Properties

Label 756.2.bp.a.193.5
Level $756$
Weight $2$
Character 756.193
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(193,756)]
 
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, 2, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.193");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.bp (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 193.5
Character \(\chi\) \(=\) 756.193
Dual form 756.2.bp.a.709.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.35655 - 1.07693i) q^{3} +(2.04264 - 0.743461i) q^{5} +(0.979055 - 2.45794i) q^{7} +(0.680440 + 2.92181i) q^{9} +O(q^{10})\) \(q+(-1.35655 - 1.07693i) q^{3} +(2.04264 - 0.743461i) q^{5} +(0.979055 - 2.45794i) q^{7} +(0.680440 + 2.92181i) q^{9} +(0.861192 + 0.313448i) q^{11} +(3.73996 - 1.36123i) q^{13} +(-3.57160 - 1.19124i) q^{15} +(1.17734 + 2.03922i) q^{17} +(0.245736 - 0.425627i) q^{19} +(-3.97516 + 2.27993i) q^{21} +(0.385571 - 2.18668i) q^{23} +(-0.210571 + 0.176690i) q^{25} +(2.22354 - 4.69637i) q^{27} +(-0.293857 - 0.106955i) q^{29} +(-1.57219 + 0.572230i) q^{31} +(-0.830685 - 1.35265i) q^{33} +(0.172480 - 5.74857i) q^{35} -0.644777 q^{37} +(-6.53939 - 2.18110i) q^{39} +(7.02951 - 2.55853i) q^{41} +(-1.47268 - 8.35201i) q^{43} +(3.56215 + 5.46234i) q^{45} +(-2.31936 - 0.844179i) q^{47} +(-5.08290 - 4.81291i) q^{49} +(0.598975 - 4.03421i) q^{51} +(0.387704 - 0.671523i) q^{53} +1.99214 q^{55} +(-0.791723 + 0.312743i) q^{57} +(0.649562 + 0.545047i) q^{59} +(-7.88514 - 2.86996i) q^{61} +(7.84782 + 1.18814i) q^{63} +(6.62738 - 5.56103i) q^{65} +(0.858765 - 4.87030i) q^{67} +(-2.87795 + 2.55110i) q^{69} +(-4.26653 + 7.38984i) q^{71} +8.22271 q^{73} +(0.475933 - 0.0129180i) q^{75} +(1.61359 - 1.80987i) q^{77} +(-2.72096 - 15.4313i) q^{79} +(-8.07400 + 3.97624i) q^{81} +(14.7930 + 5.38420i) q^{83} +(3.92097 + 3.29008i) q^{85} +(0.283448 + 0.461554i) q^{87} +(0.775187 - 1.34266i) q^{89} +(0.315801 - 10.5253i) q^{91} +(2.74900 + 0.916882i) q^{93} +(0.185513 - 1.05210i) q^{95} +(-0.191971 - 1.08872i) q^{97} +(-0.329848 + 2.72953i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(3\) −1.35655 1.07693i −0.783203 0.621766i
\(4\) 0 0
\(5\) 2.04264 0.743461i 0.913497 0.332486i 0.157849 0.987463i \(-0.449544\pi\)
0.755648 + 0.654978i \(0.227322\pi\)
\(6\) 0 0
\(7\) 0.979055 2.45794i 0.370048 0.929013i
\(8\) 0 0
\(9\) 0.680440 + 2.92181i 0.226813 + 0.973938i
\(10\) 0 0
\(11\) 0.861192 + 0.313448i 0.259659 + 0.0945082i 0.468570 0.883427i \(-0.344770\pi\)
−0.208911 + 0.977935i \(0.566992\pi\)
\(12\) 0 0
\(13\) 3.73996 1.36123i 1.03728 0.377539i 0.233431 0.972373i \(-0.425005\pi\)
0.803848 + 0.594835i \(0.202783\pi\)
\(14\) 0 0
\(15\) −3.57160 1.19124i −0.922182 0.307578i
\(16\) 0 0
\(17\) 1.17734 + 2.03922i 0.285547 + 0.494583i 0.972742 0.231891i \(-0.0744912\pi\)
−0.687194 + 0.726474i \(0.741158\pi\)
\(18\) 0 0
\(19\) 0.245736 0.425627i 0.0563757 0.0976455i −0.836460 0.548028i \(-0.815379\pi\)
0.892836 + 0.450382i \(0.148712\pi\)
\(20\) 0 0
\(21\) −3.97516 + 2.27993i −0.867451 + 0.497522i
\(22\) 0 0
\(23\) 0.385571 2.18668i 0.0803971 0.455954i −0.917858 0.396908i \(-0.870083\pi\)
0.998255 0.0590459i \(-0.0188058\pi\)
\(24\) 0 0
\(25\) −0.210571 + 0.176690i −0.0421143 + 0.0353381i
\(26\) 0 0
\(27\) 2.22354 4.69637i 0.427921 0.903816i
\(28\) 0 0
\(29\) −0.293857 0.106955i −0.0545679 0.0198611i 0.314592 0.949227i \(-0.398132\pi\)
−0.369160 + 0.929366i \(0.620355\pi\)
\(30\) 0 0
\(31\) −1.57219 + 0.572230i −0.282373 + 0.102776i −0.479324 0.877638i \(-0.659118\pi\)
0.196951 + 0.980413i \(0.436896\pi\)
\(32\) 0 0
\(33\) −0.830685 1.35265i −0.144604 0.235466i
\(34\) 0 0
\(35\) 0.172480 5.74857i 0.0291544 0.971686i
\(36\) 0 0
\(37\) −0.644777 −0.106001 −0.0530003 0.998594i \(-0.516878\pi\)
−0.0530003 + 0.998594i \(0.516878\pi\)
\(38\) 0 0
\(39\) −6.53939 2.18110i −1.04714 0.349256i
\(40\) 0 0
\(41\) 7.02951 2.55853i 1.09783 0.399576i 0.271311 0.962492i \(-0.412543\pi\)
0.826514 + 0.562916i \(0.190321\pi\)
\(42\) 0 0
\(43\) −1.47268 8.35201i −0.224582 1.27367i −0.863482 0.504379i \(-0.831721\pi\)
0.638900 0.769290i \(-0.279390\pi\)
\(44\) 0 0
\(45\) 3.56215 + 5.46234i 0.531014 + 0.814278i
\(46\) 0 0
\(47\) −2.31936 0.844179i −0.338314 0.123136i 0.167276 0.985910i \(-0.446503\pi\)
−0.505590 + 0.862774i \(0.668725\pi\)
\(48\) 0 0
\(49\) −5.08290 4.81291i −0.726129 0.687559i
\(50\) 0 0
\(51\) 0.598975 4.03421i 0.0838733 0.564902i
\(52\) 0 0
\(53\) 0.387704 0.671523i 0.0532552 0.0922408i −0.838169 0.545411i \(-0.816374\pi\)
0.891424 + 0.453170i \(0.149707\pi\)
\(54\) 0 0
\(55\) 1.99214 0.268620
\(56\) 0 0
\(57\) −0.791723 + 0.312743i −0.104866 + 0.0414238i
\(58\) 0 0
\(59\) 0.649562 + 0.545047i 0.0845657 + 0.0709591i 0.684091 0.729397i \(-0.260199\pi\)
−0.599525 + 0.800356i \(0.704644\pi\)
\(60\) 0 0
\(61\) −7.88514 2.86996i −1.00959 0.367460i −0.216314 0.976324i \(-0.569403\pi\)
−0.793275 + 0.608864i \(0.791626\pi\)
\(62\) 0 0
\(63\) 7.84782 + 1.18814i 0.988733 + 0.149691i
\(64\) 0 0
\(65\) 6.62738 5.56103i 0.822025 0.689761i
\(66\) 0 0
\(67\) 0.858765 4.87030i 0.104915 0.595001i −0.886339 0.463036i \(-0.846760\pi\)
0.991254 0.131966i \(-0.0421288\pi\)
\(68\) 0 0
\(69\) −2.87795 + 2.55110i −0.346464 + 0.307117i
\(70\) 0 0
\(71\) −4.26653 + 7.38984i −0.506344 + 0.877013i 0.493630 + 0.869672i \(0.335670\pi\)
−0.999973 + 0.00734044i \(0.997663\pi\)
\(72\) 0 0
\(73\) 8.22271 0.962396 0.481198 0.876612i \(-0.340202\pi\)
0.481198 + 0.876612i \(0.340202\pi\)
\(74\) 0 0
\(75\) 0.475933 0.0129180i 0.0549560 0.00149164i
\(76\) 0 0
\(77\) 1.61359 1.80987i 0.183886 0.206254i
\(78\) 0 0
\(79\) −2.72096 15.4313i −0.306132 1.73616i −0.618130 0.786076i \(-0.712110\pi\)
0.311999 0.950083i \(-0.399002\pi\)
\(80\) 0 0
\(81\) −8.07400 + 3.97624i −0.897111 + 0.441805i
\(82\) 0 0
\(83\) 14.7930 + 5.38420i 1.62374 + 0.590993i 0.984090 0.177673i \(-0.0568570\pi\)
0.639650 + 0.768666i \(0.279079\pi\)
\(84\) 0 0
\(85\) 3.92097 + 3.29008i 0.425288 + 0.356859i
\(86\) 0 0
\(87\) 0.283448 + 0.461554i 0.0303888 + 0.0494837i
\(88\) 0 0
\(89\) 0.775187 1.34266i 0.0821697 0.142322i −0.822012 0.569470i \(-0.807148\pi\)
0.904182 + 0.427148i \(0.140482\pi\)
\(90\) 0 0
\(91\) 0.315801 10.5253i 0.0331050 1.10335i
\(92\) 0 0
\(93\) 2.74900 + 0.916882i 0.285058 + 0.0950762i
\(94\) 0 0
\(95\) 0.185513 1.05210i 0.0190333 0.107943i
\(96\) 0 0
\(97\) −0.191971 1.08872i −0.0194917 0.110543i 0.973510 0.228646i \(-0.0734298\pi\)
−0.993001 + 0.118103i \(0.962319\pi\)
\(98\) 0 0
\(99\) −0.329848 + 2.72953i −0.0331510 + 0.274328i
\(100\) 0 0
\(101\) 2.78746 + 15.8085i 0.277363 + 1.57300i 0.731355 + 0.681997i \(0.238888\pi\)
−0.453992 + 0.891006i \(0.650001\pi\)
\(102\) 0 0
\(103\) −16.1945 + 5.89430i −1.59569 + 0.580783i −0.978539 0.206063i \(-0.933935\pi\)
−0.617150 + 0.786846i \(0.711713\pi\)
\(104\) 0 0
\(105\) −6.42479 + 7.61246i −0.626995 + 0.742900i
\(106\) 0 0
\(107\) −2.57310 4.45674i −0.248751 0.430849i 0.714429 0.699708i \(-0.246687\pi\)
−0.963179 + 0.268859i \(0.913353\pi\)
\(108\) 0 0
\(109\) −4.52203 + 7.83239i −0.433132 + 0.750207i −0.997141 0.0755615i \(-0.975925\pi\)
0.564009 + 0.825769i \(0.309258\pi\)
\(110\) 0 0
\(111\) 0.874670 + 0.694380i 0.0830200 + 0.0659076i
\(112\) 0 0
\(113\) −0.746948 + 4.23615i −0.0702669 + 0.398504i 0.929307 + 0.369309i \(0.120405\pi\)
−0.999574 + 0.0291949i \(0.990706\pi\)
\(114\) 0 0
\(115\) −0.838128 4.75326i −0.0781559 0.443244i
\(116\) 0 0
\(117\) 6.52210 + 10.0012i 0.602968 + 0.924614i
\(118\) 0 0
\(119\) 6.16495 0.897326i 0.565140 0.0822578i
\(120\) 0 0
\(121\) −7.78309 6.53079i −0.707553 0.593708i
\(122\) 0 0
\(123\) −12.2912 4.09953i −1.10826 0.369642i
\(124\) 0 0
\(125\) −5.73309 + 9.93001i −0.512784 + 0.888167i
\(126\) 0 0
\(127\) 4.36039 + 7.55242i 0.386922 + 0.670169i 0.992034 0.125972i \(-0.0402048\pi\)
−0.605112 + 0.796141i \(0.706872\pi\)
\(128\) 0 0
\(129\) −6.99677 + 12.9159i −0.616031 + 1.13718i
\(130\) 0 0
\(131\) −3.43614 + 19.4873i −0.300217 + 1.70261i 0.344991 + 0.938606i \(0.387882\pi\)
−0.645208 + 0.764007i \(0.723229\pi\)
\(132\) 0 0
\(133\) −0.805575 1.02072i −0.0698522 0.0885073i
\(134\) 0 0
\(135\) 1.05034 11.2461i 0.0903986 0.967911i
\(136\) 0 0
\(137\) 0.0527142 0.0442325i 0.00450368 0.00377904i −0.640533 0.767931i \(-0.721287\pi\)
0.645037 + 0.764152i \(0.276842\pi\)
\(138\) 0 0
\(139\) 4.91073 + 4.12059i 0.416522 + 0.349504i 0.826838 0.562440i \(-0.190137\pi\)
−0.410316 + 0.911943i \(0.634582\pi\)
\(140\) 0 0
\(141\) 2.23720 + 3.64296i 0.188406 + 0.306793i
\(142\) 0 0
\(143\) 3.64750 0.305019
\(144\) 0 0
\(145\) −0.679762 −0.0564511
\(146\) 0 0
\(147\) 1.71202 + 12.0029i 0.141205 + 0.989980i
\(148\) 0 0
\(149\) 13.1707 + 11.0515i 1.07898 + 0.905375i 0.995836 0.0911623i \(-0.0290582\pi\)
0.0831477 + 0.996537i \(0.473503\pi\)
\(150\) 0 0
\(151\) 7.96837 + 2.90025i 0.648457 + 0.236019i 0.645245 0.763976i \(-0.276755\pi\)
0.00321191 + 0.999995i \(0.498978\pi\)
\(152\) 0 0
\(153\) −5.15710 + 4.82754i −0.416927 + 0.390284i
\(154\) 0 0
\(155\) −2.78599 + 2.33772i −0.223776 + 0.187770i
\(156\) 0 0
\(157\) 1.03664 + 0.869844i 0.0827329 + 0.0694211i 0.683216 0.730216i \(-0.260581\pi\)
−0.600483 + 0.799637i \(0.705025\pi\)
\(158\) 0 0
\(159\) −1.24912 + 0.493422i −0.0990619 + 0.0391309i
\(160\) 0 0
\(161\) −4.99723 3.08859i −0.393837 0.243415i
\(162\) 0 0
\(163\) 7.57730 + 13.1243i 0.593500 + 1.02797i 0.993757 + 0.111569i \(0.0355877\pi\)
−0.400256 + 0.916403i \(0.631079\pi\)
\(164\) 0 0
\(165\) −2.70244 2.14540i −0.210384 0.167019i
\(166\) 0 0
\(167\) −4.19499 + 23.7910i −0.324618 + 1.84100i 0.187727 + 0.982221i \(0.439888\pi\)
−0.512345 + 0.858780i \(0.671223\pi\)
\(168\) 0 0
\(169\) 2.17577 1.82569i 0.167367 0.140438i
\(170\) 0 0
\(171\) 1.41081 + 0.428381i 0.107887 + 0.0327591i
\(172\) 0 0
\(173\) 18.0004 15.1041i 1.36854 1.14834i 0.395302 0.918551i \(-0.370640\pi\)
0.973240 0.229792i \(-0.0738047\pi\)
\(174\) 0 0
\(175\) 0.228133 + 0.690561i 0.0172452 + 0.0522015i
\(176\) 0 0
\(177\) −0.294183 1.43891i −0.0221122 0.108155i
\(178\) 0 0
\(179\) −3.01203 5.21699i −0.225130 0.389936i 0.731229 0.682132i \(-0.238947\pi\)
−0.956358 + 0.292196i \(0.905614\pi\)
\(180\) 0 0
\(181\) 1.25877 + 2.18025i 0.0935635 + 0.162057i 0.909008 0.416778i \(-0.136841\pi\)
−0.815445 + 0.578835i \(0.803508\pi\)
\(182\) 0 0
\(183\) 7.60582 + 12.3850i 0.562238 + 0.915524i
\(184\) 0 0
\(185\) −1.31705 + 0.479366i −0.0968313 + 0.0352437i
\(186\) 0 0
\(187\) 0.374729 + 2.12519i 0.0274029 + 0.155409i
\(188\) 0 0
\(189\) −9.36640 10.0633i −0.681305 0.731999i
\(190\) 0 0
\(191\) −2.24794 12.7487i −0.162656 0.922465i −0.951449 0.307807i \(-0.900405\pi\)
0.788793 0.614659i \(-0.210706\pi\)
\(192\) 0 0
\(193\) 3.57449 1.30101i 0.257298 0.0936487i −0.210151 0.977669i \(-0.567396\pi\)
0.467449 + 0.884020i \(0.345173\pi\)
\(194\) 0 0
\(195\) −14.9792 + 0.406573i −1.07268 + 0.0291153i
\(196\) 0 0
\(197\) 3.33263 + 5.77229i 0.237440 + 0.411258i 0.959979 0.280072i \(-0.0903583\pi\)
−0.722539 + 0.691330i \(0.757025\pi\)
\(198\) 0 0
\(199\) −6.81597 11.8056i −0.483171 0.836877i 0.516642 0.856202i \(-0.327182\pi\)
−0.999813 + 0.0193244i \(0.993848\pi\)
\(200\) 0 0
\(201\) −6.40993 + 5.68196i −0.452121 + 0.400774i
\(202\) 0 0
\(203\) −0.550591 + 0.617567i −0.0386439 + 0.0433447i
\(204\) 0 0
\(205\) 12.4566 10.4523i 0.870007 0.730022i
\(206\) 0 0
\(207\) 6.65143 0.361339i 0.462307 0.0251148i
\(208\) 0 0
\(209\) 0.345038 0.289521i 0.0238668 0.0200266i
\(210\) 0 0
\(211\) −2.13814 + 12.1260i −0.147196 + 0.834789i 0.818382 + 0.574675i \(0.194871\pi\)
−0.965578 + 0.260115i \(0.916240\pi\)
\(212\) 0 0
\(213\) 13.7461 5.42991i 0.941867 0.372052i
\(214\) 0 0
\(215\) −9.21755 15.9653i −0.628632 1.08882i
\(216\) 0 0
\(217\) −0.132755 + 4.42459i −0.00901201 + 0.300360i
\(218\) 0 0
\(219\) −11.1545 8.85529i −0.753751 0.598385i
\(220\) 0 0
\(221\) 7.17907 + 6.02395i 0.482916 + 0.405215i
\(222\) 0 0
\(223\) −2.20459 + 1.84987i −0.147630 + 0.123877i −0.713612 0.700542i \(-0.752942\pi\)
0.565981 + 0.824418i \(0.308497\pi\)
\(224\) 0 0
\(225\) −0.659538 0.495023i −0.0439692 0.0330015i
\(226\) 0 0
\(227\) 11.6442 + 4.23814i 0.772851 + 0.281295i 0.698189 0.715914i \(-0.253990\pi\)
0.0746629 + 0.997209i \(0.476212\pi\)
\(228\) 0 0
\(229\) −19.4648 16.3329i −1.28627 1.07931i −0.992347 0.123483i \(-0.960594\pi\)
−0.293926 0.955828i \(-0.594962\pi\)
\(230\) 0 0
\(231\) −4.13802 + 0.717451i −0.272262 + 0.0472048i
\(232\) 0 0
\(233\) −16.5061 −1.08135 −0.540674 0.841232i \(-0.681831\pi\)
−0.540674 + 0.841232i \(0.681831\pi\)
\(234\) 0 0
\(235\) −5.36524 −0.349990
\(236\) 0 0
\(237\) −12.9273 + 23.8636i −0.839722 + 1.55011i
\(238\) 0 0
\(239\) −19.5905 16.4384i −1.26720 1.06331i −0.994876 0.101107i \(-0.967762\pi\)
−0.272329 0.962204i \(-0.587794\pi\)
\(240\) 0 0
\(241\) 9.55019 8.01356i 0.615182 0.516199i −0.281103 0.959678i \(-0.590700\pi\)
0.896285 + 0.443479i \(0.146256\pi\)
\(242\) 0 0
\(243\) 15.2349 + 3.30118i 0.977319 + 0.211771i
\(244\) 0 0
\(245\) −13.9608 6.05212i −0.891920 0.386655i
\(246\) 0 0
\(247\) 0.339664 1.92633i 0.0216123 0.122570i
\(248\) 0 0
\(249\) −14.2690 23.2349i −0.904258 1.47245i
\(250\) 0 0
\(251\) 9.88142 + 17.1151i 0.623710 + 1.08030i 0.988789 + 0.149320i \(0.0477086\pi\)
−0.365079 + 0.930976i \(0.618958\pi\)
\(252\) 0 0
\(253\) 1.01746 1.76229i 0.0639672 0.110795i
\(254\) 0 0
\(255\) −1.77579 8.68576i −0.111204 0.543923i
\(256\) 0 0
\(257\) 17.7362 + 14.8825i 1.10636 + 0.928342i 0.997836 0.0657522i \(-0.0209447\pi\)
0.108519 + 0.994094i \(0.465389\pi\)
\(258\) 0 0
\(259\) −0.631272 + 1.58482i −0.0392253 + 0.0984759i
\(260\) 0 0
\(261\) 0.112551 0.931373i 0.00696674 0.0576505i
\(262\) 0 0
\(263\) −3.34411 18.9654i −0.206207 1.16946i −0.895530 0.445001i \(-0.853203\pi\)
0.689323 0.724454i \(-0.257908\pi\)
\(264\) 0 0
\(265\) 0.292689 1.65992i 0.0179798 0.101968i
\(266\) 0 0
\(267\) −2.49753 + 0.986564i −0.152847 + 0.0603767i
\(268\) 0 0
\(269\) 4.13138 7.15576i 0.251895 0.436294i −0.712153 0.702025i \(-0.752280\pi\)
0.964047 + 0.265730i \(0.0856130\pi\)
\(270\) 0 0
\(271\) 12.8009 + 22.1718i 0.777601 + 1.34684i 0.933321 + 0.359043i \(0.116897\pi\)
−0.155720 + 0.987801i \(0.549770\pi\)
\(272\) 0 0
\(273\) −11.7634 + 13.9380i −0.711955 + 0.843565i
\(274\) 0 0
\(275\) −0.236726 + 0.0861611i −0.0142751 + 0.00519571i
\(276\) 0 0
\(277\) 2.32599 + 13.1913i 0.139755 + 0.792591i 0.971430 + 0.237328i \(0.0762715\pi\)
−0.831674 + 0.555264i \(0.812617\pi\)
\(278\) 0 0
\(279\) −2.74173 4.20428i −0.164143 0.251703i
\(280\) 0 0
\(281\) −4.54264 25.7626i −0.270991 1.53687i −0.751415 0.659830i \(-0.770628\pi\)
0.480423 0.877037i \(-0.340483\pi\)
\(282\) 0 0
\(283\) −2.09916 + 11.9050i −0.124782 + 0.707676i 0.856654 + 0.515891i \(0.172539\pi\)
−0.981437 + 0.191785i \(0.938572\pi\)
\(284\) 0 0
\(285\) −1.38469 + 1.22744i −0.0820222 + 0.0727070i
\(286\) 0 0
\(287\) 0.593570 19.7830i 0.0350373 1.16776i
\(288\) 0 0
\(289\) 5.72773 9.92072i 0.336925 0.583572i
\(290\) 0 0
\(291\) −0.912058 + 1.68364i −0.0534658 + 0.0986966i
\(292\) 0 0
\(293\) 14.0697 + 11.8058i 0.821958 + 0.689705i 0.953430 0.301615i \(-0.0975258\pi\)
−0.131472 + 0.991320i \(0.541970\pi\)
\(294\) 0 0
\(295\) 1.73204 + 0.630412i 0.100843 + 0.0367040i
\(296\) 0 0
\(297\) 3.38696 3.34751i 0.196532 0.194242i
\(298\) 0 0
\(299\) −1.53457 8.70295i −0.0887462 0.503305i
\(300\) 0 0
\(301\) −21.9705 4.55731i −1.26636 0.262679i
\(302\) 0 0
\(303\) 13.2433 24.4469i 0.760809 1.40443i
\(304\) 0 0
\(305\) −18.2402 −1.04443
\(306\) 0 0
\(307\) 9.40312 16.2867i 0.536664 0.929530i −0.462417 0.886663i \(-0.653018\pi\)
0.999081 0.0428668i \(-0.0136491\pi\)
\(308\) 0 0
\(309\) 28.3163 + 9.44442i 1.61086 + 0.537274i
\(310\) 0 0
\(311\) 2.28943 12.9840i 0.129821 0.736254i −0.848505 0.529187i \(-0.822497\pi\)
0.978327 0.207067i \(-0.0663918\pi\)
\(312\) 0 0
\(313\) −6.84541 + 5.74398i −0.386925 + 0.324669i −0.815414 0.578878i \(-0.803491\pi\)
0.428489 + 0.903547i \(0.359046\pi\)
\(314\) 0 0
\(315\) 16.9136 3.40761i 0.952975 0.191997i
\(316\) 0 0
\(317\) 30.2370 + 11.0054i 1.69828 + 0.618122i 0.995627 0.0934144i \(-0.0297782\pi\)
0.702649 + 0.711537i \(0.252000\pi\)
\(318\) 0 0
\(319\) −0.219542 0.184218i −0.0122920 0.0103142i
\(320\) 0 0
\(321\) −1.30907 + 8.81682i −0.0730650 + 0.492107i
\(322\) 0 0
\(323\) 1.15726 0.0643917
\(324\) 0 0
\(325\) −0.547012 + 0.947452i −0.0303427 + 0.0525552i
\(326\) 0 0
\(327\) 14.5693 5.75509i 0.805684 0.318257i
\(328\) 0 0
\(329\) −4.34572 + 4.87435i −0.239587 + 0.268731i
\(330\) 0 0
\(331\) 26.8908 + 9.78746i 1.47805 + 0.537968i 0.950274 0.311414i \(-0.100803\pi\)
0.527779 + 0.849381i \(0.323025\pi\)
\(332\) 0 0
\(333\) −0.438732 1.88392i −0.0240424 0.103238i
\(334\) 0 0
\(335\) −1.86673 10.5867i −0.101990 0.578415i
\(336\) 0 0
\(337\) −12.9957 + 4.73003i −0.707919 + 0.257661i −0.670788 0.741649i \(-0.734044\pi\)
−0.0371307 + 0.999310i \(0.511822\pi\)
\(338\) 0 0
\(339\) 5.57531 4.94213i 0.302809 0.268420i
\(340\) 0 0
\(341\) −1.53332 −0.0830340
\(342\) 0 0
\(343\) −16.8063 + 7.78134i −0.907453 + 0.420153i
\(344\) 0 0
\(345\) −3.98197 + 7.35063i −0.214382 + 0.395745i
\(346\) 0 0
\(347\) −34.4899 + 12.5533i −1.85152 + 0.673897i −0.867077 + 0.498173i \(0.834004\pi\)
−0.984440 + 0.175724i \(0.943773\pi\)
\(348\) 0 0
\(349\) −14.1826 5.16203i −0.759176 0.276317i −0.0667142 0.997772i \(-0.521252\pi\)
−0.692462 + 0.721455i \(0.743474\pi\)
\(350\) 0 0
\(351\) 1.92311 20.5910i 0.102648 1.09907i
\(352\) 0 0
\(353\) −4.24502 + 3.56200i −0.225940 + 0.189586i −0.748729 0.662876i \(-0.769336\pi\)
0.522790 + 0.852462i \(0.324891\pi\)
\(354\) 0 0
\(355\) −3.22093 + 18.2668i −0.170949 + 0.969501i
\(356\) 0 0
\(357\) −9.32940 5.42196i −0.493764 0.286960i
\(358\) 0 0
\(359\) −2.89688 + 5.01755i −0.152892 + 0.264816i −0.932289 0.361713i \(-0.882192\pi\)
0.779398 + 0.626530i \(0.215525\pi\)
\(360\) 0 0
\(361\) 9.37923 + 16.2453i 0.493644 + 0.855016i
\(362\) 0 0
\(363\) 3.52492 + 17.2412i 0.185010 + 0.904926i
\(364\) 0 0
\(365\) 16.7961 6.11327i 0.879146 0.319983i
\(366\) 0 0
\(367\) 22.2206 + 8.08765i 1.15991 + 0.422172i 0.849064 0.528289i \(-0.177166\pi\)
0.310843 + 0.950461i \(0.399389\pi\)
\(368\) 0 0
\(369\) 12.2587 + 18.7980i 0.638164 + 0.978585i
\(370\) 0 0
\(371\) −1.27098 1.61041i −0.0659858 0.0836083i
\(372\) 0 0
\(373\) −4.60475 + 1.67599i −0.238425 + 0.0867796i −0.458469 0.888710i \(-0.651602\pi\)
0.220044 + 0.975490i \(0.429380\pi\)
\(374\) 0 0
\(375\) 18.4711 7.29638i 0.953846 0.376784i
\(376\) 0 0
\(377\) −1.24461 −0.0641004
\(378\) 0 0
\(379\) −2.93187 −0.150600 −0.0753000 0.997161i \(-0.523991\pi\)
−0.0753000 + 0.997161i \(0.523991\pi\)
\(380\) 0 0
\(381\) 2.21836 14.9411i 0.113650 0.765454i
\(382\) 0 0
\(383\) −26.8697 + 9.77979i −1.37298 + 0.499724i −0.920043 0.391819i \(-0.871846\pi\)
−0.452937 + 0.891542i \(0.649624\pi\)
\(384\) 0 0
\(385\) 1.95042 4.89656i 0.0994025 0.249552i
\(386\) 0 0
\(387\) 23.4009 9.98595i 1.18954 0.507614i
\(388\) 0 0
\(389\) −26.1371 9.51313i −1.32520 0.482335i −0.420081 0.907486i \(-0.637998\pi\)
−0.905122 + 0.425152i \(0.860221\pi\)
\(390\) 0 0
\(391\) 4.91306 1.78821i 0.248464 0.0904336i
\(392\) 0 0
\(393\) 25.6477 22.7350i 1.29376 1.14683i
\(394\) 0 0
\(395\) −17.0305 29.4977i −0.856898 1.48419i
\(396\) 0 0
\(397\) 8.05330 13.9487i 0.404184 0.700066i −0.590043 0.807372i \(-0.700889\pi\)
0.994226 + 0.107306i \(0.0342224\pi\)
\(398\) 0 0
\(399\) −0.00643936 + 2.25220i −0.000322371 + 0.112751i
\(400\) 0 0
\(401\) −2.69554 + 15.2872i −0.134609 + 0.763406i 0.840522 + 0.541777i \(0.182248\pi\)
−0.975131 + 0.221629i \(0.928863\pi\)
\(402\) 0 0
\(403\) −5.10099 + 4.28024i −0.254098 + 0.213214i
\(404\) 0 0
\(405\) −13.5361 + 14.1247i −0.672615 + 0.701864i
\(406\) 0 0
\(407\) −0.555277 0.202104i −0.0275240 0.0100179i
\(408\) 0 0
\(409\) −9.70699 + 3.53305i −0.479980 + 0.174698i −0.570668 0.821181i \(-0.693316\pi\)
0.0906882 + 0.995879i \(0.471093\pi\)
\(410\) 0 0
\(411\) −0.119145 + 0.00323388i −0.00587697 + 0.000159516i
\(412\) 0 0
\(413\) 1.97565 1.06295i 0.0972152 0.0523043i
\(414\) 0 0
\(415\) 34.2197 1.67978
\(416\) 0 0
\(417\) −2.22404 10.8783i −0.108912 0.532712i
\(418\) 0 0
\(419\) 19.4103 7.06476i 0.948254 0.345136i 0.178834 0.983879i \(-0.442768\pi\)
0.769420 + 0.638743i \(0.220545\pi\)
\(420\) 0 0
\(421\) −5.55192 31.4865i −0.270584 1.53456i −0.752649 0.658422i \(-0.771224\pi\)
0.482065 0.876135i \(-0.339887\pi\)
\(422\) 0 0
\(423\) 0.888346 7.35116i 0.0431929 0.357426i
\(424\) 0 0
\(425\) −0.608224 0.221376i −0.0295032 0.0107383i
\(426\) 0 0
\(427\) −14.7742 + 16.5713i −0.714972 + 0.801943i
\(428\) 0 0
\(429\) −4.94801 3.92811i −0.238892 0.189651i
\(430\) 0 0
\(431\) −10.7881 + 18.6856i −0.519646 + 0.900053i 0.480093 + 0.877217i \(0.340603\pi\)
−0.999739 + 0.0228358i \(0.992731\pi\)
\(432\) 0 0
\(433\) 11.5628 0.555671 0.277836 0.960629i \(-0.410383\pi\)
0.277836 + 0.960629i \(0.410383\pi\)
\(434\) 0 0
\(435\) 0.922129 + 0.732056i 0.0442127 + 0.0350994i
\(436\) 0 0
\(437\) −0.835962 0.701455i −0.0399895 0.0335551i
\(438\) 0 0
\(439\) −31.9568 11.6313i −1.52522 0.555133i −0.562772 0.826612i \(-0.690265\pi\)
−0.962444 + 0.271479i \(0.912487\pi\)
\(440\) 0 0
\(441\) 10.6038 18.1262i 0.504944 0.863152i
\(442\) 0 0
\(443\) −6.32517 + 5.30745i −0.300518 + 0.252165i −0.780560 0.625081i \(-0.785066\pi\)
0.480042 + 0.877246i \(0.340621\pi\)
\(444\) 0 0
\(445\) 0.585212 3.31890i 0.0277417 0.157331i
\(446\) 0 0
\(447\) −5.96493 29.1758i −0.282132 1.37997i
\(448\) 0 0
\(449\) 0.496435 0.859850i 0.0234282 0.0405788i −0.854074 0.520152i \(-0.825875\pi\)
0.877502 + 0.479573i \(0.159209\pi\)
\(450\) 0 0
\(451\) 6.85573 0.322823
\(452\) 0 0
\(453\) −7.68610 12.5157i −0.361125 0.588039i
\(454\) 0 0
\(455\) −7.18009 21.7342i −0.336608 1.01892i
\(456\) 0 0
\(457\) −5.45136 30.9162i −0.255004 1.44620i −0.796063 0.605214i \(-0.793088\pi\)
0.541059 0.840985i \(-0.318024\pi\)
\(458\) 0 0
\(459\) 12.1948 0.994946i 0.569204 0.0464401i
\(460\) 0 0
\(461\) 11.7389 + 4.27260i 0.546734 + 0.198995i 0.600595 0.799554i \(-0.294931\pi\)
−0.0538610 + 0.998548i \(0.517153\pi\)
\(462\) 0 0
\(463\) 9.14281 + 7.67173i 0.424902 + 0.356535i 0.830024 0.557727i \(-0.188326\pi\)
−0.405122 + 0.914263i \(0.632771\pi\)
\(464\) 0 0
\(465\) 6.29689 0.170913i 0.292011 0.00792592i
\(466\) 0 0
\(467\) 8.23637 14.2658i 0.381134 0.660143i −0.610091 0.792331i \(-0.708867\pi\)
0.991225 + 0.132188i \(0.0422004\pi\)
\(468\) 0 0
\(469\) −11.1301 6.87908i −0.513940 0.317646i
\(470\) 0 0
\(471\) −0.469489 2.29637i −0.0216329 0.105811i
\(472\) 0 0
\(473\) 1.34966 7.65429i 0.0620573 0.351945i
\(474\) 0 0
\(475\) 0.0234592 + 0.133044i 0.00107638 + 0.00610448i
\(476\) 0 0
\(477\) 2.22588 + 0.675868i 0.101916 + 0.0309459i
\(478\) 0 0
\(479\) −0.525860 2.98230i −0.0240272 0.136265i 0.970435 0.241365i \(-0.0775949\pi\)
−0.994462 + 0.105100i \(0.966484\pi\)
\(480\) 0 0
\(481\) −2.41144 + 0.877692i −0.109952 + 0.0400193i
\(482\) 0 0
\(483\) 3.45278 + 9.57148i 0.157107 + 0.435518i
\(484\) 0 0
\(485\) −1.20155 2.08114i −0.0545594 0.0944997i
\(486\) 0 0
\(487\) −13.4221 + 23.2478i −0.608214 + 1.05346i 0.383321 + 0.923615i \(0.374780\pi\)
−0.991535 + 0.129842i \(0.958553\pi\)
\(488\) 0 0
\(489\) 3.85497 25.9639i 0.174328 1.17413i
\(490\) 0 0
\(491\) −2.98415 + 16.9239i −0.134673 + 0.763766i 0.840414 + 0.541944i \(0.182312\pi\)
−0.975087 + 0.221822i \(0.928800\pi\)
\(492\) 0 0
\(493\) −0.127865 0.725161i −0.00575877 0.0326596i
\(494\) 0 0
\(495\) 1.35553 + 5.82067i 0.0609267 + 0.261620i
\(496\) 0 0
\(497\) 13.9866 + 17.7219i 0.627384 + 0.794936i
\(498\) 0 0
\(499\) 28.3206 + 23.7638i 1.26781 + 1.06382i 0.994805 + 0.101801i \(0.0324606\pi\)
0.273001 + 0.962014i \(0.411984\pi\)
\(500\) 0 0
\(501\) 31.3119 27.7559i 1.39891 1.24004i
\(502\) 0 0
\(503\) −3.27791 + 5.67751i −0.146155 + 0.253148i −0.929803 0.368057i \(-0.880023\pi\)
0.783648 + 0.621205i \(0.213356\pi\)
\(504\) 0 0
\(505\) 17.4468 + 30.2187i 0.776371 + 1.34471i
\(506\) 0 0
\(507\) −4.91768 + 0.133478i −0.218402 + 0.00592797i
\(508\) 0 0
\(509\) 0.896915 5.08666i 0.0397550 0.225462i −0.958457 0.285238i \(-0.907927\pi\)
0.998212 + 0.0597757i \(0.0190385\pi\)
\(510\) 0 0
\(511\) 8.05049 20.2109i 0.356133 0.894078i
\(512\) 0 0
\(513\) −1.45250 2.10047i −0.0641293 0.0927378i
\(514\) 0 0
\(515\) −28.6973 + 24.0799i −1.26455 + 1.06109i
\(516\) 0 0
\(517\) −1.73281 1.45400i −0.0762089 0.0639468i
\(518\) 0 0
\(519\) −40.6844 + 1.10428i −1.78585 + 0.0484724i
\(520\) 0 0
\(521\) −15.7393 −0.689549 −0.344775 0.938685i \(-0.612045\pi\)
−0.344775 + 0.938685i \(0.612045\pi\)
\(522\) 0 0
\(523\) 25.3835 1.10994 0.554972 0.831869i \(-0.312729\pi\)
0.554972 + 0.831869i \(0.312729\pi\)
\(524\) 0 0
\(525\) 0.434213 1.18246i 0.0189506 0.0516068i
\(526\) 0 0
\(527\) −3.01791 2.53232i −0.131462 0.110310i
\(528\) 0 0
\(529\) 16.9800 + 6.18022i 0.738262 + 0.268705i
\(530\) 0 0
\(531\) −1.15054 + 2.26877i −0.0499291 + 0.0984563i
\(532\) 0 0
\(533\) 22.8073 19.1376i 0.987895 0.828943i
\(534\) 0 0
\(535\) −8.56932 7.19052i −0.370484 0.310873i
\(536\) 0 0
\(537\) −1.53238 + 10.3208i −0.0661269 + 0.445377i
\(538\) 0 0
\(539\) −2.86875 5.73807i −0.123566 0.247156i
\(540\) 0 0
\(541\) −1.35804 2.35220i −0.0583868 0.101129i 0.835355 0.549711i \(-0.185262\pi\)
−0.893741 + 0.448583i \(0.851929\pi\)
\(542\) 0 0
\(543\) 0.640400 4.31322i 0.0274822 0.185098i
\(544\) 0 0
\(545\) −3.41382 + 19.3607i −0.146232 + 0.829323i
\(546\) 0 0
\(547\) −21.5876 + 18.1142i −0.923019 + 0.774505i −0.974551 0.224166i \(-0.928034\pi\)
0.0515315 + 0.998671i \(0.483590\pi\)
\(548\) 0 0
\(549\) 3.02011 24.9918i 0.128895 1.06662i
\(550\) 0 0
\(551\) −0.117734 + 0.0987908i −0.00501565 + 0.00420863i
\(552\) 0 0
\(553\) −40.5931 8.42017i −1.72620 0.358062i
\(554\) 0 0
\(555\) 2.30288 + 0.768086i 0.0977519 + 0.0326035i
\(556\) 0 0
\(557\) 17.5892 + 30.4654i 0.745278 + 1.29086i 0.950065 + 0.312052i \(0.101016\pi\)
−0.204788 + 0.978806i \(0.565650\pi\)
\(558\) 0 0
\(559\) −16.8768 29.2315i −0.713813 1.23636i
\(560\) 0 0
\(561\) 1.78035 3.28648i 0.0751664 0.138755i
\(562\) 0 0
\(563\) −24.1266 + 8.78135i −1.01681 + 0.370090i −0.796046 0.605236i \(-0.793079\pi\)
−0.220768 + 0.975326i \(0.570856\pi\)
\(564\) 0 0
\(565\) 1.62367 + 9.20826i 0.0683081 + 0.387395i
\(566\) 0 0
\(567\) 1.86845 + 23.7383i 0.0784676 + 0.996917i
\(568\) 0 0
\(569\) −1.39253 7.89743i −0.0583779 0.331077i 0.941606 0.336716i \(-0.109316\pi\)
−0.999984 + 0.00563874i \(0.998205\pi\)
\(570\) 0 0
\(571\) 20.7749 7.56144i 0.869401 0.316436i 0.131477 0.991319i \(-0.458028\pi\)
0.737925 + 0.674883i \(0.235806\pi\)
\(572\) 0 0
\(573\) −10.6801 + 19.7151i −0.446166 + 0.823611i
\(574\) 0 0
\(575\) 0.305175 + 0.528579i 0.0127267 + 0.0220433i
\(576\) 0 0
\(577\) 21.1011 + 36.5482i 0.878451 + 1.52152i 0.853040 + 0.521845i \(0.174756\pi\)
0.0254109 + 0.999677i \(0.491911\pi\)
\(578\) 0 0
\(579\) −6.25006 2.08460i −0.259744 0.0866331i
\(580\) 0 0
\(581\) 27.7172 31.0888i 1.14990 1.28978i
\(582\) 0 0
\(583\) 0.544375 0.456785i 0.0225457 0.0189181i
\(584\) 0 0
\(585\) 20.7578 + 15.5800i 0.858231 + 0.644154i
\(586\) 0 0
\(587\) −2.04599 + 1.71679i −0.0844471 + 0.0708595i −0.684034 0.729450i \(-0.739776\pi\)
0.599587 + 0.800310i \(0.295332\pi\)
\(588\) 0 0
\(589\) −0.142787 + 0.809784i −0.00588342 + 0.0333665i
\(590\) 0 0
\(591\) 1.69548 11.4194i 0.0697428 0.469731i
\(592\) 0 0
\(593\) −21.0319 36.4283i −0.863677 1.49593i −0.868355 0.495943i \(-0.834823\pi\)
0.00467857 0.999989i \(-0.498511\pi\)
\(594\) 0 0
\(595\) 11.9257 6.41631i 0.488904 0.263043i
\(596\) 0 0
\(597\) −3.46764 + 23.3552i −0.141921 + 0.955864i
\(598\) 0 0
\(599\) −15.7818 13.2425i −0.644826 0.541073i 0.260670 0.965428i \(-0.416056\pi\)
−0.905496 + 0.424355i \(0.860501\pi\)
\(600\) 0 0
\(601\) 32.5157 27.2839i 1.32634 1.11293i 0.341424 0.939909i \(-0.389091\pi\)
0.984918 0.173024i \(-0.0553537\pi\)
\(602\) 0 0
\(603\) 14.8144 0.804795i 0.603291 0.0327738i
\(604\) 0 0
\(605\) −20.7534 7.55363i −0.843747 0.307099i
\(606\) 0 0
\(607\) 20.9845 + 17.6081i 0.851736 + 0.714692i 0.960171 0.279412i \(-0.0901395\pi\)
−0.108435 + 0.994104i \(0.534584\pi\)
\(608\) 0 0
\(609\) 1.41198 0.244810i 0.0572163 0.00992019i
\(610\) 0 0
\(611\) −9.82345 −0.397414
\(612\) 0 0
\(613\) −15.4798 −0.625225 −0.312612 0.949881i \(-0.601204\pi\)
−0.312612 + 0.949881i \(0.601204\pi\)
\(614\) 0 0
\(615\) −28.1544 + 0.764181i −1.13530 + 0.0308148i
\(616\) 0 0
\(617\) −29.5496 24.7951i −1.18962 0.998212i −0.999866 0.0163810i \(-0.994786\pi\)
−0.189757 0.981831i \(-0.560770\pi\)
\(618\) 0 0
\(619\) −23.7500 + 19.9286i −0.954593 + 0.800999i −0.980065 0.198677i \(-0.936336\pi\)
0.0254717 + 0.999676i \(0.491891\pi\)
\(620\) 0 0
\(621\) −9.41212 6.67296i −0.377695 0.267777i
\(622\) 0 0
\(623\) −2.54123 3.21990i −0.101812 0.129003i
\(624\) 0 0
\(625\) −4.08942 + 23.1923i −0.163577 + 0.927690i
\(626\) 0 0
\(627\) −0.779854 + 0.0211672i −0.0311444 + 0.000845336i
\(628\) 0 0
\(629\) −0.759123 1.31484i −0.0302682 0.0524261i
\(630\) 0 0
\(631\) −20.9592 + 36.3024i −0.834372 + 1.44517i 0.0601695 + 0.998188i \(0.480836\pi\)
−0.894541 + 0.446986i \(0.852497\pi\)
\(632\) 0 0
\(633\) 15.9594 14.1469i 0.634328 0.562288i
\(634\) 0 0
\(635\) 14.5216 + 12.1851i 0.576274 + 0.483551i
\(636\) 0 0
\(637\) −25.5614 11.0811i −1.01278 0.439048i
\(638\) 0 0
\(639\) −24.4949 7.43765i −0.969002 0.294229i
\(640\) 0 0
\(641\) −2.30244 13.0578i −0.0909408 0.515751i −0.995916 0.0902863i \(-0.971222\pi\)
0.904975 0.425465i \(-0.139889\pi\)
\(642\) 0 0
\(643\) −0.800161 + 4.53794i −0.0315553 + 0.178959i −0.996512 0.0834505i \(-0.973406\pi\)
0.964957 + 0.262409i \(0.0845171\pi\)
\(644\) 0 0
\(645\) −4.68945 + 31.5843i −0.184647 + 1.24363i
\(646\) 0 0
\(647\) −7.66162 + 13.2703i −0.301209 + 0.521710i −0.976410 0.215924i \(-0.930724\pi\)
0.675201 + 0.737634i \(0.264057\pi\)
\(648\) 0 0
\(649\) 0.388553 + 0.672994i 0.0152520 + 0.0264173i
\(650\) 0 0
\(651\) 4.94506 5.85919i 0.193812 0.229640i
\(652\) 0 0
\(653\) −22.4735 + 8.17968i −0.879456 + 0.320096i −0.741990 0.670411i \(-0.766118\pi\)
−0.137466 + 0.990507i \(0.543896\pi\)
\(654\) 0 0
\(655\) 7.46925 + 42.3602i 0.291848 + 1.65515i
\(656\) 0 0
\(657\) 5.59507 + 24.0252i 0.218284 + 0.937314i
\(658\) 0 0
\(659\) 8.65033 + 49.0584i 0.336969 + 1.91105i 0.406860 + 0.913491i \(0.366624\pi\)
−0.0698911 + 0.997555i \(0.522265\pi\)
\(660\) 0 0
\(661\) −5.07549 + 28.7845i −0.197414 + 1.11959i 0.711526 + 0.702660i \(0.248005\pi\)
−0.908939 + 0.416928i \(0.863107\pi\)
\(662\) 0 0
\(663\) −3.25136 15.9031i −0.126272 0.617627i
\(664\) 0 0
\(665\) −2.40436 1.48604i −0.0932372 0.0576263i
\(666\) 0 0
\(667\) −0.347180 + 0.601333i −0.0134428 + 0.0232837i
\(668\) 0 0
\(669\) 4.98281 0.135246i 0.192647 0.00522891i
\(670\) 0 0
\(671\) −5.89104 4.94317i −0.227421 0.190829i
\(672\) 0 0
\(673\) 7.37079 + 2.68275i 0.284123 + 0.103412i 0.480151 0.877186i \(-0.340582\pi\)
−0.196027 + 0.980598i \(0.562804\pi\)
\(674\) 0 0
\(675\) 0.361588 + 1.38180i 0.0139175 + 0.0531855i
\(676\) 0 0
\(677\) −6.71900 38.1053i −0.258232 1.46451i −0.787638 0.616138i \(-0.788696\pi\)
0.529406 0.848369i \(-0.322415\pi\)
\(678\) 0 0
\(679\) −2.86395 0.594065i −0.109908 0.0227981i
\(680\) 0 0
\(681\) −11.2317 18.2892i −0.430400 0.700844i
\(682\) 0 0
\(683\) −29.0563 −1.11181 −0.555905 0.831246i \(-0.687628\pi\)
−0.555905 + 0.831246i \(0.687628\pi\)
\(684\) 0 0
\(685\) 0.0747911 0.129542i 0.00285762 0.00494955i
\(686\) 0 0
\(687\) 8.81553 + 43.1187i 0.336333 + 1.64508i
\(688\) 0 0
\(689\) 0.535897 3.03923i 0.0204161 0.115785i
\(690\) 0 0
\(691\) −14.9798 + 12.5696i −0.569860 + 0.478169i −0.881599 0.471998i \(-0.843533\pi\)
0.311739 + 0.950168i \(0.399088\pi\)
\(692\) 0 0
\(693\) 6.38606 + 3.48310i 0.242586 + 0.132312i
\(694\) 0 0
\(695\) 13.0944 + 4.76595i 0.496697 + 0.180783i
\(696\) 0 0
\(697\) 13.4935 + 11.3224i 0.511104 + 0.428868i
\(698\) 0 0
\(699\) 22.3912 + 17.7759i 0.846915 + 0.672346i
\(700\) 0 0
\(701\) 13.2829 0.501688 0.250844 0.968028i \(-0.419292\pi\)
0.250844 + 0.968028i \(0.419292\pi\)
\(702\) 0 0
\(703\) −0.158445 + 0.274434i −0.00597586 + 0.0103505i
\(704\) 0 0
\(705\) 7.27820 + 5.77799i 0.274113 + 0.217612i
\(706\) 0 0
\(707\) 41.5853 + 8.62597i 1.56398 + 0.324413i
\(708\) 0 0
\(709\) −16.8649 6.13833i −0.633375 0.230530i 0.00532452 0.999986i \(-0.498305\pi\)
−0.638700 + 0.769456i \(0.720527\pi\)
\(710\) 0 0
\(711\) 43.2360 18.4502i 1.62148 0.691937i
\(712\) 0 0
\(713\) 0.645094 + 3.65851i 0.0241590 + 0.137012i
\(714\) 0 0
\(715\) 7.45054 2.71177i 0.278634 0.101415i
\(716\) 0 0
\(717\) 8.87244 + 43.3971i 0.331347 + 1.62069i
\(718\) 0 0
\(719\) −4.15770 −0.155056 −0.0775280 0.996990i \(-0.524703\pi\)
−0.0775280 + 0.996990i \(0.524703\pi\)
\(720\) 0 0
\(721\) −1.36746 + 45.5758i −0.0509267 + 1.69733i
\(722\) 0 0
\(723\) −21.5853 + 0.585880i −0.802767 + 0.0217891i
\(724\) 0 0
\(725\) 0.0807758 0.0294000i 0.00299994 0.00109189i
\(726\) 0 0
\(727\) −23.1268 8.41747i −0.857726 0.312187i −0.124540 0.992215i \(-0.539745\pi\)
−0.733186 + 0.680028i \(0.761968\pi\)
\(728\) 0 0
\(729\) −17.1117 20.8851i −0.633767 0.773524i
\(730\) 0 0
\(731\) 15.2977 12.8363i 0.565806 0.474767i
\(732\) 0 0
\(733\) 1.60656 9.11124i 0.0593396 0.336531i −0.940656 0.339360i \(-0.889789\pi\)
0.999996 + 0.00282903i \(0.000900510\pi\)
\(734\) 0 0
\(735\) 12.4207 + 23.2447i 0.458145 + 0.857395i
\(736\) 0 0
\(737\) 2.26615 3.92508i 0.0834746 0.144582i
\(738\) 0 0
\(739\) 7.81739 + 13.5401i 0.287567 + 0.498081i 0.973229 0.229840i \(-0.0738202\pi\)
−0.685661 + 0.727921i \(0.740487\pi\)
\(740\) 0 0
\(741\) −2.53530 + 2.24737i −0.0931365 + 0.0825590i
\(742\) 0 0
\(743\) 1.39183 0.506586i 0.0510614 0.0185848i −0.316363 0.948638i \(-0.602462\pi\)
0.367425 + 0.930053i \(0.380240\pi\)
\(744\) 0 0
\(745\) 35.1193 + 12.7824i 1.28667 + 0.468311i
\(746\) 0 0
\(747\) −5.66590 + 46.8860i −0.207305 + 1.71547i
\(748\) 0 0
\(749\) −13.4736 + 1.96112i −0.492314 + 0.0716577i
\(750\) 0 0
\(751\) 26.6022 9.68241i 0.970728 0.353316i 0.192500 0.981297i \(-0.438341\pi\)
0.778229 + 0.627981i \(0.216118\pi\)
\(752\) 0 0
\(753\) 5.02719 33.8591i 0.183201 1.23389i
\(754\) 0 0
\(755\) 18.4327 0.670836
\(756\) 0 0
\(757\) −9.48414 −0.344707 −0.172353 0.985035i \(-0.555137\pi\)
−0.172353 + 0.985035i \(0.555137\pi\)
\(758\) 0 0
\(759\) −3.27810 + 1.29490i −0.118988 + 0.0470019i
\(760\) 0 0
\(761\) −10.7036 + 3.89577i −0.388003 + 0.141222i −0.528654 0.848838i \(-0.677303\pi\)
0.140650 + 0.990059i \(0.455081\pi\)
\(762\) 0 0
\(763\) 14.8242 + 18.7832i 0.536672 + 0.679998i
\(764\) 0 0
\(765\) −6.94502 + 13.6950i −0.251098 + 0.495145i
\(766\) 0 0
\(767\) 3.17127 + 1.15425i 0.114508 + 0.0416775i
\(768\) 0 0
\(769\) 37.3493 13.5940i 1.34685 0.490213i 0.434887 0.900485i \(-0.356788\pi\)
0.911963 + 0.410272i \(0.134566\pi\)
\(770\) 0 0
\(771\) −8.03265 39.2894i −0.289289 1.41497i
\(772\) 0 0
\(773\) −4.13102 7.15513i −0.148582 0.257352i 0.782121 0.623126i \(-0.214138\pi\)
−0.930704 + 0.365774i \(0.880804\pi\)
\(774\) 0 0
\(775\) 0.229950 0.398286i 0.00826006 0.0143069i
\(776\) 0 0
\(777\) 2.56309 1.47005i 0.0919504 0.0527376i
\(778\) 0 0
\(779\) 0.638422 3.62067i 0.0228739 0.129724i
\(780\) 0 0
\(781\) −5.99063 + 5.02674i −0.214362 + 0.179871i
\(782\) 0 0
\(783\) −1.15570 + 1.14224i −0.0413015 + 0.0408204i
\(784\) 0 0
\(785\) 2.76418 + 1.00608i 0.0986578 + 0.0359085i
\(786\) 0 0
\(787\) 15.5434 5.65733i 0.554062 0.201662i −0.0497885 0.998760i \(-0.515855\pi\)
0.603850 + 0.797098i \(0.293632\pi\)
\(788\) 0 0
\(789\) −15.8880 + 29.3288i −0.565626 + 1.04413i
\(790\) 0 0
\(791\) 9.68089 + 5.98338i 0.344213 + 0.212744i
\(792\) 0 0
\(793\) −33.3968 −1.18596
\(794\) 0 0
\(795\) −2.18467 + 1.93656i −0.0774822 + 0.0686826i
\(796\) 0 0
\(797\) 50.9520 18.5450i 1.80481 0.656898i 0.807019 0.590526i \(-0.201080\pi\)
0.997795 0.0663722i \(-0.0211425\pi\)
\(798\) 0 0
\(799\) −1.00922 5.72357i −0.0357036 0.202485i
\(800\) 0 0
\(801\) 4.45048 + 1.35135i 0.157250 + 0.0477476i
\(802\) 0 0
\(803\) 7.08133 + 2.57740i 0.249895 + 0.0909543i
\(804\) 0 0
\(805\) −12.5038 2.59364i −0.440701 0.0914138i
\(806\) 0 0
\(807\) −13.3107 + 5.25792i −0.468558 + 0.185087i
\(808\) 0 0
\(809\) −13.0155 + 22.5436i −0.457602 + 0.792590i −0.998834 0.0482838i \(-0.984625\pi\)
0.541232 + 0.840873i \(0.317958\pi\)
\(810\) 0 0
\(811\) −0.752228 −0.0264143 −0.0132072 0.999913i \(-0.504204\pi\)
−0.0132072 + 0.999913i \(0.504204\pi\)
\(812\) 0 0
\(813\) 6.51249 43.8629i 0.228403 1.53834i
\(814\) 0 0
\(815\) 25.2351 + 21.1748i 0.883947 + 0.741720i
\(816\) 0 0
\(817\) −3.91673 1.42557i −0.137029 0.0498745i
\(818\) 0 0
\(819\) 30.9679 6.23913i 1.08211 0.218013i
\(820\) 0 0
\(821\) −26.9525 + 22.6158i −0.940648 + 0.789297i −0.977698 0.210016i \(-0.932648\pi\)
0.0370502 + 0.999313i \(0.488204\pi\)
\(822\) 0 0
\(823\) 6.54189 37.1009i 0.228036 1.29326i −0.628759 0.777600i \(-0.716437\pi\)
0.856795 0.515657i \(-0.172452\pi\)
\(824\) 0 0
\(825\) 0.413919 + 0.138056i 0.0144108 + 0.00480648i
\(826\) 0 0
\(827\) −7.74484 + 13.4145i −0.269314 + 0.466466i −0.968685 0.248293i \(-0.920130\pi\)
0.699371 + 0.714759i \(0.253464\pi\)
\(828\) 0 0
\(829\) −19.0359 −0.661146 −0.330573 0.943781i \(-0.607242\pi\)
−0.330573 + 0.943781i \(0.607242\pi\)
\(830\) 0 0
\(831\) 11.0508 20.3996i 0.383350 0.707655i
\(832\) 0 0
\(833\) 3.83025 16.0316i 0.132710 0.555461i
\(834\) 0 0
\(835\) 9.11879 + 51.7152i 0.315569 + 1.78968i
\(836\) 0 0
\(837\) −0.808428 + 8.65595i −0.0279433 + 0.299194i
\(838\) 0 0
\(839\) −6.80913 2.47832i −0.235077 0.0855611i 0.221795 0.975093i \(-0.428808\pi\)
−0.456873 + 0.889532i \(0.651030\pi\)
\(840\) 0 0
\(841\) −22.1404 18.5780i −0.763461 0.640620i
\(842\) 0 0
\(843\) −21.5822 + 39.8403i −0.743331 + 1.37217i
\(844\) 0 0
\(845\) 3.08699 5.34683i 0.106196 0.183937i
\(846\) 0 0
\(847\) −23.6723 + 12.7363i −0.813391 + 0.437626i
\(848\) 0 0
\(849\) 15.6684 13.8890i 0.537739 0.476668i
\(850\) 0 0
\(851\) −0.248607 + 1.40992i −0.00852214 + 0.0483315i
\(852\) 0 0
\(853\) −4.80413 27.2456i −0.164490 0.932872i −0.949588 0.313500i \(-0.898498\pi\)
0.785098 0.619372i \(-0.212613\pi\)
\(854\) 0 0
\(855\) 3.20027 0.173855i 0.109447 0.00594570i
\(856\) 0 0
\(857\) 4.37631 + 24.8193i 0.149492 + 0.847811i 0.963650 + 0.267168i \(0.0860878\pi\)
−0.814158 + 0.580643i \(0.802801\pi\)
\(858\) 0 0
\(859\) −6.35293 + 2.31228i −0.216759 + 0.0788938i −0.448117 0.893975i \(-0.647905\pi\)
0.231358 + 0.972869i \(0.425683\pi\)
\(860\) 0 0
\(861\) −22.1102 + 26.1974i −0.753512 + 0.892805i
\(862\) 0 0
\(863\) 7.12740 + 12.3450i 0.242620 + 0.420230i 0.961460 0.274946i \(-0.0886600\pi\)
−0.718840 + 0.695176i \(0.755327\pi\)
\(864\) 0 0
\(865\) 25.5390 44.2348i 0.868352 1.50403i
\(866\) 0 0
\(867\) −18.4539 + 7.28955i −0.626726 + 0.247566i
\(868\) 0 0
\(869\) 2.49365 14.1422i 0.0845913 0.479741i
\(870\) 0 0
\(871\) −3.41787 19.3837i −0.115810 0.656792i
\(872\) 0 0
\(873\) 3.05041 1.30171i 0.103241 0.0440562i
\(874\) 0 0
\(875\) 18.7943 + 23.8136i 0.635364 + 0.805047i
\(876\) 0 0
\(877\) −28.3008 23.7472i −0.955650 0.801886i 0.0245896 0.999698i \(-0.492172\pi\)
−0.980240 + 0.197812i \(0.936617\pi\)
\(878\) 0 0
\(879\) −6.37208 31.1672i −0.214925 1.05124i
\(880\) 0 0
\(881\) −21.5123 + 37.2604i −0.724768 + 1.25533i 0.234302 + 0.972164i \(0.424720\pi\)
−0.959069 + 0.283171i \(0.908614\pi\)
\(882\) 0 0
\(883\) −3.95611 6.85218i −0.133134 0.230594i 0.791749 0.610846i \(-0.209171\pi\)
−0.924883 + 0.380252i \(0.875837\pi\)
\(884\) 0 0
\(885\) −1.67069 2.72047i −0.0561595 0.0914477i
\(886\) 0 0
\(887\) 3.81832 21.6547i 0.128206 0.727095i −0.851145 0.524931i \(-0.824091\pi\)
0.979352 0.202165i \(-0.0647976\pi\)
\(888\) 0 0
\(889\) 22.8324 3.32333i 0.765775 0.111461i
\(890\) 0 0
\(891\) −8.19961 + 0.893525i −0.274697 + 0.0299342i
\(892\) 0 0
\(893\) −0.929256 + 0.779738i −0.0310964 + 0.0260929i
\(894\) 0 0
\(895\) −10.0311 8.41712i −0.335304 0.281353i
\(896\) 0 0
\(897\) −7.29077 + 13.4586i −0.243432 + 0.449369i
\(898\) 0 0
\(899\) 0.523202 0.0174498
\(900\) 0 0
\(901\) 1.82584 0.0608276
\(902\) 0 0
\(903\) 24.8962 + 29.8430i 0.828492 + 0.993111i
\(904\) 0 0
\(905\) 4.19214 + 3.51762i 0.139351 + 0.116930i
\(906\) 0 0
\(907\) 12.0346 + 4.38024i 0.399603 + 0.145444i 0.534001 0.845484i \(-0.320688\pi\)
−0.134398 + 0.990927i \(0.542910\pi\)
\(908\) 0 0
\(909\) −44.2927 + 18.9012i −1.46910 + 0.626912i
\(910\) 0 0
\(911\) −25.9130 + 21.7436i −0.858536 + 0.720397i −0.961652 0.274272i \(-0.911563\pi\)
0.103116 + 0.994669i \(0.467119\pi\)
\(912\) 0 0
\(913\) 11.0519 + 9.27366i 0.365765 + 0.306913i
\(914\) 0 0
\(915\) 24.7437 + 19.6434i 0.818002 + 0.649392i
\(916\) 0 0
\(917\) 44.5344 + 27.5249i 1.47065 + 0.908954i
\(918\) 0 0
\(919\) −18.6409 32.2870i −0.614907 1.06505i −0.990401 0.138225i \(-0.955860\pi\)
0.375494 0.926825i \(-0.377473\pi\)
\(920\) 0 0
\(921\) −30.2954 + 11.9671i −0.998267 + 0.394331i
\(922\) 0 0
\(923\) −5.89734 + 33.4455i −0.194113 + 1.10087i
\(924\) 0 0
\(925\) 0.135772 0.113926i 0.00446414 0.00374586i
\(926\) 0 0
\(927\) −28.2414 43.3065i −0.927570 1.42237i
\(928\) 0 0
\(929\) 27.1449 22.7773i 0.890595 0.747298i −0.0777341 0.996974i \(-0.524769\pi\)
0.968329 + 0.249676i \(0.0803241\pi\)
\(930\) 0 0
\(931\) −3.29756 + 0.980715i −0.108073 + 0.0321416i
\(932\) 0 0
\(933\) −17.0886 + 15.1478i −0.559454 + 0.495918i
\(934\) 0 0
\(935\) 2.34543 + 4.06241i 0.0767039 + 0.132855i
\(936\) 0 0
\(937\) −8.54931 14.8078i −0.279294 0.483751i 0.691916 0.721978i \(-0.256767\pi\)
−0.971209 + 0.238227i \(0.923434\pi\)
\(938\) 0 0
\(939\) 15.4720 0.419948i 0.504909 0.0137045i
\(940\) 0 0
\(941\) −34.1779 + 12.4397i −1.11417 + 0.405524i −0.832521 0.553994i \(-0.813103\pi\)
−0.281648 + 0.959518i \(0.590881\pi\)
\(942\) 0 0
\(943\) −2.88432 16.3578i −0.0939264 0.532683i
\(944\) 0 0
\(945\) −26.6139 13.5922i −0.865750 0.442155i
\(946\) 0 0
\(947\) 4.88894 + 27.7266i 0.158869 + 0.900993i 0.955163 + 0.296082i \(0.0956801\pi\)
−0.796293 + 0.604911i \(0.793209\pi\)
\(948\) 0 0
\(949\) 30.7526 11.1930i 0.998273 0.363342i
\(950\) 0 0
\(951\) −29.1659 47.4924i −0.945768 1.54005i
\(952\) 0 0
\(953\) −22.5144 38.9960i −0.729312 1.26320i −0.957175 0.289511i \(-0.906507\pi\)
0.227863 0.973693i \(-0.426826\pi\)
\(954\) 0 0
\(955\) −14.0699 24.3698i −0.455292 0.788589i
\(956\) 0 0
\(957\) 0.0994296 + 0.486332i 0.00321410 + 0.0157209i
\(958\) 0 0
\(959\) −0.0571105 0.172874i −0.00184419 0.00558240i
\(960\) 0 0
\(961\) −21.6030 + 18.1271i −0.696872 + 0.584745i
\(962\) 0 0
\(963\) 11.2709 10.5507i 0.363200 0.339990i
\(964\) 0 0
\(965\) 6.33416 5.31499i 0.203904 0.171096i
\(966\) 0 0
\(967\) −0.219291 + 1.24366i −0.00705192 + 0.0399934i −0.988131 0.153616i \(-0.950908\pi\)
0.981079 + 0.193609i \(0.0620193\pi\)
\(968\) 0 0
\(969\) −1.56988 1.24629i −0.0504318 0.0400366i
\(970\) 0 0
\(971\) −25.3239 43.8622i −0.812682 1.40761i −0.910981 0.412449i \(-0.864674\pi\)
0.0982991 0.995157i \(-0.468660\pi\)
\(972\) 0 0
\(973\) 14.9360 8.03597i 0.478827 0.257621i
\(974\) 0 0
\(975\) 1.76239 0.696170i 0.0564416 0.0222953i
\(976\) 0 0
\(977\) 40.1670 + 33.7041i 1.28506 + 1.07829i 0.992526 + 0.122033i \(0.0389414\pi\)
0.292530 + 0.956256i \(0.405503\pi\)
\(978\) 0 0
\(979\) 1.08844 0.913310i 0.0347867 0.0291895i
\(980\) 0 0
\(981\) −25.9618 7.88307i −0.828896 0.251687i
\(982\) 0 0
\(983\) 30.9421 + 11.2620i 0.986901 + 0.359203i 0.784519 0.620104i \(-0.212910\pi\)
0.202381 + 0.979307i \(0.435132\pi\)
\(984\) 0 0
\(985\) 11.0988 + 9.31303i 0.353638 + 0.296738i
\(986\) 0 0
\(987\) 11.1445 1.93224i 0.354734 0.0615039i
\(988\) 0 0
\(989\) −18.8310 −0.598791
\(990\) 0 0
\(991\) −9.48076 −0.301166 −0.150583 0.988597i \(-0.548115\pi\)
−0.150583 + 0.988597i \(0.548115\pi\)
\(992\) 0 0
\(993\) −25.9383 42.2367i −0.823126 1.34034i
\(994\) 0 0
\(995\) −22.6996 19.0472i −0.719625 0.603837i
\(996\) 0 0
\(997\) 1.33794 1.12266i 0.0423729 0.0355551i −0.621355 0.783529i \(-0.713418\pi\)
0.663728 + 0.747974i \(0.268973\pi\)
\(998\) 0 0
\(999\) −1.43369 + 3.02811i −0.0453599 + 0.0958051i
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.bp.a.193.5 144
7.2 even 3 756.2.bq.a.625.22 yes 144
27.7 even 9 756.2.bq.a.277.22 yes 144
189.142 even 9 inner 756.2.bp.a.709.5 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.bp.a.193.5 144 1.1 even 1 trivial
756.2.bp.a.709.5 yes 144 189.142 even 9 inner
756.2.bq.a.277.22 yes 144 27.7 even 9
756.2.bq.a.625.22 yes 144 7.2 even 3