Properties

Label 260.2.bk.c.197.2
Level $260$
Weight $2$
Character 260.197
Analytic conductor $2.076$
Analytic rank $0$
Dimension $20$
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] = [260,2,Mod(33,260)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(260, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 9, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("260.33");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.bk (of order \(12\), degree \(4\), 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: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + 6399 x^{4} + 666 x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 197.2
Root \(1.86950i\) of defining polynomial
Character \(\chi\) \(=\) 260.197
Dual form 260.2.bk.c.33.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.41732 - 0.647720i) q^{3} +(-2.18528 + 0.473860i) q^{5} +(3.34088 + 1.92886i) q^{7} +(2.82584 + 1.63150i) q^{9} +O(q^{10})\) \(q+(-2.41732 - 0.647720i) q^{3} +(-2.18528 + 0.473860i) q^{5} +(3.34088 + 1.92886i) q^{7} +(2.82584 + 1.63150i) q^{9} +(1.17419 - 4.38214i) q^{11} +(2.93090 + 2.09996i) q^{13} +(5.58946 + 0.269977i) q^{15} +(1.34075 + 5.00375i) q^{17} +(6.75335 - 1.80956i) q^{19} +(-6.82663 - 6.82663i) q^{21} +(0.490083 - 1.82902i) q^{23} +(4.55091 - 2.07104i) q^{25} +(-0.465395 - 0.465395i) q^{27} +(-1.71600 + 0.990731i) q^{29} +(-2.74684 + 2.74684i) q^{31} +(-5.67679 + 9.83250i) q^{33} +(-8.21477 - 2.63199i) q^{35} +(-10.2855 + 5.93836i) q^{37} +(-5.72474 - 6.97469i) q^{39} +(7.04912 + 1.88880i) q^{41} +(5.07520 - 1.35990i) q^{43} +(-6.94835 - 2.22623i) q^{45} -2.88429i q^{47} +(3.94098 + 6.82598i) q^{49} -12.9641i q^{51} +(3.37298 - 3.37298i) q^{53} +(-0.489416 + 10.1326i) q^{55} -17.4971 q^{57} +(-1.22940 - 4.58817i) q^{59} +(1.59692 - 2.76595i) q^{61} +(6.29385 + 10.9013i) q^{63} +(-7.39992 - 3.20018i) q^{65} +(-1.60567 - 2.78111i) q^{67} +(-2.36938 + 4.10389i) q^{69} +(1.70510 + 6.36353i) q^{71} +3.35146 q^{73} +(-12.3425 + 2.05865i) q^{75} +(12.3753 - 12.3753i) q^{77} -0.191160i q^{79} +(-4.07093 - 7.05105i) q^{81} +7.50696i q^{83} +(-5.30100 - 10.2993i) q^{85} +(4.78983 - 1.28343i) q^{87} +(10.5771 + 2.83413i) q^{89} +(5.74124 + 12.6690i) q^{91} +(8.41918 - 4.86082i) q^{93} +(-13.9005 + 7.15454i) q^{95} +(3.13619 - 5.43203i) q^{97} +(10.4675 - 10.4675i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{1}{12}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) −2.41732 0.647720i −1.39564 0.373961i −0.518864 0.854857i \(-0.673645\pi\)
−0.876778 + 0.480895i \(0.840312\pi\)
\(4\) 0 0
\(5\) −2.18528 + 0.473860i −0.977288 + 0.211917i
\(6\) 0 0
\(7\) 3.34088 + 1.92886i 1.26273 + 0.729040i 0.973603 0.228250i \(-0.0733003\pi\)
0.289131 + 0.957290i \(0.406634\pi\)
\(8\) 0 0
\(9\) 2.82584 + 1.63150i 0.941945 + 0.543832i
\(10\) 0 0
\(11\) 1.17419 4.38214i 0.354032 1.32126i −0.527667 0.849451i \(-0.676933\pi\)
0.881699 0.471813i \(-0.156400\pi\)
\(12\) 0 0
\(13\) 2.93090 + 2.09996i 0.812885 + 0.582425i
\(14\) 0 0
\(15\) 5.58946 + 0.269977i 1.44319 + 0.0697078i
\(16\) 0 0
\(17\) 1.34075 + 5.00375i 0.325180 + 1.21359i 0.914131 + 0.405419i \(0.132875\pi\)
−0.588951 + 0.808169i \(0.700459\pi\)
\(18\) 0 0
\(19\) 6.75335 1.80956i 1.54933 0.415141i 0.620061 0.784554i \(-0.287108\pi\)
0.929265 + 0.369413i \(0.120441\pi\)
\(20\) 0 0
\(21\) −6.82663 6.82663i −1.48969 1.48969i
\(22\) 0 0
\(23\) 0.490083 1.82902i 0.102189 0.381376i −0.895822 0.444414i \(-0.853412\pi\)
0.998011 + 0.0630374i \(0.0200788\pi\)
\(24\) 0 0
\(25\) 4.55091 2.07104i 0.910183 0.414207i
\(26\) 0 0
\(27\) −0.465395 0.465395i −0.0895652 0.0895652i
\(28\) 0 0
\(29\) −1.71600 + 0.990731i −0.318652 + 0.183974i −0.650792 0.759256i \(-0.725563\pi\)
0.332139 + 0.943230i \(0.392230\pi\)
\(30\) 0 0
\(31\) −2.74684 + 2.74684i −0.493347 + 0.493347i −0.909359 0.416012i \(-0.863427\pi\)
0.416012 + 0.909359i \(0.363427\pi\)
\(32\) 0 0
\(33\) −5.67679 + 9.83250i −0.988203 + 1.71162i
\(34\) 0 0
\(35\) −8.21477 2.63199i −1.38855 0.444887i
\(36\) 0 0
\(37\) −10.2855 + 5.93836i −1.69093 + 0.976260i −0.737165 + 0.675712i \(0.763836\pi\)
−0.953767 + 0.300548i \(0.902830\pi\)
\(38\) 0 0
\(39\) −5.72474 6.97469i −0.916692 1.11684i
\(40\) 0 0
\(41\) 7.04912 + 1.88880i 1.10089 + 0.294982i 0.763126 0.646250i \(-0.223664\pi\)
0.337761 + 0.941232i \(0.390330\pi\)
\(42\) 0 0
\(43\) 5.07520 1.35990i 0.773961 0.207382i 0.149841 0.988710i \(-0.452124\pi\)
0.624121 + 0.781328i \(0.285457\pi\)
\(44\) 0 0
\(45\) −6.94835 2.22623i −1.03580 0.331867i
\(46\) 0 0
\(47\) 2.88429i 0.420717i −0.977624 0.210358i \(-0.932537\pi\)
0.977624 0.210358i \(-0.0674631\pi\)
\(48\) 0 0
\(49\) 3.94098 + 6.82598i 0.562997 + 0.975140i
\(50\) 0 0
\(51\) 12.9641i 1.81534i
\(52\) 0 0
\(53\) 3.37298 3.37298i 0.463315 0.463315i −0.436425 0.899740i \(-0.643756\pi\)
0.899740 + 0.436425i \(0.143756\pi\)
\(54\) 0 0
\(55\) −0.489416 + 10.1326i −0.0659928 + 1.36628i
\(56\) 0 0
\(57\) −17.4971 −2.31755
\(58\) 0 0
\(59\) −1.22940 4.58817i −0.160054 0.597329i −0.998619 0.0525286i \(-0.983272\pi\)
0.838565 0.544801i \(-0.183395\pi\)
\(60\) 0 0
\(61\) 1.59692 2.76595i 0.204465 0.354144i −0.745497 0.666509i \(-0.767788\pi\)
0.949962 + 0.312365i \(0.101121\pi\)
\(62\) 0 0
\(63\) 6.29385 + 10.9013i 0.792950 + 1.37343i
\(64\) 0 0
\(65\) −7.39992 3.20018i −0.917848 0.396933i
\(66\) 0 0
\(67\) −1.60567 2.78111i −0.196164 0.339767i 0.751117 0.660169i \(-0.229515\pi\)
−0.947282 + 0.320402i \(0.896182\pi\)
\(68\) 0 0
\(69\) −2.36938 + 4.10389i −0.285240 + 0.494050i
\(70\) 0 0
\(71\) 1.70510 + 6.36353i 0.202358 + 0.755212i 0.990239 + 0.139383i \(0.0445120\pi\)
−0.787880 + 0.615829i \(0.788821\pi\)
\(72\) 0 0
\(73\) 3.35146 0.392259 0.196129 0.980578i \(-0.437163\pi\)
0.196129 + 0.980578i \(0.437163\pi\)
\(74\) 0 0
\(75\) −12.3425 + 2.05865i −1.42519 + 0.237712i
\(76\) 0 0
\(77\) 12.3753 12.3753i 1.41030 1.41030i
\(78\) 0 0
\(79\) 0.191160i 0.0215072i −0.999942 0.0107536i \(-0.996577\pi\)
0.999942 0.0107536i \(-0.00342304\pi\)
\(80\) 0 0
\(81\) −4.07093 7.05105i −0.452325 0.783450i
\(82\) 0 0
\(83\) 7.50696i 0.823996i 0.911185 + 0.411998i \(0.135169\pi\)
−0.911185 + 0.411998i \(0.864831\pi\)
\(84\) 0 0
\(85\) −5.30100 10.2993i −0.574974 1.11711i
\(86\) 0 0
\(87\) 4.78983 1.28343i 0.513524 0.137598i
\(88\) 0 0
\(89\) 10.5771 + 2.83413i 1.12117 + 0.300418i 0.771358 0.636401i \(-0.219578\pi\)
0.349816 + 0.936819i \(0.386244\pi\)
\(90\) 0 0
\(91\) 5.74124 + 12.6690i 0.601846 + 1.32807i
\(92\) 0 0
\(93\) 8.41918 4.86082i 0.873029 0.504043i
\(94\) 0 0
\(95\) −13.9005 + 7.15454i −1.42616 + 0.734040i
\(96\) 0 0
\(97\) 3.13619 5.43203i 0.318431 0.551539i −0.661730 0.749743i \(-0.730177\pi\)
0.980161 + 0.198203i \(0.0635106\pi\)
\(98\) 0 0
\(99\) 10.4675 10.4675i 1.05202 1.05202i
\(100\) 0 0
\(101\) −5.84851 + 3.37664i −0.581949 + 0.335988i −0.761907 0.647686i \(-0.775737\pi\)
0.179959 + 0.983674i \(0.442404\pi\)
\(102\) 0 0
\(103\) −7.17259 7.17259i −0.706736 0.706736i 0.259111 0.965847i \(-0.416570\pi\)
−0.965847 + 0.259111i \(0.916570\pi\)
\(104\) 0 0
\(105\) 18.1530 + 11.6832i 1.77155 + 1.14017i
\(106\) 0 0
\(107\) −0.595458 + 2.22228i −0.0575651 + 0.214836i −0.988717 0.149796i \(-0.952138\pi\)
0.931152 + 0.364632i \(0.118805\pi\)
\(108\) 0 0
\(109\) 1.63415 + 1.63415i 0.156523 + 0.156523i 0.781024 0.624501i \(-0.214698\pi\)
−0.624501 + 0.781024i \(0.714698\pi\)
\(110\) 0 0
\(111\) 28.7099 7.69279i 2.72502 0.730167i
\(112\) 0 0
\(113\) −2.65149 9.89551i −0.249432 0.930891i −0.971104 0.238657i \(-0.923293\pi\)
0.721672 0.692235i \(-0.243374\pi\)
\(114\) 0 0
\(115\) −0.204272 + 4.22915i −0.0190485 + 0.394370i
\(116\) 0 0
\(117\) 4.85615 + 10.7159i 0.448951 + 0.990685i
\(118\) 0 0
\(119\) −5.17224 + 19.3031i −0.474138 + 1.76951i
\(120\) 0 0
\(121\) −8.29812 4.79092i −0.754375 0.435538i
\(122\) 0 0
\(123\) −15.8166 9.13170i −1.42613 0.823378i
\(124\) 0 0
\(125\) −8.96365 + 6.68229i −0.801733 + 0.597683i
\(126\) 0 0
\(127\) 6.33875 + 1.69846i 0.562473 + 0.150714i 0.528842 0.848720i \(-0.322626\pi\)
0.0336308 + 0.999434i \(0.489293\pi\)
\(128\) 0 0
\(129\) −13.1492 −1.15773
\(130\) 0 0
\(131\) −9.05372 −0.791027 −0.395514 0.918460i \(-0.629433\pi\)
−0.395514 + 0.918460i \(0.629433\pi\)
\(132\) 0 0
\(133\) 26.0525 + 6.98075i 2.25904 + 0.605308i
\(134\) 0 0
\(135\) 1.23755 + 0.796486i 0.106511 + 0.0685506i
\(136\) 0 0
\(137\) −2.92353 1.68790i −0.249774 0.144207i 0.369887 0.929077i \(-0.379396\pi\)
−0.619661 + 0.784870i \(0.712730\pi\)
\(138\) 0 0
\(139\) 8.53706 + 4.92888i 0.724104 + 0.418062i 0.816261 0.577683i \(-0.196043\pi\)
−0.0921571 + 0.995744i \(0.529376\pi\)
\(140\) 0 0
\(141\) −1.86821 + 6.97226i −0.157332 + 0.587170i
\(142\) 0 0
\(143\) 12.6438 10.3778i 1.05732 0.867838i
\(144\) 0 0
\(145\) 3.28047 2.97817i 0.272428 0.247323i
\(146\) 0 0
\(147\) −5.10530 19.0533i −0.421078 1.57149i
\(148\) 0 0
\(149\) 2.20843 0.591746i 0.180921 0.0484777i −0.167221 0.985919i \(-0.553479\pi\)
0.348142 + 0.937442i \(0.386813\pi\)
\(150\) 0 0
\(151\) −13.2429 13.2429i −1.07769 1.07769i −0.996716 0.0809746i \(-0.974197\pi\)
−0.0809746 0.996716i \(-0.525803\pi\)
\(152\) 0 0
\(153\) −4.37486 + 16.3272i −0.353687 + 1.31998i
\(154\) 0 0
\(155\) 4.70100 7.30424i 0.377593 0.586690i
\(156\) 0 0
\(157\) −1.52992 1.52992i −0.122101 0.122101i 0.643416 0.765517i \(-0.277517\pi\)
−0.765517 + 0.643416i \(0.777517\pi\)
\(158\) 0 0
\(159\) −10.3383 + 5.96884i −0.819884 + 0.473360i
\(160\) 0 0
\(161\) 5.16522 5.16522i 0.407076 0.407076i
\(162\) 0 0
\(163\) −7.70822 + 13.3510i −0.603755 + 1.04573i 0.388492 + 0.921452i \(0.372996\pi\)
−0.992247 + 0.124282i \(0.960337\pi\)
\(164\) 0 0
\(165\) 7.74617 24.1768i 0.603038 1.88216i
\(166\) 0 0
\(167\) −12.1902 + 7.03801i −0.943306 + 0.544618i −0.890995 0.454013i \(-0.849992\pi\)
−0.0523106 + 0.998631i \(0.516659\pi\)
\(168\) 0 0
\(169\) 4.18031 + 12.3095i 0.321562 + 0.946888i
\(170\) 0 0
\(171\) 22.0362 + 5.90457i 1.68515 + 0.451534i
\(172\) 0 0
\(173\) −10.2249 + 2.73977i −0.777388 + 0.208301i −0.625633 0.780118i \(-0.715159\pi\)
−0.151755 + 0.988418i \(0.548493\pi\)
\(174\) 0 0
\(175\) 19.1988 + 1.85898i 1.45129 + 0.140526i
\(176\) 0 0
\(177\) 11.8874i 0.893512i
\(178\) 0 0
\(179\) −7.94948 13.7689i −0.594172 1.02914i −0.993663 0.112399i \(-0.964146\pi\)
0.399491 0.916737i \(-0.369187\pi\)
\(180\) 0 0
\(181\) 18.0258i 1.33985i 0.742430 + 0.669923i \(0.233673\pi\)
−0.742430 + 0.669923i \(0.766327\pi\)
\(182\) 0 0
\(183\) −5.65184 + 5.65184i −0.417796 + 0.417796i
\(184\) 0 0
\(185\) 19.6628 17.8509i 1.44564 1.31242i
\(186\) 0 0
\(187\) 23.5014 1.71859
\(188\) 0 0
\(189\) −0.657147 2.45251i −0.0478004 0.178394i
\(190\) 0 0
\(191\) 7.25135 12.5597i 0.524689 0.908788i −0.474898 0.880041i \(-0.657515\pi\)
0.999587 0.0287469i \(-0.00915169\pi\)
\(192\) 0 0
\(193\) −0.660752 1.14446i −0.0475620 0.0823798i 0.841264 0.540624i \(-0.181812\pi\)
−0.888826 + 0.458244i \(0.848478\pi\)
\(194\) 0 0
\(195\) 15.8152 + 12.5289i 1.13255 + 0.897216i
\(196\) 0 0
\(197\) 6.96097 + 12.0568i 0.495949 + 0.859009i 0.999989 0.00467150i \(-0.00148699\pi\)
−0.504040 + 0.863680i \(0.668154\pi\)
\(198\) 0 0
\(199\) 6.73532 11.6659i 0.477454 0.826975i −0.522212 0.852816i \(-0.674893\pi\)
0.999666 + 0.0258407i \(0.00822625\pi\)
\(200\) 0 0
\(201\) 2.08005 + 7.76287i 0.146716 + 0.547550i
\(202\) 0 0
\(203\) −7.64391 −0.536498
\(204\) 0 0
\(205\) −16.2993 0.787275i −1.13839 0.0549857i
\(206\) 0 0
\(207\) 4.36893 4.36893i 0.303661 0.303661i
\(208\) 0 0
\(209\) 31.7189i 2.19404i
\(210\) 0 0
\(211\) −9.02243 15.6273i −0.621129 1.07583i −0.989276 0.146060i \(-0.953341\pi\)
0.368146 0.929768i \(-0.379993\pi\)
\(212\) 0 0
\(213\) 16.4871i 1.12968i
\(214\) 0 0
\(215\) −10.4464 + 5.37670i −0.712435 + 0.366688i
\(216\) 0 0
\(217\) −14.4751 + 3.87860i −0.982635 + 0.263296i
\(218\) 0 0
\(219\) −8.10156 2.17081i −0.547453 0.146690i
\(220\) 0 0
\(221\) −6.57809 + 17.4810i −0.442490 + 1.17590i
\(222\) 0 0
\(223\) −3.73310 + 2.15531i −0.249987 + 0.144330i −0.619758 0.784793i \(-0.712769\pi\)
0.369771 + 0.929123i \(0.379436\pi\)
\(224\) 0 0
\(225\) 16.2390 + 1.57239i 1.08260 + 0.104826i
\(226\) 0 0
\(227\) −10.6548 + 18.4546i −0.707182 + 1.22488i 0.258716 + 0.965953i \(0.416701\pi\)
−0.965898 + 0.258922i \(0.916633\pi\)
\(228\) 0 0
\(229\) −1.68567 + 1.68567i −0.111392 + 0.111392i −0.760606 0.649214i \(-0.775098\pi\)
0.649214 + 0.760606i \(0.275098\pi\)
\(230\) 0 0
\(231\) −37.9310 + 21.8995i −2.49567 + 1.44088i
\(232\) 0 0
\(233\) −19.8733 19.8733i −1.30195 1.30195i −0.927079 0.374867i \(-0.877688\pi\)
−0.374867 0.927079i \(-0.622312\pi\)
\(234\) 0 0
\(235\) 1.36675 + 6.30298i 0.0891569 + 0.411161i
\(236\) 0 0
\(237\) −0.123818 + 0.462096i −0.00804286 + 0.0300164i
\(238\) 0 0
\(239\) 0.515620 + 0.515620i 0.0333527 + 0.0333527i 0.723586 0.690234i \(-0.242492\pi\)
−0.690234 + 0.723586i \(0.742492\pi\)
\(240\) 0 0
\(241\) −13.9645 + 3.74178i −0.899533 + 0.241029i −0.678816 0.734309i \(-0.737506\pi\)
−0.220717 + 0.975338i \(0.570840\pi\)
\(242\) 0 0
\(243\) 5.78468 + 21.5887i 0.371087 + 1.38492i
\(244\) 0 0
\(245\) −11.8467 13.0492i −0.756859 0.833684i
\(246\) 0 0
\(247\) 23.5934 + 8.87817i 1.50121 + 0.564905i
\(248\) 0 0
\(249\) 4.86241 18.1467i 0.308143 1.15000i
\(250\) 0 0
\(251\) −12.3324 7.12014i −0.778417 0.449419i 0.0574522 0.998348i \(-0.481702\pi\)
−0.835869 + 0.548929i \(0.815036\pi\)
\(252\) 0 0
\(253\) −7.43955 4.29522i −0.467720 0.270038i
\(254\) 0 0
\(255\) 6.14318 + 28.3303i 0.384701 + 1.77411i
\(256\) 0 0
\(257\) −9.08035 2.43307i −0.566417 0.151771i −0.0357640 0.999360i \(-0.511386\pi\)
−0.530653 + 0.847589i \(0.678053\pi\)
\(258\) 0 0
\(259\) −45.8170 −2.84693
\(260\) 0 0
\(261\) −6.46550 −0.400204
\(262\) 0 0
\(263\) −19.2807 5.16623i −1.18890 0.318564i −0.390446 0.920626i \(-0.627679\pi\)
−0.798449 + 0.602062i \(0.794346\pi\)
\(264\) 0 0
\(265\) −5.77260 + 8.96924i −0.354608 + 0.550976i
\(266\) 0 0
\(267\) −23.7326 13.7020i −1.45241 0.838551i
\(268\) 0 0
\(269\) 18.8136 + 10.8620i 1.14708 + 0.662270i 0.948175 0.317748i \(-0.102927\pi\)
0.198909 + 0.980018i \(0.436260\pi\)
\(270\) 0 0
\(271\) −1.58261 + 5.90638i −0.0961367 + 0.358787i −0.997189 0.0749226i \(-0.976129\pi\)
0.901053 + 0.433710i \(0.142796\pi\)
\(272\) 0 0
\(273\) −5.67248 34.3438i −0.343314 2.07858i
\(274\) 0 0
\(275\) −3.73193 22.3745i −0.225044 1.34923i
\(276\) 0 0
\(277\) −5.11654 19.0952i −0.307423 1.14732i −0.930839 0.365429i \(-0.880922\pi\)
0.623416 0.781891i \(-0.285744\pi\)
\(278\) 0 0
\(279\) −12.2436 + 3.28066i −0.733004 + 0.196408i
\(280\) 0 0
\(281\) 14.1598 + 14.1598i 0.844700 + 0.844700i 0.989466 0.144766i \(-0.0462429\pi\)
−0.144766 + 0.989466i \(0.546243\pi\)
\(282\) 0 0
\(283\) 8.46917 31.6074i 0.503440 1.87886i 0.0270400 0.999634i \(-0.491392\pi\)
0.476400 0.879229i \(-0.341941\pi\)
\(284\) 0 0
\(285\) 38.2362 8.29119i 2.26491 0.491128i
\(286\) 0 0
\(287\) 19.9070 + 19.9070i 1.17507 + 1.17507i
\(288\) 0 0
\(289\) −8.51750 + 4.91758i −0.501029 + 0.289269i
\(290\) 0 0
\(291\) −11.0996 + 11.0996i −0.650671 + 0.650671i
\(292\) 0 0
\(293\) −6.02783 + 10.4405i −0.352150 + 0.609941i −0.986626 0.163001i \(-0.947883\pi\)
0.634476 + 0.772943i \(0.281216\pi\)
\(294\) 0 0
\(295\) 4.86073 + 9.44389i 0.283003 + 0.549845i
\(296\) 0 0
\(297\) −2.58588 + 1.49296i −0.150048 + 0.0866304i
\(298\) 0 0
\(299\) 5.27725 4.33150i 0.305191 0.250497i
\(300\) 0 0
\(301\) 19.5787 + 5.24609i 1.12850 + 0.302380i
\(302\) 0 0
\(303\) 16.3249 4.37423i 0.937839 0.251293i
\(304\) 0 0
\(305\) −2.17905 + 6.80110i −0.124772 + 0.389430i
\(306\) 0 0
\(307\) 25.5219i 1.45661i −0.685252 0.728306i \(-0.740308\pi\)
0.685252 0.728306i \(-0.259692\pi\)
\(308\) 0 0
\(309\) 12.6926 + 21.9843i 0.722059 + 1.25064i
\(310\) 0 0
\(311\) 18.9993i 1.07735i 0.842513 + 0.538676i \(0.181075\pi\)
−0.842513 + 0.538676i \(0.818925\pi\)
\(312\) 0 0
\(313\) 16.2567 16.2567i 0.918883 0.918883i −0.0780653 0.996948i \(-0.524874\pi\)
0.996948 + 0.0780653i \(0.0248743\pi\)
\(314\) 0 0
\(315\) −18.9195 20.8399i −1.06599 1.17420i
\(316\) 0 0
\(317\) 20.9422 1.17623 0.588115 0.808777i \(-0.299870\pi\)
0.588115 + 0.808777i \(0.299870\pi\)
\(318\) 0 0
\(319\) 2.32661 + 8.68303i 0.130265 + 0.486157i
\(320\) 0 0
\(321\) 2.87883 4.98628i 0.160681 0.278307i
\(322\) 0 0
\(323\) 18.1091 + 31.3660i 1.00762 + 1.74525i
\(324\) 0 0
\(325\) 17.6874 + 3.48675i 0.981118 + 0.193410i
\(326\) 0 0
\(327\) −2.89179 5.00873i −0.159916 0.276983i
\(328\) 0 0
\(329\) 5.56338 9.63606i 0.306719 0.531253i
\(330\) 0 0
\(331\) 2.54739 + 9.50699i 0.140017 + 0.522551i 0.999927 + 0.0121049i \(0.00385320\pi\)
−0.859910 + 0.510446i \(0.829480\pi\)
\(332\) 0 0
\(333\) −38.7537 −2.12369
\(334\) 0 0
\(335\) 4.82671 + 5.31664i 0.263711 + 0.290479i
\(336\) 0 0
\(337\) −8.77242 + 8.77242i −0.477864 + 0.477864i −0.904448 0.426584i \(-0.859717\pi\)
0.426584 + 0.904448i \(0.359717\pi\)
\(338\) 0 0
\(339\) 25.6381i 1.39247i
\(340\) 0 0
\(341\) 8.81171 + 15.2623i 0.477181 + 0.826502i
\(342\) 0 0
\(343\) 3.40236i 0.183710i
\(344\) 0 0
\(345\) 3.23309 10.0909i 0.174064 0.543276i
\(346\) 0 0
\(347\) 1.16045 0.310942i 0.0622963 0.0166922i −0.227536 0.973770i \(-0.573067\pi\)
0.289833 + 0.957077i \(0.406400\pi\)
\(348\) 0 0
\(349\) −18.3696 4.92212i −0.983303 0.263475i −0.268868 0.963177i \(-0.586650\pi\)
−0.714435 + 0.699702i \(0.753316\pi\)
\(350\) 0 0
\(351\) −0.386712 2.34133i −0.0206412 0.124971i
\(352\) 0 0
\(353\) −8.40342 + 4.85172i −0.447269 + 0.258231i −0.706676 0.707537i \(-0.749806\pi\)
0.259407 + 0.965768i \(0.416473\pi\)
\(354\) 0 0
\(355\) −6.74155 13.0981i −0.357804 0.695176i
\(356\) 0 0
\(357\) 25.0059 43.3116i 1.32345 2.29229i
\(358\) 0 0
\(359\) 24.3084 24.3084i 1.28295 1.28295i 0.343969 0.938981i \(-0.388228\pi\)
0.938981 0.343969i \(-0.111772\pi\)
\(360\) 0 0
\(361\) 25.8788 14.9411i 1.36204 0.786376i
\(362\) 0 0
\(363\) 16.9561 + 16.9561i 0.889963 + 0.889963i
\(364\) 0 0
\(365\) −7.32389 + 1.58812i −0.383350 + 0.0831262i
\(366\) 0 0
\(367\) 1.97860 7.38424i 0.103282 0.385454i −0.894862 0.446342i \(-0.852726\pi\)
0.998145 + 0.0608877i \(0.0193931\pi\)
\(368\) 0 0
\(369\) 16.8381 + 16.8381i 0.876554 + 0.876554i
\(370\) 0 0
\(371\) 17.7747 4.76273i 0.922818 0.247268i
\(372\) 0 0
\(373\) −1.11739 4.17016i −0.0578563 0.215923i 0.930945 0.365159i \(-0.118985\pi\)
−0.988802 + 0.149236i \(0.952319\pi\)
\(374\) 0 0
\(375\) 25.9963 10.3473i 1.34244 0.534334i
\(376\) 0 0
\(377\) −7.10990 0.699798i −0.366179 0.0360414i
\(378\) 0 0
\(379\) −3.78500 + 14.1258i −0.194422 + 0.725594i 0.797993 + 0.602666i \(0.205895\pi\)
−0.992416 + 0.122928i \(0.960772\pi\)
\(380\) 0 0
\(381\) −14.2227 8.21147i −0.728650 0.420686i
\(382\) 0 0
\(383\) 2.93423 + 1.69408i 0.149932 + 0.0865635i 0.573089 0.819493i \(-0.305745\pi\)
−0.423157 + 0.906056i \(0.639078\pi\)
\(384\) 0 0
\(385\) −21.1794 + 32.9078i −1.07940 + 1.67714i
\(386\) 0 0
\(387\) 16.5604 + 4.43734i 0.841810 + 0.225562i
\(388\) 0 0
\(389\) 22.8218 1.15711 0.578555 0.815643i \(-0.303617\pi\)
0.578555 + 0.815643i \(0.303617\pi\)
\(390\) 0 0
\(391\) 9.80902 0.496064
\(392\) 0 0
\(393\) 21.8858 + 5.86427i 1.10399 + 0.295814i
\(394\) 0 0
\(395\) 0.0905832 + 0.417739i 0.00455774 + 0.0210187i
\(396\) 0 0
\(397\) −8.77734 5.06760i −0.440522 0.254335i 0.263297 0.964715i \(-0.415190\pi\)
−0.703819 + 0.710379i \(0.748523\pi\)
\(398\) 0 0
\(399\) −58.4558 33.7495i −2.92645 1.68959i
\(400\) 0 0
\(401\) 8.05785 30.0723i 0.402390 1.50174i −0.406430 0.913682i \(-0.633226\pi\)
0.808819 0.588057i \(-0.200107\pi\)
\(402\) 0 0
\(403\) −13.8190 + 2.28244i −0.688372 + 0.113697i
\(404\) 0 0
\(405\) 12.2373 + 13.4795i 0.608078 + 0.669801i
\(406\) 0 0
\(407\) 13.9455 + 52.0454i 0.691254 + 2.57979i
\(408\) 0 0
\(409\) −16.1424 + 4.32535i −0.798192 + 0.213875i −0.634790 0.772685i \(-0.718913\pi\)
−0.163402 + 0.986560i \(0.552247\pi\)
\(410\) 0 0
\(411\) 5.97383 + 5.97383i 0.294667 + 0.294667i
\(412\) 0 0
\(413\) 4.74267 17.6999i 0.233371 0.870954i
\(414\) 0 0
\(415\) −3.55725 16.4048i −0.174619 0.805281i
\(416\) 0 0
\(417\) −17.4443 17.4443i −0.854252 0.854252i
\(418\) 0 0
\(419\) 3.80652 2.19769i 0.185960 0.107364i −0.404130 0.914702i \(-0.632426\pi\)
0.590090 + 0.807337i \(0.299092\pi\)
\(420\) 0 0
\(421\) −14.0586 + 14.0586i −0.685175 + 0.685175i −0.961161 0.275987i \(-0.910995\pi\)
0.275987 + 0.961161i \(0.410995\pi\)
\(422\) 0 0
\(423\) 4.70571 8.15053i 0.228799 0.396292i
\(424\) 0 0
\(425\) 16.4646 + 19.9949i 0.798650 + 0.969895i
\(426\) 0 0
\(427\) 10.6703 6.16047i 0.516370 0.298126i
\(428\) 0 0
\(429\) −37.2860 + 16.8970i −1.80018 + 0.815794i
\(430\) 0 0
\(431\) −1.45418 0.389648i −0.0700456 0.0187687i 0.223626 0.974675i \(-0.428211\pi\)
−0.293672 + 0.955906i \(0.594877\pi\)
\(432\) 0 0
\(433\) −14.3146 + 3.83559i −0.687917 + 0.184327i −0.585812 0.810447i \(-0.699224\pi\)
−0.102105 + 0.994774i \(0.532558\pi\)
\(434\) 0 0
\(435\) −9.85897 + 5.07437i −0.472701 + 0.243297i
\(436\) 0 0
\(437\) 13.2388i 0.633299i
\(438\) 0 0
\(439\) 3.62582 + 6.28011i 0.173051 + 0.299733i 0.939485 0.342590i \(-0.111304\pi\)
−0.766434 + 0.642323i \(0.777971\pi\)
\(440\) 0 0
\(441\) 25.7188i 1.22470i
\(442\) 0 0
\(443\) 12.2198 12.2198i 0.580581 0.580581i −0.354482 0.935063i \(-0.615343\pi\)
0.935063 + 0.354482i \(0.115343\pi\)
\(444\) 0 0
\(445\) −24.4570 1.18130i −1.15937 0.0559990i
\(446\) 0 0
\(447\) −5.72177 −0.270630
\(448\) 0 0
\(449\) 9.84620 + 36.7465i 0.464671 + 1.73417i 0.657979 + 0.753037i \(0.271412\pi\)
−0.193308 + 0.981138i \(0.561922\pi\)
\(450\) 0 0
\(451\) 16.5540 28.6724i 0.779497 1.35013i
\(452\) 0 0
\(453\) 23.4347 + 40.5900i 1.10106 + 1.90709i
\(454\) 0 0
\(455\) −18.5496 24.9648i −0.869617 1.17037i
\(456\) 0 0
\(457\) −6.35050 10.9994i −0.297064 0.514530i 0.678399 0.734694i \(-0.262674\pi\)
−0.975463 + 0.220164i \(0.929341\pi\)
\(458\) 0 0
\(459\) 1.70474 2.95270i 0.0795705 0.137820i
\(460\) 0 0
\(461\) 7.37555 + 27.5259i 0.343513 + 1.28201i 0.894339 + 0.447389i \(0.147646\pi\)
−0.550826 + 0.834620i \(0.685687\pi\)
\(462\) 0 0
\(463\) 11.9895 0.557201 0.278601 0.960407i \(-0.410129\pi\)
0.278601 + 0.960407i \(0.410129\pi\)
\(464\) 0 0
\(465\) −16.0949 + 14.6118i −0.746385 + 0.677605i
\(466\) 0 0
\(467\) −2.12252 + 2.12252i −0.0982186 + 0.0982186i −0.754509 0.656290i \(-0.772125\pi\)
0.656290 + 0.754509i \(0.272125\pi\)
\(468\) 0 0
\(469\) 12.3885i 0.572046i
\(470\) 0 0
\(471\) 2.70736 + 4.68928i 0.124748 + 0.216071i
\(472\) 0 0
\(473\) 23.8370i 1.09603i
\(474\) 0 0
\(475\) 26.9863 22.2216i 1.23822 1.01960i
\(476\) 0 0
\(477\) 15.0345 4.02848i 0.688383 0.184452i
\(478\) 0 0
\(479\) −36.2773 9.72046i −1.65755 0.444139i −0.695837 0.718199i \(-0.744967\pi\)
−0.961713 + 0.274060i \(0.911633\pi\)
\(480\) 0 0
\(481\) −42.6162 4.19453i −1.94313 0.191254i
\(482\) 0 0
\(483\) −15.8316 + 9.14039i −0.720364 + 0.415902i
\(484\) 0 0
\(485\) −4.27943 + 13.3566i −0.194319 + 0.606494i
\(486\) 0 0
\(487\) −1.64663 + 2.85205i −0.0746160 + 0.129239i −0.900919 0.433987i \(-0.857106\pi\)
0.826303 + 0.563225i \(0.190440\pi\)
\(488\) 0 0
\(489\) 27.2810 27.2810i 1.23369 1.23369i
\(490\) 0 0
\(491\) 17.1647 9.91005i 0.774633 0.447234i −0.0598922 0.998205i \(-0.519076\pi\)
0.834525 + 0.550971i \(0.185742\pi\)
\(492\) 0 0
\(493\) −7.25810 7.25810i −0.326888 0.326888i
\(494\) 0 0
\(495\) −17.9143 + 27.8346i −0.805189 + 1.25107i
\(496\) 0 0
\(497\) −6.57780 + 24.5487i −0.295055 + 1.10116i
\(498\) 0 0
\(499\) 6.58653 + 6.58653i 0.294854 + 0.294854i 0.838994 0.544141i \(-0.183144\pi\)
−0.544141 + 0.838994i \(0.683144\pi\)
\(500\) 0 0
\(501\) 34.0263 9.11732i 1.52018 0.407332i
\(502\) 0 0
\(503\) 0.767145 + 2.86302i 0.0342053 + 0.127656i 0.980917 0.194425i \(-0.0622842\pi\)
−0.946712 + 0.322081i \(0.895618\pi\)
\(504\) 0 0
\(505\) 11.1806 10.1503i 0.497530 0.451682i
\(506\) 0 0
\(507\) −2.13203 32.4638i −0.0946867 1.44177i
\(508\) 0 0
\(509\) 5.86672 21.8949i 0.260038 0.970475i −0.705180 0.709028i \(-0.749134\pi\)
0.965218 0.261446i \(-0.0841995\pi\)
\(510\) 0 0
\(511\) 11.1968 + 6.46449i 0.495318 + 0.285972i
\(512\) 0 0
\(513\) −3.98513 2.30082i −0.175948 0.101584i
\(514\) 0 0
\(515\) 19.0729 + 12.2753i 0.840454 + 0.540915i
\(516\) 0 0
\(517\) −12.6393 3.38670i −0.555878 0.148947i
\(518\) 0 0
\(519\) 26.4916 1.16285
\(520\) 0 0
\(521\) −31.4316 −1.37704 −0.688521 0.725216i \(-0.741740\pi\)
−0.688521 + 0.725216i \(0.741740\pi\)
\(522\) 0 0
\(523\) 32.5167 + 8.71283i 1.42186 + 0.380985i 0.886142 0.463414i \(-0.153376\pi\)
0.535715 + 0.844399i \(0.320042\pi\)
\(524\) 0 0
\(525\) −45.2056 16.9292i −1.97293 0.738850i
\(526\) 0 0
\(527\) −17.4273 10.0617i −0.759147 0.438294i
\(528\) 0 0
\(529\) 16.8135 + 9.70726i 0.731020 + 0.422055i
\(530\) 0 0
\(531\) 4.01152 14.9712i 0.174085 0.649694i
\(532\) 0 0
\(533\) 16.6938 + 20.3388i 0.723089 + 0.880970i
\(534\) 0 0
\(535\) 0.248194 5.13847i 0.0107304 0.222155i
\(536\) 0 0
\(537\) 10.2981 + 38.4329i 0.444395 + 1.65850i
\(538\) 0 0
\(539\) 34.5398 9.25492i 1.48774 0.398638i
\(540\) 0 0
\(541\) −2.00796 2.00796i −0.0863288 0.0863288i 0.662624 0.748953i \(-0.269443\pi\)
−0.748953 + 0.662624i \(0.769443\pi\)
\(542\) 0 0
\(543\) 11.6757 43.5742i 0.501051 1.86995i
\(544\) 0 0
\(545\) −4.34543 2.79671i −0.186138 0.119798i
\(546\) 0 0
\(547\) −9.19675 9.19675i −0.393224 0.393224i 0.482611 0.875835i \(-0.339689\pi\)
−0.875835 + 0.482611i \(0.839689\pi\)
\(548\) 0 0
\(549\) 9.02528 5.21075i 0.385190 0.222389i
\(550\) 0 0
\(551\) −9.79595 + 9.79595i −0.417321 + 0.417321i
\(552\) 0 0
\(553\) 0.368721 0.638643i 0.0156796 0.0271579i
\(554\) 0 0
\(555\) −59.0938 + 30.4154i −2.50839 + 1.29106i
\(556\) 0 0
\(557\) −17.3556 + 10.0203i −0.735381 + 0.424572i −0.820387 0.571808i \(-0.806242\pi\)
0.0850066 + 0.996380i \(0.472909\pi\)
\(558\) 0 0
\(559\) 17.7306 + 6.67202i 0.749926 + 0.282197i
\(560\) 0 0
\(561\) −56.8105 15.2223i −2.39854 0.642688i
\(562\) 0 0
\(563\) −31.9878 + 8.57109i −1.34812 + 0.361229i −0.859442 0.511234i \(-0.829189\pi\)
−0.488682 + 0.872462i \(0.662522\pi\)
\(564\) 0 0
\(565\) 10.4834 + 20.3680i 0.441038 + 0.856890i
\(566\) 0 0
\(567\) 31.4089i 1.31905i
\(568\) 0 0
\(569\) 18.5265 + 32.0889i 0.776672 + 1.34524i 0.933850 + 0.357665i \(0.116427\pi\)
−0.157178 + 0.987570i \(0.550240\pi\)
\(570\) 0 0
\(571\) 24.2209i 1.01361i −0.862060 0.506807i \(-0.830826\pi\)
0.862060 0.506807i \(-0.169174\pi\)
\(572\) 0 0
\(573\) −25.6640 + 25.6640i −1.07213 + 1.07213i
\(574\) 0 0
\(575\) −1.55763 9.33867i −0.0649577 0.389449i
\(576\) 0 0
\(577\) −2.85093 −0.118686 −0.0593429 0.998238i \(-0.518901\pi\)
−0.0593429 + 0.998238i \(0.518901\pi\)
\(578\) 0 0
\(579\) 0.855965 + 3.19450i 0.0355727 + 0.132759i
\(580\) 0 0
\(581\) −14.4799 + 25.0798i −0.600726 + 1.04049i
\(582\) 0 0
\(583\) −10.8204 18.7414i −0.448133 0.776189i
\(584\) 0 0
\(585\) −15.6899 21.1161i −0.648697 0.873044i
\(586\) 0 0
\(587\) 1.91874 + 3.32335i 0.0791947 + 0.137169i 0.902903 0.429845i \(-0.141432\pi\)
−0.823708 + 0.567014i \(0.808098\pi\)
\(588\) 0 0
\(589\) −13.5798 + 23.5209i −0.559547 + 0.969164i
\(590\) 0 0
\(591\) −9.01752 33.6539i −0.370931 1.38433i
\(592\) 0 0
\(593\) −16.4597 −0.675919 −0.337960 0.941161i \(-0.609737\pi\)
−0.337960 + 0.941161i \(0.609737\pi\)
\(594\) 0 0
\(595\) 2.15585 44.6335i 0.0883811 1.82980i
\(596\) 0 0
\(597\) −23.8377 + 23.8377i −0.975612 + 0.975612i
\(598\) 0 0
\(599\) 37.2957i 1.52386i −0.647659 0.761931i \(-0.724252\pi\)
0.647659 0.761931i \(-0.275748\pi\)
\(600\) 0 0
\(601\) −0.218654 0.378720i −0.00891908 0.0154483i 0.861531 0.507704i \(-0.169506\pi\)
−0.870450 + 0.492256i \(0.836172\pi\)
\(602\) 0 0
\(603\) 10.4786i 0.426722i
\(604\) 0 0
\(605\) 20.4040 + 6.53737i 0.829539 + 0.265782i
\(606\) 0 0
\(607\) −31.2280 + 8.36751i −1.26750 + 0.339627i −0.829074 0.559139i \(-0.811132\pi\)
−0.438430 + 0.898765i \(0.644465\pi\)
\(608\) 0 0
\(609\) 18.4778 + 4.95111i 0.748759 + 0.200629i
\(610\) 0 0
\(611\) 6.05690 8.45355i 0.245036 0.341994i
\(612\) 0 0
\(613\) −25.2582 + 14.5828i −1.02017 + 0.588996i −0.914153 0.405369i \(-0.867143\pi\)
−0.106017 + 0.994364i \(0.533810\pi\)
\(614\) 0 0
\(615\) 38.8908 + 12.4605i 1.56823 + 0.502456i
\(616\) 0 0
\(617\) 20.3229 35.2002i 0.818168 1.41711i −0.0888631 0.996044i \(-0.528323\pi\)
0.907031 0.421064i \(-0.138343\pi\)
\(618\) 0 0
\(619\) −14.2874 + 14.2874i −0.574260 + 0.574260i −0.933316 0.359056i \(-0.883099\pi\)
0.359056 + 0.933316i \(0.383099\pi\)
\(620\) 0 0
\(621\) −1.07930 + 0.623132i −0.0433107 + 0.0250054i
\(622\) 0 0
\(623\) 29.8703 + 29.8703i 1.19673 + 1.19673i
\(624\) 0 0
\(625\) 16.4216 18.8502i 0.656865 0.754008i
\(626\) 0 0
\(627\) −20.5450 + 76.6748i −0.820486 + 3.06210i
\(628\) 0 0
\(629\) −43.5044 43.5044i −1.73464 1.73464i
\(630\) 0 0
\(631\) −30.8788 + 8.27394i −1.22926 + 0.329380i −0.814293 0.580454i \(-0.802875\pi\)
−0.414971 + 0.909834i \(0.636208\pi\)
\(632\) 0 0
\(633\) 11.6880 + 43.6202i 0.464557 + 1.73375i
\(634\) 0 0
\(635\) −14.6568 0.707939i −0.581637 0.0280937i
\(636\) 0 0
\(637\) −2.78369 + 28.2822i −0.110294 + 1.12058i
\(638\) 0 0
\(639\) −5.56374 + 20.7641i −0.220098 + 0.821417i
\(640\) 0 0
\(641\) 30.7120 + 17.7316i 1.21305 + 0.700354i 0.963422 0.267988i \(-0.0863587\pi\)
0.249627 + 0.968342i \(0.419692\pi\)
\(642\) 0 0
\(643\) −25.3268 14.6224i −0.998790 0.576652i −0.0909000 0.995860i \(-0.528974\pi\)
−0.907890 + 0.419208i \(0.862308\pi\)
\(644\) 0 0
\(645\) 28.7348 6.23090i 1.13143 0.245342i
\(646\) 0 0
\(647\) 21.0890 + 5.65079i 0.829095 + 0.222155i 0.648319 0.761369i \(-0.275472\pi\)
0.180776 + 0.983524i \(0.442139\pi\)
\(648\) 0 0
\(649\) −21.5496 −0.845894
\(650\) 0 0
\(651\) 37.5033 1.46987
\(652\) 0 0
\(653\) −9.64542 2.58448i −0.377454 0.101139i 0.0651035 0.997879i \(-0.479262\pi\)
−0.442558 + 0.896740i \(0.645929\pi\)
\(654\) 0 0
\(655\) 19.7849 4.29020i 0.773061 0.167632i
\(656\) 0 0
\(657\) 9.47068 + 5.46790i 0.369486 + 0.213323i
\(658\) 0 0
\(659\) −17.9408 10.3581i −0.698873 0.403494i 0.108055 0.994145i \(-0.465538\pi\)
−0.806927 + 0.590651i \(0.798871\pi\)
\(660\) 0 0
\(661\) 11.9997 44.7834i 0.466734 1.74187i −0.184343 0.982862i \(-0.559016\pi\)
0.651077 0.759012i \(-0.274318\pi\)
\(662\) 0 0
\(663\) 27.2242 37.9965i 1.05730 1.47566i
\(664\) 0 0
\(665\) −60.2400 2.90966i −2.33601 0.112832i
\(666\) 0 0
\(667\) 0.971081 + 3.62412i 0.0376004 + 0.140327i
\(668\) 0 0
\(669\) 10.4201 2.79207i 0.402866 0.107948i
\(670\) 0 0
\(671\) −10.2457 10.2457i −0.395530 0.395530i
\(672\) 0 0
\(673\) 4.44409 16.5856i 0.171307 0.639327i −0.825844 0.563898i \(-0.809301\pi\)
0.997151 0.0754282i \(-0.0240324\pi\)
\(674\) 0 0
\(675\) −3.08182 1.15412i −0.118619 0.0444221i
\(676\) 0 0
\(677\) 16.9842 + 16.9842i 0.652756 + 0.652756i 0.953656 0.300900i \(-0.0972870\pi\)
−0.300900 + 0.953656i \(0.597287\pi\)
\(678\) 0 0
\(679\) 20.9552 12.0985i 0.804188 0.464298i
\(680\) 0 0
\(681\) 37.7095 37.7095i 1.44503 1.44503i
\(682\) 0 0
\(683\) −18.7675 + 32.5062i −0.718117 + 1.24382i 0.243628 + 0.969869i \(0.421662\pi\)
−0.961745 + 0.273946i \(0.911671\pi\)
\(684\) 0 0
\(685\) 7.18856 + 2.30319i 0.274661 + 0.0880005i
\(686\) 0 0
\(687\) 5.16665 2.98297i 0.197120 0.113807i
\(688\) 0 0
\(689\) 16.9690 2.80273i 0.646468 0.106775i
\(690\) 0 0
\(691\) −29.8582 8.00047i −1.13586 0.304352i −0.358573 0.933502i \(-0.616737\pi\)
−0.777284 + 0.629149i \(0.783403\pi\)
\(692\) 0 0
\(693\) 55.1610 14.7803i 2.09539 0.561459i
\(694\) 0 0
\(695\) −20.9915 6.72561i −0.796253 0.255117i
\(696\) 0 0
\(697\) 37.8044i 1.43195i
\(698\) 0 0
\(699\) 35.1679 + 60.9126i 1.33017 + 2.30393i
\(700\) 0 0
\(701\) 38.2090i 1.44313i −0.692345 0.721566i \(-0.743423\pi\)
0.692345 0.721566i \(-0.256577\pi\)
\(702\) 0 0
\(703\) −58.7161 + 58.7161i −2.21452 + 2.21452i
\(704\) 0 0
\(705\) 0.778692 16.1216i 0.0293272 0.607175i
\(706\) 0 0
\(707\) −26.0522 −0.979795
\(708\) 0 0
\(709\) −9.62682 35.9278i −0.361543 1.34930i −0.872048 0.489421i \(-0.837208\pi\)
0.510505 0.859875i \(-0.329458\pi\)
\(710\) 0 0
\(711\) 0.311877 0.540187i 0.0116963 0.0202586i
\(712\) 0 0
\(713\) 3.67783 + 6.37019i 0.137736 + 0.238566i
\(714\) 0 0
\(715\) −22.7125 + 28.6699i −0.849400 + 1.07219i
\(716\) 0 0
\(717\) −0.912443 1.58040i −0.0340758 0.0590210i
\(718\) 0 0
\(719\) 22.5751 39.1012i 0.841908 1.45823i −0.0463715 0.998924i \(-0.514766\pi\)
0.888280 0.459303i \(-0.151901\pi\)
\(720\) 0 0
\(721\) −10.1279 37.7977i −0.377181 1.40766i
\(722\) 0 0
\(723\) 36.1803 1.34556
\(724\) 0 0
\(725\) −5.75751 + 8.06262i −0.213829 + 0.299438i
\(726\) 0 0
\(727\) 2.21203 2.21203i 0.0820398 0.0820398i −0.664896 0.746936i \(-0.731524\pi\)
0.746936 + 0.664896i \(0.231524\pi\)
\(728\) 0 0
\(729\) 31.5082i 1.16697i
\(730\) 0 0
\(731\) 13.6092 + 23.5718i 0.503354 + 0.871834i
\(732\) 0 0
\(733\) 17.9002i 0.661161i 0.943778 + 0.330580i \(0.107244\pi\)
−0.943778 + 0.330580i \(0.892756\pi\)
\(734\) 0 0
\(735\) 20.1851 + 39.2175i 0.744539 + 1.44656i
\(736\) 0 0
\(737\) −14.0726 + 3.77073i −0.518370 + 0.138897i
\(738\) 0 0
\(739\) −15.0511 4.03294i −0.553665 0.148354i −0.0288707 0.999583i \(-0.509191\pi\)
−0.524794 + 0.851229i \(0.675858\pi\)
\(740\) 0 0
\(741\) −51.2823 36.7433i −1.88390 1.34980i
\(742\) 0 0
\(743\) 3.81686 2.20366i 0.140027 0.0808446i −0.428350 0.903613i \(-0.640905\pi\)
0.568377 + 0.822768i \(0.307572\pi\)
\(744\) 0 0
\(745\) −4.54563 + 2.33962i −0.166539 + 0.0857170i
\(746\) 0 0
\(747\) −12.2476 + 21.2134i −0.448116 + 0.776159i
\(748\) 0 0
\(749\) −6.27581 + 6.27581i −0.229313 + 0.229313i
\(750\) 0 0
\(751\) −37.2400 + 21.5005i −1.35891 + 0.784565i −0.989476 0.144694i \(-0.953780\pi\)
−0.369429 + 0.929259i \(0.620447\pi\)
\(752\) 0 0
\(753\) 25.1996 + 25.1996i 0.918326 + 0.918326i
\(754\) 0 0
\(755\) 35.2147 + 22.6642i 1.28159 + 0.824833i
\(756\) 0 0
\(757\) 7.50026 27.9914i 0.272602 1.01736i −0.684830 0.728703i \(-0.740124\pi\)
0.957432 0.288660i \(-0.0932098\pi\)
\(758\) 0 0
\(759\) 15.2017 + 15.2017i 0.551786 + 0.551786i
\(760\) 0 0
\(761\) 9.09438 2.43683i 0.329671 0.0883350i −0.0901872 0.995925i \(-0.528747\pi\)
0.419858 + 0.907590i \(0.362080\pi\)
\(762\) 0 0
\(763\) 2.30745 + 8.61152i 0.0835353 + 0.311758i
\(764\) 0 0
\(765\) 1.82349 37.7526i 0.0659285 1.36495i
\(766\) 0 0
\(767\) 6.03176 16.0292i 0.217794 0.578779i
\(768\) 0 0
\(769\) 3.95609 14.7643i 0.142660 0.532416i −0.857188 0.515004i \(-0.827791\pi\)
0.999848 0.0174122i \(-0.00554276\pi\)
\(770\) 0 0
\(771\) 20.3742 + 11.7630i 0.733759 + 0.423636i
\(772\) 0 0
\(773\) 14.8233 + 8.55826i 0.533158 + 0.307819i 0.742302 0.670066i \(-0.233734\pi\)
−0.209143 + 0.977885i \(0.567067\pi\)
\(774\) 0 0
\(775\) −6.81182 + 18.1894i −0.244688 + 0.653384i
\(776\) 0 0
\(777\) 110.754 + 29.6766i 3.97329 + 1.06464i
\(778\) 0 0
\(779\) 51.0231 1.82809
\(780\) 0 0
\(781\) 29.8880 1.06948
\(782\) 0 0
\(783\) 1.25970 + 0.337534i 0.0450179 + 0.0120625i
\(784\) 0 0
\(785\) 4.06828 + 2.61834i 0.145203 + 0.0934527i
\(786\) 0 0
\(787\) 12.5805 + 7.26333i 0.448445 + 0.258910i 0.707173 0.707040i \(-0.249970\pi\)
−0.258728 + 0.965950i \(0.583303\pi\)
\(788\) 0 0
\(789\) 43.2613 + 24.9769i 1.54014 + 0.889202i
\(790\) 0 0
\(791\) 10.2287 38.1741i 0.363691 1.35731i
\(792\) 0 0
\(793\) 10.4888 4.75324i 0.372469 0.168793i
\(794\) 0 0
\(795\) 19.7638 17.9425i 0.700949 0.636356i
\(796\) 0 0
\(797\) −12.4168 46.3403i −0.439827 1.64146i −0.729244 0.684253i \(-0.760128\pi\)
0.289418 0.957203i \(-0.406538\pi\)
\(798\) 0 0
\(799\) 14.4323 3.86712i 0.510577 0.136809i
\(800\) 0 0
\(801\) 25.2654 + 25.2654i 0.892708 + 0.892708i
\(802\) 0 0
\(803\) 3.93525 14.6866i 0.138872 0.518277i
\(804\) 0 0
\(805\) −8.83987 + 13.7351i −0.311564 + 0.484097i
\(806\) 0 0
\(807\) −38.4430 38.4430i −1.35326 1.35326i
\(808\) 0 0
\(809\) −39.5328 + 22.8242i −1.38990 + 0.802458i −0.993303 0.115536i \(-0.963141\pi\)
−0.396594 + 0.917994i \(0.629808\pi\)
\(810\) 0 0
\(811\) 35.2035 35.2035i 1.23616 1.23616i 0.274606 0.961557i \(-0.411452\pi\)
0.961557 0.274606i \(-0.0885475\pi\)
\(812\) 0 0
\(813\) 7.65136 13.2525i 0.268345 0.464787i
\(814\) 0 0
\(815\) 10.5181 32.8284i 0.368433 1.14993i
\(816\) 0 0
\(817\) 31.8138 18.3677i 1.11303 0.642606i
\(818\) 0 0
\(819\) −4.44563 + 45.1673i −0.155343 + 1.57827i
\(820\) 0 0
\(821\) 47.3788 + 12.6951i 1.65353 + 0.443062i 0.960599 0.277940i \(-0.0896515\pi\)
0.692933 + 0.721002i \(0.256318\pi\)
\(822\) 0 0
\(823\) 32.3492 8.66794i 1.12762 0.302145i 0.353658 0.935375i \(-0.384938\pi\)
0.773964 + 0.633230i \(0.218271\pi\)
\(824\) 0 0
\(825\) −5.47114 + 56.5037i −0.190481 + 1.96721i
\(826\) 0 0
\(827\) 0.102239i 0.00355520i −0.999998 0.00177760i \(-0.999434\pi\)
0.999998 0.00177760i \(-0.000565828\pi\)
\(828\) 0 0
\(829\) −21.0347 36.4332i −0.730567 1.26538i −0.956641 0.291268i \(-0.905923\pi\)
0.226075 0.974110i \(-0.427411\pi\)
\(830\) 0 0
\(831\) 49.4734i 1.71621i
\(832\) 0 0
\(833\) −28.8716 + 28.8716i −1.00034 + 1.00034i
\(834\) 0 0
\(835\) 23.3040 21.1565i 0.806467 0.732150i
\(836\) 0 0
\(837\) 2.55673 0.0883735
\(838\) 0 0
\(839\) 1.59501 + 5.95267i 0.0550660 + 0.205509i 0.987978 0.154596i \(-0.0494076\pi\)
−0.932912 + 0.360105i \(0.882741\pi\)
\(840\) 0 0
\(841\) −12.5369 + 21.7146i −0.432307 + 0.748778i
\(842\) 0 0
\(843\) −25.0571 43.4002i −0.863014 1.49478i
\(844\) 0 0
\(845\) −14.9682 24.9189i −0.514921 0.857238i
\(846\) 0 0
\(847\) −18.4820 32.0118i −0.635049 1.09994i
\(848\) 0 0
\(849\) −40.9454 + 70.9196i −1.40524 + 2.43395i
\(850\) 0 0
\(851\) 5.82058 + 21.7227i 0.199527 + 0.744645i
\(852\) 0 0
\(853\) −44.1436 −1.51145 −0.755724 0.654890i \(-0.772715\pi\)
−0.755724 + 0.654890i \(0.772715\pi\)
\(854\) 0 0
\(855\) −50.9531 2.46109i −1.74256 0.0841676i
\(856\) 0 0
\(857\) −24.9216 + 24.9216i −0.851305 + 0.851305i −0.990294 0.138989i \(-0.955615\pi\)
0.138989 + 0.990294i \(0.455615\pi\)
\(858\) 0 0
\(859\) 38.2383i 1.30467i 0.757929 + 0.652337i \(0.226211\pi\)
−0.757929 + 0.652337i \(0.773789\pi\)
\(860\) 0 0
\(861\) −35.2275 61.0158i −1.20055 2.07941i
\(862\) 0 0
\(863\) 0.948734i 0.0322953i 0.999870 + 0.0161476i \(0.00514018\pi\)
−0.999870 + 0.0161476i \(0.994860\pi\)
\(864\) 0 0
\(865\) 21.0461 10.8324i 0.715590 0.368311i
\(866\) 0 0
\(867\) 23.7748 6.37043i 0.807433 0.216351i
\(868\) 0 0
\(869\) −0.837690 0.224458i −0.0284167 0.00761423i
\(870\) 0 0
\(871\) 1.13416 11.5230i 0.0384296 0.390442i
\(872\) 0 0
\(873\) 17.7247 10.2334i 0.599890 0.346347i
\(874\) 0 0
\(875\) −42.8356 + 5.03514i −1.44811 + 0.170219i
\(876\) 0 0
\(877\) −20.8949 + 36.1910i −0.705569 + 1.22208i 0.260916 + 0.965361i \(0.415975\pi\)
−0.966486 + 0.256721i \(0.917358\pi\)
\(878\) 0 0
\(879\) 21.3338 21.3338i 0.719570 0.719570i
\(880\) 0 0
\(881\) 27.5194 15.8883i 0.927151 0.535291i 0.0412419 0.999149i \(-0.486869\pi\)
0.885910 + 0.463858i \(0.153535\pi\)
\(882\) 0 0
\(883\) 10.2531 + 10.2531i 0.345043 + 0.345043i 0.858259 0.513217i \(-0.171546\pi\)
−0.513217 + 0.858259i \(0.671546\pi\)
\(884\) 0 0
\(885\) −5.63297 25.9773i −0.189350 0.873218i
\(886\) 0 0
\(887\) −2.69367 + 10.0529i −0.0904447 + 0.337544i −0.996289 0.0860657i \(-0.972571\pi\)
0.905845 + 0.423610i \(0.139237\pi\)
\(888\) 0 0
\(889\) 17.9009 + 17.9009i 0.600377 + 0.600377i
\(890\) 0 0
\(891\) −35.6787 + 9.56008i −1.19528 + 0.320275i
\(892\) 0 0
\(893\) −5.21928 19.4786i −0.174657 0.651827i
\(894\) 0 0
\(895\) 23.8964 + 26.3220i 0.798768 + 0.879847i
\(896\) 0 0
\(897\) −15.5624 + 7.05246i −0.519614 + 0.235475i
\(898\) 0 0
\(899\) 1.99219 7.43494i 0.0664432 0.247969i
\(900\) 0 0
\(901\) 21.3999 + 12.3552i 0.712934 + 0.411613i
\(902\) 0 0
\(903\) −43.9300 25.3630i −1.46190 0.844028i
\(904\) 0 0
\(905\) −8.54170 39.3914i −0.283936 1.30942i
\(906\) 0 0
\(907\) −11.1887 2.99801i −0.371516 0.0995473i 0.0682301 0.997670i \(-0.478265\pi\)
−0.439746 + 0.898122i \(0.644931\pi\)
\(908\) 0 0
\(909\) −22.0359 −0.730885
\(910\) 0 0
\(911\) −16.9445 −0.561397 −0.280699 0.959796i \(-0.590566\pi\)
−0.280699 + 0.959796i \(0.590566\pi\)
\(912\) 0 0
\(913\) 32.8965 + 8.81460i 1.08872 + 0.291721i
\(914\) 0 0
\(915\) 9.67268 15.0291i 0.319769 0.496845i
\(916\) 0 0
\(917\) −30.2474 17.4633i −0.998857 0.576690i
\(918\) 0 0
\(919\) −2.13979 1.23541i −0.0705851 0.0407523i 0.464292 0.885682i \(-0.346309\pi\)
−0.534877 + 0.844930i \(0.679642\pi\)
\(920\) 0 0
\(921\) −16.5310 + 61.6947i −0.544717 + 2.03291i
\(922\) 0 0
\(923\) −8.36569 + 22.2315i −0.275360 + 0.731758i
\(924\) 0 0
\(925\) −34.5100 + 48.3267i −1.13468 + 1.58897i
\(926\) 0 0
\(927\) −8.56650 31.9706i −0.281361 1.05005i
\(928\) 0 0
\(929\) 6.19975 1.66122i 0.203407 0.0545028i −0.155677 0.987808i \(-0.549756\pi\)
0.359084 + 0.933305i \(0.383089\pi\)
\(930\) 0 0
\(931\) 38.9668 + 38.9668i 1.27709 + 1.27709i
\(932\) 0 0
\(933\) 12.3062 45.9275i 0.402888 1.50360i
\(934\) 0 0
\(935\) −51.3572 + 11.1364i −1.67956 + 0.364199i
\(936\) 0 0
\(937\) −29.9242 29.9242i −0.977581 0.977581i 0.0221727 0.999754i \(-0.492942\pi\)
−0.999754 + 0.0221727i \(0.992942\pi\)
\(938\) 0 0
\(939\) −49.8275 + 28.7679i −1.62606 + 0.938805i
\(940\) 0 0
\(941\) −10.0049 + 10.0049i −0.326150 + 0.326150i −0.851121 0.524970i \(-0.824076\pi\)
0.524970 + 0.851121i \(0.324076\pi\)
\(942\) 0 0
\(943\) 6.90931 11.9673i 0.224998 0.389708i
\(944\) 0 0
\(945\) 2.59820 + 5.04802i 0.0845194 + 0.164212i
\(946\) 0 0
\(947\) −8.33687 + 4.81329i −0.270912 + 0.156411i −0.629302 0.777161i \(-0.716659\pi\)
0.358390 + 0.933572i \(0.383326\pi\)
\(948\) 0 0
\(949\) 9.82279 + 7.03794i 0.318861 + 0.228461i
\(950\) 0 0
\(951\) −50.6241 13.5647i −1.64160 0.439865i
\(952\) 0 0
\(953\) 7.91919 2.12194i 0.256528 0.0687364i −0.128263 0.991740i \(-0.540940\pi\)
0.384791 + 0.923004i \(0.374274\pi\)
\(954\) 0 0
\(955\) −9.89469 + 30.8826i −0.320185 + 0.999338i
\(956\) 0 0
\(957\) 22.4967i 0.727215i
\(958\) 0 0
\(959\) −6.51143 11.2781i −0.210265 0.364190i
\(960\) 0 0
\(961\) 15.9097i 0.513218i
\(962\) 0 0
\(963\) −5.30831 + 5.30831i −0.171058 + 0.171058i
\(964\) 0 0
\(965\) 1.98624 + 2.18786i 0.0639394 + 0.0704296i
\(966\) 0 0
\(967\) 53.8159 1.73060 0.865301 0.501252i \(-0.167127\pi\)
0.865301 + 0.501252i \(0.167127\pi\)
\(968\) 0 0
\(969\) −23.4593 87.5513i −0.753621 2.81255i
\(970\) 0 0
\(971\) −28.7496 + 49.7958i −0.922619 + 1.59802i −0.127272 + 0.991868i \(0.540622\pi\)
−0.795347 + 0.606154i \(0.792711\pi\)
\(972\) 0 0
\(973\) 19.0142 + 32.9336i 0.609567 + 1.05580i
\(974\) 0 0
\(975\) −40.4976 19.8851i −1.29696 0.636832i
\(976\) 0 0
\(977\) −3.46271 5.99759i −0.110782 0.191880i 0.805304 0.592862i \(-0.202002\pi\)
−0.916086 + 0.400982i \(0.868669\pi\)
\(978\) 0 0
\(979\) 24.8391 43.0226i 0.793862 1.37501i
\(980\) 0 0
\(981\) 1.95172 + 7.28393i 0.0623138 + 0.232558i
\(982\) 0 0
\(983\) −33.9827 −1.08388 −0.541941 0.840417i \(-0.682310\pi\)
−0.541941 + 0.840417i \(0.682310\pi\)
\(984\) 0 0
\(985\) −20.9249 23.0489i −0.666723 0.734399i
\(986\) 0 0
\(987\) −19.6900 + 19.6900i −0.626738 + 0.626738i
\(988\) 0 0
\(989\) 9.94909i 0.316363i
\(990\) 0 0
\(991\) −7.93170 13.7381i −0.251959 0.436405i 0.712106 0.702072i \(-0.247741\pi\)
−0.964065 + 0.265666i \(0.914408\pi\)
\(992\) 0 0
\(993\) 24.6315i 0.781656i
\(994\) 0 0
\(995\) −9.19056 + 28.6849i −0.291360 + 0.909373i
\(996\) 0 0
\(997\) 19.5993 5.25161i 0.620715 0.166320i 0.0652620 0.997868i \(-0.479212\pi\)
0.555453 + 0.831548i \(0.312545\pi\)
\(998\) 0 0
\(999\) 7.55051 + 2.02315i 0.238888 + 0.0640098i
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 260.2.bk.c.197.2 yes 20
5.2 odd 4 1300.2.bn.d.93.2 20
5.3 odd 4 260.2.bf.c.93.4 20
5.4 even 2 1300.2.bs.d.457.4 20
13.7 odd 12 260.2.bf.c.137.4 yes 20
65.7 even 12 1300.2.bs.d.293.4 20
65.33 even 12 inner 260.2.bk.c.33.2 yes 20
65.59 odd 12 1300.2.bn.d.657.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
260.2.bf.c.93.4 20 5.3 odd 4
260.2.bf.c.137.4 yes 20 13.7 odd 12
260.2.bk.c.33.2 yes 20 65.33 even 12 inner
260.2.bk.c.197.2 yes 20 1.1 even 1 trivial
1300.2.bn.d.93.2 20 5.2 odd 4
1300.2.bn.d.657.2 20 65.59 odd 12
1300.2.bs.d.293.4 20 65.7 even 12
1300.2.bs.d.457.4 20 5.4 even 2