Properties

Label 792.2.h.i.307.13
Level $792$
Weight $2$
Character 792.307
Analytic conductor $6.324$
Analytic rank $0$
Dimension $16$
Inner twists $8$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [792,2,Mod(307,792)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(792, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 1])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("792.307"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 792.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [16,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.32415184009\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: 16.0.3342602057661458415616.4
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 20x^{14} + 164x^{12} - 666x^{10} + 1300x^{8} - 924x^{6} + 273x^{4} + 404x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 307.13
Root \(-2.34517 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 792.307
Dual form 792.2.h.i.307.16

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.37491 - 0.331077i) q^{2} +(1.78078 - 0.910404i) q^{4} -2.00000i q^{5} -3.02045 q^{7} +(2.14700 - 1.84130i) q^{8} +(-0.662153 - 2.74983i) q^{10} +(2.33205 - 2.35829i) q^{11} -1.32431 q^{13} +(-4.15286 + 1.00000i) q^{14} +(2.34233 - 3.24245i) q^{16} +1.69614i q^{17} -7.04383i q^{19} +(-1.82081 - 3.56155i) q^{20} +(2.42559 - 4.01454i) q^{22} +3.12311i q^{23} +1.00000 q^{25} +(-1.82081 + 0.438447i) q^{26} +(-5.37874 + 2.74983i) q^{28} -1.54417 q^{29} -8.30571i q^{31} +(2.14700 - 5.23358i) q^{32} +(0.561553 + 2.33205i) q^{34} +6.04090i q^{35} +4.66410i q^{37} +(-2.33205 - 9.68466i) q^{38} +(-3.68260 - 4.29400i) q^{40} +7.73704i q^{41} +3.95548i q^{43} +(2.00586 - 6.32270i) q^{44} +(1.03399 + 4.29400i) q^{46} -6.00000i q^{47} +2.12311 q^{49} +(1.37491 - 0.331077i) q^{50} +(-2.35829 + 1.20565i) q^{52} +8.24621i q^{53} +(-4.71659 - 4.66410i) q^{55} +(-6.48490 + 5.56155i) q^{56} +(-2.12311 + 0.511240i) q^{58} +11.9473 q^{59} +8.10887 q^{61} +(-2.74983 - 11.4196i) q^{62} +(1.21922 - 7.90655i) q^{64} +2.64861i q^{65} +6.24621 q^{67} +(1.54417 + 3.02045i) q^{68} +(2.00000 + 8.30571i) q^{70} +12.2462i q^{71} +3.08835i q^{73} +(1.54417 + 6.41273i) q^{74} +(-6.41273 - 12.5435i) q^{76} +(-7.04383 + 7.12311i) q^{77} -12.4536 q^{79} +(-6.48490 - 4.68466i) q^{80} +(2.56155 + 10.6378i) q^{82} +4.71659i q^{83} +3.39228 q^{85} +(1.30957 + 5.43845i) q^{86} +(0.664579 - 9.35726i) q^{88} +16.6114 q^{89} +4.00000 q^{91} +(2.84329 + 5.56155i) q^{92} +(-1.98646 - 8.24948i) q^{94} -14.0877 q^{95} -13.3693 q^{97} +(2.91909 - 0.702911i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 12 q^{4} - 12 q^{16} + 4 q^{22} + 16 q^{25} - 24 q^{34} - 32 q^{49} + 32 q^{58} + 36 q^{64} - 32 q^{67} + 32 q^{70} + 8 q^{82} - 20 q^{88} + 64 q^{91} - 16 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/792\mathbb{Z}\right)^\times\).

\(n\) \(145\) \(199\) \(353\) \(397\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.37491 0.331077i 0.972211 0.234107i
\(3\) 0 0
\(4\) 1.78078 0.910404i 0.890388 0.455202i
\(5\) 2.00000i 0.894427i −0.894427 0.447214i \(-0.852416\pi\)
0.894427 0.447214i \(-0.147584\pi\)
\(6\) 0 0
\(7\) −3.02045 −1.14162 −0.570811 0.821081i \(-0.693371\pi\)
−0.570811 + 0.821081i \(0.693371\pi\)
\(8\) 2.14700 1.84130i 0.759079 0.650998i
\(9\) 0 0
\(10\) −0.662153 2.74983i −0.209391 0.869572i
\(11\) 2.33205 2.35829i 0.703139 0.711053i
\(12\) 0 0
\(13\) −1.32431 −0.367297 −0.183648 0.982992i \(-0.558791\pi\)
−0.183648 + 0.982992i \(0.558791\pi\)
\(14\) −4.15286 + 1.00000i −1.10990 + 0.267261i
\(15\) 0 0
\(16\) 2.34233 3.24245i 0.585582 0.810613i
\(17\) 1.69614i 0.411375i 0.978618 + 0.205687i \(0.0659430\pi\)
−0.978618 + 0.205687i \(0.934057\pi\)
\(18\) 0 0
\(19\) 7.04383i 1.61597i −0.589206 0.807983i \(-0.700559\pi\)
0.589206 0.807983i \(-0.299441\pi\)
\(20\) −1.82081 3.56155i −0.407145 0.796387i
\(21\) 0 0
\(22\) 2.42559 4.01454i 0.517137 0.855903i
\(23\) 3.12311i 0.651213i 0.945505 + 0.325606i \(0.105568\pi\)
−0.945505 + 0.325606i \(0.894432\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −1.82081 + 0.438447i −0.357090 + 0.0859866i
\(27\) 0 0
\(28\) −5.37874 + 2.74983i −1.01649 + 0.519669i
\(29\) −1.54417 −0.286746 −0.143373 0.989669i \(-0.545795\pi\)
−0.143373 + 0.989669i \(0.545795\pi\)
\(30\) 0 0
\(31\) 8.30571i 1.49175i −0.666086 0.745875i \(-0.732032\pi\)
0.666086 0.745875i \(-0.267968\pi\)
\(32\) 2.14700 5.23358i 0.379540 0.925175i
\(33\) 0 0
\(34\) 0.561553 + 2.33205i 0.0963055 + 0.399943i
\(35\) 6.04090i 1.02110i
\(36\) 0 0
\(37\) 4.66410i 0.766773i 0.923588 + 0.383386i \(0.125242\pi\)
−0.923588 + 0.383386i \(0.874758\pi\)
\(38\) −2.33205 9.68466i −0.378308 1.57106i
\(39\) 0 0
\(40\) −3.68260 4.29400i −0.582270 0.678941i
\(41\) 7.73704i 1.20832i 0.796862 + 0.604161i \(0.206492\pi\)
−0.796862 + 0.604161i \(0.793508\pi\)
\(42\) 0 0
\(43\) 3.95548i 0.603205i 0.953434 + 0.301603i \(0.0975216\pi\)
−0.953434 + 0.301603i \(0.902478\pi\)
\(44\) 2.00586 6.32270i 0.302394 0.953183i
\(45\) 0 0
\(46\) 1.03399 + 4.29400i 0.152453 + 0.633116i
\(47\) 6.00000i 0.875190i −0.899172 0.437595i \(-0.855830\pi\)
0.899172 0.437595i \(-0.144170\pi\)
\(48\) 0 0
\(49\) 2.12311 0.303301
\(50\) 1.37491 0.331077i 0.194442 0.0468213i
\(51\) 0 0
\(52\) −2.35829 + 1.20565i −0.327037 + 0.167194i
\(53\) 8.24621i 1.13270i 0.824163 + 0.566352i \(0.191646\pi\)
−0.824163 + 0.566352i \(0.808354\pi\)
\(54\) 0 0
\(55\) −4.71659 4.66410i −0.635985 0.628907i
\(56\) −6.48490 + 5.56155i −0.866582 + 0.743194i
\(57\) 0 0
\(58\) −2.12311 + 0.511240i −0.278777 + 0.0671291i
\(59\) 11.9473 1.55541 0.777705 0.628630i \(-0.216384\pi\)
0.777705 + 0.628630i \(0.216384\pi\)
\(60\) 0 0
\(61\) 8.10887 1.03823 0.519117 0.854703i \(-0.326261\pi\)
0.519117 + 0.854703i \(0.326261\pi\)
\(62\) −2.74983 11.4196i −0.349228 1.45030i
\(63\) 0 0
\(64\) 1.21922 7.90655i 0.152403 0.988318i
\(65\) 2.64861i 0.328520i
\(66\) 0 0
\(67\) 6.24621 0.763096 0.381548 0.924349i \(-0.375391\pi\)
0.381548 + 0.924349i \(0.375391\pi\)
\(68\) 1.54417 + 3.02045i 0.187259 + 0.366283i
\(69\) 0 0
\(70\) 2.00000 + 8.30571i 0.239046 + 0.992722i
\(71\) 12.2462i 1.45336i 0.686977 + 0.726679i \(0.258937\pi\)
−0.686977 + 0.726679i \(0.741063\pi\)
\(72\) 0 0
\(73\) 3.08835i 0.361464i 0.983532 + 0.180732i \(0.0578466\pi\)
−0.983532 + 0.180732i \(0.942153\pi\)
\(74\) 1.54417 + 6.41273i 0.179507 + 0.745465i
\(75\) 0 0
\(76\) −6.41273 12.5435i −0.735591 1.43884i
\(77\) −7.04383 + 7.12311i −0.802719 + 0.811753i
\(78\) 0 0
\(79\) −12.4536 −1.40114 −0.700571 0.713583i \(-0.747071\pi\)
−0.700571 + 0.713583i \(0.747071\pi\)
\(80\) −6.48490 4.68466i −0.725034 0.523761i
\(81\) 0 0
\(82\) 2.56155 + 10.6378i 0.282876 + 1.17474i
\(83\) 4.71659i 0.517713i 0.965916 + 0.258856i \(0.0833457\pi\)
−0.965916 + 0.258856i \(0.916654\pi\)
\(84\) 0 0
\(85\) 3.39228 0.367945
\(86\) 1.30957 + 5.43845i 0.141214 + 0.586443i
\(87\) 0 0
\(88\) 0.664579 9.35726i 0.0708444 0.997487i
\(89\) 16.6114 1.76081 0.880404 0.474225i \(-0.157272\pi\)
0.880404 + 0.474225i \(0.157272\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) 2.84329 + 5.56155i 0.296433 + 0.579832i
\(93\) 0 0
\(94\) −1.98646 8.24948i −0.204888 0.850869i
\(95\) −14.0877 −1.44536
\(96\) 0 0
\(97\) −13.3693 −1.35745 −0.678724 0.734393i \(-0.737467\pi\)
−0.678724 + 0.734393i \(0.737467\pi\)
\(98\) 2.91909 0.702911i 0.294872 0.0710047i
\(99\) 0 0
\(100\) 1.78078 0.910404i 0.178078 0.0910404i
\(101\) 1.54417 0.153651 0.0768255 0.997045i \(-0.475522\pi\)
0.0768255 + 0.997045i \(0.475522\pi\)
\(102\) 0 0
\(103\) 8.30571i 0.818386i −0.912448 0.409193i \(-0.865810\pi\)
0.912448 0.409193i \(-0.134190\pi\)
\(104\) −2.84329 + 2.43845i −0.278807 + 0.239109i
\(105\) 0 0
\(106\) 2.73013 + 11.3378i 0.265174 + 1.10123i
\(107\) 8.10887i 0.783914i 0.919984 + 0.391957i \(0.128202\pi\)
−0.919984 + 0.391957i \(0.871798\pi\)
\(108\) 0 0
\(109\) 16.7984 1.60899 0.804497 0.593957i \(-0.202435\pi\)
0.804497 + 0.593957i \(0.202435\pi\)
\(110\) −8.02908 4.85118i −0.765542 0.462542i
\(111\) 0 0
\(112\) −7.07488 + 9.79366i −0.668514 + 0.925414i
\(113\) 7.28323 0.685149 0.342574 0.939491i \(-0.388701\pi\)
0.342574 + 0.939491i \(0.388701\pi\)
\(114\) 0 0
\(115\) 6.24621 0.582462
\(116\) −2.74983 + 1.40582i −0.255315 + 0.130527i
\(117\) 0 0
\(118\) 16.4265 3.95548i 1.51219 0.364132i
\(119\) 5.12311i 0.469634i
\(120\) 0 0
\(121\) −0.123106 10.9993i −0.0111914 0.999937i
\(122\) 11.1490 2.68466i 1.00938 0.243058i
\(123\) 0 0
\(124\) −7.56155 14.7906i −0.679047 1.32824i
\(125\) 12.0000i 1.07331i
\(126\) 0 0
\(127\) 2.27678 0.202032 0.101016 0.994885i \(-0.467791\pi\)
0.101016 + 0.994885i \(0.467791\pi\)
\(128\) −0.941346 11.2745i −0.0832041 0.996533i
\(129\) 0 0
\(130\) 0.876894 + 3.64162i 0.0769087 + 0.319391i
\(131\) 3.97292i 0.347116i 0.984824 + 0.173558i \(0.0555264\pi\)
−0.984824 + 0.173558i \(0.944474\pi\)
\(132\) 0 0
\(133\) 21.2755i 1.84482i
\(134\) 8.58800 2.06798i 0.741890 0.178646i
\(135\) 0 0
\(136\) 3.12311 + 3.64162i 0.267804 + 0.312266i
\(137\) −7.28323 −0.622248 −0.311124 0.950369i \(-0.600706\pi\)
−0.311124 + 0.950369i \(0.600706\pi\)
\(138\) 0 0
\(139\) 3.95548i 0.335500i 0.985830 + 0.167750i \(0.0536501\pi\)
−0.985830 + 0.167750i \(0.946350\pi\)
\(140\) 5.49966 + 10.7575i 0.464806 + 0.909173i
\(141\) 0 0
\(142\) 4.05444 + 16.8375i 0.340241 + 1.41297i
\(143\) −3.08835 + 3.12311i −0.258261 + 0.261167i
\(144\) 0 0
\(145\) 3.08835i 0.256473i
\(146\) 1.02248 + 4.24621i 0.0846210 + 0.351419i
\(147\) 0 0
\(148\) 4.24621 + 8.30571i 0.349036 + 0.682725i
\(149\) −12.5435 −1.02760 −0.513801 0.857909i \(-0.671763\pi\)
−0.513801 + 0.857909i \(0.671763\pi\)
\(150\) 0 0
\(151\) −7.15640 −0.582379 −0.291190 0.956665i \(-0.594051\pi\)
−0.291190 + 0.956665i \(0.594051\pi\)
\(152\) −12.9698 15.1231i −1.05199 1.22665i
\(153\) 0 0
\(154\) −7.32636 + 12.1257i −0.590375 + 0.977117i
\(155\) −16.6114 −1.33426
\(156\) 0 0
\(157\) 7.28323i 0.581265i 0.956835 + 0.290633i \(0.0938657\pi\)
−0.956835 + 0.290633i \(0.906134\pi\)
\(158\) −17.1227 + 4.12311i −1.36221 + 0.328017i
\(159\) 0 0
\(160\) −10.4672 4.29400i −0.827502 0.339471i
\(161\) 9.43318i 0.743439i
\(162\) 0 0
\(163\) −20.4924 −1.60509 −0.802545 0.596591i \(-0.796521\pi\)
−0.802545 + 0.596591i \(0.796521\pi\)
\(164\) 7.04383 + 13.7779i 0.550031 + 1.07588i
\(165\) 0 0
\(166\) 1.56155 + 6.48490i 0.121200 + 0.503326i
\(167\) 14.0877 1.09014 0.545068 0.838392i \(-0.316504\pi\)
0.545068 + 0.838392i \(0.316504\pi\)
\(168\) 0 0
\(169\) −11.2462 −0.865093
\(170\) 4.66410 1.12311i 0.357720 0.0861383i
\(171\) 0 0
\(172\) 3.60109 + 7.04383i 0.274580 + 0.537087i
\(173\) 12.5435 0.953663 0.476832 0.878995i \(-0.341785\pi\)
0.476832 + 0.878995i \(0.341785\pi\)
\(174\) 0 0
\(175\) −3.02045 −0.228324
\(176\) −2.18423 13.0855i −0.164643 0.986353i
\(177\) 0 0
\(178\) 22.8393 5.49966i 1.71188 0.412217i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 25.9396i 1.92808i 0.265764 + 0.964038i \(0.414376\pi\)
−0.265764 + 0.964038i \(0.585624\pi\)
\(182\) 5.49966 1.32431i 0.407662 0.0981642i
\(183\) 0 0
\(184\) 5.75058 + 6.70531i 0.423938 + 0.494322i
\(185\) 9.32819 0.685822
\(186\) 0 0
\(187\) 4.00000 + 3.95548i 0.292509 + 0.289253i
\(188\) −5.46242 10.6847i −0.398388 0.779259i
\(189\) 0 0
\(190\) −19.3693 + 4.66410i −1.40520 + 0.338369i
\(191\) 4.24621i 0.307245i −0.988130 0.153623i \(-0.950906\pi\)
0.988130 0.153623i \(-0.0490940\pi\)
\(192\) 0 0
\(193\) 25.0870i 1.80580i 0.429851 + 0.902900i \(0.358566\pi\)
−0.429851 + 0.902900i \(0.641434\pi\)
\(194\) −18.3817 + 4.42627i −1.31973 + 0.317788i
\(195\) 0 0
\(196\) 3.78078 1.93288i 0.270055 0.138063i
\(197\) 15.6318 1.11372 0.556861 0.830606i \(-0.312006\pi\)
0.556861 + 0.830606i \(0.312006\pi\)
\(198\) 0 0
\(199\) 1.02248i 0.0724817i −0.999343 0.0362408i \(-0.988462\pi\)
0.999343 0.0362408i \(-0.0115383\pi\)
\(200\) 2.14700 1.84130i 0.151816 0.130200i
\(201\) 0 0
\(202\) 2.12311 0.511240i 0.149381 0.0359707i
\(203\) 4.66410 0.327355
\(204\) 0 0
\(205\) 15.4741 1.08076
\(206\) −2.74983 11.4196i −0.191590 0.795644i
\(207\) 0 0
\(208\) −3.10196 + 4.29400i −0.215082 + 0.297735i
\(209\) −16.6114 16.4265i −1.14904 1.13625i
\(210\) 0 0
\(211\) 7.04383i 0.484917i −0.970162 0.242459i \(-0.922046\pi\)
0.970162 0.242459i \(-0.0779539\pi\)
\(212\) 7.50738 + 14.6847i 0.515609 + 1.00855i
\(213\) 0 0
\(214\) 2.68466 + 11.1490i 0.183519 + 0.762130i
\(215\) 7.91096 0.539523
\(216\) 0 0
\(217\) 25.0870i 1.70301i
\(218\) 23.0963 5.56155i 1.56428 0.376676i
\(219\) 0 0
\(220\) −12.6454 4.01171i −0.852553 0.270469i
\(221\) 2.24621i 0.151097i
\(222\) 0 0
\(223\) 10.3507i 0.693132i −0.938026 0.346566i \(-0.887348\pi\)
0.938026 0.346566i \(-0.112652\pi\)
\(224\) −6.48490 + 15.8078i −0.433291 + 1.05620i
\(225\) 0 0
\(226\) 10.0138 2.41131i 0.666109 0.160398i
\(227\) 24.7442i 1.64233i −0.570690 0.821166i \(-0.693324\pi\)
0.570690 0.821166i \(-0.306676\pi\)
\(228\) 0 0
\(229\) 19.2306i 1.27079i −0.772187 0.635396i \(-0.780837\pi\)
0.772187 0.635396i \(-0.219163\pi\)
\(230\) 8.58800 2.06798i 0.566276 0.136358i
\(231\) 0 0
\(232\) −3.31534 + 2.84329i −0.217663 + 0.186671i
\(233\) 19.8188i 1.29837i 0.760629 + 0.649187i \(0.224891\pi\)
−0.760629 + 0.649187i \(0.775109\pi\)
\(234\) 0 0
\(235\) −12.0000 −0.782794
\(236\) 21.2755 10.8769i 1.38492 0.708026i
\(237\) 0 0
\(238\) −1.69614 7.04383i −0.109944 0.456584i
\(239\) −7.91096 −0.511718 −0.255859 0.966714i \(-0.582358\pi\)
−0.255859 + 0.966714i \(0.582358\pi\)
\(240\) 0 0
\(241\) 18.9103i 1.21812i −0.793125 0.609059i \(-0.791547\pi\)
0.793125 0.609059i \(-0.208453\pi\)
\(242\) −3.81088 15.0823i −0.244972 0.969530i
\(243\) 0 0
\(244\) 14.4401 7.38235i 0.924432 0.472606i
\(245\) 4.24621i 0.271280i
\(246\) 0 0
\(247\) 9.32819i 0.593539i
\(248\) −15.2933 17.8324i −0.971126 1.13236i
\(249\) 0 0
\(250\) −3.97292 16.4990i −0.251270 1.04349i
\(251\) −16.6114 −1.04850 −0.524252 0.851563i \(-0.675655\pi\)
−0.524252 + 0.851563i \(0.675655\pi\)
\(252\) 0 0
\(253\) 7.36520 + 7.28323i 0.463046 + 0.457893i
\(254\) 3.13038 0.753789i 0.196417 0.0472969i
\(255\) 0 0
\(256\) −5.02699 15.1898i −0.314187 0.949361i
\(257\) −25.9396 −1.61807 −0.809034 0.587761i \(-0.800009\pi\)
−0.809034 + 0.587761i \(0.800009\pi\)
\(258\) 0 0
\(259\) 14.0877i 0.875364i
\(260\) 2.41131 + 4.71659i 0.149543 + 0.292510i
\(261\) 0 0
\(262\) 1.31534 + 5.46242i 0.0812621 + 0.337470i
\(263\) 20.2644 1.24955 0.624777 0.780803i \(-0.285190\pi\)
0.624777 + 0.780803i \(0.285190\pi\)
\(264\) 0 0
\(265\) 16.4924 1.01312
\(266\) 7.04383 + 29.2520i 0.431885 + 1.79356i
\(267\) 0 0
\(268\) 11.1231 5.68658i 0.679452 0.347363i
\(269\) 16.2462i 0.990549i 0.868737 + 0.495274i \(0.164933\pi\)
−0.868737 + 0.495274i \(0.835067\pi\)
\(270\) 0 0
\(271\) −6.41273 −0.389546 −0.194773 0.980848i \(-0.562397\pi\)
−0.194773 + 0.980848i \(0.562397\pi\)
\(272\) 5.49966 + 3.97292i 0.333466 + 0.240894i
\(273\) 0 0
\(274\) −10.0138 + 2.41131i −0.604957 + 0.145672i
\(275\) 2.33205 2.35829i 0.140628 0.142211i
\(276\) 0 0
\(277\) 4.71659 0.283392 0.141696 0.989910i \(-0.454744\pi\)
0.141696 + 0.989910i \(0.454744\pi\)
\(278\) 1.30957 + 5.43845i 0.0785427 + 0.326176i
\(279\) 0 0
\(280\) 11.1231 + 12.9698i 0.664733 + 0.775094i
\(281\) 15.6829i 0.935562i −0.883844 0.467781i \(-0.845054\pi\)
0.883844 0.467781i \(-0.154946\pi\)
\(282\) 0 0
\(283\) 14.9548i 0.888970i −0.895786 0.444485i \(-0.853387\pi\)
0.895786 0.444485i \(-0.146613\pi\)
\(284\) 11.1490 + 21.8078i 0.661571 + 1.29405i
\(285\) 0 0
\(286\) −3.21222 + 5.31648i −0.189943 + 0.314370i
\(287\) 23.3693i 1.37945i
\(288\) 0 0
\(289\) 14.1231 0.830771
\(290\) 1.02248 + 4.24621i 0.0600421 + 0.249346i
\(291\) 0 0
\(292\) 2.81164 + 5.49966i 0.164539 + 0.321843i
\(293\) 6.36679 0.371952 0.185976 0.982554i \(-0.440455\pi\)
0.185976 + 0.982554i \(0.440455\pi\)
\(294\) 0 0
\(295\) 23.8947i 1.39120i
\(296\) 8.58800 + 10.0138i 0.499168 + 0.582041i
\(297\) 0 0
\(298\) −17.2462 + 4.15286i −0.999046 + 0.240568i
\(299\) 4.13595i 0.239188i
\(300\) 0 0
\(301\) 11.9473i 0.688633i
\(302\) −9.83943 + 2.36932i −0.566196 + 0.136339i
\(303\) 0 0
\(304\) −22.8393 16.4990i −1.30992 0.946281i
\(305\) 16.2177i 0.928625i
\(306\) 0 0
\(307\) 18.0431i 1.02978i 0.857257 + 0.514888i \(0.172167\pi\)
−0.857257 + 0.514888i \(0.827833\pi\)
\(308\) −6.05858 + 19.0974i −0.345220 + 1.08817i
\(309\) 0 0
\(310\) −22.8393 + 5.49966i −1.29718 + 0.312359i
\(311\) 4.87689i 0.276543i 0.990394 + 0.138272i \(0.0441547\pi\)
−0.990394 + 0.138272i \(0.955845\pi\)
\(312\) 0 0
\(313\) 3.12311 0.176528 0.0882642 0.996097i \(-0.471868\pi\)
0.0882642 + 0.996097i \(0.471868\pi\)
\(314\) 2.41131 + 10.0138i 0.136078 + 0.565112i
\(315\) 0 0
\(316\) −22.1771 + 11.3378i −1.24756 + 0.637803i
\(317\) 10.4924i 0.589313i −0.955603 0.294657i \(-0.904795\pi\)
0.955603 0.294657i \(-0.0952053\pi\)
\(318\) 0 0
\(319\) −3.60109 + 3.64162i −0.201622 + 0.203891i
\(320\) −15.8131 2.43845i −0.883979 0.136313i
\(321\) 0 0
\(322\) −3.12311 12.9698i −0.174044 0.722779i
\(323\) 11.9473 0.664767
\(324\) 0 0
\(325\) −1.32431 −0.0734593
\(326\) −28.1753 + 6.78456i −1.56049 + 0.375762i
\(327\) 0 0
\(328\) 14.2462 + 16.6114i 0.786615 + 0.917212i
\(329\) 18.1227i 0.999136i
\(330\) 0 0
\(331\) 18.2462 1.00290 0.501451 0.865186i \(-0.332800\pi\)
0.501451 + 0.865186i \(0.332800\pi\)
\(332\) 4.29400 + 8.39919i 0.235664 + 0.460965i
\(333\) 0 0
\(334\) 19.3693 4.66410i 1.05984 0.255208i
\(335\) 12.4924i 0.682534i
\(336\) 0 0
\(337\) 31.2637i 1.70304i −0.524322 0.851520i \(-0.675681\pi\)
0.524322 0.851520i \(-0.324319\pi\)
\(338\) −15.4626 + 3.72336i −0.841053 + 0.202524i
\(339\) 0 0
\(340\) 6.04090 3.08835i 0.327614 0.167489i
\(341\) −19.5873 19.3693i −1.06071 1.04891i
\(342\) 0 0
\(343\) 14.7304 0.795367
\(344\) 7.28323 + 8.49242i 0.392686 + 0.457881i
\(345\) 0 0
\(346\) 17.2462 4.15286i 0.927162 0.223259i
\(347\) 20.9343i 1.12381i −0.827200 0.561907i \(-0.810068\pi\)
0.827200 0.561907i \(-0.189932\pi\)
\(348\) 0 0
\(349\) −15.3110 −0.819581 −0.409791 0.912180i \(-0.634398\pi\)
−0.409791 + 0.912180i \(0.634398\pi\)
\(350\) −4.15286 + 1.00000i −0.221979 + 0.0534522i
\(351\) 0 0
\(352\) −7.33542 17.2682i −0.390979 0.920399i
\(353\) −9.32819 −0.496490 −0.248245 0.968697i \(-0.579854\pi\)
−0.248245 + 0.968697i \(0.579854\pi\)
\(354\) 0 0
\(355\) 24.4924 1.29992
\(356\) 29.5812 15.1231i 1.56780 0.801523i
\(357\) 0 0
\(358\) 0 0
\(359\) −36.0863 −1.90456 −0.952281 0.305224i \(-0.901269\pi\)
−0.952281 + 0.305224i \(0.901269\pi\)
\(360\) 0 0
\(361\) −30.6155 −1.61134
\(362\) 8.58800 + 35.6647i 0.451375 + 1.87450i
\(363\) 0 0
\(364\) 7.12311 3.64162i 0.373352 0.190873i
\(365\) 6.17669 0.323303
\(366\) 0 0
\(367\) 6.26075i 0.326809i −0.986559 0.163404i \(-0.947753\pi\)
0.986559 0.163404i \(-0.0522475\pi\)
\(368\) 10.1265 + 7.31534i 0.527881 + 0.381339i
\(369\) 0 0
\(370\) 12.8255 3.08835i 0.666764 0.160556i
\(371\) 24.9073i 1.29312i
\(372\) 0 0
\(373\) −23.5829 −1.22108 −0.610539 0.791986i \(-0.709047\pi\)
−0.610539 + 0.791986i \(0.709047\pi\)
\(374\) 6.80922 + 4.11414i 0.352097 + 0.212737i
\(375\) 0 0
\(376\) −11.0478 12.8820i −0.569747 0.664339i
\(377\) 2.04496 0.105321
\(378\) 0 0
\(379\) 2.24621 0.115380 0.0576901 0.998335i \(-0.481626\pi\)
0.0576901 + 0.998335i \(0.481626\pi\)
\(380\) −25.0870 + 12.8255i −1.28693 + 0.657932i
\(381\) 0 0
\(382\) −1.40582 5.83817i −0.0719281 0.298707i
\(383\) 25.3693i 1.29631i 0.761508 + 0.648156i \(0.224459\pi\)
−0.761508 + 0.648156i \(0.775541\pi\)
\(384\) 0 0
\(385\) 14.2462 + 14.0877i 0.726054 + 0.717974i
\(386\) 8.30571 + 34.4924i 0.422750 + 1.75562i
\(387\) 0 0
\(388\) −23.8078 + 12.1715i −1.20866 + 0.617913i
\(389\) 2.49242i 0.126371i −0.998002 0.0631854i \(-0.979874\pi\)
0.998002 0.0631854i \(-0.0201260\pi\)
\(390\) 0 0
\(391\) −5.29723 −0.267892
\(392\) 4.55831 3.90928i 0.230229 0.197448i
\(393\) 0 0
\(394\) 21.4924 5.17534i 1.08277 0.260730i
\(395\) 24.9073i 1.25322i
\(396\) 0 0
\(397\) 13.9923i 0.702253i −0.936328 0.351126i \(-0.885799\pi\)
0.936328 0.351126i \(-0.114201\pi\)
\(398\) −0.338519 1.40582i −0.0169684 0.0704675i
\(399\) 0 0
\(400\) 2.34233 3.24245i 0.117116 0.162123i
\(401\) −18.6564 −0.931655 −0.465828 0.884875i \(-0.654243\pi\)
−0.465828 + 0.884875i \(0.654243\pi\)
\(402\) 0 0
\(403\) 10.9993i 0.547915i
\(404\) 2.74983 1.40582i 0.136809 0.0699422i
\(405\) 0 0
\(406\) 6.41273 1.54417i 0.318258 0.0766360i
\(407\) 10.9993 + 10.8769i 0.545216 + 0.539148i
\(408\) 0 0
\(409\) 6.17669i 0.305418i −0.988271 0.152709i \(-0.951200\pi\)
0.988271 0.152709i \(-0.0487997\pi\)
\(410\) 21.2755 5.12311i 1.05072 0.253012i
\(411\) 0 0
\(412\) −7.56155 14.7906i −0.372531 0.728681i
\(413\) −36.0863 −1.77569
\(414\) 0 0
\(415\) 9.43318 0.463056
\(416\) −2.84329 + 6.93087i −0.139404 + 0.339814i
\(417\) 0 0
\(418\) −28.2777 17.0854i −1.38311 0.835676i
\(419\) −16.6114 −0.811521 −0.405761 0.913979i \(-0.632993\pi\)
−0.405761 + 0.913979i \(0.632993\pi\)
\(420\) 0 0
\(421\) 7.28323i 0.354963i 0.984124 + 0.177481i \(0.0567950\pi\)
−0.984124 + 0.177481i \(0.943205\pi\)
\(422\) −2.33205 9.68466i −0.113522 0.471442i
\(423\) 0 0
\(424\) 15.1838 + 17.7046i 0.737388 + 0.859812i
\(425\) 1.69614i 0.0822749i
\(426\) 0 0
\(427\) −24.4924 −1.18527
\(428\) 7.38235 + 14.4401i 0.356839 + 0.697988i
\(429\) 0 0
\(430\) 10.8769 2.61914i 0.524530 0.126306i
\(431\) 28.1753 1.35716 0.678579 0.734528i \(-0.262596\pi\)
0.678579 + 0.734528i \(0.262596\pi\)
\(432\) 0 0
\(433\) −15.1231 −0.726770 −0.363385 0.931639i \(-0.618379\pi\)
−0.363385 + 0.931639i \(0.618379\pi\)
\(434\) 8.30571 + 34.4924i 0.398687 + 1.65569i
\(435\) 0 0
\(436\) 29.9142 15.2933i 1.43263 0.732417i
\(437\) 21.9986 1.05234
\(438\) 0 0
\(439\) −23.0481 −1.10002 −0.550012 0.835156i \(-0.685377\pi\)
−0.550012 + 0.835156i \(0.685377\pi\)
\(440\) −18.7145 1.32916i −0.892180 0.0633651i
\(441\) 0 0
\(442\) −0.743668 3.08835i −0.0353727 0.146898i
\(443\) −4.66410 −0.221598 −0.110799 0.993843i \(-0.535341\pi\)
−0.110799 + 0.993843i \(0.535341\pi\)
\(444\) 0 0
\(445\) 33.2228i 1.57491i
\(446\) −3.42687 14.2313i −0.162267 0.673871i
\(447\) 0 0
\(448\) −3.68260 + 23.8813i −0.173987 + 1.12829i
\(449\) −2.04496 −0.0965076 −0.0482538 0.998835i \(-0.515366\pi\)
−0.0482538 + 0.998835i \(0.515366\pi\)
\(450\) 0 0
\(451\) 18.2462 + 18.0431i 0.859181 + 0.849618i
\(452\) 12.9698 6.63068i 0.610048 0.311881i
\(453\) 0 0
\(454\) −8.19224 34.0212i −0.384481 1.59669i
\(455\) 8.00000i 0.375046i
\(456\) 0 0
\(457\) 28.1753i 1.31799i −0.752149 0.658993i \(-0.770983\pi\)
0.752149 0.658993i \(-0.229017\pi\)
\(458\) −6.36679 26.4404i −0.297501 1.23548i
\(459\) 0 0
\(460\) 11.1231 5.68658i 0.518617 0.265138i
\(461\) 32.8078 1.52801 0.764007 0.645208i \(-0.223229\pi\)
0.764007 + 0.645208i \(0.223229\pi\)
\(462\) 0 0
\(463\) 34.2453i 1.59152i 0.605615 + 0.795758i \(0.292927\pi\)
−0.605615 + 0.795758i \(0.707073\pi\)
\(464\) −3.61696 + 5.00691i −0.167913 + 0.232440i
\(465\) 0 0
\(466\) 6.56155 + 27.2492i 0.303958 + 1.26229i
\(467\) 4.66410 0.215829 0.107914 0.994160i \(-0.465583\pi\)
0.107914 + 0.994160i \(0.465583\pi\)
\(468\) 0 0
\(469\) −18.8664 −0.871167
\(470\) −16.4990 + 3.97292i −0.761041 + 0.183257i
\(471\) 0 0
\(472\) 25.6509 21.9986i 1.18068 1.01257i
\(473\) 9.32819 + 9.22437i 0.428911 + 0.424137i
\(474\) 0 0
\(475\) 7.04383i 0.323193i
\(476\) −4.66410 9.12311i −0.213778 0.418157i
\(477\) 0 0
\(478\) −10.8769 + 2.61914i −0.497498 + 0.119796i
\(479\) 21.9986 1.00514 0.502571 0.864536i \(-0.332387\pi\)
0.502571 + 0.864536i \(0.332387\pi\)
\(480\) 0 0
\(481\) 6.17669i 0.281633i
\(482\) −6.26075 26.0000i −0.285169 1.18427i
\(483\) 0 0
\(484\) −10.2330 19.4752i −0.465138 0.885238i
\(485\) 26.7386i 1.21414i
\(486\) 0 0
\(487\) 32.2004i 1.45914i 0.683907 + 0.729569i \(0.260279\pi\)
−0.683907 + 0.729569i \(0.739721\pi\)
\(488\) 17.4098 14.9309i 0.788102 0.675889i
\(489\) 0 0
\(490\) −1.40582 5.83817i −0.0635086 0.263742i
\(491\) 9.27015i 0.418356i −0.977878 0.209178i \(-0.932921\pi\)
0.977878 0.209178i \(-0.0670788\pi\)
\(492\) 0 0
\(493\) 2.61914i 0.117960i
\(494\) 3.08835 + 12.8255i 0.138951 + 0.577045i
\(495\) 0 0
\(496\) −26.9309 19.4547i −1.20923 0.873542i
\(497\) 36.9890i 1.65919i
\(498\) 0 0
\(499\) −14.7386 −0.659792 −0.329896 0.944017i \(-0.607014\pi\)
−0.329896 + 0.944017i \(0.607014\pi\)
\(500\) −10.9248 21.3693i −0.488574 0.955665i
\(501\) 0 0
\(502\) −22.8393 + 5.49966i −1.01937 + 0.245462i
\(503\) −28.1753 −1.25628 −0.628138 0.778102i \(-0.716183\pi\)
−0.628138 + 0.778102i \(0.716183\pi\)
\(504\) 0 0
\(505\) 3.08835i 0.137430i
\(506\) 12.5378 + 7.57537i 0.557374 + 0.336766i
\(507\) 0 0
\(508\) 4.05444 2.07279i 0.179886 0.0919652i
\(509\) 10.0000i 0.443242i −0.975133 0.221621i \(-0.928865\pi\)
0.975133 0.221621i \(-0.0711348\pi\)
\(510\) 0 0
\(511\) 9.32819i 0.412655i
\(512\) −11.9407 19.2203i −0.527707 0.849426i
\(513\) 0 0
\(514\) −35.6647 + 8.58800i −1.57310 + 0.378801i
\(515\) −16.6114 −0.731987
\(516\) 0 0
\(517\) −14.1498 13.9923i −0.622306 0.615380i
\(518\) −4.66410 19.3693i −0.204929 0.851039i
\(519\) 0 0
\(520\) 4.87689 + 5.68658i 0.213866 + 0.249373i
\(521\) 18.6564 0.817351 0.408675 0.912680i \(-0.365991\pi\)
0.408675 + 0.912680i \(0.365991\pi\)
\(522\) 0 0
\(523\) 25.9541i 1.13489i −0.823410 0.567447i \(-0.807931\pi\)
0.823410 0.567447i \(-0.192069\pi\)
\(524\) 3.61696 + 7.07488i 0.158008 + 0.309068i
\(525\) 0 0
\(526\) 27.8617 6.70906i 1.21483 0.292529i
\(527\) 14.0877 0.613668
\(528\) 0 0
\(529\) 13.2462 0.575922
\(530\) 22.6757 5.46026i 0.984968 0.237178i
\(531\) 0 0
\(532\) 19.3693 + 37.8869i 0.839766 + 1.64261i
\(533\) 10.2462i 0.443813i
\(534\) 0 0
\(535\) 16.2177 0.701154
\(536\) 13.4106 11.5012i 0.579251 0.496774i
\(537\) 0 0
\(538\) 5.37874 + 22.3371i 0.231894 + 0.963023i
\(539\) 4.95118 5.00691i 0.213263 0.215663i
\(540\) 0 0
\(541\) 10.0138 0.430528 0.215264 0.976556i \(-0.430939\pi\)
0.215264 + 0.976556i \(0.430939\pi\)
\(542\) −8.81695 + 2.12311i −0.378720 + 0.0911952i
\(543\) 0 0
\(544\) 8.87689 + 3.64162i 0.380594 + 0.156133i
\(545\) 33.5968i 1.43913i
\(546\) 0 0
\(547\) 0.867135i 0.0370760i −0.999828 0.0185380i \(-0.994099\pi\)
0.999828 0.0185380i \(-0.00590117\pi\)
\(548\) −12.9698 + 6.63068i −0.554043 + 0.283249i
\(549\) 0 0
\(550\) 2.42559 4.01454i 0.103427 0.171181i
\(551\) 10.8769i 0.463371i
\(552\) 0 0
\(553\) 37.6155 1.59957
\(554\) 6.48490 1.56155i 0.275517 0.0663440i
\(555\) 0 0
\(556\) 3.60109 + 7.04383i 0.152720 + 0.298725i
\(557\) 28.3654 1.20188 0.600941 0.799294i \(-0.294793\pi\)
0.600941 + 0.799294i \(0.294793\pi\)
\(558\) 0 0
\(559\) 5.23827i 0.221555i
\(560\) 19.5873 + 14.1498i 0.827715 + 0.597937i
\(561\) 0 0
\(562\) −5.19224 21.5626i −0.219021 0.909564i
\(563\) 38.3134i 1.61472i 0.590062 + 0.807358i \(0.299103\pi\)
−0.590062 + 0.807358i \(0.700897\pi\)
\(564\) 0 0
\(565\) 14.5665i 0.612816i
\(566\) −4.95118 20.5616i −0.208114 0.864267i
\(567\) 0 0
\(568\) 22.5490 + 26.2926i 0.946133 + 1.10321i
\(569\) 24.3724i 1.02174i 0.859657 + 0.510872i \(0.170677\pi\)
−0.859657 + 0.510872i \(0.829323\pi\)
\(570\) 0 0
\(571\) 10.1322i 0.424018i 0.977268 + 0.212009i \(0.0680007\pi\)
−0.977268 + 0.212009i \(0.931999\pi\)
\(572\) −2.65637 + 8.37320i −0.111068 + 0.350101i
\(573\) 0 0
\(574\) −7.73704 32.1308i −0.322938 1.34111i
\(575\) 3.12311i 0.130243i
\(576\) 0 0
\(577\) −8.24621 −0.343294 −0.171647 0.985158i \(-0.554909\pi\)
−0.171647 + 0.985158i \(0.554909\pi\)
\(578\) 19.4181 4.67583i 0.807685 0.194489i
\(579\) 0 0
\(580\) 2.81164 + 5.49966i 0.116747 + 0.228361i
\(581\) 14.2462i 0.591032i
\(582\) 0 0
\(583\) 19.4470 + 19.2306i 0.805412 + 0.796448i
\(584\) 5.68658 + 6.63068i 0.235312 + 0.274380i
\(585\) 0 0
\(586\) 8.75379 2.10790i 0.361616 0.0870764i
\(587\) −26.5138 −1.09434 −0.547171 0.837021i \(-0.684295\pi\)
−0.547171 + 0.837021i \(0.684295\pi\)
\(588\) 0 0
\(589\) −58.5040 −2.41062
\(590\) −7.91096 32.8531i −0.325689 1.35254i
\(591\) 0 0
\(592\) 15.1231 + 10.9248i 0.621556 + 0.449008i
\(593\) 19.0752i 0.783323i 0.920109 + 0.391661i \(0.128100\pi\)
−0.920109 + 0.391661i \(0.871900\pi\)
\(594\) 0 0
\(595\) −10.2462 −0.420054
\(596\) −22.3371 + 11.4196i −0.914965 + 0.467767i
\(597\) 0 0
\(598\) −1.36932 5.68658i −0.0559955 0.232541i
\(599\) 33.3693i 1.36343i −0.731616 0.681717i \(-0.761234\pi\)
0.731616 0.681717i \(-0.238766\pi\)
\(600\) 0 0
\(601\) 31.2637i 1.27527i 0.770338 + 0.637636i \(0.220087\pi\)
−0.770338 + 0.637636i \(0.779913\pi\)
\(602\) −3.95548 16.4265i −0.161213 0.669496i
\(603\) 0 0
\(604\) −12.7439 + 6.51521i −0.518544 + 0.265100i
\(605\) −21.9986 + 0.246211i −0.894371 + 0.0100099i
\(606\) 0 0
\(607\) 32.8073 1.33161 0.665804 0.746127i \(-0.268089\pi\)
0.665804 + 0.746127i \(0.268089\pi\)
\(608\) −36.8645 15.1231i −1.49505 0.613323i
\(609\) 0 0
\(610\) −5.36932 22.2980i −0.217397 0.902820i
\(611\) 7.94584i 0.321454i
\(612\) 0 0
\(613\) 18.7033 0.755420 0.377710 0.925924i \(-0.376712\pi\)
0.377710 + 0.925924i \(0.376712\pi\)
\(614\) 5.97366 + 24.8078i 0.241077 + 1.00116i
\(615\) 0 0
\(616\) −2.00733 + 28.2631i −0.0808775 + 1.13875i
\(617\) 11.3732 0.457866 0.228933 0.973442i \(-0.426476\pi\)
0.228933 + 0.973442i \(0.426476\pi\)
\(618\) 0 0
\(619\) 24.4924 0.984434 0.492217 0.870473i \(-0.336187\pi\)
0.492217 + 0.870473i \(0.336187\pi\)
\(620\) −29.5812 + 15.1231i −1.18801 + 0.607359i
\(621\) 0 0
\(622\) 1.61463 + 6.70531i 0.0647406 + 0.268858i
\(623\) −50.1739 −2.01018
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 4.29400 1.03399i 0.171623 0.0413265i
\(627\) 0 0
\(628\) 6.63068 + 12.9698i 0.264593 + 0.517552i
\(629\) −7.91096 −0.315431
\(630\) 0 0
\(631\) 10.3507i 0.412054i 0.978546 + 0.206027i \(0.0660534\pi\)
−0.978546 + 0.206027i \(0.933947\pi\)
\(632\) −26.7379 + 22.9309i −1.06358 + 0.912141i
\(633\) 0 0
\(634\) −3.47380 14.4262i −0.137962 0.572937i
\(635\) 4.55356i 0.180702i
\(636\) 0 0
\(637\) −2.81164 −0.111401
\(638\) −3.74553 + 6.19914i −0.148287 + 0.245426i
\(639\) 0 0
\(640\) −22.5490 + 1.88269i −0.891326 + 0.0744200i
\(641\) −42.5510 −1.68066 −0.840332 0.542071i \(-0.817640\pi\)
−0.840332 + 0.542071i \(0.817640\pi\)
\(642\) 0 0
\(643\) −28.9848 −1.14305 −0.571525 0.820584i \(-0.693648\pi\)
−0.571525 + 0.820584i \(0.693648\pi\)
\(644\) −8.58800 16.7984i −0.338415 0.661949i
\(645\) 0 0
\(646\) 16.4265 3.95548i 0.646294 0.155626i
\(647\) 36.8769i 1.44978i −0.688864 0.724890i \(-0.741890\pi\)
0.688864 0.724890i \(-0.258110\pi\)
\(648\) 0 0
\(649\) 27.8617 28.1753i 1.09367 1.10598i
\(650\) −1.82081 + 0.438447i −0.0714180 + 0.0171973i
\(651\) 0 0
\(652\) −36.4924 + 18.6564i −1.42915 + 0.730640i
\(653\) 42.9848i 1.68213i 0.540936 + 0.841063i \(0.318070\pi\)
−0.540936 + 0.841063i \(0.681930\pi\)
\(654\) 0 0
\(655\) 7.94584 0.310470
\(656\) 25.0870 + 18.1227i 0.979482 + 0.707572i
\(657\) 0 0
\(658\) 6.00000 + 24.9171i 0.233904 + 0.971371i
\(659\) 10.7575i 0.419052i 0.977803 + 0.209526i \(0.0671921\pi\)
−0.977803 + 0.209526i \(0.932808\pi\)
\(660\) 0 0
\(661\) 11.3732i 0.442364i −0.975233 0.221182i \(-0.929008\pi\)
0.975233 0.221182i \(-0.0709915\pi\)
\(662\) 25.0870 6.04090i 0.975033 0.234786i
\(663\) 0 0
\(664\) 8.68466 + 10.1265i 0.337030 + 0.392985i
\(665\) 42.5510 1.65006
\(666\) 0 0
\(667\) 4.82262i 0.186732i
\(668\) 25.0870 12.8255i 0.970644 0.496232i
\(669\) 0 0
\(670\) −4.13595 17.1760i −0.159786 0.663567i
\(671\) 18.9103 19.1231i 0.730023 0.738239i
\(672\) 0 0
\(673\) 21.9986i 0.847985i 0.905666 + 0.423992i \(0.139372\pi\)
−0.905666 + 0.423992i \(0.860628\pi\)
\(674\) −10.3507 42.9848i −0.398693 1.65571i
\(675\) 0 0
\(676\) −20.0270 + 10.2386i −0.770269 + 0.393792i
\(677\) −34.5421 −1.32756 −0.663781 0.747927i \(-0.731049\pi\)
−0.663781 + 0.747927i \(0.731049\pi\)
\(678\) 0 0
\(679\) 40.3813 1.54969
\(680\) 7.28323 6.24621i 0.279299 0.239531i
\(681\) 0 0
\(682\) −33.3436 20.1462i −1.27679 0.771439i
\(683\) 49.8343 1.90686 0.953428 0.301622i \(-0.0975280\pi\)
0.953428 + 0.301622i \(0.0975280\pi\)
\(684\) 0 0
\(685\) 14.5665i 0.556556i
\(686\) 20.2530 4.87689i 0.773265 0.186201i
\(687\) 0 0
\(688\) 12.8255 + 9.26504i 0.488966 + 0.353226i
\(689\) 10.9205i 0.416038i
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 22.3371 11.4196i 0.849131 0.434110i
\(693\) 0 0
\(694\) −6.93087 28.7829i −0.263092 1.09258i
\(695\) 7.91096 0.300080
\(696\) 0 0
\(697\) −13.1231 −0.497073
\(698\) −21.0514 + 5.06913i −0.796806 + 0.191869i
\(699\) 0 0
\(700\) −5.37874 + 2.74983i −0.203297 + 0.103934i
\(701\) 6.36679 0.240470 0.120235 0.992745i \(-0.461635\pi\)
0.120235 + 0.992745i \(0.461635\pi\)
\(702\) 0 0
\(703\) 32.8531 1.23908
\(704\) −15.8027 21.3137i −0.595586 0.803292i
\(705\) 0 0
\(706\) −12.8255 + 3.08835i −0.482693 + 0.116231i
\(707\) −4.66410 −0.175411
\(708\) 0 0
\(709\) 13.9923i 0.525491i −0.964865 0.262746i \(-0.915372\pi\)
0.964865 0.262746i \(-0.0846280\pi\)
\(710\) 33.6750 8.10887i 1.26380 0.304321i
\(711\) 0 0
\(712\) 35.6647 30.5866i 1.33659 1.14628i
\(713\) 25.9396 0.971446
\(714\) 0 0
\(715\) 6.24621 + 6.17669i 0.233595 + 0.230995i
\(716\) 0 0
\(717\) 0 0
\(718\) −49.6155 + 11.9473i −1.85164 + 0.445870i
\(719\) 50.9848i 1.90141i 0.310091 + 0.950707i \(0.399641\pi\)
−0.310091 + 0.950707i \(0.600359\pi\)
\(720\) 0 0
\(721\) 25.0870i 0.934288i
\(722\) −42.0937 + 10.1361i −1.56657 + 0.377226i
\(723\) 0 0
\(724\) 23.6155 + 46.1927i 0.877664 + 1.71674i
\(725\) −1.54417 −0.0573492
\(726\) 0 0
\(727\) 1.02248i 0.0379217i −0.999820 0.0189608i \(-0.993964\pi\)
0.999820 0.0189608i \(-0.00603578\pi\)
\(728\) 8.58800 7.36520i 0.318293 0.272973i
\(729\) 0 0
\(730\) 8.49242 2.04496i 0.314319 0.0756874i
\(731\) −6.70906 −0.248143
\(732\) 0 0
\(733\) −15.6371 −0.577570 −0.288785 0.957394i \(-0.593251\pi\)
−0.288785 + 0.957394i \(0.593251\pi\)
\(734\) −2.07279 8.60799i −0.0765080 0.317727i
\(735\) 0 0
\(736\) 16.3450 + 6.70531i 0.602486 + 0.247161i
\(737\) 14.5665 14.7304i 0.536563 0.542601i
\(738\) 0 0
\(739\) 35.2191i 1.29556i 0.761829 + 0.647779i \(0.224302\pi\)
−0.761829 + 0.647779i \(0.775698\pi\)
\(740\) 16.6114 8.49242i 0.610648 0.312188i
\(741\) 0 0
\(742\) −8.24621 34.2453i −0.302728 1.25719i
\(743\) 15.8219 0.580450 0.290225 0.956958i \(-0.406270\pi\)
0.290225 + 0.956958i \(0.406270\pi\)
\(744\) 0 0
\(745\) 25.0870i 0.919115i
\(746\) −32.4245 + 7.80776i −1.18715 + 0.285863i
\(747\) 0 0
\(748\) 10.7242 + 3.40221i 0.392115 + 0.124397i
\(749\) 24.4924i 0.894934i
\(750\) 0 0
\(751\) 48.8118i 1.78117i 0.454819 + 0.890584i \(0.349704\pi\)
−0.454819 + 0.890584i \(0.650296\pi\)
\(752\) −19.4547 14.0540i −0.709440 0.512496i
\(753\) 0 0
\(754\) 2.81164 0.677039i 0.102394 0.0246563i
\(755\) 14.3128i 0.520896i
\(756\) 0 0
\(757\) 40.5061i 1.47222i −0.676863 0.736109i \(-0.736661\pi\)
0.676863 0.736109i \(-0.263339\pi\)
\(758\) 3.08835 0.743668i 0.112174 0.0270112i
\(759\) 0 0
\(760\) −30.2462 + 25.9396i −1.09715 + 0.940929i
\(761\) 42.8211i 1.55226i 0.630570 + 0.776132i \(0.282821\pi\)
−0.630570 + 0.776132i \(0.717179\pi\)
\(762\) 0 0
\(763\) −50.7386 −1.83686
\(764\) −3.86577 7.56155i −0.139859 0.273567i
\(765\) 0 0
\(766\) 8.39919 + 34.8806i 0.303475 + 1.26029i
\(767\) −15.8219 −0.571297
\(768\) 0 0
\(769\) 9.26504i 0.334106i −0.985948 0.167053i \(-0.946575\pi\)
0.985948 0.167053i \(-0.0534251\pi\)
\(770\) 24.2514 + 14.6527i 0.873960 + 0.528048i
\(771\) 0 0
\(772\) 22.8393 + 44.6743i 0.822004 + 1.60786i
\(773\) 33.2311i 1.19524i 0.801780 + 0.597619i \(0.203886\pi\)
−0.801780 + 0.597619i \(0.796114\pi\)
\(774\) 0 0
\(775\) 8.30571i 0.298350i
\(776\) −28.7039 + 24.6169i −1.03041 + 0.883696i
\(777\) 0 0
\(778\) −0.825183 3.42687i −0.0295842 0.122859i
\(779\) 54.4984 1.95261
\(780\) 0 0
\(781\) 28.8802 + 28.5588i 1.03341 + 1.02191i
\(782\) −7.28323 + 1.75379i −0.260448 + 0.0627154i
\(783\) 0 0
\(784\) 4.97301 6.88407i 0.177608 0.245860i
\(785\) 14.5665 0.519899
\(786\) 0 0
\(787\) 30.3965i 1.08352i 0.840533 + 0.541760i \(0.182242\pi\)
−0.840533 + 0.541760i \(0.817758\pi\)
\(788\) 27.8368 14.2313i 0.991645 0.506968i
\(789\) 0 0
\(790\) 8.24621 + 34.2453i 0.293387 + 1.21839i
\(791\) −21.9986 −0.782181
\(792\) 0 0
\(793\) −10.7386 −0.381340
\(794\) −4.63252 19.2382i −0.164402 0.682738i
\(795\) 0 0
\(796\) −0.930870 1.82081i −0.0329938 0.0645368i
\(797\) 28.2462i 1.00053i −0.865872 0.500266i \(-0.833236\pi\)
0.865872 0.500266i \(-0.166764\pi\)
\(798\) 0 0
\(799\) 10.1768 0.360031
\(800\) 2.14700 5.23358i 0.0759079 0.185035i
\(801\) 0 0
\(802\) −25.6509 + 6.17669i −0.905765 + 0.218107i
\(803\) 7.28323 + 7.20217i 0.257020 + 0.254159i
\(804\) 0 0
\(805\) −18.8664 −0.664952
\(806\) 3.64162 + 15.1231i 0.128270 + 0.532689i
\(807\) 0 0
\(808\) 3.31534 2.84329i 0.116633 0.100027i
\(809\) 31.4830i 1.10688i 0.832888 + 0.553442i \(0.186686\pi\)
−0.832888 + 0.553442i \(0.813314\pi\)
\(810\) 0 0
\(811\) 11.8664i 0.416687i 0.978056 + 0.208344i \(0.0668072\pi\)
−0.978056 + 0.208344i \(0.933193\pi\)
\(812\) 8.30571 4.24621i 0.291473 0.149013i
\(813\) 0 0
\(814\) 18.7242 + 11.3132i 0.656283 + 0.396527i
\(815\) 40.9848i 1.43564i
\(816\) 0 0
\(817\) 27.8617 0.974759
\(818\) −2.04496 8.49242i −0.0715003 0.296931i
\(819\) 0 0
\(820\) 27.5559 14.0877i 0.962293 0.491962i
\(821\) 31.4538 1.09774 0.548872 0.835906i \(-0.315057\pi\)
0.548872 + 0.835906i \(0.315057\pi\)
\(822\) 0 0
\(823\) 45.6185i 1.59016i 0.606504 + 0.795080i \(0.292571\pi\)
−0.606504 + 0.795080i \(0.707429\pi\)
\(824\) −15.2933 17.8324i −0.532768 0.621220i
\(825\) 0 0
\(826\) −49.6155 + 11.9473i −1.72635 + 0.415701i
\(827\) 5.13420i 0.178534i 0.996008 + 0.0892668i \(0.0284524\pi\)
−0.996008 + 0.0892668i \(0.971548\pi\)
\(828\) 0 0
\(829\) 19.2306i 0.667905i −0.942590 0.333952i \(-0.891617\pi\)
0.942590 0.333952i \(-0.108383\pi\)
\(830\) 12.9698 3.12311i 0.450189 0.108405i
\(831\) 0 0
\(832\) −1.61463 + 10.4707i −0.0559771 + 0.363006i
\(833\) 3.60109i 0.124770i
\(834\) 0 0
\(835\) 28.1753i 0.975047i
\(836\) −44.5360 14.1289i −1.54031 0.488658i
\(837\) 0 0
\(838\) −22.8393 + 5.49966i −0.788970 + 0.189982i
\(839\) 27.1231i 0.936394i 0.883624 + 0.468197i \(0.155096\pi\)
−0.883624 + 0.468197i \(0.844904\pi\)
\(840\) 0 0
\(841\) −26.6155 −0.917777
\(842\) 2.41131 + 10.0138i 0.0830992 + 0.345099i
\(843\) 0 0
\(844\) −6.41273 12.5435i −0.220735 0.431765i
\(845\) 22.4924i 0.773763i
\(846\) 0 0
\(847\) 0.371834 + 33.2228i 0.0127764 + 1.14155i
\(848\) 26.7379 + 19.3153i 0.918185 + 0.663292i
\(849\) 0 0
\(850\) 0.561553 + 2.33205i 0.0192611 + 0.0799886i
\(851\) −14.5665 −0.499332
\(852\) 0 0
\(853\) 43.6106 1.49320 0.746599 0.665274i \(-0.231685\pi\)
0.746599 + 0.665274i \(0.231685\pi\)
\(854\) −33.6750 + 8.10887i −1.15233 + 0.277480i
\(855\) 0 0
\(856\) 14.9309 + 17.4098i 0.510327 + 0.595053i
\(857\) 26.6034i 0.908755i 0.890809 + 0.454377i \(0.150138\pi\)
−0.890809 + 0.454377i \(0.849862\pi\)
\(858\) 0 0
\(859\) 24.0000 0.818869 0.409435 0.912339i \(-0.365726\pi\)
0.409435 + 0.912339i \(0.365726\pi\)
\(860\) 14.0877 7.20217i 0.480385 0.245592i
\(861\) 0 0
\(862\) 38.7386 9.32819i 1.31944 0.317719i
\(863\) 42.3542i 1.44175i 0.693064 + 0.720876i \(0.256260\pi\)
−0.693064 + 0.720876i \(0.743740\pi\)
\(864\) 0 0
\(865\) 25.0870i 0.852983i
\(866\) −20.7930 + 5.00691i −0.706574 + 0.170142i
\(867\) 0 0
\(868\) 22.8393 + 44.6743i 0.775216 + 1.51634i
\(869\) −29.0425 + 29.3693i −0.985198 + 0.996286i
\(870\) 0 0
\(871\) −8.27190 −0.280283
\(872\) 36.0661 30.9309i 1.22135 1.04745i
\(873\) 0 0
\(874\) 30.2462 7.28323i 1.02309 0.246359i
\(875\) 36.2454i 1.22532i
\(876\) 0 0
\(877\) −49.9775 −1.68762 −0.843811 0.536641i \(-0.819693\pi\)
−0.843811 + 0.536641i \(0.819693\pi\)
\(878\) −31.6891 + 7.63068i −1.06946 + 0.257523i
\(879\) 0 0
\(880\) −26.1709 + 4.36846i −0.882221 + 0.147261i
\(881\) −27.9846 −0.942824 −0.471412 0.881913i \(-0.656256\pi\)
−0.471412 + 0.881913i \(0.656256\pi\)
\(882\) 0 0
\(883\) 22.2462 0.748645 0.374322 0.927299i \(-0.377875\pi\)
0.374322 + 0.927299i \(0.377875\pi\)
\(884\) −2.04496 4.00000i −0.0687794 0.134535i
\(885\) 0 0
\(886\) −6.41273 + 1.54417i −0.215440 + 0.0518775i
\(887\) −43.9972 −1.47728 −0.738641 0.674099i \(-0.764532\pi\)
−0.738641 + 0.674099i \(0.764532\pi\)
\(888\) 0 0
\(889\) −6.87689 −0.230644
\(890\) −10.9993 45.6786i −0.368698 1.53115i
\(891\) 0 0
\(892\) −9.42329 18.4322i −0.315515 0.617157i
\(893\) −42.2630 −1.41428
\(894\) 0 0
\(895\) 0 0
\(896\) 2.84329 + 34.0540i 0.0949876 + 1.13766i
\(897\) 0 0
\(898\) −2.81164 + 0.677039i −0.0938258 + 0.0225931i
\(899\) 12.8255i 0.427753i
\(900\) 0 0
\(901\) −13.9867 −0.465966
\(902\) 31.0606 + 18.7669i 1.03421 + 0.624868i
\(903\) 0 0
\(904\) 15.6371 13.4106i 0.520082 0.446031i
\(905\) 51.8792 1.72452
\(906\) 0 0
\(907\) −18.7386 −0.622206 −0.311103 0.950376i \(-0.600698\pi\)
−0.311103 + 0.950376i \(0.600698\pi\)
\(908\) −22.5272 44.0639i −0.747593 1.46231i
\(909\) 0 0
\(910\) −2.64861 10.9993i −0.0878007 0.364624i
\(911\) 0.738634i 0.0244720i −0.999925 0.0122360i \(-0.996105\pi\)
0.999925 0.0122360i \(-0.00389494\pi\)
\(912\) 0 0
\(913\) 11.1231 + 10.9993i 0.368121 + 0.364024i
\(914\) −9.32819 38.7386i −0.308549 1.28136i
\(915\) 0 0
\(916\) −17.5076 34.2453i −0.578467 1.13150i
\(917\) 12.0000i 0.396275i
\(918\) 0 0
\(919\) −7.57401 −0.249843 −0.124922 0.992167i \(-0.539868\pi\)
−0.124922 + 0.992167i \(0.539868\pi\)
\(920\) 13.4106 11.5012i 0.442135 0.379182i
\(921\) 0 0
\(922\) 45.1080 10.8619i 1.48555 0.357718i
\(923\) 16.2177i 0.533813i
\(924\) 0 0
\(925\) 4.66410i 0.153355i
\(926\) 11.3378 + 47.0844i 0.372584 + 1.54729i
\(927\) 0 0
\(928\) −3.31534 + 8.08156i −0.108831 + 0.265290i
\(929\) −2.04496 −0.0670929 −0.0335465 0.999437i \(-0.510680\pi\)
−0.0335465 + 0.999437i \(0.510680\pi\)
\(930\) 0 0
\(931\) 14.9548i 0.490124i
\(932\) 18.0431 + 35.2929i 0.591023 + 1.15606i
\(933\) 0 0
\(934\) 6.41273 1.54417i 0.209831 0.0505269i
\(935\) 7.91096 8.00000i 0.258716 0.261628i
\(936\) 0 0
\(937\) 21.9986i 0.718664i −0.933210 0.359332i \(-0.883005\pi\)
0.933210 0.359332i \(-0.116995\pi\)
\(938\) −25.9396 + 6.24621i −0.846958 + 0.203946i
\(939\) 0 0
\(940\) −21.3693 + 10.9248i −0.696990 + 0.356329i
\(941\) −34.5421 −1.12604 −0.563020 0.826443i \(-0.690361\pi\)
−0.563020 + 0.826443i \(0.690361\pi\)
\(942\) 0 0
\(943\) −24.1636 −0.786875
\(944\) 27.9846 38.7386i 0.910820 1.26084i
\(945\) 0 0
\(946\) 15.8794 + 9.59437i 0.516285 + 0.311940i
\(947\) 33.2228 1.07960 0.539799 0.841794i \(-0.318500\pi\)
0.539799 + 0.841794i \(0.318500\pi\)
\(948\) 0 0
\(949\) 4.08992i 0.132764i
\(950\) −2.33205 9.68466i −0.0756616 0.314212i
\(951\) 0 0
\(952\) −9.43318 10.9993i −0.305731 0.356490i
\(953\) 54.5769i 1.76792i 0.467564 + 0.883959i \(0.345132\pi\)
−0.467564 + 0.883959i \(0.654868\pi\)
\(954\) 0 0
\(955\) −8.49242 −0.274808
\(956\) −14.0877 + 7.20217i −0.455627 + 0.232935i
\(957\) 0 0
\(958\) 30.2462 7.28323i 0.977211 0.235311i
\(959\) 21.9986 0.710373
\(960\) 0 0
\(961\) −37.9848 −1.22532
\(962\) −2.04496 8.49242i −0.0659321 0.273807i
\(963\) 0 0
\(964\) −17.2160 33.6750i −0.554490 1.08460i
\(965\) 50.1739 1.61516
\(966\) 0 0
\(967\) 38.1045 1.22536 0.612680 0.790331i \(-0.290092\pi\)
0.612680 + 0.790331i \(0.290092\pi\)
\(968\) −20.5173 23.3889i −0.659453 0.751746i
\(969\) 0 0
\(970\) 8.85254 + 36.7633i 0.284238 + 1.18040i
\(971\) 23.3205 0.748390 0.374195 0.927350i \(-0.377919\pi\)
0.374195 + 0.927350i \(0.377919\pi\)
\(972\) 0 0
\(973\) 11.9473i 0.383014i
\(974\) 10.6608 + 44.2727i 0.341594 + 1.41859i
\(975\) 0 0
\(976\) 18.9936 26.2926i 0.607972 0.841606i
\(977\) −61.2074 −1.95820 −0.979099 0.203382i \(-0.934807\pi\)
−0.979099 + 0.203382i \(0.934807\pi\)
\(978\) 0 0
\(979\) 38.7386 39.1746i 1.23809 1.25203i
\(980\) −3.86577 7.56155i −0.123487 0.241545i
\(981\) 0 0
\(982\) −3.06913 12.7457i −0.0979399 0.406730i
\(983\) 22.6307i 0.721807i −0.932603 0.360903i \(-0.882468\pi\)
0.932603 0.360903i \(-0.117532\pi\)
\(984\) 0 0
\(985\) 31.2637i 0.996143i
\(986\) −0.867135 3.60109i −0.0276152 0.114682i
\(987\) 0 0
\(988\) 8.49242 + 16.6114i 0.270180 + 0.528480i
\(989\) −12.3534 −0.392815
\(990\) 0 0
\(991\) 45.6185i 1.44912i −0.689212 0.724559i \(-0.742043\pi\)
0.689212 0.724559i \(-0.257957\pi\)
\(992\) −43.4686 17.8324i −1.38013 0.566178i
\(993\) 0 0
\(994\) −12.2462 50.8567i −0.388426 1.61308i
\(995\) −2.04496 −0.0648296
\(996\) 0 0
\(997\) −3.22925 −0.102271 −0.0511357 0.998692i \(-0.516284\pi\)
−0.0511357 + 0.998692i \(0.516284\pi\)
\(998\) −20.2644 + 4.87962i −0.641457 + 0.154462i
\(999\) 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 792.2.h.i.307.13 yes 16
3.2 odd 2 inner 792.2.h.i.307.4 yes 16
4.3 odd 2 3168.2.h.i.2287.7 16
8.3 odd 2 inner 792.2.h.i.307.2 yes 16
8.5 even 2 3168.2.h.i.2287.9 16
11.10 odd 2 inner 792.2.h.i.307.3 yes 16
12.11 even 2 3168.2.h.i.2287.16 16
24.5 odd 2 3168.2.h.i.2287.2 16
24.11 even 2 inner 792.2.h.i.307.15 yes 16
33.32 even 2 inner 792.2.h.i.307.14 yes 16
44.43 even 2 3168.2.h.i.2287.1 16
88.21 odd 2 3168.2.h.i.2287.15 16
88.43 even 2 inner 792.2.h.i.307.16 yes 16
132.131 odd 2 3168.2.h.i.2287.10 16
264.131 odd 2 inner 792.2.h.i.307.1 16
264.197 even 2 3168.2.h.i.2287.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
792.2.h.i.307.1 16 264.131 odd 2 inner
792.2.h.i.307.2 yes 16 8.3 odd 2 inner
792.2.h.i.307.3 yes 16 11.10 odd 2 inner
792.2.h.i.307.4 yes 16 3.2 odd 2 inner
792.2.h.i.307.13 yes 16 1.1 even 1 trivial
792.2.h.i.307.14 yes 16 33.32 even 2 inner
792.2.h.i.307.15 yes 16 24.11 even 2 inner
792.2.h.i.307.16 yes 16 88.43 even 2 inner
3168.2.h.i.2287.1 16 44.43 even 2
3168.2.h.i.2287.2 16 24.5 odd 2
3168.2.h.i.2287.7 16 4.3 odd 2
3168.2.h.i.2287.8 16 264.197 even 2
3168.2.h.i.2287.9 16 8.5 even 2
3168.2.h.i.2287.10 16 132.131 odd 2
3168.2.h.i.2287.15 16 88.21 odd 2
3168.2.h.i.2287.16 16 12.11 even 2