LMFDB - Embedded newform 29.18.a.b.1.2

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			1.2
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)

$f(q)$	$=$	$q-687.348 q^{2} -21372.9 q^{3} +341375. q^{4} -1.16997e6 q^{5} +1.46906e7 q^{6} -9.37855e6 q^{7} -1.44551e8 q^{8} +3.27660e8 q^{9} +O(q^{10})$	\(q-687.348 q^{2} -21372.9 q^{3} +341375. q^{4} -1.16997e6 q^{5} +1.46906e7 q^{6} -9.37855e6 q^{7} -1.44551e8 q^{8} +3.27660e8 q^{9} +8.04176e8 q^{10} +8.41895e8 q^{11} -7.29616e9 q^{12} +4.06492e9 q^{13} +6.44633e9 q^{14} +2.50056e10 q^{15} +5.46121e10 q^{16} +1.44158e10 q^{17} -2.25216e11 q^{18} -2.26386e9 q^{19} -3.99398e11 q^{20} +2.00447e11 q^{21} -5.78675e11 q^{22} -2.37009e11 q^{23} +3.08947e12 q^{24} +6.05889e11 q^{25} -2.79401e12 q^{26} -4.24295e12 q^{27} -3.20160e12 q^{28} +5.00246e11 q^{29} -1.71876e13 q^{30} +7.30920e12 q^{31} -1.85909e13 q^{32} -1.79937e13 q^{33} -9.90864e12 q^{34} +1.09726e13 q^{35} +1.11855e14 q^{36} +1.73834e12 q^{37} +1.55606e12 q^{38} -8.68790e13 q^{39} +1.69120e14 q^{40} -2.43176e13 q^{41} -1.37777e14 q^{42} +8.01944e13 q^{43} +2.87402e14 q^{44} -3.83352e14 q^{45} +1.62907e14 q^{46} +9.47943e13 q^{47} -1.16722e15 q^{48} -1.44673e14 q^{49} -4.16456e14 q^{50} -3.08107e14 q^{51} +1.38766e15 q^{52} -5.06029e14 q^{53} +2.91638e15 q^{54} -9.84992e14 q^{55} +1.35568e15 q^{56} +4.83852e13 q^{57} -3.43843e14 q^{58} +1.89499e15 q^{59} +8.53629e15 q^{60} +5.95411e14 q^{61} -5.02396e15 q^{62} -3.07298e15 q^{63} +5.62029e15 q^{64} -4.75583e15 q^{65} +1.23679e16 q^{66} +7.78620e14 q^{67} +4.92118e15 q^{68} +5.06556e15 q^{69} -7.54200e15 q^{70} -2.17222e15 q^{71} -4.73636e16 q^{72} +1.29421e16 q^{73} -1.19485e15 q^{74} -1.29496e16 q^{75} -7.72824e14 q^{76} -7.89576e15 q^{77} +5.97161e16 q^{78} +1.99974e16 q^{79} -6.38945e16 q^{80} +4.83700e16 q^{81} +1.67147e16 q^{82} -2.62251e16 q^{83} +6.84274e16 q^{84} -1.68660e16 q^{85} -5.51214e16 q^{86} -1.06917e16 q^{87} -1.21697e17 q^{88} -3.29297e15 q^{89} +2.63496e17 q^{90} -3.81230e16 q^{91} -8.09087e16 q^{92} -1.56219e17 q^{93} -6.51566e16 q^{94} +2.64865e15 q^{95} +3.97341e17 q^{96} -5.04465e16 q^{97} +9.94408e16 q^{98} +2.75856e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−687.348	−1.89855	−0.949274	−	0.314451i	$-0.898179\pi$
$2$	−687.348	−1.89855	−0.949274	+	0.314451i	$0.898179\pi$
$3$	−21372.9	−1.88076	−0.940378	−	0.340130i	$-0.889529\pi$
$3$	−21372.9	−1.88076	−0.940378	+	0.340130i	$0.889529\pi$
$4$	341375.	2.60448
$5$	−1.16997e6	−1.33946	−0.669730	−	0.742605i	$-0.733590\pi$
$5$	−1.16997e6	−1.33946	−0.669730	+	0.742605i	$0.733590\pi$
$6$	1.46906e7	3.57071
$7$	−9.37855e6	−0.614897	−0.307449	−	0.951565i	$-0.599475\pi$
$7$	−9.37855e6	−0.614897	−0.307449	+	0.951565i	$0.599475\pi$
$8$	−1.44551e8	−3.04618
$9$	3.27660e8	2.53725
$10$	8.04176e8	2.54303
$11$	8.41895e8	1.18419	0.592093	−	0.805869i	$-0.298302\pi$
$11$	8.41895e8	1.18419	0.592093	+	0.805869i	$0.298302\pi$
$12$	−7.29616e9	−4.89840
$13$	4.06492e9	1.38208	0.691040	−	0.722817i	$-0.257153\pi$
$13$	4.06492e9	1.38208	0.691040	+	0.722817i	$0.257153\pi$
$14$	6.44633e9	1.16741
$15$	2.50056e10	2.51920
$16$	5.46121e10	3.17884
$17$	1.44158e10	0.501212	0.250606	−	0.968089i	$-0.419370\pi$
$17$	1.44158e10	0.501212	0.250606	+	0.968089i	$0.419370\pi$
$18$	−2.25216e11	−4.81708
$19$	−2.26386e9	−0.0305804	−0.0152902	−	0.999883i	$-0.504867\pi$
$19$	−2.26386e9	−0.0305804	−0.0152902	+	0.999883i	$0.504867\pi$
$20$	−3.99398e11	−3.48860
$21$	2.00447e11	1.15647
$22$	−5.78675e11	−2.24823
$23$	−2.37009e11	−0.631070	−0.315535	−	0.948914i	$-0.602184\pi$
$23$	−2.37009e11	−0.631070	−0.315535	+	0.948914i	$0.602184\pi$
$24$	3.08947e12	5.72913
$25$	6.05889e11	0.794151
$26$	−2.79401e12	−2.62394
$27$	−4.24295e12	−2.89118
$28$	−3.20160e12	−1.60149
$29$	5.00246e11	0.185695
$29$	5.00246e11	0.185695
$30$	−1.71876e13	−4.78281
$31$	7.30920e12	1.53920	0.769601	−	0.638526i	$-0.220455\pi$
$31$	7.30920e12	1.53920	0.769601	+	0.638526i	$0.220455\pi$
$32$	−1.85909e13	−2.98900
$33$	−1.79937e13	−2.22717
$34$	−9.90864e12	−0.951576
$35$	1.09726e13	0.823630
$36$	1.11855e14	6.60821
$37$	1.73834e12	0.0813619	0.0406810	−	0.999172i	$-0.487047\pi$
$37$	1.73834e12	0.0813619	0.0406810	+	0.999172i	$0.487047\pi$
$38$	1.55606e12	0.0580584
$39$	−8.68790e13	−2.59935
$40$	1.69120e14	4.08024
$41$	−2.43176e13	−0.475618	−0.237809	−	0.971312i	$-0.576429\pi$
$41$	−2.43176e13	−0.475618	−0.237809	+	0.971312i	$0.576429\pi$
$42$	−1.37777e14	−2.19562
$43$	8.01944e13	1.04631	0.523157	−	0.852236i	$-0.324754\pi$
$43$	8.01944e13	1.04631	0.523157	+	0.852236i	$0.324754\pi$
$44$	2.87402e14	3.08419
$45$	−3.83352e14	−3.39854
$46$	1.62907e14	1.19812
$47$	9.47943e13	0.580698	0.290349	−	0.956921i	$-0.406229\pi$
$47$	9.47943e13	0.580698	0.290349	+	0.956921i	$0.406229\pi$
$48$	−1.16722e15	−5.97863
$49$	−1.44673e14	−0.621901
$50$	−4.16456e14	−1.50773
$51$	−3.08107e14	−0.942659
$52$	1.38766e15	3.59960
$53$	−5.06029e14	−1.11643	−0.558214	−	0.829697i	$-0.688513\pi$
$53$	−5.06029e14	−1.11643	−0.558214	+	0.829697i	$0.688513\pi$
$54$	2.91638e15	5.48905
$55$	−9.84992e14	−1.58617
$56$	1.35568e15	1.87309
$57$	4.83852e13	0.0575144
$58$	−3.43843e14	−0.352551
$59$	1.89499e15	1.68022	0.840108	−	0.542419i	$-0.182491\pi$
$59$	1.89499e15	1.68022	0.840108	+	0.542419i	$0.182491\pi$
$60$	8.53629e15	6.56120
$61$	5.95411e14	0.397661	0.198831	−	0.980034i	$-0.436286\pi$
$61$	5.95411e14	0.397661	0.198831	+	0.980034i	$0.436286\pi$
$62$	−5.02396e15	−2.92225
$63$	−3.07298e15	−1.56014
$64$	5.62029e15	2.49591
$65$	−4.75583e15	−1.85124
$66$	1.23679e16	4.22838
$67$	7.78620e14	0.234256	0.117128	−	0.993117i	$-0.462631\pi$
$67$	7.78620e14	0.234256	0.117128	+	0.993117i	$0.462631\pi$
$68$	4.92118e15	1.30540
$69$	5.06556e15	1.18689
$70$	−7.54200e15	−1.56370
$71$	−2.17222e15	−0.399215	−0.199608	−	0.979876i	$-0.563967\pi$
$71$	−2.17222e15	−0.399215	−0.199608	+	0.979876i	$0.563967\pi$
$72$	−4.73636e16	−7.72891
$73$	1.29421e16	1.87829	0.939143	−	0.343527i	$-0.111622\pi$
$73$	1.29421e16	1.87829	0.939143	+	0.343527i	$0.111622\pi$
$74$	−1.19485e15	−0.154469
$75$	−1.29496e16	−1.49360
$76$	−7.72824e14	−0.0796462
$77$	−7.89576e15	−0.728153
$78$	5.97161e16	4.93500
$79$	1.99974e16	1.48301	0.741504	−	0.670948i	$-0.234113\pi$
$79$	1.99974e16	1.48301	0.741504	+	0.670948i	$0.234113\pi$
$80$	−6.38945e16	−4.25793
$81$	4.83700e16	2.90037
$82$	1.67147e16	0.902983
$83$	−2.62251e16	−1.27807	−0.639034	−	0.769178i	$-0.720666\pi$
$83$	−2.62251e16	−1.27807	−0.639034	+	0.769178i	$0.720666\pi$
$84$	6.84274e16	3.01201
$85$	−1.68660e16	−0.671354
$86$	−5.51214e16	−1.98648
$87$	−1.06917e16	−0.349248
$88$	−1.21697e17	−3.60725
$89$	−3.29297e15	−0.0886693	−0.0443347	−	0.999017i	$-0.514117\pi$
$89$	−3.29297e15	−0.0886693	−0.0443347	+	0.999017i	$0.514117\pi$
$90$	2.63496e17	6.45228
$91$	−3.81230e16	−0.849837
$92$	−8.09087e16	−1.64361
$93$	−1.56219e17	−2.89486
$94$	−6.51566e16	−1.10248
$95$	2.64865e15	0.0409612
$96$	3.97341e17	5.62158
$97$	−5.04465e16	−0.653539	−0.326769	−	0.945104i	$-0.605960\pi$
$97$	−5.04465e16	−0.653539	−0.326769	+	0.945104i	$0.605960\pi$
$98$	9.94408e16	1.18071
$99$	2.75856e17	3.00457
$100$	2.06835e17	2.06835
$101$	−8.81990e16	−0.810460	−0.405230	−	0.914215i	$-0.632809\pi$
$101$	−8.81990e16	−0.810460	−0.405230	+	0.914215i	$0.632809\pi$
$102$	2.11776e17	1.78968
$103$	−1.15173e16	−0.0895848	−0.0447924	−	0.998996i	$-0.514263\pi$
$103$	−1.15173e16	−0.0895848	−0.0447924	+	0.998996i	$0.514263\pi$
$104$	−5.87587e17	−4.21007
$105$	−2.34517e17	−1.54905
$106$	3.47818e17	2.11959
$107$	9.87881e16	0.555831	0.277915	−	0.960606i	$-0.410357\pi$
$107$	9.87881e16	0.555831	0.277915	+	0.960606i	$0.410357\pi$
$108$	−1.44843e18	−7.53003
$109$	−2.17356e17	−1.04483	−0.522417	−	0.852690i	$-0.674969\pi$
$109$	−2.17356e17	−1.04483	−0.522417	+	0.852690i	$0.674969\pi$
$110$	6.77032e17	3.01142
$111$	−3.71535e16	−0.153022
$112$	−5.12182e17	−1.95466
$113$	6.64718e16	0.235218	0.117609	−	0.993060i	$-0.462477\pi$
$113$	6.64718e16	0.235218	0.117609	+	0.993060i	$0.462477\pi$
$114$	−3.32574e16	−0.109194
$115$	2.77293e17	0.845292
$116$	1.70771e17	0.483640
$117$	1.33191e18	3.50667
$118$	−1.30252e18	−3.18997
$119$	−1.35199e17	−0.308194
$120$	−3.61459e18	−7.67394
$121$	2.03341e17	0.402298
$122$	−4.09254e17	−0.754978
$123$	5.19738e17	0.894522
$124$	2.49517e18	4.00882
$125$	1.83744e17	0.275726
$126$	2.11220e18	2.96201
$127$	1.32550e17	0.173799	0.0868997	−	0.996217i	$-0.472304\pi$
$127$	1.32550e17	0.173799	0.0868997	+	0.996217i	$0.472304\pi$
$128$	−1.42635e18	−1.74961
$129$	−1.71399e18	−1.96786
$130$	3.26891e18	3.51466
$131$	−1.73136e18	−1.74414	−0.872071	−	0.489380i	$-0.837223\pi$
$131$	−1.73136e18	−1.74414	−0.872071	+	0.489380i	$0.837223\pi$
$132$	−6.14260e18	−5.80062
$133$	2.12317e16	0.0188038
$134$	−5.35183e17	−0.444745
$135$	4.96412e18	3.87262
$136$	−2.08381e18	−1.52679
$137$	2.19249e17	0.150943	0.0754713	−	0.997148i	$-0.475954\pi$
$137$	2.19249e17	0.150943	0.0754713	+	0.997148i	$0.475954\pi$
$138$	−3.48180e18	−2.25336
$139$	2.34745e18	1.42879	0.714397	−	0.699740i	$-0.246701\pi$
$139$	2.34745e18	1.42879	0.714397	+	0.699740i	$0.246701\pi$
$140$	3.74577e18	2.14513
$141$	−2.02603e18	−1.09215
$142$	1.49307e18	0.757929
$143$	3.42223e18	1.63664
$144$	1.78942e19	8.06550
$145$	−5.85273e17	−0.248731
$146$	−8.89574e18	−3.56601
$147$	3.09209e18	1.16965
$148$	5.93427e17	0.211906
$149$	1.95450e18	0.659100	0.329550	−	0.944138i	$-0.393103\pi$
$149$	1.95450e18	0.659100	0.329550	+	0.944138i	$0.393103\pi$
$150$	8.90088e18	2.83568
$151$	1.84272e18	0.554824	0.277412	−	0.960751i	$-0.410523\pi$
$151$	1.84272e18	0.554824	0.277412	+	0.960751i	$0.410523\pi$
$152$	3.27243e17	0.0931536
$153$	4.72347e18	1.27170
$154$	5.42713e18	1.38243
$155$	−8.55154e18	−2.06170
$156$	−2.96583e19	−6.76997
$157$	−3.13944e17	−0.0678743	−0.0339372	−	0.999424i	$-0.510805\pi$
$157$	−3.13944e17	−0.0678743	−0.0339372	+	0.999424i	$0.510805\pi$
$158$	−1.37452e19	−2.81556
$159$	1.08153e19	2.09973
$160$	2.17508e19	4.00364
$161$	2.22280e18	0.388043
$162$	−3.32470e19	−5.50648
$163$	−2.83376e18	−0.445419	−0.222710	−	0.974885i	$-0.571490\pi$
$163$	−2.83376e18	−0.445419	−0.222710	+	0.974885i	$0.571490\pi$
$164$	−8.30142e18	−1.23874
$165$	2.10521e19	2.98320
$166$	1.80258e19	2.42647
$167$	−8.86986e18	−1.13456	−0.567279	−	0.823526i	$-0.692004\pi$
$167$	−8.86986e18	−1.13456	−0.567279	+	0.823526i	$0.692004\pi$
$168$	−2.89748e19	−3.52283
$169$	7.87312e18	0.910144
$170$	1.15928e19	1.27460
$171$	−7.41776e17	−0.0775901
$172$	2.73763e19	2.72510
$173$	9.67216e18	0.916498	0.458249	−	0.888824i	$-0.348477\pi$
$173$	9.67216e18	0.916498	0.458249	+	0.888824i	$0.348477\pi$
$174$	7.34892e18	0.663063
$175$	−5.68236e18	−0.488321
$176$	4.59777e19	3.76434
$177$	−4.05014e19	−3.16008
$178$	2.26342e18	0.168343
$179$	−2.55136e19	−1.80934	−0.904670	−	0.426112i	$-0.859883\pi$
$179$	−2.55136e19	−1.80934	−0.904670	+	0.426112i	$0.859883\pi$
$180$	−1.30867e20	−8.85142
$181$	−7.12996e18	−0.460065	−0.230033	−	0.973183i	$-0.573883\pi$
$181$	−7.12996e18	−0.460065	−0.230033	+	0.973183i	$0.573883\pi$
$182$	2.62038e19	1.61346
$183$	−1.27256e19	−0.747904
$184$	3.42598e19	1.92235
$185$	−2.03381e18	−0.108981
$186$	1.07377e20	5.49603
$187$	1.21366e19	0.593529
$188$	3.23604e19	1.51242
$189$	3.97927e19	1.77778
$190$	−1.82054e18	−0.0777669
$191$	7.07241e18	0.288924	0.144462	−	0.989510i	$-0.453855\pi$
$191$	7.07241e18	0.288924	0.144462	+	0.989510i	$0.453855\pi$
$192$	−1.20122e20	−4.69420
$193$	−3.38792e19	−1.26676	−0.633382	−	0.773840i	$-0.718334\pi$
$193$	−3.38792e19	−1.26676	−0.633382	+	0.773840i	$0.718334\pi$
$194$	3.46743e19	1.24077
$195$	1.01646e20	3.48173
$196$	−4.93878e19	−1.61973
$197$	2.07684e19	0.652289	0.326144	−	0.945320i	$-0.394250\pi$
$197$	2.07684e19	0.652289	0.326144	+	0.945320i	$0.394250\pi$
$198$	−1.89609e20	−5.70432
$199$	−1.07855e19	−0.310878	−0.155439	−	0.987845i	$-0.549679\pi$
$199$	−1.07855e19	−0.310878	−0.155439	+	0.987845i	$0.549679\pi$
$200$	−8.75818e19	−2.41913
$201$	−1.66414e19	−0.440578
$202$	6.06233e19	1.53870
$203$	−4.69159e18	−0.114184
$204$	−1.05180e20	−2.45514
$205$	2.84509e19	0.637071
$206$	7.91639e18	0.170081
$207$	−7.76583e19	−1.60118
$208$	2.21994e20	4.39341
$209$	−1.90593e18	−0.0362130
$210$	1.61194e20	2.94094
$211$	4.11001e18	0.0720181	0.0360091	−	0.999351i	$-0.488535\pi$
$211$	4.11001e18	0.0720181	0.0360091	+	0.999351i	$0.488535\pi$
$212$	−1.72746e20	−2.90772
$213$	4.64265e19	0.750827
$214$	−6.79018e19	−1.05527
$215$	−9.38250e19	−1.40149
$216$	6.13322e20	8.80708
$217$	−6.85497e19	−0.946450
$218$	1.49399e20	1.98367
$219$	−2.76611e20	−3.53260
$220$	−3.36251e20	−4.13115
$221$	5.85989e19	0.692715
$222$	2.55373e19	0.290519
$223$	−1.23930e20	−1.35701	−0.678507	−	0.734594i	$-0.737372\pi$
$223$	−1.23930e20	−1.35701	−0.678507	+	0.734594i	$0.737372\pi$
$224$	1.74356e20	1.83793
$225$	1.98526e20	2.01496
$226$	−4.56892e19	−0.446572
$227$	1.40492e20	1.32261	0.661304	−	0.750118i	$-0.270003\pi$
$227$	1.40492e20	1.32261	0.661304	+	0.750118i	$0.270003\pi$
$228$	1.65175e19	0.149795
$229$	−3.71721e19	−0.324800	−0.162400	−	0.986725i	$-0.551923\pi$
$229$	−3.71721e19	−0.324800	−0.162400	+	0.986725i	$0.551923\pi$
$230$	−1.90596e20	−1.60483
$231$	1.68755e20	1.36948
$232$	−7.23111e19	−0.565662
$233$	−5.78190e18	−0.0436059	−0.0218029	−	0.999762i	$-0.506941\pi$
$233$	−5.78190e18	−0.0436059	−0.0218029	+	0.999762i	$0.506941\pi$
$234$	−9.15486e20	−6.65759
$235$	−1.10906e20	−0.777821
$236$	6.46902e20	4.37609
$237$	−4.27402e20	−2.78918
$238$	9.29287e19	0.585121
$239$	−1.40901e20	−0.856115	−0.428057	−	0.903752i	$-0.640802\pi$
$239$	−1.40901e20	−0.856115	−0.428057	+	0.903752i	$0.640802\pi$
$240$	1.36561e21	8.00813
$241$	1.92876e20	1.09177	0.545887	−	0.837859i	$-0.316193\pi$
$241$	1.92876e20	1.09177	0.545887	+	0.837859i	$0.316193\pi$
$242$	−1.39766e20	−0.763783
$243$	−4.85871e20	−2.56370
$244$	2.03258e20	1.03570
$245$	1.69263e20	0.833012
$246$	−3.57241e20	−1.69829
$247$	−9.20239e18	−0.0422646
$248$	−1.05655e21	−4.68869
$249$	5.60507e20	2.40374
$250$	−1.26296e20	−0.523480
$251$	4.84963e20	1.94304	0.971521	−	0.236952i	$-0.0761483\pi$
$251$	4.84963e20	1.94304	0.971521	+	0.236952i	$0.0761483\pi$
$252$	−1.04904e21	−4.06337
$253$	−1.99536e20	−0.747304
$254$	−9.11080e19	−0.329966
$255$	3.60475e20	1.26265
$256$	2.43734e20	0.825802
$257$	−2.70164e20	−0.885514	−0.442757	−	0.896642i	$-0.646000\pi$
$257$	−2.70164e20	−0.885514	−0.442757	+	0.896642i	$0.646000\pi$
$258$	1.17810e21	3.73608
$259$	−1.63032e19	−0.0500292
$260$	−1.62352e21	−4.82152
$261$	1.63911e20	0.471155
$262$	1.19005e21	3.31133
$263$	4.41737e20	1.18998	0.594991	−	0.803733i	$-0.297156\pi$
$263$	4.41737e20	1.18998	0.594991	+	0.803733i	$0.297156\pi$
$264$	2.60101e21	6.78436
$265$	5.92039e20	1.49541
$266$	−1.45936e19	−0.0357000
$267$	7.03804e19	0.166765
$268$	2.65801e20	0.610114
$269$	1.90827e20	0.424371	0.212186	−	0.977229i	$-0.431942\pi$
$269$	1.90827e20	0.424371	0.212186	+	0.977229i	$0.431942\pi$
$270$	−3.41208e21	−7.35236
$271$	−9.03682e19	−0.188702	−0.0943510	−	0.995539i	$-0.530078\pi$
$271$	−9.03682e19	−0.188702	−0.0943510	+	0.995539i	$0.530078\pi$
$272$	7.87275e20	1.59328
$273$	8.14799e20	1.59834
$274$	−1.50700e20	−0.286572
$275$	5.10095e20	0.940423
$276$	1.72925e21	3.09123
$277$	−1.10542e20	−0.191623	−0.0958117	−	0.995399i	$-0.530545\pi$
$277$	−1.10542e20	−0.191623	−0.0958117	+	0.995399i	$0.530545\pi$
$278$	−1.61351e21	−2.71263
$279$	2.39493e21	3.90533
$280$	−1.58610e21	−2.50893
$281$	−1.15804e21	−1.77713	−0.888567	−	0.458748i	$-0.848298\pi$
$281$	−1.15804e21	−1.77713	−0.888567	+	0.458748i	$0.848298\pi$
$282$	1.39258e21	2.07350
$283$	6.66784e20	0.963386	0.481693	−	0.876340i	$-0.340022\pi$
$283$	6.66784e20	0.963386	0.481693	+	0.876340i	$0.340022\pi$
$284$	−7.41539e20	−1.03975
$285$	−5.66092e19	−0.0770381
$286$	−2.35226e21	−3.10724
$287$	2.28064e20	0.292456
$288$	−6.09150e21	−7.58382
$289$	−6.19426e20	−0.748786
$290$	4.02286e20	0.472228
$291$	1.07819e21	1.22915
$292$	4.41812e21	4.89196
$293$	7.96814e20	0.857003	0.428502	−	0.903541i	$-0.359042\pi$
$293$	7.96814e20	0.857003	0.428502	+	0.903541i	$0.359042\pi$
$294$	−2.12534e21	−2.22063
$295$	−2.21708e21	−2.25058
$296$	−2.51279e20	−0.247843
$297$	−3.57212e21	−3.42370
$298$	−1.34342e21	−1.25133
$299$	−9.63420e20	−0.872188
$300$	−4.42066e21	−3.89007
$301$	−7.52107e20	−0.643375
$302$	−1.26659e21	−1.05336
$303$	1.88507e21	1.52428
$304$	−1.23634e20	−0.0972104
$305$	−6.96612e20	−0.532651
$306$	−3.24667e21	−2.41438
$307$	−1.18009e21	−0.853568	−0.426784	−	0.904354i	$-0.640354\pi$
$307$	−1.18009e21	−0.853568	−0.426784	+	0.904354i	$0.640354\pi$
$308$	−2.69541e21	−1.89646
$309$	2.46158e20	0.168487
$310$	5.87788e21	3.91423
$311$	2.73278e21	1.77069	0.885343	−	0.464939i	$-0.153924\pi$
$311$	2.73278e21	1.77069	0.885343	+	0.464939i	$0.153924\pi$
$312$	1.25584e22	7.91811
$313$	2.00382e20	0.122951	0.0614755	−	0.998109i	$-0.480419\pi$
$313$	2.00382e20	0.122951	0.0614755	+	0.998109i	$0.480419\pi$
$314$	2.15789e20	0.128863
$315$	3.59529e21	2.08975
$316$	6.82661e21	3.86247
$317$	1.57164e21	0.865666	0.432833	−	0.901474i	$-0.357514\pi$
$317$	1.57164e21	0.865666	0.432833	+	0.901474i	$0.357514\pi$
$318$	−7.43388e21	−3.98644
$319$	4.21155e20	0.219898
$320$	−6.57557e21	−3.34317
$321$	−2.11139e21	−1.04538
$322$	−1.52783e21	−0.736718
$323$	−3.26353e19	−0.0153273
$324$	1.65123e22	7.55395
$325$	2.46289e21	1.09758
$326$	1.94778e21	0.845650
$327$	4.64553e21	1.96508
$328$	3.51514e21	1.44882
$329$	−8.89033e20	−0.357069
$330$	−1.44701e22	−5.66374
$331$	3.70721e21	1.41419	0.707097	−	0.707117i	$-0.250004\pi$
$331$	3.70721e21	1.41419	0.707097	+	0.707117i	$0.250004\pi$
$332$	−8.95260e21	−3.32870
$333$	5.69586e20	0.206435
$334$	6.09668e21	2.15401
$335$	−9.10962e20	−0.313776
$336$	1.09468e22	3.67624
$337$	−1.59611e21	−0.522648	−0.261324	−	0.965251i	$-0.584159\pi$
$337$	−1.59611e21	−0.522648	−0.261324	+	0.965251i	$0.584159\pi$
$338$	−5.41157e21	−1.72795
$339$	−1.42069e21	−0.442388
$340$	−5.75763e21	−1.74853
$341$	6.15358e21	1.82270
$342$	5.09858e20	0.147308
$343$	3.53856e21	0.997303
$344$	−1.15922e22	−3.18726
$345$	−5.92655e21	−1.58979
$346$	−6.64813e21	−1.74001
$347$	2.65739e21	0.678665	0.339333	−	0.940666i	$-0.389799\pi$
$347$	2.65739e21	0.678665	0.339333	+	0.940666i	$0.389799\pi$
$348$	−3.64988e21	−0.909609
$349$	−2.90036e21	−0.705401	−0.352701	−	0.935736i	$-0.614737\pi$
$349$	−2.90036e21	−0.705401	−0.352701	+	0.935736i	$0.614737\pi$
$350$	3.90576e21	0.927101
$351$	−1.72472e22	−3.99585
$352$	−1.56516e22	−3.53953
$353$	2.61779e21	0.577896	0.288948	−	0.957345i	$-0.406695\pi$
$353$	2.61779e21	0.577896	0.288948	+	0.957345i	$0.406695\pi$
$354$	2.78386e22	5.99956
$355$	2.54143e21	0.534733
$356$	−1.12414e21	−0.230938
$357$	2.88959e21	0.579638
$358$	1.75367e22	3.43512
$359$	2.58164e21	0.493847	0.246924	−	0.969035i	$-0.420580\pi$
$359$	2.58164e21	0.493847	0.246924	+	0.969035i	$0.420580\pi$
$360$	5.54140e22	10.3526
$361$	−5.47526e21	−0.999065
$362$	4.90076e21	0.873455
$363$	−4.34597e21	−0.756625
$364$	−1.30142e22	−2.21338
$365$	−1.51419e22	−2.51589
$366$	8.74694e21	1.41993
$367$	8.30226e21	1.31685	0.658423	−	0.752648i	$-0.271224\pi$
$367$	8.30226e21	1.31685	0.658423	+	0.752648i	$0.271224\pi$
$368$	−1.29435e22	−2.00607
$369$	−7.96792e21	−1.20676
$370$	1.39793e21	0.206906
$371$	4.74582e21	0.686489
$372$	−5.33291e22	−7.53962
$373$	9.06960e21	1.25332	0.626661	−	0.779292i	$-0.284421\pi$
$373$	9.06960e21	1.25332	0.626661	+	0.779292i	$0.284421\pi$
$374$	−8.34204e21	−1.12684
$375$	−3.92714e21	−0.518574
$376$	−1.37026e22	−1.76891
$377$	2.03346e21	0.256646
$378$	−2.73514e22	−3.37520
$379$	4.74499e21	0.572535	0.286267	−	0.958150i	$-0.407585\pi$
$379$	4.74499e21	0.572535	0.286267	+	0.958150i	$0.407585\pi$
$380$	9.04180e20	0.106683
$381$	−2.83298e21	−0.326874
$382$	−4.86120e21	−0.548536
$383$	−1.67466e22	−1.84815	−0.924077	−	0.382207i	$-0.875164\pi$
$383$	−1.67466e22	−1.84815	−0.924077	+	0.382207i	$0.875164\pi$
$384$	3.04852e22	3.29059
$385$	9.23780e21	0.975331
$386$	2.32868e22	2.40501
$387$	2.62765e22	2.65475
$388$	−1.72212e22	−1.70213
$389$	−1.95067e22	−1.88631	−0.943153	−	0.332358i	$-0.892156\pi$
$389$	−1.95067e22	−1.88631	−0.943153	+	0.332358i	$0.892156\pi$
$390$	−6.98660e22	−6.61023
$391$	−3.41666e21	−0.316300
$392$	2.09127e22	1.89443
$393$	3.70042e22	3.28031
$394$	−1.42751e22	−1.23840
$395$	−2.33964e22	−1.98643
$396$	9.41701e22	7.82535
$397$	1.61283e20	0.0131180	0.00655902	−	0.999978i	$-0.497912\pi$
$397$	1.61283e20	0.0131180	0.00655902	+	0.999978i	$0.497912\pi$
$398$	7.41341e21	0.590217
$399$	−4.53783e20	−0.0353654
$400$	3.30889e22	2.52448
$401$	−1.38546e22	−1.03483	−0.517413	−	0.855736i	$-0.673105\pi$
$401$	−1.38546e22	−1.03483	−0.517413	+	0.855736i	$0.673105\pi$
$402$	1.14384e22	0.836458
$403$	2.97113e22	2.12730
$404$	−3.01089e22	−2.11083
$405$	−5.65914e22	−3.88492
$406$	3.22475e21	0.216783
$407$	1.46350e21	0.0963477
$408$	4.45371e22	2.87151
$409$	8.57698e20	0.0541609	0.0270805	−	0.999633i	$-0.491379\pi$
$409$	8.57698e20	0.0541609	0.0270805	+	0.999633i	$0.491379\pi$
$410$	−1.95556e22	−1.20951
$411$	−4.68598e21	−0.283886
$412$	−3.93172e21	−0.233322
$413$	−1.77723e22	−1.03316
$414$	5.33782e22	3.03991
$415$	3.06826e22	1.71192
$416$	−7.55704e22	−4.13103
$417$	−5.01717e22	−2.68721
$418$	1.31004e21	0.0687520
$419$	3.23264e22	1.66241	0.831205	−	0.555966i	$-0.187652\pi$
$419$	3.23264e22	1.66241	0.831205	+	0.555966i	$0.187652\pi$
$420$	−8.00580e22	−4.03446
$421$	−1.49065e21	−0.0736171	−0.0368086	−	0.999322i	$-0.511719\pi$
$421$	−1.49065e21	−0.0736171	−0.0368086	+	0.999322i	$0.511719\pi$
$422$	−2.82500e21	−0.136730
$423$	3.10603e22	1.47337
$424$	7.31470e22	3.40085
$425$	8.73435e21	0.398038
$426$	−3.19112e22	−1.42548
$427$	−5.58409e21	−0.244521
$428$	3.37238e22	1.44765
$429$	−7.31430e22	−3.07812
$430$	6.44903e22	2.66080
$431$	2.87893e22	1.16459	0.582297	−	0.812976i	$-0.302154\pi$
$431$	2.87893e22	1.16459	0.582297	+	0.812976i	$0.302154\pi$
$432$	−2.31716e23	−9.19062
$433$	−5.12762e21	−0.199420	−0.0997099	−	0.995017i	$-0.531791\pi$
$433$	−5.12762e21	−0.199420	−0.0997099	+	0.995017i	$0.531791\pi$
$434$	4.71175e22	1.79688
$435$	1.25090e22	0.467803
$436$	−7.41999e22	−2.72125
$437$	5.36554e20	0.0192984
$438$	1.90128e23	6.70680
$439$	−9.40876e21	−0.325525	−0.162762	−	0.986665i	$-0.552040\pi$
$439$	−9.40876e21	−0.325525	−0.162762	+	0.986665i	$0.552040\pi$
$440$	1.42381e23	4.83176
$441$	−4.74037e22	−1.57792
$442$	−4.02778e22	−1.31515
$443$	4.10051e22	1.31343	0.656713	−	0.754140i	$-0.271946\pi$
$443$	4.10051e22	1.31343	0.656713	+	0.754140i	$0.271946\pi$
$444$	−1.26832e22	−0.398543
$445$	3.85268e21	0.118769
$446$	8.51828e22	2.57635
$447$	−4.17732e22	−1.23961
$448$	−5.27102e22	−1.53473
$449$	1.16331e22	0.332355	0.166177	−	0.986096i	$-0.446858\pi$
$449$	1.16331e22	0.332355	0.166177	+	0.986096i	$0.446858\pi$
$450$	−1.36456e23	−3.82549
$451$	−2.04729e22	−0.563221
$452$	2.26918e22	0.612621
$453$	−3.93843e22	−1.04349
$454$	−9.65667e22	−2.51103
$455$	4.46028e22	1.13832
$456$	−6.99413e21	−0.175199
$457$	4.03849e21	0.0992959	0.0496479	−	0.998767i	$-0.484190\pi$
$457$	4.03849e21	0.0992959	0.0496479	+	0.998767i	$0.484190\pi$
$458$	2.55501e22	0.616647
$459$	−6.11653e22	−1.44910
$460$	9.46607e22	2.20155
$461$	5.71596e21	0.130506	0.0652531	−	0.997869i	$-0.479215\pi$
$461$	5.71596e21	0.130506	0.0652531	+	0.997869i	$0.479215\pi$
$462$	−1.15993e23	−2.60002
$463$	−2.97167e22	−0.653977	−0.326988	−	0.945028i	$-0.606034\pi$
$463$	−2.97167e22	−0.653977	−0.326988	+	0.945028i	$0.606034\pi$
$464$	2.73195e22	0.590296
$465$	1.82771e23	3.87755
$466$	3.97417e21	0.0827879
$467$	9.82343e21	0.200942	0.100471	−	0.994940i	$-0.467965\pi$
$467$	9.82343e21	0.200942	0.100471	+	0.994940i	$0.467965\pi$
$468$	4.54681e23	9.13307
$469$	−7.30233e21	−0.144043
$470$	7.62312e22	1.47673
$471$	6.70990e21	0.127655
$472$	−2.73923e23	−5.11825
$473$	6.75153e22	1.23903
$474$	2.93774e23	5.29538
$475$	−1.37165e21	−0.0242855
$476$	−4.61535e22	−0.802686
$477$	−1.65806e23	−2.83265
$478$	9.68480e22	1.62537
$479$	−9.02271e22	−1.48760	−0.743798	−	0.668404i	$-0.766978\pi$
$479$	−9.02271e22	−1.48760	−0.743798	+	0.668404i	$0.766978\pi$
$480$	−4.64877e23	−7.52987
$481$	7.06622e21	0.112449
$482$	−1.32573e23	−2.07278
$483$	−4.75076e22	−0.729814
$484$	6.94153e22	1.04778
$485$	5.90209e22	0.875388
$486$	3.33962e23	4.86731
$487$	−5.49419e22	−0.786878	−0.393439	−	0.919351i	$-0.628715\pi$
$487$	−5.49419e22	−0.786878	−0.393439	+	0.919351i	$0.628715\pi$
$488$	−8.60672e22	−1.21135
$489$	6.05657e22	0.837725
$490$	−1.16343e23	−1.58151
$491$	1.84297e21	0.0246221	0.0123111	−	0.999924i	$-0.496081\pi$
$491$	1.84297e21	0.0246221	0.0123111	+	0.999924i	$0.496081\pi$
$492$	1.77425e23	2.32977
$493$	7.21143e21	0.0930728
$494$	6.32524e21	0.0802413
$495$	−3.22743e23	−4.02450
$496$	3.99171e23	4.89288
$497$	2.03722e22	0.245476
$498$	−3.85263e23	−4.56360
$499$	1.42761e23	1.66247	0.831236	−	0.555919i	$-0.187634\pi$
$499$	1.42761e23	1.66247	0.831236	+	0.555919i	$0.187634\pi$
$500$	6.27256e22	0.718124
$501$	1.89575e23	2.13383
$502$	−3.33338e23	−3.68896
$503$	−3.50135e22	−0.380985	−0.190493	−	0.981689i	$-0.561009\pi$
$503$	−3.50135e22	−0.380985	−0.190493	+	0.981689i	$0.561009\pi$
$504$	4.44202e23	4.75249
$505$	1.03190e23	1.08558
$506$	1.37151e23	1.41879
$507$	−1.68271e23	−1.71176
$508$	4.52492e22	0.452657
$509$	9.02728e22	0.888087	0.444044	−	0.896005i	$-0.353544\pi$
$509$	9.02728e22	0.888087	0.444044	+	0.896005i	$0.353544\pi$
$510$	−2.47772e23	−2.39721
$511$	−1.21378e23	−1.15495
$512$	1.94245e22	0.181784
$513$	9.60543e21	0.0884137
$514$	1.85696e23	1.68119
$515$	1.34749e22	0.119995
$516$	−5.85111e23	−5.12526
$517$	7.98068e22	0.687655
$518$	1.12059e22	0.0949828
$519$	−2.06722e23	−1.72371
$520$	6.87459e23	5.63921
$521$	−5.91132e22	−0.477050	−0.238525	−	0.971136i	$-0.576664\pi$
$521$	−5.91132e22	−0.477050	−0.238525	+	0.971136i	$0.576664\pi$
$522$	−1.12664e23	−0.894509
$523$	8.05353e22	0.629103	0.314552	−	0.949240i	$-0.398146\pi$
$523$	8.05353e22	0.629103	0.314552	+	0.949240i	$0.398146\pi$
$524$	−5.91043e23	−4.54258
$525$	1.21449e23	0.918413
$526$	−3.03627e23	−2.25924
$527$	1.05368e23	0.771467
$528$	−9.82675e23	−7.07981
$529$	−8.48770e22	−0.601751
$530$	−4.06937e23	−2.83911
$531$	6.20913e23	4.26312
$532$	7.24797e21	0.0489742
$533$	−9.88491e22	−0.657342
$534$	−4.83758e22	−0.316612
$535$	−1.15579e23	−0.744513
$536$	−1.12550e23	−0.713586
$537$	5.45299e23	3.40293
$538$	−1.31165e23	−0.805689
$539$	−1.21800e23	−0.736447
$540$	1.69462e24	10.0862
$541$	−8.96982e22	−0.525542	−0.262771	−	0.964858i	$-0.584636\pi$
$541$	−8.96982e22	−0.525542	−0.262771	+	0.964858i	$0.584636\pi$
$542$	6.21143e22	0.358260
$543$	1.52388e23	0.865271
$544$	−2.68002e23	−1.49812
$545$	2.54300e23	1.39951
$546$	−5.60050e23	−3.03452
$547$	1.79289e23	0.956450	0.478225	−	0.878237i	$-0.341280\pi$
$547$	1.79289e23	0.956450	0.478225	+	0.878237i	$0.341280\pi$
$548$	7.48459e22	0.393127
$549$	1.95092e23	1.00896
$550$	−3.50613e23	−1.78544
$551$	−1.13249e21	−0.00567864
$552$	−7.32231e23	−3.61548
$553$	−1.87547e23	−0.911897
$554$	7.59806e22	0.363806
$555$	4.34684e22	0.204967
$556$	8.01358e23	3.72127
$557$	−3.64921e23	−1.66890	−0.834450	−	0.551084i	$-0.814214\pi$
$557$	−3.64921e23	−1.66890	−0.834450	+	0.551084i	$0.814214\pi$
$558$	−1.64615e24	−7.41445
$559$	3.25983e23	1.44609
$560$	5.99238e23	2.61819
$561$	−2.59393e23	−1.11628
$562$	7.95976e23	3.37397
$563$	2.04537e23	0.853987	0.426994	−	0.904255i	$-0.359573\pi$
$563$	2.04537e23	0.853987	0.426994	+	0.904255i	$0.359573\pi$
$564$	−6.91634e23	−2.84449
$565$	−7.77699e22	−0.315065
$566$	−4.58312e23	−1.82903
$567$	−4.53640e23	−1.78343
$568$	3.13996e23	1.21608
$569$	−2.68877e21	−0.0102589	−0.00512943	−	0.999987i	$-0.501633\pi$
$569$	−2.68877e21	−0.0102589	−0.00512943	+	0.999987i	$0.501633\pi$
$570$	3.89102e22	0.146261
$571$	−2.01589e23	−0.746553	−0.373276	−	0.927720i	$-0.621766\pi$
$571$	−2.01589e23	−0.746553	−0.373276	+	0.927720i	$0.621766\pi$
$572$	1.16826e24	4.26260
$573$	−1.51158e23	−0.543396
$574$	−1.56759e23	−0.555242
$575$	−1.43601e23	−0.501165
$576$	1.84155e24	6.33274
$577$	2.26835e23	0.768628	0.384314	−	0.923202i	$-0.374438\pi$
$577$	2.26835e23	0.768628	0.384314	+	0.923202i	$0.374438\pi$
$578$	4.25761e23	1.42161
$579$	7.24095e23	2.38247
$580$	−1.99797e23	−0.647816
$581$	2.45954e23	0.785881
$582$	−7.41089e23	−2.33359
$583$	−4.26024e23	−1.32206
$584$	−1.87080e24	−5.72160
$585$	−1.55830e24	−4.69705
$586$	−5.47688e23	−1.62706
$587$	−5.40188e23	−1.58169	−0.790844	−	0.612017i	$-0.790358\pi$
$587$	−5.40188e23	−1.58169	−0.790844	+	0.612017i	$0.790358\pi$
$588$	1.05556e24	3.04632
$589$	−1.65470e22	−0.0470694
$590$	1.52391e24	4.27283
$591$	−4.43881e23	−1.22680
$592$	9.49346e22	0.258637
$593$	2.61741e23	0.702921	0.351460	−	0.936203i	$-0.385685\pi$
$593$	2.61741e23	0.702921	0.351460	+	0.936203i	$0.385685\pi$
$594$	2.45529e24	6.50006
$595$	1.58179e23	0.412813
$596$	6.67215e23	1.71661
$597$	2.30518e23	0.584687
$598$	6.62204e23	1.65589
$599$	−3.31672e23	−0.817675	−0.408838	−	0.912607i	$-0.634066\pi$
$599$	−3.31672e23	−0.817675	−0.408838	+	0.912607i	$0.634066\pi$
$600$	1.87188e24	4.54979
$601$	−4.68717e23	−1.12325	−0.561627	−	0.827391i	$-0.689824\pi$
$601$	−4.68717e23	−1.12325	−0.561627	+	0.827391i	$0.689824\pi$
$602$	5.16959e23	1.22148
$603$	2.55123e23	0.594364
$604$	6.29058e23	1.44503
$605$	−2.37902e23	−0.538862
$606$	−1.29570e24	−2.89392
$607$	−1.64951e23	−0.363288	−0.181644	−	0.983364i	$-0.558142\pi$
$607$	−1.64951e23	−0.363288	−0.181644	+	0.983364i	$0.558142\pi$
$608$	4.20872e22	0.0914049
$609$	1.00273e23	0.214751
$610$	4.78815e23	1.01126
$611$	3.85331e23	0.802571
$612$	1.61247e24	3.31212
$613$	1.81599e22	0.0367874	0.0183937	−	0.999831i	$-0.494145\pi$
$613$	1.81599e22	0.0367874	0.0183937	+	0.999831i	$0.494145\pi$
$614$	8.11131e23	1.62054
$615$	−6.08077e23	−1.19818
$616$	1.14134e24	2.21809
$617$	−4.73421e23	−0.907451	−0.453726	−	0.891141i	$-0.649905\pi$
$617$	−4.73421e23	−0.907451	−0.453726	+	0.891141i	$0.649905\pi$
$618$	−1.69196e23	−0.319881
$619$	8.41475e22	0.156917	0.0784586	−	0.996917i	$-0.475000\pi$
$619$	8.41475e22	0.156917	0.0784586	+	0.996917i	$0.475000\pi$
$620$	−2.91928e24	−5.36965
$621$	1.00561e24	1.82454
$622$	−1.87837e24	−3.36173
$623$	3.08833e22	0.0545225
$624$	−4.74464e24	−8.26294
$625$	−6.77232e23	−1.16348
$626$	−1.37732e23	−0.233428
$627$	4.07353e22	0.0681077
$628$	−1.07173e23	−0.176777
$629$	2.50596e22	0.0407796
$630$	−2.47121e24	−3.96749
$631$	−5.94010e23	−0.940902	−0.470451	−	0.882426i	$-0.655909\pi$
$631$	−5.94010e23	−0.940902	−0.470451	+	0.882426i	$0.655909\pi$
$632$	−2.89064e24	−4.51751
$633$	−8.78427e22	−0.135449
$634$	−1.08027e24	−1.64351
$635$	−1.55080e23	−0.232797
$636$	3.69207e24	5.46871
$637$	−5.88085e23	−0.859517
$638$	−2.89480e23	−0.417487
$639$	−7.11749e23	−1.01291
$640$	1.66878e24	2.34353
$641$	1.78206e23	0.246962	0.123481	−	0.992347i	$-0.460594\pi$
$641$	1.78206e23	0.246962	0.123481	+	0.992347i	$0.460594\pi$
$642$	1.45126e24	1.98471
$643$	1.09047e24	1.47171	0.735855	−	0.677139i	$-0.236780\pi$
$643$	1.09047e24	1.47171	0.735855	+	0.677139i	$0.236780\pi$
$644$	7.58806e23	1.01065
$645$	2.00531e24	2.63587
$646$	2.24318e22	0.0290996
$647$	4.67565e23	0.598626	0.299313	−	0.954155i	$-0.403243\pi$
$647$	4.67565e23	0.598626	0.299313	+	0.954155i	$0.403243\pi$
$648$	−6.99192e24	−8.83505
$649$	1.59538e24	1.98969
$650$	−1.69286e24	−2.08381
$651$	1.46511e24	1.78004
$652$	−9.67375e23	−1.16009
$653$	1.75695e23	0.207969	0.103984	−	0.994579i	$-0.466841\pi$
$653$	1.75695e23	0.207969	0.103984	+	0.994579i	$0.466841\pi$
$654$	−3.19309e24	−3.73079
$655$	2.02564e24	2.33621
$656$	−1.32804e24	−1.51191
$657$	4.24062e24	4.76567
$658$	6.11075e23	0.677913
$659$	−5.51681e22	−0.0604174	−0.0302087	−	0.999544i	$-0.509617\pi$
$659$	−5.51681e22	−0.0604174	−0.0302087	+	0.999544i	$0.509617\pi$
$660$	7.18666e24	7.76969
$661$	−1.41922e24	−1.51473	−0.757366	−	0.652990i	$-0.773514\pi$
$661$	−1.41922e24	−1.51473	−0.757366	+	0.652990i	$0.773514\pi$
$662$	−2.54814e24	−2.68491
$663$	−1.25243e24	−1.30283
$664$	3.79087e24	3.89323
$665$	−2.48405e22	−0.0251870
$666$	−3.91504e23	−0.391927
$667$	−1.18563e23	−0.117187
$668$	−3.02795e24	−2.95494
$669$	2.64874e24	2.55221
$670$	6.26148e23	0.595718
$671$	5.01273e23	0.470905
$672$	−3.72649e24	−3.45669
$673$	1.56049e23	0.142933	0.0714667	−	0.997443i	$-0.477232\pi$
$673$	1.56049e23	0.142933	0.0714667	+	0.997443i	$0.477232\pi$
$674$	1.09708e24	0.992272
$675$	−2.57076e24	−2.29604
$676$	2.68768e24	2.37045
$677$	1.81271e24	1.57879	0.789394	−	0.613887i	$-0.210395\pi$
$677$	1.81271e24	1.57879	0.789394	+	0.613887i	$0.210395\pi$
$678$	9.76510e23	0.839894
$679$	4.73115e23	0.401859
$680$	2.43800e24	2.04507
$681$	−3.00271e24	−2.48750
$682$	−4.22965e24	−3.46049
$683$	−2.04896e22	−0.0165561	−0.00827805	−	0.999966i	$-0.502635\pi$
$683$	−2.04896e22	−0.0165561	−0.00827805	+	0.999966i	$0.502635\pi$
$684$	−2.53224e23	−0.202082
$685$	−2.56514e23	−0.202181
$686$	−2.43222e24	−1.89343
$687$	7.94475e23	0.610869
$688$	4.37958e24	3.32607
$689$	−2.05697e24	−1.54299
$690$	4.07360e24	3.01829
$691$	1.33185e24	0.974746	0.487373	−	0.873194i	$-0.337955\pi$
$691$	1.33185e24	0.974746	0.487373	+	0.873194i	$0.337955\pi$
$692$	3.30183e24	2.38700
$693$	−2.58713e24	−1.84750
$694$	−1.82655e24	−1.28848
$695$	−2.74644e24	−1.91381
$696$	1.54550e24	1.06387
$697$	−3.50557e23	−0.238386
$698$	1.99356e24	1.33924
$699$	1.23576e23	0.0820121
$700$	−1.93981e24	−1.27182
$701$	−1.48023e24	−0.958796	−0.479398	−	0.877598i	$-0.659145\pi$
$701$	−1.48023e24	−0.958796	−0.479398	+	0.877598i	$0.659145\pi$
$702$	1.18548e25	7.58630
$703$	−3.93537e21	−0.00248808
$704$	4.73170e24	2.95563
$705$	2.37039e24	1.46289
$706$	−1.79933e24	−1.09716
$707$	8.27179e23	0.498350
$708$	−1.38262e25	−8.23036
$709$	−4.36708e23	−0.256861	−0.128431	−	0.991718i	$-0.540994\pi$
$709$	−4.36708e23	−0.256861	−0.128431	+	0.991718i	$0.540994\pi$
$710$	−1.74684e24	−1.01521
$711$	6.55236e24	3.76275
$712$	4.76003e23	0.270103
$713$	−1.73234e24	−0.971343
$714$	−1.98616e24	−1.10047
$715$	−4.00391e24	−2.19221
$716$	−8.70968e24	−4.71239
$717$	3.01146e24	1.61014
$718$	−1.77448e24	−0.937593
$719$	2.20556e24	1.15166	0.575830	−	0.817570i	$-0.304679\pi$
$719$	2.20556e24	1.15166	0.575830	+	0.817570i	$0.304679\pi$
$720$	−2.09357e25	−10.8034
$721$	1.08016e23	0.0550855
$722$	3.76341e24	1.89677
$723$	−4.12231e24	−2.05336
$724$	−2.43399e24	−1.19823
$725$	3.03094e23	0.147470
$726$	2.98719e24	1.43649
$727$	2.71744e24	1.29157	0.645783	−	0.763521i	$-0.276531\pi$
$727$	2.71744e24	1.29157	0.645783	+	0.763521i	$0.276531\pi$
$728$	5.51072e24	2.58876
$729$	4.13796e24	1.92133
$730$	1.04077e25	4.77653
$731$	1.15606e24	0.524426
$732$	−4.34421e24	−1.94790
$733$	−1.99267e24	−0.883186	−0.441593	−	0.897216i	$-0.645586\pi$
$733$	−1.99267e24	−0.883186	−0.441593	+	0.897216i	$0.645586\pi$
$734$	−5.70654e24	−2.50009
$735$	−3.61765e24	−1.56669
$736$	4.40620e24	1.88627
$737$	6.55517e23	0.277402
$738$	5.47673e24	2.29109
$739$	4.76635e24	1.97110	0.985550	−	0.169385i	$-0.0541781\pi$
$739$	4.76635e24	1.97110	0.985550	+	0.169385i	$0.0541781\pi$
$740$	−6.94291e23	−0.283839
$741$	1.96682e23	0.0794894
$742$	−3.26203e24	−1.30333
$743$	−1.39092e24	−0.549410	−0.274705	−	0.961529i	$-0.588580\pi$
$743$	−1.39092e24	−0.549410	−0.274705	+	0.961529i	$0.588580\pi$
$744$	2.25816e25	8.81828
$745$	−2.28670e24	−0.882838
$746$	−6.23396e24	−2.37949
$747$	−8.59294e24	−3.24277
$748$	4.14311e24	1.54584
$749$	−9.26490e23	−0.341779
$750$	2.69931e24	0.984538
$751$	−4.08147e24	−1.47190	−0.735949	−	0.677037i	$-0.763264\pi$
$751$	−4.08147e24	−1.47190	−0.735949	+	0.677037i	$0.763264\pi$
$752$	5.17691e24	1.84595
$753$	−1.03651e25	−3.65439
$754$	−1.39769e24	−0.487254
$755$	−2.15593e24	−0.743165
$756$	1.35842e25	4.63020
$757$	3.54143e24	1.19361	0.596806	−	0.802385i	$-0.296436\pi$
$757$	3.54143e24	1.19361	0.596806	+	0.802385i	$0.296436\pi$
$758$	−3.26146e24	−1.08698
$759$	4.26467e24	1.40550
$760$	−3.82864e23	−0.124775
$761$	4.24643e24	1.36853	0.684265	−	0.729234i	$-0.260123\pi$
$761$	4.24643e24	1.36853	0.684265	+	0.729234i	$0.260123\pi$
$762$	1.94724e24	0.620587
$763$	2.03849e24	0.642465
$764$	2.41434e24	0.752497
$765$	−5.52632e24	−1.70339
$766$	1.15108e25	3.50881
$767$	7.70298e24	2.32219
$768$	−5.20929e24	−1.55313
$769$	−4.79103e24	−1.41272	−0.706358	−	0.707855i	$-0.749663\pi$
$769$	−4.79103e24	−1.41272	−0.706358	+	0.707855i	$0.749663\pi$
$770$	−6.34958e24	−1.85171
$771$	5.77418e24	1.66544
$772$	−1.15655e25	−3.29926
$773$	−2.04679e24	−0.577493	−0.288747	−	0.957406i	$-0.593239\pi$
$773$	−2.04679e24	−0.577493	−0.288747	+	0.957406i	$0.593239\pi$
$774$	−1.80611e25	−5.04018
$775$	4.42856e24	1.22236
$776$	7.29209e24	1.99080
$777$	3.48446e23	0.0940928
$778$	1.34079e25	3.58124
$779$	5.50517e22	0.0145446
$780$	3.46993e25	9.06810
$781$	−1.82878e24	−0.472745
$782$	2.34843e24	0.600510
$783$	−2.12252e24	−0.536879
$784$	−7.90091e24	−1.97693
$785$	3.67305e23	0.0909149
$786$	−2.54347e25	−6.22781
$787$	−4.98402e24	−1.20724	−0.603621	−	0.797271i	$-0.706276\pi$
$787$	−4.98402e24	−1.20724	−0.603621	+	0.797271i	$0.706276\pi$
$788$	7.08980e24	1.69887
$789$	−9.44120e24	−2.23807
$790$	1.60814e25	3.77133
$791$	−6.23409e23	−0.144635
$792$	−3.98752e25	−9.15248
$793$	2.42029e24	0.549599
$794$	−1.10857e23	−0.0249052
$795$	−1.26536e25	−2.81250
$796$	−3.68191e24	−0.809677
$797$	7.29954e24	1.58818	0.794090	−	0.607800i	$-0.207948\pi$
$797$	7.29954e24	1.58818	0.794090	+	0.607800i	$0.207948\pi$
$798$	3.11907e23	0.0671429
$799$	1.36653e24	0.291053
$800$	−1.12640e25	−2.37372
$801$	−1.07898e24	−0.224976
$802$	9.52293e24	1.96467
$803$	1.08959e25	2.22424
$804$	−5.68094e24	−1.14748
$805$	−2.60060e24	−0.519768
$806$	−2.04220e25	−4.03878
$807$	−4.07853e24	−0.798139
$808$	1.27492e25	2.46881
$809$	2.51784e24	0.482464	0.241232	−	0.970467i	$-0.422448\pi$
$809$	2.51784e24	0.482464	0.241232	+	0.970467i	$0.422448\pi$
$810$	3.88979e25	7.37571
$811$	1.40479e24	0.263593	0.131796	−	0.991277i	$-0.457926\pi$
$811$	1.40479e24	0.263593	0.131796	+	0.991277i	$0.457926\pi$
$812$	−1.60159e24	−0.297389
$813$	1.93143e24	0.354903
$814$	−1.00594e24	−0.182921
$815$	3.31542e24	0.596621
$816$	−1.68263e25	−2.99656
$817$	−1.81549e23	−0.0319967
$818$	−5.89536e23	−0.102827
$819$	−1.24914e25	−2.15624
$820$	9.71241e24	1.65924
$821$	2.53580e24	0.428744	0.214372	−	0.976752i	$-0.431229\pi$
$821$	2.53580e24	0.428744	0.214372	+	0.976752i	$0.431229\pi$
$822$	3.22089e24	0.538972
$823$	−3.15106e24	−0.521864	−0.260932	−	0.965357i	$-0.584030\pi$
$823$	−3.15106e24	−0.521864	−0.260932	+	0.965357i	$0.584030\pi$
$824$	1.66484e24	0.272892
$825$	−1.09022e25	−1.76871
$826$	1.22157e25	1.96150
$827$	3.54565e24	0.563507	0.281754	−	0.959487i	$-0.409084\pi$
$827$	3.54565e24	0.563507	0.281754	+	0.959487i	$0.409084\pi$
$828$	−2.65106e25	−4.17024
$829$	−9.47300e24	−1.47494	−0.737470	−	0.675380i	$-0.763980\pi$
$829$	−9.47300e24	−1.47494	−0.737470	+	0.675380i	$0.763980\pi$
$830$	−2.10896e25	−3.25016
$831$	2.36260e24	0.360397
$832$	2.28460e25	3.44955
$833$	−2.08558e24	−0.311705
$834$	3.44854e25	5.10180
$835$	1.03775e25	1.51969
$836$	−6.50637e23	−0.0943160
$837$	−3.10125e25	−4.45011
$838$	−2.22195e25	−3.15616
$839$	−6.93284e24	−0.974843	−0.487421	−	0.873167i	$-0.662062\pi$
$839$	−6.93284e24	−0.974843	−0.487421	+	0.873167i	$0.662062\pi$
$840$	3.38996e25	4.71868
$841$	2.50246e23	0.0344828
$842$	1.02460e24	0.139766
$843$	2.47507e25	3.34235
$844$	1.40305e24	0.187570
$845$	−9.21131e24	−1.21910
$846$	−2.13492e25	−2.79727
$847$	−1.90704e24	−0.247372
$848$	−2.76353e25	−3.54895
$849$	−1.42511e25	−1.81189
$850$	−6.00354e24	−0.755695
$851$	−4.12003e23	−0.0513451
$852$	1.58488e25	1.95551
$853$	−2.16504e24	−0.264484	−0.132242	−	0.991217i	$-0.542218\pi$
$853$	−2.16504e24	−0.264484	−0.132242	+	0.991217i	$0.542218\pi$
$854$	3.83821e24	0.464234
$855$	8.67856e23	0.103929
$856$	−1.42799e25	−1.69316
$857$	1.57593e25	1.85012	0.925058	−	0.379825i	$-0.124016\pi$
$857$	1.57593e25	1.85012	0.925058	+	0.379825i	$0.124016\pi$
$858$	5.02747e25	5.84396
$859$	−6.13555e24	−0.706173	−0.353087	−	0.935591i	$-0.614868\pi$
$859$	−6.13555e24	−0.706173	−0.353087	+	0.935591i	$0.614868\pi$
$860$	−3.20295e25	−3.65017
$861$	−4.87439e24	−0.550039
$862$	−1.97883e25	−2.21104
$863$	1.98669e24	0.219805	0.109903	−	0.993942i	$-0.464946\pi$
$863$	1.98669e24	0.219805	0.109903	+	0.993942i	$0.464946\pi$
$864$	7.88802e25	8.64174
$865$	−1.13161e25	−1.22761
$866$	3.52445e24	0.378608
$867$	1.32389e25	1.40828
$868$	−2.34011e25	−2.46501
$869$	1.68357e25	1.75616
$870$	−8.59801e24	−0.888146
$871$	3.16503e24	0.323760
$872$	3.14191e25	3.18275
$873$	−1.65293e25	−1.65819
$874$	−3.68799e23	−0.0366389
$875$	−1.72325e24	−0.169543
$876$	−9.44279e25	−9.20058
$877$	−1.30941e25	−1.26351	−0.631757	−	0.775166i	$-0.717666\pi$
$877$	−1.30941e25	−1.26351	−0.631757	+	0.775166i	$0.717666\pi$
$878$	6.46709e24	0.618024
$879$	−1.70302e25	−1.61181
$880$	−5.37925e25	−5.04218
$881$	1.13551e25	1.05414	0.527068	−	0.849823i	$-0.323291\pi$
$881$	1.13551e25	1.05414	0.527068	+	0.849823i	$0.323291\pi$
$882$	3.25828e25	2.99575
$883$	5.35270e24	0.487424	0.243712	−	0.969848i	$-0.421635\pi$
$883$	5.35270e24	0.487424	0.243712	+	0.969848i	$0.421635\pi$
$884$	2.00042e25	1.80416
$885$	4.73855e25	4.23280
$886$	−2.81847e25	−2.49360
$887$	1.19457e25	1.04679	0.523397	−	0.852089i	$-0.324665\pi$
$887$	1.19457e25	1.04679	0.523397	+	0.852089i	$0.324665\pi$
$888$	5.37057e24	0.466133
$889$	−1.24313e24	−0.106869
$890$	−2.64813e24	−0.225488
$891$	4.07224e25	3.43458
$892$	−4.23064e25	−3.53432
$893$	−2.14601e23	−0.0177580
$894$	2.87127e25	2.35345
$895$	2.98501e25	2.42354
$896$	1.33771e25	1.07583
$897$	2.05911e25	1.64037
$898$	−7.99599e24	−0.630991
$899$	3.65640e24	0.285822
$900$	6.77717e25	5.24791
$901$	−7.29480e24	−0.559568
$902$	1.40720e25	1.06930
$903$	1.60747e25	1.21003
$904$	−9.60856e24	−0.716517
$905$	8.34184e24	0.616239
$906$	2.70707e25	1.98111
$907$	−1.15845e25	−0.839878	−0.419939	−	0.907552i	$-0.637949\pi$
$907$	−1.15845e25	−0.839878	−0.419939	+	0.907552i	$0.637949\pi$
$908$	4.79603e25	3.44471
$909$	−2.88993e25	−2.05634
$910$	−3.06576e25	−2.16116
$911$	−1.97637e25	−1.38026	−0.690131	−	0.723685i	$-0.742447\pi$
$911$	−1.97637e25	−1.38026	−0.690131	+	0.723685i	$0.742447\pi$
$912$	2.64242e24	0.182829
$913$	−2.20788e25	−1.51347
$914$	−2.77585e24	−0.188518
$915$	1.48886e25	1.00179
$916$	−1.26896e25	−0.845934
$917$	1.62377e25	1.07247
$918$	4.20418e25	2.75118
$919$	2.59306e25	1.68124	0.840621	−	0.541623i	$-0.182190\pi$
$919$	2.59306e25	1.68124	0.840621	+	0.541623i	$0.182190\pi$
$920$	−4.00829e25	−2.57492
$921$	2.52219e25	1.60535
$922$	−3.92885e24	−0.247772
$923$	−8.82988e24	−0.551747
$924$	5.76087e25	3.56678
$925$	1.05324e24	0.0646137
$926$	2.04257e25	1.24161
$927$	−3.77376e24	−0.227299
$928$	−9.30003e24	−0.555043
$929$	2.52659e25	1.49418	0.747088	−	0.664725i	$-0.231451\pi$
$929$	2.52659e25	1.49418	0.747088	+	0.664725i	$0.231451\pi$
$930$	−1.25627e26	−7.36171
$931$	3.27520e23	0.0190180
$932$	−1.97379e24	−0.113571
$933$	−5.84074e25	−3.33023
$934$	−6.75211e24	−0.381497
$935$	−1.41994e25	−0.795008
$936$	−1.92529e26	−10.6820
$937$	2.92873e25	1.61025	0.805125	−	0.593106i	$-0.202098\pi$
$937$	2.92873e25	1.61025	0.805125	+	0.593106i	$0.202098\pi$
$938$	5.01924e24	0.273473
$939$	−4.28274e24	−0.231241
$940$	−3.78606e25	−2.02582
$941$	3.39276e25	1.79904	0.899521	−	0.436878i	$-0.143916\pi$
$941$	3.39276e25	1.79904	0.899521	+	0.436878i	$0.143916\pi$
$942$	−4.61203e24	−0.242359
$943$	5.76348e24	0.300148
$944$	1.03489e26	5.34114
$945$	−4.65563e25	−2.38126
$946$	−4.64064e25	−2.35236
$947$	−1.67626e25	−0.842104	−0.421052	−	0.907036i	$-0.638339\pi$
$947$	−1.67626e25	−0.842104	−0.421052	+	0.907036i	$0.638339\pi$
$948$	−1.45904e26	−7.26436
$949$	5.26087e25	2.59594
$950$	9.42798e23	0.0461071
$951$	−3.35906e25	−1.62811
$952$	1.95431e25	0.938816
$953$	−2.11052e23	−0.0100485	−0.00502423	−	0.999987i	$-0.501599\pi$
$953$	−2.11052e23	−0.0100485	−0.00502423	+	0.999987i	$0.501599\pi$
$954$	1.13966e26	5.37793
$955$	−8.27450e24	−0.387002
$956$	−4.81000e25	−2.22974
$957$	−9.00130e24	−0.413575
$958$	6.20174e25	2.82427
$959$	−2.05623e24	−0.0928142
$960$	1.40539e26	6.28769
$961$	3.08743e25	1.36914
$962$	−4.85695e24	−0.213489
$963$	3.23689e25	1.41028
$964$	6.58429e25	2.84351
$965$	3.96376e25	1.69678
$966$	3.26542e25	1.38559
$967$	2.06300e25	0.867708	0.433854	−	0.900983i	$-0.357153\pi$
$967$	2.06300e25	0.867708	0.433854	+	0.900983i	$0.357153\pi$
$968$	−2.93931e25	−1.22547
$969$	6.97510e23	0.0288269
$970$	−4.05678e25	−1.66197
$971$	4.56860e25	1.85532	0.927662	−	0.373421i	$-0.121815\pi$
$971$	4.56860e25	1.85532	0.927662	+	0.373421i	$0.121815\pi$
$972$	−1.65864e26	−6.67711
$973$	−2.20156e25	−0.878562
$974$	3.77642e25	1.49392
$975$	−5.26390e25	−2.06428
$976$	3.25166e25	1.26410
$977$	−2.48939e25	−0.959379	−0.479689	−	0.877438i	$-0.659251\pi$
$977$	−2.48939e25	−0.959379	−0.479689	+	0.877438i	$0.659251\pi$
$978$	−4.16297e25	−1.59046
$979$	−2.77234e24	−0.105001
$980$	5.77822e25	2.16956
$981$	−7.12190e25	−2.65100
$982$	−1.26676e24	−0.0467463
$983$	−3.55038e25	−1.29888	−0.649442	−	0.760411i	$-0.724998\pi$
$983$	−3.55038e25	−1.29888	−0.649442	+	0.760411i	$0.724998\pi$
$984$	−7.51286e25	−2.72488
$985$	−2.42984e25	−0.873714
$986$	−4.95676e24	−0.176703
$987$	1.90012e25	0.671561
$988$	−3.14146e24	−0.110077
$989$	−1.90067e25	−0.660297
$990$	2.21836e26	7.64071
$991$	−1.10853e25	−0.378549	−0.189275	−	0.981924i	$-0.560614\pi$
$991$	−1.10853e25	−0.378549	−0.189275	+	0.981924i	$0.560614\pi$
$992$	−1.35885e26	−4.60067
$993$	−7.92337e25	−2.65975
$994$	−1.40028e25	−0.466048
$995$	1.26187e25	0.416409
$996$	1.91343e26	6.26048
$997$	2.84170e25	0.921870	0.460935	−	0.887434i	$-0.347514\pi$
$997$	2.84170e25	0.921870	0.460935	+	0.887434i	$0.347514\pi$
$998$	−9.81263e25	−3.15628
$999$	−7.37571e24	−0.235232

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.b.1.2	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.b.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-687.348 q^{2} -21372.9 q^{3} +341375. q^{4} -1.16997e6 q^{5} +1.46906e7 q^{6} -9.37855e6 q^{7} -1.44551e8 q^{8} +3.27660e8 q^{9} +O(q^{10})\)	\(q-687.348 q^{2} -21372.9 q^{3} +341375. q^{4} -1.16997e6 q^{5} +1.46906e7 q^{6} -9.37855e6 q^{7} -1.44551e8 q^{8} +3.27660e8 q^{9} +8.04176e8 q^{10} +8.41895e8 q^{11} -7.29616e9 q^{12} +4.06492e9 q^{13} +6.44633e9 q^{14} +2.50056e10 q^{15} +5.46121e10 q^{16} +1.44158e10 q^{17} -2.25216e11 q^{18} -2.26386e9 q^{19} -3.99398e11 q^{20} +2.00447e11 q^{21} -5.78675e11 q^{22} -2.37009e11 q^{23} +3.08947e12 q^{24} +6.05889e11 q^{25} -2.79401e12 q^{26} -4.24295e12 q^{27} -3.20160e12 q^{28} +5.00246e11 q^{29} -1.71876e13 q^{30} +7.30920e12 q^{31} -1.85909e13 q^{32} -1.79937e13 q^{33} -9.90864e12 q^{34} +1.09726e13 q^{35} +1.11855e14 q^{36} +1.73834e12 q^{37} +1.55606e12 q^{38} -8.68790e13 q^{39} +1.69120e14 q^{40} -2.43176e13 q^{41} -1.37777e14 q^{42} +8.01944e13 q^{43} +2.87402e14 q^{44} -3.83352e14 q^{45} +1.62907e14 q^{46} +9.47943e13 q^{47} -1.16722e15 q^{48} -1.44673e14 q^{49} -4.16456e14 q^{50} -3.08107e14 q^{51} +1.38766e15 q^{52} -5.06029e14 q^{53} +2.91638e15 q^{54} -9.84992e14 q^{55} +1.35568e15 q^{56} +4.83852e13 q^{57} -3.43843e14 q^{58} +1.89499e15 q^{59} +8.53629e15 q^{60} +5.95411e14 q^{61} -5.02396e15 q^{62} -3.07298e15 q^{63} +5.62029e15 q^{64} -4.75583e15 q^{65} +1.23679e16 q^{66} +7.78620e14 q^{67} +4.92118e15 q^{68} +5.06556e15 q^{69} -7.54200e15 q^{70} -2.17222e15 q^{71} -4.73636e16 q^{72} +1.29421e16 q^{73} -1.19485e15 q^{74} -1.29496e16 q^{75} -7.72824e14 q^{76} -7.89576e15 q^{77} +5.97161e16 q^{78} +1.99974e16 q^{79} -6.38945e16 q^{80} +4.83700e16 q^{81} +1.67147e16 q^{82} -2.62251e16 q^{83} +6.84274e16 q^{84} -1.68660e16 q^{85} -5.51214e16 q^{86} -1.06917e16 q^{87} -1.21697e17 q^{88} -3.29297e15 q^{89} +2.63496e17 q^{90} -3.81230e16 q^{91} -8.09087e16 q^{92} -1.56219e17 q^{93} -6.51566e16 q^{94} +2.64865e15 q^{95} +3.97341e17 q^{96} -5.04465e16 q^{97} +9.94408e16 q^{98} +2.75856e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) \) 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

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more