LMFDB - Embedded newform 22.20.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,20,Mod(1,22)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 20, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("22.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	22.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:	$50.3396732424$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{51151}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 51151 $ x^2 - 51151
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$226.166$ of defining polynomial
Character	$\chi$	$=$	22.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+512.000 q^{2} +16629.0 q^{3} +262144. q^{4} -5.53619e6 q^{5} +8.51403e6 q^{6} +9.09776e7 q^{7} +1.34218e8 q^{8} -8.85739e8 q^{9} +O(q^{10})$	\(q+512.000 q^{2} +16629.0 q^{3} +262144. q^{4} -5.53619e6 q^{5} +8.51403e6 q^{6} +9.09776e7 q^{7} +1.34218e8 q^{8} -8.85739e8 q^{9} -2.83453e9 q^{10} -2.35795e9 q^{11} +4.35919e9 q^{12} +6.07578e10 q^{13} +4.65805e10 q^{14} -9.20612e10 q^{15} +6.87195e10 q^{16} -3.96908e11 q^{17} -4.53498e11 q^{18} -1.40248e12 q^{19} -1.45128e12 q^{20} +1.51286e12 q^{21} -1.20727e12 q^{22} -1.26465e13 q^{23} +2.23190e12 q^{24} +1.15760e13 q^{25} +3.11080e13 q^{26} -3.40561e13 q^{27} +2.38492e13 q^{28} -6.35686e13 q^{29} -4.71353e13 q^{30} -2.46099e13 q^{31} +3.51844e13 q^{32} -3.92102e13 q^{33} -2.03217e14 q^{34} -5.03669e14 q^{35} -2.32191e14 q^{36} +2.11887e14 q^{37} -7.18072e14 q^{38} +1.01034e15 q^{39} -7.43055e14 q^{40} +5.84790e14 q^{41} +7.74586e14 q^{42} +6.66795e14 q^{43} -6.18122e14 q^{44} +4.90362e15 q^{45} -6.47501e15 q^{46} -1.05191e16 q^{47} +1.14273e15 q^{48} -3.12198e15 q^{49} +5.92689e15 q^{50} -6.60017e15 q^{51} +1.59273e16 q^{52} -3.56138e16 q^{53} -1.74367e16 q^{54} +1.30541e16 q^{55} +1.22108e16 q^{56} -2.33219e16 q^{57} -3.25471e16 q^{58} +1.26702e17 q^{59} -2.41333e16 q^{60} -9.76304e16 q^{61} -1.26003e16 q^{62} -8.05824e16 q^{63} +1.80144e16 q^{64} -3.36367e17 q^{65} -2.00756e16 q^{66} -1.91145e17 q^{67} -1.04047e17 q^{68} -2.10298e17 q^{69} -2.57879e17 q^{70} -1.94283e17 q^{71} -1.18882e17 q^{72} -4.71910e17 q^{73} +1.08486e17 q^{74} +1.92496e17 q^{75} -3.67653e17 q^{76} -2.14520e17 q^{77} +5.17294e17 q^{78} +1.46951e18 q^{79} -3.80444e17 q^{80} +4.63142e17 q^{81} +2.99412e17 q^{82} -1.08775e18 q^{83} +3.96588e17 q^{84} +2.19736e18 q^{85} +3.41399e17 q^{86} -1.05708e18 q^{87} -3.16478e17 q^{88} -1.57292e18 q^{89} +2.51065e18 q^{90} +5.52760e18 q^{91} -3.31520e18 q^{92} -4.09237e17 q^{93} -5.38579e18 q^{94} +7.76442e18 q^{95} +5.85080e17 q^{96} +1.34559e19 q^{97} -1.59845e18 q^{98} +2.08853e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 1024 q^{2} + 16974 q^{3} + 524288 q^{4} - 2948510 q^{5} + 8690688 q^{6} + 84929956 q^{7} + 268435456 q^{8} - 2047881204 q^{9}+O(q^{10}) $ 2 * q + 1024 * q^2 + 16974 * q^3 + 524288 * q^4 - 2948510 * q^5 + 8690688 * q^6 + 84929956 * q^7 + 268435456 * q^8 - 2047881204 * q^9	$ 2 q + 1024 q^{2} + 16974 q^{3} + 524288 q^{4} - 2948510 q^{5} + 8690688 q^{6} + 84929956 q^{7} + 268435456 q^{8} - 2047881204 q^{9} - 1509637120 q^{10} - 4715895382 q^{11} + 4449632256 q^{12} + 12931357856 q^{13} + 43484137472 q^{14} - 91168385490 q^{15} + 137438953472 q^{16} - 459787304876 q^{17} - 1048515176448 q^{18} - 1766628927912 q^{19} - 772934205440 q^{20} + 1510776580572 q^{21} - 2414538435584 q^{22} - 3266600096146 q^{23} + 2278211715072 q^{24} - 801420243000 q^{25} + 6620855222272 q^{26} - 34858123423398 q^{27} + 22263878385664 q^{28} - 97113536421264 q^{29} - 46678213370880 q^{30} - 154254203154130 q^{31} + 70368744177664 q^{32} - 40023804107034 q^{33} - 235411100096512 q^{34} - 519318683122780 q^{35} - 536839770341376 q^{36} - 571392764844202 q^{37} - 904514011090944 q^{38} + 993838018166208 q^{39} - 395742313185280 q^{40} - 184921680043224 q^{41} + 773517609252864 q^{42} + 21\!\cdots\!04 q^{43}+ \cdots + 48\!\cdots\!64 q^{99}+O(q^{100}) $ 2 * q + 1024 * q^2 + 16974 * q^3 + 524288 * q^4 - 2948510 * q^5 + 8690688 * q^6 + 84929956 * q^7 + 268435456 * q^8 - 2047881204 * q^9 - 1509637120 * q^10 - 4715895382 * q^11 + 4449632256 * q^12 + 12931357856 * q^13 + 43484137472 * q^14 - 91168385490 * q^15 + 137438953472 * q^16 - 459787304876 * q^17 - 1048515176448 * q^18 - 1766628927912 * q^19 - 772934205440 * q^20 + 1510776580572 * q^21 - 2414538435584 * q^22 - 3266600096146 * q^23 + 2278211715072 * q^24 - 801420243000 * q^25 + 6620855222272 * q^26 - 34858123423398 * q^27 + 22263878385664 * q^28 - 97113536421264 * q^29 - 46678213370880 * q^30 - 154254203154130 * q^31 + 70368744177664 * q^32 - 40023804107034 * q^33 - 235411100096512 * q^34 - 519318683122780 * q^35 - 536839770341376 * q^36 - 571392764844202 * q^37 - 904514011090944 * q^38 + 993838018166208 * q^39 - 395742313185280 * q^40 - 184921680043224 * q^41 + 773517609252864 * q^42 + 2116703700483204 * q^43 - 1236243679019008 * q^44 + 1896364379272140 * q^45 - 1672499249226752 * q^46 - 7456201298413488 * q^47 + 1166444398116864 * q^48 - 14484301062165318 * q^49 - 410327164416000 * q^50 - 6621865965055188 * q^51 + 3389877873803264 * q^52 - 14846639027241356 * q^53 - 17847359192779776 * q^54 + 6952432346390410 * q^55 + 11399105733459968 * q^56 - 23447497932939960 * q^57 - 49722130647687168 * q^58 + 27278259292488522 * q^59 - 23899245245890560 * q^60 - 221405767994019480 * q^61 - 78978152014914560 * q^62 - 73554176903617512 * q^63 + 36028797018963968 * q^64 - 460126589237118240 * q^65 - 20492187702801408 * q^66 - 211824895464439422 * q^67 - 120530483249414144 * q^68 - 207061904815621470 * q^69 - 265891165758863360 * q^70 - 752788827699476886 * q^71 - 274861962414784512 * q^72 - 1171002362670305344 * q^73 - 292553095600231424 * q^74 + 188225715573790200 * q^75 - 463111173678563328 * q^76 - 200260393646931596 * q^77 + 508845065301098496 * q^78 + 1558374634535268220 * q^79 - 202620064350863360 * q^80 + 1813578176100871890 * q^81 - 94679900182130688 * q^82 + 974129749376372 * q^83 + 396041015937466368 * q^84 + 2034647452871174740 * q^85 + 1083752294647400448 * q^86 - 1068654199999982256 * q^87 - 632956763657732096 * q^88 + 3903208985507920622 * q^89 + 970938562187335680 * q^90 + 5816830265117419168 * q^91 - 856319615604097024 * q^92 - 453968381403456030 * q^93 - 3817575064787705856 * q^94 + 6822127176303479320 * q^95 + 597219531835834368 * q^96 + 17667658647655093842 * q^97 - 7415962143828642816 * q^98 + 4828796756414099964 * 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 $

$2$	512.000	0.707107
$2$	512.000	0.707107
$3$	16629.0	0.487768	0.243884	−	0.969804i	$-0.421578\pi$
$3$	16629.0	0.487768	0.243884	+	0.969804i	$0.421578\pi$
$4$	262144.	0.500000
$5$	−5.53619e6	−1.26764	−0.633820	−	0.773480i	$-0.718514\pi$
$5$	−5.53619e6	−1.26764	−0.633820	+	0.773480i	$0.718514\pi$
$6$	8.51403e6	0.344904
$7$	9.09776e7	0.852124	0.426062	−	0.904694i	$-0.359901\pi$
$7$	9.09776e7	0.852124	0.426062	+	0.904694i	$0.359901\pi$
$8$	1.34218e8	0.353553
$9$	−8.85739e8	−0.762082
$10$	−2.83453e9	−0.896358
$11$	−2.35795e9	−0.301511
$11$	−2.35795e9	−0.301511
$12$	4.35919e9	0.243884
$13$	6.07578e10	1.58906	0.794530	−	0.607225i	$-0.207717\pi$
$13$	6.07578e10	1.58906	0.794530	+	0.607225i	$0.207717\pi$
$14$	4.65805e10	0.602543
$15$	−9.20612e10	−0.618315
$16$	6.87195e10	0.250000
$17$	−3.96908e11	−0.811755	−0.405878	−	0.913927i	$-0.633034\pi$
$17$	−3.96908e11	−0.811755	−0.405878	+	0.913927i	$0.633034\pi$
$18$	−4.53498e11	−0.538873
$19$	−1.40248e12	−0.997100	−0.498550	−	0.866861i	$-0.666134\pi$
$19$	−1.40248e12	−0.997100	−0.498550	+	0.866861i	$0.666134\pi$
$20$	−1.45128e12	−0.633820
$21$	1.51286e12	0.415639
$22$	−1.20727e12	−0.213201
$23$	−1.26465e13	−1.46405	−0.732025	−	0.681278i	$-0.761425\pi$
$23$	−1.26465e13	−1.46405	−0.732025	+	0.681278i	$0.761425\pi$
$24$	2.23190e12	0.172452
$25$	1.15760e13	0.606914
$26$	3.11080e13	1.12363
$27$	−3.40561e13	−0.859488
$28$	2.38492e13	0.426062
$29$	−6.35686e13	−0.813695	−0.406847	−	0.913496i	$-0.633372\pi$
$29$	−6.35686e13	−0.813695	−0.406847	+	0.913496i	$0.633372\pi$
$30$	−4.71353e13	−0.437215
$31$	−2.46099e13	−0.167176	−0.0835880	−	0.996500i	$-0.526638\pi$
$31$	−2.46099e13	−0.167176	−0.0835880	+	0.996500i	$0.526638\pi$
$32$	3.51844e13	0.176777
$33$	−3.92102e13	−0.147068
$34$	−2.03217e14	−0.573998
$35$	−5.03669e14	−1.08019
$36$	−2.32191e14	−0.381041
$37$	2.11887e14	0.268033	0.134016	−	0.990979i	$-0.457213\pi$
$37$	2.11887e14	0.268033	0.134016	+	0.990979i	$0.457213\pi$
$38$	−7.18072e14	−0.705056
$39$	1.01034e15	0.775093
$40$	−7.43055e14	−0.448179
$41$	5.84790e14	0.278967	0.139484	−	0.990224i	$-0.455456\pi$
$41$	5.84790e14	0.278967	0.139484	+	0.990224i	$0.455456\pi$
$42$	7.74586e14	0.293901
$43$	6.66795e14	0.202321	0.101161	−	0.994870i	$-0.467744\pi$
$43$	6.66795e14	0.202321	0.101161	+	0.994870i	$0.467744\pi$
$44$	−6.18122e14	−0.150756
$45$	4.90362e15	0.966047
$46$	−6.47501e15	−1.03524
$47$	−1.05191e16	−1.37104	−0.685520	−	0.728054i	$-0.740425\pi$
$47$	−1.05191e16	−1.37104	−0.685520	+	0.728054i	$0.740425\pi$
$48$	1.14273e15	0.121942
$49$	−3.12198e15	−0.273884
$50$	5.92689e15	0.429153
$51$	−6.60017e15	−0.395948
$52$	1.59273e16	0.794530
$53$	−3.56138e16	−1.48251	−0.741254	−	0.671224i	$-0.765769\pi$
$53$	−3.56138e16	−1.48251	−0.741254	+	0.671224i	$0.765769\pi$
$54$	−1.74367e16	−0.607750
$55$	1.30541e16	0.382208
$56$	1.22108e16	0.301271
$57$	−2.33219e16	−0.486353
$58$	−3.25471e16	−0.575369
$59$	1.26702e17	1.90410	0.952050	−	0.305942i	$-0.0989712\pi$
$59$	1.26702e17	1.90410	0.952050	+	0.305942i	$0.0989712\pi$
$60$	−2.41333e16	−0.309157
$61$	−9.76304e16	−1.06894	−0.534468	−	0.845189i	$-0.679488\pi$
$61$	−9.76304e16	−1.06894	−0.534468	+	0.845189i	$0.679488\pi$
$62$	−1.26003e16	−0.118211
$63$	−8.05824e16	−0.649389
$64$	1.80144e16	0.125000
$65$	−3.36367e17	−2.01436
$66$	−2.00756e16	−0.103993
$67$	−1.91145e17	−0.858327	−0.429163	−	0.903227i	$-0.641192\pi$
$67$	−1.91145e17	−0.858327	−0.429163	+	0.903227i	$0.641192\pi$
$68$	−1.04047e17	−0.405878
$69$	−2.10298e17	−0.714117
$70$	−2.57879e17	−0.763808
$71$	−1.94283e17	−0.502898	−0.251449	−	0.967871i	$-0.580907\pi$
$71$	−1.94283e17	−0.502898	−0.251449	+	0.967871i	$0.580907\pi$
$72$	−1.18882e17	−0.269437
$73$	−4.71910e17	−0.938192	−0.469096	−	0.883147i	$-0.655420\pi$
$73$	−4.71910e17	−0.938192	−0.469096	+	0.883147i	$0.655420\pi$
$74$	1.08486e17	0.189528
$75$	1.92496e17	0.296033
$76$	−3.67653e17	−0.498550
$77$	−2.14520e17	−0.256925
$78$	5.17294e17	0.548073
$79$	1.46951e18	1.37948	0.689742	−	0.724056i	$-0.257724\pi$
$79$	1.46951e18	1.37948	0.689742	+	0.724056i	$0.257724\pi$
$80$	−3.80444e17	−0.316910
$81$	4.63142e17	0.342851
$82$	2.99412e17	0.197260
$83$	−1.08775e18	−0.638686	−0.319343	−	0.947639i	$-0.603462\pi$
$83$	−1.08775e18	−0.638686	−0.319343	+	0.947639i	$0.603462\pi$
$84$	3.96588e17	0.207820
$85$	2.19736e18	1.02901
$86$	3.41399e17	0.143063
$87$	−1.05708e18	−0.396894
$88$	−3.16478e17	−0.106600
$89$	−1.57292e18	−0.475884	−0.237942	−	0.971279i	$-0.576473\pi$
$89$	−1.57292e18	−0.475884	−0.237942	+	0.971279i	$0.576473\pi$
$90$	2.51065e18	0.683098
$91$	5.52760e18	1.35408
$92$	−3.31520e18	−0.732025
$93$	−4.09237e17	−0.0815431
$94$	−5.38579e18	−0.969471
$95$	7.76442e18	1.26396
$96$	5.85080e17	0.0862260
$97$	1.34559e19	1.79714	0.898571	−	0.438828i	$-0.144606\pi$
$97$	1.34559e19	1.79714	0.898571	+	0.438828i	$0.144606\pi$
$98$	−1.59845e18	−0.193666
$99$	2.08853e18	0.229776
$100$	3.03457e18	0.303457
$101$	−1.69621e19	−1.54321	−0.771607	−	0.636099i	$-0.780547\pi$
$101$	−1.69621e19	−1.54321	−0.771607	+	0.636099i	$0.780547\pi$
$102$	−3.37929e18	−0.279978
$103$	2.44595e19	1.84711	0.923557	−	0.383461i	$-0.125268\pi$
$103$	2.44595e19	1.84711	0.923557	+	0.383461i	$0.125268\pi$
$104$	8.15477e18	0.561817
$105$	−8.37550e18	−0.526881
$106$	−1.82342e19	−1.04829
$107$	−6.22257e18	−0.327208	−0.163604	−	0.986526i	$-0.552312\pi$
$107$	−6.22257e18	−0.327208	−0.163604	+	0.986526i	$0.552312\pi$
$108$	−8.92761e18	−0.429744
$109$	7.29381e18	0.321664	0.160832	−	0.986982i	$-0.448582\pi$
$109$	7.29381e18	0.321664	0.160832	+	0.986982i	$0.448582\pi$
$110$	6.68368e18	0.270262
$111$	3.52346e18	0.130738
$112$	6.25193e18	0.213031
$113$	4.86452e19	1.52333	0.761666	−	0.647969i	$-0.224382\pi$
$113$	4.86452e19	1.52333	0.761666	+	0.647969i	$0.224382\pi$
$114$	−1.19408e19	−0.343904
$115$	7.00135e19	1.85589
$116$	−1.66641e19	−0.406847
$117$	−5.38155e19	−1.21099
$118$	6.48715e19	1.34640
$119$	−3.61097e19	−0.691716
$120$	−1.23562e19	−0.218607
$121$	5.55992e18	0.0909091
$122$	−4.99868e19	−0.755852
$123$	9.72446e18	0.136071
$124$	−6.45134e18	−0.0835880
$125$	4.15078e19	0.498292
$126$	−4.12582e19	−0.459187
$127$	−4.73330e19	−0.488684	−0.244342	−	0.969689i	$-0.578572\pi$
$127$	−4.73330e19	−0.488684	−0.244342	+	0.969689i	$0.578572\pi$
$128$	9.22337e18	0.0883883
$129$	1.10881e19	0.0986860
$130$	−1.72220e20	−1.42437
$131$	1.35138e19	0.103920	0.0519601	−	0.998649i	$-0.483453\pi$
$131$	1.35138e19	0.103920	0.0519601	+	0.998649i	$0.483453\pi$
$132$	−1.02787e19	−0.0735338
$133$	−1.27595e20	−0.849653
$134$	−9.78663e19	−0.606929
$135$	1.88541e20	1.08952
$136$	−5.32721e19	−0.286999
$137$	1.31306e20	0.659839	0.329920	−	0.944009i	$-0.392978\pi$
$137$	1.31306e20	0.659839	0.329920	+	0.944009i	$0.392978\pi$
$138$	−1.07673e20	−0.504957
$139$	2.15715e19	0.0944582	0.0472291	−	0.998884i	$-0.484961\pi$
$139$	2.15715e19	0.0944582	0.0472291	+	0.998884i	$0.484961\pi$
$140$	−1.32034e20	−0.540094
$141$	−1.74922e20	−0.668750
$142$	−9.94727e19	−0.355602
$143$	−1.43264e20	−0.479119
$144$	−6.08675e19	−0.190521
$145$	3.51928e20	1.03147
$146$	−2.41618e20	−0.663402
$147$	−5.19153e19	−0.133592
$148$	5.55449e19	0.134016
$149$	−6.98435e20	−1.58073	−0.790363	−	0.612639i	$-0.790108\pi$
$149$	−6.98435e20	−1.58073	−0.790363	+	0.612639i	$0.790108\pi$
$150$	9.85581e19	0.209327
$151$	3.15154e20	0.628408	0.314204	−	0.949356i	$-0.398262\pi$
$151$	3.15154e20	0.628408	0.314204	+	0.949356i	$0.398262\pi$
$152$	−1.88238e20	−0.352528
$153$	3.51557e20	0.618624
$154$	−1.09834e20	−0.181673
$155$	1.36245e20	0.211919
$156$	2.64854e20	0.387546
$157$	8.52293e20	1.17366	0.586830	−	0.809710i	$-0.300376\pi$
$157$	8.52293e20	1.17366	0.586830	+	0.809710i	$0.300376\pi$
$158$	7.52391e20	0.975442
$159$	−5.92220e20	−0.723120
$160$	−1.94788e20	−0.224089
$161$	−1.15055e21	−1.24755
$162$	2.37128e20	0.242433
$163$	−7.92319e20	−0.764043	−0.382021	−	0.924153i	$-0.624772\pi$
$163$	−7.92319e20	−0.764043	−0.382021	+	0.924153i	$0.624772\pi$
$164$	1.53299e20	0.139484
$165$	2.17076e20	0.186429
$166$	−5.56928e20	−0.451619
$167$	1.33047e21	1.01906	0.509530	−	0.860453i	$-0.329819\pi$
$167$	1.33047e21	1.01906	0.509530	+	0.860453i	$0.329819\pi$
$168$	2.03053e20	0.146951
$169$	2.22959e21	1.52511
$170$	1.12505e21	0.727623
$171$	1.24223e21	0.759872
$172$	1.74796e20	0.101161
$173$	2.08220e21	1.14047	0.570234	−	0.821482i	$-0.306852\pi$
$173$	2.08220e21	1.14047	0.570234	+	0.821482i	$0.306852\pi$
$174$	−5.41225e20	−0.280647
$175$	1.05315e21	0.517166
$176$	−1.62037e20	−0.0753778
$177$	2.10693e21	0.928760
$178$	−8.05335e20	−0.336501
$179$	1.65328e21	0.655002	0.327501	−	0.944851i	$-0.393793\pi$
$179$	1.65328e21	0.655002	0.327501	+	0.944851i	$0.393793\pi$
$180$	1.28546e21	0.483023
$181$	−4.47883e21	−1.59668	−0.798340	−	0.602207i	$-0.794288\pi$
$181$	−4.47883e21	−1.59668	−0.798340	+	0.602207i	$0.794288\pi$
$182$	2.83013e21	0.957476
$183$	−1.62349e21	−0.521393
$184$	−1.69738e21	−0.517620
$185$	−1.17305e21	−0.339769
$186$	−2.09530e20	−0.0576597
$187$	9.35888e20	0.244753
$188$	−2.75753e21	−0.685520
$189$	−3.09834e21	−0.732390
$190$	3.97538e21	0.893758
$191$	−3.43047e21	−0.733730	−0.366865	−	0.930274i	$-0.619569\pi$
$191$	−3.43047e21	−0.733730	−0.366865	+	0.930274i	$0.619569\pi$
$192$	2.99561e20	0.0609710
$193$	−2.78212e21	−0.538991	−0.269496	−	0.963002i	$-0.586857\pi$
$193$	−2.78212e21	−0.538991	−0.269496	+	0.963002i	$0.586857\pi$
$194$	6.88944e21	1.27077
$195$	−5.59344e21	−0.982539
$196$	−8.18408e20	−0.136942
$197$	−5.60564e21	−0.893708	−0.446854	−	0.894607i	$-0.647456\pi$
$197$	−5.60564e21	−0.893708	−0.446854	+	0.894607i	$0.647456\pi$
$198$	1.06933e21	0.162476
$199$	−2.30749e21	−0.334223	−0.167112	−	0.985938i	$-0.553444\pi$
$199$	−2.30749e21	−0.334223	−0.167112	+	0.985938i	$0.553444\pi$
$200$	1.55370e21	0.214576
$201$	−3.17855e21	−0.418665
$202$	−8.68459e21	−1.09122
$203$	−5.78331e21	−0.693369
$204$	−1.73020e21	−0.197974
$205$	−3.23751e21	−0.353630
$206$	1.25233e22	1.30611
$207$	1.12015e22	1.11573
$208$	4.17524e21	0.397265
$209$	3.30698e21	0.300637
$210$	−4.28826e21	−0.372561
$211$	1.14190e21	0.0948301	0.0474150	−	0.998875i	$-0.484902\pi$
$211$	1.14190e21	0.0948301	0.0474150	+	0.998875i	$0.484902\pi$
$212$	−9.33594e21	−0.741254
$213$	−3.23072e21	−0.245297
$214$	−3.18596e21	−0.231371
$215$	−3.69151e21	−0.256471
$216$	−4.57094e21	−0.303875
$217$	−2.23895e21	−0.142455
$218$	3.73443e21	0.227451
$219$	−7.84738e21	−0.457620
$220$	3.42204e21	0.191104
$221$	−2.41152e22	−1.28993
$222$	1.80401e21	0.0924456
$223$	−3.08095e22	−1.51282	−0.756411	−	0.654096i	$-0.773049\pi$
$223$	−3.08095e22	−1.51282	−0.756411	+	0.654096i	$0.773049\pi$
$224$	3.20099e21	0.150636
$225$	−1.02533e22	−0.462518
$226$	2.49063e22	1.07716
$227$	4.10574e22	1.70273	0.851365	−	0.524574i	$-0.175775\pi$
$227$	4.10574e22	1.70273	0.851365	+	0.524574i	$0.175775\pi$
$228$	−6.11368e21	−0.243177
$229$	1.89086e22	0.721475	0.360738	−	0.932667i	$-0.382525\pi$
$229$	1.89086e22	0.721475	0.360738	+	0.932667i	$0.382525\pi$
$230$	3.58469e22	1.31231
$231$	−3.56725e21	−0.125320
$232$	−8.53203e21	−0.287685
$233$	−5.11138e21	−0.165446	−0.0827231	−	0.996573i	$-0.526362\pi$
$233$	−5.11138e21	−0.165446	−0.0827231	+	0.996573i	$0.526362\pi$
$234$	−2.75536e22	−0.856302
$235$	5.82359e22	1.73799
$236$	3.32142e22	0.952050
$237$	2.44365e22	0.672868
$238$	−1.84882e22	−0.489117
$239$	−1.83206e22	−0.465757	−0.232878	−	0.972506i	$-0.574814\pi$
$239$	−1.83206e22	−0.465757	−0.232878	+	0.972506i	$0.574814\pi$
$240$	−6.32640e21	−0.154579
$241$	−3.02286e22	−0.709996	−0.354998	−	0.934867i	$-0.615518\pi$
$241$	−3.02286e22	−0.709996	−0.354998	+	0.934867i	$0.615518\pi$
$242$	2.84668e21	0.0642824
$243$	4.72837e22	1.02672
$244$	−2.55932e22	−0.534468
$245$	1.72839e22	0.347187
$246$	4.97892e21	0.0962170
$247$	−8.52118e22	−1.58445
$248$	−3.30309e21	−0.0591056
$249$	−1.80882e22	−0.311531
$250$	2.12520e22	0.352346
$251$	−3.95395e22	−0.631147	−0.315574	−	0.948901i	$-0.602197\pi$
$251$	−3.95395e22	−0.631147	−0.315574	+	0.948901i	$0.602197\pi$
$252$	−2.11242e22	−0.324694
$253$	2.98198e22	0.441428
$254$	−2.42345e22	−0.345552
$255$	3.65398e22	0.501920
$256$	4.72237e21	0.0625000
$257$	9.03097e22	1.15178	0.575890	−	0.817527i	$-0.304656\pi$
$257$	9.03097e22	1.15178	0.575890	+	0.817527i	$0.304656\pi$
$258$	5.67712e21	0.0697815
$259$	1.92770e22	0.228397
$260$	−8.81766e22	−1.00718
$261$	5.63052e22	0.620102
$262$	6.91906e21	0.0734827
$263$	1.15698e23	1.18507	0.592536	−	0.805544i	$-0.298127\pi$
$263$	1.15698e23	1.18507	0.592536	+	0.805544i	$0.298127\pi$
$264$	−5.26271e21	−0.0519963
$265$	1.97165e23	1.87929
$266$	−6.53284e22	−0.600795
$267$	−2.61560e22	−0.232121
$268$	−5.01076e22	−0.429163
$269$	5.31945e22	0.439765	0.219882	−	0.975526i	$-0.429433\pi$
$269$	5.31945e22	0.439765	0.219882	+	0.975526i	$0.429433\pi$
$270$	9.65332e22	0.770408
$271$	2.06257e22	0.158928	0.0794640	−	0.996838i	$-0.474679\pi$
$271$	2.06257e22	0.158928	0.0794640	+	0.996838i	$0.474679\pi$
$272$	−2.72753e22	−0.202939
$273$	9.19182e22	0.660475
$274$	6.72285e22	0.466577
$275$	−2.72955e22	−0.182991
$276$	−5.51284e22	−0.357058
$277$	2.07373e21	0.0129776	0.00648881	−	0.999979i	$-0.497935\pi$
$277$	2.07373e21	0.0129776	0.00648881	+	0.999979i	$0.497935\pi$
$278$	1.10446e22	0.0667921
$279$	2.17979e22	0.127402
$280$	−6.76014e22	−0.381904
$281$	−3.56381e23	−1.94628	−0.973138	−	0.230222i	$-0.926055\pi$
$281$	−3.56381e23	−1.94628	−0.973138	+	0.230222i	$0.926055\pi$
$282$	−8.95602e22	−0.472877
$283$	−2.25371e23	−1.15060	−0.575302	−	0.817941i	$-0.695115\pi$
$283$	−2.25371e23	−1.15060	−0.575302	+	0.817941i	$0.695115\pi$
$284$	−5.09300e22	−0.251449
$285$	1.29114e23	0.616522
$286$	−7.33510e22	−0.338789
$287$	5.32028e22	0.237715
$288$	−3.11642e22	−0.134718
$289$	−8.15365e22	−0.341054
$290$	1.80187e23	0.729362
$291$	2.23758e23	0.876589
$292$	−1.23708e23	−0.469096
$293$	−2.20919e22	−0.0810943	−0.0405472	−	0.999178i	$-0.512910\pi$
$293$	−2.20919e22	−0.0810943	−0.0405472	+	0.999178i	$0.512910\pi$
$294$	−2.65806e22	−0.0944639
$295$	−7.01448e23	−2.41372
$296$	2.84390e22	0.0947639
$297$	8.03026e22	0.259145
$298$	−3.57599e23	−1.11774
$299$	−7.68373e23	−2.32646
$300$	5.04617e22	0.148017
$301$	6.06634e22	0.172403
$302$	1.61359e23	0.444351
$303$	−2.82062e23	−0.752731
$304$	−9.63779e22	−0.249275
$305$	5.40501e23	1.35503
$306$	1.79997e23	0.437433
$307$	−3.34855e23	−0.788936	−0.394468	−	0.918910i	$-0.629071\pi$
$307$	−3.34855e23	−0.788936	−0.394468	+	0.918910i	$0.629071\pi$
$308$	−5.62352e22	−0.128463
$309$	4.06736e23	0.900963
$310$	6.97575e22	0.149849
$311$	7.38742e23	1.53911	0.769554	−	0.638581i	$-0.220478\pi$
$311$	7.38742e23	1.53911	0.769554	+	0.638581i	$0.220478\pi$
$312$	1.35605e23	0.274037
$313$	−4.37290e23	−0.857231	−0.428616	−	0.903487i	$-0.640998\pi$
$313$	−4.37290e23	−0.857231	−0.428616	+	0.903487i	$0.640998\pi$
$314$	4.36374e23	0.829903
$315$	4.46120e23	0.823192
$316$	3.85224e23	0.689742
$317$	−6.48121e23	−1.12614	−0.563071	−	0.826409i	$-0.690380\pi$
$317$	−6.48121e23	−1.12614	−0.563071	+	0.826409i	$0.690380\pi$
$318$	−3.03217e23	−0.511323
$319$	1.49891e23	0.245338
$320$	−9.97312e22	−0.158455
$321$	−1.03475e23	−0.159602
$322$	−5.89080e23	−0.882153
$323$	5.56657e23	0.809401
$324$	1.21410e23	0.171426
$325$	7.03330e23	0.964422
$326$	−4.05667e23	−0.540260
$327$	1.21289e23	0.156898
$328$	7.84892e22	0.0986298
$329$	−9.57004e23	−1.16830
$330$	1.11143e23	0.131825
$331$	6.75202e23	0.778158	0.389079	−	0.921204i	$-0.372793\pi$
$331$	6.75202e23	0.778158	0.389079	+	0.921204i	$0.372793\pi$
$332$	−2.85147e23	−0.319343
$333$	−1.87677e23	−0.204263
$334$	6.81202e23	0.720584
$335$	1.05822e24	1.08805
$336$	1.03963e23	0.103910
$337$	−7.50787e23	−0.729513	−0.364756	−	0.931103i	$-0.618848\pi$
$337$	−7.50787e23	−0.729513	−0.364756	+	0.931103i	$0.618848\pi$
$338$	1.14155e24	1.07842
$339$	8.08920e23	0.743033
$340$	5.76025e23	0.514507
$341$	5.80289e22	0.0504054
$342$	6.36024e23	0.537311
$343$	−1.32107e24	−1.08551
$344$	8.94957e22	0.0715315
$345$	1.16425e24	0.905244
$346$	1.06608e24	0.806433
$347$	2.31604e24	1.70457	0.852286	−	0.523076i	$-0.175216\pi$
$347$	2.31604e24	1.70457	0.852286	+	0.523076i	$0.175216\pi$
$348$	−2.77107e23	−0.198447
$349$	−1.78550e24	−1.24428	−0.622139	−	0.782907i	$-0.713736\pi$
$349$	−1.78550e24	−1.24428	−0.622139	+	0.782907i	$0.713736\pi$
$350$	5.39214e23	0.365691
$351$	−2.06918e24	−1.36578
$352$	−8.29629e22	−0.0533002
$353$	−1.46906e24	−0.918713	−0.459357	−	0.888252i	$-0.651920\pi$
$353$	−1.46906e24	−0.918713	−0.459357	+	0.888252i	$0.651920\pi$
$354$	1.07875e24	0.656732
$355$	1.07559e24	0.637493
$356$	−4.12331e23	−0.237942
$357$	−6.00467e23	−0.337397
$358$	8.46480e23	0.463156
$359$	−1.03516e24	−0.551584	−0.275792	−	0.961217i	$-0.588940\pi$
$359$	−1.03516e24	−0.551584	−0.275792	+	0.961217i	$0.588940\pi$
$360$	6.58153e23	0.341549
$361$	−1.14598e22	−0.00579239
$362$	−2.29316e24	−1.12902
$363$	9.24557e22	0.0443426
$364$	1.44903e24	0.677038
$365$	2.61258e24	1.18929
$366$	−8.31228e23	−0.368680
$367$	−3.77144e24	−1.62997	−0.814984	−	0.579483i	$-0.803254\pi$
$367$	−3.77144e24	−1.62997	−0.814984	+	0.579483i	$0.803254\pi$
$368$	−8.69061e23	−0.366012
$369$	−5.17971e23	−0.212596
$370$	−6.00600e23	−0.240253
$371$	−3.24005e24	−1.26328
$372$	−1.07279e23	−0.0407716
$373$	5.00723e24	1.85509	0.927543	−	0.373717i	$-0.121917\pi$
$373$	5.00723e24	1.85509	0.927543	+	0.373717i	$0.121917\pi$
$374$	4.79175e23	0.173067
$375$	6.90232e23	0.243051
$376$	−1.41185e24	−0.484736
$377$	−3.86229e24	−1.29301
$378$	−1.58635e24	−0.517878
$379$	−2.53521e24	−0.807125	−0.403563	−	0.914952i	$-0.632228\pi$
$379$	−2.53521e24	−0.807125	−0.403563	+	0.914952i	$0.632228\pi$
$380$	2.03540e24	0.631982
$381$	−7.87098e23	−0.238365
$382$	−1.75640e24	−0.518826
$383$	−2.48507e24	−0.716063	−0.358031	−	0.933710i	$-0.616552\pi$
$383$	−2.48507e24	−0.716063	−0.358031	+	0.933710i	$0.616552\pi$
$384$	1.53375e23	0.0431130
$385$	1.18763e24	0.325689
$386$	−1.42445e24	−0.381124
$387$	−5.90606e23	−0.154186
$388$	3.52739e24	0.898571
$389$	4.57128e24	1.13636	0.568181	−	0.822904i	$-0.307648\pi$
$389$	4.57128e24	1.13636	0.568181	+	0.822904i	$0.307648\pi$
$390$	−2.86384e24	−0.694760
$391$	5.01950e24	1.18845
$392$	−4.19025e23	−0.0968328
$393$	2.24720e23	0.0506890
$394$	−2.87009e24	−0.631947
$395$	−8.13552e24	−1.74869
$396$	5.47494e23	0.114888
$397$	7.27391e24	1.49025	0.745123	−	0.666927i	$-0.232391\pi$
$397$	7.27391e24	1.49025	0.745123	+	0.666927i	$0.232391\pi$
$398$	−1.18144e24	−0.236331
$399$	−2.12177e24	−0.414434
$400$	7.95494e23	0.151728
$401$	1.13014e23	0.0210504	0.0105252	−	0.999945i	$-0.496650\pi$
$401$	1.13014e23	0.0210504	0.0105252	+	0.999945i	$0.496650\pi$
$402$	−1.62742e24	−0.296041
$403$	−1.49524e24	−0.265653
$404$	−4.44651e24	−0.771607
$405$	−2.56404e24	−0.434613
$406$	−2.96106e24	−0.490286
$407$	−4.99618e23	−0.0808149
$408$	−8.85860e23	−0.139989
$409$	−2.61011e24	−0.402983	−0.201492	−	0.979490i	$-0.564579\pi$
$409$	−2.61011e24	−0.402983	−0.201492	+	0.979490i	$0.564579\pi$
$410$	−1.65761e24	−0.250054
$411$	2.18348e24	0.321849
$412$	6.41191e24	0.923557
$413$	1.15271e25	1.62253
$414$	5.73516e24	0.788938
$415$	6.02200e24	0.809625
$416$	2.13772e24	0.280909
$417$	3.58712e23	0.0460737
$418$	1.69318e24	0.212582
$419$	−8.00901e23	−0.0982982	−0.0491491	−	0.998791i	$-0.515651\pi$
$419$	−8.00901e23	−0.0982982	−0.0491491	+	0.998791i	$0.515651\pi$
$420$	−2.19559e24	−0.263441
$421$	2.73247e24	0.320535	0.160268	−	0.987074i	$-0.448764\pi$
$421$	2.73247e24	0.320535	0.160268	+	0.987074i	$0.448764\pi$
$422$	5.84655e23	0.0670550
$423$	9.31720e24	1.04484
$424$	−4.78000e24	−0.524146
$425$	−4.59459e24	−0.492665
$426$	−1.65413e24	−0.173451
$427$	−8.88217e24	−0.910866
$428$	−1.63121e24	−0.163604
$429$	−2.38233e24	−0.233699
$430$	−1.89005e24	−0.181352
$431$	6.50460e24	0.610501	0.305250	−	0.952272i	$-0.401260\pi$
$431$	6.50460e24	0.610501	0.305250	+	0.952272i	$0.401260\pi$
$432$	−2.34032e24	−0.214872
$433$	1.24767e25	1.12064	0.560320	−	0.828276i	$-0.310678\pi$
$433$	1.24767e25	1.12064	0.560320	+	0.828276i	$0.310678\pi$
$434$	−1.14634e24	−0.100731
$435$	5.85220e24	0.503120
$436$	1.91203e24	0.160832
$437$	1.77365e25	1.45980
$438$	−4.01786e24	−0.323587
$439$	4.27242e24	0.336714	0.168357	−	0.985726i	$-0.446154\pi$
$439$	4.27242e24	0.336714	0.168357	+	0.985726i	$0.446154\pi$
$440$	1.75209e24	0.135131
$441$	2.76526e24	0.208722
$442$	−1.23470e25	−0.912116
$443$	−1.20018e25	−0.867783	−0.433891	−	0.900965i	$-0.642860\pi$
$443$	−1.20018e25	−0.867783	−0.433891	+	0.900965i	$0.642860\pi$
$444$	9.23655e23	0.0653689
$445$	8.70799e24	0.603250
$446$	−1.57745e25	−1.06973
$447$	−1.16143e25	−0.771028
$448$	1.63891e24	0.106516
$449$	−3.78323e24	−0.240726	−0.120363	−	0.992730i	$-0.538406\pi$
$449$	−3.78323e24	−0.240726	−0.120363	+	0.992730i	$0.538406\pi$
$450$	−5.24968e24	−0.327050
$451$	−1.37890e24	−0.0841118
$452$	1.27520e25	0.761666
$453$	5.24068e24	0.306517
$454$	2.10214e25	1.20401
$455$	−3.06018e25	−1.71648
$456$	−3.13021e24	−0.171952
$457$	−2.05765e25	−1.10705	−0.553526	−	0.832832i	$-0.686718\pi$
$457$	−2.05765e25	−1.10705	−0.553526	+	0.832832i	$0.686718\pi$
$458$	9.68119e24	0.510160
$459$	1.35172e25	0.697693
$460$	1.83536e25	0.927945
$461$	3.18626e25	1.57806	0.789028	−	0.614358i	$-0.210585\pi$
$461$	3.18626e25	1.57806	0.789028	+	0.614358i	$0.210585\pi$
$462$	−1.82643e24	−0.0886145
$463$	1.60669e25	0.763683	0.381842	−	0.924228i	$-0.375290\pi$
$463$	1.60669e25	0.763683	0.381842	+	0.924228i	$0.375290\pi$
$464$	−4.36840e24	−0.203424
$465$	2.26562e24	0.103367
$466$	−2.61702e24	−0.116988
$467$	−1.00139e25	−0.438625	−0.219312	−	0.975655i	$-0.570381\pi$
$467$	−1.00139e25	−0.438625	−0.219312	+	0.975655i	$0.570381\pi$
$468$	−1.41074e25	−0.605497
$469$	−1.73899e25	−0.731401
$470$	2.98168e25	1.22894
$471$	1.41728e25	0.572474
$472$	1.70057e25	0.673201
$473$	−1.57227e24	−0.0610022
$474$	1.25115e25	0.475790
$475$	−1.62351e25	−0.605153
$476$	−9.46595e24	−0.345858
$477$	3.15445e25	1.12979
$478$	−9.38014e24	−0.329340
$479$	−4.44906e25	−1.53137	−0.765687	−	0.643213i	$-0.777601\pi$
$479$	−4.44906e25	−1.53137	−0.765687	+	0.643213i	$0.777601\pi$
$480$	−3.23912e24	−0.109304
$481$	1.28738e25	0.425920
$482$	−1.54770e25	−0.502043
$483$	−1.91324e25	−0.608516
$484$	1.45750e24	0.0454545
$485$	−7.44947e25	−2.27813
$486$	2.42093e25	0.726000
$487$	2.83315e25	0.833190	0.416595	−	0.909092i	$-0.363223\pi$
$487$	2.83315e25	0.833190	0.416595	+	0.909092i	$0.363223\pi$
$488$	−1.31037e25	−0.377926
$489$	−1.31754e25	−0.372676
$490$	8.84935e24	0.245498
$491$	−3.31546e25	−0.902132	−0.451066	−	0.892491i	$-0.648956\pi$
$491$	−3.31546e25	−0.902132	−0.451066	+	0.892491i	$0.648956\pi$
$492$	2.54921e24	0.0680357
$493$	2.52309e25	0.660521
$494$	−4.36284e25	−1.12038
$495$	−1.15625e25	−0.291274
$496$	−1.69118e24	−0.0417940
$497$	−1.76754e25	−0.428531
$498$	−9.26115e24	−0.220286
$499$	−3.68845e25	−0.860773	−0.430386	−	0.902645i	$-0.641623\pi$
$499$	−3.68845e25	−0.860773	−0.430386	+	0.902645i	$0.641623\pi$
$500$	1.08810e25	0.249146
$501$	2.21244e25	0.497065
$502$	−2.02442e25	−0.446289
$503$	−6.25558e25	−1.35323	−0.676615	−	0.736337i	$-0.736554\pi$
$503$	−6.25558e25	−1.35323	−0.676615	+	0.736337i	$0.736554\pi$
$504$	−1.08156e25	−0.229594
$505$	9.39054e25	1.95624
$506$	1.52677e25	0.312136
$507$	3.70758e25	0.743900
$508$	−1.24080e25	−0.244342
$509$	−7.10631e25	−1.37349	−0.686745	−	0.726899i	$-0.740961\pi$
$509$	−7.10631e25	−1.37349	−0.686745	+	0.726899i	$0.740961\pi$
$510$	1.87084e25	0.354911
$511$	−4.29332e25	−0.799456
$512$	2.41785e24	0.0441942
$513$	4.77632e25	0.856995
$514$	4.62386e25	0.814432
$515$	−1.35412e26	−2.34148
$516$	2.90668e24	0.0493430
$517$	2.48036e25	0.413384
$518$	9.86980e24	0.161501
$519$	3.46248e25	0.556284
$520$	−4.51464e25	−0.712183
$521$	−6.25674e25	−0.969148	−0.484574	−	0.874750i	$-0.661025\pi$
$521$	−6.25674e25	−0.969148	−0.484574	+	0.874750i	$0.661025\pi$
$522$	2.88282e25	0.438479
$523$	2.02579e25	0.302571	0.151286	−	0.988490i	$-0.451659\pi$
$523$	2.02579e25	0.302571	0.151286	+	0.988490i	$0.451659\pi$
$524$	3.54256e24	0.0519601
$525$	1.75128e25	0.252257
$526$	5.92371e25	0.837972
$527$	9.76787e24	0.135706
$528$	−2.69451e24	−0.0367669
$529$	8.53184e25	1.14344
$530$	1.00948e26	1.32886
$531$	−1.12225e26	−1.45108
$532$	−3.34481e25	−0.424826
$533$	3.55305e25	0.443296
$534$	−1.33919e25	−0.164134
$535$	3.44494e25	0.414782
$536$	−2.56551e25	−0.303464
$537$	2.74924e25	0.319489
$538$	2.72356e25	0.310961
$539$	7.36146e24	0.0825792
$540$	4.94250e25	0.544761
$541$	9.83691e25	1.06533	0.532666	−	0.846326i	$-0.321190\pi$
$541$	9.83691e25	1.06533	0.532666	+	0.846326i	$0.321190\pi$
$542$	1.05604e25	0.112379
$543$	−7.44783e25	−0.778810
$544$	−1.39650e25	−0.143499
$545$	−4.03800e25	−0.407755
$546$	4.70621e25	0.467026
$547$	1.33140e25	0.129846	0.0649229	−	0.997890i	$-0.479320\pi$
$547$	1.33140e25	0.129846	0.0649229	+	0.997890i	$0.479320\pi$
$548$	3.44210e25	0.329920
$549$	8.64750e25	0.814617
$550$	−1.39753e25	−0.129394
$551$	8.91539e25	0.811335
$552$	−2.82258e25	−0.252478
$553$	1.33693e26	1.17549
$554$	1.06175e24	0.00917656
$555$	−1.95066e25	−0.165729
$556$	5.65484e24	0.0472291
$557$	1.72025e26	1.41243	0.706215	−	0.707997i	$-0.250401\pi$
$557$	1.72025e26	1.41243	0.706215	+	0.707997i	$0.250401\pi$
$558$	1.11605e25	0.0900867
$559$	4.05130e25	0.321501
$560$	−3.46119e25	−0.270047
$561$	1.55629e25	0.119383
$562$	−1.82467e26	−1.37623
$563$	2.52833e26	1.87501	0.937506	−	0.347969i	$-0.113129\pi$
$563$	2.52833e26	1.87501	0.937506	+	0.347969i	$0.113129\pi$
$564$	−4.58548e25	−0.334375
$565$	−2.69309e26	−1.93104
$566$	−1.15390e26	−0.813600
$567$	4.21355e25	0.292152
$568$	−2.60762e25	−0.177801
$569$	2.40443e26	1.61230	0.806150	−	0.591711i	$-0.201548\pi$
$569$	2.40443e26	1.61230	0.806150	+	0.591711i	$0.201548\pi$
$570$	6.61065e25	0.435947
$571$	−5.68149e25	−0.368485	−0.184242	−	0.982881i	$-0.558983\pi$
$571$	−5.68149e25	−0.368485	−0.184242	+	0.982881i	$0.558983\pi$
$572$	−3.75557e25	−0.239560
$573$	−5.70452e25	−0.357890
$574$	2.72398e25	0.168090
$575$	−1.46395e26	−0.888552
$576$	−1.59561e25	−0.0952603
$577$	−1.08033e26	−0.634435	−0.317217	−	0.948353i	$-0.602748\pi$
$577$	−1.08033e26	−0.634435	−0.317217	+	0.948353i	$0.602748\pi$
$578$	−4.17467e25	−0.241161
$579$	−4.62638e25	−0.262903
$580$	9.22558e25	0.515736
$581$	−9.89609e25	−0.544240
$582$	1.14564e26	0.619842
$583$	8.39754e25	0.446993
$584$	−6.33387e25	−0.331701
$585$	2.97933e26	1.53511
$586$	−1.13110e25	−0.0573423
$587$	−2.11762e26	−1.05630	−0.528150	−	0.849151i	$-0.677114\pi$
$587$	−2.11762e26	−1.05630	−0.528150	+	0.849151i	$0.677114\pi$
$588$	−1.36093e25	−0.0667960
$589$	3.45150e25	0.166691
$590$	−3.59141e26	−1.70675
$591$	−9.32159e25	−0.435922
$592$	1.45608e25	0.0670082
$593$	−1.87886e26	−0.850892	−0.425446	−	0.904984i	$-0.639883\pi$
$593$	−1.87886e26	−0.850892	−0.425446	+	0.904984i	$0.639883\pi$
$594$	4.11149e25	0.183243
$595$	1.99910e26	0.876848
$596$	−1.83091e26	−0.790363
$597$	−3.83713e25	−0.163023
$598$	−3.93407e26	−1.64506
$599$	−7.05164e25	−0.290225	−0.145113	−	0.989415i	$-0.546354\pi$
$599$	−7.05164e25	−0.290225	−0.145113	+	0.989415i	$0.546354\pi$
$600$	2.58364e25	0.104664
$601$	−3.61449e26	−1.44125	−0.720626	−	0.693324i	$-0.756145\pi$
$601$	−3.61449e26	−1.44125	−0.720626	+	0.693324i	$0.756145\pi$
$602$	3.10597e25	0.121907
$603$	1.69305e26	0.654116
$604$	8.26157e25	0.314204
$605$	−3.07808e25	−0.115240
$606$	−1.44416e26	−0.532261
$607$	−2.18220e26	−0.791777	−0.395888	−	0.918299i	$-0.629563\pi$
$607$	−2.18220e26	−0.791777	−0.395888	+	0.918299i	$0.629563\pi$
$608$	−4.93455e25	−0.176264
$609$	−9.61706e25	−0.338203
$610$	2.76736e26	0.958148
$611$	−6.39119e26	−2.17866
$612$	9.21585e25	0.309312
$613$	5.46902e26	1.80732	0.903660	−	0.428251i	$-0.140870\pi$
$613$	5.46902e26	1.80732	0.903660	+	0.428251i	$0.140870\pi$
$614$	−1.71446e26	−0.557862
$615$	−5.38365e25	−0.172490
$616$	−2.87924e25	−0.0908367
$617$	4.80766e26	1.49357	0.746783	−	0.665068i	$-0.231597\pi$
$617$	4.80766e26	1.49357	0.746783	+	0.665068i	$0.231597\pi$
$618$	2.08249e26	0.637077
$619$	2.01621e26	0.607401	0.303701	−	0.952768i	$-0.401778\pi$
$619$	2.01621e26	0.607401	0.303701	+	0.952768i	$0.401778\pi$
$620$	3.57159e25	0.105960
$621$	4.30691e26	1.25833
$622$	3.78236e26	1.08831
$623$	−1.43100e26	−0.405512
$624$	6.94300e25	0.193773
$625$	−4.50589e26	−1.23857
$626$	−2.23892e26	−0.606154
$627$	5.49917e25	0.146641
$628$	2.23424e26	0.586830
$629$	−8.40996e25	−0.217577
$630$	2.28413e26	0.582084
$631$	8.30818e25	0.208558	0.104279	−	0.994548i	$-0.466747\pi$
$631$	8.30818e25	0.208558	0.104279	+	0.994548i	$0.466747\pi$
$632$	1.97235e26	0.487721
$633$	1.89887e25	0.0462551
$634$	−3.31838e26	−0.796302
$635$	2.62044e26	0.619476
$636$	−1.55247e26	−0.361560
$637$	−1.89685e26	−0.435219
$638$	7.67444e25	0.173480
$639$	1.72084e26	0.383249
$640$	−5.10624e25	−0.112045
$641$	1.08313e26	0.234169	0.117084	−	0.993122i	$-0.462645\pi$
$641$	1.08313e26	0.234169	0.117084	+	0.993122i	$0.462645\pi$
$642$	−5.29792e25	−0.112855
$643$	−5.95121e26	−1.24911	−0.624556	−	0.780980i	$-0.714720\pi$
$643$	−5.95121e26	−1.24911	−0.624556	+	0.780980i	$0.714720\pi$
$644$	−3.01609e26	−0.623776
$645$	−6.13860e25	−0.125098
$646$	2.85008e26	0.572333
$647$	−1.01838e26	−0.201521	−0.100760	−	0.994911i	$-0.532128\pi$
$647$	−1.01838e26	−0.201521	−0.100760	+	0.994911i	$0.532128\pi$
$648$	6.21618e25	0.121216
$649$	−2.98757e26	−0.574108
$650$	3.60105e26	0.681949
$651$	−3.72314e25	−0.0694849
$652$	−2.07702e26	−0.382021
$653$	−6.18708e26	−1.12153	−0.560765	−	0.827975i	$-0.689493\pi$
$653$	−6.18708e26	−1.12153	−0.560765	+	0.827975i	$0.689493\pi$
$654$	6.20998e25	0.110943
$655$	−7.48150e25	−0.131733
$656$	4.01865e25	0.0697418
$657$	4.17989e26	0.714980
$658$	−4.89986e26	−0.826110
$659$	6.58470e25	0.109427	0.0547135	−	0.998502i	$-0.482575\pi$
$659$	6.58470e25	0.109427	0.0547135	+	0.998502i	$0.482575\pi$
$660$	5.69050e25	0.0932145
$661$	8.76254e26	1.41487	0.707435	−	0.706779i	$-0.249852\pi$
$661$	8.76254e26	1.41487	0.707435	+	0.706779i	$0.249852\pi$
$662$	3.45704e26	0.550241
$663$	−4.01012e26	−0.629185
$664$	−1.45995e26	−0.225810
$665$	7.06388e26	1.07705
$666$	−9.60904e25	−0.144436
$667$	8.03920e26	1.19129
$668$	3.48775e26	0.509530
$669$	−5.12330e26	−0.737907
$670$	5.41807e26	0.769368
$671$	2.30207e26	0.322296
$672$	5.32291e25	0.0734753
$673$	8.11161e26	1.10399	0.551994	−	0.833848i	$-0.313867\pi$
$673$	8.11161e26	1.10399	0.551994	+	0.833848i	$0.313867\pi$
$674$	−3.84403e26	−0.515843
$675$	−3.94232e26	−0.521635
$676$	5.84473e26	0.762555
$677$	−5.30323e26	−0.682258	−0.341129	−	0.940017i	$-0.610809\pi$
$677$	−5.30323e26	−0.682258	−0.341129	+	0.940017i	$0.610809\pi$
$678$	4.14167e26	0.525404
$679$	1.22419e27	1.53139
$680$	2.94925e26	0.363811
$681$	6.82742e26	0.830538
$682$	2.97108e25	0.0356420
$683$	−2.38888e26	−0.282617	−0.141308	−	0.989966i	$-0.545131\pi$
$683$	−2.38888e26	−0.282617	−0.141308	+	0.989966i	$0.545131\pi$
$684$	3.25644e26	0.379936
$685$	−7.26934e26	−0.836439
$686$	−6.76390e26	−0.767570
$687$	3.14430e26	0.351913
$688$	4.58218e25	0.0505804
$689$	−2.16381e27	−2.35579
$690$	5.96097e26	0.640104
$691$	−7.28740e26	−0.771846	−0.385923	−	0.922531i	$-0.626117\pi$
$691$	−7.28740e26	−0.771846	−0.385923	+	0.922531i	$0.626117\pi$
$692$	5.45835e26	0.570234
$693$	1.90009e26	0.195798
$694$	1.18581e27	1.20531
$695$	−1.19424e26	−0.119739
$696$	−1.41879e26	−0.140323
$697$	−2.32108e26	−0.226453
$698$	−9.14174e26	−0.879838
$699$	−8.49969e25	−0.0806994
$700$	2.76078e26	0.258583
$701$	−9.69213e25	−0.0895567	−0.0447784	−	0.998997i	$-0.514258\pi$
$701$	−9.69213e25	−0.0895567	−0.0447784	+	0.998997i	$0.514258\pi$
$702$	−1.05942e27	−0.965750
$703$	−2.97168e26	−0.267255
$704$	−4.24770e25	−0.0376889
$705$	9.68404e26	0.847734
$706$	−7.52159e26	−0.649629
$707$	−1.54317e27	−1.31501
$708$	5.52318e26	0.464380
$709$	−2.46232e26	−0.204270	−0.102135	−	0.994771i	$-0.532567\pi$
$709$	−2.46232e26	−0.204270	−0.102135	+	0.994771i	$0.532567\pi$
$710$	5.50700e26	0.450776
$711$	−1.30161e27	−1.05128
$712$	−2.11114e26	−0.168250
$713$	3.11229e26	0.244754
$714$	−3.07439e26	−0.238576
$715$	7.93136e26	0.607351
$716$	4.33398e26	0.327501
$717$	−3.04653e26	−0.227181
$718$	−5.30004e26	−0.390029
$719$	−1.00505e27	−0.729897	−0.364949	−	0.931028i	$-0.618913\pi$
$719$	−1.00505e27	−0.729897	−0.364949	+	0.931028i	$0.618913\pi$
$720$	3.36974e26	0.241512
$721$	2.22526e27	1.57397
$722$	−5.86741e24	−0.00409584
$723$	−5.02670e26	−0.346313
$724$	−1.17410e27	−0.798340
$725$	−7.35867e26	−0.493842
$726$	4.73373e25	0.0313549
$727$	2.55019e27	1.66723	0.833614	−	0.552347i	$-0.186268\pi$
$727$	2.55019e27	1.66723	0.833614	+	0.552347i	$0.186268\pi$
$728$	7.41901e26	0.478738
$729$	2.47988e26	0.157950
$730$	1.33764e27	0.840956
$731$	−2.64656e26	−0.164236
$732$	−4.25589e26	−0.260696
$733$	−2.60469e27	−1.57496	−0.787478	−	0.616342i	$-0.788614\pi$
$733$	−2.60469e27	−1.57496	−0.787478	+	0.616342i	$0.788614\pi$
$734$	−1.93097e27	−1.15256
$735$	2.87413e26	0.169347
$736$	−4.44959e26	−0.258810
$737$	4.50710e26	0.258795
$738$	−2.65201e26	−0.150328
$739$	−2.41892e26	−0.135363	−0.0676814	−	0.997707i	$-0.521560\pi$
$739$	−2.41892e26	−0.135363	−0.0676814	+	0.997707i	$0.521560\pi$
$740$	−3.07507e26	−0.169885
$741$	−1.41698e27	−0.772844
$742$	−1.65891e27	−0.893275
$743$	2.58193e27	1.37262	0.686311	−	0.727309i	$-0.259229\pi$
$743$	2.58193e27	1.37262	0.686311	+	0.727309i	$0.259229\pi$
$744$	−5.49269e25	−0.0288298
$745$	3.86667e27	2.00379
$746$	2.56370e27	1.31174
$747$	9.63463e26	0.486731
$748$	2.45337e26	0.122377
$749$	−5.66114e26	−0.278822
$750$	3.53399e26	0.171863
$751$	−3.92785e27	−1.88615	−0.943073	−	0.332585i	$-0.892079\pi$
$751$	−3.92785e27	−1.88615	−0.943073	+	0.332585i	$0.892079\pi$
$752$	−7.22869e26	−0.342760
$753$	−6.57501e26	−0.307854
$754$	−1.97749e27	−0.914296
$755$	−1.74475e27	−0.796595
$756$	−8.12212e26	−0.366195
$757$	−1.01968e27	−0.453996	−0.226998	−	0.973895i	$-0.572891\pi$
$757$	−1.01968e27	−0.453996	−0.226998	+	0.973895i	$0.572891\pi$
$758$	−1.29803e27	−0.570724
$759$	4.95872e26	0.215314
$760$	1.04212e27	0.446879
$761$	−3.84308e27	−1.62752	−0.813758	−	0.581204i	$-0.802582\pi$
$761$	−3.84308e27	−1.62752	−0.813758	+	0.581204i	$0.802582\pi$
$762$	−4.02994e26	−0.168549
$763$	6.63573e26	0.274098
$764$	−8.99277e26	−0.366865
$765$	−1.94629e27	−0.784193
$766$	−1.27236e27	−0.506333
$767$	7.69814e27	3.02573
$768$	7.85281e25	0.0304855
$769$	−3.88639e26	−0.149020	−0.0745102	−	0.997220i	$-0.523739\pi$
$769$	−3.88639e26	−0.149020	−0.0745102	+	0.997220i	$0.523739\pi$
$770$	6.08065e26	0.230297
$771$	1.50176e27	0.561802
$772$	−7.29317e26	−0.269496
$773$	−2.46263e27	−0.898863	−0.449432	−	0.893315i	$-0.648373\pi$
$773$	−2.46263e27	−0.898863	−0.449432	+	0.893315i	$0.648373\pi$
$774$	−3.02390e26	−0.109026
$775$	−2.84883e26	−0.101461
$776$	1.80602e27	0.635386
$777$	3.20556e26	0.111405
$778$	2.34049e27	0.803529
$779$	−8.20158e26	−0.278158
$780$	−1.46629e27	−0.491270
$781$	4.58108e26	0.151629
$782$	2.56998e27	0.840361
$783$	2.16490e27	0.699361
$784$	−2.14541e26	−0.0684711
$785$	−4.71846e27	−1.48778
$786$	1.15057e26	0.0358425
$787$	5.61887e27	1.72937	0.864687	−	0.502310i	$-0.167516\pi$
$787$	5.61887e27	1.72937	0.864687	+	0.502310i	$0.167516\pi$
$788$	−1.46948e27	−0.446854
$789$	1.92393e27	0.578040
$790$	−4.16538e27	−1.23651
$791$	4.42562e27	1.29807
$792$	2.80317e26	0.0812382
$793$	−5.93181e27	−1.69860
$794$	3.72424e27	1.05376
$795$	3.27865e27	0.916657
$796$	−6.04896e26	−0.167112
$797$	5.93729e27	1.62082	0.810409	−	0.585864i	$-0.199245\pi$
$797$	5.93729e27	1.62082	0.810409	+	0.585864i	$0.199245\pi$
$798$	−1.08634e27	−0.293049
$799$	4.17512e27	1.11295
$800$	4.07293e26	0.107288
$801$	1.39320e27	0.362663
$802$	5.78632e25	0.0148849
$803$	1.11274e27	0.282876
$804$	−8.33237e26	−0.209332
$805$	6.36965e27	1.58145
$806$	−7.65565e26	−0.187845
$807$	8.84571e26	0.214503
$808$	−2.27661e27	−0.545609
$809$	−6.80607e27	−1.61208	−0.806038	−	0.591863i	$-0.798392\pi$
$809$	−6.80607e27	−1.61208	−0.806038	+	0.591863i	$0.798392\pi$
$810$	−1.31279e27	−0.307318
$811$	3.32837e27	0.770077	0.385038	−	0.922901i	$-0.374188\pi$
$811$	3.32837e27	0.770077	0.385038	+	0.922901i	$0.374188\pi$
$812$	−1.51606e27	−0.346685
$813$	3.42984e26	0.0775200
$814$	−2.55805e26	−0.0571448
$815$	4.38643e27	0.968532
$816$	−4.53560e26	−0.0989871
$817$	−9.35169e26	−0.201735
$818$	−1.33638e27	−0.284952
$819$	−4.89601e27	−1.03192
$820$	−8.48694e26	−0.176815
$821$	3.69915e27	0.761803	0.380901	−	0.924616i	$-0.375614\pi$
$821$	3.69915e27	0.761803	0.380901	+	0.924616i	$0.375614\pi$
$822$	1.11794e27	0.227581
$823$	−4.91961e27	−0.989994	−0.494997	−	0.868895i	$-0.664831\pi$
$823$	−4.91961e27	−0.989994	−0.494997	+	0.868895i	$0.664831\pi$
$824$	3.28290e27	0.653053
$825$	−4.53896e26	−0.0892573
$826$	5.90185e27	1.14730
$827$	1.64283e27	0.315711	0.157856	−	0.987462i	$-0.449542\pi$
$827$	1.64283e27	0.315711	0.157856	+	0.987462i	$0.449542\pi$
$828$	2.93640e27	0.557863
$829$	5.51231e27	1.03530	0.517649	−	0.855593i	$-0.326807\pi$
$829$	5.51231e27	1.03530	0.517649	+	0.855593i	$0.326807\pi$
$830$	3.08326e27	0.572491
$831$	3.44840e25	0.00633007
$832$	1.09452e27	0.198632
$833$	1.23914e27	0.222327
$834$	1.83660e26	0.0325790
$835$	−7.36575e27	−1.29180
$836$	8.66906e26	0.150318
$837$	8.38118e26	0.143686
$838$	−4.10061e26	−0.0695073
$839$	1.46432e27	0.245413	0.122706	−	0.992443i	$-0.460843\pi$
$839$	1.46432e27	0.245413	0.122706	+	0.992443i	$0.460843\pi$
$840$	−1.12414e27	−0.186281
$841$	−2.06230e27	−0.337901
$842$	1.39903e27	0.226653
$843$	−5.92625e27	−0.949332
$844$	2.99343e26	0.0474150
$845$	−1.23434e28	−1.93329
$846$	4.77041e27	0.738817
$847$	5.05828e26	0.0774658
$848$	−2.44736e27	−0.370627
$849$	−3.74768e27	−0.561228
$850$	−2.35243e27	−0.348367
$851$	−2.67963e27	−0.392413
$852$	−8.46914e26	−0.122649
$853$	−6.30007e27	−0.902255	−0.451128	−	0.892459i	$-0.648978\pi$
$853$	−6.30007e27	−0.902255	−0.451128	+	0.892459i	$0.648978\pi$
$854$	−4.54767e27	−0.644079
$855$	−6.87725e27	−0.963245
$856$	−8.35180e26	−0.115686
$857$	−3.66852e27	−0.502542	−0.251271	−	0.967917i	$-0.580849\pi$
$857$	−3.66852e27	−0.502542	−0.251271	+	0.967917i	$0.580849\pi$
$858$	−1.21975e27	−0.165250
$859$	6.16141e27	0.825553	0.412777	−	0.910832i	$-0.364559\pi$
$859$	6.16141e27	0.825553	0.412777	+	0.910832i	$0.364559\pi$
$860$	−9.67706e26	−0.128236
$861$	8.84707e26	0.115950
$862$	3.33035e27	0.431689
$863$	7.22501e27	0.926266	0.463133	−	0.886289i	$-0.346725\pi$
$863$	7.22501e27	0.926266	0.463133	+	0.886289i	$0.346725\pi$
$864$	−1.19824e27	−0.151937
$865$	−1.15274e28	−1.44571
$866$	6.38809e27	0.792412
$867$	−1.35587e27	−0.166355
$868$	−5.86927e26	−0.0712273
$869$	−3.46504e27	−0.415930
$870$	2.99633e27	0.355759
$871$	−1.16136e28	−1.36393
$872$	9.78959e26	0.113726
$873$	−1.19184e28	−1.36957
$874$	9.08109e27	1.03224
$875$	3.77628e27	0.424607
$876$	−2.05714e27	−0.228810
$877$	5.67688e27	0.624616	0.312308	−	0.949981i	$-0.398898\pi$
$877$	5.67688e27	0.624616	0.312308	+	0.949981i	$0.398898\pi$
$878$	2.18748e27	0.238092
$879$	−3.67365e26	−0.0395552
$880$	8.97068e26	0.0955520
$881$	7.68746e27	0.810050	0.405025	−	0.914306i	$-0.367263\pi$
$881$	7.68746e27	0.810050	0.405025	+	0.914306i	$0.367263\pi$
$882$	1.41581e27	0.147589
$883$	−4.02169e27	−0.414746	−0.207373	−	0.978262i	$-0.566491\pi$
$883$	−4.02169e27	−0.414746	−0.207373	+	0.978262i	$0.566491\pi$
$884$	−6.32167e27	−0.644964
$885$	−1.16644e28	−1.17733
$886$	−6.14492e27	−0.613615
$887$	−6.97948e27	−0.689522	−0.344761	−	0.938690i	$-0.612040\pi$
$887$	−6.97948e27	−0.689522	−0.344761	+	0.938690i	$0.612040\pi$
$888$	4.72911e26	0.0462228
$889$	−4.30624e27	−0.416420
$890$	4.45849e27	0.426562
$891$	−1.09206e27	−0.103374
$892$	−8.07652e27	−0.756411
$893$	1.47529e28	1.36706
$894$	−5.94650e27	−0.545199
$895$	−9.15288e27	−0.830308
$896$	8.39120e26	0.0753178
$897$	−1.27773e28	−1.13477
$898$	−1.93702e27	−0.170219
$899$	1.56442e27	0.136030
$900$	−2.68783e27	−0.231259
$901$	1.41354e28	1.20343
$902$	−7.05999e26	−0.0594760
$903$	1.00877e27	0.0840927
$904$	6.52905e27	0.538579
$905$	2.47957e28	2.02402
$906$	2.68323e27	0.216740
$907$	3.72744e27	0.297948	0.148974	−	0.988841i	$-0.452403\pi$
$907$	3.72744e27	0.297948	0.148974	+	0.988841i	$0.452403\pi$
$908$	1.07630e28	0.851365
$909$	1.50240e28	1.17606
$910$	−1.56681e28	−1.21374
$911$	2.33604e28	1.79083	0.895417	−	0.445227i	$-0.146877\pi$
$911$	2.33604e28	1.79083	0.895417	+	0.445227i	$0.146877\pi$
$912$	−1.60267e27	−0.121588
$913$	2.56486e27	0.192571
$914$	−1.05352e28	−0.782804
$915$	8.98797e27	0.660939
$916$	4.95677e27	0.360738
$917$	1.22945e27	0.0885529
$918$	6.92078e27	0.493344
$919$	1.36233e28	0.961137	0.480569	−	0.876957i	$-0.340430\pi$
$919$	1.36233e28	0.961137	0.480569	+	0.876957i	$0.340430\pi$
$920$	9.39705e27	0.656156
$921$	−5.56829e27	−0.384818
$922$	1.63136e28	1.11585
$923$	−1.18042e28	−0.799134
$924$	−9.35134e26	−0.0626599
$925$	2.45279e27	0.162673
$926$	8.22626e27	0.540006
$927$	−2.16647e28	−1.40765
$928$	−2.23662e27	−0.143842
$929$	−9.91907e27	−0.631425	−0.315712	−	0.948855i	$-0.602243\pi$
$929$	−9.91907e27	−0.631425	−0.315712	+	0.948855i	$0.602243\pi$
$930$	1.16000e27	0.0730918
$931$	4.37852e27	0.273090
$932$	−1.33992e27	−0.0827231
$933$	1.22845e28	0.750728
$934$	−5.12712e27	−0.310154
$935$	−5.18126e27	−0.310259
$936$	−7.22300e27	−0.428151
$937$	7.25562e26	0.0425744	0.0212872	−	0.999773i	$-0.493224\pi$
$937$	7.25562e26	0.0425744	0.0212872	+	0.999773i	$0.493224\pi$
$938$	−8.90364e27	−0.517179
$939$	−7.27168e27	−0.418130
$940$	1.52662e28	0.868993
$941$	−3.02283e28	−1.70338	−0.851691	−	0.524045i	$-0.824423\pi$
$941$	−3.02283e28	−1.70338	−0.851691	+	0.524045i	$0.824423\pi$
$942$	7.25645e27	0.404800
$943$	−7.39555e27	−0.408422
$944$	8.70691e27	0.476025
$945$	1.71530e28	0.928408
$946$	−8.05001e26	−0.0431351
$947$	1.94047e28	1.02939	0.514697	−	0.857372i	$-0.327905\pi$
$947$	1.94047e28	1.02939	0.514697	+	0.857372i	$0.327905\pi$
$948$	6.40588e27	0.336434
$949$	−2.86722e28	−1.49084
$950$	−8.31237e27	−0.427908
$951$	−1.07776e28	−0.549296
$952$	−4.84656e27	−0.244559
$953$	2.71812e28	1.35796	0.678978	−	0.734158i	$-0.262423\pi$
$953$	2.71812e28	1.35796	0.678978	+	0.734158i	$0.262423\pi$
$954$	1.61508e28	0.798885
$955$	1.89917e28	0.930106
$956$	−4.80263e27	−0.232878
$957$	2.49254e27	0.119668
$958$	−2.27792e28	−1.08284
$959$	1.19459e28	0.562265
$960$	−1.65843e27	−0.0772894
$961$	−2.10650e28	−0.972052
$962$	6.59138e27	0.301171
$963$	5.51157e27	0.249359
$964$	−7.92424e27	−0.354998
$965$	1.54024e28	0.683247
$966$	−9.79580e27	−0.430286
$967$	−1.17983e28	−0.513180	−0.256590	−	0.966520i	$-0.582599\pi$
$967$	−1.17983e28	−0.513180	−0.256590	+	0.966520i	$0.582599\pi$
$968$	7.46239e26	0.0321412
$969$	9.25663e27	0.394800
$970$	−3.81413e28	−1.61088
$971$	3.75278e28	1.56953	0.784766	−	0.619792i	$-0.212783\pi$
$971$	3.75278e28	1.56953	0.784766	+	0.619792i	$0.212783\pi$
$972$	1.23951e28	0.513360
$973$	1.96252e27	0.0804901
$974$	1.45057e28	0.589155
$975$	1.16956e28	0.470414
$976$	−6.70911e27	−0.267234
$977$	6.88365e27	0.271532	0.135766	−	0.990741i	$-0.456651\pi$
$977$	6.88365e27	0.271532	0.135766	+	0.990741i	$0.456651\pi$
$978$	−6.74583e27	−0.263522
$979$	3.70886e27	0.143484
$980$	4.53087e27	0.173594
$981$	−6.46041e27	−0.245135
$982$	−1.69752e28	−0.637904
$983$	−4.49594e27	−0.167325	−0.0836627	−	0.996494i	$-0.526662\pi$
$983$	−4.49594e27	−0.167325	−0.0836627	+	0.996494i	$0.526662\pi$
$984$	1.30519e27	0.0481085
$985$	3.10339e28	1.13290
$986$	1.29182e28	0.467059
$987$	−1.59140e28	−0.569858
$988$	−2.23378e28	−0.792225
$989$	−8.43262e27	−0.296209
$990$	−5.91999e27	−0.205962
$991$	−2.89277e28	−0.996815	−0.498408	−	0.866943i	$-0.666082\pi$
$991$	−2.89277e28	−0.996815	−0.498408	+	0.866943i	$0.666082\pi$
$992$	−8.65884e26	−0.0295528
$993$	1.12279e28	0.379561
$994$	−9.04978e27	−0.303017
$995$	1.27747e28	0.423675
$996$	−4.74171e27	−0.155765
$997$	2.16606e28	0.704801	0.352401	−	0.935849i	$-0.385365\pi$
$997$	2.16606e28	0.704801	0.352401	+	0.935849i	$0.385365\pi$
$998$	−1.88849e28	−0.608658
$999$	−7.21605e27	−0.230371

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.20.a.b.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.20.a.b.1.2	✓	2	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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	22.a (trivial)

\(f(q)\)	\(=\)	\(q+512.000 q^{2} +16629.0 q^{3} +262144. q^{4} -5.53619e6 q^{5} +8.51403e6 q^{6} +9.09776e7 q^{7} +1.34218e8 q^{8} -8.85739e8 q^{9} +O(q^{10})\)	\(q+512.000 q^{2} +16629.0 q^{3} +262144. q^{4} -5.53619e6 q^{5} +8.51403e6 q^{6} +9.09776e7 q^{7} +1.34218e8 q^{8} -8.85739e8 q^{9} -2.83453e9 q^{10} -2.35795e9 q^{11} +4.35919e9 q^{12} +6.07578e10 q^{13} +4.65805e10 q^{14} -9.20612e10 q^{15} +6.87195e10 q^{16} -3.96908e11 q^{17} -4.53498e11 q^{18} -1.40248e12 q^{19} -1.45128e12 q^{20} +1.51286e12 q^{21} -1.20727e12 q^{22} -1.26465e13 q^{23} +2.23190e12 q^{24} +1.15760e13 q^{25} +3.11080e13 q^{26} -3.40561e13 q^{27} +2.38492e13 q^{28} -6.35686e13 q^{29} -4.71353e13 q^{30} -2.46099e13 q^{31} +3.51844e13 q^{32} -3.92102e13 q^{33} -2.03217e14 q^{34} -5.03669e14 q^{35} -2.32191e14 q^{36} +2.11887e14 q^{37} -7.18072e14 q^{38} +1.01034e15 q^{39} -7.43055e14 q^{40} +5.84790e14 q^{41} +7.74586e14 q^{42} +6.66795e14 q^{43} -6.18122e14 q^{44} +4.90362e15 q^{45} -6.47501e15 q^{46} -1.05191e16 q^{47} +1.14273e15 q^{48} -3.12198e15 q^{49} +5.92689e15 q^{50} -6.60017e15 q^{51} +1.59273e16 q^{52} -3.56138e16 q^{53} -1.74367e16 q^{54} +1.30541e16 q^{55} +1.22108e16 q^{56} -2.33219e16 q^{57} -3.25471e16 q^{58} +1.26702e17 q^{59} -2.41333e16 q^{60} -9.76304e16 q^{61} -1.26003e16 q^{62} -8.05824e16 q^{63} +1.80144e16 q^{64} -3.36367e17 q^{65} -2.00756e16 q^{66} -1.91145e17 q^{67} -1.04047e17 q^{68} -2.10298e17 q^{69} -2.57879e17 q^{70} -1.94283e17 q^{71} -1.18882e17 q^{72} -4.71910e17 q^{73} +1.08486e17 q^{74} +1.92496e17 q^{75} -3.67653e17 q^{76} -2.14520e17 q^{77} +5.17294e17 q^{78} +1.46951e18 q^{79} -3.80444e17 q^{80} +4.63142e17 q^{81} +2.99412e17 q^{82} -1.08775e18 q^{83} +3.96588e17 q^{84} +2.19736e18 q^{85} +3.41399e17 q^{86} -1.05708e18 q^{87} -3.16478e17 q^{88} -1.57292e18 q^{89} +2.51065e18 q^{90} +5.52760e18 q^{91} -3.31520e18 q^{92} -4.09237e17 q^{93} -5.38579e18 q^{94} +7.76442e18 q^{95} +5.85080e17 q^{96} +1.34559e19 q^{97} -1.59845e18 q^{98} +2.08853e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 1024 q^{2} + 16974 q^{3} + 524288 q^{4} - 2948510 q^{5} + 8690688 q^{6} + 84929956 q^{7} + 268435456 q^{8} - 2047881204 q^{9}+O(q^{10}) \) 2 * q + 1024 * q^2 + 16974 * q^3 + 524288 * q^4 - 2948510 * q^5 + 8690688 * q^6 + 84929956 * q^7 + 268435456 * q^8 - 2047881204 * q^9	\( 2 q + 1024 q^{2} + 16974 q^{3} + 524288 q^{4} - 2948510 q^{5} + 8690688 q^{6} + 84929956 q^{7} + 268435456 q^{8} - 2047881204 q^{9} - 1509637120 q^{10} - 4715895382 q^{11} + 4449632256 q^{12} + 12931357856 q^{13} + 43484137472 q^{14} - 91168385490 q^{15} + 137438953472 q^{16} - 459787304876 q^{17} - 1048515176448 q^{18} - 1766628927912 q^{19} - 772934205440 q^{20} + 1510776580572 q^{21} - 2414538435584 q^{22} - 3266600096146 q^{23} + 2278211715072 q^{24} - 801420243000 q^{25} + 6620855222272 q^{26} - 34858123423398 q^{27} + 22263878385664 q^{28} - 97113536421264 q^{29} - 46678213370880 q^{30} - 154254203154130 q^{31} + 70368744177664 q^{32} - 40023804107034 q^{33} - 235411100096512 q^{34} - 519318683122780 q^{35} - 536839770341376 q^{36} - 571392764844202 q^{37} - 904514011090944 q^{38} + 993838018166208 q^{39} - 395742313185280 q^{40} - 184921680043224 q^{41} + 773517609252864 q^{42} + 21\!\cdots\!04 q^{43}+ \cdots + 48\!\cdots\!64 q^{99}+O(q^{100}) \) 2 * q + 1024 * q^2 + 16974 * q^3 + 524288 * q^4 - 2948510 * q^5 + 8690688 * q^6 + 84929956 * q^7 + 268435456 * q^8 - 2047881204 * q^9 - 1509637120 * q^10 - 4715895382 * q^11 + 4449632256 * q^12 + 12931357856 * q^13 + 43484137472 * q^14 - 91168385490 * q^15 + 137438953472 * q^16 - 459787304876 * q^17 - 1048515176448 * q^18 - 1766628927912 * q^19 - 772934205440 * q^20 + 1510776580572 * q^21 - 2414538435584 * q^22 - 3266600096146 * q^23 + 2278211715072 * q^24 - 801420243000 * q^25 + 6620855222272 * q^26 - 34858123423398 * q^27 + 22263878385664 * q^28 - 97113536421264 * q^29 - 46678213370880 * q^30 - 154254203154130 * q^31 + 70368744177664 * q^32 - 40023804107034 * q^33 - 235411100096512 * q^34 - 519318683122780 * q^35 - 536839770341376 * q^36 - 571392764844202 * q^37 - 904514011090944 * q^38 + 993838018166208 * q^39 - 395742313185280 * q^40 - 184921680043224 * q^41 + 773517609252864 * q^42 + 2116703700483204 * q^43 - 1236243679019008 * q^44 + 1896364379272140 * q^45 - 1672499249226752 * q^46 - 7456201298413488 * q^47 + 1166444398116864 * q^48 - 14484301062165318 * q^49 - 410327164416000 * q^50 - 6621865965055188 * q^51 + 3389877873803264 * q^52 - 14846639027241356 * q^53 - 17847359192779776 * q^54 + 6952432346390410 * q^55 + 11399105733459968 * q^56 - 23447497932939960 * q^57 - 49722130647687168 * q^58 + 27278259292488522 * q^59 - 23899245245890560 * q^60 - 221405767994019480 * q^61 - 78978152014914560 * q^62 - 73554176903617512 * q^63 + 36028797018963968 * q^64 - 460126589237118240 * q^65 - 20492187702801408 * q^66 - 211824895464439422 * q^67 - 120530483249414144 * q^68 - 207061904815621470 * q^69 - 265891165758863360 * q^70 - 752788827699476886 * q^71 - 274861962414784512 * q^72 - 1171002362670305344 * q^73 - 292553095600231424 * q^74 + 188225715573790200 * q^75 - 463111173678563328 * q^76 - 200260393646931596 * q^77 + 508845065301098496 * q^78 + 1558374634535268220 * q^79 - 202620064350863360 * q^80 + 1813578176100871890 * q^81 - 94679900182130688 * q^82 + 974129749376372 * q^83 + 396041015937466368 * q^84 + 2034647452871174740 * q^85 + 1083752294647400448 * q^86 - 1068654199999982256 * q^87 - 632956763657732096 * q^88 + 3903208985507920622 * q^89 + 970938562187335680 * q^90 + 5816830265117419168 * q^91 - 856319615604097024 * q^92 - 453968381403456030 * q^93 - 3817575064787705856 * q^94 + 6822127176303479320 * q^95 + 597219531835834368 * q^96 + 17667658647655093842 * q^97 - 7415962143828642816 * q^98 + 4828796756414099964 * q^99

Introduction

L-functions

Modular forms

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