LMFDB - Embedded newform 29.18.a.b.1.11

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			1.11
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)

$f(q)$	$=$	$q-3.42944 q^{2} -6754.54 q^{3} -131060. q^{4} +511876. q^{5} +23164.3 q^{6} -1.86320e7 q^{7} +898966. q^{8} -8.35164e7 q^{9} +O(q^{10})$	\(q-3.42944 q^{2} -6754.54 q^{3} -131060. q^{4} +511876. q^{5} +23164.3 q^{6} -1.86320e7 q^{7} +898966. q^{8} -8.35164e7 q^{9} -1.75545e6 q^{10} -3.73240e8 q^{11} +8.85251e8 q^{12} -1.25316e9 q^{13} +6.38972e7 q^{14} -3.45749e9 q^{15} +1.71752e10 q^{16} -2.47656e10 q^{17} +2.86414e8 q^{18} -1.19897e11 q^{19} -6.70866e10 q^{20} +1.25850e11 q^{21} +1.28000e9 q^{22} -5.78063e11 q^{23} -6.07210e9 q^{24} -5.00922e11 q^{25} +4.29765e9 q^{26} +1.43640e12 q^{27} +2.44191e12 q^{28} +5.00246e11 q^{29} +1.18572e10 q^{30} -5.22626e11 q^{31} -1.76731e11 q^{32} +2.52106e12 q^{33} +8.49320e10 q^{34} -9.53726e12 q^{35} +1.09457e13 q^{36} -1.62265e13 q^{37} +4.11179e11 q^{38} +8.46454e12 q^{39} +4.60160e11 q^{40} -1.89639e13 q^{41} -4.31596e11 q^{42} +8.14686e13 q^{43} +4.89169e13 q^{44} -4.27501e13 q^{45} +1.98243e12 q^{46} +1.46847e14 q^{47} -1.16011e14 q^{48} +1.14519e14 q^{49} +1.71788e12 q^{50} +1.67280e14 q^{51} +1.64240e14 q^{52} -2.00234e14 q^{53} -4.92603e12 q^{54} -1.91053e14 q^{55} -1.67495e13 q^{56} +8.09848e14 q^{57} -1.71556e12 q^{58} +9.31474e14 q^{59} +4.53139e14 q^{60} +3.72712e14 q^{61} +1.79231e12 q^{62} +1.55607e15 q^{63} -2.25059e15 q^{64} -6.41465e14 q^{65} -8.64583e12 q^{66} +3.15629e15 q^{67} +3.24578e15 q^{68} +3.90455e15 q^{69} +3.27074e13 q^{70} +9.53111e15 q^{71} -7.50784e13 q^{72} -3.79981e14 q^{73} +5.56478e13 q^{74} +3.38350e15 q^{75} +1.57137e16 q^{76} +6.95419e15 q^{77} -2.90286e13 q^{78} -1.81233e16 q^{79} +8.79160e15 q^{80} +1.08312e15 q^{81} +6.50354e13 q^{82} -2.82171e16 q^{83} -1.64940e16 q^{84} -1.26769e16 q^{85} -2.79391e14 q^{86} -3.37893e15 q^{87} -3.35530e14 q^{88} +5.52201e16 q^{89} +1.46609e14 q^{90} +2.33489e16 q^{91} +7.57611e16 q^{92} +3.53010e15 q^{93} -5.03604e14 q^{94} -6.13724e16 q^{95} +1.19373e15 q^{96} -5.77435e16 q^{97} -3.92737e14 q^{98} +3.11716e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.42944	−0.00947257	−0.00473629	−	0.999989i	$-0.501508\pi$
$2$	−3.42944	−0.00947257	−0.00473629	+	0.999989i	$0.501508\pi$
$3$	−6754.54	−0.594381	−0.297191	−	0.954818i	$-0.596050\pi$
$3$	−6754.54	−0.594381	−0.297191	+	0.954818i	$0.596050\pi$
$4$	−131060.	−0.999910
$5$	511876.	0.586030	0.293015	−	0.956108i	$-0.405341\pi$
$5$	511876.	0.586030	0.293015	+	0.956108i	$0.405341\pi$
$6$	23164.3	0.00563032
$7$	−1.86320e7	−1.22159	−0.610795	−	0.791789i	$-0.709150\pi$
$7$	−1.86320e7	−1.22159	−0.610795	+	0.791789i	$0.709150\pi$
$8$	898966.	0.0189443
$9$	−8.35164e7	−0.646711
$10$	−1.75545e6	−0.00555121
$11$	−3.73240e8	−0.524989	−0.262494	−	0.964934i	$-0.584545\pi$
$11$	−3.73240e8	−0.524989	−0.262494	+	0.964934i	$0.584545\pi$
$12$	8.85251e8	0.594328
$13$	−1.25316e9	−0.426078	−0.213039	−	0.977044i	$-0.568336\pi$
$13$	−1.25316e9	−0.426078	−0.213039	+	0.977044i	$0.568336\pi$
$14$	6.38972e7	0.0115716
$15$	−3.45749e9	−0.348325
$16$	1.71752e10	0.999731
$17$	−2.47656e10	−0.861058	−0.430529	−	0.902577i	$-0.641673\pi$
$17$	−2.47656e10	−0.861058	−0.430529	+	0.902577i	$0.641673\pi$
$18$	2.86414e8	0.00612602
$19$	−1.19897e11	−1.61958	−0.809790	−	0.586720i	$-0.800419\pi$
$19$	−1.19897e11	−1.61958	−0.809790	+	0.586720i	$0.800419\pi$
$20$	−6.70866e10	−0.585978
$21$	1.25850e11	0.726090
$22$	1.28000e9	0.00497300
$23$	−5.78063e11	−1.53918	−0.769589	−	0.638540i	$-0.779539\pi$
$23$	−5.78063e11	−1.53918	−0.769589	+	0.638540i	$0.779539\pi$
$24$	−6.07210e9	−0.0112601
$25$	−5.00922e11	−0.656569
$26$	4.29765e9	0.00403606
$27$	1.43640e12	0.978774
$28$	2.44191e12	1.22148
$29$	5.00246e11	0.185695
$29$	5.00246e11	0.185695
$30$	1.18572e10	0.00329954
$31$	−5.22626e11	−0.110057	−0.0550284	−	0.998485i	$-0.517525\pi$
$31$	−5.22626e11	−0.110057	−0.0550284	+	0.998485i	$0.517525\pi$
$32$	−1.76731e11	−0.0284143
$33$	2.52106e12	0.312043
$34$	8.49320e10	0.00815644
$35$	−9.53726e12	−0.715888
$36$	1.09457e13	0.646653
$37$	−1.62265e13	−0.759470	−0.379735	−	0.925095i	$-0.623985\pi$
$37$	−1.62265e13	−0.759470	−0.379735	+	0.925095i	$0.623985\pi$
$38$	4.11179e11	0.0153416
$39$	8.46454e12	0.253253
$40$	4.60160e11	0.0111019
$41$	−1.89639e13	−0.370906	−0.185453	−	0.982653i	$-0.559375\pi$
$41$	−1.89639e13	−0.370906	−0.185453	+	0.982653i	$0.559375\pi$
$42$	−4.31596e11	−0.00687794
$43$	8.14686e13	1.06294	0.531469	−	0.847077i	$-0.321640\pi$
$43$	8.14686e13	1.06294	0.531469	+	0.847077i	$0.321640\pi$
$44$	4.89169e13	0.524942
$45$	−4.27501e13	−0.378992
$46$	1.98243e12	0.0145800
$47$	1.46847e14	0.899568	0.449784	−	0.893137i	$-0.351501\pi$
$47$	1.46847e14	0.899568	0.449784	+	0.893137i	$0.351501\pi$
$48$	−1.16011e14	−0.594221
$49$	1.14519e14	0.492281
$50$	1.71788e12	0.00621939
$51$	1.67280e14	0.511797
$52$	1.64240e14	0.426040
$53$	−2.00234e14	−0.441768	−0.220884	−	0.975300i	$-0.570894\pi$
$53$	−2.00234e14	−0.441768	−0.220884	+	0.975300i	$0.570894\pi$
$54$	−4.92603e12	−0.00927151
$55$	−1.91053e14	−0.307659
$56$	−1.67495e13	−0.0231422
$57$	8.09848e14	0.962648
$58$	−1.71556e12	−0.00175901
$59$	9.31474e14	0.825903	0.412951	−	0.910753i	$-0.364498\pi$
$59$	9.31474e14	0.825903	0.412951	+	0.910753i	$0.364498\pi$
$60$	4.53139e14	0.348294
$61$	3.72712e14	0.248926	0.124463	−	0.992224i	$-0.460279\pi$
$61$	3.72712e14	0.248926	0.124463	+	0.992224i	$0.460279\pi$
$62$	1.79231e12	0.00104252
$63$	1.55607e15	0.790015
$64$	−2.25059e15	−0.999462
$65$	−6.41465e14	−0.249695
$66$	−8.64583e12	−0.00295585
$67$	3.15629e15	0.949601	0.474801	−	0.880093i	$-0.342520\pi$
$67$	3.15629e15	0.949601	0.474801	+	0.880093i	$0.342520\pi$
$68$	3.24578e15	0.860981
$69$	3.90455e15	0.914858
$70$	3.27074e13	0.00678131
$71$	9.53111e15	1.75165	0.875825	−	0.482629i	$-0.160318\pi$
$71$	9.53111e15	1.75165	0.875825	+	0.482629i	$0.160318\pi$
$72$	−7.50784e13	−0.0122515
$73$	−3.79981e14	−0.0551465	−0.0275732	−	0.999620i	$-0.508778\pi$
$73$	−3.79981e14	−0.0551465	−0.0275732	+	0.999620i	$0.508778\pi$
$74$	5.56478e13	0.00719413
$75$	3.38350e15	0.390252
$76$	1.57137e16	1.61943
$77$	6.95419e15	0.641321
$78$	−2.90286e13	−0.00239896
$79$	−1.81233e16	−1.34402	−0.672011	−	0.740541i	$-0.734569\pi$
$79$	−1.81233e16	−1.34402	−0.672011	+	0.740541i	$0.734569\pi$
$80$	8.79160e15	0.585873
$81$	1.08312e15	0.0649465
$82$	6.50354e13	0.00351343
$83$	−2.82171e16	−1.37515	−0.687573	−	0.726116i	$-0.741324\pi$
$83$	−2.82171e16	−1.37515	−0.687573	+	0.726116i	$0.741324\pi$
$84$	−1.64940e16	−0.726024
$85$	−1.26769e16	−0.504606
$86$	−2.79391e14	−0.0100688
$87$	−3.37893e15	−0.110374
$88$	−3.35530e14	−0.00994555
$89$	5.52201e16	1.48690	0.743451	−	0.668790i	$-0.233188\pi$
$89$	5.52201e16	1.48690	0.743451	+	0.668790i	$0.233188\pi$
$90$	1.46609e14	0.00359003
$91$	2.33489e16	0.520493
$92$	7.57611e16	1.53904
$93$	3.53010e15	0.0654157
$94$	−5.03604e14	−0.00852123
$95$	−6.13724e16	−0.949123
$96$	1.19373e15	0.0168889
$97$	−5.77435e16	−0.748071	−0.374036	−	0.927414i	$-0.622026\pi$
$97$	−5.77435e16	−0.748071	−0.374036	+	0.927414i	$0.622026\pi$
$98$	−3.92737e14	−0.00466316
$99$	3.11716e16	0.339516
$100$	6.56510e16	0.656510
$101$	−2.69807e16	−0.247925	−0.123963	−	0.992287i	$-0.539560\pi$
$101$	−2.69807e16	−0.247925	−0.123963	+	0.992287i	$0.539560\pi$
$102$	−5.73676e14	−0.00484803
$103$	−2.05801e17	−1.60078	−0.800390	−	0.599479i	$-0.795374\pi$
$103$	−2.05801e17	−1.60078	−0.800390	+	0.599479i	$0.795374\pi$
$104$	−1.12655e15	−0.00807175
$105$	6.44198e16	0.425510
$106$	6.86691e14	0.00418468
$107$	1.89943e17	1.06871	0.534355	−	0.845260i	$-0.320554\pi$
$107$	1.89943e17	1.06871	0.534355	+	0.845260i	$0.320554\pi$
$108$	−1.88254e17	−0.978686
$109$	−3.84746e17	−1.84948	−0.924739	−	0.380602i	$-0.875717\pi$
$109$	−3.84746e17	−1.84948	−0.924739	+	0.380602i	$0.875717\pi$
$110$	6.55203e14	0.00291433
$111$	1.09603e17	0.451414
$112$	−3.20009e17	−1.22126
$113$	−3.00563e17	−1.06358	−0.531788	−	0.846877i	$-0.678480\pi$
$113$	−3.00563e17	−1.06358	−0.531788	+	0.846877i	$0.678480\pi$
$114$	−2.77732e15	−0.00911875
$115$	−2.95897e17	−0.902005
$116$	−6.55624e16	−0.185679
$117$	1.04660e17	0.275550
$118$	−3.19443e15	−0.00782342
$119$	4.61431e17	1.05186
$120$	−3.10817e15	−0.00659878
$121$	−3.66139e17	−0.724387
$122$	−1.27819e15	−0.00235797
$123$	1.28092e17	0.220460
$124$	6.84955e16	0.110047
$125$	−6.46941e17	−0.970799
$126$	−5.33646e15	−0.00748348
$127$	7.04500e16	0.0923739	0.0461870	−	0.998933i	$-0.485293\pi$
$127$	7.04500e16	0.0923739	0.0461870	+	0.998933i	$0.485293\pi$
$128$	3.08827e16	0.0378818
$129$	−5.50283e17	−0.631791
$130$	2.19986e15	0.00236525
$131$	−2.64333e17	−0.266285	−0.133142	−	0.991097i	$-0.542507\pi$
$131$	−2.64333e17	−0.266285	−0.133142	+	0.991097i	$0.542507\pi$
$132$	−3.30411e17	−0.312015
$133$	2.23391e18	1.97846
$134$	−1.08243e16	−0.00899517
$135$	7.35257e17	0.573591
$136$	−2.22634e16	−0.0163121
$137$	1.16056e18	0.798990	0.399495	−	0.916735i	$-0.369185\pi$
$137$	1.16056e18	0.798990	0.399495	+	0.916735i	$0.369185\pi$
$138$	−1.33904e16	−0.00866606
$139$	3.45837e17	0.210497	0.105248	−	0.994446i	$-0.466436\pi$
$139$	3.45837e17	0.210497	0.105248	+	0.994446i	$0.466436\pi$
$140$	1.24996e18	0.715824
$141$	−9.91886e17	−0.534686
$142$	−3.26863e16	−0.0165926
$143$	4.67731e17	0.223686
$144$	−1.43441e18	−0.646537
$145$	2.56064e17	0.108823
$146$	1.30312e15	0.000522379 0
$147$	−7.73526e17	−0.292602
$148$	2.12665e18	0.759402
$149$	1.12796e18	0.380373	0.190187	−	0.981748i	$-0.439091\pi$
$149$	1.12796e18	0.380373	0.190187	+	0.981748i	$0.439091\pi$
$150$	−1.16035e16	−0.00369669
$151$	7.30363e17	0.219905	0.109952	−	0.993937i	$-0.464930\pi$
$151$	7.30363e17	0.219905	0.109952	+	0.993937i	$0.464930\pi$
$152$	−1.07783e17	−0.0306818
$153$	2.06833e18	0.556856
$154$	−2.38490e16	−0.00607496
$155$	−2.67520e17	−0.0644966
$156$	−1.10936e18	−0.253230
$157$	−6.82573e18	−1.47571	−0.737857	−	0.674957i	$-0.764162\pi$
$157$	−6.82573e18	−1.47571	−0.737857	+	0.674957i	$0.764162\pi$
$158$	6.21526e16	0.0127313
$159$	1.35249e18	0.262578
$160$	−9.04643e16	−0.0166517
$161$	1.07705e19	1.88024
$162$	−3.71451e15	−0.000615210 0
$163$	1.16311e18	0.182821	0.0914106	−	0.995813i	$-0.470862\pi$
$163$	1.16311e18	0.182821	0.0914106	+	0.995813i	$0.470862\pi$
$164$	2.48541e18	0.370873
$165$	1.29047e18	0.182867
$166$	9.67688e16	0.0130262
$167$	1.33697e19	1.71015	0.855073	−	0.518508i	$-0.173512\pi$
$167$	1.33697e19	1.71015	0.855073	+	0.518508i	$0.173512\pi$
$168$	1.13135e17	0.0137553
$169$	−7.08000e18	−0.818457
$170$	4.34747e16	0.00477992
$171$	1.00134e19	1.04740
$172$	−1.06773e19	−1.06284
$173$	2.28215e17	0.0216248	0.0108124	−	0.999942i	$-0.496558\pi$
$173$	2.28215e17	0.0216248	0.0108124	+	0.999942i	$0.496558\pi$
$174$	1.15878e16	0.00104552
$175$	9.33316e18	0.802057
$176$	−6.41048e18	−0.524848
$177$	−6.29168e18	−0.490901
$178$	−1.89374e17	−0.0140848
$179$	−6.77644e18	−0.480564	−0.240282	−	0.970703i	$-0.577240\pi$
$179$	−6.77644e18	−0.480564	−0.240282	+	0.970703i	$0.577240\pi$
$180$	5.60283e18	0.378958
$181$	−1.04893e19	−0.676829	−0.338414	−	0.940997i	$-0.609891\pi$
$181$	−1.04893e19	−0.676829	−0.338414	+	0.940997i	$0.609891\pi$
$182$	−8.00736e16	−0.00493040
$183$	−2.51750e18	−0.147957
$184$	−5.19659e17	−0.0291586
$185$	−8.30597e18	−0.445072
$186$	−1.21063e16	−0.000619655 0
$187$	9.24350e18	0.452046
$188$	−1.92458e19	−0.899488
$189$	−2.67629e19	−1.19566
$190$	2.10473e17	0.00899063
$191$	−2.92078e19	−1.19321	−0.596603	−	0.802536i	$-0.703483\pi$
$191$	−2.92078e19	−1.19321	−0.596603	+	0.802536i	$0.703483\pi$
$192$	1.52017e19	0.594061
$193$	−9.23243e18	−0.345206	−0.172603	−	0.984991i	$-0.555218\pi$
$193$	−9.23243e18	−0.345206	−0.172603	+	0.984991i	$0.555218\pi$
$194$	1.98028e17	0.00708616
$195$	4.33280e18	0.148414
$196$	−1.50090e19	−0.492236
$197$	−5.92054e18	−0.185951	−0.0929755	−	0.995668i	$-0.529638\pi$
$197$	−5.92054e18	−0.185951	−0.0929755	+	0.995668i	$0.529638\pi$
$198$	−1.06901e17	−0.00321609
$199$	2.88969e19	0.832913	0.416456	−	0.909156i	$-0.363272\pi$
$199$	2.88969e19	0.832913	0.416456	+	0.909156i	$0.363272\pi$
$200$	−4.50312e17	−0.0124382
$201$	−2.13193e19	−0.564425
$202$	9.25285e16	0.00234849
$203$	−9.32057e18	−0.226843
$204$	−2.19238e19	−0.511751
$205$	−9.70715e18	−0.217362
$206$	7.05783e17	0.0151635
$207$	4.82777e19	0.995403
$208$	−2.15234e19	−0.425964
$209$	4.47503e19	0.850261
$210$	−2.20924e17	−0.00403068
$211$	−1.03087e20	−1.80635	−0.903175	−	0.429272i	$-0.858770\pi$
$211$	−1.03087e20	−1.80635	−0.903175	+	0.429272i	$0.858770\pi$
$212$	2.62428e19	0.441728
$213$	−6.43782e19	−1.04115
$214$	−6.51396e17	−0.0101234
$215$	4.17018e19	0.622914
$216$	1.29127e18	0.0185422
$217$	9.73755e18	0.134444
$218$	1.31946e18	0.0175193
$219$	2.56660e18	0.0327780
$220$	2.50394e19	0.307632
$221$	3.10353e19	0.366878
$222$	−3.75875e17	−0.00427606
$223$	1.04565e20	1.14497	0.572484	−	0.819916i	$-0.305980\pi$
$223$	1.04565e20	1.14497	0.572484	+	0.819916i	$0.305980\pi$
$224$	3.29284e18	0.0347106
$225$	4.18352e19	0.424610
$226$	1.03076e18	0.0100748
$227$	5.14533e19	0.484388	0.242194	−	0.970228i	$-0.422133\pi$
$227$	5.14533e19	0.484388	0.242194	+	0.970228i	$0.422133\pi$
$228$	−1.06139e20	−0.962561
$229$	1.35059e20	1.18011	0.590053	−	0.807365i	$-0.299107\pi$
$229$	1.35059e20	1.18011	0.590053	+	0.807365i	$0.299107\pi$
$230$	1.01476e18	0.00854431
$231$	−4.69723e19	−0.381189
$232$	4.49705e17	0.00351787
$233$	−2.19325e20	−1.65411	−0.827054	−	0.562123i	$-0.809985\pi$
$233$	−2.19325e20	−1.65411	−0.827054	+	0.562123i	$0.809985\pi$
$234$	−3.58924e17	−0.00261016
$235$	7.51677e19	0.527174
$236$	−1.22079e20	−0.825828
$237$	1.22414e20	0.798861
$238$	−1.58245e18	−0.00996382
$239$	2.05696e20	1.24981	0.624904	−	0.780702i	$-0.285138\pi$
$239$	2.05696e20	1.24981	0.624904	+	0.780702i	$0.285138\pi$
$240$	−5.93832e19	−0.348232
$241$	2.49893e20	1.41452	0.707260	−	0.706953i	$-0.249931\pi$
$241$	2.49893e20	1.41452	0.707260	+	0.706953i	$0.249931\pi$
$242$	1.25565e18	0.00686181
$243$	−1.92813e20	−1.01738
$244$	−4.88477e19	−0.248903
$245$	5.86198e19	0.288491
$246$	−4.39284e17	−0.00208832
$247$	1.50250e20	0.690068
$248$	−4.69823e17	−0.00208495
$249$	1.90593e20	0.817360
$250$	2.21864e18	0.00919597
$251$	3.02119e20	1.21046	0.605231	−	0.796050i	$-0.293081\pi$
$251$	3.02119e20	1.21046	0.605231	+	0.796050i	$0.293081\pi$
$252$	−2.03939e20	−0.789945
$253$	2.15756e20	0.808051
$254$	−2.41604e17	−0.000875019 0
$255$	8.56267e19	0.299928
$256$	2.94883e20	0.999103
$257$	−4.60871e20	−1.51060	−0.755298	−	0.655382i	$-0.772508\pi$
$257$	−4.60871e20	−1.51060	−0.755298	+	0.655382i	$0.772508\pi$
$258$	1.88716e18	0.00598468
$259$	3.02332e20	0.927760
$260$	8.40705e19	0.249672
$261$	−4.17788e19	−0.120091
$262$	9.06515e17	0.00252240
$263$	−1.43435e20	−0.386395	−0.193198	−	0.981160i	$-0.561886\pi$
$263$	−1.43435e20	−0.386395	−0.193198	+	0.981160i	$0.561886\pi$
$264$	2.26635e18	0.00591144
$265$	−1.02495e20	−0.258889
$266$	−7.66107e18	−0.0187411
$267$	−3.72987e20	−0.883787
$268$	−4.13664e20	−0.949516
$269$	3.64514e20	0.810625	0.405312	−	0.914178i	$-0.367163\pi$
$269$	3.64514e20	0.810625	0.405312	+	0.914178i	$0.367163\pi$
$270$	−2.52152e18	−0.00543338
$271$	−6.10309e20	−1.27442	−0.637208	−	0.770692i	$-0.719911\pi$
$271$	−6.10309e20	−1.27442	−0.637208	+	0.770692i	$0.719911\pi$
$272$	−4.25355e20	−0.860826
$273$	−1.57711e20	−0.309371
$274$	−3.98006e18	−0.00756849
$275$	1.86964e20	0.344691
$276$	−5.11731e20	−0.914776
$277$	7.06050e20	1.22393	0.611966	−	0.790884i	$-0.290379\pi$
$277$	7.06050e20	1.22393	0.611966	+	0.790884i	$0.290379\pi$
$278$	−1.18603e18	−0.00199395
$279$	4.36479e19	0.0711750
$280$	−8.57368e18	−0.0135620
$281$	5.45596e20	0.837273	0.418637	−	0.908154i	$-0.362508\pi$
$281$	5.45596e20	0.837273	0.418637	+	0.908154i	$0.362508\pi$
$282$	3.40161e18	0.00506486
$283$	−4.81264e19	−0.0695342	−0.0347671	−	0.999395i	$-0.511069\pi$
$283$	−4.81264e19	−0.0695342	−0.0347671	+	0.999395i	$0.511069\pi$
$284$	−1.24915e21	−1.75149
$285$	4.14542e20	0.564141
$286$	−1.60405e18	−0.00211889
$287$	3.53334e20	0.453095
$288$	1.47599e19	0.0183759
$289$	−2.13907e20	−0.258579
$290$	−8.78157e17	−0.00103083
$291$	3.90030e20	0.444639
$292$	4.98004e19	0.0551415
$293$	−5.81083e20	−0.624976	−0.312488	−	0.949922i	$-0.601162\pi$
$293$	−5.81083e20	−0.624976	−0.312488	+	0.949922i	$0.601162\pi$
$294$	2.65276e18	0.00277170
$295$	4.76800e20	0.484004
$296$	−1.45871e19	−0.0143876
$297$	−5.36120e20	−0.513845
$298$	−3.86827e18	−0.00360311
$299$	7.24408e20	0.655810
$300$	−4.43442e20	−0.390217
$301$	−1.51792e21	−1.29847
$302$	−2.50474e18	−0.00208307
$303$	1.82242e20	0.147362
$304$	−2.05926e21	−1.61914
$305$	1.90782e20	0.145878
$306$	−7.09321e18	−0.00527486
$307$	−2.35169e21	−1.70100	−0.850498	−	0.525978i	$-0.823700\pi$
$307$	−2.35169e21	−1.70100	−0.850498	+	0.525978i	$0.823700\pi$
$308$	−9.11418e20	−0.641263
$309$	1.39009e21	0.951474
$310$	9.17443e17	0.000610949 0
$311$	−1.67101e21	−1.08272	−0.541360	−	0.840791i	$-0.682091\pi$
$311$	−1.67101e21	−1.08272	−0.541360	+	0.840791i	$0.682091\pi$
$312$	7.60934e18	0.00479770
$313$	−2.12466e20	−0.130366	−0.0651829	−	0.997873i	$-0.520763\pi$
$313$	−2.12466e20	−0.130366	−0.0651829	+	0.997873i	$0.520763\pi$
$314$	2.34084e19	0.0139788
$315$	7.96518e20	0.462973
$316$	2.37524e21	1.34390
$317$	1.86015e21	1.02458	0.512288	−	0.858814i	$-0.328798\pi$
$317$	1.86015e21	1.02458	0.512288	+	0.858814i	$0.328798\pi$
$318$	−4.63828e18	−0.00248729
$319$	−1.86712e20	−0.0974880
$320$	−1.15202e21	−0.585715
$321$	−1.28297e21	−0.635222
$322$	−3.69366e19	−0.0178107
$323$	2.96931e21	1.39455
$324$	−1.41954e20	−0.0649406
$325$	6.27737e20	0.279750
$326$	−3.98882e18	−0.00173179
$327$	2.59878e21	1.09929
$328$	−1.70479e19	−0.00702655
$329$	−2.73605e21	−1.09890
$330$	−4.42559e18	−0.00173222
$331$	−1.08446e21	−0.413691	−0.206845	−	0.978374i	$-0.566320\pi$
$331$	−1.08446e21	−0.413691	−0.206845	+	0.978374i	$0.566320\pi$
$332$	3.69814e21	1.37502
$333$	1.35518e21	0.491158
$334$	−4.58507e19	−0.0161995
$335$	1.61563e21	0.556495
$336$	2.16151e21	0.725894
$337$	1.21083e21	0.396488	0.198244	−	0.980153i	$-0.436476\pi$
$337$	1.21083e21	0.396488	0.198244	+	0.980153i	$0.436476\pi$
$338$	2.42804e19	0.00775290
$339$	2.03016e21	0.632170
$340$	1.66144e21	0.504561
$341$	1.95065e20	0.0577786
$342$	−3.43402e19	−0.00992158
$343$	2.20064e21	0.620225
$344$	7.32375e19	0.0201366
$345$	1.99865e21	0.536134
$346$	−7.82648e17	−0.000204842 0
$347$	−3.88478e20	−0.0992124	−0.0496062	−	0.998769i	$-0.515797\pi$
$347$	−3.88478e20	−0.0992124	−0.0496062	+	0.998769i	$0.515797\pi$
$348$	4.42844e20	0.110364
$349$	−7.18525e21	−1.74753	−0.873767	−	0.486344i	$-0.838330\pi$
$349$	−7.18525e21	−1.74753	−0.873767	+	0.486344i	$0.838330\pi$
$350$	−3.20075e19	−0.00759755
$351$	−1.80004e21	−0.417034
$352$	6.59629e19	0.0149172
$353$	−6.09324e20	−0.134513	−0.0672564	−	0.997736i	$-0.521425\pi$
$353$	−6.09324e20	−0.134513	−0.0672564	+	0.997736i	$0.521425\pi$
$354$	2.15769e19	0.00465009
$355$	4.87875e21	1.02652
$356$	−7.23716e21	−1.48677
$357$	−3.11675e21	−0.625205
$358$	2.32394e19	0.00455217
$359$	5.73421e21	1.09691	0.548455	−	0.836180i	$-0.315216\pi$
$359$	5.73421e21	1.09691	0.548455	+	0.836180i	$0.315216\pi$
$360$	−3.84309e19	−0.00717974
$361$	8.89488e21	1.62304
$362$	3.59724e19	0.00641131
$363$	2.47310e21	0.430562
$364$	−3.06011e21	−0.520446
$365$	−1.94503e20	−0.0323175
$366$	8.63360e18	0.00140153
$367$	−5.41307e21	−0.858582	−0.429291	−	0.903166i	$-0.641237\pi$
$367$	−5.41307e21	−0.858582	−0.429291	+	0.903166i	$0.641237\pi$
$368$	−9.92838e21	−1.53876
$369$	1.58379e21	0.239869
$370$	2.84848e19	0.00421598
$371$	3.73076e21	0.539659
$372$	−4.62656e20	−0.0654098
$373$	−7.62704e21	−1.05398	−0.526989	−	0.849872i	$-0.676679\pi$
$373$	−7.62704e21	−1.05398	−0.526989	+	0.849872i	$0.676679\pi$
$374$	−3.17000e19	−0.00428204
$375$	4.36979e21	0.577025
$376$	1.32011e20	0.0170417
$377$	−6.26891e20	−0.0791207
$378$	9.17817e19	0.0113260
$379$	1.66580e21	0.200997	0.100499	−	0.994937i	$-0.467956\pi$
$379$	1.66580e21	0.200997	0.100499	+	0.994937i	$0.467956\pi$
$380$	8.04348e21	0.949038
$381$	−4.75857e20	−0.0549053
$382$	1.00166e20	0.0113027
$383$	2.42994e20	0.0268168	0.0134084	−	0.999910i	$-0.495732\pi$
$383$	2.42994e20	0.0268168	0.0134084	+	0.999910i	$0.495732\pi$
$384$	−2.08598e20	−0.0225162
$385$	3.55969e21	0.375833
$386$	3.16620e19	0.00326999
$387$	−6.80396e21	−0.687414
$388$	7.56787e21	0.748004
$389$	−1.97111e22	−1.90607	−0.953037	−	0.302853i	$-0.902061\pi$
$389$	−1.97111e22	−1.90607	−0.953037	+	0.302853i	$0.902061\pi$
$390$	−1.48591e19	−0.00140586
$391$	1.43161e22	1.32532
$392$	1.02949e20	0.00932591
$393$	1.78545e21	0.158274
$394$	2.03041e19	0.00176144
$395$	−9.27687e21	−0.787637
$396$	−4.08536e21	−0.339486
$397$	6.88365e21	0.559886	0.279943	−	0.960017i	$-0.409684\pi$
$397$	6.88365e21	0.559886	0.279943	+	0.960017i	$0.409684\pi$
$398$	−9.91000e19	−0.00788983
$399$	−1.50891e22	−1.17596
$400$	−8.60346e21	−0.656392
$401$	−3.16226e21	−0.236195	−0.118098	−	0.993002i	$-0.537680\pi$
$401$	−3.16226e21	−0.236195	−0.118098	+	0.993002i	$0.537680\pi$
$402$	7.31132e19	0.00534656
$403$	6.54936e20	0.0468928
$404$	3.53609e21	0.247903
$405$	5.54425e20	0.0380606
$406$	3.19643e19	0.00214879
$407$	6.05638e21	0.398713
$408$	1.50379e20	0.00969563
$409$	−1.96146e22	−1.23860	−0.619301	−	0.785154i	$-0.712584\pi$
$409$	−1.96146e22	−1.23860	−0.619301	+	0.785154i	$0.712584\pi$
$410$	3.32901e19	0.00205898
$411$	−7.83902e21	−0.474905
$412$	2.69724e22	1.60064
$413$	−1.73552e22	−1.00891
$414$	−1.65566e20	−0.00942903
$415$	−1.44437e22	−0.805877
$416$	2.21473e20	0.0121067
$417$	−2.33597e21	−0.125115
$418$	−1.53468e20	−0.00805416
$419$	−5.98847e21	−0.307962	−0.153981	−	0.988074i	$-0.549209\pi$
$419$	−5.98847e21	−0.307962	−0.153981	+	0.988074i	$0.549209\pi$
$420$	−8.44287e21	−0.425472
$421$	−1.91425e22	−0.945368	−0.472684	−	0.881232i	$-0.656715\pi$
$421$	−1.91425e22	−0.945368	−0.472684	+	0.881232i	$0.656715\pi$
$422$	3.53530e20	0.0171108
$423$	−1.22642e22	−0.581761
$424$	−1.80004e20	−0.00836898
$425$	1.24056e22	0.565344
$426$	2.20781e20	0.00986235
$427$	−6.94436e21	−0.304085
$428$	−2.48939e22	−1.06862
$429$	−3.15930e21	−0.132955
$430$	−1.43014e20	−0.00590060
$431$	−9.85235e21	−0.398550	−0.199275	−	0.979944i	$-0.563859\pi$
$431$	−9.85235e21	−0.398550	−0.199275	+	0.979944i	$0.563859\pi$
$432$	2.46705e22	0.978510
$433$	1.17810e22	0.458179	0.229089	−	0.973405i	$-0.426425\pi$
$433$	1.17810e22	0.458179	0.229089	+	0.973405i	$0.426425\pi$
$434$	−3.33943e19	−0.00127353
$435$	−1.72960e21	−0.0646824
$436$	5.04249e22	1.84931
$437$	6.93080e22	2.49282
$438$	−8.80199e18	−0.000310492 0
$439$	−4.86071e22	−1.68171	−0.840855	−	0.541261i	$-0.817947\pi$
$439$	−4.86071e22	−1.68171	−0.840855	+	0.541261i	$0.817947\pi$
$440$	−1.71750e20	−0.00582839
$441$	−9.56425e21	−0.318363
$442$	−1.06434e20	−0.00347528
$443$	3.04164e22	0.974263	0.487132	−	0.873329i	$-0.338043\pi$
$443$	3.04164e22	0.974263	0.487132	+	0.873329i	$0.338043\pi$
$444$	−1.43645e22	−0.451374
$445$	2.82659e22	0.871370
$446$	−3.58598e20	−0.0108458
$447$	−7.61884e21	−0.226087
$448$	4.19329e22	1.22093
$449$	1.59762e22	0.456435	0.228218	−	0.973610i	$-0.426710\pi$
$449$	1.59762e22	0.456435	0.228218	+	0.973610i	$0.426710\pi$
$450$	−1.43471e20	−0.00402215
$451$	7.07807e21	0.194722
$452$	3.93919e22	1.06348
$453$	−4.93327e21	−0.130707
$454$	−1.76456e20	−0.00458841
$455$	1.19518e22	0.305024
$456$	7.28026e20	0.0182367
$457$	−1.14043e21	−0.0280403	−0.0140201	−	0.999902i	$-0.504463\pi$
$457$	−1.14043e21	−0.0280403	−0.0140201	+	0.999902i	$0.504463\pi$
$458$	−4.63175e20	−0.0111786
$459$	−3.55732e22	−0.842781
$460$	3.87803e22	0.901924
$461$	2.64525e22	0.603960	0.301980	−	0.953314i	$-0.402352\pi$
$461$	2.64525e22	0.603960	0.301980	+	0.953314i	$0.402352\pi$
$462$	1.61089e20	0.00361084
$463$	5.61913e22	1.23660	0.618302	−	0.785941i	$-0.287821\pi$
$463$	5.61913e22	1.23660	0.618302	+	0.785941i	$0.287821\pi$
$464$	8.59185e21	0.185645
$465$	1.80697e21	0.0383356
$466$	7.52163e20	0.0156687
$467$	−9.13087e22	−1.86775	−0.933874	−	0.357601i	$-0.883595\pi$
$467$	−9.13087e22	−1.86775	−0.933874	+	0.357601i	$0.883595\pi$
$468$	−1.37167e22	−0.275525
$469$	−5.88079e22	−1.16002
$470$	−2.57783e20	−0.00499370
$471$	4.61047e22	0.877136
$472$	8.37364e20	0.0156461
$473$	−3.04073e22	−0.558031
$474$	−4.19812e20	−0.00756727
$475$	6.00590e22	1.06337
$476$	−6.04753e22	−1.05177
$477$	1.67229e22	0.285696
$478$	−7.05421e20	−0.0118389
$479$	−4.57233e22	−0.753851	−0.376926	−	0.926244i	$-0.623019\pi$
$479$	−4.57233e22	−0.753851	−0.376926	+	0.926244i	$0.623019\pi$
$480$	6.11044e20	0.00989743
$481$	2.03345e22	0.323594
$482$	−8.56993e20	−0.0133992
$483$	−7.27494e22	−1.11758
$484$	4.79863e22	0.724322
$485$	−2.95575e22	−0.438392
$486$	6.61239e20	0.00963718
$487$	1.29964e23	1.86134	0.930671	−	0.365858i	$-0.119224\pi$
$487$	1.29964e23	1.86134	0.930671	+	0.365858i	$0.119224\pi$
$488$	3.35056e20	0.00471572
$489$	−7.85628e21	−0.108665
$490$	−2.01033e20	−0.00273276
$491$	1.09533e23	1.46337	0.731683	−	0.681645i	$-0.238735\pi$
$491$	1.09533e23	1.46337	0.731683	+	0.681645i	$0.238735\pi$
$492$	−1.67878e22	−0.220440
$493$	−1.23889e22	−0.159894
$494$	−5.15275e20	−0.00653672
$495$	1.59560e22	0.198967
$496$	−8.97624e21	−0.110027
$497$	−1.77583e23	−2.13980
$498$	−6.53628e20	−0.00774251
$499$	3.44291e22	0.400932	0.200466	−	0.979701i	$-0.435754\pi$
$499$	3.44291e22	0.400932	0.200466	+	0.979701i	$0.435754\pi$
$500$	8.47882e22	0.970712
$501$	−9.03064e22	−1.01648
$502$	−1.03610e21	−0.0114662
$503$	−2.48272e22	−0.270147	−0.135074	−	0.990836i	$-0.543127\pi$
$503$	−2.48272e22	−0.270147	−0.135074	+	0.990836i	$0.543127\pi$
$504$	1.39886e21	0.0149663
$505$	−1.38108e22	−0.145292
$506$	−7.39922e20	−0.00765432
$507$	4.78221e22	0.486476
$508$	−9.23320e21	−0.0923656
$509$	1.64901e22	0.162227	0.0811135	−	0.996705i	$-0.474152\pi$
$509$	1.64901e22	0.162227	0.0811135	+	0.996705i	$0.474152\pi$
$510$	−2.93651e20	−0.00284109
$511$	7.07979e21	0.0673663
$512$	−5.05914e21	−0.0473459
$513$	−1.72219e23	−1.58520
$514$	1.58053e21	0.0143092
$515$	−1.05345e23	−0.938106
$516$	7.21202e22	0.631734
$517$	−5.48093e22	−0.472263
$518$	−1.03683e21	−0.00878828
$519$	−1.54148e21	−0.0128534
$520$	−5.76655e20	−0.00473029
$521$	8.92259e21	0.0720063	0.0360031	−	0.999352i	$-0.488537\pi$
$521$	8.92259e21	0.0720063	0.0360031	+	0.999352i	$0.488537\pi$
$522$	1.43278e20	0.00113757
$523$	−8.73757e22	−0.682537	−0.341269	−	0.939966i	$-0.610857\pi$
$523$	−8.73757e22	−0.682537	−0.341269	+	0.939966i	$0.610857\pi$
$524$	3.46436e22	0.266261
$525$	−6.30412e22	−0.476728
$526$	4.91902e20	0.00366016
$527$	1.29431e22	0.0947653
$528$	4.32999e22	0.311959
$529$	1.93107e23	1.36907
$530$	3.51501e20	0.00245235
$531$	−7.77934e22	−0.534120
$532$	−2.92777e23	−1.97828
$533$	2.37648e22	0.158035
$534$	1.27913e21	0.00837173
$535$	9.72271e22	0.626297
$536$	2.83740e21	0.0179895
$537$	4.57717e22	0.285638
$538$	−1.25008e21	−0.00767870
$539$	−4.27432e22	−0.258442
$540$	−9.63630e22	−0.573540
$541$	3.42492e22	0.200666	0.100333	−	0.994954i	$-0.468009\pi$
$541$	3.42492e22	0.200666	0.100333	+	0.994954i	$0.468009\pi$
$542$	2.09302e21	0.0120720
$543$	7.08504e22	0.402294
$544$	4.37684e21	0.0244664
$545$	−1.96943e23	−1.08385
$546$	5.40860e20	0.00293054
$547$	6.63782e22	0.354106	0.177053	−	0.984201i	$-0.443344\pi$
$547$	6.63782e22	0.354106	0.177053	+	0.984201i	$0.443344\pi$
$548$	−1.52103e23	−0.798919
$549$	−3.11276e22	−0.160983
$550$	−6.41182e20	−0.00326511
$551$	−5.99780e22	−0.300748
$552$	3.51006e21	0.0173313
$553$	3.37672e23	1.64184
$554$	−2.42135e21	−0.0115938
$555$	5.61030e22	0.264543
$556$	−4.53255e22	−0.210478
$557$	7.56476e22	0.345960	0.172980	−	0.984925i	$-0.444660\pi$
$557$	7.56476e22	0.345960	0.172980	+	0.984925i	$0.444660\pi$
$558$	−1.49688e20	−0.000674210 0
$559$	−1.02093e23	−0.452895
$560$	−1.63805e23	−0.715696
$561$	−6.24355e22	−0.268688
$562$	−1.87109e21	−0.00793113
$563$	−3.16720e23	−1.32237	−0.661187	−	0.750221i	$-0.729947\pi$
$563$	−3.16720e23	−1.32237	−0.661187	+	0.750221i	$0.729947\pi$
$564$	1.29997e23	0.534638
$565$	−1.53851e23	−0.623288
$566$	1.65046e20	0.000658668 0
$567$	−2.01807e22	−0.0793379
$568$	8.56814e21	0.0331838
$569$	−2.00150e22	−0.0763663	−0.0381831	−	0.999271i	$-0.512157\pi$
$569$	−2.00150e22	−0.0763663	−0.0381831	+	0.999271i	$0.512157\pi$
$570$	−1.42165e21	−0.00534386
$571$	7.51493e22	0.278303	0.139151	−	0.990271i	$-0.455563\pi$
$571$	7.51493e22	0.278303	0.139151	+	0.990271i	$0.455563\pi$
$572$	−6.13009e22	−0.223666
$573$	1.97285e23	0.709219
$574$	−1.21174e21	−0.00429197
$575$	2.89565e23	1.01058
$576$	1.87961e23	0.646363
$577$	5.67298e23	1.92228	0.961140	−	0.276060i	$-0.0890288\pi$
$577$	5.67298e23	1.92228	0.961140	+	0.276060i	$0.0890288\pi$
$578$	7.33581e20	0.00244941
$579$	6.23608e22	0.205184
$580$	−3.35599e22	−0.108813
$581$	5.25740e23	1.67986
$582$	−1.33758e21	−0.00421188
$583$	7.47354e22	0.231923
$584$	−3.41590e20	−0.00104471
$585$	5.35728e22	0.161480
$586$	1.99279e21	0.00592013
$587$	−1.42251e23	−0.416517	−0.208259	−	0.978074i	$-0.566780\pi$
$587$	−1.42251e23	−0.416517	−0.208259	+	0.978074i	$0.566780\pi$
$588$	1.01379e23	0.292576
$589$	6.26613e22	0.178246
$590$	−1.63516e21	−0.00458476
$591$	3.99905e22	0.110526
$592$	−2.78694e23	−0.759265
$593$	1.74110e23	0.467583	0.233791	−	0.972287i	$-0.424887\pi$
$593$	1.74110e23	0.467583	0.233791	+	0.972287i	$0.424887\pi$
$594$	1.83859e21	0.00486744
$595$	2.36196e23	0.616421
$596$	−1.47831e23	−0.380339
$597$	−1.95185e23	−0.495068
$598$	−2.48431e21	−0.00621221
$599$	7.03769e23	1.73501	0.867505	−	0.497428i	$-0.165722\pi$
$599$	7.03769e23	1.73501	0.867505	+	0.497428i	$0.165722\pi$
$600$	3.04165e21	0.00739305
$601$	2.15830e23	0.517224	0.258612	−	0.965981i	$-0.416735\pi$
$601$	2.15830e23	0.517224	0.258612	+	0.965981i	$0.416735\pi$
$602$	5.20561e21	0.0122999
$603$	−2.63602e23	−0.614118
$604$	−9.57216e22	−0.219885
$605$	−1.87418e23	−0.424513
$606$	−6.24987e20	−0.00139590
$607$	3.20290e23	0.705406	0.352703	−	0.935735i	$-0.385263\pi$
$607$	3.20290e23	0.705406	0.352703	+	0.935735i	$0.385263\pi$
$608$	2.11895e22	0.0460193
$609$	6.29562e22	0.134831
$610$	−6.54277e20	−0.00138184
$611$	−1.84024e23	−0.383287
$612$	−2.71076e23	−0.556806
$613$	−3.36623e23	−0.681915	−0.340957	−	0.940079i	$-0.610751\pi$
$613$	−3.36623e23	−0.681915	−0.340957	+	0.940079i	$0.610751\pi$
$614$	8.06497e21	0.0161128
$615$	6.55673e22	0.129196
$616$	6.25158e21	0.0121494
$617$	6.95589e22	0.133330	0.0666651	−	0.997775i	$-0.478764\pi$
$617$	6.95589e22	0.133330	0.0666651	+	0.997775i	$0.478764\pi$
$618$	−4.76724e21	−0.00901290
$619$	−5.07620e22	−0.0946604	−0.0473302	−	0.998879i	$-0.515071\pi$
$619$	−5.07620e22	−0.0946604	−0.0473302	+	0.998879i	$0.515071\pi$
$620$	3.50612e22	0.0644908
$621$	−8.30328e23	−1.50651
$622$	5.73064e21	0.0102562
$623$	−1.02886e24	−1.81638
$624$	1.45381e23	0.253185
$625$	5.10195e22	0.0876508
$626$	7.28640e20	0.00123490
$627$	−3.02268e23	−0.505379
$628$	8.94582e23	1.47558
$629$	4.01859e23	0.653948
$630$	−2.73161e21	−0.00438555
$631$	1.10928e24	1.75708	0.878540	−	0.477668i	$-0.158518\pi$
$631$	1.10928e24	1.75708	0.878540	+	0.477668i	$0.158518\pi$
$632$	−1.62922e22	−0.0254616
$633$	6.96303e23	1.07366
$634$	−6.37927e21	−0.00970538
$635$	3.60617e22	0.0541339
$636$	−1.77258e23	−0.262555
$637$	−1.43512e23	−0.209750
$638$	6.40317e20	0.000923462 0
$639$	−7.96004e23	−1.13281
$640$	1.58081e22	0.0221999
$641$	7.28063e23	1.00896	0.504482	−	0.863422i	$-0.331684\pi$
$641$	7.28063e23	1.00896	0.504482	+	0.863422i	$0.331684\pi$
$642$	4.39988e21	0.00601718
$643$	8.58846e23	1.15910	0.579552	−	0.814936i	$-0.303228\pi$
$643$	8.58846e23	1.15910	0.579552	+	0.814936i	$0.303228\pi$
$644$	−1.41158e24	−1.88007
$645$	−2.81677e23	−0.370248
$646$	−1.01831e22	−0.0132100
$647$	−1.41945e24	−1.81732	−0.908662	−	0.417533i	$-0.862895\pi$
$647$	−1.41945e24	−1.81732	−0.908662	+	0.417533i	$0.862895\pi$
$648$	9.73692e20	0.00123036
$649$	−3.47663e23	−0.433590
$650$	−2.15279e21	−0.00264995
$651$	−6.57727e22	−0.0799111
$652$	−1.52438e23	−0.182805
$653$	−8.68942e23	−1.02856	−0.514279	−	0.857623i	$-0.671940\pi$
$653$	−8.68942e23	−1.02856	−0.514279	+	0.857623i	$0.671940\pi$
$654$	−8.91237e21	−0.0104132
$655$	−1.35306e23	−0.156051
$656$	−3.25709e23	−0.370806
$657$	3.17346e22	0.0356638
$658$	9.38313e21	0.0104094
$659$	4.73723e23	0.518798	0.259399	−	0.965770i	$-0.416476\pi$
$659$	4.73723e23	0.518798	0.259399	+	0.965770i	$0.416476\pi$
$660$	−1.69130e23	−0.182850
$661$	3.47025e23	0.370381	0.185191	−	0.982703i	$-0.440710\pi$
$661$	3.47025e23	0.370381	0.185191	+	0.982703i	$0.440710\pi$
$662$	3.71909e21	0.00391872
$663$	−2.09629e23	−0.218065
$664$	−2.53662e22	−0.0260512
$665$	1.14349e24	1.15944
$666$	−4.64750e21	−0.00465253
$667$	−2.89174e23	−0.285818
$668$	−1.75224e24	−1.70999
$669$	−7.06286e23	−0.680548
$670$	−5.54071e21	−0.00527144
$671$	−1.39111e23	−0.130683
$672$	−2.22416e22	−0.0206313
$673$	1.71256e24	1.56862	0.784308	−	0.620371i	$-0.213018\pi$
$673$	1.71256e24	1.56862	0.784308	+	0.620371i	$0.213018\pi$
$674$	−4.15248e21	−0.00375576
$675$	−7.19523e23	−0.642632
$676$	9.27906e23	0.818384
$677$	−1.17905e24	−1.02690	−0.513450	−	0.858119i	$-0.671633\pi$
$677$	−1.17905e24	−1.02690	−0.513450	+	0.858119i	$0.671633\pi$
$678$	−6.96232e21	−0.00598827
$679$	1.07587e24	0.913836
$680$	−1.13961e22	−0.00955941
$681$	−3.47544e23	−0.287911
$682$	−6.68963e20	−0.000547312 0
$683$	−1.32715e24	−1.07237	−0.536185	−	0.844100i	$-0.680135\pi$
$683$	−1.32715e24	−1.07237	−0.536185	+	0.844100i	$0.680135\pi$
$684$	−1.31235e24	−1.04731
$685$	5.94061e23	0.468232
$686$	−7.54696e21	−0.00587512
$687$	−9.12259e23	−0.701432
$688$	1.39924e24	1.06265
$689$	2.50926e23	0.188228
$690$	−6.85424e21	−0.00507857
$691$	−7.04462e23	−0.515577	−0.257789	−	0.966201i	$-0.582994\pi$
$691$	−7.04462e23	−0.515577	−0.257789	+	0.966201i	$0.582994\pi$
$692$	−2.99099e22	−0.0216228
$693$	−5.80789e23	−0.414749
$694$	1.33226e21	0.000939797 0
$695$	1.77026e23	0.123358
$696$	−3.03755e21	−0.00209095
$697$	4.69651e23	0.319372
$698$	2.46414e22	0.0165537
$699$	1.48144e24	0.983170
$700$	−1.22321e24	−0.801985
$701$	1.02907e24	0.666561	0.333280	−	0.942828i	$-0.391844\pi$
$701$	1.02907e24	0.666561	0.333280	+	0.942828i	$0.391844\pi$
$702$	6.17313e21	0.00395039
$703$	1.94551e24	1.23002
$704$	8.40009e23	0.524706
$705$	−5.07723e23	−0.313342
$706$	2.08964e21	0.00127418
$707$	5.02703e23	0.302863
$708$	8.24589e23	0.490857
$709$	−1.50256e24	−0.883771	−0.441886	−	0.897071i	$-0.645690\pi$
$709$	−1.50256e24	−0.883771	−0.441886	+	0.897071i	$0.645690\pi$
$710$	−1.67314e22	−0.00972379
$711$	1.51359e24	0.869194
$712$	4.96410e22	0.0281683
$713$	3.02111e23	0.169397
$714$	1.06887e22	0.00592230
$715$	2.39420e23	0.131087
$716$	8.88122e23	0.480521
$717$	−1.38938e24	−0.742862
$718$	−1.96651e22	−0.0103906
$719$	−1.29790e24	−0.677715	−0.338858	−	0.940838i	$-0.610040\pi$
$719$	−1.29790e24	−0.677715	−0.338858	+	0.940838i	$0.610040\pi$
$720$	−7.34243e23	−0.378890
$721$	3.83448e24	1.95550
$722$	−3.05044e22	−0.0153744
$723$	−1.68791e24	−0.840764
$724$	1.37473e24	0.676768
$725$	−2.50584e23	−0.121922
$726$	−8.48134e21	−0.00407853
$727$	6.38437e23	0.303442	0.151721	−	0.988423i	$-0.451518\pi$
$727$	6.38437e23	0.303442	0.151721	+	0.988423i	$0.451518\pi$
$728$	2.09899e22	0.00986037
$729$	1.16248e24	0.539763
$730$	6.67037e20	0.000306130 0
$731$	−2.01762e24	−0.915252
$732$	3.29944e23	0.147943
$733$	−9.70112e23	−0.429970	−0.214985	−	0.976617i	$-0.568970\pi$
$733$	−9.70112e23	−0.429970	−0.214985	+	0.976617i	$0.568970\pi$
$734$	1.85638e22	0.00813298
$735$	−3.95950e23	−0.171474
$736$	1.02162e23	0.0437347
$737$	−1.17805e24	−0.498530
$738$	−5.43152e21	−0.00227218
$739$	2.98392e24	1.23399	0.616993	−	0.786969i	$-0.288351\pi$
$739$	2.98392e24	1.23399	0.616993	+	0.786969i	$0.288351\pi$
$740$	1.08858e24	0.445032
$741$	−1.01487e24	−0.410163
$742$	−1.27944e22	−0.00511196
$743$	4.48536e24	1.77171	0.885854	−	0.463965i	$-0.153574\pi$
$743$	4.48536e24	1.77171	0.885854	+	0.463965i	$0.153574\pi$
$744$	3.17344e21	0.00123925
$745$	5.77375e23	0.222910
$746$	2.61565e22	0.00998388
$747$	2.35659e24	0.889322
$748$	−1.21145e24	−0.452005
$749$	−3.53900e24	−1.30553
$750$	−1.49859e22	−0.00546591
$751$	−2.88722e24	−1.04121	−0.520607	−	0.853796i	$-0.674294\pi$
$751$	−2.88722e24	−1.04121	−0.520607	+	0.853796i	$0.674294\pi$
$752$	2.52214e24	0.899326
$753$	−2.04067e24	−0.719476
$754$	2.14988e21	0.000749477 0
$755$	3.73856e23	0.128871
$756$	3.50755e24	1.19555
$757$	−6.11135e23	−0.205979	−0.102989	−	0.994682i	$-0.532841\pi$
$757$	−6.11135e23	−0.205979	−0.102989	+	0.994682i	$0.532841\pi$
$758$	−5.71276e21	−0.00190396
$759$	−1.45733e24	−0.480290
$760$	−5.51717e22	−0.0179805
$761$	−2.08647e24	−0.672422	−0.336211	−	0.941787i	$-0.609146\pi$
$761$	−2.08647e24	−0.672422	−0.336211	+	0.941787i	$0.609146\pi$
$762$	1.63192e21	0.000520095 0
$763$	7.16858e24	2.25930
$764$	3.82798e24	1.19310
$765$	1.05873e24	0.326334
$766$	−8.33333e20	−0.000254024 0
$767$	−1.16729e24	−0.351899
$768$	−1.99180e24	−0.593848
$769$	−5.48432e24	−1.61714	−0.808572	−	0.588397i	$-0.799759\pi$
$769$	−5.48432e24	−1.61714	−0.808572	+	0.588397i	$0.799759\pi$
$770$	−1.22077e22	−0.00356011
$771$	3.11297e24	0.897869
$772$	1.21000e24	0.345175
$773$	−5.47763e23	−0.154549	−0.0772747	−	0.997010i	$-0.524622\pi$
$773$	−5.47763e23	−0.154549	−0.0772747	+	0.997010i	$0.524622\pi$
$774$	2.33338e22	0.00651158
$775$	2.61795e23	0.0722598
$776$	−5.19094e22	−0.0141717
$777$	−2.04211e24	−0.551443
$778$	6.75981e22	0.0180554
$779$	2.27371e24	0.600712
$780$	−5.67858e23	−0.148401
$781$	−3.55739e24	−0.919597
$782$	−4.90961e22	−0.0125542
$783$	7.18552e23	0.181754
$784$	1.96690e24	0.492148
$785$	−3.49393e24	−0.864813
$786$	−6.12309e21	−0.00149927
$787$	−4.94659e24	−1.19818	−0.599089	−	0.800683i	$-0.704470\pi$
$787$	−4.94659e24	−1.19818	−0.599089	+	0.800683i	$0.704470\pi$
$788$	7.75948e23	0.185934
$789$	9.68838e23	0.229666
$790$	3.18145e22	0.00746095
$791$	5.60008e24	1.29925
$792$	2.80223e22	0.00643190
$793$	−4.67069e23	−0.106062
$794$	−2.36071e22	−0.00530356
$795$	6.92308e23	0.153879
$796$	−3.78723e24	−0.832838
$797$	2.01271e24	0.437910	0.218955	−	0.975735i	$-0.429735\pi$
$797$	2.01271e24	0.437910	0.218955	+	0.975735i	$0.429735\pi$
$798$	5.17470e22	0.0111394
$799$	−3.63676e24	−0.774581
$800$	8.85283e22	0.0186559
$801$	−4.61179e24	−0.961596
$802$	1.08448e22	0.00223738
$803$	1.41824e23	0.0289513
$804$	2.79411e24	0.564374
$805$	5.51314e24	1.10188
$806$	−2.24606e21	−0.000444196 0
$807$	−2.46212e24	−0.481820
$808$	−2.42547e22	−0.00469677
$809$	−7.23390e24	−1.38615	−0.693074	−	0.720866i	$-0.743744\pi$
$809$	−7.23390e24	−1.38615	−0.693074	+	0.720866i	$0.743744\pi$
$810$	−1.90137e21	−0.000360532 0
$811$	−9.10229e24	−1.70794	−0.853972	−	0.520319i	$-0.825813\pi$
$811$	−9.10229e24	−1.70794	−0.853972	+	0.520319i	$0.825813\pi$
$812$	1.22156e24	0.226823
$813$	4.12236e24	0.757488
$814$	−2.07700e22	−0.00377684
$815$	5.95369e23	0.107139
$816$	2.87307e24	0.511659
$817$	−9.76783e24	−1.72151
$818$	6.72671e22	0.0117327
$819$	−1.95002e24	−0.336608
$820$	1.27222e24	0.217343
$821$	−3.84841e24	−0.650676	−0.325338	−	0.945598i	$-0.605478\pi$
$821$	−3.84841e24	−0.650676	−0.325338	+	0.945598i	$0.605478\pi$
$822$	2.68834e22	0.00449857
$823$	−4.92532e24	−0.815711	−0.407855	−	0.913047i	$-0.633723\pi$
$823$	−4.92532e24	−0.815711	−0.407855	+	0.913047i	$0.633723\pi$
$824$	−1.85008e23	−0.0303257
$825$	−1.26286e24	−0.204878
$826$	5.95186e22	0.00955701
$827$	−8.38249e24	−1.33222	−0.666110	−	0.745853i	$-0.732042\pi$
$827$	−8.38249e24	−1.33222	−0.666110	+	0.745853i	$0.732042\pi$
$828$	−6.32729e24	−0.995314
$829$	−1.69341e24	−0.263662	−0.131831	−	0.991272i	$-0.542086\pi$
$829$	−1.69341e24	−0.263662	−0.131831	+	0.991272i	$0.542086\pi$
$830$	4.95337e22	0.00763373
$831$	−4.76904e24	−0.727482
$832$	2.82035e24	0.425849
$833$	−2.83614e24	−0.423882
$834$	8.01107e21	0.00118517
$835$	6.84366e24	1.00220
$836$	−5.86498e24	−0.850185
$837$	−7.50699e23	−0.107721
$838$	2.05371e22	0.00291719
$839$	1.04997e25	1.47638	0.738192	−	0.674591i	$-0.235680\pi$
$839$	1.04997e25	1.47638	0.738192	+	0.674591i	$0.235680\pi$
$840$	5.79112e22	0.00806100
$841$	2.50246e23	0.0344828
$842$	6.56481e22	0.00895507
$843$	−3.68525e24	−0.497659
$844$	1.35106e25	1.80619
$845$	−3.62408e24	−0.479641
$846$	4.20592e22	0.00551077
$847$	6.82189e24	0.884903
$848$	−3.43907e24	−0.441649
$849$	3.25072e23	0.0413298
$850$	−4.25443e22	−0.00535526
$851$	9.37995e24	1.16896
$852$	8.43742e24	1.04105
$853$	5.99593e24	0.732470	0.366235	−	0.930522i	$-0.380647\pi$
$853$	5.99593e24	0.732470	0.366235	+	0.930522i	$0.380647\pi$
$854$	2.38152e22	0.00288047
$855$	5.12560e24	0.613808
$856$	1.70752e23	0.0202460
$857$	2.49140e24	0.292487	0.146243	−	0.989249i	$-0.453282\pi$
$857$	2.49140e24	0.292487	0.146243	+	0.989249i	$0.453282\pi$
$858$	1.08346e22	0.00125943
$859$	1.28997e25	1.48469	0.742346	−	0.670017i	$-0.233713\pi$
$859$	1.28997e25	1.48469	0.742346	+	0.670017i	$0.233713\pi$
$860$	−5.46545e24	−0.622858
$861$	−2.38661e24	−0.269311
$862$	3.37880e22	0.00377529
$863$	−9.14758e24	−1.01208	−0.506040	−	0.862510i	$-0.668891\pi$
$863$	−9.14758e24	−1.01208	−0.506040	+	0.862510i	$0.668891\pi$
$864$	−2.53855e23	−0.0278112
$865$	1.16818e23	0.0126728
$866$	−4.04022e22	−0.00434013
$867$	1.44484e24	0.153694
$868$	−1.27621e24	−0.134432
$869$	6.76433e24	0.705597
$870$	5.93154e21	0.000612709 0
$871$	−3.95535e24	−0.404604
$872$	−3.45874e23	−0.0350371
$873$	4.82252e24	0.483786
$874$	−2.37687e23	−0.0236134
$875$	1.20538e25	1.18592
$876$	−3.36379e23	−0.0327751
$877$	3.58663e23	0.0346091	0.0173045	−	0.999850i	$-0.494492\pi$
$877$	3.58663e23	0.0346091	0.0173045	+	0.999850i	$0.494492\pi$
$878$	1.66695e23	0.0159301
$879$	3.92494e24	0.371474
$880$	−3.28138e24	−0.307577
$881$	9.05050e24	0.840190	0.420095	−	0.907480i	$-0.361997\pi$
$881$	9.05050e24	0.840190	0.420095	+	0.907480i	$0.361997\pi$
$882$	3.28000e22	0.00301572
$883$	−9.56791e24	−0.871266	−0.435633	−	0.900124i	$-0.643476\pi$
$883$	−9.56791e24	−0.871266	−0.435633	+	0.900124i	$0.643476\pi$
$884$	−4.06750e24	−0.366845
$885$	−3.22056e24	−0.287683
$886$	−1.04311e23	−0.00922878
$887$	1.64860e25	1.44466	0.722328	−	0.691551i	$-0.243072\pi$
$887$	1.64860e25	1.44466	0.722328	+	0.691551i	$0.243072\pi$
$888$	9.85290e22	0.00855173
$889$	−1.31262e24	−0.112843
$890$	−9.69361e22	−0.00825411
$891$	−4.04265e23	−0.0340962
$892$	−1.37043e25	−1.14487
$893$	−1.76065e25	−1.45692
$894$	2.61283e22	0.00214162
$895$	−3.46870e24	−0.281625
$896$	−5.75405e23	−0.0462760
$897$	−4.89304e24	−0.389801
$898$	−5.47893e22	−0.00432362
$899$	−2.61442e23	−0.0204370
$900$	−5.48293e24	−0.424572
$901$	4.95892e24	0.380388
$902$	−2.42738e22	−0.00184451
$903$	1.02528e25	0.771789
$904$	−2.70196e23	−0.0201487
$905$	−5.36923e24	−0.396642
$906$	1.69183e22	0.00123813
$907$	−1.02873e24	−0.0745830	−0.0372915	−	0.999304i	$-0.511873\pi$
$907$	−1.02873e24	−0.0745830	−0.0372915	+	0.999304i	$0.511873\pi$
$908$	−6.74349e24	−0.484345
$909$	2.25333e24	0.160336
$910$	−4.09878e22	−0.00288937
$911$	1.84842e25	1.29091	0.645453	−	0.763800i	$-0.276669\pi$
$911$	1.84842e25	1.29091	0.645453	+	0.763800i	$0.276669\pi$
$912$	1.39093e25	0.962388
$913$	1.05317e25	0.721936
$914$	3.91105e21	0.000265614 0
$915$	−1.28865e24	−0.0867071
$916$	−1.77008e25	−1.18000
$917$	4.92505e24	0.325290
$918$	1.21996e23	0.00798331
$919$	5.70687e24	0.370012	0.185006	−	0.982737i	$-0.440770\pi$
$919$	5.70687e24	0.370012	0.185006	+	0.982737i	$0.440770\pi$
$920$	−2.66001e23	−0.0170878
$921$	1.58846e25	1.01104
$922$	−9.07171e22	−0.00572106
$923$	−1.19440e25	−0.746340
$924$	6.15621e24	0.381155
$925$	8.12822e24	0.498644
$926$	−1.92705e23	−0.0117138
$927$	1.71878e25	1.03524
$928$	−8.84089e22	−0.00527641
$929$	−2.76557e25	−1.63550	−0.817751	−	0.575573i	$-0.804779\pi$
$929$	−2.76557e25	−1.63550	−0.817751	+	0.575573i	$0.804779\pi$
$930$	−6.19691e21	−0.000363136 0
$931$	−1.37305e25	−0.797288
$932$	2.87448e25	1.65396
$933$	1.12869e25	0.643549
$934$	3.13137e23	0.0176924
$935$	4.73153e24	0.264913
$936$	9.40855e22	0.00522009
$937$	1.72166e25	0.946586	0.473293	−	0.880905i	$-0.343065\pi$
$937$	1.72166e25	0.946586	0.473293	+	0.880905i	$0.343065\pi$
$938$	2.01678e23	0.0109884
$939$	1.43511e24	0.0774869
$940$	−9.85149e24	−0.527127
$941$	1.43971e25	0.763421	0.381711	−	0.924282i	$-0.375335\pi$
$941$	1.43971e25	0.763421	0.381711	+	0.924282i	$0.375335\pi$
$942$	−1.58113e23	−0.00830874
$943$	1.09623e25	0.570890
$944$	1.59983e25	0.825680
$945$	−1.36993e25	−0.700693
$946$	1.04280e23	0.00528599
$947$	1.42930e25	0.718039	0.359019	−	0.933330i	$-0.383111\pi$
$947$	1.42930e25	0.718039	0.359019	+	0.933330i	$0.383111\pi$
$948$	−1.60437e25	−0.798789
$949$	4.76179e23	0.0234967
$950$	−2.05969e23	−0.0100728
$951$	−1.25645e25	−0.608989
$952$	4.14811e23	0.0199267
$953$	−1.88198e25	−0.896035	−0.448017	−	0.894025i	$-0.647870\pi$
$953$	−1.88198e25	−0.896035	−0.448017	+	0.894025i	$0.647870\pi$
$954$	−5.73500e22	−0.00270628
$955$	−1.49508e25	−0.699255
$956$	−2.69585e25	−1.24970
$957$	1.26115e24	0.0579450
$958$	1.56805e23	0.00714091
$959$	−2.16234e25	−0.976038
$960$	7.78138e24	0.348138
$961$	−2.22770e25	−0.987888
$962$	−6.97358e22	−0.00306526
$963$	−1.58633e25	−0.691147
$964$	−3.27510e25	−1.41439
$965$	−4.72586e24	−0.202301
$966$	2.49490e23	0.0105864
$967$	−3.33944e24	−0.140459	−0.0702294	−	0.997531i	$-0.522373\pi$
$967$	−3.33944e24	−0.140459	−0.0702294	+	0.997531i	$0.522373\pi$
$968$	−3.29147e23	−0.0137230
$969$	−2.00563e25	−0.828895
$970$	1.01366e23	0.00415270
$971$	8.70669e24	0.353581	0.176791	−	0.984248i	$-0.443428\pi$
$971$	8.70669e24	0.353581	0.176791	+	0.984248i	$0.443428\pi$
$972$	2.52701e25	1.01729
$973$	−6.44363e24	−0.257141
$974$	−4.45703e23	−0.0176317
$975$	−4.24008e24	−0.166278
$976$	6.40142e24	0.248859
$977$	1.36248e25	0.525080	0.262540	−	0.964921i	$-0.415440\pi$
$977$	1.36248e25	0.525080	0.262540	+	0.964921i	$0.415440\pi$
$978$	2.69426e22	0.00102934
$979$	−2.06104e25	−0.780607
$980$	−7.68273e24	−0.288465
$981$	3.21326e25	1.19608
$982$	−3.75637e23	−0.0138618
$983$	4.01641e25	1.46938	0.734689	−	0.678404i	$-0.237328\pi$
$983$	4.01641e25	1.46938	0.734689	+	0.678404i	$0.237328\pi$
$984$	1.15150e23	0.00417645
$985$	−3.03059e24	−0.108973
$986$	4.24869e22	0.00151461
$987$	1.84808e25	0.653167
$988$	−1.96919e25	−0.690006
$989$	−4.70940e25	−1.63605
$990$	−5.47202e22	−0.00188473
$991$	−1.87250e25	−0.639434	−0.319717	−	0.947513i	$-0.603588\pi$
$991$	−1.87250e25	−0.639434	−0.319717	+	0.947513i	$0.603588\pi$
$992$	9.23641e22	0.00312719
$993$	7.32503e24	0.245890
$994$	6.09011e23	0.0202694
$995$	1.47916e25	0.488112
$996$	−2.49792e25	−0.817287
$997$	−5.61599e25	−1.82187	−0.910935	−	0.412549i	$-0.864639\pi$
$997$	−5.61599e25	−1.82187	−0.910935	+	0.412549i	$0.864639\pi$
$998$	−1.18072e23	−0.00379786
$999$	−2.33077e25	−0.743349

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.b.1.11	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.b.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-3.42944 q^{2} -6754.54 q^{3} -131060. q^{4} +511876. q^{5} +23164.3 q^{6} -1.86320e7 q^{7} +898966. q^{8} -8.35164e7 q^{9} +O(q^{10})\)	\(q-3.42944 q^{2} -6754.54 q^{3} -131060. q^{4} +511876. q^{5} +23164.3 q^{6} -1.86320e7 q^{7} +898966. q^{8} -8.35164e7 q^{9} -1.75545e6 q^{10} -3.73240e8 q^{11} +8.85251e8 q^{12} -1.25316e9 q^{13} +6.38972e7 q^{14} -3.45749e9 q^{15} +1.71752e10 q^{16} -2.47656e10 q^{17} +2.86414e8 q^{18} -1.19897e11 q^{19} -6.70866e10 q^{20} +1.25850e11 q^{21} +1.28000e9 q^{22} -5.78063e11 q^{23} -6.07210e9 q^{24} -5.00922e11 q^{25} +4.29765e9 q^{26} +1.43640e12 q^{27} +2.44191e12 q^{28} +5.00246e11 q^{29} +1.18572e10 q^{30} -5.22626e11 q^{31} -1.76731e11 q^{32} +2.52106e12 q^{33} +8.49320e10 q^{34} -9.53726e12 q^{35} +1.09457e13 q^{36} -1.62265e13 q^{37} +4.11179e11 q^{38} +8.46454e12 q^{39} +4.60160e11 q^{40} -1.89639e13 q^{41} -4.31596e11 q^{42} +8.14686e13 q^{43} +4.89169e13 q^{44} -4.27501e13 q^{45} +1.98243e12 q^{46} +1.46847e14 q^{47} -1.16011e14 q^{48} +1.14519e14 q^{49} +1.71788e12 q^{50} +1.67280e14 q^{51} +1.64240e14 q^{52} -2.00234e14 q^{53} -4.92603e12 q^{54} -1.91053e14 q^{55} -1.67495e13 q^{56} +8.09848e14 q^{57} -1.71556e12 q^{58} +9.31474e14 q^{59} +4.53139e14 q^{60} +3.72712e14 q^{61} +1.79231e12 q^{62} +1.55607e15 q^{63} -2.25059e15 q^{64} -6.41465e14 q^{65} -8.64583e12 q^{66} +3.15629e15 q^{67} +3.24578e15 q^{68} +3.90455e15 q^{69} +3.27074e13 q^{70} +9.53111e15 q^{71} -7.50784e13 q^{72} -3.79981e14 q^{73} +5.56478e13 q^{74} +3.38350e15 q^{75} +1.57137e16 q^{76} +6.95419e15 q^{77} -2.90286e13 q^{78} -1.81233e16 q^{79} +8.79160e15 q^{80} +1.08312e15 q^{81} +6.50354e13 q^{82} -2.82171e16 q^{83} -1.64940e16 q^{84} -1.26769e16 q^{85} -2.79391e14 q^{86} -3.37893e15 q^{87} -3.35530e14 q^{88} +5.52201e16 q^{89} +1.46609e14 q^{90} +2.33489e16 q^{91} +7.57611e16 q^{92} +3.53010e15 q^{93} -5.03604e14 q^{94} -6.13724e16 q^{95} +1.19373e15 q^{96} -5.77435e16 q^{97} -3.92737e14 q^{98} +3.11716e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) \) 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

Varieties

Fields

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