.332432i
\(713\) −16.8493 29.1838i −0.631010 1.09294i
\(714\) 0 0
\(715\) 21.7279 37.6339i 0.812578 1.40743i
\(716\) 16.2189 9.36396i 0.606127 0.349948i
\(717\) 0 0
\(718\) 1.24264 2.15232i 0.0463749 0.0803237i
\(719\) 5.52938 9.57716i 0.206211 0.357168i −0.744307 0.667838i \(-0.767220\pi\)
0.950518 + 0.310670i \(0.100553\pi\)
\(720\) 0 0
\(721\) −12.9853 + 10.0696i −0.483597 + 0.375013i
\(722\) 4.33013 2.50000i 0.161151 0.0930404i
\(723\) 0 0
\(724\) 9.79796i 0.364138i
\(725\) 10.2426i 0.380402i
\(726\) 0 0
\(727\) −39.3198 + 22.7013i −1.45829 + 0.841945i −0.998927 0.0463038i \(-0.985256\pi\)
−0.459363 + 0.888248i \(0.651922\pi\)
\(728\) −4.18154 + 10.2426i −0.154978 + 0.379618i
\(729\) 0 0
\(730\) 18.7279 32.4377i 0.693151 1.20057i
\(731\) −8.57321 + 14.8492i −0.317092 + 0.549219i
\(732\) 0 0
\(733\) −13.8640 + 8.00436i −0.512077 + 0.295648i −0.733687 0.679488i \(-0.762202\pi\)
0.221610 + 0.975135i \(0.428869\pi\)
\(734\) −4.60181 + 7.97056i −0.169856 + 0.294199i
\(735\) 0 0
\(736\) 3.00000 + 5.19615i 0.110581 + 0.191533i
\(737\) −12.8057 7.39340i −0.471706 0.272339i
\(738\) 0 0
\(739\) −21.2279 36.7678i −0.780882 1.35253i −0.931429 0.363924i \(-0.881437\pi\)
0.150547 0.988603i \(-0.451897\pi\)
\(740\) 7.94282 0.291984
\(741\) 0 0
\(742\) −4.02944 5.19615i −0.147925 0.190757i
\(743\) −5.82655 3.36396i −0.213755 0.123412i 0.389300 0.921111i \(-0.372717\pi\)
−0.603055 + 0.797699i \(0.706050\pi\)
\(744\) 0 0
\(745\) 16.4558 + 9.50079i 0.602895 + 0.348082i
\(746\) 19.0526 11.0000i 0.697564 0.402739i
\(747\) 0 0
\(748\) 10.3923i 0.379980i
\(749\) 35.4815 + 14.4853i 1.29647 + 0.529281i
\(750\) 0 0
\(751\) −1.27208 2.20330i −0.0464188 0.0803997i 0.841882 0.539661i \(-0.181448\pi\)
−0.888301 + 0.459261i \(0.848114\pi\)
\(752\) −7.94282 −0.289645
\(753\) 0 0
\(754\) 42.8300i 1.55978i
\(755\) 42.2357 1.53711
\(756\) 0 0
\(757\) 41.2426 1.49899 0.749495 0.662010i \(-0.230297\pi\)
0.749495 + 0.662010i \(0.230297\pi\)
\(758\) 9.48528i 0.344521i
\(759\) 0 0
\(760\) 12.0000 0.435286
\(761\) 12.2474 + 21.2132i 0.443970 + 0.768978i 0.997980 0.0635319i \(-0.0202365\pi\)
−0.554010 + 0.832510i \(0.686903\pi\)
\(762\) 0 0
\(763\) −12.5294 16.1573i −0.453596 0.584934i
\(764\) 21.2132i 0.767467i
\(765\) 0 0
\(766\) −13.2426 + 7.64564i −0.478476 + 0.276248i
\(767\) −8.87039 5.12132i −0.320291 0.184920i
\(768\) 0 0
\(769\) −1.02944 0.594346i −0.0371225 0.0214327i 0.481324 0.876543i \(-0.340156\pi\)
−0.518446 + 0.855110i \(0.673489\pi\)
\(770\) −27.2416 + 3.72792i −0.981718 + 0.134345i
\(771\) 0 0
\(772\) −15.4853 −0.557327
\(773\) −4.89898 8.48528i −0.176204 0.305194i 0.764373 0.644774i \(-0.223049\pi\)
−0.940577 + 0.339580i \(0.889715\pi\)
\(774\) 0 0
\(775\) −4.86396 2.80821i −0.174719 0.100874i
\(776\) 3.31552 + 5.74264i 0.119020 + 0.206149i
\(777\) 0 0
\(778\) −16.2426 + 28.1331i −0.582327 + 1.00862i
\(779\) 10.3923 6.00000i 0.372343 0.214972i
\(780\) 0 0
\(781\) 27.0000 46.7654i 0.966136 1.67340i
\(782\) 7.34847 12.7279i 0.262781 0.455150i
\(783\) 0 0
\(784\) 6.74264 1.88064i 0.240809 0.0671656i
\(785\) −22.0454 + 12.7279i −0.786834 + 0.454279i
\(786\) 0 0
\(787\) 10.9357i 0.389814i 0.980822 + 0.194907i \(0.0624406\pi\)
−0.980822 + 0.194907i \(0.937559\pi\)
\(788\) 16.9706i 0.604551i
\(789\) 0 0
\(790\) −19.6066 + 11.3199i −0.697572 + 0.402743i
\(791\) 4.30463 + 1.75736i 0.153055 + 0.0624845i
\(792\) 0 0
\(793\) −1.50000 + 2.59808i −0.0532666 + 0.0922604i
\(794\) −14.9326 + 25.8640i −0.529937 + 0.917878i
\(795\) 0 0
\(796\) −3.10660 + 1.79360i −0.110111 + 0.0635724i
\(797\) 1.52192 2.63604i 0.0539091 0.0933733i −0.837812 0.545960i \(-0.816165\pi\)
0.891721 + 0.452586i \(0.149499\pi\)
\(798\) 0 0
\(799\) 9.72792 + 16.8493i 0.344149 + 0.596084i
\(800\) 0.866025 + 0.500000i 0.0306186 + 0.0176777i
\(801\) 0 0
\(802\) −14.1213 24.4588i −0.498641 0.863672i
\(803\) −64.8754 −2.28940
\(804\) 0 0
\(805\) 36.0000 + 14.6969i 1.26883 + 0.517999i
\(806\) 20.3389 + 11.7426i 0.716405 + 0.413617i
\(807\) 0 0
\(808\) −6.36396 3.67423i −0.223883 0.129259i
\(809\) −2.15232 + 1.24264i −0.0756714 + 0.0436889i −0.537358 0.843354i \(-0.680578\pi\)
0.461687 + 0.887043i \(0.347244\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) −21.4150 + 16.6066i −0.751519 + 0.582777i
\(813\) 0 0
\(814\) −6.87868 11.9142i −0.241098 0.417593i
\(815\) 18.3351 0.642251
\(816\) 0 0
\(817\) 34.2929i 1.19976i
\(818\) −13.5592 −0.474087
\(819\) 0 0
\(820\) 6.00000 0.209529
\(821\) 10.9706i 0.382875i 0.981505 + 0.191438i \(0.0613150\pi\)
−0.981505 + 0.191438i \(0.938685\pi\)
\(822\) 0 0
\(823\) −11.2426 −0.391894 −0.195947 0.980615i \(-0.562778\pi\)
−0.195947 + 0.980615i \(0.562778\pi\)
\(824\) −3.10538 5.37868i −0.108181 0.187375i
\(825\) 0 0
\(826\) 0.878680 + 6.42090i 0.0305732 + 0.223412i
\(827\) 20.4853i 0.712343i 0.934421 + 0.356172i \(0.115918\pi\)
−0.934421 + 0.356172i \(0.884082\pi\)
\(828\) 0 0
\(829\) −8.48528 + 4.89898i −0.294706 + 0.170149i −0.640062 0.768323i \(-0.721091\pi\)
0.345356 + 0.938472i \(0.387758\pi\)
\(830\) −11.6531 6.72792i −0.404485 0.233530i
\(831\) 0 0
\(832\) −3.62132 2.09077i −0.125547 0.0724844i
\(833\) −12.2474 12.0000i −0.424349 0.415775i
\(834\) 0 0
\(835\) 49.4558 1.71149
\(836\) −10.3923 18.0000i −0.359425 0.622543i
\(837\) 0 0
\(838\) 11.1213 + 6.42090i 0.384180 + 0.221806i
\(839\) −2.74666 4.75736i −0.0948253 0.164242i 0.814710 0.579868i \(-0.196896\pi\)
−0.909536 + 0.415626i \(0.863563\pi\)
\(840\) 0 0
\(841\) 37.9558 65.7415i 1.30882 2.26695i
\(842\) −23.7775 + 13.7279i −0.819425 + 0.473095i
\(843\) 0 0
\(844\) −6.74264 + 11.6786i −0.232091 + 0.401994i
\(845\) 5.49333 9.51472i 0.188976 0.327316i
\(846\) 0 0
\(847\) 11.3492 + 14.6354i 0.389965 + 0.502878i
\(848\) 2.15232 1.24264i 0.0739109 0.0426725i
\(849\) 0 0
\(850\) 2.44949i 0.0840168i
\(851\) 19.4558i 0.666938i
\(852\) 0 0
\(853\) −44.4853 + 25.6836i −1.52315 + 0.879389i −0.523522 + 0.852012i \(0.675382\pi\)
−0.999625 + 0.0273771i \(0.991285\pi\)
\(854\) 1.88064 0.257359i 0.0643541 0.00880665i
\(855\) 0 0
\(856\) −7.24264 + 12.5446i −0.247548 + 0.428766i
\(857\) −3.37706 + 5.84924i −0.115358 + 0.199806i −0.917923 0.396759i \(-0.870135\pi\)
0.802565 + 0.596565i \(0.203468\pi\)
\(858\) 0 0
\(859\) 9.47056 5.46783i 0.323131 0.186560i −0.329656 0.944101i \(-0.606933\pi\)
0.652787 + 0.757541i \(0.273599\pi\)
\(860\) 8.57321 14.8492i 0.292344 0.506355i
\(861\) 0 0
\(862\) −5.12132 8.87039i −0.174433 0.302127i
\(863\) −11.6531 6.72792i −0.396676 0.229021i 0.288373 0.957518i \(-0.406886\pi\)
−0.685049 + 0.728497i \(0.740219\pi\)
\(864\) 0 0
\(865\) 25.4558 + 44.0908i 0.865525 + 1.49913i
\(866\) 26.8213 0.911425
\(867\) 0 0
\(868\) −2.01472 14.7224i −0.0683840 0.499712i
\(869\) 33.9596 + 19.6066i 1.15200 + 0.665108i
\(870\) 0 0
\(871\) −12.6213 7.28692i −0.427657 0.246908i
\(872\) 6.69258 3.86396i 0.226639 0.130850i
\(873\) 0 0
\(874\) 29.3939i 0.994263i
\(875\) −25.6836 + 3.51472i −0.868264 + 0.118819i
\(876\) 0 0
\(877\) 1.89340 + 3.27946i 0.0639355 + 0.110740i 0.896221 0.443607i \(-0.146301\pi\)
−0.832286 + 0.554347i \(0.812968\pi\)
\(878\) 25.0892 0.846721
\(879\) 0 0
\(880\) 10.3923i 0.350325i
\(881\) 4.30463 0.145027 0.0725134 0.997367i \(-0.476898\pi\)
0.0725134 + 0.997367i \(0.476898\pi\)
\(882\) 0 0
\(883\) −2.00000 −0.0673054 −0.0336527 0.999434i \(-0.510714\pi\)
−0.0336527 + 0.999434i \(0.510714\pi\)
\(884\) 10.2426i 0.344497i
\(885\) 0 0
\(886\) −25.4558 −0.855206
\(887\) 14.9941 + 25.9706i 0.503453 + 0.872006i 0.999992 + 0.00399177i \(0.00127062\pi\)
−0.496539 + 0.868014i \(0.665396\pi\)
\(888\) 0 0
\(889\) 46.4706 6.35935i 1.55857 0.213286i
\(890\) 43.4558i 1.45664i
\(891\) 0 0
\(892\) −9.00000 + 5.19615i −0.301342 + 0.173980i
\(893\) −33.6985 19.4558i −1.12768 0.651065i
\(894\) 0 0
\(895\) 39.7279 + 22.9369i 1.32796 + 0.766697i
\(896\) 0.358719 + 2.62132i 0.0119840 + 0.0875722i
\(897\) 0 0
\(898\) −30.7279 −1.02540
\(899\) 28.7635 + 49.8198i 0.959316 + 1.66158i
\(900\) 0 0
\(901\) −5.27208 3.04384i −0.175638 0.101405i
\(902\) −5.19615 9.00000i −0.173013 0.299667i
\(903\) 0 0
\(904\) −0.878680 + 1.52192i −0.0292245 + 0.0506182i
\(905\) −20.7846 + 12.0000i −0.690904 + 0.398893i
\(906\) 0 0
\(907\) −1.74264 + 3.01834i −0.0578634 + 0.100222i −0.893506 0.449051i \(-0.851762\pi\)
0.835643 + 0.549273i \(0.185095\pi\)
\(908\) −2.15232 + 3.72792i −0.0714271 + 0.123715i
\(909\) 0 0
\(910\) −26.8492 + 3.67423i −0.890044 + 0.121800i
\(911\) 1.52192 0.878680i 0.0504234 0.0291120i −0.474576 0.880214i \(-0.657399\pi\)
0.525000 + 0.851102i \(0.324065\pi\)
\(912\) 0 0
\(913\) 23.3062i 0.771323i
\(914\) 23.0000i 0.760772i
\(915\) 0 0
\(916\) 7.86396 4.54026i 0.259833 0.150014i
\(917\) 0 0
\(918\) 0 0
\(919\) −0.136039 + 0.235626i −0.00448751 + 0.00777260i −0.868260 0.496109i \(-0.834762\pi\)
0.863773 + 0.503881i \(0.168095\pi\)
\(920\) −7.34847 + 12.7279i −0.242272 + 0.419627i
\(921\) 0 0
\(922\) 36.5772 21.1178i 1.20460 0.695479i
\(923\) 26.6112 46.0919i 0.875917 1.51713i
\(924\) 0 0
\(925\) 1.62132 + 2.80821i 0.0533087 + 0.0923334i
\(926\) −19.0526 11.0000i −0.626106 0.361482i
\(927\) 0 0
\(928\) −5.12132 8.87039i −0.168116 0.291185i
\(929\) 33.6264 1.10325 0.551623 0.834093i \(-0.314009\pi\)
0.551623 + 0.834093i \(0.314009\pi\)
\(930\) 0 0
\(931\) 33.2132 + 8.53716i 1.08852 + 0.279794i
\(932\) −3.04384 1.75736i −0.0997042 0.0575642i
\(933\) 0 0
\(934\) 2.63604 + 1.52192i 0.0862538 + 0.0497987i
\(935\) −22.0454 + 12.7279i −0.720962 + 0.416248i
\(936\) 0 0
\(937\) 53.0992i 1.73468i 0.497719 + 0.867338i \(0.334171\pi\)
−0.497719 + 0.867338i \(0.665829\pi\)
\(938\) 1.25024 + 9.13604i 0.0408217 + 0.298302i
\(939\) 0 0
\(940\) −9.72792 16.8493i −0.317290 0.549562i
\(941\) −21.4511 −0.699285 −0.349642 0.936883i \(-0.613697\pi\)
−0.349642 + 0.936883i \(0.613697\pi\)
\(942\) 0 0
\(943\) 14.6969i 0.478598i
\(944\) −2.44949 −0.0797241
\(945\) 0 0
\(946\) −29.6985 −0.965581
\(947\) 7.75736i 0.252080i 0.992025 + 0.126040i \(0.0402268\pi\)
−0.992025 + 0.126040i \(0.959773\pi\)
\(948\) 0 0
\(949\) −63.9411 −2.07562
\(950\) 2.44949 + 4.24264i 0.0794719 + 0.137649i
\(951\) 0 0
\(952\) 5.12132 3.97141i 0.165983 0.128714i
\(953\) 34.9706i 1.13281i 0.824128 + 0.566404i \(0.191666\pi\)
−0.824128 + 0.566404i \(0.808334\pi\)
\(954\) 0 0
\(955\) 45.0000 25.9808i 1.45617 0.840718i
\(956\) −6.71807 3.87868i −0.217278 0.125445i
\(957\) 0 0
\(958\) −2.12132 1.22474i −0.0685367 0.0395697i
\(959\) 14.6969 + 6.00000i 0.474589 + 0.193750i
\(960\) 0 0
\(961\) −0.544156 −0.0175534
\(962\) −6.77962 11.7426i −0.218584 0.378598i
\(963\) 0 0
\(964\) 15.9853 + 9.22911i 0.514851 + 0.297250i
\(965\) −18.9655 32.8492i −0.610522 1.05745i
\(966\) 0 0
\(967\) −8.34924 + 14.4613i −0.268494 + 0.465044i −0.968473 0.249119i \(-0.919859\pi\)
0.699979 + 0.714163i \(0.253192\pi\)
\(968\) −6.06218 + 3.50000i −0.194846 + 0.112494i
\(969\) 0 0
\(970\) −8.12132 + 14.0665i −0.260760 + 0.451649i
\(971\) 0.594346 1.02944i 0.0190735 0.0330362i −0.856331 0.516427i \(-0.827262\pi\)
0.875405 + 0.483391i \(0.160595\pi\)
\(972\) 0 0
\(973\) −28.2426 11.5300i −0.905417 0.369635i
\(974\) −19.0526 + 11.0000i −0.610483 + 0.352463i
\(975\) 0 0
\(976\) 0.717439i 0.0229647i
\(977\) 6.00000i 0.191957i −0.995383 0.0959785i \(-0.969402\pi\)
0.995383 0.0959785i \(-0.0305980\pi\)
\(978\) 0 0
\(979\) 65.1838 37.6339i 2.08328 1.20278i
\(980\) 12.2474 + 12.0000i 0.391230 + 0.383326i
\(981\) 0 0
\(982\) 0.514719 0.891519i 0.0164253 0.0284495i
\(983\) −9.16756 + 15.8787i −0.292400 + 0.506451i −0.974377 0.224922i \(-0.927787\pi\)
0.681977 + 0.731374i \(0.261120\pi\)
\(984\) 0 0
\(985\) 36.0000 20.7846i 1.14706 0.662253i
\(986\) −12.5446 + 21.7279i −0.399502 + 0.691958i
\(987\) 0 0
\(988\) −10.2426 17.7408i −0.325862 0.564409i
\(989\) 36.3731 + 21.0000i 1.15660 + 0.667761i
\(990\) 0 0
\(991\) −11.1066 19.2372i −0.352813 0.611090i 0.633928 0.773392i \(-0.281441\pi\)
−0.986741 + 0.162302i \(0.948108\pi\)
\(992\) 5.61642 0.178321
\(993\) 0 0
\(994\) −33.3640 + 4.56575i −1.05824 + 0.144817i
\(995\) −7.60959 4.39340i −0.241240 0.139280i
\(996\) 0 0
\(997\) −4.13604 2.38794i −0.130990 0.0756269i 0.433073 0.901359i \(-0.357429\pi\)
−0.564063 + 0.825732i \(0.690762\pi\)
\(998\) −22.9114 + 13.2279i −0.725249 + 0.418723i
\(999\) 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 1134.2.l.e.215.1 8
3.2 odd 2 inner 1134.2.l.e.215.4 8
7.3 odd 6 1134.2.t.f.1025.3 8
9.2 odd 6 1134.2.t.f.593.3 8
9.4 even 3 378.2.k.d.215.3 yes 8
9.5 odd 6 378.2.k.d.215.2 8
9.7 even 3 1134.2.t.f.593.2 8
21.17 even 6 1134.2.t.f.1025.2 8
63.5 even 6 2646.2.d.d.2645.8 8
63.23 odd 6 2646.2.d.d.2645.6 8
63.31 odd 6 378.2.k.d.269.2 yes 8
63.38 even 6 inner 1134.2.l.e.269.3 8
63.40 odd 6 2646.2.d.d.2645.1 8
63.52 odd 6 inner 1134.2.l.e.269.2 8
63.58 even 3 2646.2.d.d.2645.3 8
63.59 even 6 378.2.k.d.269.3 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.k.d.215.2 8 9.5 odd 6
378.2.k.d.215.3 yes 8 9.4 even 3
378.2.k.d.269.2 yes 8 63.31 odd 6
378.2.k.d.269.3 yes 8 63.59 even 6
1134.2.l.e.215.1 8 1.1 even 1 trivial
1134.2.l.e.215.4 8 3.2 odd 2 inner
1134.2.l.e.269.2 8 63.52 odd 6 inner
1134.2.l.e.269.3 8 63.38 even 6 inner
1134.2.t.f.593.2 8 9.7 even 3
1134.2.t.f.593.3 8 9.2 odd 6
1134.2.t.f.1025.2 8 21.17 even 6
1134.2.t.f.1025.3 8 7.3 odd 6
2646.2.d.d.2645.1 8 63.40 odd 6
2646.2.d.d.2645.3 8 63.58 even 3
2646.2.d.d.2645.6 8 63.23 odd 6
2646.2.d.d.2645.8 8 63.5 even 6