LMFDB - Embedded newform 5.18.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,18,Mod(1,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, 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("5.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	5.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:	$9.16110436723$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 50686x + 2014936 $ x^3 - x^2 - 50686*x + 2014936
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$41.0886$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-42.1772 q^{2} -13886.4 q^{3} -129293. q^{4} +390625. q^{5} +585688. q^{6} +3.78919e6 q^{7} +1.09815e7 q^{8} +6.36910e7 q^{9} +O(q^{10})$	\(q-42.1772 q^{2} -13886.4 q^{3} -129293. q^{4} +390625. q^{5} +585688. q^{6} +3.78919e6 q^{7} +1.09815e7 q^{8} +6.36910e7 q^{9} -1.64755e7 q^{10} +1.01532e9 q^{11} +1.79541e9 q^{12} +5.30372e8 q^{13} -1.59817e8 q^{14} -5.42436e9 q^{15} +1.64835e10 q^{16} +3.99398e8 q^{17} -2.68631e9 q^{18} -1.38618e11 q^{19} -5.05051e10 q^{20} -5.26180e10 q^{21} -4.28235e10 q^{22} +6.06190e11 q^{23} -1.52493e11 q^{24} +1.52588e11 q^{25} -2.23696e10 q^{26} +9.08851e11 q^{27} -4.89916e11 q^{28} +2.50344e12 q^{29} +2.28784e11 q^{30} -8.40914e11 q^{31} -2.13459e12 q^{32} -1.40992e13 q^{33} -1.68455e10 q^{34} +1.48015e12 q^{35} -8.23481e12 q^{36} +1.79717e13 q^{37} +5.84651e12 q^{38} -7.36493e12 q^{39} +4.28964e12 q^{40} +2.61986e13 q^{41} +2.21928e12 q^{42} +1.23806e14 q^{43} -1.31274e14 q^{44} +2.48793e13 q^{45} -2.55674e13 q^{46} +2.31632e14 q^{47} -2.28896e14 q^{48} -2.18273e14 q^{49} -6.43573e12 q^{50} -5.54619e12 q^{51} -6.85734e13 q^{52} -6.10408e14 q^{53} -3.83328e13 q^{54} +3.96611e14 q^{55} +4.16108e13 q^{56} +1.92490e15 q^{57} -1.05588e14 q^{58} -1.81598e14 q^{59} +7.01333e14 q^{60} -1.07634e15 q^{61} +3.54674e13 q^{62} +2.41337e14 q^{63} -2.07050e15 q^{64} +2.07176e14 q^{65} +5.94663e14 q^{66} +4.63577e15 q^{67} -5.16394e13 q^{68} -8.41778e15 q^{69} -6.24286e13 q^{70} -4.09643e15 q^{71} +6.99421e14 q^{72} -3.39518e15 q^{73} -7.57996e14 q^{74} -2.11889e15 q^{75} +1.79223e16 q^{76} +3.84725e15 q^{77} +3.10632e14 q^{78} +1.66069e16 q^{79} +6.43888e15 q^{80} -2.08457e16 q^{81} -1.10498e15 q^{82} -2.02111e15 q^{83} +6.80315e15 q^{84} +1.56015e14 q^{85} -5.22178e15 q^{86} -3.47637e16 q^{87} +1.11497e16 q^{88} +2.41537e16 q^{89} -1.04934e15 q^{90} +2.00968e15 q^{91} -7.83762e16 q^{92} +1.16772e16 q^{93} -9.76959e15 q^{94} -5.41476e16 q^{95} +2.96417e16 q^{96} +3.35090e16 q^{97} +9.20612e15 q^{98} +6.46670e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 118 q^{2} + 15944 q^{3} + 16916 q^{4} + 1171875 q^{5} - 2419064 q^{6} + 2139308 q^{7} + 65050440 q^{8} + 323892439 q^{9}+O(q^{10}) $ 3 * q + 118 * q^2 + 15944 * q^3 + 16916 * q^4 + 1171875 * q^5 - 2419064 * q^6 + 2139308 * q^7 + 65050440 * q^8 + 323892439 * q^9	\( 3 q + 118 q^{2} + 15944 q^{3} + 16916 q^{4} + 1171875 q^{5} - 2419064 q^{6} + 2139308 q^{7} + 65050440 q^{8} + 323892439 q^{9} + 46093750 q^{10} + 1789747516 q^{11} + 3112179088 q^{12} + 5414696794 q^{13} + 10507173312 q^{14} + 6228125000 q^{15} - 16203699952 q^{16} - 27402303962 q^{17} - 142746901186 q^{18} - 29956565300 q^{19} + 6607812500 q^{20} - 224495442624 q^{21} - 294714945304 q^{22} + 16254077844 q^{23} + 897428301600 q^{24} + 457763671875 q^{25} + 2017382699956 q^{26} + 3131715461840 q^{27} + 1119244517216 q^{28} - 2528278831750 q^{29} - 944946875000 q^{30} - 521256054664 q^{31} - 10880399775712 q^{32} + 1732417161568 q^{33} - 32147385667828 q^{34} + 835667187500 q^{35} - 14985377520892 q^{36} + 31762746900498 q^{37} - 40258035935240 q^{38} + 43003853320688 q^{39} + 25410328125000 q^{40} + 86833482954446 q^{41} + 153974403759936 q^{42} + 89258046385744 q^{43} - 124942202946448 q^{44} + 126520483984375 q^{45} - 323339762673024 q^{46} + 348182738140228 q^{47} - 729510516165056 q^{48} - 387320833396229 q^{49} + 18005371093750 q^{50} - 12409602773744 q^{51} + 552556858385688 q^{52} + 44014499212594 q^{53} - 22\!\cdots\!00 q^{54}+ \cdots + 29\!\cdots\!08 q^{99}+O(q^{100}) \) 3 * q + 118 * q^2 + 15944 * q^3 + 16916 * q^4 + 1171875 * q^5 - 2419064 * q^6 + 2139308 * q^7 + 65050440 * q^8 + 323892439 * q^9 + 46093750 * q^10 + 1789747516 * q^11 + 3112179088 * q^12 + 5414696794 * q^13 + 10507173312 * q^14 + 6228125000 * q^15 - 16203699952 * q^16 - 27402303962 * q^17 - 142746901186 * q^18 - 29956565300 * q^19 + 6607812500 * q^20 - 224495442624 * q^21 - 294714945304 * q^22 + 16254077844 * q^23 + 897428301600 * q^24 + 457763671875 * q^25 + 2017382699956 * q^26 + 3131715461840 * q^27 + 1119244517216 * q^28 - 2528278831750 * q^29 - 944946875000 * q^30 - 521256054664 * q^31 - 10880399775712 * q^32 + 1732417161568 * q^33 - 32147385667828 * q^34 + 835667187500 * q^35 - 14985377520892 * q^36 + 31762746900498 * q^37 - 40258035935240 * q^38 + 43003853320688 * q^39 + 25410328125000 * q^40 + 86833482954446 * q^41 + 153974403759936 * q^42 + 89258046385744 * q^43 - 124942202946448 * q^44 + 126520483984375 * q^45 - 323339762673024 * q^46 + 348182738140228 * q^47 - 729510516165056 * q^48 - 387320833396229 * q^49 + 18005371093750 * q^50 - 12409602773744 * q^51 + 552556858385688 * q^52 + 44014499212594 * q^53 - 2265337034433200 * q^54 + 699120123437500 * q^55 - 490455582129600 * q^56 + 4293013923032480 * q^57 + 597742677475540 * q^58 - 2133293278957100 * q^59 + 1215694956250000 * q^60 + 2822990449991866 * q^61 + 5338539124096416 * q^62 - 4366406213760516 * q^63 - 2533946722090944 * q^64 + 2115115935156250 * q^65 - 4908048881135008 * q^66 + 374173462156688 * q^67 - 6873999340144024 * q^68 - 13800336843711552 * q^69 + 4104364575000000 * q^70 - 9029705707562224 * q^71 + 14996701114647720 * q^72 - 5906564941861106 * q^73 + 2774091820866692 * q^74 + 2432861328125000 * q^75 + 17087125269517200 * q^76 - 5362490012556624 * q^77 + 15760779344737648 * q^78 + 9183397142621600 * q^79 - 6329570293750000 * q^80 + 11504008140536443 * q^81 + 34156701290034076 * q^82 + 15992201117651544 * q^83 + 20750744922079872 * q^84 - 10704024985156250 * q^85 - 41302213526621384 * q^86 - 124899722203208080 * q^87 + 46255695387619680 * q^88 - 31272661736951250 * q^89 - 55760508275781250 * q^90 + 42991889981897896 * q^91 - 161631619485465312 * q^92 - 55524596752956672 * q^93 + 206283262927378352 * q^94 - 11701783320312500 * q^95 - 45608798390141824 * q^96 + 28207632381796278 * q^97 - 22149964169860474 * q^98 + 293120596614370508 * 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 $

$2$	−42.1772	−0.116499	−0.0582496	−	0.998302i	$-0.518552\pi$
$2$	−42.1772	−0.116499	−0.0582496	+	0.998302i	$0.518552\pi$
$3$	−13886.4	−1.22196	−0.610981	−	0.791645i	$-0.709225\pi$
$3$	−13886.4	−1.22196	−0.610981	+	0.791645i	$0.709225\pi$
$4$	−129293.	−0.986428
$5$	390625.	0.447214
$5$	390625.	0.447214
$6$	585688.	0.142358
$7$	3.78919e6	0.248435	0.124217	−	0.992255i	$-0.460358\pi$
$7$	3.78919e6	0.248435	0.124217	+	0.992255i	$0.460358\pi$
$8$	1.09815e7	0.231417
$9$	6.36910e7	0.493193
$10$	−1.64755e7	−0.0521000
$11$	1.01532e9	1.42813	0.714063	−	0.700081i	$-0.246853\pi$
$11$	1.01532e9	1.42813	0.714063	+	0.700081i	$0.246853\pi$
$12$	1.79541e9	1.20538
$13$	5.30372e8	0.180327	0.0901637	−	0.995927i	$-0.471261\pi$
$13$	5.30372e8	0.180327	0.0901637	+	0.995927i	$0.471261\pi$
$14$	−1.59817e8	−0.0289425
$15$	−5.42436e9	−0.546478
$16$	1.64835e10	0.959468
$17$	3.99398e8	0.0138864	0.00694321	−	0.999976i	$-0.497790\pi$
$17$	3.99398e8	0.0138864	0.00694321	+	0.999976i	$0.497790\pi$
$18$	−2.68631e9	−0.0574566
$19$	−1.38618e11	−1.87246	−0.936232	−	0.351381i	$-0.885712\pi$
$19$	−1.38618e11	−1.87246	−0.936232	+	0.351381i	$0.885712\pi$
$20$	−5.05051e10	−0.441144
$21$	−5.26180e10	−0.303578
$22$	−4.28235e10	−0.166375
$23$	6.06190e11	1.61407	0.807035	−	0.590504i	$-0.201071\pi$
$23$	6.06190e11	1.61407	0.807035	+	0.590504i	$0.201071\pi$
$24$	−1.52493e11	−0.282783
$25$	1.52588e11	0.200000
$26$	−2.23696e10	−0.0210080
$27$	9.08851e11	0.619299
$28$	−4.89916e11	−0.245063
$29$	2.50344e12	0.929297	0.464649	−	0.885495i	$-0.346181\pi$
$29$	2.50344e12	0.929297	0.464649	+	0.885495i	$0.346181\pi$
$30$	2.28784e11	0.0636643
$31$	−8.40914e11	−0.177083	−0.0885415	−	0.996072i	$-0.528221\pi$
$31$	−8.40914e11	−0.177083	−0.0885415	+	0.996072i	$0.528221\pi$
$32$	−2.13459e12	−0.343194
$33$	−1.40992e13	−1.74512
$34$	−1.68455e10	−0.00161776
$35$	1.48015e12	0.111103
$36$	−8.23481e12	−0.486499
$37$	1.79717e13	0.841152	0.420576	−	0.907257i	$-0.361828\pi$
$37$	1.79717e13	0.841152	0.420576	+	0.907257i	$0.361828\pi$
$38$	5.84651e12	0.218141
$39$	−7.36493e12	−0.220353
$40$	4.28964e12	0.103493
$41$	2.61986e13	0.512407	0.256204	−	0.966623i	$-0.417528\pi$
$41$	2.61986e13	0.512407	0.256204	+	0.966623i	$0.417528\pi$
$42$	2.21928e12	0.0353666
$43$	1.23806e14	1.61532	0.807660	−	0.589648i	$-0.200734\pi$
$43$	1.23806e14	1.61532	0.807660	+	0.589648i	$0.200734\pi$
$44$	−1.31274e14	−1.40874
$45$	2.48793e13	0.220563
$46$	−2.55674e13	−0.188038
$47$	2.31632e14	1.41895	0.709474	−	0.704731i	$-0.248932\pi$
$47$	2.31632e14	1.41895	0.709474	+	0.704731i	$0.248932\pi$
$48$	−2.28896e14	−1.17243
$49$	−2.18273e14	−0.938280
$50$	−6.43573e12	−0.0232998
$51$	−5.54619e12	−0.0169687
$52$	−6.85734e13	−0.177880
$53$	−6.10408e14	−1.34671	−0.673356	−	0.739318i	$-0.735148\pi$
$53$	−6.10408e14	−1.34671	−0.673356	+	0.739318i	$0.735148\pi$
$54$	−3.83328e13	−0.0721478
$55$	3.96611e14	0.638677
$56$	4.16108e13	0.0574921
$57$	1.92490e15	2.28808
$58$	−1.05588e14	−0.108262
$59$	−1.81598e14	−0.161016	−0.0805082	−	0.996754i	$-0.525654\pi$
$59$	−1.81598e14	−0.161016	−0.0805082	+	0.996754i	$0.525654\pi$
$60$	7.01333e14	0.539062
$61$	−1.07634e15	−0.718862	−0.359431	−	0.933172i	$-0.617029\pi$
$61$	−1.07634e15	−0.718862	−0.359431	+	0.933172i	$0.617029\pi$
$62$	3.54674e13	0.0206300
$63$	2.41337e14	0.122526
$64$	−2.07050e15	−0.919486
$65$	2.07176e14	0.0806449
$66$	5.94663e14	0.203305
$67$	4.63577e15	1.39472	0.697359	−	0.716722i	$-0.254358\pi$
$67$	4.63577e15	1.39472	0.697359	+	0.716722i	$0.254358\pi$
$68$	−5.16394e13	−0.0136980
$69$	−8.41778e15	−1.97233
$70$	−6.24286e13	−0.0129435
$71$	−4.09643e15	−0.752852	−0.376426	−	0.926447i	$-0.622847\pi$
$71$	−4.09643e15	−0.752852	−0.376426	+	0.926447i	$0.622847\pi$
$72$	6.99421e14	0.114133
$73$	−3.39518e15	−0.492740	−0.246370	−	0.969176i	$-0.579238\pi$
$73$	−3.39518e15	−0.492740	−0.246370	+	0.969176i	$0.579238\pi$
$74$	−7.57996e14	−0.0979935
$75$	−2.11889e15	−0.244393
$76$	1.79223e16	1.84705
$77$	3.84725e15	0.354796
$78$	3.10632e14	0.0256710
$79$	1.66069e16	1.23157	0.615786	−	0.787914i	$-0.288839\pi$
$79$	1.66069e16	1.23157	0.615786	+	0.787914i	$0.288839\pi$
$80$	6.43888e15	0.429087
$81$	−2.08457e16	−1.24995
$82$	−1.10498e15	−0.0596950
$83$	−2.02111e15	−0.0984977	−0.0492488	−	0.998787i	$-0.515683\pi$
$83$	−2.02111e15	−0.0984977	−0.0492488	+	0.998787i	$0.515683\pi$
$84$	6.80315e15	0.299458
$85$	1.56015e14	0.00621020
$86$	−5.22178e15	−0.188183
$87$	−3.47637e16	−1.13557
$88$	1.11497e16	0.330493
$89$	2.41537e16	0.650382	0.325191	−	0.945648i	$-0.394571\pi$
$89$	2.41537e16	0.650382	0.325191	+	0.945648i	$0.394571\pi$
$90$	−1.04934e15	−0.0256954
$91$	2.00968e15	0.0447996
$92$	−7.83762e16	−1.59216
$93$	1.16772e16	0.216389
$94$	−9.76959e15	−0.165306
$95$	−5.41476e16	−0.837392
$96$	2.96417e16	0.419371
$97$	3.35090e16	0.434111	0.217056	−	0.976159i	$-0.430355\pi$
$97$	3.35090e16	0.434111	0.217056	+	0.976159i	$0.430355\pi$
$98$	9.20612e15	0.109309
$99$	6.46670e16	0.704342
$100$	−1.97286e16	−0.197286
$101$	8.44564e16	0.776070	0.388035	−	0.921645i	$-0.373154\pi$
$101$	8.44564e16	0.776070	0.388035	+	0.921645i	$0.373154\pi$
$102$	2.33923e14	0.00197684
$103$	1.86200e17	1.44831	0.724156	−	0.689636i	$-0.242229\pi$
$103$	1.86200e17	1.44831	0.724156	+	0.689636i	$0.242229\pi$
$104$	5.82426e15	0.0417308
$105$	−2.05539e16	−0.135764
$106$	2.57453e16	0.156891
$107$	−2.24733e17	−1.26446	−0.632228	−	0.774782i	$-0.717859\pi$
$107$	−2.24733e17	−1.26446	−0.632228	+	0.774782i	$0.717859\pi$
$108$	−1.17508e17	−0.610894
$109$	1.59942e17	0.768845	0.384422	−	0.923157i	$-0.374401\pi$
$109$	1.59942e17	0.768845	0.384422	+	0.923157i	$0.374401\pi$
$110$	−1.67279e16	−0.0744053
$111$	−2.49562e17	−1.02786
$112$	6.24592e16	0.238365
$113$	−1.51067e17	−0.534568	−0.267284	−	0.963618i	$-0.586126\pi$
$113$	−1.51067e17	−0.534568	−0.267284	+	0.963618i	$0.586126\pi$
$114$	−8.11868e16	−0.266560
$115$	2.36793e17	0.721834
$116$	−3.23678e17	−0.916685
$117$	3.37799e16	0.0889362
$118$	7.65931e15	0.0187583
$119$	1.51340e15	0.00344987
$120$	−5.95675e16	−0.126464
$121$	5.25434e17	1.03954
$122$	4.53969e16	0.0837468
$123$	−3.63803e17	−0.626143
$124$	1.08724e17	0.174680
$125$	5.96046e16	0.0894427
$126$	−1.01789e16	−0.0142742
$127$	1.14947e18	1.50719	0.753594	−	0.657340i	$-0.228318\pi$
$127$	1.14947e18	1.50719	0.753594	+	0.657340i	$0.228318\pi$
$128$	3.67113e17	0.450314
$129$	−1.71921e18	−1.97386
$130$	−8.73812e15	−0.00939506
$131$	8.25777e17	0.831872	0.415936	−	0.909394i	$-0.363454\pi$
$131$	8.25777e17	0.831872	0.415936	+	0.909394i	$0.363454\pi$
$132$	1.82292e18	1.72143
$133$	−5.25249e17	−0.465186
$134$	−1.95524e17	−0.162483
$135$	3.55020e17	0.276959
$136$	4.38598e15	0.00321356
$137$	−1.97835e18	−1.36200	−0.681000	−	0.732283i	$-0.738455\pi$
$137$	−1.97835e18	−1.36200	−0.681000	+	0.732283i	$0.738455\pi$
$138$	3.55038e17	0.229775
$139$	−2.06244e18	−1.25532	−0.627662	−	0.778486i	$-0.715988\pi$
$139$	−2.06244e18	−1.25532	−0.627662	+	0.778486i	$0.715988\pi$
$140$	−1.91373e17	−0.109596
$141$	−3.21653e18	−1.73390
$142$	1.72776e17	0.0877066
$143$	5.38499e17	0.257530
$144$	1.04985e18	0.473203
$145$	9.77907e17	0.415594
$146$	1.43199e17	0.0574038
$147$	3.03101e18	1.14654
$148$	−2.32362e18	−0.829736
$149$	3.08686e18	1.04096	0.520479	−	0.853874i	$-0.325753\pi$
$149$	3.08686e18	1.04096	0.520479	+	0.853874i	$0.325753\pi$
$150$	8.93689e16	0.0284715
$151$	1.83595e18	0.552785	0.276393	−	0.961045i	$-0.410861\pi$
$151$	1.83595e18	0.552785	0.276393	+	0.961045i	$0.410861\pi$
$152$	−1.52223e18	−0.433320
$153$	2.54381e16	0.00684869
$154$	−1.62266e17	−0.0413335
$155$	−3.28482e17	−0.0791939
$156$	9.52235e17	0.217363
$157$	−4.03280e18	−0.871885	−0.435943	−	0.899974i	$-0.643585\pi$
$157$	−4.03280e18	−0.871885	−0.435943	+	0.899974i	$0.643585\pi$
$158$	−7.00434e17	−0.143477
$159$	8.47634e18	1.64563
$160$	−8.33825e17	−0.153481
$161$	2.29697e18	0.400991
$162$	8.79213e17	0.145619
$163$	4.47792e18	0.703853	0.351926	−	0.936028i	$-0.385527\pi$
$163$	4.47792e18	0.703853	0.351926	+	0.936028i	$0.385527\pi$
$164$	−3.38730e18	−0.505453
$165$	−5.50748e18	−0.780440
$166$	8.52447e16	0.0114749
$167$	−6.08424e18	−0.778245	−0.389122	−	0.921186i	$-0.627222\pi$
$167$	−6.08424e18	−0.778245	−0.389122	+	0.921186i	$0.627222\pi$
$168$	−5.77823e17	−0.0702532
$169$	−8.36912e18	−0.967482
$170$	−6.58027e15	−0.000723483 0
$171$	−8.82872e18	−0.923487
$172$	−1.60072e19	−1.59340
$173$	1.30121e19	1.23298	0.616491	−	0.787362i	$-0.288554\pi$
$173$	1.30121e19	1.23298	0.616491	+	0.787362i	$0.288554\pi$
$174$	1.46624e18	0.132293
$175$	5.78184e17	0.0496870
$176$	1.67361e19	1.37024
$177$	2.52174e18	0.196756
$178$	−1.01874e18	−0.0757690
$179$	1.79247e19	1.27116	0.635580	−	0.772035i	$-0.280761\pi$
$179$	1.79247e19	1.27116	0.635580	+	0.772035i	$0.280761\pi$
$180$	−3.21672e18	−0.217569
$181$	−1.14651e19	−0.739794	−0.369897	−	0.929073i	$-0.620607\pi$
$181$	−1.14651e19	−0.739794	−0.369897	+	0.929073i	$0.620607\pi$
$182$	−8.47625e16	−0.00521912
$183$	1.49464e19	0.878422
$184$	6.65686e18	0.373523
$185$	7.02020e18	0.376175
$186$	−4.92513e17	−0.0252091
$187$	4.05518e17	0.0198316
$188$	−2.99484e19	−1.39969
$189$	3.44380e18	0.153856
$190$	2.28379e18	0.0975554
$191$	2.17524e18	0.0888636	0.0444318	−	0.999012i	$-0.485852\pi$
$191$	2.17524e18	0.0888636	0.0444318	+	0.999012i	$0.485852\pi$
$192$	2.87517e19	1.12358
$193$	−3.00822e19	−1.12479	−0.562396	−	0.826868i	$-0.690120\pi$
$193$	−3.00822e19	−1.12479	−0.562396	+	0.826868i	$0.690120\pi$
$194$	−1.41331e18	−0.0505736
$195$	−2.87693e18	−0.0985450
$196$	2.82211e19	0.925546
$197$	−4.06840e18	−0.127779	−0.0638896	−	0.997957i	$-0.520351\pi$
$197$	−4.06840e18	−0.127779	−0.0638896	+	0.997957i	$0.520351\pi$
$198$	−2.72747e18	−0.0820552
$199$	−2.36604e19	−0.681979	−0.340990	−	0.940067i	$-0.610762\pi$
$199$	−2.36604e19	−0.681979	−0.340990	+	0.940067i	$0.610762\pi$
$200$	1.67564e18	0.0462834
$201$	−6.43741e19	−1.70429
$202$	−3.56213e18	−0.0904114
$203$	9.48601e18	0.230870
$204$	7.17084e17	0.0167384
$205$	1.02338e19	0.229155
$206$	−7.85338e18	−0.168727
$207$	3.86089e19	0.796048
$208$	8.74240e18	0.173018
$209$	−1.40742e20	−2.67412
$210$	8.66907e17	0.0158164
$211$	4.58187e19	0.802865	0.401432	−	0.915889i	$-0.368513\pi$
$211$	4.58187e19	0.802865	0.401432	+	0.915889i	$0.368513\pi$
$212$	7.89215e19	1.32844
$213$	5.68846e19	0.919957
$214$	9.47859e18	0.147308
$215$	4.83616e19	0.722393
$216$	9.98051e18	0.143316
$217$	−3.18638e18	−0.0439936
$218$	−6.74592e18	−0.0895697
$219$	4.71467e19	0.602110
$220$	−5.12790e19	−0.630009
$221$	2.11830e17	0.00250410
$222$	1.05258e19	0.119744
$223$	5.43096e19	0.594683	0.297341	−	0.954771i	$-0.403900\pi$
$223$	5.43096e19	0.594683	0.297341	+	0.954771i	$0.403900\pi$
$224$	−8.08837e18	−0.0852615
$225$	9.71848e18	0.0986386
$226$	6.37159e18	0.0622767
$227$	−2.64296e19	−0.248812	−0.124406	−	0.992231i	$-0.539703\pi$
$227$	−2.64296e19	−0.248812	−0.124406	+	0.992231i	$0.539703\pi$
$228$	−2.48876e20	−2.25703
$229$	3.64008e19	0.318061	0.159030	−	0.987274i	$-0.449163\pi$
$229$	3.64008e19	0.318061	0.159030	+	0.987274i	$0.449163\pi$
$230$	−9.98726e18	−0.0840930
$231$	−5.34243e19	−0.433548
$232$	2.74915e19	0.215055
$233$	−3.64819e19	−0.275139	−0.137569	−	0.990492i	$-0.543929\pi$
$233$	−3.64819e19	−0.275139	−0.137569	+	0.990492i	$0.543929\pi$
$234$	−1.42474e18	−0.0103610
$235$	9.04812e19	0.634573
$236$	2.34794e19	0.158831
$237$	−2.30610e20	−1.50493
$238$	−6.38307e16	−0.000401907 0
$239$	1.51343e20	0.919560	0.459780	−	0.888033i	$-0.347928\pi$
$239$	1.51343e20	0.919560	0.459780	+	0.888033i	$0.347928\pi$
$240$	−8.94127e19	−0.524329
$241$	9.78430e18	0.0553841	0.0276920	−	0.999617i	$-0.491184\pi$
$241$	9.78430e18	0.0553841	0.0276920	+	0.999617i	$0.491184\pi$
$242$	−2.21613e19	−0.121106
$243$	1.72102e20	0.908098
$244$	1.39163e20	0.709105
$245$	−8.52627e19	−0.419612
$246$	1.53442e19	0.0729451
$247$	−7.35190e19	−0.337657
$248$	−9.23447e18	−0.0409800
$249$	2.80659e19	0.120361
$250$	−2.51396e18	−0.0104200
$251$	−1.76177e20	−0.705865	−0.352933	−	0.935649i	$-0.614816\pi$
$251$	−1.76177e20	−0.705865	−0.352933	+	0.935649i	$0.614816\pi$
$252$	−3.12032e19	−0.120863
$253$	6.15479e20	2.30509
$254$	−4.84816e19	−0.175586
$255$	−2.16648e18	−0.00758863
$256$	2.55901e20	0.867025
$257$	−1.26700e20	−0.415285	−0.207643	−	0.978205i	$-0.566579\pi$
$257$	−1.26700e20	−0.415285	−0.207643	+	0.978205i	$0.566579\pi$
$258$	7.25115e19	0.229953
$259$	6.80981e19	0.208972
$260$	−2.67865e19	−0.0795504
$261$	1.59447e20	0.458323
$262$	−3.48289e19	−0.0969124
$263$	−1.55965e20	−0.420149	−0.210074	−	0.977685i	$-0.567371\pi$
$263$	−1.55965e20	−0.420149	−0.210074	+	0.977685i	$0.567371\pi$
$264$	−1.54829e20	−0.403850
$265$	−2.38440e20	−0.602268
$266$	2.21535e19	0.0541937
$267$	−3.35407e20	−0.794743
$268$	−5.99373e20	−1.37579
$269$	7.52340e19	0.167309	0.0836546	−	0.996495i	$-0.473341\pi$
$269$	7.52340e19	0.167309	0.0836546	+	0.996495i	$0.473341\pi$
$270$	−1.49737e19	−0.0322655
$271$	−7.50387e20	−1.56692	−0.783459	−	0.621443i	$-0.786547\pi$
$271$	−7.50387e20	−1.56692	−0.783459	+	0.621443i	$0.786547\pi$
$272$	6.58350e18	0.0133236
$273$	−2.79071e19	−0.0547435
$274$	8.34411e19	0.158672
$275$	1.54926e20	0.285625
$276$	1.08836e21	1.94556
$277$	6.13765e20	1.06396	0.531979	−	0.846758i	$-0.321449\pi$
$277$	6.13765e20	1.06396	0.531979	+	0.846758i	$0.321449\pi$
$278$	8.69879e19	0.146244
$279$	−5.35587e19	−0.0873361
$280$	1.62542e19	0.0257112
$281$	−6.85305e20	−1.05167	−0.525836	−	0.850586i	$-0.676247\pi$
$281$	−6.85305e20	−1.05167	−0.525836	+	0.850586i	$0.676247\pi$
$282$	1.35664e20	0.201998
$283$	−7.53488e20	−1.08866	−0.544329	−	0.838872i	$-0.683216\pi$
$283$	−7.53488e20	−1.08866	−0.544329	+	0.838872i	$0.683216\pi$
$284$	5.29640e20	0.742635
$285$	7.51914e20	1.02326
$286$	−2.27124e19	−0.0300020
$287$	9.92714e19	0.127300
$288$	−1.35954e20	−0.169261
$289$	−8.27081e20	−0.999807
$290$	−4.12454e19	−0.0484164
$291$	−4.65318e20	−0.530468
$292$	4.38973e20	0.486053
$293$	1.65093e21	1.77563	0.887817	−	0.460197i	$-0.152221\pi$
$293$	1.65093e21	1.77563	0.887817	+	0.460197i	$0.152221\pi$
$294$	−1.27840e20	−0.133571
$295$	−7.09369e19	−0.0720087
$296$	1.97356e20	0.194657
$297$	9.22777e20	0.884437
$298$	−1.30195e20	−0.121271
$299$	3.21506e20	0.291061
$300$	2.73958e20	0.241076
$301$	4.69123e20	0.401302
$302$	−7.74351e19	−0.0643990
$303$	−1.17279e21	−0.948328
$304$	−2.28491e21	−1.79657
$305$	−4.20445e20	−0.321485
$306$	−1.07291e18	−0.000797866 0
$307$	5.65284e20	0.408875	0.204437	−	0.978880i	$-0.434464\pi$
$307$	5.65284e20	0.408875	0.204437	+	0.978880i	$0.434464\pi$
$308$	−4.97423e20	−0.349981
$309$	−2.58564e21	−1.76978
$310$	1.38544e19	0.00922603
$311$	1.90250e20	0.123271	0.0616357	−	0.998099i	$-0.480368\pi$
$311$	1.90250e20	0.123271	0.0616357	+	0.998099i	$0.480368\pi$
$312$	−8.08778e19	−0.0509935
$313$	5.24312e20	0.321709	0.160854	−	0.986978i	$-0.448575\pi$
$313$	5.24312e20	0.321709	0.160854	+	0.986978i	$0.448575\pi$
$314$	1.70092e20	0.101574
$315$	9.42724e19	0.0547955
$316$	−2.14716e21	−1.21486
$317$	1.01628e21	0.559771	0.279886	−	0.960033i	$-0.409703\pi$
$317$	1.01628e21	0.559771	0.279886	+	0.960033i	$0.409703\pi$
$318$	−3.57508e20	−0.191715
$319$	2.54180e21	1.32715
$320$	−8.08789e20	−0.411207
$321$	3.12072e21	1.54512
$322$	−9.68796e19	−0.0467151
$323$	−5.53638e19	−0.0260018
$324$	2.69521e21	1.23299
$325$	8.09283e19	0.0360655
$326$	−1.88866e20	−0.0819983
$327$	−2.22102e21	−0.939500
$328$	2.87699e20	0.118580
$329$	8.77697e20	0.352516
$330$	2.32290e20	0.0909206
$331$	−8.05098e20	−0.307122	−0.153561	−	0.988139i	$-0.549074\pi$
$331$	−8.05098e20	−0.307122	−0.153561	+	0.988139i	$0.549074\pi$
$332$	2.61315e20	0.0971609
$333$	1.14464e21	0.414851
$334$	2.56616e20	0.0906648
$335$	1.81085e21	0.623737
$336$	−8.67331e20	−0.291274
$337$	−3.18366e21	−1.04249	−0.521246	−	0.853407i	$-0.674532\pi$
$337$	−3.18366e21	−1.04249	−0.521246	+	0.853407i	$0.674532\pi$
$338$	3.52986e20	0.112711
$339$	2.09777e21	0.653222
$340$	−2.01717e19	−0.00612591
$341$	−8.53799e20	−0.252897
$342$	3.72370e20	0.107585
$343$	−1.70856e21	−0.481536
$344$	1.35957e21	0.373813
$345$	−3.28819e21	−0.882054
$346$	−5.48815e20	−0.143641
$347$	−5.49531e21	−1.40343	−0.701717	−	0.712456i	$-0.747583\pi$
$347$	−5.49531e21	−1.40343	−0.701717	+	0.712456i	$0.747583\pi$
$348$	4.49471e21	1.12015
$349$	1.02212e21	0.248591	0.124296	−	0.992245i	$-0.460333\pi$
$349$	1.02212e21	0.248591	0.124296	+	0.992245i	$0.460333\pi$
$350$	−2.43862e19	−0.00578849
$351$	4.82028e20	0.111677
$352$	−2.16730e21	−0.490125
$353$	−1.55835e20	−0.0344016	−0.0172008	−	0.999852i	$-0.505475\pi$
$353$	−1.55835e20	−0.0344016	−0.0172008	+	0.999852i	$0.505475\pi$
$354$	−1.06360e20	−0.0229219
$355$	−1.60017e21	−0.336686
$356$	−3.12291e21	−0.641555
$357$	−2.10156e19	−0.00421562
$358$	−7.56011e20	−0.148089
$359$	−5.81313e21	−1.11201	−0.556003	−	0.831180i	$-0.687666\pi$
$359$	−5.81313e21	−1.11201	−0.556003	+	0.831180i	$0.687666\pi$
$360$	2.73211e20	0.0510420
$361$	1.37345e22	2.50612
$362$	4.83566e20	0.0861853
$363$	−7.29637e21	−1.27028
$364$	−2.59837e20	−0.0441916
$365$	−1.32624e21	−0.220360
$366$	−6.30399e20	−0.102335
$367$	7.28071e21	1.15481	0.577407	−	0.816456i	$-0.304064\pi$
$367$	7.28071e21	1.15481	0.577407	+	0.816456i	$0.304064\pi$
$368$	9.99216e21	1.54865
$369$	1.66862e21	0.252716
$370$	−2.96092e20	−0.0438240
$371$	−2.31295e21	−0.334571
$372$	−1.50979e21	−0.213452
$373$	5.23119e21	0.722896	0.361448	−	0.932392i	$-0.382283\pi$
$373$	5.23119e21	0.722896	0.361448	+	0.932392i	$0.382283\pi$
$374$	−1.71036e19	−0.00231036
$375$	−8.27692e20	−0.109296
$376$	2.54366e21	0.328369
$377$	1.32775e21	0.167578
$378$	−1.45250e20	−0.0179240
$379$	7.81275e21	0.942693	0.471347	−	0.881948i	$-0.343768\pi$
$379$	7.81275e21	0.942693	0.471347	+	0.881948i	$0.343768\pi$
$380$	7.00091e21	0.826027
$381$	−1.59620e22	−1.84173
$382$	−9.17456e19	−0.0103525
$383$	−9.53032e21	−1.05176	−0.525881	−	0.850558i	$-0.676264\pi$
$383$	−9.53032e21	−1.05176	−0.525881	+	0.850558i	$0.676264\pi$
$384$	−5.09787e21	−0.550267
$385$	1.50283e21	0.158670
$386$	1.26878e21	0.131037
$387$	7.88531e21	0.796665
$388$	−4.33248e21	−0.428220
$389$	−1.23478e22	−1.19404	−0.597020	−	0.802226i	$-0.703649\pi$
$389$	−1.23478e22	−1.19404	−0.597020	+	0.802226i	$0.703649\pi$
$390$	1.21341e20	0.0114804
$391$	2.42111e20	0.0224137
$392$	−2.39695e21	−0.217134
$393$	−1.14670e22	−1.01652
$394$	1.71593e20	0.0148862
$395$	6.48709e21	0.550775
$396$	−8.36100e21	−0.694783
$397$	9.04594e21	0.735757	0.367879	−	0.929874i	$-0.380084\pi$
$397$	9.04594e21	0.735757	0.367879	+	0.929874i	$0.380084\pi$
$398$	9.97929e20	0.0794500
$399$	7.29380e21	0.568440
$400$	2.51519e21	0.191894
$401$	−7.60801e20	−0.0568256	−0.0284128	−	0.999596i	$-0.509045\pi$
$401$	−7.60801e20	−0.0568256	−0.0284128	+	0.999596i	$0.509045\pi$
$402$	2.71512e21	0.198549
$403$	−4.45997e20	−0.0319329
$404$	−1.09196e22	−0.765537
$405$	−8.14285e21	−0.558996
$406$	−4.00093e20	−0.0268961
$407$	1.82471e22	1.20127
$408$	−6.09053e19	−0.00392685
$409$	−1.20477e22	−0.760775	−0.380388	−	0.924827i	$-0.624209\pi$
$409$	−1.20477e22	−0.760775	−0.380388	+	0.924827i	$0.624209\pi$
$410$	−4.31634e20	−0.0266964
$411$	2.74720e22	1.66431
$412$	−2.40743e22	−1.42866
$413$	−6.88110e20	−0.0400021
$414$	−1.62841e21	−0.0927389
$415$	−7.89496e20	−0.0440495
$416$	−1.13213e21	−0.0618873
$417$	2.86398e22	1.53396
$418$	5.93610e21	0.311532
$419$	7.03075e21	0.361562	0.180781	−	0.983523i	$-0.442138\pi$
$419$	7.03075e21	0.361562	0.180781	+	0.983523i	$0.442138\pi$
$420$	2.65748e21	0.133922
$421$	1.26652e22	0.625480	0.312740	−	0.949839i	$-0.398753\pi$
$421$	1.26652e22	0.625480	0.312740	+	0.949839i	$0.398753\pi$
$422$	−1.93251e21	−0.0935330
$423$	1.47529e22	0.699816
$424$	−6.70317e21	−0.311652
$425$	6.09434e19	0.00277729
$426$	−2.39923e21	−0.107174
$427$	−4.07845e21	−0.178590
$428$	2.90564e22	1.24729
$429$	−7.47779e21	−0.314692
$430$	−2.03976e21	−0.0841582
$431$	−1.44245e22	−0.583505	−0.291753	−	0.956494i	$-0.594238\pi$
$431$	−1.44245e22	−0.583505	−0.291753	+	0.956494i	$0.594238\pi$
$432$	1.49811e22	0.594198
$433$	−4.63518e22	−1.80268	−0.901341	−	0.433110i	$-0.857416\pi$
$433$	−4.63518e22	−1.80268	−0.901341	+	0.433110i	$0.857416\pi$
$434$	1.34392e20	0.00512522
$435$	−1.35796e22	−0.507841
$436$	−2.06795e22	−0.758410
$437$	−8.40288e22	−3.02229
$438$	−1.98851e21	−0.0701453
$439$	1.55581e22	0.538281	0.269140	−	0.963101i	$-0.413260\pi$
$439$	1.55581e22	0.538281	0.269140	+	0.963101i	$0.413260\pi$
$440$	4.35537e21	0.147801
$441$	−1.39020e22	−0.462753
$442$	−8.93437e18	−0.000291726 0
$443$	4.68453e22	1.50049	0.750247	−	0.661158i	$-0.229935\pi$
$443$	4.68453e22	1.50049	0.750247	+	0.661158i	$0.229935\pi$
$444$	3.22666e22	1.01391
$445$	9.43504e21	0.290860
$446$	−2.29063e21	−0.0692800
$447$	−4.28653e22	−1.27201
$448$	−7.84551e21	−0.228433
$449$	4.57919e22	1.30826	0.654131	−	0.756381i	$-0.273034\pi$
$449$	4.57919e22	1.30826	0.654131	+	0.756381i	$0.273034\pi$
$450$	−4.09898e20	−0.0114913
$451$	2.66000e22	0.731782
$452$	1.95319e22	0.527313
$453$	−2.54947e22	−0.675483
$454$	1.11473e21	0.0289864
$455$	7.85030e20	0.0200350
$456$	2.11382e22	0.529501
$457$	1.82733e22	0.449293	0.224646	−	0.974440i	$-0.427877\pi$
$457$	1.82733e22	0.449293	0.224646	+	0.974440i	$0.427877\pi$
$458$	−1.53529e21	−0.0370538
$459$	3.62993e20	0.00859985
$460$	−3.06157e22	−0.712037
$461$	−2.76015e22	−0.630194	−0.315097	−	0.949060i	$-0.602037\pi$
$461$	−2.76015e22	−0.630194	−0.315097	+	0.949060i	$0.602037\pi$
$462$	2.25329e21	0.0505080
$463$	−3.71212e22	−0.816927	−0.408464	−	0.912775i	$-0.633935\pi$
$463$	−3.71212e22	−0.816927	−0.408464	+	0.912775i	$0.633935\pi$
$464$	4.12656e22	0.891631
$465$	4.56142e21	0.0967721
$466$	1.53870e21	0.0320534
$467$	−1.89794e20	−0.00388229	−0.00194115	−	0.999998i	$-0.500618\pi$
$467$	−1.89794e20	−0.00388229	−0.00194115	+	0.999998i	$0.500618\pi$
$468$	−4.36751e21	−0.0877292
$469$	1.75658e22	0.346497
$470$	−3.81624e21	−0.0739272
$471$	5.60009e22	1.06541
$472$	−1.99422e21	−0.0372619
$473$	1.25703e23	2.30688
$474$	9.72649e21	0.175324
$475$	−2.11514e22	−0.374493
$476$	−1.95672e20	−0.00340305
$477$	−3.88775e22	−0.664190
$478$	−6.38322e21	−0.107128
$479$	−1.03721e23	−1.71008	−0.855041	−	0.518561i	$-0.826468\pi$
$479$	−1.03721e23	−1.71008	−0.855041	+	0.518561i	$0.826468\pi$
$480$	1.15788e22	0.187548
$481$	9.53168e21	0.151683
$482$	−4.12674e20	−0.00645220
$483$	−3.18965e22	−0.489996
$484$	−6.79350e22	−1.02543
$485$	1.30894e22	0.194141
$486$	−7.25878e21	−0.105793
$487$	3.53131e22	0.505754	0.252877	−	0.967498i	$-0.418623\pi$
$487$	3.53131e22	0.505754	0.252877	+	0.967498i	$0.418623\pi$
$488$	−1.18198e22	−0.166357
$489$	−6.21821e22	−0.860082
$490$	3.59614e21	0.0488844
$491$	−1.28065e23	−1.71095	−0.855477	−	0.517840i	$-0.826736\pi$
$491$	−1.28065e23	−1.71095	−0.855477	+	0.517840i	$0.826736\pi$
$492$	4.70373e22	0.617645
$493$	9.99871e20	0.0129046
$494$	3.10082e21	0.0393367
$495$	2.52605e22	0.314991
$496$	−1.38612e22	−0.169906
$497$	−1.55221e22	−0.187035
$498$	−1.18374e21	−0.0140219
$499$	−1.20072e22	−0.139825	−0.0699127	−	0.997553i	$-0.522272\pi$
$499$	−1.20072e22	−0.139825	−0.0699127	+	0.997553i	$0.522272\pi$
$500$	−7.70647e21	−0.0882288
$501$	8.44879e22	0.950986
$502$	7.43064e21	0.0822327
$503$	7.06784e22	0.769057	0.384529	−	0.923113i	$-0.374364\pi$
$503$	7.06784e22	0.769057	0.384529	+	0.923113i	$0.374364\pi$
$504$	2.65024e21	0.0283547
$505$	3.29908e22	0.347069
$506$	−2.59592e22	−0.268541
$507$	1.16217e23	1.18223
$508$	−1.48619e23	−1.48673
$509$	1.64610e23	1.61941	0.809703	−	0.586840i	$-0.199628\pi$
$509$	1.64610e23	1.61941	0.809703	+	0.586840i	$0.199628\pi$
$510$	9.13761e19	0.000884069 0
$511$	−1.28650e22	−0.122414
$512$	−5.89114e22	−0.551321
$513$	−1.25983e23	−1.15962
$514$	5.34387e21	0.0483804
$515$	7.27342e22	0.647705
$516$	2.22282e23	1.94707
$517$	2.35181e23	2.02644
$518$	−2.87219e21	−0.0243450
$519$	−1.80691e23	−1.50666
$520$	2.27510e21	0.0186626
$521$	−2.16722e23	−1.74897	−0.874484	−	0.485055i	$-0.838800\pi$
$521$	−2.16722e23	−1.74897	−0.874484	+	0.485055i	$0.838800\pi$
$522$	−6.72502e21	−0.0533942
$523$	1.50353e23	1.17448	0.587241	−	0.809412i	$-0.300214\pi$
$523$	1.50353e23	1.17448	0.587241	+	0.809412i	$0.300214\pi$
$524$	−1.06767e23	−0.820582
$525$	−8.02888e21	−0.0607157
$526$	6.57816e21	0.0489469
$527$	−3.35860e20	−0.00245905
$528$	−2.32404e23	−1.67438
$529$	2.26416e23	1.60522
$530$	1.00567e22	0.0701637
$531$	−1.15662e22	−0.0794122
$532$	6.79111e22	0.458872
$533$	1.38950e22	0.0924011
$534$	1.41465e22	0.0925868
$535$	−8.77861e22	−0.565482
$536$	5.09076e22	0.322762
$537$	−2.48908e23	−1.55331
$538$	−3.17316e21	−0.0194914
$539$	−2.21617e23	−1.33998
$540$	−4.59016e22	−0.273200
$541$	1.91778e22	0.112363	0.0561813	−	0.998421i	$-0.482108\pi$
$541$	1.91778e22	0.112363	0.0561813	+	0.998421i	$0.482108\pi$
$542$	3.16492e22	0.182545
$543$	1.59209e23	0.904001
$544$	−8.52553e20	−0.00476574
$545$	6.24775e22	0.343838
$546$	1.17704e21	0.00637757
$547$	−1.66096e23	−0.886066	−0.443033	−	0.896505i	$-0.646098\pi$
$547$	−1.66096e23	−0.886066	−0.443033	+	0.896505i	$0.646098\pi$
$548$	2.55786e23	1.34352
$549$	−6.85531e22	−0.354538
$550$	−6.53434e21	−0.0332751
$551$	−3.47022e23	−1.74008
$552$	−9.24396e22	−0.456432
$553$	6.29268e22	0.305965
$554$	−2.58869e22	−0.123950
$555$	−9.74850e22	−0.459672
$556$	2.66659e23	1.23829
$557$	1.16314e23	0.531942	0.265971	−	0.963981i	$-0.414307\pi$
$557$	1.16314e23	0.531942	0.265971	+	0.963981i	$0.414307\pi$
$558$	2.25895e21	0.0101746
$559$	6.56630e22	0.291287
$560$	2.43981e22	0.106600
$561$	−5.63118e21	−0.0242334
$562$	2.89042e22	0.122519
$563$	1.33619e23	0.557889	0.278945	−	0.960307i	$-0.410015\pi$
$563$	1.33619e23	0.557889	0.278945	+	0.960307i	$0.410015\pi$
$564$	4.15875e23	1.71037
$565$	−5.90106e22	−0.239066
$566$	3.17800e22	0.126828
$567$	−7.89883e22	−0.310532
$568$	−4.49848e22	−0.174223
$569$	1.20840e23	0.461059	0.230530	−	0.973065i	$-0.425954\pi$
$569$	1.20840e23	0.461059	0.230530	+	0.973065i	$0.425954\pi$
$570$	−3.17136e22	−0.119209
$571$	3.87857e23	1.43637	0.718183	−	0.695854i	$-0.244974\pi$
$571$	3.87857e23	1.43637	0.718183	+	0.695854i	$0.244974\pi$
$572$	−6.96241e22	−0.254035
$573$	−3.02062e22	−0.108588
$574$	−4.18699e21	−0.0148303
$575$	9.24973e22	0.322814
$576$	−1.31872e23	−0.453484
$577$	−3.96262e23	−1.34273	−0.671363	−	0.741129i	$-0.734291\pi$
$577$	−3.96262e23	−1.34273	−0.671363	+	0.741129i	$0.734291\pi$
$578$	3.48839e22	0.116477
$579$	4.17732e23	1.37445
$580$	−1.26437e23	−0.409954
$581$	−7.65836e21	−0.0244703
$582$	1.96258e22	0.0617991
$583$	−6.19761e23	−1.92328
$584$	−3.72840e22	−0.114029
$585$	1.31953e22	0.0397735
$586$	−6.96315e22	−0.206860
$587$	−4.74902e23	−1.39053	−0.695265	−	0.718754i	$-0.744713\pi$
$587$	−4.74902e23	−1.39053	−0.695265	+	0.718754i	$0.744713\pi$
$588$	−3.91889e23	−1.13098
$589$	1.16566e23	0.331582
$590$	2.99192e21	0.00838895
$591$	5.64952e22	0.156141
$592$	2.96237e23	0.807059
$593$	4.97577e23	1.33627	0.668137	−	0.744038i	$-0.267092\pi$
$593$	4.97577e23	1.33627	0.668137	+	0.744038i	$0.267092\pi$
$594$	−3.89201e22	−0.103036
$595$	5.91170e20	0.00154283
$596$	−3.99109e23	−1.02683
$597$	3.28557e23	0.833353
$598$	−1.35602e22	−0.0339083
$599$	−2.34667e23	−0.578527	−0.289263	−	0.957250i	$-0.593410\pi$
$599$	−2.34667e23	−0.578527	−0.289263	+	0.957250i	$0.593410\pi$
$600$	−2.32685e22	−0.0565566
$601$	−1.32229e23	−0.316880	−0.158440	−	0.987369i	$-0.550646\pi$
$601$	−1.32229e23	−0.316880	−0.158440	+	0.987369i	$0.550646\pi$
$602$	−1.97863e22	−0.0467513
$603$	2.95257e23	0.687865
$604$	−2.37375e23	−0.545283
$605$	2.05248e23	0.464898
$606$	4.94651e22	0.110479
$607$	−1.30209e23	−0.286772	−0.143386	−	0.989667i	$-0.545799\pi$
$607$	−1.30209e23	−0.286772	−0.143386	+	0.989667i	$0.545799\pi$
$608$	2.95893e23	0.642619
$609$	−1.31726e23	−0.282114
$610$	1.77332e22	0.0374527
$611$	1.22851e23	0.255875
$612$	−3.28897e21	−0.00675574
$613$	−9.71711e22	−0.196844	−0.0984222	−	0.995145i	$-0.531380\pi$
$613$	−9.71711e22	−0.196844	−0.0984222	+	0.995145i	$0.531380\pi$
$614$	−2.38421e22	−0.0476335
$615$	−1.42111e23	−0.280019
$616$	4.22484e22	0.0821060
$617$	1.73762e22	0.0333066	0.0166533	−	0.999861i	$-0.494699\pi$
$617$	1.73762e22	0.0333066	0.0166533	+	0.999861i	$0.494699\pi$
$618$	1.09055e23	0.206178
$619$	−6.73878e23	−1.25664	−0.628319	−	0.777955i	$-0.716257\pi$
$619$	−6.73878e23	−1.25664	−0.628319	+	0.777955i	$0.716257\pi$
$620$	4.24704e22	0.0781191
$621$	5.50936e23	0.999592
$622$	−8.02423e21	−0.0143610
$623$	9.15229e22	0.161578
$624$	−1.21400e23	−0.211422
$625$	2.32831e22	0.0400000
$626$	−2.21140e22	−0.0374788
$627$	1.95439e24	3.26767
$628$	5.21413e23	0.860052
$629$	7.17787e21	0.0116806
$630$	−3.97614e21	−0.00638362
$631$	1.85677e23	0.294109	0.147055	−	0.989128i	$-0.453021\pi$
$631$	1.85677e23	0.294109	0.147055	+	0.989128i	$0.453021\pi$
$632$	1.82369e23	0.285007
$633$	−6.36256e23	−0.981071
$634$	−4.28639e22	−0.0652129
$635$	4.49013e23	0.674035
$636$	−1.09593e24	−1.62330
$637$	−1.15766e23	−0.169198
$638$	−1.07206e23	−0.154612
$639$	−2.60906e23	−0.371302
$640$	1.43404e23	0.201386
$641$	2.46674e23	0.341846	0.170923	−	0.985284i	$-0.445325\pi$
$641$	2.46674e23	0.341846	0.170923	+	0.985284i	$0.445325\pi$
$642$	−1.31623e23	−0.180005
$643$	−1.45215e24	−1.95983	−0.979916	−	0.199409i	$-0.936098\pi$
$643$	−1.45215e24	−1.95983	−0.979916	+	0.199409i	$0.936098\pi$
$644$	−2.96982e23	−0.395549
$645$	−6.71567e23	−0.882738
$646$	2.33509e21	0.00302919
$647$	−8.41846e22	−0.107782	−0.0538910	−	0.998547i	$-0.517162\pi$
$647$	−8.41846e22	−0.107782	−0.0538910	+	0.998547i	$0.517162\pi$
$648$	−2.28916e23	−0.289261
$649$	−1.84381e23	−0.229952
$650$	−3.41333e21	−0.00420160
$651$	4.42472e22	0.0537586
$652$	−5.78964e23	−0.694300
$653$	−1.67703e23	−0.198508	−0.0992540	−	0.995062i	$-0.531646\pi$
$653$	−1.67703e23	−0.198508	−0.0992540	+	0.995062i	$0.531646\pi$
$654$	9.36764e22	0.109451
$655$	3.22569e23	0.372025
$656$	4.31846e23	0.491638
$657$	−2.16242e23	−0.243016
$658$	−3.70188e22	−0.0410679
$659$	1.50378e24	1.64686	0.823431	−	0.567417i	$-0.192057\pi$
$659$	1.50378e24	1.64686	0.823431	+	0.567417i	$0.192057\pi$
$660$	7.12079e23	0.769848
$661$	−6.16515e23	−0.658008	−0.329004	−	0.944329i	$-0.606713\pi$
$661$	−6.16515e23	−0.658008	−0.329004	+	0.944329i	$0.606713\pi$
$662$	3.39568e22	0.0357794
$663$	−2.94154e21	−0.00305992
$664$	−2.21947e22	−0.0227941
$665$	−2.05175e23	−0.208037
$666$	−4.82776e22	−0.0483297
$667$	1.51756e24	1.49995
$668$	7.86650e23	0.767682
$669$	−7.54163e23	−0.726680
$670$	−7.63765e22	−0.0726648
$671$	−1.09283e24	−1.02663
$672$	1.12318e23	0.104186
$673$	1.11017e23	0.101686	0.0508429	−	0.998707i	$-0.483809\pi$
$673$	1.11017e23	0.101686	0.0508429	+	0.998707i	$0.483809\pi$
$674$	1.34278e23	0.121449
$675$	1.38680e23	0.123860
$676$	1.08207e24	0.954351
$677$	−1.95012e24	−1.69847	−0.849236	−	0.528013i	$-0.822937\pi$
$677$	−1.95012e24	−1.69847	−0.849236	+	0.528013i	$0.822937\pi$
$678$	−8.84782e22	−0.0760998
$679$	1.26972e23	0.107848
$680$	1.71327e21	0.00143715
$681$	3.67012e23	0.304039
$682$	3.60108e22	0.0294623
$683$	1.45259e24	1.17373	0.586864	−	0.809686i	$-0.300362\pi$
$683$	1.45259e24	1.17373	0.586864	+	0.809686i	$0.300362\pi$
$684$	1.14149e24	0.910953
$685$	−7.72791e23	−0.609105
$686$	7.20621e22	0.0560986
$687$	−5.05475e23	−0.388658
$688$	2.04076e24	1.54985
$689$	−3.23743e23	−0.242849
$690$	1.38687e23	0.102759
$691$	1.18404e24	0.866569	0.433285	−	0.901257i	$-0.357354\pi$
$691$	1.18404e24	0.866569	0.433285	+	0.901257i	$0.357354\pi$
$692$	−1.68238e24	−1.21625
$693$	2.45035e23	0.174983
$694$	2.31777e23	0.163499
$695$	−8.05641e23	−0.561398
$696$	−3.81757e23	−0.262790
$697$	1.04637e22	0.00711550
$698$	−4.31102e22	−0.0289607
$699$	5.06601e23	0.336209
$700$	−7.47552e22	−0.0490126
$701$	−7.28112e21	−0.00471623	−0.00235811	−	0.999997i	$-0.500751\pi$
$701$	−7.28112e21	−0.00471623	−0.00235811	+	0.999997i	$0.500751\pi$
$702$	−2.03306e22	−0.0130102
$703$	−2.49120e24	−1.57503
$704$	−2.10223e24	−1.31314
$705$	−1.25646e24	−0.775425
$706$	6.57266e21	0.00400776
$707$	3.20021e23	0.192803
$708$	−3.26044e23	−0.194086
$709$	6.82414e23	0.401379	0.200689	−	0.979655i	$-0.435682\pi$
$709$	6.82414e23	0.401379	0.200689	+	0.979655i	$0.435682\pi$
$710$	6.74906e22	0.0392236
$711$	1.05771e24	0.607402
$712$	2.65243e23	0.150510
$713$	−5.09754e23	−0.285824
$714$	8.86377e20	0.000491116 0
$715$	2.10351e23	0.115171
$716$	−2.31753e24	−1.25391
$717$	−2.10160e24	−1.12367
$718$	2.45181e23	0.129548
$719$	2.44746e24	1.27797	0.638984	−	0.769220i	$-0.279355\pi$
$719$	2.44746e24	1.27797	0.638984	+	0.769220i	$0.279355\pi$
$720$	4.10099e23	0.211623
$721$	7.05545e23	0.359812
$722$	−5.79284e23	−0.291961
$723$	−1.35868e23	−0.0676773
$724$	1.48236e24	0.729753
$725$	3.81995e23	0.185859
$726$	3.07740e23	0.147987
$727$	5.64598e22	0.0268347	0.0134174	−	0.999910i	$-0.495729\pi$
$727$	5.64598e22	0.0268347	0.0134174	+	0.999910i	$0.495729\pi$
$728$	2.20692e22	0.0103674
$729$	3.02146e23	0.140292
$730$	5.59371e22	0.0256718
$731$	4.94478e22	0.0224310
$732$	−1.93247e24	−0.866500
$733$	2.99425e24	1.32710	0.663551	−	0.748131i	$-0.269049\pi$
$733$	2.99425e24	1.32710	0.663551	+	0.748131i	$0.269049\pi$
$734$	−3.07080e23	−0.134535
$735$	1.18399e24	0.512750
$736$	−1.29397e24	−0.553939
$737$	4.70681e24	1.99183
$738$	−7.03775e22	−0.0294412
$739$	1.54200e24	0.637687	0.318843	−	0.947807i	$-0.396706\pi$
$739$	1.54200e24	0.637687	0.318843	+	0.947807i	$0.396706\pi$
$740$	−9.07663e23	−0.371069
$741$	1.02091e24	0.412604
$742$	9.75537e22	0.0389772
$743$	−3.51345e24	−1.38781	−0.693904	−	0.720068i	$-0.744111\pi$
$743$	−3.51345e24	−1.38781	−0.693904	+	0.720068i	$0.744111\pi$
$744$	1.28233e23	0.0500761
$745$	1.20580e24	0.465531
$746$	−2.20637e23	−0.0842167
$747$	−1.28727e23	−0.0485784
$748$	−5.24307e22	−0.0195624
$749$	−8.51553e23	−0.314135
$750$	3.49097e22	0.0127329
$751$	−4.37586e24	−1.57806	−0.789030	−	0.614354i	$-0.789417\pi$
$751$	−4.37586e24	−1.57806	−0.789030	+	0.614354i	$0.789417\pi$
$752$	3.81811e24	1.36144
$753$	2.44645e24	0.862541
$754$	−5.60010e22	−0.0195227
$755$	7.17167e23	0.247213
$756$	−4.45260e23	−0.151767
$757$	−2.28839e24	−0.771285	−0.385642	−	0.922648i	$-0.626020\pi$
$757$	−2.28839e24	−0.771285	−0.385642	+	0.922648i	$0.626020\pi$
$758$	−3.29520e23	−0.109823
$759$	−8.54677e24	−2.81674
$760$	−5.94620e23	−0.193787
$761$	5.32807e24	1.71712	0.858560	−	0.512714i	$-0.171360\pi$
$761$	5.32807e24	1.71712	0.858560	+	0.512714i	$0.171360\pi$
$762$	6.73233e23	0.214560
$763$	6.06052e23	0.191008
$764$	−2.81244e23	−0.0876576
$765$	9.93676e21	0.00306283
$766$	4.01962e23	0.122529
$767$	−9.63146e22	−0.0290357
$768$	−3.55353e24	−1.05947
$769$	−3.77315e23	−0.111258	−0.0556288	−	0.998452i	$-0.517716\pi$
$769$	−3.77315e23	−0.111258	−0.0556288	+	0.998452i	$0.517716\pi$
$770$	−6.33852e22	−0.0184849
$771$	1.75941e24	0.507463
$772$	3.88942e24	1.10953
$773$	−2.76711e24	−0.780730	−0.390365	−	0.920660i	$-0.627651\pi$
$773$	−2.76711e24	−0.780730	−0.390365	+	0.920660i	$0.627651\pi$
$774$	−3.32580e23	−0.0928108
$775$	−1.28313e23	−0.0354166
$776$	3.67978e23	0.100461
$777$	−9.45636e23	−0.255356
$778$	5.20797e23	0.139105
$779$	−3.63159e24	−0.959464
$780$	3.71967e23	0.0972076
$781$	−4.15920e24	−1.07517
$782$	−1.02116e22	−0.00261117
$783$	2.27525e24	0.575513
$784$	−3.59790e24	−0.900250
$785$	−1.57531e24	−0.389919
$786$	4.83647e23	0.118423
$787$	3.31614e24	0.803244	0.401622	−	0.915806i	$-0.368447\pi$
$787$	3.31614e24	0.803244	0.401622	+	0.915806i	$0.368447\pi$
$788$	5.26015e23	0.126045
$789$	2.16579e24	0.513406
$790$	−2.73607e23	−0.0641649
$791$	−5.72421e23	−0.132805
$792$	7.10138e23	0.162997
$793$	−5.70860e23	−0.129630
$794$	−3.81532e23	−0.0857150
$795$	3.31107e24	0.735950
$796$	3.05913e24	0.672723
$797$	4.86851e24	1.05926	0.529628	−	0.848230i	$-0.322332\pi$
$797$	4.86851e24	1.05926	0.529628	+	0.848230i	$0.322332\pi$
$798$	−3.07632e23	−0.0662227
$799$	9.25134e22	0.0197041
$800$	−3.25713e23	−0.0686389
$801$	1.53837e24	0.320764
$802$	3.20884e22	0.00662013
$803$	−3.44720e24	−0.703695
$804$	8.32312e24	1.68116
$805$	8.97253e23	0.179329
$806$	1.88109e22	0.00372016
$807$	−1.04473e24	−0.204446
$808$	9.27455e23	0.179596
$809$	4.89499e24	0.937972	0.468986	−	0.883206i	$-0.344620\pi$
$809$	4.89499e24	0.937972	0.468986	+	0.883206i	$0.344620\pi$
$810$	3.43443e23	0.0651226
$811$	−3.18460e24	−0.597555	−0.298778	−	0.954323i	$-0.596579\pi$
$811$	−3.18460e24	−0.597555	−0.298778	+	0.954323i	$0.596579\pi$
$812$	−1.22648e24	−0.227737
$813$	1.04202e25	1.91472
$814$	−7.69611e23	−0.139947
$815$	1.74919e24	0.314773
$816$	−9.14209e22	−0.0162809
$817$	−1.71617e25	−3.02463
$818$	5.08139e23	0.0886297
$819$	1.27998e23	0.0220949
$820$	−1.32316e24	−0.226045
$821$	−8.79210e24	−1.48654	−0.743268	−	0.668993i	$-0.766725\pi$
$821$	−8.79210e24	−1.48654	−0.743268	+	0.668993i	$0.766725\pi$
$822$	−1.15869e24	−0.193891
$823$	−7.30298e24	−1.20949	−0.604744	−	0.796420i	$-0.706725\pi$
$823$	−7.30298e24	−1.20949	−0.604744	+	0.796420i	$0.706725\pi$
$824$	2.04475e24	0.335164
$825$	−2.15136e24	−0.349023
$826$	2.90226e22	0.00466021
$827$	5.65189e24	0.898249	0.449125	−	0.893469i	$-0.351736\pi$
$827$	5.65189e24	0.898249	0.449125	+	0.893469i	$0.351736\pi$
$828$	−4.99186e24	−0.785244
$829$	4.60010e24	0.716232	0.358116	−	0.933677i	$-0.383419\pi$
$829$	4.60010e24	0.716232	0.358116	+	0.933677i	$0.383419\pi$
$830$	3.32987e22	0.00513173
$831$	−8.52297e24	−1.30012
$832$	−1.09813e24	−0.165809
$833$	−8.71777e22	−0.0130294
$834$	−1.20795e24	−0.178705
$835$	−2.37665e24	−0.348042
$836$	1.81970e25	2.63782
$837$	−7.64265e23	−0.109667
$838$	−2.96537e23	−0.0421216
$839$	−4.39181e24	−0.617543	−0.308772	−	0.951136i	$-0.599918\pi$
$839$	−4.39181e24	−0.617543	−0.308772	+	0.951136i	$0.599918\pi$
$840$	−2.25712e23	−0.0314182
$841$	−9.89925e23	−0.136407
$842$	−5.34181e23	−0.0728679
$843$	9.51640e24	1.28510
$844$	−5.92405e24	−0.791968
$845$	−3.26919e24	−0.432671
$846$	−6.22235e23	−0.0815279
$847$	1.99097e24	0.258259
$848$	−1.00617e25	−1.29213
$849$	1.04632e25	1.33030
$850$	−2.57042e21	−0.000323551 0
$851$	1.08943e25	1.35768
$852$	−7.35478e24	−0.907472
$853$	1.45514e25	1.77761	0.888807	−	0.458282i	$-0.151535\pi$
$853$	1.45514e25	1.77761	0.888807	+	0.458282i	$0.151535\pi$
$854$	1.72018e23	0.0208056
$855$	−3.44872e24	−0.412996
$856$	−2.46789e24	−0.292617
$857$	−1.40588e25	−1.65048	−0.825242	−	0.564779i	$-0.808961\pi$
$857$	−1.40588e25	−1.65048	−0.825242	+	0.564779i	$0.808961\pi$
$858$	3.15392e23	0.0366614
$859$	−2.70465e24	−0.311292	−0.155646	−	0.987813i	$-0.549746\pi$
$859$	−2.70465e24	−0.311292	−0.155646	+	0.987813i	$0.549746\pi$
$860$	−6.25282e24	−0.712589
$861$	−1.37852e24	−0.155556
$862$	6.08386e23	0.0679778
$863$	3.31545e24	0.366818	0.183409	−	0.983037i	$-0.441287\pi$
$863$	3.31545e24	0.366818	0.183409	+	0.983037i	$0.441287\pi$
$864$	−1.94003e24	−0.212540
$865$	5.08286e24	0.551406
$866$	1.95499e24	0.210011
$867$	1.14851e25	1.22173
$868$	4.11977e23	0.0433965
$869$	1.68614e25	1.75884
$870$	5.72748e23	0.0591630
$871$	2.45868e24	0.251506
$872$	1.75640e24	0.177924
$873$	2.13422e24	0.214101
$874$	3.54410e24	0.352094
$875$	2.25853e23	0.0222207
$876$	−6.09574e24	−0.593938
$877$	4.75079e24	0.458426	0.229213	−	0.973376i	$-0.426385\pi$
$877$	4.75079e24	0.458426	0.229213	+	0.973376i	$0.426385\pi$
$878$	−6.56198e23	−0.0627092
$879$	−2.29254e25	−2.16976
$880$	6.53755e24	0.612790
$881$	6.55529e24	0.608551	0.304275	−	0.952584i	$-0.401586\pi$
$881$	6.55529e24	0.608551	0.304275	+	0.952584i	$0.401586\pi$
$882$	5.86348e23	0.0539104
$883$	1.39612e25	1.27132	0.635661	−	0.771968i	$-0.280728\pi$
$883$	1.39612e25	1.27132	0.635661	+	0.771968i	$0.280728\pi$
$884$	−2.73881e22	−0.00247012
$885$	9.85056e23	0.0879920
$886$	−1.97580e24	−0.174806
$887$	−5.14755e24	−0.451076	−0.225538	−	0.974234i	$-0.572414\pi$
$887$	−5.14755e24	−0.451076	−0.225538	+	0.974234i	$0.572414\pi$
$888$	−2.74055e24	−0.237864
$889$	4.35557e24	0.374438
$890$	−3.97943e23	−0.0338849
$891$	−2.11651e25	−1.78509
$892$	−7.02186e24	−0.586612
$893$	−3.21083e25	−2.65693
$894$	1.80794e24	0.148188
$895$	7.00182e24	0.568480
$896$	1.39106e24	0.111874
$897$	−4.46455e24	−0.355666
$898$	−1.93137e24	−0.152411
$899$	−2.10518e24	−0.164563
$900$	−1.25653e24	−0.0972999
$901$	−2.43796e23	−0.0187010
$902$	−1.12192e24	−0.0852520
$903$	−6.51441e24	−0.490376
$904$	−1.65894e24	−0.123708
$905$	−4.47856e24	−0.330846
$906$	1.07529e24	0.0786932
$907$	9.49790e24	0.688598	0.344299	−	0.938860i	$-0.388117\pi$
$907$	9.49790e24	0.688598	0.344299	+	0.938860i	$0.388117\pi$
$908$	3.41717e24	0.245435
$909$	5.37911e24	0.382752
$910$	−3.31104e22	−0.00233406
$911$	3.16103e24	0.220761	0.110380	−	0.993889i	$-0.464793\pi$
$911$	3.16103e24	0.220761	0.110380	+	0.993889i	$0.464793\pi$
$912$	3.17291e25	2.19534
$913$	−2.05208e24	−0.140667
$914$	−7.70716e23	−0.0523422
$915$	5.83845e24	0.392842
$916$	−4.70638e24	−0.313744
$917$	3.12902e24	0.206666
$918$	−1.53100e22	−0.00100188
$919$	−1.63003e25	−1.05685	−0.528426	−	0.848979i	$-0.677218\pi$
$919$	−1.63003e25	−1.05685	−0.528426	+	0.848979i	$0.677218\pi$
$920$	2.60033e24	0.167045
$921$	−7.84974e24	−0.499630
$922$	1.16415e24	0.0734170
$923$	−2.17263e24	−0.135760
$924$	6.90739e24	0.427664
$925$	2.74226e24	0.168230
$926$	1.56567e24	0.0951713
$927$	1.18592e25	0.714298
$928$	−5.34383e24	−0.318929
$929$	−2.23143e25	−1.31962	−0.659811	−	0.751432i	$-0.729364\pi$
$929$	−2.23143e25	−1.31962	−0.659811	+	0.751432i	$0.729364\pi$
$930$	−1.92388e23	−0.0112739
$931$	3.02565e25	1.75690
$932$	4.71685e24	0.271404
$933$	−2.64189e24	−0.150633
$934$	8.00496e21	0.000452284 0
$935$	1.58406e23	0.00886895
$936$	3.70953e23	0.0205814
$937$	−7.91639e23	−0.0435252	−0.0217626	−	0.999763i	$-0.506928\pi$
$937$	−7.91639e23	−0.0435252	−0.0217626	+	0.999763i	$0.506928\pi$
$938$	−7.40876e23	−0.0403666
$939$	−7.28079e24	−0.393116
$940$	−1.16986e25	−0.625961
$941$	1.96151e25	1.04011	0.520054	−	0.854133i	$-0.325912\pi$
$941$	1.96151e25	1.04011	0.520054	+	0.854133i	$0.325912\pi$
$942$	−2.36196e24	−0.124119
$943$	1.58813e25	0.827061
$944$	−2.99338e24	−0.154490
$945$	1.34524e24	0.0688063
$946$	−5.30179e24	−0.268750
$947$	1.92926e25	0.969203	0.484602	−	0.874735i	$-0.338965\pi$
$947$	1.92926e25	0.969203	0.484602	+	0.874735i	$0.338965\pi$
$948$	2.98163e25	1.48451
$949$	−1.80070e24	−0.0888546
$950$	8.92107e23	0.0436281
$951$	−1.41125e25	−0.684020
$952$	1.66193e22	0.000798360 0
$953$	−3.70005e24	−0.176164	−0.0880822	−	0.996113i	$-0.528074\pi$
$953$	−3.70005e24	−0.176164	−0.0880822	+	0.996113i	$0.528074\pi$
$954$	1.63974e24	0.0773775
$955$	8.49704e23	0.0397410
$956$	−1.95676e25	−0.907079
$957$	−3.52964e25	−1.62173
$958$	4.37468e24	0.199223
$959$	−7.49632e24	−0.338369
$960$	1.12311e25	0.502479
$961$	−2.18430e25	−0.968642
$962$	−4.02020e23	−0.0176709
$963$	−1.43134e25	−0.623621
$964$	−1.26504e24	−0.0546324
$965$	−1.17509e25	−0.503022
$966$	1.34531e24	0.0570842
$967$	2.10463e25	0.885220	0.442610	−	0.896714i	$-0.354053\pi$
$967$	2.10463e25	0.885220	0.442610	+	0.896714i	$0.354053\pi$
$968$	5.77004e24	0.240568
$969$	7.68801e23	0.0317733
$970$	−5.52076e23	−0.0226172
$971$	1.32196e25	0.536854	0.268427	−	0.963300i	$-0.413496\pi$
$971$	1.32196e25	0.536854	0.268427	+	0.963300i	$0.413496\pi$
$972$	−2.22516e25	−0.895773
$973$	−7.81497e24	−0.311866
$974$	−1.48941e24	−0.0589200
$975$	−1.12380e24	−0.0440707
$976$	−1.77419e25	−0.689725
$977$	−4.35449e25	−1.67816	−0.839081	−	0.544007i	$-0.816907\pi$
$977$	−4.35449e25	−1.67816	−0.839081	+	0.544007i	$0.816907\pi$
$978$	2.62267e24	0.100199
$979$	2.45238e25	0.928828
$980$	1.10239e25	0.413917
$981$	1.01869e25	0.379189
$982$	5.40143e24	0.199325
$983$	−3.72688e25	−1.36345	−0.681727	−	0.731607i	$-0.738771\pi$
$983$	−3.72688e25	−1.36345	−0.681727	+	0.731607i	$0.738771\pi$
$984$	−3.99509e24	−0.144900
$985$	−1.58922e24	−0.0571446
$986$	−4.21717e22	−0.00150338
$987$	−1.21880e25	−0.430762
$988$	9.50550e24	0.333074
$989$	7.50498e25	2.60724
$990$	−1.06542e24	−0.0366962
$991$	3.59188e25	1.22658	0.613290	−	0.789857i	$-0.289846\pi$
$991$	3.59188e25	1.22658	0.613290	+	0.789857i	$0.289846\pi$
$992$	1.79501e24	0.0607739
$993$	1.11799e25	0.375291
$994$	6.54680e23	0.0217894
$995$	−9.24235e24	−0.304990
$996$	−3.62872e24	−0.118727
$997$	−2.59316e25	−0.841241	−0.420620	−	0.907237i	$-0.638188\pi$
$997$	−2.59316e25	−0.841241	−0.420620	+	0.907237i	$0.638188\pi$
$998$	5.06428e23	0.0162895
$999$	1.63336e25	0.520925

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.18.a.b.1.2	✓	3
3.2	odd	2		45.18.a.c.1.2		3
4.3	odd	2		80.18.a.g.1.3		3
5.2	odd	4		25.18.b.c.24.3		6
5.3	odd	4		25.18.b.c.24.4		6
5.4	even	2		25.18.a.c.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.18.a.b.1.2	✓	3	1.1	even	1	trivial
25.18.a.c.1.2		3	5.4	even	2
25.18.b.c.24.3		6	5.2	odd	4
25.18.b.c.24.4		6	5.3	odd	4
45.18.a.c.1.2		3	3.2	odd	2
80.18.a.g.1.3		3	4.3	odd	2

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q-42.1772 q^{2} -13886.4 q^{3} -129293. q^{4} +390625. q^{5} +585688. q^{6} +3.78919e6 q^{7} +1.09815e7 q^{8} +6.36910e7 q^{9} +O(q^{10})\)	\(q-42.1772 q^{2} -13886.4 q^{3} -129293. q^{4} +390625. q^{5} +585688. q^{6} +3.78919e6 q^{7} +1.09815e7 q^{8} +6.36910e7 q^{9} -1.64755e7 q^{10} +1.01532e9 q^{11} +1.79541e9 q^{12} +5.30372e8 q^{13} -1.59817e8 q^{14} -5.42436e9 q^{15} +1.64835e10 q^{16} +3.99398e8 q^{17} -2.68631e9 q^{18} -1.38618e11 q^{19} -5.05051e10 q^{20} -5.26180e10 q^{21} -4.28235e10 q^{22} +6.06190e11 q^{23} -1.52493e11 q^{24} +1.52588e11 q^{25} -2.23696e10 q^{26} +9.08851e11 q^{27} -4.89916e11 q^{28} +2.50344e12 q^{29} +2.28784e11 q^{30} -8.40914e11 q^{31} -2.13459e12 q^{32} -1.40992e13 q^{33} -1.68455e10 q^{34} +1.48015e12 q^{35} -8.23481e12 q^{36} +1.79717e13 q^{37} +5.84651e12 q^{38} -7.36493e12 q^{39} +4.28964e12 q^{40} +2.61986e13 q^{41} +2.21928e12 q^{42} +1.23806e14 q^{43} -1.31274e14 q^{44} +2.48793e13 q^{45} -2.55674e13 q^{46} +2.31632e14 q^{47} -2.28896e14 q^{48} -2.18273e14 q^{49} -6.43573e12 q^{50} -5.54619e12 q^{51} -6.85734e13 q^{52} -6.10408e14 q^{53} -3.83328e13 q^{54} +3.96611e14 q^{55} +4.16108e13 q^{56} +1.92490e15 q^{57} -1.05588e14 q^{58} -1.81598e14 q^{59} +7.01333e14 q^{60} -1.07634e15 q^{61} +3.54674e13 q^{62} +2.41337e14 q^{63} -2.07050e15 q^{64} +2.07176e14 q^{65} +5.94663e14 q^{66} +4.63577e15 q^{67} -5.16394e13 q^{68} -8.41778e15 q^{69} -6.24286e13 q^{70} -4.09643e15 q^{71} +6.99421e14 q^{72} -3.39518e15 q^{73} -7.57996e14 q^{74} -2.11889e15 q^{75} +1.79223e16 q^{76} +3.84725e15 q^{77} +3.10632e14 q^{78} +1.66069e16 q^{79} +6.43888e15 q^{80} -2.08457e16 q^{81} -1.10498e15 q^{82} -2.02111e15 q^{83} +6.80315e15 q^{84} +1.56015e14 q^{85} -5.22178e15 q^{86} -3.47637e16 q^{87} +1.11497e16 q^{88} +2.41537e16 q^{89} -1.04934e15 q^{90} +2.00968e15 q^{91} -7.83762e16 q^{92} +1.16772e16 q^{93} -9.76959e15 q^{94} -5.41476e16 q^{95} +2.96417e16 q^{96} +3.35090e16 q^{97} +9.20612e15 q^{98} +6.46670e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 118 q^{2} + 15944 q^{3} + 16916 q^{4} + 1171875 q^{5} - 2419064 q^{6} + 2139308 q^{7} + 65050440 q^{8} + 323892439 q^{9}+O(q^{10}) \) 3 * q + 118 * q^2 + 15944 * q^3 + 16916 * q^4 + 1171875 * q^5 - 2419064 * q^6 + 2139308 * q^7 + 65050440 * q^8 + 323892439 * q^9	\( 3 q + 118 q^{2} + 15944 q^{3} + 16916 q^{4} + 1171875 q^{5} - 2419064 q^{6} + 2139308 q^{7} + 65050440 q^{8} + 323892439 q^{9} + 46093750 q^{10} + 1789747516 q^{11} + 3112179088 q^{12} + 5414696794 q^{13} + 10507173312 q^{14} + 6228125000 q^{15} - 16203699952 q^{16} - 27402303962 q^{17} - 142746901186 q^{18} - 29956565300 q^{19} + 6607812500 q^{20} - 224495442624 q^{21} - 294714945304 q^{22} + 16254077844 q^{23} + 897428301600 q^{24} + 457763671875 q^{25} + 2017382699956 q^{26} + 3131715461840 q^{27} + 1119244517216 q^{28} - 2528278831750 q^{29} - 944946875000 q^{30} - 521256054664 q^{31} - 10880399775712 q^{32} + 1732417161568 q^{33} - 32147385667828 q^{34} + 835667187500 q^{35} - 14985377520892 q^{36} + 31762746900498 q^{37} - 40258035935240 q^{38} + 43003853320688 q^{39} + 25410328125000 q^{40} + 86833482954446 q^{41} + 153974403759936 q^{42} + 89258046385744 q^{43} - 124942202946448 q^{44} + 126520483984375 q^{45} - 323339762673024 q^{46} + 348182738140228 q^{47} - 729510516165056 q^{48} - 387320833396229 q^{49} + 18005371093750 q^{50} - 12409602773744 q^{51} + 552556858385688 q^{52} + 44014499212594 q^{53} - 22\!\cdots\!00 q^{54}+ \cdots + 29\!\cdots\!08 q^{99}+O(q^{100}) \) 3 * q + 118 * q^2 + 15944 * q^3 + 16916 * q^4 + 1171875 * q^5 - 2419064 * q^6 + 2139308 * q^7 + 65050440 * q^8 + 323892439 * q^9 + 46093750 * q^10 + 1789747516 * q^11 + 3112179088 * q^12 + 5414696794 * q^13 + 10507173312 * q^14 + 6228125000 * q^15 - 16203699952 * q^16 - 27402303962 * q^17 - 142746901186 * q^18 - 29956565300 * q^19 + 6607812500 * q^20 - 224495442624 * q^21 - 294714945304 * q^22 + 16254077844 * q^23 + 897428301600 * q^24 + 457763671875 * q^25 + 2017382699956 * q^26 + 3131715461840 * q^27 + 1119244517216 * q^28 - 2528278831750 * q^29 - 944946875000 * q^30 - 521256054664 * q^31 - 10880399775712 * q^32 + 1732417161568 * q^33 - 32147385667828 * q^34 + 835667187500 * q^35 - 14985377520892 * q^36 + 31762746900498 * q^37 - 40258035935240 * q^38 + 43003853320688 * q^39 + 25410328125000 * q^40 + 86833482954446 * q^41 + 153974403759936 * q^42 + 89258046385744 * q^43 - 124942202946448 * q^44 + 126520483984375 * q^45 - 323339762673024 * q^46 + 348182738140228 * q^47 - 729510516165056 * q^48 - 387320833396229 * q^49 + 18005371093750 * q^50 - 12409602773744 * q^51 + 552556858385688 * q^52 + 44014499212594 * q^53 - 2265337034433200 * q^54 + 699120123437500 * q^55 - 490455582129600 * q^56 + 4293013923032480 * q^57 + 597742677475540 * q^58 - 2133293278957100 * q^59 + 1215694956250000 * q^60 + 2822990449991866 * q^61 + 5338539124096416 * q^62 - 4366406213760516 * q^63 - 2533946722090944 * q^64 + 2115115935156250 * q^65 - 4908048881135008 * q^66 + 374173462156688 * q^67 - 6873999340144024 * q^68 - 13800336843711552 * q^69 + 4104364575000000 * q^70 - 9029705707562224 * q^71 + 14996701114647720 * q^72 - 5906564941861106 * q^73 + 2774091820866692 * q^74 + 2432861328125000 * q^75 + 17087125269517200 * q^76 - 5362490012556624 * q^77 + 15760779344737648 * q^78 + 9183397142621600 * q^79 - 6329570293750000 * q^80 + 11504008140536443 * q^81 + 34156701290034076 * q^82 + 15992201117651544 * q^83 + 20750744922079872 * q^84 - 10704024985156250 * q^85 - 41302213526621384 * q^86 - 124899722203208080 * q^87 + 46255695387619680 * q^88 - 31272661736951250 * q^89 - 55760508275781250 * q^90 + 42991889981897896 * q^91 - 161631619485465312 * q^92 - 55524596752956672 * q^93 + 206283262927378352 * q^94 - 11701783320312500 * q^95 - 45608798390141824 * q^96 + 28207632381796278 * q^97 - 22149964169860474 * q^98 + 293120596614370508 * q^99

Introduction

L-functions

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