Properties

Label 448.2.i.a.193.1
Level $448$
Weight $2$
Character 448.193
Analytic conductor $3.577$
Analytic rank $1$
Dimension $2$
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] = [448,2,Mod(65,448)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(448, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("448.65");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 448.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.57729801055\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 448.193
Dual form 448.2.i.a.65.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(q+(-1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(-3.00000 - 5.19615i) q^{9} +(0.500000 - 0.866025i) q^{11} -2.00000 q^{13} +3.00000 q^{15} +(-1.50000 + 2.59808i) q^{17} +(-2.50000 - 4.33013i) q^{19} +(-1.50000 - 7.79423i) q^{21} +(-1.50000 - 2.59808i) q^{23} +(2.00000 - 3.46410i) q^{25} +9.00000 q^{27} +6.00000 q^{29} +(-0.500000 + 0.866025i) q^{31} +(1.50000 + 2.59808i) q^{33} +(2.50000 + 0.866025i) q^{35} +(-2.50000 - 4.33013i) q^{37} +(3.00000 - 5.19615i) q^{39} -10.0000 q^{41} -4.00000 q^{43} +(-3.00000 + 5.19615i) q^{45} +(0.500000 + 0.866025i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-4.50000 - 7.79423i) q^{51} +(-4.50000 + 7.79423i) q^{53} -1.00000 q^{55} +15.0000 q^{57} +(-1.50000 + 2.59808i) q^{59} +(1.50000 + 2.59808i) q^{61} +(15.0000 + 5.19615i) q^{63} +(1.00000 + 1.73205i) q^{65} +(-5.50000 + 9.52628i) q^{67} +9.00000 q^{69} -16.0000 q^{71} +(-3.50000 + 6.06218i) q^{73} +(6.00000 + 10.3923i) q^{75} +(0.500000 + 2.59808i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(-4.50000 + 7.79423i) q^{81} -4.00000 q^{83} +3.00000 q^{85} +(-9.00000 + 15.5885i) q^{87} +(4.50000 + 7.79423i) q^{89} +(4.00000 - 3.46410i) q^{91} +(-1.50000 - 2.59808i) q^{93} +(-2.50000 + 4.33013i) q^{95} +6.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{3} - q^{5} - 4 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{3} - q^{5} - 4 q^{7} - 6 q^{9} + q^{11} - 4 q^{13} + 6 q^{15} - 3 q^{17} - 5 q^{19} - 3 q^{21} - 3 q^{23} + 4 q^{25} + 18 q^{27} + 12 q^{29} - q^{31} + 3 q^{33} + 5 q^{35} - 5 q^{37} + 6 q^{39} - 20 q^{41} - 8 q^{43} - 6 q^{45} + q^{47} + 2 q^{49} - 9 q^{51} - 9 q^{53} - 2 q^{55} + 30 q^{57} - 3 q^{59} + 3 q^{61} + 30 q^{63} + 2 q^{65} - 11 q^{67} + 18 q^{69} - 32 q^{71} - 7 q^{73} + 12 q^{75} + q^{77} - 11 q^{79} - 9 q^{81} - 8 q^{83} + 6 q^{85} - 18 q^{87} + 9 q^{89} + 8 q^{91} - 3 q^{93} - 5 q^{95} + 12 q^{97} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.50000 + 2.59808i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i 0.732294 0.680989i \(-0.238450\pi\)
−0.955901 + 0.293691i \(0.905116\pi\)
\(6\) 0 0
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) 0 0
\(9\) −3.00000 5.19615i −1.00000 1.73205i
\(10\) 0 0
\(11\) 0.500000 0.866025i 0.150756 0.261116i −0.780750 0.624844i \(-0.785163\pi\)
0.931505 + 0.363727i \(0.118496\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 3.00000 0.774597
\(16\) 0 0
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 0 0
\(19\) −2.50000 4.33013i −0.573539 0.993399i −0.996199 0.0871106i \(-0.972237\pi\)
0.422659 0.906289i \(-0.361097\pi\)
\(20\) 0 0
\(21\) −1.50000 7.79423i −0.327327 1.70084i
\(22\) 0 0
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 0 0
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) 0 0
\(27\) 9.00000 1.73205
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −0.500000 + 0.866025i −0.0898027 + 0.155543i −0.907428 0.420208i \(-0.861957\pi\)
0.817625 + 0.575751i \(0.195290\pi\)
\(32\) 0 0
\(33\) 1.50000 + 2.59808i 0.261116 + 0.452267i
\(34\) 0 0
\(35\) 2.50000 + 0.866025i 0.422577 + 0.146385i
\(36\) 0 0
\(37\) −2.50000 4.33013i −0.410997 0.711868i 0.584002 0.811752i \(-0.301486\pi\)
−0.994999 + 0.0998840i \(0.968153\pi\)
\(38\) 0 0
\(39\) 3.00000 5.19615i 0.480384 0.832050i
\(40\) 0 0
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) −3.00000 + 5.19615i −0.447214 + 0.774597i
\(46\) 0 0
\(47\) 0.500000 + 0.866025i 0.0729325 + 0.126323i 0.900185 0.435507i \(-0.143431\pi\)
−0.827253 + 0.561830i \(0.810098\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) −4.50000 7.79423i −0.630126 1.09141i
\(52\) 0 0
\(53\) −4.50000 + 7.79423i −0.618123 + 1.07062i 0.371706 + 0.928351i \(0.378773\pi\)
−0.989828 + 0.142269i \(0.954560\pi\)
\(54\) 0 0
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) 15.0000 1.98680
\(58\) 0 0
\(59\) −1.50000 + 2.59808i −0.195283 + 0.338241i −0.946993 0.321253i \(-0.895896\pi\)
0.751710 + 0.659494i \(0.229229\pi\)
\(60\) 0 0
\(61\) 1.50000 + 2.59808i 0.192055 + 0.332650i 0.945931 0.324367i \(-0.105151\pi\)
−0.753876 + 0.657017i \(0.771818\pi\)
\(62\) 0 0
\(63\) 15.0000 + 5.19615i 1.88982 + 0.654654i
\(64\) 0 0
\(65\) 1.00000 + 1.73205i 0.124035 + 0.214834i
\(66\) 0 0
\(67\) −5.50000 + 9.52628i −0.671932 + 1.16382i 0.305424 + 0.952217i \(0.401202\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) 0 0
\(69\) 9.00000 1.08347
\(70\) 0 0
\(71\) −16.0000 −1.89885 −0.949425 0.313993i \(-0.898333\pi\)
−0.949425 + 0.313993i \(0.898333\pi\)
\(72\) 0 0
\(73\) −3.50000 + 6.06218i −0.409644 + 0.709524i −0.994850 0.101361i \(-0.967680\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 0 0
\(75\) 6.00000 + 10.3923i 0.692820 + 1.20000i
\(76\) 0 0
\(77\) 0.500000 + 2.59808i 0.0569803 + 0.296078i
\(78\) 0 0
\(79\) −5.50000 9.52628i −0.618798 1.07179i −0.989705 0.143120i \(-0.954286\pi\)
0.370907 0.928670i \(-0.379047\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) 3.00000 0.325396
\(86\) 0 0
\(87\) −9.00000 + 15.5885i −0.964901 + 1.67126i
\(88\) 0 0
\(89\) 4.50000 + 7.79423i 0.476999 + 0.826187i 0.999653 0.0263586i \(-0.00839118\pi\)
−0.522654 + 0.852545i \(0.675058\pi\)
\(90\) 0 0
\(91\) 4.00000 3.46410i 0.419314 0.363137i
\(92\) 0 0
\(93\) −1.50000 2.59808i −0.155543 0.269408i
\(94\) 0 0
\(95\) −2.50000 + 4.33013i −0.256495 + 0.444262i
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) −6.00000 −0.603023
\(100\) 0 0
\(101\) −6.50000 + 11.2583i −0.646774 + 1.12025i 0.337115 + 0.941464i \(0.390549\pi\)
−0.983889 + 0.178782i \(0.942784\pi\)
\(102\) 0 0
\(103\) 2.50000 + 4.33013i 0.246332 + 0.426660i 0.962505 0.271263i \(-0.0874412\pi\)
−0.716173 + 0.697923i \(0.754108\pi\)
\(104\) 0 0
\(105\) −6.00000 + 5.19615i −0.585540 + 0.507093i
\(106\) 0 0
\(107\) 1.50000 + 2.59808i 0.145010 + 0.251166i 0.929377 0.369132i \(-0.120345\pi\)
−0.784366 + 0.620298i \(0.787012\pi\)
\(108\) 0 0
\(109\) 5.50000 9.52628i 0.526804 0.912452i −0.472708 0.881219i \(-0.656723\pi\)
0.999512 0.0312328i \(-0.00994332\pi\)
\(110\) 0 0
\(111\) 15.0000 1.42374
\(112\) 0 0
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) −1.50000 + 2.59808i −0.139876 + 0.242272i
\(116\) 0 0
\(117\) 6.00000 + 10.3923i 0.554700 + 0.960769i
\(118\) 0 0
\(119\) −1.50000 7.79423i −0.137505 0.714496i
\(120\) 0 0
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 0 0
\(123\) 15.0000 25.9808i 1.35250 2.34261i
\(124\) 0 0
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) 6.00000 10.3923i 0.528271 0.914991i
\(130\) 0 0
\(131\) −8.50000 14.7224i −0.742648 1.28630i −0.951285 0.308312i \(-0.900236\pi\)
0.208637 0.977993i \(-0.433097\pi\)
\(132\) 0 0
\(133\) 12.5000 + 4.33013i 1.08389 + 0.375470i
\(134\) 0 0
\(135\) −4.50000 7.79423i −0.387298 0.670820i
\(136\) 0 0
\(137\) −1.50000 + 2.59808i −0.128154 + 0.221969i −0.922961 0.384893i \(-0.874238\pi\)
0.794808 + 0.606861i \(0.207572\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) 0 0
\(143\) −1.00000 + 1.73205i −0.0836242 + 0.144841i
\(144\) 0 0
\(145\) −3.00000 5.19615i −0.249136 0.431517i
\(146\) 0 0
\(147\) 16.5000 + 12.9904i 1.36090 + 1.07143i
\(148\) 0 0
\(149\) 7.50000 + 12.9904i 0.614424 + 1.06421i 0.990485 + 0.137619i \(0.0439449\pi\)
−0.376061 + 0.926595i \(0.622722\pi\)
\(150\) 0 0
\(151\) 7.50000 12.9904i 0.610341 1.05714i −0.380841 0.924640i \(-0.624366\pi\)
0.991183 0.132502i \(-0.0423010\pi\)
\(152\) 0 0
\(153\) 18.0000 1.45521
\(154\) 0 0
\(155\) 1.00000 0.0803219
\(156\) 0 0
\(157\) 7.50000 12.9904i 0.598565 1.03675i −0.394468 0.918910i \(-0.629071\pi\)
0.993033 0.117836i \(-0.0375956\pi\)
\(158\) 0 0
\(159\) −13.5000 23.3827i −1.07062 1.85437i
\(160\) 0 0
\(161\) 7.50000 + 2.59808i 0.591083 + 0.204757i
\(162\) 0 0
\(163\) −4.50000 7.79423i −0.352467 0.610491i 0.634214 0.773158i \(-0.281324\pi\)
−0.986681 + 0.162667i \(0.947991\pi\)
\(164\) 0 0
\(165\) 1.50000 2.59808i 0.116775 0.202260i
\(166\) 0 0
\(167\) 20.0000 1.54765 0.773823 0.633402i \(-0.218342\pi\)
0.773823 + 0.633402i \(0.218342\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −15.0000 + 25.9808i −1.14708 + 1.98680i
\(172\) 0 0
\(173\) −10.5000 18.1865i −0.798300 1.38270i −0.920722 0.390218i \(-0.872399\pi\)
0.122422 0.992478i \(-0.460934\pi\)
\(174\) 0 0
\(175\) 2.00000 + 10.3923i 0.151186 + 0.785584i
\(176\) 0 0
\(177\) −4.50000 7.79423i −0.338241 0.585850i
\(178\) 0 0
\(179\) 0.500000 0.866025i 0.0373718 0.0647298i −0.846735 0.532016i \(-0.821435\pi\)
0.884106 + 0.467286i \(0.154768\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) −9.00000 −0.665299
\(184\) 0 0
\(185\) −2.50000 + 4.33013i −0.183804 + 0.318357i
\(186\) 0 0
\(187\) 1.50000 + 2.59808i 0.109691 + 0.189990i
\(188\) 0 0
\(189\) −18.0000 + 15.5885i −1.30931 + 1.13389i
\(190\) 0 0
\(191\) 8.50000 + 14.7224i 0.615038 + 1.06528i 0.990378 + 0.138390i \(0.0441928\pi\)
−0.375339 + 0.926887i \(0.622474\pi\)
\(192\) 0 0
\(193\) 2.50000 4.33013i 0.179954 0.311689i −0.761911 0.647682i \(-0.775738\pi\)
0.941865 + 0.335993i \(0.109072\pi\)
\(194\) 0 0
\(195\) −6.00000 −0.429669
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −4.50000 + 7.79423i −0.318997 + 0.552518i −0.980279 0.197619i \(-0.936679\pi\)
0.661282 + 0.750137i \(0.270013\pi\)
\(200\) 0 0
\(201\) −16.5000 28.5788i −1.16382 2.01580i
\(202\) 0 0
\(203\) −12.0000 + 10.3923i −0.842235 + 0.729397i
\(204\) 0 0
\(205\) 5.00000 + 8.66025i 0.349215 + 0.604858i
\(206\) 0 0
\(207\) −9.00000 + 15.5885i −0.625543 + 1.08347i
\(208\) 0 0
\(209\) −5.00000 −0.345857
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 0 0
\(213\) 24.0000 41.5692i 1.64445 2.84828i
\(214\) 0 0
\(215\) 2.00000 + 3.46410i 0.136399 + 0.236250i
\(216\) 0 0
\(217\) −0.500000 2.59808i −0.0339422 0.176369i
\(218\) 0 0
\(219\) −10.5000 18.1865i −0.709524 1.22893i
\(220\) 0 0
\(221\) 3.00000 5.19615i 0.201802 0.349531i
\(222\) 0 0
\(223\) −24.0000 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) −24.0000 −1.60000
\(226\) 0 0
\(227\) −3.50000 + 6.06218i −0.232303 + 0.402361i −0.958485 0.285141i \(-0.907959\pi\)
0.726182 + 0.687502i \(0.241293\pi\)
\(228\) 0 0
\(229\) 3.50000 + 6.06218i 0.231287 + 0.400600i 0.958187 0.286143i \(-0.0923732\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) −7.50000 2.59808i −0.493464 0.170941i
\(232\) 0 0
\(233\) 6.50000 + 11.2583i 0.425829 + 0.737558i 0.996497 0.0836229i \(-0.0266491\pi\)
−0.570668 + 0.821181i \(0.693316\pi\)
\(234\) 0 0
\(235\) 0.500000 0.866025i 0.0326164 0.0564933i
\(236\) 0 0
\(237\) 33.0000 2.14358
\(238\) 0 0
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 0 0
\(241\) 8.50000 14.7224i 0.547533 0.948355i −0.450910 0.892570i \(-0.648900\pi\)
0.998443 0.0557856i \(-0.0177663\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −6.50000 + 2.59808i −0.415270 + 0.165985i
\(246\) 0 0
\(247\) 5.00000 + 8.66025i 0.318142 + 0.551039i
\(248\) 0 0
\(249\) 6.00000 10.3923i 0.380235 0.658586i
\(250\) 0 0
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) −3.00000 −0.188608
\(254\) 0 0
\(255\) −4.50000 + 7.79423i −0.281801 + 0.488094i
\(256\) 0 0
\(257\) 6.50000 + 11.2583i 0.405459 + 0.702275i 0.994375 0.105919i \(-0.0337784\pi\)
−0.588916 + 0.808194i \(0.700445\pi\)
\(258\) 0 0
\(259\) 12.5000 + 4.33013i 0.776712 + 0.269061i
\(260\) 0 0
\(261\) −18.0000 31.1769i −1.11417 1.92980i
\(262\) 0 0
\(263\) 1.50000 2.59808i 0.0924940 0.160204i −0.816066 0.577959i \(-0.803849\pi\)
0.908560 + 0.417755i \(0.137183\pi\)
\(264\) 0 0
\(265\) 9.00000 0.552866
\(266\) 0 0
\(267\) −27.0000 −1.65237
\(268\) 0 0
\(269\) −8.50000 + 14.7224i −0.518254 + 0.897643i 0.481521 + 0.876435i \(0.340085\pi\)
−0.999775 + 0.0212079i \(0.993249\pi\)
\(270\) 0 0
\(271\) −1.50000 2.59808i −0.0911185 0.157822i 0.816864 0.576831i \(-0.195711\pi\)
−0.907982 + 0.419009i \(0.862378\pi\)
\(272\) 0 0
\(273\) 3.00000 + 15.5885i 0.181568 + 0.943456i
\(274\) 0 0
\(275\) −2.00000 3.46410i −0.120605 0.208893i
\(276\) 0 0
\(277\) 3.50000 6.06218i 0.210295 0.364241i −0.741512 0.670940i \(-0.765891\pi\)
0.951807 + 0.306699i \(0.0992243\pi\)
\(278\) 0 0
\(279\) 6.00000 0.359211
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) 8.50000 14.7224i 0.505273 0.875158i −0.494709 0.869059i \(-0.664725\pi\)
0.999981 0.00609896i \(-0.00194137\pi\)
\(284\) 0 0
\(285\) −7.50000 12.9904i −0.444262 0.769484i
\(286\) 0 0
\(287\) 20.0000 17.3205i 1.18056 1.02240i
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) −9.00000 + 15.5885i −0.527589 + 0.913812i
\(292\) 0 0
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 0 0
\(295\) 3.00000 0.174667
\(296\) 0 0
\(297\) 4.50000 7.79423i 0.261116 0.452267i
\(298\) 0 0
\(299\) 3.00000 + 5.19615i 0.173494 + 0.300501i
\(300\) 0 0
\(301\) 8.00000 6.92820i 0.461112 0.399335i
\(302\) 0 0
\(303\) −19.5000 33.7750i −1.12025 1.94032i
\(304\) 0 0
\(305\) 1.50000 2.59808i 0.0858898 0.148765i
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) −15.0000 −0.853320
\(310\) 0 0
\(311\) 5.50000 9.52628i 0.311876 0.540186i −0.666892 0.745154i \(-0.732376\pi\)
0.978769 + 0.204968i \(0.0657092\pi\)
\(312\) 0 0
\(313\) −15.5000 26.8468i −0.876112 1.51747i −0.855574 0.517681i \(-0.826795\pi\)
−0.0205381 0.999789i \(-0.506538\pi\)
\(314\) 0 0
\(315\) −3.00000 15.5885i −0.169031 0.878310i
\(316\) 0 0
\(317\) 13.5000 + 23.3827i 0.758236 + 1.31330i 0.943750 + 0.330661i \(0.107272\pi\)
−0.185514 + 0.982642i \(0.559395\pi\)
\(318\) 0 0
\(319\) 3.00000 5.19615i 0.167968 0.290929i
\(320\) 0 0
\(321\) −9.00000 −0.502331
\(322\) 0 0
\(323\) 15.0000 0.834622
\(324\) 0 0
\(325\) −4.00000 + 6.92820i −0.221880 + 0.384308i
\(326\) 0 0
\(327\) 16.5000 + 28.5788i 0.912452 + 1.58041i
\(328\) 0 0
\(329\) −2.50000 0.866025i −0.137829 0.0477455i
\(330\) 0 0
\(331\) 3.50000 + 6.06218i 0.192377 + 0.333207i 0.946038 0.324057i \(-0.105047\pi\)
−0.753660 + 0.657264i \(0.771714\pi\)
\(332\) 0 0
\(333\) −15.0000 + 25.9808i −0.821995 + 1.42374i
\(334\) 0 0
\(335\) 11.0000 0.600994
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) 15.0000 25.9808i 0.814688 1.41108i
\(340\) 0 0
\(341\) 0.500000 + 0.866025i 0.0270765 + 0.0468979i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 0 0
\(345\) −4.50000 7.79423i −0.242272 0.419627i
\(346\) 0 0
\(347\) −1.50000 + 2.59808i −0.0805242 + 0.139472i −0.903475 0.428640i \(-0.858993\pi\)
0.822951 + 0.568112i \(0.192326\pi\)
\(348\) 0 0
\(349\) 6.00000 0.321173 0.160586 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(350\) 0 0
\(351\) −18.0000 −0.960769
\(352\) 0 0
\(353\) 2.50000 4.33013i 0.133062 0.230469i −0.791794 0.610789i \(-0.790853\pi\)
0.924855 + 0.380319i \(0.124186\pi\)
\(354\) 0 0
\(355\) 8.00000 + 13.8564i 0.424596 + 0.735422i
\(356\) 0 0
\(357\) 22.5000 + 7.79423i 1.19083 + 0.412514i
\(358\) 0 0
\(359\) −7.50000 12.9904i −0.395835 0.685606i 0.597372 0.801964i \(-0.296211\pi\)
−0.993207 + 0.116358i \(0.962878\pi\)
\(360\) 0 0
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) 0 0
\(363\) −30.0000 −1.57459
\(364\) 0 0
\(365\) 7.00000 0.366397
\(366\) 0 0
\(367\) 9.50000 16.4545i 0.495896 0.858917i −0.504093 0.863649i \(-0.668173\pi\)
0.999989 + 0.00473247i \(0.00150640\pi\)
\(368\) 0 0
\(369\) 30.0000 + 51.9615i 1.56174 + 2.70501i
\(370\) 0 0
\(371\) −4.50000 23.3827i −0.233628 1.21397i
\(372\) 0 0
\(373\) 9.50000 + 16.4545i 0.491891 + 0.851981i 0.999956 0.00933789i \(-0.00297238\pi\)
−0.508065 + 0.861319i \(0.669639\pi\)
\(374\) 0 0
\(375\) 13.5000 23.3827i 0.697137 1.20748i
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) −12.0000 + 20.7846i −0.614779 + 1.06483i
\(382\) 0 0
\(383\) 4.50000 + 7.79423i 0.229939 + 0.398266i 0.957790 0.287469i \(-0.0928139\pi\)
−0.727851 + 0.685736i \(0.759481\pi\)
\(384\) 0 0
\(385\) 2.00000 1.73205i 0.101929 0.0882735i
\(386\) 0 0
\(387\) 12.0000 + 20.7846i 0.609994 + 1.05654i
\(388\) 0 0
\(389\) 9.50000 16.4545i 0.481669 0.834275i −0.518110 0.855314i \(-0.673364\pi\)
0.999779 + 0.0210389i \(0.00669738\pi\)
\(390\) 0 0
\(391\) 9.00000 0.455150
\(392\) 0 0
\(393\) 51.0000 2.57261
\(394\) 0 0
\(395\) −5.50000 + 9.52628i −0.276735 + 0.479319i
\(396\) 0 0
\(397\) −8.50000 14.7224i −0.426603 0.738898i 0.569966 0.821668i \(-0.306956\pi\)
−0.996569 + 0.0827707i \(0.973623\pi\)
\(398\) 0 0
\(399\) −30.0000 + 25.9808i −1.50188 + 1.30066i
\(400\) 0 0
\(401\) −1.50000 2.59808i −0.0749064 0.129742i 0.826139 0.563466i \(-0.190532\pi\)
−0.901046 + 0.433724i \(0.857199\pi\)
\(402\) 0 0
\(403\) 1.00000 1.73205i 0.0498135 0.0862796i
\(404\) 0 0
\(405\) 9.00000 0.447214
\(406\) 0 0
\(407\) −5.00000 −0.247841
\(408\) 0 0
\(409\) −9.50000 + 16.4545i −0.469745 + 0.813622i −0.999402 0.0345902i \(-0.988987\pi\)
0.529657 + 0.848212i \(0.322321\pi\)
\(410\) 0 0
\(411\) −4.50000 7.79423i −0.221969 0.384461i
\(412\) 0 0
\(413\) −1.50000 7.79423i −0.0738102 0.383529i
\(414\) 0 0
\(415\) 2.00000 + 3.46410i 0.0981761 + 0.170046i
\(416\) 0 0
\(417\) −6.00000 + 10.3923i −0.293821 + 0.508913i
\(418\) 0 0
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 0 0
\(423\) 3.00000 5.19615i 0.145865 0.252646i
\(424\) 0 0
\(425\) 6.00000 + 10.3923i 0.291043 + 0.504101i
\(426\) 0 0
\(427\) −7.50000 2.59808i −0.362950 0.125730i
\(428\) 0 0
\(429\) −3.00000 5.19615i −0.144841 0.250873i
\(430\) 0 0
\(431\) −20.5000 + 35.5070i −0.987450 + 1.71031i −0.356953 + 0.934122i \(0.616185\pi\)
−0.630497 + 0.776192i \(0.717149\pi\)
\(432\) 0 0
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 0 0
\(435\) 18.0000 0.863034
\(436\) 0 0
\(437\) −7.50000 + 12.9904i −0.358774 + 0.621414i
\(438\) 0 0
\(439\) −7.50000 12.9904i −0.357955 0.619997i 0.629664 0.776868i \(-0.283193\pi\)
−0.987619 + 0.156871i \(0.949859\pi\)
\(440\) 0 0
\(441\) −39.0000 + 15.5885i −1.85714 + 0.742307i
\(442\) 0 0
\(443\) 13.5000 + 23.3827i 0.641404 + 1.11094i 0.985119 + 0.171871i \(0.0549812\pi\)
−0.343715 + 0.939074i \(0.611685\pi\)
\(444\) 0 0
\(445\) 4.50000 7.79423i 0.213320 0.369482i
\(446\) 0 0
\(447\) −45.0000 −2.12843
\(448\) 0 0
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 0 0
\(451\) −5.00000 + 8.66025i −0.235441 + 0.407795i
\(452\) 0 0
\(453\) 22.5000 + 38.9711i 1.05714 + 1.83102i
\(454\) 0 0
\(455\) −5.00000 1.73205i −0.234404 0.0811998i
\(456\) 0 0
\(457\) 8.50000 + 14.7224i 0.397613 + 0.688686i 0.993431 0.114433i \(-0.0365053\pi\)
−0.595818 + 0.803120i \(0.703172\pi\)
\(458\) 0 0
\(459\) −13.5000 + 23.3827i −0.630126 + 1.09141i
\(460\) 0 0
\(461\) 6.00000 0.279448 0.139724 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 0 0
\(465\) −1.50000 + 2.59808i −0.0695608 + 0.120483i
\(466\) 0 0
\(467\) −12.5000 21.6506i −0.578431 1.00187i −0.995660 0.0930703i \(-0.970332\pi\)
0.417229 0.908802i \(-0.363001\pi\)
\(468\) 0 0
\(469\) −5.50000 28.5788i −0.253966 1.31965i
\(470\) 0 0
\(471\) 22.5000 + 38.9711i 1.03675 + 1.79570i
\(472\) 0 0
\(473\) −2.00000 + 3.46410i −0.0919601 + 0.159280i
\(474\) 0 0
\(475\) −20.0000 −0.917663
\(476\) 0 0
\(477\) 54.0000 2.47249
\(478\) 0 0
\(479\) −10.5000 + 18.1865i −0.479757 + 0.830964i −0.999730 0.0232187i \(-0.992609\pi\)
0.519973 + 0.854183i \(0.325942\pi\)
\(480\) 0 0
\(481\) 5.00000 + 8.66025i 0.227980 + 0.394874i
\(482\) 0 0
\(483\) −18.0000 + 15.5885i −0.819028 + 0.709299i
\(484\) 0 0
\(485\) −3.00000 5.19615i −0.136223 0.235945i
\(486\) 0 0
\(487\) −6.50000 + 11.2583i −0.294543 + 0.510164i −0.974879 0.222737i \(-0.928501\pi\)
0.680335 + 0.732901i \(0.261834\pi\)
\(488\) 0 0
\(489\) 27.0000 1.22098
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) −9.00000 + 15.5885i −0.405340 + 0.702069i
\(494\) 0 0
\(495\) 3.00000 + 5.19615i 0.134840 + 0.233550i
\(496\) 0 0
\(497\) 32.0000 27.7128i 1.43540 1.24309i
\(498\) 0 0
\(499\) 3.50000 + 6.06218i 0.156682 + 0.271380i 0.933670 0.358134i \(-0.116587\pi\)
−0.776989 + 0.629515i \(0.783254\pi\)
\(500\) 0 0
\(501\) −30.0000 + 51.9615i −1.34030 + 2.32147i
\(502\) 0 0
\(503\) −16.0000 −0.713405 −0.356702 0.934218i \(-0.616099\pi\)
−0.356702 + 0.934218i \(0.616099\pi\)
\(504\) 0 0
\(505\) 13.0000 0.578492
\(506\) 0 0
\(507\) 13.5000 23.3827i 0.599556 1.03846i
\(508\) 0 0
\(509\) 3.50000 + 6.06218i 0.155135 + 0.268701i 0.933108 0.359596i \(-0.117085\pi\)
−0.777973 + 0.628297i \(0.783752\pi\)
\(510\) 0 0
\(511\) −3.50000 18.1865i −0.154831 0.804525i
\(512\) 0 0
\(513\) −22.5000 38.9711i −0.993399 1.72062i
\(514\) 0 0
\(515\) 2.50000 4.33013i 0.110163 0.190808i
\(516\) 0 0
\(517\) 1.00000 0.0439799
\(518\) 0 0
\(519\) 63.0000 2.76539
\(520\) 0 0
\(521\) −7.50000 + 12.9904i −0.328581 + 0.569119i −0.982231 0.187678i \(-0.939904\pi\)
0.653650 + 0.756797i \(0.273237\pi\)
\(522\) 0 0
\(523\) −6.50000 11.2583i −0.284225 0.492292i 0.688196 0.725525i \(-0.258403\pi\)
−0.972421 + 0.233233i \(0.925070\pi\)
\(524\) 0 0
\(525\) −30.0000 10.3923i −1.30931 0.453557i
\(526\) 0 0
\(527\) −1.50000 2.59808i −0.0653410 0.113174i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) 18.0000 0.781133
\(532\) 0 0
\(533\) 20.0000 0.866296
\(534\) 0 0
\(535\) 1.50000 2.59808i 0.0648507 0.112325i
\(536\) 0 0
\(537\) 1.50000 + 2.59808i 0.0647298 + 0.112115i
\(538\) 0 0
\(539\) −5.50000 4.33013i −0.236902 0.186512i
\(540\) 0 0
\(541\) −12.5000 21.6506i −0.537417 0.930834i −0.999042 0.0437584i \(-0.986067\pi\)
0.461625 0.887075i \(-0.347267\pi\)
\(542\) 0 0
\(543\) 33.0000 57.1577i 1.41617 2.45287i
\(544\) 0 0
\(545\) −11.0000 −0.471188
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) 9.00000 15.5885i 0.384111 0.665299i
\(550\) 0 0
\(551\) −15.0000 25.9808i −0.639021 1.10682i
\(552\) 0 0
\(553\) 27.5000 + 9.52628i 1.16942 + 0.405099i
\(554\) 0 0
\(555\) −7.50000 12.9904i −0.318357 0.551411i
\(556\) 0 0
\(557\) 5.50000 9.52628i 0.233042 0.403641i −0.725660 0.688054i \(-0.758465\pi\)
0.958702 + 0.284413i \(0.0917985\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) −9.00000 −0.379980
\(562\) 0 0
\(563\) −5.50000 + 9.52628i −0.231797 + 0.401485i −0.958337 0.285640i \(-0.907794\pi\)
0.726540 + 0.687124i \(0.241127\pi\)
\(564\) 0 0
\(565\) 5.00000 + 8.66025i 0.210352 + 0.364340i
\(566\) 0 0
\(567\) −4.50000 23.3827i −0.188982 0.981981i
\(568\) 0 0
\(569\) 0.500000 + 0.866025i 0.0209611 + 0.0363057i 0.876316 0.481737i \(-0.159994\pi\)
−0.855355 + 0.518043i \(0.826661\pi\)
\(570\) 0 0
\(571\) 8.50000 14.7224i 0.355714 0.616115i −0.631526 0.775355i \(-0.717571\pi\)
0.987240 + 0.159240i \(0.0509044\pi\)
\(572\) 0 0
\(573\) −51.0000 −2.13056
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) −15.5000 + 26.8468i −0.645273 + 1.11765i 0.338965 + 0.940799i \(0.389923\pi\)
−0.984238 + 0.176847i \(0.943410\pi\)
\(578\) 0 0
\(579\) 7.50000 + 12.9904i 0.311689 + 0.539862i
\(580\) 0 0
\(581\) 8.00000 6.92820i 0.331896 0.287430i
\(582\) 0 0
\(583\) 4.50000 + 7.79423i 0.186371 + 0.322804i
\(584\) 0 0
\(585\) 6.00000 10.3923i 0.248069 0.429669i
\(586\) 0 0
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) 5.00000 0.206021
\(590\) 0 0
\(591\) 27.0000 46.7654i 1.11063 1.92367i
\(592\) 0 0
\(593\) −21.5000 37.2391i −0.882899 1.52923i −0.848103 0.529832i \(-0.822255\pi\)
−0.0347964 0.999394i \(-0.511078\pi\)
\(594\) 0 0
\(595\) −6.00000 + 5.19615i −0.245976 + 0.213021i
\(596\) 0 0
\(597\) −13.5000 23.3827i −0.552518 0.956990i
\(598\) 0 0
\(599\) −10.5000 + 18.1865i −0.429018 + 0.743082i −0.996786 0.0801071i \(-0.974474\pi\)
0.567768 + 0.823189i \(0.307807\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) 0 0
\(603\) 66.0000 2.68773
\(604\) 0 0
\(605\) 5.00000 8.66025i 0.203279 0.352089i
\(606\) 0 0
\(607\) −3.50000 6.06218i −0.142061 0.246056i 0.786212 0.617957i \(-0.212039\pi\)
−0.928272 + 0.371901i \(0.878706\pi\)
\(608\) 0 0
\(609\) −9.00000 46.7654i −0.364698 1.89503i
\(610\) 0 0
\(611\) −1.00000 1.73205i −0.0404557 0.0700713i
\(612\) 0 0
\(613\) −10.5000 + 18.1865i −0.424091 + 0.734547i −0.996335 0.0855362i \(-0.972740\pi\)
0.572244 + 0.820083i \(0.306073\pi\)
\(614\) 0 0
\(615\) −30.0000 −1.20972
\(616\) 0 0
\(617\) 22.0000 0.885687 0.442843 0.896599i \(-0.353970\pi\)
0.442843 + 0.896599i \(0.353970\pi\)
\(618\) 0 0
\(619\) 2.50000 4.33013i 0.100483 0.174042i −0.811400 0.584491i \(-0.801294\pi\)
0.911884 + 0.410448i \(0.134628\pi\)
\(620\) 0 0
\(621\) −13.5000 23.3827i −0.541736 0.938315i
\(622\) 0 0
\(623\) −22.5000 7.79423i −0.901443 0.312269i
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 0 0
\(627\) 7.50000 12.9904i 0.299521 0.518786i
\(628\) 0 0
\(629\) 15.0000 0.598089
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) −18.0000 + 31.1769i −0.715436 + 1.23917i
\(634\) 0 0
\(635\) −4.00000 6.92820i −0.158735 0.274937i
\(636\) 0 0
\(637\) −2.00000 + 13.8564i −0.0792429 + 0.549011i
\(638\) 0 0
\(639\) 48.0000 + 83.1384i 1.89885 + 3.28891i
\(640\) 0 0
\(641\) −7.50000 + 12.9904i −0.296232 + 0.513089i −0.975271 0.221013i \(-0.929064\pi\)
0.679039 + 0.734103i \(0.262397\pi\)
\(642\) 0 0
\(643\) −44.0000 −1.73519 −0.867595 0.497271i \(-0.834335\pi\)
−0.867595 + 0.497271i \(0.834335\pi\)
\(644\) 0 0
\(645\) −12.0000 −0.472500
\(646\) 0 0
\(647\) 21.5000 37.2391i 0.845252 1.46402i −0.0401498 0.999194i \(-0.512784\pi\)
0.885402 0.464826i \(-0.153883\pi\)
\(648\) 0 0
\(649\) 1.50000 + 2.59808i 0.0588802 + 0.101983i
\(650\) 0 0
\(651\) 7.50000 + 2.59808i 0.293948 + 0.101827i
\(652\) 0 0
\(653\) −2.50000 4.33013i −0.0978326 0.169451i 0.812955 0.582327i \(-0.197858\pi\)
−0.910787 + 0.412876i \(0.864524\pi\)
\(654\) 0 0
\(655\) −8.50000 + 14.7224i −0.332122 + 0.575253i
\(656\) 0 0
\(657\) 42.0000 1.63858
\(658\) 0 0
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) −0.500000 + 0.866025i −0.0194477 + 0.0336845i −0.875585 0.483063i \(-0.839524\pi\)
0.856138 + 0.516748i \(0.172857\pi\)
\(662\) 0 0
\(663\) 9.00000 + 15.5885i 0.349531 + 0.605406i
\(664\) 0 0
\(665\) −2.50000 12.9904i −0.0969458 0.503745i
\(666\) 0 0
\(667\) −9.00000 15.5885i −0.348481 0.603587i
\(668\) 0 0
\(669\) 36.0000 62.3538i 1.39184 2.41074i
\(670\) 0 0
\(671\) 3.00000 0.115814
\(672\) 0 0
\(673\) −2.00000 −0.0770943 −0.0385472 0.999257i \(-0.512273\pi\)
−0.0385472 + 0.999257i \(0.512273\pi\)
\(674\) 0 0
\(675\) 18.0000 31.1769i 0.692820 1.20000i
\(676\) 0 0
\(677\) −4.50000 7.79423i −0.172949 0.299557i 0.766501 0.642244i \(-0.221996\pi\)
−0.939450 + 0.342687i \(0.888663\pi\)
\(678\) 0 0
\(679\) −12.0000 + 10.3923i −0.460518 + 0.398820i
\(680\) 0 0
\(681\) −10.5000 18.1865i −0.402361 0.696909i
\(682\) 0 0
\(683\) −19.5000 + 33.7750i −0.746147 + 1.29236i 0.203510 + 0.979073i \(0.434765\pi\)
−0.949657 + 0.313291i \(0.898568\pi\)
\(684\) 0 0
\(685\) 3.00000 0.114624
\(686\) 0 0
\(687\) −21.0000 −0.801200
\(688\) 0 0
\(689\) 9.00000 15.5885i 0.342873 0.593873i
\(690\) 0 0
\(691\) 23.5000 + 40.7032i 0.893982 + 1.54842i 0.835059 + 0.550160i \(0.185433\pi\)
0.0589228 + 0.998263i \(0.481233\pi\)
\(692\) 0 0
\(693\) 12.0000 10.3923i 0.455842 0.394771i
\(694\) 0 0
\(695\) −2.00000 3.46410i −0.0758643 0.131401i
\(696\) 0 0
\(697\) 15.0000 25.9808i 0.568166 0.984092i
\(698\) 0 0
\(699\) −39.0000 −1.47512
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) −12.5000 + 21.6506i −0.471446 + 0.816569i
\(704\) 0 0
\(705\) 1.50000 + 2.59808i 0.0564933 + 0.0978492i
\(706\) 0 0
\(707\) −6.50000 33.7750i −0.244458 1.27024i
\(708\) 0 0
\(709\) 13.5000 + 23.3827i 0.507003 + 0.878155i 0.999967 + 0.00810550i \(0.00258009\pi\)
−0.492964 + 0.870050i \(0.664087\pi\)
\(710\) 0 0
\(711\) −33.0000 + 57.1577i −1.23760 + 2.14358i
\(712\) 0 0
\(713\) 3.00000 0.112351
\(714\) 0 0
\(715\) 2.00000 0.0747958
\(716\) 0 0
\(717\) −6.00000 + 10.3923i −0.224074 + 0.388108i
\(718\) 0 0
\(719\) 14.5000 + 25.1147i 0.540759 + 0.936622i 0.998861 + 0.0477220i \(0.0151961\pi\)
−0.458102 + 0.888900i \(0.651471\pi\)
\(720\) 0 0
\(721\) −12.5000 4.33013i −0.465524 0.161262i
\(722\) 0 0
\(723\) 25.5000 + 44.1673i 0.948355 + 1.64260i
\(724\) 0 0
\(725\) 12.0000 20.7846i 0.445669 0.771921i
\(726\) 0 0
\(727\) −16.0000 −0.593407 −0.296704 0.954970i \(-0.595887\pi\)
−0.296704 + 0.954970i \(0.595887\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 6.00000 10.3923i 0.221918 0.384373i
\(732\) 0 0
\(733\) 5.50000 + 9.52628i 0.203147 + 0.351861i 0.949541 0.313644i \(-0.101550\pi\)
−0.746394 + 0.665505i \(0.768216\pi\)
\(734\) 0 0
\(735\) 3.00000 20.7846i 0.110657 0.766652i
\(736\) 0 0
\(737\) 5.50000 + 9.52628i 0.202595 + 0.350905i
\(738\) 0 0
\(739\) 20.5000 35.5070i 0.754105 1.30615i −0.191714 0.981451i \(-0.561404\pi\)
0.945818 0.324697i \(-0.105262\pi\)
\(740\) 0 0
\(741\) −30.0000 −1.10208
\(742\) 0 0
\(743\) −32.0000 −1.17397 −0.586983 0.809599i \(-0.699684\pi\)
−0.586983 + 0.809599i \(0.699684\pi\)
\(744\) 0 0
\(745\) 7.50000 12.9904i 0.274779 0.475931i
\(746\) 0 0
\(747\) 12.0000 + 20.7846i 0.439057 + 0.760469i
\(748\) 0 0
\(749\) −7.50000 2.59808i −0.274044 0.0949316i
\(750\) 0 0
\(751\) −23.5000 40.7032i −0.857527 1.48528i −0.874281 0.485421i \(-0.838666\pi\)
0.0167534 0.999860i \(-0.494667\pi\)
\(752\) 0 0
\(753\) −36.0000 + 62.3538i −1.31191 + 2.27230i
\(754\) 0 0
\(755\) −15.0000 −0.545906
\(756\) 0 0
\(757\) −34.0000 −1.23575 −0.617876 0.786276i \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) 0 0
\(759\) 4.50000 7.79423i 0.163340 0.282913i
\(760\) 0 0
\(761\) −13.5000 23.3827i −0.489375 0.847622i 0.510551 0.859848i \(-0.329442\pi\)
−0.999925 + 0.0122260i \(0.996108\pi\)
\(762\) 0 0
\(763\) 5.50000 + 28.5788i 0.199113 + 1.03462i
\(764\) 0 0
\(765\) −9.00000 15.5885i −0.325396 0.563602i
\(766\) 0 0
\(767\) 3.00000 5.19615i 0.108324 0.187622i
\(768\) 0 0
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) −39.0000 −1.40455
\(772\) 0 0
\(773\) 17.5000 30.3109i 0.629431 1.09021i −0.358235 0.933632i \(-0.616621\pi\)
0.987666 0.156575i \(-0.0500454\pi\)
\(774\) 0 0
\(775\) 2.00000 + 3.46410i 0.0718421 + 0.124434i
\(776\) 0 0
\(777\) −30.0000 + 25.9808i −1.07624 + 0.932055i
\(778\) 0 0
\(779\) 25.0000 + 43.3013i 0.895718 + 1.55143i
\(780\) 0 0
\(781\) −8.00000 + 13.8564i −0.286263 + 0.495821i
\(782\) 0 0
\(783\) 54.0000 1.92980
\(784\) 0 0
\(785\) −15.0000 −0.535373
\(786\) 0 0
\(787\) 6.50000 11.2583i 0.231700 0.401316i −0.726609 0.687052i \(-0.758905\pi\)
0.958308 + 0.285736i \(0.0922379\pi\)
\(788\) 0 0
\(789\) 4.50000 + 7.79423i 0.160204 + 0.277482i
\(790\) 0 0
\(791\) 20.0000 17.3205i 0.711118 0.615846i
\(792\) 0 0
\(793\) −3.00000 5.19615i −0.106533 0.184521i
\(794\) 0 0
\(795\) −13.5000 + 23.3827i −0.478796 + 0.829298i
\(796\) 0 0
\(797\) −42.0000 −1.48772 −0.743858 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 0 0
\(799\) −3.00000 −0.106132
\(800\) 0 0
\(801\) 27.0000 46.7654i 0.953998 1.65237i
\(802\) 0 0
\(803\) 3.50000 + 6.06218i 0.123512 + 0.213930i
\(804\) 0 0
\(805\) −1.50000 7.79423i −0.0528681 0.274710i
\(806\) 0 0
\(807\) −25.5000 44.1673i −0.897643 1.55476i
\(808\) 0 0
\(809\) 12.5000 21.6506i 0.439477 0.761196i −0.558173 0.829725i \(-0.688497\pi\)
0.997649 + 0.0685291i \(0.0218306\pi\)
\(810\) 0 0
\(811\) −20.0000 −0.702295 −0.351147 0.936320i \(-0.614208\pi\)
−0.351147 + 0.936320i \(0.614208\pi\)
\(812\) 0 0
\(813\) 9.00000 0.315644
\(814\) 0 0
\(815\) −4.50000 + 7.79423i −0.157628 + 0.273020i
\(816\) 0 0
\(817\) 10.0000 + 17.3205i 0.349856 + 0.605968i
\(818\) 0 0
\(819\) −30.0000 10.3923i −1.04828 0.363137i
\(820\) 0 0
\(821\) −12.5000 21.6506i −0.436253 0.755612i 0.561144 0.827718i \(-0.310361\pi\)
−0.997397 + 0.0721058i \(0.977028\pi\)
\(822\) 0 0
\(823\) −10.5000 + 18.1865i −0.366007 + 0.633943i −0.988937 0.148335i \(-0.952609\pi\)
0.622930 + 0.782277i \(0.285942\pi\)
\(824\) 0 0
\(825\) 12.0000 0.417786
\(826\) 0 0
\(827\) −4.00000 −0.139094 −0.0695468 0.997579i \(-0.522155\pi\)
−0.0695468 + 0.997579i \(0.522155\pi\)
\(828\) 0 0
\(829\) −18.5000 + 32.0429i −0.642532 + 1.11290i 0.342334 + 0.939578i \(0.388783\pi\)
−0.984866 + 0.173319i \(0.944551\pi\)
\(830\) 0 0
\(831\) 10.5000 + 18.1865i 0.364241 + 0.630884i
\(832\) 0 0
\(833\) 16.5000 + 12.9904i 0.571691 + 0.450090i
\(834\) 0 0
\(835\) −10.0000 17.3205i −0.346064 0.599401i
\(836\) 0 0
\(837\) −4.50000 + 7.79423i −0.155543 + 0.269408i
\(838\) 0 0
\(839\) 24.0000 0.828572 0.414286 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) 27.0000 46.7654i 0.929929 1.61068i
\(844\) 0 0
\(845\) 4.50000 + 7.79423i 0.154805 + 0.268130i
\(846\) 0 0
\(847\) −25.0000 8.66025i −0.859010 0.297570i
\(848\) 0 0
\(849\) 25.5000 + 44.1673i 0.875158 + 1.51582i
\(850\) 0 0
\(851\) −7.50000 + 12.9904i −0.257097 + 0.445305i
\(852\) 0 0
\(853\) 22.0000 0.753266 0.376633 0.926363i \(-0.377082\pi\)
0.376633 + 0.926363i \(0.377082\pi\)
\(854\) 0 0
\(855\) 30.0000 1.02598
\(856\) 0 0
\(857\) 28.5000 49.3634i 0.973541 1.68622i 0.288875 0.957367i \(-0.406719\pi\)
0.684667 0.728856i \(-0.259948\pi\)
\(858\) 0 0
\(859\) −2.50000 4.33013i −0.0852989 0.147742i 0.820220 0.572049i \(-0.193851\pi\)
−0.905519 + 0.424307i \(0.860518\pi\)
\(860\) 0 0
\(861\) 15.0000 + 77.9423i 0.511199 + 2.65627i
\(862\) 0 0
\(863\) 18.5000 + 32.0429i 0.629747 + 1.09075i 0.987602 + 0.156977i \(0.0501749\pi\)
−0.357855 + 0.933777i \(0.616492\pi\)
\(864\) 0 0
\(865\) −10.5000 + 18.1865i −0.357011 + 0.618361i
\(866\) 0 0
\(867\) −24.0000 −0.815083
\(868\) 0 0
\(869\) −11.0000 −0.373149
\(870\) 0 0
\(871\) 11.0000 19.0526i 0.372721 0.645571i
\(872\) 0 0
\(873\) −18.0000 31.1769i −0.609208 1.05518i
\(874\) 0 0
\(875\) 18.0000 15.5885i 0.608511 0.526986i
\(876\) 0 0
\(877\) 19.5000 + 33.7750i 0.658468 + 1.14050i 0.981012 + 0.193946i \(0.0621286\pi\)
−0.322544 + 0.946554i \(0.604538\pi\)
\(878\) 0 0
\(879\) 9.00000 15.5885i 0.303562 0.525786i
\(880\) 0 0
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 0 0
\(883\) 28.0000 0.942275 0.471138 0.882060i \(-0.343844\pi\)
0.471138 + 0.882060i \(0.343844\pi\)
\(884\) 0 0
\(885\) −4.50000 + 7.79423i −0.151266 + 0.262000i
\(886\) 0 0
\(887\) −27.5000 47.6314i −0.923360 1.59931i −0.794178 0.607685i \(-0.792098\pi\)
−0.129181 0.991621i \(-0.541235\pi\)
\(888\) 0 0
\(889\) −16.0000 + 13.8564i −0.536623 + 0.464729i
\(890\) 0 0
\(891\) 4.50000 + 7.79423i 0.150756 + 0.261116i
\(892\) 0 0
\(893\) 2.50000 4.33013i 0.0836593 0.144902i
\(894\) 0 0
\(895\) −1.00000 −0.0334263
\(896\) 0 0
\(897\) −18.0000 −0.601003
\(898\) 0 0
\(899\) −3.00000 + 5.19615i −0.100056 + 0.173301i
\(900\) 0 0
\(901\) −13.5000 23.3827i −0.449750 0.778990i
\(902\) 0 0
\(903\) 6.00000 + 31.1769i 0.199667 + 1.03750i
\(904\) 0 0
\(905\) 11.0000 + 19.0526i 0.365652 + 0.633328i
\(906\) 0 0
\(907\) 6.50000 11.2583i 0.215829 0.373827i −0.737700 0.675129i \(-0.764088\pi\)
0.953529 + 0.301302i \(0.0974213\pi\)
\(908\) 0 0
\(909\) 78.0000 2.58710
\(910\) 0 0
\(911\) 48.0000 1.59031 0.795155 0.606406i \(-0.207389\pi\)
0.795155 + 0.606406i \(0.207389\pi\)
\(912\) 0 0
\(913\) −2.00000 + 3.46410i −0.0661903 + 0.114645i
\(914\) 0 0
\(915\) 4.50000 + 7.79423i 0.148765 + 0.257669i
\(916\) 0 0
\(917\) 42.5000 + 14.7224i 1.40347 + 0.486178i
\(918\) 0 0
\(919\) 8.50000 + 14.7224i 0.280389 + 0.485648i 0.971481 0.237119i \(-0.0762032\pi\)
−0.691091 + 0.722767i \(0.742870\pi\)
\(920\) 0 0
\(921\) −6.00000 + 10.3923i −0.197707 + 0.342438i
\(922\) 0 0
\(923\) 32.0000 1.05329
\(924\) 0 0
\(925\) −20.0000 −0.657596
\(926\) 0 0
\(927\) 15.0000 25.9808i 0.492665 0.853320i
\(928\) 0 0
\(929\) 20.5000 + 35.5070i 0.672583 + 1.16495i 0.977169 + 0.212463i \(0.0681486\pi\)
−0.304586 + 0.952485i \(0.598518\pi\)
\(930\) 0 0
\(931\) −32.5000 + 12.9904i −1.06514 + 0.425743i
\(932\) 0 0
\(933\) 16.5000 + 28.5788i 0.540186 + 0.935629i
\(934\) 0 0
\(935\) 1.50000 2.59808i 0.0490552 0.0849662i
\(936\) 0 0
\(937\) −38.0000 −1.24141 −0.620703 0.784046i \(-0.713153\pi\)
−0.620703 + 0.784046i \(0.713153\pi\)
\(938\) 0 0
\(939\) 93.0000 3.03494
\(940\) 0 0
\(941\) 19.5000 33.7750i 0.635682 1.10103i −0.350688 0.936492i \(-0.614052\pi\)
0.986370 0.164541i \(-0.0526143\pi\)
\(942\) 0 0
\(943\) 15.0000 + 25.9808i 0.488467 + 0.846050i
\(944\) 0 0
\(945\) 22.5000 + 7.79423i 0.731925 + 0.253546i
\(946\) 0 0
\(947\) −24.5000 42.4352i −0.796143 1.37896i −0.922111 0.386926i \(-0.873537\pi\)
0.125968 0.992034i \(-0.459796\pi\)
\(948\) 0 0
\(949\) 7.00000 12.1244i 0.227230 0.393573i
\(950\) 0 0
\(951\) −81.0000 −2.62660
\(952\) 0 0
\(953\) 30.0000 0.971795 0.485898 0.874016i \(-0.338493\pi\)
0.485898 + 0.874016i \(0.338493\pi\)
\(954\) 0 0
\(955\) 8.50000 14.7224i 0.275054 0.476407i
\(956\) 0 0
\(957\) 9.00000 + 15.5885i 0.290929 + 0.503903i
\(958\) 0 0
\(959\) −1.50000 7.79423i −0.0484375 0.251689i
\(960\) 0 0
\(961\) 15.0000 + 25.9808i 0.483871 + 0.838089i
\(962\) 0 0
\(963\) 9.00000 15.5885i 0.290021 0.502331i
\(964\) 0 0
\(965\) −5.00000 −0.160956
\(966\) 0 0
\(967\) −32.0000 −1.02905 −0.514525 0.857475i \(-0.672032\pi\)
−0.514525 + 0.857475i \(0.672032\pi\)
\(968\) 0 0
\(969\) −22.5000 + 38.9711i −0.722804 + 1.25193i
\(970\) 0 0
\(971\) −28.5000 49.3634i −0.914609 1.58415i −0.807473 0.589904i \(-0.799166\pi\)
−0.107135 0.994244i \(-0.534168\pi\)
\(972\) 0 0
\(973\) −8.00000 + 6.92820i −0.256468 + 0.222108i
\(974\) 0 0
\(975\) −12.0000 20.7846i −0.384308 0.665640i
\(976\) 0 0
\(977\) 18.5000 32.0429i 0.591867 1.02514i −0.402113 0.915590i \(-0.631724\pi\)
0.993981 0.109555i \(-0.0349424\pi\)
\(978\) 0 0
\(979\) 9.00000 0.287641
\(980\) 0 0
\(981\) −66.0000 −2.10722
\(982\) 0 0
\(983\) −16.5000 + 28.5788i −0.526268 + 0.911523i 0.473263 + 0.880921i \(0.343076\pi\)
−0.999532 + 0.0306024i \(0.990257\pi\)
\(984\) 0 0
\(985\) 9.00000 + 15.5885i 0.286764 + 0.496690i
\(986\) 0 0
\(987\) 6.00000 5.19615i 0.190982 0.165395i
\(988\) 0 0
\(989\) 6.00000 + 10.3923i 0.190789 + 0.330456i
\(990\) 0 0
\(991\) 29.5000 51.0955i 0.937098 1.62310i 0.166250 0.986084i \(-0.446834\pi\)
0.770849 0.637018i \(-0.219832\pi\)
\(992\) 0 0
\(993\) −21.0000 −0.666415
\(994\) 0 0
\(995\) 9.00000 0.285319
\(996\) 0 0
\(997\) 15.5000 26.8468i 0.490890 0.850246i −0.509055 0.860734i \(-0.670005\pi\)
0.999945 + 0.0104877i \(0.00333839\pi\)
\(998\) 0 0
\(999\) −22.5000 38.9711i −0.711868 1.23299i
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 448.2.i.a.193.1 2
4.3 odd 2 448.2.i.f.193.1 2
7.2 even 3 inner 448.2.i.a.65.1 2
7.3 odd 6 3136.2.a.a.1.1 1
7.4 even 3 3136.2.a.bc.1.1 1
8.3 odd 2 56.2.i.a.25.1 yes 2
8.5 even 2 112.2.i.c.81.1 2
24.5 odd 2 1008.2.s.e.865.1 2
24.11 even 2 504.2.s.e.361.1 2
28.3 even 6 3136.2.a.bb.1.1 1
28.11 odd 6 3136.2.a.b.1.1 1
28.23 odd 6 448.2.i.f.65.1 2
40.3 even 4 1400.2.bh.f.249.1 4
40.19 odd 2 1400.2.q.g.1201.1 2
40.27 even 4 1400.2.bh.f.249.2 4
56.3 even 6 392.2.a.a.1.1 1
56.5 odd 6 784.2.i.a.177.1 2
56.11 odd 6 392.2.a.f.1.1 1
56.13 odd 2 784.2.i.a.753.1 2
56.19 even 6 392.2.i.f.177.1 2
56.27 even 2 392.2.i.f.361.1 2
56.37 even 6 112.2.i.c.65.1 2
56.45 odd 6 784.2.a.j.1.1 1
56.51 odd 6 56.2.i.a.9.1 2
56.53 even 6 784.2.a.a.1.1 1
168.11 even 6 3528.2.a.r.1.1 1
168.53 odd 6 7056.2.a.bi.1.1 1
168.59 odd 6 3528.2.a.k.1.1 1
168.83 odd 2 3528.2.s.o.361.1 2
168.101 even 6 7056.2.a.s.1.1 1
168.107 even 6 504.2.s.e.289.1 2
168.131 odd 6 3528.2.s.o.3313.1 2
168.149 odd 6 1008.2.s.e.289.1 2
280.59 even 6 9800.2.a.bp.1.1 1
280.107 even 12 1400.2.bh.f.849.1 4
280.163 even 12 1400.2.bh.f.849.2 4
280.179 odd 6 9800.2.a.b.1.1 1
280.219 odd 6 1400.2.q.g.401.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.2.i.a.9.1 2 56.51 odd 6
56.2.i.a.25.1 yes 2 8.3 odd 2
112.2.i.c.65.1 2 56.37 even 6
112.2.i.c.81.1 2 8.5 even 2
392.2.a.a.1.1 1 56.3 even 6
392.2.a.f.1.1 1 56.11 odd 6
392.2.i.f.177.1 2 56.19 even 6
392.2.i.f.361.1 2 56.27 even 2
448.2.i.a.65.1 2 7.2 even 3 inner
448.2.i.a.193.1 2 1.1 even 1 trivial
448.2.i.f.65.1 2 28.23 odd 6
448.2.i.f.193.1 2 4.3 odd 2
504.2.s.e.289.1 2 168.107 even 6
504.2.s.e.361.1 2 24.11 even 2
784.2.a.a.1.1 1 56.53 even 6
784.2.a.j.1.1 1 56.45 odd 6
784.2.i.a.177.1 2 56.5 odd 6
784.2.i.a.753.1 2 56.13 odd 2
1008.2.s.e.289.1 2 168.149 odd 6
1008.2.s.e.865.1 2 24.5 odd 2
1400.2.q.g.401.1 2 280.219 odd 6
1400.2.q.g.1201.1 2 40.19 odd 2
1400.2.bh.f.249.1 4 40.3 even 4
1400.2.bh.f.249.2 4 40.27 even 4
1400.2.bh.f.849.1 4 280.107 even 12
1400.2.bh.f.849.2 4 280.163 even 12
3136.2.a.a.1.1 1 7.3 odd 6
3136.2.a.b.1.1 1 28.11 odd 6
3136.2.a.bb.1.1 1 28.3 even 6
3136.2.a.bc.1.1 1 7.4 even 3
3528.2.a.k.1.1 1 168.59 odd 6
3528.2.a.r.1.1 1 168.11 even 6
3528.2.s.o.361.1 2 168.83 odd 2
3528.2.s.o.3313.1 2 168.131 odd 6
7056.2.a.s.1.1 1 168.101 even 6
7056.2.a.bi.1.1 1 168.53 odd 6
9800.2.a.b.1.1 1 280.179 odd 6
9800.2.a.bp.1.1 1 280.59 even 6