Properties

Label 29.9.c.a.12.10
Level $29$
Weight $9$
Character 29.12
Analytic conductor $11.814$
Analytic rank $0$
Dimension $38$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [29,9,Mod(12,29)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(29, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.12");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 29.c (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.8139796918\)
Analytic rank: \(0\)
Dimension: \(38\)
Relative dimension: \(19\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 12.10
Character \(\chi\) \(=\) 29.12
Dual form 29.9.c.a.17.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.384989 + 0.384989i) q^{2} +(93.7530 + 93.7530i) q^{3} -255.704i q^{4} +802.752i q^{5} +72.1877i q^{6} +2726.98 q^{7} +(197.000 - 197.000i) q^{8} +11018.2i q^{9} +O(q^{10})\) \(q+(0.384989 + 0.384989i) q^{2} +(93.7530 + 93.7530i) q^{3} -255.704i q^{4} +802.752i q^{5} +72.1877i q^{6} +2726.98 q^{7} +(197.000 - 197.000i) q^{8} +11018.2i q^{9} +(-309.050 + 309.050i) q^{10} +(-10332.7 - 10332.7i) q^{11} +(23973.0 - 23973.0i) q^{12} +21024.9i q^{13} +(1049.86 + 1049.86i) q^{14} +(-75260.4 + 75260.4i) q^{15} -65308.4 q^{16} +(75820.3 + 75820.3i) q^{17} +(-4241.90 + 4241.90i) q^{18} +(49482.1 + 49482.1i) q^{19} +205266. q^{20} +(255663. + 255663. i) q^{21} -7955.94i q^{22} -10519.0 q^{23} +36938.7 q^{24} -253785. q^{25} +(-8094.35 + 8094.35i) q^{26} +(-417880. + 417880. i) q^{27} -697299. i q^{28} +(-290625. + 644813. i) q^{29} -57948.8 q^{30} +(-1.05254e6 - 1.05254e6i) q^{31} +(-75575.1 - 75575.1i) q^{32} -1.93744e6i q^{33} +58379.9i q^{34} +2.18909e6i q^{35} +2.81741e6 q^{36} +(2.43856e6 - 2.43856e6i) q^{37} +38100.1i q^{38} +(-1.97115e6 + 1.97115e6i) q^{39} +(158142. + 158142. i) q^{40} +(3.64219e6 - 3.64219e6i) q^{41} +196855. i q^{42} +(-2.65043e6 - 2.65043e6i) q^{43} +(-2.64211e6 + 2.64211e6i) q^{44} -8.84492e6 q^{45} +(-4049.71 - 4049.71i) q^{46} +(2.80524e6 - 2.80524e6i) q^{47} +(-6.12286e6 - 6.12286e6i) q^{48} +1.67162e6 q^{49} +(-97704.5 - 97704.5i) q^{50} +1.42168e7i q^{51} +5.37614e6 q^{52} +5.48448e6 q^{53} -321759. q^{54} +(8.29459e6 - 8.29459e6i) q^{55} +(537216. - 537216. i) q^{56} +9.27819e6i q^{57} +(-360133. + 136358. i) q^{58} -4.51198e6 q^{59} +(1.92443e7 + 1.92443e7i) q^{60} +(-9.36984e6 - 9.36984e6i) q^{61} -810429. i q^{62} +3.00466e7i q^{63} +1.66608e7i q^{64} -1.68778e7 q^{65} +(745893. - 745893. i) q^{66} -9.67617e6i q^{67} +(1.93875e7 - 1.93875e7i) q^{68} +(-986191. - 986191. i) q^{69} +(-842775. + 842775. i) q^{70} -5.43326e6i q^{71} +(2.17060e6 + 2.17060e6i) q^{72} +(-1.88608e7 + 1.88608e7i) q^{73} +1.87764e6 q^{74} +(-2.37931e7 - 2.37931e7i) q^{75} +(1.26527e7 - 1.26527e7i) q^{76} +(-2.81771e7 - 2.81771e7i) q^{77} -1.51774e6 q^{78} +(7.39724e6 + 7.39724e6i) q^{79} -5.24265e7i q^{80} -6.06434e6 q^{81} +2.80441e6 q^{82} +6.15697e7 q^{83} +(6.53738e7 - 6.53738e7i) q^{84} +(-6.08649e7 + 6.08649e7i) q^{85} -2.04077e6i q^{86} +(-8.77001e7 + 3.32061e7i) q^{87} -4.07108e6 q^{88} +(5.11006e7 + 5.11006e7i) q^{89} +(-3.40519e6 - 3.40519e6i) q^{90} +5.73345e7i q^{91} +2.68976e6i q^{92} -1.97357e8i q^{93} +2.15997e6 q^{94} +(-3.97218e7 + 3.97218e7i) q^{95} -1.41708e7i q^{96} +(6.15776e7 - 6.15776e7i) q^{97} +(643557. + 643557. i) q^{98} +(1.13848e8 - 1.13848e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + 15870 q^{10} - 8390 q^{11} + 5022 q^{12} + 12728 q^{14} - 35530 q^{15} - 245912 q^{16} + 76234 q^{17} - 465022 q^{18} - 164488 q^{19} + 4092 q^{20} - 514620 q^{21} + 733568 q^{23} - 482376 q^{24} - 1528354 q^{25} + 1405470 q^{26} - 1279754 q^{27} + 1420996 q^{29} + 3659852 q^{30} + 291062 q^{31} + 1592134 q^{32} - 10223688 q^{36} + 7994574 q^{37} - 309930 q^{39} + 9093994 q^{40} + 9561658 q^{41} - 5181022 q^{43} - 11400526 q^{44} + 9526060 q^{45} - 32561820 q^{46} + 5445034 q^{47} - 17683542 q^{48} + 45106458 q^{49} + 3122002 q^{50} + 56198616 q^{52} - 25331452 q^{53} - 42307016 q^{54} + 3037606 q^{55} - 25661184 q^{56} - 33846328 q^{58} + 27333008 q^{59} + 30592014 q^{60} - 49572406 q^{61} - 121974972 q^{65} + 133443354 q^{66} + 21192980 q^{68} - 28739184 q^{69} - 17976124 q^{70} - 186114192 q^{72} + 45787870 q^{73} + 91919252 q^{74} - 159074460 q^{75} + 243795016 q^{76} + 59851916 q^{77} + 163580208 q^{78} - 99827470 q^{79} - 75138586 q^{81} - 18178416 q^{82} - 177270160 q^{83} - 9436684 q^{84} + 156307616 q^{85} - 20584526 q^{87} + 563433236 q^{88} - 388451858 q^{89} + 306402752 q^{90} + 81569204 q^{94} - 44386260 q^{95} - 121157834 q^{97} - 129908712 q^{98} - 216447384 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.384989 + 0.384989i 0.0240618 + 0.0240618i 0.719035 0.694974i \(-0.244584\pi\)
−0.694974 + 0.719035i \(0.744584\pi\)
\(3\) 93.7530 + 93.7530i 1.15744 + 1.15744i 0.985023 + 0.172421i \(0.0551590\pi\)
0.172421 + 0.985023i \(0.444841\pi\)
\(4\) 255.704i 0.998842i
\(5\) 802.752i 1.28440i 0.766536 + 0.642201i \(0.221979\pi\)
−0.766536 + 0.642201i \(0.778021\pi\)
\(6\) 72.1877i 0.0557004i
\(7\) 2726.98 1.13577 0.567884 0.823108i \(-0.307762\pi\)
0.567884 + 0.823108i \(0.307762\pi\)
\(8\) 197.000 197.000i 0.0480957 0.0480957i
\(9\) 11018.2i 1.67935i
\(10\) −309.050 + 309.050i −0.0309050 + 0.0309050i
\(11\) −10332.7 10332.7i −0.705737 0.705737i 0.259899 0.965636i \(-0.416311\pi\)
−0.965636 + 0.259899i \(0.916311\pi\)
\(12\) 23973.0 23973.0i 1.15610 1.15610i
\(13\) 21024.9i 0.736140i 0.929798 + 0.368070i \(0.119981\pi\)
−0.929798 + 0.368070i \(0.880019\pi\)
\(14\) 1049.86 + 1049.86i 0.0273286 + 0.0273286i
\(15\) −75260.4 + 75260.4i −1.48662 + 1.48662i
\(16\) −65308.4 −0.996528
\(17\) 75820.3 + 75820.3i 0.907799 + 0.907799i 0.996094 0.0882951i \(-0.0281418\pi\)
−0.0882951 + 0.996094i \(0.528142\pi\)
\(18\) −4241.90 + 4241.90i −0.0404083 + 0.0404083i
\(19\) 49482.1 + 49482.1i 0.379694 + 0.379694i 0.870992 0.491298i \(-0.163477\pi\)
−0.491298 + 0.870992i \(0.663477\pi\)
\(20\) 205266. 1.28292
\(21\) 255663. + 255663.i 1.31459 + 1.31459i
\(22\) 7955.94i 0.0339626i
\(23\) −10519.0 −0.0375893 −0.0187947 0.999823i \(-0.505983\pi\)
−0.0187947 + 0.999823i \(0.505983\pi\)
\(24\) 36938.7 0.111336
\(25\) −253785. −0.649691
\(26\) −8094.35 + 8094.35i −0.0177129 + 0.0177129i
\(27\) −417880. + 417880.i −0.786316 + 0.786316i
\(28\) 697299.i 1.13445i
\(29\) −290625. + 644813.i −0.410905 + 0.911678i
\(30\) −57948.8 −0.0715417
\(31\) −1.05254e6 1.05254e6i −1.13970 1.13970i −0.988504 0.151195i \(-0.951688\pi\)
−0.151195 0.988504i \(-0.548312\pi\)
\(32\) −75575.1 75575.1i −0.0720740 0.0720740i
\(33\) 1.93744e6i 1.63370i
\(34\) 58379.9i 0.0436866i
\(35\) 2.18909e6i 1.45878i
\(36\) 2.81741e6 1.67741
\(37\) 2.43856e6 2.43856e6i 1.30115 1.30115i 0.373533 0.927617i \(-0.378146\pi\)
0.927617 0.373533i \(-0.121854\pi\)
\(38\) 38100.1i 0.0182722i
\(39\) −1.97115e6 + 1.97115e6i −0.852041 + 0.852041i
\(40\) 158142. + 158142.i 0.0617743 + 0.0617743i
\(41\) 3.64219e6 3.64219e6i 1.28892 1.28892i 0.353484 0.935441i \(-0.384997\pi\)
0.935441 0.353484i \(-0.115003\pi\)
\(42\) 196855.i 0.0632628i
\(43\) −2.65043e6 2.65043e6i −0.775252 0.775252i 0.203767 0.979019i \(-0.434681\pi\)
−0.979019 + 0.203767i \(0.934681\pi\)
\(44\) −2.64211e6 + 2.64211e6i −0.704920 + 0.704920i
\(45\) −8.84492e6 −2.15697
\(46\) −4049.71 4049.71i −0.000904467 0.000904467i
\(47\) 2.80524e6 2.80524e6i 0.574882 0.574882i −0.358607 0.933489i \(-0.616748\pi\)
0.933489 + 0.358607i \(0.116748\pi\)
\(48\) −6.12286e6 6.12286e6i −1.15343 1.15343i
\(49\) 1.67162e6 0.289971
\(50\) −97704.5 97704.5i −0.0156327 0.0156327i
\(51\) 1.42168e7i 2.10145i
\(52\) 5.37614e6 0.735288
\(53\) 5.48448e6 0.695075 0.347538 0.937666i \(-0.387018\pi\)
0.347538 + 0.937666i \(0.387018\pi\)
\(54\) −321759. −0.0378403
\(55\) 8.29459e6 8.29459e6i 0.906450 0.906450i
\(56\) 537216. 537216.i 0.0546257 0.0546257i
\(57\) 9.27819e6i 0.878949i
\(58\) −360133. + 136358.i −0.0318237 + 0.0120495i
\(59\) −4.51198e6 −0.372357 −0.186178 0.982516i \(-0.559610\pi\)
−0.186178 + 0.982516i \(0.559610\pi\)
\(60\) 1.92443e7 + 1.92443e7i 1.48490 + 1.48490i
\(61\) −9.36984e6 9.36984e6i −0.676726 0.676726i 0.282532 0.959258i \(-0.408826\pi\)
−0.959258 + 0.282532i \(0.908826\pi\)
\(62\) 810429.i 0.0548464i
\(63\) 3.00466e7i 1.90736i
\(64\) 1.66608e7i 0.993059i
\(65\) −1.68778e7 −0.945500
\(66\) 745893. 745893.i 0.0393098 0.0393098i
\(67\) 9.67617e6i 0.480180i −0.970751 0.240090i \(-0.922823\pi\)
0.970751 0.240090i \(-0.0771770\pi\)
\(68\) 1.93875e7 1.93875e7i 0.906748 0.906748i
\(69\) −986191. 986191.i −0.0435076 0.0435076i
\(70\) −842775. + 842775.i −0.0351010 + 0.0351010i
\(71\) 5.43326e6i 0.213809i −0.994269 0.106905i \(-0.965906\pi\)
0.994269 0.106905i \(-0.0340940\pi\)
\(72\) 2.17060e6 + 2.17060e6i 0.0807698 + 0.0807698i
\(73\) −1.88608e7 + 1.88608e7i −0.664154 + 0.664154i −0.956356 0.292202i \(-0.905612\pi\)
0.292202 + 0.956356i \(0.405612\pi\)
\(74\) 1.87764e6 0.0626160
\(75\) −2.37931e7 2.37931e7i −0.751981 0.751981i
\(76\) 1.26527e7 1.26527e7i 0.379254 0.379254i
\(77\) −2.81771e7 2.81771e7i −0.801554 0.801554i
\(78\) −1.51774e6 −0.0410033
\(79\) 7.39724e6 + 7.39724e6i 0.189916 + 0.189916i 0.795660 0.605744i \(-0.207124\pi\)
−0.605744 + 0.795660i \(0.707124\pi\)
\(80\) 5.24265e7i 1.27994i
\(81\) −6.06434e6 −0.140878
\(82\) 2.80441e6 0.0620277
\(83\) 6.15697e7 1.29734 0.648671 0.761069i \(-0.275325\pi\)
0.648671 + 0.761069i \(0.275325\pi\)
\(84\) 6.53738e7 6.53738e7i 1.31307 1.31307i
\(85\) −6.08649e7 + 6.08649e7i −1.16598 + 1.16598i
\(86\) 2.04077e6i 0.0373079i
\(87\) −8.77001e7 + 3.32061e7i −1.53082 + 0.579617i
\(88\) −4.07108e6 −0.0678859
\(89\) 5.11006e7 + 5.11006e7i 0.814454 + 0.814454i 0.985298 0.170844i \(-0.0546496\pi\)
−0.170844 + 0.985298i \(0.554650\pi\)
\(90\) −3.40519e6 3.40519e6i −0.0519005 0.0519005i
\(91\) 5.73345e7i 0.836085i
\(92\) 2.68976e6i 0.0375458i
\(93\) 1.97357e8i 2.63828i
\(94\) 2.15997e6 0.0276654
\(95\) −3.97218e7 + 3.97218e7i −0.487680 + 0.487680i
\(96\) 1.41708e7i 0.166843i
\(97\) 6.15776e7 6.15776e7i 0.695562 0.695562i −0.267888 0.963450i \(-0.586326\pi\)
0.963450 + 0.267888i \(0.0863257\pi\)
\(98\) 643557. + 643557.i 0.00697722 + 0.00697722i
\(99\) 1.13848e8 1.13848e8i 1.18518 1.18518i
\(100\) 6.48938e7i 0.648938i
\(101\) 3.53918e7 + 3.53918e7i 0.340108 + 0.340108i 0.856408 0.516300i \(-0.172691\pi\)
−0.516300 + 0.856408i \(0.672691\pi\)
\(102\) −5.47329e6 + 5.47329e6i −0.0505648 + 0.0505648i
\(103\) −1.06856e8 −0.949406 −0.474703 0.880146i \(-0.657444\pi\)
−0.474703 + 0.880146i \(0.657444\pi\)
\(104\) 4.14191e6 + 4.14191e6i 0.0354052 + 0.0354052i
\(105\) −2.05234e8 + 2.05234e8i −1.68846 + 1.68846i
\(106\) 2.11146e6 + 2.11146e6i 0.0167248 + 0.0167248i
\(107\) −2.30440e8 −1.75802 −0.879008 0.476807i \(-0.841794\pi\)
−0.879008 + 0.476807i \(0.841794\pi\)
\(108\) 1.06853e8 + 1.06853e8i 0.785405 + 0.785405i
\(109\) 1.37188e8i 0.971873i −0.873994 0.485936i \(-0.838479\pi\)
0.873994 0.485936i \(-0.161521\pi\)
\(110\) 6.38665e6 0.0436217
\(111\) 4.57245e8 3.01202
\(112\) −1.78095e8 −1.13182
\(113\) −8.21417e7 + 8.21417e7i −0.503790 + 0.503790i −0.912614 0.408823i \(-0.865939\pi\)
0.408823 + 0.912614i \(0.365939\pi\)
\(114\) −3.57200e6 + 3.57200e6i −0.0211491 + 0.0211491i
\(115\) 8.44418e6i 0.0482799i
\(116\) 1.64881e8 + 7.43139e7i 0.910623 + 0.410429i
\(117\) −2.31658e8 −1.23624
\(118\) −1.73706e6 1.73706e6i −0.00895958 0.00895958i
\(119\) 2.06761e8 + 2.06761e8i 1.03105 + 1.03105i
\(120\) 2.96526e7i 0.143001i
\(121\) 829827.i 0.00387120i
\(122\) 7.21457e6i 0.0325665i
\(123\) 6.82933e8 2.98372
\(124\) −2.69137e8 + 2.69137e8i −1.13838 + 1.13838i
\(125\) 1.09848e8i 0.449938i
\(126\) −1.15676e7 + 1.15676e7i −0.0458945 + 0.0458945i
\(127\) 5.82442e7 + 5.82442e7i 0.223892 + 0.223892i 0.810135 0.586243i \(-0.199394\pi\)
−0.586243 + 0.810135i \(0.699394\pi\)
\(128\) −2.57614e7 + 2.57614e7i −0.0959688 + 0.0959688i
\(129\) 4.96972e8i 1.79462i
\(130\) −6.49776e6 6.49776e6i −0.0227504 0.0227504i
\(131\) −4.54145e7 + 4.54145e7i −0.154209 + 0.154209i −0.779995 0.625786i \(-0.784778\pi\)
0.625786 + 0.779995i \(0.284778\pi\)
\(132\) −4.95411e8 −1.63181
\(133\) 1.34937e8 + 1.34937e8i 0.431245 + 0.431245i
\(134\) 3.72522e6 3.72522e6i 0.0115540 0.0115540i
\(135\) −3.35454e8 3.35454e8i −1.00995 1.00995i
\(136\) 2.98732e7 0.0873226
\(137\) −2.83150e8 2.83150e8i −0.803775 0.803775i 0.179909 0.983683i \(-0.442420\pi\)
−0.983683 + 0.179909i \(0.942420\pi\)
\(138\) 759345.i 0.00209374i
\(139\) −4.91187e8 −1.31579 −0.657897 0.753108i \(-0.728554\pi\)
−0.657897 + 0.753108i \(0.728554\pi\)
\(140\) 5.59758e8 1.45710
\(141\) 5.26000e8 1.33079
\(142\) 2.09174e6 2.09174e6i 0.00514464 0.00514464i
\(143\) 2.17244e8 2.17244e8i 0.519521 0.519521i
\(144\) 7.19584e8i 1.67352i
\(145\) −5.17625e8 2.33300e8i −1.17096 0.527767i
\(146\) −1.45224e7 −0.0319615
\(147\) 1.56720e8 + 1.56720e8i 0.335625 + 0.335625i
\(148\) −6.23549e8 6.23549e8i −1.29964 1.29964i
\(149\) 3.37753e8i 0.685259i 0.939471 + 0.342629i \(0.111318\pi\)
−0.939471 + 0.342629i \(0.888682\pi\)
\(150\) 1.83202e7i 0.0361880i
\(151\) 4.47050e8i 0.859900i 0.902853 + 0.429950i \(0.141469\pi\)
−0.902853 + 0.429950i \(0.858531\pi\)
\(152\) 1.94960e7 0.0365233
\(153\) −8.35407e8 + 8.35407e8i −1.52452 + 1.52452i
\(154\) 2.16957e7i 0.0385737i
\(155\) 8.44925e8 8.44925e8i 1.46383 1.46383i
\(156\) 5.04029e8 + 5.04029e8i 0.851055 + 0.851055i
\(157\) 4.12641e8 4.12641e8i 0.679162 0.679162i −0.280649 0.959811i \(-0.590550\pi\)
0.959811 + 0.280649i \(0.0905496\pi\)
\(158\) 5.69571e6i 0.00913944i
\(159\) 5.14186e8 + 5.14186e8i 0.804511 + 0.804511i
\(160\) 6.06680e7 6.06680e7i 0.0925720 0.0925720i
\(161\) −2.86852e7 −0.0426928
\(162\) −2.33470e6 2.33470e6i −0.00338978 0.00338978i
\(163\) −8.01327e8 + 8.01327e8i −1.13517 + 1.13517i −0.145861 + 0.989305i \(0.546595\pi\)
−0.989305 + 0.145861i \(0.953405\pi\)
\(164\) −9.31322e8 9.31322e8i −1.28743 1.28743i
\(165\) 1.55528e9 2.09833
\(166\) 2.37037e7 + 2.37037e7i 0.0312164 + 0.0312164i
\(167\) 8.76082e8i 1.12636i −0.826333 0.563182i \(-0.809577\pi\)
0.826333 0.563182i \(-0.190423\pi\)
\(168\) 1.00731e8 0.126452
\(169\) 3.73684e8 0.458098
\(170\) −4.68646e7 −0.0561112
\(171\) −5.45206e8 + 5.45206e8i −0.637641 + 0.637641i
\(172\) −6.77725e8 + 6.77725e8i −0.774355 + 0.774355i
\(173\) 9.38376e7i 0.104759i 0.998627 + 0.0523796i \(0.0166806\pi\)
−0.998627 + 0.0523796i \(0.983319\pi\)
\(174\) −4.65476e7 2.09796e7i −0.0507808 0.0228876i
\(175\) −6.92068e8 −0.737898
\(176\) 6.74812e8 + 6.74812e8i 0.703286 + 0.703286i
\(177\) −4.23012e8 4.23012e8i −0.430982 0.430982i
\(178\) 3.93464e7i 0.0391944i
\(179\) 5.27432e8i 0.513753i −0.966444 0.256877i \(-0.917307\pi\)
0.966444 0.256877i \(-0.0826934\pi\)
\(180\) 2.26168e9i 2.15447i
\(181\) 1.00453e8 0.0935939 0.0467969 0.998904i \(-0.485099\pi\)
0.0467969 + 0.998904i \(0.485099\pi\)
\(182\) −2.20731e7 + 2.20731e7i −0.0201177 + 0.0201177i
\(183\) 1.75690e9i 1.56654i
\(184\) −2.07225e6 + 2.07225e6i −0.00180789 + 0.00180789i
\(185\) 1.95756e9 + 1.95756e9i 1.67120 + 1.67120i
\(186\) 7.59802e7 7.59802e7i 0.0634817 0.0634817i
\(187\) 1.56686e9i 1.28133i
\(188\) −7.17310e8 7.17310e8i −0.574217 0.574217i
\(189\) −1.13955e9 + 1.13955e9i −0.893073 + 0.893073i
\(190\) −3.05849e7 −0.0234689
\(191\) −3.80660e7 3.80660e7i −0.0286025 0.0286025i 0.692661 0.721263i \(-0.256438\pi\)
−0.721263 + 0.692661i \(0.756438\pi\)
\(192\) −1.56200e9 + 1.56200e9i −1.14941 + 1.14941i
\(193\) 1.91551e9 + 1.91551e9i 1.38056 + 1.38056i 0.843627 + 0.536930i \(0.180416\pi\)
0.536930 + 0.843627i \(0.319584\pi\)
\(194\) 4.74134e7 0.0334730
\(195\) −1.58234e9 1.58234e9i −1.09436 1.09436i
\(196\) 4.27440e8i 0.289635i
\(197\) 1.51393e9 1.00517 0.502586 0.864527i \(-0.332382\pi\)
0.502586 + 0.864527i \(0.332382\pi\)
\(198\) 8.76605e7 0.0570353
\(199\) −2.13226e9 −1.35965 −0.679827 0.733372i \(-0.737945\pi\)
−0.679827 + 0.733372i \(0.737945\pi\)
\(200\) −4.99958e7 + 4.99958e7i −0.0312474 + 0.0312474i
\(201\) 9.07170e8 9.07170e8i 0.555782 0.555782i
\(202\) 2.72509e7i 0.0163672i
\(203\) −7.92529e8 + 1.75839e9i −0.466693 + 1.03546i
\(204\) 3.63528e9 2.09902
\(205\) 2.92378e9 + 2.92378e9i 1.65550 + 1.65550i
\(206\) −4.11385e7 4.11385e7i −0.0228444 0.0228444i
\(207\) 1.15901e8i 0.0631259i
\(208\) 1.37310e9i 0.733584i
\(209\) 1.02257e9i 0.535928i
\(210\) −1.58025e8 −0.0812549
\(211\) 5.04224e8 5.04224e8i 0.254387 0.254387i −0.568380 0.822766i \(-0.692430\pi\)
0.822766 + 0.568380i \(0.192430\pi\)
\(212\) 1.40240e9i 0.694271i
\(213\) 5.09384e8 5.09384e8i 0.247473 0.247473i
\(214\) −8.87168e7 8.87168e7i −0.0423010 0.0423010i
\(215\) 2.12764e9 2.12764e9i 0.995736 0.995736i
\(216\) 1.64645e8i 0.0756369i
\(217\) −2.87025e9 2.87025e9i −1.29443 1.29443i
\(218\) 5.28158e7 5.28158e7i 0.0233850 0.0233850i
\(219\) −3.53651e9 −1.53744
\(220\) −2.12096e9 2.12096e9i −0.905401 0.905401i
\(221\) −1.59411e9 + 1.59411e9i −0.668268 + 0.668268i
\(222\) 1.76034e8 + 1.76034e8i 0.0724746 + 0.0724746i
\(223\) −4.05878e9 −1.64126 −0.820628 0.571463i \(-0.806376\pi\)
−0.820628 + 0.571463i \(0.806376\pi\)
\(224\) −2.06092e8 2.06092e8i −0.0818594 0.0818594i
\(225\) 2.79627e9i 1.09106i
\(226\) −6.32473e7 −0.0242442
\(227\) −1.26056e9 −0.474744 −0.237372 0.971419i \(-0.576286\pi\)
−0.237372 + 0.971419i \(0.576286\pi\)
\(228\) 2.37247e9 0.877931
\(229\) −3.83854e9 + 3.83854e9i −1.39580 + 1.39580i −0.584178 + 0.811626i \(0.698583\pi\)
−0.811626 + 0.584178i \(0.801417\pi\)
\(230\) 3.25091e6 3.25091e6i 0.00116170 0.00116170i
\(231\) 5.28337e9i 1.85551i
\(232\) 6.97750e7 + 1.84281e8i 0.0240851 + 0.0636106i
\(233\) 2.44354e9 0.829079 0.414539 0.910031i \(-0.363943\pi\)
0.414539 + 0.910031i \(0.363943\pi\)
\(234\) −8.91856e7 8.91856e7i −0.0297462 0.0297462i
\(235\) 2.25191e9 + 2.25191e9i 0.738380 + 0.738380i
\(236\) 1.15373e9i 0.371926i
\(237\) 1.38703e9i 0.439634i
\(238\) 1.59201e8i 0.0496179i
\(239\) 3.12903e8 0.0958999 0.0479499 0.998850i \(-0.484731\pi\)
0.0479499 + 0.998850i \(0.484731\pi\)
\(240\) 4.91514e9 4.91514e9i 1.48146 1.48146i
\(241\) 2.35690e9i 0.698671i −0.936998 0.349336i \(-0.886407\pi\)
0.936998 0.349336i \(-0.113593\pi\)
\(242\) 319474. 319474.i 9.31481e−5 9.31481e-5i
\(243\) 2.17316e9 + 2.17316e9i 0.623257 + 0.623257i
\(244\) −2.39590e9 + 2.39590e9i −0.675942 + 0.675942i
\(245\) 1.34190e9i 0.372439i
\(246\) 2.62922e8 + 2.62922e8i 0.0717936 + 0.0717936i
\(247\) −1.04036e9 + 1.04036e9i −0.279508 + 0.279508i
\(248\) −4.14700e8 −0.109629
\(249\) 5.77234e9 + 5.77234e9i 1.50160 + 1.50160i
\(250\) −4.22904e7 + 4.22904e7i −0.0108263 + 0.0108263i
\(251\) 1.52610e9 + 1.52610e9i 0.384492 + 0.384492i 0.872717 0.488226i \(-0.162356\pi\)
−0.488226 + 0.872717i \(0.662356\pi\)
\(252\) 7.68301e9 1.90515
\(253\) 1.08690e8 + 1.08690e8i 0.0265282 + 0.0265282i
\(254\) 4.48467e7i 0.0107745i
\(255\) −1.14125e10 −2.69911
\(256\) 4.24532e9 0.988441
\(257\) 1.14264e9 0.261924 0.130962 0.991387i \(-0.458193\pi\)
0.130962 + 0.991387i \(0.458193\pi\)
\(258\) 1.91329e8 1.91329e8i 0.0431819 0.0431819i
\(259\) 6.64992e9 6.64992e9i 1.47781 1.47781i
\(260\) 4.31571e9i 0.944406i
\(261\) −7.10471e9 3.20218e9i −1.53103 0.690055i
\(262\) −3.49681e7 −0.00742108
\(263\) −3.38727e9 3.38727e9i −0.707989 0.707989i 0.258123 0.966112i \(-0.416896\pi\)
−0.966112 + 0.258123i \(0.916896\pi\)
\(264\) −3.81676e8 3.81676e8i −0.0785741 0.0785741i
\(265\) 4.40268e9i 0.892757i
\(266\) 1.03898e8i 0.0207530i
\(267\) 9.58168e9i 1.88537i
\(268\) −2.47423e9 −0.479624
\(269\) −6.36007e9 + 6.36007e9i −1.21466 + 1.21466i −0.245177 + 0.969478i \(0.578846\pi\)
−0.969478 + 0.245177i \(0.921154\pi\)
\(270\) 2.58292e8i 0.0486022i
\(271\) −2.36975e9 + 2.36975e9i −0.439366 + 0.439366i −0.891798 0.452433i \(-0.850556\pi\)
0.452433 + 0.891798i \(0.350556\pi\)
\(272\) −4.95170e9 4.95170e9i −0.904647 0.904647i
\(273\) −5.37528e9 + 5.37528e9i −0.967722 + 0.967722i
\(274\) 2.18019e8i 0.0386805i
\(275\) 2.62229e9 + 2.62229e9i 0.458511 + 0.458511i
\(276\) −2.52173e8 + 2.52173e8i −0.0434572 + 0.0434572i
\(277\) 4.94342e9 0.839670 0.419835 0.907600i \(-0.362088\pi\)
0.419835 + 0.907600i \(0.362088\pi\)
\(278\) −1.89102e8 1.89102e8i −0.0316604 0.0316604i
\(279\) 1.15971e10 1.15971e10i 1.91396 1.91396i
\(280\) 4.31251e8 + 4.31251e8i 0.0701613 + 0.0701613i
\(281\) −8.54127e9 −1.36993 −0.684963 0.728577i \(-0.740182\pi\)
−0.684963 + 0.728577i \(0.740182\pi\)
\(282\) 2.02504e8 + 2.02504e8i 0.0320212 + 0.0320212i
\(283\) 3.36436e9i 0.524513i −0.964998 0.262257i \(-0.915533\pi\)
0.964998 0.262257i \(-0.0844667\pi\)
\(284\) −1.38930e9 −0.213562
\(285\) −7.44808e9 −1.12892
\(286\) 1.67273e8 0.0250012
\(287\) 9.93219e9 9.93219e9i 1.46392 1.46392i
\(288\) 8.32705e8 8.32705e8i 0.121038 0.121038i
\(289\) 4.52168e9i 0.648199i
\(290\) −1.09462e8 2.89098e8i −0.0154764 0.0408745i
\(291\) 1.15462e10 1.61015
\(292\) 4.82278e9 + 4.82278e9i 0.663385 + 0.663385i
\(293\) 6.59250e9 + 6.59250e9i 0.894499 + 0.894499i 0.994943 0.100444i \(-0.0320263\pi\)
−0.100444 + 0.994943i \(0.532026\pi\)
\(294\) 1.20671e8i 0.0161515i
\(295\) 3.62200e9i 0.478256i
\(296\) 9.60795e8i 0.125160i
\(297\) 8.63566e9 1.10986
\(298\) −1.30031e8 + 1.30031e8i −0.0164886 + 0.0164886i
\(299\) 2.21162e8i 0.0276710i
\(300\) −6.08399e9 + 6.08399e9i −0.751110 + 0.751110i
\(301\) −7.22768e9 7.22768e9i −0.880508 0.880508i
\(302\) −1.72109e8 + 1.72109e8i −0.0206908 + 0.0206908i
\(303\) 6.63618e9i 0.787313i
\(304\) −3.23160e9 3.23160e9i −0.378375 0.378375i
\(305\) 7.52165e9 7.52165e9i 0.869188 0.869188i
\(306\) −6.43245e8 −0.0733653
\(307\) 1.92561e9 + 1.92561e9i 0.216778 + 0.216778i 0.807139 0.590361i \(-0.201015\pi\)
−0.590361 + 0.807139i \(0.701015\pi\)
\(308\) −7.20497e9 + 7.20497e9i −0.800626 + 0.800626i
\(309\) −1.00181e10 1.00181e10i −1.09888 1.09888i
\(310\) 6.50574e8 0.0704449
\(311\) −5.70463e9 5.70463e9i −0.609798 0.609798i 0.333095 0.942893i \(-0.391907\pi\)
−0.942893 + 0.333095i \(0.891907\pi\)
\(312\) 7.76633e8i 0.0819591i
\(313\) 1.73518e10 1.80787 0.903933 0.427674i \(-0.140667\pi\)
0.903933 + 0.427674i \(0.140667\pi\)
\(314\) 3.17724e8 0.0326837
\(315\) −2.41199e10 −2.44982
\(316\) 1.89150e9 1.89150e9i 0.189696 0.189696i
\(317\) −5.25464e9 + 5.25464e9i −0.520363 + 0.520363i −0.917681 0.397318i \(-0.869941\pi\)
0.397318 + 0.917681i \(0.369941\pi\)
\(318\) 3.95912e8i 0.0387160i
\(319\) 9.66559e9 3.65971e9i 0.933396 0.353414i
\(320\) −1.33745e10 −1.27549
\(321\) −2.16044e10 2.16044e10i −2.03481 2.03481i
\(322\) −1.10435e7 1.10435e7i −0.00102727 0.00102727i
\(323\) 7.50349e9i 0.689372i
\(324\) 1.55067e9i 0.140715i
\(325\) 5.33581e9i 0.478263i
\(326\) −6.17004e8 −0.0546283
\(327\) 1.28618e10 1.28618e10i 1.12489 1.12489i
\(328\) 1.43503e9i 0.123984i
\(329\) 7.64984e9 7.64984e9i 0.652933 0.652933i
\(330\) 5.98767e8 + 5.98767e8i 0.0504896 + 0.0504896i
\(331\) 8.71393e8 8.71393e8i 0.0725942 0.0725942i −0.669877 0.742472i \(-0.733653\pi\)
0.742472 + 0.669877i \(0.233653\pi\)
\(332\) 1.57436e10i 1.29584i
\(333\) 2.68687e10 + 2.68687e10i 2.18509 + 2.18509i
\(334\) 3.37282e8 3.37282e8i 0.0271024 0.0271024i
\(335\) 7.76756e9 0.616745
\(336\) −1.66969e10 1.66969e10i −1.31002 1.31002i
\(337\) 5.79665e9 5.79665e9i 0.449426 0.449426i −0.445738 0.895163i \(-0.647059\pi\)
0.895163 + 0.445738i \(0.147059\pi\)
\(338\) 1.43864e8 + 1.43864e8i 0.0110227 + 0.0110227i
\(339\) −1.54021e10 −1.16622
\(340\) 1.55634e10 + 1.55634e10i 1.16463 + 1.16463i
\(341\) 2.17511e10i 1.60866i
\(342\) −4.19796e8 −0.0306856
\(343\) −1.11620e10 −0.806429
\(344\) −1.04427e9 −0.0745727
\(345\) 7.91667e8 7.91667e8i 0.0558813 0.0558813i
\(346\) −3.61264e7 + 3.61264e7i −0.00252070 + 0.00252070i
\(347\) 1.44331e10i 0.995500i 0.867321 + 0.497750i \(0.165840\pi\)
−0.867321 + 0.497750i \(0.834160\pi\)
\(348\) 8.49093e9 + 2.24252e10i 0.578946 + 1.52904i
\(349\) 4.35187e8 0.0293342 0.0146671 0.999892i \(-0.495331\pi\)
0.0146671 + 0.999892i \(0.495331\pi\)
\(350\) −2.66438e8 2.66438e8i −0.0177552 0.0177552i
\(351\) −8.78589e9 8.78589e9i −0.578838 0.578838i
\(352\) 1.56179e9i 0.101731i
\(353\) 4.34810e9i 0.280028i 0.990150 + 0.140014i \(0.0447147\pi\)
−0.990150 + 0.140014i \(0.955285\pi\)
\(354\) 3.25710e8i 0.0207404i
\(355\) 4.36156e9 0.274617
\(356\) 1.30666e10 1.30666e10i 0.813510 0.813510i
\(357\) 3.87688e10i 2.38677i
\(358\) 2.03056e8 2.03056e8i 0.0123618 0.0123618i
\(359\) −5.31301e9 5.31301e9i −0.319862 0.319862i 0.528852 0.848714i \(-0.322623\pi\)
−0.848714 + 0.528852i \(0.822623\pi\)
\(360\) −1.74245e9 + 1.74245e9i −0.103741 + 0.103741i
\(361\) 1.20866e10i 0.711665i
\(362\) 3.86732e7 + 3.86732e7i 0.00225204 + 0.00225204i
\(363\) 7.77987e7 7.77987e7i 0.00448070 0.00448070i
\(364\) 1.46606e10 0.835117
\(365\) −1.51405e10 1.51405e10i −0.853041 0.853041i
\(366\) 6.76387e8 6.76387e8i 0.0376939 0.0376939i
\(367\) 8.06359e9 + 8.06359e9i 0.444492 + 0.444492i 0.893519 0.449026i \(-0.148229\pi\)
−0.449026 + 0.893519i \(0.648229\pi\)
\(368\) 6.86982e8 0.0374588
\(369\) 4.01306e10 + 4.01306e10i 2.16456 + 2.16456i
\(370\) 1.50728e9i 0.0804242i
\(371\) 1.49561e10 0.789445
\(372\) −5.04648e10 −2.63522
\(373\) −9.26204e9 −0.478488 −0.239244 0.970959i \(-0.576900\pi\)
−0.239244 + 0.970959i \(0.576900\pi\)
\(374\) 6.03222e8 6.03222e8i 0.0308312 0.0308312i
\(375\) −1.02986e10 + 1.02986e10i −0.520779 + 0.520779i
\(376\) 1.10527e9i 0.0552988i
\(377\) −1.35571e10 6.11037e9i −0.671123 0.302484i
\(378\) −8.77429e8 −0.0429779
\(379\) 4.45713e9 + 4.45713e9i 0.216022 + 0.216022i 0.806820 0.590797i \(-0.201187\pi\)
−0.590797 + 0.806820i \(0.701187\pi\)
\(380\) 1.01570e10 + 1.01570e10i 0.487115 + 0.487115i
\(381\) 1.09211e10i 0.518284i
\(382\) 2.93100e7i 0.00137646i
\(383\) 2.49677e10i 1.16033i −0.814498 0.580167i \(-0.802987\pi\)
0.814498 0.580167i \(-0.197013\pi\)
\(384\) −4.83042e9 −0.222157
\(385\) 2.26192e10 2.26192e10i 1.02952 1.02952i
\(386\) 1.47490e9i 0.0664374i
\(387\) 2.92031e10 2.92031e10i 1.30192 1.30192i
\(388\) −1.57456e10 1.57456e10i −0.694757 0.694757i
\(389\) −1.83603e10 + 1.83603e10i −0.801829 + 0.801829i −0.983381 0.181553i \(-0.941888\pi\)
0.181553 + 0.983381i \(0.441888\pi\)
\(390\) 1.21837e9i 0.0526648i
\(391\) −7.97557e8 7.97557e8i −0.0341236 0.0341236i
\(392\) 3.29310e8 3.29310e8i 0.0139464 0.0139464i
\(393\) −8.51548e9 −0.356976
\(394\) 5.82846e8 + 5.82846e8i 0.0241863 + 0.0241863i
\(395\) −5.93815e9 + 5.93815e9i −0.243929 + 0.243929i
\(396\) −2.91114e10 2.91114e10i −1.18381 1.18381i
\(397\) 1.00393e9 0.0404151 0.0202075 0.999796i \(-0.493567\pi\)
0.0202075 + 0.999796i \(0.493567\pi\)
\(398\) −8.20898e8 8.20898e8i −0.0327158 0.0327158i
\(399\) 2.53014e10i 0.998283i
\(400\) 1.65743e10 0.647435
\(401\) 6.28405e9 0.243031 0.121516 0.992590i \(-0.461225\pi\)
0.121516 + 0.992590i \(0.461225\pi\)
\(402\) 6.98501e8 0.0267462
\(403\) 2.21295e10 2.21295e10i 0.838978 0.838978i
\(404\) 9.04981e9 9.04981e9i 0.339715 0.339715i
\(405\) 4.86816e9i 0.180944i
\(406\) −9.82076e8 + 3.71846e8i −0.0361444 + 0.0136855i
\(407\) −5.03939e10 −1.83654
\(408\) 2.80070e9 + 2.80070e9i 0.101071 + 0.101071i
\(409\) 1.83804e9 + 1.83804e9i 0.0656845 + 0.0656845i 0.739186 0.673501i \(-0.235210\pi\)
−0.673501 + 0.739186i \(0.735210\pi\)
\(410\) 2.25124e9i 0.0796686i
\(411\) 5.30923e10i 1.86065i
\(412\) 2.73236e10i 0.948306i
\(413\) −1.23041e10 −0.422911
\(414\) 4.46207e7 4.46207e7i 0.00151892 0.00151892i
\(415\) 4.94252e10i 1.66631i
\(416\) 1.58896e9 1.58896e9i 0.0530566 0.0530566i
\(417\) −4.60503e10 4.60503e10i −1.52296 1.52296i
\(418\) 3.93677e8 3.93677e8i 0.0128954 0.0128954i
\(419\) 2.03704e10i 0.660911i −0.943822 0.330455i \(-0.892798\pi\)
0.943822 0.330455i \(-0.107202\pi\)
\(420\) 5.24790e10 + 5.24790e10i 1.68651 + 1.68651i
\(421\) 1.07169e10 1.07169e10i 0.341147 0.341147i −0.515652 0.856798i \(-0.672450\pi\)
0.856798 + 0.515652i \(0.172450\pi\)
\(422\) 3.88242e8 0.0122420
\(423\) 3.09089e10 + 3.09089e10i 0.965431 + 0.965431i
\(424\) 1.08044e9 1.08044e9i 0.0334302 0.0334302i
\(425\) −1.92421e10 1.92421e10i −0.589789 0.589789i
\(426\) 3.92214e8 0.0119093
\(427\) −2.55514e10 2.55514e10i −0.768604 0.768604i
\(428\) 5.89243e10i 1.75598i
\(429\) 4.07345e10 1.20263
\(430\) 1.63824e9 0.0479184
\(431\) 2.98922e10 0.866261 0.433130 0.901331i \(-0.357409\pi\)
0.433130 + 0.901331i \(0.357409\pi\)
\(432\) 2.72911e10 2.72911e10i 0.783585 0.783585i
\(433\) 3.95905e10 3.95905e10i 1.12626 1.12626i 0.135483 0.990780i \(-0.456741\pi\)
0.990780 0.135483i \(-0.0432586\pi\)
\(434\) 2.21003e9i 0.0622929i
\(435\) −2.66563e10 7.04014e10i −0.744462 1.96618i
\(436\) −3.50794e10 −0.970747
\(437\) −5.20504e8 5.20504e8i −0.0142724 0.0142724i
\(438\) −1.36152e9 1.36152e9i −0.0369936 0.0369936i
\(439\) 4.59391e9i 0.123687i 0.998086 + 0.0618435i \(0.0196980\pi\)
−0.998086 + 0.0618435i \(0.980302\pi\)
\(440\) 3.26807e9i 0.0871928i
\(441\) 1.84184e10i 0.486964i
\(442\) −1.22743e9 −0.0321594
\(443\) 7.38201e9 7.38201e9i 0.191672 0.191672i −0.604746 0.796418i \(-0.706725\pi\)
0.796418 + 0.604746i \(0.206725\pi\)
\(444\) 1.16919e11i 3.00853i
\(445\) −4.10211e10 + 4.10211e10i −1.04609 + 1.04609i
\(446\) −1.56259e9 1.56259e9i −0.0394916 0.0394916i
\(447\) −3.16654e10 + 3.16654e10i −0.793149 + 0.793149i
\(448\) 4.54336e10i 1.12789i
\(449\) 3.68491e10 + 3.68491e10i 0.906654 + 0.906654i 0.996001 0.0893470i \(-0.0284780\pi\)
−0.0893470 + 0.996001i \(0.528478\pi\)
\(450\) 1.07653e9 1.07653e9i 0.0262529 0.0262529i
\(451\) −7.52673e10 −1.81928
\(452\) 2.10039e10 + 2.10039e10i 0.503207 + 0.503207i
\(453\) −4.19123e10 + 4.19123e10i −0.995287 + 0.995287i
\(454\) −4.85301e8 4.85301e8i −0.0114232 0.0114232i
\(455\) −4.60254e10 −1.07387
\(456\) 1.82780e9 + 1.82780e9i 0.0422737 + 0.0422737i
\(457\) 6.58821e10i 1.51044i −0.655473 0.755218i \(-0.727531\pi\)
0.655473 0.755218i \(-0.272469\pi\)
\(458\) −2.95559e9 −0.0671711
\(459\) −6.33676e10 −1.42763
\(460\) −2.15921e9 −0.0482240
\(461\) −2.82917e10 + 2.82917e10i −0.626405 + 0.626405i −0.947162 0.320756i \(-0.896063\pi\)
0.320756 + 0.947162i \(0.396063\pi\)
\(462\) 2.03404e9 2.03404e9i 0.0446469 0.0446469i
\(463\) 4.28979e10i 0.933494i 0.884391 + 0.466747i \(0.154574\pi\)
−0.884391 + 0.466747i \(0.845426\pi\)
\(464\) 1.89803e10 4.21117e10i 0.409478 0.908512i
\(465\) 1.58429e11 3.38861
\(466\) 9.40736e8 + 9.40736e8i 0.0199491 + 0.0199491i
\(467\) 2.73491e10 + 2.73491e10i 0.575011 + 0.575011i 0.933525 0.358513i \(-0.116716\pi\)
−0.358513 + 0.933525i \(0.616716\pi\)
\(468\) 5.92357e10i 1.23481i
\(469\) 2.63867e10i 0.545374i
\(470\) 1.73392e9i 0.0355335i
\(471\) 7.73726e10 1.57218
\(472\) −8.88861e8 + 8.88861e8i −0.0179088 + 0.0179088i
\(473\) 5.47722e10i 1.09425i
\(474\) −5.33990e8 + 5.33990e8i −0.0105784 + 0.0105784i
\(475\) −1.25578e10 1.25578e10i −0.246684 0.246684i
\(476\) 5.28694e10 5.28694e10i 1.02986 1.02986i
\(477\) 6.04293e10i 1.16728i
\(478\) 1.20464e8 + 1.20464e8i 0.00230752 + 0.00230752i
\(479\) −6.03446e10 + 6.03446e10i −1.14630 + 1.14630i −0.159020 + 0.987275i \(0.550834\pi\)
−0.987275 + 0.159020i \(0.949166\pi\)
\(480\) 1.13756e10 0.214294
\(481\) 5.12706e10 + 5.12706e10i 0.957828 + 0.957828i
\(482\) 9.07380e8 9.07380e8i 0.0168113 0.0168113i
\(483\) −2.68933e9 2.68933e9i −0.0494145 0.0494145i
\(484\) −2.12190e8 −0.00386672
\(485\) 4.94315e10 + 4.94315e10i 0.893382 + 0.893382i
\(486\) 1.67329e9i 0.0299934i
\(487\) −4.88736e10 −0.868878 −0.434439 0.900701i \(-0.643053\pi\)
−0.434439 + 0.900701i \(0.643053\pi\)
\(488\) −3.69172e9 −0.0650953
\(489\) −1.50254e11 −2.62778
\(490\) −5.16616e8 + 5.16616e8i −0.00896157 + 0.00896157i
\(491\) 3.31464e10 3.31464e10i 0.570310 0.570310i −0.361905 0.932215i \(-0.617874\pi\)
0.932215 + 0.361905i \(0.117874\pi\)
\(492\) 1.74628e11i 2.98026i
\(493\) −7.09252e10 + 2.68546e10i −1.20064 + 0.454602i
\(494\) −8.01051e8 −0.0134509
\(495\) 9.13918e10 + 9.13918e10i 1.52225 + 1.52225i
\(496\) 6.87395e10 + 6.87395e10i 1.13574 + 1.13574i
\(497\) 1.48164e10i 0.242838i
\(498\) 4.44458e9i 0.0722625i
\(499\) 2.25994e10i 0.364497i −0.983252 0.182249i \(-0.941662\pi\)
0.983252 0.182249i \(-0.0583376\pi\)
\(500\) 2.80886e10 0.449417
\(501\) 8.21353e10 8.21353e10i 1.30370 1.30370i
\(502\) 1.17506e9i 0.0185031i
\(503\) 2.07414e10 2.07414e10i 0.324015 0.324015i −0.526290 0.850305i \(-0.676417\pi\)
0.850305 + 0.526290i \(0.176417\pi\)
\(504\) 5.91918e9 + 5.91918e9i 0.0917359 + 0.0917359i
\(505\) −2.84108e10 + 2.84108e10i −0.436836 + 0.436836i
\(506\) 8.36889e7i 0.00127663i
\(507\) 3.50340e10 + 3.50340e10i 0.530223 + 0.530223i
\(508\) 1.48933e10 1.48933e10i 0.223632 0.223632i
\(509\) −8.66687e10 −1.29119 −0.645596 0.763679i \(-0.723391\pi\)
−0.645596 + 0.763679i \(0.723391\pi\)
\(510\) −4.39370e9 4.39370e9i −0.0649455 0.0649455i
\(511\) −5.14331e10 + 5.14331e10i −0.754325 + 0.754325i
\(512\) 8.22933e9 + 8.22933e9i 0.119752 + 0.119752i
\(513\) −4.13552e10 −0.597118
\(514\) 4.39902e8 + 4.39902e8i 0.00630236 + 0.00630236i
\(515\) 8.57792e10i 1.21942i
\(516\) −1.27078e11 −1.79254
\(517\) −5.79714e10 −0.811431
\(518\) 5.12029e9 0.0711173
\(519\) −8.79756e9 + 8.79756e9i −0.121253 + 0.121253i
\(520\) −3.32492e9 + 3.32492e9i −0.0454746 + 0.0454746i
\(521\) 1.21697e11i 1.65169i −0.563900 0.825843i \(-0.690700\pi\)
0.563900 0.825843i \(-0.309300\pi\)
\(522\) −1.50243e9 3.96804e9i −0.0202354 0.0534433i
\(523\) 5.55302e10 0.742203 0.371101 0.928592i \(-0.378980\pi\)
0.371101 + 0.928592i \(0.378980\pi\)
\(524\) 1.16126e10 + 1.16126e10i 0.154030 + 0.154030i
\(525\) −6.48834e10 6.48834e10i −0.854076 0.854076i
\(526\) 2.60812e9i 0.0340710i
\(527\) 1.59607e11i 2.06924i
\(528\) 1.26531e11i 1.62803i
\(529\) −7.82003e10 −0.998587
\(530\) −1.69498e9 + 1.69498e9i −0.0214813 + 0.0214813i
\(531\) 4.97141e10i 0.625319i
\(532\) 3.45038e10 3.45038e10i 0.430745 0.430745i
\(533\) 7.65767e10 + 7.65767e10i 0.948829 + 0.948829i
\(534\) −3.68884e9 + 3.68884e9i −0.0453654 + 0.0453654i
\(535\) 1.84986e11i 2.25800i
\(536\) −1.90621e9 1.90621e9i −0.0230946 0.0230946i
\(537\) 4.94483e10 4.94483e10i 0.594641 0.594641i
\(538\) −4.89711e9 −0.0584536
\(539\) −1.72724e10 1.72724e10i −0.204643 0.204643i
\(540\) −8.57768e10 + 8.57768e10i −1.00878 + 1.00878i
\(541\) 2.00767e9 + 2.00767e9i 0.0234370 + 0.0234370i 0.718728 0.695291i \(-0.244725\pi\)
−0.695291 + 0.718728i \(0.744725\pi\)
\(542\) −1.82466e9 −0.0211439
\(543\) 9.41775e9 + 9.41775e9i 0.108330 + 0.108330i
\(544\) 1.14602e10i 0.130857i
\(545\) 1.10128e11 1.24828
\(546\) −4.13885e9 −0.0465703
\(547\) 4.07148e10 0.454782 0.227391 0.973804i \(-0.426980\pi\)
0.227391 + 0.973804i \(0.426980\pi\)
\(548\) −7.24025e10 + 7.24025e10i −0.802844 + 0.802844i
\(549\) 1.03239e11 1.03239e11i 1.13646 1.13646i
\(550\) 2.01910e9i 0.0220652i
\(551\) −4.62874e10 + 1.75259e10i −0.502177 + 0.190141i
\(552\) −3.88560e8 −0.00418506
\(553\) 2.01721e10 + 2.01721e10i 0.215701 + 0.215701i
\(554\) 1.90316e9 + 1.90316e9i 0.0202040 + 0.0202040i
\(555\) 3.67054e11i 3.86864i
\(556\) 1.25598e11i 1.31427i
\(557\) 9.69776e10i 1.00751i 0.863846 + 0.503756i \(0.168049\pi\)
−0.863846 + 0.503756i \(0.831951\pi\)
\(558\) 8.92951e9 0.0921066
\(559\) 5.57251e10 5.57251e10i 0.570694 0.570694i
\(560\) 1.42966e11i 1.45372i
\(561\) 1.46897e11 1.46897e11i 1.48307 1.48307i
\(562\) −3.28830e9 3.28830e9i −0.0329629 0.0329629i
\(563\) 5.73948e10 5.73948e10i 0.571266 0.571266i −0.361216 0.932482i \(-0.617638\pi\)
0.932482 + 0.361216i \(0.117638\pi\)
\(564\) 1.34500e11i 1.32925i
\(565\) −6.59394e10 6.59394e10i −0.647070 0.647070i
\(566\) 1.29524e9 1.29524e9i 0.0126207 0.0126207i
\(567\) −1.65373e10 −0.160005
\(568\) −1.07035e9 1.07035e9i −0.0102833 0.0102833i
\(569\) −8.28425e10 + 8.28425e10i −0.790322 + 0.790322i −0.981546 0.191224i \(-0.938754\pi\)
0.191224 + 0.981546i \(0.438754\pi\)
\(570\) −2.86743e9 2.86743e9i −0.0271640 0.0271640i
\(571\) −2.04986e10 −0.192832 −0.0964162 0.995341i \(-0.530738\pi\)
−0.0964162 + 0.995341i \(0.530738\pi\)
\(572\) −5.55500e10 5.55500e10i −0.518920 0.518920i
\(573\) 7.13761e9i 0.0662117i
\(574\) 7.64757e9 0.0704491
\(575\) 2.66958e9 0.0244214
\(576\) −1.83572e11 −1.66770
\(577\) 6.21525e10 6.21525e10i 0.560732 0.560732i −0.368783 0.929515i \(-0.620226\pi\)
0.929515 + 0.368783i \(0.120226\pi\)
\(578\) −1.74080e9 + 1.74080e9i −0.0155968 + 0.0155968i
\(579\) 3.59169e11i 3.19584i
\(580\) −5.96556e10 + 1.32358e11i −0.527156 + 1.16961i
\(581\) 1.67899e11 1.47348
\(582\) 4.44515e9 + 4.44515e9i 0.0387431 + 0.0387431i
\(583\) −5.66694e10 5.66694e10i −0.490540 0.490540i
\(584\) 7.43116e9i 0.0638860i
\(585\) 1.85963e11i 1.58783i
\(586\) 5.07608e9i 0.0430465i
\(587\) 1.35471e11 1.14102 0.570512 0.821289i \(-0.306745\pi\)
0.570512 + 0.821289i \(0.306745\pi\)
\(588\) 4.00738e10 4.00738e10i 0.335237 0.335237i
\(589\) 1.04163e11i 0.865474i
\(590\) 1.39443e9 1.39443e9i 0.0115077 0.0115077i
\(591\) 1.41935e11 + 1.41935e11i 1.16343 + 1.16343i
\(592\) −1.59259e11 + 1.59259e11i −1.29663 + 1.29663i
\(593\) 1.26193e10i 0.102050i −0.998697 0.0510252i \(-0.983751\pi\)
0.998697 0.0510252i \(-0.0162489\pi\)
\(594\) 3.32463e9 + 3.32463e9i 0.0267053 + 0.0267053i
\(595\) −1.65977e11 + 1.65977e11i −1.32428 + 1.32428i
\(596\) 8.63648e10 0.684465
\(597\) −1.99906e11 1.99906e11i −1.57372 1.57372i
\(598\) 8.51448e7 8.51448e7i 0.000665815 0.000665815i
\(599\) −5.38002e10 5.38002e10i −0.417904 0.417904i 0.466577 0.884481i \(-0.345487\pi\)
−0.884481 + 0.466577i \(0.845487\pi\)
\(600\) −9.37450e9 −0.0723341
\(601\) −1.01554e11 1.01554e11i −0.778397 0.778397i 0.201161 0.979558i \(-0.435529\pi\)
−0.979558 + 0.201161i \(0.935529\pi\)
\(602\) 5.56515e9i 0.0423732i
\(603\) 1.06614e11 0.806393
\(604\) 1.14312e11 0.858905
\(605\) 6.66145e8 0.00497218
\(606\) −2.55485e9 + 2.55485e9i −0.0189442 + 0.0189442i
\(607\) 7.32554e10 7.32554e10i 0.539616 0.539616i −0.383800 0.923416i \(-0.625385\pi\)
0.923416 + 0.383800i \(0.125385\pi\)
\(608\) 7.47922e9i 0.0547321i
\(609\) −2.39157e11 + 9.05525e10i −1.73865 + 0.658311i
\(610\) 5.79151e9 0.0418285
\(611\) 5.89799e10 + 5.89799e10i 0.423194 + 0.423194i
\(612\) 2.13617e11 + 2.13617e11i 1.52275 + 1.52275i
\(613\) 4.76968e10i 0.337791i 0.985634 + 0.168895i \(0.0540200\pi\)
−0.985634 + 0.168895i \(0.945980\pi\)
\(614\) 1.48268e9i 0.0104322i
\(615\) 5.48226e11i 3.83229i
\(616\) −1.11018e10 −0.0771027
\(617\) −1.21988e11 + 1.21988e11i −0.841739 + 0.841739i −0.989085 0.147346i \(-0.952927\pi\)
0.147346 + 0.989085i \(0.452927\pi\)
\(618\) 7.71372e9i 0.0528823i
\(619\) 6.31992e10 6.31992e10i 0.430476 0.430476i −0.458314 0.888790i \(-0.651547\pi\)
0.888790 + 0.458314i \(0.151547\pi\)
\(620\) −2.16050e11 2.16050e11i −1.46214 1.46214i
\(621\) 4.39570e9 4.39570e9i 0.0295571 0.0295571i
\(622\) 4.39244e9i 0.0293457i
\(623\) 1.39350e11 + 1.39350e11i 0.925031 + 0.925031i
\(624\) 1.28733e11 1.28733e11i 0.849083 0.849083i
\(625\) −1.87316e11 −1.22759
\(626\) 6.68024e9 + 6.68024e9i 0.0435005 + 0.0435005i
\(627\) 9.58687e10 9.58687e10i 0.620307 0.620307i
\(628\) −1.05514e11 1.05514e11i −0.678375 0.678375i
\(629\) 3.69785e11 2.36237
\(630\) −9.28590e9 9.28590e9i −0.0589470 0.0589470i
\(631\) 1.01804e11i 0.642167i −0.947051 0.321083i \(-0.895953\pi\)
0.947051 0.321083i \(-0.104047\pi\)
\(632\) 2.91452e9 0.0182683
\(633\) 9.45451e10 0.588876
\(634\) −4.04596e9 −0.0250417
\(635\) −4.67556e10 + 4.67556e10i −0.287567 + 0.287567i
\(636\) 1.31479e11 1.31479e11i 0.803579 0.803579i
\(637\) 3.51457e10i 0.213459i
\(638\) 5.13009e9 + 2.31220e9i 0.0309630 + 0.0139554i
\(639\) 5.98650e10 0.359062
\(640\) −2.06800e10 2.06800e10i −0.123263 0.123263i
\(641\) −1.41113e11 1.41113e11i −0.835866 0.835866i 0.152446 0.988312i \(-0.451285\pi\)
−0.988312 + 0.152446i \(0.951285\pi\)
\(642\) 1.66349e10i 0.0979222i
\(643\) 1.87106e11i 1.09457i 0.836947 + 0.547284i \(0.184338\pi\)
−0.836947 + 0.547284i \(0.815662\pi\)
\(644\) 7.33491e9i 0.0426434i
\(645\) 3.98945e11 2.30502
\(646\) −2.88876e9 + 2.88876e9i −0.0165875 + 0.0165875i
\(647\) 3.07155e10i 0.175283i 0.996152 + 0.0876417i \(0.0279331\pi\)
−0.996152 + 0.0876417i \(0.972067\pi\)
\(648\) −1.19468e9 + 1.19468e9i −0.00677563 + 0.00677563i
\(649\) 4.66209e10 + 4.66209e10i 0.262786 + 0.262786i
\(650\) 2.05423e9 2.05423e9i 0.0115079 0.0115079i
\(651\) 5.38188e11i 2.99647i
\(652\) 2.04902e11 + 2.04902e11i 1.13385 + 1.13385i
\(653\) −1.12901e11 + 1.12901e11i −0.620934 + 0.620934i −0.945770 0.324836i \(-0.894691\pi\)
0.324836 + 0.945770i \(0.394691\pi\)
\(654\) 9.90327e9 0.0541337
\(655\) −3.64565e10 3.64565e10i −0.198066 0.198066i
\(656\) −2.37866e11 + 2.37866e11i −1.28445 + 1.28445i
\(657\) −2.07813e11 2.07813e11i −1.11535 1.11535i
\(658\) 5.89021e9 0.0314215
\(659\) 1.50790e11 + 1.50790e11i 0.799522 + 0.799522i 0.983020 0.183498i \(-0.0587421\pi\)
−0.183498 + 0.983020i \(0.558742\pi\)
\(660\) 3.97692e11i 2.09590i
\(661\) −2.80608e11 −1.46992 −0.734962 0.678109i \(-0.762800\pi\)
−0.734962 + 0.678109i \(0.762800\pi\)
\(662\) 6.70953e8 0.00349349
\(663\) −2.98906e11 −1.54696
\(664\) 1.21292e10 1.21292e10i 0.0623967 0.0623967i
\(665\) −1.08321e11 + 1.08321e11i −0.553892 + 0.553892i
\(666\) 2.06883e10i 0.105155i
\(667\) 3.05710e9 6.78281e9i 0.0154456 0.0342694i
\(668\) −2.24017e11 −1.12506
\(669\) −3.80523e11 3.80523e11i −1.89966 1.89966i
\(670\) 2.99042e9 + 2.99042e9i 0.0148400 + 0.0148400i
\(671\) 1.93631e11i 0.955180i
\(672\) 3.86434e10i 0.189495i
\(673\) 1.05430e11i 0.513930i −0.966421 0.256965i \(-0.917277\pi\)
0.966421 0.256965i \(-0.0827226\pi\)
\(674\) 4.46329e9 0.0216280
\(675\) 1.06052e11 1.06052e11i 0.510862 0.510862i
\(676\) 9.55524e10i 0.457567i
\(677\) −2.99102e9 + 2.99102e9i −0.0142385 + 0.0142385i −0.714190 0.699952i \(-0.753205\pi\)
0.699952 + 0.714190i \(0.253205\pi\)
\(678\) −5.92962e9 5.92962e9i −0.0280613 0.0280613i
\(679\) 1.67921e11 1.67921e11i 0.789998 0.789998i
\(680\) 2.39808e10i 0.112157i
\(681\) −1.18181e11 1.18181e11i −0.549489 0.549489i
\(682\) −8.37392e9 + 8.37392e9i −0.0387072 + 0.0387072i
\(683\) 1.49572e9 0.00687333 0.00343666 0.999994i \(-0.498906\pi\)
0.00343666 + 0.999994i \(0.498906\pi\)
\(684\) 1.39411e11 + 1.39411e11i 0.636902 + 0.636902i
\(685\) 2.27299e11 2.27299e11i 1.03237 1.03237i
\(686\) −4.29725e9 4.29725e9i −0.0194041 0.0194041i
\(687\) −7.19749e11 −3.23113
\(688\) 1.73096e11 + 1.73096e11i 0.772560 + 0.772560i
\(689\) 1.15311e11i 0.511673i
\(690\) 6.09566e8 0.00268921
\(691\) −2.43095e11 −1.06626 −0.533132 0.846032i \(-0.678985\pi\)
−0.533132 + 0.846032i \(0.678985\pi\)
\(692\) 2.39946e10 0.104638
\(693\) 3.10462e11 3.10462e11i 1.34609 1.34609i
\(694\) −5.55658e9 + 5.55658e9i −0.0239535 + 0.0239535i
\(695\) 3.94302e11i 1.69001i
\(696\) −1.07353e10 + 2.38186e10i −0.0457486 + 0.101503i
\(697\) 5.52304e11 2.34017
\(698\) 1.67542e8 + 1.67542e8i 0.000705833 + 0.000705833i
\(699\) 2.29089e11 + 2.29089e11i 0.959612 + 0.959612i
\(700\) 1.76964e11i 0.737044i
\(701\) 3.29493e9i 0.0136450i −0.999977 0.00682250i \(-0.997828\pi\)
0.999977 0.00682250i \(-0.00217169\pi\)
\(702\) 6.76494e9i 0.0278558i
\(703\) 2.41330e11 0.988077
\(704\) 1.72151e11 1.72151e11i 0.700838 0.700838i
\(705\) 4.22247e11i 1.70927i
\(706\) −1.67397e9 + 1.67397e9i −0.00673797 + 0.00673797i
\(707\) 9.65128e10 + 9.65128e10i 0.386284 + 0.386284i
\(708\) −1.08166e11 + 1.08166e11i −0.430483 + 0.430483i
\(709\) 4.66187e11i 1.84491i 0.386107 + 0.922454i \(0.373820\pi\)
−0.386107 + 0.922454i \(0.626180\pi\)
\(710\) 1.67915e9 + 1.67915e9i 0.00660779 + 0.00660779i
\(711\) −8.15047e10 + 8.15047e10i −0.318936 + 0.318936i
\(712\) 2.01337e10 0.0783435
\(713\) 1.10717e10 + 1.10717e10i 0.0428405 + 0.0428405i
\(714\) −1.49256e10 + 1.49256e10i −0.0574299 + 0.0574299i
\(715\) 1.74393e11 + 1.74393e11i 0.667274 + 0.667274i
\(716\) −1.34866e11 −0.513158
\(717\) 2.93356e10 + 2.93356e10i 0.110999 + 0.110999i
\(718\) 4.09090e9i 0.0153929i
\(719\) −2.67420e11 −1.00064 −0.500320 0.865841i \(-0.666784\pi\)
−0.500320 + 0.865841i \(0.666784\pi\)
\(720\) 5.77648e11 2.14948
\(721\) −2.91396e11 −1.07831
\(722\) 4.65321e9 4.65321e9i 0.0171239 0.0171239i
\(723\) 2.20966e11 2.20966e11i 0.808673 0.808673i
\(724\) 2.56861e10i 0.0934855i
\(725\) 7.37564e10 1.63644e11i 0.266961 0.592309i
\(726\) 5.99033e7 0.000215628
\(727\) 1.53119e11 + 1.53119e11i 0.548141 + 0.548141i 0.925903 0.377762i \(-0.123306\pi\)
−0.377762 + 0.925903i \(0.623306\pi\)
\(728\) 1.12949e10 + 1.12949e10i 0.0402121 + 0.0402121i
\(729\) 4.47269e11i 1.58365i
\(730\) 1.16579e10i 0.0410514i
\(731\) 4.01913e11i 1.40755i
\(732\) −4.49246e11 −1.56473
\(733\) −1.52946e10 + 1.52946e10i −0.0529811 + 0.0529811i −0.733101 0.680120i \(-0.761928\pi\)
0.680120 + 0.733101i \(0.261928\pi\)
\(734\) 6.20879e9i 0.0213906i
\(735\) −1.25807e11 + 1.25807e11i −0.431078 + 0.431078i
\(736\) 7.94977e8 + 7.94977e8i 0.00270921 + 0.00270921i
\(737\) −9.99809e10 + 9.99809e10i −0.338881 + 0.338881i
\(738\) 3.08997e10i 0.104167i
\(739\) −1.00402e10 1.00402e10i −0.0336641 0.0336641i 0.690074 0.723738i \(-0.257578\pi\)
−0.723738 + 0.690074i \(0.757578\pi\)
\(740\) 5.00555e11 5.00555e11i 1.66927 1.66927i
\(741\) −1.95073e11 −0.647030
\(742\) 5.75792e9 + 5.75792e9i 0.0189955 + 0.0189955i
\(743\) −1.39158e11 + 1.39158e11i −0.456618 + 0.456618i −0.897544 0.440926i \(-0.854650\pi\)
0.440926 + 0.897544i \(0.354650\pi\)
\(744\) −3.88793e10 3.88793e10i −0.126890 0.126890i
\(745\) −2.71132e11 −0.880148
\(746\) −3.56578e9 3.56578e9i −0.0115133 0.0115133i
\(747\) 6.78390e11i 2.17870i
\(748\) −4.00651e11 −1.27985
\(749\) −6.28406e11 −1.99670
\(750\) −7.92969e9 −0.0250618
\(751\) 2.94916e11 2.94916e11i 0.927125 0.927125i −0.0703940 0.997519i \(-0.522426\pi\)
0.997519 + 0.0703940i \(0.0224257\pi\)
\(752\) −1.83206e11 + 1.83206e11i −0.572886 + 0.572886i
\(753\) 2.86152e11i 0.890056i
\(754\) −2.86692e9 7.57176e9i −0.00887013 0.0234267i
\(755\) −3.58870e11 −1.10446
\(756\) 2.91387e11 + 2.91387e11i 0.892039 + 0.892039i
\(757\) 1.92054e11 + 1.92054e11i 0.584844 + 0.584844i 0.936231 0.351386i \(-0.114290\pi\)
−0.351386 + 0.936231i \(0.614290\pi\)
\(758\) 3.43189e9i 0.0103958i
\(759\) 2.03800e10i 0.0614098i
\(760\) 1.56504e10i 0.0469107i
\(761\) 8.05148e10 0.240070 0.120035 0.992770i \(-0.461699\pi\)
0.120035 + 0.992770i \(0.461699\pi\)
\(762\) −4.20452e9 + 4.20452e9i −0.0124709 + 0.0124709i
\(763\) 3.74108e11i 1.10382i
\(764\) −9.73362e9 + 9.73362e9i −0.0285694 + 0.0285694i
\(765\) −6.70624e11 6.70624e11i −1.95809 1.95809i
\(766\) 9.61227e9 9.61227e9i 0.0279197 0.0279197i
\(767\) 9.48640e10i 0.274107i
\(768\) 3.98012e11 + 3.98012e11i 1.14407 + 1.14407i
\(769\) −5.67272e10 + 5.67272e10i −0.162213 + 0.162213i −0.783546 0.621333i \(-0.786591\pi\)
0.621333 + 0.783546i \(0.286591\pi\)
\(770\) 1.74163e10 0.0495441
\(771\) 1.07125e11 + 1.07125e11i 0.303162 + 0.303162i
\(772\) 4.89802e11 4.89802e11i 1.37896 1.37896i
\(773\) −2.20080e10 2.20080e10i −0.0616399 0.0616399i 0.675615 0.737255i \(-0.263878\pi\)
−0.737255 + 0.675615i \(0.763878\pi\)
\(774\) 2.24858e10 0.0626533
\(775\) 2.67118e11 + 2.67118e11i 0.740452 + 0.740452i
\(776\) 2.42616e10i 0.0669071i
\(777\) 1.24690e12 3.42095
\(778\) −1.41370e10 −0.0385869
\(779\) 3.60447e11 0.978794
\(780\) −4.04610e11 + 4.04610e11i −1.09310 + 1.09310i
\(781\) −5.61402e10 + 5.61402e10i −0.150893 + 0.150893i
\(782\) 6.14101e8i 0.00164215i
\(783\) −1.48008e11 3.90901e11i −0.393766 1.03997i
\(784\) −1.09171e11 −0.288964
\(785\) 3.31248e11 + 3.31248e11i 0.872317 + 0.872317i
\(786\) −3.27837e9 3.27837e9i −0.00858949 0.00858949i
\(787\) 6.14633e11i 1.60220i −0.598530 0.801101i \(-0.704248\pi\)
0.598530 0.801101i \(-0.295752\pi\)
\(788\) 3.87117e11i 1.00401i
\(789\) 6.35133e11i 1.63892i
\(790\) −4.57224e9 −0.0117387
\(791\) −2.23999e11 + 2.23999e11i −0.572189 + 0.572189i
\(792\) 4.48562e10i 0.114004i
\(793\) 1.97000e11 1.97000e11i 0.498165 0.498165i
\(794\) 3.86504e8 + 3.86504e8i 0.000972460 + 0.000972460i
\(795\) −4.12764e11 + 4.12764e11i −1.03332 + 1.03332i
\(796\) 5.45228e11i 1.35808i
\(797\) 2.44620e11 + 2.44620e11i 0.606259 + 0.606259i 0.941966 0.335707i \(-0.108975\pi\)
−0.335707 + 0.941966i \(0.608975\pi\)
\(798\) −9.74077e9 + 9.74077e9i −0.0240205 + 0.0240205i
\(799\) 4.25389e11 1.04376
\(800\) 1.91798e10 + 1.91798e10i 0.0468258 + 0.0468258i
\(801\) −5.63040e11 + 5.63040e11i −1.36776 + 1.36776i
\(802\) 2.41929e9 + 2.41929e9i 0.00584777 + 0.00584777i
\(803\) 3.89766e11 0.937436
\(804\) −2.31967e11 2.31967e11i −0.555138 0.555138i
\(805\) 2.30271e10i 0.0548348i
\(806\) 1.70392e10 0.0403747
\(807\) −1.19255e12 −2.81179
\(808\) 1.39444e10 0.0327155
\(809\) 2.32790e11 2.32790e11i 0.543463 0.543463i −0.381080 0.924542i \(-0.624448\pi\)
0.924542 + 0.381080i \(0.124448\pi\)
\(810\) 1.87419e9 1.87419e9i 0.00435384 0.00435384i
\(811\) 5.46311e9i 0.0126286i −0.999980 0.00631432i \(-0.997990\pi\)
0.999980 0.00631432i \(-0.00200992\pi\)
\(812\) 4.49627e11 + 2.02653e11i 1.03426 + 0.466153i
\(813\) −4.44343e11 −1.01708
\(814\) −1.94011e10 1.94011e10i −0.0441904 0.0441904i
\(815\) −6.43267e11 6.43267e11i −1.45801 1.45801i
\(816\) 9.28474e11i 2.09416i
\(817\) 2.62298e11i 0.588717i
\(818\) 1.41525e9i 0.00316097i
\(819\) −6.31726e11 −1.40408
\(820\) 7.47620e11 7.47620e11i 1.65358 1.65358i
\(821\) 3.30921e11i 0.728369i 0.931327 + 0.364185i \(0.118652\pi\)
−0.931327 + 0.364185i \(0.881348\pi\)
\(822\) 2.04400e10 2.04400e10i 0.0447706 0.0447706i
\(823\) −2.87737e11 2.87737e11i −0.627186 0.627186i 0.320173 0.947359i \(-0.396259\pi\)
−0.947359 + 0.320173i \(0.896259\pi\)
\(824\) −2.10507e10 + 2.10507e10i −0.0456624 + 0.0456624i
\(825\) 4.91694e11i 1.06140i
\(826\) −4.73694e9 4.73694e9i −0.0101760 0.0101760i
\(827\) −4.78666e11 + 4.78666e11i −1.02332 + 1.02332i −0.0235963 + 0.999722i \(0.507512\pi\)
−0.999722 + 0.0235963i \(0.992488\pi\)
\(828\) −2.96364e10 −0.0630528
\(829\) 1.00884e11 + 1.00884e11i 0.213602 + 0.213602i 0.805796 0.592193i \(-0.201738\pi\)
−0.592193 + 0.805796i \(0.701738\pi\)
\(830\) −1.90281e10 + 1.90281e10i −0.0400944 + 0.0400944i
\(831\) 4.63461e11 + 4.63461e11i 0.971871 + 0.971871i
\(832\) −3.50291e11 −0.731031
\(833\) 1.26743e11 + 1.26743e11i 0.263235 + 0.263235i
\(834\) 3.54577e10i 0.0732903i
\(835\) 7.03277e11 1.44671
\(836\) −2.61474e11 −0.535307
\(837\) 8.79668e11 1.79233
\(838\) 7.84237e9 7.84237e9i 0.0159027 0.0159027i
\(839\) 3.47996e11 3.47996e11i 0.702306 0.702306i −0.262599 0.964905i \(-0.584580\pi\)
0.964905 + 0.262599i \(0.0845798\pi\)
\(840\) 8.08621e10i 0.162416i
\(841\) −3.31320e11 3.74798e11i −0.662314 0.749226i
\(842\) 8.25178e9 0.0164172
\(843\) −8.00770e11 8.00770e11i −1.58561 1.58561i
\(844\) −1.28932e11 1.28932e11i −0.254092 0.254092i
\(845\) 2.99976e11i 0.588382i
\(846\) 2.37991e10i 0.0464600i
\(847\) 2.26292e9i 0.00439679i
\(848\) −3.58183e11 −0.692662
\(849\) 3.15419e11 3.15419e11i 0.607095 0.607095i
\(850\) 1.48160e10i 0.0283828i
\(851\) −2.56514e10 + 2.56514e10i −0.0489094 + 0.0489094i
\(852\) −1.30251e11 1.30251e11i −0.247186 0.247186i
\(853\) 5.53587e11 5.53587e11i 1.04566 1.04566i 0.0467510 0.998907i \(-0.485113\pi\)
0.998907 0.0467510i \(-0.0148867\pi\)
\(854\) 1.96740e10i 0.0369880i
\(855\) −4.37665e11 4.37665e11i −0.818988 0.818988i
\(856\) −4.53967e10 + 4.53967e10i −0.0845531 + 0.0845531i
\(857\) −4.23255e11 −0.784656 −0.392328 0.919825i \(-0.628330\pi\)
−0.392328 + 0.919825i \(0.628330\pi\)
\(858\) 1.56823e10 + 1.56823e10i 0.0289375 + 0.0289375i
\(859\) 3.43252e11 3.43252e11i 0.630435 0.630435i −0.317742 0.948177i \(-0.602925\pi\)
0.948177 + 0.317742i \(0.102925\pi\)
\(860\) −5.44045e11 5.44045e11i −0.994583 0.994583i
\(861\) 1.86235e12 3.38881
\(862\) 1.15082e10 + 1.15082e10i 0.0208438 + 0.0208438i
\(863\) 8.57111e11i 1.54523i 0.634874 + 0.772616i \(0.281052\pi\)
−0.634874 + 0.772616i \(0.718948\pi\)
\(864\) 6.31627e10 0.113346
\(865\) −7.53283e10 −0.134553
\(866\) 3.04838e10 0.0541998
\(867\) −4.23921e11 + 4.23921e11i −0.750254 + 0.750254i
\(868\) −7.33932e11 + 7.33932e11i −1.29294 + 1.29294i
\(869\) 1.52867e11i 0.268061i
\(870\) 1.68414e10 3.73661e10i 0.0293969 0.0652231i
\(871\) 2.03440e11 0.353480
\(872\) −2.70260e10 2.70260e10i −0.0467429 0.0467429i
\(873\) 6.78477e11 + 6.78477e11i 1.16810 + 1.16810i
\(874\) 4.00777e8i 0.000686842i
\(875\) 2.99554e11i 0.511026i
\(876\) 9.04299e11i 1.53566i
\(877\) −5.33654e11 −0.902114 −0.451057 0.892495i \(-0.648953\pi\)
−0.451057 + 0.892495i \(0.648953\pi\)
\(878\) −1.76860e9 + 1.76860e9i −0.00297613 + 0.00297613i
\(879\) 1.23613e12i 2.07067i
\(880\) −5.41706e11 + 5.41706e11i −0.903303 + 0.903303i
\(881\) 2.27315e10 + 2.27315e10i 0.0377333 + 0.0377333i 0.725722 0.687988i \(-0.241506\pi\)
−0.687988 + 0.725722i \(0.741506\pi\)
\(882\) −7.09087e9 + 7.09087e9i −0.0117172 + 0.0117172i
\(883\) 3.04160e11i 0.500333i −0.968203 0.250167i \(-0.919515\pi\)
0.968203 0.250167i \(-0.0804854\pi\)
\(884\) 4.07621e11 + 4.07621e11i 0.667494 + 0.667494i
\(885\) 3.39573e11 3.39573e11i 0.553555 0.553555i
\(886\) 5.68398e9 0.00922397
\(887\) −2.74403e11 2.74403e11i −0.443296 0.443296i 0.449822 0.893118i \(-0.351487\pi\)
−0.893118 + 0.449822i \(0.851487\pi\)
\(888\) 9.00774e10 9.00774e10i 0.144865 0.144865i
\(889\) 1.58831e11 + 1.58831e11i 0.254289 + 0.254289i
\(890\) −3.15854e10 −0.0503415
\(891\) 6.26609e10 + 6.26609e10i 0.0994228 + 0.0994228i
\(892\) 1.03785e12i 1.63936i
\(893\) 2.77618e11 0.436559
\(894\) −2.43816e10 −0.0381692
\(895\) 4.23397e11 0.659866
\(896\) −7.02509e10 + 7.02509e10i −0.108998 + 0.108998i
\(897\) 2.07346e10 2.07346e10i 0.0320277 0.0320277i
\(898\) 2.83730e10i 0.0436314i
\(899\) 9.84582e11 3.72795e11i 1.50735 0.570731i
\(900\) −7.15016e11 −1.08980
\(901\) 4.15835e11 + 4.15835e11i 0.630989 + 0.630989i
\(902\) −2.89771e10 2.89771e10i −0.0437752 0.0437752i
\(903\) 1.35523e12i 2.03828i
\(904\) 3.23638e10i 0.0484603i
\(905\) 8.06386e10i 0.120212i
\(906\) −3.22715e10 −0.0478968
\(907\) 5.12278e10 5.12278e10i 0.0756966 0.0756966i −0.668245 0.743941i \(-0.732954\pi\)
0.743941 + 0.668245i \(0.232954\pi\)
\(908\) 3.22329e11i 0.474194i
\(909\) −3.89956e11 + 3.89956e11i −0.571163 + 0.571163i
\(910\) −1.77193e10 1.77193e10i −0.0258393 0.0258393i
\(911\) −1.66277e11 + 1.66277e11i −0.241412 + 0.241412i −0.817434 0.576022i \(-0.804604\pi\)
0.576022 + 0.817434i \(0.304604\pi\)
\(912\) 6.05944e11i 0.875897i
\(913\) −6.36181e11 6.36181e11i −0.915582 0.915582i
\(914\) 2.53639e10 2.53639e10i 0.0363438 0.0363438i
\(915\) 1.41035e12 2.01207
\(916\) 9.81529e11 + 9.81529e11i 1.39419 + 1.39419i
\(917\) −1.23844e11 + 1.23844e11i −0.175145 + 0.175145i
\(918\) −2.43958e10 2.43958e10i −0.0343514 0.0343514i
\(919\) −1.25364e12 −1.75756 −0.878779 0.477229i \(-0.841641\pi\)
−0.878779 + 0.477229i \(0.841641\pi\)
\(920\) −1.66350e9 1.66350e9i −0.00232206 0.00232206i
\(921\) 3.61064e11i 0.501818i
\(922\) −2.17840e10 −0.0301449
\(923\) 1.14234e11 0.157394
\(924\) −1.35098e12 −1.85336
\(925\) −6.18872e11 + 6.18872e11i −0.845345 + 0.845345i
\(926\) −1.65152e10 + 1.65152e10i −0.0224616 + 0.0224616i
\(927\) 1.17737e12i 1.59439i
\(928\) 7.06958e10 2.67677e10i 0.0953239 0.0360927i
\(929\) −7.21060e11 −0.968075 −0.484037 0.875047i \(-0.660830\pi\)
−0.484037 + 0.875047i \(0.660830\pi\)
\(930\) 6.09932e10 + 6.09932e10i 0.0815361 + 0.0815361i
\(931\) 8.27155e10 + 8.27155e10i 0.110100 + 0.110100i
\(932\) 6.24822e11i 0.828119i
\(933\) 1.06965e12i 1.41161i
\(934\) 2.10582e10i 0.0276716i
\(935\) 1.25780e12 1.64575
\(936\) −4.56366e10 + 4.56366e10i −0.0594579 + 0.0594579i
\(937\) 3.37163e11i 0.437402i 0.975792 + 0.218701i \(0.0701820\pi\)
−0.975792 + 0.218701i \(0.929818\pi\)
\(938\) 1.01586e10 1.01586e10i 0.0131227 0.0131227i
\(939\) 1.62678e12 + 1.62678e12i 2.09250 + 2.09250i
\(940\) 5.75822e11 5.75822e11i 0.737525 0.737525i
\(941\) 2.70865e11i 0.345457i −0.984969 0.172729i \(-0.944742\pi\)
0.984969 0.172729i \(-0.0552584\pi\)
\(942\) 2.97876e10 + 2.97876e10i 0.0378296 + 0.0378296i
\(943\) −3.83124e10 + 3.83124e10i −0.0484498 + 0.0484498i
\(944\) 2.94670e11 0.371064
\(945\) −9.14777e11 9.14777e11i −1.14707 1.14707i
\(946\) −2.10867e10 + 2.10867e10i −0.0263296 + 0.0263296i
\(947\) 1.60874e11 + 1.60874e11i 0.200025 + 0.200025i 0.800011 0.599986i \(-0.204827\pi\)
−0.599986 + 0.800011i \(0.704827\pi\)
\(948\) 3.54668e11 0.439125
\(949\) −3.96547e11 3.96547e11i −0.488910 0.488910i
\(950\) 9.66925e9i 0.0118713i
\(951\) −9.85277e11 −1.20458
\(952\) 8.14637e10 0.0991783
\(953\) −3.75674e11 −0.455449 −0.227724 0.973726i \(-0.573129\pi\)
−0.227724 + 0.973726i \(0.573129\pi\)
\(954\) −2.32646e10 + 2.32646e10i −0.0280868 + 0.0280868i
\(955\) 3.05576e10 3.05576e10i 0.0367372 0.0367372i
\(956\) 8.00104e10i 0.0957888i
\(957\) 1.24929e12 + 5.63069e11i 1.48941 + 0.671296i
\(958\) −4.64640e10 −0.0551639
\(959\) −7.72145e11 7.72145e11i −0.912902 0.912902i
\(960\) −1.25390e12 1.25390e12i −1.47631 1.47631i
\(961\) 1.36277e12i 1.59783i
\(962\) 3.94772e10i 0.0460942i
\(963\) 2.53904e12i 2.95233i
\(964\) −6.02668e11 −0.697862
\(965\) −1.53768e12 + 1.53768e12i −1.77319 + 1.77319i
\(966\) 2.07072e9i 0.00237801i
\(967\) −5.07328e11 + 5.07328e11i −0.580207 + 0.580207i −0.934960 0.354753i \(-0.884565\pi\)
0.354753 + 0.934960i \(0.384565\pi\)
\(968\) −1.63476e8 1.63476e8i −0.000186188 0.000186188i
\(969\) −7.03475e11 + 7.03475e11i −0.797909 + 0.797909i
\(970\) 3.80612e10i 0.0429928i
\(971\) −1.17516e11 1.17516e11i −0.132197 0.132197i 0.637912 0.770109i \(-0.279798\pi\)
−0.770109 + 0.637912i \(0.779798\pi\)
\(972\) 5.55686e11 5.55686e11i 0.622535 0.622535i
\(973\) −1.33946e12 −1.49444
\(974\) −1.88158e10 1.88158e10i −0.0209068 0.0209068i
\(975\) 5.00248e11 5.00248e11i 0.553563 0.553563i
\(976\) 6.11929e11 + 6.11929e11i 0.674376 + 0.674376i
\(977\) 1.61586e11 0.177348 0.0886739 0.996061i \(-0.471737\pi\)
0.0886739 + 0.996061i \(0.471737\pi\)
\(978\) −5.78460e10 5.78460e10i −0.0632292 0.0632292i
\(979\) 1.05601e12i 1.14958i
\(980\) 3.43129e11 0.372008
\(981\) 1.51157e12 1.63212
\(982\) 2.55220e10 0.0274454
\(983\) 1.22639e12 1.22639e12i 1.31345 1.31345i 0.394598 0.918854i \(-0.370884\pi\)
0.918854 0.394598i \(-0.129116\pi\)
\(984\) 1.34538e11 1.34538e11i 0.143504 0.143504i
\(985\) 1.21531e12i 1.29105i
\(986\) −3.76441e10 1.69667e10i −0.0398281 0.0179510i
\(987\) 1.43439e12 1.51147
\(988\) 2.66023e11 + 2.66023e11i 0.279184 + 0.279184i
\(989\) 2.78800e10 + 2.78800e10i 0.0291412 + 0.0291412i
\(990\) 7.03697e10i 0.0732562i
\(991\) 1.40982e12i 1.46174i 0.682519 + 0.730868i \(0.260884\pi\)
−0.682519 + 0.730868i \(0.739116\pi\)
\(992\) 1.59091e11i 0.164285i
\(993\) 1.63391e11 0.168047
\(994\) 5.70415e9 5.70415e9i 0.00584312 0.00584312i
\(995\) 1.71168e12i 1.74634i
\(996\) 1.47601e12 1.47601e12i 1.49986 1.49986i
\(997\) −6.96211e11 6.96211e11i −0.704629 0.704629i 0.260772 0.965401i \(-0.416023\pi\)
−0.965401 + 0.260772i \(0.916023\pi\)
\(998\) 8.70051e9 8.70051e9i 0.00877046 0.00877046i
\(999\) 2.03806e12i 2.04623i
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 29.9.c.a.12.10 38
29.17 odd 4 inner 29.9.c.a.17.10 yes 38
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.9.c.a.12.10 38 1.1 even 1 trivial
29.9.c.a.17.10 yes 38 29.17 odd 4 inner