Properties

Label 197.14.a.b.1.5
Level $197$
Weight $14$
Character 197.1
Self dual yes
Analytic conductor $211.245$
Analytic rank $0$
Dimension $109$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [197,14,Mod(1,197)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(197, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("197.1");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 197.a (trivial)

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: yes
Analytic conductor: \(211.244930035\)
Analytic rank: \(0\)
Dimension: \(109\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 197.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-172.035 q^{2} -63.8588 q^{3} +21404.1 q^{4} -26311.4 q^{5} +10986.0 q^{6} -168215. q^{7} -2.27295e6 q^{8} -1.59025e6 q^{9} +O(q^{10})\) \(q-172.035 q^{2} -63.8588 q^{3} +21404.1 q^{4} -26311.4 q^{5} +10986.0 q^{6} -168215. q^{7} -2.27295e6 q^{8} -1.59025e6 q^{9} +4.52650e6 q^{10} +7.08307e6 q^{11} -1.36684e6 q^{12} -1.35177e7 q^{13} +2.89389e7 q^{14} +1.68022e6 q^{15} +2.15685e8 q^{16} +1.48916e8 q^{17} +2.73578e8 q^{18} +3.64027e8 q^{19} -5.63173e8 q^{20} +1.07420e7 q^{21} -1.21854e9 q^{22} +6.00850e8 q^{23} +1.45148e8 q^{24} -5.28411e8 q^{25} +2.32552e9 q^{26} +2.03363e8 q^{27} -3.60049e9 q^{28} +3.66758e9 q^{29} -2.89056e8 q^{30} -3.03901e9 q^{31} -1.84854e10 q^{32} -4.52316e8 q^{33} -2.56189e10 q^{34} +4.42597e9 q^{35} -3.40378e10 q^{36} +1.64898e10 q^{37} -6.26254e10 q^{38} +8.63224e8 q^{39} +5.98046e10 q^{40} +2.85360e9 q^{41} -1.84800e9 q^{42} +4.65537e10 q^{43} +1.51607e11 q^{44} +4.18416e10 q^{45} -1.03367e11 q^{46} -5.12739e10 q^{47} -1.37734e10 q^{48} -6.85928e10 q^{49} +9.09053e10 q^{50} -9.50961e9 q^{51} -2.89335e11 q^{52} +2.79882e10 q^{53} -3.49855e10 q^{54} -1.86366e11 q^{55} +3.82344e11 q^{56} -2.32463e10 q^{57} -6.30952e11 q^{58} +3.35418e11 q^{59} +3.59636e10 q^{60} +5.64009e10 q^{61} +5.22817e11 q^{62} +2.67503e11 q^{63} +1.41325e12 q^{64} +3.55670e11 q^{65} +7.78143e10 q^{66} +7.15230e10 q^{67} +3.18742e12 q^{68} -3.83695e10 q^{69} -7.61424e11 q^{70} -8.56849e11 q^{71} +3.61455e12 q^{72} +2.39608e12 q^{73} -2.83683e12 q^{74} +3.37437e10 q^{75} +7.79167e12 q^{76} -1.19148e12 q^{77} -1.48505e11 q^{78} +1.85526e12 q^{79} -5.67499e12 q^{80} +2.52238e12 q^{81} -4.90921e11 q^{82} +3.36851e12 q^{83} +2.29923e11 q^{84} -3.91820e12 q^{85} -8.00888e12 q^{86} -2.34207e11 q^{87} -1.60995e13 q^{88} -8.44395e12 q^{89} -7.19824e12 q^{90} +2.27388e12 q^{91} +1.28607e13 q^{92} +1.94067e11 q^{93} +8.82091e12 q^{94} -9.57807e12 q^{95} +1.18046e12 q^{96} -7.81335e12 q^{97} +1.18004e13 q^{98} -1.12638e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 109 q + 192 q^{2} + 8018 q^{3} + 471040 q^{4} + 88496 q^{5} + 383232 q^{6} + 1680731 q^{7} + 1820859 q^{8} + 59521391 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 109 q + 192 q^{2} + 8018 q^{3} + 471040 q^{4} + 88496 q^{5} + 383232 q^{6} + 1680731 q^{7} + 1820859 q^{8} + 59521391 q^{9} + 16373653 q^{10} + 21199298 q^{11} + 63225856 q^{12} + 59695238 q^{13} + 37888529 q^{14} + 87246239 q^{15} + 2130706432 q^{16} + 228353715 q^{17} + 400647337 q^{18} + 1139301305 q^{19} + 1109969259 q^{20} + 539982398 q^{21} + 1613315649 q^{22} + 920306804 q^{23} + 5542439613 q^{24} + 31241700999 q^{25} + 1864366110 q^{26} + 17825460755 q^{27} + 20413389070 q^{28} + 7185436621 q^{29} + 2050251883 q^{30} + 28475592572 q^{31} + 8334714660 q^{32} + 19623425846 q^{33} + 37845014194 q^{34} + 25255003636 q^{35} + 287968706746 q^{36} + 71523920490 q^{37} + 67778214914 q^{38} + 44951568463 q^{39} + 169184871486 q^{40} + 69139231052 q^{41} + 58715177635 q^{42} + 247544146139 q^{43} + 63861560722 q^{44} + 257443045479 q^{45} + 160530477869 q^{46} + 308496573061 q^{47} + 412228130018 q^{48} + 1736616239908 q^{49} + 1680360028531 q^{50} + 756579032995 q^{51} + 928015404666 q^{52} + 342783723680 q^{53} - 597894730601 q^{54} + 59276330527 q^{55} - 3822929869144 q^{56} - 562905761941 q^{57} + 62740419347 q^{58} + 827401964151 q^{59} - 2247133283907 q^{60} + 988213134514 q^{61} + 1937380192071 q^{62} + 1788190111357 q^{63} + 11682175668457 q^{64} + 2494670804291 q^{65} + 11819807890512 q^{66} + 8038740399790 q^{67} + 10126245189885 q^{68} + 5225665164579 q^{69} + 11464042631319 q^{70} + 4867145119603 q^{71} + 18133468947055 q^{72} + 9684156738615 q^{73} + 16996786880941 q^{74} + 16718732018262 q^{75} + 21454522032798 q^{76} + 6593100920650 q^{77} + 33749579076633 q^{78} + 7591753073823 q^{79} + 24349241260570 q^{80} + 38778649605417 q^{81} + 25555033184251 q^{82} + 16945724819556 q^{83} + 21855489402730 q^{84} + 15544906794766 q^{85} + 18664144286914 q^{86} + 19049540636401 q^{87} + 17318749473003 q^{88} + 11289674998576 q^{89} + 20983303956671 q^{90} + 47242561944227 q^{91} - 25046698097386 q^{92} - 5411884145985 q^{93} + 18338784709341 q^{94} + 6784117894603 q^{95} - 36827486682955 q^{96} + 45969533477736 q^{97} - 42983409526150 q^{98} + 12084396239183 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −172.035 −1.90074 −0.950369 0.311124i \(-0.899295\pi\)
−0.950369 + 0.311124i \(0.899295\pi\)
\(3\) −63.8588 −0.0505746 −0.0252873 0.999680i \(-0.508050\pi\)
−0.0252873 + 0.999680i \(0.508050\pi\)
\(4\) 21404.1 2.61281
\(5\) −26311.4 −0.753077 −0.376539 0.926401i \(-0.622886\pi\)
−0.376539 + 0.926401i \(0.622886\pi\)
\(6\) 10986.0 0.0961291
\(7\) −168215. −0.540414 −0.270207 0.962802i \(-0.587092\pi\)
−0.270207 + 0.962802i \(0.587092\pi\)
\(8\) −2.27295e6 −3.06553
\(9\) −1.59025e6 −0.997442
\(10\) 4.52650e6 1.43140
\(11\) 7.08307e6 1.20551 0.602753 0.797928i \(-0.294070\pi\)
0.602753 + 0.797928i \(0.294070\pi\)
\(12\) −1.36684e6 −0.132142
\(13\) −1.35177e7 −0.776732 −0.388366 0.921505i \(-0.626960\pi\)
−0.388366 + 0.921505i \(0.626960\pi\)
\(14\) 2.89389e7 1.02719
\(15\) 1.68022e6 0.0380866
\(16\) 2.15685e8 3.21396
\(17\) 1.48916e8 1.49632 0.748160 0.663518i \(-0.230938\pi\)
0.748160 + 0.663518i \(0.230938\pi\)
\(18\) 2.73578e8 1.89588
\(19\) 3.64027e8 1.77515 0.887574 0.460664i \(-0.152389\pi\)
0.887574 + 0.460664i \(0.152389\pi\)
\(20\) −5.63173e8 −1.96765
\(21\) 1.07420e7 0.0273312
\(22\) −1.21854e9 −2.29135
\(23\) 6.00850e8 0.846320 0.423160 0.906055i \(-0.360921\pi\)
0.423160 + 0.906055i \(0.360921\pi\)
\(24\) 1.45148e8 0.155038
\(25\) −5.28411e8 −0.432874
\(26\) 2.32552e9 1.47636
\(27\) 2.03363e8 0.101020
\(28\) −3.60049e9 −1.41200
\(29\) 3.66758e9 1.14496 0.572482 0.819917i \(-0.305981\pi\)
0.572482 + 0.819917i \(0.305981\pi\)
\(30\) −2.89056e8 −0.0723926
\(31\) −3.03901e9 −0.615009 −0.307504 0.951547i \(-0.599494\pi\)
−0.307504 + 0.951547i \(0.599494\pi\)
\(32\) −1.84854e10 −3.04337
\(33\) −4.52316e8 −0.0609680
\(34\) −2.56189e10 −2.84411
\(35\) 4.42597e9 0.406974
\(36\) −3.40378e10 −2.60613
\(37\) 1.64898e10 1.05659 0.528293 0.849062i \(-0.322832\pi\)
0.528293 + 0.849062i \(0.322832\pi\)
\(38\) −6.26254e10 −3.37409
\(39\) 8.63224e8 0.0392829
\(40\) 5.98046e10 2.30858
\(41\) 2.85360e9 0.0938207 0.0469104 0.998899i \(-0.485062\pi\)
0.0469104 + 0.998899i \(0.485062\pi\)
\(42\) −1.84800e9 −0.0519495
\(43\) 4.65537e10 1.12308 0.561539 0.827451i \(-0.310210\pi\)
0.561539 + 0.827451i \(0.310210\pi\)
\(44\) 1.51607e11 3.14976
\(45\) 4.18416e10 0.751151
\(46\) −1.03367e11 −1.60863
\(47\) −5.12739e10 −0.693841 −0.346920 0.937895i \(-0.612773\pi\)
−0.346920 + 0.937895i \(0.612773\pi\)
\(48\) −1.37734e10 −0.162545
\(49\) −6.85928e10 −0.707952
\(50\) 9.09053e10 0.822781
\(51\) −9.50961e9 −0.0756757
\(52\) −2.89335e11 −2.02945
\(53\) 2.79882e10 0.173453 0.0867264 0.996232i \(-0.472359\pi\)
0.0867264 + 0.996232i \(0.472359\pi\)
\(54\) −3.49855e10 −0.192012
\(55\) −1.86366e11 −0.907839
\(56\) 3.82344e11 1.65666
\(57\) −2.32463e10 −0.0897774
\(58\) −6.30952e11 −2.17628
\(59\) 3.35418e11 1.03526 0.517628 0.855606i \(-0.326815\pi\)
0.517628 + 0.855606i \(0.326815\pi\)
\(60\) 3.59636e10 0.0995129
\(61\) 5.64009e10 0.140166 0.0700829 0.997541i \(-0.477674\pi\)
0.0700829 + 0.997541i \(0.477674\pi\)
\(62\) 5.22817e11 1.16897
\(63\) 2.67503e11 0.539032
\(64\) 1.41325e12 2.57069
\(65\) 3.55670e11 0.584939
\(66\) 7.78143e10 0.115884
\(67\) 7.15230e10 0.0965961 0.0482981 0.998833i \(-0.484620\pi\)
0.0482981 + 0.998833i \(0.484620\pi\)
\(68\) 3.18742e12 3.90960
\(69\) −3.83695e10 −0.0428023
\(70\) −7.61424e11 −0.773551
\(71\) −8.56849e11 −0.793825 −0.396913 0.917856i \(-0.629918\pi\)
−0.396913 + 0.917856i \(0.629918\pi\)
\(72\) 3.61455e12 3.05769
\(73\) 2.39608e12 1.85312 0.926558 0.376151i \(-0.122753\pi\)
0.926558 + 0.376151i \(0.122753\pi\)
\(74\) −2.83683e12 −2.00830
\(75\) 3.37437e10 0.0218924
\(76\) 7.79167e12 4.63812
\(77\) −1.19148e12 −0.651473
\(78\) −1.48505e11 −0.0746665
\(79\) 1.85526e12 0.858673 0.429337 0.903144i \(-0.358747\pi\)
0.429337 + 0.903144i \(0.358747\pi\)
\(80\) −5.67499e12 −2.42036
\(81\) 2.52238e12 0.992333
\(82\) −4.90921e11 −0.178329
\(83\) 3.36851e12 1.13092 0.565458 0.824777i \(-0.308699\pi\)
0.565458 + 0.824777i \(0.308699\pi\)
\(84\) 2.29923e11 0.0714113
\(85\) −3.91820e12 −1.12684
\(86\) −8.00888e12 −2.13468
\(87\) −2.34207e11 −0.0579061
\(88\) −1.60995e13 −3.69551
\(89\) −8.44395e12 −1.80099 −0.900493 0.434870i \(-0.856794\pi\)
−0.900493 + 0.434870i \(0.856794\pi\)
\(90\) −7.19824e12 −1.42774
\(91\) 2.27388e12 0.419757
\(92\) 1.28607e13 2.21127
\(93\) 1.94067e11 0.0311038
\(94\) 8.82091e12 1.31881
\(95\) −9.57807e12 −1.33682
\(96\) 1.18046e12 0.153917
\(97\) −7.81335e12 −0.952404 −0.476202 0.879336i \(-0.657987\pi\)
−0.476202 + 0.879336i \(0.657987\pi\)
\(98\) 1.18004e13 1.34563
\(99\) −1.12638e13 −1.20242
\(100\) −1.13102e13 −1.13102
\(101\) −1.52078e13 −1.42553 −0.712765 0.701403i \(-0.752557\pi\)
−0.712765 + 0.701403i \(0.752557\pi\)
\(102\) 1.63599e12 0.143840
\(103\) 1.30991e13 1.08093 0.540467 0.841365i \(-0.318248\pi\)
0.540467 + 0.841365i \(0.318248\pi\)
\(104\) 3.07251e13 2.38109
\(105\) −2.82637e11 −0.0205825
\(106\) −4.81495e12 −0.329688
\(107\) −1.28498e13 −0.827753 −0.413876 0.910333i \(-0.635825\pi\)
−0.413876 + 0.910333i \(0.635825\pi\)
\(108\) 4.35280e12 0.263945
\(109\) −1.26119e13 −0.720290 −0.360145 0.932896i \(-0.617273\pi\)
−0.360145 + 0.932896i \(0.617273\pi\)
\(110\) 3.20615e13 1.72557
\(111\) −1.05302e12 −0.0534364
\(112\) −3.62814e13 −1.73687
\(113\) −1.11804e13 −0.505182 −0.252591 0.967573i \(-0.581283\pi\)
−0.252591 + 0.967573i \(0.581283\pi\)
\(114\) 3.99918e12 0.170643
\(115\) −1.58092e13 −0.637345
\(116\) 7.85012e13 2.99157
\(117\) 2.14965e13 0.774745
\(118\) −5.77037e13 −1.96775
\(119\) −2.50499e13 −0.808633
\(120\) −3.81905e12 −0.116755
\(121\) 1.56472e13 0.453244
\(122\) −9.70294e12 −0.266419
\(123\) −1.82228e11 −0.00474494
\(124\) −6.50474e13 −1.60690
\(125\) 4.60217e13 1.07907
\(126\) −4.60199e13 −1.02456
\(127\) 3.75142e13 0.793362 0.396681 0.917957i \(-0.370162\pi\)
0.396681 + 0.917957i \(0.370162\pi\)
\(128\) −9.16967e13 −1.84285
\(129\) −2.97286e12 −0.0567992
\(130\) −6.11878e13 −1.11182
\(131\) −6.86287e13 −1.18643 −0.593215 0.805044i \(-0.702142\pi\)
−0.593215 + 0.805044i \(0.702142\pi\)
\(132\) −9.68144e12 −0.159298
\(133\) −6.12347e13 −0.959316
\(134\) −1.23045e13 −0.183604
\(135\) −5.35076e12 −0.0760757
\(136\) −3.38480e14 −4.58701
\(137\) 5.99220e13 0.774288 0.387144 0.922019i \(-0.373462\pi\)
0.387144 + 0.922019i \(0.373462\pi\)
\(138\) 6.60091e12 0.0813560
\(139\) 9.78581e13 1.15080 0.575401 0.817871i \(-0.304846\pi\)
0.575401 + 0.817871i \(0.304846\pi\)
\(140\) 9.47341e13 1.06334
\(141\) 3.27428e12 0.0350907
\(142\) 1.47408e14 1.50885
\(143\) −9.57469e13 −0.936355
\(144\) −3.42992e14 −3.20574
\(145\) −9.64992e13 −0.862247
\(146\) −4.12210e14 −3.52229
\(147\) 4.38025e12 0.0358044
\(148\) 3.52951e14 2.76066
\(149\) −7.83903e13 −0.586883 −0.293442 0.955977i \(-0.594801\pi\)
−0.293442 + 0.955977i \(0.594801\pi\)
\(150\) −5.80510e12 −0.0416118
\(151\) −3.08346e13 −0.211684 −0.105842 0.994383i \(-0.533754\pi\)
−0.105842 + 0.994383i \(0.533754\pi\)
\(152\) −8.27415e14 −5.44177
\(153\) −2.36814e14 −1.49249
\(154\) 2.04976e14 1.23828
\(155\) 7.99608e13 0.463149
\(156\) 1.84765e13 0.102639
\(157\) 2.70280e14 1.44034 0.720172 0.693795i \(-0.244063\pi\)
0.720172 + 0.693795i \(0.244063\pi\)
\(158\) −3.19170e14 −1.63211
\(159\) −1.78729e12 −0.00877230
\(160\) 4.86379e14 2.29189
\(161\) −1.01072e14 −0.457364
\(162\) −4.33938e14 −1.88617
\(163\) −1.75321e14 −0.732173 −0.366086 0.930581i \(-0.619303\pi\)
−0.366086 + 0.930581i \(0.619303\pi\)
\(164\) 6.10789e13 0.245136
\(165\) 1.19011e13 0.0459136
\(166\) −5.79503e14 −2.14958
\(167\) 3.60391e14 1.28563 0.642816 0.766020i \(-0.277766\pi\)
0.642816 + 0.766020i \(0.277766\pi\)
\(168\) −2.44160e13 −0.0837847
\(169\) −1.20147e14 −0.396688
\(170\) 6.74069e14 2.14184
\(171\) −5.78892e14 −1.77061
\(172\) 9.96442e14 2.93439
\(173\) −3.27747e14 −0.929479 −0.464739 0.885447i \(-0.653852\pi\)
−0.464739 + 0.885447i \(0.653852\pi\)
\(174\) 4.02918e13 0.110064
\(175\) 8.88866e13 0.233932
\(176\) 1.52771e15 3.87445
\(177\) −2.14194e13 −0.0523577
\(178\) 1.45266e15 3.42320
\(179\) 4.61583e13 0.104883 0.0524415 0.998624i \(-0.483300\pi\)
0.0524415 + 0.998624i \(0.483300\pi\)
\(180\) 8.95584e14 1.96261
\(181\) 1.40907e14 0.297866 0.148933 0.988847i \(-0.452416\pi\)
0.148933 + 0.988847i \(0.452416\pi\)
\(182\) −3.91187e14 −0.797849
\(183\) −3.60169e12 −0.00708882
\(184\) −1.36570e15 −2.59442
\(185\) −4.33871e14 −0.795692
\(186\) −3.33864e13 −0.0591202
\(187\) 1.05479e15 1.80382
\(188\) −1.09747e15 −1.81287
\(189\) −3.42086e13 −0.0545926
\(190\) 1.64777e15 2.54095
\(191\) −8.93595e14 −1.33175 −0.665877 0.746062i \(-0.731942\pi\)
−0.665877 + 0.746062i \(0.731942\pi\)
\(192\) −9.02486e13 −0.130012
\(193\) 7.79283e14 1.08536 0.542679 0.839940i \(-0.317410\pi\)
0.542679 + 0.839940i \(0.317410\pi\)
\(194\) 1.34417e15 1.81027
\(195\) −2.27127e13 −0.0295831
\(196\) −1.46817e15 −1.84974
\(197\) 5.84517e13 0.0712470
\(198\) 1.93777e15 2.28549
\(199\) −9.47463e14 −1.08148 −0.540738 0.841191i \(-0.681855\pi\)
−0.540738 + 0.841191i \(0.681855\pi\)
\(200\) 1.20105e15 1.32699
\(201\) −4.56737e12 −0.00488531
\(202\) 2.61627e15 2.70956
\(203\) −6.16940e14 −0.618755
\(204\) −2.03545e14 −0.197726
\(205\) −7.50825e13 −0.0706543
\(206\) −2.25351e15 −2.05457
\(207\) −9.55498e14 −0.844156
\(208\) −2.91557e15 −2.49638
\(209\) 2.57843e15 2.13995
\(210\) 4.86236e13 0.0391220
\(211\) 1.38881e15 1.08345 0.541724 0.840557i \(-0.317772\pi\)
0.541724 + 0.840557i \(0.317772\pi\)
\(212\) 5.99062e14 0.453199
\(213\) 5.47173e13 0.0401474
\(214\) 2.21061e15 1.57334
\(215\) −1.22490e15 −0.845764
\(216\) −4.62233e14 −0.309679
\(217\) 5.11207e14 0.332360
\(218\) 2.16969e15 1.36908
\(219\) −1.53011e14 −0.0937206
\(220\) −3.98900e15 −2.37201
\(221\) −2.01301e15 −1.16224
\(222\) 1.81157e14 0.101569
\(223\) −1.18057e15 −0.642851 −0.321426 0.946935i \(-0.604162\pi\)
−0.321426 + 0.946935i \(0.604162\pi\)
\(224\) 3.10952e15 1.64468
\(225\) 8.40303e14 0.431767
\(226\) 1.92342e15 0.960219
\(227\) −8.98384e14 −0.435807 −0.217903 0.975970i \(-0.569922\pi\)
−0.217903 + 0.975970i \(0.569922\pi\)
\(228\) −4.97567e14 −0.234571
\(229\) 2.00568e13 0.00919032 0.00459516 0.999989i \(-0.498537\pi\)
0.00459516 + 0.999989i \(0.498537\pi\)
\(230\) 2.71974e15 1.21143
\(231\) 7.60863e13 0.0329480
\(232\) −8.33622e15 −3.50992
\(233\) −2.49792e15 −1.02274 −0.511369 0.859361i \(-0.670862\pi\)
−0.511369 + 0.859361i \(0.670862\pi\)
\(234\) −3.69815e15 −1.47259
\(235\) 1.34909e15 0.522516
\(236\) 7.17932e15 2.70493
\(237\) −1.18474e14 −0.0434271
\(238\) 4.30947e15 1.53700
\(239\) −7.52534e14 −0.261180 −0.130590 0.991436i \(-0.541687\pi\)
−0.130590 + 0.991436i \(0.541687\pi\)
\(240\) 3.62398e14 0.122409
\(241\) 5.34556e15 1.75745 0.878723 0.477331i \(-0.158396\pi\)
0.878723 + 0.477331i \(0.158396\pi\)
\(242\) −2.69187e15 −0.861499
\(243\) −4.85301e14 −0.151207
\(244\) 1.20721e15 0.366226
\(245\) 1.80478e15 0.533143
\(246\) 3.13496e13 0.00901890
\(247\) −4.92080e15 −1.37881
\(248\) 6.90753e15 1.88533
\(249\) −2.15109e14 −0.0571956
\(250\) −7.91736e15 −2.05102
\(251\) 1.16407e15 0.293832 0.146916 0.989149i \(-0.453065\pi\)
0.146916 + 0.989149i \(0.453065\pi\)
\(252\) 5.72566e15 1.40839
\(253\) 4.25586e15 1.02024
\(254\) −6.45376e15 −1.50797
\(255\) 2.50212e14 0.0569897
\(256\) 4.19770e15 0.932076
\(257\) −9.44364e14 −0.204444 −0.102222 0.994762i \(-0.532595\pi\)
−0.102222 + 0.994762i \(0.532595\pi\)
\(258\) 5.11437e14 0.107960
\(259\) −2.77383e15 −0.570995
\(260\) 7.61281e15 1.52833
\(261\) −5.83234e15 −1.14204
\(262\) 1.18066e16 2.25509
\(263\) 4.27412e15 0.796405 0.398202 0.917298i \(-0.369634\pi\)
0.398202 + 0.917298i \(0.369634\pi\)
\(264\) 1.02809e15 0.186899
\(265\) −7.36409e14 −0.130623
\(266\) 1.05345e16 1.82341
\(267\) 5.39220e14 0.0910841
\(268\) 1.53089e15 0.252387
\(269\) −6.63891e15 −1.06833 −0.534167 0.845379i \(-0.679375\pi\)
−0.534167 + 0.845379i \(0.679375\pi\)
\(270\) 9.20520e14 0.144600
\(271\) 7.41915e14 0.113777 0.0568884 0.998381i \(-0.481882\pi\)
0.0568884 + 0.998381i \(0.481882\pi\)
\(272\) 3.21191e16 4.80911
\(273\) −1.45207e14 −0.0212290
\(274\) −1.03087e16 −1.47172
\(275\) −3.74277e15 −0.521833
\(276\) −8.21266e14 −0.111834
\(277\) 4.98961e15 0.663664 0.331832 0.943339i \(-0.392333\pi\)
0.331832 + 0.943339i \(0.392333\pi\)
\(278\) −1.68350e16 −2.18737
\(279\) 4.83277e15 0.613436
\(280\) −1.00600e16 −1.24759
\(281\) 9.37190e15 1.13563 0.567815 0.823156i \(-0.307789\pi\)
0.567815 + 0.823156i \(0.307789\pi\)
\(282\) −5.63292e14 −0.0666983
\(283\) 5.30685e15 0.614080 0.307040 0.951697i \(-0.400661\pi\)
0.307040 + 0.951697i \(0.400661\pi\)
\(284\) −1.83401e16 −2.07411
\(285\) 6.11643e14 0.0676093
\(286\) 1.64718e16 1.77977
\(287\) −4.80019e14 −0.0507021
\(288\) 2.93964e16 3.03559
\(289\) 1.22715e16 1.23897
\(290\) 1.66013e16 1.63891
\(291\) 4.98951e14 0.0481674
\(292\) 5.12860e16 4.84184
\(293\) 3.77760e15 0.348800 0.174400 0.984675i \(-0.444202\pi\)
0.174400 + 0.984675i \(0.444202\pi\)
\(294\) −7.53557e14 −0.0680548
\(295\) −8.82533e15 −0.779628
\(296\) −3.74806e16 −3.23900
\(297\) 1.44043e15 0.121780
\(298\) 1.34859e16 1.11551
\(299\) −8.12210e15 −0.657364
\(300\) 7.22254e14 0.0572008
\(301\) −7.83103e15 −0.606927
\(302\) 5.30463e15 0.402356
\(303\) 9.71149e14 0.0720956
\(304\) 7.85152e16 5.70526
\(305\) −1.48399e15 −0.105556
\(306\) 4.07403e16 2.83684
\(307\) −2.77133e16 −1.88925 −0.944624 0.328156i \(-0.893573\pi\)
−0.944624 + 0.328156i \(0.893573\pi\)
\(308\) −2.55025e16 −1.70217
\(309\) −8.36492e14 −0.0546678
\(310\) −1.37561e16 −0.880326
\(311\) −2.22649e16 −1.39533 −0.697666 0.716424i \(-0.745778\pi\)
−0.697666 + 0.716424i \(0.745778\pi\)
\(312\) −1.96207e15 −0.120423
\(313\) −2.18947e16 −1.31613 −0.658067 0.752959i \(-0.728626\pi\)
−0.658067 + 0.752959i \(0.728626\pi\)
\(314\) −4.64977e16 −2.73772
\(315\) −7.03838e15 −0.405933
\(316\) 3.97102e16 2.24355
\(317\) 5.02815e15 0.278306 0.139153 0.990271i \(-0.455562\pi\)
0.139153 + 0.990271i \(0.455562\pi\)
\(318\) 3.07477e14 0.0166739
\(319\) 2.59777e16 1.38026
\(320\) −3.71847e16 −1.93593
\(321\) 8.20570e14 0.0418632
\(322\) 1.73879e16 0.869329
\(323\) 5.42095e16 2.65619
\(324\) 5.39893e16 2.59278
\(325\) 7.14290e15 0.336227
\(326\) 3.01613e16 1.39167
\(327\) 8.05378e14 0.0364283
\(328\) −6.48610e15 −0.287610
\(329\) 8.62502e15 0.374962
\(330\) −2.04741e15 −0.0872698
\(331\) −4.07285e16 −1.70222 −0.851111 0.524985i \(-0.824071\pi\)
−0.851111 + 0.524985i \(0.824071\pi\)
\(332\) 7.21001e16 2.95487
\(333\) −2.62229e16 −1.05388
\(334\) −6.20000e16 −2.44365
\(335\) −1.88187e15 −0.0727444
\(336\) 2.31689e15 0.0878415
\(337\) 4.09748e16 1.52378 0.761890 0.647707i \(-0.224272\pi\)
0.761890 + 0.647707i \(0.224272\pi\)
\(338\) 2.06695e16 0.754000
\(339\) 7.13967e14 0.0255494
\(340\) −8.38657e16 −2.94423
\(341\) −2.15255e16 −0.741397
\(342\) 9.95898e16 3.36546
\(343\) 2.78365e16 0.923002
\(344\) −1.05814e17 −3.44282
\(345\) 1.00956e15 0.0322334
\(346\) 5.63841e16 1.76670
\(347\) −1.30655e16 −0.401776 −0.200888 0.979614i \(-0.564383\pi\)
−0.200888 + 0.979614i \(0.564383\pi\)
\(348\) −5.01299e15 −0.151298
\(349\) −7.64906e15 −0.226591 −0.113296 0.993561i \(-0.536141\pi\)
−0.113296 + 0.993561i \(0.536141\pi\)
\(350\) −1.52916e16 −0.444643
\(351\) −2.74899e15 −0.0784653
\(352\) −1.30934e17 −3.66880
\(353\) 2.31293e16 0.636248 0.318124 0.948049i \(-0.396947\pi\)
0.318124 + 0.948049i \(0.396947\pi\)
\(354\) 3.68489e15 0.0995183
\(355\) 2.25449e16 0.597812
\(356\) −1.80735e17 −4.70563
\(357\) 1.59966e15 0.0408963
\(358\) −7.94086e15 −0.199355
\(359\) −6.06805e16 −1.49601 −0.748007 0.663691i \(-0.768989\pi\)
−0.748007 + 0.663691i \(0.768989\pi\)
\(360\) −9.51040e16 −2.30268
\(361\) 9.04624e16 2.15115
\(362\) −2.42409e16 −0.566166
\(363\) −9.99212e14 −0.0229226
\(364\) 4.86704e16 1.09674
\(365\) −6.30443e16 −1.39554
\(366\) 6.19618e14 0.0134740
\(367\) −2.38532e16 −0.509585 −0.254792 0.966996i \(-0.582007\pi\)
−0.254792 + 0.966996i \(0.582007\pi\)
\(368\) 1.29594e17 2.72004
\(369\) −4.53793e15 −0.0935807
\(370\) 7.46412e16 1.51240
\(371\) −4.70802e15 −0.0937364
\(372\) 4.15384e15 0.0812683
\(373\) 4.49041e16 0.863333 0.431666 0.902033i \(-0.357926\pi\)
0.431666 + 0.902033i \(0.357926\pi\)
\(374\) −1.81460e17 −3.42860
\(375\) −2.93889e15 −0.0545733
\(376\) 1.16543e17 2.12699
\(377\) −4.95772e16 −0.889330
\(378\) 5.88508e15 0.103766
\(379\) −2.06523e16 −0.357942 −0.178971 0.983854i \(-0.557277\pi\)
−0.178971 + 0.983854i \(0.557277\pi\)
\(380\) −2.05010e17 −3.49287
\(381\) −2.39561e15 −0.0401240
\(382\) 1.53730e17 2.53132
\(383\) 6.19958e16 1.00362 0.501811 0.864977i \(-0.332667\pi\)
0.501811 + 0.864977i \(0.332667\pi\)
\(384\) 5.85564e15 0.0932012
\(385\) 3.13495e16 0.490609
\(386\) −1.34064e17 −2.06298
\(387\) −7.40318e16 −1.12020
\(388\) −1.67238e17 −2.48845
\(389\) 1.66800e16 0.244075 0.122037 0.992525i \(-0.461057\pi\)
0.122037 + 0.992525i \(0.461057\pi\)
\(390\) 3.90738e15 0.0562297
\(391\) 8.94763e16 1.26637
\(392\) 1.55908e17 2.17025
\(393\) 4.38254e15 0.0600032
\(394\) −1.00558e16 −0.135422
\(395\) −4.88145e16 −0.646648
\(396\) −2.41092e17 −3.14170
\(397\) −9.05295e16 −1.16052 −0.580259 0.814432i \(-0.697049\pi\)
−0.580259 + 0.814432i \(0.697049\pi\)
\(398\) 1.62997e17 2.05560
\(399\) 3.91037e15 0.0485170
\(400\) −1.13970e17 −1.39124
\(401\) −5.44307e16 −0.653740 −0.326870 0.945069i \(-0.605994\pi\)
−0.326870 + 0.945069i \(0.605994\pi\)
\(402\) 7.85749e14 0.00928570
\(403\) 4.10804e16 0.477697
\(404\) −3.25509e17 −3.72464
\(405\) −6.63674e16 −0.747304
\(406\) 1.06136e17 1.17609
\(407\) 1.16799e17 1.27372
\(408\) 2.16149e16 0.231986
\(409\) −3.72472e15 −0.0393452 −0.0196726 0.999806i \(-0.506262\pi\)
−0.0196726 + 0.999806i \(0.506262\pi\)
\(410\) 1.29168e16 0.134295
\(411\) −3.82655e15 −0.0391593
\(412\) 2.80375e17 2.82427
\(413\) −5.64222e16 −0.559468
\(414\) 1.64379e17 1.60452
\(415\) −8.86304e16 −0.851668
\(416\) 2.49881e17 2.36388
\(417\) −6.24910e15 −0.0582013
\(418\) −4.43580e17 −4.06749
\(419\) 3.64682e16 0.329248 0.164624 0.986356i \(-0.447359\pi\)
0.164624 + 0.986356i \(0.447359\pi\)
\(420\) −6.04960e15 −0.0537782
\(421\) 1.52315e17 1.33324 0.666619 0.745399i \(-0.267741\pi\)
0.666619 + 0.745399i \(0.267741\pi\)
\(422\) −2.38925e17 −2.05935
\(423\) 8.15380e16 0.692066
\(424\) −6.36157e16 −0.531724
\(425\) −7.86891e16 −0.647718
\(426\) −9.41330e15 −0.0763097
\(427\) −9.48746e15 −0.0757476
\(428\) −2.75038e17 −2.16276
\(429\) 6.11428e15 0.0473557
\(430\) 2.10725e17 1.60758
\(431\) 4.15615e16 0.312312 0.156156 0.987732i \(-0.450090\pi\)
0.156156 + 0.987732i \(0.450090\pi\)
\(432\) 4.38623e16 0.324674
\(433\) 1.11089e17 0.810026 0.405013 0.914311i \(-0.367267\pi\)
0.405013 + 0.914311i \(0.367267\pi\)
\(434\) −8.79456e16 −0.631729
\(435\) 6.16232e15 0.0436078
\(436\) −2.69946e17 −1.88198
\(437\) 2.18725e17 1.50234
\(438\) 2.63232e16 0.178138
\(439\) 1.52657e17 1.01788 0.508942 0.860801i \(-0.330037\pi\)
0.508942 + 0.860801i \(0.330037\pi\)
\(440\) 4.23601e17 2.78301
\(441\) 1.09079e17 0.706141
\(442\) 3.46308e17 2.20911
\(443\) −1.84693e17 −1.16098 −0.580491 0.814267i \(-0.697139\pi\)
−0.580491 + 0.814267i \(0.697139\pi\)
\(444\) −2.25390e16 −0.139619
\(445\) 2.22172e17 1.35628
\(446\) 2.03100e17 1.22189
\(447\) 5.00591e15 0.0296814
\(448\) −2.37730e17 −1.38924
\(449\) 3.14842e17 1.81339 0.906695 0.421787i \(-0.138597\pi\)
0.906695 + 0.421787i \(0.138597\pi\)
\(450\) −1.44562e17 −0.820677
\(451\) 2.02123e16 0.113101
\(452\) −2.39307e17 −1.31994
\(453\) 1.96906e15 0.0107058
\(454\) 1.54554e17 0.828355
\(455\) −5.98290e16 −0.316110
\(456\) 5.28377e16 0.275215
\(457\) 2.69381e17 1.38329 0.691644 0.722239i \(-0.256887\pi\)
0.691644 + 0.722239i \(0.256887\pi\)
\(458\) −3.45047e15 −0.0174684
\(459\) 3.02840e16 0.151158
\(460\) −3.38383e17 −1.66526
\(461\) 3.66421e17 1.77797 0.888986 0.457935i \(-0.151411\pi\)
0.888986 + 0.457935i \(0.151411\pi\)
\(462\) −1.30895e16 −0.0626255
\(463\) 3.66603e17 1.72950 0.864749 0.502204i \(-0.167478\pi\)
0.864749 + 0.502204i \(0.167478\pi\)
\(464\) 7.91042e17 3.67987
\(465\) −5.10620e15 −0.0234236
\(466\) 4.29730e17 1.94396
\(467\) −6.94235e16 −0.309704 −0.154852 0.987938i \(-0.549490\pi\)
−0.154852 + 0.987938i \(0.549490\pi\)
\(468\) 4.60113e17 2.02426
\(469\) −1.20312e16 −0.0522020
\(470\) −2.32091e17 −0.993166
\(471\) −1.72598e16 −0.0728448
\(472\) −7.62388e17 −3.17361
\(473\) 3.29744e17 1.35388
\(474\) 2.03818e16 0.0825435
\(475\) −1.92356e17 −0.768416
\(476\) −5.36172e17 −2.11280
\(477\) −4.45080e16 −0.173009
\(478\) 1.29462e17 0.496435
\(479\) 3.67023e17 1.38839 0.694196 0.719786i \(-0.255760\pi\)
0.694196 + 0.719786i \(0.255760\pi\)
\(480\) −3.10595e16 −0.115912
\(481\) −2.22905e17 −0.820684
\(482\) −9.19624e17 −3.34045
\(483\) 6.45432e15 0.0231310
\(484\) 3.34915e17 1.18424
\(485\) 2.05581e17 0.717234
\(486\) 8.34890e16 0.287404
\(487\) −2.68060e17 −0.910528 −0.455264 0.890357i \(-0.650455\pi\)
−0.455264 + 0.890357i \(0.650455\pi\)
\(488\) −1.28196e17 −0.429682
\(489\) 1.11958e16 0.0370293
\(490\) −3.10485e17 −1.01337
\(491\) −5.16026e17 −1.66204 −0.831021 0.556240i \(-0.812243\pi\)
−0.831021 + 0.556240i \(0.812243\pi\)
\(492\) −3.90042e15 −0.0123976
\(493\) 5.46162e17 1.71323
\(494\) 8.46552e17 2.62077
\(495\) 2.96367e17 0.905517
\(496\) −6.55470e17 −1.97661
\(497\) 1.44135e17 0.428995
\(498\) 3.70063e16 0.108714
\(499\) −4.94534e17 −1.43398 −0.716989 0.697085i \(-0.754480\pi\)
−0.716989 + 0.697085i \(0.754480\pi\)
\(500\) 9.85055e17 2.81939
\(501\) −2.30141e16 −0.0650203
\(502\) −2.00261e17 −0.558498
\(503\) −7.50547e16 −0.206626 −0.103313 0.994649i \(-0.532944\pi\)
−0.103313 + 0.994649i \(0.532944\pi\)
\(504\) −6.08021e17 −1.65242
\(505\) 4.00138e17 1.07353
\(506\) −7.32158e17 −1.93922
\(507\) 7.67243e15 0.0200623
\(508\) 8.02959e17 2.07290
\(509\) −6.81044e17 −1.73584 −0.867920 0.496704i \(-0.834543\pi\)
−0.867920 + 0.496704i \(0.834543\pi\)
\(510\) −4.30452e16 −0.108323
\(511\) −4.03056e17 −1.00145
\(512\) 2.90276e16 0.0712126
\(513\) 7.40294e16 0.179325
\(514\) 1.62464e17 0.388595
\(515\) −3.44656e17 −0.814027
\(516\) −6.36316e16 −0.148405
\(517\) −3.63176e17 −0.836429
\(518\) 4.77197e17 1.08531
\(519\) 2.09295e16 0.0470080
\(520\) −8.08421e17 −1.79315
\(521\) 1.06572e17 0.233452 0.116726 0.993164i \(-0.462760\pi\)
0.116726 + 0.993164i \(0.462760\pi\)
\(522\) 1.00337e18 2.17071
\(523\) −1.69125e17 −0.361365 −0.180683 0.983541i \(-0.557831\pi\)
−0.180683 + 0.983541i \(0.557831\pi\)
\(524\) −1.46894e18 −3.09992
\(525\) −5.67619e15 −0.0118310
\(526\) −7.35299e17 −1.51376
\(527\) −4.52559e17 −0.920250
\(528\) −9.75579e16 −0.195949
\(529\) −1.43016e17 −0.283742
\(530\) 1.26688e17 0.248281
\(531\) −5.33396e17 −1.03261
\(532\) −1.31067e18 −2.50651
\(533\) −3.85742e16 −0.0728735
\(534\) −9.27648e16 −0.173127
\(535\) 3.38096e17 0.623362
\(536\) −1.62568e17 −0.296118
\(537\) −2.94761e15 −0.00530441
\(538\) 1.14213e18 2.03062
\(539\) −4.85848e17 −0.853441
\(540\) −1.14528e17 −0.198771
\(541\) 4.94957e17 0.848761 0.424380 0.905484i \(-0.360492\pi\)
0.424380 + 0.905484i \(0.360492\pi\)
\(542\) −1.27636e17 −0.216260
\(543\) −8.99813e15 −0.0150645
\(544\) −2.75278e18 −4.55386
\(545\) 3.31836e17 0.542434
\(546\) 2.49807e16 0.0403509
\(547\) 6.84775e17 1.09303 0.546513 0.837451i \(-0.315955\pi\)
0.546513 + 0.837451i \(0.315955\pi\)
\(548\) 1.28258e18 2.02307
\(549\) −8.96912e16 −0.139807
\(550\) 6.43889e17 0.991868
\(551\) 1.33510e18 2.03248
\(552\) 8.72120e16 0.131212
\(553\) −3.12082e17 −0.464040
\(554\) −8.58389e17 −1.26145
\(555\) 2.77065e16 0.0402418
\(556\) 2.09457e18 3.00682
\(557\) −4.24245e17 −0.601947 −0.300974 0.953632i \(-0.597312\pi\)
−0.300974 + 0.953632i \(0.597312\pi\)
\(558\) −8.31407e17 −1.16598
\(559\) −6.29300e17 −0.872330
\(560\) 9.54617e17 1.30800
\(561\) −6.73573e16 −0.0912276
\(562\) −1.61230e18 −2.15853
\(563\) 1.08909e18 1.44131 0.720657 0.693292i \(-0.243840\pi\)
0.720657 + 0.693292i \(0.243840\pi\)
\(564\) 7.00832e16 0.0916853
\(565\) 2.94173e17 0.380441
\(566\) −9.12966e17 −1.16721
\(567\) −4.24301e17 −0.536271
\(568\) 1.94758e18 2.43349
\(569\) 1.51324e18 1.86930 0.934649 0.355572i \(-0.115714\pi\)
0.934649 + 0.355572i \(0.115714\pi\)
\(570\) −1.05224e17 −0.128508
\(571\) 1.41235e18 1.70533 0.852666 0.522456i \(-0.174984\pi\)
0.852666 + 0.522456i \(0.174984\pi\)
\(572\) −2.04938e18 −2.44652
\(573\) 5.70639e16 0.0673529
\(574\) 8.25801e16 0.0963714
\(575\) −3.17496e17 −0.366350
\(576\) −2.24742e18 −2.56412
\(577\) 1.34945e17 0.152235 0.0761174 0.997099i \(-0.475748\pi\)
0.0761174 + 0.997099i \(0.475748\pi\)
\(578\) −2.11113e18 −2.35496
\(579\) −4.97640e16 −0.0548915
\(580\) −2.06548e18 −2.25289
\(581\) −5.66634e17 −0.611164
\(582\) −8.58372e16 −0.0915537
\(583\) 1.98242e17 0.209098
\(584\) −5.44617e18 −5.68078
\(585\) −5.65603e17 −0.583443
\(586\) −6.49880e17 −0.662977
\(587\) 1.91612e17 0.193319 0.0966595 0.995318i \(-0.469184\pi\)
0.0966595 + 0.995318i \(0.469184\pi\)
\(588\) 9.37554e16 0.0935500
\(589\) −1.10628e18 −1.09173
\(590\) 1.51827e18 1.48187
\(591\) −3.73265e15 −0.00360329
\(592\) 3.55661e18 3.39583
\(593\) 1.86646e18 1.76264 0.881319 0.472521i \(-0.156656\pi\)
0.881319 + 0.472521i \(0.156656\pi\)
\(594\) −2.47805e17 −0.231472
\(595\) 6.59100e17 0.608963
\(596\) −1.67788e18 −1.53341
\(597\) 6.05038e16 0.0546952
\(598\) 1.39729e18 1.24948
\(599\) −1.06545e18 −0.942452 −0.471226 0.882013i \(-0.656188\pi\)
−0.471226 + 0.882013i \(0.656188\pi\)
\(600\) −7.66977e16 −0.0671119
\(601\) 1.83640e18 1.58959 0.794793 0.606881i \(-0.207580\pi\)
0.794793 + 0.606881i \(0.207580\pi\)
\(602\) 1.34721e18 1.15361
\(603\) −1.13739e17 −0.0963491
\(604\) −6.59987e17 −0.553089
\(605\) −4.11701e17 −0.341328
\(606\) −1.67072e17 −0.137035
\(607\) 8.60353e17 0.698152 0.349076 0.937094i \(-0.386495\pi\)
0.349076 + 0.937094i \(0.386495\pi\)
\(608\) −6.72919e18 −5.40244
\(609\) 3.93971e16 0.0312933
\(610\) 2.55298e17 0.200634
\(611\) 6.93105e17 0.538928
\(612\) −5.06879e18 −3.89960
\(613\) 1.19125e18 0.906795 0.453398 0.891308i \(-0.350212\pi\)
0.453398 + 0.891308i \(0.350212\pi\)
\(614\) 4.76766e18 3.59097
\(615\) 4.79467e15 0.00357331
\(616\) 2.70817e18 1.99711
\(617\) 9.56470e17 0.697940 0.348970 0.937134i \(-0.386532\pi\)
0.348970 + 0.937134i \(0.386532\pi\)
\(618\) 1.43906e17 0.103909
\(619\) 8.06377e17 0.576168 0.288084 0.957605i \(-0.406982\pi\)
0.288084 + 0.957605i \(0.406982\pi\)
\(620\) 1.71149e18 1.21012
\(621\) 1.22190e17 0.0854951
\(622\) 3.83034e18 2.65216
\(623\) 1.42040e18 0.973279
\(624\) 1.86185e17 0.126254
\(625\) −5.65865e17 −0.379745
\(626\) 3.76665e18 2.50163
\(627\) −1.64655e17 −0.108227
\(628\) 5.78511e18 3.76334
\(629\) 2.45561e18 1.58099
\(630\) 1.21085e18 0.771573
\(631\) −1.28671e16 −0.00811502 −0.00405751 0.999992i \(-0.501292\pi\)
−0.00405751 + 0.999992i \(0.501292\pi\)
\(632\) −4.21691e18 −2.63229
\(633\) −8.86878e16 −0.0547949
\(634\) −8.65020e17 −0.528988
\(635\) −9.87053e17 −0.597463
\(636\) −3.82554e16 −0.0229203
\(637\) 9.27217e17 0.549889
\(638\) −4.46908e18 −2.62352
\(639\) 1.36260e18 0.791795
\(640\) 2.41267e18 1.38781
\(641\) −1.98043e18 −1.12767 −0.563835 0.825888i \(-0.690674\pi\)
−0.563835 + 0.825888i \(0.690674\pi\)
\(642\) −1.41167e17 −0.0795711
\(643\) −8.02979e17 −0.448056 −0.224028 0.974583i \(-0.571921\pi\)
−0.224028 + 0.974583i \(0.571921\pi\)
\(644\) −2.16335e18 −1.19500
\(645\) 7.82203e16 0.0427742
\(646\) −9.32595e18 −5.04872
\(647\) −2.75749e18 −1.47787 −0.738936 0.673776i \(-0.764671\pi\)
−0.738936 + 0.673776i \(0.764671\pi\)
\(648\) −5.73324e18 −3.04203
\(649\) 2.37579e18 1.24801
\(650\) −1.22883e18 −0.639080
\(651\) −3.26450e16 −0.0168089
\(652\) −3.75258e18 −1.91303
\(653\) 3.49617e18 1.76464 0.882320 0.470649i \(-0.155980\pi\)
0.882320 + 0.470649i \(0.155980\pi\)
\(654\) −1.38553e17 −0.0692408
\(655\) 1.80572e18 0.893474
\(656\) 6.15480e17 0.301536
\(657\) −3.81035e18 −1.84838
\(658\) −1.48381e18 −0.712704
\(659\) 2.57366e18 1.22404 0.612020 0.790843i \(-0.290357\pi\)
0.612020 + 0.790843i \(0.290357\pi\)
\(660\) 2.54733e17 0.119963
\(661\) −1.58831e18 −0.740673 −0.370336 0.928898i \(-0.620758\pi\)
−0.370336 + 0.928898i \(0.620758\pi\)
\(662\) 7.00674e18 3.23548
\(663\) 1.28548e17 0.0587798
\(664\) −7.65647e18 −3.46686
\(665\) 1.61117e18 0.722439
\(666\) 4.51126e18 2.00316
\(667\) 2.20366e18 0.969007
\(668\) 7.71385e18 3.35911
\(669\) 7.53898e16 0.0325119
\(670\) 3.23749e17 0.138268
\(671\) 3.99492e17 0.168971
\(672\) −1.98570e17 −0.0831791
\(673\) −4.61407e18 −1.91419 −0.957097 0.289768i \(-0.906422\pi\)
−0.957097 + 0.289768i \(0.906422\pi\)
\(674\) −7.04910e18 −2.89631
\(675\) −1.07459e17 −0.0437289
\(676\) −2.57164e18 −1.03647
\(677\) −2.72951e18 −1.08958 −0.544790 0.838573i \(-0.683391\pi\)
−0.544790 + 0.838573i \(0.683391\pi\)
\(678\) −1.22828e17 −0.0485627
\(679\) 1.31432e18 0.514693
\(680\) 8.90589e18 3.45437
\(681\) 5.73697e16 0.0220407
\(682\) 3.70315e18 1.40920
\(683\) −2.16774e18 −0.817095 −0.408548 0.912737i \(-0.633965\pi\)
−0.408548 + 0.912737i \(0.633965\pi\)
\(684\) −1.23907e19 −4.62626
\(685\) −1.57663e18 −0.583099
\(686\) −4.78886e18 −1.75439
\(687\) −1.28080e15 −0.000464797 0
\(688\) 1.00410e19 3.60952
\(689\) −3.78336e17 −0.134726
\(690\) −1.73679e17 −0.0612674
\(691\) 1.57881e18 0.551725 0.275863 0.961197i \(-0.411037\pi\)
0.275863 + 0.961197i \(0.411037\pi\)
\(692\) −7.01515e18 −2.42855
\(693\) 1.89474e18 0.649806
\(694\) 2.24773e18 0.763672
\(695\) −2.57479e18 −0.866643
\(696\) 5.32341e17 0.177513
\(697\) 4.24948e17 0.140386
\(698\) 1.31591e18 0.430691
\(699\) 1.59514e17 0.0517246
\(700\) 1.90254e18 0.611218
\(701\) 8.34232e17 0.265534 0.132767 0.991147i \(-0.457614\pi\)
0.132767 + 0.991147i \(0.457614\pi\)
\(702\) 4.72924e17 0.149142
\(703\) 6.00274e18 1.87560
\(704\) 1.00102e19 3.09899
\(705\) −8.61511e16 −0.0264260
\(706\) −3.97905e18 −1.20934
\(707\) 2.55817e18 0.770377
\(708\) −4.58463e17 −0.136801
\(709\) 4.44918e18 1.31546 0.657732 0.753252i \(-0.271516\pi\)
0.657732 + 0.753252i \(0.271516\pi\)
\(710\) −3.87852e18 −1.13628
\(711\) −2.95031e18 −0.856477
\(712\) 1.91927e19 5.52097
\(713\) −1.82599e18 −0.520494
\(714\) −2.75198e17 −0.0777331
\(715\) 2.51924e18 0.705148
\(716\) 9.87978e17 0.274039
\(717\) 4.80559e16 0.0132091
\(718\) 1.04392e19 2.84353
\(719\) 5.55360e18 1.49912 0.749561 0.661936i \(-0.230265\pi\)
0.749561 + 0.661936i \(0.230265\pi\)
\(720\) 9.02462e18 2.41417
\(721\) −2.20346e18 −0.584152
\(722\) −1.55627e19 −4.08878
\(723\) −3.41361e17 −0.0888821
\(724\) 3.01599e18 0.778267
\(725\) −1.93799e18 −0.495626
\(726\) 1.71900e17 0.0435700
\(727\) 6.78768e18 1.70509 0.852545 0.522653i \(-0.175058\pi\)
0.852545 + 0.522653i \(0.175058\pi\)
\(728\) −5.16841e18 −1.28678
\(729\) −3.99049e18 −0.984686
\(730\) 1.08458e19 2.65256
\(731\) 6.93261e18 1.68048
\(732\) −7.70910e16 −0.0185217
\(733\) −6.28285e18 −1.49617 −0.748085 0.663603i \(-0.769026\pi\)
−0.748085 + 0.663603i \(0.769026\pi\)
\(734\) 4.10358e18 0.968588
\(735\) −1.15251e17 −0.0269635
\(736\) −1.11070e19 −2.57567
\(737\) 5.06603e17 0.116447
\(738\) 7.80684e17 0.177873
\(739\) −3.01382e18 −0.680658 −0.340329 0.940307i \(-0.610538\pi\)
−0.340329 + 0.940307i \(0.610538\pi\)
\(740\) −9.28664e18 −2.07899
\(741\) 3.14236e17 0.0697330
\(742\) 8.09946e17 0.178168
\(743\) −1.90536e18 −0.415479 −0.207739 0.978184i \(-0.566611\pi\)
−0.207739 + 0.978184i \(0.566611\pi\)
\(744\) −4.41106e17 −0.0953496
\(745\) 2.06256e18 0.441969
\(746\) −7.72508e18 −1.64097
\(747\) −5.35676e18 −1.12802
\(748\) 2.25768e19 4.71304
\(749\) 2.16152e18 0.447329
\(750\) 5.05593e17 0.103730
\(751\) −5.17090e18 −1.05174 −0.525868 0.850566i \(-0.676260\pi\)
−0.525868 + 0.850566i \(0.676260\pi\)
\(752\) −1.10590e19 −2.22998
\(753\) −7.43359e16 −0.0148604
\(754\) 8.52902e18 1.69038
\(755\) 8.11302e17 0.159414
\(756\) −7.32205e17 −0.142640
\(757\) −8.59437e18 −1.65993 −0.829967 0.557813i \(-0.811641\pi\)
−0.829967 + 0.557813i \(0.811641\pi\)
\(758\) 3.55292e18 0.680354
\(759\) −2.71774e17 −0.0515984
\(760\) 2.17705e19 4.09807
\(761\) −4.75000e18 −0.886529 −0.443265 0.896391i \(-0.646180\pi\)
−0.443265 + 0.896391i \(0.646180\pi\)
\(762\) 4.12129e17 0.0762652
\(763\) 2.12150e18 0.389255
\(764\) −1.91266e19 −3.47962
\(765\) 6.23091e18 1.12396
\(766\) −1.06655e19 −1.90762
\(767\) −4.53408e18 −0.804117
\(768\) −2.68060e17 −0.0471394
\(769\) 6.03880e18 1.05300 0.526501 0.850174i \(-0.323503\pi\)
0.526501 + 0.850174i \(0.323503\pi\)
\(770\) −5.39322e18 −0.932521
\(771\) 6.03059e16 0.0103397
\(772\) 1.66799e19 2.83583
\(773\) 4.42542e18 0.746085 0.373042 0.927814i \(-0.378315\pi\)
0.373042 + 0.927814i \(0.378315\pi\)
\(774\) 1.27361e19 2.12922
\(775\) 1.60585e18 0.266222
\(776\) 1.77594e19 2.91962
\(777\) 1.77134e17 0.0288778
\(778\) −2.86955e18 −0.463923
\(779\) 1.03879e18 0.166546
\(780\) −4.86145e17 −0.0772949
\(781\) −6.06912e18 −0.956961
\(782\) −1.53931e19 −2.40703
\(783\) 7.45847e17 0.115664
\(784\) −1.47944e19 −2.27533
\(785\) −7.11146e18 −1.08469
\(786\) −7.53952e17 −0.114050
\(787\) 2.40013e18 0.360080 0.180040 0.983659i \(-0.442377\pi\)
0.180040 + 0.983659i \(0.442377\pi\)
\(788\) 1.25111e18 0.186155
\(789\) −2.72940e17 −0.0402778
\(790\) 8.39781e18 1.22911
\(791\) 1.88071e18 0.273008
\(792\) 2.56021e19 3.68606
\(793\) −7.62410e17 −0.108871
\(794\) 1.55743e19 2.20584
\(795\) 4.70262e16 0.00660622
\(796\) −2.02796e19 −2.82569
\(797\) −8.80632e17 −0.121707 −0.0608535 0.998147i \(-0.519382\pi\)
−0.0608535 + 0.998147i \(0.519382\pi\)
\(798\) −6.72721e17 −0.0922182
\(799\) −7.63552e18 −1.03821
\(800\) 9.76791e18 1.31740
\(801\) 1.34279e19 1.79638
\(802\) 9.36400e18 1.24259
\(803\) 1.69716e19 2.23394
\(804\) −9.77606e16 −0.0127644
\(805\) 2.65934e18 0.344430
\(806\) −7.06729e18 −0.907977
\(807\) 4.23952e17 0.0540305
\(808\) 3.45665e19 4.37000
\(809\) 6.40994e18 0.803875 0.401937 0.915667i \(-0.368337\pi\)
0.401937 + 0.915667i \(0.368337\pi\)
\(810\) 1.14175e19 1.42043
\(811\) −1.26952e19 −1.56677 −0.783385 0.621537i \(-0.786509\pi\)
−0.783385 + 0.621537i \(0.786509\pi\)
\(812\) −1.32051e19 −1.61669
\(813\) −4.73778e16 −0.00575422
\(814\) −2.00935e19 −2.42101
\(815\) 4.61294e18 0.551383
\(816\) −2.05108e18 −0.243219
\(817\) 1.69468e19 1.99363
\(818\) 6.40783e17 0.0747850
\(819\) −3.61602e18 −0.418683
\(820\) −1.60707e18 −0.184606
\(821\) −1.01610e19 −1.15799 −0.578996 0.815331i \(-0.696555\pi\)
−0.578996 + 0.815331i \(0.696555\pi\)
\(822\) 6.58301e17 0.0744316
\(823\) −5.57992e18 −0.625934 −0.312967 0.949764i \(-0.601323\pi\)
−0.312967 + 0.949764i \(0.601323\pi\)
\(824\) −2.97736e19 −3.31363
\(825\) 2.39009e17 0.0263915
\(826\) 9.70661e18 1.06340
\(827\) −4.02076e17 −0.0437041 −0.0218521 0.999761i \(-0.506956\pi\)
−0.0218521 + 0.999761i \(0.506956\pi\)
\(828\) −2.04516e19 −2.20562
\(829\) −8.10479e18 −0.867236 −0.433618 0.901097i \(-0.642763\pi\)
−0.433618 + 0.901097i \(0.642763\pi\)
\(830\) 1.52476e19 1.61880
\(831\) −3.18630e17 −0.0335645
\(832\) −1.91039e19 −1.99674
\(833\) −1.02146e19 −1.05932
\(834\) 1.07506e18 0.110626
\(835\) −9.48241e18 −0.968181
\(836\) 5.51890e19 5.59129
\(837\) −6.18021e17 −0.0621281
\(838\) −6.27381e18 −0.625814
\(839\) 1.47569e19 1.46064 0.730320 0.683105i \(-0.239371\pi\)
0.730320 + 0.683105i \(0.239371\pi\)
\(840\) 6.42421e17 0.0630963
\(841\) 3.19048e18 0.310944
\(842\) −2.62035e19 −2.53414
\(843\) −5.98478e17 −0.0574340
\(844\) 2.97263e19 2.83084
\(845\) 3.16124e18 0.298737
\(846\) −1.40274e19 −1.31544
\(847\) −2.63210e18 −0.244940
\(848\) 6.03663e18 0.557470
\(849\) −3.38889e17 −0.0310569
\(850\) 1.35373e19 1.23114
\(851\) 9.90791e18 0.894211
\(852\) 1.17118e18 0.104897
\(853\) 2.75384e18 0.244777 0.122388 0.992482i \(-0.460945\pi\)
0.122388 + 0.992482i \(0.460945\pi\)
\(854\) 1.63218e18 0.143976
\(855\) 1.52315e19 1.33341
\(856\) 2.92069e19 2.53750
\(857\) −4.04490e18 −0.348765 −0.174382 0.984678i \(-0.555793\pi\)
−0.174382 + 0.984678i \(0.555793\pi\)
\(858\) −1.05187e18 −0.0900109
\(859\) −8.44802e18 −0.717463 −0.358732 0.933441i \(-0.616791\pi\)
−0.358732 + 0.933441i \(0.616791\pi\)
\(860\) −2.62178e19 −2.20982
\(861\) 3.06534e16 0.00256424
\(862\) −7.15005e18 −0.593624
\(863\) 1.25169e19 1.03140 0.515700 0.856769i \(-0.327532\pi\)
0.515700 + 0.856769i \(0.327532\pi\)
\(864\) −3.75925e18 −0.307441
\(865\) 8.62351e18 0.699970
\(866\) −1.91112e19 −1.53965
\(867\) −7.83643e17 −0.0626605
\(868\) 1.09419e19 0.868392
\(869\) 1.31409e19 1.03514
\(870\) −1.06014e18 −0.0828870
\(871\) −9.66827e17 −0.0750293
\(872\) 2.86662e19 2.20807
\(873\) 1.24251e19 0.949968
\(874\) −3.76285e19 −2.85557
\(875\) −7.74153e18 −0.583143
\(876\) −3.27506e18 −0.244874
\(877\) −1.36834e17 −0.0101554 −0.00507770 0.999987i \(-0.501616\pi\)
−0.00507770 + 0.999987i \(0.501616\pi\)
\(878\) −2.62624e19 −1.93473
\(879\) −2.41233e17 −0.0176404
\(880\) −4.01964e19 −2.91776
\(881\) 1.43457e19 1.03366 0.516830 0.856088i \(-0.327112\pi\)
0.516830 + 0.856088i \(0.327112\pi\)
\(882\) −1.87655e19 −1.34219
\(883\) 1.93837e18 0.137624 0.0688118 0.997630i \(-0.478079\pi\)
0.0688118 + 0.997630i \(0.478079\pi\)
\(884\) −4.30867e19 −3.03671
\(885\) 5.63574e17 0.0394294
\(886\) 3.17736e19 2.20672
\(887\) −1.02952e19 −0.709791 −0.354895 0.934906i \(-0.615483\pi\)
−0.354895 + 0.934906i \(0.615483\pi\)
\(888\) 2.39346e18 0.163811
\(889\) −6.31044e18 −0.428744
\(890\) −3.82215e19 −2.57794
\(891\) 1.78662e19 1.19626
\(892\) −2.52691e19 −1.67965
\(893\) −1.86650e19 −1.23167
\(894\) −8.61193e17 −0.0564166
\(895\) −1.21449e18 −0.0789850
\(896\) 1.54247e19 0.995901
\(897\) 5.18668e17 0.0332459
\(898\) −5.41639e19 −3.44678
\(899\) −1.11458e19 −0.704163
\(900\) 1.79860e19 1.12812
\(901\) 4.16790e18 0.259541
\(902\) −3.47723e18 −0.214976
\(903\) 5.00080e17 0.0306951
\(904\) 2.54125e19 1.54865
\(905\) −3.70746e18 −0.224316
\(906\) −3.38747e17 −0.0203490
\(907\) 1.38977e19 0.828890 0.414445 0.910074i \(-0.363976\pi\)
0.414445 + 0.910074i \(0.363976\pi\)
\(908\) −1.92291e19 −1.13868
\(909\) 2.41841e19 1.42188
\(910\) 1.02927e19 0.600842
\(911\) −7.03802e18 −0.407926 −0.203963 0.978979i \(-0.565382\pi\)
−0.203963 + 0.978979i \(0.565382\pi\)
\(912\) −5.01388e18 −0.288541
\(913\) 2.38594e19 1.36333
\(914\) −4.63431e19 −2.62927
\(915\) 9.47657e16 0.00533843
\(916\) 4.29298e17 0.0240125
\(917\) 1.15444e19 0.641164
\(918\) −5.20992e18 −0.287312
\(919\) −6.39596e18 −0.350231 −0.175116 0.984548i \(-0.556030\pi\)
−0.175116 + 0.984548i \(0.556030\pi\)
\(920\) 3.59336e19 1.95380
\(921\) 1.76974e18 0.0955479
\(922\) −6.30374e19 −3.37946
\(923\) 1.15826e19 0.616589
\(924\) 1.62856e18 0.0860867
\(925\) −8.71341e18 −0.457369
\(926\) −6.30687e19 −3.28732
\(927\) −2.08308e19 −1.07817
\(928\) −6.77967e19 −3.48455
\(929\) −8.05207e18 −0.410966 −0.205483 0.978661i \(-0.565876\pi\)
−0.205483 + 0.978661i \(0.565876\pi\)
\(930\) 8.78446e17 0.0445221
\(931\) −2.49696e19 −1.25672
\(932\) −5.34658e19 −2.67222
\(933\) 1.42181e18 0.0705683
\(934\) 1.19433e19 0.588667
\(935\) −2.77529e19 −1.35842
\(936\) −4.88604e19 −2.37500
\(937\) 1.55596e19 0.751087 0.375544 0.926805i \(-0.377456\pi\)
0.375544 + 0.926805i \(0.377456\pi\)
\(938\) 2.06980e18 0.0992223
\(939\) 1.39817e18 0.0665629
\(940\) 2.88761e19 1.36523
\(941\) −1.57748e19 −0.740681 −0.370340 0.928896i \(-0.620759\pi\)
−0.370340 + 0.928896i \(0.620759\pi\)
\(942\) 2.96929e18 0.138459
\(943\) 1.71459e18 0.0794024
\(944\) 7.23446e19 3.32727
\(945\) 9.00077e17 0.0411124
\(946\) −5.67275e19 −2.57336
\(947\) −2.78601e19 −1.25518 −0.627592 0.778542i \(-0.715960\pi\)
−0.627592 + 0.778542i \(0.715960\pi\)
\(948\) −2.53584e18 −0.113467
\(949\) −3.23895e19 −1.43937
\(950\) 3.30920e19 1.46056
\(951\) −3.21092e17 −0.0140752
\(952\) 5.69373e19 2.47889
\(953\) −3.74684e19 −1.62017 −0.810086 0.586311i \(-0.800580\pi\)
−0.810086 + 0.586311i \(0.800580\pi\)
\(954\) 7.65695e18 0.328845
\(955\) 2.35118e19 1.00291
\(956\) −1.61073e19 −0.682413
\(957\) −1.65890e18 −0.0698061
\(958\) −6.31408e19 −2.63897
\(959\) −1.00798e19 −0.418437
\(960\) 2.37457e18 0.0979089
\(961\) −1.51820e19 −0.621764
\(962\) 3.83475e19 1.55991
\(963\) 2.04343e19 0.825635
\(964\) 1.14417e20 4.59187
\(965\) −2.05041e19 −0.817358
\(966\) −1.11037e18 −0.0439660
\(967\) −4.43213e19 −1.74317 −0.871586 0.490243i \(-0.836908\pi\)
−0.871586 + 0.490243i \(0.836908\pi\)
\(968\) −3.55654e19 −1.38943
\(969\) −3.46175e18 −0.134336
\(970\) −3.53671e19 −1.36327
\(971\) 7.78932e18 0.298246 0.149123 0.988819i \(-0.452355\pi\)
0.149123 + 0.988819i \(0.452355\pi\)
\(972\) −1.03875e19 −0.395074
\(973\) −1.64612e19 −0.621910
\(974\) 4.61157e19 1.73068
\(975\) −4.56137e17 −0.0170046
\(976\) 1.21648e19 0.450487
\(977\) 1.51495e19 0.557292 0.278646 0.960394i \(-0.410114\pi\)
0.278646 + 0.960394i \(0.410114\pi\)
\(978\) −1.92606e18 −0.0703831
\(979\) −5.98091e19 −2.17110
\(980\) 3.86296e19 1.39300
\(981\) 2.00560e19 0.718447
\(982\) 8.87747e19 3.15911
\(983\) −2.28813e19 −0.808879 −0.404440 0.914565i \(-0.632533\pi\)
−0.404440 + 0.914565i \(0.632533\pi\)
\(984\) 4.14195e17 0.0145458
\(985\) −1.53795e18 −0.0536545
\(986\) −9.39591e19 −3.25641
\(987\) −5.50783e17 −0.0189635
\(988\) −1.05326e20 −3.60258
\(989\) 2.79718e19 0.950483
\(990\) −5.09857e19 −1.72115
\(991\) −6.43960e18 −0.215964 −0.107982 0.994153i \(-0.534439\pi\)
−0.107982 + 0.994153i \(0.534439\pi\)
\(992\) 5.61774e19 1.87170
\(993\) 2.60087e18 0.0860892
\(994\) −2.47962e19 −0.815407
\(995\) 2.49291e19 0.814436
\(996\) −4.60422e18 −0.149441
\(997\) 2.43126e19 0.783994 0.391997 0.919966i \(-0.371784\pi\)
0.391997 + 0.919966i \(0.371784\pi\)
\(998\) 8.50773e19 2.72562
\(999\) 3.35341e18 0.106736
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 197.14.a.b.1.5 109
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.14.a.b.1.5 109 1.1 even 1 trivial