Properties

Label 756.2.bx.a.41.7
Level $756$
Weight $2$
Character 756.41
Analytic conductor $6.037$
Analytic rank $0$
Dimension $144$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [756,2,Mod(41,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 17, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.bx (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 41.7
Character \(\chi\) \(=\) 756.41
Dual form 756.2.bx.a.461.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.885631 + 1.48851i) q^{3} +(0.580812 + 0.487359i) q^{5} +(-1.90191 + 1.83923i) q^{7} +(-1.43132 - 2.63654i) q^{9} +O(q^{10})\) \(q+(-0.885631 + 1.48851i) q^{3} +(0.580812 + 0.487359i) q^{5} +(-1.90191 + 1.83923i) q^{7} +(-1.43132 - 2.63654i) q^{9} +(2.03560 + 2.42593i) q^{11} +(-3.63164 - 0.640357i) q^{13} +(-1.23982 + 0.432924i) q^{15} +(-1.64486 + 2.84899i) q^{17} +(0.322117 - 0.185975i) q^{19} +(-1.05332 - 4.45988i) q^{21} +(-1.58709 - 4.36050i) q^{23} +(-0.768417 - 4.35791i) q^{25} +(5.19213 + 0.204470i) q^{27} +(-10.5919 + 1.86764i) q^{29} +(2.98491 + 8.20097i) q^{31} +(-5.41381 + 0.881527i) q^{33} +(-2.00101 + 0.141333i) q^{35} +(-2.91021 + 5.04063i) q^{37} +(4.16947 - 4.83861i) q^{39} +(1.27317 - 7.22051i) q^{41} +(5.33314 - 4.47504i) q^{43} +(0.453615 - 2.22890i) q^{45} +(-9.81459 - 3.57222i) q^{47} +(0.234493 - 6.99607i) q^{49} +(-2.78400 - 4.97154i) q^{51} -2.23537i q^{53} +2.40108i q^{55} +(-0.00845222 + 0.644179i) q^{57} +(-7.93795 - 6.66073i) q^{59} +(-3.02231 + 8.30373i) q^{61} +(7.57142 + 2.38193i) q^{63} +(-1.79722 - 2.14184i) q^{65} +(-1.68948 + 9.58153i) q^{67} +(7.89622 + 1.49939i) q^{69} +(6.78533 + 3.91751i) q^{71} +(-8.24898 + 4.76255i) q^{73} +(7.16732 + 2.71570i) q^{75} +(-8.33336 - 0.869968i) q^{77} +(-0.249457 - 1.41474i) q^{79} +(-4.90266 + 7.54744i) q^{81} +(0.0799053 + 0.453166i) q^{83} +(-2.34384 + 0.853087i) q^{85} +(6.60053 - 17.4202i) q^{87} +(-2.54964 - 4.41610i) q^{89} +(8.08481 - 5.46152i) q^{91} +(-14.8507 - 2.81997i) q^{93} +(0.277726 + 0.0489706i) q^{95} +(2.99639 + 3.57096i) q^{97} +(3.48247 - 8.83921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(-1\) \(1\)

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
\(3\) −0.885631 + 1.48851i −0.511319 + 0.859391i
\(4\) 0 0
\(5\) 0.580812 + 0.487359i 0.259747 + 0.217954i 0.763356 0.645978i \(-0.223550\pi\)
−0.503609 + 0.863932i \(0.667995\pi\)
\(6\) 0 0
\(7\) −1.90191 + 1.83923i −0.718853 + 0.695162i
\(8\) 0 0
\(9\) −1.43132 2.63654i −0.477106 0.878846i
\(10\) 0 0
\(11\) 2.03560 + 2.42593i 0.613756 + 0.731446i 0.979983 0.199079i \(-0.0637951\pi\)
−0.366227 + 0.930525i \(0.619351\pi\)
\(12\) 0 0
\(13\) −3.63164 0.640357i −1.00724 0.177603i −0.354394 0.935096i \(-0.615313\pi\)
−0.652843 + 0.757493i \(0.726424\pi\)
\(14\) 0 0
\(15\) −1.23982 + 0.432924i −0.320121 + 0.111780i
\(16\) 0 0
\(17\) −1.64486 + 2.84899i −0.398938 + 0.690981i −0.993595 0.112998i \(-0.963954\pi\)
0.594657 + 0.803979i \(0.297288\pi\)
\(18\) 0 0
\(19\) 0.322117 0.185975i 0.0738988 0.0426655i −0.462595 0.886570i \(-0.653082\pi\)
0.536494 + 0.843904i \(0.319748\pi\)
\(20\) 0 0
\(21\) −1.05332 4.45988i −0.229853 0.973225i
\(22\) 0 0
\(23\) −1.58709 4.36050i −0.330931 0.909227i −0.987870 0.155283i \(-0.950371\pi\)
0.656939 0.753944i \(-0.271851\pi\)
\(24\) 0 0
\(25\) −0.768417 4.35791i −0.153683 0.871582i
\(26\) 0 0
\(27\) 5.19213 + 0.204470i 0.999225 + 0.0393503i
\(28\) 0 0
\(29\) −10.5919 + 1.86764i −1.96687 + 0.346812i −0.974271 + 0.225381i \(0.927637\pi\)
−0.992600 + 0.121431i \(0.961252\pi\)
\(30\) 0 0
\(31\) 2.98491 + 8.20097i 0.536106 + 1.47294i 0.851693 + 0.524042i \(0.175576\pi\)
−0.315587 + 0.948897i \(0.602201\pi\)
\(32\) 0 0
\(33\) −5.41381 + 0.881527i −0.942423 + 0.153454i
\(34\) 0 0
\(35\) −2.00101 + 0.141333i −0.338233 + 0.0238897i
\(36\) 0 0
\(37\) −2.91021 + 5.04063i −0.478435 + 0.828674i −0.999694 0.0247245i \(-0.992129\pi\)
0.521259 + 0.853398i \(0.325462\pi\)
\(38\) 0 0
\(39\) 4.16947 4.83861i 0.667650 0.774798i
\(40\) 0 0
\(41\) 1.27317 7.22051i 0.198836 1.12765i −0.708013 0.706199i \(-0.750408\pi\)
0.906849 0.421456i \(-0.138481\pi\)
\(42\) 0 0
\(43\) 5.33314 4.47504i 0.813296 0.682437i −0.138096 0.990419i \(-0.544098\pi\)
0.951392 + 0.307982i \(0.0996538\pi\)
\(44\) 0 0
\(45\) 0.453615 2.22890i 0.0676209 0.332264i
\(46\) 0 0
\(47\) −9.81459 3.57222i −1.43160 0.521062i −0.494214 0.869340i \(-0.664544\pi\)
−0.937391 + 0.348279i \(0.886766\pi\)
\(48\) 0 0
\(49\) 0.234493 6.99607i 0.0334990 0.999439i
\(50\) 0 0
\(51\) −2.78400 4.97154i −0.389838 0.696155i
\(52\) 0 0
\(53\) 2.23537i 0.307052i −0.988145 0.153526i \(-0.950937\pi\)
0.988145 0.153526i \(-0.0490629\pi\)
\(54\) 0 0
\(55\) 2.40108i 0.323761i
\(56\) 0 0
\(57\) −0.00845222 + 0.644179i −0.00111952 + 0.0853236i
\(58\) 0 0
\(59\) −7.93795 6.66073i −1.03343 0.867153i −0.0421777 0.999110i \(-0.513430\pi\)
−0.991255 + 0.131957i \(0.957874\pi\)
\(60\) 0 0
\(61\) −3.02231 + 8.30373i −0.386967 + 1.06318i 0.581392 + 0.813623i \(0.302508\pi\)
−0.968359 + 0.249560i \(0.919714\pi\)
\(62\) 0 0
\(63\) 7.57142 + 2.38193i 0.953909 + 0.300095i
\(64\) 0 0
\(65\) −1.79722 2.14184i −0.222917 0.265663i
\(66\) 0 0
\(67\) −1.68948 + 9.58153i −0.206403 + 1.17057i 0.688814 + 0.724939i \(0.258132\pi\)
−0.895217 + 0.445631i \(0.852979\pi\)
\(68\) 0 0
\(69\) 7.89622 + 1.49939i 0.950593 + 0.180505i
\(70\) 0 0
\(71\) 6.78533 + 3.91751i 0.805271 + 0.464923i 0.845311 0.534275i \(-0.179415\pi\)
−0.0400400 + 0.999198i \(0.512749\pi\)
\(72\) 0 0
\(73\) −8.24898 + 4.76255i −0.965470 + 0.557414i −0.897852 0.440297i \(-0.854873\pi\)
−0.0676176 + 0.997711i \(0.521540\pi\)
\(74\) 0 0
\(75\) 7.16732 + 2.71570i 0.827611 + 0.313582i
\(76\) 0 0
\(77\) −8.33336 0.869968i −0.949674 0.0991421i
\(78\) 0 0
\(79\) −0.249457 1.41474i −0.0280661 0.159171i 0.967554 0.252666i \(-0.0813073\pi\)
−0.995620 + 0.0934947i \(0.970196\pi\)
\(80\) 0 0
\(81\) −4.90266 + 7.54744i −0.544740 + 0.838605i
\(82\) 0 0
\(83\) 0.0799053 + 0.453166i 0.00877075 + 0.0497414i 0.988879 0.148722i \(-0.0475160\pi\)
−0.980108 + 0.198463i \(0.936405\pi\)
\(84\) 0 0
\(85\) −2.34384 + 0.853087i −0.254225 + 0.0925302i
\(86\) 0 0
\(87\) 6.60053 17.4202i 0.707651 1.86764i
\(88\) 0 0
\(89\) −2.54964 4.41610i −0.270261 0.468106i 0.698668 0.715446i \(-0.253777\pi\)
−0.968929 + 0.247341i \(0.920443\pi\)
\(90\) 0 0
\(91\) 8.08481 5.46152i 0.847518 0.572522i
\(92\) 0 0
\(93\) −14.8507 2.81997i −1.53995 0.292417i
\(94\) 0 0
\(95\) 0.277726 + 0.0489706i 0.0284941 + 0.00502428i
\(96\) 0 0
\(97\) 2.99639 + 3.57096i 0.304238 + 0.362576i 0.896403 0.443240i \(-0.146171\pi\)
−0.592165 + 0.805817i \(0.701727\pi\)
\(98\) 0 0
\(99\) 3.48247 8.83921i 0.350002 0.888374i
\(100\) 0 0
\(101\) 7.14051 + 2.59893i 0.710507 + 0.258603i 0.671890 0.740651i \(-0.265483\pi\)
0.0386167 + 0.999254i \(0.487705\pi\)
\(102\) 0 0
\(103\) −8.98237 + 10.7048i −0.885059 + 1.05477i 0.113068 + 0.993587i \(0.463932\pi\)
−0.998126 + 0.0611847i \(0.980512\pi\)
\(104\) 0 0
\(105\) 1.56178 3.10370i 0.152414 0.302890i
\(106\) 0 0
\(107\) 14.1706i 1.36993i 0.728577 + 0.684963i \(0.240182\pi\)
−0.728577 + 0.684963i \(0.759818\pi\)
\(108\) 0 0
\(109\) 18.1324 1.73677 0.868384 0.495892i \(-0.165159\pi\)
0.868384 + 0.495892i \(0.165159\pi\)
\(110\) 0 0
\(111\) −4.92565 8.79600i −0.467522 0.834880i
\(112\) 0 0
\(113\) −2.80894 + 3.34756i −0.264243 + 0.314912i −0.881809 0.471607i \(-0.843674\pi\)
0.617566 + 0.786519i \(0.288119\pi\)
\(114\) 0 0
\(115\) 1.20333 3.30611i 0.112211 0.308297i
\(116\) 0 0
\(117\) 3.50971 + 10.4915i 0.324473 + 0.969941i
\(118\) 0 0
\(119\) −2.11156 8.44378i −0.193566 0.774040i
\(120\) 0 0
\(121\) 0.168645 0.956433i 0.0153314 0.0869485i
\(122\) 0 0
\(123\) 9.62024 + 8.28983i 0.867428 + 0.747469i
\(124\) 0 0
\(125\) 3.57305 6.18871i 0.319583 0.553535i
\(126\) 0 0
\(127\) 9.97682 + 17.2804i 0.885300 + 1.53338i 0.845370 + 0.534181i \(0.179380\pi\)
0.0399295 + 0.999202i \(0.487287\pi\)
\(128\) 0 0
\(129\) 1.93794 + 11.9017i 0.170626 + 1.04788i
\(130\) 0 0
\(131\) −10.4263 + 3.79485i −0.910947 + 0.331557i −0.754631 0.656150i \(-0.772184\pi\)
−0.156316 + 0.987707i \(0.549962\pi\)
\(132\) 0 0
\(133\) −0.270588 + 0.946153i −0.0234629 + 0.0820418i
\(134\) 0 0
\(135\) 2.91600 + 2.64919i 0.250969 + 0.228006i
\(136\) 0 0
\(137\) 5.88144 1.03706i 0.502485 0.0886017i 0.0833406 0.996521i \(-0.473441\pi\)
0.419145 + 0.907919i \(0.362330\pi\)
\(138\) 0 0
\(139\) 2.14512 + 5.89367i 0.181947 + 0.499895i 0.996815 0.0797520i \(-0.0254128\pi\)
−0.814868 + 0.579647i \(0.803191\pi\)
\(140\) 0 0
\(141\) 14.0094 11.4454i 1.17980 0.963880i
\(142\) 0 0
\(143\) −5.83911 10.1136i −0.488291 0.845744i
\(144\) 0 0
\(145\) −7.06213 4.07732i −0.586478 0.338603i
\(146\) 0 0
\(147\) 10.2060 + 6.54498i 0.841780 + 0.539821i
\(148\) 0 0
\(149\) 9.52983 + 1.68037i 0.780714 + 0.137661i 0.549781 0.835309i \(-0.314711\pi\)
0.230933 + 0.972970i \(0.425822\pi\)
\(150\) 0 0
\(151\) 3.33262 2.79640i 0.271205 0.227568i −0.497034 0.867731i \(-0.665578\pi\)
0.768239 + 0.640163i \(0.221133\pi\)
\(152\) 0 0
\(153\) 9.86578 + 0.258941i 0.797601 + 0.0209341i
\(154\) 0 0
\(155\) −2.26315 + 6.21795i −0.181780 + 0.499437i
\(156\) 0 0
\(157\) −1.14269 + 1.36181i −0.0911967 + 0.108684i −0.809713 0.586826i \(-0.800377\pi\)
0.718516 + 0.695510i \(0.244822\pi\)
\(158\) 0 0
\(159\) 3.32737 + 1.97971i 0.263878 + 0.157001i
\(160\) 0 0
\(161\) 11.0384 + 5.37424i 0.869951 + 0.423549i
\(162\) 0 0
\(163\) 14.6403 1.14672 0.573359 0.819304i \(-0.305640\pi\)
0.573359 + 0.819304i \(0.305640\pi\)
\(164\) 0 0
\(165\) −3.57403 2.12647i −0.278238 0.165545i
\(166\) 0 0
\(167\) 5.85974 + 4.91691i 0.453441 + 0.380482i 0.840711 0.541484i \(-0.182138\pi\)
−0.387270 + 0.921966i \(0.626582\pi\)
\(168\) 0 0
\(169\) 0.562775 + 0.204833i 0.0432904 + 0.0157564i
\(170\) 0 0
\(171\) −0.951381 0.583086i −0.0727539 0.0445897i
\(172\) 0 0
\(173\) −14.0203 + 11.7644i −1.06594 + 0.894432i −0.994679 0.103026i \(-0.967148\pi\)
−0.0712635 + 0.997458i \(0.522703\pi\)
\(174\) 0 0
\(175\) 9.47664 + 6.87504i 0.716367 + 0.519704i
\(176\) 0 0
\(177\) 16.9446 5.91676i 1.27364 0.444731i
\(178\) 0 0
\(179\) 15.2922 + 8.82896i 1.14299 + 0.659907i 0.947170 0.320732i \(-0.103929\pi\)
0.195823 + 0.980639i \(0.437262\pi\)
\(180\) 0 0
\(181\) 19.6886 11.3672i 1.46344 0.844920i 0.464276 0.885691i \(-0.346315\pi\)
0.999169 + 0.0407705i \(0.0129812\pi\)
\(182\) 0 0
\(183\) −9.68352 11.8528i −0.715827 0.876182i
\(184\) 0 0
\(185\) −4.14688 + 1.50934i −0.304885 + 0.110969i
\(186\) 0 0
\(187\) −10.2597 + 1.80907i −0.750266 + 0.132292i
\(188\) 0 0
\(189\) −10.2510 + 9.16062i −0.745651 + 0.666337i
\(190\) 0 0
\(191\) −22.7735 + 4.01558i −1.64783 + 0.290557i −0.919036 0.394175i \(-0.871031\pi\)
−0.728795 + 0.684732i \(0.759919\pi\)
\(192\) 0 0
\(193\) −12.7613 + 4.64473i −0.918578 + 0.334335i −0.757673 0.652635i \(-0.773664\pi\)
−0.160905 + 0.986970i \(0.551441\pi\)
\(194\) 0 0
\(195\) 4.77982 0.778295i 0.342290 0.0557349i
\(196\) 0 0
\(197\) −13.5242 + 7.80820i −0.963560 + 0.556311i −0.897267 0.441489i \(-0.854450\pi\)
−0.0662928 + 0.997800i \(0.521117\pi\)
\(198\) 0 0
\(199\) 5.52621 + 3.19056i 0.391743 + 0.226173i 0.682915 0.730498i \(-0.260712\pi\)
−0.291172 + 0.956671i \(0.594045\pi\)
\(200\) 0 0
\(201\) −12.7659 11.0005i −0.900439 0.775916i
\(202\) 0 0
\(203\) 16.7098 23.0330i 1.17280 1.61660i
\(204\) 0 0
\(205\) 4.25846 3.57327i 0.297423 0.249568i
\(206\) 0 0
\(207\) −9.22499 + 10.4257i −0.641181 + 0.724635i
\(208\) 0 0
\(209\) 1.10686 + 0.402865i 0.0765633 + 0.0278668i
\(210\) 0 0
\(211\) 17.6446 + 14.8056i 1.21470 + 1.01926i 0.999084 + 0.0427808i \(0.0136217\pi\)
0.215620 + 0.976477i \(0.430823\pi\)
\(212\) 0 0
\(213\) −11.8406 + 6.63056i −0.811301 + 0.454318i
\(214\) 0 0
\(215\) 5.27850 0.359991
\(216\) 0 0
\(217\) −20.7605 10.1076i −1.40931 0.686146i
\(218\) 0 0
\(219\) 0.216450 16.4965i 0.0146263 1.11473i
\(220\) 0 0
\(221\) 7.79793 9.29321i 0.524545 0.625129i
\(222\) 0 0
\(223\) −1.29796 + 3.56610i −0.0869176 + 0.238804i −0.975535 0.219846i \(-0.929445\pi\)
0.888617 + 0.458650i \(0.151667\pi\)
\(224\) 0 0
\(225\) −10.3899 + 8.26351i −0.692663 + 0.550901i
\(226\) 0 0
\(227\) 6.50525 5.45855i 0.431769 0.362297i −0.400850 0.916144i \(-0.631285\pi\)
0.832619 + 0.553847i \(0.186841\pi\)
\(228\) 0 0
\(229\) 8.95145 + 1.57838i 0.591529 + 0.104302i 0.461396 0.887194i \(-0.347349\pi\)
0.130132 + 0.991497i \(0.458460\pi\)
\(230\) 0 0
\(231\) 8.67523 11.6338i 0.570788 0.765448i
\(232\) 0 0
\(233\) −1.89811 1.09588i −0.124350 0.0717932i 0.436535 0.899687i \(-0.356206\pi\)
−0.560885 + 0.827894i \(0.689539\pi\)
\(234\) 0 0
\(235\) −3.95948 6.85802i −0.258288 0.447368i
\(236\) 0 0
\(237\) 2.32678 + 0.881620i 0.151141 + 0.0572674i
\(238\) 0 0
\(239\) −0.443055 1.21728i −0.0286588 0.0787395i 0.924538 0.381090i \(-0.124451\pi\)
−0.953197 + 0.302350i \(0.902229\pi\)
\(240\) 0 0
\(241\) −14.8370 + 2.61616i −0.955733 + 0.168521i −0.629701 0.776837i \(-0.716823\pi\)
−0.326031 + 0.945359i \(0.605712\pi\)
\(242\) 0 0
\(243\) −6.89249 13.9819i −0.442153 0.896939i
\(244\) 0 0
\(245\) 3.54580 3.94912i 0.226533 0.252300i
\(246\) 0 0
\(247\) −1.28891 + 0.469123i −0.0820111 + 0.0298496i
\(248\) 0 0
\(249\) −0.745308 0.282398i −0.0472320 0.0178962i
\(250\) 0 0
\(251\) −10.9824 19.0220i −0.693201 1.20066i −0.970783 0.239958i \(-0.922866\pi\)
0.277582 0.960702i \(-0.410467\pi\)
\(252\) 0 0
\(253\) 7.34759 12.7264i 0.461939 0.800102i
\(254\) 0 0
\(255\) 0.805946 4.24434i 0.0504703 0.265791i
\(256\) 0 0
\(257\) 0.495949 2.81267i 0.0309365 0.175449i −0.965425 0.260683i \(-0.916052\pi\)
0.996361 + 0.0852332i \(0.0271635\pi\)
\(258\) 0 0
\(259\) −3.73591 14.9393i −0.232138 0.928285i
\(260\) 0 0
\(261\) 20.0845 + 25.2528i 1.24320 + 1.56311i
\(262\) 0 0
\(263\) −2.49305 + 6.84959i −0.153728 + 0.422364i −0.992519 0.122089i \(-0.961041\pi\)
0.838791 + 0.544453i \(0.183263\pi\)
\(264\) 0 0
\(265\) 1.08943 1.29833i 0.0669231 0.0797558i
\(266\) 0 0
\(267\) 8.83144 + 0.115877i 0.540475 + 0.00709153i
\(268\) 0 0
\(269\) 13.7990 0.841341 0.420670 0.907214i \(-0.361795\pi\)
0.420670 + 0.907214i \(0.361795\pi\)
\(270\) 0 0
\(271\) 6.87579i 0.417675i −0.977950 0.208837i \(-0.933032\pi\)
0.977950 0.208837i \(-0.0669679\pi\)
\(272\) 0 0
\(273\) 0.969364 + 16.8712i 0.0586686 + 1.02109i
\(274\) 0 0
\(275\) 9.00781 10.7351i 0.543191 0.647350i
\(276\) 0 0
\(277\) −24.4022 8.88168i −1.46619 0.533649i −0.519125 0.854698i \(-0.673742\pi\)
−0.947062 + 0.321049i \(0.895964\pi\)
\(278\) 0 0
\(279\) 17.3498 19.6080i 1.03871 1.17390i
\(280\) 0 0
\(281\) −10.8817 12.9683i −0.649150 0.773627i 0.336636 0.941635i \(-0.390711\pi\)
−0.985786 + 0.168008i \(0.946266\pi\)
\(282\) 0 0
\(283\) −7.55158 1.33155i −0.448895 0.0791522i −0.0553692 0.998466i \(-0.517634\pi\)
−0.393525 + 0.919314i \(0.628745\pi\)
\(284\) 0 0
\(285\) −0.318856 + 0.370028i −0.0188874 + 0.0219185i
\(286\) 0 0
\(287\) 10.8587 + 16.0744i 0.640969 + 0.948841i
\(288\) 0 0
\(289\) 3.08885 + 5.35004i 0.181697 + 0.314708i
\(290\) 0 0
\(291\) −7.96910 + 1.29760i −0.467157 + 0.0760669i
\(292\) 0 0
\(293\) 0.905744 0.329664i 0.0529142 0.0192592i −0.315427 0.948950i \(-0.602148\pi\)
0.368342 + 0.929691i \(0.379926\pi\)
\(294\) 0 0
\(295\) −1.36429 7.73726i −0.0794319 0.450481i
\(296\) 0 0
\(297\) 10.0731 + 13.0120i 0.584498 + 0.755031i
\(298\) 0 0
\(299\) 2.97148 + 16.8521i 0.171845 + 0.974581i
\(300\) 0 0
\(301\) −1.91253 + 18.3199i −0.110236 + 1.05594i
\(302\) 0 0
\(303\) −10.1924 + 8.32701i −0.585537 + 0.478374i
\(304\) 0 0
\(305\) −5.80229 + 3.34995i −0.332238 + 0.191818i
\(306\) 0 0
\(307\) 1.50572 + 0.869326i 0.0859358 + 0.0496151i 0.542352 0.840151i \(-0.317534\pi\)
−0.456416 + 0.889766i \(0.650867\pi\)
\(308\) 0 0
\(309\) −7.97908 22.8508i −0.453914 1.29994i
\(310\) 0 0
\(311\) −5.38235 + 30.5248i −0.305205 + 1.73090i 0.317334 + 0.948314i \(0.397213\pi\)
−0.622538 + 0.782589i \(0.713899\pi\)
\(312\) 0 0
\(313\) −8.97130 10.6916i −0.507088 0.604324i 0.450389 0.892832i \(-0.351285\pi\)
−0.957477 + 0.288508i \(0.906841\pi\)
\(314\) 0 0
\(315\) 3.23672 + 5.07345i 0.182368 + 0.285857i
\(316\) 0 0
\(317\) 0.819774 2.25231i 0.0460431 0.126502i −0.914540 0.404496i \(-0.867447\pi\)
0.960583 + 0.277993i \(0.0896693\pi\)
\(318\) 0 0
\(319\) −26.0917 21.8935i −1.46085 1.22580i
\(320\) 0 0
\(321\) −21.0931 12.5499i −1.17730 0.700470i
\(322\) 0 0
\(323\) 1.22361i 0.0680835i
\(324\) 0 0
\(325\) 16.3184i 0.905184i
\(326\) 0 0
\(327\) −16.0586 + 26.9902i −0.888043 + 1.49256i
\(328\) 0 0
\(329\) 25.2365 11.2572i 1.39134 0.620631i
\(330\) 0 0
\(331\) −8.54493 3.11010i −0.469672 0.170947i 0.0963319 0.995349i \(-0.469289\pi\)
−0.566004 + 0.824403i \(0.691511\pi\)
\(332\) 0 0
\(333\) 17.4552 + 0.458136i 0.956541 + 0.0251057i
\(334\) 0 0
\(335\) −5.65092 + 4.74168i −0.308742 + 0.259066i
\(336\) 0 0
\(337\) −2.82194 + 16.0040i −0.153721 + 0.871793i 0.806225 + 0.591608i \(0.201507\pi\)
−0.959946 + 0.280185i \(0.909604\pi\)
\(338\) 0 0
\(339\) −2.49520 7.14583i −0.135520 0.388108i
\(340\) 0 0
\(341\) −13.8189 + 23.9351i −0.748337 + 1.29616i
\(342\) 0 0
\(343\) 12.4214 + 13.7372i 0.670691 + 0.741737i
\(344\) 0 0
\(345\) 3.85547 + 4.71916i 0.207572 + 0.254071i
\(346\) 0 0
\(347\) −9.78183 26.8754i −0.525116 1.44275i −0.864757 0.502190i \(-0.832528\pi\)
0.339641 0.940555i \(-0.389694\pi\)
\(348\) 0 0
\(349\) 6.58677 1.16143i 0.352582 0.0621697i 0.00544760 0.999985i \(-0.498266\pi\)
0.347134 + 0.937815i \(0.387155\pi\)
\(350\) 0 0
\(351\) −18.7250 4.06738i −0.999468 0.217101i
\(352\) 0 0
\(353\) 0.525929 + 2.98269i 0.0279924 + 0.158753i 0.995600 0.0937069i \(-0.0298717\pi\)
−0.967607 + 0.252460i \(0.918761\pi\)
\(354\) 0 0
\(355\) 2.03177 + 5.58223i 0.107835 + 0.296274i
\(356\) 0 0
\(357\) 14.4387 + 4.33500i 0.764177 + 0.229433i
\(358\) 0 0
\(359\) −10.7244 + 6.19172i −0.566011 + 0.326787i −0.755555 0.655086i \(-0.772633\pi\)
0.189544 + 0.981872i \(0.439299\pi\)
\(360\) 0 0
\(361\) −9.43083 + 16.3347i −0.496359 + 0.859720i
\(362\) 0 0
\(363\) 1.27430 + 1.09808i 0.0668835 + 0.0576341i
\(364\) 0 0
\(365\) −7.11218 1.25407i −0.372268 0.0656409i
\(366\) 0 0
\(367\) −0.689314 0.821493i −0.0359819 0.0428816i 0.747753 0.663977i \(-0.231133\pi\)
−0.783735 + 0.621095i \(0.786688\pi\)
\(368\) 0 0
\(369\) −20.8595 + 6.97808i −1.08590 + 0.363264i
\(370\) 0 0
\(371\) 4.11135 + 4.25147i 0.213451 + 0.220725i
\(372\) 0 0
\(373\) 5.67292 + 4.76015i 0.293733 + 0.246471i 0.777730 0.628598i \(-0.216371\pi\)
−0.483997 + 0.875070i \(0.660816\pi\)
\(374\) 0 0
\(375\) 6.04754 + 10.7994i 0.312294 + 0.557680i
\(376\) 0 0
\(377\) 39.6620 2.04270
\(378\) 0 0
\(379\) 26.9337 1.38349 0.691745 0.722142i \(-0.256842\pi\)
0.691745 + 0.722142i \(0.256842\pi\)
\(380\) 0 0
\(381\) −34.5577 0.453429i −1.77045 0.0232299i
\(382\) 0 0
\(383\) −26.6839 22.3904i −1.36348 1.14410i −0.974890 0.222689i \(-0.928517\pi\)
−0.388593 0.921409i \(-0.627039\pi\)
\(384\) 0 0
\(385\) −4.41613 4.56663i −0.225067 0.232737i
\(386\) 0 0
\(387\) −19.4320 7.65583i −0.987785 0.389168i
\(388\) 0 0
\(389\) −13.0365 15.5363i −0.660977 0.787722i 0.326548 0.945181i \(-0.394114\pi\)
−0.987526 + 0.157458i \(0.949670\pi\)
\(390\) 0 0
\(391\) 15.0336 + 2.65082i 0.760279 + 0.134058i
\(392\) 0 0
\(393\) 3.58515 18.8804i 0.180847 0.952391i
\(394\) 0 0
\(395\) 0.544600 0.943275i 0.0274018 0.0474613i
\(396\) 0 0
\(397\) −7.02081 + 4.05347i −0.352364 + 0.203438i −0.665726 0.746196i \(-0.731878\pi\)
0.313362 + 0.949634i \(0.398545\pi\)
\(398\) 0 0
\(399\) −1.16872 1.24071i −0.0585090 0.0621134i
\(400\) 0 0
\(401\) −1.96007 5.38524i −0.0978811 0.268926i 0.881082 0.472964i \(-0.156816\pi\)
−0.978963 + 0.204037i \(0.934594\pi\)
\(402\) 0 0
\(403\) −5.58858 31.6944i −0.278387 1.57881i
\(404\) 0 0
\(405\) −6.52584 + 1.99429i −0.324272 + 0.0990970i
\(406\) 0 0
\(407\) −18.1522 + 3.20073i −0.899773 + 0.158654i
\(408\) 0 0
\(409\) −10.2787 28.2404i −0.508247 1.39640i −0.883044 0.469290i \(-0.844510\pi\)
0.374797 0.927107i \(-0.377712\pi\)
\(410\) 0 0
\(411\) −3.66512 + 9.67303i −0.180787 + 0.477135i
\(412\) 0 0
\(413\) 27.3478 1.93160i 1.34570 0.0950479i
\(414\) 0 0
\(415\) −0.174444 + 0.302147i −0.00856314 + 0.0148318i
\(416\) 0 0
\(417\) −10.6726 2.02658i −0.522638 0.0992422i
\(418\) 0 0
\(419\) −2.02546 + 11.4870i −0.0989504 + 0.561176i 0.894515 + 0.447039i \(0.147521\pi\)
−0.993465 + 0.114137i \(0.963590\pi\)
\(420\) 0 0
\(421\) 0.622585 0.522411i 0.0303429 0.0254608i −0.627490 0.778625i \(-0.715918\pi\)
0.657833 + 0.753164i \(0.271473\pi\)
\(422\) 0 0
\(423\) 4.62950 + 30.9895i 0.225094 + 1.50676i
\(424\) 0 0
\(425\) 13.6796 + 4.97896i 0.663557 + 0.241515i
\(426\) 0 0
\(427\) −9.52429 21.3516i −0.460913 1.03328i
\(428\) 0 0
\(429\) 20.2255 + 0.265377i 0.976497 + 0.0128125i
\(430\) 0 0
\(431\) 17.3542i 0.835924i −0.908465 0.417962i \(-0.862745\pi\)
0.908465 0.417962i \(-0.137255\pi\)
\(432\) 0 0
\(433\) 30.4315i 1.46245i −0.682139 0.731223i \(-0.738950\pi\)
0.682139 0.731223i \(-0.261050\pi\)
\(434\) 0 0
\(435\) 12.3236 6.90104i 0.590870 0.330879i
\(436\) 0 0
\(437\) −1.32217 1.10943i −0.0632480 0.0530714i
\(438\) 0 0
\(439\) −9.18800 + 25.2438i −0.438519 + 1.20482i 0.501936 + 0.864905i \(0.332621\pi\)
−0.940455 + 0.339917i \(0.889601\pi\)
\(440\) 0 0
\(441\) −18.7810 + 9.39535i −0.894335 + 0.447397i
\(442\) 0 0
\(443\) 7.22306 + 8.60810i 0.343178 + 0.408983i 0.909835 0.414970i \(-0.136208\pi\)
−0.566657 + 0.823954i \(0.691764\pi\)
\(444\) 0 0
\(445\) 0.671367 3.80751i 0.0318259 0.180493i
\(446\) 0 0
\(447\) −10.9412 + 12.6971i −0.517499 + 0.600550i
\(448\) 0 0
\(449\) 3.02045 + 1.74385i 0.142544 + 0.0822976i 0.569576 0.821939i \(-0.307108\pi\)
−0.427032 + 0.904236i \(0.640441\pi\)
\(450\) 0 0
\(451\) 20.1081 11.6094i 0.946856 0.546667i
\(452\) 0 0
\(453\) 1.21100 + 7.43721i 0.0568976 + 0.349431i
\(454\) 0 0
\(455\) 7.35747 + 0.768090i 0.344924 + 0.0360086i
\(456\) 0 0
\(457\) −2.04648 11.6062i −0.0957303 0.542913i −0.994521 0.104536i \(-0.966664\pi\)
0.898791 0.438378i \(-0.144447\pi\)
\(458\) 0 0
\(459\) −9.12288 + 14.4560i −0.425819 + 0.674747i
\(460\) 0 0
\(461\) 3.51700 + 19.9459i 0.163803 + 0.928973i 0.950290 + 0.311366i \(0.100787\pi\)
−0.786487 + 0.617607i \(0.788102\pi\)
\(462\) 0 0
\(463\) −34.2382 + 12.4617i −1.59119 + 0.579144i −0.977598 0.210481i \(-0.932497\pi\)
−0.613589 + 0.789626i \(0.710275\pi\)
\(464\) 0 0
\(465\) −7.25116 8.87552i −0.336264 0.411592i
\(466\) 0 0
\(467\) 1.66258 + 2.87968i 0.0769351 + 0.133255i 0.901926 0.431890i \(-0.142153\pi\)
−0.824991 + 0.565146i \(0.808820\pi\)
\(468\) 0 0
\(469\) −14.4094 21.3305i −0.665362 0.984951i
\(470\) 0 0
\(471\) −1.01506 2.90696i −0.0467714 0.133946i
\(472\) 0 0
\(473\) 21.7123 + 3.82846i 0.998331 + 0.176033i
\(474\) 0 0
\(475\) −1.05798 1.26085i −0.0485435 0.0578519i
\(476\) 0 0
\(477\) −5.89364 + 3.19953i −0.269851 + 0.146496i
\(478\) 0 0
\(479\) 2.58586 + 0.941175i 0.118151 + 0.0430034i 0.400419 0.916332i \(-0.368865\pi\)
−0.282268 + 0.959336i \(0.591087\pi\)
\(480\) 0 0
\(481\) 13.7966 16.4422i 0.629072 0.749699i
\(482\) 0 0
\(483\) −17.7756 + 11.6712i −0.808817 + 0.531059i
\(484\) 0 0
\(485\) 3.53438i 0.160488i
\(486\) 0 0
\(487\) −6.75517 −0.306106 −0.153053 0.988218i \(-0.548911\pi\)
−0.153053 + 0.988218i \(0.548911\pi\)
\(488\) 0 0
\(489\) −12.9659 + 21.7922i −0.586339 + 0.985479i
\(490\) 0 0
\(491\) −6.44850 + 7.68503i −0.291017 + 0.346820i −0.891667 0.452691i \(-0.850464\pi\)
0.600650 + 0.799512i \(0.294908\pi\)
\(492\) 0 0
\(493\) 12.1014 33.2483i 0.545019 1.49743i
\(494\) 0 0
\(495\) 6.33053 3.43670i 0.284536 0.154468i
\(496\) 0 0
\(497\) −20.1103 + 5.02902i −0.902068 + 0.225582i
\(498\) 0 0
\(499\) −0.778363 + 4.41432i −0.0348443 + 0.197612i −0.997261 0.0739660i \(-0.976434\pi\)
0.962416 + 0.271578i \(0.0875455\pi\)
\(500\) 0 0
\(501\) −12.5084 + 4.36772i −0.558835 + 0.195135i
\(502\) 0 0
\(503\) −7.20120 + 12.4728i −0.321086 + 0.556137i −0.980712 0.195457i \(-0.937381\pi\)
0.659627 + 0.751593i \(0.270714\pi\)
\(504\) 0 0
\(505\) 2.88068 + 4.98948i 0.128189 + 0.222029i
\(506\) 0 0
\(507\) −0.803308 + 0.656289i −0.0356761 + 0.0291468i
\(508\) 0 0
\(509\) 39.0931 14.2287i 1.73277 0.630677i 0.733950 0.679204i \(-0.237675\pi\)
0.998822 + 0.0485267i \(0.0154526\pi\)
\(510\) 0 0
\(511\) 6.92937 24.2297i 0.306537 1.07186i
\(512\) 0 0
\(513\) 1.71050 0.899740i 0.0755204 0.0397245i
\(514\) 0 0
\(515\) −10.4341 + 1.83982i −0.459783 + 0.0810721i
\(516\) 0 0
\(517\) −11.3126 31.0811i −0.497528 1.36695i
\(518\) 0 0
\(519\) −5.09464 31.2882i −0.223630 1.37340i
\(520\) 0 0
\(521\) −8.77828 15.2044i −0.384583 0.666118i 0.607128 0.794604i \(-0.292322\pi\)
−0.991711 + 0.128486i \(0.958988\pi\)
\(522\) 0 0
\(523\) −9.12872 5.27047i −0.399171 0.230462i 0.286955 0.957944i \(-0.407357\pi\)
−0.686126 + 0.727482i \(0.740690\pi\)
\(524\) 0 0
\(525\) −18.6264 + 8.01732i −0.812921 + 0.349904i
\(526\) 0 0
\(527\) −28.2742 4.98551i −1.23165 0.217172i
\(528\) 0 0
\(529\) 1.12394 0.943099i 0.0488671 0.0410043i
\(530\) 0 0
\(531\) −6.19955 + 30.4623i −0.269037 + 1.32195i
\(532\) 0 0
\(533\) −9.24741 + 25.4070i −0.400550 + 1.10050i
\(534\) 0 0
\(535\) −6.90619 + 8.23047i −0.298581 + 0.355834i
\(536\) 0 0
\(537\) −26.6852 + 14.9434i −1.15155 + 0.644855i
\(538\) 0 0
\(539\) 17.4493 13.6723i 0.751596 0.588909i
\(540\) 0 0
\(541\) 6.04178 0.259756 0.129878 0.991530i \(-0.458541\pi\)
0.129878 + 0.991530i \(0.458541\pi\)
\(542\) 0 0
\(543\) −0.516621 + 39.3739i −0.0221703 + 1.68969i
\(544\) 0 0
\(545\) 10.5315 + 8.83699i 0.451120 + 0.378535i
\(546\) 0 0
\(547\) 32.8469 + 11.9553i 1.40443 + 0.511172i 0.929491 0.368845i \(-0.120247\pi\)
0.474942 + 0.880017i \(0.342469\pi\)
\(548\) 0 0
\(549\) 26.2190 3.91683i 1.11900 0.167166i
\(550\) 0 0
\(551\) −3.06451 + 2.57143i −0.130552 + 0.109546i
\(552\) 0 0
\(553\) 3.07648 + 2.23190i 0.130825 + 0.0949100i
\(554\) 0 0
\(555\) 1.42594 7.50938i 0.0605276 0.318756i
\(556\) 0 0
\(557\) 26.9399 + 15.5538i 1.14148 + 0.659034i 0.946797 0.321832i \(-0.104299\pi\)
0.194684 + 0.980866i \(0.437632\pi\)
\(558\) 0 0
\(559\) −22.2337 + 12.8366i −0.940385 + 0.542931i
\(560\) 0 0
\(561\) 6.39352 16.8739i 0.269935 0.712415i
\(562\) 0 0
\(563\) 2.93215 1.06721i 0.123575 0.0449777i −0.279492 0.960148i \(-0.590166\pi\)
0.403068 + 0.915170i \(0.367944\pi\)
\(564\) 0 0
\(565\) −3.26293 + 0.575343i −0.137273 + 0.0242048i
\(566\) 0 0
\(567\) −4.55705 23.3716i −0.191378 0.981516i
\(568\) 0 0
\(569\) 17.8105 3.14048i 0.746656 0.131656i 0.212641 0.977130i \(-0.431794\pi\)
0.534015 + 0.845475i \(0.320683\pi\)
\(570\) 0 0
\(571\) −7.02115 + 2.55549i −0.293826 + 0.106944i −0.484727 0.874665i \(-0.661081\pi\)
0.190901 + 0.981609i \(0.438859\pi\)
\(572\) 0 0
\(573\) 14.1917 37.4548i 0.592865 1.56470i
\(574\) 0 0
\(575\) −17.7831 + 10.2671i −0.741607 + 0.428167i
\(576\) 0 0
\(577\) 16.7017 + 9.64275i 0.695302 + 0.401433i 0.805595 0.592466i \(-0.201846\pi\)
−0.110293 + 0.993899i \(0.535179\pi\)
\(578\) 0 0
\(579\) 4.38807 23.1088i 0.182362 0.960369i
\(580\) 0 0
\(581\) −0.985447 0.714915i −0.0408832 0.0296597i
\(582\) 0 0
\(583\) 5.42286 4.55032i 0.224592 0.188455i
\(584\) 0 0
\(585\) −3.07466 + 7.80409i −0.127121 + 0.322659i
\(586\) 0 0
\(587\) 15.9146 + 5.79243i 0.656864 + 0.239079i 0.648882 0.760889i \(-0.275237\pi\)
0.00798237 + 0.999968i \(0.497459\pi\)
\(588\) 0 0
\(589\) 2.48666 + 2.08656i 0.102461 + 0.0859751i
\(590\) 0 0
\(591\) 0.354869 27.0461i 0.0145974 1.11253i
\(592\) 0 0
\(593\) 44.1513 1.81308 0.906538 0.422125i \(-0.138716\pi\)
0.906538 + 0.422125i \(0.138716\pi\)
\(594\) 0 0
\(595\) 2.88874 5.93334i 0.118427 0.243243i
\(596\) 0 0
\(597\) −9.64336 + 5.40016i −0.394676 + 0.221014i
\(598\) 0 0
\(599\) 23.6707 28.2097i 0.967160 1.15262i −0.0210911 0.999778i \(-0.506714\pi\)
0.988251 0.152839i \(-0.0488415\pi\)
\(600\) 0 0
\(601\) 8.31816 22.8540i 0.339305 0.932233i −0.646287 0.763094i \(-0.723679\pi\)
0.985592 0.169138i \(-0.0540985\pi\)
\(602\) 0 0
\(603\) 27.6802 9.25982i 1.12723 0.377089i
\(604\) 0 0
\(605\) 0.564078 0.473317i 0.0229330 0.0192431i
\(606\) 0 0
\(607\) 13.5872 + 2.39579i 0.551487 + 0.0972420i 0.442446 0.896795i \(-0.354111\pi\)
0.109041 + 0.994037i \(0.465222\pi\)
\(608\) 0 0
\(609\) 19.4861 + 45.2715i 0.789618 + 1.83449i
\(610\) 0 0
\(611\) 33.3556 + 19.2579i 1.34942 + 0.779090i
\(612\) 0 0
\(613\) −17.8206 30.8661i −0.719766 1.24667i −0.961092 0.276228i \(-0.910916\pi\)
0.241326 0.970444i \(-0.422418\pi\)
\(614\) 0 0
\(615\) 1.54742 + 9.50335i 0.0623981 + 0.383212i
\(616\) 0 0
\(617\) −0.342056 0.939792i −0.0137707 0.0378346i 0.932617 0.360868i \(-0.117520\pi\)
−0.946388 + 0.323034i \(0.895297\pi\)
\(618\) 0 0
\(619\) 24.7736 4.36825i 0.995735 0.175575i 0.348044 0.937478i \(-0.386846\pi\)
0.647691 + 0.761903i \(0.275735\pi\)
\(620\) 0 0
\(621\) −7.34879 22.9648i −0.294897 0.921545i
\(622\) 0 0
\(623\) 12.9714 + 3.70965i 0.519687 + 0.148624i
\(624\) 0 0
\(625\) −15.7000 + 5.71432i −0.627998 + 0.228573i
\(626\) 0 0
\(627\) −1.57994 + 1.29079i −0.0630967 + 0.0515490i
\(628\) 0 0
\(629\) −9.57379 16.5823i −0.381732 0.661179i
\(630\) 0 0
\(631\) −8.81809 + 15.2734i −0.351043 + 0.608024i −0.986432 0.164168i \(-0.947506\pi\)
0.635390 + 0.772192i \(0.280839\pi\)
\(632\) 0 0
\(633\) −37.6648 + 13.1519i −1.49704 + 0.522740i
\(634\) 0 0
\(635\) −2.62708 + 14.8989i −0.104253 + 0.591246i
\(636\) 0 0
\(637\) −5.33158 + 25.2571i −0.211245 + 1.00072i
\(638\) 0 0
\(639\) 0.616710 23.4970i 0.0243967 0.929527i
\(640\) 0 0
\(641\) 14.5683 40.0260i 0.575411 1.58093i −0.220416 0.975406i \(-0.570741\pi\)
0.795827 0.605524i \(-0.207036\pi\)
\(642\) 0 0
\(643\) −18.0323 + 21.4901i −0.711126 + 0.847487i −0.993737 0.111748i \(-0.964355\pi\)
0.282611 + 0.959235i \(0.408800\pi\)
\(644\) 0 0
\(645\) −4.67480 + 7.85709i −0.184070 + 0.309373i
\(646\) 0 0
\(647\) 1.52315 0.0598813 0.0299407 0.999552i \(-0.490468\pi\)
0.0299407 + 0.999552i \(0.490468\pi\)
\(648\) 0 0
\(649\) 32.8155i 1.28812i
\(650\) 0 0
\(651\) 33.4313 21.9506i 1.31028 0.860311i
\(652\) 0 0
\(653\) 9.91571 11.8171i 0.388032 0.462438i −0.536300 0.844027i \(-0.680179\pi\)
0.924332 + 0.381589i \(0.124623\pi\)
\(654\) 0 0
\(655\) −7.90515 2.87724i −0.308880 0.112423i
\(656\) 0 0
\(657\) 24.3635 + 14.9320i 0.950512 + 0.582554i
\(658\) 0 0
\(659\) −9.37220 11.1694i −0.365089 0.435096i 0.551960 0.833871i \(-0.313880\pi\)
−0.917049 + 0.398774i \(0.869436\pi\)
\(660\) 0 0
\(661\) −22.4478 3.95815i −0.873118 0.153954i −0.280905 0.959736i \(-0.590635\pi\)
−0.592213 + 0.805781i \(0.701746\pi\)
\(662\) 0 0
\(663\) 6.92694 + 19.8376i 0.269020 + 0.770430i
\(664\) 0 0
\(665\) −0.618277 + 0.417663i −0.0239757 + 0.0161963i
\(666\) 0 0
\(667\) 24.9542 + 43.2219i 0.966230 + 1.67356i
\(668\) 0 0
\(669\) −4.15867 5.09027i −0.160783 0.196801i
\(670\) 0 0
\(671\) −26.2965 + 9.57114i −1.01517 + 0.369490i
\(672\) 0 0
\(673\) 7.00771 + 39.7427i 0.270127 + 1.53197i 0.754026 + 0.656845i \(0.228109\pi\)
−0.483898 + 0.875124i \(0.660780\pi\)
\(674\) 0 0
\(675\) −3.09866 22.7839i −0.119267 0.876955i
\(676\) 0 0
\(677\) −4.58819 26.0209i −0.176338 1.00006i −0.936588 0.350433i \(-0.886034\pi\)
0.760249 0.649631i \(-0.225077\pi\)
\(678\) 0 0
\(679\) −12.2667 1.28059i −0.470751 0.0491445i
\(680\) 0 0
\(681\) 2.36386 + 14.5174i 0.0905831 + 0.556307i
\(682\) 0 0
\(683\) 19.4784 11.2459i 0.745322 0.430312i −0.0786790 0.996900i \(-0.525070\pi\)
0.824001 + 0.566588i \(0.191737\pi\)
\(684\) 0 0
\(685\) 3.92143 + 2.26404i 0.149830 + 0.0865045i
\(686\) 0 0
\(687\) −10.2771 + 11.9265i −0.392096 + 0.455022i
\(688\) 0 0
\(689\) −1.43144 + 8.11807i −0.0545333 + 0.309274i
\(690\) 0 0
\(691\) −2.74733 3.27414i −0.104513 0.124554i 0.711252 0.702937i \(-0.248128\pi\)
−0.815765 + 0.578383i \(0.803684\pi\)
\(692\) 0 0
\(693\) 9.63397 + 23.2164i 0.365964 + 0.881919i
\(694\) 0 0
\(695\) −1.62642 + 4.46856i −0.0616937 + 0.169502i
\(696\) 0 0
\(697\) 18.4770 + 15.5040i 0.699865 + 0.587256i
\(698\) 0 0
\(699\) 3.31225 1.85482i 0.125281 0.0701556i
\(700\) 0 0
\(701\) 23.7848i 0.898340i 0.893446 + 0.449170i \(0.148280\pi\)
−0.893446 + 0.449170i \(0.851720\pi\)
\(702\) 0 0
\(703\) 2.16490i 0.0816507i
\(704\) 0 0
\(705\) 13.7149 + 0.179951i 0.516531 + 0.00677736i
\(706\) 0 0
\(707\) −18.3606 + 8.19008i −0.690521 + 0.308020i
\(708\) 0 0
\(709\) −4.38703 1.59675i −0.164758 0.0599672i 0.258324 0.966058i \(-0.416830\pi\)
−0.423083 + 0.906091i \(0.639052\pi\)
\(710\) 0 0
\(711\) −3.37297 + 2.68265i −0.126496 + 0.100607i
\(712\) 0 0
\(713\) 31.0230 26.0314i 1.16182 0.974883i
\(714\) 0 0
\(715\) 1.53755 8.71986i 0.0575010 0.326104i
\(716\) 0 0
\(717\) 2.20432 + 0.418572i 0.0823218 + 0.0156319i
\(718\) 0 0
\(719\) −11.7175 + 20.2952i −0.436988 + 0.756885i −0.997456 0.0712912i \(-0.977288\pi\)
0.560468 + 0.828176i \(0.310621\pi\)
\(720\) 0 0
\(721\) −2.60487 36.8801i −0.0970105 1.37349i
\(722\) 0 0
\(723\) 9.24589 24.4019i 0.343858 0.907516i
\(724\) 0 0
\(725\) 16.2780 + 44.7235i 0.604551 + 1.66099i
\(726\) 0 0
\(727\) −13.2926 + 2.34385i −0.492996 + 0.0869285i −0.414619 0.909995i \(-0.636085\pi\)
−0.0783772 + 0.996924i \(0.524974\pi\)
\(728\) 0 0
\(729\) 26.9164 + 2.12327i 0.996903 + 0.0786397i
\(730\) 0 0
\(731\) 3.97703 + 22.5549i 0.147096 + 0.834222i
\(732\) 0 0
\(733\) 7.19663 + 19.7726i 0.265813 + 0.730317i 0.998748 + 0.0500177i \(0.0159278\pi\)
−0.732935 + 0.680299i \(0.761850\pi\)
\(734\) 0 0
\(735\) 2.73803 + 8.77541i 0.100994 + 0.323686i
\(736\) 0 0
\(737\) −26.6832 + 15.4056i −0.982890 + 0.567472i
\(738\) 0 0
\(739\) −11.7112 + 20.2844i −0.430803 + 0.746173i −0.996943 0.0781363i \(-0.975103\pi\)
0.566139 + 0.824310i \(0.308436\pi\)
\(740\) 0 0
\(741\) 0.443200 2.33402i 0.0162814 0.0857423i
\(742\) 0 0
\(743\) −31.0839 5.48093i −1.14036 0.201076i −0.428596 0.903496i \(-0.640992\pi\)
−0.711762 + 0.702420i \(0.752103\pi\)
\(744\) 0 0
\(745\) 4.71610 + 5.62043i 0.172784 + 0.205917i
\(746\) 0 0
\(747\) 1.08042 0.859297i 0.0395305 0.0314400i
\(748\) 0 0
\(749\) −26.0630 26.9512i −0.952321 0.984776i
\(750\) 0 0
\(751\) 0.0408859 + 0.0343073i 0.00149195 + 0.00125189i 0.643533 0.765418i \(-0.277468\pi\)
−0.642041 + 0.766670i \(0.721912\pi\)
\(752\) 0 0
\(753\) 38.0408 + 0.499130i 1.38628 + 0.0181893i
\(754\) 0 0
\(755\) 3.29848 0.120044
\(756\) 0 0
\(757\) 21.5650 0.783794 0.391897 0.920009i \(-0.371819\pi\)
0.391897 + 0.920009i \(0.371819\pi\)
\(758\) 0 0
\(759\) 12.4361 + 22.2078i 0.451402 + 0.806094i
\(760\) 0 0
\(761\) 1.36733 + 1.14732i 0.0495656 + 0.0415905i 0.667234 0.744848i \(-0.267478\pi\)
−0.617668 + 0.786439i \(0.711923\pi\)
\(762\) 0 0
\(763\) −34.4861 + 33.3496i −1.24848 + 1.20734i
\(764\) 0 0
\(765\) 5.60397 + 4.95858i 0.202612 + 0.179278i
\(766\) 0 0
\(767\) 24.5626 + 29.2725i 0.886903 + 1.05697i
\(768\) 0 0
\(769\) 16.3648 + 2.88555i 0.590128 + 0.104056i 0.460735 0.887538i \(-0.347586\pi\)
0.129393 + 0.991593i \(0.458697\pi\)
\(770\) 0 0
\(771\) 3.74745 + 3.22921i 0.134961 + 0.116297i
\(772\) 0 0
\(773\) −18.1663 + 31.4649i −0.653395 + 1.13171i 0.328898 + 0.944365i \(0.393323\pi\)
−0.982293 + 0.187349i \(0.940011\pi\)
\(774\) 0 0
\(775\) 33.4455 19.3097i 1.20140 0.693626i
\(776\) 0 0
\(777\) 25.5460 + 7.66979i 0.916456 + 0.275152i
\(778\) 0 0
\(779\) −0.932721 2.56263i −0.0334182 0.0918158i
\(780\) 0 0
\(781\) 4.30859 + 24.4352i 0.154174 + 0.874362i
\(782\) 0 0
\(783\) −55.3765 + 7.53130i −1.97899 + 0.269147i
\(784\) 0 0
\(785\) −1.32738 + 0.234052i −0.0473761 + 0.00835369i
\(786\) 0 0
\(787\) 7.16754 + 19.6927i 0.255495 + 0.701967i 0.999431 + 0.0337166i \(0.0107344\pi\)
−0.743936 + 0.668251i \(0.767043\pi\)
\(788\) 0 0
\(789\) −7.98776 9.77713i −0.284372 0.348075i
\(790\) 0 0
\(791\) −0.814588 11.5330i −0.0289634 0.410067i
\(792\) 0 0
\(793\) 16.2933 28.2208i 0.578592 1.00215i
\(794\) 0 0
\(795\) 0.967745 + 2.77146i 0.0343224 + 0.0982937i
\(796\) 0 0
\(797\) 5.73543 32.5273i 0.203160 1.15217i −0.697150 0.716925i \(-0.745549\pi\)
0.900310 0.435250i \(-0.143340\pi\)
\(798\) 0 0
\(799\) 26.3209 22.0858i 0.931165 0.781340i
\(800\) 0 0
\(801\) −7.99388 + 13.0431i −0.282450 + 0.460854i
\(802\) 0 0
\(803\) −28.3452 10.3168i −1.00028 0.364073i
\(804\) 0 0
\(805\) 3.79207 + 8.50110i 0.133653 + 0.299625i
\(806\) 0 0
\(807\) −12.2208 + 20.5400i −0.430194 + 0.723041i
\(808\) 0 0
\(809\) 3.11659i 0.109573i −0.998498 0.0547867i \(-0.982552\pi\)
0.998498 0.0547867i \(-0.0174479\pi\)
\(810\) 0 0
\(811\) 30.6649i 1.07679i 0.842692 + 0.538395i \(0.180969\pi\)
−0.842692 + 0.538395i \(0.819031\pi\)
\(812\) 0 0
\(813\) 10.2347 + 6.08941i 0.358946 + 0.213565i
\(814\) 0 0
\(815\) 8.50327 + 7.13509i 0.297857 + 0.249931i
\(816\) 0 0
\(817\) 0.885654 2.43331i 0.0309851 0.0851309i
\(818\) 0 0
\(819\) −25.9714 13.4987i −0.907515 0.471684i
\(820\) 0 0
\(821\) 12.8376 + 15.2993i 0.448036 + 0.533949i 0.942035 0.335514i \(-0.108910\pi\)
−0.493999 + 0.869462i \(0.664465\pi\)
\(822\) 0 0
\(823\) 1.58071 8.96463i 0.0551000 0.312487i −0.944784 0.327693i \(-0.893729\pi\)
0.999884 + 0.0152050i \(0.00484010\pi\)
\(824\) 0 0
\(825\) 8.00168 + 22.9155i 0.278583 + 0.797816i
\(826\) 0 0
\(827\) −7.71719 4.45552i −0.268353 0.154934i 0.359786 0.933035i \(-0.382850\pi\)
−0.628139 + 0.778101i \(0.716183\pi\)
\(828\) 0 0
\(829\) −11.0653 + 6.38856i −0.384314 + 0.221884i −0.679694 0.733496i \(-0.737887\pi\)
0.295379 + 0.955380i \(0.404554\pi\)
\(830\) 0 0
\(831\) 34.8318 28.4570i 1.20830 0.987164i
\(832\) 0 0
\(833\) 19.5460 + 12.1757i 0.677229 + 0.421861i
\(834\) 0 0
\(835\) 1.00711 + 5.71160i 0.0348524 + 0.197658i
\(836\) 0 0
\(837\) 13.8212 + 43.1908i 0.477730 + 1.49289i
\(838\) 0 0
\(839\) −4.35684 24.7089i −0.150415 0.853044i −0.962859 0.270005i \(-0.912975\pi\)
0.812444 0.583039i \(-0.198137\pi\)
\(840\) 0 0
\(841\) 81.4496 29.6452i 2.80861 1.02225i
\(842\) 0 0
\(843\) 28.9407 4.71239i 0.996770 0.162303i
\(844\) 0 0
\(845\) 0.227039 + 0.393243i 0.00781039 + 0.0135280i
\(846\) 0 0
\(847\) 1.43835 + 2.12922i 0.0494223 + 0.0731610i
\(848\) 0 0
\(849\) 8.66993 10.0613i 0.297551 0.345304i
\(850\) 0 0
\(851\) 26.5984 + 4.69002i 0.911782 + 0.160772i
\(852\) 0 0
\(853\) −12.5040 14.9017i −0.428130 0.510226i 0.508252 0.861209i \(-0.330292\pi\)
−0.936382 + 0.350983i \(0.885848\pi\)
\(854\) 0 0
\(855\) −0.268401 0.802327i −0.00917912 0.0274390i
\(856\) 0 0
\(857\) 54.8203 + 19.9530i 1.87263 + 0.681581i 0.965292 + 0.261172i \(0.0841089\pi\)
0.907335 + 0.420409i \(0.138113\pi\)
\(858\) 0 0
\(859\) 20.4664 24.3909i 0.698304 0.832206i −0.294029 0.955796i \(-0.594996\pi\)
0.992333 + 0.123590i \(0.0394408\pi\)
\(860\) 0 0
\(861\) −33.5437 + 1.92731i −1.14317 + 0.0656826i
\(862\) 0 0
\(863\) 56.3306i 1.91751i −0.284226 0.958757i \(-0.591737\pi\)
0.284226 0.958757i \(-0.408263\pi\)
\(864\) 0 0
\(865\) −13.8766 −0.471820
\(866\) 0 0
\(867\) −10.6992 0.140383i −0.363362 0.00476765i
\(868\) 0 0
\(869\) 2.92428 3.48502i 0.0991993 0.118221i
\(870\) 0 0
\(871\) 12.2712 33.7148i 0.415793 1.14238i
\(872\) 0 0
\(873\) 5.12619 13.0113i 0.173495 0.440365i
\(874\) 0 0
\(875\) 4.58682 + 18.3420i 0.155063 + 0.620072i
\(876\) 0 0
\(877\) −2.43349 + 13.8010i −0.0821732 + 0.466027i 0.915758 + 0.401731i \(0.131591\pi\)
−0.997931 + 0.0642962i \(0.979520\pi\)
\(878\) 0 0
\(879\) −0.311447 + 1.64017i −0.0105049 + 0.0553215i
\(880\) 0 0
\(881\) −25.9828 + 45.0035i −0.875383 + 1.51621i −0.0190281 + 0.999819i \(0.506057\pi\)
−0.856355 + 0.516388i \(0.827276\pi\)
\(882\) 0 0
\(883\) −5.33882 9.24711i −0.179666 0.311190i 0.762100 0.647459i \(-0.224168\pi\)
−0.941766 + 0.336269i \(0.890835\pi\)
\(884\) 0 0
\(885\) 12.7252 + 4.82160i 0.427754 + 0.162076i
\(886\) 0 0
\(887\) 42.6916 15.5385i 1.43344 0.521731i 0.495527 0.868593i \(-0.334975\pi\)
0.937916 + 0.346862i \(0.112753\pi\)
\(888\) 0 0
\(889\) −50.7575 14.5160i −1.70235 0.486851i
\(890\) 0 0
\(891\) −28.2894 + 3.47004i −0.947732 + 0.116251i
\(892\) 0 0
\(893\) −3.82579 + 0.674590i −0.128025 + 0.0225743i
\(894\) 0 0
\(895\) 4.57902 + 12.5808i 0.153060 + 0.420528i
\(896\) 0 0
\(897\) −27.7161 10.5016i −0.925414 0.350640i
\(898\) 0 0
\(899\) −46.9324 81.2893i −1.56528 2.71115i
\(900\) 0 0
\(901\) 6.36854 + 3.67688i 0.212167 + 0.122495i
\(902\) 0 0
\(903\) −25.5756 19.0715i −0.851103 0.634660i
\(904\) 0 0
\(905\) 16.9753 + 2.99321i 0.564279 + 0.0994976i
\(906\) 0 0
\(907\) −26.4373 + 22.1835i −0.877836 + 0.736592i −0.965733 0.259538i \(-0.916430\pi\)
0.0878972 + 0.996130i \(0.471985\pi\)
\(908\) 0 0
\(909\) −3.36815 22.5461i −0.111714 0.747807i
\(910\) 0 0
\(911\) −12.5484 + 34.4764i −0.415747 + 1.14226i 0.538341 + 0.842727i \(0.319051\pi\)
−0.954087 + 0.299528i \(0.903171\pi\)
\(912\) 0 0
\(913\) −0.936694 + 1.11631i −0.0310001 + 0.0369444i
\(914\) 0 0
\(915\) 0.152250 11.6036i 0.00503322 0.383603i
\(916\) 0 0
\(917\) 12.8502 26.3937i 0.424350 0.871597i
\(918\) 0 0
\(919\) −44.2554 −1.45985 −0.729926 0.683526i \(-0.760445\pi\)
−0.729926 + 0.683526i \(0.760445\pi\)
\(920\) 0 0
\(921\) −2.62751 + 1.47137i −0.0865794 + 0.0484833i
\(922\) 0 0
\(923\) −22.1333 18.5720i −0.728527 0.611306i
\(924\) 0 0
\(925\) 24.2029 + 8.80912i 0.795785 + 0.289642i
\(926\) 0 0
\(927\) 41.0801 + 8.36043i 1.34925 + 0.274593i
\(928\) 0 0
\(929\) 0.123460 0.103595i 0.00405058 0.00339884i −0.640760 0.767741i \(-0.721381\pi\)
0.644811 + 0.764342i \(0.276936\pi\)
\(930\) 0 0
\(931\) −1.22556 2.29717i −0.0401660 0.0752866i
\(932\) 0 0
\(933\) −40.6697 35.0454i −1.33147 1.14733i
\(934\) 0 0
\(935\) −6.84064 3.94945i −0.223713 0.129161i
\(936\) 0 0
\(937\) −28.3872 + 16.3894i −0.927369 + 0.535417i −0.885979 0.463726i \(-0.846512\pi\)
−0.0413907 + 0.999143i \(0.513179\pi\)
\(938\) 0 0
\(939\) 23.8598 3.88507i 0.778634 0.126785i
\(940\) 0 0
\(941\) −47.1036 + 17.1443i −1.53553 + 0.558889i −0.964969 0.262363i \(-0.915498\pi\)
−0.570565 + 0.821252i \(0.693276\pi\)
\(942\) 0 0
\(943\) −33.5057 + 5.90795i −1.09109 + 0.192389i
\(944\) 0 0
\(945\) −10.4184 + 0.324674i −0.338911 + 0.0105616i
\(946\) 0 0
\(947\) −54.5111 + 9.61177i −1.77137 + 0.312341i −0.961610 0.274419i \(-0.911514\pi\)
−0.809761 + 0.586760i \(0.800403\pi\)
\(948\) 0 0
\(949\) 33.0071 12.0136i 1.07146 0.389978i
\(950\) 0 0
\(951\) 2.62657 + 3.21496i 0.0851723 + 0.104252i
\(952\) 0 0
\(953\) −40.8446 + 23.5816i −1.32309 + 0.763884i −0.984220 0.176951i \(-0.943377\pi\)
−0.338866 + 0.940835i \(0.610043\pi\)
\(954\) 0 0
\(955\) −15.1841 8.76656i −0.491347 0.283679i
\(956\) 0 0
\(957\) 55.6963 19.4481i 1.80041 0.628669i
\(958\) 0 0
\(959\) −9.27857 + 12.7897i −0.299621 + 0.413001i
\(960\) 0 0
\(961\) −34.5989 + 29.0319i −1.11609 + 0.936514i
\(962\) 0 0
\(963\) 37.3614 20.2827i 1.20395 0.653600i
\(964\) 0 0
\(965\) −9.67556 3.52162i −0.311467 0.113365i
\(966\) 0 0
\(967\) 7.46649 + 6.26513i 0.240106 + 0.201473i 0.754898 0.655842i \(-0.227686\pi\)
−0.514792 + 0.857315i \(0.672131\pi\)
\(968\) 0 0
\(969\) −1.82136 1.08367i −0.0585104 0.0348124i
\(970\) 0 0
\(971\) 49.8838 1.60085 0.800424 0.599434i \(-0.204608\pi\)
0.800424 + 0.599434i \(0.204608\pi\)
\(972\) 0 0
\(973\) −14.9196 7.26385i −0.478301 0.232868i
\(974\) 0 0
\(975\) −24.2901 14.4521i −0.777907 0.462838i
\(976\) 0 0
\(977\) −10.0973 + 12.0335i −0.323041 + 0.384986i −0.902986 0.429670i \(-0.858630\pi\)
0.579945 + 0.814656i \(0.303074\pi\)
\(978\) 0 0
\(979\) 5.52312 15.1747i 0.176520 0.484984i
\(980\) 0 0
\(981\) −25.9532 47.8067i −0.828622 1.52635i
\(982\) 0 0
\(983\) 42.7711 35.8892i 1.36418 1.14469i 0.389520 0.921018i \(-0.372641\pi\)
0.974665 0.223669i \(-0.0718034\pi\)
\(984\) 0 0
\(985\) −11.6604 2.05605i −0.371532 0.0655111i
\(986\) 0 0
\(987\) −5.59377 + 47.5346i −0.178052 + 1.51304i
\(988\) 0 0
\(989\) −27.9776 16.1529i −0.889635 0.513631i
\(990\) 0 0
\(991\) −6.17459 10.6947i −0.196142 0.339728i 0.751132 0.660152i \(-0.229508\pi\)
−0.947274 + 0.320424i \(0.896175\pi\)
\(992\) 0 0
\(993\) 12.1971 9.96480i 0.387062 0.316223i
\(994\) 0 0
\(995\) 1.65474 + 4.54636i 0.0524588 + 0.144129i
\(996\) 0 0
\(997\) 49.4777 8.72425i 1.56697 0.276300i 0.678281 0.734802i \(-0.262725\pi\)
0.888693 + 0.458502i \(0.151614\pi\)
\(998\) 0 0
\(999\) −16.1408 + 25.5765i −0.510673 + 0.809206i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 756.2.bx.a.41.7 144
7.6 odd 2 inner 756.2.bx.a.41.18 yes 144
27.2 odd 18 inner 756.2.bx.a.461.18 yes 144
189.83 even 18 inner 756.2.bx.a.461.7 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.bx.a.41.7 144 1.1 even 1 trivial
756.2.bx.a.41.18 yes 144 7.6 odd 2 inner
756.2.bx.a.461.7 yes 144 189.83 even 18 inner
756.2.bx.a.461.18 yes 144 27.2 odd 18 inner