Properties

Label 896.2.ba.e.737.7
Level $896$
Weight $2$
Character 896.737
Analytic conductor $7.155$
Analytic rank $0$
Dimension $48$
Inner twists $4$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [896,2,Mod(289,896)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("896.289"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(896, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 4])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 896 = 2^{7} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 896.ba (of order \(12\), degree \(4\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [48,0,0,0,-4,0,0,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.15459602111\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 112)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 737.7
Character \(\chi\) \(=\) 896.737
Dual form 896.2.ba.e.417.7

$q$-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)
 
\(f(q)\) \(=\) \(q+(0.827840 + 0.221819i) q^{3} +(-4.10878 + 1.10095i) q^{5} +(2.50325 - 0.856573i) q^{7} +(-1.96196 - 1.13274i) q^{9} +(-0.318576 + 1.18894i) q^{11} +(1.73092 - 1.73092i) q^{13} -3.64563 q^{15} +(-0.931914 - 1.61412i) q^{17} +(-0.989804 - 3.69400i) q^{19} +(2.26230 - 0.153836i) q^{21} +(-1.23305 - 0.711901i) q^{23} +(11.3399 - 6.54709i) q^{25} +(-3.19099 - 3.19099i) q^{27} +(0.181826 - 0.181826i) q^{29} +(-3.23200 - 5.59799i) q^{31} +(-0.527459 + 0.913587i) q^{33} +(-9.34229 + 6.27542i) q^{35} +(-0.238000 + 0.0637719i) q^{37} +(1.81687 - 1.04897i) q^{39} +0.440182i q^{41} +(-5.54503 - 5.54503i) q^{43} +(9.30835 + 2.49417i) q^{45} +(3.61427 - 6.26009i) q^{47} +(5.53257 - 4.28844i) q^{49} +(-0.413433 - 1.54295i) q^{51} +(2.59716 - 9.69274i) q^{53} -5.23583i q^{55} -3.27760i q^{57} +(-0.438601 + 1.63688i) q^{59} +(-2.41596 - 9.01647i) q^{61} +(-5.88156 - 1.15497i) q^{63} +(-5.20632 + 9.01761i) q^{65} +(9.59422 + 2.57076i) q^{67} +(-0.862854 - 0.862854i) q^{69} +11.2912i q^{71} +(-8.13092 + 4.69439i) q^{73} +(10.8399 - 2.90454i) q^{75} +(0.220938 + 3.24910i) q^{77} +(-6.52948 + 11.3094i) q^{79} +(1.46441 + 2.53643i) q^{81} +(-3.06926 + 3.06926i) q^{83} +(5.60609 + 5.60609i) q^{85} +(0.190855 - 0.110190i) q^{87} +(-5.66084 - 3.26829i) q^{89} +(2.85027 - 5.81558i) q^{91} +(-1.43384 - 5.35117i) q^{93} +(8.13378 + 14.0881i) q^{95} +1.70409 q^{97} +(1.97179 - 1.97179i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 4 q^{5} - 4 q^{11} + 24 q^{13} + 40 q^{15} + 8 q^{17} - 4 q^{19} + 8 q^{21} - 24 q^{27} - 24 q^{29} - 28 q^{31} + 16 q^{33} + 28 q^{35} + 24 q^{37} - 40 q^{43} + 28 q^{45} + 20 q^{47} + 24 q^{51}+ \cdots - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(645\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.827840 + 0.221819i 0.477954 + 0.128067i 0.489750 0.871863i \(-0.337088\pi\)
−0.0117959 + 0.999930i \(0.503755\pi\)
\(4\) 0 0
\(5\) −4.10878 + 1.10095i −1.83750 + 0.492358i −0.998647 0.0519945i \(-0.983442\pi\)
−0.838857 + 0.544352i \(0.816775\pi\)
\(6\) 0 0
\(7\) 2.50325 0.856573i 0.946141 0.323754i
\(8\) 0 0
\(9\) −1.96196 1.13274i −0.653987 0.377579i
\(10\) 0 0
\(11\) −0.318576 + 1.18894i −0.0960542 + 0.358479i −0.997177 0.0750845i \(-0.976077\pi\)
0.901123 + 0.433564i \(0.142744\pi\)
\(12\) 0 0
\(13\) 1.73092 1.73092i 0.480070 0.480070i −0.425084 0.905154i \(-0.639755\pi\)
0.905154 + 0.425084i \(0.139755\pi\)
\(14\) 0 0
\(15\) −3.64563 −0.941297
\(16\) 0 0
\(17\) −0.931914 1.61412i −0.226022 0.391482i 0.730603 0.682802i \(-0.239239\pi\)
−0.956626 + 0.291320i \(0.905906\pi\)
\(18\) 0 0
\(19\) −0.989804 3.69400i −0.227077 0.847462i −0.981562 0.191145i \(-0.938780\pi\)
0.754485 0.656317i \(-0.227887\pi\)
\(20\) 0 0
\(21\) 2.26230 0.153836i 0.493674 0.0335697i
\(22\) 0 0
\(23\) −1.23305 0.711901i −0.257108 0.148442i 0.365906 0.930652i \(-0.380759\pi\)
−0.623015 + 0.782210i \(0.714092\pi\)
\(24\) 0 0
\(25\) 11.3399 6.54709i 2.26798 1.30942i
\(26\) 0 0
\(27\) −3.19099 3.19099i −0.614106 0.614106i
\(28\) 0 0
\(29\) 0.181826 0.181826i 0.0337642 0.0337642i −0.690023 0.723787i \(-0.742400\pi\)
0.723787 + 0.690023i \(0.242400\pi\)
\(30\) 0 0
\(31\) −3.23200 5.59799i −0.580485 1.00543i −0.995422 0.0955792i \(-0.969530\pi\)
0.414937 0.909850i \(-0.363804\pi\)
\(32\) 0 0
\(33\) −0.527459 + 0.913587i −0.0918189 + 0.159035i
\(34\) 0 0
\(35\) −9.34229 + 6.27542i −1.57914 + 1.06074i
\(36\) 0 0
\(37\) −0.238000 + 0.0637719i −0.0391269 + 0.0104840i −0.278329 0.960486i \(-0.589781\pi\)
0.239202 + 0.970970i \(0.423114\pi\)
\(38\) 0 0
\(39\) 1.81687 1.04897i 0.290933 0.167970i
\(40\) 0 0
\(41\) 0.440182i 0.0687448i 0.999409 + 0.0343724i \(0.0109432\pi\)
−0.999409 + 0.0343724i \(0.989057\pi\)
\(42\) 0 0
\(43\) −5.54503 5.54503i −0.845609 0.845609i 0.143972 0.989582i \(-0.454012\pi\)
−0.989582 + 0.143972i \(0.954012\pi\)
\(44\) 0 0
\(45\) 9.30835 + 2.49417i 1.38761 + 0.371808i
\(46\) 0 0
\(47\) 3.61427 6.26009i 0.527195 0.913128i −0.472303 0.881436i \(-0.656577\pi\)
0.999498 0.0316918i \(-0.0100895\pi\)
\(48\) 0 0
\(49\) 5.53257 4.28844i 0.790366 0.612634i
\(50\) 0 0
\(51\) −0.413433 1.54295i −0.0578921 0.216056i
\(52\) 0 0
\(53\) 2.59716 9.69274i 0.356747 1.33140i −0.521524 0.853237i \(-0.674636\pi\)
0.878271 0.478163i \(-0.158697\pi\)
\(54\) 0 0
\(55\) 5.23583i 0.706000i
\(56\) 0 0
\(57\) 3.27760i 0.434129i
\(58\) 0 0
\(59\) −0.438601 + 1.63688i −0.0571010 + 0.213104i −0.988581 0.150688i \(-0.951851\pi\)
0.931480 + 0.363791i \(0.118518\pi\)
\(60\) 0 0
\(61\) −2.41596 9.01647i −0.309331 1.15444i −0.929152 0.369697i \(-0.879461\pi\)
0.619821 0.784743i \(-0.287205\pi\)
\(62\) 0 0
\(63\) −5.88156 1.15497i −0.741007 0.145513i
\(64\) 0 0
\(65\) −5.20632 + 9.01761i −0.645765 + 1.11850i
\(66\) 0 0
\(67\) 9.59422 + 2.57076i 1.17212 + 0.314069i 0.791797 0.610785i \(-0.209146\pi\)
0.380324 + 0.924853i \(0.375813\pi\)
\(68\) 0 0
\(69\) −0.862854 0.862854i −0.103875 0.103875i
\(70\) 0 0
\(71\) 11.2912i 1.34002i 0.742352 + 0.670010i \(0.233710\pi\)
−0.742352 + 0.670010i \(0.766290\pi\)
\(72\) 0 0
\(73\) −8.13092 + 4.69439i −0.951652 + 0.549437i −0.893594 0.448877i \(-0.851824\pi\)
−0.0580583 + 0.998313i \(0.518491\pi\)
\(74\) 0 0
\(75\) 10.8399 2.90454i 1.25168 0.335388i
\(76\) 0 0
\(77\) 0.220938 + 3.24910i 0.0251783 + 0.370270i
\(78\) 0 0
\(79\) −6.52948 + 11.3094i −0.734624 + 1.27241i 0.220264 + 0.975440i \(0.429308\pi\)
−0.954888 + 0.296966i \(0.904025\pi\)
\(80\) 0 0
\(81\) 1.46441 + 2.53643i 0.162712 + 0.281825i
\(82\) 0 0
\(83\) −3.06926 + 3.06926i −0.336895 + 0.336895i −0.855198 0.518302i \(-0.826564\pi\)
0.518302 + 0.855198i \(0.326564\pi\)
\(84\) 0 0
\(85\) 5.60609 + 5.60609i 0.608066 + 0.608066i
\(86\) 0 0
\(87\) 0.190855 0.110190i 0.0204618 0.0118137i
\(88\) 0 0
\(89\) −5.66084 3.26829i −0.600047 0.346438i 0.169013 0.985614i \(-0.445942\pi\)
−0.769060 + 0.639176i \(0.779275\pi\)
\(90\) 0 0
\(91\) 2.85027 5.81558i 0.298789 0.609639i
\(92\) 0 0
\(93\) −1.43384 5.35117i −0.148682 0.554890i
\(94\) 0 0
\(95\) 8.13378 + 14.0881i 0.834508 + 1.44541i
\(96\) 0 0
\(97\) 1.70409 0.173024 0.0865122 0.996251i \(-0.472428\pi\)
0.0865122 + 0.996251i \(0.472428\pi\)
\(98\) 0 0
\(99\) 1.97179 1.97179i 0.198172 0.198172i
\(100\) 0 0
\(101\) −0.632838 + 2.36178i −0.0629697 + 0.235006i −0.990237 0.139394i \(-0.955485\pi\)
0.927267 + 0.374400i \(0.122151\pi\)
\(102\) 0 0
\(103\) −12.6328 7.29353i −1.24474 0.718653i −0.274687 0.961534i \(-0.588574\pi\)
−0.970056 + 0.242881i \(0.921908\pi\)
\(104\) 0 0
\(105\) −9.12593 + 3.12275i −0.890600 + 0.304749i
\(106\) 0 0
\(107\) −4.80256 + 1.28684i −0.464281 + 0.124404i −0.483374 0.875414i \(-0.660589\pi\)
0.0190927 + 0.999818i \(0.493922\pi\)
\(108\) 0 0
\(109\) 9.76613 + 2.61683i 0.935426 + 0.250647i 0.694167 0.719814i \(-0.255773\pi\)
0.241259 + 0.970461i \(0.422440\pi\)
\(110\) 0 0
\(111\) −0.211172 −0.0200435
\(112\) 0 0
\(113\) 5.22780 0.491791 0.245895 0.969296i \(-0.420918\pi\)
0.245895 + 0.969296i \(0.420918\pi\)
\(114\) 0 0
\(115\) 5.85009 + 1.56753i 0.545524 + 0.146173i
\(116\) 0 0
\(117\) −5.35667 + 1.43532i −0.495224 + 0.132695i
\(118\) 0 0
\(119\) −3.71543 3.24230i −0.340593 0.297222i
\(120\) 0 0
\(121\) 8.21419 + 4.74247i 0.746745 + 0.431133i
\(122\) 0 0
\(123\) −0.0976407 + 0.364400i −0.00880396 + 0.0328568i
\(124\) 0 0
\(125\) −24.3460 + 24.3460i −2.17757 + 2.17757i
\(126\) 0 0
\(127\) 1.20463 0.106893 0.0534467 0.998571i \(-0.482979\pi\)
0.0534467 + 0.998571i \(0.482979\pi\)
\(128\) 0 0
\(129\) −3.36041 5.82039i −0.295867 0.512457i
\(130\) 0 0
\(131\) −0.809509 3.02113i −0.0707272 0.263957i 0.921503 0.388370i \(-0.126962\pi\)
−0.992231 + 0.124413i \(0.960295\pi\)
\(132\) 0 0
\(133\) −5.64191 8.39918i −0.489216 0.728301i
\(134\) 0 0
\(135\) 16.6242 + 9.59798i 1.43078 + 0.826063i
\(136\) 0 0
\(137\) 0.286357 0.165329i 0.0244652 0.0141250i −0.487718 0.873001i \(-0.662170\pi\)
0.512183 + 0.858877i \(0.328837\pi\)
\(138\) 0 0
\(139\) −2.41295 2.41295i −0.204663 0.204663i 0.597331 0.801995i \(-0.296228\pi\)
−0.801995 + 0.597331i \(0.796228\pi\)
\(140\) 0 0
\(141\) 4.38064 4.38064i 0.368917 0.368917i
\(142\) 0 0
\(143\) 1.50653 + 2.60939i 0.125982 + 0.218208i
\(144\) 0 0
\(145\) −0.546903 + 0.947264i −0.0454179 + 0.0786660i
\(146\) 0 0
\(147\) 5.53134 2.32291i 0.456217 0.191591i
\(148\) 0 0
\(149\) 2.36381 0.633381i 0.193651 0.0518886i −0.160690 0.987005i \(-0.551372\pi\)
0.354341 + 0.935116i \(0.384705\pi\)
\(150\) 0 0
\(151\) −11.4320 + 6.60029i −0.930326 + 0.537124i −0.886915 0.461934i \(-0.847156\pi\)
−0.0434110 + 0.999057i \(0.513823\pi\)
\(152\) 0 0
\(153\) 4.22246i 0.341365i
\(154\) 0 0
\(155\) 19.4427 + 19.4427i 1.56167 + 1.56167i
\(156\) 0 0
\(157\) 3.45433 + 0.925585i 0.275685 + 0.0738697i 0.394013 0.919105i \(-0.371087\pi\)
−0.118327 + 0.992975i \(0.537753\pi\)
\(158\) 0 0
\(159\) 4.30007 7.44794i 0.341018 0.590660i
\(160\) 0 0
\(161\) −3.69643 0.725873i −0.291319 0.0572068i
\(162\) 0 0
\(163\) −2.90781 10.8521i −0.227757 0.850001i −0.981281 0.192581i \(-0.938314\pi\)
0.753524 0.657420i \(-0.228352\pi\)
\(164\) 0 0
\(165\) 1.16141 4.33443i 0.0904155 0.337435i
\(166\) 0 0
\(167\) 11.7171i 0.906693i −0.891334 0.453346i \(-0.850230\pi\)
0.891334 0.453346i \(-0.149770\pi\)
\(168\) 0 0
\(169\) 7.00785i 0.539065i
\(170\) 0 0
\(171\) −2.24238 + 8.36867i −0.171479 + 0.639968i
\(172\) 0 0
\(173\) −2.83415 10.5772i −0.215476 0.804169i −0.985998 0.166755i \(-0.946671\pi\)
0.770522 0.637413i \(-0.219996\pi\)
\(174\) 0 0
\(175\) 22.7786 26.1025i 1.72190 1.97316i
\(176\) 0 0
\(177\) −0.726183 + 1.25779i −0.0545833 + 0.0945410i
\(178\) 0 0
\(179\) −16.1464 4.32641i −1.20684 0.323371i −0.401317 0.915939i \(-0.631447\pi\)
−0.805520 + 0.592568i \(0.798114\pi\)
\(180\) 0 0
\(181\) 15.9791 + 15.9791i 1.18772 + 1.18772i 0.977696 + 0.210025i \(0.0673544\pi\)
0.210025 + 0.977696i \(0.432646\pi\)
\(182\) 0 0
\(183\) 8.00010i 0.591385i
\(184\) 0 0
\(185\) 0.907680 0.524050i 0.0667340 0.0385289i
\(186\) 0 0
\(187\) 2.21598 0.593770i 0.162048 0.0434208i
\(188\) 0 0
\(189\) −10.7212 5.25454i −0.779851 0.382212i
\(190\) 0 0
\(191\) −4.97963 + 8.62497i −0.360313 + 0.624081i −0.988012 0.154375i \(-0.950664\pi\)
0.627699 + 0.778456i \(0.283997\pi\)
\(192\) 0 0
\(193\) −4.02312 6.96824i −0.289590 0.501585i 0.684122 0.729368i \(-0.260186\pi\)
−0.973712 + 0.227783i \(0.926852\pi\)
\(194\) 0 0
\(195\) −6.31028 + 6.31028i −0.451889 + 0.451889i
\(196\) 0 0
\(197\) −6.01951 6.01951i −0.428873 0.428873i 0.459372 0.888244i \(-0.348075\pi\)
−0.888244 + 0.459372i \(0.848075\pi\)
\(198\) 0 0
\(199\) −12.7812 + 7.37922i −0.906035 + 0.523099i −0.879153 0.476539i \(-0.841891\pi\)
−0.0268814 + 0.999639i \(0.508558\pi\)
\(200\) 0 0
\(201\) 7.37224 + 4.25636i 0.519998 + 0.300221i
\(202\) 0 0
\(203\) 0.299410 0.610904i 0.0210144 0.0428771i
\(204\) 0 0
\(205\) −0.484616 1.80861i −0.0338470 0.126319i
\(206\) 0 0
\(207\) 1.61279 + 2.79344i 0.112097 + 0.194158i
\(208\) 0 0
\(209\) 4.70727 0.325609
\(210\) 0 0
\(211\) 14.5016 14.5016i 0.998329 0.998329i −0.00166940 0.999999i \(-0.500531\pi\)
0.999999 + 0.00166940i \(0.000531387\pi\)
\(212\) 0 0
\(213\) −2.50461 + 9.34732i −0.171613 + 0.640468i
\(214\) 0 0
\(215\) 28.8881 + 16.6786i 1.97015 + 1.13747i
\(216\) 0 0
\(217\) −12.8856 11.2448i −0.874733 0.763344i
\(218\) 0 0
\(219\) −7.77241 + 2.08261i −0.525211 + 0.140730i
\(220\) 0 0
\(221\) −4.40698 1.18085i −0.296445 0.0794323i
\(222\) 0 0
\(223\) −4.72461 −0.316383 −0.158192 0.987408i \(-0.550566\pi\)
−0.158192 + 0.987408i \(0.550566\pi\)
\(224\) 0 0
\(225\) −29.6646 −1.97764
\(226\) 0 0
\(227\) 15.9081 + 4.26257i 1.05586 + 0.282917i 0.744671 0.667431i \(-0.232606\pi\)
0.311189 + 0.950348i \(0.399273\pi\)
\(228\) 0 0
\(229\) 13.3085 3.56601i 0.879453 0.235649i 0.209282 0.977855i \(-0.432887\pi\)
0.670171 + 0.742207i \(0.266221\pi\)
\(230\) 0 0
\(231\) −0.537812 + 2.73875i −0.0353854 + 0.180196i
\(232\) 0 0
\(233\) 12.0806 + 6.97475i 0.791428 + 0.456931i 0.840465 0.541866i \(-0.182282\pi\)
−0.0490370 + 0.998797i \(0.515615\pi\)
\(234\) 0 0
\(235\) −7.95822 + 29.7005i −0.519137 + 1.93745i
\(236\) 0 0
\(237\) −7.91401 + 7.91401i −0.514070 + 0.514070i
\(238\) 0 0
\(239\) 23.1794 1.49935 0.749674 0.661807i \(-0.230210\pi\)
0.749674 + 0.661807i \(0.230210\pi\)
\(240\) 0 0
\(241\) 2.09690 + 3.63195i 0.135073 + 0.233954i 0.925626 0.378441i \(-0.123540\pi\)
−0.790552 + 0.612395i \(0.790206\pi\)
\(242\) 0 0
\(243\) 4.15362 + 15.5015i 0.266455 + 0.994422i
\(244\) 0 0
\(245\) −18.0108 + 23.7113i −1.15067 + 1.51486i
\(246\) 0 0
\(247\) −8.10728 4.68074i −0.515854 0.297828i
\(248\) 0 0
\(249\) −3.22168 + 1.86004i −0.204166 + 0.117875i
\(250\) 0 0
\(251\) −16.5937 16.5937i −1.04739 1.04739i −0.998820 0.0485679i \(-0.984534\pi\)
−0.0485679 0.998820i \(-0.515466\pi\)
\(252\) 0 0
\(253\) 1.23923 1.23923i 0.0779095 0.0779095i
\(254\) 0 0
\(255\) 3.39741 + 5.88449i 0.212754 + 0.368501i
\(256\) 0 0
\(257\) 5.52727 9.57351i 0.344782 0.597179i −0.640532 0.767931i \(-0.721286\pi\)
0.985314 + 0.170752i \(0.0546196\pi\)
\(258\) 0 0
\(259\) −0.541149 + 0.363501i −0.0336254 + 0.0225869i
\(260\) 0 0
\(261\) −0.562697 + 0.150774i −0.0348301 + 0.00933269i
\(262\) 0 0
\(263\) 14.1936 8.19466i 0.875213 0.505304i 0.00613562 0.999981i \(-0.498047\pi\)
0.869077 + 0.494677i \(0.164714\pi\)
\(264\) 0 0
\(265\) 42.6847i 2.62210i
\(266\) 0 0
\(267\) −3.96130 3.96130i −0.242428 0.242428i
\(268\) 0 0
\(269\) 1.24494 + 0.333581i 0.0759055 + 0.0203388i 0.296572 0.955011i \(-0.404157\pi\)
−0.220666 + 0.975349i \(0.570823\pi\)
\(270\) 0 0
\(271\) −10.0688 + 17.4397i −0.611639 + 1.05939i 0.379326 + 0.925263i \(0.376156\pi\)
−0.990964 + 0.134126i \(0.957177\pi\)
\(272\) 0 0
\(273\) 3.64958 4.18213i 0.220882 0.253114i
\(274\) 0 0
\(275\) 4.17149 + 15.5682i 0.251550 + 0.938798i
\(276\) 0 0
\(277\) −8.35382 + 31.1769i −0.501932 + 1.87324i −0.0148319 + 0.999890i \(0.504721\pi\)
−0.487100 + 0.873346i \(0.661945\pi\)
\(278\) 0 0
\(279\) 14.6441i 0.876717i
\(280\) 0 0
\(281\) 13.6466i 0.814089i −0.913408 0.407044i \(-0.866559\pi\)
0.913408 0.407044i \(-0.133441\pi\)
\(282\) 0 0
\(283\) −4.86306 + 18.1492i −0.289079 + 1.07886i 0.656728 + 0.754128i \(0.271940\pi\)
−0.945807 + 0.324730i \(0.894727\pi\)
\(284\) 0 0
\(285\) 3.60846 + 13.4669i 0.213747 + 0.797713i
\(286\) 0 0
\(287\) 0.377048 + 1.10189i 0.0222564 + 0.0650423i
\(288\) 0 0
\(289\) 6.76307 11.7140i 0.397828 0.689058i
\(290\) 0 0
\(291\) 1.41072 + 0.378000i 0.0826977 + 0.0221588i
\(292\) 0 0
\(293\) −2.19433 2.19433i −0.128194 0.128194i 0.640099 0.768293i \(-0.278893\pi\)
−0.768293 + 0.640099i \(0.778893\pi\)
\(294\) 0 0
\(295\) 7.20847i 0.419693i
\(296\) 0 0
\(297\) 4.81047 2.77733i 0.279132 0.161157i
\(298\) 0 0
\(299\) −3.36655 + 0.902063i −0.194692 + 0.0521677i
\(300\) 0 0
\(301\) −18.6303 9.13090i −1.07384 0.526296i
\(302\) 0 0
\(303\) −1.04778 + 1.81480i −0.0601932 + 0.104258i
\(304\) 0 0
\(305\) 19.8533 + 34.3869i 1.13680 + 1.96899i
\(306\) 0 0
\(307\) −8.28029 + 8.28029i −0.472581 + 0.472581i −0.902749 0.430168i \(-0.858454\pi\)
0.430168 + 0.902749i \(0.358454\pi\)
\(308\) 0 0
\(309\) −8.84007 8.84007i −0.502894 0.502894i
\(310\) 0 0
\(311\) 7.36500 4.25218i 0.417631 0.241119i −0.276432 0.961033i \(-0.589152\pi\)
0.694063 + 0.719914i \(0.255819\pi\)
\(312\) 0 0
\(313\) −14.1001 8.14069i −0.796984 0.460139i 0.0454317 0.998967i \(-0.485534\pi\)
−0.842415 + 0.538829i \(0.818867\pi\)
\(314\) 0 0
\(315\) 25.4376 1.72975i 1.43325 0.0974605i
\(316\) 0 0
\(317\) 5.85666 + 21.8574i 0.328943 + 1.22763i 0.910288 + 0.413975i \(0.135860\pi\)
−0.581345 + 0.813657i \(0.697474\pi\)
\(318\) 0 0
\(319\) 0.158255 + 0.274106i 0.00886058 + 0.0153470i
\(320\) 0 0
\(321\) −4.26120 −0.237837
\(322\) 0 0
\(323\) −5.04015 + 5.04015i −0.280442 + 0.280442i
\(324\) 0 0
\(325\) 8.29595 30.9609i 0.460177 1.71740i
\(326\) 0 0
\(327\) 7.50434 + 4.33263i 0.414991 + 0.239595i
\(328\) 0 0
\(329\) 3.68520 18.7665i 0.203172 1.03463i
\(330\) 0 0
\(331\) 11.2314 3.00945i 0.617334 0.165414i 0.0634183 0.997987i \(-0.479800\pi\)
0.553915 + 0.832573i \(0.313133\pi\)
\(332\) 0 0
\(333\) 0.539183 + 0.144474i 0.0295470 + 0.00791711i
\(334\) 0 0
\(335\) −42.2509 −2.30841
\(336\) 0 0
\(337\) 15.7590 0.858445 0.429223 0.903199i \(-0.358788\pi\)
0.429223 + 0.903199i \(0.358788\pi\)
\(338\) 0 0
\(339\) 4.32779 + 1.15963i 0.235053 + 0.0629823i
\(340\) 0 0
\(341\) 7.68532 2.05928i 0.416183 0.111516i
\(342\) 0 0
\(343\) 10.1761 15.4741i 0.549455 0.835523i
\(344\) 0 0
\(345\) 4.49523 + 2.59533i 0.242015 + 0.139728i
\(346\) 0 0
\(347\) 3.95167 14.7478i 0.212137 0.791706i −0.775018 0.631939i \(-0.782259\pi\)
0.987155 0.159766i \(-0.0510741\pi\)
\(348\) 0 0
\(349\) 6.62124 6.62124i 0.354427 0.354427i −0.507327 0.861754i \(-0.669366\pi\)
0.861754 + 0.507327i \(0.169366\pi\)
\(350\) 0 0
\(351\) −11.0467 −0.589628
\(352\) 0 0
\(353\) −10.9032 18.8849i −0.580319 1.00514i −0.995441 0.0953759i \(-0.969595\pi\)
0.415123 0.909765i \(-0.363739\pi\)
\(354\) 0 0
\(355\) −12.4310 46.3931i −0.659769 2.46229i
\(356\) 0 0
\(357\) −2.35658 3.50826i −0.124723 0.185677i
\(358\) 0 0
\(359\) −29.8216 17.2175i −1.57392 0.908704i −0.995681 0.0928386i \(-0.970406\pi\)
−0.578241 0.815866i \(-0.696261\pi\)
\(360\) 0 0
\(361\) 3.78856 2.18733i 0.199398 0.115123i
\(362\) 0 0
\(363\) 5.74807 + 5.74807i 0.301695 + 0.301695i
\(364\) 0 0
\(365\) 28.2399 28.2399i 1.47815 1.47815i
\(366\) 0 0
\(367\) 1.65812 + 2.87195i 0.0865533 + 0.149915i 0.906052 0.423166i \(-0.139081\pi\)
−0.819499 + 0.573081i \(0.805748\pi\)
\(368\) 0 0
\(369\) 0.498611 0.863619i 0.0259566 0.0449582i
\(370\) 0 0
\(371\) −1.80118 26.4880i −0.0935127 1.37519i
\(372\) 0 0
\(373\) 22.4918 6.02667i 1.16458 0.312049i 0.375789 0.926705i \(-0.377372\pi\)
0.788795 + 0.614656i \(0.210705\pi\)
\(374\) 0 0
\(375\) −25.5550 + 14.7542i −1.31966 + 0.761903i
\(376\) 0 0
\(377\) 0.629452i 0.0324184i
\(378\) 0 0
\(379\) 2.77271 + 2.77271i 0.142425 + 0.142425i 0.774724 0.632299i \(-0.217889\pi\)
−0.632299 + 0.774724i \(0.717889\pi\)
\(380\) 0 0
\(381\) 0.997239 + 0.267209i 0.0510901 + 0.0136895i
\(382\) 0 0
\(383\) 10.6953 18.5248i 0.546504 0.946572i −0.452007 0.892014i \(-0.649292\pi\)
0.998511 0.0545578i \(-0.0173749\pi\)
\(384\) 0 0
\(385\) −4.48487 13.1066i −0.228570 0.667975i
\(386\) 0 0
\(387\) 4.59806 + 17.1602i 0.233733 + 0.872302i
\(388\) 0 0
\(389\) 6.51295 24.3067i 0.330220 1.23240i −0.578740 0.815512i \(-0.696455\pi\)
0.908959 0.416885i \(-0.136878\pi\)
\(390\) 0 0
\(391\) 2.65372i 0.134204i
\(392\) 0 0
\(393\) 2.68058i 0.135217i
\(394\) 0 0
\(395\) 14.3772 53.6564i 0.723395 2.69975i
\(396\) 0 0
\(397\) −0.101204 0.377699i −0.00507929 0.0189562i 0.963340 0.268285i \(-0.0864568\pi\)
−0.968419 + 0.249328i \(0.919790\pi\)
\(398\) 0 0
\(399\) −2.80750 8.20466i −0.140551 0.410747i
\(400\) 0 0
\(401\) −9.92701 + 17.1941i −0.495731 + 0.858631i −0.999988 0.00492242i \(-0.998433\pi\)
0.504257 + 0.863554i \(0.331766\pi\)
\(402\) 0 0
\(403\) −15.2840 4.09534i −0.761350 0.204003i
\(404\) 0 0
\(405\) −8.80940 8.80940i −0.437743 0.437743i
\(406\) 0 0
\(407\) 0.303284i 0.0150332i
\(408\) 0 0
\(409\) 30.4501 17.5804i 1.50566 0.869295i 0.505685 0.862718i \(-0.331240\pi\)
0.999978 0.00657643i \(-0.00209336\pi\)
\(410\) 0 0
\(411\) 0.273731 0.0733461i 0.0135022 0.00361789i
\(412\) 0 0
\(413\) 0.304178 + 4.47322i 0.0149676 + 0.220113i
\(414\) 0 0
\(415\) 9.23185 15.9900i 0.453174 0.784920i
\(416\) 0 0
\(417\) −1.46230 2.53277i −0.0716089 0.124030i
\(418\) 0 0
\(419\) −17.1877 + 17.1877i −0.839673 + 0.839673i −0.988816 0.149142i \(-0.952349\pi\)
0.149142 + 0.988816i \(0.452349\pi\)
\(420\) 0 0
\(421\) −12.9543 12.9543i −0.631352 0.631352i 0.317055 0.948407i \(-0.397306\pi\)
−0.948407 + 0.317055i \(0.897306\pi\)
\(422\) 0 0
\(423\) −14.1821 + 8.18803i −0.689557 + 0.398116i
\(424\) 0 0
\(425\) −21.1356 12.2026i −1.02523 0.591915i
\(426\) 0 0
\(427\) −13.7710 20.5011i −0.666426 0.992117i
\(428\) 0 0
\(429\) 0.668354 + 2.49433i 0.0322685 + 0.120427i
\(430\) 0 0
\(431\) −2.85225 4.94025i −0.137388 0.237963i 0.789119 0.614240i \(-0.210537\pi\)
−0.926507 + 0.376277i \(0.877204\pi\)
\(432\) 0 0
\(433\) −8.09187 −0.388870 −0.194435 0.980915i \(-0.562287\pi\)
−0.194435 + 0.980915i \(0.562287\pi\)
\(434\) 0 0
\(435\) −0.662870 + 0.662870i −0.0317822 + 0.0317822i
\(436\) 0 0
\(437\) −1.40928 + 5.25952i −0.0674152 + 0.251597i
\(438\) 0 0
\(439\) −6.11379 3.52980i −0.291795 0.168468i 0.346956 0.937881i \(-0.387215\pi\)
−0.638751 + 0.769413i \(0.720549\pi\)
\(440\) 0 0
\(441\) −15.7124 + 2.14680i −0.748207 + 0.102229i
\(442\) 0 0
\(443\) −14.7590 + 3.95466i −0.701221 + 0.187891i −0.591777 0.806102i \(-0.701573\pi\)
−0.109443 + 0.993993i \(0.534907\pi\)
\(444\) 0 0
\(445\) 26.8574 + 7.19641i 1.27316 + 0.341142i
\(446\) 0 0
\(447\) 2.09735 0.0992014
\(448\) 0 0
\(449\) 19.5020 0.920356 0.460178 0.887827i \(-0.347786\pi\)
0.460178 + 0.887827i \(0.347786\pi\)
\(450\) 0 0
\(451\) −0.523350 0.140231i −0.0246436 0.00660322i
\(452\) 0 0
\(453\) −10.9280 + 2.92814i −0.513441 + 0.137576i
\(454\) 0 0
\(455\) −5.30850 + 27.0330i −0.248866 + 1.26733i
\(456\) 0 0
\(457\) −8.72578 5.03783i −0.408175 0.235660i 0.281830 0.959464i \(-0.409058\pi\)
−0.690005 + 0.723804i \(0.742392\pi\)
\(458\) 0 0
\(459\) −2.17692 + 8.12437i −0.101610 + 0.379213i
\(460\) 0 0
\(461\) 15.9419 15.9419i 0.742487 0.742487i −0.230569 0.973056i \(-0.574059\pi\)
0.973056 + 0.230569i \(0.0740587\pi\)
\(462\) 0 0
\(463\) 8.23452 0.382690 0.191345 0.981523i \(-0.438715\pi\)
0.191345 + 0.981523i \(0.438715\pi\)
\(464\) 0 0
\(465\) 11.7827 + 20.4082i 0.546409 + 0.946408i
\(466\) 0 0
\(467\) 8.94417 + 33.3801i 0.413887 + 1.54465i 0.787055 + 0.616882i \(0.211605\pi\)
−0.373169 + 0.927764i \(0.621729\pi\)
\(468\) 0 0
\(469\) 26.2188 1.78288i 1.21067 0.0823255i
\(470\) 0 0
\(471\) 2.65432 + 1.53247i 0.122305 + 0.0706126i
\(472\) 0 0
\(473\) 8.35922 4.82620i 0.384357 0.221909i
\(474\) 0 0
\(475\) −35.4092 35.4092i −1.62469 1.62469i
\(476\) 0 0
\(477\) −16.0749 + 16.0749i −0.736017 + 0.736017i
\(478\) 0 0
\(479\) −3.70229 6.41255i −0.169162 0.292997i 0.768964 0.639293i \(-0.220773\pi\)
−0.938125 + 0.346296i \(0.887439\pi\)
\(480\) 0 0
\(481\) −0.301574 + 0.522342i −0.0137506 + 0.0238167i
\(482\) 0 0
\(483\) −2.89904 1.42085i −0.131911 0.0646507i
\(484\) 0 0
\(485\) −7.00175 + 1.87611i −0.317933 + 0.0851899i
\(486\) 0 0
\(487\) 29.4458 17.0005i 1.33432 0.770368i 0.348359 0.937361i \(-0.386739\pi\)
0.985958 + 0.166993i \(0.0534056\pi\)
\(488\) 0 0
\(489\) 9.62880i 0.435429i
\(490\) 0 0
\(491\) 2.03871 + 2.03871i 0.0920055 + 0.0920055i 0.751612 0.659606i \(-0.229277\pi\)
−0.659606 + 0.751612i \(0.729277\pi\)
\(492\) 0 0
\(493\) −0.462935 0.124043i −0.0208496 0.00558662i
\(494\) 0 0
\(495\) −5.93083 + 10.2725i −0.266571 + 0.461714i
\(496\) 0 0
\(497\) 9.67175 + 28.2648i 0.433837 + 1.26785i
\(498\) 0 0
\(499\) −3.72332 13.8956i −0.166679 0.622053i −0.997820 0.0659922i \(-0.978979\pi\)
0.831141 0.556061i \(-0.187688\pi\)
\(500\) 0 0
\(501\) 2.59907 9.69985i 0.116118 0.433357i
\(502\) 0 0
\(503\) 27.2980i 1.21716i −0.793494 0.608579i \(-0.791740\pi\)
0.793494 0.608579i \(-0.208260\pi\)
\(504\) 0 0
\(505\) 10.4008i 0.462828i
\(506\) 0 0
\(507\) −1.55447 + 5.80138i −0.0690366 + 0.257648i
\(508\) 0 0
\(509\) −5.34620 19.9523i −0.236966 0.884370i −0.977253 0.212078i \(-0.931977\pi\)
0.740286 0.672292i \(-0.234690\pi\)
\(510\) 0 0
\(511\) −16.3327 + 18.7160i −0.722515 + 0.827946i
\(512\) 0 0
\(513\) −8.62906 + 14.9460i −0.380982 + 0.659881i
\(514\) 0 0
\(515\) 59.9351 + 16.0596i 2.64106 + 0.707669i
\(516\) 0 0
\(517\) 6.29146 + 6.29146i 0.276698 + 0.276698i
\(518\) 0 0
\(519\) 9.38489i 0.411951i
\(520\) 0 0
\(521\) −9.46400 + 5.46404i −0.414625 + 0.239384i −0.692775 0.721154i \(-0.743612\pi\)
0.278150 + 0.960538i \(0.410279\pi\)
\(522\) 0 0
\(523\) 11.8976 3.18796i 0.520247 0.139400i 0.0108660 0.999941i \(-0.496541\pi\)
0.509381 + 0.860541i \(0.329875\pi\)
\(524\) 0 0
\(525\) 24.6471 16.5560i 1.07569 0.722562i
\(526\) 0 0
\(527\) −6.02390 + 10.4337i −0.262405 + 0.454499i
\(528\) 0 0
\(529\) −10.4864 18.1630i −0.455930 0.789694i
\(530\) 0 0
\(531\) 2.71468 2.71468i 0.117807 0.117807i
\(532\) 0 0
\(533\) 0.761918 + 0.761918i 0.0330023 + 0.0330023i
\(534\) 0 0
\(535\) 18.3160 10.5747i 0.791868 0.457185i
\(536\) 0 0
\(537\) −12.4069 7.16316i −0.535399 0.309113i
\(538\) 0 0
\(539\) 3.33616 + 7.94408i 0.143699 + 0.342176i
\(540\) 0 0
\(541\) −4.34231 16.2057i −0.186691 0.696739i −0.994262 0.106969i \(-0.965885\pi\)
0.807572 0.589769i \(-0.200781\pi\)
\(542\) 0 0
\(543\) 9.68370 + 16.7727i 0.415567 + 0.719784i
\(544\) 0 0
\(545\) −43.0079 −1.84226
\(546\) 0 0
\(547\) −23.2429 + 23.2429i −0.993797 + 0.993797i −0.999981 0.00618416i \(-0.998032\pi\)
0.00618416 + 0.999981i \(0.498032\pi\)
\(548\) 0 0
\(549\) −5.47329 + 20.4266i −0.233594 + 0.871786i
\(550\) 0 0
\(551\) −0.851637 0.491693i −0.0362810 0.0209468i
\(552\) 0 0
\(553\) −6.65763 + 33.9033i −0.283111 + 1.44171i
\(554\) 0 0
\(555\) 0.867659 0.232488i 0.0368301 0.00986858i
\(556\) 0 0
\(557\) 22.7871 + 6.10578i 0.965519 + 0.258710i 0.706935 0.707279i \(-0.250077\pi\)
0.258584 + 0.965989i \(0.416744\pi\)
\(558\) 0 0
\(559\) −19.1960 −0.811904
\(560\) 0 0
\(561\) 1.96619 0.0830125
\(562\) 0 0
\(563\) −37.6366 10.0847i −1.58620 0.425020i −0.645358 0.763880i \(-0.723292\pi\)
−0.940837 + 0.338860i \(0.889959\pi\)
\(564\) 0 0
\(565\) −21.4799 + 5.75553i −0.903667 + 0.242137i
\(566\) 0 0
\(567\) 5.83842 + 5.09495i 0.245191 + 0.213968i
\(568\) 0 0
\(569\) 10.2086 + 5.89395i 0.427968 + 0.247087i 0.698481 0.715629i \(-0.253860\pi\)
−0.270513 + 0.962716i \(0.587193\pi\)
\(570\) 0 0
\(571\) −0.732074 + 2.73214i −0.0306363 + 0.114336i −0.979551 0.201197i \(-0.935517\pi\)
0.948914 + 0.315534i \(0.102183\pi\)
\(572\) 0 0
\(573\) −6.03552 + 6.03552i −0.252138 + 0.252138i
\(574\) 0 0
\(575\) −18.6435 −0.777489
\(576\) 0 0
\(577\) 21.6020 + 37.4157i 0.899302 + 1.55764i 0.828389 + 0.560154i \(0.189258\pi\)
0.0709133 + 0.997482i \(0.477409\pi\)
\(578\) 0 0
\(579\) −1.78481 6.66100i −0.0741741 0.276822i
\(580\) 0 0
\(581\) −5.05410 + 10.3122i −0.209679 + 0.427822i
\(582\) 0 0
\(583\) 10.6967 + 6.17574i 0.443012 + 0.255773i
\(584\) 0 0
\(585\) 20.4292 11.7948i 0.844643 0.487655i
\(586\) 0 0
\(587\) 28.1127 + 28.1127i 1.16034 + 1.16034i 0.984402 + 0.175935i \(0.0562948\pi\)
0.175935 + 0.984402i \(0.443705\pi\)
\(588\) 0 0
\(589\) −17.4799 + 17.4799i −0.720248 + 0.720248i
\(590\) 0 0
\(591\) −3.64795 6.31844i −0.150057 0.259906i
\(592\) 0 0
\(593\) 8.44544 14.6279i 0.346812 0.600697i −0.638869 0.769316i \(-0.720597\pi\)
0.985681 + 0.168619i \(0.0539307\pi\)
\(594\) 0 0
\(595\) 18.8355 + 9.23145i 0.772180 + 0.378452i
\(596\) 0 0
\(597\) −12.2176 + 3.27371i −0.500035 + 0.133984i
\(598\) 0 0
\(599\) −25.7194 + 14.8491i −1.05087 + 0.606718i −0.922892 0.385059i \(-0.874181\pi\)
−0.127975 + 0.991777i \(0.540848\pi\)
\(600\) 0 0
\(601\) 30.4663i 1.24275i −0.783515 0.621373i \(-0.786575\pi\)
0.783515 0.621373i \(-0.213425\pi\)
\(602\) 0 0
\(603\) −15.9115 15.9115i −0.647966 0.647966i
\(604\) 0 0
\(605\) −38.9715 10.4424i −1.58442 0.424544i
\(606\) 0 0
\(607\) 16.6272 28.7992i 0.674879 1.16892i −0.301626 0.953426i \(-0.597529\pi\)
0.976504 0.215498i \(-0.0691373\pi\)
\(608\) 0 0
\(609\) 0.383374 0.439316i 0.0155351 0.0178020i
\(610\) 0 0
\(611\) −4.57971 17.0917i −0.185275 0.691456i
\(612\) 0 0
\(613\) 5.29950 19.7780i 0.214045 0.798827i −0.772456 0.635069i \(-0.780972\pi\)
0.986501 0.163758i \(-0.0523616\pi\)
\(614\) 0 0
\(615\) 1.60474i 0.0647093i
\(616\) 0 0
\(617\) 2.64884i 0.106638i 0.998578 + 0.0533192i \(0.0169801\pi\)
−0.998578 + 0.0533192i \(0.983020\pi\)
\(618\) 0 0
\(619\) −9.69816 + 36.1940i −0.389802 + 1.45476i 0.440654 + 0.897677i \(0.354747\pi\)
−0.830456 + 0.557084i \(0.811920\pi\)
\(620\) 0 0
\(621\) 1.66298 + 6.20631i 0.0667330 + 0.249051i
\(622\) 0 0
\(623\) −16.9700 3.33243i −0.679890 0.133511i
\(624\) 0 0
\(625\) 40.4934 70.1366i 1.61974 2.80546i
\(626\) 0 0
\(627\) 3.89687 + 1.04416i 0.155626 + 0.0416999i
\(628\) 0 0
\(629\) 0.324731 + 0.324731i 0.0129479 + 0.0129479i
\(630\) 0 0
\(631\) 10.0919i 0.401753i 0.979617 + 0.200877i \(0.0643791\pi\)
−0.979617 + 0.200877i \(0.935621\pi\)
\(632\) 0 0
\(633\) 15.2217 8.78826i 0.605009 0.349302i
\(634\) 0 0
\(635\) −4.94955 + 1.32623i −0.196417 + 0.0526298i
\(636\) 0 0
\(637\) 2.15348 16.9994i 0.0853239 0.673539i
\(638\) 0 0
\(639\) 12.7900 22.1529i 0.505964 0.876355i
\(640\) 0 0
\(641\) −15.3814 26.6413i −0.607528 1.05227i −0.991646 0.128986i \(-0.958828\pi\)
0.384118 0.923284i \(-0.374505\pi\)
\(642\) 0 0
\(643\) 22.2297 22.2297i 0.876653 0.876653i −0.116533 0.993187i \(-0.537178\pi\)
0.993187 + 0.116533i \(0.0371782\pi\)
\(644\) 0 0
\(645\) 20.2151 + 20.2151i 0.795970 + 0.795970i
\(646\) 0 0
\(647\) 14.3410 8.27978i 0.563803 0.325512i −0.190867 0.981616i \(-0.561130\pi\)
0.754670 + 0.656104i \(0.227797\pi\)
\(648\) 0 0
\(649\) −1.80643 1.04294i −0.0709085 0.0409390i
\(650\) 0 0
\(651\) −8.17293 12.1671i −0.320322 0.476868i
\(652\) 0 0
\(653\) 9.67497 + 36.1075i 0.378611 + 1.41300i 0.847996 + 0.530002i \(0.177809\pi\)
−0.469385 + 0.882993i \(0.655524\pi\)
\(654\) 0 0
\(655\) 6.65220 + 11.5219i 0.259923 + 0.450200i
\(656\) 0 0
\(657\) 21.2701 0.829824
\(658\) 0 0
\(659\) −14.8808 + 14.8808i −0.579674 + 0.579674i −0.934813 0.355139i \(-0.884433\pi\)
0.355139 + 0.934813i \(0.384433\pi\)
\(660\) 0 0
\(661\) 2.96488 11.0651i 0.115321 0.430382i −0.883990 0.467506i \(-0.845153\pi\)
0.999311 + 0.0371232i \(0.0118194\pi\)
\(662\) 0 0
\(663\) −3.38634 1.95510i −0.131515 0.0759299i
\(664\) 0 0
\(665\) 32.4284 + 28.2990i 1.25752 + 1.09739i
\(666\) 0 0
\(667\) −0.353642 + 0.0947582i −0.0136931 + 0.00366905i
\(668\) 0 0
\(669\) −3.91122 1.04801i −0.151217 0.0405183i
\(670\) 0 0
\(671\) 11.4897 0.443555
\(672\) 0 0
\(673\) 20.7704 0.800639 0.400319 0.916376i \(-0.368899\pi\)
0.400319 + 0.916376i \(0.368899\pi\)
\(674\) 0 0
\(675\) −57.0772 15.2938i −2.19690 0.588658i
\(676\) 0 0
\(677\) −26.5605 + 7.11687i −1.02080 + 0.273524i −0.730137 0.683301i \(-0.760544\pi\)
−0.290667 + 0.956824i \(0.593877\pi\)
\(678\) 0 0
\(679\) 4.26578 1.45968i 0.163706 0.0560174i
\(680\) 0 0
\(681\) 12.2239 + 7.05746i 0.468420 + 0.270442i
\(682\) 0 0
\(683\) −0.558762 + 2.08533i −0.0213804 + 0.0797928i −0.975792 0.218702i \(-0.929818\pi\)
0.954411 + 0.298495i \(0.0964845\pi\)
\(684\) 0 0
\(685\) −0.994563 + 0.994563i −0.0380003 + 0.0380003i
\(686\) 0 0
\(687\) 11.8083 0.450517
\(688\) 0 0
\(689\) −12.2819 21.2728i −0.467902 0.810429i
\(690\) 0 0
\(691\) −0.631272 2.35594i −0.0240147 0.0896242i 0.952878 0.303352i \(-0.0981059\pi\)
−0.976893 + 0.213728i \(0.931439\pi\)
\(692\) 0 0
\(693\) 3.24691 6.62488i 0.123340 0.251658i
\(694\) 0 0
\(695\) 12.5708 + 7.25775i 0.476837 + 0.275302i
\(696\) 0 0
\(697\) 0.710506 0.410211i 0.0269124 0.0155379i
\(698\) 0 0
\(699\) 8.45369 + 8.45369i 0.319748 + 0.319748i
\(700\) 0 0
\(701\) −6.81795 + 6.81795i −0.257510 + 0.257510i −0.824041 0.566530i \(-0.808285\pi\)
0.566530 + 0.824041i \(0.308285\pi\)
\(702\) 0 0
\(703\) 0.471146 + 0.816049i 0.0177696 + 0.0307779i
\(704\) 0 0
\(705\) −13.1763 + 22.8220i −0.496247 + 0.859525i
\(706\) 0 0
\(707\) 0.438885 + 6.45421i 0.0165060 + 0.242736i
\(708\) 0 0
\(709\) −11.3630 + 3.04470i −0.426745 + 0.114346i −0.465798 0.884891i \(-0.654233\pi\)
0.0390527 + 0.999237i \(0.487566\pi\)
\(710\) 0 0
\(711\) 25.6212 14.7924i 0.960869 0.554758i
\(712\) 0 0
\(713\) 9.20346i 0.344672i
\(714\) 0 0
\(715\) −9.06280 9.06280i −0.338929 0.338929i
\(716\) 0 0
\(717\) 19.1888 + 5.14163i 0.716619 + 0.192018i
\(718\) 0 0
\(719\) 16.4827 28.5490i 0.614703 1.06470i −0.375734 0.926728i \(-0.622609\pi\)
0.990437 0.137969i \(-0.0440573\pi\)
\(720\) 0 0
\(721\) −37.8705 7.43668i −1.41037 0.276956i
\(722\) 0 0
\(723\) 0.930267 + 3.47180i 0.0345970 + 0.129118i
\(724\) 0 0
\(725\) 0.871457 3.25232i 0.0323651 0.120788i
\(726\) 0 0
\(727\) 13.8871i 0.515045i 0.966272 + 0.257523i \(0.0829062\pi\)
−0.966272 + 0.257523i \(0.917094\pi\)
\(728\) 0 0
\(729\) 4.96768i 0.183988i
\(730\) 0 0
\(731\) −3.78286 + 14.1178i −0.139914 + 0.522167i
\(732\) 0 0
\(733\) 2.86505 + 10.6925i 0.105823 + 0.394936i 0.998437 0.0558846i \(-0.0177979\pi\)
−0.892614 + 0.450821i \(0.851131\pi\)
\(734\) 0 0
\(735\) −20.1697 + 15.6341i −0.743970 + 0.576671i
\(736\) 0 0
\(737\) −6.11297 + 10.5880i −0.225174 + 0.390013i
\(738\) 0 0
\(739\) 10.7856 + 2.88999i 0.396754 + 0.106310i 0.451679 0.892181i \(-0.350825\pi\)
−0.0549249 + 0.998490i \(0.517492\pi\)
\(740\) 0 0
\(741\) −5.67325 5.67325i −0.208412 0.208412i
\(742\) 0 0
\(743\) 49.5292i 1.81705i 0.417832 + 0.908524i \(0.362790\pi\)
−0.417832 + 0.908524i \(0.637210\pi\)
\(744\) 0 0
\(745\) −9.01507 + 5.20485i −0.330287 + 0.190691i
\(746\) 0 0
\(747\) 9.49845 2.54510i 0.347530 0.0931204i
\(748\) 0 0
\(749\) −10.9198 + 7.33504i −0.398999 + 0.268017i
\(750\) 0 0
\(751\) −0.523146 + 0.906116i −0.0190899 + 0.0330646i −0.875413 0.483377i \(-0.839410\pi\)
0.856323 + 0.516441i \(0.172744\pi\)
\(752\) 0 0
\(753\) −10.0562 17.4178i −0.366467 0.634739i
\(754\) 0 0
\(755\) 39.7052 39.7052i 1.44502 1.44502i
\(756\) 0 0
\(757\) 29.5274 + 29.5274i 1.07319 + 1.07319i 0.997101 + 0.0760892i \(0.0242434\pi\)
0.0760892 + 0.997101i \(0.475757\pi\)
\(758\) 0 0
\(759\) 1.30077 0.750998i 0.0472148 0.0272595i
\(760\) 0 0
\(761\) 33.9144 + 19.5805i 1.22940 + 0.709793i 0.966904 0.255141i \(-0.0821220\pi\)
0.262493 + 0.964934i \(0.415455\pi\)
\(762\) 0 0
\(763\) 26.6886 1.81482i 0.966193 0.0657009i
\(764\) 0 0
\(765\) −4.64869 17.3492i −0.168074 0.627260i
\(766\) 0 0
\(767\) 2.07412 + 3.59249i 0.0748923 + 0.129717i
\(768\) 0 0
\(769\) 28.7025 1.03504 0.517519 0.855672i \(-0.326856\pi\)
0.517519 + 0.855672i \(0.326856\pi\)
\(770\) 0 0
\(771\) 6.69929 6.69929i 0.241269 0.241269i
\(772\) 0 0
\(773\) −3.90180 + 14.5617i −0.140338 + 0.523748i 0.859581 + 0.511000i \(0.170725\pi\)
−0.999919 + 0.0127485i \(0.995942\pi\)
\(774\) 0 0
\(775\) −73.3012 42.3205i −2.63306 1.52020i
\(776\) 0 0
\(777\) −0.528616 + 0.180884i −0.0189640 + 0.00648917i
\(778\) 0 0
\(779\) 1.62603 0.435693i 0.0582586 0.0156103i
\(780\) 0 0
\(781\) −13.4246 3.59710i −0.480369 0.128715i
\(782\) 0 0
\(783\) −1.16041 −0.0414697
\(784\) 0 0
\(785\) −15.2121 −0.542944
\(786\) 0 0
\(787\) 22.6434 + 6.06728i 0.807150 + 0.216275i 0.638721 0.769438i \(-0.279464\pi\)
0.168429 + 0.985714i \(0.446131\pi\)
\(788\) 0 0
\(789\) 13.5677 3.63546i 0.483024 0.129426i
\(790\) 0 0
\(791\) 13.0865 4.47800i 0.465303 0.159219i
\(792\) 0 0
\(793\) −19.7886 11.4249i −0.702713 0.405712i
\(794\) 0 0
\(795\) −9.46828 + 35.3361i −0.335805 + 1.25324i
\(796\) 0 0
\(797\) −3.81531 + 3.81531i −0.135145 + 0.135145i −0.771443 0.636298i \(-0.780465\pi\)
0.636298 + 0.771443i \(0.280465\pi\)
\(798\) 0 0
\(799\) −13.4727 −0.476631
\(800\) 0 0
\(801\) 7.40422 + 12.8245i 0.261615 + 0.453131i
\(802\) 0 0
\(803\) −2.99104 11.1627i −0.105551 0.393923i
\(804\) 0 0
\(805\) 15.9870 1.08711i 0.563467 0.0383156i
\(806\) 0 0
\(807\) 0.956619 + 0.552304i 0.0336746 + 0.0194420i
\(808\) 0 0
\(809\) −24.7881 + 14.3114i −0.871505 + 0.503164i −0.867848 0.496830i \(-0.834497\pi\)
−0.00365682 + 0.999993i \(0.501164\pi\)
\(810\) 0 0
\(811\) 9.30808 + 9.30808i 0.326851 + 0.326851i 0.851388 0.524537i \(-0.175762\pi\)
−0.524537 + 0.851388i \(0.675762\pi\)
\(812\) 0 0
\(813\) −12.2039 + 12.2039i −0.428008 + 0.428008i
\(814\) 0 0
\(815\) 23.8951 + 41.3875i 0.837009 + 1.44974i
\(816\) 0 0
\(817\) −14.9948 + 25.9718i −0.524603 + 0.908639i
\(818\) 0 0
\(819\) −12.1797 + 8.18134i −0.425592 + 0.285879i
\(820\) 0 0
\(821\) 16.1169 4.31850i 0.562482 0.150717i 0.0336357 0.999434i \(-0.489291\pi\)
0.528846 + 0.848718i \(0.322625\pi\)
\(822\) 0 0
\(823\) −9.41497 + 5.43573i −0.328185 + 0.189478i −0.655035 0.755598i \(-0.727346\pi\)
0.326850 + 0.945076i \(0.394013\pi\)
\(824\) 0 0
\(825\) 13.8133i 0.480918i
\(826\) 0 0
\(827\) 9.97483 + 9.97483i 0.346859 + 0.346859i 0.858938 0.512079i \(-0.171125\pi\)
−0.512079 + 0.858938i \(0.671125\pi\)
\(828\) 0 0
\(829\) −24.9645 6.68921i −0.867052 0.232326i −0.202240 0.979336i \(-0.564822\pi\)
−0.664813 + 0.747010i \(0.731489\pi\)
\(830\) 0 0
\(831\) −13.8312 + 23.9564i −0.479801 + 0.831039i
\(832\) 0 0
\(833\) −12.0779 4.93378i −0.418476 0.170945i
\(834\) 0 0
\(835\) 12.8998 + 48.1428i 0.446417 + 1.66605i
\(836\) 0 0
\(837\) −7.54985 + 28.1764i −0.260961 + 0.973920i
\(838\) 0 0
\(839\) 35.9931i 1.24262i 0.783565 + 0.621310i \(0.213399\pi\)
−0.783565 + 0.621310i \(0.786601\pi\)
\(840\) 0 0
\(841\) 28.9339i 0.997720i
\(842\) 0 0
\(843\) 3.02708 11.2972i 0.104258 0.389097i
\(844\) 0 0
\(845\) −7.71526 28.7937i −0.265413 0.990535i
\(846\) 0 0
\(847\) 24.6245 + 4.83554i 0.846107 + 0.166151i
\(848\) 0 0
\(849\) −8.05167 + 13.9459i −0.276333 + 0.478622i
\(850\) 0 0
\(851\) 0.338864 + 0.0907985i 0.0116161 + 0.00311253i
\(852\) 0 0
\(853\) −11.5045 11.5045i −0.393906 0.393906i 0.482171 0.876077i \(-0.339848\pi\)
−0.876077 + 0.482171i \(0.839848\pi\)
\(854\) 0 0
\(855\) 36.8538i 1.26037i
\(856\) 0 0
\(857\) −46.8795 + 27.0659i −1.60137 + 0.924554i −0.610161 + 0.792277i \(0.708895\pi\)
−0.991213 + 0.132276i \(0.957771\pi\)
\(858\) 0 0
\(859\) −6.87557 + 1.84230i −0.234591 + 0.0628586i −0.374199 0.927348i \(-0.622082\pi\)
0.139608 + 0.990207i \(0.455416\pi\)
\(860\) 0 0
\(861\) 0.0677157 + 0.995822i 0.00230775 + 0.0339375i
\(862\) 0 0
\(863\) 8.29596 14.3690i 0.282398 0.489127i −0.689577 0.724212i \(-0.742204\pi\)
0.971975 + 0.235085i \(0.0755369\pi\)
\(864\) 0 0
\(865\) 23.2898 + 40.3391i 0.791877 + 1.37157i
\(866\) 0 0
\(867\) 8.19713 8.19713i 0.278389 0.278389i
\(868\) 0 0
\(869\) −11.3661 11.3661i −0.385567 0.385567i
\(870\) 0 0
\(871\) 21.0566 12.1570i 0.713475 0.411925i
\(872\) 0 0
\(873\) −3.34336 1.93029i −0.113156 0.0653305i
\(874\) 0 0
\(875\) −40.0901 + 81.7984i −1.35529 + 2.76529i
\(876\) 0 0
\(877\) 7.85634 + 29.3202i 0.265290 + 0.990074i 0.962073 + 0.272793i \(0.0879473\pi\)
−0.696783 + 0.717282i \(0.745386\pi\)
\(878\) 0 0
\(879\) −1.32981 2.30330i −0.0448534 0.0776883i
\(880\) 0 0
\(881\) −48.7213 −1.64146 −0.820731 0.571314i \(-0.806434\pi\)
−0.820731 + 0.571314i \(0.806434\pi\)
\(882\) 0 0
\(883\) 2.32744 2.32744i 0.0783247 0.0783247i −0.666859 0.745184i \(-0.732362\pi\)
0.745184 + 0.666859i \(0.232362\pi\)
\(884\) 0 0
\(885\) 1.59898 5.96746i 0.0537490 0.200594i
\(886\) 0 0
\(887\) 45.9577 + 26.5337i 1.54311 + 0.890914i 0.998640 + 0.0521315i \(0.0166015\pi\)
0.544467 + 0.838782i \(0.316732\pi\)
\(888\) 0 0
\(889\) 3.01549 1.03185i 0.101136 0.0346072i
\(890\) 0 0
\(891\) −3.48219 + 0.933049i −0.116658 + 0.0312583i
\(892\) 0 0
\(893\) −26.7022 7.15483i −0.893555 0.239427i
\(894\) 0 0
\(895\) 71.1052 2.37678
\(896\) 0 0
\(897\) −2.98706 −0.0997350
\(898\) 0 0
\(899\) −1.60552 0.430199i −0.0535472 0.0143479i
\(900\) 0 0
\(901\) −18.0656 + 4.84066i −0.601852 + 0.161266i
\(902\) 0 0
\(903\) −13.3975 11.6915i −0.445842 0.389069i
\(904\) 0 0
\(905\) −83.2470 48.0627i −2.76723 1.59766i
\(906\) 0 0
\(907\) 14.4466 53.9154i 0.479691 1.79023i −0.123172 0.992385i \(-0.539307\pi\)
0.602863 0.797845i \(-0.294027\pi\)
\(908\) 0 0
\(909\) 3.91688 3.91688i 0.129915 0.129915i
\(910\) 0 0
\(911\) 44.7554 1.48281 0.741406 0.671057i \(-0.234159\pi\)
0.741406 + 0.671057i \(0.234159\pi\)
\(912\) 0 0
\(913\) −2.67138 4.62696i −0.0884097 0.153130i
\(914\) 0 0
\(915\) 8.80768 + 32.8707i 0.291173 + 1.08667i
\(916\) 0 0
\(917\) −4.61423 6.86925i −0.152375 0.226843i
\(918\) 0 0
\(919\) −19.8098 11.4372i −0.653464 0.377277i 0.136318 0.990665i \(-0.456473\pi\)
−0.789782 + 0.613388i \(0.789806\pi\)
\(920\) 0 0
\(921\) −8.69148 + 5.01803i −0.286394 + 0.165350i
\(922\) 0 0
\(923\) 19.5442 + 19.5442i 0.643304 + 0.643304i
\(924\) 0 0
\(925\) −2.28137 + 2.28137i −0.0750111 + 0.0750111i
\(926\) 0 0
\(927\) 16.5233 + 28.6192i 0.542697 + 0.939979i
\(928\) 0 0
\(929\) 13.2871 23.0139i 0.435935 0.755062i −0.561436 0.827520i \(-0.689751\pi\)
0.997371 + 0.0724577i \(0.0230842\pi\)
\(930\) 0 0
\(931\) −21.3177 16.1926i −0.698658 0.530690i
\(932\) 0 0
\(933\) 7.04026 1.88643i 0.230488 0.0617590i
\(934\) 0 0
\(935\) −8.45127 + 4.87934i −0.276386 + 0.159572i
\(936\) 0 0
\(937\) 11.8582i 0.387391i −0.981062 0.193696i \(-0.937953\pi\)
0.981062 0.193696i \(-0.0620474\pi\)
\(938\) 0 0
\(939\) −9.86686 9.86686i −0.321993 0.321993i
\(940\) 0 0
\(941\) 2.04535 + 0.548049i 0.0666764 + 0.0178659i 0.292003 0.956417i \(-0.405678\pi\)
−0.225327 + 0.974283i \(0.572345\pi\)
\(942\) 0 0
\(943\) 0.313366 0.542765i 0.0102046 0.0176749i
\(944\) 0 0
\(945\) 49.8360 + 9.78636i 1.62116 + 0.318350i
\(946\) 0 0
\(947\) 1.38876 + 5.18291i 0.0451285 + 0.168422i 0.984812 0.173623i \(-0.0555473\pi\)
−0.939684 + 0.342045i \(0.888881\pi\)
\(948\) 0 0
\(949\) −5.94835 + 22.1995i −0.193092 + 0.720628i
\(950\) 0 0
\(951\) 19.3935i 0.628878i
\(952\) 0 0
\(953\) 3.43130i 0.111151i 0.998454 + 0.0555753i \(0.0176993\pi\)
−0.998454 + 0.0555753i \(0.982301\pi\)
\(954\) 0 0
\(955\) 10.9646 40.9205i 0.354806 1.32415i
\(956\) 0 0
\(957\) 0.0702080 + 0.262020i 0.00226950 + 0.00846989i
\(958\) 0 0
\(959\) 0.575210 0.659145i 0.0185745 0.0212849i
\(960\) 0 0
\(961\) −5.39169 + 9.33869i −0.173926 + 0.301248i
\(962\) 0 0
\(963\) 10.8801 + 2.91531i 0.350606 + 0.0939446i
\(964\) 0 0
\(965\) 24.2018 + 24.2018i 0.779083 + 0.779083i
\(966\) 0 0
\(967\) 19.4110i 0.624217i −0.950046 0.312108i \(-0.898965\pi\)
0.950046 0.312108i \(-0.101035\pi\)
\(968\) 0 0
\(969\) −5.29044 + 3.05444i −0.169954 + 0.0981227i
\(970\) 0 0
\(971\) 19.4567 5.21341i 0.624396 0.167306i 0.0672705 0.997735i \(-0.478571\pi\)
0.557125 + 0.830428i \(0.311904\pi\)
\(972\) 0 0
\(973\) −8.10708 3.97335i −0.259901 0.127380i
\(974\) 0 0
\(975\) 13.7354 23.7905i 0.439886 0.761905i
\(976\) 0 0
\(977\) −8.78731 15.2201i −0.281131 0.486933i 0.690533 0.723301i \(-0.257376\pi\)
−0.971664 + 0.236368i \(0.924043\pi\)
\(978\) 0 0
\(979\) 5.68920 5.68920i 0.181828 0.181828i
\(980\) 0 0
\(981\) −16.1966 16.1966i −0.517117 0.517117i
\(982\) 0 0
\(983\) −47.7497 + 27.5683i −1.52298 + 0.879292i −0.523347 + 0.852119i \(0.675317\pi\)
−0.999631 + 0.0271723i \(0.991350\pi\)
\(984\) 0 0
\(985\) 31.3600 + 18.1057i 0.999214 + 0.576896i
\(986\) 0 0
\(987\) 7.21352 14.7182i 0.229609 0.468486i
\(988\) 0 0
\(989\) 2.88978 + 10.7848i 0.0918896 + 0.342937i
\(990\) 0 0
\(991\) −18.4719 31.9943i −0.586781 1.01633i −0.994651 0.103294i \(-0.967062\pi\)
0.407870 0.913040i \(-0.366272\pi\)
\(992\) 0 0
\(993\) 9.96536 0.316241
\(994\) 0 0
\(995\) 44.3910 44.3910i 1.40729 1.40729i
\(996\) 0 0
\(997\) 0.959891 3.58236i 0.0304001 0.113455i −0.949059 0.315100i \(-0.897962\pi\)
0.979459 + 0.201645i \(0.0646287\pi\)
\(998\) 0 0
\(999\) 0.962950 + 0.555960i 0.0304664 + 0.0175898i
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 896.2.ba.e.737.7 48
4.3 odd 2 896.2.ba.f.737.6 48
7.4 even 3 inner 896.2.ba.e.865.6 48
8.3 odd 2 112.2.w.c.37.7 48
8.5 even 2 448.2.ba.c.177.6 48
16.3 odd 4 896.2.ba.f.289.7 48
16.5 even 4 448.2.ba.c.401.7 48
16.11 odd 4 112.2.w.c.93.2 yes 48
16.13 even 4 inner 896.2.ba.e.289.6 48
28.11 odd 6 896.2.ba.f.865.7 48
56.3 even 6 784.2.x.o.165.2 48
56.11 odd 6 112.2.w.c.53.2 yes 48
56.19 even 6 784.2.m.k.197.9 24
56.27 even 2 784.2.x.o.373.7 48
56.51 odd 6 784.2.m.j.197.9 24
56.53 even 6 448.2.ba.c.305.7 48
112.11 odd 12 112.2.w.c.109.7 yes 48
112.27 even 4 784.2.x.o.765.2 48
112.53 even 12 448.2.ba.c.81.6 48
112.59 even 12 784.2.x.o.557.7 48
112.67 odd 12 896.2.ba.f.417.6 48
112.75 even 12 784.2.m.k.589.9 24
112.107 odd 12 784.2.m.j.589.9 24
112.109 even 12 inner 896.2.ba.e.417.7 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.w.c.37.7 48 8.3 odd 2
112.2.w.c.53.2 yes 48 56.11 odd 6
112.2.w.c.93.2 yes 48 16.11 odd 4
112.2.w.c.109.7 yes 48 112.11 odd 12
448.2.ba.c.81.6 48 112.53 even 12
448.2.ba.c.177.6 48 8.5 even 2
448.2.ba.c.305.7 48 56.53 even 6
448.2.ba.c.401.7 48 16.5 even 4
784.2.m.j.197.9 24 56.51 odd 6
784.2.m.j.589.9 24 112.107 odd 12
784.2.m.k.197.9 24 56.19 even 6
784.2.m.k.589.9 24 112.75 even 12
784.2.x.o.165.2 48 56.3 even 6
784.2.x.o.373.7 48 56.27 even 2
784.2.x.o.557.7 48 112.59 even 12
784.2.x.o.765.2 48 112.27 even 4
896.2.ba.e.289.6 48 16.13 even 4 inner
896.2.ba.e.417.7 48 112.109 even 12 inner
896.2.ba.e.737.7 48 1.1 even 1 trivial
896.2.ba.e.865.6 48 7.4 even 3 inner
896.2.ba.f.289.7 48 16.3 odd 4
896.2.ba.f.417.6 48 112.67 odd 12
896.2.ba.f.737.6 48 4.3 odd 2
896.2.ba.f.865.7 48 28.11 odd 6