Properties

Label 1008.2.t.l.193.8
Level $1008$
Weight $2$
Character 1008.193
Analytic conductor $8.049$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,2,Mod(193,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.193");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.t (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.8
Character \(\chi\) \(=\) 1008.193
Dual form 1008.2.t.l.961.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.04208 + 1.38350i) q^{3} -0.0619693 q^{5} +(1.63689 + 2.07860i) q^{7} +(-0.828124 + 2.88344i) q^{9} +O(q^{10})\) \(q+(1.04208 + 1.38350i) q^{3} -0.0619693 q^{5} +(1.63689 + 2.07860i) q^{7} +(-0.828124 + 2.88344i) q^{9} +3.18053 q^{11} +(-0.252417 + 0.437198i) q^{13} +(-0.0645772 - 0.0857342i) q^{15} +(-0.554700 + 0.960769i) q^{17} +(-0.933573 - 1.61700i) q^{19} +(-1.16996 + 4.43071i) q^{21} +6.20496 q^{23} -4.99616 q^{25} +(-4.85220 + 1.85908i) q^{27} +(2.39645 + 4.15077i) q^{29} +(-1.26858 - 2.19724i) q^{31} +(3.31438 + 4.40026i) q^{33} +(-0.101437 - 0.128809i) q^{35} +(-4.26085 - 7.38001i) q^{37} +(-0.867902 + 0.106380i) q^{39} +(-4.94516 + 8.56527i) q^{41} +(3.95574 + 6.85154i) q^{43} +(0.0513182 - 0.178684i) q^{45} +(3.29168 - 5.70136i) q^{47} +(-1.64116 + 6.80489i) q^{49} +(-1.90726 + 0.233776i) q^{51} +(-1.58258 + 2.74112i) q^{53} -0.197095 q^{55} +(1.26425 - 2.97664i) q^{57} +(4.50652 + 7.80552i) q^{59} +(6.94094 - 12.0221i) q^{61} +(-7.34906 + 2.99854i) q^{63} +(0.0156421 - 0.0270929i) q^{65} +(1.66642 + 2.88632i) q^{67} +(6.46609 + 8.58454i) q^{69} -2.25651 q^{71} +(2.07503 - 3.59406i) q^{73} +(-5.20642 - 6.91217i) q^{75} +(5.20619 + 6.61106i) q^{77} +(-1.48925 + 2.57946i) q^{79} +(-7.62842 - 4.77569i) q^{81} +(-2.17289 - 3.76355i) q^{83} +(0.0343744 - 0.0595381i) q^{85} +(-3.24528 + 7.64093i) q^{87} +(-4.30077 - 7.44915i) q^{89} +(-1.32194 + 0.190974i) q^{91} +(1.71791 - 4.04478i) q^{93} +(0.0578528 + 0.100204i) q^{95} +(-3.27671 - 5.67542i) q^{97} +(-2.63388 + 9.17087i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 2 q^{3} - 2 q^{5} + q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 2 q^{3} - 2 q^{5} + q^{7} + 6 q^{11} + 7 q^{13} + q^{15} - q^{17} - 13 q^{19} + 33 q^{21} + 44 q^{25} + 2 q^{27} - 7 q^{29} - 6 q^{31} + 9 q^{33} - 2 q^{35} + 6 q^{37} + 4 q^{39} + 4 q^{41} - 2 q^{43} - 17 q^{47} + 29 q^{49} + 25 q^{51} + q^{53} - 2 q^{55} - 21 q^{57} + 21 q^{59} + 31 q^{61} + 7 q^{63} - 3 q^{65} + 26 q^{67} - 40 q^{69} + 32 q^{71} + 17 q^{73} + 16 q^{75} - 4 q^{77} + 16 q^{79} + 36 q^{83} + 28 q^{85} - 7 q^{87} - 2 q^{89} - 15 q^{91} - 56 q^{93} + 24 q^{95} + 19 q^{97} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.04208 + 1.38350i 0.601647 + 0.798762i
\(4\) 0 0
\(5\) −0.0619693 −0.0277135 −0.0138567 0.999904i \(-0.504411\pi\)
−0.0138567 + 0.999904i \(0.504411\pi\)
\(6\) 0 0
\(7\) 1.63689 + 2.07860i 0.618688 + 0.785637i
\(8\) 0 0
\(9\) −0.828124 + 2.88344i −0.276041 + 0.961146i
\(10\) 0 0
\(11\) 3.18053 0.958967 0.479483 0.877551i \(-0.340824\pi\)
0.479483 + 0.877551i \(0.340824\pi\)
\(12\) 0 0
\(13\) −0.252417 + 0.437198i −0.0700078 + 0.121257i −0.898904 0.438145i \(-0.855636\pi\)
0.828897 + 0.559402i \(0.188969\pi\)
\(14\) 0 0
\(15\) −0.0645772 0.0857342i −0.0166737 0.0221365i
\(16\) 0 0
\(17\) −0.554700 + 0.960769i −0.134535 + 0.233021i −0.925420 0.378944i \(-0.876287\pi\)
0.790885 + 0.611965i \(0.209621\pi\)
\(18\) 0 0
\(19\) −0.933573 1.61700i −0.214176 0.370964i 0.738841 0.673880i \(-0.235373\pi\)
−0.953017 + 0.302915i \(0.902040\pi\)
\(20\) 0 0
\(21\) −1.16996 + 4.43071i −0.255305 + 0.966860i
\(22\) 0 0
\(23\) 6.20496 1.29382 0.646912 0.762565i \(-0.276060\pi\)
0.646912 + 0.762565i \(0.276060\pi\)
\(24\) 0 0
\(25\) −4.99616 −0.999232
\(26\) 0 0
\(27\) −4.85220 + 1.85908i −0.933806 + 0.357779i
\(28\) 0 0
\(29\) 2.39645 + 4.15077i 0.445010 + 0.770779i 0.998053 0.0623731i \(-0.0198669\pi\)
−0.553043 + 0.833153i \(0.686534\pi\)
\(30\) 0 0
\(31\) −1.26858 2.19724i −0.227843 0.394636i 0.729325 0.684167i \(-0.239834\pi\)
−0.957169 + 0.289531i \(0.906501\pi\)
\(32\) 0 0
\(33\) 3.31438 + 4.40026i 0.576960 + 0.765986i
\(34\) 0 0
\(35\) −0.101437 0.128809i −0.0171460 0.0217728i
\(36\) 0 0
\(37\) −4.26085 7.38001i −0.700479 1.21327i −0.968298 0.249797i \(-0.919636\pi\)
0.267819 0.963469i \(-0.413697\pi\)
\(38\) 0 0
\(39\) −0.867902 + 0.106380i −0.138976 + 0.0170344i
\(40\) 0 0
\(41\) −4.94516 + 8.56527i −0.772305 + 1.33767i 0.163992 + 0.986462i \(0.447563\pi\)
−0.936297 + 0.351210i \(0.885770\pi\)
\(42\) 0 0
\(43\) 3.95574 + 6.85154i 0.603244 + 1.04485i 0.992326 + 0.123646i \(0.0394589\pi\)
−0.389082 + 0.921203i \(0.627208\pi\)
\(44\) 0 0
\(45\) 0.0513182 0.178684i 0.00765007 0.0266367i
\(46\) 0 0
\(47\) 3.29168 5.70136i 0.480141 0.831628i −0.519600 0.854410i \(-0.673919\pi\)
0.999740 + 0.0227816i \(0.00725224\pi\)
\(48\) 0 0
\(49\) −1.64116 + 6.80489i −0.234451 + 0.972128i
\(50\) 0 0
\(51\) −1.90726 + 0.233776i −0.267070 + 0.0327352i
\(52\) 0 0
\(53\) −1.58258 + 2.74112i −0.217385 + 0.376521i −0.954008 0.299782i \(-0.903086\pi\)
0.736623 + 0.676304i \(0.236419\pi\)
\(54\) 0 0
\(55\) −0.197095 −0.0265763
\(56\) 0 0
\(57\) 1.26425 2.97664i 0.167454 0.394266i
\(58\) 0 0
\(59\) 4.50652 + 7.80552i 0.586699 + 1.01619i 0.994661 + 0.103194i \(0.0329062\pi\)
−0.407962 + 0.912999i \(0.633760\pi\)
\(60\) 0 0
\(61\) 6.94094 12.0221i 0.888697 1.53927i 0.0472794 0.998882i \(-0.484945\pi\)
0.841417 0.540386i \(-0.181722\pi\)
\(62\) 0 0
\(63\) −7.34906 + 2.99854i −0.925895 + 0.377781i
\(64\) 0 0
\(65\) 0.0156421 0.0270929i 0.00194016 0.00336046i
\(66\) 0 0
\(67\) 1.66642 + 2.88632i 0.203585 + 0.352620i 0.949681 0.313219i \(-0.101407\pi\)
−0.746096 + 0.665839i \(0.768074\pi\)
\(68\) 0 0
\(69\) 6.46609 + 8.58454i 0.778425 + 1.03346i
\(70\) 0 0
\(71\) −2.25651 −0.267798 −0.133899 0.990995i \(-0.542750\pi\)
−0.133899 + 0.990995i \(0.542750\pi\)
\(72\) 0 0
\(73\) 2.07503 3.59406i 0.242864 0.420652i −0.718665 0.695356i \(-0.755247\pi\)
0.961529 + 0.274704i \(0.0885799\pi\)
\(74\) 0 0
\(75\) −5.20642 6.91217i −0.601185 0.798148i
\(76\) 0 0
\(77\) 5.20619 + 6.61106i 0.593301 + 0.753400i
\(78\) 0 0
\(79\) −1.48925 + 2.57946i −0.167554 + 0.290211i −0.937559 0.347826i \(-0.886920\pi\)
0.770006 + 0.638037i \(0.220253\pi\)
\(80\) 0 0
\(81\) −7.62842 4.77569i −0.847602 0.530632i
\(82\) 0 0
\(83\) −2.17289 3.76355i −0.238506 0.413104i 0.721780 0.692122i \(-0.243324\pi\)
−0.960286 + 0.279019i \(0.909991\pi\)
\(84\) 0 0
\(85\) 0.0343744 0.0595381i 0.00372842 0.00645782i
\(86\) 0 0
\(87\) −3.24528 + 7.64093i −0.347930 + 0.819194i
\(88\) 0 0
\(89\) −4.30077 7.44915i −0.455880 0.789608i 0.542858 0.839824i \(-0.317342\pi\)
−0.998738 + 0.0502166i \(0.984009\pi\)
\(90\) 0 0
\(91\) −1.32194 + 0.190974i −0.138577 + 0.0200195i
\(92\) 0 0
\(93\) 1.71791 4.04478i 0.178139 0.419424i
\(94\) 0 0
\(95\) 0.0578528 + 0.100204i 0.00593558 + 0.0102807i
\(96\) 0 0
\(97\) −3.27671 5.67542i −0.332699 0.576252i 0.650341 0.759642i \(-0.274626\pi\)
−0.983040 + 0.183391i \(0.941293\pi\)
\(98\) 0 0
\(99\) −2.63388 + 9.17087i −0.264714 + 0.921707i
\(100\) 0 0
\(101\) 6.51654 0.648420 0.324210 0.945985i \(-0.394902\pi\)
0.324210 + 0.945985i \(0.394902\pi\)
\(102\) 0 0
\(103\) −17.0196 −1.67699 −0.838494 0.544911i \(-0.816563\pi\)
−0.838494 + 0.544911i \(0.816563\pi\)
\(104\) 0 0
\(105\) 0.0725013 0.274568i 0.00707540 0.0267951i
\(106\) 0 0
\(107\) 8.86075 + 15.3473i 0.856601 + 1.48368i 0.875152 + 0.483848i \(0.160761\pi\)
−0.0185508 + 0.999828i \(0.505905\pi\)
\(108\) 0 0
\(109\) 6.62928 11.4822i 0.634970 1.09980i −0.351552 0.936168i \(-0.614346\pi\)
0.986522 0.163631i \(-0.0523208\pi\)
\(110\) 0 0
\(111\) 5.77005 13.5855i 0.547669 1.28947i
\(112\) 0 0
\(113\) 1.10094 1.90689i 0.103568 0.179385i −0.809584 0.587004i \(-0.800307\pi\)
0.913152 + 0.407619i \(0.133641\pi\)
\(114\) 0 0
\(115\) −0.384517 −0.0358564
\(116\) 0 0
\(117\) −1.05160 1.08988i −0.0972207 0.100760i
\(118\) 0 0
\(119\) −2.90504 + 0.419676i −0.266305 + 0.0384717i
\(120\) 0 0
\(121\) −0.884207 −0.0803825
\(122\) 0 0
\(123\) −17.0033 + 2.08412i −1.53314 + 0.187918i
\(124\) 0 0
\(125\) 0.619455 0.0554057
\(126\) 0 0
\(127\) 4.61290 0.409329 0.204664 0.978832i \(-0.434390\pi\)
0.204664 + 0.978832i \(0.434390\pi\)
\(128\) 0 0
\(129\) −5.35687 + 12.6126i −0.471646 + 1.11048i
\(130\) 0 0
\(131\) 0.152139 0.0132925 0.00664623 0.999978i \(-0.497884\pi\)
0.00664623 + 0.999978i \(0.497884\pi\)
\(132\) 0 0
\(133\) 1.83293 4.58738i 0.158935 0.397776i
\(134\) 0 0
\(135\) 0.300687 0.115206i 0.0258790 0.00991532i
\(136\) 0 0
\(137\) −3.55540 −0.303759 −0.151879 0.988399i \(-0.548533\pi\)
−0.151879 + 0.988399i \(0.548533\pi\)
\(138\) 0 0
\(139\) 7.60945 13.1800i 0.645425 1.11791i −0.338778 0.940866i \(-0.610013\pi\)
0.984203 0.177043i \(-0.0566532\pi\)
\(140\) 0 0
\(141\) 11.3180 1.38726i 0.953148 0.116829i
\(142\) 0 0
\(143\) −0.802820 + 1.39052i −0.0671352 + 0.116281i
\(144\) 0 0
\(145\) −0.148506 0.257220i −0.0123328 0.0213610i
\(146\) 0 0
\(147\) −11.1248 + 4.82073i −0.917556 + 0.397607i
\(148\) 0 0
\(149\) 0.366914 0.0300588 0.0150294 0.999887i \(-0.495216\pi\)
0.0150294 + 0.999887i \(0.495216\pi\)
\(150\) 0 0
\(151\) 12.5832 1.02401 0.512005 0.858983i \(-0.328903\pi\)
0.512005 + 0.858983i \(0.328903\pi\)
\(152\) 0 0
\(153\) −2.31096 2.39508i −0.186830 0.193631i
\(154\) 0 0
\(155\) 0.0786128 + 0.136161i 0.00631434 + 0.0109368i
\(156\) 0 0
\(157\) 2.72734 + 4.72389i 0.217666 + 0.377008i 0.954094 0.299508i \(-0.0968225\pi\)
−0.736428 + 0.676516i \(0.763489\pi\)
\(158\) 0 0
\(159\) −5.44151 + 0.666973i −0.431540 + 0.0528944i
\(160\) 0 0
\(161\) 10.1569 + 12.8976i 0.800473 + 1.01648i
\(162\) 0 0
\(163\) −3.83559 6.64343i −0.300426 0.520354i 0.675806 0.737079i \(-0.263796\pi\)
−0.976233 + 0.216726i \(0.930462\pi\)
\(164\) 0 0
\(165\) −0.205390 0.272681i −0.0159896 0.0212282i
\(166\) 0 0
\(167\) 9.47493 16.4111i 0.733192 1.26993i −0.222320 0.974974i \(-0.571363\pi\)
0.955512 0.294952i \(-0.0953037\pi\)
\(168\) 0 0
\(169\) 6.37257 + 11.0376i 0.490198 + 0.849048i
\(170\) 0 0
\(171\) 5.43562 1.35283i 0.415672 0.103453i
\(172\) 0 0
\(173\) 11.9959 20.7776i 0.912034 1.57969i 0.100846 0.994902i \(-0.467845\pi\)
0.811187 0.584787i \(-0.198822\pi\)
\(174\) 0 0
\(175\) −8.17818 10.3850i −0.618212 0.785034i
\(176\) 0 0
\(177\) −6.10274 + 14.3688i −0.458710 + 1.08002i
\(178\) 0 0
\(179\) 4.27901 7.41146i 0.319828 0.553959i −0.660624 0.750717i \(-0.729708\pi\)
0.980452 + 0.196758i \(0.0630415\pi\)
\(180\) 0 0
\(181\) 0.632669 0.0470259 0.0235130 0.999724i \(-0.492515\pi\)
0.0235130 + 0.999724i \(0.492515\pi\)
\(182\) 0 0
\(183\) 23.8655 2.92523i 1.76419 0.216239i
\(184\) 0 0
\(185\) 0.264042 + 0.457334i 0.0194127 + 0.0336238i
\(186\) 0 0
\(187\) −1.76424 + 3.05576i −0.129014 + 0.223459i
\(188\) 0 0
\(189\) −11.8068 7.04267i −0.858819 0.512279i
\(190\) 0 0
\(191\) 11.7915 20.4235i 0.853205 1.47780i −0.0250944 0.999685i \(-0.507989\pi\)
0.878300 0.478110i \(-0.158678\pi\)
\(192\) 0 0
\(193\) −12.8030 22.1754i −0.921577 1.59622i −0.796976 0.604011i \(-0.793568\pi\)
−0.124600 0.992207i \(-0.539765\pi\)
\(194\) 0 0
\(195\) 0.0537832 0.00659228i 0.00385150 0.000472083i
\(196\) 0 0
\(197\) 9.45810 0.673862 0.336931 0.941529i \(-0.390611\pi\)
0.336931 + 0.941529i \(0.390611\pi\)
\(198\) 0 0
\(199\) −4.15133 + 7.19032i −0.294280 + 0.509708i −0.974817 0.223005i \(-0.928413\pi\)
0.680537 + 0.732714i \(0.261747\pi\)
\(200\) 0 0
\(201\) −2.25666 + 5.31327i −0.159173 + 0.374769i
\(202\) 0 0
\(203\) −4.70507 + 11.7756i −0.330231 + 0.826488i
\(204\) 0 0
\(205\) 0.306448 0.530784i 0.0214033 0.0370715i
\(206\) 0 0
\(207\) −5.13848 + 17.8916i −0.357149 + 1.24355i
\(208\) 0 0
\(209\) −2.96926 5.14291i −0.205388 0.355742i
\(210\) 0 0
\(211\) 10.1164 17.5222i 0.696444 1.20628i −0.273247 0.961944i \(-0.588098\pi\)
0.969691 0.244333i \(-0.0785689\pi\)
\(212\) 0 0
\(213\) −2.35147 3.12187i −0.161120 0.213907i
\(214\) 0 0
\(215\) −0.245134 0.424585i −0.0167180 0.0289564i
\(216\) 0 0
\(217\) 2.49066 6.23352i 0.169077 0.423159i
\(218\) 0 0
\(219\) 7.13472 0.874512i 0.482120 0.0590940i
\(220\) 0 0
\(221\) −0.280031 0.485028i −0.0188369 0.0326265i
\(222\) 0 0
\(223\) 2.41918 + 4.19014i 0.162000 + 0.280593i 0.935586 0.353099i \(-0.114872\pi\)
−0.773586 + 0.633692i \(0.781539\pi\)
\(224\) 0 0
\(225\) 4.13744 14.4061i 0.275829 0.960408i
\(226\) 0 0
\(227\) −0.672213 −0.0446163 −0.0223082 0.999751i \(-0.507101\pi\)
−0.0223082 + 0.999751i \(0.507101\pi\)
\(228\) 0 0
\(229\) −6.13553 −0.405447 −0.202724 0.979236i \(-0.564979\pi\)
−0.202724 + 0.979236i \(0.564979\pi\)
\(230\) 0 0
\(231\) −3.72108 + 14.0920i −0.244829 + 0.927187i
\(232\) 0 0
\(233\) 12.1492 + 21.0431i 0.795922 + 1.37858i 0.922252 + 0.386589i \(0.126347\pi\)
−0.126330 + 0.991988i \(0.540320\pi\)
\(234\) 0 0
\(235\) −0.203983 + 0.353309i −0.0133064 + 0.0230473i
\(236\) 0 0
\(237\) −5.12059 + 0.627637i −0.332618 + 0.0407694i
\(238\) 0 0
\(239\) −13.5978 + 23.5521i −0.879569 + 1.52346i −0.0277545 + 0.999615i \(0.508836\pi\)
−0.851815 + 0.523843i \(0.824498\pi\)
\(240\) 0 0
\(241\) −25.8054 −1.66227 −0.831135 0.556070i \(-0.812309\pi\)
−0.831135 + 0.556070i \(0.812309\pi\)
\(242\) 0 0
\(243\) −1.34231 15.5306i −0.0861092 0.996286i
\(244\) 0 0
\(245\) 0.101701 0.421694i 0.00649747 0.0269411i
\(246\) 0 0
\(247\) 0.942598 0.0599760
\(248\) 0 0
\(249\) 2.94253 6.92812i 0.186475 0.439052i
\(250\) 0 0
\(251\) 27.0741 1.70890 0.854450 0.519533i \(-0.173894\pi\)
0.854450 + 0.519533i \(0.173894\pi\)
\(252\) 0 0
\(253\) 19.7351 1.24073
\(254\) 0 0
\(255\) 0.118192 0.0144869i 0.00740146 0.000907206i
\(256\) 0 0
\(257\) −13.5215 −0.843445 −0.421723 0.906725i \(-0.638574\pi\)
−0.421723 + 0.906725i \(0.638574\pi\)
\(258\) 0 0
\(259\) 8.36553 20.9369i 0.519809 1.30096i
\(260\) 0 0
\(261\) −13.9531 + 3.47266i −0.863672 + 0.214952i
\(262\) 0 0
\(263\) 13.3745 0.824710 0.412355 0.911023i \(-0.364706\pi\)
0.412355 + 0.911023i \(0.364706\pi\)
\(264\) 0 0
\(265\) 0.0980716 0.169865i 0.00602449 0.0104347i
\(266\) 0 0
\(267\) 5.82411 13.7127i 0.356430 0.839205i
\(268\) 0 0
\(269\) 3.91594 6.78261i 0.238759 0.413543i −0.721599 0.692311i \(-0.756593\pi\)
0.960359 + 0.278768i \(0.0899260\pi\)
\(270\) 0 0
\(271\) −15.1737 26.2816i −0.921735 1.59649i −0.796730 0.604335i \(-0.793439\pi\)
−0.125005 0.992156i \(-0.539895\pi\)
\(272\) 0 0
\(273\) −1.64178 1.62989i −0.0993653 0.0986453i
\(274\) 0 0
\(275\) −15.8905 −0.958230
\(276\) 0 0
\(277\) −22.6924 −1.36346 −0.681728 0.731606i \(-0.738771\pi\)
−0.681728 + 0.731606i \(0.738771\pi\)
\(278\) 0 0
\(279\) 7.38615 1.83828i 0.442197 0.110055i
\(280\) 0 0
\(281\) −10.0826 17.4635i −0.601475 1.04179i −0.992598 0.121447i \(-0.961246\pi\)
0.391122 0.920339i \(-0.372087\pi\)
\(282\) 0 0
\(283\) −8.45297 14.6410i −0.502477 0.870316i −0.999996 0.00286255i \(-0.999089\pi\)
0.497519 0.867453i \(-0.334245\pi\)
\(284\) 0 0
\(285\) −0.0783444 + 0.184460i −0.00464072 + 0.0109265i
\(286\) 0 0
\(287\) −25.8985 + 3.74142i −1.52874 + 0.220849i
\(288\) 0 0
\(289\) 7.88462 + 13.6566i 0.463801 + 0.803327i
\(290\) 0 0
\(291\) 4.43732 10.4476i 0.260120 0.612448i
\(292\) 0 0
\(293\) 2.40597 4.16727i 0.140558 0.243454i −0.787149 0.616763i \(-0.788444\pi\)
0.927707 + 0.373309i \(0.121777\pi\)
\(294\) 0 0
\(295\) −0.279266 0.483703i −0.0162595 0.0281623i
\(296\) 0 0
\(297\) −15.4326 + 5.91286i −0.895489 + 0.343099i
\(298\) 0 0
\(299\) −1.56624 + 2.71280i −0.0905777 + 0.156885i
\(300\) 0 0
\(301\) −7.76649 + 19.4376i −0.447653 + 1.12037i
\(302\) 0 0
\(303\) 6.79078 + 9.01561i 0.390120 + 0.517933i
\(304\) 0 0
\(305\) −0.430125 + 0.744999i −0.0246289 + 0.0426585i
\(306\) 0 0
\(307\) −15.9188 −0.908534 −0.454267 0.890866i \(-0.650099\pi\)
−0.454267 + 0.890866i \(0.650099\pi\)
\(308\) 0 0
\(309\) −17.7358 23.5465i −1.00896 1.33951i
\(310\) 0 0
\(311\) −0.131435 0.227651i −0.00745297 0.0129089i 0.862275 0.506441i \(-0.169039\pi\)
−0.869728 + 0.493532i \(0.835706\pi\)
\(312\) 0 0
\(313\) 3.12534 5.41325i 0.176655 0.305975i −0.764078 0.645124i \(-0.776806\pi\)
0.940733 + 0.339149i \(0.110139\pi\)
\(314\) 0 0
\(315\) 0.455416 0.185817i 0.0256598 0.0104696i
\(316\) 0 0
\(317\) 9.83961 17.0427i 0.552648 0.957214i −0.445435 0.895314i \(-0.646951\pi\)
0.998082 0.0618994i \(-0.0197158\pi\)
\(318\) 0 0
\(319\) 7.62199 + 13.2017i 0.426750 + 0.739152i
\(320\) 0 0
\(321\) −11.9992 + 28.2519i −0.669733 + 1.57687i
\(322\) 0 0
\(323\) 2.07141 0.115256
\(324\) 0 0
\(325\) 1.26111 2.18431i 0.0699540 0.121164i
\(326\) 0 0
\(327\) 22.7939 2.79388i 1.26051 0.154502i
\(328\) 0 0
\(329\) 17.2390 2.49043i 0.950415 0.137302i
\(330\) 0 0
\(331\) 12.2669 21.2469i 0.674249 1.16783i −0.302439 0.953169i \(-0.597801\pi\)
0.976688 0.214665i \(-0.0688659\pi\)
\(332\) 0 0
\(333\) 24.8083 6.17433i 1.35949 0.338351i
\(334\) 0 0
\(335\) −0.103267 0.178863i −0.00564206 0.00977233i
\(336\) 0 0
\(337\) −6.89471 + 11.9420i −0.375579 + 0.650521i −0.990413 0.138135i \(-0.955889\pi\)
0.614835 + 0.788656i \(0.289223\pi\)
\(338\) 0 0
\(339\) 3.78545 0.463988i 0.205598 0.0252004i
\(340\) 0 0
\(341\) −4.03475 6.98840i −0.218494 0.378443i
\(342\) 0 0
\(343\) −16.8311 + 7.72757i −0.908792 + 0.417250i
\(344\) 0 0
\(345\) −0.400699 0.531978i −0.0215729 0.0286407i
\(346\) 0 0
\(347\) −9.84786 17.0570i −0.528661 0.915667i −0.999441 0.0334170i \(-0.989361\pi\)
0.470781 0.882250i \(-0.343972\pi\)
\(348\) 0 0
\(349\) 5.34712 + 9.26149i 0.286225 + 0.495756i 0.972905 0.231203i \(-0.0742662\pi\)
−0.686681 + 0.726959i \(0.740933\pi\)
\(350\) 0 0
\(351\) 0.411990 2.59064i 0.0219904 0.138278i
\(352\) 0 0
\(353\) −11.6615 −0.620677 −0.310338 0.950626i \(-0.600442\pi\)
−0.310338 + 0.950626i \(0.600442\pi\)
\(354\) 0 0
\(355\) 0.139834 0.00742162
\(356\) 0 0
\(357\) −3.60792 3.58177i −0.190951 0.189568i
\(358\) 0 0
\(359\) 8.82159 + 15.2794i 0.465586 + 0.806418i 0.999228 0.0392925i \(-0.0125104\pi\)
−0.533642 + 0.845710i \(0.679177\pi\)
\(360\) 0 0
\(361\) 7.75688 13.4353i 0.408257 0.707122i
\(362\) 0 0
\(363\) −0.921418 1.22330i −0.0483619 0.0642064i
\(364\) 0 0
\(365\) −0.128588 + 0.222721i −0.00673061 + 0.0116578i
\(366\) 0 0
\(367\) −3.38292 −0.176587 −0.0882934 0.996095i \(-0.528141\pi\)
−0.0882934 + 0.996095i \(0.528141\pi\)
\(368\) 0 0
\(369\) −20.6022 21.3522i −1.07251 1.11155i
\(370\) 0 0
\(371\) −8.28821 + 1.19736i −0.430302 + 0.0621636i
\(372\) 0 0
\(373\) 13.3902 0.693320 0.346660 0.937991i \(-0.387316\pi\)
0.346660 + 0.937991i \(0.387316\pi\)
\(374\) 0 0
\(375\) 0.645524 + 0.857013i 0.0333347 + 0.0442560i
\(376\) 0 0
\(377\) −2.41962 −0.124617
\(378\) 0 0
\(379\) 27.6131 1.41839 0.709194 0.705013i \(-0.249059\pi\)
0.709194 + 0.705013i \(0.249059\pi\)
\(380\) 0 0
\(381\) 4.80703 + 6.38193i 0.246271 + 0.326956i
\(382\) 0 0
\(383\) −25.0040 −1.27764 −0.638822 0.769354i \(-0.720578\pi\)
−0.638822 + 0.769354i \(0.720578\pi\)
\(384\) 0 0
\(385\) −0.322624 0.409682i −0.0164424 0.0208793i
\(386\) 0 0
\(387\) −23.0318 + 5.73220i −1.17077 + 0.291384i
\(388\) 0 0
\(389\) −0.136646 −0.00692821 −0.00346411 0.999994i \(-0.501103\pi\)
−0.00346411 + 0.999994i \(0.501103\pi\)
\(390\) 0 0
\(391\) −3.44189 + 5.96153i −0.174064 + 0.301488i
\(392\) 0 0
\(393\) 0.158542 + 0.210484i 0.00799737 + 0.0106175i
\(394\) 0 0
\(395\) 0.0922877 0.159847i 0.00464350 0.00804277i
\(396\) 0 0
\(397\) 7.91030 + 13.7010i 0.397006 + 0.687635i 0.993355 0.115090i \(-0.0367157\pi\)
−0.596349 + 0.802726i \(0.703382\pi\)
\(398\) 0 0
\(399\) 8.25668 2.24458i 0.413351 0.112369i
\(400\) 0 0
\(401\) −11.0549 −0.552055 −0.276028 0.961150i \(-0.589018\pi\)
−0.276028 + 0.961150i \(0.589018\pi\)
\(402\) 0 0
\(403\) 1.28084 0.0638032
\(404\) 0 0
\(405\) 0.472728 + 0.295946i 0.0234900 + 0.0147057i
\(406\) 0 0
\(407\) −13.5518 23.4724i −0.671737 1.16348i
\(408\) 0 0
\(409\) 18.0064 + 31.1880i 0.890358 + 1.54215i 0.839446 + 0.543443i \(0.182880\pi\)
0.0509122 + 0.998703i \(0.483787\pi\)
\(410\) 0 0
\(411\) −3.70503 4.91889i −0.182756 0.242631i
\(412\) 0 0
\(413\) −8.84787 + 22.1441i −0.435375 + 1.08964i
\(414\) 0 0
\(415\) 0.134652 + 0.233225i 0.00660982 + 0.0114485i
\(416\) 0 0
\(417\) 26.1641 3.20697i 1.28126 0.157046i
\(418\) 0 0
\(419\) −16.4877 + 28.5576i −0.805477 + 1.39513i 0.110491 + 0.993877i \(0.464758\pi\)
−0.915968 + 0.401251i \(0.868576\pi\)
\(420\) 0 0
\(421\) 14.9800 + 25.9461i 0.730080 + 1.26454i 0.956849 + 0.290587i \(0.0938505\pi\)
−0.226769 + 0.973949i \(0.572816\pi\)
\(422\) 0 0
\(423\) 13.7136 + 14.2128i 0.666777 + 0.691049i
\(424\) 0 0
\(425\) 2.77137 4.80016i 0.134431 0.232842i
\(426\) 0 0
\(427\) 36.3507 5.25139i 1.75913 0.254133i
\(428\) 0 0
\(429\) −2.76039 + 0.338345i −0.133273 + 0.0163354i
\(430\) 0 0
\(431\) 12.4021 21.4811i 0.597389 1.03471i −0.395816 0.918330i \(-0.629538\pi\)
0.993205 0.116379i \(-0.0371286\pi\)
\(432\) 0 0
\(433\) −5.00906 −0.240720 −0.120360 0.992730i \(-0.538405\pi\)
−0.120360 + 0.992730i \(0.538405\pi\)
\(434\) 0 0
\(435\) 0.201108 0.473503i 0.00964237 0.0227027i
\(436\) 0 0
\(437\) −5.79278 10.0334i −0.277106 0.479962i
\(438\) 0 0
\(439\) −20.2918 + 35.1464i −0.968475 + 1.67745i −0.268502 + 0.963279i \(0.586529\pi\)
−0.699973 + 0.714169i \(0.746805\pi\)
\(440\) 0 0
\(441\) −18.2624 10.3675i −0.869638 0.493689i
\(442\) 0 0
\(443\) −14.1332 + 24.4795i −0.671490 + 1.16305i 0.305992 + 0.952034i \(0.401012\pi\)
−0.977482 + 0.211021i \(0.932321\pi\)
\(444\) 0 0
\(445\) 0.266515 + 0.461618i 0.0126340 + 0.0218828i
\(446\) 0 0
\(447\) 0.382355 + 0.507624i 0.0180848 + 0.0240098i
\(448\) 0 0
\(449\) 36.6443 1.72935 0.864676 0.502329i \(-0.167523\pi\)
0.864676 + 0.502329i \(0.167523\pi\)
\(450\) 0 0
\(451\) −15.7283 + 27.2421i −0.740615 + 1.28278i
\(452\) 0 0
\(453\) 13.1128 + 17.4089i 0.616092 + 0.817939i
\(454\) 0 0
\(455\) 0.0819197 0.0118345i 0.00384045 0.000554811i
\(456\) 0 0
\(457\) 3.19154 5.52791i 0.149294 0.258585i −0.781673 0.623689i \(-0.785633\pi\)
0.930967 + 0.365104i \(0.118967\pi\)
\(458\) 0 0
\(459\) 0.905373 5.69307i 0.0422592 0.265730i
\(460\) 0 0
\(461\) 7.24366 + 12.5464i 0.337371 + 0.584343i 0.983937 0.178514i \(-0.0571291\pi\)
−0.646567 + 0.762858i \(0.723796\pi\)
\(462\) 0 0
\(463\) −13.2527 + 22.9544i −0.615907 + 1.06678i 0.374317 + 0.927301i \(0.377877\pi\)
−0.990225 + 0.139482i \(0.955456\pi\)
\(464\) 0 0
\(465\) −0.106458 + 0.250652i −0.00493686 + 0.0116237i
\(466\) 0 0
\(467\) 11.6879 + 20.2440i 0.540851 + 0.936782i 0.998855 + 0.0478318i \(0.0152311\pi\)
−0.458004 + 0.888950i \(0.651436\pi\)
\(468\) 0 0
\(469\) −3.27176 + 8.18841i −0.151076 + 0.378106i
\(470\) 0 0
\(471\) −3.69337 + 8.69596i −0.170182 + 0.400689i
\(472\) 0 0
\(473\) 12.5814 + 21.7915i 0.578491 + 1.00198i
\(474\) 0 0
\(475\) 4.66428 + 8.07877i 0.214012 + 0.370679i
\(476\) 0 0
\(477\) −6.59326 6.83327i −0.301885 0.312874i
\(478\) 0 0
\(479\) −9.29606 −0.424748 −0.212374 0.977188i \(-0.568119\pi\)
−0.212374 + 0.977188i \(0.568119\pi\)
\(480\) 0 0
\(481\) 4.30204 0.196156
\(482\) 0 0
\(483\) −7.25953 + 27.4924i −0.330320 + 1.25095i
\(484\) 0 0
\(485\) 0.203055 + 0.351702i 0.00922026 + 0.0159700i
\(486\) 0 0
\(487\) −2.04947 + 3.54979i −0.0928704 + 0.160856i −0.908718 0.417411i \(-0.862938\pi\)
0.815847 + 0.578267i \(0.196271\pi\)
\(488\) 0 0
\(489\) 5.19416 12.2295i 0.234888 0.553038i
\(490\) 0 0
\(491\) −4.98703 + 8.63778i −0.225061 + 0.389818i −0.956338 0.292264i \(-0.905592\pi\)
0.731277 + 0.682081i \(0.238925\pi\)
\(492\) 0 0
\(493\) −5.31725 −0.239477
\(494\) 0 0
\(495\) 0.163219 0.568312i 0.00733616 0.0255437i
\(496\) 0 0
\(497\) −3.69366 4.69037i −0.165683 0.210392i
\(498\) 0 0
\(499\) 11.2083 0.501752 0.250876 0.968019i \(-0.419281\pi\)
0.250876 + 0.968019i \(0.419281\pi\)
\(500\) 0 0
\(501\) 32.5783 3.99317i 1.45549 0.178402i
\(502\) 0 0
\(503\) 1.69350 0.0755094 0.0377547 0.999287i \(-0.487979\pi\)
0.0377547 + 0.999287i \(0.487979\pi\)
\(504\) 0 0
\(505\) −0.403825 −0.0179700
\(506\) 0 0
\(507\) −8.62975 + 20.3185i −0.383261 + 0.902378i
\(508\) 0 0
\(509\) −40.9555 −1.81532 −0.907659 0.419707i \(-0.862133\pi\)
−0.907659 + 0.419707i \(0.862133\pi\)
\(510\) 0 0
\(511\) 10.8672 1.56993i 0.480737 0.0694496i
\(512\) 0 0
\(513\) 7.53600 + 6.11040i 0.332723 + 0.269781i
\(514\) 0 0
\(515\) 1.05469 0.0464752
\(516\) 0 0
\(517\) 10.4693 18.1334i 0.460439 0.797504i
\(518\) 0 0
\(519\) 41.2464 5.05563i 1.81052 0.221918i
\(520\) 0 0
\(521\) 15.5075 26.8598i 0.679396 1.17675i −0.295767 0.955260i \(-0.595575\pi\)
0.975163 0.221488i \(-0.0710914\pi\)
\(522\) 0 0
\(523\) 3.67840 + 6.37117i 0.160845 + 0.278592i 0.935172 0.354194i \(-0.115245\pi\)
−0.774327 + 0.632786i \(0.781911\pi\)
\(524\) 0 0
\(525\) 5.84529 22.1365i 0.255109 0.966118i
\(526\) 0 0
\(527\) 2.81472 0.122611
\(528\) 0 0
\(529\) 15.5015 0.673980
\(530\) 0 0
\(531\) −26.2387 + 6.53033i −1.13866 + 0.283392i
\(532\) 0 0
\(533\) −2.49648 4.32404i −0.108135 0.187295i
\(534\) 0 0
\(535\) −0.549094 0.951059i −0.0237394 0.0411179i
\(536\) 0 0
\(537\) 14.7128 1.80337i 0.634905 0.0778211i
\(538\) 0 0
\(539\) −5.21976 + 21.6432i −0.224831 + 0.932238i
\(540\) 0 0
\(541\) −14.4735 25.0688i −0.622262 1.07779i −0.989063 0.147491i \(-0.952880\pi\)
0.366801 0.930299i \(-0.380453\pi\)
\(542\) 0 0
\(543\) 0.659294 + 0.875295i 0.0282930 + 0.0375625i
\(544\) 0 0
\(545\) −0.410812 + 0.711546i −0.0175972 + 0.0304793i
\(546\) 0 0
\(547\) −9.34891 16.1928i −0.399731 0.692354i 0.593962 0.804493i \(-0.297563\pi\)
−0.993692 + 0.112140i \(0.964230\pi\)
\(548\) 0 0
\(549\) 28.9169 + 29.9695i 1.23414 + 1.27907i
\(550\) 0 0
\(551\) 4.47452 7.75010i 0.190621 0.330165i
\(552\) 0 0
\(553\) −7.79940 + 1.12674i −0.331664 + 0.0479138i
\(554\) 0 0
\(555\) −0.357566 + 0.841881i −0.0151778 + 0.0357358i
\(556\) 0 0
\(557\) −17.1787 + 29.7544i −0.727886 + 1.26074i 0.229889 + 0.973217i \(0.426164\pi\)
−0.957775 + 0.287519i \(0.907170\pi\)
\(558\) 0 0
\(559\) −3.99397 −0.168927
\(560\) 0 0
\(561\) −6.06612 + 0.743532i −0.256112 + 0.0313919i
\(562\) 0 0
\(563\) −7.37355 12.7714i −0.310758 0.538249i 0.667769 0.744369i \(-0.267250\pi\)
−0.978527 + 0.206120i \(0.933916\pi\)
\(564\) 0 0
\(565\) −0.0682247 + 0.118169i −0.00287024 + 0.00497139i
\(566\) 0 0
\(567\) −2.56017 23.6737i −0.107517 0.994203i
\(568\) 0 0
\(569\) −1.66821 + 2.88942i −0.0699349 + 0.121131i −0.898872 0.438210i \(-0.855613\pi\)
0.828938 + 0.559341i \(0.188946\pi\)
\(570\) 0 0
\(571\) 9.40360 + 16.2875i 0.393528 + 0.681611i 0.992912 0.118851i \(-0.0379210\pi\)
−0.599384 + 0.800462i \(0.704588\pi\)
\(572\) 0 0
\(573\) 40.5437 4.96949i 1.69374 0.207603i
\(574\) 0 0
\(575\) −31.0010 −1.29283
\(576\) 0 0
\(577\) −17.6961 + 30.6505i −0.736697 + 1.27600i 0.217277 + 0.976110i \(0.430282\pi\)
−0.953975 + 0.299887i \(0.903051\pi\)
\(578\) 0 0
\(579\) 17.3378 40.8214i 0.720534 1.69648i
\(580\) 0 0
\(581\) 4.26614 10.6771i 0.176989 0.442961i
\(582\) 0 0
\(583\) −5.03346 + 8.71821i −0.208465 + 0.361072i
\(584\) 0 0
\(585\) 0.0651670 + 0.0675392i 0.00269432 + 0.00279240i
\(586\) 0 0
\(587\) 17.2921 + 29.9508i 0.713722 + 1.23620i 0.963450 + 0.267887i \(0.0863256\pi\)
−0.249728 + 0.968316i \(0.580341\pi\)
\(588\) 0 0
\(589\) −2.36862 + 4.10257i −0.0975973 + 0.169043i
\(590\) 0 0
\(591\) 9.85613 + 13.0852i 0.405427 + 0.538255i
\(592\) 0 0
\(593\) −15.9787 27.6759i −0.656166 1.13651i −0.981600 0.190949i \(-0.938844\pi\)
0.325434 0.945565i \(-0.394490\pi\)
\(594\) 0 0
\(595\) 0.180023 0.0260070i 0.00738023 0.00106618i
\(596\) 0 0
\(597\) −14.2738 + 1.74956i −0.584188 + 0.0716047i
\(598\) 0 0
\(599\) −4.92476 8.52993i −0.201220 0.348524i 0.747702 0.664035i \(-0.231157\pi\)
−0.948922 + 0.315511i \(0.897824\pi\)
\(600\) 0 0
\(601\) −3.77340 6.53572i −0.153920 0.266598i 0.778745 0.627340i \(-0.215857\pi\)
−0.932665 + 0.360743i \(0.882523\pi\)
\(602\) 0 0
\(603\) −9.70252 + 2.41478i −0.395117 + 0.0983374i
\(604\) 0 0
\(605\) 0.0547937 0.00222768
\(606\) 0 0
\(607\) −10.8584 −0.440730 −0.220365 0.975417i \(-0.570725\pi\)
−0.220365 + 0.975417i \(0.570725\pi\)
\(608\) 0 0
\(609\) −21.1946 + 5.76176i −0.858850 + 0.233478i
\(610\) 0 0
\(611\) 1.66175 + 2.87823i 0.0672272 + 0.116441i
\(612\) 0 0
\(613\) −23.8823 + 41.3653i −0.964596 + 1.67073i −0.253899 + 0.967231i \(0.581713\pi\)
−0.710697 + 0.703499i \(0.751620\pi\)
\(614\) 0 0
\(615\) 1.05368 0.129151i 0.0424886 0.00520788i
\(616\) 0 0
\(617\) −18.7769 + 32.5225i −0.755929 + 1.30931i 0.188982 + 0.981980i \(0.439481\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(618\) 0 0
\(619\) −35.9657 −1.44558 −0.722792 0.691065i \(-0.757142\pi\)
−0.722792 + 0.691065i \(0.757142\pi\)
\(620\) 0 0
\(621\) −30.1077 + 11.5355i −1.20818 + 0.462904i
\(622\) 0 0
\(623\) 8.44390 21.1330i 0.338298 0.846677i
\(624\) 0 0
\(625\) 24.9424 0.997696
\(626\) 0 0
\(627\) 4.02098 9.46730i 0.160582 0.378088i
\(628\) 0 0
\(629\) 9.45398 0.376955
\(630\) 0 0
\(631\) 31.8848 1.26931 0.634656 0.772794i \(-0.281142\pi\)
0.634656 + 0.772794i \(0.281142\pi\)
\(632\) 0 0
\(633\) 34.7840 4.26353i 1.38254 0.169460i
\(634\) 0 0
\(635\) −0.285858 −0.0113439
\(636\) 0 0
\(637\) −2.56083 2.43518i −0.101464 0.0964854i
\(638\) 0 0
\(639\) 1.86867 6.50649i 0.0739233 0.257393i
\(640\) 0 0
\(641\) 16.6788 0.658772 0.329386 0.944195i \(-0.393158\pi\)
0.329386 + 0.944195i \(0.393158\pi\)
\(642\) 0 0
\(643\) −23.5295 + 40.7544i −0.927915 + 1.60720i −0.141109 + 0.989994i \(0.545067\pi\)
−0.786805 + 0.617201i \(0.788266\pi\)
\(644\) 0 0
\(645\) 0.331961 0.781595i 0.0130710 0.0307753i
\(646\) 0 0
\(647\) 12.2324 21.1872i 0.480906 0.832954i −0.518854 0.854863i \(-0.673641\pi\)
0.999760 + 0.0219091i \(0.00697444\pi\)
\(648\) 0 0
\(649\) 14.3331 + 24.8257i 0.562625 + 0.974495i
\(650\) 0 0
\(651\) 11.2195 3.05003i 0.439728 0.119540i
\(652\) 0 0
\(653\) −11.8261 −0.462792 −0.231396 0.972860i \(-0.574329\pi\)
−0.231396 + 0.972860i \(0.574329\pi\)
\(654\) 0 0
\(655\) −0.00942795 −0.000368380
\(656\) 0 0
\(657\) 8.64486 + 8.95954i 0.337268 + 0.349545i
\(658\) 0 0
\(659\) −3.51539 6.08883i −0.136940 0.237187i 0.789397 0.613883i \(-0.210393\pi\)
−0.926337 + 0.376696i \(0.877060\pi\)
\(660\) 0 0
\(661\) −7.43024 12.8696i −0.289003 0.500568i 0.684569 0.728948i \(-0.259990\pi\)
−0.973572 + 0.228380i \(0.926657\pi\)
\(662\) 0 0
\(663\) 0.379219 0.892862i 0.0147276 0.0346759i
\(664\) 0 0
\(665\) −0.113585 + 0.284276i −0.00440465 + 0.0110238i
\(666\) 0 0
\(667\) 14.8699 + 25.7554i 0.575764 + 0.997253i
\(668\) 0 0
\(669\) −3.27606 + 7.71341i −0.126660 + 0.298218i
\(670\) 0 0
\(671\) 22.0759 38.2366i 0.852231 1.47611i
\(672\) 0 0
\(673\) 7.81679 + 13.5391i 0.301315 + 0.521893i 0.976434 0.215816i \(-0.0692411\pi\)
−0.675119 + 0.737709i \(0.735908\pi\)
\(674\) 0 0
\(675\) 24.2424 9.28824i 0.933089 0.357505i
\(676\) 0 0
\(677\) −12.3561 + 21.4014i −0.474883 + 0.822522i −0.999586 0.0287634i \(-0.990843\pi\)
0.524703 + 0.851285i \(0.324176\pi\)
\(678\) 0 0
\(679\) 6.43332 16.1010i 0.246888 0.617901i
\(680\) 0 0
\(681\) −0.700502 0.930004i −0.0268433 0.0356378i
\(682\) 0 0
\(683\) 16.7467 29.0061i 0.640794 1.10989i −0.344462 0.938800i \(-0.611939\pi\)
0.985256 0.171087i \(-0.0547279\pi\)
\(684\) 0 0
\(685\) 0.220326 0.00841821
\(686\) 0 0
\(687\) −6.39373 8.48848i −0.243936 0.323856i
\(688\) 0 0
\(689\) −0.798941 1.38381i −0.0304372 0.0527189i
\(690\) 0 0
\(691\) −1.33836 + 2.31811i −0.0509137 + 0.0881851i −0.890359 0.455259i \(-0.849547\pi\)
0.839445 + 0.543444i \(0.182880\pi\)
\(692\) 0 0
\(693\) −23.3739 + 9.53696i −0.887903 + 0.362279i
\(694\) 0 0
\(695\) −0.471552 + 0.816752i −0.0178870 + 0.0309812i
\(696\) 0 0
\(697\) −5.48617 9.50232i −0.207803 0.359926i
\(698\) 0 0
\(699\) −16.4525 + 38.7370i −0.622291 + 1.46517i
\(700\) 0 0
\(701\) −36.3715 −1.37373 −0.686866 0.726784i \(-0.741014\pi\)
−0.686866 + 0.726784i \(0.741014\pi\)
\(702\) 0 0
\(703\) −7.95563 + 13.7796i −0.300052 + 0.519706i
\(704\) 0 0
\(705\) −0.701369 + 0.0859677i −0.0264151 + 0.00323773i
\(706\) 0 0
\(707\) 10.6669 + 13.5453i 0.401169 + 0.509423i
\(708\) 0 0
\(709\) 5.95369 10.3121i 0.223596 0.387279i −0.732302 0.680980i \(-0.761554\pi\)
0.955897 + 0.293702i \(0.0948872\pi\)
\(710\) 0 0
\(711\) −6.20442 6.43027i −0.232684 0.241154i
\(712\) 0 0
\(713\) −7.87148 13.6338i −0.294789 0.510590i
\(714\) 0 0
\(715\) 0.0497501 0.0861698i 0.00186055 0.00322257i
\(716\) 0 0
\(717\) −46.7543 + 5.73073i −1.74607 + 0.214018i
\(718\) 0 0
\(719\) −8.44050 14.6194i −0.314778 0.545211i 0.664613 0.747188i \(-0.268597\pi\)
−0.979390 + 0.201977i \(0.935263\pi\)
\(720\) 0 0
\(721\) −27.8592 35.3769i −1.03753 1.31750i
\(722\) 0 0
\(723\) −26.8914 35.7016i −1.00010 1.32776i
\(724\) 0 0
\(725\) −11.9731 20.7379i −0.444668 0.770187i
\(726\) 0 0
\(727\) −1.24570 2.15762i −0.0462006 0.0800218i 0.842000 0.539477i \(-0.181378\pi\)
−0.888201 + 0.459455i \(0.848045\pi\)
\(728\) 0 0
\(729\) 20.0877 18.0412i 0.743988 0.668193i
\(730\) 0 0
\(731\) −8.77699 −0.324629
\(732\) 0 0
\(733\) −12.5131 −0.462181 −0.231090 0.972932i \(-0.574229\pi\)
−0.231090 + 0.972932i \(0.574229\pi\)
\(734\) 0 0
\(735\) 0.689394 0.298737i 0.0254287 0.0110191i
\(736\) 0 0
\(737\) 5.30009 + 9.18003i 0.195231 + 0.338151i
\(738\) 0 0
\(739\) 10.0051 17.3294i 0.368044 0.637472i −0.621215 0.783640i \(-0.713361\pi\)
0.989260 + 0.146168i \(0.0466941\pi\)
\(740\) 0 0
\(741\) 0.982265 + 1.30408i 0.0360844 + 0.0479066i
\(742\) 0 0
\(743\) −5.49879 + 9.52419i −0.201731 + 0.349408i −0.949086 0.315016i \(-0.897990\pi\)
0.747355 + 0.664425i \(0.231323\pi\)
\(744\) 0 0
\(745\) −0.0227374 −0.000833034
\(746\) 0 0
\(747\) 12.6514 3.14870i 0.462890 0.115205i
\(748\) 0 0
\(749\) −17.3967 + 43.5398i −0.635663 + 1.59091i
\(750\) 0 0
\(751\) −28.8670 −1.05337 −0.526686 0.850060i \(-0.676566\pi\)
−0.526686 + 0.850060i \(0.676566\pi\)
\(752\) 0 0
\(753\) 28.2135 + 37.4569i 1.02816 + 1.36500i
\(754\) 0 0
\(755\) −0.779774 −0.0283789
\(756\) 0 0
\(757\) −17.3626 −0.631053 −0.315527 0.948917i \(-0.602181\pi\)
−0.315527 + 0.948917i \(0.602181\pi\)
\(758\) 0 0
\(759\) 20.5656 + 27.3034i 0.746484 + 0.991051i
\(760\) 0 0
\(761\) −52.0039 −1.88514 −0.942571 0.334006i \(-0.891599\pi\)
−0.942571 + 0.334006i \(0.891599\pi\)
\(762\) 0 0
\(763\) 34.7184 5.01559i 1.25689 0.181577i
\(764\) 0 0
\(765\) 0.143208 + 0.148421i 0.00517771 + 0.00536618i
\(766\) 0 0
\(767\) −4.55008 −0.164294
\(768\) 0 0
\(769\) 13.5839 23.5280i 0.489849 0.848443i −0.510083 0.860125i \(-0.670385\pi\)
0.999932 + 0.0116822i \(0.00371865\pi\)
\(770\) 0 0
\(771\) −14.0905 18.7069i −0.507457 0.673712i
\(772\) 0 0
\(773\) 12.2452 21.2093i 0.440428 0.762845i −0.557293 0.830316i \(-0.688160\pi\)
0.997721 + 0.0674716i \(0.0214932\pi\)
\(774\) 0 0
\(775\) 6.33802 + 10.9778i 0.227668 + 0.394333i
\(776\) 0 0
\(777\) 37.6837 10.2443i 1.35189 0.367513i
\(778\) 0 0
\(779\) 18.4667 0.661638
\(780\) 0 0
\(781\) −7.17689 −0.256809
\(782\) 0 0
\(783\) −19.3447 15.6852i −0.691322 0.560543i
\(784\) 0 0
\(785\) −0.169011 0.292736i −0.00603227 0.0104482i
\(786\) 0 0
\(787\) 0.939312 + 1.62694i 0.0334828 + 0.0579940i 0.882281 0.470723i \(-0.156007\pi\)
−0.848798 + 0.528717i \(0.822673\pi\)
\(788\) 0 0
\(789\) 13.9374 + 18.5036i 0.496184 + 0.658747i
\(790\) 0 0
\(791\) 5.76579 0.832955i 0.205008 0.0296165i
\(792\) 0 0
\(793\) 3.50402 + 6.06914i 0.124431 + 0.215521i
\(794\) 0 0
\(795\) 0.337206 0.0413318i 0.0119595 0.00146589i
\(796\) 0 0
\(797\) 17.6067 30.4957i 0.623662 1.08021i −0.365137 0.930954i \(-0.618978\pi\)
0.988798 0.149259i \(-0.0476890\pi\)
\(798\) 0 0
\(799\) 3.65179 + 6.32509i 0.129191 + 0.223765i
\(800\) 0 0
\(801\) 25.0407 6.23218i 0.884770 0.220203i
\(802\) 0 0
\(803\) 6.59970 11.4310i 0.232898 0.403392i
\(804\) 0 0
\(805\) −0.629413 0.799257i −0.0221839 0.0281701i
\(806\) 0 0
\(807\) 13.4645 1.65036i 0.473971 0.0580953i
\(808\) 0 0
\(809\) 1.53614 2.66067i 0.0540077 0.0935441i −0.837758 0.546042i \(-0.816134\pi\)
0.891765 + 0.452498i \(0.149467\pi\)
\(810\) 0 0
\(811\) 14.8034 0.519818 0.259909 0.965633i \(-0.416307\pi\)
0.259909 + 0.965633i \(0.416307\pi\)
\(812\) 0 0
\(813\) 20.5482 48.3803i 0.720657 1.69677i
\(814\) 0 0
\(815\) 0.237688 + 0.411689i 0.00832586 + 0.0144208i
\(816\) 0 0
\(817\) 7.38594 12.7928i 0.258401 0.447564i
\(818\) 0 0
\(819\) 0.544069 3.96988i 0.0190113 0.138719i
\(820\) 0 0
\(821\) −12.5061 + 21.6612i −0.436467 + 0.755982i −0.997414 0.0718690i \(-0.977104\pi\)
0.560947 + 0.827851i \(0.310437\pi\)
\(822\) 0 0
\(823\) 19.7480 + 34.2046i 0.688374 + 1.19230i 0.972364 + 0.233471i \(0.0750084\pi\)
−0.283990 + 0.958827i \(0.591658\pi\)
\(824\) 0 0
\(825\) −16.5592 21.9844i −0.576517 0.765398i
\(826\) 0 0
\(827\) −12.4528 −0.433026 −0.216513 0.976280i \(-0.569468\pi\)
−0.216513 + 0.976280i \(0.569468\pi\)
\(828\) 0 0
\(829\) −14.2995 + 24.7675i −0.496643 + 0.860211i −0.999993 0.00387209i \(-0.998767\pi\)
0.503350 + 0.864083i \(0.332101\pi\)
\(830\) 0 0
\(831\) −23.6474 31.3949i −0.820320 1.08908i
\(832\) 0 0
\(833\) −5.62758 5.35145i −0.194984 0.185417i
\(834\) 0 0
\(835\) −0.587154 + 1.01698i −0.0203193 + 0.0351941i
\(836\) 0 0
\(837\) 10.2402 + 8.30307i 0.353954 + 0.286996i
\(838\) 0 0
\(839\) −21.0794 36.5107i −0.727743 1.26049i −0.957835 0.287319i \(-0.907236\pi\)
0.230092 0.973169i \(-0.426097\pi\)
\(840\) 0 0
\(841\) 3.01405 5.22048i 0.103933 0.180017i
\(842\) 0 0
\(843\) 13.6538 32.1476i 0.470263 1.10722i
\(844\) 0 0
\(845\) −0.394904 0.683993i −0.0135851 0.0235301i
\(846\) 0 0
\(847\) −1.44735 1.83791i −0.0497316 0.0631514i
\(848\) 0 0
\(849\) 11.4470 26.9518i 0.392861 0.924983i
\(850\) 0 0
\(851\) −26.4384 45.7927i −0.906297 1.56975i
\(852\) 0 0
\(853\) −25.6206 44.3761i −0.877232 1.51941i −0.854366 0.519671i \(-0.826054\pi\)
−0.0228654 0.999739i \(-0.507279\pi\)
\(854\) 0 0
\(855\) −0.336841 + 0.0838337i −0.0115197 + 0.00286705i
\(856\) 0 0
\(857\) −37.8058 −1.29142 −0.645710 0.763582i \(-0.723439\pi\)
−0.645710 + 0.763582i \(0.723439\pi\)
\(858\) 0 0
\(859\) 44.6224 1.52250 0.761249 0.648460i \(-0.224587\pi\)
0.761249 + 0.648460i \(0.224587\pi\)
\(860\) 0 0
\(861\) −32.1646 31.9316i −1.09617 1.08823i
\(862\) 0 0
\(863\) 15.4848 + 26.8205i 0.527109 + 0.912980i 0.999501 + 0.0315912i \(0.0100575\pi\)
−0.472392 + 0.881389i \(0.656609\pi\)
\(864\) 0 0
\(865\) −0.743379 + 1.28757i −0.0252756 + 0.0437787i
\(866\) 0 0
\(867\) −10.6774 + 25.1396i −0.362622 + 0.853786i
\(868\) 0 0
\(869\) −4.73661 + 8.20405i −0.160678 + 0.278303i
\(870\) 0 0
\(871\) −1.68253 −0.0570102
\(872\) 0 0
\(873\) 19.0782 4.74823i 0.645701 0.160703i
\(874\) 0 0
\(875\) 1.01398 + 1.28760i 0.0342788 + 0.0435288i
\(876\) 0 0
\(877\) 23.1686 0.782347 0.391174 0.920317i \(-0.372069\pi\)
0.391174 + 0.920317i \(0.372069\pi\)
\(878\) 0 0
\(879\) 8.27263 1.01399i 0.279029 0.0342009i
\(880\) 0 0
\(881\) 14.0143 0.472155 0.236077 0.971734i \(-0.424138\pi\)
0.236077 + 0.971734i \(0.424138\pi\)
\(882\) 0 0
\(883\) 39.9269 1.34365 0.671824 0.740711i \(-0.265511\pi\)
0.671824 + 0.740711i \(0.265511\pi\)
\(884\) 0 0
\(885\) 0.378182 0.890422i 0.0127125 0.0299312i
\(886\) 0 0
\(887\) 26.8441 0.901338 0.450669 0.892691i \(-0.351186\pi\)
0.450669 + 0.892691i \(0.351186\pi\)
\(888\) 0 0
\(889\) 7.55082 + 9.58837i 0.253246 + 0.321584i
\(890\) 0 0
\(891\) −24.2625 15.1892i −0.812823 0.508858i
\(892\) 0 0
\(893\) −12.2921 −0.411339
\(894\) 0 0
\(895\) −0.265167 + 0.459283i −0.00886356 + 0.0153521i
\(896\) 0 0
\(897\) −5.38530 + 0.660083i −0.179810 + 0.0220395i
\(898\) 0 0
\(899\) 6.08017 10.5312i 0.202785 0.351234i
\(900\) 0 0
\(901\) −1.75572 3.04100i −0.0584915 0.101310i
\(902\) 0 0
\(903\) −34.9852 + 9.51073i −1.16424 + 0.316497i
\(904\) 0 0
\(905\) −0.0392060 −0.00130325
\(906\) 0 0
\(907\) −37.7617 −1.25386 −0.626928 0.779077i \(-0.715688\pi\)
−0.626928 + 0.779077i \(0.715688\pi\)
\(908\) 0 0
\(909\) −5.39650 + 18.7900i −0.178991 + 0.623226i
\(910\) 0 0
\(911\) −7.93650 13.7464i −0.262948 0.455439i 0.704076 0.710125i \(-0.251361\pi\)
−0.967024 + 0.254685i \(0.918028\pi\)
\(912\) 0 0
\(913\) −6.91094 11.9701i −0.228719 0.396153i
\(914\) 0 0
\(915\) −1.47893 + 0.181274i −0.0488919 + 0.00599274i
\(916\) 0 0
\(917\) 0.249035 + 0.316236i 0.00822388 + 0.0104430i
\(918\) 0 0
\(919\) −5.22203 9.04482i −0.172259 0.298361i 0.766950 0.641706i \(-0.221773\pi\)
−0.939209 + 0.343345i \(0.888440\pi\)
\(920\) 0 0
\(921\) −16.5887 22.0236i −0.546617 0.725702i
\(922\) 0 0
\(923\) 0.569580 0.986541i 0.0187479 0.0324724i
\(924\) 0 0
\(925\) 21.2879 + 36.8717i 0.699941 + 1.21233i
\(926\) 0 0
\(927\) 14.0943 49.0749i 0.462918 1.61183i
\(928\) 0 0
\(929\) 9.58169 16.5960i 0.314365 0.544496i −0.664937 0.746899i \(-0.731542\pi\)
0.979302 + 0.202403i \(0.0648751\pi\)
\(930\) 0 0
\(931\) 12.5356 3.69912i 0.410839 0.121234i
\(932\) 0 0
\(933\) 0.177989 0.419071i 0.00582710 0.0137198i
\(934\) 0 0
\(935\) 0.109329 0.189363i 0.00357543 0.00619283i
\(936\) 0 0
\(937\) 3.09451 0.101093 0.0505467 0.998722i \(-0.483904\pi\)
0.0505467 + 0.998722i \(0.483904\pi\)
\(938\) 0 0
\(939\) 10.7461 1.31716i 0.350685 0.0429839i
\(940\) 0 0
\(941\) −7.65564 13.2600i −0.249567 0.432262i 0.713839 0.700310i \(-0.246955\pi\)
−0.963406 + 0.268048i \(0.913622\pi\)
\(942\) 0 0
\(943\) −30.6845 + 53.1472i −0.999226 + 1.73071i
\(944\) 0 0
\(945\) 0.731659 + 0.436429i 0.0238009 + 0.0141970i
\(946\) 0 0
\(947\) 0.507747 0.879443i 0.0164995 0.0285781i −0.857658 0.514221i \(-0.828081\pi\)
0.874157 + 0.485643i \(0.161414\pi\)
\(948\) 0 0
\(949\) 1.04754 + 1.81440i 0.0340047 + 0.0588979i
\(950\) 0 0
\(951\) 33.8322 4.14686i 1.09708 0.134471i
\(952\) 0 0
\(953\) −35.4930 −1.14973 −0.574865 0.818248i \(-0.694945\pi\)
−0.574865 + 0.818248i \(0.694945\pi\)
\(954\) 0 0
\(955\) −0.730713 + 1.26563i −0.0236453 + 0.0409549i
\(956\) 0 0
\(957\) −10.3217 + 24.3022i −0.333654 + 0.785580i
\(958\) 0 0
\(959\) −5.81982 7.39026i −0.187932 0.238644i
\(960\) 0 0
\(961\) 12.2814 21.2720i 0.396175 0.686195i
\(962\) 0 0
\(963\) −51.5907 + 12.8400i −1.66249 + 0.413763i
\(964\) 0 0
\(965\) 0.793390 + 1.37419i 0.0255401 + 0.0442368i
\(966\) 0 0
\(967\) −6.87762 + 11.9124i −0.221169 + 0.383077i −0.955163 0.296079i \(-0.904321\pi\)
0.733994 + 0.679156i \(0.237654\pi\)
\(968\) 0 0
\(969\) 2.15859 + 2.86579i 0.0693437 + 0.0920625i
\(970\) 0 0
\(971\) 21.6567 + 37.5104i 0.694995 + 1.20377i 0.970182 + 0.242376i \(0.0779269\pi\)
−0.275187 + 0.961391i \(0.588740\pi\)
\(972\) 0 0
\(973\) 39.8517 5.75718i 1.27759 0.184567i
\(974\) 0 0
\(975\) 4.33618 0.531491i 0.138869 0.0170213i
\(976\) 0 0
\(977\) 4.78420 + 8.28648i 0.153060 + 0.265108i 0.932351 0.361554i \(-0.117754\pi\)
−0.779291 + 0.626662i \(0.784421\pi\)
\(978\) 0 0
\(979\) −13.6787 23.6923i −0.437174 0.757208i
\(980\) 0 0
\(981\) 27.6185 + 28.6238i 0.881790 + 0.913889i
\(982\) 0 0
\(983\) −17.1329 −0.546454 −0.273227 0.961950i \(-0.588091\pi\)
−0.273227 + 0.961950i \(0.588091\pi\)
\(984\) 0 0
\(985\) −0.586111 −0.0186751
\(986\) 0 0
\(987\) 21.4099 + 21.2548i 0.681486 + 0.676548i
\(988\) 0 0
\(989\) 24.5452 + 42.5135i 0.780492 + 1.35185i
\(990\) 0 0
\(991\) −6.32891 + 10.9620i −0.201044 + 0.348219i −0.948865 0.315682i \(-0.897767\pi\)
0.747821 + 0.663901i \(0.231100\pi\)
\(992\) 0 0
\(993\) 42.1781 5.16982i 1.33848 0.164059i
\(994\) 0 0
\(995\) 0.257255 0.445579i 0.00815553 0.0141258i
\(996\) 0 0
\(997\) −25.6704 −0.812989 −0.406495 0.913653i \(-0.633249\pi\)
−0.406495 + 0.913653i \(0.633249\pi\)
\(998\) 0 0
\(999\) 34.3945 + 27.8880i 1.08819 + 0.882338i
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 1008.2.t.l.193.8 22
3.2 odd 2 3024.2.t.k.1873.6 22
4.3 odd 2 504.2.t.c.193.4 yes 22
7.2 even 3 1008.2.q.l.625.1 22
9.2 odd 6 3024.2.q.l.2881.6 22
9.7 even 3 1008.2.q.l.529.1 22
12.11 even 2 1512.2.t.c.361.6 22
21.2 odd 6 3024.2.q.l.2305.6 22
28.23 odd 6 504.2.q.c.121.11 yes 22
36.7 odd 6 504.2.q.c.25.11 22
36.11 even 6 1512.2.q.d.1369.6 22
63.2 odd 6 3024.2.t.k.289.6 22
63.16 even 3 inner 1008.2.t.l.961.8 22
84.23 even 6 1512.2.q.d.793.6 22
252.79 odd 6 504.2.t.c.457.4 yes 22
252.191 even 6 1512.2.t.c.289.6 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.q.c.25.11 22 36.7 odd 6
504.2.q.c.121.11 yes 22 28.23 odd 6
504.2.t.c.193.4 yes 22 4.3 odd 2
504.2.t.c.457.4 yes 22 252.79 odd 6
1008.2.q.l.529.1 22 9.7 even 3
1008.2.q.l.625.1 22 7.2 even 3
1008.2.t.l.193.8 22 1.1 even 1 trivial
1008.2.t.l.961.8 22 63.16 even 3 inner
1512.2.q.d.793.6 22 84.23 even 6
1512.2.q.d.1369.6 22 36.11 even 6
1512.2.t.c.289.6 22 252.191 even 6
1512.2.t.c.361.6 22 12.11 even 2
3024.2.q.l.2305.6 22 21.2 odd 6
3024.2.q.l.2881.6 22 9.2 odd 6
3024.2.t.k.289.6 22 63.2 odd 6
3024.2.t.k.1873.6 22 3.2 odd 2