Properties

Label 756.2.bq.a.25.15
Level $756$
Weight $2$
Character 756.25
Analytic conductor $6.037$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [756,2,Mod(25,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 10, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.bq (of order \(9\), degree \(6\), 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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 25.15
Character \(\chi\) \(=\) 756.25
Dual form 756.2.bq.a.121.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.568135 - 1.63622i) q^{3} +(0.924390 + 0.336451i) q^{5} +(-1.51517 - 2.16893i) q^{7} +(-2.35445 - 1.85919i) q^{9} +O(q^{10})\) \(q+(0.568135 - 1.63622i) q^{3} +(0.924390 + 0.336451i) q^{5} +(-1.51517 - 2.16893i) q^{7} +(-2.35445 - 1.85919i) q^{9} +(2.17655 - 0.792199i) q^{11} +(-0.0760705 - 0.431417i) q^{13} +(1.07569 - 1.32136i) q^{15} -0.0707882 q^{17} -0.639828 q^{19} +(-4.40967 + 1.24692i) q^{21} +(-1.21450 - 6.88778i) q^{23} +(-3.08892 - 2.59191i) q^{25} +(-4.37969 + 2.79613i) q^{27} +(0.0761311 - 0.431761i) q^{29} +(3.69688 - 3.10205i) q^{31} +(-0.0596402 - 4.01140i) q^{33} +(-0.670876 - 2.51472i) q^{35} +(-2.48013 + 4.29572i) q^{37} +(-0.749113 - 0.120635i) q^{39} +(-0.764696 - 4.33681i) q^{41} +(6.62677 + 5.56052i) q^{43} +(-1.55090 - 2.51077i) q^{45} +(3.02798 + 2.54078i) q^{47} +(-2.40849 + 6.57261i) q^{49} +(-0.0402172 + 0.115825i) q^{51} +(-2.26738 + 3.92722i) q^{53} +2.27852 q^{55} +(-0.363509 + 1.04690i) q^{57} +(-1.82083 - 10.3264i) q^{59} +(-0.973637 - 0.816979i) q^{61} +(-0.465050 + 7.92362i) q^{63} +(0.0748317 - 0.424392i) q^{65} +(8.87117 + 3.22884i) q^{67} +(-11.9599 - 1.92599i) q^{69} +(-3.96925 - 6.87494i) q^{71} +(-1.70862 - 2.95941i) q^{73} +(-5.99587 + 3.58161i) q^{75} +(-5.01608 - 3.52046i) q^{77} +(-0.214314 + 0.0780040i) q^{79} +(2.08683 + 8.75472i) q^{81} +(1.32377 - 7.50749i) q^{83} +(-0.0654359 - 0.0238167i) q^{85} +(-0.663204 - 0.369866i) q^{87} +1.64267 q^{89} +(-0.820453 + 0.818664i) q^{91} +(-2.97532 - 7.81131i) q^{93} +(-0.591451 - 0.215271i) q^{95} +(8.80304 + 7.38663i) q^{97} +(-6.59742 - 2.18143i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.568135 1.63622i 0.328013 0.944673i
\(4\) 0 0
\(5\) 0.924390 + 0.336451i 0.413400 + 0.150465i 0.540343 0.841445i \(-0.318294\pi\)
−0.126943 + 0.991910i \(0.540517\pi\)
\(6\) 0 0
\(7\) −1.51517 2.16893i −0.572682 0.819777i
\(8\) 0 0
\(9\) −2.35445 1.85919i −0.784815 0.619730i
\(10\) 0 0
\(11\) 2.17655 0.792199i 0.656255 0.238857i 0.00763609 0.999971i \(-0.497569\pi\)
0.648618 + 0.761114i \(0.275347\pi\)
\(12\) 0 0
\(13\) −0.0760705 0.431417i −0.0210982 0.119654i 0.972440 0.233154i \(-0.0749047\pi\)
−0.993538 + 0.113501i \(0.963794\pi\)
\(14\) 0 0
\(15\) 1.07569 1.32136i 0.277741 0.341173i
\(16\) 0 0
\(17\) −0.0707882 −0.0171687 −0.00858433 0.999963i \(-0.502733\pi\)
−0.00858433 + 0.999963i \(0.502733\pi\)
\(18\) 0 0
\(19\) −0.639828 −0.146787 −0.0733933 0.997303i \(-0.523383\pi\)
−0.0733933 + 0.997303i \(0.523383\pi\)
\(20\) 0 0
\(21\) −4.40967 + 1.24692i −0.962269 + 0.272100i
\(22\) 0 0
\(23\) −1.21450 6.88778i −0.253241 1.43620i −0.800548 0.599269i \(-0.795458\pi\)
0.547307 0.836932i \(-0.315653\pi\)
\(24\) 0 0
\(25\) −3.08892 2.59191i −0.617785 0.518383i
\(26\) 0 0
\(27\) −4.37969 + 2.79613i −0.842872 + 0.538115i
\(28\) 0 0
\(29\) 0.0761311 0.431761i 0.0141372 0.0801759i −0.976923 0.213592i \(-0.931484\pi\)
0.991060 + 0.133416i \(0.0425947\pi\)
\(30\) 0 0
\(31\) 3.69688 3.10205i 0.663980 0.557145i −0.247297 0.968940i \(-0.579542\pi\)
0.911277 + 0.411794i \(0.135098\pi\)
\(32\) 0 0
\(33\) −0.0596402 4.01140i −0.0103820 0.698294i
\(34\) 0 0
\(35\) −0.670876 2.51472i −0.113399 0.425065i
\(36\) 0 0
\(37\) −2.48013 + 4.29572i −0.407732 + 0.706212i −0.994635 0.103445i \(-0.967013\pi\)
0.586904 + 0.809657i \(0.300347\pi\)
\(38\) 0 0
\(39\) −0.749113 0.120635i −0.119954 0.0193171i
\(40\) 0 0
\(41\) −0.764696 4.33681i −0.119425 0.677295i −0.984464 0.175589i \(-0.943817\pi\)
0.865038 0.501706i \(-0.167294\pi\)
\(42\) 0 0
\(43\) 6.62677 + 5.56052i 1.01057 + 0.847972i 0.988414 0.151783i \(-0.0485014\pi\)
0.0221594 + 0.999754i \(0.492946\pi\)
\(44\) 0 0
\(45\) −1.55090 2.51077i −0.231195 0.374284i
\(46\) 0 0
\(47\) 3.02798 + 2.54078i 0.441677 + 0.370611i 0.836336 0.548217i \(-0.184693\pi\)
−0.394660 + 0.918827i \(0.629137\pi\)
\(48\) 0 0
\(49\) −2.40849 + 6.57261i −0.344070 + 0.938944i
\(50\) 0 0
\(51\) −0.0402172 + 0.115825i −0.00563154 + 0.0162188i
\(52\) 0 0
\(53\) −2.26738 + 3.92722i −0.311449 + 0.539445i −0.978676 0.205409i \(-0.934147\pi\)
0.667228 + 0.744854i \(0.267481\pi\)
\(54\) 0 0
\(55\) 2.27852 0.307235
\(56\) 0 0
\(57\) −0.363509 + 1.04690i −0.0481479 + 0.138665i
\(58\) 0 0
\(59\) −1.82083 10.3264i −0.237052 1.34439i −0.838249 0.545288i \(-0.816420\pi\)
0.601197 0.799101i \(-0.294691\pi\)
\(60\) 0 0
\(61\) −0.973637 0.816979i −0.124661 0.104603i 0.578326 0.815806i \(-0.303706\pi\)
−0.702987 + 0.711203i \(0.748151\pi\)
\(62\) 0 0
\(63\) −0.465050 + 7.92362i −0.0585908 + 0.998282i
\(64\) 0 0
\(65\) 0.0748317 0.424392i 0.00928174 0.0526393i
\(66\) 0 0
\(67\) 8.87117 + 3.22884i 1.08379 + 0.394466i 0.821315 0.570474i \(-0.193241\pi\)
0.262470 + 0.964940i \(0.415463\pi\)
\(68\) 0 0
\(69\) −11.9599 1.92599i −1.43981 0.231862i
\(70\) 0 0
\(71\) −3.96925 6.87494i −0.471063 0.815905i 0.528389 0.849002i \(-0.322796\pi\)
−0.999452 + 0.0330973i \(0.989463\pi\)
\(72\) 0 0
\(73\) −1.70862 2.95941i −0.199979 0.346373i 0.748543 0.663087i \(-0.230754\pi\)
−0.948521 + 0.316714i \(0.897421\pi\)
\(74\) 0 0
\(75\) −5.99587 + 3.58161i −0.692344 + 0.413568i
\(76\) 0 0
\(77\) −5.01608 3.52046i −0.571635 0.401193i
\(78\) 0 0
\(79\) −0.214314 + 0.0780040i −0.0241122 + 0.00877614i −0.354048 0.935227i \(-0.615195\pi\)
0.329936 + 0.944003i \(0.392973\pi\)
\(80\) 0 0
\(81\) 2.08683 + 8.75472i 0.231870 + 0.972747i
\(82\) 0 0
\(83\) 1.32377 7.50749i 0.145303 0.824055i −0.821820 0.569747i \(-0.807041\pi\)
0.967123 0.254308i \(-0.0818476\pi\)
\(84\) 0 0
\(85\) −0.0654359 0.0238167i −0.00709752 0.00258329i
\(86\) 0 0
\(87\) −0.663204 0.369866i −0.0711029 0.0396538i
\(88\) 0 0
\(89\) 1.64267 0.174123 0.0870614 0.996203i \(-0.472252\pi\)
0.0870614 + 0.996203i \(0.472252\pi\)
\(90\) 0 0
\(91\) −0.820453 + 0.818664i −0.0860068 + 0.0858193i
\(92\) 0 0
\(93\) −2.97532 7.81131i −0.308526 0.809995i
\(94\) 0 0
\(95\) −0.591451 0.215271i −0.0606816 0.0220863i
\(96\) 0 0
\(97\) 8.80304 + 7.38663i 0.893813 + 0.749998i 0.968971 0.247173i \(-0.0795017\pi\)
−0.0751579 + 0.997172i \(0.523946\pi\)
\(98\) 0 0
\(99\) −6.59742 2.18143i −0.663065 0.219242i
\(100\) 0 0
\(101\) 0.978500 5.54935i 0.0973644 0.552181i −0.896633 0.442775i \(-0.853994\pi\)
0.993997 0.109406i \(-0.0348949\pi\)
\(102\) 0 0
\(103\) 11.3798 + 4.14192i 1.12129 + 0.408116i 0.835122 0.550064i \(-0.185397\pi\)
0.286166 + 0.958180i \(0.407619\pi\)
\(104\) 0 0
\(105\) −4.49578 0.330996i −0.438743 0.0323019i
\(106\) 0 0
\(107\) 5.75760 + 9.97246i 0.556609 + 0.964074i 0.997776 + 0.0666497i \(0.0212310\pi\)
−0.441168 + 0.897425i \(0.645436\pi\)
\(108\) 0 0
\(109\) −4.26485 + 7.38694i −0.408499 + 0.707541i −0.994722 0.102609i \(-0.967281\pi\)
0.586223 + 0.810150i \(0.300614\pi\)
\(110\) 0 0
\(111\) 5.61970 + 6.49860i 0.533398 + 0.616820i
\(112\) 0 0
\(113\) 12.1155 10.1661i 1.13973 0.956344i 0.140297 0.990110i \(-0.455194\pi\)
0.999430 + 0.0337656i \(0.0107500\pi\)
\(114\) 0 0
\(115\) 1.19472 6.77561i 0.111409 0.631829i
\(116\) 0 0
\(117\) −0.622983 + 1.15718i −0.0575948 + 0.106981i
\(118\) 0 0
\(119\) 0.107256 + 0.153534i 0.00983218 + 0.0140745i
\(120\) 0 0
\(121\) −4.31670 + 3.62214i −0.392427 + 0.329285i
\(122\) 0 0
\(123\) −7.53043 1.21268i −0.678996 0.109344i
\(124\) 0 0
\(125\) −4.44261 7.69482i −0.397359 0.688246i
\(126\) 0 0
\(127\) −2.41882 + 4.18953i −0.214636 + 0.371760i −0.953160 0.302467i \(-0.902190\pi\)
0.738524 + 0.674227i \(0.235523\pi\)
\(128\) 0 0
\(129\) 12.8631 7.68374i 1.13254 0.676516i
\(130\) 0 0
\(131\) 1.93441 + 10.9706i 0.169010 + 0.958504i 0.944833 + 0.327553i \(0.106224\pi\)
−0.775823 + 0.630951i \(0.782665\pi\)
\(132\) 0 0
\(133\) 0.969452 + 1.38774i 0.0840621 + 0.120332i
\(134\) 0 0
\(135\) −4.98930 + 1.11116i −0.429411 + 0.0956336i
\(136\) 0 0
\(137\) 15.8464 + 13.2967i 1.35385 + 1.13602i 0.977829 + 0.209405i \(0.0671529\pi\)
0.376022 + 0.926611i \(0.377292\pi\)
\(138\) 0 0
\(139\) 20.1891 + 7.34824i 1.71242 + 0.623269i 0.997140 0.0755707i \(-0.0240778\pi\)
0.715278 + 0.698840i \(0.246300\pi\)
\(140\) 0 0
\(141\) 5.87758 3.51095i 0.494982 0.295675i
\(142\) 0 0
\(143\) −0.507340 0.878738i −0.0424259 0.0734838i
\(144\) 0 0
\(145\) 0.215641 0.373501i 0.0179080 0.0310176i
\(146\) 0 0
\(147\) 9.38590 + 7.67495i 0.774136 + 0.633019i
\(148\) 0 0
\(149\) 0.710501 0.596181i 0.0582065 0.0488410i −0.613220 0.789912i \(-0.710126\pi\)
0.671427 + 0.741071i \(0.265682\pi\)
\(150\) 0 0
\(151\) −2.76803 + 1.00748i −0.225259 + 0.0819877i −0.452184 0.891925i \(-0.649355\pi\)
0.226925 + 0.973912i \(0.427133\pi\)
\(152\) 0 0
\(153\) 0.166667 + 0.131609i 0.0134742 + 0.0106399i
\(154\) 0 0
\(155\) 4.46105 1.62369i 0.358320 0.130418i
\(156\) 0 0
\(157\) 0.711723 + 4.03638i 0.0568017 + 0.322138i 0.999948 0.0102407i \(-0.00325978\pi\)
−0.943146 + 0.332379i \(0.892149\pi\)
\(158\) 0 0
\(159\) 5.13762 + 5.94113i 0.407440 + 0.471162i
\(160\) 0 0
\(161\) −13.0989 + 13.0704i −1.03234 + 1.03009i
\(162\) 0 0
\(163\) 4.17014 + 7.22289i 0.326630 + 0.565740i 0.981841 0.189706i \(-0.0607535\pi\)
−0.655211 + 0.755446i \(0.727420\pi\)
\(164\) 0 0
\(165\) 1.29451 3.72816i 0.100777 0.290237i
\(166\) 0 0
\(167\) 14.4476 12.1230i 1.11799 0.938107i 0.119491 0.992835i \(-0.461874\pi\)
0.998501 + 0.0547283i \(0.0174293\pi\)
\(168\) 0 0
\(169\) 12.0357 4.38063i 0.925821 0.336971i
\(170\) 0 0
\(171\) 1.50644 + 1.18956i 0.115200 + 0.0909681i
\(172\) 0 0
\(173\) 1.44042 8.16901i 0.109513 0.621078i −0.879809 0.475328i \(-0.842329\pi\)
0.989321 0.145750i \(-0.0465596\pi\)
\(174\) 0 0
\(175\) −0.941414 + 10.6269i −0.0711642 + 0.803315i
\(176\) 0 0
\(177\) −17.9308 2.88753i −1.34776 0.217040i
\(178\) 0 0
\(179\) 1.83453 0.137120 0.0685598 0.997647i \(-0.478160\pi\)
0.0685598 + 0.997647i \(0.478160\pi\)
\(180\) 0 0
\(181\) 5.56664 9.64170i 0.413765 0.716662i −0.581533 0.813523i \(-0.697547\pi\)
0.995298 + 0.0968610i \(0.0308802\pi\)
\(182\) 0 0
\(183\) −1.88992 + 1.12893i −0.139707 + 0.0834531i
\(184\) 0 0
\(185\) −3.73791 + 3.13648i −0.274817 + 0.230599i
\(186\) 0 0
\(187\) −0.154074 + 0.0560784i −0.0112670 + 0.00410086i
\(188\) 0 0
\(189\) 12.7006 + 5.26261i 0.923832 + 0.382799i
\(190\) 0 0
\(191\) −0.565067 + 0.205667i −0.0408868 + 0.0148816i −0.362383 0.932029i \(-0.618037\pi\)
0.321496 + 0.946911i \(0.395814\pi\)
\(192\) 0 0
\(193\) −16.2542 + 13.6389i −1.17000 + 0.981750i −0.999993 0.00369161i \(-0.998825\pi\)
−0.170011 + 0.985442i \(0.554380\pi\)
\(194\) 0 0
\(195\) −0.651885 0.363553i −0.0466824 0.0260346i
\(196\) 0 0
\(197\) −7.86191 + 13.6172i −0.560138 + 0.970188i 0.437346 + 0.899293i \(0.355919\pi\)
−0.997484 + 0.0708942i \(0.977415\pi\)
\(198\) 0 0
\(199\) −20.1373 −1.42750 −0.713749 0.700402i \(-0.753004\pi\)
−0.713749 + 0.700402i \(0.753004\pi\)
\(200\) 0 0
\(201\) 10.3231 12.6808i 0.728137 0.894433i
\(202\) 0 0
\(203\) −1.05181 + 0.489070i −0.0738225 + 0.0343260i
\(204\) 0 0
\(205\) 0.752243 4.26618i 0.0525390 0.297963i
\(206\) 0 0
\(207\) −9.94621 + 18.4749i −0.691309 + 1.28409i
\(208\) 0 0
\(209\) −1.39262 + 0.506871i −0.0963294 + 0.0350610i
\(210\) 0 0
\(211\) −11.8097 + 9.90955i −0.813017 + 0.682202i −0.951326 0.308187i \(-0.900278\pi\)
0.138309 + 0.990389i \(0.455833\pi\)
\(212\) 0 0
\(213\) −13.5040 + 2.58868i −0.925278 + 0.177373i
\(214\) 0 0
\(215\) 4.25488 + 7.36967i 0.290181 + 0.502608i
\(216\) 0 0
\(217\) −12.3296 3.31812i −0.836985 0.225249i
\(218\) 0 0
\(219\) −5.81298 + 1.11433i −0.392805 + 0.0752996i
\(220\) 0 0
\(221\) 0.00538489 + 0.0305392i 0.000362227 + 0.00205429i
\(222\) 0 0
\(223\) 17.0256 6.19682i 1.14012 0.414970i 0.298163 0.954515i \(-0.403626\pi\)
0.841957 + 0.539545i \(0.181404\pi\)
\(224\) 0 0
\(225\) 2.45384 + 11.8454i 0.163589 + 0.789695i
\(226\) 0 0
\(227\) 15.3048 5.57050i 1.01582 0.369727i 0.220153 0.975465i \(-0.429344\pi\)
0.795664 + 0.605738i \(0.207122\pi\)
\(228\) 0 0
\(229\) 0.341403 0.286471i 0.0225605 0.0189305i −0.631438 0.775427i \(-0.717535\pi\)
0.653998 + 0.756496i \(0.273090\pi\)
\(230\) 0 0
\(231\) −8.61006 + 6.20732i −0.566500 + 0.408412i
\(232\) 0 0
\(233\) 11.8701 20.5596i 0.777634 1.34690i −0.155668 0.987810i \(-0.549753\pi\)
0.933302 0.359093i \(-0.116914\pi\)
\(234\) 0 0
\(235\) 1.94419 + 3.36744i 0.126825 + 0.219668i
\(236\) 0 0
\(237\) 0.00587248 + 0.394983i 0.000381458 + 0.0256569i
\(238\) 0 0
\(239\) −7.43765 2.70709i −0.481102 0.175107i 0.0900730 0.995935i \(-0.471290\pi\)
−0.571175 + 0.820828i \(0.693512\pi\)
\(240\) 0 0
\(241\) −1.10082 0.923694i −0.0709097 0.0595003i 0.606644 0.794974i \(-0.292515\pi\)
−0.677554 + 0.735473i \(0.736960\pi\)
\(242\) 0 0
\(243\) 15.5103 + 1.55935i 0.994984 + 0.100032i
\(244\) 0 0
\(245\) −4.43774 + 5.26532i −0.283517 + 0.336389i
\(246\) 0 0
\(247\) 0.0486720 + 0.276033i 0.00309693 + 0.0175636i
\(248\) 0 0
\(249\) −11.5318 6.43126i −0.730801 0.407564i
\(250\) 0 0
\(251\) 8.96367 15.5255i 0.565782 0.979962i −0.431195 0.902259i \(-0.641908\pi\)
0.996977 0.0777036i \(-0.0247588\pi\)
\(252\) 0 0
\(253\) −8.09992 14.0295i −0.509237 0.882025i
\(254\) 0 0
\(255\) −0.0761459 + 0.0935366i −0.00476844 + 0.00585749i
\(256\) 0 0
\(257\) −17.7194 + 14.8683i −1.10530 + 0.927460i −0.997770 0.0667413i \(-0.978740\pi\)
−0.107534 + 0.994201i \(0.534295\pi\)
\(258\) 0 0
\(259\) 13.0749 1.12954i 0.812437 0.0701859i
\(260\) 0 0
\(261\) −0.981971 + 0.875015i −0.0607825 + 0.0541621i
\(262\) 0 0
\(263\) −2.72362 + 15.4464i −0.167945 + 0.952465i 0.778030 + 0.628227i \(0.216219\pi\)
−0.945975 + 0.324238i \(0.894892\pi\)
\(264\) 0 0
\(265\) −3.41726 + 2.86742i −0.209920 + 0.176144i
\(266\) 0 0
\(267\) 0.933259 2.68778i 0.0571145 0.164489i
\(268\) 0 0
\(269\) −9.94507 + 17.2254i −0.606362 + 1.05025i 0.385473 + 0.922719i \(0.374038\pi\)
−0.991835 + 0.127530i \(0.959295\pi\)
\(270\) 0 0
\(271\) 1.36148 + 2.35815i 0.0827038 + 0.143247i 0.904410 0.426663i \(-0.140311\pi\)
−0.821707 + 0.569911i \(0.806978\pi\)
\(272\) 0 0
\(273\) 0.873389 + 1.80755i 0.0528599 + 0.109398i
\(274\) 0 0
\(275\) −8.77651 3.19439i −0.529244 0.192629i
\(276\) 0 0
\(277\) −0.705456 + 4.00084i −0.0423867 + 0.240387i −0.998639 0.0521564i \(-0.983391\pi\)
0.956252 + 0.292544i \(0.0945017\pi\)
\(278\) 0 0
\(279\) −14.4714 + 0.430408i −0.866381 + 0.0257679i
\(280\) 0 0
\(281\) 11.2218 + 9.41620i 0.669436 + 0.561724i 0.912898 0.408187i \(-0.133839\pi\)
−0.243462 + 0.969910i \(0.578283\pi\)
\(282\) 0 0
\(283\) 26.9033 + 9.79201i 1.59924 + 0.582074i 0.979271 0.202555i \(-0.0649244\pi\)
0.619965 + 0.784629i \(0.287147\pi\)
\(284\) 0 0
\(285\) −0.688254 + 0.845442i −0.0407687 + 0.0500797i
\(286\) 0 0
\(287\) −8.24757 + 8.22959i −0.486839 + 0.485777i
\(288\) 0 0
\(289\) −16.9950 −0.999705
\(290\) 0 0
\(291\) 17.0875 10.2071i 1.00169 0.598352i
\(292\) 0 0
\(293\) 5.06330 + 1.84289i 0.295801 + 0.107663i 0.485658 0.874149i \(-0.338580\pi\)
−0.189857 + 0.981812i \(0.560802\pi\)
\(294\) 0 0
\(295\) 1.79118 10.1583i 0.104287 0.591438i
\(296\) 0 0
\(297\) −7.31753 + 9.55549i −0.424606 + 0.554466i
\(298\) 0 0
\(299\) −2.87912 + 1.04791i −0.166504 + 0.0606024i
\(300\) 0 0
\(301\) 2.01965 22.7981i 0.116411 1.31406i
\(302\) 0 0
\(303\) −8.52405 4.75382i −0.489694 0.273100i
\(304\) 0 0
\(305\) −0.625148 1.08279i −0.0357959 0.0620002i
\(306\) 0 0
\(307\) 5.61320 + 9.72235i 0.320362 + 0.554884i 0.980563 0.196206i \(-0.0628620\pi\)
−0.660200 + 0.751089i \(0.729529\pi\)
\(308\) 0 0
\(309\) 13.2424 16.2668i 0.753333 0.925384i
\(310\) 0 0
\(311\) −12.0130 4.37236i −0.681193 0.247934i −0.0218333 0.999762i \(-0.506950\pi\)
−0.659360 + 0.751828i \(0.729173\pi\)
\(312\) 0 0
\(313\) 2.98614 16.9353i 0.168787 0.957237i −0.776287 0.630380i \(-0.782899\pi\)
0.945074 0.326857i \(-0.105990\pi\)
\(314\) 0 0
\(315\) −3.09579 + 7.16805i −0.174428 + 0.403874i
\(316\) 0 0
\(317\) −20.0577 16.8304i −1.12655 0.945290i −0.127636 0.991821i \(-0.540739\pi\)
−0.998917 + 0.0465309i \(0.985183\pi\)
\(318\) 0 0
\(319\) −0.176338 1.00006i −0.00987300 0.0559926i
\(320\) 0 0
\(321\) 19.5883 3.75501i 1.09331 0.209584i
\(322\) 0 0
\(323\) 0.0452923 0.00252013
\(324\) 0 0
\(325\) −0.883221 + 1.52978i −0.0489923 + 0.0848571i
\(326\) 0 0
\(327\) 9.66366 + 11.1750i 0.534402 + 0.617980i
\(328\) 0 0
\(329\) 0.922842 10.4172i 0.0508779 0.574319i
\(330\) 0 0
\(331\) −18.4058 15.4443i −1.01167 0.848896i −0.0231161 0.999733i \(-0.507359\pi\)
−0.988559 + 0.150837i \(0.951803\pi\)
\(332\) 0 0
\(333\) 13.8259 5.50300i 0.757655 0.301562i
\(334\) 0 0
\(335\) 7.11408 + 5.96942i 0.388683 + 0.326144i
\(336\) 0 0
\(337\) 0.216639 + 1.22862i 0.0118011 + 0.0669272i 0.990140 0.140084i \(-0.0447374\pi\)
−0.978339 + 0.207011i \(0.933626\pi\)
\(338\) 0 0
\(339\) −9.75074 25.5993i −0.529588 1.39036i
\(340\) 0 0
\(341\) 5.58901 9.68045i 0.302662 0.524226i
\(342\) 0 0
\(343\) 17.9048 4.73481i 0.966768 0.255656i
\(344\) 0 0
\(345\) −10.4076 5.80430i −0.560329 0.312493i
\(346\) 0 0
\(347\) 21.3643 17.9268i 1.14689 0.962359i 0.147252 0.989099i \(-0.452957\pi\)
0.999642 + 0.0267405i \(0.00851279\pi\)
\(348\) 0 0
\(349\) 4.39046 24.8995i 0.235016 1.33284i −0.607565 0.794270i \(-0.707854\pi\)
0.842581 0.538570i \(-0.181035\pi\)
\(350\) 0 0
\(351\) 1.53946 + 1.67677i 0.0821704 + 0.0894994i
\(352\) 0 0
\(353\) 17.1107 + 14.3576i 0.910712 + 0.764178i 0.972254 0.233926i \(-0.0751574\pi\)
−0.0615422 + 0.998104i \(0.519602\pi\)
\(354\) 0 0
\(355\) −1.35606 7.69058i −0.0719720 0.408174i
\(356\) 0 0
\(357\) 0.312152 0.0882672i 0.0165209 0.00467159i
\(358\) 0 0
\(359\) −33.7116 −1.77923 −0.889615 0.456711i \(-0.849027\pi\)
−0.889615 + 0.456711i \(0.849027\pi\)
\(360\) 0 0
\(361\) −18.5906 −0.978454
\(362\) 0 0
\(363\) 3.47416 + 9.12094i 0.182346 + 0.478725i
\(364\) 0 0
\(365\) −0.583734 3.31052i −0.0305540 0.173281i
\(366\) 0 0
\(367\) 11.4582 4.17046i 0.598115 0.217696i −0.0251797 0.999683i \(-0.508016\pi\)
0.623295 + 0.781987i \(0.285794\pi\)
\(368\) 0 0
\(369\) −6.26251 + 11.6325i −0.326013 + 0.605563i
\(370\) 0 0
\(371\) 11.9533 1.03264i 0.620586 0.0536120i
\(372\) 0 0
\(373\) −4.30247 1.56597i −0.222773 0.0810829i 0.228222 0.973609i \(-0.426709\pi\)
−0.450996 + 0.892526i \(0.648931\pi\)
\(374\) 0 0
\(375\) −15.1144 + 2.89740i −0.780506 + 0.149621i
\(376\) 0 0
\(377\) −0.192060 −0.00989161
\(378\) 0 0
\(379\) −18.2509 −0.937486 −0.468743 0.883334i \(-0.655293\pi\)
−0.468743 + 0.883334i \(0.655293\pi\)
\(380\) 0 0
\(381\) 5.48078 + 6.33795i 0.280789 + 0.324703i
\(382\) 0 0
\(383\) −24.3184 8.85116i −1.24261 0.452273i −0.364712 0.931120i \(-0.618833\pi\)
−0.877898 + 0.478847i \(0.841055\pi\)
\(384\) 0 0
\(385\) −3.45235 4.94194i −0.175948 0.251865i
\(386\) 0 0
\(387\) −5.26431 25.4124i −0.267600 1.29178i
\(388\) 0 0
\(389\) 16.6769 6.06989i 0.845552 0.307756i 0.117326 0.993093i \(-0.462568\pi\)
0.728225 + 0.685338i \(0.240345\pi\)
\(390\) 0 0
\(391\) 0.0859723 + 0.487573i 0.00434781 + 0.0246576i
\(392\) 0 0
\(393\) 19.0493 + 3.06765i 0.960911 + 0.154742i
\(394\) 0 0
\(395\) −0.224355 −0.0112885
\(396\) 0 0
\(397\) −6.40127 −0.321270 −0.160635 0.987014i \(-0.551354\pi\)
−0.160635 + 0.987014i \(0.551354\pi\)
\(398\) 0 0
\(399\) 2.82143 0.797814i 0.141248 0.0399407i
\(400\) 0 0
\(401\) 0.543269 + 3.08103i 0.0271296 + 0.153859i 0.995363 0.0961878i \(-0.0306649\pi\)
−0.968234 + 0.250047i \(0.919554\pi\)
\(402\) 0 0
\(403\) −1.61950 1.35893i −0.0806732 0.0676929i
\(404\) 0 0
\(405\) −1.01649 + 8.79489i −0.0505097 + 0.437022i
\(406\) 0 0
\(407\) −1.99507 + 11.3146i −0.0988920 + 0.560844i
\(408\) 0 0
\(409\) −16.3666 + 13.7332i −0.809277 + 0.679064i −0.950435 0.310923i \(-0.899362\pi\)
0.141158 + 0.989987i \(0.454918\pi\)
\(410\) 0 0
\(411\) 30.7593 18.3739i 1.51724 0.906319i
\(412\) 0 0
\(413\) −19.6384 + 19.5956i −0.966344 + 0.964238i
\(414\) 0 0
\(415\) 3.74958 6.49447i 0.184060 0.318801i
\(416\) 0 0
\(417\) 23.4935 28.8591i 1.15048 1.41324i
\(418\) 0 0
\(419\) −5.11435 29.0049i −0.249852 1.41698i −0.808948 0.587880i \(-0.799963\pi\)
0.559096 0.829103i \(-0.311148\pi\)
\(420\) 0 0
\(421\) −1.53987 1.29210i −0.0750487 0.0629733i 0.604492 0.796612i \(-0.293376\pi\)
−0.679540 + 0.733638i \(0.737821\pi\)
\(422\) 0 0
\(423\) −2.40543 11.6117i −0.116956 0.564581i
\(424\) 0 0
\(425\) 0.218659 + 0.183477i 0.0106065 + 0.00889994i
\(426\) 0 0
\(427\) −0.296736 + 3.34961i −0.0143601 + 0.162099i
\(428\) 0 0
\(429\) −1.72605 + 0.330879i −0.0833344 + 0.0159750i
\(430\) 0 0
\(431\) −11.8904 + 20.5947i −0.572739 + 0.992014i 0.423544 + 0.905876i \(0.360786\pi\)
−0.996283 + 0.0861382i \(0.972547\pi\)
\(432\) 0 0
\(433\) 7.91761 0.380496 0.190248 0.981736i \(-0.439071\pi\)
0.190248 + 0.981736i \(0.439071\pi\)
\(434\) 0 0
\(435\) −0.488617 0.565035i −0.0234274 0.0270914i
\(436\) 0 0
\(437\) 0.777072 + 4.40699i 0.0371724 + 0.210815i
\(438\) 0 0
\(439\) −29.7095 24.9292i −1.41796 1.18981i −0.952423 0.304778i \(-0.901418\pi\)
−0.465535 0.885030i \(-0.654138\pi\)
\(440\) 0 0
\(441\) 17.8904 10.9970i 0.851923 0.523667i
\(442\) 0 0
\(443\) 2.51368 14.2558i 0.119429 0.677313i −0.865033 0.501714i \(-0.832703\pi\)
0.984462 0.175598i \(-0.0561860\pi\)
\(444\) 0 0
\(445\) 1.51847 + 0.552678i 0.0719824 + 0.0261994i
\(446\) 0 0
\(447\) −0.571824 1.50125i −0.0270463 0.0710066i
\(448\) 0 0
\(449\) 8.12221 + 14.0681i 0.383311 + 0.663914i 0.991533 0.129853i \(-0.0414505\pi\)
−0.608222 + 0.793767i \(0.708117\pi\)
\(450\) 0 0
\(451\) −5.10001 8.83348i −0.240150 0.415953i
\(452\) 0 0
\(453\) 0.0758475 + 5.10150i 0.00356363 + 0.239689i
\(454\) 0 0
\(455\) −1.03386 + 0.480723i −0.0484680 + 0.0225367i
\(456\) 0 0
\(457\) −11.9071 + 4.33383i −0.556990 + 0.202728i −0.605150 0.796112i \(-0.706887\pi\)
0.0481593 + 0.998840i \(0.484664\pi\)
\(458\) 0 0
\(459\) 0.310030 0.197933i 0.0144710 0.00923870i
\(460\) 0 0
\(461\) −1.95397 + 11.0815i −0.0910055 + 0.516118i 0.904893 + 0.425639i \(0.139951\pi\)
−0.995898 + 0.0904786i \(0.971160\pi\)
\(462\) 0 0
\(463\) −34.9431 12.7183i −1.62394 0.591068i −0.639817 0.768527i \(-0.720990\pi\)
−0.984128 + 0.177460i \(0.943212\pi\)
\(464\) 0 0
\(465\) −0.122238 8.22175i −0.00566867 0.381274i
\(466\) 0 0
\(467\) −38.0252 −1.75960 −0.879799 0.475345i \(-0.842323\pi\)
−0.879799 + 0.475345i \(0.842323\pi\)
\(468\) 0 0
\(469\) −6.43825 24.1332i −0.297291 1.11437i
\(470\) 0 0
\(471\) 7.00877 + 1.12867i 0.322947 + 0.0520065i
\(472\) 0 0
\(473\) 18.8285 + 6.85303i 0.865737 + 0.315103i
\(474\) 0 0
\(475\) 1.97638 + 1.65838i 0.0906825 + 0.0760917i
\(476\) 0 0
\(477\) 12.6399 5.03093i 0.578740 0.230350i
\(478\) 0 0
\(479\) 0.506346 2.87163i 0.0231355 0.131208i −0.971052 0.238867i \(-0.923224\pi\)
0.994188 + 0.107658i \(0.0343353\pi\)
\(480\) 0 0
\(481\) 2.04191 + 0.743196i 0.0931032 + 0.0338868i
\(482\) 0 0
\(483\) 13.9441 + 28.8584i 0.634476 + 1.31310i
\(484\) 0 0
\(485\) 5.65221 + 9.78992i 0.256654 + 0.444537i
\(486\) 0 0
\(487\) −17.4368 + 30.2014i −0.790136 + 1.36856i 0.135746 + 0.990744i \(0.456657\pi\)
−0.925882 + 0.377812i \(0.876677\pi\)
\(488\) 0 0
\(489\) 14.1874 2.71969i 0.641579 0.122989i
\(490\) 0 0
\(491\) −19.9781 + 16.7636i −0.901599 + 0.756531i −0.970502 0.241092i \(-0.922494\pi\)
0.0689034 + 0.997623i \(0.478050\pi\)
\(492\) 0 0
\(493\) −0.00538918 + 0.0305635i −0.000242716 + 0.00137651i
\(494\) 0 0
\(495\) −5.36465 4.23620i −0.241123 0.190403i
\(496\) 0 0
\(497\) −8.89713 + 19.0257i −0.399091 + 0.853421i
\(498\) 0 0
\(499\) 18.8204 15.7922i 0.842517 0.706956i −0.115611 0.993295i \(-0.536883\pi\)
0.958129 + 0.286339i \(0.0924382\pi\)
\(500\) 0 0
\(501\) −11.6277 30.5271i −0.519489 1.36385i
\(502\) 0 0
\(503\) −13.4101 23.2270i −0.597929 1.03564i −0.993126 0.117047i \(-0.962657\pi\)
0.395198 0.918596i \(-0.370676\pi\)
\(504\) 0 0
\(505\) 2.77160 4.80055i 0.123335 0.213622i
\(506\) 0 0
\(507\) −0.329792 22.1818i −0.0146466 0.985129i
\(508\) 0 0
\(509\) 2.69329 + 15.2744i 0.119378 + 0.677027i 0.984489 + 0.175446i \(0.0561369\pi\)
−0.865111 + 0.501581i \(0.832752\pi\)
\(510\) 0 0
\(511\) −3.82990 + 8.18990i −0.169425 + 0.362300i
\(512\) 0 0
\(513\) 2.80225 1.78904i 0.123722 0.0789880i
\(514\) 0 0
\(515\) 9.12586 + 7.65750i 0.402133 + 0.337430i
\(516\) 0 0
\(517\) 8.60336 + 3.13137i 0.378376 + 0.137717i
\(518\) 0 0
\(519\) −12.5480 6.99794i −0.550795 0.307176i
\(520\) 0 0
\(521\) 3.33632 + 5.77867i 0.146167 + 0.253168i 0.929808 0.368046i \(-0.119973\pi\)
−0.783641 + 0.621214i \(0.786640\pi\)
\(522\) 0 0
\(523\) −0.871304 + 1.50914i −0.0380995 + 0.0659902i −0.884446 0.466642i \(-0.845464\pi\)
0.846347 + 0.532632i \(0.178797\pi\)
\(524\) 0 0
\(525\) 16.8530 + 7.57785i 0.735527 + 0.330724i
\(526\) 0 0
\(527\) −0.261696 + 0.219589i −0.0113996 + 0.00956544i
\(528\) 0 0
\(529\) −24.3535 + 8.86396i −1.05885 + 0.385390i
\(530\) 0 0
\(531\) −14.9118 + 27.6983i −0.647116 + 1.20201i
\(532\) 0 0
\(533\) −1.81280 + 0.659806i −0.0785212 + 0.0285794i
\(534\) 0 0
\(535\) 1.96703 + 11.1556i 0.0850422 + 0.482298i
\(536\) 0 0
\(537\) 1.04226 3.00171i 0.0449770 0.129533i
\(538\) 0 0
\(539\) −0.0353816 + 16.2136i −0.00152399 + 0.698370i
\(540\) 0 0
\(541\) −2.64106 4.57445i −0.113548 0.196671i 0.803650 0.595102i \(-0.202888\pi\)
−0.917198 + 0.398431i \(0.869555\pi\)
\(542\) 0 0
\(543\) −12.6134 14.5860i −0.541291 0.625947i
\(544\) 0 0
\(545\) −6.42773 + 5.39350i −0.275334 + 0.231032i
\(546\) 0 0
\(547\) 0.0366163 0.0133272i 0.00156560 0.000569832i −0.341237 0.939977i \(-0.610846\pi\)
0.342803 + 0.939407i \(0.388624\pi\)
\(548\) 0 0
\(549\) 0.773457 + 3.73371i 0.0330104 + 0.159351i
\(550\) 0 0
\(551\) −0.0487108 + 0.276253i −0.00207515 + 0.0117688i
\(552\) 0 0
\(553\) 0.493909 + 0.346642i 0.0210031 + 0.0147407i
\(554\) 0 0
\(555\) 3.00834 + 7.89799i 0.127697 + 0.335251i
\(556\) 0 0
\(557\) 25.4419 1.07801 0.539003 0.842304i \(-0.318801\pi\)
0.539003 + 0.842304i \(0.318801\pi\)
\(558\) 0 0
\(559\) 1.89480 3.28190i 0.0801416 0.138809i
\(560\) 0 0
\(561\) 0.00422182 + 0.283959i 0.000178245 + 0.0119888i
\(562\) 0 0
\(563\) 24.2182 20.3215i 1.02068 0.856448i 0.0309629 0.999521i \(-0.490143\pi\)
0.989712 + 0.143072i \(0.0456982\pi\)
\(564\) 0 0
\(565\) 14.6198 5.32117i 0.615059 0.223863i
\(566\) 0 0
\(567\) 15.8264 17.7911i 0.664648 0.747156i
\(568\) 0 0
\(569\) 15.8922 5.78428i 0.666235 0.242490i 0.0133088 0.999911i \(-0.495764\pi\)
0.652926 + 0.757422i \(0.273541\pi\)
\(570\) 0 0
\(571\) 10.9549 9.19222i 0.458447 0.384682i −0.384112 0.923286i \(-0.625493\pi\)
0.842559 + 0.538604i \(0.181048\pi\)
\(572\) 0 0
\(573\) 0.0154835 + 1.04142i 0.000646834 + 0.0435060i
\(574\) 0 0
\(575\) −14.1010 + 24.4237i −0.588054 + 1.01854i
\(576\) 0 0
\(577\) −30.1251 −1.25413 −0.627063 0.778969i \(-0.715743\pi\)
−0.627063 + 0.778969i \(0.715743\pi\)
\(578\) 0 0
\(579\) 13.0817 + 34.3443i 0.543657 + 1.42730i
\(580\) 0 0
\(581\) −18.2890 + 8.50400i −0.758754 + 0.352805i
\(582\) 0 0
\(583\) −1.82393 + 10.3440i −0.0755393 + 0.428405i
\(584\) 0 0
\(585\) −0.965212 + 0.860081i −0.0399066 + 0.0355600i
\(586\) 0 0
\(587\) −3.93620 + 1.43266i −0.162464 + 0.0591322i −0.421972 0.906609i \(-0.638662\pi\)
0.259508 + 0.965741i \(0.416440\pi\)
\(588\) 0 0
\(589\) −2.36537 + 1.98478i −0.0974634 + 0.0817815i
\(590\) 0 0
\(591\) 17.8142 + 20.6003i 0.732778 + 0.847381i
\(592\) 0 0
\(593\) 21.7491 + 37.6706i 0.893129 + 1.54694i 0.836103 + 0.548572i \(0.184828\pi\)
0.0570258 + 0.998373i \(0.481838\pi\)
\(594\) 0 0
\(595\) 0.0474901 + 0.178012i 0.00194690 + 0.00729779i
\(596\) 0 0
\(597\) −11.4407 + 32.9491i −0.468237 + 1.34852i
\(598\) 0 0
\(599\) −1.85508 10.5207i −0.0757965 0.429864i −0.998966 0.0454696i \(-0.985522\pi\)
0.923169 0.384394i \(-0.125590\pi\)
\(600\) 0 0
\(601\) 7.03554 2.56073i 0.286986 0.104454i −0.194516 0.980899i \(-0.562314\pi\)
0.481502 + 0.876445i \(0.340091\pi\)
\(602\) 0 0
\(603\) −14.8837 24.0953i −0.606109 0.981237i
\(604\) 0 0
\(605\) −5.20899 + 1.89592i −0.211775 + 0.0770799i
\(606\) 0 0
\(607\) 22.6747 19.0263i 0.920338 0.772256i −0.0537192 0.998556i \(-0.517108\pi\)
0.974058 + 0.226301i \(0.0726631\pi\)
\(608\) 0 0
\(609\) 0.202658 + 1.99885i 0.00821212 + 0.0809975i
\(610\) 0 0
\(611\) 0.865796 1.49960i 0.0350264 0.0606674i
\(612\) 0 0
\(613\) 12.8537 + 22.2632i 0.519155 + 0.899202i 0.999752 + 0.0222609i \(0.00708645\pi\)
−0.480598 + 0.876941i \(0.659580\pi\)
\(614\) 0 0
\(615\) −6.55305 3.65461i −0.264244 0.147368i
\(616\) 0 0
\(617\) 12.4910 + 4.54635i 0.502868 + 0.183029i 0.580983 0.813915i \(-0.302668\pi\)
−0.0781155 + 0.996944i \(0.524890\pi\)
\(618\) 0 0
\(619\) −13.0690 10.9662i −0.525288 0.440769i 0.341183 0.939997i \(-0.389172\pi\)
−0.866471 + 0.499228i \(0.833617\pi\)
\(620\) 0 0
\(621\) 24.5782 + 26.7704i 0.986290 + 1.07426i
\(622\) 0 0
\(623\) −2.48894 3.56284i −0.0997171 0.142742i
\(624\) 0 0
\(625\) 1.98323 + 11.2475i 0.0793294 + 0.449899i
\(626\) 0 0
\(627\) 0.0381595 + 2.56660i 0.00152394 + 0.102500i
\(628\) 0 0
\(629\) 0.175564 0.304086i 0.00700020 0.0121247i
\(630\) 0 0
\(631\) −7.55606 13.0875i −0.300802 0.521004i 0.675516 0.737345i \(-0.263921\pi\)
−0.976318 + 0.216341i \(0.930588\pi\)
\(632\) 0 0
\(633\) 9.50470 + 24.9533i 0.377778 + 0.991806i
\(634\) 0 0
\(635\) −3.64551 + 3.05894i −0.144667 + 0.121390i
\(636\) 0 0
\(637\) 3.01875 + 0.539082i 0.119607 + 0.0213592i
\(638\) 0 0
\(639\) −3.43644 + 23.5662i −0.135943 + 0.932266i
\(640\) 0 0
\(641\) −5.53943 + 31.4157i −0.218794 + 1.24084i 0.655405 + 0.755278i \(0.272498\pi\)
−0.874199 + 0.485567i \(0.838613\pi\)
\(642\) 0 0
\(643\) 9.81337 8.23439i 0.387002 0.324733i −0.428442 0.903569i \(-0.640937\pi\)
0.815444 + 0.578836i \(0.196493\pi\)
\(644\) 0 0
\(645\) 14.4758 2.77496i 0.569983 0.109264i
\(646\) 0 0
\(647\) −6.43583 + 11.1472i −0.253019 + 0.438241i −0.964355 0.264610i \(-0.914757\pi\)
0.711337 + 0.702851i \(0.248090\pi\)
\(648\) 0 0
\(649\) −12.1437 21.0336i −0.476683 0.825640i
\(650\) 0 0
\(651\) −12.4340 + 18.2888i −0.487328 + 0.716793i
\(652\) 0 0
\(653\) 7.35391 + 2.67660i 0.287781 + 0.104744i 0.481877 0.876239i \(-0.339955\pi\)
−0.194096 + 0.980982i \(0.562177\pi\)
\(654\) 0 0
\(655\) −1.90291 + 10.7919i −0.0743528 + 0.421676i
\(656\) 0 0
\(657\) −1.47926 + 10.1444i −0.0577116 + 0.395772i
\(658\) 0 0
\(659\) 27.7152 + 23.2559i 1.07963 + 0.905919i 0.995890 0.0905680i \(-0.0288683\pi\)
0.0837424 + 0.996487i \(0.473313\pi\)
\(660\) 0 0
\(661\) −9.22697 3.35834i −0.358887 0.130624i 0.156282 0.987712i \(-0.450049\pi\)
−0.515170 + 0.857088i \(0.672271\pi\)
\(662\) 0 0
\(663\) 0.0530283 + 0.00853953i 0.00205945 + 0.000331648i
\(664\) 0 0
\(665\) 0.429245 + 1.60899i 0.0166454 + 0.0623938i
\(666\) 0 0
\(667\) −3.06633 −0.118729
\(668\) 0 0
\(669\) −0.466523 31.3783i −0.0180368 1.21316i
\(670\) 0 0
\(671\) −2.76638 1.00688i −0.106795 0.0388702i
\(672\) 0 0
\(673\) −0.805359 + 4.56742i −0.0310443 + 0.176061i −0.996388 0.0849225i \(-0.972936\pi\)
0.965343 + 0.260984i \(0.0840468\pi\)
\(674\) 0 0
\(675\) 20.7758 + 2.71477i 0.799663 + 0.104491i
\(676\) 0 0
\(677\) −39.6213 + 14.4210i −1.52277 + 0.554243i −0.961838 0.273618i \(-0.911780\pi\)
−0.560932 + 0.827862i \(0.689557\pi\)
\(678\) 0 0
\(679\) 2.68291 30.2852i 0.102961 1.16224i
\(680\) 0 0
\(681\) −0.419371 28.2069i −0.0160703 1.08089i
\(682\) 0 0
\(683\) −16.2839 28.2046i −0.623087 1.07922i −0.988908 0.148533i \(-0.952545\pi\)
0.365821 0.930685i \(-0.380788\pi\)
\(684\) 0 0
\(685\) 10.1746 + 17.6229i 0.388751 + 0.673336i
\(686\) 0 0
\(687\) −0.274767 0.721365i −0.0104830 0.0275218i
\(688\) 0 0
\(689\) 1.86675 + 0.679441i 0.0711175 + 0.0258847i
\(690\) 0 0
\(691\) 6.12694 34.7476i 0.233080 1.32186i −0.613541 0.789663i \(-0.710255\pi\)
0.846620 0.532197i \(-0.178634\pi\)
\(692\) 0 0
\(693\) 5.26488 + 17.6146i 0.199996 + 0.669122i
\(694\) 0 0
\(695\) 16.1903 + 13.5853i 0.614133 + 0.515319i
\(696\) 0 0
\(697\) 0.0541314 + 0.306995i 0.00205037 + 0.0116282i
\(698\) 0 0
\(699\) −26.8962 31.1027i −1.01731 1.17641i
\(700\) 0 0
\(701\) 11.6825 0.441243 0.220621 0.975360i \(-0.429192\pi\)
0.220621 + 0.975360i \(0.429192\pi\)
\(702\) 0 0
\(703\) 1.58686 2.74852i 0.0598496 0.103662i
\(704\) 0 0
\(705\) 6.61444 1.26797i 0.249114 0.0477545i
\(706\) 0 0
\(707\) −13.5187 + 6.28594i −0.508424 + 0.236407i
\(708\) 0 0
\(709\) 38.1091 + 31.9774i 1.43122 + 1.20093i 0.944988 + 0.327104i \(0.106073\pi\)
0.486230 + 0.873831i \(0.338372\pi\)
\(710\) 0 0
\(711\) 0.649616 + 0.214795i 0.0243625 + 0.00805543i
\(712\) 0 0
\(713\) −25.8561 21.6959i −0.968320 0.812517i
\(714\) 0 0
\(715\) −0.173328 0.982992i −0.00648210 0.0367618i
\(716\) 0 0
\(717\) −8.65498 + 10.6317i −0.323226 + 0.397047i
\(718\) 0 0
\(719\) 19.0285 32.9583i 0.709643 1.22914i −0.255347 0.966850i \(-0.582190\pi\)
0.964990 0.262288i \(-0.0844771\pi\)
\(720\) 0 0
\(721\) −8.25891 30.9578i −0.307578 1.15293i
\(722\) 0 0
\(723\) −2.13678 + 1.27640i −0.0794677 + 0.0474697i
\(724\) 0 0
\(725\) −1.35425 + 1.13635i −0.0502956 + 0.0422030i
\(726\) 0 0
\(727\) −7.75664 + 43.9901i −0.287678 + 1.63150i 0.407883 + 0.913034i \(0.366267\pi\)
−0.695561 + 0.718467i \(0.744844\pi\)
\(728\) 0 0
\(729\) 11.3634 24.4923i 0.420866 0.907123i
\(730\) 0 0
\(731\) −0.469097 0.393619i −0.0173502 0.0145585i
\(732\) 0 0
\(733\) 4.55055 + 25.8075i 0.168078 + 0.953220i 0.945833 + 0.324653i \(0.105247\pi\)
−0.777755 + 0.628568i \(0.783641\pi\)
\(734\) 0 0
\(735\) 6.09399 + 10.2525i 0.224780 + 0.378171i
\(736\) 0 0
\(737\) 21.8664 0.805460
\(738\) 0 0
\(739\) 32.5923 1.19893 0.599464 0.800402i \(-0.295381\pi\)
0.599464 + 0.800402i \(0.295381\pi\)
\(740\) 0 0
\(741\) 0.479303 + 0.0771856i 0.0176077 + 0.00283549i
\(742\) 0 0
\(743\) −6.00324 34.0461i −0.220237 1.24903i −0.871583 0.490248i \(-0.836906\pi\)
0.651346 0.758781i \(-0.274205\pi\)
\(744\) 0 0
\(745\) 0.857365 0.312055i 0.0314114 0.0114328i
\(746\) 0 0
\(747\) −17.0746 + 15.2148i −0.624727 + 0.556682i
\(748\) 0 0
\(749\) 12.9058 27.5978i 0.471566 1.00840i
\(750\) 0 0
\(751\) 32.2590 + 11.7413i 1.17715 + 0.428447i 0.855194 0.518308i \(-0.173438\pi\)
0.321955 + 0.946755i \(0.395660\pi\)
\(752\) 0 0
\(753\) −20.3106 23.4871i −0.740161 0.855919i
\(754\) 0 0
\(755\) −2.89771 −0.105458
\(756\) 0 0
\(757\) 10.6867 0.388415 0.194208 0.980960i \(-0.437786\pi\)
0.194208 + 0.980960i \(0.437786\pi\)
\(758\) 0 0
\(759\) −27.5572 + 5.28263i −1.00026 + 0.191747i
\(760\) 0 0
\(761\) 18.6670 + 6.79422i 0.676677 + 0.246290i 0.657420 0.753524i \(-0.271648\pi\)
0.0192571 + 0.999815i \(0.493870\pi\)
\(762\) 0 0
\(763\) 22.4837 1.94235i 0.813966 0.0703179i
\(764\) 0 0
\(765\) 0.109785 + 0.177733i 0.00396930 + 0.00642595i
\(766\) 0 0
\(767\) −4.31650 + 1.57108i −0.155860 + 0.0567283i
\(768\) 0 0
\(769\) 2.05123 + 11.6331i 0.0739694 + 0.419501i 0.999196 + 0.0400869i \(0.0127635\pi\)
−0.925227 + 0.379415i \(0.876125\pi\)
\(770\) 0 0
\(771\) 14.2609 + 37.4400i 0.513593 + 1.34837i
\(772\) 0 0
\(773\) 29.1843 1.04969 0.524844 0.851199i \(-0.324124\pi\)
0.524844 + 0.851199i \(0.324124\pi\)
\(774\) 0 0
\(775\) −19.4597 −0.699012
\(776\) 0 0
\(777\) 5.58016 22.0352i 0.200187 0.790510i
\(778\) 0 0
\(779\) 0.489274 + 2.77481i 0.0175301 + 0.0994179i
\(780\) 0 0
\(781\) −14.0856 11.8192i −0.504022 0.422925i
\(782\) 0 0
\(783\) 0.873826 + 2.10385i 0.0312280 + 0.0751855i
\(784\) 0 0
\(785\) −0.700133 + 3.97065i −0.0249888 + 0.141719i
\(786\) 0 0
\(787\) −10.7783 + 9.04406i −0.384205 + 0.322386i −0.814350 0.580373i \(-0.802907\pi\)
0.430146 + 0.902759i \(0.358462\pi\)
\(788\) 0 0
\(789\) 23.7263 + 13.2321i 0.844680 + 0.471074i
\(790\) 0 0
\(791\) −40.4065 10.8742i −1.43669 0.386641i
\(792\) 0 0
\(793\) −0.278394 + 0.482192i −0.00988605 + 0.0171231i
\(794\) 0 0
\(795\) 2.75027 + 7.22047i 0.0975421 + 0.256084i
\(796\) 0 0
\(797\) 3.34584 + 18.9752i 0.118516 + 0.672137i 0.984949 + 0.172844i \(0.0552957\pi\)
−0.866433 + 0.499293i \(0.833593\pi\)
\(798\) 0 0
\(799\) −0.214345 0.179857i −0.00758300 0.00636289i
\(800\) 0 0
\(801\) −3.86758 3.05404i −0.136654 0.107909i
\(802\) 0 0
\(803\) −6.06334 5.08775i −0.213971 0.179543i
\(804\) 0 0
\(805\) −16.5060 + 7.67497i −0.581761 + 0.270507i
\(806\) 0 0
\(807\) 22.5344 + 26.0587i 0.793248 + 0.917309i
\(808\) 0 0
\(809\) −4.36780 + 7.56525i −0.153564 + 0.265980i −0.932535 0.361079i \(-0.882408\pi\)
0.778971 + 0.627059i \(0.215742\pi\)
\(810\) 0 0
\(811\) 5.30542 0.186298 0.0931492 0.995652i \(-0.470307\pi\)
0.0931492 + 0.995652i \(0.470307\pi\)
\(812\) 0 0
\(813\) 4.63196 0.887933i 0.162450 0.0311412i
\(814\) 0 0
\(815\) 1.42469 + 8.07981i 0.0499047 + 0.283023i
\(816\) 0 0
\(817\) −4.23999 3.55778i −0.148339 0.124471i
\(818\) 0 0
\(819\) 3.45376 0.402123i 0.120684 0.0140513i
\(820\) 0 0
\(821\) −0.270945 + 1.53661i −0.00945605 + 0.0536279i −0.989171 0.146770i \(-0.953112\pi\)
0.979715 + 0.200398i \(0.0642234\pi\)
\(822\) 0 0
\(823\) −30.6784 11.1660i −1.06938 0.389224i −0.253437 0.967352i \(-0.581561\pi\)
−0.815946 + 0.578128i \(0.803783\pi\)
\(824\) 0 0
\(825\) −10.2130 + 12.5455i −0.355570 + 0.436777i
\(826\) 0 0
\(827\) 9.60466 + 16.6358i 0.333987 + 0.578482i 0.983290 0.182048i \(-0.0582726\pi\)
−0.649303 + 0.760530i \(0.724939\pi\)
\(828\) 0 0
\(829\) 16.3738 + 28.3603i 0.568686 + 0.984993i 0.996696 + 0.0812190i \(0.0258813\pi\)
−0.428010 + 0.903774i \(0.640785\pi\)
\(830\) 0 0
\(831\) 6.14547 + 3.42730i 0.213184 + 0.118892i
\(832\) 0 0
\(833\) 0.170493 0.465263i 0.00590722 0.0161204i
\(834\) 0 0
\(835\) 17.4341 6.34548i 0.603330 0.219594i
\(836\) 0 0
\(837\) −7.51748 + 23.9230i −0.259842 + 0.826900i
\(838\) 0 0
\(839\) 5.17751 29.3631i 0.178748 1.01373i −0.754981 0.655747i \(-0.772354\pi\)
0.933729 0.357982i \(-0.116535\pi\)
\(840\) 0 0
\(841\) 27.0705 + 9.85284i 0.933464 + 0.339753i
\(842\) 0 0
\(843\) 21.7825 13.0117i 0.750229 0.448146i
\(844\) 0 0
\(845\) 12.5995 0.433437
\(846\) 0 0
\(847\) 14.3967 + 3.87443i 0.494677 + 0.133127i
\(848\) 0 0
\(849\) 31.3066 38.4566i 1.07444 1.31983i
\(850\) 0 0
\(851\) 32.6001 + 11.8655i 1.11752 + 0.406743i
\(852\) 0 0
\(853\) −13.4587 11.2932i −0.460818 0.386672i 0.382614 0.923908i \(-0.375024\pi\)
−0.843432 + 0.537236i \(0.819468\pi\)
\(854\) 0 0
\(855\) 0.992310 + 1.60646i 0.0339363 + 0.0549398i
\(856\) 0 0
\(857\) 7.18190 40.7306i 0.245329 1.39133i −0.574398 0.818576i \(-0.694764\pi\)
0.819727 0.572754i \(-0.194125\pi\)
\(858\) 0 0
\(859\) −4.37585 1.59268i −0.149302 0.0543415i 0.266288 0.963893i \(-0.414203\pi\)
−0.415590 + 0.909552i \(0.636425\pi\)
\(860\) 0 0
\(861\) 8.77971 + 18.1704i 0.299212 + 0.619245i
\(862\) 0 0
\(863\) 17.7776 + 30.7917i 0.605157 + 1.04816i 0.992027 + 0.126028i \(0.0402230\pi\)
−0.386870 + 0.922134i \(0.626444\pi\)
\(864\) 0 0
\(865\) 4.07998 7.06672i 0.138723 0.240276i
\(866\) 0 0
\(867\) −9.65545 + 27.8076i −0.327916 + 0.944395i
\(868\) 0 0
\(869\) −0.404671 + 0.339559i −0.0137275 + 0.0115188i
\(870\) 0 0
\(871\) 0.718144 4.07279i 0.0243334 0.138001i
\(872\) 0 0
\(873\) −6.99314 33.7579i −0.236682 1.14253i
\(874\) 0 0
\(875\) −9.95818 + 21.2947i −0.336648 + 0.719892i
\(876\) 0 0
\(877\) −32.3016 + 27.1043i −1.09075 + 0.915246i −0.996768 0.0803282i \(-0.974403\pi\)
−0.0939792 + 0.995574i \(0.529959\pi\)
\(878\) 0 0
\(879\) 5.89201 7.23767i 0.198733 0.244121i
\(880\) 0 0
\(881\) −16.6310 28.8057i −0.560312 0.970489i −0.997469 0.0711039i \(-0.977348\pi\)
0.437157 0.899385i \(-0.355986\pi\)
\(882\) 0 0
\(883\) 12.3693 21.4242i 0.416259 0.720981i −0.579301 0.815114i \(-0.696674\pi\)
0.995560 + 0.0941324i \(0.0300077\pi\)
\(884\) 0 0
\(885\) −15.6036 8.70205i −0.524509 0.292516i
\(886\) 0 0
\(887\) 4.66231 + 26.4412i 0.156545 + 0.887810i 0.957360 + 0.288898i \(0.0932890\pi\)
−0.800815 + 0.598912i \(0.795600\pi\)
\(888\) 0 0
\(889\) 12.7517 1.10161i 0.427679 0.0369469i
\(890\) 0 0
\(891\) 11.4776 + 17.4019i 0.384513 + 0.582986i
\(892\) 0 0
\(893\) −1.93739 1.62566i −0.0648323 0.0544007i
\(894\) 0 0
\(895\) 1.69583 + 0.617230i 0.0566852 + 0.0206317i
\(896\) 0 0
\(897\) 0.0788914 + 5.30623i 0.00263411 + 0.177170i
\(898\) 0 0
\(899\) −1.05790 1.83233i −0.0352829 0.0611117i
\(900\) 0 0
\(901\) 0.160504 0.278001i 0.00534715 0.00926154i
\(902\) 0 0
\(903\) −36.1554 16.2570i −1.20318 0.541000i
\(904\) 0 0
\(905\) 8.38970 7.03979i 0.278883 0.234011i
\(906\) 0 0
\(907\) −41.8685 + 15.2389i −1.39022 + 0.505999i −0.925260 0.379333i \(-0.876153\pi\)
−0.464960 + 0.885332i \(0.653931\pi\)
\(908\) 0 0
\(909\) −12.6211 + 11.2464i −0.418616 + 0.373020i
\(910\) 0 0
\(911\) −26.0255 + 9.47251i −0.862263 + 0.313838i −0.735030 0.678035i \(-0.762832\pi\)
−0.127233 + 0.991873i \(0.540610\pi\)
\(912\) 0 0
\(913\) −3.06617 17.3891i −0.101476 0.575496i
\(914\) 0 0
\(915\) −2.12685 + 0.407711i −0.0703115 + 0.0134785i
\(916\) 0 0
\(917\) 20.8634 20.8179i 0.688971 0.687469i
\(918\) 0 0
\(919\) 24.2124 + 41.9372i 0.798695 + 1.38338i 0.920466 + 0.390822i \(0.127809\pi\)
−0.121772 + 0.992558i \(0.538858\pi\)
\(920\) 0 0
\(921\) 19.0970 3.66084i 0.629267 0.120629i
\(922\) 0 0
\(923\) −2.66402 + 2.23538i −0.0876874 + 0.0735785i
\(924\) 0 0
\(925\) 18.7951 6.84085i 0.617979 0.224926i
\(926\) 0 0
\(927\) −19.0926 30.9092i −0.627083 1.01519i
\(928\) 0 0
\(929\) 3.90527 22.1479i 0.128128 0.726648i −0.851273 0.524723i \(-0.824169\pi\)
0.979401 0.201926i \(-0.0647199\pi\)
\(930\) 0 0
\(931\) 1.54102 4.20534i 0.0505049 0.137824i
\(932\) 0 0
\(933\) −13.9791 + 17.1718i −0.457657 + 0.562179i
\(934\) 0 0
\(935\) −0.161292 −0.00527482
\(936\) 0 0
\(937\) −17.0154 + 29.4715i −0.555868 + 0.962791i 0.441968 + 0.897031i \(0.354281\pi\)
−0.997835 + 0.0657601i \(0.979053\pi\)
\(938\) 0 0
\(939\) −26.0133 14.5075i −0.848912 0.473434i
\(940\) 0 0
\(941\) −33.2276 + 27.8813i −1.08319 + 0.908903i −0.996182 0.0873045i \(-0.972175\pi\)
−0.0870069 + 0.996208i \(0.527730\pi\)
\(942\) 0 0
\(943\) −28.9422 + 10.5341i −0.942489 + 0.343038i
\(944\) 0 0
\(945\) 9.96969 + 9.13782i 0.324314 + 0.297253i
\(946\) 0 0
\(947\) 7.30894 2.66024i 0.237509 0.0864460i −0.220524 0.975382i \(-0.570777\pi\)
0.458032 + 0.888936i \(0.348554\pi\)
\(948\) 0 0
\(949\) −1.14677 + 0.962252i −0.0372256 + 0.0312360i
\(950\) 0 0
\(951\) −38.9338 + 23.2569i −1.26251 + 0.754157i
\(952\) 0 0
\(953\) 10.5593 18.2892i 0.342049 0.592447i −0.642764 0.766064i \(-0.722212\pi\)
0.984813 + 0.173618i \(0.0555457\pi\)
\(954\) 0 0
\(955\) −0.591539 −0.0191418
\(956\) 0 0
\(957\) −1.73650 0.279641i −0.0561332 0.00903953i
\(958\) 0 0
\(959\) 4.82953 54.5166i 0.155954 1.76043i
\(960\) 0 0
\(961\) −1.33888 + 7.59316i −0.0431897 + 0.244941i
\(962\) 0 0
\(963\) 4.98474 34.1841i 0.160631 1.10157i
\(964\) 0 0
\(965\) −19.6141 + 7.13894i −0.631399 + 0.229810i
\(966\) 0 0
\(967\) −46.1741 + 38.7447i −1.48486 + 1.24594i −0.584059 + 0.811711i \(0.698536\pi\)
−0.900800 + 0.434234i \(0.857019\pi\)
\(968\) 0 0
\(969\) 0.0257321 0.0741082i 0.000826635 0.00238070i
\(970\) 0 0
\(971\) 7.65835 + 13.2647i 0.245768 + 0.425683i 0.962347 0.271823i \(-0.0876264\pi\)
−0.716579 + 0.697506i \(0.754293\pi\)
\(972\) 0 0
\(973\) −14.6523 54.9226i −0.469730 1.76074i
\(974\) 0 0
\(975\) 2.00128 + 2.31427i 0.0640922 + 0.0741159i
\(976\) 0 0
\(977\) 3.76272 + 21.3395i 0.120380 + 0.682710i 0.983945 + 0.178472i \(0.0571154\pi\)
−0.863565 + 0.504238i \(0.831773\pi\)
\(978\) 0 0
\(979\) 3.57536 1.30132i 0.114269 0.0415905i
\(980\) 0 0
\(981\) 23.7751 9.46298i 0.759080 0.302130i
\(982\) 0 0
\(983\) −4.59558 + 1.67265i −0.146576 + 0.0533494i −0.414266 0.910156i \(-0.635962\pi\)
0.267690 + 0.963505i \(0.413740\pi\)
\(984\) 0 0
\(985\) −11.8490 + 9.94249i −0.377541 + 0.316794i
\(986\) 0 0
\(987\) −16.5206 7.42835i −0.525855 0.236447i
\(988\) 0 0
\(989\) 30.2514 52.3970i 0.961939 1.66613i
\(990\) 0 0
\(991\) 5.78837 + 10.0258i 0.183874 + 0.318479i 0.943196 0.332236i \(-0.107803\pi\)
−0.759323 + 0.650714i \(0.774470\pi\)
\(992\) 0 0
\(993\) −35.7273 + 21.3415i −1.13377 + 0.677253i
\(994\) 0 0
\(995\) −18.6147 6.77521i −0.590127 0.214789i
\(996\) 0 0
\(997\) 38.9099 + 32.6493i 1.23229 + 1.03401i 0.998087 + 0.0618253i \(0.0196921\pi\)
0.234202 + 0.972188i \(0.424752\pi\)
\(998\) 0 0
\(999\) −1.14915 25.7487i −0.0363574 0.814652i
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 756.2.bq.a.25.15 yes 144
7.2 even 3 756.2.bp.a.457.18 yes 144
27.13 even 9 756.2.bp.a.445.18 144
189.121 even 9 inner 756.2.bq.a.121.15 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.bp.a.445.18 144 27.13 even 9
756.2.bp.a.457.18 yes 144 7.2 even 3
756.2.bq.a.25.15 yes 144 1.1 even 1 trivial
756.2.bq.a.121.15 yes 144 189.121 even 9 inner