LMFDB - Embedded newform 29.18.a.b.1.20

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			1.20
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)

$f(q)$	$=$	$q+652.859 q^{2} +4140.75 q^{3} +295153. q^{4} +358296. q^{5} +2.70332e6 q^{6} +1.05214e7 q^{7} +1.07122e8 q^{8} -1.11994e8 q^{9} +O(q^{10})$	\(q+652.859 q^{2} +4140.75 q^{3} +295153. q^{4} +358296. q^{5} +2.70332e6 q^{6} +1.05214e7 q^{7} +1.07122e8 q^{8} -1.11994e8 q^{9} +2.33917e8 q^{10} +1.15705e9 q^{11} +1.22215e9 q^{12} -2.51476e9 q^{13} +6.86899e9 q^{14} +1.48361e9 q^{15} +3.12492e10 q^{16} +1.45392e10 q^{17} -7.31166e10 q^{18} +1.40302e11 q^{19} +1.05752e11 q^{20} +4.35664e10 q^{21} +7.55391e11 q^{22} -5.22017e11 q^{23} +4.43565e11 q^{24} -6.34564e11 q^{25} -1.64179e12 q^{26} -9.98477e11 q^{27} +3.10542e12 q^{28} +5.00246e11 q^{29} +9.68589e11 q^{30} +5.44856e12 q^{31} +6.36066e12 q^{32} +4.79105e12 q^{33} +9.49202e12 q^{34} +3.76977e12 q^{35} -3.30555e13 q^{36} +2.38708e13 q^{37} +9.15975e13 q^{38} -1.04130e13 q^{39} +3.83813e13 q^{40} -5.39518e13 q^{41} +2.84428e13 q^{42} +5.68631e13 q^{43} +3.41507e14 q^{44} -4.01271e13 q^{45} -3.40803e14 q^{46} -1.71515e14 q^{47} +1.29395e14 q^{48} -1.21931e14 q^{49} -4.14281e14 q^{50} +6.02029e13 q^{51} -7.42240e14 q^{52} +6.93926e14 q^{53} -6.51865e14 q^{54} +4.14566e14 q^{55} +1.12707e15 q^{56} +5.80955e14 q^{57} +3.26591e14 q^{58} -1.52517e15 q^{59} +4.37893e14 q^{60} -2.52379e14 q^{61} +3.55714e15 q^{62} -1.17834e15 q^{63} +5.67187e13 q^{64} -9.01028e14 q^{65} +3.12788e15 q^{66} -9.07675e14 q^{67} +4.29128e15 q^{68} -2.16154e15 q^{69} +2.46113e15 q^{70} +1.43297e14 q^{71} -1.19971e16 q^{72} +5.43727e15 q^{73} +1.55842e16 q^{74} -2.62757e15 q^{75} +4.14106e16 q^{76} +1.21738e16 q^{77} -6.79822e15 q^{78} -6.13389e15 q^{79} +1.11965e16 q^{80} +1.03285e16 q^{81} -3.52229e16 q^{82} -1.62223e16 q^{83} +1.28588e16 q^{84} +5.20931e15 q^{85} +3.71236e16 q^{86} +2.07139e15 q^{87} +1.23945e17 q^{88} +4.92142e16 q^{89} -2.61973e16 q^{90} -2.64588e16 q^{91} -1.54075e17 q^{92} +2.25611e16 q^{93} -1.11975e17 q^{94} +5.02696e16 q^{95} +2.63379e16 q^{96} -7.93342e16 q^{97} -7.96036e16 q^{98} -1.29583e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	652.859	1.80329	0.901643	−	0.432481i	$-0.142362\pi$
$2$	652.859	1.80329	0.901643	+	0.432481i	$0.142362\pi$
$3$	4140.75	0.364374	0.182187	−	0.983264i	$-0.441682\pi$
$3$	4140.75	0.364374	0.182187	+	0.983264i	$0.441682\pi$
$4$	295153.	2.25184
$5$	358296.	0.410201	0.205100	−	0.978741i	$-0.434248\pi$
$5$	358296.	0.410201	0.205100	+	0.978741i	$0.434248\pi$
$6$	2.70332e6	0.657071
$7$	1.05214e7	0.689827	0.344913	−	0.938634i	$-0.387908\pi$
$7$	1.05214e7	0.689827	0.344913	+	0.938634i	$0.387908\pi$
$8$	1.07122e8	2.25743
$9$	−1.11994e8	−0.867231
$10$	2.33917e8	0.739709
$11$	1.15705e9	1.62747	0.813737	−	0.581233i	$-0.197430\pi$
$11$	1.15705e9	1.62747	0.813737	+	0.581233i	$0.197430\pi$
$12$	1.22215e9	0.820513
$13$	−2.51476e9	−0.855024	−0.427512	−	0.904010i	$-0.640610\pi$
$13$	−2.51476e9	−0.855024	−0.427512	+	0.904010i	$0.640610\pi$
$14$	6.86899e9	1.24396
$15$	1.48361e9	0.149467
$16$	3.12492e10	1.81894
$17$	1.45392e10	0.505503	0.252751	−	0.967531i	$-0.418665\pi$
$17$	1.45392e10	0.505503	0.252751	+	0.967531i	$0.418665\pi$
$18$	−7.31166e10	−1.56387
$19$	1.40302e11	1.89521	0.947607	−	0.319438i	$-0.103494\pi$
$19$	1.40302e11	1.89521	0.947607	+	0.319438i	$0.103494\pi$
$20$	1.05752e11	0.923706
$21$	4.35664e10	0.251355
$22$	7.55391e11	2.93480
$23$	−5.22017e11	−1.38995	−0.694973	−	0.719036i	$-0.744584\pi$
$23$	−5.22017e11	−1.38995	−0.694973	+	0.719036i	$0.744584\pi$
$24$	4.43565e11	0.822548
$25$	−6.34564e11	−0.831735
$26$	−1.64179e12	−1.54185
$27$	−9.98477e11	−0.680371
$28$	3.10542e12	1.55338
$29$	5.00246e11	0.185695
$29$	5.00246e11	0.185695
$30$	9.68589e11	0.269531
$31$	5.44856e12	1.14738	0.573690	−	0.819073i	$-0.305511\pi$
$31$	5.44856e12	1.14738	0.573690	+	0.819073i	$0.305511\pi$
$32$	6.36066e12	1.02265
$33$	4.79105e12	0.593010
$34$	9.49202e12	0.911566
$35$	3.76977e12	0.282967
$36$	−3.30555e13	−1.95287
$37$	2.38708e13	1.11725	0.558626	−	0.829419i	$-0.311329\pi$
$37$	2.38708e13	1.11725	0.558626	+	0.829419i	$0.311329\pi$
$38$	9.15975e13	3.41761
$39$	−1.04130e13	−0.311549
$40$	3.83813e13	0.925998
$41$	−5.39518e13	−1.05522	−0.527610	−	0.849487i	$-0.676912\pi$
$41$	−5.39518e13	−1.05522	−0.527610	+	0.849487i	$0.676912\pi$
$42$	2.84428e13	0.453266
$43$	5.68631e13	0.741905	0.370953	−	0.928652i	$-0.379031\pi$
$43$	5.68631e13	0.741905	0.370953	+	0.928652i	$0.379031\pi$
$44$	3.41507e14	3.66481
$45$	−4.01271e13	−0.355739
$46$	−3.40803e14	−2.50647
$47$	−1.71515e14	−1.05068	−0.525339	−	0.850893i	$-0.676061\pi$
$47$	−1.71515e14	−1.05068	−0.525339	+	0.850893i	$0.676061\pi$
$48$	1.29395e14	0.662777
$49$	−1.21931e14	−0.524139
$50$	−4.14281e14	−1.49986
$51$	6.02029e13	0.184192
$52$	−7.42240e14	−1.92538
$53$	6.93926e14	1.53098	0.765488	−	0.643451i	$-0.222498\pi$
$53$	6.93926e14	1.53098	0.765488	+	0.643451i	$0.222498\pi$
$54$	−6.51865e14	−1.22690
$55$	4.14566e14	0.667591
$56$	1.12707e15	1.55723
$57$	5.80955e14	0.690568
$58$	3.26591e14	0.334862
$59$	−1.52517e15	−1.35231	−0.676153	−	0.736761i	$-0.736354\pi$
$59$	−1.52517e15	−1.35231	−0.676153	+	0.736761i	$0.736354\pi$
$60$	4.37893e14	0.336575
$61$	−2.52379e14	−0.168558	−0.0842790	−	0.996442i	$-0.526859\pi$
$61$	−2.52379e14	−0.168558	−0.0842790	+	0.996442i	$0.526859\pi$
$62$	3.55714e15	2.06905
$63$	−1.17834e15	−0.598239
$64$	5.67187e13	0.0251882
$65$	−9.01028e14	−0.350731
$66$	3.12788e15	1.06937
$67$	−9.07675e14	−0.273083	−0.136542	−	0.990634i	$-0.543599\pi$
$67$	−9.07675e14	−0.273083	−0.136542	+	0.990634i	$0.543599\pi$
$68$	4.29128e15	1.13831
$69$	−2.16154e15	−0.506461
$70$	2.46113e15	0.510271
$71$	1.43297e14	0.0263354	0.0131677	−	0.999913i	$-0.495808\pi$
$71$	1.43297e14	0.0263354	0.0131677	+	0.999913i	$0.495808\pi$
$72$	−1.19971e16	−1.95771
$73$	5.43727e15	0.789108	0.394554	−	0.918873i	$-0.370899\pi$
$73$	5.43727e15	0.789108	0.394554	+	0.918873i	$0.370899\pi$
$74$	1.55842e16	2.01473
$75$	−2.62757e15	−0.303063
$76$	4.14106e16	4.26772
$77$	1.21738e16	1.12268
$78$	−6.79822e15	−0.561812
$79$	−6.13389e15	−0.454889	−0.227445	−	0.973791i	$-0.573037\pi$
$79$	−6.13389e15	−0.454889	−0.227445	+	0.973791i	$0.573037\pi$
$80$	1.11965e16	0.746132
$81$	1.03285e16	0.619321
$82$	−3.52229e16	−1.90286
$83$	−1.62223e16	−0.790584	−0.395292	−	0.918556i	$-0.629357\pi$
$83$	−1.62223e16	−0.790584	−0.395292	+	0.918556i	$0.629357\pi$
$84$	1.28588e16	0.566012
$85$	5.20931e15	0.207357
$86$	3.71236e16	1.33787
$87$	2.07139e15	0.0676626
$88$	1.23945e17	3.67390
$89$	4.92142e16	1.32518	0.662590	−	0.748982i	$-0.269457\pi$
$89$	4.92142e16	1.32518	0.662590	+	0.748982i	$0.269457\pi$
$90$	−2.61973e16	−0.641499
$91$	−2.64588e16	−0.589819
$92$	−1.54075e17	−3.12994
$93$	2.25611e16	0.418076
$94$	−1.11975e17	−1.89467
$95$	5.02696e16	0.777418
$96$	2.63379e16	0.372628
$97$	−7.93342e16	−1.02778	−0.513891	−	0.857856i	$-0.671796\pi$
$97$	−7.93342e16	−1.02778	−0.513891	+	0.857856i	$0.671796\pi$
$98$	−7.96036e16	−0.945172
$99$	−1.29583e17	−1.41140
$100$	−1.87294e17	−1.87294
$101$	−6.32559e16	−0.581259	−0.290629	−	0.956836i	$-0.593865\pi$
$101$	−6.32559e16	−0.581259	−0.290629	+	0.956836i	$0.593865\pi$
$102$	3.93041e16	0.332151
$103$	−1.77368e17	−1.37961	−0.689807	−	0.723993i	$-0.742305\pi$
$103$	−1.77368e17	−1.37961	−0.689807	+	0.723993i	$0.742305\pi$
$104$	−2.69386e17	−1.93015
$105$	1.56097e16	0.103106
$106$	4.53036e17	2.76079
$107$	−1.42311e17	−0.800714	−0.400357	−	0.916359i	$-0.631114\pi$
$107$	−1.42311e17	−0.800714	−0.400357	+	0.916359i	$0.631114\pi$
$108$	−2.94704e17	−1.53209
$109$	−1.29421e17	−0.622128	−0.311064	−	0.950389i	$-0.600685\pi$
$109$	−1.29421e17	−0.622128	−0.311064	+	0.950389i	$0.600685\pi$
$110$	2.70653e17	1.20386
$111$	9.88427e16	0.407098
$112$	3.28786e17	1.25476
$113$	1.59967e17	0.566063	0.283032	−	0.959111i	$-0.408660\pi$
$113$	1.59967e17	0.566063	0.283032	+	0.959111i	$0.408660\pi$
$114$	3.79282e17	1.24529
$115$	−1.87036e17	−0.570157
$116$	1.47649e17	0.418156
$117$	2.81639e17	0.741504
$118$	−9.95718e17	−2.43859
$119$	1.52972e17	0.348709
$120$	1.58927e17	0.337410
$121$	8.33317e17	1.64867
$122$	−1.64768e17	−0.303958
$123$	−2.23401e17	−0.384495
$124$	1.60816e18	2.58372
$125$	−5.00719e17	−0.751379
$126$	−7.69289e17	−1.07880
$127$	−6.38435e17	−0.837115	−0.418558	−	0.908190i	$-0.637464\pi$
$127$	−6.38435e17	−0.837115	−0.418558	+	0.908190i	$0.637464\pi$
$128$	−7.96676e17	−0.977230
$129$	2.35456e17	0.270331
$130$	−5.88244e17	−0.632469
$131$	−1.43449e18	−1.44508	−0.722538	−	0.691332i	$-0.757024\pi$
$131$	−1.43449e18	−1.44508	−0.722538	+	0.691332i	$0.757024\pi$
$132$	1.41409e18	1.33536
$133$	1.47617e18	1.30737
$134$	−5.92584e17	−0.492447
$135$	−3.57750e17	−0.279089
$136$	1.55746e18	1.14113
$137$	−2.34038e18	−1.61124	−0.805622	−	0.592431i	$-0.798168\pi$
$137$	−2.34038e18	−1.61124	−0.805622	+	0.592431i	$0.798168\pi$
$138$	−1.41118e18	−0.913293
$139$	6.13804e17	0.373597	0.186799	−	0.982398i	$-0.440189\pi$
$139$	6.13804e17	0.373597	0.186799	+	0.982398i	$0.440189\pi$
$140$	1.11266e18	0.637198
$141$	−7.10199e17	−0.382840
$142$	9.35526e16	0.0474903
$143$	−2.90970e18	−1.39153
$144$	−3.49974e18	−1.57745
$145$	1.79236e17	0.0761724
$146$	3.54977e18	1.42299
$147$	−5.04884e17	−0.190983
$148$	7.04553e18	2.51588
$149$	−3.00916e18	−1.01476	−0.507379	−	0.861723i	$-0.669386\pi$
$149$	−3.00916e18	−1.01476	−0.507379	+	0.861723i	$0.669386\pi$
$150$	−1.71543e18	−0.546509
$151$	2.14548e17	0.0645983	0.0322991	−	0.999478i	$-0.489717\pi$
$151$	2.14548e17	0.0645983	0.0322991	+	0.999478i	$0.489717\pi$
$152$	1.50294e19	4.27831
$153$	−1.62830e18	−0.438388
$154$	7.94777e18	2.02451
$155$	1.95219e18	0.470656
$156$	−3.07343e18	−0.701558
$157$	−5.18646e18	−1.12131	−0.560653	−	0.828051i	$-0.689450\pi$
$157$	−5.18646e18	−1.12131	−0.560653	+	0.828051i	$0.689450\pi$
$158$	−4.00457e18	−0.820295
$159$	2.87337e18	0.557848
$160$	2.27900e18	0.419492
$161$	−5.49235e18	−0.958822
$162$	6.74308e18	1.11681
$163$	−2.17414e18	−0.341737	−0.170869	−	0.985294i	$-0.554657\pi$
$163$	−2.17414e18	−0.341737	−0.170869	+	0.985294i	$0.554657\pi$
$164$	−1.59240e19	−2.37619
$165$	1.71661e18	0.243253
$166$	−1.05909e19	−1.42565
$167$	7.99349e18	1.02246	0.511230	−	0.859444i	$-0.329190\pi$
$167$	7.99349e18	1.02246	0.511230	+	0.859444i	$0.329190\pi$
$168$	4.66692e18	0.567416
$169$	−2.32639e18	−0.268934
$170$	3.40095e18	0.373925
$171$	−1.57130e19	−1.64359
$172$	1.67833e19	1.67065
$173$	5.81820e18	0.551311	0.275656	−	0.961256i	$-0.411105\pi$
$173$	5.81820e18	0.551311	0.275656	+	0.961256i	$0.411105\pi$
$174$	1.35233e18	0.122015
$175$	−6.67650e18	−0.573753
$176$	3.61569e19	2.96029
$177$	−6.31532e18	−0.492746
$178$	3.21299e19	2.38968
$179$	2.24434e19	1.59161	0.795806	−	0.605552i	$-0.207048\pi$
$179$	2.24434e19	1.59161	0.795806	+	0.605552i	$0.207048\pi$
$180$	−1.18436e19	−0.801067
$181$	1.47666e19	0.952822	0.476411	−	0.879223i	$-0.341937\pi$
$181$	1.47666e19	0.952822	0.476411	+	0.879223i	$0.341937\pi$
$182$	−1.72739e19	−1.06361
$183$	−1.04504e18	−0.0614182
$184$	−5.59195e19	−3.13770
$185$	8.55279e18	0.458298
$186$	1.47292e19	0.753910
$187$	1.68225e19	0.822692
$188$	−5.06231e19	−2.36596
$189$	−1.05054e19	−0.469338
$190$	3.28190e19	1.40191
$191$	−8.66002e18	−0.353781	−0.176891	−	0.984230i	$-0.556604\pi$
$191$	−8.66002e18	−0.353781	−0.176891	+	0.984230i	$0.556604\pi$
$192$	2.34858e17	0.00917793
$193$	4.09075e19	1.52956	0.764779	−	0.644293i	$-0.222848\pi$
$193$	4.09075e19	1.52956	0.764779	+	0.644293i	$0.222848\pi$
$194$	−5.17941e19	−1.85338
$195$	−3.73093e18	−0.127798
$196$	−3.59882e19	−1.18028
$197$	−4.27580e19	−1.34293	−0.671466	−	0.741035i	$-0.734335\pi$
$197$	−4.27580e19	−1.34293	−0.671466	+	0.741035i	$0.734335\pi$
$198$	−8.45995e19	−2.54515
$199$	1.19856e19	0.345467	0.172734	−	0.984969i	$-0.444740\pi$
$199$	1.19856e19	0.345467	0.172734	+	0.984969i	$0.444740\pi$
$200$	−6.79757e19	−1.87758
$201$	−3.75845e18	−0.0995045
$202$	−4.12972e19	−1.04818
$203$	5.26329e18	0.128098
$204$	1.77691e19	0.414771
$205$	−1.93307e19	−0.432852
$206$	−1.15796e20	−2.48784
$207$	5.84629e19	1.20540
$208$	−7.85844e19	−1.55524
$209$	1.62336e20	3.08441
$210$	1.01909e19	0.185930
$211$	−5.40899e19	−0.947798	−0.473899	−	0.880579i	$-0.657154\pi$
$211$	−5.40899e19	−0.947798	−0.473899	+	0.880579i	$0.657154\pi$
$212$	2.04814e20	3.44751
$213$	5.93355e17	0.00959596
$214$	−9.29093e19	−1.44392
$215$	2.03738e19	0.304330
$216$	−1.06959e20	−1.53589
$217$	5.73265e19	0.791494
$218$	−8.44937e19	−1.12187
$219$	2.25144e19	0.287531
$220$	1.22360e20	1.50331
$221$	−3.65625e19	−0.432217
$222$	6.45304e19	0.734115
$223$	−1.98803e19	−0.217686	−0.108843	−	0.994059i	$-0.534715\pi$
$223$	−1.98803e19	−0.217686	−0.108843	+	0.994059i	$0.534715\pi$
$224$	6.69231e19	0.705453
$225$	7.10676e19	0.721307
$226$	1.04436e20	1.02077
$227$	1.25506e20	1.18153	0.590764	−	0.806845i	$-0.298826\pi$
$227$	1.25506e20	1.18153	0.590764	+	0.806845i	$0.298826\pi$
$228$	1.71471e20	1.55505
$229$	−4.26961e19	−0.373067	−0.186533	−	0.982449i	$-0.559725\pi$
$229$	−4.26961e19	−0.373067	−0.186533	+	0.982449i	$0.559725\pi$
$230$	−1.22108e20	−1.02816
$231$	5.04085e19	0.409074
$232$	5.35874e19	0.419194
$233$	8.91859e18	0.0672621	0.0336311	−	0.999434i	$-0.489293\pi$
$233$	8.91859e18	0.0672621	0.0336311	+	0.999434i	$0.489293\pi$
$234$	1.83871e20	1.33714
$235$	−6.14529e19	−0.430989
$236$	−4.50158e20	−3.04518
$237$	−2.53989e19	−0.165750
$238$	9.98694e19	0.628823
$239$	2.26702e20	1.37744	0.688720	−	0.725027i	$-0.258173\pi$
$239$	2.26702e20	1.37744	0.688720	+	0.725027i	$0.258173\pi$
$240$	4.63617e19	0.271872
$241$	1.86486e20	1.05560	0.527802	−	0.849368i	$-0.323016\pi$
$241$	1.86486e20	1.05560	0.527802	+	0.849368i	$0.323016\pi$
$242$	5.44039e20	2.97303
$243$	1.71711e20	0.906036
$244$	−7.44904e19	−0.379566
$245$	−4.36872e19	−0.215002
$246$	−1.45849e20	−0.693355
$247$	−3.52826e20	−1.62045
$248$	5.83660e20	2.59013
$249$	−6.71723e19	−0.288069
$250$	−3.26899e20	−1.35495
$251$	3.50739e20	1.40526	0.702631	−	0.711554i	$-0.252009\pi$
$251$	3.50739e20	1.40526	0.702631	+	0.711554i	$0.252009\pi$
$252$	−3.47790e20	−1.34714
$253$	−6.03999e20	−2.26210
$254$	−4.16808e20	−1.50956
$255$	2.15704e19	0.0755558
$256$	−5.27551e20	−1.78741
$257$	6.98794e19	0.229043	0.114522	−	0.993421i	$-0.463466\pi$
$257$	6.98794e19	0.229043	0.114522	+	0.993421i	$0.463466\pi$
$258$	1.53719e20	0.487485
$259$	2.51154e20	0.770711
$260$	−2.65941e20	−0.789791
$261$	−5.60248e19	−0.161041
$262$	−9.36518e20	−2.60588
$263$	3.37246e20	0.908496	0.454248	−	0.890875i	$-0.349908\pi$
$263$	3.37246e20	0.908496	0.454248	+	0.890875i	$0.349908\pi$
$264$	5.13226e20	1.33868
$265$	2.48631e20	0.628007
$266$	9.63734e20	2.35756
$267$	2.03783e20	0.482862
$268$	−2.67903e20	−0.614939
$269$	5.58156e20	1.24126	0.620628	−	0.784105i	$-0.286878\pi$
$269$	5.58156e20	1.24126	0.620628	+	0.784105i	$0.286878\pi$
$270$	−2.33560e20	−0.503277
$271$	5.37531e20	1.12244	0.561221	−	0.827666i	$-0.310332\pi$
$271$	5.37531e20	1.12244	0.561221	+	0.827666i	$0.310332\pi$
$272$	4.54337e20	0.919481
$273$	−1.09559e20	−0.214915
$274$	−1.52794e21	−2.90553
$275$	−7.34222e20	−1.35363
$276$	−6.37985e20	−1.14047
$277$	1.98272e19	0.0343703	0.0171852	−	0.999852i	$-0.494530\pi$
$277$	1.98272e19	0.0343703	0.0171852	+	0.999852i	$0.494530\pi$
$278$	4.00727e20	0.673703
$279$	−6.10208e20	−0.995044
$280$	4.03825e20	0.638778
$281$	1.12948e21	1.73330	0.866649	−	0.498918i	$-0.166269\pi$
$281$	1.12948e21	1.73330	0.866649	+	0.498918i	$0.166269\pi$
$282$	−4.63660e20	−0.690370
$283$	7.43230e19	0.107384	0.0536919	−	0.998558i	$-0.482901\pi$
$283$	7.43230e19	0.107384	0.0536919	+	0.998558i	$0.482901\pi$
$284$	4.22945e19	0.0593032
$285$	2.08154e20	0.283271
$286$	−1.89963e21	−2.50933
$287$	−5.67648e20	−0.727919
$288$	−7.12359e20	−0.886875
$289$	−6.15853e20	−0.744467
$290$	1.17016e20	0.137361
$291$	−3.28503e20	−0.374497
$292$	1.60483e21	1.77695
$293$	5.50391e20	0.591966	0.295983	−	0.955193i	$-0.404353\pi$
$293$	5.50391e20	0.591966	0.295983	+	0.955193i	$0.404353\pi$
$294$	−3.29618e20	−0.344397
$295$	−5.46460e20	−0.554717
$296$	2.55708e21	2.52212
$297$	−1.15529e21	−1.10729
$298$	−1.96456e21	−1.82990
$299$	1.31275e21	1.18844
$300$	−7.75535e20	−0.682450
$301$	5.98279e20	0.511786
$302$	1.40070e20	0.116489
$303$	−2.61927e20	−0.211796
$304$	4.38433e21	3.44729
$305$	−9.04262e19	−0.0691426
$306$	−1.06305e21	−0.790538
$307$	−5.62539e20	−0.406889	−0.203445	−	0.979086i	$-0.565214\pi$
$307$	−5.62539e20	−0.406889	−0.203445	+	0.979086i	$0.565214\pi$
$308$	3.59313e21	2.52809
$309$	−7.34434e20	−0.502696
$310$	1.27451e21	0.848727
$311$	−1.38771e21	−0.899156	−0.449578	−	0.893241i	$-0.648426\pi$
$311$	−1.38771e21	−0.899156	−0.449578	+	0.893241i	$0.648426\pi$
$312$	−1.11546e21	−0.703299
$313$	2.65655e21	1.63001	0.815007	−	0.579451i	$-0.196733\pi$
$313$	2.65655e21	1.63001	0.815007	+	0.579451i	$0.196733\pi$
$314$	−3.38603e21	−2.02204
$315$	−4.22193e20	−0.245398
$316$	−1.81044e21	−1.02434
$317$	−1.53955e21	−0.847988	−0.423994	−	0.905665i	$-0.639372\pi$
$317$	−1.53955e21	−0.847988	−0.423994	+	0.905665i	$0.639372\pi$
$318$	1.87591e21	1.00596
$319$	5.78810e20	0.302214
$320$	2.03221e19	0.0103322
$321$	−5.89275e20	−0.291760
$322$	−3.58573e21	−1.72903
$323$	2.03987e21	0.958036
$324$	3.04850e21	1.39461
$325$	1.59578e21	0.711154
$326$	−1.41941e21	−0.616250
$327$	−5.35900e20	−0.226688
$328$	−5.77942e21	−2.38208
$329$	−1.80457e21	−0.724786
$330$	1.12071e21	0.438655
$331$	3.77688e21	1.44077	0.720385	−	0.693574i	$-0.243965\pi$
$331$	3.77688e21	1.44077	0.720385	+	0.693574i	$0.243965\pi$
$332$	−4.78806e21	−1.78027
$333$	−2.67339e21	−0.968917
$334$	5.21863e21	1.84379
$335$	−3.25216e20	−0.112019
$336$	1.36142e21	0.457201
$337$	−1.21175e21	−0.396788	−0.198394	−	0.980122i	$-0.563573\pi$
$337$	−1.21175e21	−0.396788	−0.198394	+	0.980122i	$0.563573\pi$
$338$	−1.51881e21	−0.484965
$339$	6.62384e20	0.206259
$340$	1.53755e21	0.466936
$341$	6.30425e21	1.86733
$342$	−1.02584e22	−2.96386
$343$	−3.73048e21	−1.05139
$344$	6.09128e21	1.67480
$345$	−7.74470e20	−0.207751
$346$	3.79847e21	0.994172
$347$	−7.01646e21	−1.79192	−0.895958	−	0.444138i	$-0.853510\pi$
$347$	−7.01646e21	−1.79192	−0.895958	+	0.444138i	$0.853510\pi$
$348$	6.11378e20	0.152365
$349$	−7.19973e20	−0.175106	−0.0875528	−	0.996160i	$-0.527905\pi$
$349$	−7.19973e20	−0.175106	−0.0875528	+	0.996160i	$0.527905\pi$
$350$	−4.35881e21	−1.03464
$351$	2.51093e21	0.581734
$352$	7.35960e21	1.66434
$353$	−3.89749e21	−0.860400	−0.430200	−	0.902734i	$-0.641557\pi$
$353$	−3.89749e21	−0.860400	−0.430200	+	0.902734i	$0.641557\pi$
$354$	−4.12302e21	−0.888561
$355$	5.13426e19	0.0108028
$356$	1.45257e22	2.98409
$357$	6.33419e20	0.127061
$358$	1.46524e22	2.87013
$359$	2.13839e21	0.409057	0.204529	−	0.978861i	$-0.434434\pi$
$359$	2.13839e21	0.409057	0.204529	+	0.978861i	$0.434434\pi$
$360$	−4.29849e21	−0.803054
$361$	1.42043e22	2.59184
$362$	9.64049e21	1.71821
$363$	3.45055e21	0.600734
$364$	−7.80940e21	−1.32818
$365$	1.94815e21	0.323693
$366$	−6.82262e20	−0.110755
$367$	−2.17384e21	−0.344799	−0.172399	−	0.985027i	$-0.555152\pi$
$367$	−2.17384e21	−0.344799	−0.172399	+	0.985027i	$0.555152\pi$
$368$	−1.63126e22	−2.52823
$369$	6.04229e21	0.915119
$370$	5.58377e21	0.826442
$371$	7.30107e21	1.05611
$372$	6.65898e21	0.941440
$373$	3.19905e21	0.442074	0.221037	−	0.975265i	$-0.429056\pi$
$373$	3.19905e21	0.442074	0.221037	+	0.975265i	$0.429056\pi$
$374$	1.09827e22	1.48355
$375$	−2.07335e21	−0.273783
$376$	−1.83730e22	−2.37183
$377$	−1.25800e21	−0.158774
$378$	−6.85853e21	−0.846352
$379$	−1.31984e22	−1.59253	−0.796266	−	0.604947i	$-0.793194\pi$
$379$	−1.31984e22	−1.59253	−0.796266	+	0.604947i	$0.793194\pi$
$380$	1.48372e22	1.75062
$381$	−2.64360e21	−0.305023
$382$	−5.65377e21	−0.637969
$383$	4.70891e20	0.0519673	0.0259837	−	0.999662i	$-0.491728\pi$
$383$	4.70891e20	0.0519673	0.0259837	+	0.999662i	$0.491728\pi$
$384$	−3.29883e21	−0.356078
$385$	4.36181e21	0.460522
$386$	2.67068e22	2.75823
$387$	−6.36835e21	−0.643404
$388$	−2.34157e22	−2.31440
$389$	7.19164e21	0.695434	0.347717	−	0.937599i	$-0.386957\pi$
$389$	7.19164e21	0.695434	0.347717	+	0.937599i	$0.386957\pi$
$390$	−2.43577e21	−0.230456
$391$	−7.58968e21	−0.702621
$392$	−1.30615e22	−1.18320
$393$	−5.93984e21	−0.526548
$394$	−2.79149e22	−2.42169
$395$	−2.19774e21	−0.186596
$396$	−3.82469e22	−3.17824
$397$	9.34349e21	0.759959	0.379979	−	0.924995i	$-0.375931\pi$
$397$	9.34349e21	0.759959	0.379979	+	0.924995i	$0.375931\pi$
$398$	7.82488e21	0.622977
$399$	6.11246e21	0.476372
$400$	−1.98296e22	−1.51288
$401$	−1.18885e22	−0.887977	−0.443988	−	0.896033i	$-0.646437\pi$
$401$	−1.18885e22	−0.887977	−0.443988	+	0.896033i	$0.646437\pi$
$402$	−2.45374e21	−0.179435
$403$	−1.37018e22	−0.981037
$404$	−1.86702e22	−1.30890
$405$	3.70067e21	0.254046
$406$	3.43619e21	0.230997
$407$	2.76196e22	1.81830
$408$	6.44906e21	0.415800
$409$	2.42965e22	1.53425	0.767123	−	0.641500i	$-0.221688\pi$
$409$	2.42965e22	1.53425	0.767123	+	0.641500i	$0.221688\pi$
$410$	−1.26202e22	−0.780556
$411$	−9.69091e21	−0.587096
$412$	−5.23506e22	−3.10667
$413$	−1.60469e22	−0.932857
$414$	3.81681e22	2.17369
$415$	−5.81237e21	−0.324298
$416$	−1.59956e22	−0.874391
$417$	2.54161e21	0.136129
$418$	1.05983e23	5.56208
$419$	2.77211e21	0.142558	0.0712788	−	0.997456i	$-0.477292\pi$
$419$	2.77211e21	0.142558	0.0712788	+	0.997456i	$0.477292\pi$
$420$	4.60724e21	0.232179
$421$	−2.03291e22	−1.00397	−0.501985	−	0.864877i	$-0.667397\pi$
$421$	−2.03291e22	−1.00397	−0.501985	+	0.864877i	$0.667397\pi$
$422$	−3.53131e22	−1.70915
$423$	1.92087e22	0.911180
$424$	7.43347e22	3.45606
$425$	−9.22602e21	−0.420444
$426$	3.87378e20	0.0173043
$427$	−2.65538e21	−0.116276
$428$	−4.20037e22	−1.80308
$429$	−1.20483e22	−0.507038
$430$	1.33012e22	0.548794
$431$	−1.04255e22	−0.421737	−0.210868	−	0.977514i	$-0.567629\pi$
$431$	−1.04255e22	−0.421737	−0.210868	+	0.977514i	$0.567629\pi$
$432$	−3.12016e22	−1.23756
$433$	3.20282e21	0.124562	0.0622809	−	0.998059i	$-0.480163\pi$
$433$	3.20282e21	0.124562	0.0622809	+	0.998059i	$0.480163\pi$
$434$	3.74261e22	1.42729
$435$	7.42171e20	0.0277553
$436$	−3.81990e22	−1.40093
$437$	−7.32400e22	−2.63425
$438$	1.46987e22	0.518500
$439$	2.99418e22	1.03593	0.517964	−	0.855402i	$-0.326690\pi$
$439$	2.99418e22	1.03593	0.517964	+	0.855402i	$0.326690\pi$
$440$	4.44091e22	1.50704
$441$	1.36556e22	0.454550
$442$	−2.38702e22	−0.779410
$443$	5.67436e22	1.81754	0.908772	−	0.417292i	$-0.137021\pi$
$443$	5.67436e22	1.81754	0.908772	+	0.417292i	$0.137021\pi$
$444$	2.91737e22	0.916721
$445$	1.76332e22	0.543590
$446$	−1.29790e22	−0.392551
$447$	−1.24602e22	−0.369752
$448$	5.96761e20	0.0173755
$449$	−2.47369e22	−0.706725	−0.353363	−	0.935486i	$-0.614962\pi$
$449$	−2.47369e22	−0.706725	−0.353363	+	0.935486i	$0.614962\pi$
$450$	4.63971e22	1.30072
$451$	−6.24249e22	−1.71734
$452$	4.72149e22	1.27468
$453$	8.88390e20	0.0235380
$454$	8.19376e22	2.13063
$455$	−9.48007e21	−0.241944
$456$	6.22330e22	1.55891
$457$	5.72597e22	1.40787	0.703933	−	0.710266i	$-0.251425\pi$
$457$	5.72597e22	1.40787	0.703933	+	0.710266i	$0.251425\pi$
$458$	−2.78745e22	−0.672746
$459$	−1.45170e22	−0.343929
$460$	−5.52044e22	−1.28390
$461$	−3.33732e22	−0.761973	−0.380987	−	0.924581i	$-0.624416\pi$
$461$	−3.33732e22	−0.761973	−0.380987	+	0.924581i	$0.624416\pi$
$462$	3.29097e22	0.737678
$463$	1.36245e22	0.299834	0.149917	−	0.988699i	$-0.452099\pi$
$463$	1.36245e22	0.299834	0.149917	+	0.988699i	$0.452099\pi$
$464$	1.56323e22	0.337770
$465$	8.08354e21	0.171495
$466$	5.82258e21	0.121293
$467$	4.49094e22	0.918637	0.459319	−	0.888272i	$-0.348094\pi$
$467$	4.49094e22	0.918637	0.459319	+	0.888272i	$0.348094\pi$
$468$	8.31267e22	1.66975
$469$	−9.55002e21	−0.188380
$470$	−4.01201e22	−0.777196
$471$	−2.14758e22	−0.408575
$472$	−1.63379e23	−3.05273
$473$	6.57934e22	1.20743
$474$	−1.65819e22	−0.298895
$475$	−8.90306e22	−1.57632
$476$	4.51503e22	0.785238
$477$	−7.77158e22	−1.32771
$478$	1.48004e23	2.48392
$479$	−4.24649e22	−0.700130	−0.350065	−	0.936725i	$-0.613840\pi$
$479$	−4.24649e22	−0.700130	−0.350065	+	0.936725i	$0.613840\pi$
$480$	9.43675e21	0.152852
$481$	−6.00293e22	−0.955278
$482$	1.21749e23	1.90355
$483$	−2.27424e22	−0.349370
$484$	2.45956e23	3.71255
$485$	−2.84251e22	−0.421597
$486$	1.12103e23	1.63384
$487$	−1.28110e23	−1.83480	−0.917399	−	0.397968i	$-0.869715\pi$
$487$	−1.28110e23	−1.83480	−0.917399	+	0.397968i	$0.869715\pi$
$488$	−2.70353e22	−0.380507
$489$	−9.00255e21	−0.124520
$490$	−2.85216e22	−0.387710
$491$	−8.27365e22	−1.10536	−0.552681	−	0.833393i	$-0.686395\pi$
$491$	−8.27365e22	−1.10536	−0.552681	+	0.833393i	$0.686395\pi$
$492$	−6.59374e22	−0.865821
$493$	7.27316e21	0.0938695
$494$	−2.30346e23	−2.92214
$495$	−4.64290e22	−0.578956
$496$	1.70263e23	2.08702
$497$	1.50768e21	0.0181669
$498$	−4.38541e22	−0.519470
$499$	3.00550e22	0.349995	0.174998	−	0.984569i	$-0.444008\pi$
$499$	3.00550e22	0.349995	0.174998	+	0.984569i	$0.444008\pi$
$500$	−1.47789e23	−1.69199
$501$	3.30990e22	0.372559
$502$	2.28983e23	2.53409
$503$	1.76283e23	1.91815	0.959074	−	0.283156i	$-0.0913815\pi$
$503$	1.76283e23	1.91815	0.959074	+	0.283156i	$0.0913815\pi$
$504$	−1.26226e23	−1.35048
$505$	−2.26643e22	−0.238433
$506$	−3.94327e23	−4.07921
$507$	−9.63299e21	−0.0979927
$508$	−1.88436e23	−1.88505
$509$	1.20073e23	1.18126	0.590628	−	0.806944i	$-0.298880\pi$
$509$	1.20073e23	1.18126	0.590628	+	0.806944i	$0.298880\pi$
$510$	1.40825e22	0.136249
$511$	5.72077e22	0.544348
$512$	−2.39995e23	−2.24599
$513$	−1.40088e23	−1.28945
$514$	4.56214e22	0.413031
$515$	−6.35500e22	−0.565919
$516$	6.94955e22	0.608743
$517$	−1.98451e23	−1.70995
$518$	1.63968e23	1.38981
$519$	2.40917e22	0.200884
$520$	−9.65199e22	−0.791750
$521$	−1.57336e23	−1.26972	−0.634860	−	0.772627i	$-0.718942\pi$
$521$	−1.57336e23	−1.26972	−0.634860	+	0.772627i	$0.718942\pi$
$522$	−3.65763e22	−0.290403
$523$	9.85721e22	0.769998	0.384999	−	0.922917i	$-0.374202\pi$
$523$	9.85721e22	0.769998	0.384999	+	0.922917i	$0.374202\pi$
$524$	−4.23393e23	−3.25408
$525$	−2.76457e22	−0.209061
$526$	2.20174e23	1.63828
$527$	7.92174e22	0.580003
$528$	1.49717e23	1.07865
$529$	1.31451e23	0.931949
$530$	1.62321e23	1.13248
$531$	1.70810e23	1.17276
$532$	4.35697e23	2.94399
$533$	1.35676e23	0.902238
$534$	1.33042e23	0.870738
$535$	−5.09895e22	−0.328454
$536$	−9.72320e22	−0.616465
$537$	9.29322e22	0.579942
$538$	3.64397e23	2.23834
$539$	−1.41080e23	−0.853022
$540$	−1.05591e23	−0.628463
$541$	1.45163e23	0.850507	0.425254	−	0.905074i	$-0.360185\pi$
$541$	1.45163e23	0.850507	0.425254	+	0.905074i	$0.360185\pi$
$542$	3.50932e23	2.02409
$543$	6.11446e22	0.347184
$544$	9.24787e22	0.516953
$545$	−4.63710e22	−0.255197
$546$	−7.15267e22	−0.387553
$547$	1.29272e23	0.689624	0.344812	−	0.938672i	$-0.387943\pi$
$547$	1.29272e23	0.689624	0.344812	+	0.938672i	$0.387943\pi$
$548$	−6.90770e23	−3.62826
$549$	2.82650e22	0.146179
$550$	−4.79343e23	−2.44098
$551$	7.01856e22	0.351933
$552$	−2.31548e23	−1.14330
$553$	−6.45371e22	−0.313795
$554$	1.29444e22	0.0619795
$555$	3.54149e22	0.166992
$556$	1.81166e23	0.841282
$557$	3.02733e22	0.138449	0.0692247	−	0.997601i	$-0.477947\pi$
$557$	3.02733e22	0.138449	0.0692247	+	0.997601i	$0.477947\pi$
$558$	−3.98380e23	−1.79435
$559$	−1.42997e23	−0.634347
$560$	1.17802e23	0.514702
$561$	6.96578e22	0.299768
$562$	7.37389e23	3.12563
$563$	−1.19493e23	−0.498907	−0.249454	−	0.968387i	$-0.580251\pi$
$563$	−1.19493e23	−0.498907	−0.249454	+	0.968387i	$0.580251\pi$
$564$	−2.09617e23	−0.862095
$565$	5.73156e22	0.232199
$566$	4.85225e22	0.193644
$567$	1.08671e23	0.427225
$568$	1.53502e22	0.0594503
$569$	7.01391e22	0.267612	0.133806	−	0.991008i	$-0.457280\pi$
$569$	7.01391e22	0.267612	0.133806	+	0.991008i	$0.457280\pi$
$570$	1.35895e23	0.510819
$571$	−3.81222e23	−1.41179	−0.705896	−	0.708315i	$-0.749456\pi$
$571$	−3.81222e23	−1.41179	−0.705896	+	0.708315i	$0.749456\pi$
$572$	−8.58808e23	−3.13350
$573$	−3.58589e22	−0.128909
$574$	−3.70594e23	−1.31265
$575$	3.31253e23	1.15607
$576$	−6.35218e21	−0.0218440
$577$	−3.85101e23	−1.30491	−0.652455	−	0.757827i	$-0.726261\pi$
$577$	−3.85101e23	−1.30491	−0.652455	+	0.757827i	$0.726261\pi$
$578$	−4.02065e23	−1.34249
$579$	1.69388e23	0.557332
$580$	5.29021e22	0.171528
$581$	−1.70681e23	−0.545366
$582$	−2.14466e23	−0.675326
$583$	8.02907e23	2.49162
$584$	5.82451e23	1.78135
$585$	1.00910e23	0.304165
$586$	3.59328e23	1.06748
$587$	−6.75340e23	−1.97742	−0.988709	−	0.149846i	$-0.952122\pi$
$587$	−6.75340e23	−1.97742	−0.988709	+	0.149846i	$0.952122\pi$
$588$	−1.49018e23	−0.430063
$589$	7.64444e23	2.17453
$590$	−3.56762e23	−1.00031
$591$	−1.77050e23	−0.489330
$592$	7.45943e23	2.03222
$593$	−1.56859e23	−0.421255	−0.210627	−	0.977566i	$-0.567551\pi$
$593$	−1.56859e23	−0.421255	−0.210627	+	0.977566i	$0.567551\pi$
$594$	−7.54240e23	−1.99675
$595$	5.48093e22	0.143041
$596$	−8.88164e23	−2.28507
$597$	4.96292e22	0.125880
$598$	8.57039e23	2.14309
$599$	7.90605e23	1.94909	0.974544	−	0.224195i	$-0.0719754\pi$
$599$	7.90605e23	1.94909	0.974544	+	0.224195i	$0.0719754\pi$
$600$	−2.81470e23	−0.684143
$601$	1.62928e23	0.390449	0.195224	−	0.980759i	$-0.437457\pi$
$601$	1.62928e23	0.390449	0.195224	+	0.980759i	$0.437457\pi$
$602$	3.90592e23	0.922897
$603$	1.01655e23	0.236826
$604$	6.33246e22	0.145465
$605$	2.98574e23	0.676287
$606$	−1.71001e23	−0.381928
$607$	−1.01319e23	−0.223144	−0.111572	−	0.993756i	$-0.535589\pi$
$607$	−1.01319e23	−0.223144	−0.111572	+	0.993756i	$0.535589\pi$
$608$	8.92414e23	1.93814
$609$	2.17940e22	0.0466755
$610$	−5.90356e22	−0.124684
$611$	4.31318e23	0.898354
$612$	−4.80599e23	−0.987179
$613$	−7.22991e22	−0.146460	−0.0732300	−	0.997315i	$-0.523331\pi$
$613$	−7.22991e22	−0.146460	−0.0732300	+	0.997315i	$0.523331\pi$
$614$	−3.67258e23	−0.733737
$615$	−8.00434e22	−0.157720
$616$	1.30408e24	2.53436
$617$	6.35382e22	0.121790	0.0608949	−	0.998144i	$-0.480605\pi$
$617$	6.35382e22	0.121790	0.0608949	+	0.998144i	$0.480605\pi$
$618$	−4.79482e23	−0.906505
$619$	−8.00300e22	−0.149239	−0.0746195	−	0.997212i	$-0.523774\pi$
$619$	−8.00300e22	−0.149239	−0.0746195	+	0.997212i	$0.523774\pi$
$620$	5.76196e23	1.05984
$621$	5.21222e23	0.945679
$622$	−9.05979e23	−1.62144
$623$	5.17802e23	0.914145
$624$	−3.25398e23	−0.566690
$625$	3.04728e23	0.523519
$626$	1.73435e24	2.93938
$627$	6.72194e23	1.12388
$628$	−1.53080e24	−2.52500
$629$	3.47061e23	0.564774
$630$	−2.75633e23	−0.442523
$631$	−7.48894e23	−1.18624	−0.593118	−	0.805116i	$-0.702103\pi$
$631$	−7.48894e23	−1.18624	−0.593118	+	0.805116i	$0.702103\pi$
$632$	−6.57074e23	−1.02688
$633$	−2.23973e23	−0.345353
$634$	−1.00511e24	−1.52916
$635$	−2.28749e23	−0.343385
$636$	8.48085e23	1.25619
$637$	3.06627e23	0.448151
$638$	3.77881e23	0.544979
$639$	−1.60484e22	−0.0228389
$640$	−2.85445e23	−0.400860
$641$	−2.64145e23	−0.366057	−0.183029	−	0.983108i	$-0.558590\pi$
$641$	−2.64145e23	−0.366057	−0.183029	+	0.983108i	$0.558590\pi$
$642$	−3.84714e23	−0.526126
$643$	4.21965e23	0.569486	0.284743	−	0.958604i	$-0.408092\pi$
$643$	4.21965e23	0.569486	0.284743	+	0.958604i	$0.408092\pi$
$644$	−1.62108e24	−2.15911
$645$	8.43627e22	0.110890
$646$	1.33175e24	1.72761
$647$	−8.02812e23	−1.02784	−0.513922	−	0.857837i	$-0.671808\pi$
$647$	−8.02812e23	−1.02784	−0.513922	+	0.857837i	$0.671808\pi$
$648$	1.10641e24	1.39807
$649$	−1.76469e24	−2.20084
$650$	1.04182e24	1.28241
$651$	2.37374e23	0.288400
$652$	−6.41704e23	−0.769538
$653$	−4.64489e23	−0.549811	−0.274905	−	0.961471i	$-0.588647\pi$
$653$	−4.64489e23	−0.549811	−0.274905	+	0.961471i	$0.588647\pi$
$654$	−3.49867e23	−0.408782
$655$	−5.13970e23	−0.592771
$656$	−1.68595e24	−1.91939
$657$	−6.08944e23	−0.684339
$658$	−1.17813e24	−1.30700
$659$	9.29904e23	1.01838	0.509192	−	0.860653i	$-0.329944\pi$
$659$	9.29904e23	1.01838	0.509192	+	0.860653i	$0.329944\pi$
$660$	5.06663e23	0.547767
$661$	3.40182e23	0.363078	0.181539	−	0.983384i	$-0.441892\pi$
$661$	3.40182e23	0.363078	0.181539	+	0.983384i	$0.441892\pi$
$662$	2.46577e24	2.59812
$663$	−1.51396e23	−0.157489
$664$	−1.73776e24	−1.78468
$665$	5.28907e23	0.536284
$666$	−1.74535e24	−1.74723
$667$	−2.61137e23	−0.258106
$668$	2.35931e24	2.30242
$669$	−8.23192e22	−0.0793194
$670$	−2.12320e23	−0.202002
$671$	−2.92015e23	−0.274324
$672$	2.77111e23	0.257049
$673$	−2.17086e23	−0.198840	−0.0994202	−	0.995046i	$-0.531699\pi$
$673$	−2.17086e23	−0.198840	−0.0994202	+	0.995046i	$0.531699\pi$
$674$	−7.91101e23	−0.715522
$675$	6.33597e23	0.565889
$676$	−6.86642e23	−0.605596
$677$	1.95265e24	1.70067	0.850337	−	0.526238i	$-0.176398\pi$
$677$	1.95265e24	1.70067	0.850337	+	0.526238i	$0.176398\pi$
$678$	4.32444e23	0.371944
$679$	−8.34707e23	−0.708991
$680$	5.58032e23	0.468094
$681$	5.19687e23	0.430518
$682$	4.11579e24	3.36733
$683$	−2.17020e24	−1.75357	−0.876787	−	0.480879i	$-0.840318\pi$
$683$	−2.17020e24	−1.75357	−0.876787	+	0.480879i	$0.840318\pi$
$684$	−4.63775e24	−3.70110
$685$	−8.38547e23	−0.660933
$686$	−2.43548e24	−1.89596
$687$	−1.76794e23	−0.135936
$688$	1.77693e24	1.34949
$689$	−1.74506e24	−1.30902
$690$	−5.05620e23	−0.374634
$691$	6.12633e23	0.448370	0.224185	−	0.974547i	$-0.428028\pi$
$691$	6.12633e23	0.448370	0.224185	+	0.974547i	$0.428028\pi$
$692$	1.71726e24	1.24147
$693$	−1.36340e24	−0.973619
$694$	−4.58076e24	−3.23134
$695$	2.19923e23	0.153250
$696$	2.21892e23	0.152743
$697$	−7.84413e23	−0.533416
$698$	−4.70041e23	−0.315766
$699$	3.69296e22	0.0245086
$700$	−1.97059e24	−1.29200
$701$	−1.08874e24	−0.705212	−0.352606	−	0.935772i	$-0.614704\pi$
$701$	−1.08874e24	−0.705212	−0.352606	+	0.935772i	$0.614704\pi$
$702$	1.63928e24	1.04903
$703$	3.34912e24	2.11743
$704$	6.56264e22	0.0409931
$705$	−2.54461e23	−0.157041
$706$	−2.54452e24	−1.55155
$707$	−6.65541e23	−0.400968
$708$	−1.86399e24	−1.10958
$709$	2.72295e24	1.60157	0.800787	−	0.598950i	$-0.204415\pi$
$709$	2.72295e24	1.60157	0.800787	+	0.598950i	$0.204415\pi$
$710$	3.35195e22	0.0194806
$711$	6.86961e23	0.394494
$712$	5.27192e24	2.99150
$713$	−2.84424e24	−1.59480
$714$	4.13534e23	0.229127
$715$	−1.04253e24	−0.570806
$716$	6.62423e24	3.58405
$717$	9.38715e23	0.501904
$718$	1.39607e24	0.737647
$719$	−6.34749e23	−0.331441	−0.165721	−	0.986173i	$-0.552995\pi$
$719$	−6.34749e23	−0.331441	−0.165721	+	0.986173i	$0.552995\pi$
$720$	−1.25394e24	−0.647069
$721$	−1.86615e24	−0.951695
$722$	9.27339e24	4.67383
$723$	7.72190e23	0.384635
$724$	4.35840e24	2.14560
$725$	−3.17438e23	−0.154449
$726$	2.25273e24	1.08330
$727$	−3.59324e23	−0.170783	−0.0853913	−	0.996347i	$-0.527214\pi$
$727$	−3.59324e23	−0.170783	−0.0853913	+	0.996347i	$0.527214\pi$
$728$	−2.83432e24	−1.33147
$729$	−6.22816e23	−0.289185
$730$	1.27187e24	0.583711
$731$	8.26741e23	0.375035
$732$	−3.08446e23	−0.138304
$733$	1.35860e24	0.602154	0.301077	−	0.953600i	$-0.402654\pi$
$733$	1.35860e24	0.602154	0.301077	+	0.953600i	$0.402654\pi$
$734$	−1.41921e24	−0.621770
$735$	−1.80898e23	−0.0783413
$736$	−3.32037e24	−1.42143
$737$	−1.05023e24	−0.444436
$738$	3.94477e24	1.65022
$739$	2.92762e23	0.121070	0.0605352	−	0.998166i	$-0.480719\pi$
$739$	2.92762e23	0.121070	0.0605352	+	0.998166i	$0.480719\pi$
$740$	2.52438e24	1.03201
$741$	−1.46096e24	−0.590452
$742$	4.76657e24	1.90446
$743$	1.26938e24	0.501401	0.250701	−	0.968065i	$-0.419339\pi$
$743$	1.26938e24	0.501401	0.250701	+	0.968065i	$0.419339\pi$
$744$	2.41679e24	0.943776
$745$	−1.07817e24	−0.416255
$746$	2.08853e24	0.797187
$747$	1.81680e24	0.685619
$748$	4.96522e24	1.85257
$749$	−1.49732e24	−0.552354
$750$	−1.35361e24	−0.493710
$751$	−1.79039e24	−0.645666	−0.322833	−	0.946456i	$-0.604635\pi$
$751$	−1.79039e24	−0.645666	−0.322833	+	0.946456i	$0.604635\pi$
$752$	−5.35970e24	−1.91112
$753$	1.45232e24	0.512042
$754$	−8.21297e23	−0.286315
$755$	7.68717e22	0.0264982
$756$	−3.10069e24	−1.05688
$757$	−5.88170e24	−1.98239	−0.991193	−	0.132425i	$-0.957724\pi$
$757$	−5.88170e24	−1.98239	−0.991193	+	0.132425i	$0.957724\pi$
$758$	−8.61670e24	−2.87179
$759$	−2.50101e24	−0.824252
$760$	5.38498e24	1.75496
$761$	6.02417e24	1.94145	0.970727	−	0.240184i	$-0.0772077\pi$
$761$	6.02417e24	1.94145	0.970727	+	0.240184i	$0.0772077\pi$
$762$	−1.72590e24	−0.550045
$763$	−1.36169e24	−0.429161
$764$	−2.55603e24	−0.796659
$765$	−5.83414e23	−0.179827
$766$	3.07425e23	0.0937120
$767$	3.83543e24	1.15625
$768$	−2.18446e24	−0.651288
$769$	1.47101e24	0.433752	0.216876	−	0.976199i	$-0.430413\pi$
$769$	1.47101e24	0.433752	0.216876	+	0.976199i	$0.430413\pi$
$770$	2.84765e24	0.830453
$771$	2.89353e23	0.0834575
$772$	1.20740e25	3.44432
$773$	4.34175e24	1.22501	0.612504	−	0.790468i	$-0.290162\pi$
$773$	4.34175e24	1.22501	0.612504	+	0.790468i	$0.290162\pi$
$774$	−4.15763e24	−1.16024
$775$	−3.45746e24	−0.954316
$776$	−8.49843e24	−2.32014
$777$	1.03996e24	0.280827
$778$	4.69513e24	1.25407
$779$	−7.56954e24	−1.99987
$780$	−1.10120e24	−0.287780
$781$	1.65801e23	0.0428602
$782$	−4.95499e24	−1.26703
$783$	−4.99484e23	−0.126342
$784$	−3.81024e24	−0.953380
$785$	−1.85829e24	−0.459960
$786$	−3.87788e24	−0.949517
$787$	3.14826e24	0.762580	0.381290	−	0.924456i	$-0.375480\pi$
$787$	3.14826e24	0.762580	0.381290	+	0.924456i	$0.375480\pi$
$788$	−1.26202e25	−3.02407
$789$	1.39645e24	0.331033
$790$	−1.43482e24	−0.336486
$791$	1.68308e24	0.390486
$792$	−1.38812e25	−3.18612
$793$	6.34673e23	0.144121
$794$	6.09999e24	1.37042
$795$	1.02952e24	0.228830
$796$	3.53758e24	0.777938
$797$	−7.09934e23	−0.154462	−0.0772311	−	0.997013i	$-0.524608\pi$
$797$	−7.09934e23	−0.154462	−0.0772311	+	0.997013i	$0.524608\pi$
$798$	3.99058e24	0.859035
$799$	−2.49368e24	−0.531120
$800$	−4.03625e24	−0.850575
$801$	−5.51171e24	−1.14924
$802$	−7.76155e24	−1.60128
$803$	6.29119e24	1.28425
$804$	−1.10932e24	−0.224068
$805$	−1.96788e24	−0.393309
$806$	−8.94536e24	−1.76909
$807$	2.31118e24	0.452282
$808$	−6.77610e24	−1.31215
$809$	−2.23126e24	−0.427551	−0.213776	−	0.976883i	$-0.568576\pi$
$809$	−2.23126e24	−0.427551	−0.213776	+	0.976883i	$0.568576\pi$
$810$	2.41602e24	0.458118
$811$	8.44506e24	1.58462	0.792311	−	0.610118i	$-0.208878\pi$
$811$	8.44506e24	1.58462	0.792311	+	0.610118i	$0.208878\pi$
$812$	1.55348e24	0.288455
$813$	2.22578e24	0.408989
$814$	1.80317e25	3.27892
$815$	−7.78984e23	−0.140181
$816$	1.88130e24	0.335035
$817$	7.97801e24	1.40607
$818$	1.58622e25	2.76668
$819$	2.96324e24	0.511509
$820$	−5.70551e24	−0.974713
$821$	−1.52167e24	−0.257278	−0.128639	−	0.991691i	$-0.541061\pi$
$821$	−1.52167e24	−0.257278	−0.128639	+	0.991691i	$0.541061\pi$
$822$	−6.32680e24	−1.05870
$823$	4.82422e24	0.798967	0.399483	−	0.916740i	$-0.369190\pi$
$823$	4.82422e24	0.798967	0.399483	+	0.916740i	$0.369190\pi$
$824$	−1.90000e25	−3.11438
$825$	−3.04023e24	−0.493227
$826$	−1.04764e25	−1.68221
$827$	−1.39875e24	−0.222302	−0.111151	−	0.993804i	$-0.535454\pi$
$827$	−1.39875e24	−0.222302	−0.111151	+	0.993804i	$0.535454\pi$
$828$	1.72555e25	2.71438
$829$	2.95029e24	0.459358	0.229679	−	0.973266i	$-0.426232\pi$
$829$	2.95029e24	0.459358	0.229679	+	0.973266i	$0.426232\pi$
$830$	−3.79466e24	−0.584802
$831$	8.20995e22	0.0125237
$832$	−1.42634e23	−0.0215365
$833$	−1.77277e24	−0.264953
$834$	1.65931e24	0.245480
$835$	2.86403e24	0.419414
$836$	4.79141e25	6.94561
$837$	−5.44026e24	−0.780644
$838$	1.80979e24	0.257072
$839$	−1.00139e25	−1.40807	−0.704036	−	0.710164i	$-0.748621\pi$
$839$	−1.00139e25	−1.40807	−0.704036	+	0.710164i	$0.748621\pi$
$840$	1.67214e24	0.232754
$841$	2.50246e23	0.0344828
$842$	−1.32720e25	−1.81044
$843$	4.67687e24	0.631570
$844$	−1.59648e25	−2.13429
$845$	−8.33535e23	−0.110317
$846$	1.25406e25	1.64312
$847$	8.76766e24	1.13730
$848$	2.16847e25	2.78476
$849$	3.07753e23	0.0391279
$850$	−6.02329e24	−0.758181
$851$	−1.24609e25	−1.55292
$852$	1.75131e23	0.0216086
$853$	−1.10311e25	−1.34757	−0.673784	−	0.738929i	$-0.735332\pi$
$853$	−1.10311e25	−1.34757	−0.673784	+	0.738929i	$0.735332\pi$
$854$	−1.73359e24	−0.209679
$855$	−5.62991e24	−0.674201
$856$	−1.52447e25	−1.80755
$857$	1.11014e25	1.30328	0.651642	−	0.758527i	$-0.274080\pi$
$857$	1.11014e25	1.30328	0.651642	+	0.758527i	$0.274080\pi$
$858$	−7.86587e24	−0.914334
$859$	−9.60992e24	−1.10606	−0.553029	−	0.833162i	$-0.686528\pi$
$859$	−9.60992e24	−1.10606	−0.553029	+	0.833162i	$0.686528\pi$
$860$	6.01339e24	0.685303
$861$	−2.35049e24	−0.265235
$862$	−6.80641e24	−0.760512
$863$	−7.22439e24	−0.799299	−0.399649	−	0.916668i	$-0.630868\pi$
$863$	−7.22439e24	−0.799299	−0.399649	+	0.916668i	$0.630868\pi$
$864$	−6.35098e24	−0.695783
$865$	2.08464e24	0.226148
$866$	2.09099e24	0.224621
$867$	−2.55009e24	−0.271265
$868$	1.69201e25	1.78232
$869$	−7.09721e24	−0.740320
$870$	4.84533e23	0.0500507
$871$	2.28259e24	0.233493
$872$	−1.38638e25	−1.40441
$873$	8.88499e24	0.891324
$874$	−4.78154e25	−4.75030
$875$	−5.26827e24	−0.518322
$876$	6.64518e24	0.647474
$877$	2.91120e24	0.280915	0.140457	−	0.990087i	$-0.455143\pi$
$877$	2.91120e24	0.280915	0.140457	+	0.990087i	$0.455143\pi$
$878$	1.95478e25	1.86808
$879$	2.27903e24	0.215697
$880$	1.29549e25	1.21431
$881$	7.96627e24	0.739537	0.369769	−	0.929124i	$-0.379437\pi$
$881$	7.96627e24	0.739537	0.369769	+	0.929124i	$0.379437\pi$
$882$	8.91515e24	0.819683
$883$	1.59441e25	1.45190	0.725948	−	0.687750i	$-0.241401\pi$
$883$	1.59441e25	1.45190	0.725948	+	0.687750i	$0.241401\pi$
$884$	−1.07915e25	−0.973283
$885$	−2.26275e24	−0.202125
$886$	3.70456e25	3.27755
$887$	6.50168e24	0.569738	0.284869	−	0.958566i	$-0.408050\pi$
$887$	6.50168e24	0.569738	0.284869	+	0.958566i	$0.408050\pi$
$888$	1.05882e25	0.918995
$889$	−6.71723e24	−0.577465
$890$	1.15120e25	0.980248
$891$	1.19506e25	1.00793
$892$	−5.86773e24	−0.490195
$893$	−2.40639e25	−1.99126
$894$	−8.13475e24	−0.666769
$895$	8.04135e24	0.652880
$896$	−8.38214e24	−0.674120
$897$	5.43575e24	0.433036
$898$	−1.61497e25	−1.27443
$899$	2.72562e24	0.213063
$900$	2.09758e25	1.62427
$901$	1.00891e25	0.773912
$902$	−4.07547e25	−3.09686
$903$	2.47732e24	0.186482
$904$	1.71360e25	1.27785
$905$	5.29080e24	0.390848
$906$	5.79993e23	0.0424457
$907$	−2.19181e25	−1.58906	−0.794531	−	0.607224i	$-0.792283\pi$
$907$	−2.19181e25	−1.58906	−0.794531	+	0.607224i	$0.792283\pi$
$908$	3.70434e25	2.66061
$909$	7.08431e24	0.504086
$910$	−6.18915e24	−0.436294
$911$	−2.64085e25	−1.84433	−0.922164	−	0.386799i	$-0.873581\pi$
$911$	−2.64085e25	−1.84433	−0.922164	+	0.386799i	$0.873581\pi$
$912$	1.81544e25	1.25610
$913$	−1.87700e25	−1.28665
$914$	3.73825e25	2.53879
$915$	−3.74432e23	−0.0251938
$916$	−1.26019e25	−0.840086
$917$	−1.50928e25	−0.996852
$918$	−9.47756e24	−0.620203
$919$	1.23626e25	0.801544	0.400772	−	0.916178i	$-0.368742\pi$
$919$	1.23626e25	0.801544	0.400772	+	0.916178i	$0.368742\pi$
$920$	−2.00357e25	−1.28709
$921$	−2.32933e24	−0.148260
$922$	−2.17880e25	−1.37406
$923$	−3.60357e23	−0.0225174
$924$	1.48782e25	0.921170
$925$	−1.51475e25	−0.929259
$926$	8.89485e24	0.540686
$927$	1.98642e25	1.19644
$928$	3.18190e24	0.189902
$929$	−1.04780e24	−0.0619645	−0.0309823	−	0.999520i	$-0.509864\pi$
$929$	−1.04780e24	−0.0619645	−0.0309823	+	0.999520i	$0.509864\pi$
$930$	5.27741e24	0.309255
$931$	−1.71071e25	−0.993355
$932$	2.63235e24	0.151464
$933$	−5.74615e24	−0.327630
$934$	2.93195e25	1.65657
$935$	6.02744e24	0.337469
$936$	3.01697e25	1.67389
$937$	−7.67856e24	−0.422176	−0.211088	−	0.977467i	$-0.567701\pi$
$937$	−7.67856e24	−0.422176	−0.211088	+	0.977467i	$0.567701\pi$
$938$	−6.23482e24	−0.339703
$939$	1.10001e25	0.593935
$940$	−1.81380e25	−0.970518
$941$	−5.84057e24	−0.309701	−0.154851	−	0.987938i	$-0.549490\pi$
$941$	−5.84057e24	−0.309701	−0.154851	+	0.987938i	$0.549490\pi$
$942$	−1.40207e25	−0.736778
$943$	2.81637e25	1.46670
$944$	−4.76603e25	−2.45977
$945$	−3.76403e24	−0.192523
$946$	4.29538e25	2.17735
$947$	−7.29245e24	−0.366352	−0.183176	−	0.983080i	$-0.558638\pi$
$947$	−7.29245e24	−0.366352	−0.183176	+	0.983080i	$0.558638\pi$
$948$	−7.49656e24	−0.373243
$949$	−1.36734e25	−0.674706
$950$	−5.81244e25	−2.84255
$951$	−6.37488e24	−0.308985
$952$	1.63867e25	0.787185
$953$	1.09843e25	0.522979	0.261490	−	0.965206i	$-0.415786\pi$
$953$	1.09843e25	0.522979	0.261490	+	0.965206i	$0.415786\pi$
$954$	−5.07375e25	−2.39424
$955$	−3.10285e24	−0.145121
$956$	6.69118e25	3.10178
$957$	2.39670e24	0.110119
$958$	−2.77236e25	−1.26253
$959$	−2.46240e25	−1.11148
$960$	8.41485e22	0.00376479
$961$	7.13667e24	0.316481
$962$	−3.91907e25	−1.72264
$963$	1.59381e25	0.694405
$964$	5.50419e25	2.37705
$965$	1.46570e25	0.627426
$966$	−1.48476e25	−0.630014
$967$	2.88717e25	1.21436	0.607179	−	0.794565i	$-0.292301\pi$
$967$	2.88717e25	1.21436	0.607179	+	0.794565i	$0.292301\pi$
$968$	8.92665e25	3.72176
$969$	8.44660e24	0.349084
$970$	−1.85576e25	−0.760259
$971$	3.53970e25	1.43748	0.718742	−	0.695277i	$-0.244718\pi$
$971$	3.53970e25	1.43748	0.718742	+	0.695277i	$0.244718\pi$
$972$	5.06811e25	2.04025
$973$	6.45807e24	0.257718
$974$	−8.36381e25	−3.30867
$975$	6.60770e24	0.259126
$976$	−7.88665e24	−0.306598
$977$	−2.78359e25	−1.07276	−0.536378	−	0.843978i	$-0.680208\pi$
$977$	−2.78359e25	−1.07276	−0.536378	+	0.843978i	$0.680208\pi$
$978$	−5.87740e24	−0.224546
$979$	5.69432e25	2.15670
$980$	−1.28944e25	−0.484150
$981$	1.44944e25	0.539529
$982$	−5.40153e25	−1.99328
$983$	4.25993e25	1.55847	0.779234	−	0.626733i	$-0.215609\pi$
$983$	4.25993e25	1.55847	0.779234	+	0.626733i	$0.215609\pi$
$984$	−2.39311e25	−0.867969
$985$	−1.53200e25	−0.550872
$986$	4.74835e24	0.169273
$987$	−7.47228e24	−0.264093
$988$	−1.04138e26	−3.64900
$989$	−2.96835e25	−1.03121
$990$	−3.03116e25	−1.04402
$991$	8.47047e23	0.0289256	0.0144628	−	0.999895i	$-0.495396\pi$
$991$	8.47047e23	0.0289256	0.0144628	+	0.999895i	$0.495396\pi$
$992$	3.46564e25	1.17337
$993$	1.56391e25	0.524980
$994$	9.84304e23	0.0327601
$995$	4.29437e24	0.141711
$996$	−1.98261e25	−0.648684
$997$	−3.78529e25	−1.22798	−0.613988	−	0.789315i	$-0.710436\pi$
$997$	−3.78529e25	−1.22798	−0.613988	+	0.789315i	$0.710436\pi$
$998$	1.96217e25	0.631141
$999$	−2.38344e25	−0.760147

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.b.1.20	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.b.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+652.859 q^{2} +4140.75 q^{3} +295153. q^{4} +358296. q^{5} +2.70332e6 q^{6} +1.05214e7 q^{7} +1.07122e8 q^{8} -1.11994e8 q^{9} +O(q^{10})\)	\(q+652.859 q^{2} +4140.75 q^{3} +295153. q^{4} +358296. q^{5} +2.70332e6 q^{6} +1.05214e7 q^{7} +1.07122e8 q^{8} -1.11994e8 q^{9} +2.33917e8 q^{10} +1.15705e9 q^{11} +1.22215e9 q^{12} -2.51476e9 q^{13} +6.86899e9 q^{14} +1.48361e9 q^{15} +3.12492e10 q^{16} +1.45392e10 q^{17} -7.31166e10 q^{18} +1.40302e11 q^{19} +1.05752e11 q^{20} +4.35664e10 q^{21} +7.55391e11 q^{22} -5.22017e11 q^{23} +4.43565e11 q^{24} -6.34564e11 q^{25} -1.64179e12 q^{26} -9.98477e11 q^{27} +3.10542e12 q^{28} +5.00246e11 q^{29} +9.68589e11 q^{30} +5.44856e12 q^{31} +6.36066e12 q^{32} +4.79105e12 q^{33} +9.49202e12 q^{34} +3.76977e12 q^{35} -3.30555e13 q^{36} +2.38708e13 q^{37} +9.15975e13 q^{38} -1.04130e13 q^{39} +3.83813e13 q^{40} -5.39518e13 q^{41} +2.84428e13 q^{42} +5.68631e13 q^{43} +3.41507e14 q^{44} -4.01271e13 q^{45} -3.40803e14 q^{46} -1.71515e14 q^{47} +1.29395e14 q^{48} -1.21931e14 q^{49} -4.14281e14 q^{50} +6.02029e13 q^{51} -7.42240e14 q^{52} +6.93926e14 q^{53} -6.51865e14 q^{54} +4.14566e14 q^{55} +1.12707e15 q^{56} +5.80955e14 q^{57} +3.26591e14 q^{58} -1.52517e15 q^{59} +4.37893e14 q^{60} -2.52379e14 q^{61} +3.55714e15 q^{62} -1.17834e15 q^{63} +5.67187e13 q^{64} -9.01028e14 q^{65} +3.12788e15 q^{66} -9.07675e14 q^{67} +4.29128e15 q^{68} -2.16154e15 q^{69} +2.46113e15 q^{70} +1.43297e14 q^{71} -1.19971e16 q^{72} +5.43727e15 q^{73} +1.55842e16 q^{74} -2.62757e15 q^{75} +4.14106e16 q^{76} +1.21738e16 q^{77} -6.79822e15 q^{78} -6.13389e15 q^{79} +1.11965e16 q^{80} +1.03285e16 q^{81} -3.52229e16 q^{82} -1.62223e16 q^{83} +1.28588e16 q^{84} +5.20931e15 q^{85} +3.71236e16 q^{86} +2.07139e15 q^{87} +1.23945e17 q^{88} +4.92142e16 q^{89} -2.61973e16 q^{90} -2.64588e16 q^{91} -1.54075e17 q^{92} +2.25611e16 q^{93} -1.11975e17 q^{94} +5.02696e16 q^{95} +2.63379e16 q^{96} -7.93342e16 q^{97} -7.96036e16 q^{98} -1.29583e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) \) 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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