LMFDB - Embedded newform 29.18.a.b.1.17

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			1.17
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)

$f(q)$	$=$	$q+460.739 q^{2} +20203.5 q^{3} +81208.7 q^{4} -1.66304e6 q^{5} +9.30854e6 q^{6} +1.23855e7 q^{7} -2.29740e7 q^{8} +2.79040e8 q^{9} +O(q^{10})$	\(q+460.739 q^{2} +20203.5 q^{3} +81208.7 q^{4} -1.66304e6 q^{5} +9.30854e6 q^{6} +1.23855e7 q^{7} -2.29740e7 q^{8} +2.79040e8 q^{9} -7.66230e8 q^{10} +9.02232e8 q^{11} +1.64070e9 q^{12} +3.76021e9 q^{13} +5.70649e9 q^{14} -3.35993e10 q^{15} -2.12292e10 q^{16} -3.63569e9 q^{17} +1.28565e11 q^{18} +1.22876e11 q^{19} -1.35054e11 q^{20} +2.50230e11 q^{21} +4.15694e11 q^{22} +6.50140e10 q^{23} -4.64154e11 q^{24} +2.00278e12 q^{25} +1.73248e12 q^{26} +3.02851e12 q^{27} +1.00581e12 q^{28} +5.00246e11 q^{29} -1.54805e13 q^{30} +2.97150e12 q^{31} -6.76988e12 q^{32} +1.82282e13 q^{33} -1.67510e12 q^{34} -2.05977e13 q^{35} +2.26605e13 q^{36} -3.65243e13 q^{37} +5.66139e13 q^{38} +7.59693e13 q^{39} +3.82068e13 q^{40} -9.22379e11 q^{41} +1.15291e14 q^{42} -4.15443e13 q^{43} +7.32691e13 q^{44} -4.64057e14 q^{45} +2.99545e13 q^{46} +9.84670e13 q^{47} -4.28904e14 q^{48} -7.92297e13 q^{49} +9.22759e14 q^{50} -7.34535e13 q^{51} +3.05362e14 q^{52} -1.51452e14 q^{53} +1.39535e15 q^{54} -1.50045e15 q^{55} -2.84545e14 q^{56} +2.48253e15 q^{57} +2.30483e14 q^{58} -1.57878e14 q^{59} -2.72855e15 q^{60} -1.88634e15 q^{61} +1.36909e15 q^{62} +3.45606e15 q^{63} -3.36596e14 q^{64} -6.25340e15 q^{65} +8.39846e15 q^{66} +4.36716e15 q^{67} -2.95249e14 q^{68} +1.31351e15 q^{69} -9.49015e15 q^{70} -2.82315e15 q^{71} -6.41067e15 q^{72} -3.52665e15 q^{73} -1.68282e16 q^{74} +4.04631e16 q^{75} +9.97862e15 q^{76} +1.11746e16 q^{77} +3.50021e16 q^{78} +6.21859e15 q^{79} +3.53051e16 q^{80} +2.51511e16 q^{81} -4.24976e14 q^{82} +4.03215e15 q^{83} +2.03209e16 q^{84} +6.04631e15 q^{85} -1.91411e16 q^{86} +1.01067e16 q^{87} -2.07279e16 q^{88} -3.87727e16 q^{89} -2.13809e17 q^{90} +4.65721e16 q^{91} +5.27970e15 q^{92} +6.00346e16 q^{93} +4.53676e16 q^{94} -2.04349e17 q^{95} -1.36775e17 q^{96} -3.83177e16 q^{97} -3.65042e16 q^{98} +2.51759e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	460.739	1.27262	0.636312	−	0.771432i	$-0.280459\pi$
$2$	460.739	1.27262	0.636312	+	0.771432i	$0.280459\pi$
$3$	20203.5	1.77785	0.888926	−	0.458051i	$-0.151452\pi$
$3$	20203.5	1.77785	0.888926	+	0.458051i	$0.151452\pi$
$4$	81208.7	0.619573
$5$	−1.66304e6	−1.90396	−0.951982	−	0.306153i	$-0.900958\pi$
$5$	−1.66304e6	−1.90396	−0.951982	+	0.306153i	$0.900958\pi$
$6$	9.30854e6	2.26254
$7$	1.23855e7	0.812046	0.406023	−	0.913863i	$-0.366915\pi$
$7$	1.23855e7	0.812046	0.406023	+	0.913863i	$0.366915\pi$
$8$	−2.29740e7	−0.484141
$9$	2.79040e8	2.16076
$10$	−7.66230e8	−2.42303
$11$	9.02232e8	1.26906	0.634528	−	0.772900i	$-0.281195\pi$
$11$	9.02232e8	1.26906	0.634528	+	0.772900i	$0.281195\pi$
$12$	1.64070e9	1.10151
$13$	3.76021e9	1.27848	0.639240	−	0.769008i	$-0.279249\pi$
$13$	3.76021e9	1.27848	0.639240	+	0.769008i	$0.279249\pi$
$14$	5.70649e9	1.03343
$15$	−3.35993e10	−3.38497
$16$	−2.12292e10	−1.23570
$17$	−3.63569e9	−0.126407	−0.0632034	−	0.998001i	$-0.520132\pi$
$17$	−3.63569e9	−0.126407	−0.0632034	+	0.998001i	$0.520132\pi$
$18$	1.28565e11	2.74983
$19$	1.22876e11	1.65983	0.829913	−	0.557893i	$-0.188390\pi$
$19$	1.22876e11	1.65983	0.829913	+	0.557893i	$0.188390\pi$
$20$	−1.35054e11	−1.17965
$21$	2.50230e11	1.44370
$22$	4.15694e11	1.61503
$23$	6.50140e10	0.173109	0.0865546	−	0.996247i	$-0.472414\pi$
$23$	6.50140e10	0.173109	0.0865546	+	0.996247i	$0.472414\pi$
$24$	−4.64154e11	−0.860730
$25$	2.00278e12	2.62508
$26$	1.73248e12	1.62702
$27$	3.02851e12	2.06365
$28$	1.00581e12	0.503122
$29$	5.00246e11	0.185695
$29$	5.00246e11	0.185695
$30$	−1.54805e13	−4.30779
$31$	2.97150e12	0.625751	0.312875	−	0.949794i	$-0.398708\pi$
$31$	2.97150e12	0.625751	0.312875	+	0.949794i	$0.398708\pi$
$32$	−6.76988e12	−1.08844
$33$	1.82282e13	2.25619
$34$	−1.67510e12	−0.160868
$35$	−2.05977e13	−1.54611
$36$	2.26605e13	1.33875
$37$	−3.65243e13	−1.70949	−0.854746	−	0.519046i	$-0.826287\pi$
$37$	−3.65243e13	−1.70949	−0.854746	+	0.519046i	$0.826287\pi$
$38$	5.66139e13	2.11234
$39$	7.59693e13	2.27295
$40$	3.82068e13	0.921787
$41$	−9.22379e11	−0.0180404	−0.00902021	−	0.999959i	$-0.502871\pi$
$41$	−9.22379e11	−0.0180404	−0.00902021	+	0.999959i	$0.502871\pi$
$42$	1.15291e14	1.83728
$43$	−4.15443e13	−0.542038	−0.271019	−	0.962574i	$-0.587361\pi$
$43$	−4.15443e13	−0.542038	−0.271019	+	0.962574i	$0.587361\pi$
$44$	7.32691e13	0.786272
$45$	−4.64057e14	−4.11400
$46$	2.99545e13	0.220303
$47$	9.84670e13	0.603197	0.301598	−	0.953435i	$-0.402480\pi$
$47$	9.84670e13	0.603197	0.301598	+	0.953435i	$0.402480\pi$
$48$	−4.28904e14	−2.19690
$49$	−7.92297e13	−0.340582
$50$	9.22759e14	3.34074
$51$	−7.34535e13	−0.224733
$52$	3.05362e14	0.792111
$53$	−1.51452e14	−0.334140	−0.167070	−	0.985945i	$-0.553431\pi$
$53$	−1.51452e14	−0.334140	−0.167070	+	0.985945i	$0.553431\pi$
$54$	1.39535e15	2.62625
$55$	−1.50045e15	−2.41624
$56$	−2.84545e14	−0.393144
$57$	2.48253e15	2.95092
$58$	2.30483e14	0.236320
$59$	−1.57878e14	−0.139984	−0.0699921	−	0.997548i	$-0.522297\pi$
$59$	−1.57878e14	−0.139984	−0.0699921	+	0.997548i	$0.522297\pi$
$60$	−2.72855e15	−2.09723
$61$	−1.88634e15	−1.25984	−0.629922	−	0.776658i	$-0.716913\pi$
$61$	−1.88634e15	−1.25984	−0.629922	+	0.776658i	$0.716913\pi$
$62$	1.36909e15	0.796345
$63$	3.45606e15	1.75463
$64$	−3.36596e14	−0.149479
$65$	−6.25340e15	−2.43418
$66$	8.39846e15	2.87128
$67$	4.36716e15	1.31390	0.656951	−	0.753933i	$-0.271846\pi$
$67$	4.36716e15	1.31390	0.656951	+	0.753933i	$0.271846\pi$
$68$	−2.95249e14	−0.0783183
$69$	1.31351e15	0.307762
$70$	−9.49015e15	−1.96761
$71$	−2.82315e15	−0.518846	−0.259423	−	0.965764i	$-0.583532\pi$
$71$	−2.82315e15	−0.518846	−0.259423	+	0.965764i	$0.583532\pi$
$72$	−6.41067e15	−1.04611
$73$	−3.52665e15	−0.511821	−0.255911	−	0.966700i	$-0.582375\pi$
$73$	−3.52665e15	−0.511821	−0.255911	+	0.966700i	$0.582375\pi$
$74$	−1.68282e16	−2.17554
$75$	4.04631e16	4.66701
$76$	9.97862e15	1.02838
$77$	1.11746e16	1.03053
$78$	3.50021e16	2.89261
$79$	6.21859e15	0.461170	0.230585	−	0.973052i	$-0.425936\pi$
$79$	6.21859e15	0.461170	0.230585	+	0.973052i	$0.425936\pi$
$80$	3.53051e16	2.35273
$81$	2.51511e16	1.50811
$82$	−4.24976e14	−0.0229587
$83$	4.03215e15	0.196505	0.0982523	−	0.995162i	$-0.468675\pi$
$83$	4.03215e15	0.196505	0.0982523	+	0.995162i	$0.468675\pi$
$84$	2.03209e16	0.894476
$85$	6.04631e15	0.240674
$86$	−1.91411e16	−0.689811
$87$	1.01067e16	0.330139
$88$	−2.07279e16	−0.614401
$89$	−3.87727e16	−1.04403	−0.522013	−	0.852937i	$-0.674819\pi$
$89$	−3.87727e16	−1.04403	−0.522013	+	0.852937i	$0.674819\pi$
$90$	−2.13809e17	−5.23558
$91$	4.65721e16	1.03818
$92$	5.27970e15	0.107254
$93$	6.00346e16	1.11249
$94$	4.53676e16	0.767643
$95$	−2.04349e17	−3.16025
$96$	−1.36775e17	−1.93509
$97$	−3.83177e16	−0.496409	−0.248205	−	0.968708i	$-0.579841\pi$
$97$	−3.83177e16	−0.496409	−0.248205	+	0.968708i	$0.579841\pi$
$98$	−3.65042e16	−0.433433
$99$	2.51759e17	2.74212
$100$	1.62643e17	1.62643
$101$	−1.65336e17	−1.51927	−0.759636	−	0.650349i	$-0.774623\pi$
$101$	−1.65336e17	−1.51927	−0.759636	+	0.650349i	$0.774623\pi$
$102$	−3.38429e16	−0.286000
$103$	1.49910e17	1.16604	0.583019	−	0.812458i	$-0.301871\pi$
$103$	1.49910e17	1.16604	0.583019	+	0.812458i	$0.301871\pi$
$104$	−8.63870e16	−0.618964
$105$	−4.16144e17	−2.74875
$106$	−6.97797e16	−0.425235
$107$	1.51941e17	0.854897	0.427448	−	0.904040i	$-0.359413\pi$
$107$	1.51941e17	0.854897	0.427448	+	0.904040i	$0.359413\pi$
$108$	2.45941e17	1.27858
$109$	2.41241e17	1.15965	0.579824	−	0.814742i	$-0.303121\pi$
$109$	2.41241e17	1.15965	0.579824	+	0.814742i	$0.303121\pi$
$110$	−6.91317e17	−3.07496
$111$	−7.37918e17	−3.03922
$112$	−2.62934e17	−1.00345
$113$	−1.12905e16	−0.0399526	−0.0199763	−	0.999800i	$-0.506359\pi$
$113$	−1.12905e16	−0.0399526	−0.0199763	+	0.999800i	$0.506359\pi$
$114$	1.14380e18	3.75542
$115$	−1.08121e17	−0.329594
$116$	4.06244e16	0.115052
$117$	1.04925e18	2.76248
$118$	−7.27405e16	−0.178147
$119$	−4.50298e16	−0.102648
$120$	7.71910e17	1.63880
$121$	3.08576e17	0.610501
$122$	−8.69112e17	−1.60331
$123$	−1.86353e16	−0.0320732
$124$	2.41312e17	0.387698
$125$	−2.06191e18	−3.09410
$126$	1.59234e18	2.23299
$127$	−4.28216e17	−0.561476	−0.280738	−	0.959784i	$-0.590579\pi$
$127$	−4.28216e17	−0.561476	−0.280738	+	0.959784i	$0.590579\pi$
$128$	7.32259e17	0.898214
$129$	−8.39340e17	−0.963663
$130$	−2.88119e18	−3.09780
$131$	1.66744e17	0.167975	0.0839875	−	0.996467i	$-0.473234\pi$
$131$	1.66744e17	0.167975	0.0839875	+	0.996467i	$0.473234\pi$
$132$	1.48029e18	1.39788
$133$	1.52189e18	1.34785
$134$	2.01212e18	1.67210
$135$	−5.03654e18	−3.92912
$136$	8.35262e16	0.0611987
$137$	1.48836e18	1.02467	0.512333	−	0.858787i	$-0.328782\pi$
$137$	1.48836e18	1.02467	0.512333	+	0.858787i	$0.328782\pi$
$138$	6.05185e17	0.391666
$139$	−6.39389e17	−0.389170	−0.194585	−	0.980886i	$-0.562336\pi$
$139$	−6.39389e17	−0.389170	−0.194585	+	0.980886i	$0.562336\pi$
$140$	−1.67271e18	−0.957926
$141$	1.98938e18	1.07239
$142$	−1.30074e18	−0.660296
$143$	3.39258e18	1.62246
$144$	−5.92381e18	−2.67005
$145$	−8.31932e17	−0.353557
$146$	−1.62487e18	−0.651356
$147$	−1.60072e18	−0.605504
$148$	−2.96609e18	−1.05916
$149$	−1.86113e17	−0.0627614	−0.0313807	−	0.999508i	$-0.509990\pi$
$149$	−1.86113e17	−0.0627614	−0.0313807	+	0.999508i	$0.509990\pi$
$150$	1.86429e19	5.93935
$151$	4.97001e18	1.49642	0.748210	−	0.663462i	$-0.230913\pi$
$151$	4.97001e18	1.49642	0.748210	+	0.663462i	$0.230913\pi$
$152$	−2.82296e18	−0.803589
$153$	−1.01450e18	−0.273134
$154$	5.14858e18	1.31148
$155$	−4.94174e18	−1.19141
$156$	6.16937e18	1.40826
$157$	−2.52108e18	−0.545055	−0.272527	−	0.962148i	$-0.587859\pi$
$157$	−2.52108e18	−0.545055	−0.272527	+	0.962148i	$0.587859\pi$
$158$	2.86515e18	0.586897
$159$	−3.05985e18	−0.594052
$160$	1.12586e19	2.07236
$161$	8.05231e17	0.140573
$162$	1.15881e19	1.91926
$163$	1.83879e18	0.289027	0.144513	−	0.989503i	$-0.453838\pi$
$163$	1.83879e18	0.289027	0.144513	+	0.989503i	$0.453838\pi$
$164$	−7.49052e16	−0.0111774
$165$	−3.03144e19	−4.29571
$166$	1.85777e18	0.250077
$167$	−1.15909e19	−1.48261	−0.741303	−	0.671171i	$-0.765792\pi$
$167$	−1.15909e19	−1.48261	−0.741303	+	0.671171i	$0.765792\pi$
$168$	−5.74879e18	−0.698952
$169$	5.48877e18	0.634509
$170$	2.78577e18	0.306288
$171$	3.42875e19	3.58648
$172$	−3.37376e18	−0.335832
$173$	−1.24687e19	−1.18148	−0.590742	−	0.806860i	$-0.701165\pi$
$173$	−1.24687e19	−1.18148	−0.590742	+	0.806860i	$0.701165\pi$
$174$	4.65656e18	0.420143
$175$	2.48054e19	2.13169
$176$	−1.91537e19	−1.56817
$177$	−3.18968e18	−0.248871
$178$	−1.78641e19	−1.32865
$179$	−3.81768e18	−0.270738	−0.135369	−	0.990795i	$-0.543222\pi$
$179$	−3.81768e18	−0.270738	−0.135369	+	0.990795i	$0.543222\pi$
$180$	−3.76854e19	−2.54893
$181$	1.67540e19	1.08106	0.540531	−	0.841324i	$-0.318223\pi$
$181$	1.67540e19	1.08106	0.540531	+	0.841324i	$0.318223\pi$
$182$	2.14576e19	1.32122
$183$	−3.81107e19	−2.23982
$184$	−1.49363e18	−0.0838092
$185$	6.07415e19	3.25481
$186$	2.76603e19	1.41578
$187$	−3.28023e18	−0.160417
$188$	7.99637e18	0.373724
$189$	3.75096e19	1.67578
$190$	−9.41515e19	−4.02181
$191$	−3.94112e19	−1.61004	−0.805019	−	0.593250i	$-0.797845\pi$
$191$	−3.94112e19	−1.61004	−0.805019	+	0.593250i	$0.797845\pi$
$192$	−6.80041e18	−0.265751
$193$	3.44273e19	1.28726	0.643630	−	0.765337i	$-0.277428\pi$
$193$	3.44273e19	1.28726	0.643630	+	0.765337i	$0.277428\pi$
$194$	−1.76545e19	−0.631743
$195$	−1.26340e20	−4.32761
$196$	−6.43414e18	−0.211015
$197$	−5.79097e18	−0.181881	−0.0909407	−	0.995856i	$-0.528987\pi$
$197$	−5.79097e18	−0.181881	−0.0909407	+	0.995856i	$0.528987\pi$
$198$	1.15995e20	3.48969
$199$	−2.16629e17	−0.00624404	−0.00312202	−	0.999995i	$-0.500994\pi$
$199$	−2.16629e17	−0.00624404	−0.00312202	+	0.999995i	$0.500994\pi$
$200$	−4.60118e19	−1.27091
$201$	8.82318e19	2.33592
$202$	−7.61767e19	−1.93346
$203$	6.19581e18	0.150793
$204$	−5.96506e18	−0.139238
$205$	1.53396e18	0.0343483
$206$	6.90692e19	1.48393
$207$	1.81415e19	0.374047
$208$	−7.98263e19	−1.57982
$209$	1.10863e20	2.10641
$210$	−1.91734e20	−3.49812
$211$	−2.91427e19	−0.510657	−0.255329	−	0.966854i	$-0.582184\pi$
$211$	−2.91427e19	−0.510657	−0.255329	+	0.966854i	$0.582184\pi$
$212$	−1.22992e19	−0.207024
$213$	−5.70375e19	−0.922431
$214$	7.00053e19	1.08796
$215$	6.90901e19	1.03202
$216$	−6.95769e19	−0.999098
$217$	3.68035e19	0.508138
$218$	1.11149e20	1.47580
$219$	−7.12506e19	−0.909942
$220$	−1.21850e20	−1.49703
$221$	−1.36709e19	−0.161609
$222$	−3.39988e20	−3.86779
$223$	−1.51839e20	−1.66261	−0.831307	−	0.555814i	$-0.812407\pi$
$223$	−1.51839e20	−1.66261	−0.831307	+	0.555814i	$0.812407\pi$
$224$	−8.38484e19	−0.883867
$225$	5.58856e20	5.67216
$226$	−5.20196e18	−0.0508447
$227$	4.69796e19	0.442272	0.221136	−	0.975243i	$-0.429024\pi$
$227$	4.69796e19	0.442272	0.221136	+	0.975243i	$0.429024\pi$
$228$	2.01603e20	1.82831
$229$	7.14393e19	0.624217	0.312108	−	0.950047i	$-0.398965\pi$
$229$	7.14393e19	0.624217	0.312108	+	0.950047i	$0.398965\pi$
$230$	−4.98157e19	−0.419449
$231$	2.25766e20	1.83213
$232$	−1.14927e19	−0.0899026
$233$	−1.75134e20	−1.32083	−0.660414	−	0.750902i	$-0.729619\pi$
$233$	−1.75134e20	−1.32083	−0.660414	+	0.750902i	$0.729619\pi$
$234$	4.83431e20	3.51560
$235$	−1.63755e20	−1.14847
$236$	−1.28210e19	−0.0867304
$237$	1.25637e20	0.819893
$238$	−2.07470e19	−0.130633
$239$	−2.20043e20	−1.33698	−0.668490	−	0.743721i	$-0.733059\pi$
$239$	−2.20043e20	−1.33698	−0.668490	+	0.743721i	$0.733059\pi$
$240$	7.13286e20	4.18281
$241$	−1.56304e20	−0.884762	−0.442381	−	0.896827i	$-0.645866\pi$
$241$	−1.56304e20	−0.884762	−0.442381	+	0.896827i	$0.645866\pi$
$242$	1.42173e20	0.776938
$243$	1.17037e20	0.617546
$244$	−1.53187e20	−0.780566
$245$	1.31763e20	0.648456
$246$	−8.58600e18	−0.0408171
$247$	4.62041e20	2.12205
$248$	−6.82672e19	−0.302951
$249$	8.14634e19	0.349356
$250$	−9.50002e20	−3.93763
$251$	1.52792e20	0.612172	0.306086	−	0.952004i	$-0.400980\pi$
$251$	1.52792e20	0.612172	0.306086	+	0.952004i	$0.400980\pi$
$252$	2.80662e20	1.08712
$253$	5.86577e19	0.219685
$254$	−1.97296e20	−0.714548
$255$	1.22157e20	0.427883
$256$	3.81499e20	1.29257
$257$	−4.10329e20	−1.34493	−0.672466	−	0.740128i	$-0.734765\pi$
$257$	−4.10329e20	−1.34493	−0.672466	+	0.740128i	$0.734765\pi$
$258$	−3.86717e20	−1.22638
$259$	−4.52372e20	−1.38819
$260$	−5.07830e20	−1.50815
$261$	1.39589e20	0.401242
$262$	7.68256e19	0.213769
$263$	−1.77746e20	−0.478825	−0.239412	−	0.970918i	$-0.576955\pi$
$263$	−1.77746e20	−0.478825	−0.239412	+	0.970918i	$0.576955\pi$
$264$	−4.18775e20	−1.09231
$265$	2.51871e20	0.636191
$266$	7.01192e20	1.71531
$267$	−7.83344e20	−1.85612
$268$	3.54651e20	0.814058
$269$	−3.73241e19	−0.0830032	−0.0415016	−	0.999138i	$-0.513214\pi$
$269$	−3.73241e19	−0.0830032	−0.0415016	+	0.999138i	$0.513214\pi$
$270$	−2.32053e21	−5.00030
$271$	−8.58140e19	−0.179192	−0.0895961	−	0.995978i	$-0.528558\pi$
$271$	−8.58140e19	−0.179192	−0.0895961	+	0.995978i	$0.528558\pi$
$272$	7.71827e19	0.156201
$273$	9.40919e20	1.84574
$274$	6.85744e20	1.30401
$275$	1.80697e21	3.33137
$276$	1.06668e20	0.190681
$277$	−3.27364e20	−0.567482	−0.283741	−	0.958901i	$-0.591576\pi$
$277$	−3.27364e20	−0.567482	−0.283741	+	0.958901i	$0.591576\pi$
$278$	−2.94592e20	−0.495267
$279$	8.29168e20	1.35209
$280$	4.73210e20	0.748533
$281$	−2.39779e20	−0.367965	−0.183983	−	0.982929i	$-0.558899\pi$
$281$	−2.39779e20	−0.367965	−0.183983	+	0.982929i	$0.558899\pi$
$282$	9.16584e20	1.36475
$283$	−1.71895e20	−0.248358	−0.124179	−	0.992260i	$-0.539630\pi$
$283$	−1.71895e20	−0.248358	−0.124179	+	0.992260i	$0.539630\pi$
$284$	−2.29265e20	−0.321463
$285$	−4.12856e21	−5.61846
$286$	1.56310e21	2.06478
$287$	−1.14241e19	−0.0146496
$288$	−1.88907e21	−2.35186
$289$	−8.14022e20	−0.984021
$290$	−3.83304e20	−0.449946
$291$	−7.74151e20	−0.882542
$292$	−2.86395e20	−0.317111
$293$	1.97331e19	0.0212236	0.0106118	−	0.999944i	$-0.496622\pi$
$293$	1.97331e19	0.0212236	0.0106118	+	0.999944i	$0.496622\pi$
$294$	−7.37513e20	−0.770579
$295$	2.62558e20	0.266525
$296$	8.39108e20	0.827634
$297$	2.73242e21	2.61889
$298$	−8.57495e19	−0.0798717
$299$	2.44466e20	0.221316
$300$	3.28595e21	2.89155
$301$	−5.14548e20	−0.440160
$302$	2.28988e21	1.90438
$303$	−3.34036e21	−2.70104
$304$	−2.60857e21	−2.05105
$305$	3.13707e21	2.39870
$306$	−4.67422e20	−0.347598
$307$	6.82405e20	0.493590	0.246795	−	0.969068i	$-0.420623\pi$
$307$	6.82405e20	0.493590	0.246795	+	0.969068i	$0.420623\pi$
$308$	9.07475e20	0.638489
$309$	3.02870e21	2.07304
$310$	−2.27685e21	−1.51621
$311$	2.23157e21	1.44593	0.722966	−	0.690883i	$-0.242778\pi$
$311$	2.23157e21	1.44593	0.722966	+	0.690883i	$0.242778\pi$
$312$	−1.74532e21	−1.10043
$313$	2.21099e21	1.35663	0.678314	−	0.734773i	$-0.262711\pi$
$313$	2.21099e21	1.35663	0.678314	+	0.734773i	$0.262711\pi$
$314$	−1.16156e21	−0.693650
$315$	−5.74758e21	−3.34076
$316$	5.05003e20	0.285729
$317$	−2.95633e21	−1.62836	−0.814179	−	0.580614i	$-0.802812\pi$
$317$	−2.95633e21	−1.62836	−0.814179	+	0.580614i	$0.802812\pi$
$318$	−1.40979e21	−0.756005
$319$	4.51338e20	0.235658
$320$	5.59775e20	0.284602
$321$	3.06974e21	1.51988
$322$	3.71002e20	0.178896
$323$	−4.46740e20	−0.209813
$324$	2.04248e21	0.934385
$325$	7.53087e21	3.35611
$326$	8.47203e20	0.367822
$327$	4.87391e21	2.06168
$328$	2.11907e19	0.00873410
$329$	1.21956e21	0.489823
$330$	−1.39670e22	−5.46682
$331$	−1.91693e21	−0.731253	−0.365626	−	0.930762i	$-0.619145\pi$
$331$	−1.91693e21	−0.731253	−0.365626	+	0.930762i	$0.619145\pi$
$332$	3.27446e20	0.121749
$333$	−1.01918e22	−3.69380
$334$	−5.34037e21	−1.88680
$335$	−7.26278e21	−2.50162
$336$	−5.31219e21	−1.78398
$337$	1.65410e21	0.541635	0.270817	−	0.962631i	$-0.412706\pi$
$337$	1.65410e21	0.541635	0.270817	+	0.962631i	$0.412706\pi$
$338$	2.52889e21	0.807492
$339$	−2.28107e20	−0.0710298
$340$	4.91013e20	0.149115
$341$	2.68098e21	0.794112
$342$	1.57976e22	4.56424
$343$	−3.86255e21	−1.08861
$344$	9.54439e20	0.262423
$345$	−2.18442e21	−0.585969
$346$	−5.74480e21	−1.50359
$347$	4.73096e21	1.20823	0.604114	−	0.796898i	$-0.293527\pi$
$347$	4.73096e21	1.20823	0.604114	+	0.796898i	$0.293527\pi$
$348$	8.20753e20	0.204545
$349$	5.88546e21	1.43141	0.715705	−	0.698403i	$-0.246106\pi$
$349$	5.88546e21	1.43141	0.715705	+	0.698403i	$0.246106\pi$
$350$	1.14288e22	2.71284
$351$	1.13878e22	2.63834
$352$	−6.10800e21	−1.38130
$353$	5.33356e21	1.17742	0.588712	−	0.808343i	$-0.299635\pi$
$353$	5.33356e21	1.17742	0.588712	+	0.808343i	$0.299635\pi$
$354$	−1.46961e21	−0.316719
$355$	4.69503e21	0.987865
$356$	−3.14868e21	−0.646851
$357$	−9.09759e20	−0.182493
$358$	−1.75895e21	−0.344547
$359$	1.07155e21	0.204978	0.102489	−	0.994734i	$-0.467319\pi$
$359$	1.07155e21	0.204978	0.102489	+	0.994734i	$0.467319\pi$
$360$	1.06612e22	1.99176
$361$	9.61820e21	1.75502
$362$	7.71922e21	1.37579
$363$	6.23430e21	1.08538
$364$	3.78206e21	0.643231
$365$	5.86498e21	0.974489
$366$	−1.75591e22	−2.85045
$367$	−6.72242e21	−1.06626	−0.533131	−	0.846032i	$-0.678985\pi$
$367$	−6.72242e21	−1.06626	−0.533131	+	0.846032i	$0.678985\pi$
$368$	−1.38019e21	−0.213911
$369$	−2.57381e20	−0.0389809
$370$	2.79860e22	4.14215
$371$	−1.87580e21	−0.271337
$372$	4.87533e21	0.689270
$373$	−8.99881e21	−1.24354	−0.621770	−	0.783200i	$-0.713586\pi$
$373$	−8.99881e21	−1.24354	−0.621770	+	0.783200i	$0.713586\pi$
$374$	−1.51133e21	−0.204151
$375$	−4.16577e22	−5.50085
$376$	−2.26218e21	−0.292032
$377$	1.88103e21	0.237408
$378$	1.72821e22	2.13264
$379$	4.28477e21	0.517004	0.258502	−	0.966011i	$-0.416771\pi$
$379$	4.28477e21	0.517004	0.258502	+	0.966011i	$0.416771\pi$
$380$	−1.65949e22	−1.95801
$381$	−8.65145e21	−0.998221
$382$	−1.81583e22	−2.04897
$383$	−2.36639e21	−0.261154	−0.130577	−	0.991438i	$-0.541683\pi$
$383$	−2.36639e21	−0.261154	−0.130577	+	0.991438i	$0.541683\pi$
$384$	1.47942e22	1.59689
$385$	−1.85839e22	−1.96209
$386$	1.58620e22	1.63820
$387$	−1.15925e22	−1.17121
$388$	−3.11173e21	−0.307562
$389$	7.94802e21	0.768577	0.384288	−	0.923213i	$-0.374447\pi$
$389$	7.94802e21	0.768577	0.384288	+	0.923213i	$0.374447\pi$
$390$	−5.82100e22	−5.50742
$391$	−2.36370e20	−0.0218822
$392$	1.82022e21	0.164889
$393$	3.36881e21	0.298634
$394$	−2.66813e21	−0.231467
$395$	−1.03418e22	−0.878052
$396$	2.04450e22	1.69894
$397$	6.69632e20	0.0544649	0.0272325	−	0.999629i	$-0.491331\pi$
$397$	6.69632e20	0.0544649	0.0272325	+	0.999629i	$0.491331\pi$
$398$	−9.98095e19	−0.00794631
$399$	3.07474e22	2.39629
$400$	−4.25174e22	−3.24382
$401$	2.31632e22	1.73010	0.865049	−	0.501687i	$-0.167287\pi$
$401$	2.31632e22	1.73010	0.865049	+	0.501687i	$0.167287\pi$
$402$	4.06518e22	2.97275
$403$	1.11735e22	0.800009
$404$	−1.34267e22	−0.941300
$405$	−4.18273e22	−2.87139
$406$	2.85465e21	0.191903
$407$	−3.29534e22	−2.16944
$408$	1.68752e21	0.108802
$409$	1.72729e22	1.09073	0.545365	−	0.838199i	$-0.316391\pi$
$409$	1.72729e22	1.09073	0.545365	+	0.838199i	$0.316391\pi$
$410$	7.06754e20	0.0437125
$411$	3.00700e22	1.82170
$412$	1.21740e22	0.722446
$413$	−1.95540e21	−0.113674
$414$	8.35851e21	0.476021
$415$	−6.70564e21	−0.374138
$416$	−2.54562e22	−1.39155
$417$	−1.29179e22	−0.691887
$418$	5.10789e22	2.68067
$419$	−8.74359e21	−0.449646	−0.224823	−	0.974400i	$-0.572180\pi$
$419$	−8.74359e21	−0.449646	−0.224823	+	0.974400i	$0.572180\pi$
$420$	−3.37945e22	−1.70305
$421$	−1.83931e22	−0.908358	−0.454179	−	0.890910i	$-0.650067\pi$
$421$	−1.83931e22	−0.908358	−0.454179	+	0.890910i	$0.650067\pi$
$422$	−1.34272e22	−0.649875
$423$	2.74763e22	1.30336
$424$	3.47945e21	0.161771
$425$	−7.28148e21	−0.331828
$426$	−2.62794e22	−1.17391
$427$	−2.33633e22	−1.02305
$428$	1.23390e22	0.529671
$429$	6.85420e22	2.88449
$430$	3.18325e22	1.31338
$431$	−1.40411e22	−0.567993	−0.283996	−	0.958825i	$-0.591660\pi$
$431$	−1.40411e22	−0.567993	−0.283996	+	0.958825i	$0.591660\pi$
$432$	−6.42928e22	−2.55006
$433$	−1.38965e22	−0.540454	−0.270227	−	0.962797i	$-0.587099\pi$
$433$	−1.38965e22	−0.540454	−0.270227	+	0.962797i	$0.587099\pi$
$434$	1.69568e22	0.646669
$435$	−1.68079e22	−0.628573
$436$	1.95909e22	0.718486
$437$	7.98868e21	0.287331
$438$	−3.28280e22	−1.15801
$439$	4.98312e22	1.72406	0.862030	−	0.506856i	$-0.169193\pi$
$439$	4.98312e22	1.72406	0.862030	+	0.506856i	$0.169193\pi$
$440$	3.44714e22	1.16980
$441$	−2.21083e22	−0.735914
$442$	−6.29874e21	−0.205667
$443$	2.26060e22	0.724090	0.362045	−	0.932161i	$-0.382079\pi$
$443$	2.26060e22	0.724090	0.362045	+	0.932161i	$0.382079\pi$
$444$	−5.99253e22	−1.88302
$445$	6.44808e22	1.98779
$446$	−6.99581e22	−2.11588
$447$	−3.76013e21	−0.111581
$448$	−4.16892e21	−0.121384
$449$	−1.31159e22	−0.374719	−0.187359	−	0.982291i	$-0.559993\pi$
$449$	−1.31159e22	−0.374719	−0.187359	+	0.982291i	$0.559993\pi$
$450$	2.57487e23	7.21853
$451$	−8.32200e20	−0.0228943
$452$	−9.16884e20	−0.0247536
$453$	1.00412e23	2.66041
$454$	2.16453e22	0.562846
$455$	−7.74515e22	−1.97667
$456$	−5.70336e22	−1.42866
$457$	−2.98675e22	−0.734364	−0.367182	−	0.930149i	$-0.619677\pi$
$457$	−2.98675e22	−0.734364	−0.367182	+	0.930149i	$0.619677\pi$
$458$	3.29149e22	0.794394
$459$	−1.10107e22	−0.260860
$460$	−8.78038e21	−0.204207
$461$	−2.85329e22	−0.651461	−0.325731	−	0.945463i	$-0.605610\pi$
$461$	−2.85329e22	−0.651461	−0.325731	+	0.945463i	$0.605610\pi$
$462$	1.04019e23	2.33161
$463$	−3.09007e22	−0.680033	−0.340017	−	0.940419i	$-0.610433\pi$
$463$	−3.09007e22	−0.680033	−0.340017	+	0.940419i	$0.610433\pi$
$464$	−1.06198e22	−0.229464
$465$	−9.98403e22	−2.11814
$466$	−8.06913e22	−1.68092
$467$	−2.26799e22	−0.463925	−0.231963	−	0.972725i	$-0.574515\pi$
$467$	−2.26799e22	−0.463925	−0.231963	+	0.972725i	$0.574515\pi$
$468$	8.52083e22	1.71156
$469$	5.40895e22	1.06695
$470$	−7.54484e22	−1.46156
$471$	−5.09346e22	−0.969026
$472$	3.62708e21	0.0677720
$473$	−3.74826e22	−0.687876
$474$	5.78860e22	1.04342
$475$	2.46094e23	4.35718
$476$	−3.65681e21	−0.0635980
$477$	−4.22611e22	−0.721996
$478$	−1.01382e23	−1.70147
$479$	−3.78397e22	−0.623872	−0.311936	−	0.950103i	$-0.600977\pi$
$479$	−3.78397e22	−0.623872	−0.311936	+	0.950103i	$0.600977\pi$
$480$	2.27463e23	3.68435
$481$	−1.37339e23	−2.18555
$482$	−7.20156e22	−1.12597
$483$	1.62685e22	0.249917
$484$	2.50590e22	0.378250
$485$	6.37241e22	0.945146
$486$	5.39235e22	0.785904
$487$	3.14449e22	0.450353	0.225177	−	0.974318i	$-0.427704\pi$
$487$	3.14449e22	0.450353	0.225177	+	0.974318i	$0.427704\pi$
$488$	4.33368e22	0.609942
$489$	3.71500e22	0.513846
$490$	6.07082e22	0.825240
$491$	−1.16677e23	−1.55880	−0.779401	−	0.626525i	$-0.784477\pi$
$491$	−1.16677e23	−1.55880	−0.779401	+	0.626525i	$0.784477\pi$
$492$	−1.51334e21	−0.0198717
$493$	−1.81874e21	−0.0234732
$494$	2.12880e23	2.70058
$495$	−4.18687e23	−5.22090
$496$	−6.30826e22	−0.773241
$497$	−3.49662e22	−0.421327
$498$	3.75334e22	0.444599
$499$	−1.12590e23	−1.31113	−0.655564	−	0.755140i	$-0.727569\pi$
$499$	−1.12590e23	−1.31113	−0.655564	+	0.755140i	$0.727569\pi$
$500$	−1.67445e23	−1.91702
$501$	−2.34176e23	−2.63585
$502$	7.03972e22	0.779065
$503$	1.74880e23	1.90288	0.951440	−	0.307833i	$-0.0996038\pi$
$503$	1.74880e23	1.90288	0.951440	+	0.307833i	$0.0996038\pi$
$504$	−7.93994e22	−0.849489
$505$	2.74961e23	2.89264
$506$	2.70259e22	0.279577
$507$	1.10892e23	1.12806
$508$	−3.47748e22	−0.347875
$509$	−1.68804e23	−1.66066	−0.830332	−	0.557269i	$-0.811849\pi$
$509$	−1.68804e23	−1.66066	−0.830332	+	0.557269i	$0.811849\pi$
$510$	5.62823e22	0.544534
$511$	−4.36794e22	−0.415622
$512$	7.97928e22	0.746740
$513$	3.72132e23	3.42530
$514$	−1.89054e23	−1.71159
$515$	−2.49306e23	−2.22010
$516$	−6.81617e22	−0.597060
$517$	8.88401e22	0.765490
$518$	−2.08425e23	−1.76664
$519$	−2.51910e23	−2.10050
$520$	1.43666e23	1.17849
$521$	8.77607e22	0.708239	0.354119	−	0.935200i	$-0.384781\pi$
$521$	8.77607e22	0.708239	0.354119	+	0.935200i	$0.384781\pi$
$522$	6.43141e22	0.510631
$523$	−2.79801e22	−0.218567	−0.109284	−	0.994011i	$-0.534856\pi$
$523$	−2.79801e22	−0.218567	−0.109284	+	0.994011i	$0.534856\pi$
$524$	1.35411e22	0.104073
$525$	5.01156e23	3.78982
$526$	−8.18947e22	−0.609364
$527$	−1.08034e22	−0.0790992
$528$	−3.86971e23	−2.78798
$529$	−1.36823e23	−0.970033
$530$	1.16047e23	0.809633
$531$	−4.40543e22	−0.302472
$532$	1.23590e23	0.835094
$533$	−3.46834e21	−0.0230643
$534$	−3.60917e23	−2.36215
$535$	−2.52685e23	−1.62769
$536$	−1.00331e23	−0.636113
$537$	−7.71304e22	−0.481331
$538$	−1.71967e22	−0.105632
$539$	−7.14836e22	−0.432217
$540$	−4.09011e23	−2.43438
$541$	1.81920e23	1.06587	0.532935	−	0.846156i	$-0.321089\pi$
$541$	1.81920e23	1.06587	0.532935	+	0.846156i	$0.321089\pi$
$542$	−3.95379e22	−0.228044
$543$	3.38489e23	1.92197
$544$	2.46132e22	0.137587
$545$	−4.01195e23	−2.20793
$546$	4.33518e23	2.34893
$547$	1.08706e23	0.579911	0.289955	−	0.957040i	$-0.406359\pi$
$547$	1.08706e23	0.579911	0.289955	+	0.957040i	$0.406359\pi$
$548$	1.20867e23	0.634855
$549$	−5.26366e23	−2.72222
$550$	8.32543e23	4.23959
$551$	6.14684e22	0.308222
$552$	−3.01765e22	−0.149000
$553$	7.70204e22	0.374492
$554$	−1.50829e23	−0.722192
$555$	1.22719e24	5.78657
$556$	−5.19240e22	−0.241119
$557$	3.54816e23	1.62268	0.811341	−	0.584573i	$-0.198738\pi$
$557$	3.54816e23	1.62268	0.811341	+	0.584573i	$0.198738\pi$
$558$	3.82030e23	1.72071
$559$	−1.56215e23	−0.692984
$560$	4.37272e23	1.91053
$561$	−6.62721e22	−0.285198
$562$	−1.10475e23	−0.468282
$563$	−3.69859e23	−1.54424	−0.772119	−	0.635477i	$-0.780803\pi$
$563$	−3.69859e23	−1.54424	−0.772119	+	0.635477i	$0.780803\pi$
$564$	1.61555e23	0.664426
$565$	1.87766e22	0.0760684
$566$	−7.91986e22	−0.316066
$567$	3.11509e23	1.22466
$568$	6.48591e22	0.251194
$569$	2.33522e23	0.890990	0.445495	−	0.895284i	$-0.353028\pi$
$569$	2.33522e23	0.890990	0.445495	+	0.895284i	$0.353028\pi$
$570$	−1.90219e24	−7.15018
$571$	1.16066e23	0.429831	0.214916	−	0.976633i	$-0.431052\pi$
$571$	1.16066e23	0.429831	0.214916	+	0.976633i	$0.431052\pi$
$572$	2.75507e23	1.00523
$573$	−7.96243e23	−2.86241
$574$	−5.26355e21	−0.0186435
$575$	1.30209e23	0.454426
$576$	−9.39240e22	−0.322987
$577$	3.12163e23	1.05776	0.528881	−	0.848696i	$-0.322612\pi$
$577$	3.12163e23	1.05776	0.528881	+	0.848696i	$0.322612\pi$
$578$	−3.75052e23	−1.25229
$579$	6.95551e23	2.28856
$580$	−6.75601e22	−0.219055
$581$	4.99402e22	0.159571
$582$	−3.56682e23	−1.12314
$583$	−1.36644e23	−0.424042
$584$	8.10212e22	0.247793
$585$	−1.74495e24	−5.25967
$586$	9.09180e21	0.0270097
$587$	−4.43095e23	−1.29740	−0.648698	−	0.761046i	$-0.724686\pi$
$587$	−4.43095e23	−1.29740	−0.648698	+	0.761046i	$0.724686\pi$
$588$	−1.29992e23	−0.375154
$589$	3.65127e23	1.03864
$590$	1.20971e23	0.339186
$591$	−1.16998e23	−0.323358
$592$	7.75382e23	2.11242
$593$	6.30066e22	0.169208	0.0846041	−	0.996415i	$-0.473037\pi$
$593$	6.30066e22	0.169208	0.0846041	+	0.996415i	$0.473037\pi$
$594$	1.25893e24	3.33286
$595$	7.48866e22	0.195438
$596$	−1.51140e22	−0.0388853
$597$	−4.37666e21	−0.0111010
$598$	1.12635e23	0.281653
$599$	4.82780e23	1.19020	0.595102	−	0.803650i	$-0.297112\pi$
$599$	4.82780e23	1.19020	0.595102	+	0.803650i	$0.297112\pi$
$600$	−9.29599e23	−2.25949
$601$	3.54944e23	0.850602	0.425301	−	0.905052i	$-0.360168\pi$
$601$	3.54944e23	0.850602	0.425301	+	0.905052i	$0.360168\pi$
$602$	−2.37072e23	−0.560158
$603$	1.21861e24	2.83902
$604$	4.03608e23	0.927142
$605$	−5.13175e23	−1.16237
$606$	−1.53904e24	−3.43741
$607$	7.88543e23	1.73669	0.868344	−	0.495963i	$-0.165185\pi$
$607$	7.88543e23	1.73669	0.868344	+	0.495963i	$0.165185\pi$
$608$	−8.31858e23	−1.80663
$609$	1.25177e23	0.268088
$610$	1.44537e24	3.05264
$611$	3.70257e23	0.771174
$612$	−8.23865e22	−0.169227
$613$	−7.53363e23	−1.52613	−0.763063	−	0.646324i	$-0.776305\pi$
$613$	−7.53363e23	−1.52613	−0.763063	+	0.646324i	$0.776305\pi$
$614$	3.14411e23	0.628155
$615$	3.09913e22	0.0610662
$616$	−2.56725e23	−0.498922
$617$	−1.02961e24	−1.97356	−0.986779	−	0.162070i	$-0.948183\pi$
$617$	−1.02961e24	−1.97356	−0.986779	+	0.162070i	$0.948183\pi$
$618$	1.39544e24	2.63821
$619$	7.28626e23	1.35873	0.679367	−	0.733799i	$-0.262254\pi$
$619$	7.28626e23	1.35873	0.679367	+	0.733799i	$0.262254\pi$
$620$	−4.01312e23	−0.738164
$621$	1.96895e23	0.357237
$622$	1.02817e24	1.84013
$623$	−4.80220e23	−0.847797
$624$	−1.61277e24	−2.80868
$625$	1.90105e24	3.26597
$626$	1.01869e24	1.72648
$627$	2.23982e24	3.74488
$628$	−2.04734e23	−0.337701
$629$	1.32791e23	0.216092
$630$	−2.64814e24	−4.25153
$631$	−8.51045e23	−1.34804	−0.674020	−	0.738713i	$-0.735434\pi$
$631$	−8.51045e23	−1.34804	−0.674020	+	0.738713i	$0.735434\pi$
$632$	−1.42866e23	−0.223271
$633$	−5.88785e23	−0.907873
$634$	−1.36210e24	−2.07229
$635$	7.12142e23	1.06903
$636$	−2.48486e23	−0.368058
$637$	−2.97920e23	−0.435427
$638$	2.07949e23	0.299904
$639$	−7.87774e23	−1.12110
$640$	−1.21778e24	−1.71017
$641$	−2.98958e23	−0.414302	−0.207151	−	0.978309i	$-0.566419\pi$
$641$	−2.98958e23	−0.414302	−0.207151	+	0.978309i	$0.566419\pi$
$642$	1.41435e24	1.93424
$643$	3.37881e23	0.456006	0.228003	−	0.973660i	$-0.426780\pi$
$643$	3.37881e23	0.456006	0.228003	+	0.973660i	$0.426780\pi$
$644$	6.53918e22	0.0870950
$645$	1.39586e24	1.83478
$646$	−2.05831e23	−0.267014
$647$	2.52599e23	0.323404	0.161702	−	0.986840i	$-0.448302\pi$
$647$	2.52599e23	0.323404	0.161702	+	0.986840i	$0.448302\pi$
$648$	−5.77820e23	−0.730138
$649$	−1.42442e23	−0.177648
$650$	3.46977e24	4.27107
$651$	7.43559e23	0.903394
$652$	1.49326e23	0.179073
$653$	1.18820e24	1.40646	0.703228	−	0.710965i	$-0.251741\pi$
$653$	1.18820e24	1.40646	0.703228	+	0.710965i	$0.251741\pi$
$654$	2.24560e24	2.62375
$655$	−2.77303e23	−0.319818
$656$	1.95814e22	0.0222926
$657$	−9.84078e23	−1.10592
$658$	5.61901e23	0.623361
$659$	−5.86304e23	−0.642092	−0.321046	−	0.947064i	$-0.604034\pi$
$659$	−5.86304e23	−0.642092	−0.321046	+	0.947064i	$0.604034\pi$
$660$	−2.46179e24	−2.66151
$661$	−1.90196e23	−0.202997	−0.101498	−	0.994836i	$-0.532364\pi$
$661$	−1.90196e23	−0.202997	−0.101498	+	0.994836i	$0.532364\pi$
$662$	−8.83204e23	−0.930610
$663$	−2.76201e23	−0.287316
$664$	−9.26345e22	−0.0951359
$665$	−2.53096e24	−2.56627
$666$	−4.69574e24	−4.70081
$667$	3.25230e22	0.0321456
$668$	−9.41279e23	−0.918583
$669$	−3.06767e24	−2.95588
$670$	−3.34625e24	−3.18363
$671$	−1.70192e24	−1.59881
$672$	−1.69403e24	−1.57138
$673$	2.29048e23	0.209796	0.104898	−	0.994483i	$-0.466548\pi$
$673$	2.29048e23	0.209796	0.104898	+	0.994483i	$0.466548\pi$
$674$	7.62107e23	0.689297
$675$	6.06543e24	5.41726
$676$	4.45736e23	0.393125
$677$	−2.17691e23	−0.189600	−0.0947998	−	0.995496i	$-0.530221\pi$
$677$	−2.17691e23	−0.189600	−0.0947998	+	0.995496i	$0.530221\pi$
$678$	−1.05098e23	−0.0903943
$679$	−4.74585e23	−0.403107
$680$	−1.38908e23	−0.116520
$681$	9.49151e23	0.786294
$682$	1.23523e24	1.01061
$683$	−1.11390e24	−0.900061	−0.450030	−	0.893013i	$-0.648587\pi$
$683$	−1.11390e24	−0.900061	−0.450030	+	0.893013i	$0.648587\pi$
$684$	2.78444e24	2.22209
$685$	−2.47520e24	−1.95093
$686$	−1.77963e24	−1.38540
$687$	1.44332e24	1.10976
$688$	8.81953e23	0.669798
$689$	−5.69490e23	−0.427191
$690$	−1.00645e24	−0.745718
$691$	−2.20772e24	−1.61577	−0.807886	−	0.589338i	$-0.799389\pi$
$691$	−2.20772e24	−1.61577	−0.807886	+	0.589338i	$0.799389\pi$
$692$	−1.01256e24	−0.732016
$693$	3.11817e24	2.22673
$694$	2.17974e24	1.53762
$695$	1.06333e24	0.740966
$696$	−2.32192e23	−0.159834
$697$	3.35348e21	0.00228043
$698$	2.71166e24	1.82165
$699$	−3.53833e24	−2.34824
$700$	2.01442e24	1.32074
$701$	2.35254e24	1.52382	0.761910	−	0.647683i	$-0.224262\pi$
$701$	2.35254e24	1.52382	0.761910	+	0.647683i	$0.224262\pi$
$702$	5.24682e24	3.35761
$703$	−4.48797e24	−2.83746
$704$	−3.03688e23	−0.189697
$705$	−3.30842e24	−2.04180
$706$	2.45738e24	1.49842
$707$	−2.04777e24	−1.23372
$708$	−2.59030e23	−0.154194
$709$	−2.34326e24	−1.37825	−0.689123	−	0.724644i	$-0.742004\pi$
$709$	−2.34326e24	−1.37825	−0.689123	+	0.724644i	$0.742004\pi$
$710$	2.16319e24	1.25718
$711$	1.73524e24	0.996477
$712$	8.90764e23	0.505456
$713$	1.93189e23	0.108323
$714$	−4.19162e23	−0.232245
$715$	−5.64202e24	−3.08911
$716$	−3.10029e23	−0.167742
$717$	−4.44563e24	−2.37695
$718$	4.93703e23	0.260860
$719$	2.55641e24	1.33486	0.667429	−	0.744674i	$-0.267395\pi$
$719$	2.55641e24	1.33486	0.667429	+	0.744674i	$0.267395\pi$
$720$	9.85155e24	5.08368
$721$	1.85671e24	0.946877
$722$	4.43148e24	2.23348
$723$	−3.15789e24	−1.57298
$724$	1.36057e24	0.669797
$725$	1.00188e24	0.487465
$726$	2.87239e24	1.38128
$727$	2.48286e24	1.18008	0.590039	−	0.807375i	$-0.299112\pi$
$727$	2.48286e24	1.18008	0.590039	+	0.807375i	$0.299112\pi$
$728$	−1.06995e24	−0.502627
$729$	−8.83459e23	−0.410206
$730$	2.70223e24	1.24016
$731$	1.51042e23	0.0685173
$732$	−3.09492e24	−1.38773
$733$	1.50420e24	0.666687	0.333343	−	0.942806i	$-0.391823\pi$
$733$	1.50420e24	0.666687	0.333343	+	0.942806i	$0.391823\pi$
$734$	−3.09728e24	−1.35695
$735$	2.66206e24	1.15286
$736$	−4.40137e23	−0.188420
$737$	3.94019e24	1.66741
$738$	−1.18586e23	−0.0496081
$739$	−2.65601e24	−1.09838	−0.549189	−	0.835698i	$-0.685063\pi$
$739$	−2.65601e24	−1.09838	−0.549189	+	0.835698i	$0.685063\pi$
$740$	4.93274e24	2.01659
$741$	9.33483e24	3.77270
$742$	−8.64257e23	−0.345310
$743$	−1.69484e24	−0.669457	−0.334729	−	0.942315i	$-0.608645\pi$
$743$	−1.69484e24	−0.669457	−0.334729	+	0.942315i	$0.608645\pi$
$744$	−1.37923e24	−0.538602
$745$	3.09514e23	0.119496
$746$	−4.14610e24	−1.58256
$747$	1.12513e24	0.424599
$748$	−2.66383e23	−0.0993902
$749$	1.88187e24	0.694215
$750$	−1.91933e25	−7.00051
$751$	2.38565e24	0.860333	0.430167	−	0.902749i	$-0.358455\pi$
$751$	2.38565e24	0.860333	0.430167	+	0.902749i	$0.358455\pi$
$752$	−2.09038e24	−0.745371
$753$	3.08693e24	1.08835
$754$	8.66665e23	0.302131
$755$	−8.26536e24	−2.84913
$756$	3.04611e24	1.03827
$757$	2.23473e24	0.753200	0.376600	−	0.926376i	$-0.377093\pi$
$757$	2.23473e24	0.753200	0.376600	+	0.926376i	$0.377093\pi$
$758$	1.97416e24	0.657952
$759$	1.18509e24	0.390567
$760$	4.69471e24	1.53001
$761$	5.08484e24	1.63873	0.819366	−	0.573271i	$-0.194326\pi$
$761$	5.08484e24	1.63873	0.819366	+	0.573271i	$0.194326\pi$
$762$	−3.98606e24	−1.27036
$763$	2.98789e24	0.941687
$764$	−3.20053e24	−0.997536
$765$	1.68717e24	0.520038
$766$	−1.09029e24	−0.332351
$767$	−5.93654e23	−0.178967
$768$	7.70760e24	2.29799
$769$	−2.47180e24	−0.728853	−0.364427	−	0.931232i	$-0.618735\pi$
$769$	−2.47180e24	−0.728853	−0.364427	+	0.931232i	$0.618735\pi$
$770$	−8.56232e24	−2.49701
$771$	−8.29006e24	−2.39109
$772$	2.79580e24	0.797551
$773$	3.57180e24	1.00777	0.503885	−	0.863770i	$-0.331903\pi$
$773$	3.57180e24	1.00777	0.503885	+	0.863770i	$0.331903\pi$
$774$	−5.34114e24	−1.49051
$775$	5.95126e24	1.64265
$776$	8.80311e23	0.240332
$777$	−9.13949e24	−2.46799
$778$	3.66196e24	0.978109
$779$	−1.13338e23	−0.0299439
$780$	−1.02599e25	−2.68127
$781$	−2.54714e24	−0.658444
$782$	−1.08905e23	−0.0278478
$783$	1.51500e24	0.383211
$784$	1.68198e24	0.420858
$785$	4.19267e24	1.03776
$786$	1.55214e24	0.380050
$787$	5.61947e24	1.36116	0.680581	−	0.732673i	$-0.261727\pi$
$787$	5.61947e24	1.36116	0.680581	+	0.732673i	$0.261727\pi$
$788$	−4.70277e23	−0.112689
$789$	−3.59109e24	−0.851280
$790$	−4.76487e24	−1.11743
$791$	−1.39838e23	−0.0324433
$792$	−5.78391e24	−1.32757
$793$	−7.09305e24	−1.61069
$794$	3.08526e23	0.0693134
$795$	5.08866e24	1.13105
$796$	−1.75922e22	−0.00386864
$797$	−1.89471e24	−0.412238	−0.206119	−	0.978527i	$-0.566083\pi$
$797$	−1.89471e24	−0.412238	−0.206119	+	0.978527i	$0.566083\pi$
$798$	1.41665e25	3.04957
$799$	−3.57995e23	−0.0762482
$800$	−1.35586e25	−2.85726
$801$	−1.08192e25	−2.25589
$802$	1.06722e25	2.20177
$803$	−3.18186e24	−0.649529
$804$	7.16518e24	1.44727
$805$	−1.33914e24	−0.267645
$806$	5.14805e24	1.01811
$807$	−7.54077e23	−0.147567
$808$	3.79842e24	0.735541
$809$	2.25593e24	0.432278	0.216139	−	0.976363i	$-0.430654\pi$
$809$	2.25593e24	0.432278	0.216139	+	0.976363i	$0.430654\pi$
$810$	−1.92715e25	−3.65420
$811$	−3.95805e24	−0.742684	−0.371342	−	0.928496i	$-0.621102\pi$
$811$	−3.95805e24	−0.742684	−0.371342	+	0.928496i	$0.621102\pi$
$812$	5.03153e23	0.0934274
$813$	−1.73374e24	−0.318577
$814$	−1.51829e25	−2.76088
$815$	−3.05799e24	−0.550296
$816$	1.55936e24	0.277703
$817$	−5.10481e24	−0.899689
$818$	7.95830e24	1.38809
$819$	1.29955e25	2.24326
$820$	1.24571e23	0.0212813
$821$	−1.15347e24	−0.195024	−0.0975119	−	0.995234i	$-0.531088\pi$
$821$	−1.15347e24	−0.195024	−0.0975119	+	0.995234i	$0.531088\pi$
$822$	1.38544e25	2.31834
$823$	−1.63197e24	−0.270280	−0.135140	−	0.990827i	$-0.543148\pi$
$823$	−1.63197e24	−0.270280	−0.135140	+	0.990827i	$0.543148\pi$
$824$	−3.44402e24	−0.564527
$825$	3.65071e25	5.92269
$826$	−9.00928e23	−0.144664
$827$	9.87609e24	1.56960	0.784799	−	0.619751i	$-0.212766\pi$
$827$	9.87609e24	1.56960	0.784799	+	0.619751i	$0.212766\pi$
$828$	1.47325e24	0.231749
$829$	−1.15328e25	−1.79565	−0.897827	−	0.440348i	$-0.854855\pi$
$829$	−1.15328e25	−1.79565	−0.897827	+	0.440348i	$0.854855\pi$
$830$	−3.08955e24	−0.476137
$831$	−6.61388e24	−1.00890
$832$	−1.26567e24	−0.191105
$833$	2.88054e23	0.0430519
$834$	−5.95178e24	−0.880512
$835$	1.92761e25	2.82283
$836$	9.00303e24	1.30508
$837$	8.99921e24	1.29133
$838$	−4.02852e24	−0.572230
$839$	−1.02811e25	−1.44565	−0.722827	−	0.691029i	$-0.757158\pi$
$839$	−1.02811e25	−1.44565	−0.722827	+	0.691029i	$0.757158\pi$
$840$	9.56049e24	1.33078
$841$	2.50246e23	0.0344828
$842$	−8.47443e24	−1.15600
$843$	−4.84437e24	−0.654188
$844$	−2.36664e24	−0.316390
$845$	−9.12807e24	−1.20808
$846$	1.26594e25	1.65869
$847$	3.82187e24	0.495754
$848$	3.21520e24	0.412898
$849$	−3.47287e24	−0.441543
$850$	−3.35486e24	−0.422293
$851$	−2.37459e24	−0.295929
$852$	−4.63194e24	−0.571514
$853$	−6.62013e24	−0.808723	−0.404362	−	0.914599i	$-0.632506\pi$
$853$	−6.62013e24	−0.808723	−0.404362	+	0.914599i	$0.632506\pi$
$854$	−1.07644e25	−1.30196
$855$	−5.70216e25	−6.82853
$856$	−3.49070e24	−0.413890
$857$	−3.46347e24	−0.406606	−0.203303	−	0.979116i	$-0.565168\pi$
$857$	−3.46347e24	−0.406606	−0.203303	+	0.979116i	$0.565168\pi$
$858$	3.15800e25	3.67088
$859$	1.08759e25	1.25176	0.625881	−	0.779919i	$-0.284740\pi$
$859$	1.08759e25	1.25176	0.625881	+	0.779919i	$0.284740\pi$
$860$	5.61071e24	0.639413
$861$	−2.30807e23	−0.0260449
$862$	−6.46926e24	−0.722842
$863$	−1.27645e25	−1.41225	−0.706127	−	0.708085i	$-0.749559\pi$
$863$	−1.27645e25	−1.41225	−0.706127	+	0.708085i	$0.749559\pi$
$864$	−2.05026e25	−2.24617
$865$	2.07359e25	2.24950
$866$	−6.40267e24	−0.687795
$867$	−1.64461e25	−1.74944
$868$	2.98877e24	0.314829
$869$	5.61061e24	0.585251
$870$	−7.74407e24	−0.799937
$871$	1.64214e25	1.67980
$872$	−5.54227e24	−0.561432
$873$	−1.06922e25	−1.07262
$874$	3.68070e24	0.365665
$875$	−2.55378e25	−2.51255
$876$	−5.78617e24	−0.563776
$877$	1.89244e25	1.82610	0.913050	−	0.407847i	$-0.133720\pi$
$877$	1.89244e25	1.82610	0.913050	+	0.407847i	$0.133720\pi$
$878$	2.29592e25	2.19408
$879$	3.98676e23	0.0377325
$880$	3.18534e25	2.98575
$881$	2.02940e24	0.188396	0.0941981	−	0.995553i	$-0.469971\pi$
$881$	2.02940e24	0.188396	0.0941981	+	0.995553i	$0.469971\pi$
$882$	−1.01862e25	−0.936542
$883$	−6.80591e24	−0.619755	−0.309878	−	0.950776i	$-0.600288\pi$
$883$	−6.80591e24	−0.619755	−0.309878	+	0.950776i	$0.600288\pi$
$884$	−1.11020e24	−0.100128
$885$	5.30458e24	0.473842
$886$	1.04155e25	0.921495
$887$	7.72537e24	0.676968	0.338484	−	0.940972i	$-0.390086\pi$
$887$	7.72537e24	0.676968	0.338484	+	0.940972i	$0.390086\pi$
$888$	1.69529e25	1.47141
$889$	−5.30367e24	−0.455944
$890$	2.97088e25	2.52971
$891$	2.26921e25	1.91388
$892$	−1.23306e25	−1.03011
$893$	1.20993e25	1.00120
$894$	−1.73244e24	−0.142000
$895$	6.34897e24	0.515475
$896$	9.06940e24	0.729391
$897$	4.93907e24	0.393468
$898$	−6.04303e24	−0.476876
$899$	1.48648e24	0.116199
$900$	4.53840e25	3.51432
$901$	5.50630e23	0.0422376
$902$	−3.83427e23	−0.0291358
$903$	−1.03957e25	−0.782539
$904$	2.59387e23	0.0193427
$905$	−2.78626e25	−2.05830
$906$	4.62636e25	3.38571
$907$	1.82503e24	0.132315	0.0661575	−	0.997809i	$-0.478926\pi$
$907$	1.82503e24	0.132315	0.0661575	+	0.997809i	$0.478926\pi$
$908$	3.81515e24	0.274020
$909$	−4.61354e25	−3.28278
$910$	−3.56850e25	−2.51555
$911$	1.15848e25	0.809061	0.404531	−	0.914524i	$-0.367435\pi$
$911$	1.15848e25	0.809061	0.404531	+	0.914524i	$0.367435\pi$
$912$	−5.27021e25	−3.64646
$913$	3.63793e24	0.249375
$914$	−1.37611e25	−0.934570
$915$	6.33798e25	4.26453
$916$	5.80149e24	0.386748
$917$	2.06521e24	0.136403
$918$	−5.07306e24	−0.331977
$919$	7.77613e23	0.0504176	0.0252088	−	0.999682i	$-0.491975\pi$
$919$	7.77613e23	0.0504176	0.0252088	+	0.999682i	$0.491975\pi$
$920$	2.48397e24	0.159570
$921$	1.37870e25	0.877530
$922$	−1.31462e25	−0.829066
$923$	−1.06157e25	−0.663334
$924$	1.83341e25	1.13514
$925$	−7.31501e25	−4.48756
$926$	−1.42372e25	−0.865427
$927$	4.18308e25	2.51953
$928$	−3.38661e24	−0.202119
$929$	−1.01103e24	−0.0597905	−0.0298953	−	0.999553i	$-0.509517\pi$
$929$	−1.01103e24	−0.0597905	−0.0298953	+	0.999553i	$0.509517\pi$
$930$	−4.60003e25	−2.69560
$931$	−9.73545e24	−0.565306
$932$	−1.42224e25	−0.818349
$933$	4.50856e25	2.57065
$934$	−1.04495e25	−0.590403
$935$	5.45518e24	0.305429
$936$	−2.41055e25	−1.33743
$937$	−2.33097e25	−1.28159	−0.640797	−	0.767710i	$-0.721396\pi$
$937$	−2.33097e25	−1.28159	−0.640797	+	0.767710i	$0.721396\pi$
$938$	2.49211e25	1.35782
$939$	4.46698e25	2.41188
$940$	−1.32983e25	−0.711558
$941$	4.52403e24	0.239891	0.119945	−	0.992780i	$-0.461728\pi$
$941$	4.52403e24	0.239891	0.119945	+	0.992780i	$0.461728\pi$
$942$	−2.34676e25	−1.23321
$943$	−5.99675e22	−0.00312296
$944$	3.35162e24	0.172979
$945$	−6.23801e25	−3.19063
$946$	−1.72697e25	−0.875408
$947$	5.65355e23	0.0284018	0.0142009	−	0.999899i	$-0.495480\pi$
$947$	5.65355e23	0.0284018	0.0142009	+	0.999899i	$0.495480\pi$
$948$	1.02028e25	0.507983
$949$	−1.32610e25	−0.654353
$950$	1.13385e26	5.54505
$951$	−5.97282e25	−2.89498
$952$	1.03451e24	0.0496961
$953$	1.90879e25	0.908800	0.454400	−	0.890798i	$-0.349854\pi$
$953$	1.90879e25	0.908800	0.454400	+	0.890798i	$0.349854\pi$
$954$	−1.94713e25	−0.918829
$955$	6.55426e25	3.06545
$956$	−1.78694e25	−0.828357
$957$	9.11861e24	0.418964
$958$	−1.74342e25	−0.793955
$959$	1.84340e25	0.832075
$960$	1.13094e25	0.505981
$961$	−1.37203e25	−0.608436
$962$	−6.32775e25	−2.78138
$963$	4.23978e25	1.84722
$964$	−1.26933e25	−0.548175
$965$	−5.72542e25	−2.45090
$966$	7.49552e24	0.318051
$967$	−3.52066e25	−1.48081	−0.740404	−	0.672163i	$-0.765366\pi$
$967$	−3.52066e25	−1.48081	−0.740404	+	0.672163i	$0.765366\pi$
$968$	−7.08921e24	−0.295568
$969$	−9.02570e24	−0.373017
$970$	2.93602e25	1.20282
$971$	3.09006e25	1.25488	0.627442	−	0.778664i	$-0.284102\pi$
$971$	3.09006e25	1.25488	0.627442	+	0.778664i	$0.284102\pi$
$972$	9.50441e24	0.382615
$973$	−7.91916e24	−0.316024
$974$	1.44879e25	0.573131
$975$	1.52150e26	5.96667
$976$	4.00456e25	1.55679
$977$	3.77795e25	1.45597	0.727985	−	0.685593i	$-0.240457\pi$
$977$	3.77795e25	1.45597	0.727985	+	0.685593i	$0.240457\pi$
$978$	1.71165e25	0.653933
$979$	−3.49820e25	−1.32493
$980$	1.07003e25	0.401766
$981$	6.73160e25	2.50572
$982$	−5.37575e25	−1.98377
$983$	−3.72518e25	−1.36283	−0.681415	−	0.731897i	$-0.738635\pi$
$983$	−3.72518e25	−1.36283	−0.681415	+	0.731897i	$0.738635\pi$
$984$	4.28126e23	0.0155279
$985$	9.63064e24	0.346296
$986$	−8.37965e23	−0.0298725
$987$	2.46394e25	0.870833
$988$	3.75217e25	1.31477
$989$	−2.70096e24	−0.0938318
$990$	−1.92905e26	−6.64424
$991$	1.39883e25	0.477682	0.238841	−	0.971059i	$-0.423232\pi$
$991$	1.39883e25	0.477682	0.238841	+	0.971059i	$0.423232\pi$
$992$	−2.01167e25	−0.681095
$993$	−3.87286e25	−1.30006
$994$	−1.61103e25	−0.536191
$995$	3.60264e23	0.0118884
$996$	6.61554e24	0.216452
$997$	2.88173e25	0.934856	0.467428	−	0.884031i	$-0.345181\pi$
$997$	2.88173e25	0.934856	0.467428	+	0.884031i	$0.345181\pi$
$998$	−5.18746e25	−1.66857
$999$	−1.10614e26	−3.52780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.b.1.17	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.b.1.17	✓	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)

\(f(q)\)	\(=\)	\(q+460.739 q^{2} +20203.5 q^{3} +81208.7 q^{4} -1.66304e6 q^{5} +9.30854e6 q^{6} +1.23855e7 q^{7} -2.29740e7 q^{8} +2.79040e8 q^{9} +O(q^{10})\)	\(q+460.739 q^{2} +20203.5 q^{3} +81208.7 q^{4} -1.66304e6 q^{5} +9.30854e6 q^{6} +1.23855e7 q^{7} -2.29740e7 q^{8} +2.79040e8 q^{9} -7.66230e8 q^{10} +9.02232e8 q^{11} +1.64070e9 q^{12} +3.76021e9 q^{13} +5.70649e9 q^{14} -3.35993e10 q^{15} -2.12292e10 q^{16} -3.63569e9 q^{17} +1.28565e11 q^{18} +1.22876e11 q^{19} -1.35054e11 q^{20} +2.50230e11 q^{21} +4.15694e11 q^{22} +6.50140e10 q^{23} -4.64154e11 q^{24} +2.00278e12 q^{25} +1.73248e12 q^{26} +3.02851e12 q^{27} +1.00581e12 q^{28} +5.00246e11 q^{29} -1.54805e13 q^{30} +2.97150e12 q^{31} -6.76988e12 q^{32} +1.82282e13 q^{33} -1.67510e12 q^{34} -2.05977e13 q^{35} +2.26605e13 q^{36} -3.65243e13 q^{37} +5.66139e13 q^{38} +7.59693e13 q^{39} +3.82068e13 q^{40} -9.22379e11 q^{41} +1.15291e14 q^{42} -4.15443e13 q^{43} +7.32691e13 q^{44} -4.64057e14 q^{45} +2.99545e13 q^{46} +9.84670e13 q^{47} -4.28904e14 q^{48} -7.92297e13 q^{49} +9.22759e14 q^{50} -7.34535e13 q^{51} +3.05362e14 q^{52} -1.51452e14 q^{53} +1.39535e15 q^{54} -1.50045e15 q^{55} -2.84545e14 q^{56} +2.48253e15 q^{57} +2.30483e14 q^{58} -1.57878e14 q^{59} -2.72855e15 q^{60} -1.88634e15 q^{61} +1.36909e15 q^{62} +3.45606e15 q^{63} -3.36596e14 q^{64} -6.25340e15 q^{65} +8.39846e15 q^{66} +4.36716e15 q^{67} -2.95249e14 q^{68} +1.31351e15 q^{69} -9.49015e15 q^{70} -2.82315e15 q^{71} -6.41067e15 q^{72} -3.52665e15 q^{73} -1.68282e16 q^{74} +4.04631e16 q^{75} +9.97862e15 q^{76} +1.11746e16 q^{77} +3.50021e16 q^{78} +6.21859e15 q^{79} +3.53051e16 q^{80} +2.51511e16 q^{81} -4.24976e14 q^{82} +4.03215e15 q^{83} +2.03209e16 q^{84} +6.04631e15 q^{85} -1.91411e16 q^{86} +1.01067e16 q^{87} -2.07279e16 q^{88} -3.87727e16 q^{89} -2.13809e17 q^{90} +4.65721e16 q^{91} +5.27970e15 q^{92} +6.00346e16 q^{93} +4.53676e16 q^{94} -2.04349e17 q^{95} -1.36775e17 q^{96} -3.83177e16 q^{97} -3.65042e16 q^{98} +2.51759e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) \) 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

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