Properties

Label 150.3.b.b.149.5
Level $150$
Weight $3$
Character 150.149
Analytic conductor $4.087$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [150,3,Mod(149,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.149");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 150.b (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.08720396540\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.40960000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 7x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 30)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 149.5
Root \(-1.14412 - 1.14412i\) of defining polynomial
Character \(\chi\) \(=\) 150.149
Dual form 150.3.b.b.149.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.41421 q^{2} +(-2.94317 - 0.581139i) q^{3} +2.00000 q^{4} +(-4.16228 - 0.821854i) q^{6} -11.4868i q^{7} +2.82843 q^{8} +(8.32456 + 3.42079i) q^{9} +O(q^{10})\) \(q+1.41421 q^{2} +(-2.94317 - 0.581139i) q^{3} +2.00000 q^{4} +(-4.16228 - 0.821854i) q^{6} -11.4868i q^{7} +2.82843 q^{8} +(8.32456 + 3.42079i) q^{9} -8.48528i q^{11} +(-5.88635 - 1.16228i) q^{12} -10.0000i q^{13} -16.2448i q^{14} +4.00000 q^{16} +3.55415 q^{17} +(11.7727 + 4.83772i) q^{18} +10.9737 q^{19} +(-6.67544 + 33.8078i) q^{21} -12.0000i q^{22} -17.6590 q^{23} +(-8.32456 - 1.64371i) q^{24} -14.1421i q^{26} +(-22.5127 - 14.9057i) q^{27} -22.9737i q^{28} +26.8328i q^{29} +8.00000 q^{31} +5.65685 q^{32} +(-4.93113 + 24.9737i) q^{33} +5.02633 q^{34} +(16.6491 + 6.84157i) q^{36} +59.9473i q^{37} +15.5191 q^{38} +(-5.81139 + 29.4317i) q^{39} -20.5247i q^{41} +(-9.44050 + 47.8114i) q^{42} +42.4605i q^{43} -16.9706i q^{44} -24.9737 q^{46} +88.2952 q^{47} +(-11.7727 - 2.32456i) q^{48} -82.9473 q^{49} +(-10.4605 - 2.06546i) q^{51} -20.0000i q^{52} -3.55415 q^{53} +(-31.8377 - 21.0798i) q^{54} -32.4897i q^{56} +(-32.2974 - 6.37722i) q^{57} +37.9473i q^{58} -77.7445i q^{59} +21.9473 q^{61} +11.3137 q^{62} +(39.2940 - 95.6228i) q^{63} +8.00000 q^{64} +(-6.97367 + 35.3181i) q^{66} +53.5395i q^{67} +7.10831 q^{68} +(51.9737 + 10.2624i) q^{69} -69.2592i q^{71} +(23.5454 + 9.67544i) q^{72} +12.0527i q^{73} +84.7783i q^{74} +21.9473 q^{76} -97.4690 q^{77} +(-8.21854 + 41.6228i) q^{78} +9.02633 q^{79} +(57.5964 + 56.9530i) q^{81} -29.0263i q^{82} -0.688486 q^{83} +(-13.3509 + 67.6155i) q^{84} +60.0482i q^{86} +(15.5936 - 78.9737i) q^{87} -24.0000i q^{88} +7.10831i q^{89} -114.868 q^{91} -35.3181 q^{92} +(-23.5454 - 4.64911i) q^{93} +124.868 q^{94} +(-16.6491 - 3.28742i) q^{96} -111.947i q^{97} -117.305 q^{98} +(29.0263 - 70.6362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 16 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 16 q^{4} - 8 q^{6} + 16 q^{9} + 32 q^{16} - 64 q^{19} - 104 q^{21} - 16 q^{24} + 64 q^{31} + 192 q^{34} + 32 q^{36} + 80 q^{39} - 48 q^{46} - 360 q^{49} + 144 q^{51} - 280 q^{54} - 128 q^{61} + 64 q^{64} + 96 q^{66} + 264 q^{69} - 128 q^{76} + 224 q^{79} + 56 q^{81} - 208 q^{84} - 160 q^{91} + 240 q^{94} - 32 q^{96} + 384 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 0.707107
\(3\) −2.94317 0.581139i −0.981058 0.193713i
\(4\) 2.00000 0.500000
\(5\) 0 0
\(6\) −4.16228 0.821854i −0.693713 0.136976i
\(7\) 11.4868i 1.64098i −0.571664 0.820488i \(-0.693702\pi\)
0.571664 0.820488i \(-0.306298\pi\)
\(8\) 2.82843 0.353553
\(9\) 8.32456 + 3.42079i 0.924951 + 0.380087i
\(10\) 0 0
\(11\) 8.48528i 0.771389i −0.922627 0.385695i \(-0.873962\pi\)
0.922627 0.385695i \(-0.126038\pi\)
\(12\) −5.88635 1.16228i −0.490529 0.0968565i
\(13\) 10.0000i 0.769231i −0.923077 0.384615i \(-0.874334\pi\)
0.923077 0.384615i \(-0.125666\pi\)
\(14\) 16.2448i 1.16035i
\(15\) 0 0
\(16\) 4.00000 0.250000
\(17\) 3.55415 0.209068 0.104534 0.994521i \(-0.466665\pi\)
0.104534 + 0.994521i \(0.466665\pi\)
\(18\) 11.7727 + 4.83772i 0.654039 + 0.268762i
\(19\) 10.9737 0.577561 0.288781 0.957395i \(-0.406750\pi\)
0.288781 + 0.957395i \(0.406750\pi\)
\(20\) 0 0
\(21\) −6.67544 + 33.8078i −0.317878 + 1.60989i
\(22\) 12.0000i 0.545455i
\(23\) −17.6590 −0.767785 −0.383892 0.923378i \(-0.625417\pi\)
−0.383892 + 0.923378i \(0.625417\pi\)
\(24\) −8.32456 1.64371i −0.346856 0.0684879i
\(25\) 0 0
\(26\) 14.1421i 0.543928i
\(27\) −22.5127 14.9057i −0.833803 0.552063i
\(28\) 22.9737i 0.820488i
\(29\) 26.8328i 0.925270i 0.886549 + 0.462635i \(0.153096\pi\)
−0.886549 + 0.462635i \(0.846904\pi\)
\(30\) 0 0
\(31\) 8.00000 0.258065 0.129032 0.991640i \(-0.458813\pi\)
0.129032 + 0.991640i \(0.458813\pi\)
\(32\) 5.65685 0.176777
\(33\) −4.93113 + 24.9737i −0.149428 + 0.756778i
\(34\) 5.02633 0.147833
\(35\) 0 0
\(36\) 16.6491 + 6.84157i 0.462475 + 0.190044i
\(37\) 59.9473i 1.62020i 0.586293 + 0.810099i \(0.300587\pi\)
−0.586293 + 0.810099i \(0.699413\pi\)
\(38\) 15.5191 0.408398
\(39\) −5.81139 + 29.4317i −0.149010 + 0.754660i
\(40\) 0 0
\(41\) 20.5247i 0.500603i −0.968168 0.250301i \(-0.919470\pi\)
0.968168 0.250301i \(-0.0805297\pi\)
\(42\) −9.44050 + 47.8114i −0.224774 + 1.13837i
\(43\) 42.4605i 0.987453i 0.869617 + 0.493727i \(0.164366\pi\)
−0.869617 + 0.493727i \(0.835634\pi\)
\(44\) 16.9706i 0.385695i
\(45\) 0 0
\(46\) −24.9737 −0.542906
\(47\) 88.2952 1.87862 0.939311 0.343067i \(-0.111466\pi\)
0.939311 + 0.343067i \(0.111466\pi\)
\(48\) −11.7727 2.32456i −0.245265 0.0484282i
\(49\) −82.9473 −1.69280
\(50\) 0 0
\(51\) −10.4605 2.06546i −0.205108 0.0404992i
\(52\) 20.0000i 0.384615i
\(53\) −3.55415 −0.0670595 −0.0335298 0.999438i \(-0.510675\pi\)
−0.0335298 + 0.999438i \(0.510675\pi\)
\(54\) −31.8377 21.0798i −0.589587 0.390367i
\(55\) 0 0
\(56\) 32.4897i 0.580173i
\(57\) −32.2974 6.37722i −0.566621 0.111881i
\(58\) 37.9473i 0.654264i
\(59\) 77.7445i 1.31770i −0.752273 0.658852i \(-0.771042\pi\)
0.752273 0.658852i \(-0.228958\pi\)
\(60\) 0 0
\(61\) 21.9473 0.359792 0.179896 0.983686i \(-0.442424\pi\)
0.179896 + 0.983686i \(0.442424\pi\)
\(62\) 11.3137 0.182479
\(63\) 39.2940 95.6228i 0.623714 1.51782i
\(64\) 8.00000 0.125000
\(65\) 0 0
\(66\) −6.97367 + 35.3181i −0.105662 + 0.535123i
\(67\) 53.5395i 0.799097i 0.916712 + 0.399549i \(0.130833\pi\)
−0.916712 + 0.399549i \(0.869167\pi\)
\(68\) 7.10831 0.104534
\(69\) 51.9737 + 10.2624i 0.753242 + 0.148730i
\(70\) 0 0
\(71\) 69.2592i 0.975482i −0.872988 0.487741i \(-0.837821\pi\)
0.872988 0.487741i \(-0.162179\pi\)
\(72\) 23.5454 + 9.67544i 0.327019 + 0.134381i
\(73\) 12.0527i 0.165105i 0.996587 + 0.0825525i \(0.0263072\pi\)
−0.996587 + 0.0825525i \(0.973693\pi\)
\(74\) 84.7783i 1.14565i
\(75\) 0 0
\(76\) 21.9473 0.288781
\(77\) −97.4690 −1.26583
\(78\) −8.21854 + 41.6228i −0.105366 + 0.533625i
\(79\) 9.02633 0.114257 0.0571287 0.998367i \(-0.481805\pi\)
0.0571287 + 0.998367i \(0.481805\pi\)
\(80\) 0 0
\(81\) 57.5964 + 56.9530i 0.711067 + 0.703124i
\(82\) 29.0263i 0.353980i
\(83\) −0.688486 −0.00829501 −0.00414750 0.999991i \(-0.501320\pi\)
−0.00414750 + 0.999991i \(0.501320\pi\)
\(84\) −13.3509 + 67.6155i −0.158939 + 0.804947i
\(85\) 0 0
\(86\) 60.0482i 0.698235i
\(87\) 15.5936 78.9737i 0.179237 0.907743i
\(88\) 24.0000i 0.272727i
\(89\) 7.10831i 0.0798686i 0.999202 + 0.0399343i \(0.0127149\pi\)
−0.999202 + 0.0399343i \(0.987285\pi\)
\(90\) 0 0
\(91\) −114.868 −1.26229
\(92\) −35.3181 −0.383892
\(93\) −23.5454 4.64911i −0.253176 0.0499904i
\(94\) 124.868 1.32839
\(95\) 0 0
\(96\) −16.6491 3.28742i −0.173428 0.0342439i
\(97\) 111.947i 1.15410i −0.816710 0.577048i \(-0.804205\pi\)
0.816710 0.577048i \(-0.195795\pi\)
\(98\) −117.305 −1.19699
\(99\) 29.0263 70.6362i 0.293195 0.713497i
\(100\) 0 0
\(101\) 155.489i 1.53950i 0.638348 + 0.769748i \(0.279618\pi\)
−0.638348 + 0.769748i \(0.720382\pi\)
\(102\) −14.7934 2.92100i −0.145033 0.0286372i
\(103\) 7.59217i 0.0737104i 0.999321 + 0.0368552i \(0.0117340\pi\)
−0.999321 + 0.0368552i \(0.988266\pi\)
\(104\) 28.2843i 0.271964i
\(105\) 0 0
\(106\) −5.02633 −0.0474182
\(107\) 16.2821 0.152169 0.0760845 0.997101i \(-0.475758\pi\)
0.0760845 + 0.997101i \(0.475758\pi\)
\(108\) −45.0253 29.8114i −0.416901 0.276031i
\(109\) 93.8420 0.860936 0.430468 0.902606i \(-0.358349\pi\)
0.430468 + 0.902606i \(0.358349\pi\)
\(110\) 0 0
\(111\) 34.8377 176.435i 0.313853 1.58951i
\(112\) 45.9473i 0.410244i
\(113\) 195.738 1.73220 0.866098 0.499874i \(-0.166620\pi\)
0.866098 + 0.499874i \(0.166620\pi\)
\(114\) −45.6754 9.01876i −0.400662 0.0791119i
\(115\) 0 0
\(116\) 53.6656i 0.462635i
\(117\) 34.2079 83.2456i 0.292375 0.711500i
\(118\) 109.947i 0.931757i
\(119\) 40.8260i 0.343075i
\(120\) 0 0
\(121\) 49.0000 0.404959
\(122\) 31.0382 0.254412
\(123\) −11.9277 + 60.4078i −0.0969733 + 0.491121i
\(124\) 16.0000 0.129032
\(125\) 0 0
\(126\) 55.5701 135.231i 0.441033 1.07326i
\(127\) 77.5395i 0.610547i 0.952265 + 0.305274i \(0.0987479\pi\)
−0.952265 + 0.305274i \(0.901252\pi\)
\(128\) 11.3137 0.0883883
\(129\) 24.6754 124.969i 0.191283 0.968749i
\(130\) 0 0
\(131\) 101.600i 0.775572i −0.921749 0.387786i \(-0.873240\pi\)
0.921749 0.387786i \(-0.126760\pi\)
\(132\) −9.86225 + 49.9473i −0.0747140 + 0.378389i
\(133\) 126.053i 0.947764i
\(134\) 75.7163i 0.565047i
\(135\) 0 0
\(136\) 10.0527 0.0739167
\(137\) −176.014 −1.28477 −0.642386 0.766381i \(-0.722055\pi\)
−0.642386 + 0.766381i \(0.722055\pi\)
\(138\) 73.5019 + 14.5132i 0.532622 + 0.105168i
\(139\) −188.816 −1.35839 −0.679193 0.733960i \(-0.737670\pi\)
−0.679193 + 0.733960i \(0.737670\pi\)
\(140\) 0 0
\(141\) −259.868 51.3118i −1.84304 0.363913i
\(142\) 97.9473i 0.689770i
\(143\) −84.8528 −0.593376
\(144\) 33.2982 + 13.6831i 0.231238 + 0.0950218i
\(145\) 0 0
\(146\) 17.0450i 0.116747i
\(147\) 244.128 + 48.2039i 1.66074 + 0.327918i
\(148\) 119.895i 0.810099i
\(149\) 72.5899i 0.487181i 0.969878 + 0.243590i \(0.0783252\pi\)
−0.969878 + 0.243590i \(0.921675\pi\)
\(150\) 0 0
\(151\) 93.9473 0.622168 0.311084 0.950382i \(-0.399308\pi\)
0.311084 + 0.950382i \(0.399308\pi\)
\(152\) 31.0382 0.204199
\(153\) 29.5868 + 12.1580i 0.193378 + 0.0794641i
\(154\) −137.842 −0.895078
\(155\) 0 0
\(156\) −11.6228 + 58.8635i −0.0745050 + 0.377330i
\(157\) 123.842i 0.788803i 0.918938 + 0.394401i \(0.129048\pi\)
−0.918938 + 0.394401i \(0.870952\pi\)
\(158\) 12.7652 0.0807922
\(159\) 10.4605 + 2.06546i 0.0657893 + 0.0129903i
\(160\) 0 0
\(161\) 202.847i 1.25992i
\(162\) 81.4537 + 80.5438i 0.502800 + 0.497184i
\(163\) 159.381i 0.977801i 0.872340 + 0.488900i \(0.162602\pi\)
−0.872340 + 0.488900i \(0.837398\pi\)
\(164\) 41.0494i 0.250301i
\(165\) 0 0
\(166\) −0.973666 −0.00586546
\(167\) −10.7742 −0.0645161 −0.0322581 0.999480i \(-0.510270\pi\)
−0.0322581 + 0.999480i \(0.510270\pi\)
\(168\) −18.8810 + 95.6228i −0.112387 + 0.569183i
\(169\) 69.0000 0.408284
\(170\) 0 0
\(171\) 91.3509 + 37.5386i 0.534216 + 0.219524i
\(172\) 84.9210i 0.493727i
\(173\) −283.345 −1.63783 −0.818916 0.573913i \(-0.805425\pi\)
−0.818916 + 0.573913i \(0.805425\pi\)
\(174\) 22.0527 111.686i 0.126739 0.641871i
\(175\) 0 0
\(176\) 33.9411i 0.192847i
\(177\) −45.1804 + 228.816i −0.255256 + 1.29274i
\(178\) 10.0527i 0.0564757i
\(179\) 306.624i 1.71298i 0.516163 + 0.856491i \(0.327360\pi\)
−0.516163 + 0.856491i \(0.672640\pi\)
\(180\) 0 0
\(181\) 265.684 1.46787 0.733934 0.679221i \(-0.237682\pi\)
0.733934 + 0.679221i \(0.237682\pi\)
\(182\) −162.448 −0.892573
\(183\) −64.5948 12.7544i −0.352977 0.0696964i
\(184\) −49.9473 −0.271453
\(185\) 0 0
\(186\) −33.2982 6.57484i −0.179023 0.0353486i
\(187\) 30.1580i 0.161273i
\(188\) 176.590 0.939311
\(189\) −171.219 + 258.599i −0.905922 + 1.36825i
\(190\) 0 0
\(191\) 159.620i 0.835706i 0.908515 + 0.417853i \(0.137217\pi\)
−0.908515 + 0.417853i \(0.862783\pi\)
\(192\) −23.5454 4.64911i −0.122632 0.0242141i
\(193\) 92.0527i 0.476957i −0.971148 0.238478i \(-0.923351\pi\)
0.971148 0.238478i \(-0.0766486\pi\)
\(194\) 158.317i 0.816069i
\(195\) 0 0
\(196\) −165.895 −0.846401
\(197\) 69.8360 0.354497 0.177249 0.984166i \(-0.443280\pi\)
0.177249 + 0.984166i \(0.443280\pi\)
\(198\) 41.0494 99.8947i 0.207320 0.504519i
\(199\) −148.921 −0.748347 −0.374173 0.927359i \(-0.622074\pi\)
−0.374173 + 0.927359i \(0.622074\pi\)
\(200\) 0 0
\(201\) 31.1139 157.576i 0.154795 0.783961i
\(202\) 219.895i 1.08859i
\(203\) 308.224 1.51835
\(204\) −20.9210 4.13091i −0.102554 0.0202496i
\(205\) 0 0
\(206\) 10.7369i 0.0521211i
\(207\) −147.004 60.4078i −0.710163 0.291825i
\(208\) 40.0000i 0.192308i
\(209\) 93.1146i 0.445525i
\(210\) 0 0
\(211\) −285.842 −1.35470 −0.677351 0.735660i \(-0.736872\pi\)
−0.677351 + 0.735660i \(0.736872\pi\)
\(212\) −7.10831 −0.0335298
\(213\) −40.2492 + 203.842i −0.188963 + 0.957005i
\(214\) 23.0263 0.107600
\(215\) 0 0
\(216\) −63.6754 42.1597i −0.294794 0.195184i
\(217\) 91.8947i 0.423478i
\(218\) 132.713 0.608774
\(219\) 7.00427 35.4731i 0.0319830 0.161978i
\(220\) 0 0
\(221\) 35.5415i 0.160821i
\(222\) 49.2680 249.517i 0.221928 1.12395i
\(223\) 71.3815i 0.320096i −0.987109 0.160048i \(-0.948835\pi\)
0.987109 0.160048i \(-0.0511650\pi\)
\(224\) 64.9793i 0.290086i
\(225\) 0 0
\(226\) 276.816 1.22485
\(227\) 29.1217 0.128290 0.0641448 0.997941i \(-0.479568\pi\)
0.0641448 + 0.997941i \(0.479568\pi\)
\(228\) −64.5948 12.7544i −0.283311 0.0559406i
\(229\) 129.684 0.566306 0.283153 0.959075i \(-0.408620\pi\)
0.283153 + 0.959075i \(0.408620\pi\)
\(230\) 0 0
\(231\) 286.868 + 56.6430i 1.24185 + 0.245208i
\(232\) 75.8947i 0.327132i
\(233\) −185.876 −0.797751 −0.398875 0.917005i \(-0.630599\pi\)
−0.398875 + 0.917005i \(0.630599\pi\)
\(234\) 48.3772 117.727i 0.206740 0.503107i
\(235\) 0 0
\(236\) 155.489i 0.658852i
\(237\) −26.5661 5.24555i −0.112093 0.0221331i
\(238\) 57.7367i 0.242591i
\(239\) 302.716i 1.26659i −0.773908 0.633297i \(-0.781701\pi\)
0.773908 0.633297i \(-0.218299\pi\)
\(240\) 0 0
\(241\) −237.526 −0.985585 −0.492793 0.870147i \(-0.664024\pi\)
−0.492793 + 0.870147i \(0.664024\pi\)
\(242\) 69.2965 0.286349
\(243\) −136.419 201.094i −0.561394 0.827549i
\(244\) 43.8947 0.179896
\(245\) 0 0
\(246\) −16.8683 + 85.4296i −0.0685704 + 0.347275i
\(247\) 109.737i 0.444278i
\(248\) 22.6274 0.0912396
\(249\) 2.02633 + 0.400106i 0.00813789 + 0.00160685i
\(250\) 0 0
\(251\) 84.6294i 0.337169i −0.985687 0.168584i \(-0.946080\pi\)
0.985687 0.168584i \(-0.0539196\pi\)
\(252\) 78.5880 191.246i 0.311857 0.758911i
\(253\) 149.842i 0.592261i
\(254\) 109.657i 0.431722i
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 292.054 1.13640 0.568198 0.822892i \(-0.307641\pi\)
0.568198 + 0.822892i \(0.307641\pi\)
\(258\) 34.8963 176.732i 0.135257 0.685009i
\(259\) 688.605 2.65871
\(260\) 0 0
\(261\) −91.7893 + 223.371i −0.351683 + 0.855829i
\(262\) 143.684i 0.548412i
\(263\) −277.725 −1.05599 −0.527995 0.849247i \(-0.677056\pi\)
−0.527995 + 0.849247i \(0.677056\pi\)
\(264\) −13.9473 + 70.6362i −0.0528308 + 0.267561i
\(265\) 0 0
\(266\) 178.265i 0.670171i
\(267\) 4.13091 20.9210i 0.0154716 0.0783558i
\(268\) 107.079i 0.399549i
\(269\) 286.546i 1.06523i 0.846359 + 0.532613i \(0.178790\pi\)
−0.846359 + 0.532613i \(0.821210\pi\)
\(270\) 0 0
\(271\) −324.105 −1.19596 −0.597980 0.801511i \(-0.704030\pi\)
−0.597980 + 0.801511i \(0.704030\pi\)
\(272\) 14.2166 0.0522670
\(273\) 338.078 + 66.7544i 1.23838 + 0.244522i
\(274\) −248.921 −0.908471
\(275\) 0 0
\(276\) 103.947 + 20.5247i 0.376621 + 0.0743649i
\(277\) 415.842i 1.50123i −0.660737 0.750617i \(-0.729756\pi\)
0.660737 0.750617i \(-0.270244\pi\)
\(278\) −267.026 −0.960524
\(279\) 66.5964 + 27.3663i 0.238697 + 0.0980871i
\(280\) 0 0
\(281\) 431.726i 1.53639i −0.640216 0.768195i \(-0.721155\pi\)
0.640216 0.768195i \(-0.278845\pi\)
\(282\) −367.509 72.5658i −1.30322 0.257326i
\(283\) 141.540i 0.500140i 0.968228 + 0.250070i \(0.0804536\pi\)
−0.968228 + 0.250070i \(0.919546\pi\)
\(284\) 138.518i 0.487741i
\(285\) 0 0
\(286\) −120.000 −0.419580
\(287\) −235.764 −0.821477
\(288\) 47.0908 + 19.3509i 0.163510 + 0.0671906i
\(289\) −276.368 −0.956291
\(290\) 0 0
\(291\) −65.0569 + 329.481i −0.223563 + 1.13224i
\(292\) 24.1053i 0.0825525i
\(293\) 164.998 0.563133 0.281566 0.959542i \(-0.409146\pi\)
0.281566 + 0.959542i \(0.409146\pi\)
\(294\) 345.250 + 68.1706i 1.17432 + 0.231873i
\(295\) 0 0
\(296\) 169.557i 0.572827i
\(297\) −126.479 + 191.026i −0.425855 + 0.643186i
\(298\) 102.658i 0.344489i
\(299\) 176.590i 0.590604i
\(300\) 0 0
\(301\) 487.737 1.62039
\(302\) 132.862 0.439939
\(303\) 90.3607 457.631i 0.298220 1.51033i
\(304\) 43.8947 0.144390
\(305\) 0 0
\(306\) 41.8420 + 17.1940i 0.136739 + 0.0561896i
\(307\) 159.381i 0.519158i −0.965722 0.259579i \(-0.916416\pi\)
0.965722 0.259579i \(-0.0835838\pi\)
\(308\) −194.938 −0.632916
\(309\) 4.41210 22.3451i 0.0142787 0.0723142i
\(310\) 0 0
\(311\) 143.096i 0.460117i −0.973177 0.230058i \(-0.926108\pi\)
0.973177 0.230058i \(-0.0738917\pi\)
\(312\) −16.4371 + 83.2456i −0.0526830 + 0.266813i
\(313\) 501.684i 1.60282i −0.598113 0.801412i \(-0.704082\pi\)
0.598113 0.801412i \(-0.295918\pi\)
\(314\) 175.139i 0.557768i
\(315\) 0 0
\(316\) 18.0527 0.0571287
\(317\) 334.257 1.05444 0.527219 0.849730i \(-0.323235\pi\)
0.527219 + 0.849730i \(0.323235\pi\)
\(318\) 14.7934 + 2.92100i 0.0465201 + 0.00918553i
\(319\) 227.684 0.713743
\(320\) 0 0
\(321\) −47.9210 9.46215i −0.149287 0.0294771i
\(322\) 286.868i 0.890895i
\(323\) 39.0021 0.120750
\(324\) 115.193 + 113.906i 0.355534 + 0.351562i
\(325\) 0 0
\(326\) 225.399i 0.691409i
\(327\) −276.193 54.5352i −0.844628 0.166774i
\(328\) 58.0527i 0.176990i
\(329\) 1014.23i 3.08277i
\(330\) 0 0
\(331\) 389.421 1.17650 0.588249 0.808680i \(-0.299818\pi\)
0.588249 + 0.808680i \(0.299818\pi\)
\(332\) −1.37697 −0.00414750
\(333\) −205.067 + 499.035i −0.615817 + 1.49860i
\(334\) −15.2370 −0.0456198
\(335\) 0 0
\(336\) −26.7018 + 135.231i −0.0794696 + 0.402473i
\(337\) 129.684i 0.384819i 0.981315 + 0.192409i \(0.0616302\pi\)
−0.981315 + 0.192409i \(0.938370\pi\)
\(338\) 97.5807 0.288700
\(339\) −576.092 113.751i −1.69939 0.335549i
\(340\) 0 0
\(341\) 67.8823i 0.199068i
\(342\) 129.190 + 53.0875i 0.377748 + 0.155227i
\(343\) 389.947i 1.13687i
\(344\) 120.096i 0.349118i
\(345\) 0 0
\(346\) −400.710 −1.15812
\(347\) −346.985 −0.999956 −0.499978 0.866038i \(-0.666659\pi\)
−0.499978 + 0.866038i \(0.666659\pi\)
\(348\) 31.1872 157.947i 0.0896183 0.453872i
\(349\) −509.579 −1.46011 −0.730055 0.683388i \(-0.760506\pi\)
−0.730055 + 0.683388i \(0.760506\pi\)
\(350\) 0 0
\(351\) −149.057 + 225.127i −0.424664 + 0.641387i
\(352\) 48.0000i 0.136364i
\(353\) 637.679 1.80646 0.903229 0.429159i \(-0.141190\pi\)
0.903229 + 0.429159i \(0.141190\pi\)
\(354\) −63.8947 + 323.594i −0.180493 + 0.914108i
\(355\) 0 0
\(356\) 14.2166i 0.0399343i
\(357\) −23.7256 + 120.158i −0.0664582 + 0.336577i
\(358\) 433.631i 1.21126i
\(359\) 166.952i 0.465046i 0.972591 + 0.232523i \(0.0746982\pi\)
−0.972591 + 0.232523i \(0.925302\pi\)
\(360\) 0 0
\(361\) −240.579 −0.666423
\(362\) 375.734 1.03794
\(363\) −144.216 28.4758i −0.397288 0.0784457i
\(364\) −229.737 −0.631145
\(365\) 0 0
\(366\) −91.3509 18.0375i −0.249593 0.0492828i
\(367\) 505.828i 1.37828i 0.724629 + 0.689140i \(0.242011\pi\)
−0.724629 + 0.689140i \(0.757989\pi\)
\(368\) −70.6362 −0.191946
\(369\) 70.2107 170.859i 0.190273 0.463033i
\(370\) 0 0
\(371\) 40.8260i 0.110043i
\(372\) −47.0908 9.29822i −0.126588 0.0249952i
\(373\) 416.053i 1.11542i −0.830035 0.557711i \(-0.811680\pi\)
0.830035 0.557711i \(-0.188320\pi\)
\(374\) 42.6499i 0.114037i
\(375\) 0 0
\(376\) 249.737 0.664193
\(377\) 268.328 0.711746
\(378\) −242.141 + 365.715i −0.640583 + 0.967499i
\(379\) −82.7630 −0.218372 −0.109186 0.994021i \(-0.534824\pi\)
−0.109186 + 0.994021i \(0.534824\pi\)
\(380\) 0 0
\(381\) 45.0612 228.212i 0.118271 0.598982i
\(382\) 225.737i 0.590934i
\(383\) 334.592 0.873608 0.436804 0.899557i \(-0.356110\pi\)
0.436804 + 0.899557i \(0.356110\pi\)
\(384\) −33.2982 6.57484i −0.0867141 0.0171220i
\(385\) 0 0
\(386\) 130.182i 0.337259i
\(387\) −145.248 + 353.465i −0.375319 + 0.913346i
\(388\) 223.895i 0.577048i
\(389\) 542.964i 1.39580i 0.716197 + 0.697898i \(0.245881\pi\)
−0.716197 + 0.697898i \(0.754119\pi\)
\(390\) 0 0
\(391\) −62.7630 −0.160519
\(392\) −234.610 −0.598496
\(393\) −59.0437 + 299.026i −0.150238 + 0.760881i
\(394\) 98.7630 0.250667
\(395\) 0 0
\(396\) 58.0527 141.272i 0.146598 0.356748i
\(397\) 214.000i 0.539043i 0.962994 + 0.269521i \(0.0868655\pi\)
−0.962994 + 0.269521i \(0.913135\pi\)
\(398\) −210.606 −0.529161
\(399\) −73.2541 + 370.995i −0.183594 + 0.929812i
\(400\) 0 0
\(401\) 726.086i 1.81069i −0.424677 0.905345i \(-0.639613\pi\)
0.424677 0.905345i \(-0.360387\pi\)
\(402\) 44.0017 222.846i 0.109457 0.554344i
\(403\) 80.0000i 0.198511i
\(404\) 310.978i 0.769748i
\(405\) 0 0
\(406\) 435.895 1.07363
\(407\) 508.670 1.24980
\(408\) −29.5868 5.84200i −0.0725166 0.0143186i
\(409\) 346.158 0.846352 0.423176 0.906047i \(-0.360915\pi\)
0.423176 + 0.906047i \(0.360915\pi\)
\(410\) 0 0
\(411\) 518.039 + 102.288i 1.26044 + 0.248877i
\(412\) 15.1843i 0.0368552i
\(413\) −893.038 −2.16232
\(414\) −207.895 85.4296i −0.502161 0.206352i
\(415\) 0 0
\(416\) 56.5685i 0.135982i
\(417\) 555.717 + 109.728i 1.33266 + 0.263137i
\(418\) 131.684i 0.315033i
\(419\) 580.907i 1.38641i −0.720740 0.693206i \(-0.756198\pi\)
0.720740 0.693206i \(-0.243802\pi\)
\(420\) 0 0
\(421\) −269.315 −0.639704 −0.319852 0.947468i \(-0.603633\pi\)
−0.319852 + 0.947468i \(0.603633\pi\)
\(422\) −404.242 −0.957919
\(423\) 735.019 + 302.039i 1.73763 + 0.714041i
\(424\) −10.0527 −0.0237091
\(425\) 0 0
\(426\) −56.9210 + 288.276i −0.133617 + 0.676704i
\(427\) 252.105i 0.590411i
\(428\) 32.5642 0.0760845
\(429\) 249.737 + 49.3113i 0.582137 + 0.114945i
\(430\) 0 0
\(431\) 776.068i 1.80062i 0.435247 + 0.900311i \(0.356661\pi\)
−0.435247 + 0.900311i \(0.643339\pi\)
\(432\) −90.0507 59.6228i −0.208451 0.138016i
\(433\) 195.526i 0.451561i −0.974178 0.225781i \(-0.927507\pi\)
0.974178 0.225781i \(-0.0724932\pi\)
\(434\) 129.959i 0.299444i
\(435\) 0 0
\(436\) 187.684 0.430468
\(437\) −193.785 −0.443443
\(438\) 9.90554 50.1666i 0.0226154 0.114536i
\(439\) −598.763 −1.36392 −0.681962 0.731387i \(-0.738873\pi\)
−0.681962 + 0.731387i \(0.738873\pi\)
\(440\) 0 0
\(441\) −690.500 283.745i −1.56576 0.643413i
\(442\) 50.2633i 0.113718i
\(443\) −216.728 −0.489228 −0.244614 0.969621i \(-0.578661\pi\)
−0.244614 + 0.969621i \(0.578661\pi\)
\(444\) 69.6754 352.871i 0.156927 0.794754i
\(445\) 0 0
\(446\) 100.949i 0.226342i
\(447\) 42.1848 213.645i 0.0943732 0.477953i
\(448\) 91.8947i 0.205122i
\(449\) 246.203i 0.548336i −0.961682 0.274168i \(-0.911598\pi\)
0.961682 0.274168i \(-0.0884025\pi\)
\(450\) 0 0
\(451\) −174.158 −0.386160
\(452\) 391.476 0.866098
\(453\) −276.503 54.5964i −0.610383 0.120522i
\(454\) 41.1843 0.0907144
\(455\) 0 0
\(456\) −91.3509 18.0375i −0.200331 0.0395559i
\(457\) 553.052i 1.21018i −0.796157 0.605090i \(-0.793137\pi\)
0.796157 0.605090i \(-0.206863\pi\)
\(458\) 183.401 0.400439
\(459\) −80.0135 52.9771i −0.174321 0.115419i
\(460\) 0 0
\(461\) 124.749i 0.270605i 0.990804 + 0.135302i \(0.0432006\pi\)
−0.990804 + 0.135302i \(0.956799\pi\)
\(462\) 405.693 + 80.1053i 0.878124 + 0.173388i
\(463\) 669.723i 1.44649i 0.690593 + 0.723243i \(0.257349\pi\)
−0.690593 + 0.723243i \(0.742651\pi\)
\(464\) 107.331i 0.231317i
\(465\) 0 0
\(466\) −262.868 −0.564095
\(467\) −486.880 −1.04257 −0.521285 0.853383i \(-0.674547\pi\)
−0.521285 + 0.853383i \(0.674547\pi\)
\(468\) 68.4157 166.491i 0.146187 0.355750i
\(469\) 614.999 1.31130
\(470\) 0 0
\(471\) 71.9694 364.489i 0.152801 0.773861i
\(472\) 219.895i 0.465879i
\(473\) 360.289 0.761711
\(474\) −37.5701 7.41833i −0.0792618 0.0156505i
\(475\) 0 0
\(476\) 81.6520i 0.171538i
\(477\) −29.5868 12.1580i −0.0620267 0.0254885i
\(478\) 428.105i 0.895618i
\(479\) 520.580i 1.08680i 0.839472 + 0.543402i \(0.182864\pi\)
−0.839472 + 0.543402i \(0.817136\pi\)
\(480\) 0 0
\(481\) 599.473 1.24631
\(482\) −335.912 −0.696914
\(483\) 117.882 597.013i 0.244062 1.23605i
\(484\) 98.0000 0.202479
\(485\) 0 0
\(486\) −192.925 284.390i −0.396966 0.585165i
\(487\) 263.381i 0.540824i 0.962745 + 0.270412i \(0.0871600\pi\)
−0.962745 + 0.270412i \(0.912840\pi\)
\(488\) 62.0764 0.127206
\(489\) 92.6228 469.088i 0.189413 0.959279i
\(490\) 0 0
\(491\) 711.646i 1.44938i 0.689074 + 0.724691i \(0.258017\pi\)
−0.689074 + 0.724691i \(0.741983\pi\)
\(492\) −23.8554 + 120.816i −0.0484866 + 0.245560i
\(493\) 95.3680i 0.193444i
\(494\) 155.191i 0.314152i
\(495\) 0 0
\(496\) 32.0000 0.0645161
\(497\) −795.569 −1.60074
\(498\) 2.86567 + 0.565835i 0.00575436 + 0.00113622i
\(499\) −23.0790 −0.0462505 −0.0231253 0.999733i \(-0.507362\pi\)
−0.0231253 + 0.999733i \(0.507362\pi\)
\(500\) 0 0
\(501\) 31.7103 + 6.26130i 0.0632941 + 0.0124976i
\(502\) 119.684i 0.238414i
\(503\) 40.5844 0.0806847 0.0403423 0.999186i \(-0.487155\pi\)
0.0403423 + 0.999186i \(0.487155\pi\)
\(504\) 111.140 270.462i 0.220516 0.536631i
\(505\) 0 0
\(506\) 211.909i 0.418792i
\(507\) −203.079 40.0986i −0.400550 0.0790899i
\(508\) 155.079i 0.305274i
\(509\) 484.591i 0.952045i 0.879433 + 0.476023i \(0.157922\pi\)
−0.879433 + 0.476023i \(0.842078\pi\)
\(510\) 0 0
\(511\) 138.447 0.270933
\(512\) 22.6274 0.0441942
\(513\) −247.047 163.570i −0.481572 0.318850i
\(514\) 413.026 0.803553
\(515\) 0 0
\(516\) 49.3509 249.937i 0.0956413 0.484375i
\(517\) 749.210i 1.44915i
\(518\) 973.835 1.87999
\(519\) 833.934 + 164.663i 1.60681 + 0.317269i
\(520\) 0 0
\(521\) 539.857i 1.03619i 0.855322 + 0.518097i \(0.173359\pi\)
−0.855322 + 0.518097i \(0.826641\pi\)
\(522\) −129.810 + 315.895i −0.248678 + 0.605162i
\(523\) 266.644i 0.509836i −0.966963 0.254918i \(-0.917952\pi\)
0.966963 0.254918i \(-0.0820485\pi\)
\(524\) 203.200i 0.387786i
\(525\) 0 0
\(526\) −392.763 −0.746698
\(527\) 28.4332 0.0539530
\(528\) −19.7245 + 99.8947i −0.0373570 + 0.189194i
\(529\) −217.158 −0.410507
\(530\) 0 0
\(531\) 265.947 647.188i 0.500842 1.21881i
\(532\) 252.105i 0.473882i
\(533\) −205.247 −0.385079
\(534\) 5.84200 29.5868i 0.0109401 0.0554059i
\(535\) 0 0
\(536\) 151.433i 0.282523i
\(537\) 178.191 902.447i 0.331827 1.68053i
\(538\) 405.237i 0.753229i
\(539\) 703.831i 1.30581i
\(540\) 0 0
\(541\) −337.895 −0.624574 −0.312287 0.949988i \(-0.601095\pi\)
−0.312287 + 0.949988i \(0.601095\pi\)
\(542\) −458.354 −0.845672
\(543\) −781.954 154.399i −1.44006 0.284345i
\(544\) 20.1053 0.0369583
\(545\) 0 0
\(546\) 478.114 + 94.4050i 0.875666 + 0.172903i
\(547\) 214.566i 0.392259i 0.980578 + 0.196130i \(0.0628373\pi\)
−0.980578 + 0.196130i \(0.937163\pi\)
\(548\) −352.027 −0.642386
\(549\) 182.702 + 75.0771i 0.332790 + 0.136753i
\(550\) 0 0
\(551\) 294.454i 0.534400i
\(552\) 147.004 + 29.0263i 0.266311 + 0.0525839i
\(553\) 103.684i 0.187494i
\(554\) 588.089i 1.06153i
\(555\) 0 0
\(556\) −377.631 −0.679193
\(557\) 674.821 1.21153 0.605764 0.795644i \(-0.292867\pi\)
0.605764 + 0.795644i \(0.292867\pi\)
\(558\) 94.1816 + 38.7018i 0.168784 + 0.0693580i
\(559\) 424.605 0.759580
\(560\) 0 0
\(561\) −17.5260 + 88.7603i −0.0312406 + 0.158218i
\(562\) 610.552i 1.08639i
\(563\) −718.513 −1.27622 −0.638111 0.769944i \(-0.720284\pi\)
−0.638111 + 0.769944i \(0.720284\pi\)
\(564\) −519.737 102.624i −0.921519 0.181957i
\(565\) 0 0
\(566\) 200.167i 0.353652i
\(567\) 654.210 661.601i 1.15381 1.16684i
\(568\) 195.895i 0.344885i
\(569\) 183.122i 0.321831i 0.986968 + 0.160916i \(0.0514447\pi\)
−0.986968 + 0.160916i \(0.948555\pi\)
\(570\) 0 0
\(571\) −295.895 −0.518204 −0.259102 0.965850i \(-0.583427\pi\)
−0.259102 + 0.965850i \(0.583427\pi\)
\(572\) −169.706 −0.296688
\(573\) 92.7613 469.789i 0.161887 0.819877i
\(574\) −333.421 −0.580872
\(575\) 0 0
\(576\) 66.5964 + 27.3663i 0.115619 + 0.0475109i
\(577\) 984.947i 1.70701i 0.521082 + 0.853507i \(0.325529\pi\)
−0.521082 + 0.853507i \(0.674471\pi\)
\(578\) −390.843 −0.676200
\(579\) −53.4954 + 270.927i −0.0923927 + 0.467922i
\(580\) 0 0
\(581\) 7.90852i 0.0136119i
\(582\) −92.0044 + 465.956i −0.158083 + 0.800611i
\(583\) 30.1580i 0.0517290i
\(584\) 34.0901i 0.0583734i
\(585\) 0 0
\(586\) 233.342 0.398195
\(587\) −378.172 −0.644245 −0.322122 0.946698i \(-0.604396\pi\)
−0.322122 + 0.946698i \(0.604396\pi\)
\(588\) 488.257 + 96.4078i 0.830369 + 0.163959i
\(589\) 87.7893 0.149048
\(590\) 0 0
\(591\) −205.540 40.5844i −0.347783 0.0686707i
\(592\) 239.789i 0.405050i
\(593\) 265.221 0.447253 0.223626 0.974675i \(-0.428210\pi\)
0.223626 + 0.974675i \(0.428210\pi\)
\(594\) −178.868 + 270.152i −0.301125 + 0.454801i
\(595\) 0 0
\(596\) 145.180i 0.243590i
\(597\) 438.301 + 86.5438i 0.734172 + 0.144964i
\(598\) 249.737i 0.417620i
\(599\) 382.061i 0.637832i −0.947783 0.318916i \(-0.896681\pi\)
0.947783 0.318916i \(-0.103319\pi\)
\(600\) 0 0
\(601\) 1021.53 1.69971 0.849855 0.527016i \(-0.176689\pi\)
0.849855 + 0.527016i \(0.176689\pi\)
\(602\) 689.764 1.14579
\(603\) −183.147 + 445.693i −0.303727 + 0.739125i
\(604\) 187.895 0.311084
\(605\) 0 0
\(606\) 127.789 647.188i 0.210873 1.06797i
\(607\) 835.487i 1.37642i 0.725512 + 0.688210i \(0.241603\pi\)
−0.725512 + 0.688210i \(0.758397\pi\)
\(608\) 62.0764 0.102099
\(609\) −907.157 179.121i −1.48959 0.294123i
\(610\) 0 0
\(611\) 882.952i 1.44509i
\(612\) 59.1735 + 24.3160i 0.0966888 + 0.0397320i
\(613\) 833.263i 1.35932i 0.733528 + 0.679660i \(0.237872\pi\)
−0.733528 + 0.679660i \(0.762128\pi\)
\(614\) 225.399i 0.367100i
\(615\) 0 0
\(616\) −275.684 −0.447539
\(617\) −455.098 −0.737598 −0.368799 0.929509i \(-0.620231\pi\)
−0.368799 + 0.929509i \(0.620231\pi\)
\(618\) 6.23966 31.6007i 0.0100965 0.0511338i
\(619\) −336.710 −0.543959 −0.271979 0.962303i \(-0.587678\pi\)
−0.271979 + 0.962303i \(0.587678\pi\)
\(620\) 0 0
\(621\) 397.552 + 263.220i 0.640181 + 0.423865i
\(622\) 202.369i 0.325352i
\(623\) 81.6520 0.131063
\(624\) −23.2456 + 117.727i −0.0372525 + 0.188665i
\(625\) 0 0
\(626\) 709.488i 1.13337i
\(627\) −54.1125 + 274.053i −0.0863039 + 0.437086i
\(628\) 247.684i 0.394401i
\(629\) 213.062i 0.338731i
\(630\) 0 0
\(631\) −1100.89 −1.74468 −0.872341 0.488898i \(-0.837399\pi\)
−0.872341 + 0.488898i \(0.837399\pi\)
\(632\) 25.5303 0.0403961
\(633\) 841.283 + 166.114i 1.32904 + 0.262423i
\(634\) 472.710 0.745600
\(635\) 0 0
\(636\) 20.9210 + 4.13091i 0.0328947 + 0.00649515i
\(637\) 829.473i 1.30216i
\(638\) 321.994 0.504692
\(639\) 236.921 576.552i 0.370768 0.902273i
\(640\) 0 0
\(641\) 337.011i 0.525758i −0.964829 0.262879i \(-0.915328\pi\)
0.964829 0.262879i \(-0.0846719\pi\)
\(642\) −67.7705 13.3815i −0.105562 0.0208435i
\(643\) 599.381i 0.932164i −0.884742 0.466082i \(-0.845665\pi\)
0.884742 0.466082i \(-0.154335\pi\)
\(644\) 405.693i 0.629958i
\(645\) 0 0
\(646\) 55.1573 0.0853828
\(647\) 47.0224 0.0726775 0.0363388 0.999340i \(-0.488430\pi\)
0.0363388 + 0.999340i \(0.488430\pi\)
\(648\) 162.907 + 161.088i 0.251400 + 0.248592i
\(649\) −659.684 −1.01646
\(650\) 0 0
\(651\) −53.4036 + 270.462i −0.0820331 + 0.415456i
\(652\) 318.763i 0.488900i
\(653\) 559.228 0.856399 0.428199 0.903684i \(-0.359148\pi\)
0.428199 + 0.903684i \(0.359148\pi\)
\(654\) −390.596 77.1245i −0.597242 0.117927i
\(655\) 0 0
\(656\) 82.0989i 0.125151i
\(657\) −41.2296 + 100.333i −0.0627543 + 0.152714i
\(658\) 1434.34i 2.17985i
\(659\) 665.759i 1.01026i −0.863044 0.505129i \(-0.831445\pi\)
0.863044 0.505129i \(-0.168555\pi\)
\(660\) 0 0
\(661\) −557.947 −0.844096 −0.422048 0.906574i \(-0.638689\pi\)
−0.422048 + 0.906574i \(0.638689\pi\)
\(662\) 550.724 0.831909
\(663\) −20.6546 + 104.605i −0.0311532 + 0.157775i
\(664\) −1.94733 −0.00293273
\(665\) 0 0
\(666\) −290.009 + 705.742i −0.435448 + 1.05967i
\(667\) 473.842i 0.710408i
\(668\) −21.5484 −0.0322581
\(669\) −41.4826 + 210.088i −0.0620068 + 0.314033i
\(670\) 0 0
\(671\) 186.229i 0.277540i
\(672\) −37.7620 + 191.246i −0.0561935 + 0.284592i
\(673\) 1019.42i 1.51474i 0.652985 + 0.757370i \(0.273516\pi\)
−0.652985 + 0.757370i \(0.726484\pi\)
\(674\) 183.401i 0.272108i
\(675\) 0 0
\(676\) 138.000 0.204142
\(677\) −624.616 −0.922624 −0.461312 0.887238i \(-0.652621\pi\)
−0.461312 + 0.887238i \(0.652621\pi\)
\(678\) −814.717 160.868i −1.20165 0.237269i
\(679\) −1285.92 −1.89384
\(680\) 0 0
\(681\) −85.7103 16.9238i −0.125860 0.0248513i
\(682\) 96.0000i 0.140762i
\(683\) 525.882 0.769959 0.384980 0.922925i \(-0.374208\pi\)
0.384980 + 0.922925i \(0.374208\pi\)
\(684\) 182.702 + 75.0771i 0.267108 + 0.109762i
\(685\) 0 0
\(686\) 551.469i 0.803890i
\(687\) −381.683 75.3644i −0.555579 0.109701i
\(688\) 169.842i 0.246863i
\(689\) 35.5415i 0.0515843i
\(690\) 0 0
\(691\) 932.000 1.34877 0.674385 0.738380i \(-0.264409\pi\)
0.674385 + 0.738380i \(0.264409\pi\)
\(692\) −566.690 −0.818916
\(693\) −811.386 333.421i −1.17083 0.481126i
\(694\) −490.710 −0.707075
\(695\) 0 0
\(696\) 44.1053 223.371i 0.0633697 0.320936i
\(697\) 72.9480i 0.104660i
\(698\) −720.653 −1.03245
\(699\) 547.065 + 108.020i 0.782640 + 0.154535i
\(700\) 0 0
\(701\) 606.045i 0.864544i 0.901743 + 0.432272i \(0.142288\pi\)
−0.901743 + 0.432272i \(0.857712\pi\)
\(702\) −210.798 + 318.377i −0.300283 + 0.453529i
\(703\) 657.842i 0.935764i
\(704\) 67.8823i 0.0964237i
\(705\) 0 0
\(706\) 901.815 1.27736
\(707\) 1786.08 2.52627
\(708\) −90.3607 + 457.631i −0.127628 + 0.646372i
\(709\) −489.473 −0.690371 −0.345186 0.938534i \(-0.612184\pi\)
−0.345186 + 0.938534i \(0.612184\pi\)
\(710\) 0 0
\(711\) 75.1402 + 30.8772i 0.105682 + 0.0434278i
\(712\) 20.1053i 0.0282378i
\(713\) −141.272 −0.198138
\(714\) −33.5530 + 169.929i −0.0469930 + 0.237996i
\(715\) 0 0
\(716\) 613.247i 0.856491i
\(717\) −175.920 + 890.947i −0.245356 + 1.24260i
\(718\) 236.105i 0.328838i
\(719\) 107.778i 0.149900i −0.997187 0.0749500i \(-0.976120\pi\)
0.997187 0.0749500i \(-0.0238797\pi\)
\(720\) 0 0
\(721\) 87.2100 0.120957
\(722\) −340.230 −0.471232
\(723\) 699.080 + 138.036i 0.966916 + 0.190921i
\(724\) 531.368 0.733934
\(725\) 0 0
\(726\) −203.952 40.2709i −0.280925 0.0554695i
\(727\) 150.172i 0.206563i 0.994652 + 0.103282i \(0.0329343\pi\)
−0.994652 + 0.103282i \(0.967066\pi\)
\(728\) −324.897 −0.446287
\(729\) 284.641 + 671.134i 0.390453 + 0.920623i
\(730\) 0 0
\(731\) 150.911i 0.206445i
\(732\) −129.190 25.5089i −0.176489 0.0348482i
\(733\) 675.526i 0.921591i −0.887506 0.460795i \(-0.847564\pi\)
0.887506 0.460795i \(-0.152436\pi\)
\(734\) 715.349i 0.974591i
\(735\) 0 0
\(736\) −99.8947 −0.135726
\(737\) 454.298 0.616415
\(738\) 99.2929 241.631i 0.134543 0.327414i
\(739\) 936.921 1.26782 0.633911 0.773406i \(-0.281448\pi\)
0.633911 + 0.773406i \(0.281448\pi\)
\(740\) 0 0
\(741\) −63.7722 + 322.974i −0.0860624 + 0.435863i
\(742\) 57.7367i 0.0778122i
\(743\) 452.939 0.609608 0.304804 0.952415i \(-0.401409\pi\)
0.304804 + 0.952415i \(0.401409\pi\)
\(744\) −66.5964 13.1497i −0.0895113 0.0176743i
\(745\) 0 0
\(746\) 588.387i 0.788723i
\(747\) −5.73134 2.35516i −0.00767247 0.00315283i
\(748\) 60.3160i 0.0806364i
\(749\) 187.029i 0.249706i
\(750\) 0 0
\(751\) 654.369 0.871330 0.435665 0.900109i \(-0.356513\pi\)
0.435665 + 0.900109i \(0.356513\pi\)
\(752\) 353.181 0.469656
\(753\) −49.1814 + 249.079i −0.0653140 + 0.330782i
\(754\) 379.473 0.503280
\(755\) 0 0
\(756\) −342.438 + 517.199i −0.452961 + 0.684125i
\(757\) 123.315i 0.162900i −0.996677 0.0814500i \(-0.974045\pi\)
0.996677 0.0814500i \(-0.0259551\pi\)
\(758\) −117.045 −0.154412
\(759\) 87.0790 441.011i 0.114729 0.581042i
\(760\) 0 0
\(761\) 502.715i 0.660598i 0.943876 + 0.330299i \(0.107150\pi\)
−0.943876 + 0.330299i \(0.892850\pi\)
\(762\) 63.7262 322.741i 0.0836302 0.423545i
\(763\) 1077.95i 1.41278i
\(764\) 319.240i 0.417853i
\(765\) 0 0
\(766\) 473.184 0.617734
\(767\) −777.445 −1.01362
\(768\) −47.0908 9.29822i −0.0613161 0.0121071i
\(769\) 286.316 0.372323 0.186161 0.982519i \(-0.440395\pi\)
0.186161 + 0.982519i \(0.440395\pi\)
\(770\) 0 0
\(771\) −859.565 169.724i −1.11487 0.220135i
\(772\) 184.105i 0.238478i
\(773\) −972.030 −1.25748 −0.628739 0.777617i \(-0.716428\pi\)
−0.628739 + 0.777617i \(0.716428\pi\)
\(774\) −205.412 + 499.875i −0.265390 + 0.645833i
\(775\) 0 0
\(776\) 316.635i 0.408035i
\(777\) −2026.68 400.175i −2.60835 0.515026i
\(778\) 767.868i 0.986976i
\(779\) 225.231i 0.289129i
\(780\) 0 0
\(781\) −587.684 −0.752476
\(782\) −88.7603 −0.113504
\(783\) 399.962 604.078i 0.510807 0.771492i
\(784\) −331.789 −0.423201
\(785\) 0 0
\(786\) −83.5003 + 422.887i −0.106235 + 0.538024i
\(787\) 1492.70i 1.89669i −0.317237 0.948346i \(-0.602755\pi\)
0.317237 0.948346i \(-0.397245\pi\)
\(788\) 139.672 0.177249
\(789\) 817.394 + 161.397i 1.03599 + 0.204559i
\(790\) 0 0
\(791\) 2248.41i 2.84249i
\(792\) 82.0989 199.789i 0.103660 0.252259i
\(793\) 219.473i 0.276763i
\(794\) 302.642i 0.381161i
\(795\) 0 0
\(796\) −297.842 −0.374173
\(797\) 94.3618 0.118396 0.0591981 0.998246i \(-0.481146\pi\)
0.0591981 + 0.998246i \(0.481146\pi\)
\(798\) −103.597 + 524.666i −0.129821 + 0.657476i
\(799\) 313.815 0.392760
\(800\) 0 0
\(801\) −24.3160 + 59.1735i −0.0303571 + 0.0738746i
\(802\) 1026.84i 1.28035i
\(803\) 102.270 0.127360
\(804\) 62.2278 315.152i 0.0773977 0.391980i
\(805\) 0 0
\(806\) 113.137i 0.140369i
\(807\) 166.523 843.354i 0.206348 1.04505i
\(808\) 439.789i 0.544294i
\(809\) 1103.35i 1.36384i −0.731427 0.681920i \(-0.761145\pi\)
0.731427 0.681920i \(-0.238855\pi\)
\(810\) 0 0
\(811\) −10.1580 −0.0125253 −0.00626264 0.999980i \(-0.501993\pi\)
−0.00626264 + 0.999980i \(0.501993\pi\)
\(812\) 616.448 0.759173
\(813\) 953.899 + 188.350i 1.17331 + 0.231673i
\(814\) 719.368 0.883744
\(815\) 0 0
\(816\) −41.8420 8.26183i −0.0512770 0.0101248i
\(817\) 465.947i 0.570315i
\(818\) 489.541 0.598461
\(819\) −956.228 392.940i −1.16756 0.479780i
\(820\) 0 0
\(821\) 337.011i 0.410488i −0.978711 0.205244i \(-0.934201\pi\)
0.978711 0.205244i \(-0.0657988\pi\)
\(822\) 732.618 + 144.658i 0.891263 + 0.175983i
\(823\) 901.512i 1.09540i −0.836675 0.547699i \(-0.815504\pi\)
0.836675 0.547699i \(-0.184496\pi\)
\(824\) 21.4739i 0.0260606i
\(825\) 0 0
\(826\) −1262.95 −1.52899
\(827\) 531.354 0.642508 0.321254 0.946993i \(-0.395896\pi\)
0.321254 + 0.946993i \(0.395896\pi\)
\(828\) −294.007 120.816i −0.355081 0.145913i
\(829\) 197.631 0.238397 0.119199 0.992870i \(-0.461967\pi\)
0.119199 + 0.992870i \(0.461967\pi\)
\(830\) 0 0
\(831\) −241.662 + 1223.90i −0.290809 + 1.47280i
\(832\) 80.0000i 0.0961538i
\(833\) −294.808 −0.353911
\(834\) 785.903 + 155.179i 0.942330 + 0.186066i
\(835\) 0 0
\(836\) 186.229i 0.222762i
\(837\) −180.101 119.246i −0.215175 0.142468i
\(838\) 821.526i 0.980341i
\(839\) 943.950i 1.12509i −0.826767 0.562545i \(-0.809822\pi\)
0.826767 0.562545i \(-0.190178\pi\)
\(840\) 0 0
\(841\) 121.000 0.143876
\(842\) −380.869 −0.452339
\(843\) −250.893 + 1270.64i −0.297619 + 1.50729i
\(844\) −571.684 −0.677351
\(845\) 0 0
\(846\) 1039.47 + 427.148i 1.22869 + 0.504903i
\(847\) 562.855i 0.664528i
\(848\) −14.2166 −0.0167649
\(849\) 82.2541 416.575i 0.0968835 0.490666i
\(850\) 0 0
\(851\) 1058.61i 1.24396i
\(852\) −80.4984 + 407.684i −0.0944817 + 0.478502i
\(853\) 1196.42i 1.40260i −0.712865 0.701301i \(-0.752603\pi\)
0.712865 0.701301i \(-0.247397\pi\)
\(854\) 356.531i 0.417483i
\(855\) 0 0
\(856\) 46.0527 0.0537998
\(857\) 1266.04 1.47729 0.738645 0.674095i \(-0.235466\pi\)
0.738645 + 0.674095i \(0.235466\pi\)
\(858\) 353.181 + 69.7367i 0.411633 + 0.0812782i
\(859\) 470.868 0.548159 0.274079 0.961707i \(-0.411627\pi\)
0.274079 + 0.961707i \(0.411627\pi\)
\(860\) 0 0
\(861\) 693.895 + 137.012i 0.805917 + 0.159131i
\(862\) 1097.53i 1.27323i
\(863\) −285.057 −0.330310 −0.165155 0.986268i \(-0.552812\pi\)
−0.165155 + 0.986268i \(0.552812\pi\)
\(864\) −127.351 84.3193i −0.147397 0.0975918i
\(865\) 0 0
\(866\) 276.516i 0.319302i
\(867\) 813.399 + 160.608i 0.938177 + 0.185246i
\(868\) 183.789i 0.211739i
\(869\) 76.5910i 0.0881369i
\(870\) 0 0
\(871\) 535.395 0.614690
\(872\) 265.425 0.304387
\(873\) 382.948 931.912i 0.438657 1.06748i
\(874\) −274.053 −0.313561
\(875\) 0 0
\(876\) 14.0085 70.9462i 0.0159915 0.0809888i
\(877\) 244.579i 0.278882i −0.990230 0.139441i \(-0.955469\pi\)
0.990230 0.139441i \(-0.0445305\pi\)
\(878\) −846.779 −0.964440
\(879\) −485.618 95.8867i −0.552466 0.109086i
\(880\) 0 0
\(881\) 137.271i 0.155813i 0.996961 + 0.0779065i \(0.0248236\pi\)
−0.996961 + 0.0779065i \(0.975176\pi\)
\(882\) −976.514 401.276i −1.10716 0.454962i
\(883\) 1647.75i 1.86608i 0.359772 + 0.933040i \(0.382854\pi\)
−0.359772 + 0.933040i \(0.617146\pi\)
\(884\) 71.0831i 0.0804107i
\(885\) 0 0
\(886\) −306.500 −0.345936
\(887\) −514.419 −0.579954 −0.289977 0.957034i \(-0.593648\pi\)
−0.289977 + 0.957034i \(0.593648\pi\)
\(888\) 98.5360 499.035i 0.110964 0.561976i
\(889\) 890.683 1.00189
\(890\) 0 0
\(891\) 483.263 488.722i 0.542382 0.548510i
\(892\) 142.763i 0.160048i
\(893\) 968.923 1.08502
\(894\) 59.6584 302.139i 0.0667319 0.337964i
\(895\) 0 0
\(896\) 129.959i 0.145043i
\(897\) 102.624 519.737i 0.114408 0.579417i
\(898\) 348.184i 0.387732i
\(899\) 214.663i 0.238779i
\(900\) 0 0
\(901\) −12.6320 −0.0140200
\(902\) −246.297 −0.273056
\(903\) −1435.49 283.443i −1.58969 0.313890i
\(904\) 553.631 0.612424
\(905\) 0 0
\(906\) −391.035 77.2110i −0.431606 0.0852219i
\(907\) 347.303i 0.382914i −0.981501 0.191457i \(-0.938679\pi\)
0.981501 0.191457i \(-0.0613213\pi\)
\(908\) 58.2434 0.0641448
\(909\) −531.895 + 1294.38i −0.585143 + 1.42396i
\(910\) 0 0
\(911\) 304.540i 0.334292i −0.985932 0.167146i \(-0.946545\pi\)
0.985932 0.167146i \(-0.0534551\pi\)
\(912\) −129.190 25.5089i −0.141655 0.0279703i
\(913\) 5.84200i 0.00639868i
\(914\) 782.134i 0.855726i
\(915\) 0 0
\(916\) 259.368 0.283153
\(917\) −1167.06 −1.27270
\(918\) −113.156 74.9210i −0.123264 0.0816133i
\(919\) −244.289 −0.265820 −0.132910 0.991128i \(-0.542432\pi\)
−0.132910 + 0.991128i \(0.542432\pi\)
\(920\) 0 0
\(921\) −92.6228 + 469.088i −0.100568 + 0.509324i
\(922\) 176.421i 0.191346i
\(923\) −692.592 −0.750371
\(924\) 573.737 + 113.286i 0.620927 + 0.122604i
\(925\) 0 0
\(926\) 947.132i 1.02282i
\(927\) −25.9712 + 63.2014i −0.0280164 + 0.0681785i
\(928\) 151.789i 0.163566i
\(929\) 1025.96i 1.10437i 0.833723 + 0.552183i \(0.186205\pi\)
−0.833723 + 0.552183i \(0.813795\pi\)
\(930\) 0 0
\(931\) −910.236 −0.977697
\(932\) −371.752 −0.398875
\(933\) −83.1588 + 421.157i −0.0891305 + 0.451401i
\(934\) −688.552 −0.737208
\(935\) 0 0
\(936\) 96.7544 235.454i 0.103370 0.251553i
\(937\) 332.053i 0.354379i 0.984177 + 0.177189i \(0.0567005\pi\)
−0.984177 + 0.177189i \(0.943300\pi\)
\(938\) 869.740 0.927229
\(939\) −291.548 + 1476.54i −0.310488 + 1.57246i
\(940\) 0 0
\(941\) 1636.99i 1.73963i 0.493381 + 0.869813i \(0.335761\pi\)
−0.493381 + 0.869813i \(0.664239\pi\)
\(942\) 101.780 515.465i 0.108047 0.547203i
\(943\) 362.447i 0.384355i
\(944\) 310.978i 0.329426i
\(945\) 0 0
\(946\) 509.526 0.538611
\(947\) 1209.32 1.27700 0.638500 0.769622i \(-0.279555\pi\)
0.638500 + 0.769622i \(0.279555\pi\)
\(948\) −53.1322 10.4911i −0.0560466 0.0110666i
\(949\) 120.527 0.127004
\(950\) 0 0
\(951\) −983.776 194.250i −1.03446 0.204258i
\(952\) 115.473i 0.121296i
\(953\) 1205.26 1.26470 0.632352 0.774681i \(-0.282090\pi\)
0.632352 + 0.774681i \(0.282090\pi\)
\(954\) −41.8420 17.1940i −0.0438595 0.0180231i
\(955\) 0 0
\(956\) 605.432i 0.633297i
\(957\) −670.114 132.316i −0.700223 0.138261i
\(958\) 736.211i 0.768487i
\(959\) 2021.84i 2.10828i
\(960\) 0 0
\(961\) −897.000 −0.933403
\(962\) 847.783 0.881272
\(963\) 135.541 + 55.6975i 0.140749 + 0.0578375i
\(964\) −475.052 −0.492793
\(965\) 0 0
\(966\) 166.710 844.304i 0.172578 0.874020i
\(967\) 1845.93i 1.90893i 0.298325 + 0.954464i \(0.403572\pi\)
−0.298325 + 0.954464i \(0.596428\pi\)
\(968\) 138.593 0.143175
\(969\) −114.790 22.6656i −0.118462 0.0233908i
\(970\) 0 0
\(971\) 1057.91i 1.08950i 0.838598 + 0.544751i \(0.183376\pi\)
−0.838598 + 0.544751i \(0.816624\pi\)
\(972\) −272.838 402.189i −0.280697 0.413774i
\(973\) 2168.89i 2.22908i
\(974\) 372.478i 0.382421i
\(975\) 0 0
\(976\) 87.7893 0.0899481
\(977\) −964.028 −0.986722 −0.493361 0.869825i \(-0.664232\pi\)
−0.493361 + 0.869825i \(0.664232\pi\)
\(978\) 130.988 663.390i 0.133935 0.678313i
\(979\) 60.3160 0.0616098
\(980\) 0 0
\(981\) 781.193 + 321.013i 0.796323 + 0.327231i
\(982\) 1006.42i 1.02487i
\(983\) −460.718 −0.468685 −0.234343 0.972154i \(-0.575294\pi\)
−0.234343 + 0.972154i \(0.575294\pi\)
\(984\) −33.7367 + 170.859i −0.0342852 + 0.173637i
\(985\) 0 0
\(986\) 134.871i 0.136786i
\(987\) −589.410 + 2985.06i −0.597173 + 3.02438i
\(988\) 219.473i 0.222139i
\(989\) 749.812i 0.758152i
\(990\) 0 0
\(991\) 1237.89 1.24914 0.624568 0.780971i \(-0.285275\pi\)
0.624568 + 0.780971i \(0.285275\pi\)
\(992\) 45.2548 0.0456198
\(993\) −1146.13 226.307i −1.15421 0.227903i
\(994\) −1125.10 −1.13190
\(995\) 0 0
\(996\) 4.05267 + 0.800212i 0.00406894 + 0.000803425i
\(997\) 9.36798i 0.00939617i 0.999989 + 0.00469809i \(0.00149545\pi\)
−0.999989 + 0.00469809i \(0.998505\pi\)
\(998\) −32.6386 −0.0327040
\(999\) 893.557 1349.57i 0.894451 1.35093i
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 150.3.b.b.149.5 8
3.2 odd 2 inner 150.3.b.b.149.3 8
4.3 odd 2 1200.3.c.k.449.8 8
5.2 odd 4 30.3.d.a.11.3 yes 4
5.3 odd 4 150.3.d.c.101.2 4
5.4 even 2 inner 150.3.b.b.149.4 8
12.11 even 2 1200.3.c.k.449.2 8
15.2 even 4 30.3.d.a.11.1 4
15.8 even 4 150.3.d.c.101.4 4
15.14 odd 2 inner 150.3.b.b.149.6 8
20.3 even 4 1200.3.l.u.401.2 4
20.7 even 4 240.3.l.c.161.3 4
20.19 odd 2 1200.3.c.k.449.1 8
40.27 even 4 960.3.l.f.641.2 4
40.37 odd 4 960.3.l.e.641.3 4
45.2 even 12 810.3.h.a.701.1 8
45.7 odd 12 810.3.h.a.701.4 8
45.22 odd 12 810.3.h.a.431.1 8
45.32 even 12 810.3.h.a.431.4 8
60.23 odd 4 1200.3.l.u.401.1 4
60.47 odd 4 240.3.l.c.161.4 4
60.59 even 2 1200.3.c.k.449.7 8
120.77 even 4 960.3.l.e.641.4 4
120.107 odd 4 960.3.l.f.641.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
30.3.d.a.11.1 4 15.2 even 4
30.3.d.a.11.3 yes 4 5.2 odd 4
150.3.b.b.149.3 8 3.2 odd 2 inner
150.3.b.b.149.4 8 5.4 even 2 inner
150.3.b.b.149.5 8 1.1 even 1 trivial
150.3.b.b.149.6 8 15.14 odd 2 inner
150.3.d.c.101.2 4 5.3 odd 4
150.3.d.c.101.4 4 15.8 even 4
240.3.l.c.161.3 4 20.7 even 4
240.3.l.c.161.4 4 60.47 odd 4
810.3.h.a.431.1 8 45.22 odd 12
810.3.h.a.431.4 8 45.32 even 12
810.3.h.a.701.1 8 45.2 even 12
810.3.h.a.701.4 8 45.7 odd 12
960.3.l.e.641.3 4 40.37 odd 4
960.3.l.e.641.4 4 120.77 even 4
960.3.l.f.641.1 4 120.107 odd 4
960.3.l.f.641.2 4 40.27 even 4
1200.3.c.k.449.1 8 20.19 odd 2
1200.3.c.k.449.2 8 12.11 even 2
1200.3.c.k.449.7 8 60.59 even 2
1200.3.c.k.449.8 8 4.3 odd 2
1200.3.l.u.401.1 4 60.23 odd 4
1200.3.l.u.401.2 4 20.3 even 4