Properties

Label 1008.2.t.h.193.1
Level $1008$
Weight $2$
Character 1008.193
Analytic conductor $8.049$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,2,Mod(193,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.193");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.t (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.1
Root \(0.500000 + 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 1008.193
Dual form 1008.2.t.h.961.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.29418 - 1.15113i) q^{3} +1.58836 q^{5} +(2.64400 + 0.0963576i) q^{7} +(0.349814 + 2.97954i) q^{9} +1.58836 q^{11} +(2.40545 - 4.16635i) q^{13} +(-2.05563 - 1.82841i) q^{15} +(-2.69963 + 4.67589i) q^{17} +(3.54944 + 6.14781i) q^{19} +(-3.31089 - 3.16828i) q^{21} -0.300372 q^{23} -2.47710 q^{25} +(2.97710 - 4.25874i) q^{27} +(4.13781 + 7.16689i) q^{29} +(-1.35600 - 2.34867i) q^{31} +(-2.05563 - 1.82841i) q^{33} +(4.19963 + 0.153051i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-7.90909 + 2.62305i) q^{39} +(2.93818 - 5.08907i) q^{41} +(0.833104 + 1.44298i) q^{43} +(0.555632 + 4.73259i) q^{45} +(1.33310 - 2.30900i) q^{47} +(6.98143 + 0.509538i) q^{49} +(8.87636 - 2.94384i) q^{51} +(2.44437 - 4.23377i) q^{53} +2.52290 q^{55} +(2.48329 - 12.0422i) q^{57} +(3.23855 + 5.60933i) q^{59} +(2.23855 - 3.87728i) q^{61} +(0.637806 + 7.91159i) q^{63} +(3.82072 - 6.61769i) q^{65} +(-5.02654 - 8.70623i) q^{67} +(0.388736 + 0.345766i) q^{69} -12.7207 q^{71} +(8.02654 - 13.9024i) q^{73} +(3.20582 + 2.85146i) q^{75} +(4.19963 + 0.153051i) q^{77} +(4.19344 - 7.26325i) q^{79} +(-8.75526 + 2.08457i) q^{81} +(-1.18292 - 2.04887i) q^{83} +(-4.28799 + 7.42702i) q^{85} +(2.89493 - 14.0384i) q^{87} +(1.60507 + 2.78007i) q^{89} +(6.76145 - 10.7840i) q^{91} +(-0.948699 + 4.60054i) q^{93} +(5.63781 + 9.76497i) q^{95} +(0.712008 + 1.23323i) q^{97} +(0.555632 + 4.73259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{9} - 2 q^{11} + 8 q^{13} - 12 q^{15} - 4 q^{17} + 3 q^{19} - 7 q^{21} - 14 q^{23} - 4 q^{25} + 7 q^{27} - 5 q^{29} - 20 q^{31} - 12 q^{33} + 13 q^{35} + 3 q^{37}+ \cdots + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.29418 1.15113i −0.747196 0.664603i
\(4\) 0 0
\(5\) 1.58836 0.710338 0.355169 0.934802i \(-0.384423\pi\)
0.355169 + 0.934802i \(0.384423\pi\)
\(6\) 0 0
\(7\) 2.64400 + 0.0963576i 0.999337 + 0.0364197i
\(8\) 0 0
\(9\) 0.349814 + 2.97954i 0.116605 + 0.993178i
\(10\) 0 0
\(11\) 1.58836 0.478910 0.239455 0.970907i \(-0.423031\pi\)
0.239455 + 0.970907i \(0.423031\pi\)
\(12\) 0 0
\(13\) 2.40545 4.16635i 0.667151 1.15554i −0.311547 0.950231i \(-0.600847\pi\)
0.978697 0.205308i \(-0.0658196\pi\)
\(14\) 0 0
\(15\) −2.05563 1.82841i −0.530762 0.472093i
\(16\) 0 0
\(17\) −2.69963 + 4.67589i −0.654756 + 1.13407i 0.327199 + 0.944955i \(0.393895\pi\)
−0.981955 + 0.189115i \(0.939438\pi\)
\(18\) 0 0
\(19\) 3.54944 + 6.14781i 0.814298 + 1.41041i 0.909831 + 0.414979i \(0.136211\pi\)
−0.0955331 + 0.995426i \(0.530456\pi\)
\(20\) 0 0
\(21\) −3.31089 3.16828i −0.722496 0.691375i
\(22\) 0 0
\(23\) −0.300372 −0.0626319 −0.0313159 0.999510i \(-0.509970\pi\)
−0.0313159 + 0.999510i \(0.509970\pi\)
\(24\) 0 0
\(25\) −2.47710 −0.495420
\(26\) 0 0
\(27\) 2.97710 4.25874i 0.572943 0.819595i
\(28\) 0 0
\(29\) 4.13781 + 7.16689i 0.768371 + 1.33086i 0.938446 + 0.345427i \(0.112266\pi\)
−0.170074 + 0.985431i \(0.554401\pi\)
\(30\) 0 0
\(31\) −1.35600 2.34867i −0.243545 0.421833i 0.718176 0.695861i \(-0.244977\pi\)
−0.961722 + 0.274028i \(0.911644\pi\)
\(32\) 0 0
\(33\) −2.05563 1.82841i −0.357840 0.318285i
\(34\) 0 0
\(35\) 4.19963 + 0.153051i 0.709867 + 0.0258703i
\(36\) 0 0
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) −7.90909 + 2.62305i −1.26647 + 0.420024i
\(40\) 0 0
\(41\) 2.93818 5.08907i 0.458866 0.794780i −0.540035 0.841643i \(-0.681589\pi\)
0.998901 + 0.0468628i \(0.0149223\pi\)
\(42\) 0 0
\(43\) 0.833104 + 1.44298i 0.127047 + 0.220052i 0.922531 0.385922i \(-0.126117\pi\)
−0.795484 + 0.605974i \(0.792783\pi\)
\(44\) 0 0
\(45\) 0.555632 + 4.73259i 0.0828287 + 0.705492i
\(46\) 0 0
\(47\) 1.33310 2.30900i 0.194453 0.336803i −0.752268 0.658857i \(-0.771040\pi\)
0.946721 + 0.322055i \(0.104373\pi\)
\(48\) 0 0
\(49\) 6.98143 + 0.509538i 0.997347 + 0.0727912i
\(50\) 0 0
\(51\) 8.87636 2.94384i 1.24294 0.412220i
\(52\) 0 0
\(53\) 2.44437 4.23377i 0.335760 0.581553i −0.647871 0.761750i \(-0.724340\pi\)
0.983630 + 0.180197i \(0.0576736\pi\)
\(54\) 0 0
\(55\) 2.52290 0.340188
\(56\) 0 0
\(57\) 2.48329 12.0422i 0.328920 1.59503i
\(58\) 0 0
\(59\) 3.23855 + 5.60933i 0.421623 + 0.730273i 0.996098 0.0882491i \(-0.0281271\pi\)
−0.574475 + 0.818522i \(0.694794\pi\)
\(60\) 0 0
\(61\) 2.23855 3.87728i 0.286617 0.496435i −0.686383 0.727240i \(-0.740803\pi\)
0.973000 + 0.230805i \(0.0741360\pi\)
\(62\) 0 0
\(63\) 0.637806 + 7.91159i 0.0803560 + 0.996766i
\(64\) 0 0
\(65\) 3.82072 6.61769i 0.473902 0.820823i
\(66\) 0 0
\(67\) −5.02654 8.70623i −0.614090 1.06363i −0.990543 0.137199i \(-0.956190\pi\)
0.376454 0.926435i \(-0.377143\pi\)
\(68\) 0 0
\(69\) 0.388736 + 0.345766i 0.0467983 + 0.0416253i
\(70\) 0 0
\(71\) −12.7207 −1.50967 −0.754833 0.655917i \(-0.772282\pi\)
−0.754833 + 0.655917i \(0.772282\pi\)
\(72\) 0 0
\(73\) 8.02654 13.9024i 0.939436 1.62715i 0.172909 0.984938i \(-0.444683\pi\)
0.766527 0.642213i \(-0.221983\pi\)
\(74\) 0 0
\(75\) 3.20582 + 2.85146i 0.370176 + 0.329258i
\(76\) 0 0
\(77\) 4.19963 + 0.153051i 0.478592 + 0.0174418i
\(78\) 0 0
\(79\) 4.19344 7.26325i 0.471799 0.817179i −0.527681 0.849443i \(-0.676938\pi\)
0.999479 + 0.0322635i \(0.0102716\pi\)
\(80\) 0 0
\(81\) −8.75526 + 2.08457i −0.972807 + 0.231619i
\(82\) 0 0
\(83\) −1.18292 2.04887i −0.129842 0.224893i 0.793773 0.608214i \(-0.208114\pi\)
−0.923615 + 0.383321i \(0.874780\pi\)
\(84\) 0 0
\(85\) −4.28799 + 7.42702i −0.465098 + 0.805573i
\(86\) 0 0
\(87\) 2.89493 14.0384i 0.310369 1.50507i
\(88\) 0 0
\(89\) 1.60507 + 2.78007i 0.170138 + 0.294687i 0.938468 0.345367i \(-0.112245\pi\)
−0.768330 + 0.640054i \(0.778912\pi\)
\(90\) 0 0
\(91\) 6.76145 10.7840i 0.708793 1.13047i
\(92\) 0 0
\(93\) −0.948699 + 4.60054i −0.0983755 + 0.477053i
\(94\) 0 0
\(95\) 5.63781 + 9.76497i 0.578427 + 1.00186i
\(96\) 0 0
\(97\) 0.712008 + 1.23323i 0.0722934 + 0.125216i 0.899906 0.436084i \(-0.143635\pi\)
−0.827613 + 0.561300i \(0.810302\pi\)
\(98\) 0 0
\(99\) 0.555632 + 4.73259i 0.0558431 + 0.475643i
\(100\) 0 0
\(101\) 12.0334 1.19737 0.598685 0.800985i \(-0.295690\pi\)
0.598685 + 0.800985i \(0.295690\pi\)
\(102\) 0 0
\(103\) 6.09888 0.600941 0.300470 0.953791i \(-0.402856\pi\)
0.300470 + 0.953791i \(0.402856\pi\)
\(104\) 0 0
\(105\) −5.25890 5.03238i −0.513216 0.491110i
\(106\) 0 0
\(107\) 1.54325 + 2.67299i 0.149192 + 0.258408i 0.930929 0.365200i \(-0.118999\pi\)
−0.781737 + 0.623608i \(0.785666\pi\)
\(108\) 0 0
\(109\) 1.14400 1.98146i 0.109575 0.189789i −0.806023 0.591884i \(-0.798384\pi\)
0.915598 + 0.402095i \(0.131718\pi\)
\(110\) 0 0
\(111\) 0.349814 1.69636i 0.0332029 0.161011i
\(112\) 0 0
\(113\) −9.73236 + 16.8569i −0.915543 + 1.58577i −0.109440 + 0.993993i \(0.534906\pi\)
−0.806104 + 0.591774i \(0.798428\pi\)
\(114\) 0 0
\(115\) −0.477100 −0.0444898
\(116\) 0 0
\(117\) 13.2553 + 5.70966i 1.22545 + 0.527858i
\(118\) 0 0
\(119\) −7.58836 + 12.1029i −0.695624 + 1.10947i
\(120\) 0 0
\(121\) −8.47710 −0.770645
\(122\) 0 0
\(123\) −9.66071 + 3.20397i −0.871077 + 0.288892i
\(124\) 0 0
\(125\) −11.8764 −1.06225
\(126\) 0 0
\(127\) 13.4400 1.19260 0.596302 0.802760i \(-0.296636\pi\)
0.596302 + 0.802760i \(0.296636\pi\)
\(128\) 0 0
\(129\) 0.582863 2.82648i 0.0513182 0.248858i
\(130\) 0 0
\(131\) 3.17673 0.277552 0.138776 0.990324i \(-0.455683\pi\)
0.138776 + 0.990324i \(0.455683\pi\)
\(132\) 0 0
\(133\) 8.79232 + 16.5968i 0.762391 + 1.43913i
\(134\) 0 0
\(135\) 4.72872 6.76443i 0.406983 0.582190i
\(136\) 0 0
\(137\) −21.2632 −1.81664 −0.908320 0.418275i \(-0.862635\pi\)
−0.908320 + 0.418275i \(0.862635\pi\)
\(138\) 0 0
\(139\) −6.52654 + 11.3043i −0.553574 + 0.958818i 0.444439 + 0.895809i \(0.353403\pi\)
−0.998013 + 0.0630092i \(0.979930\pi\)
\(140\) 0 0
\(141\) −4.38323 + 1.45370i −0.369135 + 0.122424i
\(142\) 0 0
\(143\) 3.82072 6.61769i 0.319505 0.553399i
\(144\) 0 0
\(145\) 6.57234 + 11.3836i 0.545803 + 0.945359i
\(146\) 0 0
\(147\) −8.44870 8.69595i −0.696837 0.717230i
\(148\) 0 0
\(149\) 5.20877 0.426719 0.213360 0.976974i \(-0.431559\pi\)
0.213360 + 0.976974i \(0.431559\pi\)
\(150\) 0 0
\(151\) 0.522900 0.0425530 0.0212765 0.999774i \(-0.493227\pi\)
0.0212765 + 0.999774i \(0.493227\pi\)
\(152\) 0 0
\(153\) −14.8764 6.40794i −1.20268 0.518052i
\(154\) 0 0
\(155\) −2.15383 3.73054i −0.173000 0.299644i
\(156\) 0 0
\(157\) −4.43199 7.67643i −0.353711 0.612646i 0.633185 0.774000i \(-0.281747\pi\)
−0.986897 + 0.161354i \(0.948414\pi\)
\(158\) 0 0
\(159\) −8.03706 + 2.66549i −0.637381 + 0.211387i
\(160\) 0 0
\(161\) −0.794182 0.0289431i −0.0625903 0.00228104i
\(162\) 0 0
\(163\) −10.9814 19.0204i −0.860132 1.48979i −0.871801 0.489860i \(-0.837048\pi\)
0.0116689 0.999932i \(-0.496286\pi\)
\(164\) 0 0
\(165\) −3.26509 2.90418i −0.254187 0.226090i
\(166\) 0 0
\(167\) −1.65019 + 2.85821i −0.127695 + 0.221175i −0.922783 0.385319i \(-0.874091\pi\)
0.795088 + 0.606494i \(0.207425\pi\)
\(168\) 0 0
\(169\) −5.07234 8.78555i −0.390180 0.675812i
\(170\) 0 0
\(171\) −17.0760 + 12.7263i −1.30583 + 0.973203i
\(172\) 0 0
\(173\) −9.55377 + 16.5476i −0.726360 + 1.25809i 0.232052 + 0.972703i \(0.425456\pi\)
−0.958412 + 0.285389i \(0.907877\pi\)
\(174\) 0 0
\(175\) −6.54944 0.238687i −0.495091 0.0180431i
\(176\) 0 0
\(177\) 2.26578 10.9875i 0.170307 0.825870i
\(178\) 0 0
\(179\) 8.03706 13.9206i 0.600718 1.04047i −0.391994 0.919968i \(-0.628215\pi\)
0.992712 0.120507i \(-0.0384520\pi\)
\(180\) 0 0
\(181\) 8.05308 0.598581 0.299291 0.954162i \(-0.403250\pi\)
0.299291 + 0.954162i \(0.403250\pi\)
\(182\) 0 0
\(183\) −7.36033 + 2.44105i −0.544092 + 0.180448i
\(184\) 0 0
\(185\) 0.794182 + 1.37556i 0.0583894 + 0.101133i
\(186\) 0 0
\(187\) −4.28799 + 7.42702i −0.313569 + 0.543118i
\(188\) 0 0
\(189\) 8.28180 10.9732i 0.602412 0.798185i
\(190\) 0 0
\(191\) −11.9814 + 20.7524i −0.866946 + 1.50159i −0.00184390 + 0.999998i \(0.500587\pi\)
−0.865102 + 0.501596i \(0.832746\pi\)
\(192\) 0 0
\(193\) −4.88255 8.45682i −0.351453 0.608735i 0.635051 0.772470i \(-0.280979\pi\)
−0.986504 + 0.163735i \(0.947646\pi\)
\(194\) 0 0
\(195\) −12.5625 + 4.16635i −0.899620 + 0.298359i
\(196\) 0 0
\(197\) −18.2436 −1.29980 −0.649900 0.760020i \(-0.725189\pi\)
−0.649900 + 0.760020i \(0.725189\pi\)
\(198\) 0 0
\(199\) −9.04944 + 15.6741i −0.641498 + 1.11111i 0.343601 + 0.939116i \(0.388353\pi\)
−0.985098 + 0.171991i \(0.944980\pi\)
\(200\) 0 0
\(201\) −3.51671 + 17.0536i −0.248050 + 1.20287i
\(202\) 0 0
\(203\) 10.2498 + 19.3479i 0.719392 + 1.35796i
\(204\) 0 0
\(205\) 4.66690 8.08330i 0.325950 0.564562i
\(206\) 0 0
\(207\) −0.105074 0.894969i −0.00730317 0.0622046i
\(208\) 0 0
\(209\) 5.63781 + 9.76497i 0.389975 + 0.675457i
\(210\) 0 0
\(211\) −0.166208 + 0.287880i −0.0114422 + 0.0198185i −0.871690 0.490058i \(-0.836976\pi\)
0.860248 + 0.509877i \(0.170309\pi\)
\(212\) 0 0
\(213\) 16.4629 + 14.6431i 1.12802 + 1.00333i
\(214\) 0 0
\(215\) 1.32327 + 2.29197i 0.0902464 + 0.156311i
\(216\) 0 0
\(217\) −3.35896 6.34053i −0.228021 0.430423i
\(218\) 0 0
\(219\) −26.3912 + 8.75264i −1.78335 + 0.591449i
\(220\) 0 0
\(221\) 12.9876 + 22.4952i 0.873642 + 1.51319i
\(222\) 0 0
\(223\) −3.16621 5.48403i −0.212025 0.367238i 0.740323 0.672251i \(-0.234672\pi\)
−0.952348 + 0.305013i \(0.901339\pi\)
\(224\) 0 0
\(225\) −0.866524 7.38061i −0.0577683 0.492040i
\(226\) 0 0
\(227\) 23.3090 1.54707 0.773537 0.633751i \(-0.218485\pi\)
0.773537 + 0.633751i \(0.218485\pi\)
\(228\) 0 0
\(229\) −4.95420 −0.327383 −0.163691 0.986512i \(-0.552340\pi\)
−0.163691 + 0.986512i \(0.552340\pi\)
\(230\) 0 0
\(231\) −5.25890 5.03238i −0.346010 0.331106i
\(232\) 0 0
\(233\) −7.13781 12.3630i −0.467613 0.809930i 0.531702 0.846932i \(-0.321553\pi\)
−0.999315 + 0.0370017i \(0.988219\pi\)
\(234\) 0 0
\(235\) 2.11745 3.66754i 0.138127 0.239244i
\(236\) 0 0
\(237\) −13.7880 + 4.57279i −0.895626 + 0.297034i
\(238\) 0 0
\(239\) −2.48762 + 4.30868i −0.160911 + 0.278706i −0.935196 0.354132i \(-0.884776\pi\)
0.774285 + 0.632837i \(0.218110\pi\)
\(240\) 0 0
\(241\) −13.0000 −0.837404 −0.418702 0.908124i \(-0.637515\pi\)
−0.418702 + 0.908124i \(0.637515\pi\)
\(242\) 0 0
\(243\) 13.7305 + 7.38061i 0.880812 + 0.473466i
\(244\) 0 0
\(245\) 11.0891 + 0.809332i 0.708454 + 0.0517063i
\(246\) 0 0
\(247\) 34.1520 2.17304
\(248\) 0 0
\(249\) −0.827603 + 4.01330i −0.0524472 + 0.254333i
\(250\) 0 0
\(251\) −2.43268 −0.153549 −0.0767746 0.997048i \(-0.524462\pi\)
−0.0767746 + 0.997048i \(0.524462\pi\)
\(252\) 0 0
\(253\) −0.477100 −0.0299950
\(254\) 0 0
\(255\) 14.0989 4.67589i 0.882906 0.292816i
\(256\) 0 0
\(257\) −0.987620 −0.0616061 −0.0308030 0.999525i \(-0.509806\pi\)
−0.0308030 + 0.999525i \(0.509806\pi\)
\(258\) 0 0
\(259\) 1.23855 + 2.33795i 0.0769597 + 0.145273i
\(260\) 0 0
\(261\) −19.9065 + 14.8358i −1.23218 + 0.918314i
\(262\) 0 0
\(263\) −17.1854 −1.05970 −0.529848 0.848092i \(-0.677751\pi\)
−0.529848 + 0.848092i \(0.677751\pi\)
\(264\) 0 0
\(265\) 3.88255 6.72477i 0.238503 0.413099i
\(266\) 0 0
\(267\) 1.12296 5.44556i 0.0687237 0.333263i
\(268\) 0 0
\(269\) 11.4523 19.8360i 0.698262 1.20942i −0.270807 0.962634i \(-0.587291\pi\)
0.969069 0.246791i \(-0.0793761\pi\)
\(270\) 0 0
\(271\) −7.00364 12.1307i −0.425441 0.736885i 0.571021 0.820936i \(-0.306548\pi\)
−0.996462 + 0.0840504i \(0.973214\pi\)
\(272\) 0 0
\(273\) −21.1643 + 6.17323i −1.28092 + 0.373621i
\(274\) 0 0
\(275\) −3.93454 −0.237261
\(276\) 0 0
\(277\) 28.2953 1.70010 0.850049 0.526703i \(-0.176572\pi\)
0.850049 + 0.526703i \(0.176572\pi\)
\(278\) 0 0
\(279\) 6.52359 4.86186i 0.390557 0.291072i
\(280\) 0 0
\(281\) −8.79782 15.2383i −0.524834 0.909039i −0.999582 0.0289175i \(-0.990794\pi\)
0.474748 0.880122i \(-0.342539\pi\)
\(282\) 0 0
\(283\) −9.26145 16.0413i −0.550536 0.953556i −0.998236 0.0593725i \(-0.981090\pi\)
0.447700 0.894184i \(-0.352243\pi\)
\(284\) 0 0
\(285\) 3.94437 19.1275i 0.233644 1.13301i
\(286\) 0 0
\(287\) 8.25890 13.1724i 0.487508 0.777541i
\(288\) 0 0
\(289\) −6.07598 10.5239i −0.357411 0.619054i
\(290\) 0 0
\(291\) 0.498141 2.41564i 0.0292015 0.141607i
\(292\) 0 0
\(293\) −7.04256 + 12.1981i −0.411431 + 0.712619i −0.995046 0.0994108i \(-0.968304\pi\)
0.583616 + 0.812030i \(0.301638\pi\)
\(294\) 0 0
\(295\) 5.14400 + 8.90966i 0.299495 + 0.518741i
\(296\) 0 0
\(297\) 4.72872 6.76443i 0.274388 0.392512i
\(298\) 0 0
\(299\) −0.722528 + 1.25146i −0.0417849 + 0.0723736i
\(300\) 0 0
\(301\) 2.06368 + 3.89550i 0.118949 + 0.224533i
\(302\) 0 0
\(303\) −15.5734 13.8520i −0.894671 0.795776i
\(304\) 0 0
\(305\) 3.55563 6.15854i 0.203595 0.352637i
\(306\) 0 0
\(307\) 5.85532 0.334180 0.167090 0.985942i \(-0.446563\pi\)
0.167090 + 0.985942i \(0.446563\pi\)
\(308\) 0 0
\(309\) −7.89307 7.02059i −0.449021 0.399387i
\(310\) 0 0
\(311\) 0.405446 + 0.702253i 0.0229907 + 0.0398211i 0.877292 0.479957i \(-0.159348\pi\)
−0.854301 + 0.519778i \(0.826015\pi\)
\(312\) 0 0
\(313\) −5.28799 + 9.15907i −0.298895 + 0.517701i −0.975883 0.218292i \(-0.929951\pi\)
0.676988 + 0.735994i \(0.263285\pi\)
\(314\) 0 0
\(315\) 1.01307 + 12.5665i 0.0570799 + 0.708041i
\(316\) 0 0
\(317\) −6.09820 + 10.5624i −0.342509 + 0.593243i −0.984898 0.173136i \(-0.944610\pi\)
0.642389 + 0.766379i \(0.277943\pi\)
\(318\) 0 0
\(319\) 6.57234 + 11.3836i 0.367981 + 0.637361i
\(320\) 0 0
\(321\) 1.07970 5.23582i 0.0602631 0.292235i
\(322\) 0 0
\(323\) −38.3287 −2.13267
\(324\) 0 0
\(325\) −5.95853 + 10.3205i −0.330520 + 0.572477i
\(326\) 0 0
\(327\) −3.76145 + 1.24748i −0.208009 + 0.0689860i
\(328\) 0 0
\(329\) 3.74721 5.97654i 0.206590 0.329497i
\(330\) 0 0
\(331\) −7.83310 + 13.5673i −0.430546 + 0.745728i −0.996920 0.0784202i \(-0.975012\pi\)
0.566374 + 0.824148i \(0.308346\pi\)
\(332\) 0 0
\(333\) −2.40545 + 1.79272i −0.131818 + 0.0982402i
\(334\) 0 0
\(335\) −7.98398 13.8287i −0.436211 0.755540i
\(336\) 0 0
\(337\) −4.21201 + 7.29541i −0.229443 + 0.397406i −0.957643 0.287958i \(-0.907024\pi\)
0.728200 + 0.685364i \(0.240357\pi\)
\(338\) 0 0
\(339\) 31.9999 10.6128i 1.73800 0.576407i
\(340\) 0 0
\(341\) −2.15383 3.73054i −0.116636 0.202020i
\(342\) 0 0
\(343\) 18.4098 + 2.01993i 0.994035 + 0.109066i
\(344\) 0 0
\(345\) 0.617454 + 0.549202i 0.0332426 + 0.0295681i
\(346\) 0 0
\(347\) 0.283662 + 0.491316i 0.0152277 + 0.0263752i 0.873539 0.486754i \(-0.161819\pi\)
−0.858311 + 0.513130i \(0.828486\pi\)
\(348\) 0 0
\(349\) −0.00364189 0.00630794i −0.000194946 0.000337656i 0.865928 0.500169i \(-0.166729\pi\)
−0.866123 + 0.499831i \(0.833395\pi\)
\(350\) 0 0
\(351\) −10.5822 22.6478i −0.564835 1.20885i
\(352\) 0 0
\(353\) 6.65383 0.354148 0.177074 0.984198i \(-0.443337\pi\)
0.177074 + 0.984198i \(0.443337\pi\)
\(354\) 0 0
\(355\) −20.2051 −1.07237
\(356\) 0 0
\(357\) 23.7527 6.92820i 1.25713 0.366679i
\(358\) 0 0
\(359\) 0.398568 + 0.690339i 0.0210356 + 0.0364347i 0.876352 0.481672i \(-0.159970\pi\)
−0.855316 + 0.518107i \(0.826637\pi\)
\(360\) 0 0
\(361\) −15.6971 + 27.1881i −0.826162 + 1.43095i
\(362\) 0 0
\(363\) 10.9709 + 9.75822i 0.575823 + 0.512174i
\(364\) 0 0
\(365\) 12.7491 22.0820i 0.667317 1.15583i
\(366\) 0 0
\(367\) 15.4327 0.805579 0.402790 0.915293i \(-0.368041\pi\)
0.402790 + 0.915293i \(0.368041\pi\)
\(368\) 0 0
\(369\) 16.1909 + 6.97418i 0.842864 + 0.363061i
\(370\) 0 0
\(371\) 6.87085 10.9585i 0.356717 0.568939i
\(372\) 0 0
\(373\) 10.2422 0.530321 0.265160 0.964204i \(-0.414575\pi\)
0.265160 + 0.964204i \(0.414575\pi\)
\(374\) 0 0
\(375\) 15.3702 + 13.6712i 0.793712 + 0.705977i
\(376\) 0 0
\(377\) 39.8131 2.05048
\(378\) 0 0
\(379\) −25.0087 −1.28461 −0.642304 0.766450i \(-0.722021\pi\)
−0.642304 + 0.766450i \(0.722021\pi\)
\(380\) 0 0
\(381\) −17.3938 15.4711i −0.891109 0.792608i
\(382\) 0 0
\(383\) 6.26695 0.320226 0.160113 0.987099i \(-0.448814\pi\)
0.160113 + 0.987099i \(0.448814\pi\)
\(384\) 0 0
\(385\) 6.67054 + 0.243101i 0.339962 + 0.0123896i
\(386\) 0 0
\(387\) −4.00797 + 2.98704i −0.203737 + 0.151840i
\(388\) 0 0
\(389\) −21.6342 −1.09690 −0.548448 0.836185i \(-0.684781\pi\)
−0.548448 + 0.836185i \(0.684781\pi\)
\(390\) 0 0
\(391\) 0.810892 1.40451i 0.0410086 0.0710290i
\(392\) 0 0
\(393\) −4.11126 3.65682i −0.207386 0.184462i
\(394\) 0 0
\(395\) 6.66071 11.5367i 0.335137 0.580473i
\(396\) 0 0
\(397\) 2.05308 + 3.55605i 0.103041 + 0.178473i 0.912936 0.408102i \(-0.133809\pi\)
−0.809895 + 0.586575i \(0.800476\pi\)
\(398\) 0 0
\(399\) 7.72617 31.6004i 0.386792 1.58200i
\(400\) 0 0
\(401\) 16.7417 0.836041 0.418021 0.908438i \(-0.362724\pi\)
0.418021 + 0.908438i \(0.362724\pi\)
\(402\) 0 0
\(403\) −13.0472 −0.649926
\(404\) 0 0
\(405\) −13.9065 + 3.31105i −0.691022 + 0.164527i
\(406\) 0 0
\(407\) 0.794182 + 1.37556i 0.0393661 + 0.0681842i
\(408\) 0 0
\(409\) 4.38255 + 7.59079i 0.216703 + 0.375341i 0.953798 0.300449i \(-0.0971364\pi\)
−0.737095 + 0.675789i \(0.763803\pi\)
\(410\) 0 0
\(411\) 27.5185 + 24.4767i 1.35739 + 1.20735i
\(412\) 0 0
\(413\) 8.02221 + 15.1431i 0.394747 + 0.745144i
\(414\) 0 0
\(415\) −1.87890 3.25436i −0.0922318 0.159750i
\(416\) 0 0
\(417\) 21.4592 7.11695i 1.05086 0.348518i
\(418\) 0 0
\(419\) 0.210149 0.363988i 0.0102664 0.0177820i −0.860847 0.508865i \(-0.830065\pi\)
0.871113 + 0.491083i \(0.163399\pi\)
\(420\) 0 0
\(421\) 3.28799 + 5.69497i 0.160247 + 0.277556i 0.934957 0.354761i \(-0.115438\pi\)
−0.774710 + 0.632316i \(0.782104\pi\)
\(422\) 0 0
\(423\) 7.34610 + 3.16431i 0.357179 + 0.153854i
\(424\) 0 0
\(425\) 6.68725 11.5827i 0.324379 0.561841i
\(426\) 0 0
\(427\) 6.29232 10.0358i 0.304507 0.485667i
\(428\) 0 0
\(429\) −12.5625 + 4.16635i −0.606524 + 0.201154i
\(430\) 0 0
\(431\) −11.0439 + 19.1287i −0.531968 + 0.921395i 0.467336 + 0.884080i \(0.345214\pi\)
−0.999304 + 0.0373155i \(0.988119\pi\)
\(432\) 0 0
\(433\) −9.43268 −0.453306 −0.226653 0.973976i \(-0.572778\pi\)
−0.226653 + 0.973976i \(0.572778\pi\)
\(434\) 0 0
\(435\) 4.59820 22.2981i 0.220467 1.06911i
\(436\) 0 0
\(437\) −1.06615 1.84663i −0.0510010 0.0883363i
\(438\) 0 0
\(439\) −15.6032 + 27.0256i −0.744701 + 1.28986i 0.205634 + 0.978629i \(0.434074\pi\)
−0.950334 + 0.311231i \(0.899259\pi\)
\(440\) 0 0
\(441\) 0.924016 + 20.9797i 0.0440007 + 0.999031i
\(442\) 0 0
\(443\) 6.52723 11.3055i 0.310118 0.537140i −0.668270 0.743919i \(-0.732965\pi\)
0.978388 + 0.206779i \(0.0662981\pi\)
\(444\) 0 0
\(445\) 2.54944 + 4.41576i 0.120855 + 0.209327i
\(446\) 0 0
\(447\) −6.74110 5.99596i −0.318843 0.283599i
\(448\) 0 0
\(449\) −9.91706 −0.468015 −0.234008 0.972235i \(-0.575184\pi\)
−0.234008 + 0.972235i \(0.575184\pi\)
\(450\) 0 0
\(451\) 4.66690 8.08330i 0.219756 0.380628i
\(452\) 0 0
\(453\) −0.676728 0.601924i −0.0317955 0.0282809i
\(454\) 0 0
\(455\) 10.7396 17.1290i 0.503482 0.803019i
\(456\) 0 0
\(457\) 12.2615 21.2375i 0.573566 0.993446i −0.422629 0.906303i \(-0.638893\pi\)
0.996196 0.0871436i \(-0.0277739\pi\)
\(458\) 0 0
\(459\) 11.8764 + 25.4176i 0.554341 + 1.18639i
\(460\) 0 0
\(461\) 1.75526 + 3.04020i 0.0817506 + 0.141596i 0.904002 0.427528i \(-0.140616\pi\)
−0.822251 + 0.569125i \(0.807282\pi\)
\(462\) 0 0
\(463\) −8.69413 + 15.0587i −0.404050 + 0.699836i −0.994210 0.107451i \(-0.965731\pi\)
0.590160 + 0.807286i \(0.299065\pi\)
\(464\) 0 0
\(465\) −1.50688 + 7.30733i −0.0698798 + 0.338869i
\(466\) 0 0
\(467\) −6.69894 11.6029i −0.309990 0.536918i 0.668370 0.743829i \(-0.266992\pi\)
−0.978360 + 0.206911i \(0.933659\pi\)
\(468\) 0 0
\(469\) −12.4512 23.5036i −0.574945 1.08529i
\(470\) 0 0
\(471\) −3.10074 + 15.0365i −0.142875 + 0.692844i
\(472\) 0 0
\(473\) 1.32327 + 2.29197i 0.0608441 + 0.105385i
\(474\) 0 0
\(475\) −8.79232 15.2287i −0.403419 0.698743i
\(476\) 0 0
\(477\) 13.4697 + 5.80205i 0.616737 + 0.265658i
\(478\) 0 0
\(479\) −20.8058 −0.950641 −0.475321 0.879813i \(-0.657668\pi\)
−0.475321 + 0.879813i \(0.657668\pi\)
\(480\) 0 0
\(481\) 4.81089 0.219358
\(482\) 0 0
\(483\) 0.994499 + 0.951662i 0.0452513 + 0.0433021i
\(484\) 0 0
\(485\) 1.13093 + 1.95882i 0.0513528 + 0.0889456i
\(486\) 0 0
\(487\) −16.2472 + 28.1410i −0.736231 + 1.27519i 0.217950 + 0.975960i \(0.430063\pi\)
−0.954181 + 0.299230i \(0.903270\pi\)
\(488\) 0 0
\(489\) −7.68292 + 37.2569i −0.347434 + 1.68481i
\(490\) 0 0
\(491\) 9.66071 16.7328i 0.435982 0.755142i −0.561394 0.827549i \(-0.689735\pi\)
0.997375 + 0.0724067i \(0.0230679\pi\)
\(492\) 0 0
\(493\) −44.6822 −2.01238
\(494\) 0 0
\(495\) 0.882546 + 7.51707i 0.0396675 + 0.337867i
\(496\) 0 0
\(497\) −33.6334 1.22573i −1.50866 0.0549816i
\(498\) 0 0
\(499\) 11.1506 0.499169 0.249585 0.968353i \(-0.419706\pi\)
0.249585 + 0.968353i \(0.419706\pi\)
\(500\) 0 0
\(501\) 5.42580 1.79947i 0.242407 0.0803942i
\(502\) 0 0
\(503\) 40.7651 1.81763 0.908813 0.417204i \(-0.136990\pi\)
0.908813 + 0.417204i \(0.136990\pi\)
\(504\) 0 0
\(505\) 19.1135 0.850537
\(506\) 0 0
\(507\) −3.54875 + 17.2090i −0.157606 + 0.764279i
\(508\) 0 0
\(509\) 1.44506 0.0640510 0.0320255 0.999487i \(-0.489804\pi\)
0.0320255 + 0.999487i \(0.489804\pi\)
\(510\) 0 0
\(511\) 22.5617 35.9844i 0.998073 1.59186i
\(512\) 0 0
\(513\) 36.7490 + 3.18650i 1.62251 + 0.140687i
\(514\) 0 0
\(515\) 9.68725 0.426871
\(516\) 0 0
\(517\) 2.11745 3.66754i 0.0931255 0.161298i
\(518\) 0 0
\(519\) 31.4127 10.4180i 1.37887 0.457301i
\(520\) 0 0
\(521\) 9.64214 16.7007i 0.422430 0.731670i −0.573747 0.819033i \(-0.694511\pi\)
0.996177 + 0.0873630i \(0.0278440\pi\)
\(522\) 0 0
\(523\) 18.3454 + 31.7752i 0.802189 + 1.38943i 0.918173 + 0.396180i \(0.129665\pi\)
−0.115984 + 0.993251i \(0.537002\pi\)
\(524\) 0 0
\(525\) 8.20141 + 7.84814i 0.357939 + 0.342521i
\(526\) 0 0
\(527\) 14.6428 0.637851
\(528\) 0 0
\(529\) −22.9098 −0.996077
\(530\) 0 0
\(531\) −15.5803 + 11.6116i −0.676128 + 0.503900i
\(532\) 0 0
\(533\) −14.1353 24.4830i −0.612266 1.06048i
\(534\) 0 0
\(535\) 2.45125 + 4.24568i 0.105977 + 0.183557i
\(536\) 0 0
\(537\) −26.4258 + 8.76411i −1.14036 + 0.378199i
\(538\) 0 0
\(539\) 11.0891 + 0.809332i 0.477639 + 0.0348604i
\(540\) 0 0
\(541\) −1.62543 2.81532i −0.0698825 0.121040i 0.828967 0.559298i \(-0.188929\pi\)
−0.898849 + 0.438258i \(0.855596\pi\)
\(542\) 0 0
\(543\) −10.4222 9.27012i −0.447258 0.397819i
\(544\) 0 0
\(545\) 1.81708 3.14728i 0.0778352 0.134815i
\(546\) 0 0
\(547\) 2.95853 + 5.12432i 0.126498 + 0.219100i 0.922317 0.386433i \(-0.126293\pi\)
−0.795820 + 0.605534i \(0.792960\pi\)
\(548\) 0 0
\(549\) 12.3356 + 5.31351i 0.526470 + 0.226775i
\(550\) 0 0
\(551\) −29.3738 + 50.8769i −1.25137 + 2.16743i
\(552\) 0 0
\(553\) 11.7873 18.7999i 0.501247 0.799454i
\(554\) 0 0
\(555\) 0.555632 2.69443i 0.0235853 0.114372i
\(556\) 0 0
\(557\) 12.8040 22.1772i 0.542523 0.939678i −0.456235 0.889859i \(-0.650802\pi\)
0.998758 0.0498188i \(-0.0158644\pi\)
\(558\) 0 0
\(559\) 8.01594 0.339038
\(560\) 0 0
\(561\) 14.0989 4.67589i 0.595255 0.197416i
\(562\) 0 0
\(563\) −23.3189 40.3895i −0.982773 1.70221i −0.651443 0.758698i \(-0.725836\pi\)
−0.331330 0.943515i \(-0.607497\pi\)
\(564\) 0 0
\(565\) −15.4585 + 26.7750i −0.650345 + 1.12643i
\(566\) 0 0
\(567\) −23.3497 + 4.66795i −0.980597 + 0.196035i
\(568\) 0 0
\(569\) −15.5989 + 27.0181i −0.653939 + 1.13266i 0.328219 + 0.944602i \(0.393551\pi\)
−0.982159 + 0.188054i \(0.939782\pi\)
\(570\) 0 0
\(571\) −7.83812 13.5760i −0.328015 0.568139i 0.654103 0.756406i \(-0.273046\pi\)
−0.982118 + 0.188267i \(0.939713\pi\)
\(572\) 0 0
\(573\) 39.3948 13.0653i 1.64574 0.545811i
\(574\) 0 0
\(575\) 0.744051 0.0310291
\(576\) 0 0
\(577\) 6.99567 12.1169i 0.291234 0.504431i −0.682868 0.730542i \(-0.739268\pi\)
0.974102 + 0.226110i \(0.0726010\pi\)
\(578\) 0 0
\(579\) −3.41597 + 16.5651i −0.141963 + 0.688422i
\(580\) 0 0
\(581\) −2.93021 5.53120i −0.121565 0.229473i
\(582\) 0 0
\(583\) 3.88255 6.72477i 0.160799 0.278511i
\(584\) 0 0
\(585\) 21.0542 + 9.06902i 0.870483 + 0.374958i
\(586\) 0 0
\(587\) −1.44801 2.50803i −0.0597658 0.103517i 0.834594 0.550865i \(-0.185702\pi\)
−0.894360 + 0.447348i \(0.852369\pi\)
\(588\) 0 0
\(589\) 9.62612 16.6729i 0.396637 0.686996i
\(590\) 0 0
\(591\) 23.6105 + 21.0007i 0.971206 + 0.863852i
\(592\) 0 0
\(593\) −2.04394 3.54021i −0.0839346 0.145379i 0.821002 0.570925i \(-0.193415\pi\)
−0.904937 + 0.425546i \(0.860082\pi\)
\(594\) 0 0
\(595\) −12.0531 + 19.2238i −0.494128 + 0.788100i
\(596\) 0 0
\(597\) 29.7545 9.86807i 1.21777 0.403873i
\(598\) 0 0
\(599\) −9.88255 17.1171i −0.403790 0.699385i 0.590390 0.807118i \(-0.298974\pi\)
−0.994180 + 0.107734i \(0.965641\pi\)
\(600\) 0 0
\(601\) −13.4320 23.2649i −0.547902 0.948994i −0.998418 0.0562261i \(-0.982093\pi\)
0.450516 0.892768i \(-0.351240\pi\)
\(602\) 0 0
\(603\) 24.1822 18.0223i 0.984773 0.733926i
\(604\) 0 0
\(605\) −13.4647 −0.547419
\(606\) 0 0
\(607\) 15.2422 0.618661 0.309331 0.950955i \(-0.399895\pi\)
0.309331 + 0.950955i \(0.399895\pi\)
\(608\) 0 0
\(609\) 9.00688 36.8385i 0.364977 1.49277i
\(610\) 0 0
\(611\) −6.41342 11.1084i −0.259459 0.449396i
\(612\) 0 0
\(613\) −1.36033 + 2.35617i −0.0549434 + 0.0951648i −0.892189 0.451662i \(-0.850831\pi\)
0.837246 + 0.546827i \(0.184165\pi\)
\(614\) 0 0
\(615\) −15.3447 + 5.08907i −0.618759 + 0.205211i
\(616\) 0 0
\(617\) −9.21812 + 15.9663i −0.371108 + 0.642777i −0.989736 0.142906i \(-0.954355\pi\)
0.618629 + 0.785684i \(0.287689\pi\)
\(618\) 0 0
\(619\) −0.107546 −0.00432262 −0.00216131 0.999998i \(-0.500688\pi\)
−0.00216131 + 0.999998i \(0.500688\pi\)
\(620\) 0 0
\(621\) −0.894237 + 1.27921i −0.0358845 + 0.0513328i
\(622\) 0 0
\(623\) 3.97593 + 7.50516i 0.159292 + 0.300688i
\(624\) 0 0
\(625\) −6.47848 −0.259139
\(626\) 0 0
\(627\) 3.94437 19.1275i 0.157523 0.763878i
\(628\) 0 0
\(629\) −5.39926 −0.215282
\(630\) 0 0
\(631\) −35.7266 −1.42225 −0.711126 0.703064i \(-0.751815\pi\)
−0.711126 + 0.703064i \(0.751815\pi\)
\(632\) 0 0
\(633\) 0.546489 0.181243i 0.0217210 0.00720376i
\(634\) 0 0
\(635\) 21.3475 0.847152
\(636\) 0 0
\(637\) 18.9164 27.8615i 0.749494 1.10391i
\(638\) 0 0
\(639\) −4.44987 37.9017i −0.176034 1.49937i
\(640\) 0 0
\(641\) 17.3128 0.683813 0.341906 0.939734i \(-0.388927\pi\)
0.341906 + 0.939734i \(0.388927\pi\)
\(642\) 0 0
\(643\) −14.4821 + 25.0838i −0.571119 + 0.989207i 0.425332 + 0.905037i \(0.360157\pi\)
−0.996451 + 0.0841700i \(0.973176\pi\)
\(644\) 0 0
\(645\) 0.925798 4.48949i 0.0364533 0.176773i
\(646\) 0 0
\(647\) −1.27816 + 2.21384i −0.0502497 + 0.0870350i −0.890056 0.455851i \(-0.849335\pi\)
0.839807 + 0.542886i \(0.182668\pi\)
\(648\) 0 0
\(649\) 5.14400 + 8.90966i 0.201920 + 0.349735i
\(650\) 0 0
\(651\) −2.95165 + 12.0724i −0.115684 + 0.473154i
\(652\) 0 0
\(653\) 29.9766 1.17308 0.586538 0.809922i \(-0.300491\pi\)
0.586538 + 0.809922i \(0.300491\pi\)
\(654\) 0 0
\(655\) 5.04580 0.197156
\(656\) 0 0
\(657\) 44.2304 + 19.0521i 1.72559 + 0.743294i
\(658\) 0 0
\(659\) 7.63162 + 13.2183i 0.297286 + 0.514914i 0.975514 0.219937i \(-0.0705853\pi\)
−0.678228 + 0.734851i \(0.737252\pi\)
\(660\) 0 0
\(661\) 13.6261 + 23.6011i 0.529994 + 0.917977i 0.999388 + 0.0349881i \(0.0111393\pi\)
−0.469393 + 0.882989i \(0.655527\pi\)
\(662\) 0 0
\(663\) 9.08650 44.0633i 0.352891 1.71128i
\(664\) 0 0
\(665\) 13.9654 + 26.3618i 0.541555 + 1.02227i
\(666\) 0 0
\(667\) −1.24288 2.15273i −0.0481245 0.0833541i
\(668\) 0 0
\(669\) −2.21517 + 10.7420i −0.0856433 + 0.415311i
\(670\) 0 0
\(671\) 3.55563 6.15854i 0.137264 0.237748i
\(672\) 0 0
\(673\) 23.2280 + 40.2320i 0.895372 + 1.55083i 0.833344 + 0.552755i \(0.186423\pi\)
0.0620280 + 0.998074i \(0.480243\pi\)
\(674\) 0 0
\(675\) −7.37457 + 10.5493i −0.283847 + 0.406044i
\(676\) 0 0
\(677\) −2.54944 + 4.41576i −0.0979830 + 0.169712i −0.910850 0.412738i \(-0.864572\pi\)
0.812867 + 0.582450i \(0.197906\pi\)
\(678\) 0 0
\(679\) 1.76371 + 3.32927i 0.0676852 + 0.127766i
\(680\) 0 0
\(681\) −30.1661 26.8317i −1.15597 1.02819i
\(682\) 0 0
\(683\) 7.77197 13.4614i 0.297386 0.515088i −0.678151 0.734923i \(-0.737218\pi\)
0.975537 + 0.219835i \(0.0705518\pi\)
\(684\) 0 0
\(685\) −33.7738 −1.29043
\(686\) 0 0
\(687\) 6.41164 + 5.70291i 0.244619 + 0.217580i
\(688\) 0 0
\(689\) −11.7596 20.3682i −0.448005 0.775967i
\(690\) 0 0
\(691\) 11.6483 20.1755i 0.443123 0.767512i −0.554796 0.831986i \(-0.687204\pi\)
0.997919 + 0.0644744i \(0.0205371\pi\)
\(692\) 0 0
\(693\) 1.01307 + 12.5665i 0.0384833 + 0.477361i
\(694\) 0 0
\(695\) −10.3665 + 17.9553i −0.393225 + 0.681085i
\(696\) 0 0
\(697\) 15.8640 + 27.4772i 0.600891 + 1.04077i
\(698\) 0 0
\(699\) −4.99381 + 24.2165i −0.188883 + 0.915954i
\(700\) 0 0
\(701\) −45.6464 −1.72404 −0.862020 0.506874i \(-0.830801\pi\)
−0.862020 + 0.506874i \(0.830801\pi\)
\(702\) 0 0
\(703\) −3.54944 + 6.14781i −0.133870 + 0.231869i
\(704\) 0 0
\(705\) −6.96217 + 2.30900i −0.262211 + 0.0869621i
\(706\) 0 0
\(707\) 31.8163 + 1.15951i 1.19658 + 0.0436079i
\(708\) 0 0
\(709\) −9.00069 + 15.5897i −0.338028 + 0.585482i −0.984062 0.177827i \(-0.943093\pi\)
0.646034 + 0.763309i \(0.276427\pi\)
\(710\) 0 0
\(711\) 23.1080 + 9.95371i 0.866619 + 0.373293i
\(712\) 0 0
\(713\) 0.407305 + 0.705474i 0.0152537 + 0.0264202i
\(714\) 0 0
\(715\) 6.06870 10.5113i 0.226957 0.393100i
\(716\) 0 0
\(717\) 8.17928 2.71266i 0.305461 0.101306i
\(718\) 0 0
\(719\) −18.4389 31.9371i −0.687654 1.19105i −0.972595 0.232506i \(-0.925307\pi\)
0.284941 0.958545i \(-0.408026\pi\)
\(720\) 0 0
\(721\) 16.1254 + 0.587674i 0.600542 + 0.0218861i
\(722\) 0 0
\(723\) 16.8244 + 14.9646i 0.625705 + 0.556541i
\(724\) 0 0
\(725\) −10.2498 17.7531i −0.380666 0.659334i
\(726\) 0 0
\(727\) −15.2429 26.4014i −0.565327 0.979175i −0.997019 0.0771543i \(-0.975417\pi\)
0.431692 0.902021i \(-0.357917\pi\)
\(728\) 0 0
\(729\) −9.27375 25.3574i −0.343472 0.939163i
\(730\) 0 0
\(731\) −8.99628 −0.332739
\(732\) 0 0
\(733\) 6.15059 0.227177 0.113589 0.993528i \(-0.463765\pi\)
0.113589 + 0.993528i \(0.463765\pi\)
\(734\) 0 0
\(735\) −13.4196 13.8123i −0.494990 0.509475i
\(736\) 0 0
\(737\) −7.98398 13.8287i −0.294094 0.509385i
\(738\) 0 0
\(739\) 20.3912 35.3186i 0.750103 1.29922i −0.197670 0.980269i \(-0.563337\pi\)
0.947772 0.318947i \(-0.103329\pi\)
\(740\) 0 0
\(741\) −44.1989 39.3132i −1.62369 1.44421i
\(742\) 0 0
\(743\) −7.25271 + 12.5621i −0.266076 + 0.460858i −0.967845 0.251547i \(-0.919061\pi\)
0.701769 + 0.712405i \(0.252394\pi\)
\(744\) 0 0
\(745\) 8.27342 0.303115
\(746\) 0 0
\(747\) 5.69089 4.24127i 0.208219 0.155180i
\(748\) 0 0
\(749\) 3.82279 + 7.21608i 0.139682 + 0.263670i
\(750\) 0 0
\(751\) −4.18911 −0.152863 −0.0764314 0.997075i \(-0.524353\pi\)
−0.0764314 + 0.997075i \(0.524353\pi\)
\(752\) 0 0
\(753\) 3.14833 + 2.80032i 0.114731 + 0.102049i
\(754\) 0 0
\(755\) 0.830556 0.0302270
\(756\) 0 0
\(757\) 2.38688 0.0867525 0.0433763 0.999059i \(-0.486189\pi\)
0.0433763 + 0.999059i \(0.486189\pi\)
\(758\) 0 0
\(759\) 0.617454 + 0.549202i 0.0224122 + 0.0199348i
\(760\) 0 0
\(761\) 3.63416 0.131738 0.0658692 0.997828i \(-0.479018\pi\)
0.0658692 + 0.997828i \(0.479018\pi\)
\(762\) 0 0
\(763\) 3.21565 5.12874i 0.116414 0.185673i
\(764\) 0 0
\(765\) −23.6291 10.1781i −0.854311 0.367992i
\(766\) 0 0
\(767\) 31.1606 1.12515
\(768\) 0 0
\(769\) −19.9672 + 34.5842i −0.720035 + 1.24714i 0.240950 + 0.970538i \(0.422541\pi\)
−0.960985 + 0.276600i \(0.910792\pi\)
\(770\) 0 0
\(771\) 1.27816 + 1.13688i 0.0460318 + 0.0409436i
\(772\) 0 0
\(773\) 18.0698 31.2978i 0.649925 1.12570i −0.333215 0.942851i \(-0.608133\pi\)
0.983140 0.182853i \(-0.0585332\pi\)
\(774\) 0 0
\(775\) 3.35896 + 5.81788i 0.120657 + 0.208985i
\(776\) 0 0
\(777\) 1.08836 4.45146i 0.0390448 0.159695i
\(778\) 0 0
\(779\) 41.7156 1.49462
\(780\) 0 0
\(781\) −20.2051 −0.722994
\(782\) 0 0
\(783\) 42.8406 + 3.71470i 1.53100 + 0.132753i
\(784\) 0 0
\(785\) −7.03961 12.1930i −0.251254 0.435186i
\(786\) 0 0
\(787\) −22.3189 38.6574i −0.795582 1.37799i −0.922469 0.386071i \(-0.873832\pi\)
0.126888 0.991917i \(-0.459501\pi\)
\(788\) 0 0
\(789\) 22.2410 + 19.7826i 0.791801 + 0.704278i
\(790\) 0 0
\(791\) −27.3566 + 43.6319i −0.972689 + 1.55137i
\(792\) 0 0
\(793\) −10.7694 18.6532i −0.382433 0.662394i
\(794\) 0 0
\(795\) −12.7658 + 4.23377i −0.452756 + 0.150156i
\(796\) 0 0
\(797\) 26.2836 45.5245i 0.931012 1.61256i 0.149418 0.988774i \(-0.452260\pi\)
0.781595 0.623786i \(-0.214407\pi\)
\(798\) 0 0
\(799\) 7.19777 + 12.4669i 0.254639 + 0.441047i
\(800\) 0 0
\(801\) −7.72184 + 5.75488i −0.272838 + 0.203339i
\(802\) 0 0
\(803\) 12.7491 22.0820i 0.449905 0.779258i
\(804\) 0 0
\(805\) −1.26145 0.0459722i −0.0444603 0.00162031i
\(806\) 0 0
\(807\) −37.6552 + 12.4883i −1.32553 + 0.439611i
\(808\) 0 0
\(809\) 7.40290 12.8222i 0.260272 0.450804i −0.706042 0.708170i \(-0.749521\pi\)
0.966314 + 0.257365i \(0.0828544\pi\)
\(810\) 0 0
\(811\) −27.0704 −0.950571 −0.475285 0.879832i \(-0.657655\pi\)
−0.475285 + 0.879832i \(0.657655\pi\)
\(812\) 0 0
\(813\) −4.89995 + 23.7614i −0.171849 + 0.833348i
\(814\) 0 0
\(815\) −17.4425 30.2113i −0.610984 1.05826i
\(816\) 0 0
\(817\) −5.91411 + 10.2435i −0.206908 + 0.358376i
\(818\) 0 0
\(819\) 34.4967 + 16.3736i 1.20541 + 0.572139i
\(820\) 0 0
\(821\) −21.9091 + 37.9477i −0.764632 + 1.32438i 0.175808 + 0.984424i \(0.443746\pi\)
−0.940441 + 0.339958i \(0.889587\pi\)
\(822\) 0 0
\(823\) 15.6712 + 27.1434i 0.546265 + 0.946158i 0.998526 + 0.0542727i \(0.0172840\pi\)
−0.452262 + 0.891885i \(0.649383\pi\)
\(824\) 0 0
\(825\) 5.09201 + 4.52915i 0.177281 + 0.157685i
\(826\) 0 0
\(827\) 14.7665 0.513480 0.256740 0.966480i \(-0.417352\pi\)
0.256740 + 0.966480i \(0.417352\pi\)
\(828\) 0 0
\(829\) −15.0036 + 25.9871i −0.521098 + 0.902568i 0.478601 + 0.878033i \(0.341144\pi\)
−0.999699 + 0.0245357i \(0.992189\pi\)
\(830\) 0 0
\(831\) −36.6192 32.5715i −1.27031 1.12989i
\(832\) 0 0
\(833\) −21.2298 + 31.2689i −0.735569 + 1.08340i
\(834\) 0 0
\(835\) −2.62110 + 4.53987i −0.0907068 + 0.157109i
\(836\) 0 0
\(837\) −14.0393 1.21735i −0.485270 0.0420777i
\(838\) 0 0
\(839\) −18.0167 31.2059i −0.622006 1.07735i −0.989112 0.147167i \(-0.952985\pi\)
0.367106 0.930179i \(-0.380349\pi\)
\(840\) 0 0
\(841\) −19.7429 + 34.1957i −0.680789 + 1.17916i
\(842\) 0 0
\(843\) −6.15521 + 29.8485i −0.211997 + 1.02804i
\(844\) 0 0
\(845\) −8.05673 13.9547i −0.277160 0.480055i
\(846\) 0 0
\(847\) −22.4134 0.816833i −0.770134 0.0280667i
\(848\) 0 0
\(849\) −6.47957 + 31.4215i −0.222378 + 1.07838i
\(850\) 0 0
\(851\) −0.150186 0.260130i −0.00514831 0.00891713i
\(852\) 0 0
\(853\) −12.2658 21.2450i −0.419972 0.727413i 0.575964 0.817475i \(-0.304627\pi\)
−0.995936 + 0.0900617i \(0.971294\pi\)
\(854\) 0 0
\(855\) −27.1229 + 20.2140i −0.927583 + 0.691303i
\(856\) 0 0
\(857\) 29.0480 0.992260 0.496130 0.868248i \(-0.334754\pi\)
0.496130 + 0.868248i \(0.334754\pi\)
\(858\) 0 0
\(859\) −25.2953 −0.863064 −0.431532 0.902098i \(-0.642027\pi\)
−0.431532 + 0.902098i \(0.642027\pi\)
\(860\) 0 0
\(861\) −25.8516 + 7.54041i −0.881020 + 0.256976i
\(862\) 0 0
\(863\) 1.34981 + 2.33795i 0.0459482 + 0.0795846i 0.888085 0.459680i \(-0.152036\pi\)
−0.842137 + 0.539264i \(0.818702\pi\)
\(864\) 0 0
\(865\) −15.1749 + 26.2836i −0.515961 + 0.893671i
\(866\) 0 0
\(867\) −4.25093 + 20.6141i −0.144369 + 0.700091i
\(868\) 0 0
\(869\) 6.66071 11.5367i 0.225949 0.391355i
\(870\) 0 0
\(871\) −48.3643 −1.63876
\(872\) 0 0
\(873\) −3.42539 + 2.55286i −0.115932 + 0.0864011i
\(874\) 0 0
\(875\) −31.4010 1.14438i −1.06155 0.0386870i
\(876\) 0 0
\(877\) −11.0916 −0.374537 −0.187268 0.982309i \(-0.559963\pi\)
−0.187268 + 0.982309i \(0.559963\pi\)
\(878\) 0 0
\(879\) 23.1559 7.67965i 0.781029 0.259028i
\(880\) 0 0
\(881\) −40.3942 −1.36091 −0.680457 0.732788i \(-0.738219\pi\)
−0.680457 + 0.732788i \(0.738219\pi\)
\(882\) 0 0
\(883\) 33.2581 1.11923 0.559613 0.828754i \(-0.310950\pi\)
0.559613 + 0.828754i \(0.310950\pi\)
\(884\) 0 0
\(885\) 3.59888 17.4521i 0.120975 0.586646i
\(886\) 0 0
\(887\) −40.5672 −1.36211 −0.681056 0.732231i \(-0.738479\pi\)
−0.681056 + 0.732231i \(0.738479\pi\)
\(888\) 0 0
\(889\) 35.5352 + 1.29504i 1.19181 + 0.0434343i
\(890\) 0 0
\(891\) −13.9065 + 3.31105i −0.465887 + 0.110924i
\(892\) 0 0
\(893\) 18.9271 0.633371
\(894\) 0 0
\(895\) 12.7658 22.1110i 0.426713 0.739089i
\(896\) 0 0
\(897\) 2.37567 0.787890i 0.0793212 0.0263069i
\(898\) 0 0
\(899\) 11.2218 19.4367i 0.374267 0.648249i
\(900\) 0 0
\(901\) 13.1978 + 22.8592i 0.439681 + 0.761551i
\(902\) 0 0
\(903\) 1.81344 7.41705i 0.0603475 0.246824i
\(904\) 0 0
\(905\) 12.7912 0.425195
\(906\) 0 0
\(907\) −30.1135 −0.999901 −0.499950 0.866054i \(-0.666648\pi\)
−0.499950 + 0.866054i \(0.666648\pi\)
\(908\) 0 0
\(909\) 4.20946 + 35.8540i 0.139619 + 1.18920i
\(910\) 0 0
\(911\) −14.6113 25.3075i −0.484093 0.838473i 0.515740 0.856745i \(-0.327517\pi\)
−0.999833 + 0.0182717i \(0.994184\pi\)
\(912\) 0 0
\(913\) −1.87890 3.25436i −0.0621826 0.107704i
\(914\) 0 0
\(915\) −11.6909 + 3.87728i −0.386489 + 0.128179i
\(916\) 0 0
\(917\) 8.39926 + 0.306102i 0.277368 + 0.0101084i
\(918\) 0 0
\(919\) 5.52359 + 9.56714i 0.182206 + 0.315591i 0.942632 0.333835i \(-0.108343\pi\)
−0.760425 + 0.649426i \(0.775009\pi\)
\(920\) 0 0
\(921\) −7.57784 6.74021i −0.249698 0.222097i
\(922\) 0 0
\(923\) −30.5989 + 52.9988i −1.00717 + 1.74448i
\(924\) 0 0
\(925\) −1.23855 2.14523i −0.0407233 0.0705348i
\(926\) 0 0
\(927\) 2.13348 + 18.1718i 0.0700725 + 0.596842i
\(928\) 0 0
\(929\) 21.1669 36.6621i 0.694463 1.20285i −0.275898 0.961187i \(-0.588975\pi\)
0.970361 0.241659i \(-0.0776915\pi\)
\(930\) 0 0
\(931\) 21.6476 + 44.7291i 0.709473 + 1.46594i
\(932\) 0 0
\(933\) 0.283662 1.37556i 0.00928666 0.0450339i
\(934\) 0 0
\(935\) −6.81089 + 11.7968i −0.222740 + 0.385797i
\(936\) 0 0
\(937\) −11.7651 −0.384349 −0.192174 0.981361i \(-0.561554\pi\)
−0.192174 + 0.981361i \(0.561554\pi\)
\(938\) 0 0
\(939\) 17.3869 5.76636i 0.567399 0.188178i
\(940\) 0 0
\(941\) −7.28799 12.6232i −0.237582 0.411504i 0.722438 0.691436i \(-0.243021\pi\)
−0.960020 + 0.279932i \(0.909688\pi\)
\(942\) 0 0
\(943\) −0.882546 + 1.52861i −0.0287397 + 0.0497785i
\(944\) 0 0
\(945\) 13.1545 17.4295i 0.427916 0.566981i
\(946\) 0 0
\(947\) 3.12178 5.40709i 0.101444 0.175707i −0.810836 0.585274i \(-0.800987\pi\)
0.912280 + 0.409567i \(0.134320\pi\)
\(948\) 0 0
\(949\) −38.6148 66.8828i −1.25349 2.17111i
\(950\) 0 0
\(951\) 20.0508 6.64985i 0.650192 0.215636i
\(952\) 0 0
\(953\) 28.0173 0.907570 0.453785 0.891111i \(-0.350073\pi\)
0.453785 + 0.891111i \(0.350073\pi\)
\(954\) 0 0
\(955\) −19.0309 + 32.9624i −0.615825 + 1.06664i
\(956\) 0 0
\(957\) 4.59820 22.2981i 0.148639 0.720795i
\(958\) 0 0
\(959\) −56.2199 2.04887i −1.81544 0.0661616i
\(960\) 0 0
\(961\) 11.8225 20.4772i 0.381371 0.660554i
\(962\) 0 0
\(963\) −7.42442 + 5.53322i −0.239249 + 0.178306i
\(964\) 0 0
\(965\) −7.75526 13.4325i −0.249651 0.432408i
\(966\) 0 0
\(967\) −15.7837 + 27.3381i −0.507568 + 0.879134i 0.492393 + 0.870373i \(0.336122\pi\)
−0.999962 + 0.00876132i \(0.997211\pi\)
\(968\) 0 0
\(969\) 49.6043 + 44.1212i 1.59352 + 1.41738i
\(970\) 0 0
\(971\) −2.82141 4.88683i −0.0905434 0.156826i 0.817196 0.576359i \(-0.195527\pi\)
−0.907740 + 0.419533i \(0.862194\pi\)
\(972\) 0 0
\(973\) −18.3454 + 29.2596i −0.588127 + 0.938021i
\(974\) 0 0
\(975\) 19.5916 6.49755i 0.627433 0.208088i
\(976\) 0 0
\(977\) −3.24652 5.62314i −0.103865 0.179900i 0.809409 0.587246i \(-0.199788\pi\)
−0.913274 + 0.407346i \(0.866454\pi\)
\(978\) 0 0
\(979\) 2.54944 + 4.41576i 0.0814805 + 0.141128i
\(980\) 0 0
\(981\) 6.30401 + 2.71543i 0.201272 + 0.0866971i
\(982\) 0 0
\(983\) 30.3063 0.966620 0.483310 0.875449i \(-0.339434\pi\)
0.483310 + 0.875449i \(0.339434\pi\)
\(984\) 0 0
\(985\) −28.9774 −0.923298
\(986\) 0 0
\(987\) −11.7293 + 3.42122i −0.373349 + 0.108899i
\(988\) 0 0
\(989\) −0.250241 0.433430i −0.00795720 0.0137823i
\(990\) 0 0
\(991\) −11.1669 + 19.3416i −0.354728 + 0.614407i −0.987071 0.160281i \(-0.948760\pi\)
0.632343 + 0.774688i \(0.282093\pi\)
\(992\) 0 0
\(993\) 25.7552 8.54170i 0.817316 0.271063i
\(994\) 0 0
\(995\) −14.3738 + 24.8962i −0.455680 + 0.789262i
\(996\) 0 0
\(997\) −8.76509 −0.277593 −0.138797 0.990321i \(-0.544323\pi\)
−0.138797 + 0.990321i \(0.544323\pi\)
\(998\) 0 0
\(999\) 5.17673 + 0.448873i 0.163784 + 0.0142017i
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 1008.2.t.h.193.1 6
3.2 odd 2 3024.2.t.h.1873.1 6
4.3 odd 2 126.2.h.d.67.3 yes 6
7.2 even 3 1008.2.q.g.625.3 6
9.2 odd 6 3024.2.q.g.2881.3 6
9.7 even 3 1008.2.q.g.529.3 6
12.11 even 2 378.2.h.c.361.1 6
21.2 odd 6 3024.2.q.g.2305.3 6
28.3 even 6 882.2.f.o.589.1 6
28.11 odd 6 882.2.f.n.589.3 6
28.19 even 6 882.2.e.o.373.3 6
28.23 odd 6 126.2.e.c.121.1 yes 6
28.27 even 2 882.2.h.p.67.1 6
36.7 odd 6 126.2.e.c.25.1 6
36.11 even 6 378.2.e.d.235.3 6
36.23 even 6 1134.2.g.l.487.3 6
36.31 odd 6 1134.2.g.m.487.1 6
63.2 odd 6 3024.2.t.h.289.1 6
63.16 even 3 inner 1008.2.t.h.961.1 6
84.11 even 6 2646.2.f.l.1765.3 6
84.23 even 6 378.2.e.d.37.3 6
84.47 odd 6 2646.2.e.p.1549.1 6
84.59 odd 6 2646.2.f.m.1765.1 6
84.83 odd 2 2646.2.h.o.361.3 6
252.11 even 6 2646.2.f.l.883.3 6
252.23 even 6 1134.2.g.l.163.3 6
252.31 even 6 7938.2.a.bw.1.1 3
252.47 odd 6 2646.2.h.o.667.3 6
252.59 odd 6 7938.2.a.bz.1.3 3
252.67 odd 6 7938.2.a.bv.1.3 3
252.79 odd 6 126.2.h.d.79.3 yes 6
252.83 odd 6 2646.2.e.p.2125.1 6
252.95 even 6 7938.2.a.ca.1.1 3
252.115 even 6 882.2.f.o.295.1 6
252.151 odd 6 882.2.f.n.295.3 6
252.187 even 6 882.2.h.p.79.1 6
252.191 even 6 378.2.h.c.289.1 6
252.223 even 6 882.2.e.o.655.3 6
252.227 odd 6 2646.2.f.m.883.1 6
252.247 odd 6 1134.2.g.m.163.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.c.25.1 6 36.7 odd 6
126.2.e.c.121.1 yes 6 28.23 odd 6
126.2.h.d.67.3 yes 6 4.3 odd 2
126.2.h.d.79.3 yes 6 252.79 odd 6
378.2.e.d.37.3 6 84.23 even 6
378.2.e.d.235.3 6 36.11 even 6
378.2.h.c.289.1 6 252.191 even 6
378.2.h.c.361.1 6 12.11 even 2
882.2.e.o.373.3 6 28.19 even 6
882.2.e.o.655.3 6 252.223 even 6
882.2.f.n.295.3 6 252.151 odd 6
882.2.f.n.589.3 6 28.11 odd 6
882.2.f.o.295.1 6 252.115 even 6
882.2.f.o.589.1 6 28.3 even 6
882.2.h.p.67.1 6 28.27 even 2
882.2.h.p.79.1 6 252.187 even 6
1008.2.q.g.529.3 6 9.7 even 3
1008.2.q.g.625.3 6 7.2 even 3
1008.2.t.h.193.1 6 1.1 even 1 trivial
1008.2.t.h.961.1 6 63.16 even 3 inner
1134.2.g.l.163.3 6 252.23 even 6
1134.2.g.l.487.3 6 36.23 even 6
1134.2.g.m.163.1 6 252.247 odd 6
1134.2.g.m.487.1 6 36.31 odd 6
2646.2.e.p.1549.1 6 84.47 odd 6
2646.2.e.p.2125.1 6 252.83 odd 6
2646.2.f.l.883.3 6 252.11 even 6
2646.2.f.l.1765.3 6 84.11 even 6
2646.2.f.m.883.1 6 252.227 odd 6
2646.2.f.m.1765.1 6 84.59 odd 6
2646.2.h.o.361.3 6 84.83 odd 2
2646.2.h.o.667.3 6 252.47 odd 6
3024.2.q.g.2305.3 6 21.2 odd 6
3024.2.q.g.2881.3 6 9.2 odd 6
3024.2.t.h.289.1 6 63.2 odd 6
3024.2.t.h.1873.1 6 3.2 odd 2
7938.2.a.bv.1.3 3 252.67 odd 6
7938.2.a.bw.1.1 3 252.31 even 6
7938.2.a.bz.1.3 3 252.59 odd 6
7938.2.a.ca.1.1 3 252.95 even 6