Properties

Label 197.14.a.b.1.15
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 1.15
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)
 
\(f(q)\) \(=\) \(q-135.924 q^{2} -2298.95 q^{3} +10283.3 q^{4} +41046.5 q^{5} +312481. q^{6} +283206. q^{7} -284251. q^{8} +3.69083e6 q^{9} +O(q^{10})\) \(q-135.924 q^{2} -2298.95 q^{3} +10283.3 q^{4} +41046.5 q^{5} +312481. q^{6} +283206. q^{7} -284251. q^{8} +3.69083e6 q^{9} -5.57919e6 q^{10} +2.50683e6 q^{11} -2.36407e7 q^{12} +1.00648e7 q^{13} -3.84944e7 q^{14} -9.43636e7 q^{15} -4.56040e7 q^{16} -6.90987e7 q^{17} -5.01672e8 q^{18} -2.54546e8 q^{19} +4.22091e8 q^{20} -6.51076e8 q^{21} -3.40738e8 q^{22} +1.27400e9 q^{23} +6.53478e8 q^{24} +4.64108e8 q^{25} -1.36805e9 q^{26} -4.81976e9 q^{27} +2.91228e9 q^{28} +2.31906e9 q^{29} +1.28263e10 q^{30} -7.98819e8 q^{31} +8.52724e9 q^{32} -5.76308e9 q^{33} +9.39215e9 q^{34} +1.16246e10 q^{35} +3.79538e10 q^{36} -2.18141e10 q^{37} +3.45988e10 q^{38} -2.31385e10 q^{39} -1.16675e10 q^{40} +2.95945e10 q^{41} +8.84967e10 q^{42} -3.54603e10 q^{43} +2.57784e10 q^{44} +1.51496e11 q^{45} -1.73166e11 q^{46} +3.45716e10 q^{47} +1.04841e11 q^{48} -1.66833e10 q^{49} -6.30833e10 q^{50} +1.58854e11 q^{51} +1.03499e11 q^{52} -2.53893e10 q^{53} +6.55120e11 q^{54} +1.02897e11 q^{55} -8.05017e10 q^{56} +5.85187e11 q^{57} -3.15216e11 q^{58} +3.44448e10 q^{59} -9.70365e11 q^{60} +6.29561e11 q^{61} +1.08578e11 q^{62} +1.04527e12 q^{63} -7.85467e11 q^{64} +4.13126e11 q^{65} +7.83339e11 q^{66} -5.29677e11 q^{67} -7.10560e11 q^{68} -2.92885e12 q^{69} -1.58006e12 q^{70} +9.28368e11 q^{71} -1.04912e12 q^{72} -2.48962e11 q^{73} +2.96506e12 q^{74} -1.06696e12 q^{75} -2.61756e12 q^{76} +7.09951e11 q^{77} +3.14508e12 q^{78} +2.02937e12 q^{79} -1.87188e12 q^{80} +5.19600e12 q^{81} -4.02259e12 q^{82} +2.12706e12 q^{83} -6.69518e12 q^{84} -2.83626e12 q^{85} +4.81989e12 q^{86} -5.33140e12 q^{87} -7.12570e11 q^{88} -4.73010e12 q^{89} -2.05918e13 q^{90} +2.85043e12 q^{91} +1.31008e13 q^{92} +1.83644e12 q^{93} -4.69910e12 q^{94} -1.04482e13 q^{95} -1.96037e13 q^{96} +1.07707e12 q^{97} +2.26765e12 q^{98} +9.25230e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 109 q + 192 q^{2} + 8018 q^{3} + 471040 q^{4} + 88496 q^{5} + 383232 q^{6} + 1680731 q^{7} + 1820859 q^{8} + 59521391 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −135.924 −1.50176 −0.750880 0.660439i \(-0.770370\pi\)
−0.750880 + 0.660439i \(0.770370\pi\)
\(3\) −2298.95 −1.82071 −0.910355 0.413829i \(-0.864191\pi\)
−0.910355 + 0.413829i \(0.864191\pi\)
\(4\) 10283.3 1.25528
\(5\) 41046.5 1.17482 0.587409 0.809290i \(-0.300148\pi\)
0.587409 + 0.809290i \(0.300148\pi\)
\(6\) 312481. 2.73427
\(7\) 283206. 0.909841 0.454921 0.890532i \(-0.349668\pi\)
0.454921 + 0.890532i \(0.349668\pi\)
\(8\) −284251. −0.383369
\(9\) 3.69083e6 2.31498
\(10\) −5.57919e6 −1.76429
\(11\) 2.50683e6 0.426651 0.213326 0.976981i \(-0.431570\pi\)
0.213326 + 0.976981i \(0.431570\pi\)
\(12\) −2.36407e7 −2.28550
\(13\) 1.00648e7 0.578329 0.289165 0.957279i \(-0.406623\pi\)
0.289165 + 0.957279i \(0.406623\pi\)
\(14\) −3.84944e7 −1.36636
\(15\) −9.43636e7 −2.13900
\(16\) −4.56040e7 −0.679552
\(17\) −6.90987e7 −0.694308 −0.347154 0.937808i \(-0.612852\pi\)
−0.347154 + 0.937808i \(0.612852\pi\)
\(18\) −5.01672e8 −3.47655
\(19\) −2.54546e8 −1.24127 −0.620637 0.784098i \(-0.713126\pi\)
−0.620637 + 0.784098i \(0.713126\pi\)
\(20\) 4.22091e8 1.47473
\(21\) −6.51076e8 −1.65656
\(22\) −3.40738e8 −0.640727
\(23\) 1.27400e9 1.79448 0.897238 0.441548i \(-0.145570\pi\)
0.897238 + 0.441548i \(0.145570\pi\)
\(24\) 6.53478e8 0.698004
\(25\) 4.64108e8 0.380197
\(26\) −1.36805e9 −0.868511
\(27\) −4.81976e9 −2.39420
\(28\) 2.91228e9 1.14211
\(29\) 2.31906e9 0.723979 0.361989 0.932182i \(-0.382098\pi\)
0.361989 + 0.932182i \(0.382098\pi\)
\(30\) 1.28263e10 3.21227
\(31\) −7.98819e8 −0.161658 −0.0808290 0.996728i \(-0.525757\pi\)
−0.0808290 + 0.996728i \(0.525757\pi\)
\(32\) 8.52724e9 1.40389
\(33\) −5.76308e9 −0.776808
\(34\) 9.39215e9 1.04268
\(35\) 1.16246e10 1.06890
\(36\) 3.79538e10 2.90595
\(37\) −2.18141e10 −1.39774 −0.698871 0.715248i \(-0.746314\pi\)
−0.698871 + 0.715248i \(0.746314\pi\)
\(38\) 3.45988e10 1.86409
\(39\) −2.31385e10 −1.05297
\(40\) −1.16675e10 −0.450389
\(41\) 2.95945e10 0.973006 0.486503 0.873679i \(-0.338272\pi\)
0.486503 + 0.873679i \(0.338272\pi\)
\(42\) 8.84967e10 2.48775
\(43\) −3.54603e10 −0.855455 −0.427727 0.903908i \(-0.640686\pi\)
−0.427727 + 0.903908i \(0.640686\pi\)
\(44\) 2.57784e10 0.535567
\(45\) 1.51496e11 2.71968
\(46\) −1.73166e11 −2.69487
\(47\) 3.45716e10 0.467825 0.233912 0.972258i \(-0.424847\pi\)
0.233912 + 0.972258i \(0.424847\pi\)
\(48\) 1.04841e11 1.23727
\(49\) −1.66833e10 −0.172189
\(50\) −6.30833e10 −0.570965
\(51\) 1.58854e11 1.26413
\(52\) 1.03499e11 0.725965
\(53\) −2.53893e10 −0.157347 −0.0786733 0.996900i \(-0.525068\pi\)
−0.0786733 + 0.996900i \(0.525068\pi\)
\(54\) 6.55120e11 3.59552
\(55\) 1.02897e11 0.501238
\(56\) −8.05017e10 −0.348805
\(57\) 5.85187e11 2.26000
\(58\) −3.15216e11 −1.08724
\(59\) 3.44448e10 0.106313 0.0531564 0.998586i \(-0.483072\pi\)
0.0531564 + 0.998586i \(0.483072\pi\)
\(60\) −9.70365e11 −2.68505
\(61\) 6.29561e11 1.56457 0.782283 0.622923i \(-0.214055\pi\)
0.782283 + 0.622923i \(0.214055\pi\)
\(62\) 1.08578e11 0.242771
\(63\) 1.04527e12 2.10627
\(64\) −7.85467e11 −1.42876
\(65\) 4.13126e11 0.679432
\(66\) 7.83339e11 1.16658
\(67\) −5.29677e11 −0.715360 −0.357680 0.933844i \(-0.616432\pi\)
−0.357680 + 0.933844i \(0.616432\pi\)
\(68\) −7.10560e11 −0.871550
\(69\) −2.92885e12 −3.26722
\(70\) −1.58006e12 −1.60523
\(71\) 9.28368e11 0.860084 0.430042 0.902809i \(-0.358499\pi\)
0.430042 + 0.902809i \(0.358499\pi\)
\(72\) −1.04912e12 −0.887494
\(73\) −2.48962e11 −0.192546 −0.0962728 0.995355i \(-0.530692\pi\)
−0.0962728 + 0.995355i \(0.530692\pi\)
\(74\) 2.96506e12 2.09907
\(75\) −1.06696e12 −0.692229
\(76\) −2.61756e12 −1.55815
\(77\) 7.09951e11 0.388185
\(78\) 3.14508e12 1.58131
\(79\) 2.02937e12 0.939257 0.469628 0.882864i \(-0.344388\pi\)
0.469628 + 0.882864i \(0.344388\pi\)
\(80\) −1.87188e12 −0.798350
\(81\) 5.19600e12 2.04417
\(82\) −4.02259e12 −1.46122
\(83\) 2.12706e12 0.714121 0.357060 0.934081i \(-0.383779\pi\)
0.357060 + 0.934081i \(0.383779\pi\)
\(84\) −6.69518e12 −2.07944
\(85\) −2.83626e12 −0.815685
\(86\) 4.81989e12 1.28469
\(87\) −5.33140e12 −1.31816
\(88\) −7.12570e11 −0.163565
\(89\) −4.73010e12 −1.00887 −0.504436 0.863449i \(-0.668299\pi\)
−0.504436 + 0.863449i \(0.668299\pi\)
\(90\) −2.05918e13 −4.08431
\(91\) 2.85043e12 0.526188
\(92\) 1.31008e13 2.25257
\(93\) 1.83644e12 0.294332
\(94\) −4.69910e12 −0.702560
\(95\) −1.04482e13 −1.45827
\(96\) −1.96037e13 −2.55608
\(97\) 1.07707e12 0.131289 0.0656446 0.997843i \(-0.479090\pi\)
0.0656446 + 0.997843i \(0.479090\pi\)
\(98\) 2.26765e12 0.258587
\(99\) 9.25230e12 0.987691
\(100\) 4.77254e12 0.477254
\(101\) −1.12913e13 −1.05841 −0.529206 0.848494i \(-0.677510\pi\)
−0.529206 + 0.848494i \(0.677510\pi\)
\(102\) −2.15921e13 −1.89842
\(103\) −9.34018e12 −0.770749 −0.385375 0.922760i \(-0.625928\pi\)
−0.385375 + 0.922760i \(0.625928\pi\)
\(104\) −2.86094e12 −0.221714
\(105\) −2.67244e13 −1.94615
\(106\) 3.45101e12 0.236297
\(107\) 1.18948e12 0.0766235 0.0383117 0.999266i \(-0.487802\pi\)
0.0383117 + 0.999266i \(0.487802\pi\)
\(108\) −4.95628e13 −3.00540
\(109\) 1.45695e13 0.832091 0.416046 0.909344i \(-0.363416\pi\)
0.416046 + 0.909344i \(0.363416\pi\)
\(110\) −1.39861e13 −0.752738
\(111\) 5.01496e13 2.54488
\(112\) −1.29153e13 −0.618284
\(113\) 1.26616e13 0.572111 0.286055 0.958213i \(-0.407656\pi\)
0.286055 + 0.958213i \(0.407656\pi\)
\(114\) −7.95408e13 −3.39397
\(115\) 5.22931e13 2.10818
\(116\) 2.38475e13 0.908796
\(117\) 3.71476e13 1.33882
\(118\) −4.68187e12 −0.159656
\(119\) −1.95692e13 −0.631709
\(120\) 2.68230e13 0.820028
\(121\) −2.82385e13 −0.817969
\(122\) −8.55723e13 −2.34960
\(123\) −6.80361e13 −1.77156
\(124\) −8.21446e12 −0.202926
\(125\) −3.10555e13 −0.728155
\(126\) −1.42077e14 −3.16311
\(127\) 7.15485e13 1.51313 0.756565 0.653919i \(-0.226876\pi\)
0.756565 + 0.653919i \(0.226876\pi\)
\(128\) 3.69084e13 0.741755
\(129\) 8.15213e13 1.55753
\(130\) −5.61536e13 −1.02034
\(131\) 4.94564e13 0.854985 0.427493 0.904019i \(-0.359397\pi\)
0.427493 + 0.904019i \(0.359397\pi\)
\(132\) −5.92632e13 −0.975112
\(133\) −7.20890e13 −1.12936
\(134\) 7.19957e13 1.07430
\(135\) −1.97834e14 −2.81275
\(136\) 1.96414e13 0.266176
\(137\) 3.42598e13 0.442691 0.221346 0.975195i \(-0.428955\pi\)
0.221346 + 0.975195i \(0.428955\pi\)
\(138\) 3.98100e14 4.90658
\(139\) 9.32158e13 1.09621 0.548105 0.836410i \(-0.315350\pi\)
0.548105 + 0.836410i \(0.315350\pi\)
\(140\) 1.19539e14 1.34177
\(141\) −7.94782e13 −0.851773
\(142\) −1.26187e14 −1.29164
\(143\) 2.52309e13 0.246745
\(144\) −1.68317e14 −1.57315
\(145\) 9.51894e13 0.850543
\(146\) 3.38398e13 0.289157
\(147\) 3.83539e13 0.313507
\(148\) −2.24320e14 −1.75456
\(149\) −7.90059e13 −0.591492 −0.295746 0.955267i \(-0.595568\pi\)
−0.295746 + 0.955267i \(0.595568\pi\)
\(150\) 1.45025e14 1.03956
\(151\) −5.21913e13 −0.358301 −0.179150 0.983822i \(-0.557335\pi\)
−0.179150 + 0.983822i \(0.557335\pi\)
\(152\) 7.23549e13 0.475866
\(153\) −2.55032e14 −1.60731
\(154\) −9.64991e13 −0.582960
\(155\) −3.27887e13 −0.189919
\(156\) −2.37939e14 −1.32177
\(157\) −9.70806e13 −0.517350 −0.258675 0.965964i \(-0.583286\pi\)
−0.258675 + 0.965964i \(0.583286\pi\)
\(158\) −2.75839e14 −1.41054
\(159\) 5.83686e13 0.286482
\(160\) 3.50013e14 1.64932
\(161\) 3.60804e14 1.63269
\(162\) −7.06259e14 −3.06985
\(163\) 1.38754e13 0.0579462 0.0289731 0.999580i \(-0.490776\pi\)
0.0289731 + 0.999580i \(0.490776\pi\)
\(164\) 3.04327e14 1.22139
\(165\) −2.36554e14 −0.912608
\(166\) −2.89117e14 −1.07244
\(167\) 2.37760e14 0.848167 0.424083 0.905623i \(-0.360596\pi\)
0.424083 + 0.905623i \(0.360596\pi\)
\(168\) 1.85069e14 0.635073
\(169\) −2.01574e14 −0.665535
\(170\) 3.85515e14 1.22496
\(171\) −9.39486e14 −2.87353
\(172\) −3.64647e14 −1.07384
\(173\) 6.66614e14 1.89049 0.945246 0.326358i \(-0.105821\pi\)
0.945246 + 0.326358i \(0.105821\pi\)
\(174\) 7.24664e14 1.97955
\(175\) 1.31438e14 0.345919
\(176\) −1.14322e14 −0.289932
\(177\) −7.91868e13 −0.193565
\(178\) 6.42933e14 1.51508
\(179\) 6.28403e14 1.42789 0.713943 0.700204i \(-0.246907\pi\)
0.713943 + 0.700204i \(0.246907\pi\)
\(180\) 1.55787e15 3.41397
\(181\) 7.93746e14 1.67792 0.838959 0.544195i \(-0.183165\pi\)
0.838959 + 0.544195i \(0.183165\pi\)
\(182\) −3.87440e14 −0.790207
\(183\) −1.44733e15 −2.84862
\(184\) −3.62135e14 −0.687947
\(185\) −8.95393e14 −1.64209
\(186\) −2.49616e14 −0.442016
\(187\) −1.73219e14 −0.296227
\(188\) 3.55508e14 0.587251
\(189\) −1.36499e15 −2.17834
\(190\) 1.42016e15 2.18997
\(191\) −9.24881e14 −1.37838 −0.689190 0.724581i \(-0.742033\pi\)
−0.689190 + 0.724581i \(0.742033\pi\)
\(192\) 1.80575e15 2.60135
\(193\) 7.57030e14 1.05436 0.527182 0.849752i \(-0.323249\pi\)
0.527182 + 0.849752i \(0.323249\pi\)
\(194\) −1.46400e14 −0.197165
\(195\) −9.49755e14 −1.23705
\(196\) −1.71558e14 −0.216146
\(197\) 5.84517e13 0.0712470
\(198\) −1.25761e15 −1.48327
\(199\) −8.06419e13 −0.0920483 −0.0460242 0.998940i \(-0.514655\pi\)
−0.0460242 + 0.998940i \(0.514655\pi\)
\(200\) −1.31923e14 −0.145756
\(201\) 1.21770e15 1.30246
\(202\) 1.53475e15 1.58948
\(203\) 6.56773e14 0.658706
\(204\) 1.63354e15 1.58684
\(205\) 1.21475e15 1.14310
\(206\) 1.26955e15 1.15748
\(207\) 4.70211e15 4.15418
\(208\) −4.58997e14 −0.393005
\(209\) −6.38104e14 −0.529591
\(210\) 3.63247e15 2.92265
\(211\) 1.53836e15 1.20011 0.600055 0.799959i \(-0.295145\pi\)
0.600055 + 0.799959i \(0.295145\pi\)
\(212\) −2.61085e14 −0.197514
\(213\) −2.13427e15 −1.56596
\(214\) −1.61678e14 −0.115070
\(215\) −1.45552e15 −1.00500
\(216\) 1.37002e15 0.917864
\(217\) −2.26230e14 −0.147083
\(218\) −1.98033e15 −1.24960
\(219\) 5.72349e14 0.350570
\(220\) 1.05811e15 0.629194
\(221\) −6.95467e14 −0.401538
\(222\) −6.81651e15 −3.82180
\(223\) −2.65136e15 −1.44374 −0.721868 0.692031i \(-0.756716\pi\)
−0.721868 + 0.692031i \(0.756716\pi\)
\(224\) 2.41497e15 1.27732
\(225\) 1.71295e15 0.880151
\(226\) −1.72102e15 −0.859173
\(227\) 2.78776e15 1.35234 0.676172 0.736744i \(-0.263638\pi\)
0.676172 + 0.736744i \(0.263638\pi\)
\(228\) 6.01763e15 2.83693
\(229\) −1.84796e15 −0.846762 −0.423381 0.905952i \(-0.639157\pi\)
−0.423381 + 0.905952i \(0.639157\pi\)
\(230\) −7.10787e15 −3.16598
\(231\) −1.63214e15 −0.706772
\(232\) −6.59197e14 −0.277551
\(233\) −3.24217e15 −1.32746 −0.663731 0.747972i \(-0.731028\pi\)
−0.663731 + 0.747972i \(0.731028\pi\)
\(234\) −5.04924e15 −2.01059
\(235\) 1.41904e15 0.549609
\(236\) 3.54205e14 0.133452
\(237\) −4.66540e15 −1.71011
\(238\) 2.65992e15 0.948675
\(239\) −3.88510e15 −1.34839 −0.674196 0.738553i \(-0.735510\pi\)
−0.674196 + 0.738553i \(0.735510\pi\)
\(240\) 4.30335e15 1.45356
\(241\) −5.65616e15 −1.85956 −0.929781 0.368113i \(-0.880004\pi\)
−0.929781 + 0.368113i \(0.880004\pi\)
\(242\) 3.83828e15 1.22839
\(243\) −4.26106e15 −1.32763
\(244\) 6.47394e15 1.96397
\(245\) −6.84788e14 −0.202291
\(246\) 9.24772e15 2.66046
\(247\) −2.56196e15 −0.717865
\(248\) 2.27065e14 0.0619747
\(249\) −4.88999e15 −1.30021
\(250\) 4.22118e15 1.09351
\(251\) 3.32292e14 0.0838766 0.0419383 0.999120i \(-0.486647\pi\)
0.0419383 + 0.999120i \(0.486647\pi\)
\(252\) 1.07487e16 2.64396
\(253\) 3.19370e15 0.765615
\(254\) −9.72513e15 −2.27236
\(255\) 6.52040e15 1.48513
\(256\) 1.41782e15 0.314819
\(257\) 7.18806e15 1.55613 0.778065 0.628183i \(-0.216201\pi\)
0.778065 + 0.628183i \(0.216201\pi\)
\(258\) −1.10807e16 −2.33904
\(259\) −6.17790e15 −1.27172
\(260\) 4.24828e15 0.852877
\(261\) 8.55928e15 1.67600
\(262\) −6.72229e15 −1.28398
\(263\) 6.86451e14 0.127908 0.0639539 0.997953i \(-0.479629\pi\)
0.0639539 + 0.997953i \(0.479629\pi\)
\(264\) 1.63816e15 0.297804
\(265\) −1.04214e15 −0.184854
\(266\) 9.79860e15 1.69603
\(267\) 1.08743e16 1.83686
\(268\) −5.44680e15 −0.897978
\(269\) 3.23839e14 0.0521122 0.0260561 0.999660i \(-0.491705\pi\)
0.0260561 + 0.999660i \(0.491705\pi\)
\(270\) 2.68903e16 4.22408
\(271\) 1.99742e14 0.0306315 0.0153158 0.999883i \(-0.495125\pi\)
0.0153158 + 0.999883i \(0.495125\pi\)
\(272\) 3.15117e15 0.471818
\(273\) −6.55298e15 −0.958035
\(274\) −4.65672e15 −0.664816
\(275\) 1.16344e15 0.162212
\(276\) −3.01181e16 −4.10127
\(277\) 6.21216e15 0.826274 0.413137 0.910669i \(-0.364433\pi\)
0.413137 + 0.910669i \(0.364433\pi\)
\(278\) −1.26702e16 −1.64624
\(279\) −2.94831e15 −0.374236
\(280\) −3.30431e15 −0.409782
\(281\) 1.66008e15 0.201159 0.100579 0.994929i \(-0.467930\pi\)
0.100579 + 0.994929i \(0.467930\pi\)
\(282\) 1.08030e16 1.27916
\(283\) 8.26471e15 0.956348 0.478174 0.878265i \(-0.341299\pi\)
0.478174 + 0.878265i \(0.341299\pi\)
\(284\) 9.54665e15 1.07965
\(285\) 2.40199e16 2.65509
\(286\) −3.42947e15 −0.370551
\(287\) 8.38134e15 0.885281
\(288\) 3.14726e16 3.24999
\(289\) −5.12995e15 −0.517937
\(290\) −1.29385e16 −1.27731
\(291\) −2.47614e15 −0.239040
\(292\) −2.56014e15 −0.241699
\(293\) 4.93579e15 0.455740 0.227870 0.973692i \(-0.426824\pi\)
0.227870 + 0.973692i \(0.426824\pi\)
\(294\) −5.21320e15 −0.470812
\(295\) 1.41384e15 0.124898
\(296\) 6.20070e15 0.535851
\(297\) −1.20823e16 −1.02149
\(298\) 1.07388e16 0.888278
\(299\) 1.28226e16 1.03780
\(300\) −1.09718e16 −0.868942
\(301\) −1.00426e16 −0.778328
\(302\) 7.09403e15 0.538081
\(303\) 2.59581e16 1.92706
\(304\) 1.16083e16 0.843510
\(305\) 2.58413e16 1.83808
\(306\) 3.46649e16 2.41379
\(307\) 9.84951e15 0.671452 0.335726 0.941960i \(-0.391018\pi\)
0.335726 + 0.941960i \(0.391018\pi\)
\(308\) 7.30060e15 0.487281
\(309\) 2.14726e16 1.40331
\(310\) 4.45676e15 0.285212
\(311\) −8.08379e15 −0.506609 −0.253304 0.967387i \(-0.581517\pi\)
−0.253304 + 0.967387i \(0.581517\pi\)
\(312\) 6.57715e15 0.403676
\(313\) −4.41406e15 −0.265338 −0.132669 0.991160i \(-0.542355\pi\)
−0.132669 + 0.991160i \(0.542355\pi\)
\(314\) 1.31956e16 0.776935
\(315\) 4.29045e16 2.47448
\(316\) 2.08685e16 1.17903
\(317\) 1.09266e14 0.00604781 0.00302391 0.999995i \(-0.499037\pi\)
0.00302391 + 0.999995i \(0.499037\pi\)
\(318\) −7.93368e15 −0.430228
\(319\) 5.81351e15 0.308886
\(320\) −3.22406e16 −1.67853
\(321\) −2.73455e15 −0.139509
\(322\) −4.90418e16 −2.45190
\(323\) 1.75888e16 0.861826
\(324\) 5.34318e16 2.56600
\(325\) 4.67118e15 0.219879
\(326\) −1.88599e15 −0.0870212
\(327\) −3.34944e16 −1.51500
\(328\) −8.41226e15 −0.373021
\(329\) 9.79088e15 0.425646
\(330\) 3.21533e16 1.37052
\(331\) −2.94502e16 −1.23086 −0.615428 0.788193i \(-0.711017\pi\)
−0.615428 + 0.788193i \(0.711017\pi\)
\(332\) 2.18731e16 0.896421
\(333\) −8.05123e16 −3.23575
\(334\) −3.23172e16 −1.27374
\(335\) −2.17414e16 −0.840418
\(336\) 2.96916e16 1.12572
\(337\) 5.42519e15 0.201753 0.100877 0.994899i \(-0.467835\pi\)
0.100877 + 0.994899i \(0.467835\pi\)
\(338\) 2.73987e16 0.999474
\(339\) −2.91084e16 −1.04165
\(340\) −2.91659e16 −1.02391
\(341\) −2.00251e15 −0.0689716
\(342\) 1.27698e17 4.31535
\(343\) −3.21644e16 −1.06651
\(344\) 1.00796e16 0.327955
\(345\) −1.20219e17 −3.83839
\(346\) −9.06087e16 −2.83906
\(347\) 6.02544e16 1.85288 0.926440 0.376442i \(-0.122853\pi\)
0.926440 + 0.376442i \(0.122853\pi\)
\(348\) −5.48242e16 −1.65465
\(349\) 5.56245e16 1.64779 0.823894 0.566744i \(-0.191797\pi\)
0.823894 + 0.566744i \(0.191797\pi\)
\(350\) −1.78656e16 −0.519487
\(351\) −4.85101e16 −1.38464
\(352\) 2.13764e16 0.598972
\(353\) −6.91470e16 −1.90212 −0.951060 0.309006i \(-0.900004\pi\)
−0.951060 + 0.309006i \(0.900004\pi\)
\(354\) 1.07634e16 0.290688
\(355\) 3.81062e16 1.01044
\(356\) −4.86409e16 −1.26642
\(357\) 4.49885e16 1.15016
\(358\) −8.54149e16 −2.14434
\(359\) 4.60010e16 1.13411 0.567053 0.823682i \(-0.308084\pi\)
0.567053 + 0.823682i \(0.308084\pi\)
\(360\) −4.30628e16 −1.04264
\(361\) 2.27406e16 0.540761
\(362\) −1.07889e17 −2.51983
\(363\) 6.49188e16 1.48928
\(364\) 2.93117e16 0.660513
\(365\) −1.02190e16 −0.226206
\(366\) 1.96726e17 4.27794
\(367\) −5.41385e16 −1.15658 −0.578292 0.815830i \(-0.696281\pi\)
−0.578292 + 0.815830i \(0.696281\pi\)
\(368\) −5.80993e16 −1.21944
\(369\) 1.09228e17 2.25249
\(370\) 1.21705e17 2.46603
\(371\) −7.19040e15 −0.143160
\(372\) 1.88846e16 0.369470
\(373\) −5.87869e16 −1.13025 −0.565123 0.825007i \(-0.691171\pi\)
−0.565123 + 0.825007i \(0.691171\pi\)
\(374\) 2.35446e16 0.444862
\(375\) 7.13950e16 1.32576
\(376\) −9.82701e15 −0.179350
\(377\) 2.33410e16 0.418698
\(378\) 1.85534e17 3.27135
\(379\) −8.51513e16 −1.47583 −0.737915 0.674894i \(-0.764190\pi\)
−0.737915 + 0.674894i \(0.764190\pi\)
\(380\) −1.07442e17 −1.83054
\(381\) −1.64486e17 −2.75497
\(382\) 1.25713e17 2.06999
\(383\) 8.76814e16 1.41943 0.709717 0.704487i \(-0.248823\pi\)
0.709717 + 0.704487i \(0.248823\pi\)
\(384\) −8.48505e16 −1.35052
\(385\) 2.91410e16 0.456046
\(386\) −1.02898e17 −1.58340
\(387\) −1.30878e17 −1.98036
\(388\) 1.10758e16 0.164805
\(389\) −3.93493e16 −0.575790 −0.287895 0.957662i \(-0.592955\pi\)
−0.287895 + 0.957662i \(0.592955\pi\)
\(390\) 1.29094e17 1.85775
\(391\) −8.80315e16 −1.24592
\(392\) 4.74223e15 0.0660121
\(393\) −1.13698e17 −1.55668
\(394\) −7.94498e15 −0.106996
\(395\) 8.32983e16 1.10346
\(396\) 9.51438e16 1.23983
\(397\) −5.24413e16 −0.672256 −0.336128 0.941816i \(-0.609118\pi\)
−0.336128 + 0.941816i \(0.609118\pi\)
\(398\) 1.09611e16 0.138234
\(399\) 1.65729e17 2.05624
\(400\) −2.11652e16 −0.258364
\(401\) −1.36499e17 −1.63942 −0.819712 0.572776i \(-0.805867\pi\)
−0.819712 + 0.572776i \(0.805867\pi\)
\(402\) −1.65514e17 −1.95599
\(403\) −8.03999e15 −0.0934916
\(404\) −1.16111e17 −1.32860
\(405\) 2.13277e17 2.40152
\(406\) −8.92711e16 −0.989217
\(407\) −5.46844e16 −0.596348
\(408\) −4.51545e16 −0.484629
\(409\) 3.58350e15 0.0378535 0.0189267 0.999821i \(-0.493975\pi\)
0.0189267 + 0.999821i \(0.493975\pi\)
\(410\) −1.65113e17 −1.71667
\(411\) −7.87614e16 −0.806012
\(412\) −9.60474e16 −0.967506
\(413\) 9.75499e15 0.0967278
\(414\) −6.39128e17 −6.23858
\(415\) 8.73081e16 0.838962
\(416\) 8.58254e16 0.811912
\(417\) −2.14298e17 −1.99588
\(418\) 8.67335e16 0.795318
\(419\) −9.84652e16 −0.888979 −0.444489 0.895784i \(-0.646615\pi\)
−0.444489 + 0.895784i \(0.646615\pi\)
\(420\) −2.74813e17 −2.44297
\(421\) 6.86393e16 0.600813 0.300406 0.953811i \(-0.402878\pi\)
0.300406 + 0.953811i \(0.402878\pi\)
\(422\) −2.09099e17 −1.80228
\(423\) 1.27598e17 1.08301
\(424\) 7.21693e15 0.0603218
\(425\) −3.20693e16 −0.263974
\(426\) 2.90098e17 2.35170
\(427\) 1.78296e17 1.42351
\(428\) 1.22317e16 0.0961840
\(429\) −5.80044e16 −0.449251
\(430\) 1.97839e17 1.50927
\(431\) −6.98347e16 −0.524770 −0.262385 0.964963i \(-0.584509\pi\)
−0.262385 + 0.964963i \(0.584509\pi\)
\(432\) 2.19800e17 1.62699
\(433\) −1.17000e17 −0.853125 −0.426563 0.904458i \(-0.640276\pi\)
−0.426563 + 0.904458i \(0.640276\pi\)
\(434\) 3.07501e16 0.220883
\(435\) −2.18835e17 −1.54859
\(436\) 1.49821e17 1.04451
\(437\) −3.24291e17 −2.22744
\(438\) −7.77959e16 −0.526471
\(439\) 2.34231e17 1.56180 0.780898 0.624658i \(-0.214762\pi\)
0.780898 + 0.624658i \(0.214762\pi\)
\(440\) −2.92485e16 −0.192159
\(441\) −6.15751e16 −0.398615
\(442\) 9.45305e16 0.603014
\(443\) −5.03349e16 −0.316406 −0.158203 0.987407i \(-0.550570\pi\)
−0.158203 + 0.987407i \(0.550570\pi\)
\(444\) 5.15701e17 3.19454
\(445\) −1.94154e17 −1.18524
\(446\) 3.60383e17 2.16814
\(447\) 1.81630e17 1.07693
\(448\) −2.22449e17 −1.29994
\(449\) 9.14986e16 0.527003 0.263502 0.964659i \(-0.415123\pi\)
0.263502 + 0.964659i \(0.415123\pi\)
\(450\) −2.32830e17 −1.32177
\(451\) 7.41884e16 0.415134
\(452\) 1.30203e17 0.718159
\(453\) 1.19985e17 0.652361
\(454\) −3.78922e17 −2.03089
\(455\) 1.17000e17 0.618175
\(456\) −1.66340e17 −0.866414
\(457\) 1.61041e17 0.826953 0.413477 0.910515i \(-0.364314\pi\)
0.413477 + 0.910515i \(0.364314\pi\)
\(458\) 2.51181e17 1.27163
\(459\) 3.33039e17 1.66231
\(460\) 5.37743e17 2.64636
\(461\) −1.67392e17 −0.812228 −0.406114 0.913823i \(-0.633116\pi\)
−0.406114 + 0.913823i \(0.633116\pi\)
\(462\) 2.21846e17 1.06140
\(463\) 2.38660e17 1.12591 0.562955 0.826487i \(-0.309664\pi\)
0.562955 + 0.826487i \(0.309664\pi\)
\(464\) −1.05759e17 −0.491981
\(465\) 7.53794e16 0.345787
\(466\) 4.40687e17 1.99353
\(467\) −3.59768e17 −1.60495 −0.802477 0.596684i \(-0.796485\pi\)
−0.802477 + 0.596684i \(0.796485\pi\)
\(468\) 3.81999e17 1.68060
\(469\) −1.50008e17 −0.650864
\(470\) −1.92881e17 −0.825380
\(471\) 2.23183e17 0.941945
\(472\) −9.79098e15 −0.0407571
\(473\) −8.88930e16 −0.364981
\(474\) 6.34139e17 2.56818
\(475\) −1.18137e17 −0.471929
\(476\) −2.01235e17 −0.792972
\(477\) −9.37076e16 −0.364255
\(478\) 5.28077e17 2.02496
\(479\) −3.21916e17 −1.21776 −0.608880 0.793262i \(-0.708381\pi\)
−0.608880 + 0.793262i \(0.708381\pi\)
\(480\) −8.04661e17 −3.00293
\(481\) −2.19556e17 −0.808355
\(482\) 7.68806e17 2.79261
\(483\) −8.29469e17 −2.97265
\(484\) −2.90384e17 −1.02678
\(485\) 4.42101e16 0.154241
\(486\) 5.79179e17 1.99378
\(487\) 3.09460e17 1.05115 0.525577 0.850746i \(-0.323850\pi\)
0.525577 + 0.850746i \(0.323850\pi\)
\(488\) −1.78953e17 −0.599807
\(489\) −3.18987e16 −0.105503
\(490\) 9.30790e16 0.303792
\(491\) 4.75038e17 1.53003 0.765013 0.644015i \(-0.222733\pi\)
0.765013 + 0.644015i \(0.222733\pi\)
\(492\) −6.99633e17 −2.22381
\(493\) −1.60244e17 −0.502664
\(494\) 3.48232e17 1.07806
\(495\) 3.79774e17 1.16036
\(496\) 3.64293e16 0.109855
\(497\) 2.62920e17 0.782540
\(498\) 6.64666e17 1.95260
\(499\) −1.96792e17 −0.570628 −0.285314 0.958434i \(-0.592098\pi\)
−0.285314 + 0.958434i \(0.592098\pi\)
\(500\) −3.19352e17 −0.914039
\(501\) −5.46597e17 −1.54427
\(502\) −4.51664e16 −0.125962
\(503\) 5.05386e17 1.39133 0.695667 0.718365i \(-0.255109\pi\)
0.695667 + 0.718365i \(0.255109\pi\)
\(504\) −2.97118e17 −0.807478
\(505\) −4.63467e17 −1.24344
\(506\) −4.34099e17 −1.14977
\(507\) 4.63408e17 1.21175
\(508\) 7.35751e17 1.89940
\(509\) −2.34421e17 −0.597491 −0.298746 0.954333i \(-0.596568\pi\)
−0.298746 + 0.954333i \(0.596568\pi\)
\(510\) −8.86277e17 −2.23030
\(511\) −7.05075e16 −0.175186
\(512\) −4.95069e17 −1.21454
\(513\) 1.22685e18 2.97186
\(514\) −9.77027e17 −2.33693
\(515\) −3.83381e17 −0.905490
\(516\) 8.38304e17 1.95514
\(517\) 8.66652e16 0.199598
\(518\) 8.39723e17 1.90982
\(519\) −1.53251e18 −3.44204
\(520\) −1.17432e17 −0.260473
\(521\) 4.94593e17 1.08343 0.541717 0.840561i \(-0.317774\pi\)
0.541717 + 0.840561i \(0.317774\pi\)
\(522\) −1.16341e18 −2.51695
\(523\) 1.99376e17 0.426003 0.213002 0.977052i \(-0.431676\pi\)
0.213002 + 0.977052i \(0.431676\pi\)
\(524\) 5.08572e17 1.07325
\(525\) −3.02170e17 −0.629819
\(526\) −9.33050e16 −0.192087
\(527\) 5.51973e16 0.112240
\(528\) 2.62819e17 0.527881
\(529\) 1.11903e18 2.22014
\(530\) 1.41652e17 0.277606
\(531\) 1.27130e17 0.246113
\(532\) −7.41309e17 −1.41767
\(533\) 2.97864e17 0.562718
\(534\) −1.47807e18 −2.75852
\(535\) 4.88239e16 0.0900187
\(536\) 1.50561e17 0.274247
\(537\) −1.44467e18 −2.59977
\(538\) −4.40174e16 −0.0782600
\(539\) −4.18221e16 −0.0734648
\(540\) −2.03438e18 −3.53079
\(541\) −6.86151e17 −1.17662 −0.588311 0.808634i \(-0.700207\pi\)
−0.588311 + 0.808634i \(0.700207\pi\)
\(542\) −2.71496e16 −0.0460011
\(543\) −1.82478e18 −3.05500
\(544\) −5.89221e17 −0.974733
\(545\) 5.98024e17 0.977556
\(546\) 8.90705e17 1.43874
\(547\) 7.92060e17 1.26427 0.632136 0.774858i \(-0.282178\pi\)
0.632136 + 0.774858i \(0.282178\pi\)
\(548\) 3.52302e17 0.555702
\(549\) 2.32360e18 3.62195
\(550\) −1.58139e17 −0.243603
\(551\) −5.90308e17 −0.898656
\(552\) 8.32529e17 1.25255
\(553\) 5.74729e17 0.854574
\(554\) −8.44380e17 −1.24086
\(555\) 2.05846e18 2.98977
\(556\) 9.58562e17 1.37605
\(557\) 1.05547e18 1.49758 0.748788 0.662809i \(-0.230636\pi\)
0.748788 + 0.662809i \(0.230636\pi\)
\(558\) 4.00745e17 0.562012
\(559\) −3.56902e17 −0.494734
\(560\) −5.30128e17 −0.726371
\(561\) 3.98221e17 0.539344
\(562\) −2.25645e17 −0.302092
\(563\) −6.65481e17 −0.880707 −0.440353 0.897825i \(-0.645147\pi\)
−0.440353 + 0.897825i \(0.645147\pi\)
\(564\) −8.17295e17 −1.06921
\(565\) 5.19716e17 0.672126
\(566\) −1.12337e18 −1.43620
\(567\) 1.47154e18 1.85987
\(568\) −2.63890e17 −0.329730
\(569\) 4.49546e16 0.0555321 0.0277660 0.999614i \(-0.491161\pi\)
0.0277660 + 0.999614i \(0.491161\pi\)
\(570\) −3.26487e18 −3.98730
\(571\) 1.05238e17 0.127069 0.0635344 0.997980i \(-0.479763\pi\)
0.0635344 + 0.997980i \(0.479763\pi\)
\(572\) 2.59456e17 0.309734
\(573\) 2.12625e18 2.50963
\(574\) −1.13922e18 −1.32948
\(575\) 5.91273e17 0.682255
\(576\) −2.89903e18 −3.30755
\(577\) 1.43150e18 1.61491 0.807455 0.589929i \(-0.200844\pi\)
0.807455 + 0.589929i \(0.200844\pi\)
\(578\) 6.97282e17 0.777817
\(579\) −1.74037e18 −1.91969
\(580\) 9.78856e17 1.06767
\(581\) 6.02396e17 0.649736
\(582\) 3.36565e17 0.358980
\(583\) −6.36467e16 −0.0671321
\(584\) 7.07676e16 0.0738161
\(585\) 1.52478e18 1.57287
\(586\) −6.70891e17 −0.684412
\(587\) 1.54283e18 1.55657 0.778287 0.627909i \(-0.216089\pi\)
0.778287 + 0.627909i \(0.216089\pi\)
\(588\) 3.94403e17 0.393539
\(589\) 2.03336e17 0.200662
\(590\) −1.92174e17 −0.187567
\(591\) −1.34377e17 −0.129720
\(592\) 9.94811e17 0.949838
\(593\) 5.65418e17 0.533967 0.266983 0.963701i \(-0.413973\pi\)
0.266983 + 0.963701i \(0.413973\pi\)
\(594\) 1.64228e18 1.53403
\(595\) −8.03245e17 −0.742144
\(596\) −8.12437e17 −0.742488
\(597\) 1.85391e17 0.167593
\(598\) −1.74289e18 −1.55852
\(599\) −1.07258e18 −0.948757 −0.474379 0.880321i \(-0.657327\pi\)
−0.474379 + 0.880321i \(0.657327\pi\)
\(600\) 3.03285e17 0.265379
\(601\) −1.26289e18 −1.09316 −0.546578 0.837408i \(-0.684070\pi\)
−0.546578 + 0.837408i \(0.684070\pi\)
\(602\) 1.36502e18 1.16886
\(603\) −1.95495e18 −1.65605
\(604\) −5.36696e17 −0.449768
\(605\) −1.15909e18 −0.960964
\(606\) −3.52832e18 −2.89398
\(607\) 2.53882e17 0.206018 0.103009 0.994680i \(-0.467153\pi\)
0.103009 + 0.994680i \(0.467153\pi\)
\(608\) −2.17057e18 −1.74262
\(609\) −1.50989e18 −1.19931
\(610\) −3.51244e18 −2.76036
\(611\) 3.47957e17 0.270557
\(612\) −2.62256e18 −2.01763
\(613\) 2.35374e18 1.79170 0.895851 0.444355i \(-0.146567\pi\)
0.895851 + 0.444355i \(0.146567\pi\)
\(614\) −1.33878e18 −1.00836
\(615\) −2.79264e18 −2.08126
\(616\) −2.01804e17 −0.148818
\(617\) 2.31855e18 1.69186 0.845928 0.533297i \(-0.179047\pi\)
0.845928 + 0.533297i \(0.179047\pi\)
\(618\) −2.91863e18 −2.10743
\(619\) −1.00027e18 −0.714706 −0.357353 0.933969i \(-0.616321\pi\)
−0.357353 + 0.933969i \(0.616321\pi\)
\(620\) −3.37174e17 −0.238401
\(621\) −6.14036e18 −4.29634
\(622\) 1.09878e18 0.760804
\(623\) −1.33959e18 −0.917912
\(624\) 1.05521e18 0.715548
\(625\) −1.84126e18 −1.23565
\(626\) 5.99975e17 0.398474
\(627\) 1.46697e18 0.964232
\(628\) −9.98304e17 −0.649419
\(629\) 1.50733e18 0.970463
\(630\) −5.83174e18 −3.71607
\(631\) 1.33539e18 0.842203 0.421101 0.907014i \(-0.361644\pi\)
0.421101 + 0.907014i \(0.361644\pi\)
\(632\) −5.76849e17 −0.360082
\(633\) −3.53660e18 −2.18505
\(634\) −1.48518e16 −0.00908236
\(635\) 2.93681e18 1.77765
\(636\) 6.00219e17 0.359616
\(637\) −1.67914e17 −0.0995821
\(638\) −7.90193e17 −0.463873
\(639\) 3.42645e18 1.99108
\(640\) 1.51496e18 0.871427
\(641\) −1.31404e18 −0.748226 −0.374113 0.927383i \(-0.622053\pi\)
−0.374113 + 0.927383i \(0.622053\pi\)
\(642\) 3.71690e17 0.209509
\(643\) 6.04768e17 0.337456 0.168728 0.985663i \(-0.446034\pi\)
0.168728 + 0.985663i \(0.446034\pi\)
\(644\) 3.71024e18 2.04948
\(645\) 3.34616e18 1.82982
\(646\) −2.39073e18 −1.29425
\(647\) −1.14773e18 −0.615125 −0.307562 0.951528i \(-0.599513\pi\)
−0.307562 + 0.951528i \(0.599513\pi\)
\(648\) −1.47697e18 −0.783670
\(649\) 8.63474e16 0.0453585
\(650\) −6.34924e17 −0.330206
\(651\) 5.20092e17 0.267796
\(652\) 1.42684e17 0.0727387
\(653\) −2.64283e18 −1.33393 −0.666966 0.745088i \(-0.732407\pi\)
−0.666966 + 0.745088i \(0.732407\pi\)
\(654\) 4.55268e18 2.27516
\(655\) 2.03001e18 1.00445
\(656\) −1.34962e18 −0.661208
\(657\) −9.18876e17 −0.445740
\(658\) −1.33081e18 −0.639218
\(659\) 2.76702e18 1.31601 0.658003 0.753015i \(-0.271401\pi\)
0.658003 + 0.753015i \(0.271401\pi\)
\(660\) −2.43254e18 −1.14558
\(661\) 2.66733e18 1.24385 0.621925 0.783077i \(-0.286351\pi\)
0.621925 + 0.783077i \(0.286351\pi\)
\(662\) 4.00299e18 1.84845
\(663\) 1.59884e18 0.731085
\(664\) −6.04618e17 −0.273772
\(665\) −2.95900e18 −1.32679
\(666\) 1.09435e19 4.85932
\(667\) 2.95448e18 1.29916
\(668\) 2.44494e18 1.06469
\(669\) 6.09535e18 2.62862
\(670\) 2.95517e18 1.26211
\(671\) 1.57821e18 0.667524
\(672\) −5.55188e18 −2.32563
\(673\) −2.43373e18 −1.00966 −0.504828 0.863220i \(-0.668444\pi\)
−0.504828 + 0.863220i \(0.668444\pi\)
\(674\) −7.37412e17 −0.302985
\(675\) −2.23689e18 −0.910270
\(676\) −2.07284e18 −0.835433
\(677\) 1.14719e18 0.457940 0.228970 0.973434i \(-0.426464\pi\)
0.228970 + 0.973434i \(0.426464\pi\)
\(678\) 3.95653e18 1.56430
\(679\) 3.05034e17 0.119452
\(680\) 8.06209e17 0.312709
\(681\) −6.40891e18 −2.46222
\(682\) 2.72188e17 0.103579
\(683\) 2.97064e18 1.11973 0.559867 0.828582i \(-0.310852\pi\)
0.559867 + 0.828582i \(0.310852\pi\)
\(684\) −9.66097e18 −3.60708
\(685\) 1.40624e18 0.520082
\(686\) 4.37190e18 1.60163
\(687\) 4.24836e18 1.54171
\(688\) 1.61713e18 0.581326
\(689\) −2.55539e17 −0.0909981
\(690\) 1.63406e19 5.76433
\(691\) 5.48581e18 1.91705 0.958525 0.285007i \(-0.0919961\pi\)
0.958525 + 0.285007i \(0.0919961\pi\)
\(692\) 6.85497e18 2.37310
\(693\) 2.62031e18 0.898642
\(694\) −8.19001e18 −2.78258
\(695\) 3.82618e18 1.28785
\(696\) 1.51546e18 0.505340
\(697\) −2.04494e18 −0.675565
\(698\) −7.56069e18 −2.47458
\(699\) 7.45357e18 2.41692
\(700\) 1.35161e18 0.434226
\(701\) −2.08495e18 −0.663632 −0.331816 0.943344i \(-0.607661\pi\)
−0.331816 + 0.943344i \(0.607661\pi\)
\(702\) 6.59368e18 2.07939
\(703\) 5.55270e18 1.73498
\(704\) −1.96903e18 −0.609581
\(705\) −3.26230e18 −1.00068
\(706\) 9.39872e18 2.85653
\(707\) −3.19776e18 −0.962986
\(708\) −8.14298e17 −0.242978
\(709\) −6.35912e18 −1.88017 −0.940084 0.340942i \(-0.889254\pi\)
−0.940084 + 0.340942i \(0.889254\pi\)
\(710\) −5.17954e18 −1.51744
\(711\) 7.49005e18 2.17436
\(712\) 1.34454e18 0.386770
\(713\) −1.01769e18 −0.290091
\(714\) −6.11500e18 −1.72726
\(715\) 1.03564e18 0.289880
\(716\) 6.46203e18 1.79240
\(717\) 8.93164e18 2.45503
\(718\) −6.25263e18 −1.70315
\(719\) −2.39740e18 −0.647148 −0.323574 0.946203i \(-0.604884\pi\)
−0.323574 + 0.946203i \(0.604884\pi\)
\(720\) −6.90880e18 −1.84817
\(721\) −2.64520e18 −0.701259
\(722\) −3.09099e18 −0.812093
\(723\) 1.30032e19 3.38572
\(724\) 8.16229e18 2.10626
\(725\) 1.07630e18 0.275255
\(726\) −8.82400e18 −2.23655
\(727\) −1.78163e18 −0.447553 −0.223777 0.974640i \(-0.571839\pi\)
−0.223777 + 0.974640i \(0.571839\pi\)
\(728\) −8.10237e17 −0.201724
\(729\) 1.51185e18 0.373062
\(730\) 1.38900e18 0.339707
\(731\) 2.45026e18 0.593949
\(732\) −1.48832e19 −3.57582
\(733\) 4.36996e18 1.04064 0.520321 0.853971i \(-0.325812\pi\)
0.520321 + 0.853971i \(0.325812\pi\)
\(734\) 7.35871e18 1.73691
\(735\) 1.57429e18 0.368313
\(736\) 1.08637e19 2.51925
\(737\) −1.32781e18 −0.305209
\(738\) −1.48467e19 −3.38270
\(739\) −5.10948e18 −1.15395 −0.576976 0.816761i \(-0.695768\pi\)
−0.576976 + 0.816761i \(0.695768\pi\)
\(740\) −9.20756e18 −2.06129
\(741\) 5.88982e18 1.30702
\(742\) 9.77346e17 0.214992
\(743\) −4.03931e18 −0.880806 −0.440403 0.897800i \(-0.645164\pi\)
−0.440403 + 0.897800i \(0.645164\pi\)
\(744\) −5.22011e17 −0.112838
\(745\) −3.24291e18 −0.694895
\(746\) 7.99053e18 1.69736
\(747\) 7.85061e18 1.65318
\(748\) −1.78125e18 −0.371848
\(749\) 3.36868e17 0.0697152
\(750\) −9.70428e18 −1.99097
\(751\) 7.63199e18 1.55231 0.776154 0.630543i \(-0.217168\pi\)
0.776154 + 0.630543i \(0.217168\pi\)
\(752\) −1.57660e18 −0.317911
\(753\) −7.63922e17 −0.152715
\(754\) −3.17260e18 −0.628784
\(755\) −2.14227e18 −0.420938
\(756\) −1.40365e19 −2.73443
\(757\) 6.10723e18 1.17956 0.589781 0.807563i \(-0.299214\pi\)
0.589781 + 0.807563i \(0.299214\pi\)
\(758\) 1.15741e19 2.21634
\(759\) −7.34214e18 −1.39396
\(760\) 2.96991e18 0.559056
\(761\) 9.05524e18 1.69005 0.845025 0.534726i \(-0.179585\pi\)
0.845025 + 0.534726i \(0.179585\pi\)
\(762\) 2.23576e19 4.13730
\(763\) 4.12616e18 0.757071
\(764\) −9.51078e18 −1.73025
\(765\) −1.04681e19 −1.88830
\(766\) −1.19180e19 −2.13165
\(767\) 3.46682e17 0.0614839
\(768\) −3.25949e18 −0.573194
\(769\) 9.89304e17 0.172508 0.0862539 0.996273i \(-0.472510\pi\)
0.0862539 + 0.996273i \(0.472510\pi\)
\(770\) −3.96095e18 −0.684872
\(771\) −1.65250e19 −2.83326
\(772\) 7.78473e18 1.32352
\(773\) 8.42772e18 1.42083 0.710417 0.703781i \(-0.248506\pi\)
0.710417 + 0.703781i \(0.248506\pi\)
\(774\) 1.77894e19 2.97403
\(775\) −3.70738e17 −0.0614620
\(776\) −3.06159e17 −0.0503323
\(777\) 1.42027e19 2.31544
\(778\) 5.34850e18 0.864698
\(779\) −7.53315e18 −1.20777
\(780\) −9.76657e18 −1.55284
\(781\) 2.32726e18 0.366956
\(782\) 1.19656e19 1.87107
\(783\) −1.11773e19 −1.73335
\(784\) 7.60822e17 0.117012
\(785\) −3.98481e18 −0.607792
\(786\) 1.54542e19 2.33776
\(787\) −2.05174e18 −0.307812 −0.153906 0.988085i \(-0.549185\pi\)
−0.153906 + 0.988085i \(0.549185\pi\)
\(788\) 6.01074e17 0.0894350
\(789\) −1.57811e18 −0.232883
\(790\) −1.13222e19 −1.65712
\(791\) 3.58586e18 0.520530
\(792\) −2.62998e18 −0.378650
\(793\) 6.33643e18 0.904835
\(794\) 7.12801e18 1.00957
\(795\) 2.39582e18 0.336565
\(796\) −8.29261e17 −0.115546
\(797\) −1.27644e18 −0.176409 −0.0882043 0.996102i \(-0.528113\pi\)
−0.0882043 + 0.996102i \(0.528113\pi\)
\(798\) −2.25265e19 −3.08798
\(799\) −2.38885e18 −0.324814
\(800\) 3.95756e18 0.533756
\(801\) −1.74580e19 −2.33552
\(802\) 1.85535e19 2.46202
\(803\) −6.24105e17 −0.0821499
\(804\) 1.25219e19 1.63496
\(805\) 1.48097e19 1.91811
\(806\) 1.09282e18 0.140402
\(807\) −7.44489e17 −0.0948812
\(808\) 3.20956e18 0.405762
\(809\) −1.17915e19 −1.47878 −0.739392 0.673275i \(-0.764887\pi\)
−0.739392 + 0.673275i \(0.764887\pi\)
\(810\) −2.89894e19 −3.60651
\(811\) −8.89407e18 −1.09765 −0.548826 0.835937i \(-0.684925\pi\)
−0.548826 + 0.835937i \(0.684925\pi\)
\(812\) 6.75377e18 0.826860
\(813\) −4.59196e17 −0.0557711
\(814\) 7.43291e18 0.895571
\(815\) 5.69534e17 0.0680762
\(816\) −7.24438e18 −0.859044
\(817\) 9.02626e18 1.06185
\(818\) −4.87082e17 −0.0568468
\(819\) 1.05204e19 1.21812
\(820\) 1.24916e19 1.43492
\(821\) −6.60331e18 −0.752543 −0.376272 0.926509i \(-0.622794\pi\)
−0.376272 + 0.926509i \(0.622794\pi\)
\(822\) 1.07055e19 1.21044
\(823\) 7.28751e18 0.817486 0.408743 0.912650i \(-0.365967\pi\)
0.408743 + 0.912650i \(0.365967\pi\)
\(824\) 2.65496e18 0.295482
\(825\) −2.67469e18 −0.295340
\(826\) −1.32593e18 −0.145262
\(827\) 8.78024e18 0.954379 0.477189 0.878800i \(-0.341656\pi\)
0.477189 + 0.878800i \(0.341656\pi\)
\(828\) 4.83530e19 5.21466
\(829\) 6.95471e18 0.744174 0.372087 0.928198i \(-0.378642\pi\)
0.372087 + 0.928198i \(0.378642\pi\)
\(830\) −1.18672e19 −1.25992
\(831\) −1.42814e19 −1.50440
\(832\) −7.90560e18 −0.826292
\(833\) 1.15279e18 0.119552
\(834\) 2.91282e19 2.99733
\(835\) 9.75920e18 0.996442
\(836\) −6.56179e18 −0.664785
\(837\) 3.85012e18 0.387042
\(838\) 1.33837e19 1.33503
\(839\) 6.80740e18 0.673796 0.336898 0.941541i \(-0.390622\pi\)
0.336898 + 0.941541i \(0.390622\pi\)
\(840\) 7.59643e18 0.746095
\(841\) −4.88257e18 −0.475855
\(842\) −9.32971e18 −0.902276
\(843\) −3.81644e18 −0.366252
\(844\) 1.58193e19 1.50647
\(845\) −8.27390e18 −0.781883
\(846\) −1.73436e19 −1.62641
\(847\) −7.99732e18 −0.744222
\(848\) 1.15785e18 0.106925
\(849\) −1.90001e19 −1.74123
\(850\) 4.35897e18 0.396425
\(851\) −2.77912e19 −2.50821
\(852\) −2.19472e19 −1.96572
\(853\) −7.32734e18 −0.651295 −0.325647 0.945491i \(-0.605582\pi\)
−0.325647 + 0.945491i \(0.605582\pi\)
\(854\) −2.42346e19 −2.13776
\(855\) −3.85626e19 −3.37587
\(856\) −3.38111e17 −0.0293751
\(857\) −1.47181e19 −1.26905 −0.634523 0.772904i \(-0.718803\pi\)
−0.634523 + 0.772904i \(0.718803\pi\)
\(858\) 7.88418e18 0.674666
\(859\) −1.13234e19 −0.961663 −0.480831 0.876813i \(-0.659665\pi\)
−0.480831 + 0.876813i \(0.659665\pi\)
\(860\) −1.49675e19 −1.26156
\(861\) −1.92682e19 −1.61184
\(862\) 9.49219e18 0.788078
\(863\) 6.25098e18 0.515084 0.257542 0.966267i \(-0.417087\pi\)
0.257542 + 0.966267i \(0.417087\pi\)
\(864\) −4.10993e19 −3.36120
\(865\) 2.73622e19 2.22098
\(866\) 1.59030e19 1.28119
\(867\) 1.17935e19 0.943013
\(868\) −2.32639e18 −0.184631
\(869\) 5.08728e18 0.400735
\(870\) 2.97449e19 2.32561
\(871\) −5.33111e18 −0.413714
\(872\) −4.14138e18 −0.318998
\(873\) 3.97530e18 0.303933
\(874\) 4.40788e19 3.34507
\(875\) −8.79512e18 −0.662505
\(876\) 5.88562e18 0.440063
\(877\) −2.98789e17 −0.0221752 −0.0110876 0.999939i \(-0.503529\pi\)
−0.0110876 + 0.999939i \(0.503529\pi\)
\(878\) −3.18375e19 −2.34544
\(879\) −1.13471e19 −0.829771
\(880\) −4.69249e18 −0.340617
\(881\) 2.12640e19 1.53215 0.766074 0.642752i \(-0.222207\pi\)
0.766074 + 0.642752i \(0.222207\pi\)
\(882\) 8.36951e18 0.598624
\(883\) 2.28861e19 1.62490 0.812452 0.583028i \(-0.198132\pi\)
0.812452 + 0.583028i \(0.198132\pi\)
\(884\) −7.15167e18 −0.504043
\(885\) −3.25034e18 −0.227404
\(886\) 6.84171e18 0.475166
\(887\) −1.68688e18 −0.116300 −0.0581501 0.998308i \(-0.518520\pi\)
−0.0581501 + 0.998308i \(0.518520\pi\)
\(888\) −1.42551e19 −0.975630
\(889\) 2.02630e19 1.37671
\(890\) 2.63901e19 1.77994
\(891\) 1.30255e19 0.872146
\(892\) −2.72647e19 −1.81229
\(893\) −8.80005e18 −0.580699
\(894\) −2.46879e19 −1.61730
\(895\) 2.57937e19 1.67751
\(896\) 1.04527e19 0.674879
\(897\) −2.94784e19 −1.88953
\(898\) −1.24368e19 −0.791432
\(899\) −1.85251e18 −0.117037
\(900\) 1.76147e19 1.10484
\(901\) 1.75437e18 0.109247
\(902\) −1.00840e19 −0.623431
\(903\) 2.30873e19 1.41711
\(904\) −3.59909e18 −0.219330
\(905\) 3.25804e19 1.97125
\(906\) −1.63088e19 −0.979690
\(907\) 9.26728e18 0.552719 0.276360 0.961054i \(-0.410872\pi\)
0.276360 + 0.961054i \(0.410872\pi\)
\(908\) 2.86672e19 1.69757
\(909\) −4.16742e19 −2.45021
\(910\) −1.59031e19 −0.928350
\(911\) −2.08939e19 −1.21102 −0.605508 0.795839i \(-0.707030\pi\)
−0.605508 + 0.795839i \(0.707030\pi\)
\(912\) −2.66869e19 −1.53579
\(913\) 5.33218e18 0.304680
\(914\) −2.18893e19 −1.24188
\(915\) −5.94077e19 −3.34661
\(916\) −1.90030e19 −1.06292
\(917\) 1.40063e19 0.777901
\(918\) −4.52679e19 −2.49639
\(919\) −6.57630e18 −0.360106 −0.180053 0.983657i \(-0.557627\pi\)
−0.180053 + 0.983657i \(0.557627\pi\)
\(920\) −1.48644e19 −0.808212
\(921\) −2.26435e19 −1.22252
\(922\) 2.27525e19 1.21977
\(923\) 9.34388e18 0.497412
\(924\) −1.67837e19 −0.887197
\(925\) −1.01241e19 −0.531418
\(926\) −3.24396e19 −1.69085
\(927\) −3.44730e19 −1.78427
\(928\) 1.97752e19 1.01639
\(929\) −1.70376e19 −0.869572 −0.434786 0.900534i \(-0.643176\pi\)
−0.434786 + 0.900534i \(0.643176\pi\)
\(930\) −1.02459e19 −0.519289
\(931\) 4.24665e18 0.213734
\(932\) −3.33400e19 −1.66634
\(933\) 1.85842e19 0.922387
\(934\) 4.89010e19 2.41025
\(935\) −7.11002e18 −0.348013
\(936\) −1.05593e19 −0.513263
\(937\) −1.08181e18 −0.0522210 −0.0261105 0.999659i \(-0.508312\pi\)
−0.0261105 + 0.999659i \(0.508312\pi\)
\(938\) 2.03896e19 0.977441
\(939\) 1.01477e19 0.483104
\(940\) 1.45924e19 0.689913
\(941\) −1.19027e19 −0.558871 −0.279435 0.960165i \(-0.590147\pi\)
−0.279435 + 0.960165i \(0.590147\pi\)
\(942\) −3.03359e19 −1.41457
\(943\) 3.77033e19 1.74604
\(944\) −1.57082e18 −0.0722451
\(945\) −5.60279e19 −2.55916
\(946\) 1.20827e19 0.548113
\(947\) −5.44646e18 −0.245380 −0.122690 0.992445i \(-0.539152\pi\)
−0.122690 + 0.992445i \(0.539152\pi\)
\(948\) −4.79755e19 −2.14667
\(949\) −2.50576e18 −0.111355
\(950\) 1.60576e19 0.708724
\(951\) −2.51196e17 −0.0110113
\(952\) 5.56256e18 0.242178
\(953\) 3.25548e18 0.140770 0.0703851 0.997520i \(-0.477577\pi\)
0.0703851 + 0.997520i \(0.477577\pi\)
\(954\) 1.27371e19 0.547023
\(955\) −3.79631e19 −1.61934
\(956\) −3.99515e19 −1.69261
\(957\) −1.33649e19 −0.562392
\(958\) 4.37560e19 1.82878
\(959\) 9.70258e18 0.402779
\(960\) 7.41195e19 3.05611
\(961\) −2.37794e19 −0.973867
\(962\) 2.98429e19 1.21395
\(963\) 4.39016e18 0.177382
\(964\) −5.81637e19 −2.33427
\(965\) 3.10734e19 1.23869
\(966\) 1.12744e20 4.46420
\(967\) −8.33167e17 −0.0327688 −0.0163844 0.999866i \(-0.505216\pi\)
−0.0163844 + 0.999866i \(0.505216\pi\)
\(968\) 8.02682e18 0.313584
\(969\) −4.04357e19 −1.56913
\(970\) −6.00920e18 −0.231633
\(971\) −1.47868e19 −0.566172 −0.283086 0.959095i \(-0.591358\pi\)
−0.283086 + 0.959095i \(0.591358\pi\)
\(972\) −4.38176e19 −1.66655
\(973\) 2.63993e19 0.997376
\(974\) −4.20629e19 −1.57858
\(975\) −1.07388e19 −0.400336
\(976\) −2.87105e19 −1.06320
\(977\) −1.67964e19 −0.617876 −0.308938 0.951082i \(-0.599974\pi\)
−0.308938 + 0.951082i \(0.599974\pi\)
\(978\) 4.33579e18 0.158440
\(979\) −1.18576e19 −0.430436
\(980\) −7.04185e18 −0.253932
\(981\) 5.37734e19 1.92628
\(982\) −6.45689e19 −2.29773
\(983\) 1.15643e19 0.408809 0.204404 0.978887i \(-0.434474\pi\)
0.204404 + 0.978887i \(0.434474\pi\)
\(984\) 1.93393e19 0.679162
\(985\) 2.39924e18 0.0837023
\(986\) 2.17810e19 0.754880
\(987\) −2.25087e19 −0.774978
\(988\) −2.63453e19 −0.901122
\(989\) −4.51763e19 −1.53509
\(990\) −5.16203e19 −1.74258
\(991\) 4.48782e18 0.150507 0.0752535 0.997164i \(-0.476023\pi\)
0.0752535 + 0.997164i \(0.476023\pi\)
\(992\) −6.81172e18 −0.226951
\(993\) 6.77045e19 2.24103
\(994\) −3.57370e19 −1.17519
\(995\) −3.31006e18 −0.108140
\(996\) −5.02850e19 −1.63212
\(997\) −1.98245e19 −0.639268 −0.319634 0.947541i \(-0.603560\pi\)
−0.319634 + 0.947541i \(0.603560\pi\)
\(998\) 2.67486e19 0.856945
\(999\) 1.05139e20 3.34648
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.1.15 109
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.14.a.b.1.15 109 1.1 even 1 trivial