LMFDB - Embedded newform 29.18.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,18,Mod(1,29)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 18, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	29.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:	$53.1344053299$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+500.684 q^{2} -16927.2 q^{3} +119612. q^{4} -1.40156e6 q^{5} -8.47517e6 q^{6} -1.54199e7 q^{7} -5.73773e6 q^{8} +1.57390e8 q^{9} +O(q^{10})$	\(q+500.684 q^{2} -16927.2 q^{3} +119612. q^{4} -1.40156e6 q^{5} -8.47517e6 q^{6} -1.54199e7 q^{7} -5.73773e6 q^{8} +1.57390e8 q^{9} -7.01740e8 q^{10} -2.56410e8 q^{11} -2.02470e9 q^{12} -5.54885e9 q^{13} -7.72048e9 q^{14} +2.37245e10 q^{15} -1.85506e10 q^{16} +9.68450e8 q^{17} +7.88024e10 q^{18} +6.04963e10 q^{19} -1.67644e11 q^{20} +2.61015e11 q^{21} -1.28380e11 q^{22} -6.60646e11 q^{23} +9.71237e10 q^{24} +1.20144e12 q^{25} -2.77822e12 q^{26} -4.78184e11 q^{27} -1.84441e12 q^{28} +5.00246e11 q^{29} +1.18785e13 q^{30} +1.89679e12 q^{31} -8.53593e12 q^{32} +4.34030e12 q^{33} +4.84887e11 q^{34} +2.16119e13 q^{35} +1.88257e13 q^{36} -4.88697e12 q^{37} +3.02895e13 q^{38} +9.39264e13 q^{39} +8.04179e12 q^{40} +4.71702e13 q^{41} +1.30686e14 q^{42} -4.14989e13 q^{43} -3.06698e13 q^{44} -2.20592e14 q^{45} -3.30775e14 q^{46} -1.67241e14 q^{47} +3.14010e14 q^{48} +5.14205e12 q^{49} +6.01542e14 q^{50} -1.63931e13 q^{51} -6.63710e14 q^{52} -8.12313e14 q^{53} -2.39419e14 q^{54} +3.59375e14 q^{55} +8.84751e13 q^{56} -1.02403e15 q^{57} +2.50465e14 q^{58} +5.38539e14 q^{59} +2.83774e15 q^{60} +1.19007e15 q^{61} +9.49694e14 q^{62} -2.42693e15 q^{63} -1.84234e15 q^{64} +7.77706e15 q^{65} +2.17312e15 q^{66} -2.24085e15 q^{67} +1.15838e14 q^{68} +1.11829e16 q^{69} +1.08207e16 q^{70} -4.69271e15 q^{71} -9.03059e14 q^{72} -7.45113e15 q^{73} -2.44683e15 q^{74} -2.03370e16 q^{75} +7.23610e15 q^{76} +3.95381e15 q^{77} +4.70274e16 q^{78} -2.23234e16 q^{79} +2.59998e16 q^{80} -1.22310e16 q^{81} +2.36174e16 q^{82} +6.58108e15 q^{83} +3.12206e16 q^{84} -1.35734e15 q^{85} -2.07778e16 q^{86} -8.46777e15 q^{87} +1.47121e15 q^{88} +5.02131e16 q^{89} -1.10447e17 q^{90} +8.55625e16 q^{91} -7.90214e16 q^{92} -3.21074e16 q^{93} -8.37350e16 q^{94} -8.47894e16 q^{95} +1.44489e17 q^{96} +5.07934e16 q^{97} +2.57454e15 q^{98} -4.03563e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) $ 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9} - 224469478 q^{10} + 1203139534 q^{11} - 5164251122 q^{12} + 3854339312 q^{13} + 25262272904 q^{14} + 28324474306 q^{15} + 196520815922 q^{16} + 76444714794 q^{17} + 75758949126 q^{18} + 246497292428 q^{19} - 46900976670 q^{20} + 360937126704 q^{21} - 275001533522 q^{22} + 213498528140 q^{23} - 451123453870 q^{24} + 3898884886997 q^{25} - 3609347694206 q^{26} - 2718903745978 q^{27} - 5946174617200 q^{28} + 10505174672181 q^{29} - 20237658929454 q^{30} + 16670029895798 q^{31} - 42141001912046 q^{32} - 7157109761394 q^{33} + 12785761151136 q^{34} + 46677934312888 q^{35} + 132137824374868 q^{36} + 53445659988410 q^{37} + 76581637956388 q^{38} + 79233849032530 q^{39} + 193617444734146 q^{40} - 20814769309298 q^{41} + 76690667258352 q^{42} + 185498647364454 q^{43} + 315429066899678 q^{44} - 486270821438526 q^{45} + 261474367677132 q^{46} + 389503471719450 q^{47} - 101509672247630 q^{48} + 730079062141437 q^{49} + 14\!\cdots\!54 q^{50}+ \cdots - 95\!\cdots\!64 q^{99}+O(q^{100}) \) 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9 - 224469478 * q^10 + 1203139534 * q^11 - 5164251122 * q^12 + 3854339312 * q^13 + 25262272904 * q^14 + 28324474306 * q^15 + 196520815922 * q^16 + 76444714794 * q^17 + 75758949126 * q^18 + 246497292428 * q^19 - 46900976670 * q^20 + 360937126704 * q^21 - 275001533522 * q^22 + 213498528140 * q^23 - 451123453870 * q^24 + 3898884886997 * q^25 - 3609347694206 * q^26 - 2718903745978 * q^27 - 5946174617200 * q^28 + 10505174672181 * q^29 - 20237658929454 * q^30 + 16670029895798 * q^31 - 42141001912046 * q^32 - 7157109761394 * q^33 + 12785761151136 * q^34 + 46677934312888 * q^35 + 132137824374868 * q^36 + 53445659988410 * q^37 + 76581637956388 * q^38 + 79233849032530 * q^39 + 193617444734146 * q^40 - 20814769309298 * q^41 + 76690667258352 * q^42 + 185498647364454 * q^43 + 315429066899678 * q^44 - 486270821438526 * q^45 + 261474367677132 * q^46 + 389503471719450 * q^47 - 101509672247630 * q^48 + 730079062141437 * q^49 + 1482269666368354 * q^50 + 718238208473988 * q^51 + 1966802817157170 * q^52 + 747441265526156 * q^53 + 5692893333117030 * q^54 + 1639109418219546 * q^55 + 5657219329125240 * q^56 + 4694352396864932 * q^57 + 128063081718016 * q^58 + 5280258638332960 * q^59 + 15251367906033378 * q^60 + 5813675353074254 * q^61 + 6242066590947250 * q^62 + 10947760075450368 * q^63 + 24583792057508902 * q^64 + 19190799243789974 * q^65 + 41877805444482390 * q^66 + 13420580230958268 * q^67 + 24771837384165388 * q^68 + 30973047049935252 * q^69 + 8505088080182440 * q^70 + 4824462822979508 * q^71 + 1180071997284592 * q^72 + 11228916281304662 * q^73 - 89132715356772 * q^74 + 59161419576630296 * q^75 + 57466858643173460 * q^76 + 58741564492720064 * q^77 + 142050530910210210 * q^78 + 71718598015696758 * q^79 + 48350023652407550 * q^80 + 75805931446703569 * q^81 + 188661890754420812 * q^82 + 50769377111735608 * q^83 + 198832046985593048 * q^84 + 53422044849490784 * q^85 + 35014892323844118 * q^86 + 11988905533023326 * q^87 + 37459283979085258 * q^88 - 70981414576978018 * q^89 + 57211029866143724 * q^90 + 112933943315157320 * q^91 - 103019729095759724 * q^92 - 350358290646906646 * q^93 - 150286322409612578 * q^94 - 102561321856584476 * q^95 - 213770098354021866 * q^96 - 130930167251505210 * q^97 - 537387515497557296 * q^98 - 95267700931431064 * q^99

Display 100 coefficients 10 coefficients

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 $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	500.684	1.38296	0.691478	−	0.722397i	$-0.256960\pi$
$2$	500.684	1.38296	0.691478	+	0.722397i	$0.256960\pi$
$3$	−16927.2	−1.48955	−0.744773	−	0.667317i	$-0.767442\pi$
$3$	−16927.2	−1.48955	−0.744773	+	0.667317i	$0.767442\pi$
$4$	119612.	0.912569
$5$	−1.40156e6	−1.60460	−0.802302	−	0.596919i	$-0.796392\pi$
$5$	−1.40156e6	−1.60460	−0.802302	+	0.596919i	$0.796392\pi$
$6$	−8.47517e6	−2.05998
$7$	−1.54199e7	−1.01099	−0.505496	−	0.862829i	$-0.668690\pi$
$7$	−1.54199e7	−1.01099	−0.505496	+	0.862829i	$0.668690\pi$
$8$	−5.73773e6	−0.120914
$9$	1.57390e8	1.21875
$10$	−7.01740e8	−2.21910
$11$	−2.56410e8	−0.360659	−0.180330	−	0.983606i	$-0.557716\pi$
$11$	−2.56410e8	−0.360659	−0.180330	+	0.983606i	$0.557716\pi$
$12$	−2.02470e9	−1.35931
$13$	−5.54885e9	−1.88662	−0.943309	−	0.331915i	$-0.892305\pi$
$13$	−5.54885e9	−1.88662	−0.943309	+	0.331915i	$0.892305\pi$
$14$	−7.72048e9	−1.39816
$15$	2.37245e10	2.39013
$16$	−1.85506e10	−1.07979
$17$	9.68450e8	0.0336714	0.0168357	−	0.999858i	$-0.494641\pi$
$17$	9.68450e8	0.0336714	0.0168357	+	0.999858i	$0.494641\pi$
$18$	7.88024e10	1.68548
$19$	6.04963e10	0.817191	0.408595	−	0.912716i	$-0.366019\pi$
$19$	6.04963e10	0.817191	0.408595	+	0.912716i	$0.366019\pi$
$20$	−1.67644e11	−1.46431
$21$	2.61015e11	1.50592
$22$	−1.28380e11	−0.498776
$23$	−6.60646e11	−1.75907	−0.879534	−	0.475837i	$-0.842145\pi$
$23$	−6.60646e11	−1.75907	−0.879534	+	0.475837i	$0.842145\pi$
$24$	9.71237e10	0.180107
$25$	1.20144e12	1.57475
$26$	−2.77822e12	−2.60911
$27$	−4.78184e11	−0.325839
$28$	−1.84441e12	−0.922599
$29$	5.00246e11	0.185695
$29$	5.00246e11	0.185695
$30$	1.18785e13	3.30545
$31$	1.89679e12	0.399435	0.199717	−	0.979854i	$-0.435998\pi$
$31$	1.89679e12	0.399435	0.199717	+	0.979854i	$0.435998\pi$
$32$	−8.53593e12	−1.37238
$33$	4.34030e12	0.537219
$34$	4.84887e11	0.0465661
$35$	2.16119e13	1.62224
$36$	1.88257e13	1.11219
$37$	−4.88697e12	−0.228731	−0.114365	−	0.993439i	$-0.536483\pi$
$37$	−4.88697e12	−0.228731	−0.114365	+	0.993439i	$0.536483\pi$
$38$	3.02895e13	1.13014
$39$	9.39264e13	2.81021
$40$	8.04179e12	0.194018
$41$	4.71702e13	0.922582	0.461291	−	0.887249i	$-0.347386\pi$
$41$	4.71702e13	0.922582	0.461291	+	0.887249i	$0.347386\pi$
$42$	1.30686e14	2.08262
$43$	−4.14989e13	−0.541446	−0.270723	−	0.962657i	$-0.587263\pi$
$43$	−4.14989e13	−0.541446	−0.270723	+	0.962657i	$0.587263\pi$
$44$	−3.06698e13	−0.329126
$45$	−2.20592e14	−1.95561
$46$	−3.30775e14	−2.43271
$47$	−1.67241e14	−1.02450	−0.512250	−	0.858836i	$-0.671188\pi$
$47$	−1.67241e14	−1.02450	−0.512250	+	0.858836i	$0.671188\pi$
$48$	3.14010e14	1.60839
$49$	5.14205e12	0.0221039
$50$	6.01542e14	2.17781
$51$	−1.63931e13	−0.0501551
$52$	−6.63710e14	−1.72167
$53$	−8.12313e14	−1.79217	−0.896084	−	0.443884i	$-0.853600\pi$
$53$	−8.12313e14	−1.79217	−0.896084	+	0.443884i	$0.853600\pi$
$54$	−2.39419e14	−0.450621
$55$	3.59375e14	0.578715
$56$	8.84751e13	0.122243
$57$	−1.02403e15	−1.21724
$58$	2.50465e14	0.256809
$59$	5.38539e14	0.477502	0.238751	−	0.971081i	$-0.423262\pi$
$59$	5.38539e14	0.477502	0.238751	+	0.971081i	$0.423262\pi$
$60$	2.83774e15	2.18116
$61$	1.19007e15	0.794817	0.397409	−	0.917642i	$-0.369910\pi$
$61$	1.19007e15	0.794817	0.397409	+	0.917642i	$0.369910\pi$
$62$	9.49694e14	0.552401
$63$	−2.42693e15	−1.23215
$64$	−1.84234e15	−0.818162
$65$	7.77706e15	3.02727
$66$	2.17312e15	0.742951
$67$	−2.24085e15	−0.674181	−0.337091	−	0.941472i	$-0.609443\pi$
$67$	−2.24085e15	−0.674181	−0.337091	+	0.941472i	$0.609443\pi$
$68$	1.15838e14	0.0307275
$69$	1.11829e16	2.62021
$70$	1.08207e16	2.24349
$71$	−4.69271e15	−0.862439	−0.431219	−	0.902247i	$-0.641916\pi$
$71$	−4.69271e15	−0.862439	−0.431219	+	0.902247i	$0.641916\pi$
$72$	−9.03059e14	−0.147364
$73$	−7.45113e15	−1.08138	−0.540689	−	0.841222i	$-0.681836\pi$
$73$	−7.45113e15	−1.08138	−0.540689	+	0.841222i	$0.681836\pi$
$74$	−2.44683e15	−0.316325
$75$	−2.03370e16	−2.34567
$76$	7.23610e15	0.745743
$77$	3.95381e15	0.364624
$78$	4.70274e16	3.88639
$79$	−2.23234e16	−1.65550	−0.827750	−	0.561097i	$-0.810379\pi$
$79$	−2.23234e16	−1.65550	−0.827750	+	0.561097i	$0.810379\pi$
$80$	2.59998e16	1.73263
$81$	−1.22310e16	−0.733398
$82$	2.36174e16	1.27589
$83$	6.58108e15	0.320725	0.160363	−	0.987058i	$-0.448734\pi$
$83$	6.58108e15	0.320725	0.160363	+	0.987058i	$0.448734\pi$
$84$	3.12206e16	1.37425
$85$	−1.35734e15	−0.0540293
$86$	−2.07778e16	−0.748796
$87$	−8.46777e15	−0.276602
$88$	1.47121e15	0.0436086
$89$	5.02131e16	1.35208	0.676040	−	0.736865i	$-0.263695\pi$
$89$	5.02131e16	1.35208	0.676040	+	0.736865i	$0.263695\pi$
$90$	−1.10447e17	−2.70452
$91$	8.55625e16	1.90736
$92$	−7.90214e16	−1.60527
$93$	−3.21074e16	−0.594976
$94$	−8.37350e16	−1.41684
$95$	−8.47894e16	−1.31127
$96$	1.44489e17	2.04423
$97$	5.07934e16	0.658032	0.329016	−	0.944324i	$-0.393283\pi$
$97$	5.07934e16	0.658032	0.329016	+	0.944324i	$0.393283\pi$
$98$	2.57454e15	0.0305688
$99$	−4.03563e16	−0.439554
$100$	1.43707e17	1.43707
$101$	−1.45351e17	−1.33563	−0.667813	−	0.744329i	$-0.732769\pi$
$101$	−1.45351e17	−1.33563	−0.667813	+	0.744329i	$0.732769\pi$
$102$	−8.20777e15	−0.0693624
$103$	−1.44258e17	−1.12208	−0.561039	−	0.827789i	$-0.689598\pi$
$103$	−1.44258e17	−1.12208	−0.561039	+	0.827789i	$0.689598\pi$
$104$	3.18378e16	0.228118
$105$	−3.65829e17	−2.41640
$106$	−4.06712e17	−2.47849
$107$	1.47110e17	0.827712	0.413856	−	0.910342i	$-0.364182\pi$
$107$	1.47110e17	0.827712	0.413856	+	0.910342i	$0.364182\pi$
$108$	−5.71966e16	−0.297350
$109$	3.62168e17	1.74095	0.870473	−	0.492216i	$-0.163813\pi$
$109$	3.62168e17	1.74095	0.870473	+	0.492216i	$0.163813\pi$
$110$	1.79933e17	0.800338
$111$	8.27226e16	0.340705
$112$	2.86048e17	1.09166
$113$	−5.40953e17	−1.91422	−0.957112	−	0.289719i	$-0.906438\pi$
$113$	−5.40953e17	−1.91422	−0.957112	+	0.289719i	$0.906438\pi$
$114$	−5.12717e17	−1.68340
$115$	9.25938e17	2.82261
$116$	5.98356e16	0.169460
$117$	−8.73330e17	−2.29932
$118$	2.69638e17	0.660365
$119$	−1.49334e16	−0.0340415
$120$	−1.36125e17	−0.289000
$121$	−4.39701e17	−0.869925
$122$	5.95847e17	1.09920
$123$	−7.98459e17	−1.37423
$124$	2.26880e17	0.364511
$125$	−6.14588e17	−0.922250
$126$	−1.21512e18	−1.70400
$127$	−3.42469e17	−0.449045	−0.224522	−	0.974469i	$-0.572082\pi$
$127$	−3.42469e17	−0.449045	−0.224522	+	0.974469i	$0.572082\pi$
$128$	1.96393e17	0.240903
$129$	7.02460e17	0.806509
$130$	3.89385e18	4.18659
$131$	4.07079e17	0.410084	0.205042	−	0.978753i	$-0.434267\pi$
$131$	4.07079e17	0.410084	0.205042	+	0.978753i	$0.434267\pi$
$132$	5.19153e17	0.490249
$133$	−9.32846e17	−0.826173
$134$	−1.12196e18	−0.932363
$135$	6.70205e17	0.522842
$136$	−5.55670e15	−0.00407133
$137$	−2.46433e18	−1.69658	−0.848291	−	0.529530i	$-0.822368\pi$
$137$	−2.46433e18	−1.69658	−0.848291	+	0.529530i	$0.822368\pi$
$138$	5.59909e18	3.62364
$139$	−1.02318e18	−0.622767	−0.311383	−	0.950284i	$-0.600792\pi$
$139$	−1.02318e18	−0.622767	−0.311383	+	0.950284i	$0.600792\pi$
$140$	2.58505e18	1.48041
$141$	2.83093e18	1.52604
$142$	−2.34957e18	−1.19272
$143$	1.42278e18	0.680427
$144$	−2.91967e18	−1.31599
$145$	−7.01127e17	−0.297967
$146$	−3.73066e18	−1.49550
$147$	−8.70405e16	−0.0329249
$148$	−5.84541e17	−0.208733
$149$	−3.14073e18	−1.05913	−0.529563	−	0.848271i	$-0.677644\pi$
$149$	−3.14073e18	−1.05913	−0.529563	+	0.848271i	$0.677644\pi$
$150$	−1.01824e19	−3.24396
$151$	−8.59938e17	−0.258919	−0.129459	−	0.991585i	$-0.541324\pi$
$151$	−8.59938e17	−0.258919	−0.129459	+	0.991585i	$0.541324\pi$
$152$	−3.47112e17	−0.0988095
$153$	1.52424e17	0.0410370
$154$	1.97961e18	0.504259
$155$	−2.65848e18	−0.640934
$156$	1.12347e19	2.56451
$157$	2.56898e18	0.555410	0.277705	−	0.960666i	$-0.410426\pi$
$157$	2.56898e18	0.555410	0.277705	+	0.960666i	$0.410426\pi$
$158$	−1.11769e19	−2.28948
$159$	1.37502e19	2.66952
$160$	1.19636e19	2.20213
$161$	1.01871e19	1.77840
$162$	−6.12387e18	−1.01426
$163$	4.65945e18	0.732386	0.366193	−	0.930539i	$-0.380661\pi$
$163$	4.65945e18	0.732386	0.366193	+	0.930539i	$0.380661\pi$
$164$	5.64213e18	0.841920
$165$	−6.08321e18	−0.862024
$166$	3.29504e18	0.443549
$167$	−1.15871e19	−1.48213	−0.741065	−	0.671434i	$-0.765679\pi$
$167$	−1.15871e19	−1.48213	−0.741065	+	0.671434i	$0.765679\pi$
$168$	−1.49763e18	−0.182086
$169$	2.21393e19	2.55933
$170$	−6.79600e17	−0.0747201
$171$	9.52149e18	0.995951
$172$	−4.96378e18	−0.494107
$173$	3.66257e18	0.347052	0.173526	−	0.984829i	$-0.444484\pi$
$173$	3.66257e18	0.347052	0.173526	+	0.984829i	$0.444484\pi$
$174$	−4.23967e18	−0.382528
$175$	−1.85261e19	−1.59206
$176$	4.75656e18	0.389435
$177$	−9.11596e18	−0.711262
$178$	2.51409e19	1.86987
$179$	1.21501e19	0.861646	0.430823	−	0.902436i	$-0.358223\pi$
$179$	1.21501e19	0.861646	0.430823	+	0.902436i	$0.358223\pi$
$180$	−2.63854e19	−1.78463
$181$	−2.15503e19	−1.39055	−0.695273	−	0.718746i	$-0.744716\pi$
$181$	−2.15503e19	−1.39055	−0.695273	+	0.718746i	$0.744716\pi$
$182$	4.28398e19	2.63779
$183$	−2.01445e19	−1.18392
$184$	3.79061e18	0.212695
$185$	6.84940e18	0.367022
$186$	−1.60756e19	−0.822827
$187$	−2.48320e17	−0.0121439
$188$	−2.00041e19	−0.934926
$189$	7.37353e18	0.329420
$190$	−4.24527e19	−1.81343
$191$	1.34150e19	0.548034	0.274017	−	0.961725i	$-0.411647\pi$
$191$	1.34150e19	0.548034	0.274017	+	0.961725i	$0.411647\pi$
$192$	3.11856e19	1.21869
$193$	−5.95972e18	−0.222838	−0.111419	−	0.993774i	$-0.535540\pi$
$193$	−5.95972e18	−0.222838	−0.111419	+	0.993774i	$0.535540\pi$
$194$	2.54314e19	0.910030
$195$	−1.31644e20	−4.50927
$196$	6.15052e17	0.0201714
$197$	3.99342e19	1.25425	0.627123	−	0.778921i	$-0.284233\pi$
$197$	3.99342e19	1.25425	0.627123	+	0.778921i	$0.284233\pi$
$198$	−2.02057e19	−0.607884
$199$	3.05080e19	0.879351	0.439676	−	0.898157i	$-0.355093\pi$
$199$	3.05080e19	0.879351	0.439676	+	0.898157i	$0.355093\pi$
$200$	−6.89354e18	−0.190409
$201$	3.79313e19	1.00422
$202$	−7.27746e19	−1.84711
$203$	−7.71374e18	−0.187736
$204$	−1.96082e18	−0.0457700
$205$	−6.61121e19	−1.48038
$206$	−7.22276e19	−1.55179
$207$	−1.03979e20	−2.14386
$208$	1.02934e20	2.03715
$209$	−1.55119e19	−0.294727
$210$	−1.83165e20	−3.34178
$211$	−3.76481e19	−0.659693	−0.329846	−	0.944035i	$-0.606997\pi$
$211$	−3.76481e19	−0.659693	−0.329846	+	0.944035i	$0.606997\pi$
$212$	−9.71626e19	−1.63548
$213$	7.94345e19	1.28464
$214$	7.36555e19	1.14469
$215$	5.81634e19	0.868806
$216$	2.74369e18	0.0393983
$217$	−2.92483e19	−0.403825
$218$	1.81332e20	2.40765
$219$	1.26127e20	1.61076
$220$	4.29856e19	0.528118
$221$	−5.37378e18	−0.0635251
$222$	4.14179e19	0.471181
$223$	1.21598e20	1.33148	0.665738	−	0.746185i	$-0.268117\pi$
$223$	1.21598e20	1.33148	0.665738	+	0.746185i	$0.268117\pi$
$224$	1.31623e20	1.38747
$225$	1.89094e20	1.91923
$226$	−2.70846e20	−2.64729
$227$	1.42806e20	1.34440	0.672199	−	0.740370i	$-0.265350\pi$
$227$	1.42806e20	1.34440	0.672199	+	0.740370i	$0.265350\pi$
$228$	−1.22487e20	−1.11082
$229$	6.17907e19	0.539910	0.269955	−	0.962873i	$-0.412991\pi$
$229$	6.17907e19	0.539910	0.269955	+	0.962873i	$0.412991\pi$
$230$	4.63602e20	3.90354
$231$	−6.69269e19	−0.543124
$232$	−2.87028e18	−0.0224531
$233$	1.26179e20	0.951615	0.475808	−	0.879549i	$-0.342156\pi$
$233$	1.26179e20	0.951615	0.475808	+	0.879549i	$0.342156\pi$
$234$	−4.37262e20	−3.17986
$235$	2.34399e20	1.64392
$236$	6.44159e19	0.435754
$237$	3.77872e20	2.46595
$238$	−7.47690e18	−0.0470779
$239$	1.37047e20	0.832698	0.416349	−	0.909205i	$-0.363309\pi$
$239$	1.37047e20	0.832698	0.416349	+	0.909205i	$0.363309\pi$
$240$	−4.40104e20	−2.58083
$241$	−1.81757e20	−1.02883	−0.514417	−	0.857540i	$-0.671992\pi$
$241$	−1.81757e20	−1.02883	−0.514417	+	0.857540i	$0.671992\pi$
$242$	−2.20151e20	−1.20307
$243$	2.68789e20	1.41827
$244$	1.42346e20	0.725325
$245$	−7.20691e18	−0.0354681
$246$	−3.99776e20	−1.90050
$247$	−3.35685e20	−1.54173
$248$	−1.08833e19	−0.0482971
$249$	−1.11399e20	−0.477735
$250$	−3.07714e20	−1.27543
$251$	−2.64610e20	−1.06018	−0.530090	−	0.847941i	$-0.677842\pi$
$251$	−2.64610e20	−1.06018	−0.530090	+	0.847941i	$0.677842\pi$
$252$	−2.90290e20	−1.12442
$253$	1.69396e20	0.634424
$254$	−1.71469e20	−0.621010
$255$	2.29760e19	0.0804791
$256$	3.39810e20	1.15132
$257$	1.02022e20	0.334396	0.167198	−	0.985923i	$-0.446528\pi$
$257$	1.02022e20	0.334396	0.167198	+	0.985923i	$0.446528\pi$
$258$	3.51711e20	1.11537
$259$	7.53564e19	0.231245
$260$	9.30231e20	2.76260
$261$	7.87336e19	0.226316
$262$	2.03818e20	0.567128
$263$	1.61677e20	0.435537	0.217769	−	0.976000i	$-0.430122\pi$
$263$	1.61677e20	0.435537	0.217769	+	0.976000i	$0.430122\pi$
$264$	−2.49035e19	−0.0649571
$265$	1.13851e21	2.87572
$266$	−4.67061e20	−1.14256
$267$	−8.49967e20	−2.01399
$268$	−2.68033e20	−0.615237
$269$	−9.12066e19	−0.202830	−0.101415	−	0.994844i	$-0.532337\pi$
$269$	−9.12066e19	−0.202830	−0.101415	+	0.994844i	$0.532337\pi$
$270$	3.35561e20	0.723068
$271$	5.23016e20	1.09213	0.546067	−	0.837741i	$-0.316124\pi$
$271$	5.23016e20	1.09213	0.546067	+	0.837741i	$0.316124\pi$
$272$	−1.79653e19	−0.0363579
$273$	−1.44833e21	−2.84110
$274$	−1.23385e21	−2.34630
$275$	−3.08062e20	−0.567949
$276$	1.33761e21	2.39112
$277$	−4.51421e20	−0.782535	−0.391268	−	0.920277i	$-0.627963\pi$
$277$	−4.51421e20	−0.782535	−0.391268	+	0.920277i	$0.627963\pi$
$278$	−5.12289e20	−0.861260
$279$	2.98536e20	0.486811
$280$	−1.24003e20	−0.196151
$281$	−3.02965e20	−0.464932	−0.232466	−	0.972605i	$-0.574679\pi$
$281$	−3.02965e20	−0.464932	−0.232466	+	0.972605i	$0.574679\pi$
$282$	1.41740e21	2.11045
$283$	2.32757e20	0.336293	0.168147	−	0.985762i	$-0.446222\pi$
$283$	2.32757e20	0.336293	0.168147	+	0.985762i	$0.446222\pi$
$284$	−5.61306e20	−0.787035
$285$	1.43525e21	1.95319
$286$	7.12363e20	0.941001
$287$	−7.27359e20	−0.932723
$288$	−1.34347e21	−1.67259
$289$	−8.26302e20	−0.998866
$290$	−3.51043e20	−0.412076
$291$	−8.59789e20	−0.980170
$292$	−8.91246e20	−0.986832
$293$	6.62382e20	0.712416	0.356208	−	0.934407i	$-0.384069\pi$
$293$	6.62382e20	0.712416	0.356208	+	0.934407i	$0.384069\pi$
$294$	−4.35797e19	−0.0455336
$295$	−7.54797e20	−0.766202
$296$	2.80401e19	0.0276567
$297$	1.22611e20	0.117517
$298$	−1.57251e21	−1.46472
$299$	3.66582e21	3.31869
$300$	−2.43256e21	−2.14058
$301$	6.39909e20	0.547397
$302$	−4.30557e20	−0.358073
$303$	2.46038e21	1.98948
$304$	−1.12224e21	−0.882392
$305$	−1.66795e21	−1.27537
$306$	7.63162e19	0.0567524
$307$	3.22117e19	0.0232990	0.0116495	−	0.999932i	$-0.496292\pi$
$307$	3.22117e19	0.0232990	0.0116495	+	0.999932i	$0.496292\pi$
$308$	4.72924e20	0.332744
$309$	2.44188e21	1.67139
$310$	−1.33106e21	−0.886384
$311$	−1.62486e21	−1.05282	−0.526408	−	0.850232i	$-0.676461\pi$
$311$	−1.62486e21	−1.05282	−0.526408	+	0.850232i	$0.676461\pi$
$312$	−5.38924e20	−0.339792
$313$	−8.74813e20	−0.536770	−0.268385	−	0.963312i	$-0.586490\pi$
$313$	−8.74813e20	−0.536770	−0.268385	+	0.963312i	$0.586490\pi$
$314$	1.28625e21	0.768108
$315$	3.40149e21	1.97711
$316$	−2.67015e21	−1.51076
$317$	−1.28479e21	−0.707669	−0.353834	−	0.935308i	$-0.615122\pi$
$317$	−1.28479e21	−0.707669	−0.353834	+	0.935308i	$0.615122\pi$
$318$	6.88449e21	3.69183
$319$	−1.28268e20	−0.0669728
$320$	2.58215e21	1.31283
$321$	−2.49016e21	−1.23292
$322$	5.10051e21	2.45945
$323$	5.85876e19	0.0275160
$324$	−1.46298e21	−0.669276
$325$	−6.66661e21	−2.97096
$326$	2.33291e21	1.01286
$327$	−6.13049e21	−2.59322
$328$	−2.70650e20	−0.111553
$329$	2.57884e21	1.03576
$330$	−3.04576e21	−1.19214
$331$	−1.18100e21	−0.450519	−0.225260	−	0.974299i	$-0.572323\pi$
$331$	−1.18100e21	−0.450519	−0.225260	+	0.974299i	$0.572323\pi$
$332$	7.87177e20	0.292684
$333$	−7.69158e20	−0.278766
$334$	−5.80149e21	−2.04972
$335$	3.14069e21	1.08179
$336$	−4.84199e21	−1.62607
$337$	1.96904e21	0.644764	0.322382	−	0.946610i	$-0.395516\pi$
$337$	1.96904e21	0.644764	0.322382	+	0.946610i	$0.395516\pi$
$338$	1.10848e22	3.53944
$339$	9.15681e21	2.85133
$340$	−1.62355e20	−0.0493054
$341$	−4.86357e20	−0.144060
$342$	4.76726e21	1.37736
$343$	3.50784e21	0.988645
$344$	2.38110e20	0.0654682
$345$	−1.56735e22	−4.20440
$346$	1.83379e21	0.479957
$347$	2.29829e21	0.586954	0.293477	−	0.955966i	$-0.405188\pi$
$347$	2.29829e21	0.586954	0.293477	+	0.955966i	$0.405188\pi$
$348$	−1.01285e21	−0.252418
$349$	1.52352e21	0.370538	0.185269	−	0.982688i	$-0.440684\pi$
$349$	1.52352e21	0.370538	0.185269	+	0.982688i	$0.440684\pi$
$350$	−9.27570e21	−2.20175
$351$	2.65337e21	0.614733
$352$	2.18870e21	0.494963
$353$	−7.81706e21	−1.72567	−0.862836	−	0.505483i	$-0.831314\pi$
$353$	−7.81706e21	−1.72567	−0.862836	+	0.505483i	$0.831314\pi$
$354$	−4.56421e21	−0.983644
$355$	6.57714e21	1.38387
$356$	6.00611e21	1.23387
$357$	2.52780e20	0.0507064
$358$	6.08336e21	1.19162
$359$	−6.59365e21	−1.26131	−0.630657	−	0.776062i	$-0.717214\pi$
$359$	−6.59365e21	−1.26131	−0.630657	+	0.776062i	$0.717214\pi$
$360$	1.26569e21	0.236460
$361$	−1.82058e21	−0.332200
$362$	−1.07899e22	−1.92306
$363$	7.44290e21	1.29579
$364$	1.02343e22	1.74059
$365$	1.04432e22	1.73518
$366$	−1.00860e22	−1.63731
$367$	−5.97655e21	−0.947959	−0.473979	−	0.880536i	$-0.657183\pi$
$367$	−5.97655e21	−0.947959	−0.473979	+	0.880536i	$0.657183\pi$
$368$	1.22554e22	1.89942
$369$	7.42410e21	1.12440
$370$	3.42938e21	0.507576
$371$	1.25258e22	1.81187
$372$	−3.84043e21	−0.542957
$373$	9.92998e19	0.0137222	0.00686109	−	0.999976i	$-0.497816\pi$
$373$	9.92998e19	0.0137222	0.00686109	+	0.999976i	$0.497816\pi$
$374$	−1.24330e20	−0.0167945
$375$	1.04032e22	1.37373
$376$	9.59586e20	0.123876
$377$	−2.77579e21	−0.350336
$378$	3.69181e21	0.455574
$379$	−1.21448e21	−0.146540	−0.0732702	−	0.997312i	$-0.523344\pi$
$379$	−1.21448e21	−0.146540	−0.0732702	+	0.997312i	$0.523344\pi$
$380$	−1.01419e22	−1.19662
$381$	5.79704e21	0.668873
$382$	6.71668e21	0.757908
$383$	−1.25391e22	−1.38381	−0.691907	−	0.721986i	$-0.743229\pi$
$383$	−1.25391e22	−1.38381	−0.691907	+	0.721986i	$0.743229\pi$
$384$	−3.32439e21	−0.358836
$385$	−5.54152e21	−0.585076
$386$	−2.98393e21	−0.308175
$387$	−6.53150e21	−0.659887
$388$	6.07551e21	0.600500
$389$	−2.80994e21	−0.271722	−0.135861	−	0.990728i	$-0.543380\pi$
$389$	−2.80994e21	−0.271722	−0.135861	+	0.990728i	$0.543380\pi$
$390$	−6.59119e22	−6.23612
$391$	−6.39803e20	−0.0592303
$392$	−2.95037e19	−0.00267267
$393$	−6.89070e21	−0.610839
$394$	1.99944e22	1.73457
$395$	3.12876e22	2.65642
$396$	−4.82710e21	−0.401123
$397$	−1.62497e22	−1.32168	−0.660840	−	0.750527i	$-0.729800\pi$
$397$	−1.62497e22	−1.32168	−0.660840	+	0.750527i	$0.729800\pi$
$398$	1.52749e22	1.21610
$399$	1.57905e22	1.23062
$400$	−2.22874e22	−1.70040
$401$	−1.23762e22	−0.924403	−0.462202	−	0.886775i	$-0.652940\pi$
$401$	−1.23762e22	−0.924403	−0.462202	+	0.886775i	$0.652940\pi$
$402$	1.89916e22	1.38880
$403$	−1.05250e22	−0.753581
$404$	−1.73857e22	−1.21885
$405$	1.71425e22	1.17681
$406$	−3.86214e21	−0.259631
$407$	1.25307e21	0.0824939
$408$	9.40594e19	0.00606444
$409$	−7.59311e21	−0.479481	−0.239741	−	0.970837i	$-0.577062\pi$
$409$	−7.59311e21	−0.479481	−0.239741	+	0.970837i	$0.577062\pi$
$410$	−3.31012e22	−2.04730
$411$	4.17143e22	2.52714
$412$	−1.72550e22	−1.02397
$413$	−8.30421e21	−0.482751
$414$	−5.20605e22	−2.96487
$415$	−9.22380e21	−0.514637
$416$	4.73645e22	2.58917
$417$	1.73195e22	0.927641
$418$	−7.76654e21	−0.407595
$419$	−9.35565e21	−0.481121	−0.240561	−	0.970634i	$-0.577331\pi$
$419$	−9.35565e21	−0.481121	−0.240561	+	0.970634i	$0.577331\pi$
$420$	−4.37577e22	−2.20513
$421$	−4.54952e21	−0.224682	−0.112341	−	0.993670i	$-0.535835\pi$
$421$	−4.54952e21	−0.224682	−0.112341	+	0.993670i	$0.535835\pi$
$422$	−1.88498e22	−0.912326
$423$	−2.63220e22	−1.24861
$424$	4.66084e21	0.216698
$425$	1.16354e21	0.0530241
$426$	3.97715e22	1.77661
$427$	−1.83507e22	−0.803554
$428$	1.75961e22	0.755345
$429$	−2.40837e22	−1.01353
$430$	2.91215e22	1.20152
$431$	2.29322e22	0.927660	0.463830	−	0.885924i	$-0.346475\pi$
$431$	2.29322e22	0.927660	0.463830	+	0.885924i	$0.346475\pi$
$432$	8.87059e21	0.351836
$433$	−2.86402e21	−0.111385	−0.0556927	−	0.998448i	$-0.517737\pi$
$433$	−2.86402e21	−0.111385	−0.0556927	+	0.998448i	$0.517737\pi$
$434$	−1.46442e22	−0.558472
$435$	1.18681e22	0.443836
$436$	4.33198e22	1.58873
$437$	−3.99667e22	−1.43749
$438$	6.31496e22	2.22762
$439$	1.90379e21	0.0658673	0.0329336	−	0.999458i	$-0.489515\pi$
$439$	1.90379e21	0.0658673	0.0329336	+	0.999458i	$0.489515\pi$
$440$	−2.06200e21	−0.0699746
$441$	8.09305e20	0.0269392
$442$	−2.69056e21	−0.0878524
$443$	−2.27550e22	−0.728861	−0.364431	−	0.931231i	$-0.618736\pi$
$443$	−2.27550e22	−0.728861	−0.364431	+	0.931231i	$0.618736\pi$
$444$	9.89464e21	0.310917
$445$	−7.03769e22	−2.16955
$446$	6.08819e22	1.84137
$447$	5.31637e22	1.57762
$448$	2.84086e22	0.827154
$449$	4.97757e22	1.42208	0.711039	−	0.703153i	$-0.248225\pi$
$449$	4.97757e22	1.42208	0.711039	+	0.703153i	$0.248225\pi$
$450$	9.46764e22	2.65421
$451$	−1.20949e22	−0.332738
$452$	−6.47046e22	−1.74686
$453$	1.45563e22	0.385671
$454$	7.15009e22	1.85924
$455$	−1.19921e23	−3.06055
$456$	5.87562e21	0.147181
$457$	5.50178e22	1.35274	0.676372	−	0.736560i	$-0.263551\pi$
$457$	5.50178e22	1.35274	0.676372	+	0.736560i	$0.263551\pi$
$458$	3.09376e22	0.746672
$459$	−4.63097e20	−0.0109714
$460$	1.10753e23	2.57582
$461$	−8.35603e22	−1.90784	−0.953920	−	0.300061i	$-0.902993\pi$
$461$	−8.35603e22	−1.90784	−0.953920	+	0.300061i	$0.902993\pi$
$462$	−3.35092e22	−0.751117
$463$	−5.10428e22	−1.12330	−0.561650	−	0.827375i	$-0.689833\pi$
$463$	−5.10428e22	−1.12330	−0.561650	+	0.827375i	$0.689833\pi$
$464$	−9.27987e21	−0.200511
$465$	4.50005e22	0.954701
$466$	6.31757e22	1.31604
$467$	4.57207e22	0.935231	0.467616	−	0.883932i	$-0.345113\pi$
$467$	4.57207e22	0.935231	0.467616	+	0.883932i	$0.345113\pi$
$468$	−1.04461e23	−2.09828
$469$	3.45536e22	0.681592
$470$	1.17360e23	2.27346
$471$	−4.34856e22	−0.827310
$472$	−3.08999e21	−0.0577365
$473$	1.06407e22	0.195278
$474$	1.89194e23	3.41030
$475$	7.26828e22	1.28687
$476$	−1.78621e21	−0.0310652
$477$	−1.27850e23	−2.18421
$478$	6.86173e22	1.15159
$479$	−1.55465e22	−0.256319	−0.128159	−	0.991754i	$-0.540907\pi$
$479$	−1.55465e22	−0.256319	−0.128159	+	0.991754i	$0.540907\pi$
$480$	−2.02511e23	−3.28018
$481$	2.71170e22	0.431528
$482$	−9.10026e22	−1.42283
$483$	−1.72439e23	−2.64901
$484$	−5.25936e22	−0.793866
$485$	−7.11901e22	−1.05588
$486$	1.34578e23	1.96141
$487$	3.83893e22	0.549811	0.274906	−	0.961471i	$-0.411353\pi$
$487$	3.83893e22	0.549811	0.274906	+	0.961471i	$0.411353\pi$
$488$	−6.82828e21	−0.0961042
$489$	−7.88714e22	−1.09092
$490$	−3.60838e21	−0.0490508
$491$	−4.75621e22	−0.635431	−0.317716	−	0.948186i	$-0.602916\pi$
$491$	−4.75621e22	−0.635431	−0.317716	+	0.948186i	$0.602916\pi$
$492$	−9.55055e22	−1.25408
$493$	4.84463e20	0.00625262
$494$	−1.68072e23	−2.13214
$495$	5.65619e22	0.705309
$496$	−3.51867e22	−0.431304
$497$	7.23611e22	0.871918
$498$	−5.57757e22	−0.660687
$499$	3.17741e22	0.370015	0.185007	−	0.982737i	$-0.440769\pi$
$499$	3.17741e22	0.370015	0.185007	+	0.982737i	$0.440769\pi$
$500$	−7.35122e22	−0.841617
$501$	1.96138e23	2.20770
$502$	−1.32486e23	−1.46618
$503$	−1.09531e23	−1.19181	−0.595907	−	0.803054i	$-0.703207\pi$
$503$	−1.09531e23	−1.19181	−0.595907	+	0.803054i	$0.703207\pi$
$504$	1.39251e22	0.148983
$505$	2.03718e23	2.14315
$506$	8.48140e22	0.877381
$507$	−3.74756e23	−3.81224
$508$	−4.09635e22	−0.409784
$509$	−1.66614e23	−1.63912	−0.819562	−	0.572991i	$-0.805783\pi$
$509$	−1.66614e23	−1.63912	−0.819562	+	0.572991i	$0.805783\pi$
$510$	1.15037e22	0.111299
$511$	1.14895e23	1.09326
$512$	1.44395e23	1.35132
$513$	−2.89283e22	−0.266272
$514$	5.10807e22	0.462456
$515$	2.02187e23	1.80049
$516$	8.40228e22	0.735995
$517$	4.28824e22	0.369495
$518$	3.77297e22	0.319802
$519$	−6.19970e22	−0.516950
$520$	−4.46227e22	−0.366039
$521$	−3.33331e22	−0.269002	−0.134501	−	0.990913i	$-0.542943\pi$
$521$	−3.33331e22	−0.269002	−0.134501	+	0.990913i	$0.542943\pi$
$522$	3.94206e22	0.312985
$523$	−1.62984e23	−1.27315	−0.636575	−	0.771215i	$-0.719649\pi$
$523$	−1.62984e23	−1.27315	−0.636575	+	0.771215i	$0.719649\pi$
$524$	4.86916e22	0.374229
$525$	3.13594e23	2.37145
$526$	8.09493e22	0.602329
$527$	1.83695e21	0.0134495
$528$	−8.05152e22	−0.580082
$529$	2.95404e23	2.09432
$530$	5.70033e23	3.97699
$531$	8.47605e22	0.581956
$532$	−1.11580e23	−0.753939
$533$	−2.61740e23	−1.74056
$534$	−4.25565e23	−2.78526
$535$	−2.06184e23	−1.32815
$536$	1.28574e22	0.0815177
$537$	−2.05667e23	−1.28346
$538$	−4.56657e22	−0.280505
$539$	−1.31847e21	−0.00797199
$540$	8.01647e22	0.477129
$541$	1.67919e23	0.983838	0.491919	−	0.870641i	$-0.336296\pi$
$541$	1.67919e23	0.983838	0.491919	+	0.870641i	$0.336296\pi$
$542$	2.61866e23	1.51038
$543$	3.64786e23	2.07128
$544$	−8.26662e21	−0.0462101
$545$	−5.07602e23	−2.79353
$546$	−7.25157e23	−3.92911
$547$	1.42888e23	0.762263	0.381131	−	0.924521i	$-0.375535\pi$
$547$	1.42888e23	0.762263	0.381131	+	0.924521i	$0.375535\pi$
$548$	−2.94765e23	−1.54825
$549$	1.87304e23	0.968684
$550$	−1.54241e23	−0.785449
$551$	3.02631e22	0.151748
$552$	−6.41644e22	−0.316820
$553$	3.44223e23	1.67370
$554$	−2.26019e23	−1.08221
$555$	−1.15941e23	−0.546697
$556$	−1.22385e23	−0.568318
$557$	−1.71204e23	−0.782971	−0.391485	−	0.920184i	$-0.628039\pi$
$557$	−1.71204e23	−0.782971	−0.391485	+	0.920184i	$0.628039\pi$
$558$	1.49472e23	0.673238
$559$	2.30271e23	1.02150
$560$	−4.00914e23	−1.75167
$561$	4.20336e21	0.0180889
$562$	−1.51690e23	−0.642981
$563$	2.97691e23	1.24292	0.621462	−	0.783445i	$-0.286539\pi$
$563$	2.97691e23	1.24292	0.621462	+	0.783445i	$0.286539\pi$
$564$	3.38613e23	1.39262
$565$	7.58180e23	3.07157
$566$	1.16538e23	0.465079
$567$	1.88601e23	0.741459
$568$	2.69255e22	0.104281
$569$	−4.54727e23	−1.73499	−0.867494	−	0.497447i	$-0.834271\pi$
$569$	−4.54727e23	−1.73499	−0.867494	+	0.497447i	$0.834271\pi$
$570$	7.18605e23	2.70118
$571$	3.35274e23	1.24163	0.620816	−	0.783956i	$-0.286801\pi$
$571$	3.35274e23	1.24163	0.620816	+	0.783956i	$0.286801\pi$
$572$	1.70182e23	0.620936
$573$	−2.27079e23	−0.816323
$574$	−3.64177e23	−1.28992
$575$	−7.93728e23	−2.77010
$576$	−2.89965e23	−0.997135
$577$	−4.80496e23	−1.62815	−0.814077	−	0.580757i	$-0.802757\pi$
$577$	−4.80496e23	−1.62815	−0.814077	+	0.580757i	$0.802757\pi$
$578$	−4.13716e23	−1.38139
$579$	1.00881e23	0.331927
$580$	−8.38634e22	−0.271916
$581$	−1.01479e23	−0.324251
$582$	−4.30482e23	−1.35553
$583$	2.08285e23	0.646362
$584$	4.27526e22	0.130753
$585$	1.22403e24	3.68949
$586$	3.31644e23	0.985240
$587$	2.33551e23	0.683846	0.341923	−	0.939728i	$-0.388922\pi$
$587$	2.33551e23	0.683846	0.341923	+	0.939728i	$0.388922\pi$
$588$	−1.04111e22	−0.0300462
$589$	1.14749e23	0.326414
$590$	−3.77915e23	−1.05962
$591$	−6.75974e23	−1.86826
$592$	9.06562e22	0.246981
$593$	6.83788e23	1.83636	0.918178	−	0.396169i	$-0.129661\pi$
$593$	6.83788e23	1.83636	0.918178	+	0.396169i	$0.129661\pi$
$594$	6.13894e22	0.162521
$595$	2.09301e22	0.0546231
$596$	−3.75670e23	−0.966524
$597$	−5.16414e23	−1.30984
$598$	1.83542e24	4.58960
$599$	−7.94741e23	−1.95928	−0.979642	−	0.200750i	$-0.935662\pi$
$599$	−7.94741e23	−1.95928	−0.979642	+	0.200750i	$0.935662\pi$
$600$	1.16688e23	0.283623
$601$	−3.56743e23	−0.854913	−0.427457	−	0.904036i	$-0.640590\pi$
$601$	−3.56743e23	−0.854913	−0.427457	+	0.904036i	$0.640590\pi$
$602$	3.20392e23	0.757027
$603$	−3.52686e23	−0.821659
$604$	−1.02859e23	−0.236281
$605$	6.16269e23	1.39588
$606$	1.23187e24	2.75136
$607$	5.33686e23	1.17539	0.587694	−	0.809083i	$-0.300036\pi$
$607$	5.33686e23	1.17539	0.587694	+	0.809083i	$0.300036\pi$
$608$	−5.16392e23	−1.12150
$609$	1.30572e23	0.279642
$610$	−8.35117e23	−1.76378
$611$	9.27996e23	1.93284
$612$	1.82318e22	0.0374491
$613$	−9.81351e23	−1.98797	−0.993986	−	0.109507i	$-0.965073\pi$
$613$	−9.81351e23	−1.98797	−0.993986	+	0.109507i	$0.965073\pi$
$614$	1.61279e22	0.0322215
$615$	1.11909e24	2.20509
$616$	−2.26859e22	−0.0440880
$617$	3.26498e22	0.0625830	0.0312915	−	0.999510i	$-0.490038\pi$
$617$	3.26498e22	0.0625830	0.0312915	+	0.999510i	$0.490038\pi$
$618$	1.22261e24	2.31146
$619$	−1.75227e23	−0.326762	−0.163381	−	0.986563i	$-0.552240\pi$
$619$	−1.75227e23	−0.326762	−0.163381	+	0.986563i	$0.552240\pi$
$620$	−3.17986e23	−0.584896
$621$	3.15910e23	0.573172
$622$	−8.13540e23	−1.45600
$623$	−7.74280e23	−1.36694
$624$	−1.74239e24	−3.03443
$625$	−5.52430e22	−0.0949068
$626$	−4.38004e23	−0.742329
$627$	2.62572e23	0.439010
$628$	3.07281e23	0.506850
$629$	−4.73278e21	−0.00770169
$630$	1.70307e24	2.73425
$631$	7.88676e22	0.124925	0.0624625	−	0.998047i	$-0.480105\pi$
$631$	7.88676e22	0.124925	0.0624625	+	0.998047i	$0.480105\pi$
$632$	1.28085e23	0.200173
$633$	6.37276e23	0.982643
$634$	−6.43276e23	−0.978675
$635$	4.79992e23	0.720539
$636$	1.64469e24	2.43612
$637$	−2.85324e22	−0.0417017
$638$	−6.42218e22	−0.0926204
$639$	−7.38584e23	−1.05110
$640$	−2.75258e23	−0.386554
$641$	5.72727e23	0.793696	0.396848	−	0.917884i	$-0.370104\pi$
$641$	5.72727e23	0.793696	0.396848	+	0.917884i	$0.370104\pi$
$642$	−1.24678e24	−1.70507
$643$	−6.92026e23	−0.933962	−0.466981	−	0.884267i	$-0.654658\pi$
$643$	−6.92026e23	−0.933962	−0.466981	+	0.884267i	$0.654658\pi$
$644$	1.21850e24	1.62291
$645$	−9.84543e23	−1.29413
$646$	2.93339e22	0.0380534
$647$	1.18750e24	1.52037	0.760183	−	0.649709i	$-0.225109\pi$
$647$	1.18750e24	1.52037	0.760183	+	0.649709i	$0.225109\pi$
$648$	7.01783e22	0.0886778
$649$	−1.38087e23	−0.172216
$650$	−3.33786e24	−4.10871
$651$	4.95092e23	0.601516
$652$	5.57327e23	0.668353
$653$	−9.37976e19	−0.000111027 0	−5.55136e−5	−	1.00000i	$-0.500018\pi$
$653$	−9.37976e19	−0.000111027 0	−5.55136e−5		1.00000i	$0.500018\pi$
$654$	−3.06944e24	−3.58631
$655$	−5.70547e23	−0.658022
$656$	−8.75036e23	−0.996192
$657$	−1.17273e24	−1.31793
$658$	1.29118e24	1.43241
$659$	−4.53746e23	−0.496920	−0.248460	−	0.968642i	$-0.579925\pi$
$659$	−4.53746e23	−0.496920	−0.248460	+	0.968642i	$0.579925\pi$
$660$	−7.27626e23	−0.786656
$661$	9.09147e23	0.970335	0.485168	−	0.874421i	$-0.338759\pi$
$661$	9.09147e23	0.970335	0.485168	+	0.874421i	$0.338759\pi$
$662$	−5.91310e23	−0.623049
$663$	9.09629e22	0.0946236
$664$	−3.77605e22	−0.0387801
$665$	1.30744e24	1.32568
$666$	−3.85105e23	−0.385521
$667$	−3.30486e23	−0.326651
$668$	−1.38596e24	−1.35255
$669$	−2.05831e24	−1.98330
$670$	1.57249e24	1.49607
$671$	−3.05145e23	−0.286658
$672$	−2.22801e24	−2.06670
$673$	−8.08379e23	−0.740435	−0.370218	−	0.928945i	$-0.620717\pi$
$673$	−8.08379e23	−0.740435	−0.370218	+	0.928945i	$0.620717\pi$
$674$	9.85868e23	0.891681
$675$	−5.74509e23	−0.513115
$676$	2.64813e24	2.33556
$677$	−6.33598e23	−0.551836	−0.275918	−	0.961181i	$-0.588982\pi$
$677$	−6.33598e23	−0.551836	−0.275918	+	0.961181i	$0.588982\pi$
$678$	4.58467e24	3.94326
$679$	−7.83227e23	−0.665265
$680$	7.78807e21	0.00653287
$681$	−2.41731e24	−2.00254
$682$	−2.43511e23	−0.199228
$683$	1.85178e24	1.49628	0.748142	−	0.663538i	$-0.230946\pi$
$683$	1.85178e24	1.49628	0.748142	+	0.663538i	$0.230946\pi$
$684$	1.13889e24	0.908874
$685$	3.45392e24	2.72234
$686$	1.75632e24	1.36725
$687$	−1.04594e24	−0.804221
$688$	7.69830e23	0.584646
$689$	4.50740e24	3.38114
$690$	−7.84748e24	−5.81451
$691$	2.03586e24	1.48999	0.744997	−	0.667068i	$-0.232451\pi$
$691$	2.03586e24	1.48999	0.744997	+	0.667068i	$0.232451\pi$
$692$	4.38088e23	0.316708
$693$	6.22289e23	0.444385
$694$	1.15072e24	0.811732
$695$	1.43405e24	0.999294
$696$	4.85858e22	0.0334449
$697$	4.56820e22	0.0310646
$698$	7.62803e23	0.512438
$699$	−2.13585e24	−1.41748
$700$	−2.21594e24	−1.45287
$701$	−2.29073e24	−1.48379	−0.741894	−	0.670518i	$-0.766072\pi$
$701$	−2.29073e24	−1.48379	−0.741894	+	0.670518i	$0.766072\pi$
$702$	1.32850e24	0.850149
$703$	−2.95644e23	−0.186917
$704$	4.72394e23	0.295078
$705$	−3.96772e24	−2.44869
$706$	−3.91388e24	−2.38653
$707$	2.24129e24	1.35031
$708$	−1.09038e24	−0.649075
$709$	4.58438e23	0.269642	0.134821	−	0.990870i	$-0.456954\pi$
$709$	4.58438e23	0.269642	0.134821	+	0.990870i	$0.456954\pi$
$710$	3.29307e24	1.91383
$711$	−3.51346e24	−2.01764
$712$	−2.88109e23	−0.163485
$713$	−1.25311e24	−0.702632
$714$	1.26563e23	0.0701248
$715$	−1.99412e24	−1.09182
$716$	1.45330e24	0.786312
$717$	−2.31982e24	−1.24034
$718$	−3.30133e24	−1.74434
$719$	−8.39193e23	−0.438194	−0.219097	−	0.975703i	$-0.570311\pi$
$719$	−8.39193e23	−0.438194	−0.219097	+	0.975703i	$0.570311\pi$
$720$	4.09211e24	2.11164
$721$	2.22444e24	1.13441
$722$	−9.11536e23	−0.459417
$723$	3.07663e24	1.53250
$724$	−2.57768e24	−1.26897
$725$	6.01016e23	0.292424
$726$	3.72654e24	1.79203
$727$	7.45142e23	0.354158	0.177079	−	0.984197i	$-0.443335\pi$
$727$	7.45142e23	0.354158	0.177079	+	0.984197i	$0.443335\pi$
$728$	−4.90935e23	−0.230625
$729$	−2.97033e24	−1.37918
$730$	5.22875e24	2.39968
$731$	−4.01896e22	−0.0182312
$732$	−2.40952e24	−1.08041
$733$	−9.84092e23	−0.436166	−0.218083	−	0.975930i	$-0.569980\pi$
$733$	−9.84092e23	−0.436166	−0.218083	+	0.975930i	$0.569980\pi$
$734$	−2.99236e24	−1.31099
$735$	1.21993e23	0.0528313
$736$	5.63923e24	2.41412
$737$	5.74576e23	0.243150
$738$	3.71713e24	1.55499
$739$	−6.76261e23	−0.279664	−0.139832	−	0.990175i	$-0.544656\pi$
$739$	−6.76261e23	−0.279664	−0.139832	+	0.990175i	$0.544656\pi$
$740$	8.19271e23	0.334933
$741$	5.68220e24	2.29647
$742$	6.27145e24	2.50573
$743$	3.15370e24	1.24571	0.622854	−	0.782338i	$-0.285973\pi$
$743$	3.15370e24	1.24571	0.622854	+	0.782338i	$0.285973\pi$
$744$	1.84223e23	0.0719408
$745$	4.40193e24	1.69948
$746$	4.97178e22	0.0189772
$747$	1.03579e24	0.390884
$748$	−2.97021e22	−0.0110822
$749$	−2.26841e24	−0.836810
$750$	5.20873e24	1.89982
$751$	−2.12210e24	−0.765289	−0.382644	−	0.923896i	$-0.624987\pi$
$751$	−2.12210e24	−0.765289	−0.382644	+	0.923896i	$0.624987\pi$
$752$	3.10243e24	1.10624
$753$	4.47910e24	1.57919
$754$	−1.38979e24	−0.484500
$755$	1.20526e24	0.415462
$756$	8.81964e23	0.300619
$757$	1.99083e24	0.670996	0.335498	−	0.942041i	$-0.391095\pi$
$757$	1.99083e24	0.670996	0.335498	+	0.942041i	$0.391095\pi$
$758$	−6.08071e23	−0.202659
$759$	−2.86740e24	−0.945005
$760$	4.86499e23	0.158550
$761$	−3.72996e24	−1.20208	−0.601041	−	0.799218i	$-0.705247\pi$
$761$	−3.72996e24	−1.20208	−0.601041	+	0.799218i	$0.705247\pi$
$762$	2.90248e24	0.925023
$763$	−5.58459e24	−1.76008
$764$	1.60460e24	0.500119
$765$	−2.13632e23	−0.0658482
$766$	−6.27814e24	−1.91376
$767$	−2.98827e24	−0.900864
$768$	−5.75202e24	−1.71495
$769$	−3.15467e24	−0.930208	−0.465104	−	0.885256i	$-0.653983\pi$
$769$	−3.15467e24	−0.930208	−0.465104	+	0.885256i	$0.653983\pi$
$770$	−2.77455e24	−0.809135
$771$	−1.72694e24	−0.498099
$772$	−7.12855e23	−0.203355
$773$	2.31940e24	0.654409	0.327204	−	0.944954i	$-0.393893\pi$
$773$	2.31940e24	0.654409	0.327204	+	0.944954i	$0.393893\pi$
$774$	−3.27022e24	−0.912596
$775$	2.27888e24	0.629011
$776$	−2.91439e23	−0.0795651
$777$	−1.27557e24	−0.344450
$778$	−1.40689e24	−0.375780
$779$	2.85363e24	0.753926
$780$	−1.57462e25	−4.11502
$781$	1.20326e24	0.311047
$782$	−3.20339e23	−0.0819129
$783$	−2.39210e23	−0.0605067
$784$	−9.53881e22	−0.0238675
$785$	−3.60059e24	−0.891213
$786$	−3.45006e24	−0.844764
$787$	4.51975e24	1.09479	0.547393	−	0.836876i	$-0.315620\pi$
$787$	4.51975e24	1.09479	0.547393	+	0.836876i	$0.315620\pi$
$788$	4.77662e24	1.14458
$789$	−2.73674e24	−0.648754
$790$	1.56652e25	3.67372
$791$	8.34143e24	1.93526
$792$	2.31553e23	0.0531480
$793$	−6.60349e24	−1.49952
$794$	−8.13596e24	−1.82783
$795$	−1.92718e25	−4.28352
$796$	3.64913e24	0.802468
$797$	−7.87800e23	−0.171404	−0.0857019	−	0.996321i	$-0.527313\pi$
$797$	−7.87800e23	−0.171404	−0.0857019	+	0.996321i	$0.527313\pi$
$798$	7.90603e24	1.70190
$799$	−1.61965e23	−0.0344963
$800$	−1.02554e25	−2.16117
$801$	7.90303e24	1.64785
$802$	−6.19658e24	−1.27841
$803$	1.91054e24	0.390009
$804$	4.53704e24	0.916424
$805$	−1.42778e25	−2.85363
$806$	−5.26970e24	−1.04217
$807$	1.54387e24	0.302125
$808$	8.33982e23	0.161495
$809$	−3.59762e24	−0.689371	−0.344685	−	0.938718i	$-0.612014\pi$
$809$	−3.59762e24	−0.689371	−0.344685	+	0.938718i	$0.612014\pi$
$810$	8.58299e24	1.62748
$811$	7.36056e24	1.38113	0.690563	−	0.723272i	$-0.257363\pi$
$811$	7.36056e24	1.38113	0.690563	+	0.723272i	$0.257363\pi$
$812$	−9.22657e23	−0.171322
$813$	−8.85320e24	−1.62679
$814$	6.27391e23	0.114086
$815$	−6.53052e24	−1.17519
$816$	3.04102e23	0.0541569
$817$	−2.51053e24	−0.442465
$818$	−3.80175e24	−0.663102
$819$	1.34666e25	2.32459
$820$	−7.90781e24	−1.35095
$821$	−4.64818e24	−0.785898	−0.392949	−	0.919560i	$-0.628545\pi$
$821$	−4.64818e24	−0.785898	−0.392949	+	0.919560i	$0.628545\pi$
$822$	2.08857e25	3.49492
$823$	9.48298e24	1.57053	0.785265	−	0.619160i	$-0.212527\pi$
$823$	9.48298e24	1.57053	0.785265	+	0.619160i	$0.212527\pi$
$824$	8.27713e23	0.135675
$825$	5.21462e24	0.845987
$826$	−4.15778e24	−0.667623
$827$	9.77349e24	1.55329	0.776645	−	0.629938i	$-0.216920\pi$
$827$	9.77349e24	1.55329	0.776645	+	0.629938i	$0.216920\pi$
$828$	−1.24371e25	−1.95642
$829$	−6.85458e24	−1.06725	−0.533627	−	0.845720i	$-0.679171\pi$
$829$	−6.85458e24	−1.06725	−0.533627	+	0.845720i	$0.679171\pi$
$830$	−4.61821e24	−0.711721
$831$	7.64129e24	1.16562
$832$	1.02228e25	1.54356
$833$	4.97982e21	0.000744271 0
$834$	8.67161e24	1.28289
$835$	1.62401e25	2.37823
$836$	−1.85541e24	−0.268959
$837$	−9.07015e23	−0.130151
$838$	−4.68422e24	−0.665370
$839$	−6.75168e24	−0.949369	−0.474685	−	0.880156i	$-0.657438\pi$
$839$	−6.75168e24	−0.949369	−0.474685	+	0.880156i	$0.657438\pi$
$840$	2.09903e24	0.292176
$841$	2.50246e23	0.0344828
$842$	−2.27787e24	−0.310725
$843$	5.12835e24	0.692538
$844$	−4.50317e24	−0.602015
$845$	−3.10296e25	−4.10671
$846$	−1.31790e25	−1.72677
$847$	6.78013e24	0.879487
$848$	1.50689e25	1.93516
$849$	−3.93992e24	−0.500924
$850$	5.82563e23	0.0733301
$851$	3.22856e24	0.402353
$852$	9.50133e24	1.17232
$853$	1.46476e25	1.78937	0.894684	−	0.446699i	$-0.147401\pi$
$853$	1.46476e25	1.78937	0.894684	+	0.446699i	$0.147401\pi$
$854$	−9.18788e24	−1.11128
$855$	−1.33450e25	−1.59811
$856$	−8.44076e23	−0.100082
$857$	5.29536e24	0.621668	0.310834	−	0.950464i	$-0.399392\pi$
$857$	5.29536e24	0.621668	0.310834	+	0.950464i	$0.399392\pi$
$858$	−1.20583e25	−1.40166
$859$	−7.82014e24	−0.900063	−0.450031	−	0.893013i	$-0.648587\pi$
$859$	−7.82014e24	−0.900063	−0.450031	+	0.893013i	$0.648587\pi$
$860$	6.95705e24	0.792845
$861$	1.23121e25	1.38933
$862$	1.14818e25	1.28291
$863$	−1.29220e24	−0.142968	−0.0714840	−	0.997442i	$-0.522774\pi$
$863$	−1.29220e24	−0.142968	−0.0714840	+	0.997442i	$0.522774\pi$
$864$	4.08174e24	0.447176
$865$	−5.13332e24	−0.556880
$866$	−1.43397e24	−0.154041
$867$	1.39870e25	1.48786
$868$	−3.49846e24	−0.368518
$869$	5.72393e24	0.597072
$870$	5.94217e24	0.613807
$871$	1.24341e25	1.27192
$872$	−2.07802e24	−0.210504
$873$	7.99435e24	0.801977
$874$	−2.00107e25	−1.98799
$875$	9.47686e24	0.932387
$876$	1.50863e25	1.46993
$877$	2.22053e24	0.214270	0.107135	−	0.994244i	$-0.465832\pi$
$877$	2.22053e24	0.214270	0.107135	+	0.994244i	$0.465832\pi$
$878$	9.53195e23	0.0910916
$879$	−1.12123e25	−1.06118
$880$	−6.66662e24	−0.624889
$881$	4.00325e24	0.371636	0.185818	−	0.982584i	$-0.440507\pi$
$881$	4.00325e24	0.371636	0.185818	+	0.982584i	$0.440507\pi$
$882$	4.05206e23	0.0372557
$883$	−1.01102e25	−0.920650	−0.460325	−	0.887750i	$-0.652267\pi$
$883$	−1.01102e25	−0.920650	−0.460325	+	0.887750i	$0.652267\pi$
$884$	−6.42769e23	−0.0579710
$885$	1.27766e25	1.14129
$886$	−1.13931e25	−1.00798
$887$	−7.99341e24	−0.700457	−0.350228	−	0.936664i	$-0.613896\pi$
$887$	−7.99341e24	−0.700457	−0.350228	+	0.936664i	$0.613896\pi$
$888$	−4.74640e23	−0.0411959
$889$	5.28083e24	0.453981
$890$	−3.52366e25	−3.00040
$891$	3.13616e24	0.264507
$892$	1.45446e25	1.21506
$893$	−1.01175e25	−0.837212
$894$	2.66182e25	2.18178
$895$	−1.70291e25	−1.38260
$896$	−3.02836e24	−0.243551
$897$	−6.20521e25	−4.94334
$898$	2.49219e25	1.96667
$899$	9.48864e23	0.0741731
$900$	2.26180e25	1.75143
$901$	−7.86685e23	−0.0603448
$902$	−6.05573e24	−0.460162
$903$	−1.08319e25	−0.815374
$904$	3.10384e24	0.231456
$905$	3.02041e25	2.23127
$906$	7.28812e24	0.533367
$907$	1.24611e25	0.903430	0.451715	−	0.892162i	$-0.350812\pi$
$907$	1.24611e25	0.903430	0.451715	+	0.892162i	$0.350812\pi$
$908$	1.70814e25	1.22686
$909$	−2.28767e25	−1.62779
$910$	−6.00426e25	−4.23261
$911$	−8.48454e24	−0.592546	−0.296273	−	0.955103i	$-0.595744\pi$
$911$	−8.48454e24	−0.592546	−0.296273	+	0.955103i	$0.595744\pi$
$912$	1.89964e25	1.31436
$913$	−1.68745e24	−0.115673
$914$	2.75465e25	1.87079
$915$	2.82338e25	1.89972
$916$	7.39092e24	0.492705
$917$	−6.27710e24	−0.414591
$918$	−2.31865e23	−0.0151730
$919$	8.44870e24	0.547782	0.273891	−	0.961761i	$-0.411689\pi$
$919$	8.44870e24	0.547782	0.273891	+	0.961761i	$0.411689\pi$
$920$	−5.31278e24	−0.341292
$921$	−5.45253e23	−0.0347049
$922$	−4.18373e25	−2.63846
$923$	2.60391e25	1.62709
$924$	−8.00528e24	−0.495638
$925$	−5.87140e24	−0.360195
$926$	−2.55563e25	−1.55348
$927$	−2.27047e25	−1.36753
$928$	−4.27007e24	−0.254845
$929$	−1.24794e25	−0.738005	−0.369003	−	0.929428i	$-0.620301\pi$
$929$	−1.24794e25	−0.738005	−0.369003	+	0.929428i	$0.620301\pi$
$930$	2.25310e25	1.32031
$931$	3.11075e23	0.0180631
$932$	1.50925e25	0.868414
$933$	2.75043e25	1.56822
$934$	2.28916e25	1.29338
$935$	3.48037e23	0.0194862
$936$	5.01093e24	0.278019
$937$	1.67736e25	0.922229	0.461114	−	0.887341i	$-0.347450\pi$
$937$	1.67736e25	0.922229	0.461114	+	0.887341i	$0.347450\pi$
$938$	1.73004e25	0.942612
$939$	1.48081e25	0.799544
$940$	2.80370e25	1.50019
$941$	1.13249e24	0.0600513	0.0300256	−	0.999549i	$-0.490441\pi$
$941$	1.13249e24	0.0600513	0.0300256	+	0.999549i	$0.490441\pi$
$942$	−2.17725e25	−1.14413
$943$	−3.11628e25	−1.62288
$944$	−9.99023e24	−0.515601
$945$	−1.03345e25	−0.528589
$946$	5.32765e24	0.270060
$947$	−1.86402e25	−0.936429	−0.468215	−	0.883615i	$-0.655103\pi$
$947$	−1.86402e25	−0.936429	−0.468215	+	0.883615i	$0.655103\pi$
$948$	4.51981e25	2.25034
$949$	4.13452e25	2.04015
$950$	3.63911e25	1.77969
$951$	2.17480e25	1.05411
$952$	8.56837e22	0.00411608
$953$	2.41091e24	0.114787	0.0573934	−	0.998352i	$-0.481721\pi$
$953$	2.41091e24	0.114787	0.0573934	+	0.998352i	$0.481721\pi$
$954$	−6.40123e25	−3.02066
$955$	−1.88020e25	−0.879378
$956$	1.63925e25	0.759894
$957$	2.17122e24	0.0997591
$958$	−7.78387e24	−0.354478
$959$	3.79997e25	1.71523
$960$	−4.37086e25	−1.95551
$961$	−1.89523e25	−0.840452
$962$	1.35771e25	0.596784
$963$	2.31536e25	1.00877
$964$	−2.17403e25	−0.938882
$965$	8.35292e24	0.357566
$966$	−8.63373e25	−3.66347
$967$	−3.45643e24	−0.145379	−0.0726897	−	0.997355i	$-0.523158\pi$
$967$	−3.45643e24	−0.145379	−0.0726897	+	0.997355i	$0.523158\pi$
$968$	2.52289e24	0.105186
$969$	−9.91724e23	−0.0409863
$970$	−3.56437e25	−1.46024
$971$	−4.59738e25	−1.86701	−0.933505	−	0.358564i	$-0.883266\pi$
$971$	−4.59738e25	−1.86701	−0.933505	+	0.358564i	$0.883266\pi$
$972$	3.21505e25	1.29427
$973$	1.57773e25	0.629612
$974$	1.92209e25	0.760365
$975$	1.12847e26	4.42538
$976$	−2.20764e25	−0.858233
$977$	−4.16689e25	−1.60586	−0.802931	−	0.596073i	$-0.796727\pi$
$977$	−4.16689e25	−1.60586	−0.802931	+	0.596073i	$0.796727\pi$
$978$	−3.94896e25	−1.50870
$979$	−1.28752e25	−0.487640
$980$	−8.62035e23	−0.0323670
$981$	5.70015e25	2.12178
$982$	−2.38136e25	−0.878774
$983$	4.96936e25	1.81801	0.909004	−	0.416787i	$-0.136844\pi$
$983$	4.96936e25	1.81801	0.909004	+	0.416787i	$0.136844\pi$
$984$	4.58134e24	0.166163
$985$	−5.59704e25	−2.01257
$986$	2.42563e23	0.00864711
$987$	−4.36525e25	−1.54281
$988$	−4.01520e25	−1.40693
$989$	2.74161e25	0.952440
$990$	2.83196e25	0.975412
$991$	−3.07326e25	−1.04948	−0.524738	−	0.851264i	$-0.675837\pi$
$991$	−3.07326e25	−1.04948	−0.524738	+	0.851264i	$0.675837\pi$
$992$	−1.61909e25	−0.548178
$993$	1.99911e25	0.671070
$994$	3.62300e25	1.20582
$995$	−4.27589e25	−1.41101
$996$	−1.33247e25	−0.435966
$997$	−1.19644e25	−0.388136	−0.194068	−	0.980988i	$-0.562168\pi$
$997$	−1.19644e25	−0.388136	−0.194068	+	0.980988i	$0.562168\pi$
$998$	1.59088e25	0.511714
$999$	2.33687e24	0.0745294

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.b.1.18	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.b.1.18	✓	21	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+500.684 q^{2} -16927.2 q^{3} +119612. q^{4} -1.40156e6 q^{5} -8.47517e6 q^{6} -1.54199e7 q^{7} -5.73773e6 q^{8} +1.57390e8 q^{9} +O(q^{10})\)	\(q+500.684 q^{2} -16927.2 q^{3} +119612. q^{4} -1.40156e6 q^{5} -8.47517e6 q^{6} -1.54199e7 q^{7} -5.73773e6 q^{8} +1.57390e8 q^{9} -7.01740e8 q^{10} -2.56410e8 q^{11} -2.02470e9 q^{12} -5.54885e9 q^{13} -7.72048e9 q^{14} +2.37245e10 q^{15} -1.85506e10 q^{16} +9.68450e8 q^{17} +7.88024e10 q^{18} +6.04963e10 q^{19} -1.67644e11 q^{20} +2.61015e11 q^{21} -1.28380e11 q^{22} -6.60646e11 q^{23} +9.71237e10 q^{24} +1.20144e12 q^{25} -2.77822e12 q^{26} -4.78184e11 q^{27} -1.84441e12 q^{28} +5.00246e11 q^{29} +1.18785e13 q^{30} +1.89679e12 q^{31} -8.53593e12 q^{32} +4.34030e12 q^{33} +4.84887e11 q^{34} +2.16119e13 q^{35} +1.88257e13 q^{36} -4.88697e12 q^{37} +3.02895e13 q^{38} +9.39264e13 q^{39} +8.04179e12 q^{40} +4.71702e13 q^{41} +1.30686e14 q^{42} -4.14989e13 q^{43} -3.06698e13 q^{44} -2.20592e14 q^{45} -3.30775e14 q^{46} -1.67241e14 q^{47} +3.14010e14 q^{48} +5.14205e12 q^{49} +6.01542e14 q^{50} -1.63931e13 q^{51} -6.63710e14 q^{52} -8.12313e14 q^{53} -2.39419e14 q^{54} +3.59375e14 q^{55} +8.84751e13 q^{56} -1.02403e15 q^{57} +2.50465e14 q^{58} +5.38539e14 q^{59} +2.83774e15 q^{60} +1.19007e15 q^{61} +9.49694e14 q^{62} -2.42693e15 q^{63} -1.84234e15 q^{64} +7.77706e15 q^{65} +2.17312e15 q^{66} -2.24085e15 q^{67} +1.15838e14 q^{68} +1.11829e16 q^{69} +1.08207e16 q^{70} -4.69271e15 q^{71} -9.03059e14 q^{72} -7.45113e15 q^{73} -2.44683e15 q^{74} -2.03370e16 q^{75} +7.23610e15 q^{76} +3.95381e15 q^{77} +4.70274e16 q^{78} -2.23234e16 q^{79} +2.59998e16 q^{80} -1.22310e16 q^{81} +2.36174e16 q^{82} +6.58108e15 q^{83} +3.12206e16 q^{84} -1.35734e15 q^{85} -2.07778e16 q^{86} -8.46777e15 q^{87} +1.47121e15 q^{88} +5.02131e16 q^{89} -1.10447e17 q^{90} +8.55625e16 q^{91} -7.90214e16 q^{92} -3.21074e16 q^{93} -8.37350e16 q^{94} -8.47894e16 q^{95} +1.44489e17 q^{96} +5.07934e16 q^{97} +2.57454e15 q^{98} -4.03563e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) \) 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9} - 224469478 q^{10} + 1203139534 q^{11} - 5164251122 q^{12} + 3854339312 q^{13} + 25262272904 q^{14} + 28324474306 q^{15} + 196520815922 q^{16} + 76444714794 q^{17} + 75758949126 q^{18} + 246497292428 q^{19} - 46900976670 q^{20} + 360937126704 q^{21} - 275001533522 q^{22} + 213498528140 q^{23} - 451123453870 q^{24} + 3898884886997 q^{25} - 3609347694206 q^{26} - 2718903745978 q^{27} - 5946174617200 q^{28} + 10505174672181 q^{29} - 20237658929454 q^{30} + 16670029895798 q^{31} - 42141001912046 q^{32} - 7157109761394 q^{33} + 12785761151136 q^{34} + 46677934312888 q^{35} + 132137824374868 q^{36} + 53445659988410 q^{37} + 76581637956388 q^{38} + 79233849032530 q^{39} + 193617444734146 q^{40} - 20814769309298 q^{41} + 76690667258352 q^{42} + 185498647364454 q^{43} + 315429066899678 q^{44} - 486270821438526 q^{45} + 261474367677132 q^{46} + 389503471719450 q^{47} - 101509672247630 q^{48} + 730079062141437 q^{49} + 14\!\cdots\!54 q^{50}+ \cdots - 95\!\cdots\!64 q^{99}+O(q^{100}) \) 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9 - 224469478 * q^10 + 1203139534 * q^11 - 5164251122 * q^12 + 3854339312 * q^13 + 25262272904 * q^14 + 28324474306 * q^15 + 196520815922 * q^16 + 76444714794 * q^17 + 75758949126 * q^18 + 246497292428 * q^19 - 46900976670 * q^20 + 360937126704 * q^21 - 275001533522 * q^22 + 213498528140 * q^23 - 451123453870 * q^24 + 3898884886997 * q^25 - 3609347694206 * q^26 - 2718903745978 * q^27 - 5946174617200 * q^28 + 10505174672181 * q^29 - 20237658929454 * q^30 + 16670029895798 * q^31 - 42141001912046 * q^32 - 7157109761394 * q^33 + 12785761151136 * q^34 + 46677934312888 * q^35 + 132137824374868 * q^36 + 53445659988410 * q^37 + 76581637956388 * q^38 + 79233849032530 * q^39 + 193617444734146 * q^40 - 20814769309298 * q^41 + 76690667258352 * q^42 + 185498647364454 * q^43 + 315429066899678 * q^44 - 486270821438526 * q^45 + 261474367677132 * q^46 + 389503471719450 * q^47 - 101509672247630 * q^48 + 730079062141437 * q^49 + 1482269666368354 * q^50 + 718238208473988 * q^51 + 1966802817157170 * q^52 + 747441265526156 * q^53 + 5692893333117030 * q^54 + 1639109418219546 * q^55 + 5657219329125240 * q^56 + 4694352396864932 * q^57 + 128063081718016 * q^58 + 5280258638332960 * q^59 + 15251367906033378 * q^60 + 5813675353074254 * q^61 + 6242066590947250 * q^62 + 10947760075450368 * q^63 + 24583792057508902 * q^64 + 19190799243789974 * q^65 + 41877805444482390 * q^66 + 13420580230958268 * q^67 + 24771837384165388 * q^68 + 30973047049935252 * q^69 + 8505088080182440 * q^70 + 4824462822979508 * q^71 + 1180071997284592 * q^72 + 11228916281304662 * q^73 - 89132715356772 * q^74 + 59161419576630296 * q^75 + 57466858643173460 * q^76 + 58741564492720064 * q^77 + 142050530910210210 * q^78 + 71718598015696758 * q^79 + 48350023652407550 * q^80 + 75805931446703569 * q^81 + 188661890754420812 * q^82 + 50769377111735608 * q^83 + 198832046985593048 * q^84 + 53422044849490784 * q^85 + 35014892323844118 * q^86 + 11988905533023326 * q^87 + 37459283979085258 * q^88 - 70981414576978018 * q^89 + 57211029866143724 * q^90 + 112933943315157320 * q^91 - 103019729095759724 * q^92 - 350358290646906646 * q^93 - 150286322409612578 * q^94 - 102561321856584476 * q^95 - 213770098354021866 * q^96 - 130930167251505210 * q^97 - 537387515497557296 * q^98 - 95267700931431064 * q^99

Introduction

L-functions

Modular forms

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