Properties

Label 560.2.ci.b.17.1
Level $560$
Weight $2$
Character 560.17
Analytic conductor $4.472$
Analytic rank $0$
Dimension $4$
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] = [560,2,Mod(17,560)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(560, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("560.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.ci (of order \(12\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 17.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 560.17
Dual form 560.2.ci.b.33.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.86603 - 0.500000i) q^{3} +(1.86603 + 1.23205i) q^{5} +(2.50000 - 0.866025i) q^{7} +(0.633975 - 0.366025i) q^{9} +O(q^{10})\) \(q+(1.86603 - 0.500000i) q^{3} +(1.86603 + 1.23205i) q^{5} +(2.50000 - 0.866025i) q^{7} +(0.633975 - 0.366025i) q^{9} +(0.366025 - 0.633975i) q^{11} +(-2.00000 - 2.00000i) q^{13} +(4.09808 + 1.36603i) q^{15} +(0.267949 + 1.00000i) q^{17} +(1.36603 + 2.36603i) q^{19} +(4.23205 - 2.86603i) q^{21} +(-6.96410 - 1.86603i) q^{23} +(1.96410 + 4.59808i) q^{25} +(-3.09808 + 3.09808i) q^{27} -3.00000i q^{29} +(-0.464102 - 0.267949i) q^{31} +(0.366025 - 1.36603i) q^{33} +(5.73205 + 1.46410i) q^{35} +(-1.26795 + 4.73205i) q^{37} +(-4.73205 - 2.73205i) q^{39} +0.464102i q^{41} +(5.83013 - 5.83013i) q^{43} +(1.63397 + 0.0980762i) q^{45} +(-0.633975 - 0.169873i) q^{47} +(5.50000 - 4.33013i) q^{49} +(1.00000 + 1.73205i) q^{51} +(-1.83013 - 6.83013i) q^{53} +(1.46410 - 0.732051i) q^{55} +(3.73205 + 3.73205i) q^{57} +(-1.09808 + 1.90192i) q^{59} +(-7.33013 + 4.23205i) q^{61} +(1.26795 - 1.46410i) q^{63} +(-1.26795 - 6.19615i) q^{65} +(-1.13397 + 0.303848i) q^{67} -13.9282 q^{69} -4.73205 q^{71} +(3.46410 - 0.928203i) q^{73} +(5.96410 + 7.59808i) q^{75} +(0.366025 - 1.90192i) q^{77} +(5.83013 - 3.36603i) q^{79} +(-5.33013 + 9.23205i) q^{81} +(-3.09808 - 3.09808i) q^{83} +(-0.732051 + 2.19615i) q^{85} +(-1.50000 - 5.59808i) q^{87} +(8.33013 + 14.4282i) q^{89} +(-6.73205 - 3.26795i) q^{91} +(-1.00000 - 0.267949i) q^{93} +(-0.366025 + 6.09808i) q^{95} +(7.92820 - 7.92820i) q^{97} -0.535898i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{3} + 4 q^{5} + 10 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{3} + 4 q^{5} + 10 q^{7} + 6 q^{9} - 2 q^{11} - 8 q^{13} + 6 q^{15} + 8 q^{17} + 2 q^{19} + 10 q^{21} - 14 q^{23} - 6 q^{25} - 2 q^{27} + 12 q^{31} - 2 q^{33} + 16 q^{35} - 12 q^{37} - 12 q^{39} + 6 q^{43} + 10 q^{45} - 6 q^{47} + 22 q^{49} + 4 q^{51} + 10 q^{53} - 8 q^{55} + 8 q^{57} + 6 q^{59} - 12 q^{61} + 12 q^{63} - 12 q^{65} - 8 q^{67} - 28 q^{69} - 12 q^{71} + 10 q^{75} - 2 q^{77} + 6 q^{79} - 4 q^{81} - 2 q^{83} + 4 q^{85} - 6 q^{87} + 16 q^{89} - 20 q^{91} - 4 q^{93} + 2 q^{95} + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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
\(3\) 1.86603 0.500000i 1.07735 0.288675i 0.323840 0.946112i \(-0.395026\pi\)
0.753510 + 0.657437i \(0.228359\pi\)
\(4\) 0 0
\(5\) 1.86603 + 1.23205i 0.834512 + 0.550990i
\(6\) 0 0
\(7\) 2.50000 0.866025i 0.944911 0.327327i
\(8\) 0 0
\(9\) 0.633975 0.366025i 0.211325 0.122008i
\(10\) 0 0
\(11\) 0.366025 0.633975i 0.110361 0.191151i −0.805555 0.592521i \(-0.798133\pi\)
0.915916 + 0.401371i \(0.131466\pi\)
\(12\) 0 0
\(13\) −2.00000 2.00000i −0.554700 0.554700i 0.373094 0.927794i \(-0.378297\pi\)
−0.927794 + 0.373094i \(0.878297\pi\)
\(14\) 0 0
\(15\) 4.09808 + 1.36603i 1.05812 + 0.352706i
\(16\) 0 0
\(17\) 0.267949 + 1.00000i 0.0649872 + 0.242536i 0.990777 0.135503i \(-0.0432652\pi\)
−0.925790 + 0.378039i \(0.876599\pi\)
\(18\) 0 0
\(19\) 1.36603 + 2.36603i 0.313388 + 0.542803i 0.979093 0.203411i \(-0.0652027\pi\)
−0.665706 + 0.746214i \(0.731869\pi\)
\(20\) 0 0
\(21\) 4.23205 2.86603i 0.923509 0.625418i
\(22\) 0 0
\(23\) −6.96410 1.86603i −1.45212 0.389093i −0.555357 0.831612i \(-0.687418\pi\)
−0.896759 + 0.442519i \(0.854085\pi\)
\(24\) 0 0
\(25\) 1.96410 + 4.59808i 0.392820 + 0.919615i
\(26\) 0 0
\(27\) −3.09808 + 3.09808i −0.596225 + 0.596225i
\(28\) 0 0
\(29\) 3.00000i 0.557086i −0.960424 0.278543i \(-0.910149\pi\)
0.960424 0.278543i \(-0.0898515\pi\)
\(30\) 0 0
\(31\) −0.464102 0.267949i −0.0833551 0.0481251i 0.457743 0.889085i \(-0.348658\pi\)
−0.541098 + 0.840959i \(0.681991\pi\)
\(32\) 0 0
\(33\) 0.366025 1.36603i 0.0637168 0.237795i
\(34\) 0 0
\(35\) 5.73205 + 1.46410i 0.968893 + 0.247478i
\(36\) 0 0
\(37\) −1.26795 + 4.73205i −0.208450 + 0.777944i 0.779921 + 0.625878i \(0.215259\pi\)
−0.988370 + 0.152066i \(0.951407\pi\)
\(38\) 0 0
\(39\) −4.73205 2.73205i −0.757735 0.437478i
\(40\) 0 0
\(41\) 0.464102i 0.0724805i 0.999343 + 0.0362402i \(0.0115382\pi\)
−0.999343 + 0.0362402i \(0.988462\pi\)
\(42\) 0 0
\(43\) 5.83013 5.83013i 0.889086 0.889086i −0.105349 0.994435i \(-0.533596\pi\)
0.994435 + 0.105349i \(0.0335960\pi\)
\(44\) 0 0
\(45\) 1.63397 + 0.0980762i 0.243579 + 0.0146203i
\(46\) 0 0
\(47\) −0.633975 0.169873i −0.0924747 0.0247785i 0.212285 0.977208i \(-0.431909\pi\)
−0.304760 + 0.952429i \(0.598576\pi\)
\(48\) 0 0
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) 0 0
\(51\) 1.00000 + 1.73205i 0.140028 + 0.242536i
\(52\) 0 0
\(53\) −1.83013 6.83013i −0.251387 0.938190i −0.970065 0.242846i \(-0.921919\pi\)
0.718677 0.695344i \(-0.244748\pi\)
\(54\) 0 0
\(55\) 1.46410 0.732051i 0.197419 0.0987097i
\(56\) 0 0
\(57\) 3.73205 + 3.73205i 0.494322 + 0.494322i
\(58\) 0 0
\(59\) −1.09808 + 1.90192i −0.142957 + 0.247609i −0.928609 0.371060i \(-0.878995\pi\)
0.785652 + 0.618669i \(0.212328\pi\)
\(60\) 0 0
\(61\) −7.33013 + 4.23205i −0.938527 + 0.541859i −0.889498 0.456939i \(-0.848946\pi\)
−0.0490285 + 0.998797i \(0.515613\pi\)
\(62\) 0 0
\(63\) 1.26795 1.46410i 0.159747 0.184459i
\(64\) 0 0
\(65\) −1.26795 6.19615i −0.157270 0.768538i
\(66\) 0 0
\(67\) −1.13397 + 0.303848i −0.138537 + 0.0371209i −0.327421 0.944878i \(-0.606180\pi\)
0.188884 + 0.981999i \(0.439513\pi\)
\(68\) 0 0
\(69\) −13.9282 −1.67676
\(70\) 0 0
\(71\) −4.73205 −0.561591 −0.280796 0.959768i \(-0.590598\pi\)
−0.280796 + 0.959768i \(0.590598\pi\)
\(72\) 0 0
\(73\) 3.46410 0.928203i 0.405442 0.108638i −0.0503336 0.998732i \(-0.516028\pi\)
0.455776 + 0.890094i \(0.349362\pi\)
\(74\) 0 0
\(75\) 5.96410 + 7.59808i 0.688675 + 0.877350i
\(76\) 0 0
\(77\) 0.366025 1.90192i 0.0417125 0.216744i
\(78\) 0 0
\(79\) 5.83013 3.36603i 0.655941 0.378707i −0.134788 0.990874i \(-0.543035\pi\)
0.790728 + 0.612167i \(0.209702\pi\)
\(80\) 0 0
\(81\) −5.33013 + 9.23205i −0.592236 + 1.02578i
\(82\) 0 0
\(83\) −3.09808 3.09808i −0.340058 0.340058i 0.516331 0.856389i \(-0.327297\pi\)
−0.856389 + 0.516331i \(0.827297\pi\)
\(84\) 0 0
\(85\) −0.732051 + 2.19615i −0.0794021 + 0.238206i
\(86\) 0 0
\(87\) −1.50000 5.59808i −0.160817 0.600177i
\(88\) 0 0
\(89\) 8.33013 + 14.4282i 0.882992 + 1.52939i 0.847998 + 0.529999i \(0.177808\pi\)
0.0349934 + 0.999388i \(0.488859\pi\)
\(90\) 0 0
\(91\) −6.73205 3.26795i −0.705711 0.342574i
\(92\) 0 0
\(93\) −1.00000 0.267949i −0.103695 0.0277850i
\(94\) 0 0
\(95\) −0.366025 + 6.09808i −0.0375534 + 0.625649i
\(96\) 0 0
\(97\) 7.92820 7.92820i 0.804987 0.804987i −0.178883 0.983870i \(-0.557248\pi\)
0.983870 + 0.178883i \(0.0572484\pi\)
\(98\) 0 0
\(99\) 0.535898i 0.0538598i
\(100\) 0 0
\(101\) −10.1603 5.86603i −1.01098 0.583691i −0.0995037 0.995037i \(-0.531726\pi\)
−0.911479 + 0.411346i \(0.865059\pi\)
\(102\) 0 0
\(103\) 0.598076 2.23205i 0.0589302 0.219931i −0.930181 0.367102i \(-0.880350\pi\)
0.989111 + 0.147171i \(0.0470168\pi\)
\(104\) 0 0
\(105\) 11.4282 0.133975i 1.11528 0.0130746i
\(106\) 0 0
\(107\) −2.30385 + 8.59808i −0.222721 + 0.831207i 0.760583 + 0.649240i \(0.224913\pi\)
−0.983305 + 0.181967i \(0.941754\pi\)
\(108\) 0 0
\(109\) −12.2321 7.06218i −1.17162 0.676434i −0.217557 0.976048i \(-0.569809\pi\)
−0.954061 + 0.299614i \(0.903142\pi\)
\(110\) 0 0
\(111\) 9.46410i 0.898293i
\(112\) 0 0
\(113\) −4.26795 + 4.26795i −0.401495 + 0.401495i −0.878760 0.477265i \(-0.841628\pi\)
0.477265 + 0.878760i \(0.341628\pi\)
\(114\) 0 0
\(115\) −10.6962 12.0622i −0.997421 1.12480i
\(116\) 0 0
\(117\) −2.00000 0.535898i −0.184900 0.0495438i
\(118\) 0 0
\(119\) 1.53590 + 2.26795i 0.140796 + 0.207903i
\(120\) 0 0
\(121\) 5.23205 + 9.06218i 0.475641 + 0.823834i
\(122\) 0 0
\(123\) 0.232051 + 0.866025i 0.0209233 + 0.0780869i
\(124\) 0 0
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) 0 0
\(127\) 6.46410 + 6.46410i 0.573596 + 0.573596i 0.933132 0.359535i \(-0.117065\pi\)
−0.359535 + 0.933132i \(0.617065\pi\)
\(128\) 0 0
\(129\) 7.96410 13.7942i 0.701200 1.21451i
\(130\) 0 0
\(131\) −7.39230 + 4.26795i −0.645869 + 0.372892i −0.786872 0.617117i \(-0.788301\pi\)
0.141003 + 0.990009i \(0.454967\pi\)
\(132\) 0 0
\(133\) 5.46410 + 4.73205i 0.473798 + 0.410321i
\(134\) 0 0
\(135\) −9.59808 + 1.96410i −0.826071 + 0.169043i
\(136\) 0 0
\(137\) −10.4641 + 2.80385i −0.894009 + 0.239549i −0.676441 0.736496i \(-0.736479\pi\)
−0.217567 + 0.976045i \(0.569812\pi\)
\(138\) 0 0
\(139\) −11.6603 −0.989010 −0.494505 0.869175i \(-0.664651\pi\)
−0.494505 + 0.869175i \(0.664651\pi\)
\(140\) 0 0
\(141\) −1.26795 −0.106781
\(142\) 0 0
\(143\) −2.00000 + 0.535898i −0.167248 + 0.0448141i
\(144\) 0 0
\(145\) 3.69615 5.59808i 0.306949 0.464895i
\(146\) 0 0
\(147\) 8.09808 10.8301i 0.667918 0.893254i
\(148\) 0 0
\(149\) −9.69615 + 5.59808i −0.794340 + 0.458612i −0.841488 0.540276i \(-0.818320\pi\)
0.0471484 + 0.998888i \(0.484987\pi\)
\(150\) 0 0
\(151\) −6.92820 + 12.0000i −0.563809 + 0.976546i 0.433350 + 0.901226i \(0.357331\pi\)
−0.997159 + 0.0753205i \(0.976002\pi\)
\(152\) 0 0
\(153\) 0.535898 + 0.535898i 0.0433248 + 0.0433248i
\(154\) 0 0
\(155\) −0.535898 1.07180i −0.0430444 0.0860888i
\(156\) 0 0
\(157\) −6.36603 23.7583i −0.508064 1.89612i −0.438948 0.898513i \(-0.644649\pi\)
−0.0691164 0.997609i \(-0.522018\pi\)
\(158\) 0 0
\(159\) −6.83013 11.8301i −0.541664 0.938190i
\(160\) 0 0
\(161\) −19.0263 + 1.36603i −1.49948 + 0.107658i
\(162\) 0 0
\(163\) 5.36603 + 1.43782i 0.420300 + 0.112619i 0.462769 0.886479i \(-0.346856\pi\)
−0.0424696 + 0.999098i \(0.513523\pi\)
\(164\) 0 0
\(165\) 2.36603 2.09808i 0.184195 0.163335i
\(166\) 0 0
\(167\) 10.7583 10.7583i 0.832505 0.832505i −0.155354 0.987859i \(-0.549652\pi\)
0.987859 + 0.155354i \(0.0496519\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) 0 0
\(171\) 1.73205 + 1.00000i 0.132453 + 0.0764719i
\(172\) 0 0
\(173\) 6.07180 22.6603i 0.461630 1.72283i −0.206197 0.978511i \(-0.566109\pi\)
0.667827 0.744317i \(-0.267225\pi\)
\(174\) 0 0
\(175\) 8.89230 + 9.79423i 0.672195 + 0.740374i
\(176\) 0 0
\(177\) −1.09808 + 4.09808i −0.0825365 + 0.308030i
\(178\) 0 0
\(179\) −17.1962 9.92820i −1.28530 0.742069i −0.307488 0.951552i \(-0.599489\pi\)
−0.977812 + 0.209483i \(0.932822\pi\)
\(180\) 0 0
\(181\) 9.19615i 0.683545i 0.939783 + 0.341772i \(0.111027\pi\)
−0.939783 + 0.341772i \(0.888973\pi\)
\(182\) 0 0
\(183\) −11.5622 + 11.5622i −0.854701 + 0.854701i
\(184\) 0 0
\(185\) −8.19615 + 7.26795i −0.602593 + 0.534350i
\(186\) 0 0
\(187\) 0.732051 + 0.196152i 0.0535329 + 0.0143441i
\(188\) 0 0
\(189\) −5.06218 + 10.4282i −0.368219 + 0.758540i
\(190\) 0 0
\(191\) 8.36603 + 14.4904i 0.605344 + 1.04849i 0.991997 + 0.126262i \(0.0402979\pi\)
−0.386653 + 0.922225i \(0.626369\pi\)
\(192\) 0 0
\(193\) 0.830127 + 3.09808i 0.0597539 + 0.223004i 0.989346 0.145587i \(-0.0465070\pi\)
−0.929592 + 0.368591i \(0.879840\pi\)
\(194\) 0 0
\(195\) −5.46410 10.9282i −0.391292 0.782585i
\(196\) 0 0
\(197\) 14.1244 + 14.1244i 1.00632 + 1.00632i 0.999980 + 0.00633876i \(0.00201770\pi\)
0.00633876 + 0.999980i \(0.497982\pi\)
\(198\) 0 0
\(199\) 12.4641 21.5885i 0.883557 1.53037i 0.0361978 0.999345i \(-0.488475\pi\)
0.847359 0.531021i \(-0.178191\pi\)
\(200\) 0 0
\(201\) −1.96410 + 1.13397i −0.138537 + 0.0799844i
\(202\) 0 0
\(203\) −2.59808 7.50000i −0.182349 0.526397i
\(204\) 0 0
\(205\) −0.571797 + 0.866025i −0.0399360 + 0.0604858i
\(206\) 0 0
\(207\) −5.09808 + 1.36603i −0.354341 + 0.0949453i
\(208\) 0 0
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) −10.1962 −0.701932 −0.350966 0.936388i \(-0.614147\pi\)
−0.350966 + 0.936388i \(0.614147\pi\)
\(212\) 0 0
\(213\) −8.83013 + 2.36603i −0.605030 + 0.162117i
\(214\) 0 0
\(215\) 18.0622 3.69615i 1.23183 0.252076i
\(216\) 0 0
\(217\) −1.39230 0.267949i −0.0945158 0.0181896i
\(218\) 0 0
\(219\) 6.00000 3.46410i 0.405442 0.234082i
\(220\) 0 0
\(221\) 1.46410 2.53590i 0.0984861 0.170583i
\(222\) 0 0
\(223\) 6.12436 + 6.12436i 0.410117 + 0.410117i 0.881779 0.471662i \(-0.156346\pi\)
−0.471662 + 0.881779i \(0.656346\pi\)
\(224\) 0 0
\(225\) 2.92820 + 2.19615i 0.195214 + 0.146410i
\(226\) 0 0
\(227\) −0.0262794 0.0980762i −0.00174423 0.00650955i 0.965048 0.262072i \(-0.0844059\pi\)
−0.966792 + 0.255563i \(0.917739\pi\)
\(228\) 0 0
\(229\) 1.19615 + 2.07180i 0.0790440 + 0.136908i 0.902838 0.429981i \(-0.141480\pi\)
−0.823794 + 0.566890i \(0.808147\pi\)
\(230\) 0 0
\(231\) −0.267949 3.73205i −0.0176298 0.245551i
\(232\) 0 0
\(233\) 1.73205 + 0.464102i 0.113470 + 0.0304043i 0.315107 0.949056i \(-0.397959\pi\)
−0.201637 + 0.979460i \(0.564626\pi\)
\(234\) 0 0
\(235\) −0.973721 1.09808i −0.0635185 0.0716306i
\(236\) 0 0
\(237\) 9.19615 9.19615i 0.597354 0.597354i
\(238\) 0 0
\(239\) 18.3923i 1.18970i 0.803837 + 0.594850i \(0.202788\pi\)
−0.803837 + 0.594850i \(0.797212\pi\)
\(240\) 0 0
\(241\) 14.5359 + 8.39230i 0.936340 + 0.540596i 0.888811 0.458274i \(-0.151532\pi\)
0.0475286 + 0.998870i \(0.484865\pi\)
\(242\) 0 0
\(243\) −1.92820 + 7.19615i −0.123694 + 0.461633i
\(244\) 0 0
\(245\) 15.5981 1.30385i 0.996525 0.0832998i
\(246\) 0 0
\(247\) 2.00000 7.46410i 0.127257 0.474929i
\(248\) 0 0
\(249\) −7.33013 4.23205i −0.464528 0.268195i
\(250\) 0 0
\(251\) 5.85641i 0.369653i 0.982771 + 0.184827i \(0.0591723\pi\)
−0.982771 + 0.184827i \(0.940828\pi\)
\(252\) 0 0
\(253\) −3.73205 + 3.73205i −0.234632 + 0.234632i
\(254\) 0 0
\(255\) −0.267949 + 4.46410i −0.0167796 + 0.279553i
\(256\) 0 0
\(257\) 2.73205 + 0.732051i 0.170421 + 0.0456641i 0.343020 0.939328i \(-0.388550\pi\)
−0.172600 + 0.984992i \(0.555217\pi\)
\(258\) 0 0
\(259\) 0.928203 + 12.9282i 0.0576757 + 0.803319i
\(260\) 0 0
\(261\) −1.09808 1.90192i −0.0679692 0.117726i
\(262\) 0 0
\(263\) −2.16025 8.06218i −0.133207 0.497135i 0.866792 0.498670i \(-0.166178\pi\)
−0.999999 + 0.00153494i \(0.999511\pi\)
\(264\) 0 0
\(265\) 5.00000 15.0000i 0.307148 0.921443i
\(266\) 0 0
\(267\) 22.7583 + 22.7583i 1.39279 + 1.39279i
\(268\) 0 0
\(269\) −2.42820 + 4.20577i −0.148050 + 0.256430i −0.930507 0.366275i \(-0.880633\pi\)
0.782457 + 0.622705i \(0.213966\pi\)
\(270\) 0 0
\(271\) 21.4186 12.3660i 1.30109 0.751183i 0.320496 0.947250i \(-0.396150\pi\)
0.980590 + 0.196067i \(0.0628171\pi\)
\(272\) 0 0
\(273\) −14.1962 2.73205i −0.859190 0.165351i
\(274\) 0 0
\(275\) 3.63397 + 0.437822i 0.219137 + 0.0264017i
\(276\) 0 0
\(277\) 19.3923 5.19615i 1.16517 0.312207i 0.376141 0.926562i \(-0.377251\pi\)
0.789029 + 0.614356i \(0.210584\pi\)
\(278\) 0 0
\(279\) −0.392305 −0.0234867
\(280\) 0 0
\(281\) 12.9282 0.771232 0.385616 0.922659i \(-0.373989\pi\)
0.385616 + 0.922659i \(0.373989\pi\)
\(282\) 0 0
\(283\) 26.4904 7.09808i 1.57469 0.421937i 0.637413 0.770523i \(-0.280005\pi\)
0.937277 + 0.348586i \(0.113338\pi\)
\(284\) 0 0
\(285\) 2.36603 + 11.5622i 0.140151 + 0.684884i
\(286\) 0 0
\(287\) 0.401924 + 1.16025i 0.0237248 + 0.0684876i
\(288\) 0 0
\(289\) 13.7942 7.96410i 0.811425 0.468477i
\(290\) 0 0
\(291\) 10.8301 18.7583i 0.634873 1.09963i
\(292\) 0 0
\(293\) 18.3923 + 18.3923i 1.07449 + 1.07449i 0.996993 + 0.0774974i \(0.0246929\pi\)
0.0774974 + 0.996993i \(0.475307\pi\)
\(294\) 0 0
\(295\) −4.39230 + 2.19615i −0.255730 + 0.127865i
\(296\) 0 0
\(297\) 0.830127 + 3.09808i 0.0481689 + 0.179769i
\(298\) 0 0
\(299\) 10.1962 + 17.6603i 0.589659 + 1.02132i
\(300\) 0 0
\(301\) 9.52628 19.6244i 0.549086 1.13113i
\(302\) 0 0
\(303\) −21.8923 5.86603i −1.25768 0.336994i
\(304\) 0 0
\(305\) −18.8923 1.13397i −1.08177 0.0649312i
\(306\) 0 0
\(307\) 9.29423 9.29423i 0.530450 0.530450i −0.390257 0.920706i \(-0.627614\pi\)
0.920706 + 0.390257i \(0.127614\pi\)
\(308\) 0 0
\(309\) 4.46410i 0.253954i
\(310\) 0 0
\(311\) −16.2224 9.36603i −0.919890 0.531099i −0.0362898 0.999341i \(-0.511554\pi\)
−0.883600 + 0.468243i \(0.844887\pi\)
\(312\) 0 0
\(313\) 5.19615 19.3923i 0.293704 1.09612i −0.648537 0.761183i \(-0.724619\pi\)
0.942241 0.334935i \(-0.108714\pi\)
\(314\) 0 0
\(315\) 4.16987 1.16987i 0.234946 0.0659149i
\(316\) 0 0
\(317\) −1.19615 + 4.46410i −0.0671826 + 0.250729i −0.991347 0.131265i \(-0.958096\pi\)
0.924165 + 0.381994i \(0.124763\pi\)
\(318\) 0 0
\(319\) −1.90192 1.09808i −0.106487 0.0614805i
\(320\) 0 0
\(321\) 17.1962i 0.959796i
\(322\) 0 0
\(323\) −2.00000 + 2.00000i −0.111283 + 0.111283i
\(324\) 0 0
\(325\) 5.26795 13.1244i 0.292213 0.728008i
\(326\) 0 0
\(327\) −26.3564 7.06218i −1.45751 0.390539i
\(328\) 0 0
\(329\) −1.73205 + 0.124356i −0.0954911 + 0.00685595i
\(330\) 0 0
\(331\) 12.9282 + 22.3923i 0.710598 + 1.23079i 0.964633 + 0.263597i \(0.0849090\pi\)
−0.254035 + 0.967195i \(0.581758\pi\)
\(332\) 0 0
\(333\) 0.928203 + 3.46410i 0.0508652 + 0.189832i
\(334\) 0 0
\(335\) −2.49038 0.830127i −0.136064 0.0453547i
\(336\) 0 0
\(337\) 16.4641 + 16.4641i 0.896857 + 0.896857i 0.995157 0.0983001i \(-0.0313405\pi\)
−0.0983001 + 0.995157i \(0.531340\pi\)
\(338\) 0 0
\(339\) −5.83013 + 10.0981i −0.316649 + 0.548452i
\(340\) 0 0
\(341\) −0.339746 + 0.196152i −0.0183983 + 0.0106222i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) −25.9904 17.1603i −1.39928 0.923877i
\(346\) 0 0
\(347\) −7.79423 + 2.08846i −0.418416 + 0.112114i −0.461884 0.886941i \(-0.652826\pi\)
0.0434674 + 0.999055i \(0.486160\pi\)
\(348\) 0 0
\(349\) 9.73205 0.520945 0.260472 0.965481i \(-0.416122\pi\)
0.260472 + 0.965481i \(0.416122\pi\)
\(350\) 0 0
\(351\) 12.3923 0.661452
\(352\) 0 0
\(353\) 5.36603 1.43782i 0.285605 0.0765276i −0.113173 0.993575i \(-0.536101\pi\)
0.398777 + 0.917048i \(0.369435\pi\)
\(354\) 0 0
\(355\) −8.83013 5.83013i −0.468654 0.309431i
\(356\) 0 0
\(357\) 4.00000 + 3.46410i 0.211702 + 0.183340i
\(358\) 0 0
\(359\) −12.3397 + 7.12436i −0.651267 + 0.376009i −0.788941 0.614468i \(-0.789371\pi\)
0.137675 + 0.990478i \(0.456037\pi\)
\(360\) 0 0
\(361\) 5.76795 9.99038i 0.303576 0.525810i
\(362\) 0 0
\(363\) 14.2942 + 14.2942i 0.750252 + 0.750252i
\(364\) 0 0
\(365\) 7.60770 + 2.53590i 0.398205 + 0.132735i
\(366\) 0 0
\(367\) −0.500000 1.86603i −0.0260998 0.0974057i 0.951647 0.307193i \(-0.0993896\pi\)
−0.977747 + 0.209787i \(0.932723\pi\)
\(368\) 0 0
\(369\) 0.169873 + 0.294229i 0.00884323 + 0.0153169i
\(370\) 0 0
\(371\) −10.4904 15.4904i −0.544633 0.804221i
\(372\) 0 0
\(373\) 15.9282 + 4.26795i 0.824731 + 0.220986i 0.646414 0.762987i \(-0.276268\pi\)
0.178317 + 0.983973i \(0.442935\pi\)
\(374\) 0 0
\(375\) 1.76795 + 21.5263i 0.0912965 + 1.11161i
\(376\) 0 0
\(377\) −6.00000 + 6.00000i −0.309016 + 0.309016i
\(378\) 0 0
\(379\) 19.6603i 1.00988i −0.863155 0.504940i \(-0.831515\pi\)
0.863155 0.504940i \(-0.168485\pi\)
\(380\) 0 0
\(381\) 15.2942 + 8.83013i 0.783547 + 0.452381i
\(382\) 0 0
\(383\) 7.55256 28.1865i 0.385918 1.44026i −0.450797 0.892626i \(-0.648860\pi\)
0.836715 0.547638i \(-0.184473\pi\)
\(384\) 0 0
\(385\) 3.02628 3.09808i 0.154233 0.157893i
\(386\) 0 0
\(387\) 1.56218 5.83013i 0.0794100 0.296362i
\(388\) 0 0
\(389\) −7.73205 4.46410i −0.392031 0.226339i 0.291009 0.956720i \(-0.406009\pi\)
−0.683040 + 0.730381i \(0.739342\pi\)
\(390\) 0 0
\(391\) 7.46410i 0.377476i
\(392\) 0 0
\(393\) −11.6603 + 11.6603i −0.588182 + 0.588182i
\(394\) 0 0
\(395\) 15.0263 + 0.901924i 0.756054 + 0.0453807i
\(396\) 0 0
\(397\) −20.0263 5.36603i −1.00509 0.269313i −0.281514 0.959557i \(-0.590836\pi\)
−0.723577 + 0.690244i \(0.757503\pi\)
\(398\) 0 0
\(399\) 12.5622 + 6.09808i 0.628896 + 0.305286i
\(400\) 0 0
\(401\) −5.50000 9.52628i −0.274657 0.475720i 0.695392 0.718631i \(-0.255231\pi\)
−0.970049 + 0.242911i \(0.921898\pi\)
\(402\) 0 0
\(403\) 0.392305 + 1.46410i 0.0195421 + 0.0729321i
\(404\) 0 0
\(405\) −21.3205 + 10.6603i −1.05942 + 0.529712i
\(406\) 0 0
\(407\) 2.53590 + 2.53590i 0.125700 + 0.125700i
\(408\) 0 0
\(409\) 3.42820 5.93782i 0.169514 0.293606i −0.768735 0.639567i \(-0.779114\pi\)
0.938249 + 0.345961i \(0.112447\pi\)
\(410\) 0 0
\(411\) −18.1244 + 10.4641i −0.894009 + 0.516156i
\(412\) 0 0
\(413\) −1.09808 + 5.70577i −0.0540328 + 0.280763i
\(414\) 0 0
\(415\) −1.96410 9.59808i −0.0964140 0.471151i
\(416\) 0 0
\(417\) −21.7583 + 5.83013i −1.06551 + 0.285503i
\(418\) 0 0
\(419\) 3.85641 0.188398 0.0941989 0.995553i \(-0.469971\pi\)
0.0941989 + 0.995553i \(0.469971\pi\)
\(420\) 0 0
\(421\) −34.6603 −1.68924 −0.844619 0.535368i \(-0.820173\pi\)
−0.844619 + 0.535368i \(0.820173\pi\)
\(422\) 0 0
\(423\) −0.464102 + 0.124356i −0.0225654 + 0.00604638i
\(424\) 0 0
\(425\) −4.07180 + 3.19615i −0.197511 + 0.155036i
\(426\) 0 0
\(427\) −14.6603 + 16.9282i −0.709459 + 0.819213i
\(428\) 0 0
\(429\) −3.46410 + 2.00000i −0.167248 + 0.0965609i
\(430\) 0 0
\(431\) −2.09808 + 3.63397i −0.101061 + 0.175042i −0.912122 0.409919i \(-0.865557\pi\)
0.811061 + 0.584961i \(0.198890\pi\)
\(432\) 0 0
\(433\) −24.4641 24.4641i −1.17567 1.17567i −0.980836 0.194833i \(-0.937583\pi\)
−0.194833 0.980836i \(-0.562417\pi\)
\(434\) 0 0
\(435\) 4.09808 12.2942i 0.196488 0.589463i
\(436\) 0 0
\(437\) −5.09808 19.0263i −0.243874 0.910150i
\(438\) 0 0
\(439\) 15.6603 + 27.1244i 0.747423 + 1.29457i 0.949054 + 0.315113i \(0.102043\pi\)
−0.201631 + 0.979462i \(0.564624\pi\)
\(440\) 0 0
\(441\) 1.90192 4.75833i 0.0905678 0.226587i
\(442\) 0 0
\(443\) 3.50000 + 0.937822i 0.166290 + 0.0445573i 0.341003 0.940062i \(-0.389233\pi\)
−0.174713 + 0.984619i \(0.555900\pi\)
\(444\) 0 0
\(445\) −2.23205 + 37.1865i −0.105809 + 1.76281i
\(446\) 0 0
\(447\) −15.2942 + 15.2942i −0.723392 + 0.723392i
\(448\) 0 0
\(449\) 5.05256i 0.238445i 0.992868 + 0.119222i \(0.0380402\pi\)
−0.992868 + 0.119222i \(0.961960\pi\)
\(450\) 0 0
\(451\) 0.294229 + 0.169873i 0.0138547 + 0.00799901i
\(452\) 0 0
\(453\) −6.92820 + 25.8564i −0.325515 + 1.21484i
\(454\) 0 0
\(455\) −8.53590 14.3923i −0.400169 0.674722i
\(456\) 0 0
\(457\) −8.26795 + 30.8564i −0.386758 + 1.44340i 0.448618 + 0.893724i \(0.351916\pi\)
−0.835376 + 0.549678i \(0.814750\pi\)
\(458\) 0 0
\(459\) −3.92820 2.26795i −0.183353 0.105859i
\(460\) 0 0
\(461\) 26.3923i 1.22921i −0.788834 0.614606i \(-0.789315\pi\)
0.788834 0.614606i \(-0.210685\pi\)
\(462\) 0 0
\(463\) −17.7583 + 17.7583i −0.825300 + 0.825300i −0.986862 0.161563i \(-0.948347\pi\)
0.161563 + 0.986862i \(0.448347\pi\)
\(464\) 0 0
\(465\) −1.53590 1.73205i −0.0712256 0.0803219i
\(466\) 0 0
\(467\) −31.3564 8.40192i −1.45100 0.388795i −0.554629 0.832097i \(-0.687140\pi\)
−0.896372 + 0.443303i \(0.853807\pi\)
\(468\) 0 0
\(469\) −2.57180 + 1.74167i −0.118755 + 0.0804228i
\(470\) 0 0
\(471\) −23.7583 41.1506i −1.09473 1.89612i
\(472\) 0 0
\(473\) −1.56218 5.83013i −0.0718290 0.268070i
\(474\) 0 0
\(475\) −8.19615 + 10.9282i −0.376065 + 0.501420i
\(476\) 0 0
\(477\) −3.66025 3.66025i −0.167592 0.167592i
\(478\) 0 0
\(479\) −13.4641 + 23.3205i −0.615191 + 1.06554i 0.375161 + 0.926960i \(0.377588\pi\)
−0.990351 + 0.138581i \(0.955746\pi\)
\(480\) 0 0
\(481\) 12.0000 6.92820i 0.547153 0.315899i
\(482\) 0 0
\(483\) −34.8205 + 12.0622i −1.58439 + 0.548848i
\(484\) 0 0
\(485\) 24.5622 5.02628i 1.11531 0.228232i
\(486\) 0 0
\(487\) 8.29423 2.22243i 0.375847 0.100708i −0.0659498 0.997823i \(-0.521008\pi\)
0.441797 + 0.897115i \(0.354341\pi\)
\(488\) 0 0
\(489\) 10.7321 0.485320
\(490\) 0 0
\(491\) 17.7128 0.799368 0.399684 0.916653i \(-0.369120\pi\)
0.399684 + 0.916653i \(0.369120\pi\)
\(492\) 0 0
\(493\) 3.00000 0.803848i 0.135113 0.0362035i
\(494\) 0 0
\(495\) 0.660254 1.00000i 0.0296762 0.0449467i
\(496\) 0 0
\(497\) −11.8301 + 4.09808i −0.530654 + 0.183824i
\(498\) 0 0
\(499\) 29.0263 16.7583i 1.29939 0.750206i 0.319095 0.947723i \(-0.396621\pi\)
0.980300 + 0.197517i \(0.0632877\pi\)
\(500\) 0 0
\(501\) 14.6962 25.4545i 0.656576 1.13722i
\(502\) 0 0
\(503\) 19.3660 + 19.3660i 0.863488 + 0.863488i 0.991741 0.128253i \(-0.0409370\pi\)
−0.128253 + 0.991741i \(0.540937\pi\)
\(504\) 0 0
\(505\) −11.7321 23.4641i −0.522069 1.04414i
\(506\) 0 0
\(507\) −2.50000 9.33013i −0.111029 0.414365i
\(508\) 0 0
\(509\) 13.4545 + 23.3038i 0.596359 + 1.03292i 0.993353 + 0.115104i \(0.0367200\pi\)
−0.396994 + 0.917821i \(0.629947\pi\)
\(510\) 0 0
\(511\) 7.85641 5.32051i 0.347547 0.235365i
\(512\) 0 0
\(513\) −11.5622 3.09808i −0.510483 0.136783i
\(514\) 0 0
\(515\) 3.86603 3.42820i 0.170357 0.151065i
\(516\) 0 0
\(517\) −0.339746 + 0.339746i −0.0149420 + 0.0149420i
\(518\) 0 0
\(519\) 45.3205i 1.98935i
\(520\) 0 0
\(521\) −3.33975 1.92820i −0.146317 0.0844761i 0.425054 0.905168i \(-0.360255\pi\)
−0.571371 + 0.820692i \(0.693588\pi\)
\(522\) 0 0
\(523\) −3.88269 + 14.4904i −0.169778 + 0.633620i 0.827604 + 0.561312i \(0.189703\pi\)
−0.997382 + 0.0723082i \(0.976963\pi\)
\(524\) 0 0
\(525\) 21.4904 + 13.8301i 0.937917 + 0.603596i
\(526\) 0 0
\(527\) 0.143594 0.535898i 0.00625503 0.0233441i
\(528\) 0 0
\(529\) 25.0981 + 14.4904i 1.09122 + 0.630017i
\(530\) 0 0
\(531\) 1.60770i 0.0697680i
\(532\) 0 0
\(533\) 0.928203 0.928203i 0.0402049 0.0402049i
\(534\) 0 0
\(535\) −14.8923 + 13.2058i −0.643850 + 0.570935i
\(536\) 0 0
\(537\) −37.0526 9.92820i −1.59894 0.428434i
\(538\) 0 0
\(539\) −0.732051 5.07180i −0.0315317 0.218458i
\(540\) 0 0
\(541\) 9.35641 + 16.2058i 0.402263 + 0.696741i 0.993999 0.109392i \(-0.0348903\pi\)
−0.591735 + 0.806132i \(0.701557\pi\)
\(542\) 0 0
\(543\) 4.59808 + 17.1603i 0.197322 + 0.736417i
\(544\) 0 0
\(545\) −14.1244 28.2487i −0.605021 1.21004i
\(546\) 0 0
\(547\) −5.75833 5.75833i −0.246208 0.246208i 0.573204 0.819413i \(-0.305700\pi\)
−0.819413 + 0.573204i \(0.805700\pi\)
\(548\) 0 0
\(549\) −3.09808 + 5.36603i −0.132223 + 0.229016i
\(550\) 0 0
\(551\) 7.09808 4.09808i 0.302388 0.174584i
\(552\) 0 0
\(553\) 11.6603 13.4641i 0.495844 0.572552i
\(554\) 0 0
\(555\) −11.6603 + 17.6603i −0.494950 + 0.749636i
\(556\) 0 0
\(557\) 6.63397 1.77757i 0.281091 0.0753180i −0.115519 0.993305i \(-0.536853\pi\)
0.396610 + 0.917987i \(0.370187\pi\)
\(558\) 0 0
\(559\) −23.3205 −0.986352
\(560\) 0 0
\(561\) 1.46410 0.0618144
\(562\) 0 0
\(563\) −21.3564 + 5.72243i −0.900065 + 0.241172i −0.679044 0.734097i \(-0.737606\pi\)
−0.221021 + 0.975269i \(0.570939\pi\)
\(564\) 0 0
\(565\) −13.2224 + 2.70577i −0.556272 + 0.113833i
\(566\) 0 0
\(567\) −5.33013 + 27.6962i −0.223844 + 1.16313i
\(568\) 0 0
\(569\) 13.0526 7.53590i 0.547192 0.315921i −0.200797 0.979633i \(-0.564353\pi\)
0.747989 + 0.663712i \(0.231020\pi\)
\(570\) 0 0
\(571\) 10.0263 17.3660i 0.419587 0.726746i −0.576311 0.817230i \(-0.695508\pi\)
0.995898 + 0.0904849i \(0.0288417\pi\)
\(572\) 0 0
\(573\) 22.8564 + 22.8564i 0.954840 + 0.954840i
\(574\) 0 0
\(575\) −5.09808 35.6865i −0.212604 1.48823i
\(576\) 0 0
\(577\) 7.36603 + 27.4904i 0.306652 + 1.14444i 0.931514 + 0.363705i \(0.118488\pi\)
−0.624863 + 0.780735i \(0.714845\pi\)
\(578\) 0 0
\(579\) 3.09808 + 5.36603i 0.128752 + 0.223004i
\(580\) 0 0
\(581\) −10.4282 5.06218i −0.432635 0.210015i
\(582\) 0 0
\(583\) −5.00000 1.33975i −0.207079 0.0554866i
\(584\) 0 0
\(585\) −3.07180 3.46410i −0.127003 0.143223i
\(586\) 0 0
\(587\) 25.7846 25.7846i 1.06424 1.06424i 0.0664553 0.997789i \(-0.478831\pi\)
0.997789 0.0664553i \(-0.0211690\pi\)
\(588\) 0 0
\(589\) 1.46410i 0.0603273i
\(590\) 0 0
\(591\) 33.4186 + 19.2942i 1.37466 + 0.793659i
\(592\) 0 0
\(593\) −1.75833 + 6.56218i −0.0722060 + 0.269476i −0.992585 0.121550i \(-0.961213\pi\)
0.920379 + 0.391027i \(0.127880\pi\)
\(594\) 0 0
\(595\) 0.0717968 + 6.12436i 0.00294338 + 0.251074i
\(596\) 0 0
\(597\) 12.4641 46.5167i 0.510122 1.90380i
\(598\) 0 0
\(599\) 32.6603 + 18.8564i 1.33446 + 0.770452i 0.985980 0.166864i \(-0.0533640\pi\)
0.348482 + 0.937316i \(0.386697\pi\)
\(600\) 0 0
\(601\) 21.1769i 0.863824i 0.901916 + 0.431912i \(0.142161\pi\)
−0.901916 + 0.431912i \(0.857839\pi\)
\(602\) 0 0
\(603\) −0.607695 + 0.607695i −0.0247473 + 0.0247473i
\(604\) 0 0
\(605\) −1.40192 + 23.3564i −0.0569963 + 0.949573i
\(606\) 0 0
\(607\) −8.59808 2.30385i −0.348985 0.0935103i 0.0800683 0.996789i \(-0.474486\pi\)
−0.429053 + 0.903279i \(0.641153\pi\)
\(608\) 0 0
\(609\) −8.59808 12.6962i −0.348412 0.514474i
\(610\) 0 0
\(611\) 0.928203 + 1.60770i 0.0375511 + 0.0650404i
\(612\) 0 0
\(613\) 3.60770 + 13.4641i 0.145713 + 0.543810i 0.999723 + 0.0235520i \(0.00749753\pi\)
−0.854009 + 0.520258i \(0.825836\pi\)
\(614\) 0 0
\(615\) −0.633975 + 1.90192i −0.0255643 + 0.0766930i
\(616\) 0 0
\(617\) −31.9090 31.9090i −1.28461 1.28461i −0.938017 0.346590i \(-0.887340\pi\)
−0.346590 0.938017i \(-0.612660\pi\)
\(618\) 0 0
\(619\) 0.0980762 0.169873i 0.00394202 0.00682777i −0.864048 0.503410i \(-0.832079\pi\)
0.867990 + 0.496582i \(0.165412\pi\)
\(620\) 0 0
\(621\) 27.3564 15.7942i 1.09777 0.633801i
\(622\) 0 0
\(623\) 33.3205 + 28.8564i 1.33496 + 1.15611i
\(624\) 0 0
\(625\) −17.2846 + 18.0622i −0.691384 + 0.722487i
\(626\) 0 0
\(627\) 3.73205 1.00000i 0.149044 0.0399362i
\(628\) 0 0
\(629\) −5.07180 −0.202226
\(630\) 0 0
\(631\) −26.5885 −1.05847 −0.529235 0.848475i \(-0.677521\pi\)
−0.529235 + 0.848475i \(0.677521\pi\)
\(632\) 0 0
\(633\) −19.0263 + 5.09808i −0.756227 + 0.202630i
\(634\) 0 0
\(635\) 4.09808 + 20.0263i 0.162627 + 0.794719i
\(636\) 0 0
\(637\) −19.6603 2.33975i −0.778968 0.0927041i
\(638\) 0 0
\(639\) −3.00000 + 1.73205i −0.118678 + 0.0685189i
\(640\) 0 0
\(641\) 3.33013 5.76795i 0.131532 0.227820i −0.792735 0.609566i \(-0.791344\pi\)
0.924267 + 0.381746i \(0.124677\pi\)
\(642\) 0 0
\(643\) −24.4641 24.4641i −0.964770 0.964770i 0.0346302 0.999400i \(-0.488975\pi\)
−0.999400 + 0.0346302i \(0.988975\pi\)
\(644\) 0 0
\(645\) 31.8564 15.9282i 1.25434 0.627172i
\(646\) 0 0
\(647\) −1.44744 5.40192i −0.0569048 0.212372i 0.931619 0.363436i \(-0.118397\pi\)
−0.988524 + 0.151065i \(0.951730\pi\)
\(648\) 0 0
\(649\) 0.803848 + 1.39230i 0.0315538 + 0.0546527i
\(650\) 0 0
\(651\) −2.73205 + 0.196152i −0.107078 + 0.00768782i
\(652\) 0 0
\(653\) −8.73205 2.33975i −0.341712 0.0915613i 0.0838822 0.996476i \(-0.473268\pi\)
−0.425594 + 0.904914i \(0.639935\pi\)
\(654\) 0 0
\(655\) −19.0526 1.14359i −0.744445 0.0446839i
\(656\) 0 0
\(657\) 1.85641 1.85641i 0.0724253 0.0724253i
\(658\) 0 0
\(659\) 10.3397i 0.402779i 0.979511 + 0.201390i \(0.0645457\pi\)
−0.979511 + 0.201390i \(0.935454\pi\)
\(660\) 0 0
\(661\) −12.2776 7.08846i −0.477542 0.275709i 0.241850 0.970314i \(-0.422246\pi\)
−0.719392 + 0.694605i \(0.755579\pi\)
\(662\) 0 0
\(663\) 1.46410 5.46410i 0.0568610 0.212208i
\(664\) 0 0
\(665\) 4.36603 + 15.5622i 0.169307 + 0.603475i
\(666\) 0 0
\(667\) −5.59808 + 20.8923i −0.216758 + 0.808953i
\(668\) 0 0
\(669\) 14.4904 + 8.36603i 0.560230 + 0.323449i
\(670\) 0 0
\(671\) 6.19615i 0.239200i
\(672\) 0 0
\(673\) −16.3923 + 16.3923i −0.631877 + 0.631877i −0.948539 0.316662i \(-0.897438\pi\)
0.316662 + 0.948539i \(0.397438\pi\)
\(674\) 0 0
\(675\) −20.3301 8.16025i −0.782507 0.314088i
\(676\) 0 0
\(677\) 6.92820 + 1.85641i 0.266272 + 0.0713475i 0.389485 0.921033i \(-0.372653\pi\)
−0.123213 + 0.992380i \(0.539320\pi\)
\(678\) 0 0
\(679\) 12.9545 26.6865i 0.497147 1.02414i
\(680\) 0 0
\(681\) −0.0980762 0.169873i −0.00375829 0.00650955i
\(682\) 0 0
\(683\) −4.93782 18.4282i −0.188941 0.705136i −0.993753 0.111606i \(-0.964401\pi\)
0.804812 0.593530i \(-0.202266\pi\)
\(684\) 0 0
\(685\) −22.9808 7.66025i −0.878050 0.292683i
\(686\) 0 0
\(687\) 3.26795 + 3.26795i 0.124680 + 0.124680i
\(688\) 0 0
\(689\) −10.0000 + 17.3205i −0.380970 + 0.659859i
\(690\) 0 0
\(691\) 24.9737 14.4186i 0.950045 0.548509i 0.0569502 0.998377i \(-0.481862\pi\)
0.893095 + 0.449868i \(0.148529\pi\)
\(692\) 0 0
\(693\) −0.464102 1.33975i −0.0176298 0.0508927i
\(694\) 0 0
\(695\) −21.7583 14.3660i −0.825341 0.544934i
\(696\) 0 0
\(697\) −0.464102 + 0.124356i −0.0175791 + 0.00471031i
\(698\) 0 0
\(699\) 3.46410 0.131024
\(700\) 0 0
\(701\) −23.7321 −0.896347 −0.448174 0.893947i \(-0.647925\pi\)
−0.448174 + 0.893947i \(0.647925\pi\)
\(702\) 0 0
\(703\) −12.9282 + 3.46410i −0.487596 + 0.130651i
\(704\) 0 0
\(705\) −2.36603 1.56218i −0.0891097 0.0588350i
\(706\) 0 0
\(707\) −30.4808 5.86603i −1.14635 0.220615i
\(708\) 0 0
\(709\) −6.99038 + 4.03590i −0.262529 + 0.151571i −0.625488 0.780234i \(-0.715100\pi\)
0.362959 + 0.931805i \(0.381767\pi\)
\(710\) 0 0
\(711\) 2.46410 4.26795i 0.0924110 0.160061i
\(712\) 0 0
\(713\) 2.73205 + 2.73205i 0.102316 + 0.102316i
\(714\) 0 0
\(715\) −4.39230 1.46410i −0.164263 0.0547543i
\(716\) 0 0
\(717\) 9.19615 + 34.3205i 0.343437 + 1.28172i
\(718\) 0 0
\(719\) −3.70577 6.41858i −0.138202 0.239373i 0.788614 0.614888i \(-0.210799\pi\)
−0.926816 + 0.375516i \(0.877466\pi\)
\(720\) 0 0
\(721\) −0.437822 6.09808i −0.0163053 0.227104i
\(722\) 0 0
\(723\) 31.3205 + 8.39230i 1.16482 + 0.312113i
\(724\) 0 0
\(725\) 13.7942 5.89230i 0.512305 0.218835i
\(726\) 0 0
\(727\) 4.90192 4.90192i 0.181802 0.181802i −0.610338 0.792141i \(-0.708967\pi\)
0.792141 + 0.610338i \(0.208967\pi\)
\(728\) 0 0
\(729\) 17.5885i 0.651424i
\(730\) 0 0
\(731\) 7.39230 + 4.26795i 0.273414 + 0.157856i
\(732\) 0 0
\(733\) −2.63397 + 9.83013i −0.0972881 + 0.363084i −0.997356 0.0726647i \(-0.976850\pi\)
0.900068 + 0.435749i \(0.143516\pi\)
\(734\) 0 0
\(735\) 28.4545 10.2321i 1.04956 0.377415i
\(736\) 0 0
\(737\) −0.222432 + 0.830127i −0.00819338 + 0.0305781i
\(738\) 0 0
\(739\) 7.43782 + 4.29423i 0.273605 + 0.157966i 0.630525 0.776169i \(-0.282840\pi\)
−0.356920 + 0.934135i \(0.616173\pi\)
\(740\) 0 0
\(741\) 14.9282i 0.548401i
\(742\) 0 0
\(743\) 14.8301 14.8301i 0.544065 0.544065i −0.380653 0.924718i \(-0.624301\pi\)
0.924718 + 0.380653i \(0.124301\pi\)
\(744\) 0 0
\(745\) −24.9904 1.50000i −0.915577 0.0549557i
\(746\) 0 0
\(747\) −3.09808 0.830127i −0.113353 0.0303728i
\(748\) 0 0
\(749\) 1.68653 + 23.4904i 0.0616246 + 0.858320i
\(750\) 0 0
\(751\) 7.19615 + 12.4641i 0.262591 + 0.454822i 0.966930 0.255043i \(-0.0820896\pi\)
−0.704338 + 0.709864i \(0.748756\pi\)
\(752\) 0 0
\(753\) 2.92820 + 10.9282i 0.106710 + 0.398246i
\(754\) 0 0
\(755\) −27.7128 + 13.8564i −1.00857 + 0.504286i
\(756\) 0 0
\(757\) 9.26795 + 9.26795i 0.336849 + 0.336849i 0.855180 0.518331i \(-0.173446\pi\)
−0.518331 + 0.855180i \(0.673446\pi\)
\(758\) 0 0
\(759\) −5.09808 + 8.83013i −0.185048 + 0.320513i
\(760\) 0 0
\(761\) 11.0718 6.39230i 0.401352 0.231721i −0.285715 0.958315i \(-0.592231\pi\)
0.687067 + 0.726594i \(0.258898\pi\)
\(762\) 0 0
\(763\) −36.6962 7.06218i −1.32849 0.255668i
\(764\) 0 0
\(765\) 0.339746 + 1.66025i 0.0122835 + 0.0600266i
\(766\) 0 0
\(767\) 6.00000 1.60770i 0.216647 0.0580505i
\(768\) 0 0
\(769\) −47.1769 −1.70124 −0.850622 0.525778i \(-0.823774\pi\)
−0.850622 + 0.525778i \(0.823774\pi\)
\(770\) 0 0
\(771\) 5.46410 0.196785
\(772\) 0 0
\(773\) 17.9282 4.80385i 0.644833 0.172782i 0.0784412 0.996919i \(-0.475006\pi\)
0.566391 + 0.824136i \(0.308339\pi\)
\(774\) 0 0
\(775\) 0.320508 2.66025i 0.0115130 0.0955591i
\(776\) 0 0
\(777\) 8.19615 + 23.6603i 0.294035 + 0.848807i
\(778\) 0 0
\(779\) −1.09808 + 0.633975i −0.0393427 + 0.0227145i
\(780\) 0 0
\(781\) −1.73205 + 3.00000i −0.0619777 + 0.107348i
\(782\) 0 0
\(783\) 9.29423 + 9.29423i 0.332149 + 0.332149i
\(784\) 0 0
\(785\) 17.3923 52.1769i 0.620758 1.86227i
\(786\) 0 0
\(787\) 5.18653 + 19.3564i 0.184880 + 0.689981i 0.994656 + 0.103243i \(0.0329218\pi\)
−0.809776 + 0.586739i \(0.800412\pi\)
\(788\) 0 0
\(789\) −8.06218 13.9641i −0.287021 0.497135i
\(790\) 0 0
\(791\) −6.97372 + 14.3660i −0.247957 + 0.510797i
\(792\) 0 0
\(793\) 23.1244 + 6.19615i 0.821170 + 0.220032i
\(794\) 0 0
\(795\) 1.83013 30.4904i 0.0649079 1.08138i
\(796\) 0 0
\(797\) 29.4641 29.4641i 1.04367 1.04367i 0.0446702 0.999002i \(-0.485776\pi\)
0.999002 0.0446702i \(-0.0142237\pi\)
\(798\) 0 0
\(799\) 0.679492i 0.0240387i
\(800\) 0 0
\(801\) 10.5622 + 6.09808i 0.373196 + 0.215465i
\(802\) 0 0
\(803\) 0.679492 2.53590i 0.0239787 0.0894899i
\(804\) 0 0
\(805\) −37.1865 20.8923i −1.31065 0.736357i
\(806\) 0 0
\(807\) −2.42820 + 9.06218i −0.0854768 + 0.319004i
\(808\) 0 0
\(809\) 21.9904 + 12.6962i 0.773141 + 0.446373i 0.833994 0.551774i \(-0.186049\pi\)
−0.0608532 + 0.998147i \(0.519382\pi\)
\(810\) 0 0
\(811\) 29.0718i 1.02085i −0.859923 0.510424i \(-0.829488\pi\)
0.859923 0.510424i \(-0.170512\pi\)
\(812\) 0 0
\(813\) 33.7846 33.7846i 1.18488 1.18488i
\(814\) 0 0
\(815\) 8.24167 + 9.29423i 0.288693 + 0.325563i
\(816\) 0 0
\(817\) 21.7583 + 5.83013i 0.761228 + 0.203970i
\(818\) 0 0
\(819\) −5.46410 + 0.392305i −0.190931 + 0.0137082i
\(820\) 0 0
\(821\) 7.33975 + 12.7128i 0.256159 + 0.443680i 0.965210 0.261477i \(-0.0842096\pi\)
−0.709051 + 0.705157i \(0.750876\pi\)
\(822\) 0 0
\(823\) 6.61731 + 24.6962i 0.230665 + 0.860854i 0.980055 + 0.198725i \(0.0636801\pi\)
−0.749390 + 0.662129i \(0.769653\pi\)
\(824\) 0 0
\(825\) 7.00000 1.00000i 0.243709 0.0348155i
\(826\) 0 0
\(827\) 3.77757 + 3.77757i 0.131359 + 0.131359i 0.769729 0.638370i \(-0.220391\pi\)
−0.638370 + 0.769729i \(0.720391\pi\)
\(828\) 0 0
\(829\) −10.7321 + 18.5885i −0.372740 + 0.645604i −0.989986 0.141166i \(-0.954915\pi\)
0.617246 + 0.786770i \(0.288248\pi\)
\(830\) 0 0
\(831\) 33.5885 19.3923i 1.16517 0.672712i
\(832\) 0 0
\(833\) 5.80385 + 4.33975i 0.201091 + 0.150363i
\(834\) 0 0
\(835\) 33.3301 6.82051i 1.15344 0.236033i
\(836\) 0 0
\(837\) 2.26795 0.607695i 0.0783918 0.0210050i
\(838\) 0 0
\(839\) −31.1244 −1.07453 −0.537266 0.843413i \(-0.680543\pi\)
−0.537266 + 0.843413i \(0.680543\pi\)
\(840\) 0 0
\(841\) 20.0000 0.689655
\(842\) 0 0
\(843\) 24.1244 6.46410i 0.830887 0.222635i
\(844\) 0 0
\(845\) 6.16025 9.33013i 0.211919 0.320966i
\(846\) 0 0
\(847\) 20.9282 + 18.1244i 0.719102 + 0.622760i
\(848\) 0 0
\(849\) 45.8827 26.4904i 1.57469 0.909148i
\(850\) 0 0
\(851\) 17.6603 30.5885i 0.605386 1.04856i
\(852\) 0 0
\(853\) 6.12436 + 6.12436i 0.209694 + 0.209694i 0.804137 0.594443i \(-0.202628\pi\)
−0.594443 + 0.804137i \(0.702628\pi\)
\(854\) 0 0
\(855\) 2.00000 + 4.00000i 0.0683986 + 0.136797i
\(856\) 0 0
\(857\) −5.90192 22.0263i −0.201606 0.752403i −0.990457 0.137820i \(-0.955991\pi\)
0.788851 0.614584i \(-0.210676\pi\)
\(858\) 0 0
\(859\) 10.5359 + 18.2487i 0.359480 + 0.622638i 0.987874 0.155257i \(-0.0496207\pi\)
−0.628394 + 0.777895i \(0.716287\pi\)
\(860\) 0 0
\(861\) 1.33013 + 1.96410i 0.0453306 + 0.0669364i
\(862\) 0 0
\(863\) 33.3827 + 8.94486i 1.13636 + 0.304487i 0.777487 0.628900i \(-0.216494\pi\)
0.358873 + 0.933386i \(0.383161\pi\)
\(864\) 0 0
\(865\) 39.2487 34.8038i 1.33450 1.18337i
\(866\) 0 0
\(867\) 21.7583 21.7583i 0.738952 0.738952i
\(868\) 0 0
\(869\) 4.92820i 0.167178i
\(870\) 0 0
\(871\) 2.87564 + 1.66025i 0.0974375 + 0.0562556i
\(872\) 0 0
\(873\) 2.12436 7.92820i 0.0718985 0.268329i
\(874\) 0 0
\(875\) 4.52628 + 29.2321i 0.153016 + 0.988224i
\(876\) 0 0
\(877\) 4.15064 15.4904i 0.140157 0.523073i −0.859766 0.510688i \(-0.829391\pi\)
0.999923 0.0123853i \(-0.00394248\pi\)
\(878\) 0 0
\(879\) 43.5167 + 25.1244i 1.46778 + 0.847423i
\(880\) 0 0
\(881\) 52.8564i 1.78078i 0.455201 + 0.890389i \(0.349567\pi\)
−0.455201 + 0.890389i \(0.650433\pi\)
\(882\) 0 0
\(883\) −21.9282 + 21.9282i −0.737943 + 0.737943i −0.972180 0.234237i \(-0.924741\pi\)
0.234237 + 0.972180i \(0.424741\pi\)
\(884\) 0 0
\(885\) −7.09808 + 6.29423i −0.238599 + 0.211578i
\(886\) 0 0
\(887\) 36.9186 + 9.89230i 1.23960 + 0.332151i 0.818312 0.574774i \(-0.194910\pi\)
0.421292 + 0.906925i \(0.361577\pi\)
\(888\) 0 0
\(889\) 21.7583 + 10.5622i 0.729751 + 0.354244i
\(890\) 0 0
\(891\) 3.90192 + 6.75833i 0.130719 + 0.226413i
\(892\) 0 0
\(893\) −0.464102 1.73205i −0.0155306 0.0579609i
\(894\) 0 0
\(895\) −19.8564 39.7128i −0.663726 1.32745i
\(896\) 0 0
\(897\) 27.8564 + 27.8564i 0.930098 + 0.930098i
\(898\) 0 0
\(899\) −0.803848 + 1.39230i −0.0268098 + 0.0464360i
\(900\) 0 0
\(901\) 6.33975 3.66025i 0.211208 0.121941i
\(902\) 0 0
\(903\) 7.96410 41.3827i 0.265029 1.37713i
\(904\) 0 0
\(905\) −11.3301 + 17.1603i −0.376626 + 0.570426i
\(906\) 0 0
\(907\) −1.69615 + 0.454483i −0.0563198 + 0.0150908i −0.286869 0.957970i \(-0.592614\pi\)
0.230549 + 0.973061i \(0.425948\pi\)
\(908\) 0 0
\(909\) −8.58846 −0.284861
\(910\) 0 0
\(911\) −37.5167 −1.24298 −0.621491 0.783421i \(-0.713473\pi\)
−0.621491 + 0.783421i \(0.713473\pi\)
\(912\) 0 0
\(913\) −3.09808 + 0.830127i −0.102531 + 0.0274732i
\(914\) 0 0
\(915\) −35.8205 + 7.33013i −1.18419 + 0.242327i
\(916\) 0 0
\(917\) −14.7846 + 17.0718i −0.488231 + 0.563760i
\(918\) 0 0
\(919\) −39.6673 + 22.9019i −1.30850 + 0.755465i −0.981846 0.189678i \(-0.939256\pi\)
−0.326657 + 0.945143i \(0.605922\pi\)
\(920\) 0 0
\(921\) 12.6962 21.9904i 0.418352 0.724608i
\(922\) 0 0
\(923\) 9.46410 + 9.46410i 0.311515 + 0.311515i
\(924\) 0 0
\(925\) −24.2487 + 3.46410i −0.797293 + 0.113899i
\(926\) 0 0
\(927\) −0.437822 1.63397i −0.0143800 0.0536668i
\(928\) 0 0
\(929\) −0.839746 1.45448i −0.0275512 0.0477200i 0.851921 0.523670i \(-0.175438\pi\)
−0.879472 + 0.475950i \(0.842104\pi\)
\(930\) 0 0
\(931\) 17.7583 + 7.09808i 0.582006 + 0.232630i
\(932\) 0 0
\(933\) −34.9545 9.36603i −1.14436 0.306630i
\(934\) 0 0
\(935\) 1.12436 + 1.26795i 0.0367704 + 0.0414664i
\(936\) 0 0
\(937\) 30.9282 30.9282i 1.01038 1.01038i 0.0104348 0.999946i \(-0.496678\pi\)
0.999946 0.0104348i \(-0.00332156\pi\)
\(938\) 0 0
\(939\) 38.7846i 1.26569i
\(940\) 0 0
\(941\) 24.8038 + 14.3205i 0.808582 + 0.466835i 0.846463 0.532447i \(-0.178727\pi\)
−0.0378810 + 0.999282i \(0.512061\pi\)
\(942\) 0 0
\(943\) 0.866025 3.23205i 0.0282017 0.105250i
\(944\) 0 0
\(945\) −22.2942 + 13.2224i −0.725231 + 0.430126i
\(946\) 0 0
\(947\) 11.6962 43.6506i 0.380074 1.41846i −0.465714 0.884935i \(-0.654202\pi\)
0.845788 0.533520i \(-0.179131\pi\)
\(948\) 0 0
\(949\) −8.78461 5.07180i −0.285160 0.164637i
\(950\) 0 0
\(951\) 8.92820i 0.289517i
\(952\) 0 0
\(953\) −10.1436 + 10.1436i −0.328583 + 0.328583i −0.852048 0.523464i \(-0.824639\pi\)
0.523464 + 0.852048i \(0.324639\pi\)
\(954\) 0 0
\(955\) −2.24167 + 37.3468i −0.0725387 + 1.20851i
\(956\) 0 0
\(957\) −4.09808 1.09808i −0.132472 0.0354958i
\(958\) 0 0
\(959\) −23.7321 + 16.0718i −0.766348 + 0.518985i
\(960\) 0 0
\(961\) −15.3564 26.5981i −0.495368 0.858002i
\(962\) 0 0
\(963\) 1.68653 + 6.29423i 0.0543478 + 0.202829i
\(964\) 0 0
\(965\) −2.26795 + 6.80385i −0.0730079 + 0.219024i
\(966\) 0 0
\(967\) 1.43782 + 1.43782i 0.0462372 + 0.0462372i 0.729847 0.683610i \(-0.239591\pi\)
−0.683610 + 0.729847i \(0.739591\pi\)
\(968\) 0 0
\(969\) −2.73205 + 4.73205i −0.0877661 + 0.152015i
\(970\) 0 0
\(971\) −42.9282 + 24.7846i −1.37763 + 0.795376i −0.991874 0.127224i \(-0.959393\pi\)
−0.385758 + 0.922600i \(0.626060\pi\)
\(972\) 0 0
\(973\) −29.1506 + 10.0981i −0.934526 + 0.323729i
\(974\) 0 0
\(975\) 3.26795 27.1244i 0.104658 0.868675i
\(976\) 0 0
\(977\) 43.1506 11.5622i 1.38051 0.369907i 0.509204 0.860646i \(-0.329940\pi\)
0.871307 + 0.490739i \(0.163273\pi\)
\(978\) 0 0
\(979\) 12.1962 0.389791
\(980\) 0 0
\(981\) −10.3397 −0.330123
\(982\) 0 0
\(983\) −14.5000 + 3.88526i −0.462478 + 0.123921i −0.482532 0.875878i \(-0.660283\pi\)
0.0200540 + 0.999799i \(0.493616\pi\)
\(984\) 0 0
\(985\) 8.95448 + 43.7583i 0.285314 + 1.39426i
\(986\) 0 0
\(987\) −3.16987 + 1.09808i −0.100898 + 0.0349522i
\(988\) 0 0
\(989\) −51.4808 + 29.7224i −1.63699 + 0.945118i
\(990\) 0 0
\(991\) −11.8564 + 20.5359i −0.376631 + 0.652344i −0.990570 0.137009i \(-0.956251\pi\)
0.613939 + 0.789354i \(0.289584\pi\)
\(992\) 0 0
\(993\) 35.3205 + 35.3205i 1.12086 + 1.12086i
\(994\) 0 0
\(995\) 49.8564 24.9282i 1.58055 0.790277i
\(996\) 0 0
\(997\) 6.88269 + 25.6865i 0.217977 + 0.813501i 0.985097 + 0.171998i \(0.0550222\pi\)
−0.767121 + 0.641503i \(0.778311\pi\)
\(998\) 0 0
\(999\) −10.7321 18.5885i −0.339547 0.588113i
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 560.2.ci.b.17.1 4
4.3 odd 2 35.2.k.b.17.1 yes 4
5.3 odd 4 560.2.ci.a.353.1 4
7.5 odd 6 560.2.ci.a.257.1 4
12.11 even 2 315.2.bz.a.262.1 4
20.3 even 4 35.2.k.a.3.1 4
20.7 even 4 175.2.o.b.143.1 4
20.19 odd 2 175.2.o.a.157.1 4
28.3 even 6 245.2.f.a.97.2 4
28.11 odd 6 245.2.f.b.97.2 4
28.19 even 6 35.2.k.a.12.1 yes 4
28.23 odd 6 245.2.l.a.117.1 4
28.27 even 2 245.2.l.b.227.1 4
35.33 even 12 inner 560.2.ci.b.33.1 4
60.23 odd 4 315.2.bz.b.73.1 4
84.47 odd 6 315.2.bz.b.82.1 4
140.3 odd 12 245.2.f.b.48.2 4
140.19 even 6 175.2.o.b.82.1 4
140.23 even 12 245.2.l.b.68.1 4
140.47 odd 12 175.2.o.a.68.1 4
140.83 odd 4 245.2.l.a.178.1 4
140.103 odd 12 35.2.k.b.33.1 yes 4
140.123 even 12 245.2.f.a.48.2 4
420.383 even 12 315.2.bz.a.208.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.2.k.a.3.1 4 20.3 even 4
35.2.k.a.12.1 yes 4 28.19 even 6
35.2.k.b.17.1 yes 4 4.3 odd 2
35.2.k.b.33.1 yes 4 140.103 odd 12
175.2.o.a.68.1 4 140.47 odd 12
175.2.o.a.157.1 4 20.19 odd 2
175.2.o.b.82.1 4 140.19 even 6
175.2.o.b.143.1 4 20.7 even 4
245.2.f.a.48.2 4 140.123 even 12
245.2.f.a.97.2 4 28.3 even 6
245.2.f.b.48.2 4 140.3 odd 12
245.2.f.b.97.2 4 28.11 odd 6
245.2.l.a.117.1 4 28.23 odd 6
245.2.l.a.178.1 4 140.83 odd 4
245.2.l.b.68.1 4 140.23 even 12
245.2.l.b.227.1 4 28.27 even 2
315.2.bz.a.208.1 4 420.383 even 12
315.2.bz.a.262.1 4 12.11 even 2
315.2.bz.b.73.1 4 60.23 odd 4
315.2.bz.b.82.1 4 84.47 odd 6
560.2.ci.a.257.1 4 7.5 odd 6
560.2.ci.a.353.1 4 5.3 odd 4
560.2.ci.b.17.1 4 1.1 even 1 trivial
560.2.ci.b.33.1 4 35.33 even 12 inner