Properties

Label 756.2.bp.a.193.12
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 193.12
Character \(\chi\) \(=\) 756.193
Dual form 756.2.bp.a.709.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.128228 - 1.72730i) q^{3} +(3.80842 - 1.38615i) q^{5} +(-2.63217 - 0.267690i) q^{7} +(-2.96712 - 0.442975i) q^{9} +O(q^{10})\) \(q+(0.128228 - 1.72730i) q^{3} +(3.80842 - 1.38615i) q^{5} +(-2.63217 - 0.267690i) q^{7} +(-2.96712 - 0.442975i) q^{9} +(-4.19188 - 1.52572i) q^{11} +(0.0262487 - 0.00955373i) q^{13} +(-1.90595 - 6.75602i) q^{15} +(-3.72455 - 6.45111i) q^{17} +(-2.20972 + 3.82736i) q^{19} +(-0.799898 + 4.51222i) q^{21} +(0.544807 - 3.08975i) q^{23} +(8.75243 - 7.34416i) q^{25} +(-1.14562 + 5.06829i) q^{27} +(8.22017 + 2.99190i) q^{29} +(2.29370 - 0.834840i) q^{31} +(-3.17289 + 7.04498i) q^{33} +(-10.3955 + 2.62912i) q^{35} -1.31248 q^{37} +(-0.0131363 - 0.0465643i) q^{39} +(-1.58379 + 0.576451i) q^{41} +(-1.14929 - 6.51796i) q^{43} +(-11.9141 + 2.42584i) q^{45} +(11.5317 + 4.19720i) q^{47} +(6.85668 + 1.40921i) q^{49} +(-11.6206 + 5.60619i) q^{51} +(3.70846 - 6.42325i) q^{53} -18.0793 q^{55} +(6.32763 + 4.30763i) q^{57} +(2.56898 + 2.15563i) q^{59} +(1.92140 + 0.699333i) q^{61} +(7.69138 + 1.96025i) q^{63} +(0.0867230 - 0.0727693i) q^{65} +(1.09450 - 6.20720i) q^{67} +(-5.26706 - 1.33724i) q^{69} +(-1.05465 + 1.82670i) q^{71} -11.1372 q^{73} +(-11.5632 - 16.0598i) q^{75} +(10.6253 + 5.13808i) q^{77} +(-0.937848 - 5.31880i) q^{79} +(8.60755 + 2.62872i) q^{81} +(-3.56197 - 1.29645i) q^{83} +(-23.1269 - 19.4057i) q^{85} +(6.22195 - 13.8150i) q^{87} +(4.84841 - 8.39768i) q^{89} +(-0.0716485 + 0.0181206i) q^{91} +(-1.14790 - 4.06896i) q^{93} +(-3.11027 + 17.6392i) q^{95} +(-1.36290 - 7.72940i) q^{97} +(11.7619 + 6.38388i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 12 q^{9}+O(q^{10}) \) 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
\(3\) 0.128228 1.72730i 0.0740324 0.997256i
\(4\) 0 0
\(5\) 3.80842 1.38615i 1.70318 0.619906i 0.706997 0.707217i \(-0.250050\pi\)
0.996181 + 0.0873111i \(0.0278274\pi\)
\(6\) 0 0
\(7\) −2.63217 0.267690i −0.994868 0.101177i
\(8\) 0 0
\(9\) −2.96712 0.442975i −0.989038 0.147658i
\(10\) 0 0
\(11\) −4.19188 1.52572i −1.26390 0.460021i −0.378823 0.925469i \(-0.623671\pi\)
−0.885075 + 0.465448i \(0.845893\pi\)
\(12\) 0 0
\(13\) 0.0262487 0.00955373i 0.00728007 0.00264973i −0.338378 0.941010i \(-0.609878\pi\)
0.345658 + 0.938361i \(0.387656\pi\)
\(14\) 0 0
\(15\) −1.90595 6.75602i −0.492114 1.74440i
\(16\) 0 0
\(17\) −3.72455 6.45111i −0.903336 1.56462i −0.823136 0.567844i \(-0.807778\pi\)
−0.0801995 0.996779i \(-0.525556\pi\)
\(18\) 0 0
\(19\) −2.20972 + 3.82736i −0.506946 + 0.878056i 0.493022 + 0.870017i \(0.335892\pi\)
−0.999968 + 0.00803878i \(0.997441\pi\)
\(20\) 0 0
\(21\) −0.799898 + 4.51222i −0.174552 + 0.984648i
\(22\) 0 0
\(23\) 0.544807 3.08975i 0.113600 0.644258i −0.873834 0.486225i \(-0.838374\pi\)
0.987434 0.158033i \(-0.0505153\pi\)
\(24\) 0 0
\(25\) 8.75243 7.34416i 1.75049 1.46883i
\(26\) 0 0
\(27\) −1.14562 + 5.06829i −0.220474 + 0.975393i
\(28\) 0 0
\(29\) 8.22017 + 2.99190i 1.52645 + 0.555581i 0.962748 0.270400i \(-0.0871559\pi\)
0.563698 + 0.825981i \(0.309378\pi\)
\(30\) 0 0
\(31\) 2.29370 0.834840i 0.411961 0.149942i −0.127722 0.991810i \(-0.540766\pi\)
0.539683 + 0.841868i \(0.318544\pi\)
\(32\) 0 0
\(33\) −3.17289 + 7.04498i −0.552328 + 1.22637i
\(34\) 0 0
\(35\) −10.3955 + 2.62912i −1.75716 + 0.444402i
\(36\) 0 0
\(37\) −1.31248 −0.215770 −0.107885 0.994163i \(-0.534408\pi\)
−0.107885 + 0.994163i \(0.534408\pi\)
\(38\) 0 0
\(39\) −0.0131363 0.0465643i −0.00210350 0.00745626i
\(40\) 0 0
\(41\) −1.58379 + 0.576451i −0.247346 + 0.0900265i −0.462718 0.886505i \(-0.653126\pi\)
0.215372 + 0.976532i \(0.430904\pi\)
\(42\) 0 0
\(43\) −1.14929 6.51796i −0.175265 0.993980i −0.937837 0.347076i \(-0.887175\pi\)
0.762572 0.646904i \(-0.223937\pi\)
\(44\) 0 0
\(45\) −11.9141 + 2.42584i −1.77604 + 0.361622i
\(46\) 0 0
\(47\) 11.5317 + 4.19720i 1.68207 + 0.612225i 0.993592 0.113028i \(-0.0360550\pi\)
0.688482 + 0.725253i \(0.258277\pi\)
\(48\) 0 0
\(49\) 6.85668 + 1.40921i 0.979526 + 0.201316i
\(50\) 0 0
\(51\) −11.6206 + 5.60619i −1.62721 + 0.785024i
\(52\) 0 0
\(53\) 3.70846 6.42325i 0.509396 0.882301i −0.490544 0.871416i \(-0.663202\pi\)
0.999941 0.0108843i \(-0.00346465\pi\)
\(54\) 0 0
\(55\) −18.0793 −2.43781
\(56\) 0 0
\(57\) 6.32763 + 4.30763i 0.838116 + 0.570559i
\(58\) 0 0
\(59\) 2.56898 + 2.15563i 0.334453 + 0.280639i 0.794511 0.607249i \(-0.207727\pi\)
−0.460058 + 0.887889i \(0.652172\pi\)
\(60\) 0 0
\(61\) 1.92140 + 0.699333i 0.246010 + 0.0895405i 0.462082 0.886837i \(-0.347102\pi\)
−0.216072 + 0.976377i \(0.569325\pi\)
\(62\) 0 0
\(63\) 7.69138 + 1.96025i 0.969023 + 0.246969i
\(64\) 0 0
\(65\) 0.0867230 0.0727693i 0.0107567 0.00902592i
\(66\) 0 0
\(67\) 1.09450 6.20720i 0.133714 0.758330i −0.842033 0.539427i \(-0.818641\pi\)
0.975747 0.218903i \(-0.0702479\pi\)
\(68\) 0 0
\(69\) −5.26706 1.33724i −0.634080 0.160984i
\(70\) 0 0
\(71\) −1.05465 + 1.82670i −0.125163 + 0.216789i −0.921797 0.387673i \(-0.873279\pi\)
0.796633 + 0.604463i \(0.206612\pi\)
\(72\) 0 0
\(73\) −11.1372 −1.30351 −0.651754 0.758430i \(-0.725967\pi\)
−0.651754 + 0.758430i \(0.725967\pi\)
\(74\) 0 0
\(75\) −11.5632 16.0598i −1.33521 1.85442i
\(76\) 0 0
\(77\) 10.6253 + 5.13808i 1.21087 + 0.585538i
\(78\) 0 0
\(79\) −0.937848 5.31880i −0.105516 0.598412i −0.991013 0.133766i \(-0.957293\pi\)
0.885497 0.464646i \(-0.153818\pi\)
\(80\) 0 0
\(81\) 8.60755 + 2.62872i 0.956394 + 0.292080i
\(82\) 0 0
\(83\) −3.56197 1.29645i −0.390977 0.142304i 0.139049 0.990286i \(-0.455596\pi\)
−0.530026 + 0.847981i \(0.677818\pi\)
\(84\) 0 0
\(85\) −23.1269 19.4057i −2.50846 2.10485i
\(86\) 0 0
\(87\) 6.22195 13.8150i 0.667063 1.48113i
\(88\) 0 0
\(89\) 4.84841 8.39768i 0.513930 0.890153i −0.485939 0.873992i \(-0.661522\pi\)
0.999869 0.0161603i \(-0.00514421\pi\)
\(90\) 0 0
\(91\) −0.0716485 + 0.0181206i −0.00751080 + 0.00189955i
\(92\) 0 0
\(93\) −1.14790 4.06896i −0.119032 0.421931i
\(94\) 0 0
\(95\) −3.11027 + 17.6392i −0.319107 + 1.80974i
\(96\) 0 0
\(97\) −1.36290 7.72940i −0.138382 0.784802i −0.972445 0.233133i \(-0.925102\pi\)
0.834063 0.551669i \(-0.186009\pi\)
\(98\) 0 0
\(99\) 11.7619 + 6.38388i 1.18212 + 0.641604i
\(100\) 0 0
\(101\) 0.608800 + 3.45268i 0.0605779 + 0.343554i 1.00000 0.000790964i \(0.000251772\pi\)
−0.939422 + 0.342763i \(0.888637\pi\)
\(102\) 0 0
\(103\) 1.06209 0.386569i 0.104651 0.0380898i −0.289164 0.957280i \(-0.593377\pi\)
0.393815 + 0.919190i \(0.371155\pi\)
\(104\) 0 0
\(105\) 3.20828 + 18.2932i 0.313096 + 1.78524i
\(106\) 0 0
\(107\) 7.32628 + 12.6895i 0.708258 + 1.22674i 0.965503 + 0.260393i \(0.0838521\pi\)
−0.257244 + 0.966346i \(0.582815\pi\)
\(108\) 0 0
\(109\) 0.847000 1.46705i 0.0811279 0.140518i −0.822607 0.568611i \(-0.807481\pi\)
0.903735 + 0.428093i \(0.140814\pi\)
\(110\) 0 0
\(111\) −0.168296 + 2.26704i −0.0159739 + 0.215178i
\(112\) 0 0
\(113\) −2.36323 + 13.4025i −0.222314 + 1.26081i 0.645440 + 0.763811i \(0.276674\pi\)
−0.867754 + 0.496994i \(0.834437\pi\)
\(114\) 0 0
\(115\) −2.20801 12.5223i −0.205898 1.16771i
\(116\) 0 0
\(117\) −0.0821149 + 0.0167195i −0.00759152 + 0.00154572i
\(118\) 0 0
\(119\) 8.07676 + 17.9775i 0.740396 + 1.64799i
\(120\) 0 0
\(121\) 6.81752 + 5.72058i 0.619775 + 0.520053i
\(122\) 0 0
\(123\) 0.792617 + 2.80959i 0.0714679 + 0.253332i
\(124\) 0 0
\(125\) 13.0207 22.5526i 1.16461 2.01716i
\(126\) 0 0
\(127\) 6.99720 + 12.1195i 0.620901 + 1.07543i 0.989318 + 0.145772i \(0.0465666\pi\)
−0.368417 + 0.929661i \(0.620100\pi\)
\(128\) 0 0
\(129\) −11.4058 + 1.14939i −1.00423 + 0.101198i
\(130\) 0 0
\(131\) 1.19539 6.77941i 0.104442 0.592319i −0.887000 0.461770i \(-0.847215\pi\)
0.991442 0.130550i \(-0.0416742\pi\)
\(132\) 0 0
\(133\) 6.84092 9.48275i 0.593183 0.822258i
\(134\) 0 0
\(135\) 2.66243 + 20.8902i 0.229145 + 1.79794i
\(136\) 0 0
\(137\) −3.15581 + 2.64804i −0.269619 + 0.226237i −0.767566 0.640970i \(-0.778532\pi\)
0.497946 + 0.867208i \(0.334088\pi\)
\(138\) 0 0
\(139\) 1.57493 + 1.32152i 0.133584 + 0.112090i 0.707131 0.707082i \(-0.249989\pi\)
−0.573548 + 0.819172i \(0.694433\pi\)
\(140\) 0 0
\(141\) 8.72851 19.3805i 0.735073 1.63213i
\(142\) 0 0
\(143\) −0.124607 −0.0104202
\(144\) 0 0
\(145\) 35.4531 2.94422
\(146\) 0 0
\(147\) 3.31335 11.6628i 0.273280 0.961934i
\(148\) 0 0
\(149\) 13.3998 + 11.2437i 1.09775 + 0.921123i 0.997272 0.0738156i \(-0.0235176\pi\)
0.100480 + 0.994939i \(0.467962\pi\)
\(150\) 0 0
\(151\) 8.52331 + 3.10223i 0.693617 + 0.252456i 0.664683 0.747125i \(-0.268566\pi\)
0.0289341 + 0.999581i \(0.490789\pi\)
\(152\) 0 0
\(153\) 8.19348 + 20.7911i 0.662404 + 1.68086i
\(154\) 0 0
\(155\) 7.57817 6.35884i 0.608694 0.510755i
\(156\) 0 0
\(157\) −1.70912 1.43412i −0.136402 0.114455i 0.572034 0.820230i \(-0.306155\pi\)
−0.708436 + 0.705775i \(0.750599\pi\)
\(158\) 0 0
\(159\) −10.6193 7.22926i −0.842168 0.573317i
\(160\) 0 0
\(161\) −2.26112 + 7.98693i −0.178201 + 0.629458i
\(162\) 0 0
\(163\) −11.7924 20.4251i −0.923655 1.59982i −0.793710 0.608297i \(-0.791853\pi\)
−0.129946 0.991521i \(-0.541480\pi\)
\(164\) 0 0
\(165\) −2.31827 + 31.2283i −0.180477 + 2.43112i
\(166\) 0 0
\(167\) 2.84635 16.1424i 0.220257 1.24914i −0.651290 0.758829i \(-0.725772\pi\)
0.871547 0.490311i \(-0.163117\pi\)
\(168\) 0 0
\(169\) −9.95798 + 8.35574i −0.765998 + 0.642749i
\(170\) 0 0
\(171\) 8.25193 10.3774i 0.631041 0.793576i
\(172\) 0 0
\(173\) −8.64079 + 7.25049i −0.656947 + 0.551244i −0.909170 0.416425i \(-0.863283\pi\)
0.252223 + 0.967669i \(0.418838\pi\)
\(174\) 0 0
\(175\) −25.0039 + 16.9882i −1.89012 + 1.28419i
\(176\) 0 0
\(177\) 4.05283 4.16098i 0.304630 0.312759i
\(178\) 0 0
\(179\) 6.88245 + 11.9208i 0.514418 + 0.890999i 0.999860 + 0.0167298i \(0.00532549\pi\)
−0.485442 + 0.874269i \(0.661341\pi\)
\(180\) 0 0
\(181\) 7.29362 + 12.6329i 0.542130 + 0.938997i 0.998781 + 0.0493514i \(0.0157154\pi\)
−0.456651 + 0.889646i \(0.650951\pi\)
\(182\) 0 0
\(183\) 1.45433 3.22916i 0.107508 0.238706i
\(184\) 0 0
\(185\) −4.99846 + 1.81929i −0.367494 + 0.133757i
\(186\) 0 0
\(187\) 5.77027 + 32.7249i 0.421964 + 2.39308i
\(188\) 0 0
\(189\) 4.37219 13.0340i 0.318030 0.948081i
\(190\) 0 0
\(191\) −1.49639 8.48647i −0.108275 0.614060i −0.989861 0.142037i \(-0.954635\pi\)
0.881586 0.472023i \(-0.156476\pi\)
\(192\) 0 0
\(193\) 2.83258 1.03097i 0.203893 0.0742111i −0.238055 0.971252i \(-0.576510\pi\)
0.441948 + 0.897041i \(0.354288\pi\)
\(194\) 0 0
\(195\) −0.114574 0.159128i −0.00820481 0.0113954i
\(196\) 0 0
\(197\) −1.61652 2.79989i −0.115172 0.199484i 0.802676 0.596415i \(-0.203409\pi\)
−0.917849 + 0.396931i \(0.870075\pi\)
\(198\) 0 0
\(199\) 6.53332 + 11.3160i 0.463135 + 0.802173i 0.999115 0.0420573i \(-0.0133912\pi\)
−0.535980 + 0.844230i \(0.680058\pi\)
\(200\) 0 0
\(201\) −10.5813 2.68646i −0.746350 0.189488i
\(202\) 0 0
\(203\) −20.8360 10.0756i −1.46240 0.707172i
\(204\) 0 0
\(205\) −5.23268 + 4.39074i −0.365466 + 0.306662i
\(206\) 0 0
\(207\) −2.98519 + 8.92632i −0.207485 + 0.620422i
\(208\) 0 0
\(209\) 15.1024 12.6724i 1.04465 0.876567i
\(210\) 0 0
\(211\) 1.28375 7.28049i 0.0883767 0.501209i −0.908200 0.418536i \(-0.862543\pi\)
0.996577 0.0826730i \(-0.0263457\pi\)
\(212\) 0 0
\(213\) 3.02002 + 2.05592i 0.206928 + 0.140869i
\(214\) 0 0
\(215\) −13.4119 23.2300i −0.914682 1.58428i
\(216\) 0 0
\(217\) −6.26091 + 1.58344i −0.425018 + 0.107491i
\(218\) 0 0
\(219\) −1.42810 + 19.2372i −0.0965019 + 1.29993i
\(220\) 0 0
\(221\) −0.159397 0.133750i −0.0107222 0.00899697i
\(222\) 0 0
\(223\) 19.0957 16.0232i 1.27875 1.07300i 0.285330 0.958429i \(-0.407897\pi\)
0.993416 0.114566i \(-0.0365477\pi\)
\(224\) 0 0
\(225\) −29.2228 + 17.9139i −1.94818 + 1.19426i
\(226\) 0 0
\(227\) 9.22702 + 3.35836i 0.612419 + 0.222902i 0.629561 0.776951i \(-0.283235\pi\)
−0.0171425 + 0.999853i \(0.505457\pi\)
\(228\) 0 0
\(229\) −12.4235 10.4246i −0.820970 0.688875i 0.132229 0.991219i \(-0.457786\pi\)
−0.953199 + 0.302344i \(0.902231\pi\)
\(230\) 0 0
\(231\) 10.2375 17.6943i 0.673575 1.16420i
\(232\) 0 0
\(233\) 7.92115 0.518932 0.259466 0.965752i \(-0.416454\pi\)
0.259466 + 0.965752i \(0.416454\pi\)
\(234\) 0 0
\(235\) 49.7356 3.24439
\(236\) 0 0
\(237\) −9.30741 + 0.937925i −0.604582 + 0.0609248i
\(238\) 0 0
\(239\) −19.2276 16.1339i −1.24373 1.04361i −0.997223 0.0744714i \(-0.976273\pi\)
−0.246506 0.969141i \(-0.579283\pi\)
\(240\) 0 0
\(241\) 0.966642 0.811109i 0.0622669 0.0522481i −0.611123 0.791536i \(-0.709282\pi\)
0.673390 + 0.739287i \(0.264838\pi\)
\(242\) 0 0
\(243\) 5.64431 14.5307i 0.362082 0.932146i
\(244\) 0 0
\(245\) 28.0665 4.13753i 1.79310 0.264337i
\(246\) 0 0
\(247\) −0.0214368 + 0.121574i −0.00136399 + 0.00773557i
\(248\) 0 0
\(249\) −2.69610 + 5.98635i −0.170859 + 0.379369i
\(250\) 0 0
\(251\) −10.5013 18.1888i −0.662838 1.14807i −0.979867 0.199654i \(-0.936018\pi\)
0.317028 0.948416i \(-0.397315\pi\)
\(252\) 0 0
\(253\) −6.99786 + 12.1206i −0.439951 + 0.762018i
\(254\) 0 0
\(255\) −36.4850 + 37.4586i −2.28478 + 2.34575i
\(256\) 0 0
\(257\) 23.1203 + 19.4002i 1.44221 + 1.21015i 0.938031 + 0.346552i \(0.112648\pi\)
0.504175 + 0.863602i \(0.331797\pi\)
\(258\) 0 0
\(259\) 3.45466 + 0.351336i 0.214662 + 0.0218310i
\(260\) 0 0
\(261\) −23.0648 12.5186i −1.42768 0.774884i
\(262\) 0 0
\(263\) −1.55077 8.79484i −0.0956244 0.542313i −0.994554 0.104220i \(-0.966765\pi\)
0.898930 0.438093i \(-0.144346\pi\)
\(264\) 0 0
\(265\) 5.21979 29.6029i 0.320649 1.81849i
\(266\) 0 0
\(267\) −13.8836 9.45146i −0.849663 0.578420i
\(268\) 0 0
\(269\) −10.4960 + 18.1797i −0.639955 + 1.10844i 0.345487 + 0.938424i \(0.387714\pi\)
−0.985442 + 0.170012i \(0.945619\pi\)
\(270\) 0 0
\(271\) −13.6446 23.6332i −0.828853 1.43561i −0.898939 0.438074i \(-0.855661\pi\)
0.0700865 0.997541i \(-0.477672\pi\)
\(272\) 0 0
\(273\) 0.0221123 + 0.126082i 0.00133830 + 0.00763082i
\(274\) 0 0
\(275\) −47.8942 + 17.4321i −2.88813 + 1.05119i
\(276\) 0 0
\(277\) −0.494783 2.80605i −0.0297286 0.168599i 0.966329 0.257310i \(-0.0828363\pi\)
−0.996057 + 0.0887112i \(0.971725\pi\)
\(278\) 0 0
\(279\) −7.17550 + 1.46101i −0.429586 + 0.0874685i
\(280\) 0 0
\(281\) 2.46897 + 14.0022i 0.147286 + 0.835303i 0.965503 + 0.260393i \(0.0838520\pi\)
−0.818216 + 0.574910i \(0.805037\pi\)
\(282\) 0 0
\(283\) −2.79042 + 15.8253i −0.165873 + 0.940714i 0.782286 + 0.622919i \(0.214053\pi\)
−0.948160 + 0.317795i \(0.897058\pi\)
\(284\) 0 0
\(285\) 30.0693 + 7.63419i 1.78115 + 0.452211i
\(286\) 0 0
\(287\) 4.32311 1.09336i 0.255185 0.0645388i
\(288\) 0 0
\(289\) −19.2445 + 33.3325i −1.13203 + 1.96073i
\(290\) 0 0
\(291\) −13.5257 + 1.36301i −0.792893 + 0.0799012i
\(292\) 0 0
\(293\) 5.63367 + 4.72721i 0.329122 + 0.276166i 0.792342 0.610077i \(-0.208862\pi\)
−0.463220 + 0.886243i \(0.653306\pi\)
\(294\) 0 0
\(295\) 12.7718 + 4.64855i 0.743603 + 0.270649i
\(296\) 0 0
\(297\) 12.5351 19.4978i 0.727359 1.13137i
\(298\) 0 0
\(299\) −0.0152182 0.0863068i −0.000880093 0.00499125i
\(300\) 0 0
\(301\) 1.28035 + 17.4641i 0.0737980 + 1.00661i
\(302\) 0 0
\(303\) 6.04187 0.608850i 0.347096 0.0349775i
\(304\) 0 0
\(305\) 8.28689 0.474506
\(306\) 0 0
\(307\) −3.43417 + 5.94815i −0.195998 + 0.339479i −0.947227 0.320563i \(-0.896128\pi\)
0.751229 + 0.660042i \(0.229461\pi\)
\(308\) 0 0
\(309\) −0.531531 1.88411i −0.0302377 0.107184i
\(310\) 0 0
\(311\) −1.65944 + 9.41117i −0.0940984 + 0.533659i 0.900921 + 0.433982i \(0.142892\pi\)
−0.995020 + 0.0996766i \(0.968219\pi\)
\(312\) 0 0
\(313\) −8.46006 + 7.09884i −0.478191 + 0.401250i −0.849772 0.527151i \(-0.823260\pi\)
0.371581 + 0.928401i \(0.378816\pi\)
\(314\) 0 0
\(315\) 32.0092 3.19595i 1.80352 0.180071i
\(316\) 0 0
\(317\) 11.1650 + 4.06374i 0.627090 + 0.228242i 0.635964 0.771718i \(-0.280603\pi\)
−0.00887406 + 0.999961i \(0.502825\pi\)
\(318\) 0 0
\(319\) −29.8931 25.0833i −1.67369 1.40440i
\(320\) 0 0
\(321\) 22.8580 11.0275i 1.27581 0.615496i
\(322\) 0 0
\(323\) 32.9209 1.83177
\(324\) 0 0
\(325\) 0.159575 0.276393i 0.00885165 0.0153315i
\(326\) 0 0
\(327\) −2.42542 1.65114i −0.134126 0.0913081i
\(328\) 0 0
\(329\) −29.2300 14.1347i −1.61150 0.779271i
\(330\) 0 0
\(331\) 10.8070 + 3.93343i 0.594007 + 0.216201i 0.621491 0.783421i \(-0.286527\pi\)
−0.0274841 + 0.999622i \(0.508750\pi\)
\(332\) 0 0
\(333\) 3.89427 + 0.581394i 0.213404 + 0.0318602i
\(334\) 0 0
\(335\) −4.43582 25.1568i −0.242354 1.37446i
\(336\) 0 0
\(337\) 28.8940 10.5165i 1.57396 0.572873i 0.600077 0.799942i \(-0.295137\pi\)
0.973879 + 0.227069i \(0.0729145\pi\)
\(338\) 0 0
\(339\) 22.8472 + 5.80058i 1.24089 + 0.315044i
\(340\) 0 0
\(341\) −10.8887 −0.589654
\(342\) 0 0
\(343\) −17.6708 5.54476i −0.954131 0.299389i
\(344\) 0 0
\(345\) −21.9128 + 2.20819i −1.17975 + 0.118885i
\(346\) 0 0
\(347\) 16.9138 6.15613i 0.907982 0.330478i 0.154535 0.987987i \(-0.450612\pi\)
0.753447 + 0.657509i \(0.228390\pi\)
\(348\) 0 0
\(349\) −25.6012 9.31809i −1.37040 0.498786i −0.451148 0.892449i \(-0.648985\pi\)
−0.919255 + 0.393664i \(0.871208\pi\)
\(350\) 0 0
\(351\) 0.0183502 + 0.143981i 0.000979459 + 0.00768512i
\(352\) 0 0
\(353\) 25.9004 21.7330i 1.37854 1.15673i 0.408787 0.912630i \(-0.365952\pi\)
0.969750 0.244100i \(-0.0784924\pi\)
\(354\) 0 0
\(355\) −1.48445 + 8.41874i −0.0787865 + 0.446820i
\(356\) 0 0
\(357\) 32.0881 11.6458i 1.69828 0.616359i
\(358\) 0 0
\(359\) −7.64640 + 13.2440i −0.403562 + 0.698989i −0.994153 0.107982i \(-0.965561\pi\)
0.590591 + 0.806971i \(0.298895\pi\)
\(360\) 0 0
\(361\) −0.265767 0.460322i −0.0139877 0.0242275i
\(362\) 0 0
\(363\) 10.7553 11.0424i 0.564509 0.579573i
\(364\) 0 0
\(365\) −42.4151 + 15.4378i −2.22011 + 0.808053i
\(366\) 0 0
\(367\) −0.178696 0.0650401i −0.00932787 0.00339507i 0.337352 0.941379i \(-0.390469\pi\)
−0.346680 + 0.937984i \(0.612691\pi\)
\(368\) 0 0
\(369\) 4.95463 1.00882i 0.257928 0.0525170i
\(370\) 0 0
\(371\) −11.4808 + 15.9144i −0.596051 + 0.826234i
\(372\) 0 0
\(373\) −29.2189 + 10.6348i −1.51290 + 0.550650i −0.959363 0.282176i \(-0.908944\pi\)
−0.553535 + 0.832826i \(0.686722\pi\)
\(374\) 0 0
\(375\) −37.2854 25.3825i −1.92541 1.31075i
\(376\) 0 0
\(377\) 0.244352 0.0125848
\(378\) 0 0
\(379\) 29.7059 1.52589 0.762946 0.646462i \(-0.223752\pi\)
0.762946 + 0.646462i \(0.223752\pi\)
\(380\) 0 0
\(381\) 21.8312 10.5322i 1.11845 0.539581i
\(382\) 0 0
\(383\) −5.64182 + 2.05346i −0.288284 + 0.104927i −0.482114 0.876108i \(-0.660131\pi\)
0.193831 + 0.981035i \(0.437909\pi\)
\(384\) 0 0
\(385\) 47.5879 + 4.83965i 2.42530 + 0.246651i
\(386\) 0 0
\(387\) 0.522786 + 19.8487i 0.0265747 + 1.00896i
\(388\) 0 0
\(389\) 10.1180 + 3.68266i 0.513004 + 0.186718i 0.585534 0.810648i \(-0.300885\pi\)
−0.0725296 + 0.997366i \(0.523107\pi\)
\(390\) 0 0
\(391\) −21.9615 + 7.99333i −1.11064 + 0.404240i
\(392\) 0 0
\(393\) −11.5568 2.93411i −0.582962 0.148006i
\(394\) 0 0
\(395\) −10.9444 18.9562i −0.550672 0.953792i
\(396\) 0 0
\(397\) 4.79026 8.29698i 0.240416 0.416413i −0.720417 0.693542i \(-0.756049\pi\)
0.960833 + 0.277128i \(0.0893827\pi\)
\(398\) 0 0
\(399\) −15.5023 13.0323i −0.776087 0.652429i
\(400\) 0 0
\(401\) 5.17944 29.3741i 0.258649 1.46687i −0.527881 0.849319i \(-0.677013\pi\)
0.786530 0.617553i \(-0.211876\pi\)
\(402\) 0 0
\(403\) 0.0522308 0.0438269i 0.00260180 0.00218317i
\(404\) 0 0
\(405\) 36.4250 1.92010i 1.80997 0.0954105i
\(406\) 0 0
\(407\) 5.50173 + 2.00247i 0.272711 + 0.0992586i
\(408\) 0 0
\(409\) −32.0983 + 11.6828i −1.58716 + 0.577679i −0.976745 0.214402i \(-0.931220\pi\)
−0.610415 + 0.792082i \(0.708997\pi\)
\(410\) 0 0
\(411\) 4.16929 + 5.79058i 0.205656 + 0.285628i
\(412\) 0 0
\(413\) −6.18497 6.36169i −0.304342 0.313038i
\(414\) 0 0
\(415\) −15.3626 −0.754119
\(416\) 0 0
\(417\) 2.48461 2.55091i 0.121672 0.124919i
\(418\) 0 0
\(419\) −22.7096 + 8.26562i −1.10944 + 0.403802i −0.830787 0.556591i \(-0.812109\pi\)
−0.278650 + 0.960393i \(0.589887\pi\)
\(420\) 0 0
\(421\) −3.54660 20.1138i −0.172851 0.980284i −0.940596 0.339529i \(-0.889732\pi\)
0.767745 0.640755i \(-0.221379\pi\)
\(422\) 0 0
\(423\) −32.3567 17.5619i −1.57324 0.853887i
\(424\) 0 0
\(425\) −79.9768 29.1092i −3.87945 1.41200i
\(426\) 0 0
\(427\) −4.87026 2.35511i −0.235689 0.113972i
\(428\) 0 0
\(429\) −0.0159782 + 0.215234i −0.000771432 + 0.0103916i
\(430\) 0 0
\(431\) −11.5977 + 20.0879i −0.558643 + 0.967598i 0.438967 + 0.898503i \(0.355344\pi\)
−0.997610 + 0.0690948i \(0.977989\pi\)
\(432\) 0 0
\(433\) −22.5689 −1.08459 −0.542296 0.840187i \(-0.682445\pi\)
−0.542296 + 0.840187i \(0.682445\pi\)
\(434\) 0 0
\(435\) 4.54607 61.2380i 0.217967 2.93614i
\(436\) 0 0
\(437\) 10.6217 + 8.91267i 0.508105 + 0.426351i
\(438\) 0 0
\(439\) 5.52122 + 2.00956i 0.263514 + 0.0959111i 0.470398 0.882454i \(-0.344110\pi\)
−0.206885 + 0.978365i \(0.566332\pi\)
\(440\) 0 0
\(441\) −19.7203 7.21864i −0.939063 0.343745i
\(442\) 0 0
\(443\) 9.01679 7.56598i 0.428401 0.359471i −0.402947 0.915223i \(-0.632014\pi\)
0.831348 + 0.555752i \(0.187570\pi\)
\(444\) 0 0
\(445\) 6.82430 38.7025i 0.323503 1.83468i
\(446\) 0 0
\(447\) 21.1395 21.7036i 0.999865 1.02655i
\(448\) 0 0
\(449\) −6.24959 + 10.8246i −0.294937 + 0.510845i −0.974970 0.222336i \(-0.928632\pi\)
0.680034 + 0.733181i \(0.261965\pi\)
\(450\) 0 0
\(451\) 7.51854 0.354034
\(452\) 0 0
\(453\) 6.45140 14.3245i 0.303113 0.673024i
\(454\) 0 0
\(455\) −0.247750 + 0.168327i −0.0116147 + 0.00789127i
\(456\) 0 0
\(457\) −3.60433 20.4412i −0.168604 0.956199i −0.945271 0.326287i \(-0.894202\pi\)
0.776667 0.629911i \(-0.216909\pi\)
\(458\) 0 0
\(459\) 36.9630 11.4866i 1.72528 0.536148i
\(460\) 0 0
\(461\) 13.0766 + 4.75951i 0.609040 + 0.221672i 0.628083 0.778146i \(-0.283840\pi\)
−0.0190431 + 0.999819i \(0.506062\pi\)
\(462\) 0 0
\(463\) 14.7165 + 12.3486i 0.683934 + 0.573889i 0.917153 0.398535i \(-0.130481\pi\)
−0.233219 + 0.972424i \(0.574926\pi\)
\(464\) 0 0
\(465\) −10.0119 13.9051i −0.464290 0.644836i
\(466\) 0 0
\(467\) 1.73852 3.01120i 0.0804490 0.139342i −0.822994 0.568050i \(-0.807698\pi\)
0.903443 + 0.428709i \(0.141031\pi\)
\(468\) 0 0
\(469\) −4.54251 + 16.0454i −0.209754 + 0.740910i
\(470\) 0 0
\(471\) −2.69631 + 2.76826i −0.124239 + 0.127555i
\(472\) 0 0
\(473\) −5.12688 + 29.0760i −0.235734 + 1.33692i
\(474\) 0 0
\(475\) 8.76825 + 49.7272i 0.402315 + 2.28164i
\(476\) 0 0
\(477\) −13.8488 + 17.4158i −0.634092 + 0.797412i
\(478\) 0 0
\(479\) 1.00002 + 5.67140i 0.0456921 + 0.259133i 0.999093 0.0425724i \(-0.0135553\pi\)
−0.953401 + 0.301705i \(0.902444\pi\)
\(480\) 0 0
\(481\) −0.0344507 + 0.0125390i −0.00157082 + 0.000571731i
\(482\) 0 0
\(483\) 13.5059 + 4.92978i 0.614538 + 0.224313i
\(484\) 0 0
\(485\) −15.9046 27.5476i −0.722192 1.25087i
\(486\) 0 0
\(487\) −15.5970 + 27.0148i −0.706768 + 1.22416i 0.259281 + 0.965802i \(0.416514\pi\)
−0.966050 + 0.258357i \(0.916819\pi\)
\(488\) 0 0
\(489\) −36.7924 + 17.7500i −1.66381 + 0.802682i
\(490\) 0 0
\(491\) −2.68303 + 15.2162i −0.121084 + 0.686699i 0.862474 + 0.506102i \(0.168914\pi\)
−0.983557 + 0.180597i \(0.942197\pi\)
\(492\) 0 0
\(493\) −11.3154 64.1726i −0.509618 2.89019i
\(494\) 0 0
\(495\) 53.6434 + 8.00869i 2.41109 + 0.359964i
\(496\) 0 0
\(497\) 3.26500 4.52587i 0.146455 0.203013i
\(498\) 0 0
\(499\) 7.48292 + 6.27892i 0.334982 + 0.281083i 0.794726 0.606968i \(-0.207615\pi\)
−0.459744 + 0.888051i \(0.652059\pi\)
\(500\) 0 0
\(501\) −27.5178 6.98640i −1.22941 0.312129i
\(502\) 0 0
\(503\) −2.03125 + 3.51823i −0.0905690 + 0.156870i −0.907751 0.419510i \(-0.862202\pi\)
0.817182 + 0.576380i \(0.195535\pi\)
\(504\) 0 0
\(505\) 7.10450 + 12.3054i 0.316146 + 0.547581i
\(506\) 0 0
\(507\) 13.1560 + 18.2718i 0.584277 + 0.811481i
\(508\) 0 0
\(509\) −2.76007 + 15.6532i −0.122338 + 0.693814i 0.860515 + 0.509425i \(0.170142\pi\)
−0.982853 + 0.184389i \(0.940969\pi\)
\(510\) 0 0
\(511\) 29.3150 + 2.98131i 1.29682 + 0.131885i
\(512\) 0 0
\(513\) −16.8666 15.5842i −0.744681 0.688060i
\(514\) 0 0
\(515\) 3.50904 2.94444i 0.154627 0.129747i
\(516\) 0 0
\(517\) −41.9358 35.1883i −1.84433 1.54758i
\(518\) 0 0
\(519\) 11.4158 + 15.8549i 0.501096 + 0.695955i
\(520\) 0 0
\(521\) −34.1482 −1.49606 −0.748030 0.663665i \(-0.769000\pi\)
−0.748030 + 0.663665i \(0.769000\pi\)
\(522\) 0 0
\(523\) −0.302839 −0.0132422 −0.00662110 0.999978i \(-0.502108\pi\)
−0.00662110 + 0.999978i \(0.502108\pi\)
\(524\) 0 0
\(525\) 26.1374 + 45.3675i 1.14073 + 1.98000i
\(526\) 0 0
\(527\) −13.9286 11.6875i −0.606741 0.509117i
\(528\) 0 0
\(529\) 12.3632 + 4.49983i 0.537529 + 0.195645i
\(530\) 0 0
\(531\) −6.66757 7.53400i −0.289348 0.326948i
\(532\) 0 0
\(533\) −0.0360650 + 0.0302621i −0.00156215 + 0.00131080i
\(534\) 0 0
\(535\) 45.4911 + 38.1716i 1.96675 + 1.65030i
\(536\) 0 0
\(537\) 21.4732 10.3595i 0.926637 0.447044i
\(538\) 0 0
\(539\) −26.5923 16.3686i −1.14541 0.705046i
\(540\) 0 0
\(541\) 15.1584 + 26.2550i 0.651709 + 1.12879i 0.982708 + 0.185162i \(0.0592809\pi\)
−0.330999 + 0.943631i \(0.607386\pi\)
\(542\) 0 0
\(543\) 22.7561 10.9784i 0.976556 0.471126i
\(544\) 0 0
\(545\) 1.19218 6.76120i 0.0510675 0.289618i
\(546\) 0 0
\(547\) −14.5948 + 12.2465i −0.624027 + 0.523621i −0.899067 0.437812i \(-0.855754\pi\)
0.275039 + 0.961433i \(0.411309\pi\)
\(548\) 0 0
\(549\) −5.39124 2.92614i −0.230092 0.124884i
\(550\) 0 0
\(551\) −29.6154 + 24.8502i −1.26166 + 1.05866i
\(552\) 0 0
\(553\) 1.04479 + 14.2511i 0.0444291 + 0.606017i
\(554\) 0 0
\(555\) 2.50151 + 8.86711i 0.106183 + 0.376388i
\(556\) 0 0
\(557\) −7.29691 12.6386i −0.309180 0.535516i 0.669003 0.743260i \(-0.266721\pi\)
−0.978183 + 0.207744i \(0.933388\pi\)
\(558\) 0 0
\(559\) −0.0924383 0.160108i −0.00390972 0.00677184i
\(560\) 0 0
\(561\) 57.2655 5.77074i 2.41775 0.243641i
\(562\) 0 0
\(563\) 24.7837 9.02052i 1.04451 0.380170i 0.237920 0.971285i \(-0.423534\pi\)
0.806587 + 0.591115i \(0.201312\pi\)
\(564\) 0 0
\(565\) 9.57779 + 54.3183i 0.402941 + 2.28519i
\(566\) 0 0
\(567\) −21.9529 9.22340i −0.921934 0.387346i
\(568\) 0 0
\(569\) 2.38023 + 13.4990i 0.0997844 + 0.565906i 0.993176 + 0.116627i \(0.0372080\pi\)
−0.893391 + 0.449279i \(0.851681\pi\)
\(570\) 0 0
\(571\) 8.95770 3.26034i 0.374868 0.136441i −0.147713 0.989030i \(-0.547191\pi\)
0.522581 + 0.852589i \(0.324969\pi\)
\(572\) 0 0
\(573\) −14.8505 + 1.49652i −0.620391 + 0.0625179i
\(574\) 0 0
\(575\) −17.9233 31.0440i −0.747452 1.29462i
\(576\) 0 0
\(577\) −7.89500 13.6745i −0.328673 0.569279i 0.653576 0.756861i \(-0.273268\pi\)
−0.982249 + 0.187583i \(0.939935\pi\)
\(578\) 0 0
\(579\) −1.41758 5.02490i −0.0589127 0.208828i
\(580\) 0 0
\(581\) 9.02869 + 4.36599i 0.374573 + 0.181132i
\(582\) 0 0
\(583\) −25.3455 + 21.2674i −1.04970 + 0.880805i
\(584\) 0 0
\(585\) −0.289552 + 0.177499i −0.0119715 + 0.00733866i
\(586\) 0 0
\(587\) 8.03884 6.74539i 0.331798 0.278412i −0.461634 0.887071i \(-0.652737\pi\)
0.793432 + 0.608659i \(0.208292\pi\)
\(588\) 0 0
\(589\) −1.87322 + 10.6236i −0.0771849 + 0.437737i
\(590\) 0 0
\(591\) −5.04353 + 2.43319i −0.207463 + 0.100088i
\(592\) 0 0
\(593\) −8.57907 14.8594i −0.352300 0.610202i 0.634352 0.773044i \(-0.281267\pi\)
−0.986652 + 0.162843i \(0.947934\pi\)
\(594\) 0 0
\(595\) 55.6792 + 57.2701i 2.28262 + 2.34785i
\(596\) 0 0
\(597\) 20.3839 9.83396i 0.834259 0.402477i
\(598\) 0 0
\(599\) 7.01255 + 5.88423i 0.286525 + 0.240423i 0.774709 0.632317i \(-0.217896\pi\)
−0.488184 + 0.872741i \(0.662341\pi\)
\(600\) 0 0
\(601\) −27.4590 + 23.0408i −1.12007 + 0.939854i −0.998608 0.0527419i \(-0.983204\pi\)
−0.121466 + 0.992596i \(0.538760\pi\)
\(602\) 0 0
\(603\) −5.99713 + 17.9326i −0.244222 + 0.730273i
\(604\) 0 0
\(605\) 33.8936 + 12.3363i 1.37797 + 0.501540i
\(606\) 0 0
\(607\) 30.4832 + 25.5785i 1.23728 + 1.03820i 0.997732 + 0.0673126i \(0.0214425\pi\)
0.239544 + 0.970885i \(0.423002\pi\)
\(608\) 0 0
\(609\) −20.0754 + 34.6980i −0.813496 + 1.40603i
\(610\) 0 0
\(611\) 0.342791 0.0138678
\(612\) 0 0
\(613\) −43.1677 −1.74353 −0.871763 0.489928i \(-0.837023\pi\)
−0.871763 + 0.489928i \(0.837023\pi\)
\(614\) 0 0
\(615\) 6.91314 + 9.60141i 0.278765 + 0.387166i
\(616\) 0 0
\(617\) 2.40991 + 2.02216i 0.0970195 + 0.0814090i 0.690007 0.723802i \(-0.257607\pi\)
−0.592988 + 0.805211i \(0.702052\pi\)
\(618\) 0 0
\(619\) 2.96932 2.49156i 0.119347 0.100144i −0.581161 0.813789i \(-0.697401\pi\)
0.700508 + 0.713645i \(0.252957\pi\)
\(620\) 0 0
\(621\) 15.0356 + 6.30091i 0.603359 + 0.252847i
\(622\) 0 0
\(623\) −15.0098 + 20.8063i −0.601356 + 0.833587i
\(624\) 0 0
\(625\) 8.40706 47.6788i 0.336282 1.90715i
\(626\) 0 0
\(627\) −19.9524 27.7112i −0.796824 1.10668i
\(628\) 0 0
\(629\) 4.88838 + 8.46692i 0.194912 + 0.337598i
\(630\) 0 0
\(631\) −8.48331 + 14.6935i −0.337715 + 0.584940i −0.984003 0.178154i \(-0.942987\pi\)
0.646287 + 0.763094i \(0.276321\pi\)
\(632\) 0 0
\(633\) −12.4110 3.15097i −0.493291 0.125240i
\(634\) 0 0
\(635\) 43.4478 + 36.4570i 1.72417 + 1.44675i
\(636\) 0 0
\(637\) 0.193442 0.0285170i 0.00766445 0.00112988i
\(638\) 0 0
\(639\) 3.93844 4.95284i 0.155802 0.195932i
\(640\) 0 0
\(641\) 4.59160 + 26.0403i 0.181357 + 1.02853i 0.930547 + 0.366173i \(0.119332\pi\)
−0.749190 + 0.662356i \(0.769557\pi\)
\(642\) 0 0
\(643\) −0.818900 + 4.64421i −0.0322943 + 0.183150i −0.996688 0.0813208i \(-0.974086\pi\)
0.964394 + 0.264471i \(0.0851973\pi\)
\(644\) 0 0
\(645\) −41.8450 + 20.1876i −1.64764 + 0.794884i
\(646\) 0 0
\(647\) −4.45429 + 7.71506i −0.175116 + 0.303310i −0.940201 0.340619i \(-0.889363\pi\)
0.765085 + 0.643929i \(0.222697\pi\)
\(648\) 0 0
\(649\) −7.47997 12.9557i −0.293614 0.508555i
\(650\) 0 0
\(651\) 1.93226 + 11.0175i 0.0757310 + 0.431809i
\(652\) 0 0
\(653\) 29.1551 10.6116i 1.14093 0.415263i 0.298678 0.954354i \(-0.403454\pi\)
0.842247 + 0.539091i \(0.181232\pi\)
\(654\) 0 0
\(655\) −4.84473 27.4758i −0.189299 1.07357i
\(656\) 0 0
\(657\) 33.0453 + 4.93350i 1.28922 + 0.192474i
\(658\) 0 0
\(659\) −4.28545 24.3040i −0.166937 0.946749i −0.947044 0.321103i \(-0.895947\pi\)
0.780107 0.625646i \(-0.215165\pi\)
\(660\) 0 0
\(661\) 6.73711 38.2081i 0.262043 1.48612i −0.515281 0.857021i \(-0.672313\pi\)
0.777325 0.629100i \(-0.216576\pi\)
\(662\) 0 0
\(663\) −0.251464 + 0.258175i −0.00976607 + 0.0100267i
\(664\) 0 0
\(665\) 12.9086 45.5969i 0.500574 1.76817i
\(666\) 0 0
\(667\) 13.7226 23.7683i 0.531342 0.920311i
\(668\) 0 0
\(669\) −25.2283 35.0387i −0.975382 1.35467i
\(670\) 0 0
\(671\) −6.98730 5.86304i −0.269742 0.226340i
\(672\) 0 0
\(673\) 26.8884 + 9.78657i 1.03647 + 0.377245i 0.803541 0.595249i \(-0.202947\pi\)
0.232930 + 0.972494i \(0.425169\pi\)
\(674\) 0 0
\(675\) 27.1954 + 52.7735i 1.04675 + 2.03125i
\(676\) 0 0
\(677\) −0.306762 1.73973i −0.0117898 0.0668634i 0.978345 0.206980i \(-0.0663634\pi\)
−0.990135 + 0.140116i \(0.955252\pi\)
\(678\) 0 0
\(679\) 1.51831 + 20.7100i 0.0582676 + 0.794776i
\(680\) 0 0
\(681\) 6.98405 15.5072i 0.267629 0.594236i
\(682\) 0 0
\(683\) 51.2262 1.96012 0.980058 0.198710i \(-0.0636752\pi\)
0.980058 + 0.198710i \(0.0636752\pi\)
\(684\) 0 0
\(685\) −8.34808 + 14.4593i −0.318964 + 0.552461i
\(686\) 0 0
\(687\) −19.5994 + 20.1224i −0.747763 + 0.767718i
\(688\) 0 0
\(689\) 0.0359762 0.204031i 0.00137058 0.00777297i
\(690\) 0 0
\(691\) 3.33319 2.79688i 0.126801 0.106398i −0.577182 0.816615i \(-0.695848\pi\)
0.703983 + 0.710217i \(0.251403\pi\)
\(692\) 0 0
\(693\) −29.2505 19.9520i −1.11114 0.757915i
\(694\) 0 0
\(695\) 7.82981 + 2.84982i 0.297002 + 0.108100i
\(696\) 0 0
\(697\) 9.61764 + 8.07015i 0.364294 + 0.305679i
\(698\) 0 0
\(699\) 1.01571 13.6822i 0.0384178 0.517508i
\(700\) 0 0
\(701\) 15.3246 0.578803 0.289401 0.957208i \(-0.406544\pi\)
0.289401 + 0.957208i \(0.406544\pi\)
\(702\) 0 0
\(703\) 2.90021 5.02331i 0.109383 0.189458i
\(704\) 0 0
\(705\) 6.37749 85.9082i 0.240190 3.23549i
\(706\) 0 0
\(707\) −0.678222 9.25102i −0.0255072 0.347920i
\(708\) 0 0
\(709\) −11.6927 4.25580i −0.439129 0.159830i 0.112988 0.993596i \(-0.463958\pi\)
−0.552117 + 0.833766i \(0.686180\pi\)
\(710\) 0 0
\(711\) 0.426605 + 16.1969i 0.0159989 + 0.607433i
\(712\) 0 0
\(713\) −1.32982 7.54180i −0.0498023 0.282443i
\(714\) 0 0
\(715\) −0.474558 + 0.172725i −0.0177475 + 0.00645954i
\(716\) 0 0
\(717\) −30.3335 + 31.1430i −1.13283 + 1.16306i
\(718\) 0 0
\(719\) −39.0507 −1.45635 −0.728173 0.685394i \(-0.759630\pi\)
−0.728173 + 0.685394i \(0.759630\pi\)
\(720\) 0 0
\(721\) −2.89909 + 0.733207i −0.107968 + 0.0273061i
\(722\) 0 0
\(723\) −1.27708 1.77369i −0.0474950 0.0659641i
\(724\) 0 0
\(725\) 93.9194 34.1839i 3.48808 1.26956i
\(726\) 0 0
\(727\) −6.18370 2.25068i −0.229341 0.0834733i 0.224794 0.974406i \(-0.427829\pi\)
−0.454134 + 0.890933i \(0.650051\pi\)
\(728\) 0 0
\(729\) −24.3751 11.6126i −0.902782 0.430098i
\(730\) 0 0
\(731\) −37.7675 + 31.6907i −1.39688 + 1.17212i
\(732\) 0 0
\(733\) −0.388237 + 2.20180i −0.0143399 + 0.0813254i −0.991138 0.132837i \(-0.957591\pi\)
0.976798 + 0.214163i \(0.0687023\pi\)
\(734\) 0 0
\(735\) −3.54784 49.0098i −0.130864 1.80775i
\(736\) 0 0
\(737\) −14.0584 + 24.3499i −0.517849 + 0.896941i
\(738\) 0 0
\(739\) 4.88709 + 8.46468i 0.179774 + 0.311378i 0.941803 0.336165i \(-0.109130\pi\)
−0.762029 + 0.647543i \(0.775797\pi\)
\(740\) 0 0
\(741\) 0.207246 + 0.0526169i 0.00761337 + 0.00193293i
\(742\) 0 0
\(743\) −32.6538 + 11.8850i −1.19795 + 0.436019i −0.862509 0.506042i \(-0.831108\pi\)
−0.335443 + 0.942061i \(0.608886\pi\)
\(744\) 0 0
\(745\) 66.6175 + 24.2468i 2.44068 + 0.888334i
\(746\) 0 0
\(747\) 9.99449 + 5.42459i 0.365679 + 0.198475i
\(748\) 0 0
\(749\) −15.8872 35.3621i −0.580506 1.29210i
\(750\) 0 0
\(751\) 34.2653 12.4715i 1.25036 0.455093i 0.369835 0.929097i \(-0.379414\pi\)
0.880523 + 0.474004i \(0.157192\pi\)
\(752\) 0 0
\(753\) −32.7641 + 15.8066i −1.19399 + 0.576025i
\(754\) 0 0
\(755\) 36.7605 1.33785
\(756\) 0 0
\(757\) 30.3621 1.10353 0.551764 0.834000i \(-0.313955\pi\)
0.551764 + 0.834000i \(0.313955\pi\)
\(758\) 0 0
\(759\) 20.0386 + 13.6416i 0.727356 + 0.495158i
\(760\) 0 0
\(761\) −28.0536 + 10.2107i −1.01694 + 0.370137i −0.796095 0.605172i \(-0.793104\pi\)
−0.220847 + 0.975308i \(0.570882\pi\)
\(762\) 0 0
\(763\) −2.62217 + 3.63479i −0.0949288 + 0.131588i
\(764\) 0 0
\(765\) 60.0238 + 67.8237i 2.17016 + 2.45217i
\(766\) 0 0
\(767\) 0.0880267 + 0.0320391i 0.00317846 + 0.00115686i
\(768\) 0 0
\(769\) −18.2839 + 6.65479i −0.659333 + 0.239978i −0.649949 0.759978i \(-0.725210\pi\)
−0.00938486 + 0.999956i \(0.502987\pi\)
\(770\) 0 0
\(771\) 36.4747 37.4480i 1.31360 1.34866i
\(772\) 0 0
\(773\) −2.80733 4.86244i −0.100973 0.174890i 0.811113 0.584890i \(-0.198862\pi\)
−0.912086 + 0.410000i \(0.865529\pi\)
\(774\) 0 0
\(775\) 13.9443 24.1522i 0.500893 0.867573i
\(776\) 0 0
\(777\) 1.04985 5.92218i 0.0376630 0.212457i
\(778\) 0 0
\(779\) 1.29345 7.33551i 0.0463426 0.262822i
\(780\) 0 0
\(781\) 7.20797 6.04821i 0.257921 0.216422i
\(782\) 0 0
\(783\) −24.5810 + 38.2346i −0.878452 + 1.36639i
\(784\) 0 0
\(785\) −8.49695 3.09264i −0.303269 0.110381i
\(786\) 0 0
\(787\) −19.4483 + 7.07861i −0.693258 + 0.252325i −0.664529 0.747262i \(-0.731368\pi\)
−0.0287283 + 0.999587i \(0.509146\pi\)
\(788\) 0 0
\(789\) −15.3902 + 1.55089i −0.547904 + 0.0552133i
\(790\) 0 0
\(791\) 9.80816 34.6452i 0.348738 1.23184i
\(792\) 0 0
\(793\) 0.0571155 0.00202823
\(794\) 0 0
\(795\) −50.4637 12.8121i −1.78976 0.454397i
\(796\) 0 0
\(797\) 10.9875 3.99911i 0.389196 0.141656i −0.140008 0.990150i \(-0.544713\pi\)
0.529204 + 0.848495i \(0.322491\pi\)
\(798\) 0 0
\(799\) −15.8738 90.0250i −0.561576 3.18486i
\(800\) 0 0
\(801\) −18.1057 + 22.7692i −0.639735 + 0.804509i
\(802\) 0 0
\(803\) 46.6857 + 16.9922i 1.64750 + 0.599642i
\(804\) 0 0
\(805\) 2.45979 + 33.5518i 0.0866964 + 1.18255i
\(806\) 0 0
\(807\) 30.0559 + 20.4609i 1.05802 + 0.720259i
\(808\) 0 0
\(809\) 11.0776 19.1870i 0.389469 0.674579i −0.602910 0.797810i \(-0.705992\pi\)
0.992378 + 0.123230i \(0.0393253\pi\)
\(810\) 0 0
\(811\) 12.1762 0.427566 0.213783 0.976881i \(-0.431422\pi\)
0.213783 + 0.976881i \(0.431422\pi\)
\(812\) 0 0
\(813\) −42.5712 + 20.5379i −1.49304 + 0.720296i
\(814\) 0 0
\(815\) −73.2229 61.4413i −2.56489 2.15219i
\(816\) 0 0
\(817\) 27.4862 + 10.0042i 0.961620 + 0.350001i
\(818\) 0 0
\(819\) 0.220616 0.0220274i 0.00770896 0.000769698i
\(820\) 0 0
\(821\) 24.5655 20.6129i 0.857343 0.719396i −0.104051 0.994572i \(-0.533180\pi\)
0.961394 + 0.275176i \(0.0887360\pi\)
\(822\) 0 0
\(823\) −4.34862 + 24.6622i −0.151583 + 0.859671i 0.810260 + 0.586071i \(0.199326\pi\)
−0.961843 + 0.273601i \(0.911785\pi\)
\(824\) 0 0
\(825\) 23.9690 + 84.9629i 0.834494 + 2.95803i
\(826\) 0 0
\(827\) 15.8063 27.3773i 0.549638 0.952002i −0.448661 0.893702i \(-0.648099\pi\)
0.998299 0.0582995i \(-0.0185678\pi\)
\(828\) 0 0
\(829\) −12.4892 −0.433766 −0.216883 0.976198i \(-0.569589\pi\)
−0.216883 + 0.976198i \(0.569589\pi\)
\(830\) 0 0
\(831\) −4.91033 + 0.494823i −0.170337 + 0.0171652i
\(832\) 0 0
\(833\) −16.4471 49.4819i −0.569857 1.71445i
\(834\) 0 0
\(835\) −11.5358 65.4227i −0.399212 2.26405i
\(836\) 0 0
\(837\) 1.60350 + 12.5816i 0.0554252 + 0.434882i
\(838\) 0 0
\(839\) −8.71358 3.17148i −0.300826 0.109492i 0.187197 0.982322i \(-0.440060\pi\)
−0.488023 + 0.872831i \(0.662282\pi\)
\(840\) 0 0
\(841\) 36.4044 + 30.5469i 1.25532 + 1.05334i
\(842\) 0 0
\(843\) 24.5026 2.46917i 0.843915 0.0850428i
\(844\) 0 0
\(845\) −26.3419 + 45.6254i −0.906187 + 1.56956i
\(846\) 0 0
\(847\) −16.4136 16.8826i −0.563977 0.580091i
\(848\) 0 0
\(849\) 26.9771 + 6.84912i 0.925852 + 0.235061i
\(850\) 0 0
\(851\) −0.715046 + 4.05522i −0.0245114 + 0.139011i
\(852\) 0 0
\(853\) −4.64237 26.3282i −0.158952 0.901460i −0.955083 0.296337i \(-0.904235\pi\)
0.796132 0.605123i \(-0.206876\pi\)
\(854\) 0 0
\(855\) 17.0422 50.9598i 0.582833 1.74279i
\(856\) 0 0
\(857\) 0.979306 + 5.55392i 0.0334524 + 0.189718i 0.996955 0.0779816i \(-0.0248475\pi\)
−0.963502 + 0.267700i \(0.913736\pi\)
\(858\) 0 0
\(859\) −6.94252 + 2.52687i −0.236876 + 0.0862157i −0.457730 0.889091i \(-0.651338\pi\)
0.220855 + 0.975307i \(0.429115\pi\)
\(860\) 0 0
\(861\) −1.33421 7.60750i −0.0454697 0.259263i
\(862\) 0 0
\(863\) 10.8520 + 18.7962i 0.369407 + 0.639831i 0.989473 0.144719i \(-0.0462277\pi\)
−0.620066 + 0.784549i \(0.712894\pi\)
\(864\) 0 0
\(865\) −22.8575 + 39.5904i −0.777178 + 1.34611i
\(866\) 0 0
\(867\) 55.1074 + 37.5152i 1.87155 + 1.27408i
\(868\) 0 0
\(869\) −4.18365 + 23.7267i −0.141921 + 0.804872i
\(870\) 0 0
\(871\) −0.0305728 0.173387i −0.00103592 0.00587500i
\(872\) 0 0
\(873\) 0.619952 + 23.5378i 0.0209822 + 0.796632i
\(874\) 0 0
\(875\) −40.3099 + 55.8767i −1.36272 + 1.88898i
\(876\) 0 0
\(877\) 31.3185 + 26.2793i 1.05755 + 0.887390i 0.993867 0.110580i \(-0.0352710\pi\)
0.0636828 + 0.997970i \(0.479715\pi\)
\(878\) 0 0
\(879\) 8.88769 9.12486i 0.299774 0.307774i
\(880\) 0 0
\(881\) −22.6335 + 39.2023i −0.762541 + 1.32076i 0.178996 + 0.983850i \(0.442715\pi\)
−0.941537 + 0.336910i \(0.890618\pi\)
\(882\) 0 0
\(883\) 5.80328 + 10.0516i 0.195296 + 0.338263i 0.946998 0.321241i \(-0.104100\pi\)
−0.751702 + 0.659503i \(0.770767\pi\)
\(884\) 0 0
\(885\) 9.66714 21.4646i 0.324957 0.721525i
\(886\) 0 0
\(887\) 4.22367 23.9536i 0.141817 0.804284i −0.828051 0.560653i \(-0.810550\pi\)
0.969868 0.243631i \(-0.0783387\pi\)
\(888\) 0 0
\(889\) −15.1736 33.7738i −0.508906 1.13274i
\(890\) 0 0
\(891\) −32.0711 24.1520i −1.07442 0.809121i
\(892\) 0 0
\(893\) −41.5461 + 34.8613i −1.39029 + 1.16659i
\(894\) 0 0
\(895\) 42.7352 + 35.8591i 1.42848 + 1.19864i
\(896\) 0 0
\(897\) −0.151029 + 0.0152195i −0.00504271 + 0.000508163i
\(898\) 0 0
\(899\) 21.3524 0.712142
\(900\) 0 0
\(901\) −55.2494 −1.84062
\(902\) 0 0
\(903\) 30.3298 + 0.0278398i 1.00931 + 0.000926451i
\(904\) 0 0
\(905\) 45.2883 + 38.0014i 1.50543 + 1.26321i
\(906\) 0 0
\(907\) −12.0127 4.37225i −0.398874 0.145178i 0.134791 0.990874i \(-0.456964\pi\)
−0.533665 + 0.845696i \(0.679186\pi\)
\(908\) 0 0
\(909\) −0.276929 10.5142i −0.00918515 0.348733i
\(910\) 0 0
\(911\) −14.8939 + 12.4975i −0.493458 + 0.414060i −0.855264 0.518193i \(-0.826605\pi\)
0.361806 + 0.932253i \(0.382160\pi\)
\(912\) 0 0
\(913\) 12.9533 + 10.8691i 0.428693 + 0.359716i
\(914\) 0 0
\(915\) 1.06261 14.3139i 0.0351288 0.473204i
\(916\) 0 0
\(917\) −4.96126 + 17.5246i −0.163835 + 0.578713i
\(918\) 0 0
\(919\) −16.1042 27.8932i −0.531227 0.920112i −0.999336 0.0364415i \(-0.988398\pi\)
0.468109 0.883671i \(-0.344936\pi\)
\(920\) 0 0
\(921\) 9.83387 + 6.69455i 0.324037 + 0.220593i
\(922\) 0 0
\(923\) −0.0102312 + 0.0580242i −0.000336765 + 0.00190989i
\(924\) 0 0
\(925\) −11.4873 + 9.63903i −0.377702 + 0.316929i
\(926\) 0 0
\(927\) −3.32258 + 0.676515i −0.109128 + 0.0222197i
\(928\) 0 0
\(929\) 37.6440 31.5871i 1.23506 1.03634i 0.237167 0.971469i \(-0.423781\pi\)
0.997894 0.0648696i \(-0.0206632\pi\)
\(930\) 0 0
\(931\) −20.5449 + 23.1290i −0.673333 + 0.758022i
\(932\) 0 0
\(933\) 16.0431 + 4.07313i 0.525228 + 0.133348i
\(934\) 0 0
\(935\) 67.3372 + 116.632i 2.20216 + 3.81426i
\(936\) 0 0
\(937\) −29.3036 50.7553i −0.957306 1.65810i −0.729000 0.684514i \(-0.760015\pi\)
−0.228306 0.973589i \(-0.573319\pi\)
\(938\) 0 0
\(939\) 11.1770 + 15.5233i 0.364747 + 0.506584i
\(940\) 0 0
\(941\) 9.23384 3.36084i 0.301015 0.109560i −0.187097 0.982341i \(-0.559908\pi\)
0.488112 + 0.872781i \(0.337686\pi\)
\(942\) 0 0
\(943\) 0.918234 + 5.20756i 0.0299018 + 0.169582i
\(944\) 0 0
\(945\) −1.41588 55.6993i −0.0460586 1.81190i
\(946\) 0 0
\(947\) 4.23537 + 24.0200i 0.137631 + 0.780544i 0.972991 + 0.230841i \(0.0741479\pi\)
−0.835360 + 0.549703i \(0.814741\pi\)
\(948\) 0 0
\(949\) −0.292336 + 0.106402i −0.00948964 + 0.00345394i
\(950\) 0 0
\(951\) 8.45095 18.7642i 0.274041 0.608472i
\(952\) 0 0
\(953\) 7.69576 + 13.3294i 0.249290 + 0.431783i 0.963329 0.268323i \(-0.0864694\pi\)
−0.714039 + 0.700106i \(0.753136\pi\)
\(954\) 0 0
\(955\) −17.4624 30.2458i −0.565071 0.978732i
\(956\) 0 0
\(957\) −47.1595 + 48.4180i −1.52445 + 1.56513i
\(958\) 0 0
\(959\) 9.01550 6.12533i 0.291126 0.197797i
\(960\) 0 0
\(961\) −19.1833 + 16.0967i −0.618815 + 0.519247i
\(962\) 0 0
\(963\) −16.1168 40.8965i −0.519356 1.31787i
\(964\) 0 0
\(965\) 9.35856 7.85276i 0.301263 0.252789i
\(966\) 0 0
\(967\) 4.62373 26.2225i 0.148689 0.843257i −0.815642 0.578557i \(-0.803616\pi\)
0.964331 0.264700i \(-0.0852730\pi\)
\(968\) 0 0
\(969\) 4.22138 56.8642i 0.135610 1.82674i
\(970\) 0 0
\(971\) −15.1821 26.2962i −0.487217 0.843884i 0.512675 0.858583i \(-0.328654\pi\)
−0.999892 + 0.0146986i \(0.995321\pi\)
\(972\) 0 0
\(973\) −3.79172 3.90006i −0.121557 0.125030i
\(974\) 0 0
\(975\) −0.456951 0.311076i −0.0146341 0.00996239i
\(976\) 0 0
\(977\) −13.7184 11.5111i −0.438890 0.368273i 0.396404 0.918076i \(-0.370258\pi\)
−0.835294 + 0.549804i \(0.814703\pi\)
\(978\) 0 0
\(979\) −33.1364 + 27.8048i −1.05904 + 0.888644i
\(980\) 0 0
\(981\) −3.16301 + 3.97770i −0.100987 + 0.126998i
\(982\) 0 0
\(983\) 9.84149 + 3.58201i 0.313895 + 0.114248i 0.494163 0.869369i \(-0.335474\pi\)
−0.180269 + 0.983617i \(0.557697\pi\)
\(984\) 0 0
\(985\) −10.0375 8.42243i −0.319820 0.268361i
\(986\) 0 0
\(987\) −28.1629 + 48.6764i −0.896436 + 1.54939i
\(988\) 0 0
\(989\) −20.7650 −0.660290
\(990\) 0 0
\(991\) −6.42498 −0.204096 −0.102048 0.994779i \(-0.532540\pi\)
−0.102048 + 0.994779i \(0.532540\pi\)
\(992\) 0 0
\(993\) 8.17996 18.1625i 0.259583 0.576371i
\(994\) 0 0
\(995\) 40.5674 + 34.0401i 1.28607 + 1.07914i
\(996\) 0 0
\(997\) −21.8016 + 18.2937i −0.690462 + 0.579367i −0.919043 0.394158i \(-0.871036\pi\)
0.228580 + 0.973525i \(0.426592\pi\)
\(998\) 0 0
\(999\) 1.50359 6.65201i 0.0475716 0.210460i
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.193.12 144
7.2 even 3 756.2.bq.a.625.21 yes 144
27.7 even 9 756.2.bq.a.277.21 yes 144
189.142 even 9 inner 756.2.bp.a.709.12 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.bp.a.193.12 144 1.1 even 1 trivial
756.2.bp.a.709.12 yes 144 189.142 even 9 inner
756.2.bq.a.277.21 yes 144 27.7 even 9
756.2.bq.a.625.21 yes 144 7.2 even 3