LMFDB - Embedded newform 29.18.a.b.1.14

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			1.14
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)

$f(q)$	$=$	$q+290.453 q^{2} -16308.4 q^{3} -46709.2 q^{4} +805745. q^{5} -4.73681e6 q^{6} +2.28724e7 q^{7} -5.16370e7 q^{8} +1.36823e8 q^{9} +O(q^{10})$	\(q+290.453 q^{2} -16308.4 q^{3} -46709.2 q^{4} +805745. q^{5} -4.73681e6 q^{6} +2.28724e7 q^{7} -5.16370e7 q^{8} +1.36823e8 q^{9} +2.34031e8 q^{10} -1.07952e9 q^{11} +7.61751e8 q^{12} -1.42697e9 q^{13} +6.64334e9 q^{14} -1.31404e10 q^{15} -8.87585e9 q^{16} -7.26264e9 q^{17} +3.97405e10 q^{18} +2.69057e10 q^{19} -3.76357e10 q^{20} -3.73011e11 q^{21} -3.13549e11 q^{22} -1.74924e11 q^{23} +8.42116e11 q^{24} -1.13715e11 q^{25} -4.14467e11 q^{26} -1.25290e11 q^{27} -1.06835e12 q^{28} +5.00246e11 q^{29} -3.81666e12 q^{30} +5.52373e12 q^{31} +4.19015e12 q^{32} +1.76052e13 q^{33} -2.10946e12 q^{34} +1.84293e13 q^{35} -6.39088e12 q^{36} +4.02581e13 q^{37} +7.81483e12 q^{38} +2.32715e13 q^{39} -4.16063e13 q^{40} -2.76028e13 q^{41} -1.08342e14 q^{42} +3.16139e13 q^{43} +5.04234e13 q^{44} +1.10244e14 q^{45} -5.08071e13 q^{46} +2.44103e13 q^{47} +1.44751e14 q^{48} +2.90515e14 q^{49} -3.30288e13 q^{50} +1.18442e14 q^{51} +6.66525e13 q^{52} -1.46529e14 q^{53} -3.63908e13 q^{54} -8.69816e14 q^{55} -1.18106e15 q^{56} -4.38788e14 q^{57} +1.45298e14 q^{58} -1.40226e15 q^{59} +6.13777e14 q^{60} +1.67067e15 q^{61} +1.60438e15 q^{62} +3.12946e15 q^{63} +2.38042e15 q^{64} -1.14977e15 q^{65} +5.11347e15 q^{66} +5.26350e15 q^{67} +3.39232e14 q^{68} +2.85272e15 q^{69} +5.35284e15 q^{70} -3.64353e15 q^{71} -7.06512e15 q^{72} +7.68806e15 q^{73} +1.16931e16 q^{74} +1.85451e15 q^{75} -1.25674e15 q^{76} -2.46911e16 q^{77} +6.75928e15 q^{78} +2.37036e16 q^{79} -7.15167e15 q^{80} -1.56260e16 q^{81} -8.01731e15 q^{82} +6.98620e15 q^{83} +1.74230e16 q^{84} -5.85184e15 q^{85} +9.18234e15 q^{86} -8.15820e15 q^{87} +5.57431e16 q^{88} +2.61692e16 q^{89} +3.20207e16 q^{90} -3.26381e16 q^{91} +8.17055e15 q^{92} -9.00831e16 q^{93} +7.09005e15 q^{94} +2.16791e16 q^{95} -6.83346e16 q^{96} -1.14923e17 q^{97} +8.43809e16 q^{98} -1.47703e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	290.453	0.802270	0.401135	−	0.916019i	$-0.368616\pi$
$2$	290.453	0.802270	0.401135	+	0.916019i	$0.368616\pi$
$3$	−16308.4	−1.43509	−0.717546	−	0.696511i	$-0.754735\pi$
$3$	−16308.4	−1.43509	−0.717546	+	0.696511i	$0.754735\pi$
$4$	−46709.2	−0.356363
$5$	805745.	0.922470	0.461235	−	0.887278i	$-0.347406\pi$
$5$	805745.	0.922470	0.461235	+	0.887278i	$0.347406\pi$
$6$	−4.73681e6	−1.15133
$7$	2.28724e7	1.49961	0.749804	−	0.661660i	$-0.230148\pi$
$7$	2.28724e7	1.49961	0.749804	+	0.661660i	$0.230148\pi$
$8$	−5.16370e7	−1.08817
$9$	1.36823e8	1.05949
$10$	2.34031e8	0.740070
$11$	−1.07952e9	−1.51842	−0.759210	−	0.650845i	$-0.774415\pi$
$11$	−1.07952e9	−1.51842	−0.759210	+	0.650845i	$0.774415\pi$
$12$	7.61751e8	0.511414
$13$	−1.42697e9	−0.485172	−0.242586	−	0.970130i	$-0.577996\pi$
$13$	−1.42697e9	−0.485172	−0.242586	+	0.970130i	$0.577996\pi$
$14$	6.64334e9	1.20309
$15$	−1.31404e10	−1.32383
$16$	−8.87585e9	−0.516643
$17$	−7.26264e9	−0.252510	−0.126255	−	0.991998i	$-0.540296\pi$
$17$	−7.26264e9	−0.252510	−0.126255	+	0.991998i	$0.540296\pi$
$18$	3.97405e10	0.849997
$19$	2.69057e10	0.363445	0.181722	−	0.983350i	$-0.441833\pi$
$19$	2.69057e10	0.363445	0.181722	+	0.983350i	$0.441833\pi$
$20$	−3.76357e10	−0.328734
$21$	−3.73011e11	−2.15208
$22$	−3.13549e11	−1.21818
$23$	−1.74924e11	−0.465760	−0.232880	−	0.972505i	$-0.574815\pi$
$23$	−1.74924e11	−0.465760	−0.232880	+	0.972505i	$0.574815\pi$
$24$	8.42116e11	1.56162
$25$	−1.13715e11	−0.149048
$26$	−4.14467e11	−0.389239
$27$	−1.25290e11	−0.0853736
$28$	−1.06835e12	−0.534405
$29$	5.00246e11	0.185695
$29$	5.00246e11	0.185695
$30$	−3.81666e12	−1.06207
$31$	5.52373e12	1.16321	0.581605	−	0.813471i	$-0.302425\pi$
$31$	5.52373e12	1.16321	0.581605	+	0.813471i	$0.302425\pi$
$32$	4.19015e12	0.673682
$33$	1.76052e13	2.17907
$34$	−2.10946e12	−0.202581
$35$	1.84293e13	1.38334
$36$	−6.39088e12	−0.377563
$37$	4.02581e13	1.88425	0.942126	−	0.335258i	$-0.108824\pi$
$37$	4.02581e13	1.88425	0.942126	+	0.335258i	$0.108824\pi$
$38$	7.81483e12	0.291581
$39$	2.32715e13	0.696267
$40$	−4.16063e13	−1.00380
$41$	−2.76028e13	−0.539872	−0.269936	−	0.962878i	$-0.587002\pi$
$41$	−2.76028e13	−0.539872	−0.269936	+	0.962878i	$0.587002\pi$
$42$	−1.08342e14	−1.72655
$43$	3.16139e13	0.412474	0.206237	−	0.978502i	$-0.433878\pi$
$43$	3.16139e13	0.412474	0.206237	+	0.978502i	$0.433878\pi$
$44$	5.04234e13	0.541109
$45$	1.10244e14	0.977348
$46$	−5.08071e13	−0.373665
$47$	2.44103e13	0.149535	0.0747673	−	0.997201i	$-0.476179\pi$
$47$	2.44103e13	0.149535	0.0747673	+	0.997201i	$0.476179\pi$
$48$	1.44751e14	0.741430
$49$	2.90515e14	1.24883
$50$	−3.30288e13	−0.119577
$51$	1.18442e14	0.362375
$52$	6.66525e13	0.172897
$53$	−1.46529e14	−0.323279	−0.161639	−	0.986850i	$-0.551678\pi$
$53$	−1.46529e14	−0.323279	−0.161639	+	0.986850i	$0.551678\pi$
$54$	−3.63908e13	−0.0684927
$55$	−8.69816e14	−1.40070
$56$	−1.18106e15	−1.63183
$57$	−4.38788e14	−0.521577
$58$	1.45298e14	0.148978
$59$	−1.40226e15	−1.24333	−0.621667	−	0.783282i	$-0.713544\pi$
$59$	−1.40226e15	−1.24333	−0.621667	+	0.783282i	$0.713544\pi$
$60$	6.13777e14	0.471764
$61$	1.67067e15	1.11580	0.557901	−	0.829907i	$-0.311607\pi$
$61$	1.67067e15	1.11580	0.557901	+	0.829907i	$0.311607\pi$
$62$	1.60438e15	0.933209
$63$	3.12946e15	1.58882
$64$	2.38042e15	1.05712
$65$	−1.14977e15	−0.447557
$66$	5.11347e15	1.74821
$67$	5.26350e15	1.58358	0.791788	−	0.610797i	$-0.209151\pi$
$67$	5.26350e15	1.58358	0.791788	+	0.610797i	$0.209151\pi$
$68$	3.39232e14	0.0899853
$69$	2.85272e15	0.668409
$70$	5.35284e15	1.10982
$71$	−3.64353e15	−0.669616	−0.334808	−	0.942286i	$-0.608671\pi$
$71$	−3.64353e15	−0.669616	−0.334808	+	0.942286i	$0.608671\pi$
$72$	−7.06512e15	−1.15290
$73$	7.68806e15	1.11576	0.557882	−	0.829920i	$-0.311614\pi$
$73$	7.68806e15	1.11576	0.557882	+	0.829920i	$0.311614\pi$
$74$	1.16931e16	1.51168
$75$	1.85451e15	0.213898
$76$	−1.25674e15	−0.129518
$77$	−2.46911e16	−2.27704
$78$	6.75928e15	0.558594
$79$	2.37036e16	1.75786	0.878929	−	0.476953i	$-0.158259\pi$
$79$	2.37036e16	1.75786	0.878929	+	0.476953i	$0.158259\pi$
$80$	−7.15167e15	−0.476588
$81$	−1.56260e16	−0.936971
$82$	−8.01731e15	−0.433123
$83$	6.98620e15	0.340469	0.170234	−	0.985404i	$-0.445548\pi$
$83$	6.98620e15	0.340469	0.170234	+	0.985404i	$0.445548\pi$
$84$	1.74230e16	0.766920
$85$	−5.85184e15	−0.232933
$86$	9.18234e15	0.330915
$87$	−8.15820e15	−0.266490
$88$	5.57431e16	1.65230
$89$	2.61692e16	0.704652	0.352326	−	0.935877i	$-0.385391\pi$
$89$	2.61692e16	0.704652	0.352326	+	0.935877i	$0.385391\pi$
$90$	3.20207e16	0.784097
$91$	−3.26381e16	−0.727568
$92$	8.17055e15	0.165980
$93$	−9.00831e16	−1.66931
$94$	7.09005e15	0.119967
$95$	2.16791e16	0.335267
$96$	−6.83346e16	−0.966796
$97$	−1.14923e17	−1.48883	−0.744415	−	0.667717i	$-0.767272\pi$
$97$	−1.14923e17	−1.48883	−0.744415	+	0.667717i	$0.767272\pi$
$98$	8.43809e16	1.00190
$99$	−1.47703e17	−1.60875
$100$	5.31153e15	0.0531153
$101$	5.41260e16	0.497364	0.248682	−	0.968585i	$-0.420003\pi$
$101$	5.41260e16	0.497364	0.248682	+	0.968585i	$0.420003\pi$
$102$	3.44018e16	0.290723
$103$	2.47336e17	1.92385	0.961925	−	0.273312i	$-0.0881191\pi$
$103$	2.47336e17	1.92385	0.961925	+	0.273312i	$0.0881191\pi$
$104$	7.36844e16	0.527949
$105$	−3.00552e17	−1.98523
$106$	−4.25596e16	−0.259357
$107$	1.72714e17	0.971773	0.485887	−	0.874022i	$-0.338497\pi$
$107$	1.72714e17	0.971773	0.485887	+	0.874022i	$0.338497\pi$
$108$	5.85218e15	0.0304240
$109$	5.13018e15	0.0246608	0.0123304	−	0.999924i	$-0.496075\pi$
$109$	5.13018e15	0.0246608	0.0123304	+	0.999924i	$0.496075\pi$
$110$	−2.52640e17	−1.12374
$111$	−6.56545e17	−2.70408
$112$	−2.03012e17	−0.774762
$113$	4.24459e15	0.0150200	0.00750998	−	0.999972i	$-0.497609\pi$
$113$	4.24459e15	0.0150200	0.00750998	+	0.999972i	$0.497609\pi$
$114$	−1.27447e17	−0.418446
$115$	−1.40944e17	−0.429650
$116$	−2.33661e16	−0.0661749
$117$	−1.95242e17	−0.514035
$118$	−4.07292e17	−0.997490
$119$	−1.66114e17	−0.378666
$120$	6.78530e17	1.44055
$121$	6.59912e17	1.30560
$122$	4.85251e17	0.895175
$123$	4.50157e17	0.774766
$124$	−2.58009e17	−0.414525
$125$	−7.06360e17	−1.05996
$126$	9.08960e17	1.27466
$127$	−6.28454e17	−0.824028	−0.412014	−	0.911178i	$-0.635175\pi$
$127$	−6.28454e17	−0.824028	−0.412014	+	0.911178i	$0.635175\pi$
$128$	1.42187e17	0.174412
$129$	−5.15571e17	−0.591938
$130$	−3.33954e17	−0.359061
$131$	1.94473e17	0.195908	0.0979540	−	0.995191i	$-0.468770\pi$
$131$	1.94473e17	0.195908	0.0979540	+	0.995191i	$0.468770\pi$
$132$	−8.22324e17	−0.776541
$133$	6.15397e17	0.545025
$134$	1.52880e18	1.27045
$135$	−1.00952e17	−0.0787546
$136$	3.75021e17	0.274774
$137$	1.39614e18	0.961178	0.480589	−	0.876946i	$-0.340423\pi$
$137$	1.39614e18	0.961178	0.480589	+	0.876946i	$0.340423\pi$
$138$	8.28581e17	0.536244
$139$	4.97939e17	0.303075	0.151538	−	0.988452i	$-0.451578\pi$
$139$	4.97939e17	0.303075	0.151538	+	0.988452i	$0.451578\pi$
$140$	−8.60817e17	−0.492973
$141$	−3.98093e17	−0.214596
$142$	−1.05827e18	−0.537213
$143$	1.54044e18	0.736695
$144$	−1.21442e18	−0.547378
$145$	4.03071e17	0.171298
$146$	2.23302e18	0.895144
$147$	−4.73783e18	−1.79218
$148$	−1.88043e18	−0.671478
$149$	4.52991e18	1.52759	0.763795	−	0.645459i	$-0.223334\pi$
$149$	4.52991e18	1.52759	0.763795	+	0.645459i	$0.223334\pi$
$150$	5.38646e17	0.171604
$151$	2.08694e18	0.628357	0.314178	−	0.949364i	$-0.398271\pi$
$151$	2.08694e18	0.628357	0.314178	+	0.949364i	$0.398271\pi$
$152$	−1.38933e18	−0.395490
$153$	−9.93695e17	−0.267532
$154$	−7.17161e18	−1.82680
$155$	4.45072e18	1.07303
$156$	−1.08699e18	−0.248124
$157$	−6.65062e18	−1.43786	−0.718928	−	0.695085i	$-0.755367\pi$
$157$	−6.65062e18	−1.43786	−0.718928	+	0.695085i	$0.755367\pi$
$158$	6.88477e18	1.41028
$159$	2.38964e18	0.463935
$160$	3.37619e18	0.621452
$161$	−4.00092e18	−0.698458
$162$	−4.53863e18	−0.751704
$163$	9.31657e18	1.46441	0.732203	−	0.681086i	$-0.238492\pi$
$163$	9.31657e18	1.46441	0.732203	+	0.681086i	$0.238492\pi$
$164$	1.28930e18	0.192390
$165$	1.41853e19	2.01013
$166$	2.02916e18	0.273148
$167$	−1.21823e19	−1.55826	−0.779132	−	0.626860i	$-0.784340\pi$
$167$	−1.21823e19	−1.55826	−0.779132	+	0.626860i	$0.784340\pi$
$168$	1.92612e19	2.34182
$169$	−6.61418e18	−0.764608
$170$	−1.69968e18	−0.186875
$171$	3.68131e18	0.385066
$172$	−1.47666e18	−0.146990
$173$	2.80038e18	0.265353	0.132677	−	0.991159i	$-0.457643\pi$
$173$	2.80038e18	0.265353	0.132677	+	0.991159i	$0.457643\pi$
$174$	−2.36957e18	−0.213797
$175$	−2.60093e18	−0.223514
$176$	9.58164e18	0.784481
$177$	2.28686e19	1.78430
$178$	7.60091e18	0.565321
$179$	−1.47730e19	−1.04766	−0.523828	−	0.851824i	$-0.675497\pi$
$179$	−1.47730e19	−1.04766	−0.523828	+	0.851824i	$0.675497\pi$
$180$	−5.14942e18	−0.348291
$181$	−2.28833e18	−0.147656	−0.0738278	−	0.997271i	$-0.523522\pi$
$181$	−2.28833e18	−0.147656	−0.0738278	+	0.997271i	$0.523522\pi$
$182$	−9.47984e18	−0.583706
$183$	−2.72459e19	−1.60128
$184$	9.03255e18	0.506826
$185$	3.24378e19	1.73817
$186$	−2.61649e19	−1.33924
$187$	7.84016e18	0.383417
$188$	−1.14019e18	−0.0532886
$189$	−2.86567e18	−0.128027
$190$	6.29676e18	0.268975
$191$	−3.60406e19	−1.47234	−0.736171	−	0.676795i	$-0.763368\pi$
$191$	−3.60406e19	−1.47234	−0.736171	+	0.676795i	$0.763368\pi$
$192$	−3.88207e19	−1.51706
$193$	1.74235e19	0.651475	0.325738	−	0.945460i	$-0.394387\pi$
$193$	1.74235e19	0.651475	0.325738	+	0.945460i	$0.394387\pi$
$194$	−3.33796e19	−1.19444
$195$	1.87509e19	0.642285
$196$	−1.35697e19	−0.445035
$197$	−4.55647e19	−1.43108	−0.715542	−	0.698570i	$-0.753820\pi$
$197$	−4.55647e19	−1.43108	−0.715542	+	0.698570i	$0.753820\pi$
$198$	−4.29006e19	−1.29065
$199$	−1.46533e19	−0.422360	−0.211180	−	0.977447i	$-0.567731\pi$
$199$	−1.46533e19	−0.422360	−0.211180	+	0.977447i	$0.567731\pi$
$200$	5.87190e18	0.162190
$201$	−8.58391e19	−2.27258
$202$	1.57211e19	0.399020
$203$	1.14418e19	0.278470
$204$	−5.53232e18	−0.129137
$205$	−2.22408e19	−0.498016
$206$	7.18395e19	1.54345
$207$	−2.39335e19	−0.493468
$208$	1.26656e19	0.250661
$209$	−2.90452e19	−0.551862
$210$	−8.72961e19	−1.59269
$211$	9.98253e19	1.74920	0.874601	−	0.484844i	$-0.161124\pi$
$211$	9.98253e19	1.74920	0.874601	+	0.484844i	$0.161124\pi$
$212$	6.84423e18	0.115205
$213$	5.94200e19	0.960961
$214$	5.01652e19	0.779624
$215$	2.54727e19	0.380495
$216$	6.46959e18	0.0929009
$217$	1.26341e20	1.74436
$218$	1.49007e18	0.0197846
$219$	−1.25380e20	−1.60123
$220$	4.06284e19	0.499157
$221$	1.03636e19	0.122511
$222$	−1.90695e20	−2.16940
$223$	5.04871e19	0.552827	0.276413	−	0.961039i	$-0.410854\pi$
$223$	5.04871e19	0.552827	0.276413	+	0.961039i	$0.410854\pi$
$224$	9.58388e19	1.01026
$225$	−1.55588e19	−0.157915
$226$	1.23285e18	0.0120501
$227$	1.88001e20	1.76987	0.884933	−	0.465719i	$-0.154204\pi$
$227$	1.88001e20	1.76987	0.884933	+	0.465719i	$0.154204\pi$
$228$	2.04954e19	0.185871
$229$	−1.15165e20	−1.00628	−0.503139	−	0.864205i	$-0.667822\pi$
$229$	−1.15165e20	−1.00628	−0.503139	+	0.864205i	$0.667822\pi$
$230$	−4.09375e19	−0.344695
$231$	4.02672e20	3.26776
$232$	−2.58312e19	−0.202068
$233$	1.63494e20	1.23304	0.616520	−	0.787339i	$-0.288542\pi$
$233$	1.63494e20	1.23304	0.616520	+	0.787339i	$0.288542\pi$
$234$	−5.67085e19	−0.412395
$235$	1.96685e19	0.137941
$236$	6.54986e19	0.443078
$237$	−3.86567e20	−2.52269
$238$	−4.82483e19	−0.303793
$239$	8.49224e19	0.515989	0.257994	−	0.966146i	$-0.416938\pi$
$239$	8.49224e19	0.515989	0.257994	+	0.966146i	$0.416938\pi$
$240$	1.16632e20	0.683947
$241$	−3.14586e20	−1.78072	−0.890358	−	0.455262i	$-0.849546\pi$
$241$	−3.14586e20	−1.78072	−0.890358	+	0.455262i	$0.849546\pi$
$242$	1.91673e20	1.04744
$243$	2.71015e20	1.43001
$244$	−7.80357e19	−0.397630
$245$	2.34081e20	1.15200
$246$	1.30749e20	0.621571
$247$	−3.83936e19	−0.176333
$248$	−2.85229e20	−1.26577
$249$	−1.13933e20	−0.488604
$250$	−2.05164e20	−0.850377
$251$	2.44141e19	0.0978171	0.0489085	−	0.998803i	$-0.484426\pi$
$251$	2.44141e19	0.0978171	0.0489085	+	0.998803i	$0.484426\pi$
$252$	−1.46175e20	−0.566196
$253$	1.88833e20	0.707220
$254$	−1.82536e20	−0.661093
$255$	9.54339e19	0.334281
$256$	−2.70707e20	−0.917193
$257$	3.17604e20	1.04101	0.520504	−	0.853859i	$-0.325744\pi$
$257$	3.17604e20	1.04101	0.520504	+	0.853859i	$0.325744\pi$
$258$	−1.49749e20	−0.474894
$259$	9.20799e20	2.82564
$260$	5.37049e19	0.159493
$261$	6.84451e19	0.196742
$262$	5.64851e19	0.157171
$263$	3.61605e20	0.974115	0.487058	−	0.873370i	$-0.338070\pi$
$263$	3.61605e20	0.974115	0.487058	+	0.873370i	$0.338070\pi$
$264$	−9.09079e20	−2.37120
$265$	−1.18065e20	−0.298215
$266$	1.78744e20	0.437257
$267$	−4.26776e20	−1.01124
$268$	−2.45854e20	−0.564327
$269$	−6.47988e20	−1.44103	−0.720515	−	0.693440i	$-0.756094\pi$
$269$	−6.47988e20	−1.44103	−0.720515	+	0.693440i	$0.756094\pi$
$270$	−2.93217e19	−0.0631825
$271$	4.03978e20	0.843565	0.421783	−	0.906697i	$-0.361405\pi$
$271$	4.03978e20	0.843565	0.421783	+	0.906697i	$0.361405\pi$
$272$	6.44622e19	0.130458
$273$	5.32275e20	1.04413
$274$	4.05512e20	0.771124
$275$	1.22757e20	0.226318
$276$	−1.33248e20	−0.238196
$277$	−3.03761e20	−0.526568	−0.263284	−	0.964718i	$-0.584806\pi$
$277$	−3.03761e20	−0.526568	−0.263284	+	0.964718i	$0.584806\pi$
$278$	1.44628e20	0.243148
$279$	7.55772e20	1.23241
$280$	−9.51634e20	−1.50531
$281$	−3.46884e20	−0.532330	−0.266165	−	0.963928i	$-0.585757\pi$
$281$	−3.46884e20	−0.532330	−0.266165	+	0.963928i	$0.585757\pi$
$282$	−1.15627e20	−0.172164
$283$	−9.51233e20	−1.37437	−0.687183	−	0.726484i	$-0.741153\pi$
$283$	−9.51233e20	−1.37437	−0.687183	+	0.726484i	$0.741153\pi$
$284$	1.70186e20	0.238626
$285$	−3.53551e20	−0.481139
$286$	4.47424e20	0.591028
$287$	−6.31342e20	−0.809596
$288$	5.73308e20	0.713760
$289$	−7.74494e20	−0.936239
$290$	1.17073e20	0.137428
$291$	1.87420e21	2.13661
$292$	−3.59103e20	−0.397617
$293$	8.06640e20	0.867571	0.433786	−	0.901016i	$-0.357178\pi$
$293$	8.06640e20	0.867571	0.433786	+	0.901016i	$0.357178\pi$
$294$	−1.37611e21	−1.43781
$295$	−1.12987e21	−1.14694
$296$	−2.07881e21	−2.05039
$297$	1.35253e20	0.129633
$298$	1.31573e21	1.22554
$299$	2.49611e20	0.225974
$300$	−8.66225e19	−0.0762254
$301$	7.23085e20	0.618549
$302$	6.06158e20	0.504112
$303$	−8.82707e20	−0.713763
$304$	−2.38811e20	−0.187771
$305$	1.34613e21	1.02929
$306$	−2.88621e20	−0.214633
$307$	9.12901e20	0.660309	0.330155	−	0.943927i	$-0.392899\pi$
$307$	9.12901e20	0.660309	0.330155	+	0.943927i	$0.392899\pi$
$308$	1.15330e21	0.811451
$309$	−4.03365e21	−2.76090
$310$	1.29272e21	0.860857
$311$	−2.14387e21	−1.38911	−0.694554	−	0.719440i	$-0.744398\pi$
$311$	−2.14387e21	−1.38911	−0.694554	+	0.719440i	$0.744398\pi$
$312$	−1.20167e21	−0.757656
$313$	−5.26812e20	−0.323243	−0.161621	−	0.986853i	$-0.551672\pi$
$313$	−5.26812e20	−0.323243	−0.161621	+	0.986853i	$0.551672\pi$
$314$	−1.93169e21	−1.15355
$315$	2.52155e21	1.46564
$316$	−1.10718e21	−0.626435
$317$	1.87426e21	1.03235	0.516174	−	0.856484i	$-0.327356\pi$
$317$	1.87426e21	1.03235	0.516174	+	0.856484i	$0.327356\pi$
$318$	6.94078e20	0.372201
$319$	−5.40025e20	−0.281964
$320$	1.91801e21	0.975160
$321$	−2.81668e21	−1.39458
$322$	−1.16208e21	−0.560352
$323$	−1.95406e20	−0.0917735
$324$	7.29879e20	0.333902
$325$	1.62268e20	0.0723141
$326$	2.70602e21	1.17485
$327$	−8.36648e19	−0.0353905
$328$	1.42533e21	0.587472
$329$	5.58322e20	0.224243
$330$	4.12015e21	1.61267
$331$	−4.86203e21	−1.85473	−0.927363	−	0.374164i	$-0.877930\pi$
$331$	−4.86203e21	−1.85473	−0.927363	+	0.374164i	$0.877930\pi$
$332$	−3.26320e20	−0.121330
$333$	5.50823e21	1.99635
$334$	−3.53840e21	−1.25015
$335$	4.24104e21	1.46080
$336$	3.31079e21	1.11185
$337$	3.04443e21	0.996902	0.498451	−	0.866918i	$-0.333902\pi$
$337$	3.04443e21	0.996902	0.498451	+	0.866918i	$0.333902\pi$
$338$	−1.92111e21	−0.613422
$339$	−6.92223e19	−0.0215550
$340$	2.73335e20	0.0830087
$341$	−5.96297e21	−1.76624
$342$	1.06925e21	0.308927
$343$	1.32396e21	0.373142
$344$	−1.63245e21	−0.448841
$345$	2.29857e21	0.616587
$346$	8.13377e20	0.212885
$347$	5.67124e21	1.44836	0.724181	−	0.689610i	$-0.242218\pi$
$347$	5.67124e21	1.44836	0.724181	+	0.689610i	$0.242218\pi$
$348$	3.81063e20	0.0949671
$349$	3.77409e21	0.917901	0.458951	−	0.888462i	$-0.348225\pi$
$349$	3.77409e21	0.917901	0.458951	+	0.888462i	$0.348225\pi$
$350$	−7.55448e20	−0.179319
$351$	1.78784e20	0.0414209
$352$	−4.52335e21	−1.02293
$353$	−5.64887e21	−1.24703	−0.623515	−	0.781812i	$-0.714296\pi$
$353$	−5.64887e21	−1.24703	−0.623515	+	0.781812i	$0.714296\pi$
$354$	6.64226e21	1.43149
$355$	−2.93575e21	−0.617701
$356$	−1.22234e21	−0.251112
$357$	2.70905e21	0.543421
$358$	−4.29087e21	−0.840503
$359$	3.38475e21	0.647476	0.323738	−	0.946147i	$-0.395060\pi$
$359$	3.38475e21	0.647476	0.323738	+	0.946147i	$0.395060\pi$
$360$	−5.69268e21	−1.06352
$361$	−4.75647e21	−0.867908
$362$	−6.64650e20	−0.118460
$363$	−1.07621e22	−1.87366
$364$	1.52450e21	0.259278
$365$	6.19461e21	1.02926
$366$	−7.91365e21	−1.28466
$367$	3.61159e21	0.572844	0.286422	−	0.958104i	$-0.407534\pi$
$367$	3.61159e21	0.572844	0.286422	+	0.958104i	$0.407534\pi$
$368$	1.55260e21	0.240632
$369$	−3.77669e21	−0.571989
$370$	9.42164e21	1.39448
$371$	−3.35146e21	−0.484792
$372$	4.20771e21	0.594881
$373$	4.51893e21	0.624469	0.312235	−	0.950005i	$-0.398923\pi$
$373$	4.51893e21	0.624469	0.312235	+	0.950005i	$0.398923\pi$
$374$	2.27719e21	0.307604
$375$	1.15196e22	1.52114
$376$	−1.26048e21	−0.162719
$377$	−7.13836e20	−0.0900942
$378$	−8.32343e20	−0.102712
$379$	1.15862e22	1.39801	0.699003	−	0.715118i	$-0.253627\pi$
$379$	1.15862e22	1.39801	0.699003	+	0.715118i	$0.253627\pi$
$380$	−1.01261e21	−0.119477
$381$	1.02491e22	1.18256
$382$	−1.04681e22	−1.18122
$383$	9.25351e21	1.02121	0.510607	−	0.859814i	$-0.329421\pi$
$383$	9.25351e21	1.02121	0.510607	+	0.859814i	$0.329421\pi$
$384$	−2.31884e21	−0.250297
$385$	−1.98948e22	−2.10050
$386$	5.06070e21	0.522659
$387$	4.32550e21	0.437012
$388$	5.36794e21	0.530564
$389$	−2.83773e21	−0.274410	−0.137205	−	0.990543i	$-0.543812\pi$
$389$	−2.83773e21	−0.274410	−0.137205	+	0.990543i	$0.543812\pi$
$390$	5.44625e21	0.515286
$391$	1.27041e21	0.117609
$392$	−1.50013e22	−1.35893
$393$	−3.17153e21	−0.281146
$394$	−1.32344e22	−1.14812
$395$	1.90990e22	1.62157
$396$	6.89907e21	0.573299
$397$	1.46017e22	1.18763	0.593817	−	0.804600i	$-0.297620\pi$
$397$	1.46017e22	1.18763	0.593817	+	0.804600i	$0.297620\pi$
$398$	−4.25608e21	−0.338847
$399$	−1.00361e22	−0.782161
$400$	1.00932e21	0.0770048
$401$	−5.01141e21	−0.374311	−0.187155	−	0.982330i	$-0.559927\pi$
$401$	−5.01141e21	−0.374311	−0.187155	+	0.982330i	$0.559927\pi$
$402$	−2.49322e22	−1.82322
$403$	−7.88219e21	−0.564357
$404$	−2.52818e21	−0.177242
$405$	−1.25906e22	−0.864328
$406$	3.32331e21	0.223408
$407$	−4.34594e22	−2.86109
$408$	−6.11599e21	−0.394326
$409$	1.24159e22	0.784028	0.392014	−	0.919959i	$-0.371778\pi$
$409$	1.24159e22	0.784028	0.392014	+	0.919959i	$0.371778\pi$
$410$	−6.45991e21	−0.399543
$411$	−2.27687e22	−1.37938
$412$	−1.15529e22	−0.685589
$413$	−3.20731e22	−1.86451
$414$	−6.95156e21	−0.395895
$415$	5.62909e21	0.314072
$416$	−5.97921e21	−0.326852
$417$	−8.12057e21	−0.434941
$418$	−8.43625e21	−0.442742
$419$	2.18128e22	1.12174	0.560870	−	0.827904i	$-0.310467\pi$
$419$	2.18128e22	1.12174	0.560870	+	0.827904i	$0.310467\pi$
$420$	1.40385e22	0.707461
$421$	−1.26764e22	−0.626035	−0.313017	−	0.949747i	$-0.601340\pi$
$421$	−1.26764e22	−0.626035	−0.313017	+	0.949747i	$0.601340\pi$
$422$	2.89945e22	1.40333
$423$	3.33989e21	0.158430
$424$	7.56630e21	0.351782
$425$	8.25871e20	0.0376363
$426$	1.72587e22	0.770950
$427$	3.82122e22	1.67327
$428$	−8.06732e21	−0.346304
$429$	−2.51220e22	−1.05723
$430$	7.39862e21	0.305259
$431$	2.47174e22	0.999877	0.499938	−	0.866061i	$-0.333356\pi$
$431$	2.47174e22	0.999877	0.499938	+	0.866061i	$0.333356\pi$
$432$	1.11205e21	0.0441076
$433$	−7.76371e21	−0.301941	−0.150970	−	0.988538i	$-0.548240\pi$
$433$	−7.76371e21	−0.301941	−0.150970	+	0.988538i	$0.548240\pi$
$434$	3.66961e22	1.39945
$435$	−6.57343e21	−0.245829
$436$	−2.39626e20	−0.00878819
$437$	−4.70645e21	−0.169278
$438$	−3.64169e22	−1.28461
$439$	1.10474e22	0.382219	0.191109	−	0.981569i	$-0.438792\pi$
$439$	1.10474e22	0.382219	0.191109	+	0.981569i	$0.438792\pi$
$440$	4.49147e22	1.52420
$441$	3.97491e22	1.32312
$442$	3.01012e21	0.0982868
$443$	8.54955e21	0.273849	0.136925	−	0.990581i	$-0.456278\pi$
$443$	8.54955e21	0.273849	0.136925	+	0.990581i	$0.456278\pi$
$444$	3.06667e22	0.963632
$445$	2.10857e22	0.650021
$446$	1.46641e22	0.443516
$447$	−7.38755e22	−2.19223
$448$	5.44458e22	1.58526
$449$	−6.44687e22	−1.84185	−0.920927	−	0.389735i	$-0.872567\pi$
$449$	−6.44687e22	−1.84185	−0.920927	+	0.389735i	$0.872567\pi$
$450$	−4.51909e21	−0.126691
$451$	2.97977e22	0.819752
$452$	−1.98261e20	−0.00535255
$453$	−3.40346e22	−0.901750
$454$	5.46054e22	1.41991
$455$	−2.62980e22	−0.671160
$456$	2.26577e22	0.567564
$457$	−7.98467e22	−1.96322	−0.981611	−	0.190891i	$-0.938862\pi$
$457$	−7.98467e22	−1.96322	−0.981611	+	0.190891i	$0.938862\pi$
$458$	−3.34499e22	−0.807307
$459$	9.09935e20	0.0215577
$460$	6.58338e21	0.153111
$461$	8.44367e22	1.92785	0.963926	−	0.266171i	$-0.0857586\pi$
$461$	8.44367e22	1.92785	0.963926	+	0.266171i	$0.0857586\pi$
$462$	1.16957e23	2.62162
$463$	−3.57975e22	−0.787797	−0.393898	−	0.919154i	$-0.628874\pi$
$463$	−3.57975e22	−0.787797	−0.393898	+	0.919154i	$0.628874\pi$
$464$	−4.44011e21	−0.0959381
$465$	−7.25839e22	−1.53989
$466$	4.74874e22	0.989231
$467$	6.03629e22	1.23474	0.617371	−	0.786672i	$-0.288198\pi$
$467$	6.03629e22	1.23474	0.617371	+	0.786672i	$0.288198\pi$
$468$	9.11958e21	0.183183
$469$	1.20389e23	2.37474
$470$	5.71277e21	0.110666
$471$	1.08461e23	2.06346
$472$	7.24088e22	1.35296
$473$	−3.41278e22	−0.626308
$474$	−1.12279e23	−2.02388
$475$	−3.05958e21	−0.0541709
$476$	7.75905e21	0.134943
$477$	−2.00484e22	−0.342511
$478$	2.46660e22	0.413962
$479$	1.73508e22	0.286068	0.143034	−	0.989718i	$-0.454314\pi$
$479$	1.73508e22	0.286068	0.143034	+	0.989718i	$0.454314\pi$
$480$	−5.50602e22	−0.891841
$481$	−5.74471e22	−0.914187
$482$	−9.13724e22	−1.42861
$483$	6.52485e22	1.00235
$484$	−3.08240e22	−0.465268
$485$	−9.25982e22	−1.37340
$486$	7.87171e22	1.14726
$487$	−8.96174e22	−1.28350	−0.641751	−	0.766913i	$-0.721792\pi$
$487$	−8.96174e22	−1.28350	−0.641751	+	0.766913i	$0.721792\pi$
$488$	−8.62685e22	−1.21418
$489$	−1.51938e23	−2.10156
$490$	6.79895e22	0.924219
$491$	3.17435e22	0.424094	0.212047	−	0.977259i	$-0.431987\pi$
$491$	3.17435e22	0.424094	0.212047	+	0.977259i	$0.431987\pi$
$492$	−2.10265e22	−0.276098
$493$	−3.63311e21	−0.0468900
$494$	−1.11515e22	−0.141467
$495$	−1.19011e23	−1.48403
$496$	−4.90278e22	−0.600964
$497$	−8.33361e22	−1.00416
$498$	−3.30923e22	−0.391992
$499$	−2.39102e22	−0.278439	−0.139219	−	0.990262i	$-0.544459\pi$
$499$	−2.39102e22	−0.278439	−0.139219	+	0.990262i	$0.544459\pi$
$500$	3.29935e22	0.377731
$501$	1.98674e23	2.23625
$502$	7.09115e21	0.0784757
$503$	−1.62104e23	−1.76387	−0.881934	−	0.471372i	$-0.843759\pi$
$503$	−1.62104e23	−1.76387	−0.881934	+	0.471372i	$0.843759\pi$
$504$	−1.61596e23	−1.72891
$505$	4.36118e22	0.458804
$506$	5.48472e22	0.567381
$507$	1.07866e23	1.09728
$508$	2.93546e22	0.293653
$509$	−1.39759e23	−1.37493	−0.687463	−	0.726220i	$-0.741275\pi$
$509$	−1.39759e23	−1.37493	−0.687463	+	0.726220i	$0.741275\pi$
$510$	2.77190e22	0.268183
$511$	1.75844e23	1.67321
$512$	−9.72645e22	−0.910248
$513$	−3.37101e21	−0.0310286
$514$	9.22488e22	0.835169
$515$	1.99290e23	1.77470
$516$	2.40819e22	0.210945
$517$	−2.63514e22	−0.227056
$518$	2.67449e23	2.26693
$519$	−4.56696e22	−0.380806
$520$	5.93708e22	0.487017
$521$	−9.33888e22	−0.753658	−0.376829	−	0.926283i	$-0.622986\pi$
$521$	−9.33888e22	−0.753658	−0.376829	+	0.926283i	$0.622986\pi$
$522$	1.98801e22	0.157840
$523$	6.42255e22	0.501699	0.250849	−	0.968026i	$-0.419290\pi$
$523$	6.42255e22	0.501699	0.250849	+	0.968026i	$0.419290\pi$
$524$	−9.08365e21	−0.0698143
$525$	4.24169e22	0.320764
$526$	1.05029e23	0.781503
$527$	−4.01169e22	−0.293722
$528$	−1.56261e23	−1.12580
$529$	−1.10452e23	−0.783068
$530$	−3.42922e22	−0.239249
$531$	−1.91862e23	−1.31730
$532$	−2.87447e22	−0.194227
$533$	3.93883e22	0.261931
$534$	−1.23958e23	−0.811288
$535$	1.39163e23	0.896432
$536$	−2.71791e23	−1.72320
$537$	2.40924e23	1.50348
$538$	−1.88210e23	−1.15609
$539$	−3.13616e23	−1.89624
$540$	4.71536e21	0.0280652
$541$	5.39921e22	0.316340	0.158170	−	0.987412i	$-0.449441\pi$
$541$	5.39921e22	0.316340	0.158170	+	0.987412i	$0.449441\pi$
$542$	1.17337e23	0.676767
$543$	3.73188e22	0.211899
$544$	−3.04316e22	−0.170112
$545$	4.13361e21	0.0227489
$546$	1.54601e23	0.837672
$547$	−1.20758e23	−0.644203	−0.322102	−	0.946705i	$-0.604389\pi$
$547$	−1.20758e23	−0.644203	−0.322102	+	0.946705i	$0.604389\pi$
$548$	−6.52125e22	−0.342528
$549$	2.28586e23	1.18218
$550$	3.56552e22	0.181568
$551$	1.34595e22	0.0674900
$552$	−1.47306e23	−0.727342
$553$	5.42157e23	2.63610
$554$	−8.82283e22	−0.422449
$555$	−5.29007e23	−2.49443
$556$	−2.32583e22	−0.108005
$557$	2.77894e23	1.27089	0.635447	−	0.772144i	$-0.280816\pi$
$557$	2.77894e23	1.27089	0.635447	+	0.772144i	$0.280816\pi$
$558$	2.19516e23	0.988725
$559$	−4.51120e22	−0.200121
$560$	−1.63576e23	−0.714695
$561$	−1.27860e23	−0.550238
$562$	−1.00753e23	−0.427072
$563$	−1.63029e22	−0.0680679	−0.0340339	−	0.999421i	$-0.510835\pi$
$563$	−1.63029e22	−0.0680679	−0.0340339	+	0.999421i	$0.510835\pi$
$564$	1.85946e22	0.0764740
$565$	3.42005e21	0.0138555
$566$	−2.76288e23	−1.10261
$567$	−3.57405e23	−1.40509
$568$	1.88141e23	0.728656
$569$	7.08943e22	0.270493	0.135247	−	0.990812i	$-0.456817\pi$
$569$	7.08943e22	0.270493	0.135247	+	0.990812i	$0.456817\pi$
$570$	−1.02690e23	−0.386004
$571$	−1.66450e22	−0.0616420	−0.0308210	−	0.999525i	$-0.509812\pi$
$571$	−1.66450e22	−0.0616420	−0.0308210	+	0.999525i	$0.509812\pi$
$572$	−7.19526e22	−0.262531
$573$	5.87764e23	2.11295
$574$	−1.83375e23	−0.649515
$575$	1.98915e22	0.0694208
$576$	3.25695e23	1.12001
$577$	1.94899e23	0.660413	0.330206	−	0.943909i	$-0.392882\pi$
$577$	1.94899e23	0.660413	0.330206	+	0.943909i	$0.392882\pi$
$578$	−2.24954e23	−0.751116
$579$	−2.84149e23	−0.934927
$580$	−1.88271e22	−0.0610444
$581$	1.59791e23	0.510570
$582$	5.44366e23	1.71414
$583$	1.58180e23	0.490873
$584$	−3.96989e23	−1.21414
$585$	−1.57315e23	−0.474182
$586$	2.34291e23	0.696026
$587$	−3.29824e23	−0.965736	−0.482868	−	0.875693i	$-0.660405\pi$
$587$	−3.29824e23	−0.965736	−0.482868	+	0.875693i	$0.660405\pi$
$588$	2.21300e23	0.638667
$589$	1.48620e23	0.422763
$590$	−3.28173e23	−0.920155
$591$	7.43085e23	2.05374
$592$	−3.57325e23	−0.973485
$593$	3.52384e23	0.946350	0.473175	−	0.880969i	$-0.343108\pi$
$593$	3.52384e23	0.946350	0.473175	+	0.880969i	$0.343108\pi$
$594$	3.92845e22	0.104001
$595$	−1.33845e23	−0.349309
$596$	−2.11589e23	−0.544376
$597$	2.38971e23	0.606126
$598$	7.25001e22	0.181292
$599$	1.58720e23	0.391293	0.195647	−	0.980674i	$-0.437319\pi$
$599$	1.58720e23	0.391293	0.195647	+	0.980674i	$0.437319\pi$
$600$	−9.57612e22	−0.232758
$601$	4.95216e23	1.18676	0.593378	−	0.804924i	$-0.297794\pi$
$601$	4.95216e23	1.18676	0.593378	+	0.804924i	$0.297794\pi$
$602$	2.10022e23	0.496243
$603$	7.20166e23	1.67778
$604$	−9.74794e22	−0.223923
$605$	5.31721e23	1.20438
$606$	−2.56385e23	−0.572631
$607$	−6.50130e23	−1.43185	−0.715923	−	0.698180i	$-0.753994\pi$
$607$	−6.50130e23	−1.43185	−0.715923	+	0.698180i	$0.753994\pi$
$608$	1.12739e23	0.244846
$609$	−1.86597e23	−0.399631
$610$	3.90988e23	0.825772
$611$	−3.48328e22	−0.0725500
$612$	4.64147e22	0.0953385
$613$	−7.90280e23	−1.60091	−0.800455	−	0.599392i	$-0.795409\pi$
$613$	−7.90280e23	−1.60091	−0.800455	+	0.599392i	$0.795409\pi$
$614$	2.65155e23	0.529746
$615$	3.62711e23	0.714698
$616$	1.27498e24	2.47780
$617$	−6.59508e21	−0.0126414	−0.00632072	−	0.999980i	$-0.502012\pi$
$617$	−6.59508e21	−0.0126414	−0.00632072	+	0.999980i	$0.502012\pi$
$618$	−1.17159e24	−2.21499
$619$	5.53370e23	1.03192	0.515959	−	0.856613i	$-0.327436\pi$
$619$	5.53370e23	1.03192	0.515959	+	0.856613i	$0.327436\pi$
$620$	−2.07889e23	−0.382387
$621$	2.19162e22	0.0397636
$622$	−6.22694e23	−1.11444
$623$	5.98551e23	1.05670
$624$	−2.06555e23	−0.359721
$625$	−4.82388e23	−0.828736
$626$	−1.53014e23	−0.259328
$627$	4.73679e23	0.791973
$628$	3.10645e23	0.512398
$629$	−2.92381e23	−0.475793
$630$	7.32390e23	1.17584
$631$	7.01636e23	1.11138	0.555690	−	0.831390i	$-0.312454\pi$
$631$	7.01636e23	1.11138	0.555690	+	0.831390i	$0.312454\pi$
$632$	−1.22398e24	−1.91285
$633$	−1.62799e24	−2.51027
$634$	5.44384e23	0.828222
$635$	−5.06374e23	−0.760141
$636$	−1.11618e23	−0.165329
$637$	−4.14556e23	−0.605895
$638$	−1.56852e23	−0.226211
$639$	−4.98517e23	−0.709452
$640$	1.14566e23	0.160890
$641$	3.82449e23	0.530005	0.265003	−	0.964248i	$-0.414627\pi$
$641$	3.82449e23	0.530005	0.265003	+	0.964248i	$0.414627\pi$
$642$	−8.18113e23	−1.11883
$643$	8.20181e22	0.110692	0.0553460	−	0.998467i	$-0.482374\pi$
$643$	8.20181e22	0.110692	0.0553460	+	0.998467i	$0.482374\pi$
$644$	1.86880e23	0.248904
$645$	−4.15419e23	−0.546045
$646$	−5.67564e22	−0.0736272
$647$	−1.56833e23	−0.200794	−0.100397	−	0.994947i	$-0.532011\pi$
$647$	−1.56833e23	−0.200794	−0.100397	+	0.994947i	$0.532011\pi$
$648$	8.06882e23	1.01958
$649$	1.51377e24	1.88790
$650$	4.71311e22	0.0580155
$651$	−2.06041e24	−2.50332
$652$	−4.35170e23	−0.521860
$653$	−7.65071e23	−0.905607	−0.452804	−	0.891610i	$-0.649576\pi$
$653$	−7.65071e23	−0.905607	−0.452804	+	0.891610i	$0.649576\pi$
$654$	−2.43007e22	−0.0283928
$655$	1.56695e23	0.180719
$656$	2.44998e23	0.278921
$657$	1.05190e24	1.18214
$658$	1.62166e23	0.179904
$659$	1.07002e24	1.17183	0.585916	−	0.810372i	$-0.300735\pi$
$659$	1.07002e24	1.17183	0.585916	+	0.810372i	$0.300735\pi$
$660$	−6.62583e23	−0.716336
$661$	−1.16004e23	−0.123811	−0.0619055	−	0.998082i	$-0.519718\pi$
$661$	−1.16004e23	−0.123811	−0.0619055	+	0.998082i	$0.519718\pi$
$662$	−1.41219e24	−1.48799
$663$	−1.69013e23	−0.175814
$664$	−3.60747e23	−0.370487
$665$	4.95853e23	0.502769
$666$	1.59988e24	1.60161
$667$	−8.75050e22	−0.0864895
$668$	5.69028e23	0.555307
$669$	−8.23362e23	−0.793358
$670$	1.23182e24	1.17196
$671$	−1.80352e24	−1.69426
$672$	−1.56297e24	−1.44982
$673$	5.31775e23	0.487080	0.243540	−	0.969891i	$-0.421691\pi$
$673$	5.31775e23	0.487080	0.243540	+	0.969891i	$0.421691\pi$
$674$	8.84264e23	0.799784
$675$	1.42473e22	0.0127248
$676$	3.08943e23	0.272478
$677$	1.20523e24	1.04970	0.524851	−	0.851194i	$-0.324121\pi$
$677$	1.20523e24	1.04970	0.524851	+	0.851194i	$0.324121\pi$
$678$	−2.01058e22	−0.0172929
$679$	−2.62855e24	−2.23266
$680$	3.02172e23	0.253471
$681$	−3.06599e24	−2.53992
$682$	−1.73196e24	−1.41700
$683$	6.07830e21	0.00491141	0.00245570	−	0.999997i	$-0.499218\pi$
$683$	6.07830e21	0.00491141	0.00245570	+	0.999997i	$0.499218\pi$
$684$	−1.71951e23	−0.137223
$685$	1.12493e24	0.886658
$686$	3.84547e23	0.299360
$687$	1.87815e24	1.44410
$688$	−2.80600e23	−0.213101
$689$	2.09092e23	0.156846
$690$	6.67625e23	0.494669
$691$	6.63614e23	0.485682	0.242841	−	0.970066i	$-0.421921\pi$
$691$	6.63614e23	0.485682	0.242841	+	0.970066i	$0.421921\pi$
$692$	−1.30803e23	−0.0945620
$693$	−3.37831e24	−2.41250
$694$	1.64723e24	1.16198
$695$	4.01212e23	0.279578
$696$	4.21265e23	0.289986
$697$	2.00469e23	0.136323
$698$	1.09619e24	0.736405
$699$	−2.66633e24	−1.76953
$700$	1.21487e23	0.0796522
$701$	3.07649e24	1.99275	0.996374	−	0.0850821i	$-0.0271153\pi$
$701$	3.07649e24	1.99275	0.996374	+	0.0850821i	$0.0271153\pi$
$702$	5.19284e22	0.0332307
$703$	1.08317e24	0.684822
$704$	−2.56970e24	−1.60515
$705$	−3.20761e23	−0.197958
$706$	−1.64073e24	−1.00045
$707$	1.23799e24	0.745851
$708$	−1.06818e24	−0.635858
$709$	8.81025e22	0.0518197	0.0259099	−	0.999664i	$-0.491752\pi$
$709$	8.81025e22	0.0518197	0.0259099	+	0.999664i	$0.491752\pi$
$710$	−8.52697e23	−0.495563
$711$	3.24319e24	1.86243
$712$	−1.35130e24	−0.766781
$713$	−9.66232e23	−0.541777
$714$	7.86850e23	0.435971
$715$	1.24120e24	0.679579
$716$	6.90036e23	0.373346
$717$	−1.38495e24	−0.740492
$718$	9.83110e23	0.519451
$719$	8.14271e22	0.0425180	0.0212590	−	0.999774i	$-0.493233\pi$
$719$	8.14271e22	0.0425180	0.0212590	+	0.999774i	$0.493233\pi$
$720$	−9.78511e23	−0.504940
$721$	5.65717e24	2.88502
$722$	−1.38153e24	−0.696296
$723$	5.13038e24	2.55549
$724$	1.06886e23	0.0526190
$725$	−5.68855e22	−0.0276776
$726$	−3.12588e24	−1.50318
$727$	2.40276e24	1.14200	0.571002	−	0.820949i	$-0.306555\pi$
$727$	2.40276e24	1.14200	0.571002	+	0.820949i	$0.306555\pi$
$728$	1.68534e24	0.791717
$729$	−2.40186e24	−1.11523
$730$	1.79924e24	0.825744
$731$	−2.29600e23	−0.104154
$732$	1.27263e24	0.570636
$733$	1.39975e24	0.620393	0.310196	−	0.950672i	$-0.399605\pi$
$733$	1.39975e24	0.620393	0.310196	+	0.950672i	$0.399605\pi$
$734$	1.04899e24	0.459576
$735$	−3.81748e24	−1.65323
$736$	−7.32958e23	−0.313774
$737$	−5.68204e24	−2.40453
$738$	−1.09695e24	−0.458889
$739$	−2.21888e24	−0.917605	−0.458803	−	0.888538i	$-0.651722\pi$
$739$	−2.21888e24	−0.917605	−0.458803	+	0.888538i	$0.651722\pi$
$740$	−1.51514e24	−0.619418
$741$	6.26136e23	0.253055
$742$	−9.73440e23	−0.388934
$743$	3.17156e22	0.0125276	0.00626379	−	0.999980i	$-0.498006\pi$
$743$	3.17156e22	0.0125276	0.00626379	+	0.999980i	$0.498006\pi$
$744$	4.65162e24	1.81650
$745$	3.64995e24	1.40916
$746$	1.31254e24	0.500993
$747$	9.55870e23	0.360723
$748$	−3.66207e23	−0.136635
$749$	3.95037e24	1.45728
$750$	3.34589e24	1.22037
$751$	−5.00938e23	−0.180653	−0.0903263	−	0.995912i	$-0.528791\pi$
$751$	−5.00938e23	−0.180653	−0.0903263	+	0.995912i	$0.528791\pi$
$752$	−2.16663e23	−0.0772560
$753$	−3.98155e23	−0.140377
$754$	−2.07336e23	−0.0722799
$755$	1.68154e24	0.579640
$756$	1.33853e23	0.0456240
$757$	4.37145e24	1.47336	0.736682	−	0.676239i	$-0.236391\pi$
$757$	4.37145e24	1.47336	0.736682	+	0.676239i	$0.236391\pi$
$758$	3.36526e24	1.12158
$759$	−3.07956e24	−1.01493
$760$	−1.11945e24	−0.364827
$761$	−1.29118e24	−0.416117	−0.208059	−	0.978116i	$-0.566714\pi$
$761$	−1.29118e24	−0.416117	−0.208059	+	0.978116i	$0.566714\pi$
$762$	2.97687e24	0.948729
$763$	1.17339e23	0.0369815
$764$	1.68343e24	0.524688
$765$	−8.00664e23	−0.246790
$766$	2.68771e24	0.819290
$767$	2.00099e24	0.603231
$768$	4.41480e24	1.31626
$769$	−2.51351e24	−0.741150	−0.370575	−	0.928803i	$-0.620839\pi$
$769$	−2.51351e24	−0.741150	−0.370575	+	0.928803i	$0.620839\pi$
$770$	−5.77849e24	−1.68517
$771$	−5.17960e24	−1.49394
$772$	−8.13837e23	−0.232162
$773$	−4.91888e24	−1.38784	−0.693921	−	0.720051i	$-0.744118\pi$
$773$	−4.91888e24	−1.38784	−0.693921	+	0.720051i	$0.744118\pi$
$774$	1.25635e24	0.350601
$775$	−6.28131e23	−0.173375
$776$	5.93426e24	1.62010
$777$	−1.50167e25	−4.05506
$778$	−8.24226e23	−0.220151
$779$	−7.42673e23	−0.196214
$780$	−8.75839e23	−0.228887
$781$	3.93325e24	1.01676
$782$	3.68994e23	0.0943543
$783$	−6.26757e22	−0.0158535
$784$	−2.57857e24	−0.645197
$785$	−5.35871e24	−1.32638
$786$	−9.21180e23	−0.225555
$787$	−1.55789e24	−0.377356	−0.188678	−	0.982039i	$-0.560420\pi$
$787$	−1.55789e24	−0.377356	−0.188678	+	0.982039i	$0.560420\pi$
$788$	2.12829e24	0.509985
$789$	−5.89718e24	−1.39795
$790$	5.54737e24	1.30094
$791$	9.70838e22	0.0225241
$792$	7.62692e24	1.75059
$793$	−2.38399e24	−0.541356
$794$	4.24109e24	0.952804
$795$	1.92544e24	0.427966
$796$	6.84442e23	0.150513
$797$	−9.77945e23	−0.212774	−0.106387	−	0.994325i	$-0.533928\pi$
$797$	−9.77945e23	−0.212774	−0.106387	+	0.994325i	$0.533928\pi$
$798$	−2.91502e24	−0.627505
$799$	−1.77284e23	−0.0377590
$800$	−4.76483e23	−0.100411
$801$	3.58054e24	0.746572
$802$	−1.45558e24	−0.300298
$803$	−8.29940e24	−1.69420
$804$	4.00947e24	0.809862
$805$	−3.22372e24	−0.644307
$806$	−2.28940e24	−0.452767
$807$	1.05676e25	2.06801
$808$	−2.79491e24	−0.541216
$809$	−8.08604e24	−1.54944	−0.774718	−	0.632307i	$-0.782108\pi$
$809$	−8.08604e24	−1.54944	−0.774718	+	0.632307i	$0.782108\pi$
$810$	−3.65697e24	−0.693424
$811$	−3.95652e24	−0.742398	−0.371199	−	0.928553i	$-0.621053\pi$
$811$	−3.95652e24	−0.742398	−0.371199	+	0.928553i	$0.621053\pi$
$812$	−5.34438e23	−0.0992365
$813$	−6.58822e24	−1.21059
$814$	−1.26229e25	−2.29536
$815$	7.50678e24	1.35087
$816$	−1.05127e24	−0.187219
$817$	8.50594e23	0.149911
$818$	3.60625e24	0.629002
$819$	−4.46564e24	−0.770851
$820$	1.03885e24	0.177474
$821$	−1.05441e24	−0.178275	−0.0891376	−	0.996019i	$-0.528411\pi$
$821$	−1.05441e24	−0.178275	−0.0891376	+	0.996019i	$0.528411\pi$
$822$	−6.61325e24	−1.10663
$823$	8.06812e24	1.33621	0.668104	−	0.744068i	$-0.267106\pi$
$823$	8.06812e24	1.33621	0.668104	+	0.744068i	$0.267106\pi$
$824$	−1.27717e25	−2.09348
$825$	−2.00197e24	−0.324788
$826$	−9.31573e24	−1.49584
$827$	9.86275e24	1.56748	0.783739	−	0.621091i	$-0.213310\pi$
$827$	9.86275e24	1.56748	0.783739	+	0.621091i	$0.213310\pi$
$828$	1.11792e24	0.175854
$829$	5.68230e24	0.884729	0.442365	−	0.896835i	$-0.354140\pi$
$829$	5.68230e24	0.884729	0.442365	+	0.896835i	$0.354140\pi$
$830$	1.63499e24	0.251971
$831$	4.95385e24	0.755673
$832$	−3.39678e24	−0.512884
$833$	−2.10991e24	−0.315341
$834$	−2.35864e24	−0.348940
$835$	−9.81586e24	−1.43745
$836$	1.35668e24	0.196663
$837$	−6.92067e23	−0.0993074
$838$	6.33559e24	0.899938
$839$	1.01091e25	1.42146	0.710731	−	0.703464i	$-0.248364\pi$
$839$	1.01091e25	1.42146	0.710731	+	0.703464i	$0.248364\pi$
$840$	1.55196e25	2.16026
$841$	2.50246e23	0.0344828
$842$	−3.68190e24	−0.502249
$843$	5.65711e24	0.763942
$844$	−4.66276e24	−0.623350
$845$	−5.32934e24	−0.705328
$846$	9.70079e23	0.127104
$847$	1.50938e25	1.95789
$848$	1.30057e24	0.167020
$849$	1.55131e25	1.97234
$850$	2.39877e23	0.0301944
$851$	−7.04211e24	−0.877610
$852$	−2.77546e24	−0.342451
$853$	3.16445e24	0.386573	0.193286	−	0.981142i	$-0.438085\pi$
$853$	3.16445e24	0.386573	0.193286	+	0.981142i	$0.438085\pi$
$854$	1.10988e25	1.34241
$855$	2.96620e24	0.355212
$856$	−8.91843e24	−1.05745
$857$	8.79400e24	1.03240	0.516202	−	0.856467i	$-0.327346\pi$
$857$	8.79400e24	1.03240	0.516202	+	0.856467i	$0.327346\pi$
$858$	−7.29676e24	−0.848180
$859$	7.37487e24	0.848814	0.424407	−	0.905472i	$-0.360483\pi$
$859$	7.37487e24	0.848814	0.424407	+	0.905472i	$0.360483\pi$
$860$	−1.18981e24	−0.135594
$861$	1.02962e25	1.16185
$862$	7.17925e24	0.802171
$863$	1.11489e25	1.23351	0.616753	−	0.787157i	$-0.288448\pi$
$863$	1.11489e25	1.23351	0.616753	+	0.787157i	$0.288448\pi$
$864$	−5.24983e23	−0.0575147
$865$	2.25639e24	0.244780
$866$	−2.25499e24	−0.242238
$867$	1.26307e25	1.34359
$868$	−5.90128e24	−0.621625
$869$	−2.55884e25	−2.66917
$870$	−1.90927e24	−0.197221
$871$	−7.51084e24	−0.768306
$872$	−2.64907e23	−0.0268351
$873$	−1.57240e25	−1.57740
$874$	−1.36700e24	−0.135807
$875$	−1.61561e25	−1.58953
$876$	5.85639e24	0.570617
$877$	−8.85088e24	−0.854063	−0.427032	−	0.904237i	$-0.640441\pi$
$877$	−8.85088e24	−0.854063	−0.427032	+	0.904237i	$0.640441\pi$
$878$	3.20875e24	0.306642
$879$	−1.31550e25	−1.24504
$880$	7.72036e24	0.723660
$881$	−1.26442e25	−1.17380	−0.586902	−	0.809658i	$-0.699653\pi$
$881$	−1.26442e25	−1.17380	−0.586902	+	0.809658i	$0.699653\pi$
$882$	1.15452e25	1.06150
$883$	1.49551e25	1.36183	0.680916	−	0.732361i	$-0.261582\pi$
$883$	1.49551e25	1.36183	0.680916	+	0.732361i	$0.261582\pi$
$884$	−4.84074e23	−0.0436583
$885$	1.84263e25	1.64596
$886$	2.48324e24	0.219701
$887$	−4.17701e24	−0.366029	−0.183014	−	0.983110i	$-0.558585\pi$
$887$	−4.17701e24	−0.366029	−0.183014	+	0.983110i	$0.558585\pi$
$888$	3.39020e25	2.94249
$889$	−1.43742e25	−1.23572
$890$	6.12439e24	0.521492
$891$	1.68686e25	1.42272
$892$	−2.35821e24	−0.197007
$893$	6.56777e23	0.0543476
$894$	−2.14573e25	−1.75876
$895$	−1.19033e25	−0.966432
$896$	3.25216e24	0.261549
$897$	−4.07074e24	−0.324293
$898$	−1.87251e25	−1.47766
$899$	2.76323e24	0.216003
$900$	7.26738e23	0.0562752
$901$	1.06418e24	0.0816312
$902$	8.65483e24	0.657663
$903$	−1.17923e25	−0.887675
$904$	−2.19178e23	−0.0163443
$905$	−1.84381e24	−0.136208
$906$	−9.88545e24	−0.723447
$907$	−1.01823e25	−0.738213	−0.369107	−	0.929387i	$-0.620336\pi$
$907$	−1.01823e25	−0.738213	−0.369107	+	0.929387i	$0.620336\pi$
$908$	−8.78137e24	−0.630714
$909$	7.40567e24	0.526952
$910$	−7.63833e24	−0.538452
$911$	1.62257e25	1.13317	0.566587	−	0.824002i	$-0.308263\pi$
$911$	1.62257e25	1.13317	0.566587	+	0.824002i	$0.308263\pi$
$912$	3.89462e24	0.269469
$913$	−7.54173e24	−0.516974
$914$	−2.31917e25	−1.57503
$915$	−2.19532e25	−1.47713
$916$	5.37925e24	0.358600
$917$	4.44805e24	0.293785
$918$	2.64293e23	0.0172951
$919$	3.00771e25	1.95009	0.975043	−	0.222016i	$-0.0712638\pi$
$919$	3.00771e25	1.95009	0.975043	+	0.222016i	$0.0712638\pi$
$920$	7.27793e24	0.467532
$921$	−1.48879e25	−0.947605
$922$	2.45249e25	1.54666
$923$	5.19920e24	0.324879
$924$	−1.88085e25	−1.16451
$925$	−4.57795e24	−0.280845
$926$	−1.03975e25	−0.632026
$927$	3.38412e25	2.03830
$928$	2.09611e24	0.125100
$929$	1.38750e25	0.820537	0.410268	−	0.911965i	$-0.365435\pi$
$929$	1.38750e25	0.820537	0.410268	+	0.911965i	$0.365435\pi$
$930$	−2.10822e25	−1.23541
$931$	7.81651e24	0.453879
$932$	−7.63669e24	−0.439410
$933$	3.49631e25	1.99350
$934$	1.75326e25	0.990597
$935$	6.31716e24	0.353691
$936$	1.00817e25	0.559357
$937$	−3.26165e24	−0.179329	−0.0896647	−	0.995972i	$-0.528580\pi$
$937$	−3.26165e24	−0.179329	−0.0896647	+	0.995972i	$0.528580\pi$
$938$	3.49672e25	1.90518
$939$	8.59144e24	0.463883
$940$	−9.18699e23	−0.0491571
$941$	−1.04796e25	−0.555689	−0.277844	−	0.960626i	$-0.589620\pi$
$941$	−1.04796e25	−0.555689	−0.277844	+	0.960626i	$0.589620\pi$
$942$	3.15028e25	1.65545
$943$	4.82839e24	0.251451
$944$	1.24463e25	0.642359
$945$	−2.30900e24	−0.118101
$946$	−9.91250e24	−0.502468
$947$	−1.66960e25	−0.838759	−0.419379	−	0.907811i	$-0.637752\pi$
$947$	−1.66960e25	−0.838759	−0.419379	+	0.907811i	$0.637752\pi$
$948$	1.80562e25	0.898992
$949$	−1.09706e25	−0.541338
$950$	−8.88663e23	−0.0434597
$951$	−3.05661e25	−1.48152
$952$	8.57763e24	0.412053
$953$	−1.42892e25	−0.680329	−0.340165	−	0.940366i	$-0.610483\pi$
$953$	−1.42892e25	−0.680329	−0.340165	+	0.940366i	$0.610483\pi$
$954$	−5.82312e24	−0.274786
$955$	−2.90395e25	−1.35819
$956$	−3.96666e24	−0.183879
$957$	8.80693e24	0.404644
$958$	5.03960e24	0.229503
$959$	3.19330e25	1.44139
$960$	−3.12796e25	−1.39944
$961$	7.96150e24	0.353058
$962$	−1.66857e25	−0.733424
$963$	2.36312e25	1.02958
$964$	1.46941e25	0.634581
$965$	1.40389e25	0.600967
$966$	1.89516e25	0.804156
$967$	−7.78924e24	−0.327620	−0.163810	−	0.986492i	$-0.552378\pi$
$967$	−7.78924e24	−0.327620	−0.163810	+	0.986492i	$0.552378\pi$
$968$	−3.40759e25	−1.42071
$969$	3.18676e24	0.131704
$970$	−2.68954e25	−1.10184
$971$	1.23917e24	0.0503231	0.0251615	−	0.999683i	$-0.491990\pi$
$971$	1.23917e24	0.0503231	0.0251615	+	0.999683i	$0.491990\pi$
$972$	−1.26589e25	−0.509604
$973$	1.13890e25	0.454494
$974$	−2.60296e25	−1.02971
$975$	−2.64632e24	−0.103777
$976$	−1.48286e25	−0.576471
$977$	−4.33149e24	−0.166930	−0.0834649	−	0.996511i	$-0.526599\pi$
$977$	−4.33149e24	−0.166930	−0.0834649	+	0.996511i	$0.526599\pi$
$978$	−4.41308e25	−1.68602
$979$	−2.82501e25	−1.06996
$980$	−1.09337e25	−0.410532
$981$	7.01925e23	0.0261279
$982$	9.21999e24	0.340238
$983$	−2.06463e25	−0.755330	−0.377665	−	0.925942i	$-0.623273\pi$
$983$	−2.06463e25	−0.755330	−0.377665	+	0.925942i	$0.623273\pi$
$984$	−2.32448e25	−0.843076
$985$	−3.67135e25	−1.32013
$986$	−1.05525e24	−0.0376184
$987$	−9.10532e24	−0.321810
$988$	1.79333e24	0.0628386
$989$	−5.53002e24	−0.192114
$990$	−3.45669e25	−1.19059
$991$	−3.79578e25	−1.29621	−0.648105	−	0.761551i	$-0.724438\pi$
$991$	−3.79578e25	−1.29621	−0.648105	+	0.761551i	$0.724438\pi$
$992$	2.31453e25	0.783634
$993$	7.92918e25	2.66170
$994$	−2.42052e25	−0.805609
$995$	−1.18068e25	−0.389615
$996$	5.32174e24	0.174120
$997$	1.35680e25	0.440155	0.220078	−	0.975482i	$-0.429369\pi$
$997$	1.35680e25	0.440155	0.220078	+	0.975482i	$0.429369\pi$
$998$	−6.94480e24	−0.223383
$999$	−5.04393e24	−0.160865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.b.1.14	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.b.1.14	✓	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)

\(f(q)\)	\(=\)	\(q+290.453 q^{2} -16308.4 q^{3} -46709.2 q^{4} +805745. q^{5} -4.73681e6 q^{6} +2.28724e7 q^{7} -5.16370e7 q^{8} +1.36823e8 q^{9} +O(q^{10})\)	\(q+290.453 q^{2} -16308.4 q^{3} -46709.2 q^{4} +805745. q^{5} -4.73681e6 q^{6} +2.28724e7 q^{7} -5.16370e7 q^{8} +1.36823e8 q^{9} +2.34031e8 q^{10} -1.07952e9 q^{11} +7.61751e8 q^{12} -1.42697e9 q^{13} +6.64334e9 q^{14} -1.31404e10 q^{15} -8.87585e9 q^{16} -7.26264e9 q^{17} +3.97405e10 q^{18} +2.69057e10 q^{19} -3.76357e10 q^{20} -3.73011e11 q^{21} -3.13549e11 q^{22} -1.74924e11 q^{23} +8.42116e11 q^{24} -1.13715e11 q^{25} -4.14467e11 q^{26} -1.25290e11 q^{27} -1.06835e12 q^{28} +5.00246e11 q^{29} -3.81666e12 q^{30} +5.52373e12 q^{31} +4.19015e12 q^{32} +1.76052e13 q^{33} -2.10946e12 q^{34} +1.84293e13 q^{35} -6.39088e12 q^{36} +4.02581e13 q^{37} +7.81483e12 q^{38} +2.32715e13 q^{39} -4.16063e13 q^{40} -2.76028e13 q^{41} -1.08342e14 q^{42} +3.16139e13 q^{43} +5.04234e13 q^{44} +1.10244e14 q^{45} -5.08071e13 q^{46} +2.44103e13 q^{47} +1.44751e14 q^{48} +2.90515e14 q^{49} -3.30288e13 q^{50} +1.18442e14 q^{51} +6.66525e13 q^{52} -1.46529e14 q^{53} -3.63908e13 q^{54} -8.69816e14 q^{55} -1.18106e15 q^{56} -4.38788e14 q^{57} +1.45298e14 q^{58} -1.40226e15 q^{59} +6.13777e14 q^{60} +1.67067e15 q^{61} +1.60438e15 q^{62} +3.12946e15 q^{63} +2.38042e15 q^{64} -1.14977e15 q^{65} +5.11347e15 q^{66} +5.26350e15 q^{67} +3.39232e14 q^{68} +2.85272e15 q^{69} +5.35284e15 q^{70} -3.64353e15 q^{71} -7.06512e15 q^{72} +7.68806e15 q^{73} +1.16931e16 q^{74} +1.85451e15 q^{75} -1.25674e15 q^{76} -2.46911e16 q^{77} +6.75928e15 q^{78} +2.37036e16 q^{79} -7.15167e15 q^{80} -1.56260e16 q^{81} -8.01731e15 q^{82} +6.98620e15 q^{83} +1.74230e16 q^{84} -5.85184e15 q^{85} +9.18234e15 q^{86} -8.15820e15 q^{87} +5.57431e16 q^{88} +2.61692e16 q^{89} +3.20207e16 q^{90} -3.26381e16 q^{91} +8.17055e15 q^{92} -9.00831e16 q^{93} +7.09005e15 q^{94} +2.16791e16 q^{95} -6.83346e16 q^{96} -1.14923e17 q^{97} +8.43809e16 q^{98} -1.47703e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) \) 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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