Properties

Label 675.2.k.b.199.4
Level $675$
Weight $2$
Character 675.199
Analytic conductor $5.390$
Analytic rank $0$
Dimension $12$
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] = [675,2,Mod(199,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.199");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.4
Root \(-1.50511 - 0.403293i\) of defining polynomial
Character \(\chi\) \(=\) 675.199
Dual form 675.2.k.b.424.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.495361 - 0.285997i) q^{2} +(-0.836412 + 1.44871i) q^{4} +(-1.23669 + 0.714003i) q^{7} +2.10083i q^{8} +O(q^{10})\) \(q+(0.495361 - 0.285997i) q^{2} +(-0.836412 + 1.44871i) q^{4} +(-1.23669 + 0.714003i) q^{7} +2.10083i q^{8} +(1.33641 + 2.31473i) q^{11} +(-4.04678 - 2.33641i) q^{13} +(-0.408405 + 0.707378i) q^{14} +(-1.07199 - 1.85675i) q^{16} +2.67282i q^{17} -4.67282 q^{19} +(1.32401 + 0.764419i) q^{22} +(-5.12483 - 2.95882i) q^{23} -2.67282 q^{26} -2.38880i q^{28} +(4.74482 + 8.21826i) q^{29} +(-3.48040 + 6.02823i) q^{31} +(-4.70079 - 2.71400i) q^{32} +(0.764419 + 1.32401i) q^{34} +1.81681i q^{37} +(-2.31473 + 1.33641i) q^{38} +(-0.735581 + 1.27406i) q^{41} +(0.408039 - 0.235581i) q^{43} -4.47116 q^{44} -3.38485 q^{46} +(6.02480 - 3.47842i) q^{47} +(-2.48040 + 4.29618i) q^{49} +(6.76956 - 3.90841i) q^{52} +1.14399i q^{53} +(-1.50000 - 2.59808i) q^{56} +(4.70079 + 2.71400i) q^{58} +(0.571993 - 0.990721i) q^{59} +(1.26442 + 2.19004i) q^{61} +3.98153i q^{62} +1.18319 q^{64} +(-5.70751 - 3.29523i) q^{67} +(-3.87214 - 2.23558i) q^{68} +12.8745 q^{71} -1.71203i q^{73} +(0.519602 + 0.899976i) q^{74} +(3.90841 - 6.76956i) q^{76} +(-3.30545 - 1.90841i) q^{77} +(-0.143987 - 0.249392i) q^{79} +0.841495i q^{82} +(3.71007 - 2.14201i) q^{83} +(0.134751 - 0.233396i) q^{86} +(-4.86286 + 2.80757i) q^{88} -3.00000 q^{89} +6.67282 q^{91} +(8.57293 - 4.94958i) q^{92} +(1.98963 - 3.44615i) q^{94} +(-6.78555 + 3.91764i) q^{97} +2.83754i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 10 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 10 q^{4} - 4 q^{11} + 18 q^{14} - 10 q^{16} - 16 q^{19} + 8 q^{26} + 14 q^{29} - 16 q^{31} - 8 q^{34} - 26 q^{41} - 88 q^{44} - 12 q^{46} - 4 q^{49} - 18 q^{56} + 4 q^{59} - 2 q^{61} + 60 q^{64} + 40 q^{71} + 32 q^{74} + 24 q^{76} + 4 q^{79} + 56 q^{86} - 36 q^{89} + 40 q^{91} - 62 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.495361 0.285997i 0.350273 0.202230i −0.314533 0.949247i \(-0.601848\pi\)
0.664805 + 0.747017i \(0.268514\pi\)
\(3\) 0 0
\(4\) −0.836412 + 1.44871i −0.418206 + 0.724354i
\(5\) 0 0
\(6\) 0 0
\(7\) −1.23669 + 0.714003i −0.467425 + 0.269868i −0.715161 0.698960i \(-0.753647\pi\)
0.247736 + 0.968828i \(0.420313\pi\)
\(8\) 2.10083i 0.742756i
\(9\) 0 0
\(10\) 0 0
\(11\) 1.33641 + 2.31473i 0.402943 + 0.697918i 0.994080 0.108653i \(-0.0346538\pi\)
−0.591136 + 0.806572i \(0.701321\pi\)
\(12\) 0 0
\(13\) −4.04678 2.33641i −1.12238 0.648004i −0.180370 0.983599i \(-0.557729\pi\)
−0.942006 + 0.335595i \(0.891063\pi\)
\(14\) −0.408405 + 0.707378i −0.109151 + 0.189055i
\(15\) 0 0
\(16\) −1.07199 1.85675i −0.267998 0.464187i
\(17\) 2.67282i 0.648255i 0.946013 + 0.324127i \(0.105071\pi\)
−0.946013 + 0.324127i \(0.894929\pi\)
\(18\) 0 0
\(19\) −4.67282 −1.07202 −0.536010 0.844212i \(-0.680069\pi\)
−0.536010 + 0.844212i \(0.680069\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.32401 + 0.764419i 0.282280 + 0.162975i
\(23\) −5.12483 2.95882i −1.06860 0.616957i −0.140802 0.990038i \(-0.544968\pi\)
−0.927799 + 0.373081i \(0.878301\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −2.67282 −0.524184
\(27\) 0 0
\(28\) 2.38880i 0.451441i
\(29\) 4.74482 + 8.21826i 0.881090 + 1.52609i 0.850130 + 0.526573i \(0.176523\pi\)
0.0309603 + 0.999521i \(0.490143\pi\)
\(30\) 0 0
\(31\) −3.48040 + 6.02823i −0.625098 + 1.08270i 0.363424 + 0.931624i \(0.381608\pi\)
−0.988522 + 0.151078i \(0.951726\pi\)
\(32\) −4.70079 2.71400i −0.830990 0.479773i
\(33\) 0 0
\(34\) 0.764419 + 1.32401i 0.131097 + 0.227066i
\(35\) 0 0
\(36\) 0 0
\(37\) 1.81681i 0.298682i 0.988786 + 0.149341i \(0.0477152\pi\)
−0.988786 + 0.149341i \(0.952285\pi\)
\(38\) −2.31473 + 1.33641i −0.375499 + 0.216795i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.735581 + 1.27406i −0.114879 + 0.198975i −0.917731 0.397202i \(-0.869981\pi\)
0.802853 + 0.596177i \(0.203315\pi\)
\(42\) 0 0
\(43\) 0.408039 0.235581i 0.0622254 0.0359258i −0.468565 0.883429i \(-0.655229\pi\)
0.530790 + 0.847503i \(0.321895\pi\)
\(44\) −4.47116 −0.674053
\(45\) 0 0
\(46\) −3.38485 −0.499069
\(47\) 6.02480 3.47842i 0.878808 0.507380i 0.00854274 0.999964i \(-0.497281\pi\)
0.870265 + 0.492584i \(0.163947\pi\)
\(48\) 0 0
\(49\) −2.48040 + 4.29618i −0.354343 + 0.613739i
\(50\) 0 0
\(51\) 0 0
\(52\) 6.76956 3.90841i 0.938769 0.541998i
\(53\) 1.14399i 0.157139i 0.996909 + 0.0785693i \(0.0250352\pi\)
−0.996909 + 0.0785693i \(0.974965\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.50000 2.59808i −0.200446 0.347183i
\(57\) 0 0
\(58\) 4.70079 + 2.71400i 0.617244 + 0.356366i
\(59\) 0.571993 0.990721i 0.0744672 0.128981i −0.826387 0.563102i \(-0.809608\pi\)
0.900854 + 0.434121i \(0.142941\pi\)
\(60\) 0 0
\(61\) 1.26442 + 2.19004i 0.161892 + 0.280406i 0.935547 0.353201i \(-0.114907\pi\)
−0.773655 + 0.633607i \(0.781574\pi\)
\(62\) 3.98153i 0.505655i
\(63\) 0 0
\(64\) 1.18319 0.147899
\(65\) 0 0
\(66\) 0 0
\(67\) −5.70751 3.29523i −0.697283 0.402577i 0.109051 0.994036i \(-0.465219\pi\)
−0.806335 + 0.591459i \(0.798552\pi\)
\(68\) −3.87214 2.23558i −0.469566 0.271104i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.8745 1.52792 0.763960 0.645263i \(-0.223252\pi\)
0.763960 + 0.645263i \(0.223252\pi\)
\(72\) 0 0
\(73\) 1.71203i 0.200378i −0.994968 0.100189i \(-0.968055\pi\)
0.994968 0.100189i \(-0.0319447\pi\)
\(74\) 0.519602 + 0.899976i 0.0604025 + 0.104620i
\(75\) 0 0
\(76\) 3.90841 6.76956i 0.448325 0.776521i
\(77\) −3.30545 1.90841i −0.376692 0.217483i
\(78\) 0 0
\(79\) −0.143987 0.249392i −0.0161998 0.0280588i 0.857812 0.513964i \(-0.171823\pi\)
−0.874012 + 0.485905i \(0.838490\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0.841495i 0.0929276i
\(83\) 3.71007 2.14201i 0.407233 0.235116i −0.282367 0.959306i \(-0.591120\pi\)
0.689600 + 0.724190i \(0.257786\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.134751 0.233396i 0.0145306 0.0251677i
\(87\) 0 0
\(88\) −4.86286 + 2.80757i −0.518383 + 0.299288i
\(89\) −3.00000 −0.317999 −0.159000 0.987279i \(-0.550827\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(90\) 0 0
\(91\) 6.67282 0.699502
\(92\) 8.57293 4.94958i 0.893790 0.516030i
\(93\) 0 0
\(94\) 1.98963 3.44615i 0.205215 0.355443i
\(95\) 0 0
\(96\) 0 0
\(97\) −6.78555 + 3.91764i −0.688968 + 0.397776i −0.803225 0.595675i \(-0.796885\pi\)
0.114257 + 0.993451i \(0.463551\pi\)
\(98\) 2.83754i 0.286635i
\(99\) 0 0
\(100\) 0 0
\(101\) −2.10083 3.63875i −0.209040 0.362069i 0.742372 0.669988i \(-0.233701\pi\)
−0.951413 + 0.307919i \(0.900367\pi\)
\(102\) 0 0
\(103\) 1.57340 + 0.908405i 0.155032 + 0.0895078i 0.575509 0.817795i \(-0.304804\pi\)
−0.420477 + 0.907303i \(0.638137\pi\)
\(104\) 4.90841 8.50161i 0.481309 0.833651i
\(105\) 0 0
\(106\) 0.327176 + 0.566686i 0.0317782 + 0.0550414i
\(107\) 11.9176i 1.15212i 0.817407 + 0.576061i \(0.195411\pi\)
−0.817407 + 0.576061i \(0.804589\pi\)
\(108\) 0 0
\(109\) 16.6521 1.59498 0.797491 0.603331i \(-0.206160\pi\)
0.797491 + 0.603331i \(0.206160\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.65145 + 1.53081i 0.250538 + 0.144648i
\(113\) 17.4272 + 10.0616i 1.63942 + 0.946518i 0.981034 + 0.193836i \(0.0620929\pi\)
0.658384 + 0.752682i \(0.271240\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −15.8745 −1.47391
\(117\) 0 0
\(118\) 0.654353i 0.0602380i
\(119\) −1.90841 3.30545i −0.174943 0.303011i
\(120\) 0 0
\(121\) 1.92801 3.33941i 0.175273 0.303582i
\(122\) 1.25269 + 0.723239i 0.113413 + 0.0654790i
\(123\) 0 0
\(124\) −5.82209 10.0842i −0.522839 0.905584i
\(125\) 0 0
\(126\) 0 0
\(127\) 2.18714i 0.194078i −0.995281 0.0970388i \(-0.969063\pi\)
0.995281 0.0970388i \(-0.0309371\pi\)
\(128\) 9.98769 5.76640i 0.882795 0.509682i
\(129\) 0 0
\(130\) 0 0
\(131\) −3.00000 + 5.19615i −0.262111 + 0.453990i −0.966803 0.255524i \(-0.917752\pi\)
0.704692 + 0.709514i \(0.251085\pi\)
\(132\) 0 0
\(133\) 5.77883 3.33641i 0.501089 0.289304i
\(134\) −3.76970 −0.325653
\(135\) 0 0
\(136\) −5.61515 −0.481495
\(137\) −8.83490 + 5.10083i −0.754816 + 0.435793i −0.827431 0.561567i \(-0.810199\pi\)
0.0726153 + 0.997360i \(0.476865\pi\)
\(138\) 0 0
\(139\) 4.00000 6.92820i 0.339276 0.587643i −0.645021 0.764165i \(-0.723151\pi\)
0.984297 + 0.176522i \(0.0564848\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.37751 3.68206i 0.535189 0.308992i
\(143\) 12.4896i 1.04444i
\(144\) 0 0
\(145\) 0 0
\(146\) −0.489634 0.848071i −0.0405224 0.0701868i
\(147\) 0 0
\(148\) −2.63203 1.51960i −0.216351 0.124910i
\(149\) 10.0381 17.3865i 0.822351 1.42435i −0.0815762 0.996667i \(-0.525995\pi\)
0.903927 0.427687i \(-0.140671\pi\)
\(150\) 0 0
\(151\) −1.51960 2.63203i −0.123663 0.214191i 0.797546 0.603258i \(-0.206131\pi\)
−0.921210 + 0.389066i \(0.872798\pi\)
\(152\) 9.81681i 0.796248i
\(153\) 0 0
\(154\) −2.18319 −0.175926
\(155\) 0 0
\(156\) 0 0
\(157\) 0.174643 + 0.100830i 0.0139381 + 0.00804714i 0.506953 0.861974i \(-0.330772\pi\)
−0.493015 + 0.870021i \(0.664105\pi\)
\(158\) −0.142651 0.0823593i −0.0113487 0.00655216i
\(159\) 0 0
\(160\) 0 0
\(161\) 8.45043 0.665987
\(162\) 0 0
\(163\) 17.8168i 1.39552i 0.716331 + 0.697760i \(0.245820\pi\)
−0.716331 + 0.697760i \(0.754180\pi\)
\(164\) −1.23050 2.13129i −0.0960858 0.166425i
\(165\) 0 0
\(166\) 1.22522 2.12214i 0.0950952 0.164710i
\(167\) −12.2117 7.05042i −0.944968 0.545578i −0.0534538 0.998570i \(-0.517023\pi\)
−0.891514 + 0.452993i \(0.850356\pi\)
\(168\) 0 0
\(169\) 4.41764 + 7.65158i 0.339819 + 0.588583i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.788172i 0.0600976i
\(173\) −3.78140 + 2.18319i −0.287494 + 0.165985i −0.636811 0.771020i \(-0.719747\pi\)
0.349317 + 0.937005i \(0.386414\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.86525 4.96276i 0.215976 0.374082i
\(177\) 0 0
\(178\) −1.48608 + 0.857990i −0.111387 + 0.0643091i
\(179\) −15.1625 −1.13330 −0.566648 0.823960i \(-0.691760\pi\)
−0.566648 + 0.823960i \(0.691760\pi\)
\(180\) 0 0
\(181\) 3.20166 0.237978 0.118989 0.992896i \(-0.462035\pi\)
0.118989 + 0.992896i \(0.462035\pi\)
\(182\) 3.30545 1.90841i 0.245017 0.141460i
\(183\) 0 0
\(184\) 6.21598 10.7664i 0.458248 0.793709i
\(185\) 0 0
\(186\) 0 0
\(187\) −6.18687 + 3.57199i −0.452429 + 0.261210i
\(188\) 11.6376i 0.848757i
\(189\) 0 0
\(190\) 0 0
\(191\) −1.41877 2.45738i −0.102659 0.177810i 0.810121 0.586263i \(-0.199402\pi\)
−0.912779 + 0.408453i \(0.866068\pi\)
\(192\) 0 0
\(193\) 16.2710 + 9.39409i 1.17121 + 0.676201i 0.953966 0.299915i \(-0.0969584\pi\)
0.217249 + 0.976116i \(0.430292\pi\)
\(194\) −2.24086 + 3.88129i −0.160885 + 0.278660i
\(195\) 0 0
\(196\) −4.14927 7.18675i −0.296376 0.513339i
\(197\) 5.83528i 0.415747i 0.978156 + 0.207873i \(0.0666542\pi\)
−0.978156 + 0.207873i \(0.933346\pi\)
\(198\) 0 0
\(199\) −13.0761 −0.926943 −0.463472 0.886112i \(-0.653396\pi\)
−0.463472 + 0.886112i \(0.653396\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −2.08134 1.20166i −0.146442 0.0845486i
\(203\) −11.7357 6.77563i −0.823687 0.475556i
\(204\) 0 0
\(205\) 0 0
\(206\) 1.03920 0.0724047
\(207\) 0 0
\(208\) 10.0185i 0.694656i
\(209\) −6.24482 10.8163i −0.431963 0.748182i
\(210\) 0 0
\(211\) −4.19243 + 7.26149i −0.288618 + 0.499902i −0.973480 0.228771i \(-0.926529\pi\)
0.684862 + 0.728673i \(0.259863\pi\)
\(212\) −1.65730 0.956844i −0.113824 0.0657163i
\(213\) 0 0
\(214\) 3.40841 + 5.90353i 0.232994 + 0.403557i
\(215\) 0 0
\(216\) 0 0
\(217\) 9.94006i 0.674776i
\(218\) 8.24879 4.76244i 0.558679 0.322553i
\(219\) 0 0
\(220\) 0 0
\(221\) 6.24482 10.8163i 0.420072 0.727586i
\(222\) 0 0
\(223\) 7.93834 4.58321i 0.531591 0.306914i −0.210073 0.977686i \(-0.567370\pi\)
0.741664 + 0.670772i \(0.234037\pi\)
\(224\) 7.75123 0.517901
\(225\) 0 0
\(226\) 11.5104 0.765658
\(227\) −2.31473 + 1.33641i −0.153634 + 0.0887008i −0.574846 0.818261i \(-0.694938\pi\)
0.421212 + 0.906962i \(0.361605\pi\)
\(228\) 0 0
\(229\) 1.27365 2.20603i 0.0841654 0.145779i −0.820870 0.571115i \(-0.806511\pi\)
0.905035 + 0.425336i \(0.139844\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −17.2652 + 9.96806i −1.13351 + 0.654435i
\(233\) 6.22013i 0.407494i 0.979024 + 0.203747i \(0.0653121\pi\)
−0.979024 + 0.203747i \(0.934688\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.956844 + 1.65730i 0.0622852 + 0.107881i
\(237\) 0 0
\(238\) −1.89070 1.09159i −0.122556 0.0707576i
\(239\) −4.06163 + 7.03494i −0.262725 + 0.455053i −0.966965 0.254909i \(-0.917954\pi\)
0.704240 + 0.709962i \(0.251288\pi\)
\(240\) 0 0
\(241\) 13.1821 + 22.8320i 0.849131 + 1.47074i 0.881985 + 0.471278i \(0.156207\pi\)
−0.0328536 + 0.999460i \(0.510460\pi\)
\(242\) 2.20561i 0.141782i
\(243\) 0 0
\(244\) −4.23030 −0.270817
\(245\) 0 0
\(246\) 0 0
\(247\) 18.9099 + 10.9176i 1.20321 + 0.694673i
\(248\) −12.6643 7.31173i −0.804183 0.464295i
\(249\) 0 0
\(250\) 0 0
\(251\) 0.549569 0.0346885 0.0173443 0.999850i \(-0.494479\pi\)
0.0173443 + 0.999850i \(0.494479\pi\)
\(252\) 0 0
\(253\) 15.8168i 0.994394i
\(254\) −0.625515 1.08342i −0.0392483 0.0679801i
\(255\) 0 0
\(256\) 2.11515 3.66355i 0.132197 0.228972i
\(257\) 15.5885 + 9.00000i 0.972381 + 0.561405i 0.899961 0.435970i \(-0.143595\pi\)
0.0724199 + 0.997374i \(0.476928\pi\)
\(258\) 0 0
\(259\) −1.29721 2.24683i −0.0806046 0.139611i
\(260\) 0 0
\(261\) 0 0
\(262\) 3.43196i 0.212027i
\(263\) −10.3016 + 5.94761i −0.635221 + 0.366745i −0.782771 0.622309i \(-0.786195\pi\)
0.147550 + 0.989055i \(0.452861\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 1.90841 3.30545i 0.117012 0.202670i
\(267\) 0 0
\(268\) 9.54766 5.51234i 0.583216 0.336720i
\(269\) 28.5737 1.74217 0.871084 0.491134i \(-0.163417\pi\)
0.871084 + 0.491134i \(0.163417\pi\)
\(270\) 0 0
\(271\) −23.3641 −1.41927 −0.709635 0.704570i \(-0.751140\pi\)
−0.709635 + 0.704570i \(0.751140\pi\)
\(272\) 4.96276 2.86525i 0.300911 0.173731i
\(273\) 0 0
\(274\) −2.91764 + 5.05350i −0.176261 + 0.305293i
\(275\) 0 0
\(276\) 0 0
\(277\) 13.0563 7.53807i 0.784479 0.452919i −0.0535366 0.998566i \(-0.517049\pi\)
0.838015 + 0.545647i \(0.183716\pi\)
\(278\) 4.57595i 0.274447i
\(279\) 0 0
\(280\) 0 0
\(281\) 3.32605 + 5.76088i 0.198415 + 0.343665i 0.948015 0.318226i \(-0.103087\pi\)
−0.749599 + 0.661892i \(0.769754\pi\)
\(282\) 0 0
\(283\) −23.2934 13.4485i −1.38465 0.799428i −0.391943 0.919989i \(-0.628197\pi\)
−0.992706 + 0.120562i \(0.961530\pi\)
\(284\) −10.7684 + 18.6514i −0.638985 + 1.10675i
\(285\) 0 0
\(286\) −3.57199 6.18687i −0.211216 0.365838i
\(287\) 2.10083i 0.124008i
\(288\) 0 0
\(289\) 9.85601 0.579765
\(290\) 0 0
\(291\) 0 0
\(292\) 2.48023 + 1.43196i 0.145144 + 0.0837991i
\(293\) 10.7256 + 6.19243i 0.626596 + 0.361765i 0.779433 0.626486i \(-0.215507\pi\)
−0.152837 + 0.988251i \(0.548841\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −3.81681 −0.221848
\(297\) 0 0
\(298\) 11.4834i 0.665217i
\(299\) 13.8260 + 23.9474i 0.799581 + 1.38491i
\(300\) 0 0
\(301\) −0.336412 + 0.582682i −0.0193905 + 0.0335853i
\(302\) −1.50550 0.869202i −0.0866319 0.0500169i
\(303\) 0 0
\(304\) 5.00924 + 8.67625i 0.287299 + 0.497617i
\(305\) 0 0
\(306\) 0 0
\(307\) 2.49359i 0.142317i 0.997465 + 0.0711583i \(0.0226695\pi\)
−0.997465 + 0.0711583i \(0.977330\pi\)
\(308\) 5.52944 3.19243i 0.315069 0.181905i
\(309\) 0 0
\(310\) 0 0
\(311\) −12.1101 + 20.9752i −0.686699 + 1.18940i 0.286201 + 0.958170i \(0.407608\pi\)
−0.972900 + 0.231228i \(0.925726\pi\)
\(312\) 0 0
\(313\) −30.3837 + 17.5420i −1.71739 + 0.991534i −0.793770 + 0.608219i \(0.791884\pi\)
−0.923618 + 0.383315i \(0.874782\pi\)
\(314\) 0.115349 0.00650950
\(315\) 0 0
\(316\) 0.481728 0.0270993
\(317\) −9.06829 + 5.23558i −0.509326 + 0.294060i −0.732557 0.680706i \(-0.761673\pi\)
0.223231 + 0.974766i \(0.428340\pi\)
\(318\) 0 0
\(319\) −12.6821 + 21.9660i −0.710059 + 1.22986i
\(320\) 0 0
\(321\) 0 0
\(322\) 4.18601 2.41679i 0.233277 0.134683i
\(323\) 12.4896i 0.694942i
\(324\) 0 0
\(325\) 0 0
\(326\) 5.09555 + 8.82575i 0.282216 + 0.488813i
\(327\) 0 0
\(328\) −2.67659 1.54533i −0.147790 0.0853267i
\(329\) −4.96721 + 8.60346i −0.273851 + 0.474324i
\(330\) 0 0
\(331\) −8.38880 14.5298i −0.461090 0.798632i 0.537925 0.842993i \(-0.319208\pi\)
−0.999016 + 0.0443606i \(0.985875\pi\)
\(332\) 7.16641i 0.393308i
\(333\) 0 0
\(334\) −8.06558 −0.441329
\(335\) 0 0
\(336\) 0 0
\(337\) −23.5394 13.5905i −1.28227 0.740320i −0.305008 0.952350i \(-0.598659\pi\)
−0.977263 + 0.212030i \(0.931993\pi\)
\(338\) 4.37665 + 2.52686i 0.238058 + 0.137443i
\(339\) 0 0
\(340\) 0 0
\(341\) −18.6050 −1.00752
\(342\) 0 0
\(343\) 17.0801i 0.922239i
\(344\) 0.494917 + 0.857221i 0.0266841 + 0.0462182i
\(345\) 0 0
\(346\) −1.24877 + 2.16293i −0.0671343 + 0.116280i
\(347\) 20.4086 + 11.7829i 1.09559 + 0.632539i 0.935059 0.354492i \(-0.115346\pi\)
0.160530 + 0.987031i \(0.448680\pi\)
\(348\) 0 0
\(349\) −5.35601 9.27689i −0.286701 0.496580i 0.686319 0.727300i \(-0.259225\pi\)
−0.973020 + 0.230720i \(0.925892\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 14.5081i 0.773285i
\(353\) −23.6141 + 13.6336i −1.25685 + 0.725644i −0.972461 0.233064i \(-0.925125\pi\)
−0.284392 + 0.958708i \(0.591792\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 2.50924 4.34612i 0.132989 0.230344i
\(357\) 0 0
\(358\) −7.51089 + 4.33641i −0.396963 + 0.229186i
\(359\) −10.6807 −0.563707 −0.281854 0.959457i \(-0.590949\pi\)
−0.281854 + 0.959457i \(0.590949\pi\)
\(360\) 0 0
\(361\) 2.83528 0.149225
\(362\) 1.58598 0.915664i 0.0833571 0.0481262i
\(363\) 0 0
\(364\) −5.58123 + 9.66697i −0.292536 + 0.506687i
\(365\) 0 0
\(366\) 0 0
\(367\) 7.33624 4.23558i 0.382949 0.221096i −0.296152 0.955141i \(-0.595703\pi\)
0.679100 + 0.734045i \(0.262370\pi\)
\(368\) 12.6873i 0.661373i
\(369\) 0 0
\(370\) 0 0
\(371\) −0.816810 1.41476i −0.0424067 0.0734505i
\(372\) 0 0
\(373\) −8.76700 5.06163i −0.453938 0.262081i 0.255554 0.966795i \(-0.417742\pi\)
−0.709492 + 0.704714i \(0.751075\pi\)
\(374\) −2.04316 + 3.53885i −0.105649 + 0.182990i
\(375\) 0 0
\(376\) 7.30757 + 12.6571i 0.376859 + 0.652740i
\(377\) 44.3434i 2.28380i
\(378\) 0 0
\(379\) −11.9216 −0.612371 −0.306186 0.951972i \(-0.599053\pi\)
−0.306186 + 0.951972i \(0.599053\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −1.40561 0.811528i −0.0719171 0.0415214i
\(383\) 8.50161 + 4.90841i 0.434412 + 0.250808i 0.701224 0.712941i \(-0.252637\pi\)
−0.266813 + 0.963748i \(0.585970\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 10.7467 0.546993
\(387\) 0 0
\(388\) 13.1070i 0.665409i
\(389\) −4.61007 7.98487i −0.233740 0.404849i 0.725166 0.688574i \(-0.241763\pi\)
−0.958906 + 0.283725i \(0.908430\pi\)
\(390\) 0 0
\(391\) 7.90841 13.6978i 0.399945 0.692725i
\(392\) −9.02554 5.21090i −0.455858 0.263190i
\(393\) 0 0
\(394\) 1.66887 + 2.89057i 0.0840765 + 0.145625i
\(395\) 0 0
\(396\) 0 0
\(397\) 22.9793i 1.15330i 0.816993 + 0.576648i \(0.195640\pi\)
−0.816993 + 0.576648i \(0.804360\pi\)
\(398\) −6.47741 + 3.73973i −0.324683 + 0.187456i
\(399\) 0 0
\(400\) 0 0
\(401\) −5.53279 + 9.58307i −0.276294 + 0.478556i −0.970461 0.241259i \(-0.922440\pi\)
0.694167 + 0.719814i \(0.255773\pi\)
\(402\) 0 0
\(403\) 28.1688 16.2633i 1.40319 0.810132i
\(404\) 7.02864 0.349688
\(405\) 0 0
\(406\) −7.75123 −0.384687
\(407\) −4.20543 + 2.42801i −0.208455 + 0.120352i
\(408\) 0 0
\(409\) −8.81681 + 15.2712i −0.435963 + 0.755110i −0.997374 0.0724270i \(-0.976926\pi\)
0.561411 + 0.827537i \(0.310259\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −2.63203 + 1.51960i −0.129671 + 0.0748654i
\(413\) 1.63362i 0.0803852i
\(414\) 0 0
\(415\) 0 0
\(416\) 12.6821 + 21.9660i 0.621789 + 1.07697i
\(417\) 0 0
\(418\) −6.18687 3.57199i −0.302610 0.174712i
\(419\) −18.5173 + 32.0730i −0.904631 + 1.56687i −0.0832199 + 0.996531i \(0.526520\pi\)
−0.821411 + 0.570336i \(0.806813\pi\)
\(420\) 0 0
\(421\) −2.52884 4.38007i −0.123248 0.213472i 0.797799 0.602924i \(-0.205998\pi\)
−0.921047 + 0.389452i \(0.872664\pi\)
\(422\) 4.79608i 0.233469i
\(423\) 0 0
\(424\) −2.40332 −0.116716
\(425\) 0 0
\(426\) 0 0
\(427\) −3.12739 1.80560i −0.151345 0.0873790i
\(428\) −17.2652 9.96806i −0.834544 0.481824i
\(429\) 0 0
\(430\) 0 0
\(431\) 5.23030 0.251935 0.125967 0.992034i \(-0.459797\pi\)
0.125967 + 0.992034i \(0.459797\pi\)
\(432\) 0 0
\(433\) 34.3434i 1.65044i 0.564813 + 0.825219i \(0.308948\pi\)
−0.564813 + 0.825219i \(0.691052\pi\)
\(434\) −2.84283 4.92392i −0.136460 0.236356i
\(435\) 0 0
\(436\) −13.9280 + 24.1240i −0.667031 + 1.15533i
\(437\) 23.9474 + 13.8260i 1.14556 + 0.661389i
\(438\) 0 0
\(439\) −9.77365 16.9285i −0.466471 0.807952i 0.532796 0.846244i \(-0.321141\pi\)
−0.999267 + 0.0382924i \(0.987808\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 7.14399i 0.339805i
\(443\) −9.09686 + 5.25208i −0.432205 + 0.249534i −0.700286 0.713863i \(-0.746944\pi\)
0.268081 + 0.963396i \(0.413611\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 2.62156 4.54068i 0.124135 0.215007i
\(447\) 0 0
\(448\) −1.46324 + 0.844801i −0.0691315 + 0.0399131i
\(449\) 22.8560 1.07864 0.539321 0.842100i \(-0.318681\pi\)
0.539321 + 0.842100i \(0.318681\pi\)
\(450\) 0 0
\(451\) −3.93216 −0.185158
\(452\) −29.1527 + 16.8313i −1.37123 + 0.791679i
\(453\) 0 0
\(454\) −0.764419 + 1.32401i −0.0358759 + 0.0621390i
\(455\) 0 0
\(456\) 0 0
\(457\) 12.1472 7.01319i 0.568222 0.328063i −0.188217 0.982127i \(-0.560271\pi\)
0.756439 + 0.654064i \(0.226937\pi\)
\(458\) 1.45704i 0.0680832i
\(459\) 0 0
\(460\) 0 0
\(461\) −12.0513 20.8734i −0.561283 0.972171i −0.997385 0.0722736i \(-0.976975\pi\)
0.436102 0.899897i \(-0.356359\pi\)
\(462\) 0 0
\(463\) 29.3930 + 16.9700i 1.36601 + 0.788664i 0.990415 0.138121i \(-0.0441063\pi\)
0.375591 + 0.926785i \(0.377440\pi\)
\(464\) 10.1728 17.6198i 0.472261 0.817981i
\(465\) 0 0
\(466\) 1.77894 + 3.08121i 0.0824077 + 0.142734i
\(467\) 27.3720i 1.26663i −0.773896 0.633313i \(-0.781695\pi\)
0.773896 0.633313i \(-0.218305\pi\)
\(468\) 0 0
\(469\) 9.41123 0.434570
\(470\) 0 0
\(471\) 0 0
\(472\) 2.08134 + 1.20166i 0.0958013 + 0.0553109i
\(473\) 1.09062 + 0.629668i 0.0501466 + 0.0289521i
\(474\) 0 0
\(475\) 0 0
\(476\) 6.38485 0.292649
\(477\) 0 0
\(478\) 4.64645i 0.212524i
\(479\) −2.61515 4.52957i −0.119489 0.206961i 0.800076 0.599898i \(-0.204792\pi\)
−0.919565 + 0.392937i \(0.871459\pi\)
\(480\) 0 0
\(481\) 4.24482 7.35224i 0.193547 0.335233i
\(482\) 13.0597 + 7.54005i 0.594855 + 0.343440i
\(483\) 0 0
\(484\) 3.22522 + 5.58624i 0.146601 + 0.253920i
\(485\) 0 0
\(486\) 0 0
\(487\) 24.0185i 1.08838i 0.838962 + 0.544190i \(0.183163\pi\)
−0.838962 + 0.544190i \(0.816837\pi\)
\(488\) −4.60090 + 2.65633i −0.208273 + 0.120246i
\(489\) 0 0
\(490\) 0 0
\(491\) 7.38880 12.7978i 0.333452 0.577556i −0.649734 0.760161i \(-0.725120\pi\)
0.983186 + 0.182606i \(0.0584531\pi\)
\(492\) 0 0
\(493\) −21.9660 + 12.6821i −0.989298 + 0.571171i
\(494\) 12.4896 0.561935
\(495\) 0 0
\(496\) 14.9239 0.670101
\(497\) −15.9217 + 9.19243i −0.714188 + 0.412337i
\(498\) 0 0
\(499\) 12.4280 21.5259i 0.556354 0.963633i −0.441443 0.897289i \(-0.645533\pi\)
0.997797 0.0663440i \(-0.0211335\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0.272235 0.157175i 0.0121504 0.00701506i
\(503\) 38.9154i 1.73515i −0.497305 0.867576i \(-0.665677\pi\)
0.497305 0.867576i \(-0.334323\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −4.52355 7.83503i −0.201097 0.348309i
\(507\) 0 0
\(508\) 3.16853 + 1.82935i 0.140581 + 0.0811644i
\(509\) −1.01037 + 1.75001i −0.0447837 + 0.0775676i −0.887548 0.460715i \(-0.847593\pi\)
0.842765 + 0.538282i \(0.180927\pi\)
\(510\) 0 0
\(511\) 1.22239 + 2.11725i 0.0540755 + 0.0936615i
\(512\) 20.6459i 0.912428i
\(513\) 0 0
\(514\) 10.2959 0.454132
\(515\) 0 0
\(516\) 0 0
\(517\) 16.1032 + 9.29721i 0.708220 + 0.408891i
\(518\) −1.28517 0.741995i −0.0564672 0.0326014i
\(519\) 0 0
\(520\) 0 0
\(521\) 23.0290 1.00892 0.504460 0.863435i \(-0.331692\pi\)
0.504460 + 0.863435i \(0.331692\pi\)
\(522\) 0 0
\(523\) 41.1170i 1.79792i −0.438028 0.898961i \(-0.644323\pi\)
0.438028 0.898961i \(-0.355677\pi\)
\(524\) −5.01847 8.69225i −0.219233 0.379723i
\(525\) 0 0
\(526\) −3.40199 + 5.89242i −0.148334 + 0.256922i
\(527\) −16.1124 9.30249i −0.701867 0.405223i
\(528\) 0 0
\(529\) 6.00924 + 10.4083i 0.261271 + 0.452535i
\(530\) 0 0
\(531\) 0 0
\(532\) 11.1625i 0.483954i
\(533\) 5.95348 3.43724i 0.257874 0.148883i
\(534\) 0 0
\(535\) 0 0
\(536\) 6.92272 11.9905i 0.299016 0.517911i
\(537\) 0 0
\(538\) 14.1543 8.17198i 0.610234 0.352319i
\(539\) −13.2593 −0.571120
\(540\) 0 0
\(541\) 5.20957 0.223977 0.111988 0.993710i \(-0.464278\pi\)
0.111988 + 0.993710i \(0.464278\pi\)
\(542\) −11.5737 + 6.68206i −0.497132 + 0.287019i
\(543\) 0 0
\(544\) 7.25405 12.5644i 0.311015 0.538694i
\(545\) 0 0
\(546\) 0 0
\(547\) −34.6764 + 20.0204i −1.48266 + 0.856013i −0.999806 0.0196900i \(-0.993732\pi\)
−0.482851 + 0.875702i \(0.660399\pi\)
\(548\) 17.0656i 0.729005i
\(549\) 0 0
\(550\) 0 0
\(551\) −22.1717 38.4025i −0.944546 1.63600i
\(552\) 0 0
\(553\) 0.356133 + 0.205614i 0.0151443 + 0.00874359i
\(554\) 4.31173 7.46813i 0.183188 0.317290i
\(555\) 0 0
\(556\) 6.69129 + 11.5897i 0.283774 + 0.491511i
\(557\) 14.4033i 0.610288i −0.952306 0.305144i \(-0.901295\pi\)
0.952306 0.305144i \(-0.0987047\pi\)
\(558\) 0 0
\(559\) −2.20166 −0.0931203
\(560\) 0 0
\(561\) 0 0
\(562\) 3.29518 + 1.90248i 0.138999 + 0.0802511i
\(563\) 25.4335 + 14.6840i 1.07189 + 0.618858i 0.928698 0.370836i \(-0.120929\pi\)
0.143196 + 0.989694i \(0.454262\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −15.3849 −0.646674
\(567\) 0 0
\(568\) 27.0471i 1.13487i
\(569\) −23.4033 40.5357i −0.981118 1.69935i −0.658056 0.752969i \(-0.728621\pi\)
−0.323062 0.946378i \(-0.604712\pi\)
\(570\) 0 0
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) 18.0938 + 10.4465i 0.756541 + 0.436789i
\(573\) 0 0
\(574\) −0.600830 1.04067i −0.0250782 0.0434367i
\(575\) 0 0
\(576\) 0 0
\(577\) 28.2386i 1.17559i −0.809010 0.587794i \(-0.799996\pi\)
0.809010 0.587794i \(-0.200004\pi\)
\(578\) 4.88228 2.81879i 0.203076 0.117246i
\(579\) 0 0
\(580\) 0 0
\(581\) −3.05880 + 5.29801i −0.126901 + 0.219798i
\(582\) 0 0
\(583\) −2.64802 + 1.52884i −0.109670 + 0.0633180i
\(584\) 3.59668 0.148832
\(585\) 0 0
\(586\) 7.08405 0.292639
\(587\) 15.6598 9.04118i 0.646348 0.373169i −0.140707 0.990051i \(-0.544938\pi\)
0.787056 + 0.616882i \(0.211604\pi\)
\(588\) 0 0
\(589\) 16.2633 28.1688i 0.670117 1.16068i
\(590\) 0 0
\(591\) 0 0
\(592\) 3.37336 1.94761i 0.138644 0.0800462i
\(593\) 7.73840i 0.317778i 0.987296 + 0.158889i \(0.0507912\pi\)
−0.987296 + 0.158889i \(0.949209\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 16.7919 + 29.0845i 0.687824 + 1.19135i
\(597\) 0 0
\(598\) 13.6978 + 7.90841i 0.560143 + 0.323399i
\(599\) 13.9608 24.1808i 0.570423 0.988001i −0.426100 0.904676i \(-0.640113\pi\)
0.996522 0.0833249i \(-0.0265539\pi\)
\(600\) 0 0
\(601\) −19.2201 33.2902i −0.784006 1.35794i −0.929591 0.368592i \(-0.879840\pi\)
0.145586 0.989346i \(-0.453493\pi\)
\(602\) 0.384851i 0.0156853i
\(603\) 0 0
\(604\) 5.08405 0.206867
\(605\) 0 0
\(606\) 0 0
\(607\) −0.554113 0.319917i −0.0224907 0.0129850i 0.488712 0.872445i \(-0.337467\pi\)
−0.511203 + 0.859460i \(0.670800\pi\)
\(608\) 21.9660 + 12.6821i 0.890838 + 0.514325i
\(609\) 0 0
\(610\) 0 0
\(611\) −32.5081 −1.31514
\(612\) 0 0
\(613\) 42.7467i 1.72652i 0.504757 + 0.863262i \(0.331582\pi\)
−0.504757 + 0.863262i \(0.668418\pi\)
\(614\) 0.713157 + 1.23522i 0.0287807 + 0.0498496i
\(615\) 0 0
\(616\) 4.00924 6.94420i 0.161537 0.279790i
\(617\) −18.2753 10.5513i −0.735737 0.424778i 0.0847805 0.996400i \(-0.472981\pi\)
−0.820517 + 0.571622i \(0.806314\pi\)
\(618\) 0 0
\(619\) −6.82605 11.8231i −0.274362 0.475209i 0.695612 0.718418i \(-0.255133\pi\)
−0.969974 + 0.243209i \(0.921800\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 13.8538i 0.555485i
\(623\) 3.71007 2.14201i 0.148641 0.0858178i
\(624\) 0 0
\(625\) 0 0
\(626\) −10.0339 + 17.3793i −0.401036 + 0.694615i
\(627\) 0 0
\(628\) −0.292148 + 0.168672i −0.0116580 + 0.00673073i
\(629\) −4.85601 −0.193622
\(630\) 0 0
\(631\) 33.2593 1.32403 0.662017 0.749489i \(-0.269701\pi\)
0.662017 + 0.749489i \(0.269701\pi\)
\(632\) 0.523930 0.302491i 0.0208408 0.0120325i
\(633\) 0 0
\(634\) −2.99472 + 5.18700i −0.118935 + 0.206002i
\(635\) 0 0
\(636\) 0 0
\(637\) 20.0753 11.5905i 0.795411 0.459231i
\(638\) 14.5081i 0.574381i
\(639\) 0 0
\(640\) 0 0
\(641\) 13.1429 + 22.7641i 0.519112 + 0.899128i 0.999753 + 0.0222106i \(0.00707044\pi\)
−0.480642 + 0.876917i \(0.659596\pi\)
\(642\) 0 0
\(643\) −17.8250 10.2913i −0.702950 0.405848i 0.105495 0.994420i \(-0.466357\pi\)
−0.808445 + 0.588571i \(0.799691\pi\)
\(644\) −7.06804 + 12.2422i −0.278520 + 0.482410i
\(645\) 0 0
\(646\) −3.57199 6.18687i −0.140538 0.243419i
\(647\) 23.2527i 0.914159i 0.889426 + 0.457079i \(0.151104\pi\)
−0.889426 + 0.457079i \(0.848896\pi\)
\(648\) 0 0
\(649\) 3.05767 0.120024
\(650\) 0 0
\(651\) 0 0
\(652\) −25.8114 14.9022i −1.01085 0.583615i
\(653\) 16.2459 + 9.37957i 0.635751 + 0.367051i 0.782976 0.622052i \(-0.213701\pi\)
−0.147225 + 0.989103i \(0.547034\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 3.15415 0.123149
\(657\) 0 0
\(658\) 5.68242i 0.221524i
\(659\) 0.140034 + 0.242545i 0.00545494 + 0.00944823i 0.868740 0.495268i \(-0.164930\pi\)
−0.863285 + 0.504717i \(0.831597\pi\)
\(660\) 0 0
\(661\) 19.8930 34.4556i 0.773746 1.34017i −0.161750 0.986832i \(-0.551714\pi\)
0.935496 0.353336i \(-0.114953\pi\)
\(662\) −8.31097 4.79834i −0.323015 0.186493i
\(663\) 0 0
\(664\) 4.50000 + 7.79423i 0.174634 + 0.302475i
\(665\) 0 0
\(666\) 0 0
\(667\) 56.1562i 2.17438i
\(668\) 20.4280 11.7941i 0.790382 0.456327i
\(669\) 0 0
\(670\) 0 0
\(671\) −3.37957 + 5.85358i −0.130467 + 0.225975i
\(672\) 0 0
\(673\) 29.0368 16.7644i 1.11929 0.646221i 0.178068 0.984018i \(-0.443015\pi\)
0.941219 + 0.337797i \(0.109682\pi\)
\(674\) −15.5473 −0.598860
\(675\) 0 0
\(676\) −14.7799 −0.568456
\(677\) 23.8048 13.7437i 0.914891 0.528213i 0.0328897 0.999459i \(-0.489529\pi\)
0.882002 + 0.471246i \(0.156196\pi\)
\(678\) 0 0
\(679\) 5.59442 9.68981i 0.214694 0.371861i
\(680\) 0 0
\(681\) 0 0
\(682\) −9.21618 + 5.32096i −0.352906 + 0.203750i
\(683\) 34.5865i 1.32342i 0.749762 + 0.661708i \(0.230168\pi\)
−0.749762 + 0.661708i \(0.769832\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −4.88485 8.46081i −0.186504 0.323035i
\(687\) 0 0
\(688\) −0.874830 0.505083i −0.0333526 0.0192561i
\(689\) 2.67282 4.62947i 0.101826 0.176369i
\(690\) 0 0
\(691\) −20.3641 35.2717i −0.774688 1.34180i −0.934970 0.354727i \(-0.884574\pi\)
0.160282 0.987071i \(-0.448760\pi\)
\(692\) 7.30418i 0.277663i
\(693\) 0 0
\(694\) 13.4795 0.511674
\(695\) 0 0
\(696\) 0 0
\(697\) −3.40535 1.96608i −0.128987 0.0744706i
\(698\) −5.30632 3.06360i −0.200847 0.115959i
\(699\) 0 0
\(700\) 0 0
\(701\) 19.4712 0.735416 0.367708 0.929941i \(-0.380143\pi\)
0.367708 + 0.929941i \(0.380143\pi\)
\(702\) 0 0
\(703\) 8.48963i 0.320193i
\(704\) 1.58123 + 2.73877i 0.0595948 + 0.103221i
\(705\) 0 0
\(706\) −7.79834 + 13.5071i −0.293494 + 0.508347i
\(707\) 5.19615 + 3.00000i 0.195421 + 0.112827i
\(708\) 0 0
\(709\) 7.54316 + 13.0651i 0.283289 + 0.490671i 0.972193 0.234182i \(-0.0752410\pi\)
−0.688904 + 0.724853i \(0.741908\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 6.30249i 0.236196i
\(713\) 35.6729 20.5957i 1.33596 0.771317i
\(714\) 0 0
\(715\) 0 0
\(716\) 12.6821 21.9660i 0.473951 0.820907i
\(717\) 0 0
\(718\) −5.29081 + 3.05465i −0.197451 + 0.113999i
\(719\) −3.43196 −0.127990 −0.0639952 0.997950i \(-0.520384\pi\)
−0.0639952 + 0.997950i \(0.520384\pi\)
\(720\) 0 0
\(721\) −2.59442 −0.0966211
\(722\) 1.40449 0.810881i 0.0522696 0.0301779i
\(723\) 0 0
\(724\) −2.67791 + 4.63827i −0.0995236 + 0.172380i
\(725\) 0 0
\(726\) 0 0
\(727\) 30.9789 17.8857i 1.14895 0.663344i 0.200315 0.979732i \(-0.435803\pi\)
0.948630 + 0.316388i \(0.102470\pi\)
\(728\) 14.0185i 0.519559i
\(729\) 0 0
\(730\) 0 0
\(731\) 0.629668 + 1.09062i 0.0232891 + 0.0403379i
\(732\) 0 0
\(733\) 19.0526 + 11.0000i 0.703722 + 0.406294i 0.808732 0.588177i \(-0.200154\pi\)
−0.105010 + 0.994471i \(0.533487\pi\)
\(734\) 2.42272 4.19628i 0.0894244 0.154888i
\(735\) 0 0
\(736\) 16.0605 + 27.8176i 0.591998 + 1.02537i
\(737\) 17.6151i 0.648862i
\(738\) 0 0
\(739\) −6.08631 −0.223889 −0.111944 0.993714i \(-0.535708\pi\)
−0.111944 + 0.993714i \(0.535708\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.809231 0.467210i −0.0297078 0.0171518i
\(743\) −22.0853 12.7509i −0.810231 0.467787i 0.0368054 0.999322i \(-0.488282\pi\)
−0.847036 + 0.531536i \(0.821615\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −5.79043 −0.212003
\(747\) 0 0
\(748\) 11.9506i 0.436958i
\(749\) −8.50924 14.7384i −0.310921 0.538530i
\(750\) 0 0
\(751\) 9.19638 15.9286i 0.335581 0.581243i −0.648016 0.761627i \(-0.724401\pi\)
0.983596 + 0.180384i \(0.0577342\pi\)
\(752\) −12.9171 7.45769i −0.471038 0.271954i
\(753\) 0 0
\(754\) −12.6821 21.9660i −0.461853 0.799953i
\(755\) 0 0
\(756\) 0 0
\(757\) 41.8986i 1.52283i 0.648264 + 0.761415i \(0.275495\pi\)
−0.648264 + 0.761415i \(0.724505\pi\)
\(758\) −5.90549 + 3.40954i −0.214497 + 0.123840i
\(759\) 0 0
\(760\) 0 0
\(761\) −3.98568 + 6.90340i −0.144481 + 0.250248i −0.929179 0.369630i \(-0.879485\pi\)
0.784698 + 0.619878i \(0.212818\pi\)
\(762\) 0 0
\(763\) −20.5935 + 11.8896i −0.745534 + 0.430434i
\(764\) 4.74671 0.171730
\(765\) 0 0
\(766\) 5.61515 0.202884
\(767\) −4.62947 + 2.67282i −0.167160 + 0.0965101i
\(768\) 0 0
\(769\) 3.01432 5.22095i 0.108699 0.188272i −0.806544 0.591174i \(-0.798665\pi\)
0.915244 + 0.402901i \(0.131998\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −27.2186 + 15.7147i −0.979618 + 0.565583i
\(773\) 44.4033i 1.59708i −0.601944 0.798538i \(-0.705607\pi\)
0.601944 0.798538i \(-0.294393\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −8.23030 14.2553i −0.295451 0.511735i
\(777\) 0 0
\(778\) −4.56729 2.63693i −0.163745 0.0945384i
\(779\) 3.43724 5.95348i 0.123152 0.213305i
\(780\) 0 0
\(781\) 17.2056 + 29.8010i 0.615665 + 1.06636i
\(782\) 9.04711i 0.323524i
\(783\) 0 0
\(784\) 10.6359 0.379853
\(785\) 0 0
\(786\) 0 0
\(787\) 14.5817 + 8.41877i 0.519783 + 0.300097i 0.736846 0.676061i \(-0.236314\pi\)
−0.217063 + 0.976158i \(0.569648\pi\)
\(788\) −8.45362 4.88070i −0.301148 0.173868i
\(789\) 0 0
\(790\) 0 0
\(791\) −28.7361 −1.02174
\(792\) 0 0
\(793\) 11.8168i 0.419627i
\(794\) 6.57199 + 11.3830i 0.233231 + 0.403968i
\(795\) 0 0
\(796\) 10.9370 18.9435i 0.387653 0.671435i
\(797\) 28.9010 + 16.6860i 1.02373 + 0.591049i 0.915181 0.403043i \(-0.132047\pi\)
0.108545 + 0.994091i \(0.465381\pi\)
\(798\) 0 0
\(799\) 9.29721 + 16.1032i 0.328912 + 0.569692i
\(800\) 0 0
\(801\) 0 0
\(802\) 6.32944i 0.223500i
\(803\) 3.96289 2.28797i 0.139847 0.0807408i
\(804\) 0 0
\(805\) 0 0
\(806\) 9.30249 16.1124i 0.327666 0.567535i
\(807\) 0 0
\(808\) 7.64439 4.41349i 0.268929 0.155266i
\(809\) 29.1809 1.02595 0.512973 0.858404i \(-0.328544\pi\)
0.512973 + 0.858404i \(0.328544\pi\)
\(810\) 0 0
\(811\) −15.5552 −0.546217 −0.273109 0.961983i \(-0.588052\pi\)
−0.273109 + 0.961983i \(0.588052\pi\)
\(812\) 19.6318 11.3344i 0.688942 0.397761i
\(813\) 0 0
\(814\) −1.38880 + 2.40548i −0.0486775 + 0.0843120i
\(815\) 0 0
\(816\) 0 0
\(817\) −1.90669 + 1.10083i −0.0667068 + 0.0385132i
\(818\) 10.0863i 0.352660i
\(819\) 0 0
\(820\) 0 0
\(821\) −11.8588 20.5401i −0.413876 0.716855i 0.581434 0.813594i \(-0.302492\pi\)
−0.995310 + 0.0967393i \(0.969159\pi\)
\(822\) 0 0
\(823\) −16.7732 9.68404i −0.584678 0.337564i 0.178312 0.983974i \(-0.442936\pi\)
−0.762990 + 0.646410i \(0.776270\pi\)
\(824\) −1.90841 + 3.30545i −0.0664824 + 0.115151i
\(825\) 0 0
\(826\) 0.467210 + 0.809231i 0.0162563 + 0.0281568i
\(827\) 52.2241i 1.81601i 0.418960 + 0.908005i \(0.362395\pi\)
−0.418960 + 0.908005i \(0.637605\pi\)
\(828\) 0 0
\(829\) 26.6442 0.925391 0.462695 0.886517i \(-0.346882\pi\)
0.462695 + 0.886517i \(0.346882\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −4.78811 2.76442i −0.165998 0.0958390i
\(833\) −11.4829 6.62967i −0.397860 0.229704i
\(834\) 0 0
\(835\) 0 0
\(836\) 20.8930 0.722598
\(837\) 0 0
\(838\) 21.1836i 0.731775i
\(839\) 12.5196 + 21.6846i 0.432225 + 0.748635i 0.997065 0.0765655i \(-0.0243954\pi\)
−0.564840 + 0.825201i \(0.691062\pi\)
\(840\) 0 0
\(841\) −30.5266 + 52.8736i −1.05264 + 1.82323i
\(842\) −2.50537 1.44648i −0.0863409 0.0498489i
\(843\) 0 0
\(844\) −7.01319 12.1472i −0.241404 0.418124i
\(845\) 0 0
\(846\) 0 0
\(847\) 5.50641i 0.189203i
\(848\) 2.12409 1.22635i 0.0729417 0.0421129i
\(849\) 0 0
\(850\) 0 0
\(851\) 5.37562 9.31084i 0.184274 0.319171i
\(852\) 0 0
\(853\) −9.41758 + 5.43724i −0.322452 + 0.186168i −0.652485 0.757802i \(-0.726273\pi\)
0.330033 + 0.943969i \(0.392940\pi\)
\(854\) −2.06558 −0.0706827
\(855\) 0 0
\(856\) −25.0369 −0.855745
\(857\) −16.1032 + 9.29721i −0.550076 + 0.317587i −0.749153 0.662397i \(-0.769539\pi\)
0.199077 + 0.979984i \(0.436206\pi\)
\(858\) 0 0
\(859\) −2.33246 + 4.03994i −0.0795825 + 0.137841i −0.903070 0.429494i \(-0.858692\pi\)
0.823487 + 0.567335i \(0.192025\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 2.59088 1.49585i 0.0882459 0.0509488i
\(863\) 28.0594i 0.955152i 0.878590 + 0.477576i \(0.158484\pi\)
−0.878590 + 0.477576i \(0.841516\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 9.82209 + 17.0124i 0.333768 + 0.578104i
\(867\) 0 0
\(868\) 14.4002 + 8.31399i 0.488776 + 0.282195i
\(869\) 0.384851 0.666581i 0.0130552 0.0226122i
\(870\) 0 0
\(871\) 15.3980 + 26.6702i 0.521743 + 0.903685i
\(872\) 34.9832i 1.18468i
\(873\) 0 0
\(874\) 15.8168 0.535012
\(875\) 0 0
\(876\) 0 0
\(877\) 30.0236 + 17.3342i 1.01383 + 0.585333i 0.912310 0.409501i \(-0.134297\pi\)
0.101516 + 0.994834i \(0.467631\pi\)
\(878\) −9.68297 5.59046i −0.326784 0.188669i
\(879\) 0 0
\(880\) 0 0
\(881\) 5.29854 0.178512 0.0892561 0.996009i \(-0.471551\pi\)
0.0892561 + 0.996009i \(0.471551\pi\)
\(882\) 0 0
\(883\) 10.3025i 0.346706i −0.984860 0.173353i \(-0.944540\pi\)
0.984860 0.173353i \(-0.0554602\pi\)
\(884\) 10.4465 + 18.0938i 0.351353 + 0.608561i
\(885\) 0 0
\(886\) −3.00415 + 5.20334i −0.100926 + 0.174810i
\(887\) −35.8971 20.7252i −1.20531 0.695885i −0.243577 0.969882i \(-0.578321\pi\)
−0.961731 + 0.273997i \(0.911654\pi\)
\(888\) 0 0
\(889\) 1.56163 + 2.70482i 0.0523753 + 0.0907167i
\(890\) 0 0
\(891\) 0 0
\(892\) 15.3338i 0.513413i
\(893\) −28.1528 + 16.2541i −0.942099 + 0.543921i
\(894\) 0 0
\(895\) 0 0
\(896\) −8.23445 + 14.2625i −0.275094 + 0.476476i
\(897\) 0 0
\(898\) 11.3220 6.53674i 0.377819 0.218134i
\(899\) −66.0554 −2.20307
\(900\) 0 0
\(901\) −3.05767 −0.101866
\(902\) −1.94784 + 1.12458i −0.0648559 + 0.0374446i
\(903\) 0 0
\(904\) −21.1378 + 36.6117i −0.703032 + 1.21769i
\(905\) 0 0
\(906\) 0 0
\(907\) 14.5424 8.39606i 0.482873 0.278787i −0.238740 0.971083i \(-0.576734\pi\)
0.721613 + 0.692297i \(0.243401\pi\)
\(908\) 4.47116i 0.148381i
\(909\) 0 0
\(910\) 0 0
\(911\) 18.6768 + 32.3491i 0.618789 + 1.07177i 0.989707 + 0.143109i \(0.0457098\pi\)
−0.370918 + 0.928666i \(0.620957\pi\)
\(912\) 0 0
\(913\) 9.91636 + 5.72522i 0.328184 + 0.189477i
\(914\) 4.01150 6.94812i 0.132689 0.229823i
\(915\) 0 0
\(916\) 2.13060 + 3.69031i 0.0703970 + 0.121931i
\(917\) 8.56804i 0.282942i
\(918\) 0 0
\(919\) −37.1316 −1.22486 −0.612429 0.790526i \(-0.709807\pi\)
−0.612429 + 0.790526i \(0.709807\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −11.9394 6.89324i −0.393205 0.227017i
\(923\) −52.1003 30.0801i −1.71490 0.990098i
\(924\) 0 0
\(925\) 0 0
\(926\) 19.4135 0.637967
\(927\) 0 0
\(928\) 51.5098i 1.69089i
\(929\) 23.9977 + 41.5653i 0.787340 + 1.36371i 0.927591 + 0.373597i \(0.121876\pi\)
−0.140251 + 0.990116i \(0.544791\pi\)
\(930\) 0 0
\(931\) 11.5905 20.0753i 0.379862 0.657941i
\(932\) −9.01115 5.20259i −0.295170 0.170417i
\(933\) 0 0
\(934\) −7.82831 13.5590i −0.256150 0.443665i
\(935\) 0 0
\(936\) 0 0
\(937\) 22.0079i 0.718967i −0.933151 0.359483i \(-0.882953\pi\)
0.933151 0.359483i \(-0.117047\pi\)
\(938\) 4.66195 2.69158i 0.152218 0.0878832i
\(939\) 0 0
\(940\) 0 0
\(941\) 20.2921 35.1470i 0.661504 1.14576i −0.318716 0.947850i \(-0.603252\pi\)
0.980220 0.197909i \(-0.0634150\pi\)
\(942\) 0 0
\(943\) 7.53946 4.35291i 0.245518 0.141750i
\(944\) −2.45269 −0.0798283
\(945\) 0 0
\(946\) 0.720331 0.0234200
\(947\) 26.1817 15.1160i 0.850790 0.491204i −0.0101273 0.999949i \(-0.503224\pi\)
0.860917 + 0.508745i \(0.169890\pi\)
\(948\) 0 0
\(949\) −4.00000 + 6.92820i −0.129845 + 0.224899i
\(950\) 0 0
\(951\) 0 0
\(952\) 6.94420 4.00924i 0.225063 0.129940i
\(953\) 2.50811i 0.0812455i −0.999175 0.0406227i \(-0.987066\pi\)
0.999175 0.0406227i \(-0.0129342\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −6.79439 11.7682i −0.219746 0.380612i
\(957\) 0 0
\(958\) −2.59088 1.49585i −0.0837077 0.0483286i
\(959\) 7.28402 12.6163i 0.235213 0.407401i
\(960\) 0 0
\(961\) −8.72635 15.1145i −0.281495 0.487564i
\(962\) 4.85601i 0.156564i
\(963\) 0 0
\(964\) −44.1025 −1.42045
\(965\) 0 0
\(966\) 0 0
\(967\) −18.8386 10.8765i −0.605808 0.349763i 0.165515 0.986207i \(-0.447071\pi\)
−0.771323 + 0.636444i \(0.780405\pi\)
\(968\) 7.01552 + 4.05042i 0.225488 + 0.130185i
\(969\) 0 0
\(970\) 0 0
\(971\) −22.7512 −0.730122 −0.365061 0.930984i \(-0.618952\pi\)
−0.365061 + 0.930984i \(0.618952\pi\)
\(972\) 0 0
\(973\) 11.4241i 0.366238i
\(974\) 6.86920 + 11.8978i 0.220103 + 0.381230i
\(975\) 0 0
\(976\) 2.71090 4.69541i 0.0867737 0.150296i
\(977\) −34.0156 19.6389i −1.08825 0.628304i −0.155143 0.987892i \(-0.549584\pi\)
−0.933111 + 0.359588i \(0.882917\pi\)
\(978\) 0 0
\(979\) −4.00924 6.94420i −0.128136 0.221938i
\(980\) 0 0
\(981\) 0 0
\(982\) 8.45269i 0.269736i
\(983\) −29.2629 + 16.8949i −0.933341 + 0.538865i −0.887867 0.460101i \(-0.847813\pi\)
−0.0454743 + 0.998966i \(0.514480\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −7.25405 + 12.5644i −0.231016 + 0.400132i
\(987\) 0 0
\(988\) −31.6329 + 18.2633i −1.00638 + 0.581033i
\(989\) −2.78817 −0.0886587
\(990\) 0 0
\(991\) −23.7983 −0.755979 −0.377990 0.925810i \(-0.623384\pi\)
−0.377990 + 0.925810i \(0.623384\pi\)
\(992\) 32.7213 18.8916i 1.03890 0.599810i
\(993\) 0 0
\(994\) −5.25801 + 9.10713i −0.166774 + 0.288861i
\(995\) 0 0
\(996\) 0 0
\(997\) −44.7549 + 25.8392i −1.41740 + 0.818337i −0.996070 0.0885702i \(-0.971770\pi\)
−0.421331 + 0.906907i \(0.638437\pi\)
\(998\) 14.2175i 0.450046i
\(999\) 0 0
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 675.2.k.b.199.4 12
3.2 odd 2 225.2.k.b.49.3 12
5.2 odd 4 135.2.e.b.91.2 6
5.3 odd 4 675.2.e.b.226.2 6
5.4 even 2 inner 675.2.k.b.199.3 12
9.2 odd 6 225.2.k.b.124.4 12
9.4 even 3 2025.2.b.m.649.4 6
9.5 odd 6 2025.2.b.l.649.3 6
9.7 even 3 inner 675.2.k.b.424.3 12
15.2 even 4 45.2.e.b.31.2 yes 6
15.8 even 4 225.2.e.b.76.2 6
15.14 odd 2 225.2.k.b.49.4 12
20.7 even 4 2160.2.q.k.1441.2 6
45.2 even 12 45.2.e.b.16.2 6
45.4 even 6 2025.2.b.m.649.3 6
45.7 odd 12 135.2.e.b.46.2 6
45.13 odd 12 2025.2.a.o.1.2 3
45.14 odd 6 2025.2.b.l.649.4 6
45.22 odd 12 405.2.a.i.1.2 3
45.23 even 12 2025.2.a.n.1.2 3
45.29 odd 6 225.2.k.b.124.3 12
45.32 even 12 405.2.a.j.1.2 3
45.34 even 6 inner 675.2.k.b.424.4 12
45.38 even 12 225.2.e.b.151.2 6
45.43 odd 12 675.2.e.b.451.2 6
60.47 odd 4 720.2.q.i.481.2 6
180.7 even 12 2160.2.q.k.721.2 6
180.47 odd 12 720.2.q.i.241.2 6
180.67 even 12 6480.2.a.bs.1.2 3
180.167 odd 12 6480.2.a.bv.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.2.e.b.16.2 6 45.2 even 12
45.2.e.b.31.2 yes 6 15.2 even 4
135.2.e.b.46.2 6 45.7 odd 12
135.2.e.b.91.2 6 5.2 odd 4
225.2.e.b.76.2 6 15.8 even 4
225.2.e.b.151.2 6 45.38 even 12
225.2.k.b.49.3 12 3.2 odd 2
225.2.k.b.49.4 12 15.14 odd 2
225.2.k.b.124.3 12 45.29 odd 6
225.2.k.b.124.4 12 9.2 odd 6
405.2.a.i.1.2 3 45.22 odd 12
405.2.a.j.1.2 3 45.32 even 12
675.2.e.b.226.2 6 5.3 odd 4
675.2.e.b.451.2 6 45.43 odd 12
675.2.k.b.199.3 12 5.4 even 2 inner
675.2.k.b.199.4 12 1.1 even 1 trivial
675.2.k.b.424.3 12 9.7 even 3 inner
675.2.k.b.424.4 12 45.34 even 6 inner
720.2.q.i.241.2 6 180.47 odd 12
720.2.q.i.481.2 6 60.47 odd 4
2025.2.a.n.1.2 3 45.23 even 12
2025.2.a.o.1.2 3 45.13 odd 12
2025.2.b.l.649.3 6 9.5 odd 6
2025.2.b.l.649.4 6 45.14 odd 6
2025.2.b.m.649.3 6 45.4 even 6
2025.2.b.m.649.4 6 9.4 even 3
2160.2.q.k.721.2 6 180.7 even 12
2160.2.q.k.1441.2 6 20.7 even 4
6480.2.a.bs.1.2 3 180.67 even 12
6480.2.a.bv.1.2 3 180.167 odd 12