LMFDB - Embedded newform 3.22.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,22,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	3.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:	$8.38432032861$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{649}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 162 $ x^2 - x - 162
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3^{2}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$13.2377$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1271.96 q^{2} +59049.0 q^{3} -479282. q^{4} -2.12776e7 q^{5} -7.51077e7 q^{6} +6.32076e8 q^{7} +3.27711e9 q^{8} +3.48678e9 q^{9} +O(q^{10})$	\(q-1271.96 q^{2} +59049.0 q^{3} -479282. q^{4} -2.12776e7 q^{5} -7.51077e7 q^{6} +6.32076e8 q^{7} +3.27711e9 q^{8} +3.48678e9 q^{9} +2.70641e10 q^{10} +5.97585e10 q^{11} -2.83011e10 q^{12} +7.38499e11 q^{13} -8.03972e11 q^{14} -1.25642e12 q^{15} -3.16321e12 q^{16} -8.35876e12 q^{17} -4.43503e12 q^{18} +4.19061e13 q^{19} +1.01980e13 q^{20} +3.73234e13 q^{21} -7.60101e13 q^{22} +4.48926e13 q^{23} +1.93510e14 q^{24} -2.41012e13 q^{25} -9.39338e14 q^{26} +2.05891e14 q^{27} -3.02943e14 q^{28} -2.76669e15 q^{29} +1.59811e15 q^{30} +8.36452e15 q^{31} -2.84914e15 q^{32} +3.52868e15 q^{33} +1.06320e16 q^{34} -1.34490e16 q^{35} -1.67115e15 q^{36} -1.77675e16 q^{37} -5.33027e16 q^{38} +4.36077e16 q^{39} -6.97290e16 q^{40} +1.45253e17 q^{41} -4.74737e16 q^{42} +1.24744e17 q^{43} -2.86412e16 q^{44} -7.41904e16 q^{45} -5.71014e16 q^{46} +4.28566e17 q^{47} -1.86784e17 q^{48} -1.59026e17 q^{49} +3.06556e16 q^{50} -4.93577e17 q^{51} -3.53950e17 q^{52} -4.77017e17 q^{53} -2.61884e17 q^{54} -1.27152e18 q^{55} +2.07138e18 q^{56} +2.47452e18 q^{57} +3.51911e18 q^{58} +1.61959e18 q^{59} +6.02180e17 q^{60} -3.76882e18 q^{61} -1.06393e19 q^{62} +2.20391e18 q^{63} +1.02577e19 q^{64} -1.57135e19 q^{65} -4.48832e18 q^{66} -2.81797e18 q^{67} +4.00621e18 q^{68} +2.65086e18 q^{69} +1.71066e19 q^{70} +1.00228e19 q^{71} +1.14266e19 q^{72} -1.72739e19 q^{73} +2.25995e19 q^{74} -1.42315e18 q^{75} -2.00849e19 q^{76} +3.77719e19 q^{77} -5.54670e19 q^{78} -3.28276e19 q^{79} +6.73054e19 q^{80} +1.21577e19 q^{81} -1.84755e20 q^{82} +3.05240e17 q^{83} -1.78885e19 q^{84} +1.77854e20 q^{85} -1.58669e20 q^{86} -1.63370e20 q^{87} +1.95835e20 q^{88} +2.34593e20 q^{89} +9.43668e19 q^{90} +4.66787e20 q^{91} -2.15162e19 q^{92} +4.93917e20 q^{93} -5.45116e20 q^{94} -8.91662e20 q^{95} -1.68239e20 q^{96} -5.92086e20 q^{97} +2.02274e20 q^{98} +2.08365e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 666 q^{2} + 118098 q^{3} + 1179236 q^{4} + 996876 q^{5} + 39326634 q^{6} + 679896112 q^{7} + 2427055848 q^{8} + 6973568802 q^{9}+O(q^{10}) $ 2 * q + 666 * q^2 + 118098 * q^3 + 1179236 * q^4 + 996876 * q^5 + 39326634 * q^6 + 679896112 * q^7 + 2427055848 * q^8 + 6973568802 * q^9	$ 2 q + 666 q^{2} + 118098 q^{3} + 1179236 q^{4} + 996876 q^{5} + 39326634 q^{6} + 679896112 q^{7} + 2427055848 q^{8} + 6973568802 q^{9} + 70231066524 q^{10} + 219869122968 q^{11} + 69632706564 q^{12} - 48468909956 q^{13} - 711297706896 q^{14} + 58864530924 q^{15} - 8288736440560 q^{16} - 11333529041436 q^{17} + 2322198411066 q^{18} + 11960585011624 q^{19} + 47140581172824 q^{20} + 40147185517488 q^{21} + 234277148563128 q^{22} - 146508390063504 q^{23} + 143315220768552 q^{24} - 4786354247074 q^{25} - 24\!\cdots\!16 q^{26}+ \cdots + 76\!\cdots\!68 q^{99}+O(q^{100}) $ 2 * q + 666 * q^2 + 118098 * q^3 + 1179236 * q^4 + 996876 * q^5 + 39326634 * q^6 + 679896112 * q^7 + 2427055848 * q^8 + 6973568802 * q^9 + 70231066524 * q^10 + 219869122968 * q^11 + 69632706564 * q^12 - 48468909956 * q^13 - 711297706896 * q^14 + 58864530924 * q^15 - 8288736440560 * q^16 - 11333529041436 * q^17 + 2322198411066 * q^18 + 11960585011624 * q^19 + 47140581172824 * q^20 + 40147185517488 * q^21 + 234277148563128 * q^22 - 146508390063504 * q^23 + 143315220768552 * q^24 - 4786354247074 * q^25 - 2464447363969716 * q^26 + 411782264189298 * q^27 - 223631286954656 * q^28 - 1798520043674052 * q^29 + 4147074247175676 * q^30 + 11169107526944992 * q^31 - 10999491515934048 * q^32 + 12983051842137432 * q^33 + 4867007487413652 * q^34 - 12383869767948000 * q^35 + 4111741689897636 * q^36 + 12736264858660012 * q^37 - 111335877667820664 * q^38 - 2862040663991844 * q^39 - 88663459120547472 * q^40 + 122972020616468052 * q^41 - 42001418294501904 * q^42 + 288455418162270040 * q^43 + 236905239135592368 * q^44 + 3475891686531276 * q^45 - 428027981395161168 * q^46 + 837243745741596960 * q^47 - 489441598078627440 * q^48 - 715285396941470670 * q^49 + 68086886042031174 * q^50 - 669233556367754364 * q^51 - 1659150748242045896 * q^52 - 43007964012775764 * q^53 + 137123493975036234 * q^54 + 2294863118895313296 * q^55 + 2030730320050568640 * q^56 + 706260584351385576 * q^57 + 5395375030104291852 * q^58 - 3523823330903857224 * q^59 + 2783604177674084376 * q^60 - 1779023128451013860 * q^61 - 5204128043677477536 * q^62 + 2370651157622148912 * q^63 + 5211692013463482944 * q^64 - 33242791066177513752 * q^65 + 13833831345504145272 * q^66 - 16454068667621610296 * q^67 - 927498335984326008 * q^68 - 8651173924859847696 * q^69 + 19170849981674109600 * q^70 + 17379227131150420944 * q^71 + 8462620471162227048 * q^72 + 50891146268473989076 * q^73 + 81714426393675287484 * q^74 - 282629431935472626 * q^75 - 69750112936092790064 * q^76 + 45428450983816025664 * q^77 - 145523152395047760084 * q^78 - 54055785594190591040 * q^79 - 46862985896348738976 * q^80 + 24315330918113857602 * q^81 - 227933719179803895996 * q^82 + 111108429277666677288 * q^83 - 13205203863385482144 * q^84 + 111593012278262968152 * q^85 + 158596867265246585208 * q^86 - 106200810058909096548 * q^87 + 59732519594715541728 * q^88 + 226920767965448065524 * q^89 + 244880587221476492124 * q^90 + 429154174685185000352 * q^91 - 338958281810136649248 * q^92 + 659524630358574832608 * q^93 + 246883115968835119776 * q^94 - 1558683223531725831696 * q^95 - 649508974524389600352 * q^96 - 128331469252795746236 * q^97 - 875730737371150330614 * q^98 + 766636228226373222168 * 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 $

$2$	−1271.96	−0.878328	−0.439164	−	0.898407i	$-0.644725\pi$
$2$	−1271.96	−0.878328	−0.439164	+	0.898407i	$0.644725\pi$
$3$	59049.0	0.577350
$3$	59049.0	0.577350
$4$	−479282.	−0.228540
$5$	−2.12776e7	−0.974400	−0.487200	−	0.873290i	$-0.661982\pi$
$5$	−2.12776e7	−0.974400	−0.487200	+	0.873290i	$0.661982\pi$
$6$	−7.51077e7	−0.507103
$7$	6.32076e8	0.845745	0.422873	−	0.906189i	$-0.361022\pi$
$7$	6.32076e8	0.845745	0.422873	+	0.906189i	$0.361022\pi$
$8$	3.27711e9	1.07906
$9$	3.48678e9	0.333333
$10$	2.70641e10	0.855843
$11$	5.97585e10	0.694666	0.347333	−	0.937742i	$-0.387087\pi$
$11$	5.97585e10	0.694666	0.347333	+	0.937742i	$0.387087\pi$
$12$	−2.83011e10	−0.131947
$13$	7.38499e11	1.48575	0.742874	−	0.669432i	$-0.233462\pi$
$13$	7.38499e11	1.48575	0.742874	+	0.669432i	$0.233462\pi$
$14$	−8.03972e11	−0.742842
$15$	−1.25642e12	−0.562570
$16$	−3.16321e12	−0.719230
$17$	−8.35876e12	−1.00561	−0.502804	−	0.864401i	$-0.667698\pi$
$17$	−8.35876e12	−1.00561	−0.502804	+	0.864401i	$0.667698\pi$
$18$	−4.43503e12	−0.292776
$19$	4.19061e13	1.56807	0.784034	−	0.620718i	$-0.213159\pi$
$19$	4.19061e13	1.56807	0.784034	+	0.620718i	$0.213159\pi$
$20$	1.01980e13	0.222689
$21$	3.73234e13	0.488291
$22$	−7.60101e13	−0.610145
$23$	4.48926e13	0.225961	0.112980	−	0.993597i	$-0.463960\pi$
$23$	4.48926e13	0.225961	0.112980	+	0.993597i	$0.463960\pi$
$24$	1.93510e14	0.622996
$25$	−2.41012e13	−0.0505438
$26$	−9.39338e14	−1.30497
$27$	2.05891e14	0.192450
$28$	−3.02943e14	−0.193286
$29$	−2.76669e15	−1.22119	−0.610593	−	0.791945i	$-0.709069\pi$
$29$	−2.76669e15	−1.22119	−0.610593	+	0.791945i	$0.709069\pi$
$30$	1.59811e15	0.494121
$31$	8.36452e15	1.83292	0.916459	−	0.400128i	$-0.131034\pi$
$31$	8.36452e15	1.83292	0.916459	+	0.400128i	$0.131034\pi$
$32$	−2.84914e15	−0.447341
$33$	3.52868e15	0.401066
$34$	1.06320e16	0.883253
$35$	−1.34490e16	−0.824095
$36$	−1.67115e15	−0.0761798
$37$	−1.77675e16	−0.607447	−0.303724	−	0.952760i	$-0.598230\pi$
$37$	−1.77675e16	−0.607447	−0.303724	+	0.952760i	$0.598230\pi$
$38$	−5.33027e16	−1.37728
$39$	4.36077e16	0.857797
$40$	−6.97290e16	−1.05144
$41$	1.45253e17	1.69003	0.845013	−	0.534745i	$-0.179592\pi$
$41$	1.45253e17	1.69003	0.845013	+	0.534745i	$0.179592\pi$
$42$	−4.74737e16	−0.428880
$43$	1.24744e17	0.880239	0.440119	−	0.897939i	$-0.354936\pi$
$43$	1.24744e17	0.880239	0.440119	+	0.897939i	$0.354936\pi$
$44$	−2.86412e16	−0.158759
$45$	−7.41904e16	−0.324800
$46$	−5.71014e16	−0.198468
$47$	4.28566e17	1.18847	0.594237	−	0.804290i	$-0.297454\pi$
$47$	4.28566e17	1.18847	0.594237	+	0.804290i	$0.297454\pi$
$48$	−1.86784e17	−0.415248
$49$	−1.59026e17	−0.284715
$50$	3.06556e16	0.0443941
$51$	−4.93577e17	−0.580588
$52$	−3.53950e17	−0.339552
$53$	−4.77017e17	−0.374660	−0.187330	−	0.982297i	$-0.559983\pi$
$53$	−4.77017e17	−0.374660	−0.187330	+	0.982297i	$0.559983\pi$
$54$	−2.61884e17	−0.169034
$55$	−1.27152e18	−0.676883
$56$	2.07138e18	0.912611
$57$	2.47452e18	0.905324
$58$	3.51911e18	1.07260
$59$	1.61959e18	0.412533	0.206267	−	0.978496i	$-0.433869\pi$
$59$	1.61959e18	0.412533	0.206267	+	0.978496i	$0.433869\pi$
$60$	6.02180e17	0.128570
$61$	−3.76882e18	−0.676461	−0.338230	−	0.941063i	$-0.609828\pi$
$61$	−3.76882e18	−0.676461	−0.338230	+	0.941063i	$0.609828\pi$
$62$	−1.06393e19	−1.60990
$63$	2.20391e18	0.281915
$64$	1.02577e19	1.11214
$65$	−1.57135e19	−1.44771
$66$	−4.48832e18	−0.352267
$67$	−2.81797e18	−0.188865	−0.0944324	−	0.995531i	$-0.530104\pi$
$67$	−2.81797e18	−0.188865	−0.0944324	+	0.995531i	$0.530104\pi$
$68$	4.00621e18	0.229821
$69$	2.65086e18	0.130458
$70$	1.71066e19	0.723826
$71$	1.00228e19	0.365407	0.182704	−	0.983168i	$-0.441515\pi$
$71$	1.00228e19	0.365407	0.182704	+	0.983168i	$0.441515\pi$
$72$	1.14266e19	0.359687
$73$	−1.72739e19	−0.470435	−0.235218	−	0.971943i	$-0.575580\pi$
$73$	−1.72739e19	−0.470435	−0.235218	+	0.971943i	$0.575580\pi$
$74$	2.25995e19	0.533538
$75$	−1.42315e18	−0.0291815
$76$	−2.00849e19	−0.358365
$77$	3.77719e19	0.587511
$78$	−5.54670e19	−0.753427
$79$	−3.28276e19	−0.390080	−0.195040	−	0.980795i	$-0.562484\pi$
$79$	−3.28276e19	−0.390080	−0.195040	+	0.980795i	$0.562484\pi$
$80$	6.73054e19	0.700818
$81$	1.21577e19	0.111111
$82$	−1.84755e20	−1.48440
$83$	3.05240e17	0.00215934	0.00107967	−	0.999999i	$-0.499656\pi$
$83$	3.05240e17	0.00215934	0.00107967	+	0.999999i	$0.499656\pi$
$84$	−1.78885e19	−0.111594
$85$	1.77854e20	0.979864
$86$	−1.58669e20	−0.773139
$87$	−1.63370e20	−0.705052
$88$	1.95835e20	0.749587
$89$	2.34593e20	0.797480	0.398740	−	0.917064i	$-0.369448\pi$
$89$	2.34593e20	0.797480	0.398740	+	0.917064i	$0.369448\pi$
$90$	9.43668e19	0.285281
$91$	4.66787e20	1.25656
$92$	−2.15162e19	−0.0516409
$93$	4.93917e20	1.05824
$94$	−5.45116e20	−1.04387
$95$	−8.91662e20	−1.52793
$96$	−1.68239e20	−0.258272
$97$	−5.92086e20	−0.815233	−0.407616	−	0.913153i	$-0.633640\pi$
$97$	−5.92086e20	−0.815233	−0.407616	+	0.913153i	$0.633640\pi$
$98$	2.02274e20	0.250073
$99$	2.08365e20	0.231555
$100$	1.15513e19	0.0115513
$101$	−1.66229e21	−1.49739	−0.748693	−	0.662917i	$-0.769318\pi$
$101$	−1.66229e21	−1.49739	−0.748693	+	0.662917i	$0.769318\pi$
$102$	6.27807e20	0.509946
$103$	1.17919e21	0.864552	0.432276	−	0.901741i	$-0.357711\pi$
$103$	1.17919e21	0.864552	0.432276	+	0.901741i	$0.357711\pi$
$104$	2.42014e21	1.60321
$105$	−7.94153e20	−0.475791
$106$	6.06745e20	0.329075
$107$	−8.69160e20	−0.427140	−0.213570	−	0.976928i	$-0.568509\pi$
$107$	−8.69160e20	−0.427140	−0.213570	+	0.976928i	$0.568509\pi$
$108$	−9.86799e19	−0.0439825
$109$	4.12021e20	0.166702	0.0833510	−	0.996520i	$-0.473438\pi$
$109$	4.12021e20	0.166702	0.0833510	+	0.996520i	$0.473438\pi$
$110$	1.61731e21	0.594526
$111$	−1.04915e21	−0.350710
$112$	−1.99939e21	−0.608286
$113$	2.45943e21	0.681569	0.340785	−	0.940141i	$-0.389307\pi$
$113$	2.45943e21	0.681569	0.340785	+	0.940141i	$0.389307\pi$
$114$	−3.14747e21	−0.795172
$115$	−9.55207e20	−0.220176
$116$	1.32602e21	0.279089
$117$	2.57499e21	0.495249
$118$	−2.06005e21	−0.362340
$119$	−5.28337e21	−0.850487
$120$	−4.11743e21	−0.607048
$121$	−3.82917e21	−0.517439
$122$	4.79378e21	0.594155
$123$	8.57702e21	0.975737
$124$	−4.00896e21	−0.418894
$125$	1.06588e22	1.02365
$126$	−2.80328e21	−0.247614
$127$	5.53783e21	0.450195	0.225097	−	0.974336i	$-0.427730\pi$
$127$	5.53783e21	0.450195	0.225097	+	0.974336i	$0.427730\pi$
$128$	−7.07226e21	−0.529485
$129$	7.36600e21	0.508206
$130$	1.99869e22	1.27157
$131$	−2.54630e22	−1.49472	−0.747362	−	0.664417i	$-0.768680\pi$
$131$	−2.54630e22	−1.49472	−0.747362	+	0.664417i	$0.768680\pi$
$132$	−1.69123e21	−0.0916594
$133$	2.64878e22	1.32619
$134$	3.58433e21	0.165885
$135$	−4.38087e21	−0.187523
$136$	−2.73926e22	−1.08511
$137$	−4.82088e22	−1.76832	−0.884158	−	0.467188i	$-0.845267\pi$
$137$	−4.82088e22	−1.76832	−0.884158	+	0.467188i	$0.845267\pi$
$138$	−3.37178e21	−0.114585
$139$	−2.18194e22	−0.687363	−0.343682	−	0.939086i	$-0.611674\pi$
$139$	−2.18194e22	−0.687363	−0.343682	+	0.939086i	$0.611674\pi$
$140$	6.44589e21	0.188338
$141$	2.53064e22	0.686166
$142$	−1.27486e22	−0.320948
$143$	4.41316e22	1.03210
$144$	−1.10294e22	−0.239743
$145$	5.88685e22	1.18992
$146$	2.19716e22	0.413197
$147$	−9.39035e21	−0.164380
$148$	8.51565e21	0.138826
$149$	4.84140e22	0.735386	0.367693	−	0.929947i	$-0.380148\pi$
$149$	4.84140e22	0.735386	0.367693	+	0.929947i	$0.380148\pi$
$150$	1.81018e21	0.0256309
$151$	−1.22948e23	−1.62354	−0.811770	−	0.583977i	$-0.801496\pi$
$151$	−1.22948e23	−1.62354	−0.811770	+	0.583977i	$0.801496\pi$
$152$	1.37331e23	1.69204
$153$	−2.91452e22	−0.335202
$154$	−4.80441e22	−0.516027
$155$	−1.77977e23	−1.78600
$156$	−2.09004e22	−0.196040
$157$	5.89828e22	0.517344	0.258672	−	0.965965i	$-0.416715\pi$
$157$	5.89828e22	0.517344	0.258672	+	0.965965i	$0.416715\pi$
$158$	4.17552e22	0.342619
$159$	−2.81674e22	−0.216310
$160$	6.06228e22	0.435889
$161$	2.83755e22	0.191105
$162$	−1.54640e22	−0.0975920
$163$	−3.18244e22	−0.188274	−0.0941369	−	0.995559i	$-0.530009\pi$
$163$	−3.18244e22	−0.188274	−0.0941369	+	0.995559i	$0.530009\pi$
$164$	−6.96170e22	−0.386238
$165$	−7.50818e22	−0.390799
$166$	−3.88252e20	−0.00189661
$167$	−3.62822e22	−0.166407	−0.0832033	−	0.996533i	$-0.526515\pi$
$167$	−3.62822e22	−0.166407	−0.0832033	+	0.996533i	$0.526515\pi$
$168$	1.22313e23	0.526896
$169$	2.98317e23	1.20744
$170$	−2.26223e23	−0.860642
$171$	1.46118e23	0.522689
$172$	−5.97875e22	−0.201169
$173$	3.21510e23	1.01791	0.508956	−	0.860792i	$-0.330031\pi$
$173$	3.21510e23	1.01791	0.508956	+	0.860792i	$0.330031\pi$
$174$	2.07800e23	0.619267
$175$	−1.52338e22	−0.0427472
$176$	−1.89028e23	−0.499625
$177$	9.56351e22	0.238176
$178$	−2.98392e23	−0.700449
$179$	−1.80418e23	−0.399321	−0.199661	−	0.979865i	$-0.563984\pi$
$179$	−1.80418e23	−0.399321	−0.199661	+	0.979865i	$0.563984\pi$
$180$	3.55581e22	0.0742297
$181$	−6.36646e21	−0.0125393	−0.00626965	−	0.999980i	$-0.501996\pi$
$181$	−6.36646e21	−0.0125393	−0.00626965	+	0.999980i	$0.501996\pi$
$182$	−5.93733e23	−1.10368
$183$	−2.22545e23	−0.390555
$184$	1.47118e23	0.243825
$185$	3.78050e23	0.591897
$186$	−6.28240e23	−0.929479
$187$	−4.99507e23	−0.698561
$188$	−2.05404e23	−0.271613
$189$	1.30139e23	0.162764
$190$	1.13415e24	1.34202
$191$	8.17882e23	0.915883	0.457942	−	0.888982i	$-0.348587\pi$
$191$	8.17882e23	0.915883	0.457942	+	0.888982i	$0.348587\pi$
$192$	6.05707e23	0.642096
$193$	−1.80064e23	−0.180748	−0.0903742	−	0.995908i	$-0.528806\pi$
$193$	−1.80064e23	−0.180748	−0.0903742	+	0.995908i	$0.528806\pi$
$194$	7.53107e23	0.716042
$195$	−9.27866e23	−0.835837
$196$	7.62185e22	0.0650686
$197$	1.65216e24	1.33708	0.668541	−	0.743675i	$-0.266919\pi$
$197$	1.65216e24	1.33708	0.668541	+	0.743675i	$0.266919\pi$
$198$	−2.65031e23	−0.203382
$199$	−1.52537e24	−1.11024	−0.555120	−	0.831770i	$-0.687328\pi$
$199$	−1.52537e24	−1.11024	−0.555120	+	0.831770i	$0.687328\pi$
$200$	−7.89822e22	−0.0545399
$201$	−1.66398e23	−0.109041
$202$	2.11436e24	1.31520
$203$	−1.74876e24	−1.03281
$204$	2.36562e23	0.132687
$205$	−3.09063e24	−1.64676
$206$	−1.49987e24	−0.759361
$207$	1.56531e23	0.0753202
$208$	−2.33603e24	−1.06859
$209$	2.50425e24	1.08928
$210$	1.01013e24	0.417901
$211$	1.35748e24	0.534277	0.267138	−	0.963658i	$-0.413922\pi$
$211$	1.35748e24	0.534277	0.267138	+	0.963658i	$0.413922\pi$
$212$	2.28626e23	0.0856247
$213$	5.91838e23	0.210968
$214$	1.10553e24	0.375169
$215$	−2.65425e24	−0.857705
$216$	6.74728e23	0.207665
$217$	5.28701e24	1.55018
$218$	−5.24072e23	−0.146419
$219$	−1.02001e24	−0.271606
$220$	6.09415e23	0.154695
$221$	−6.17294e24	−1.49408
$222$	1.33448e24	0.308038
$223$	4.73192e24	1.04192	0.520962	−	0.853580i	$-0.325573\pi$
$223$	4.73192e24	1.04192	0.520962	+	0.853580i	$0.325573\pi$
$224$	−1.80087e24	−0.378336
$225$	−8.40356e22	−0.0168479
$226$	−3.12828e24	−0.598642
$227$	8.00226e24	1.46198	0.730989	−	0.682389i	$-0.239059\pi$
$227$	8.00226e24	1.46198	0.730989	+	0.682389i	$0.239059\pi$
$228$	−1.18599e24	−0.206902
$229$	2.72111e24	0.453391	0.226696	−	0.973966i	$-0.427208\pi$
$229$	2.72111e24	0.453391	0.226696	+	0.973966i	$0.427208\pi$
$230$	1.21498e24	0.193387
$231$	2.23039e24	0.339200
$232$	−9.06674e24	−1.31773
$233$	−6.60115e24	−0.917028	−0.458514	−	0.888687i	$-0.651618\pi$
$233$	−6.60115e24	−0.917028	−0.458514	+	0.888687i	$0.651618\pi$
$234$	−3.27527e24	−0.434991
$235$	−9.11885e24	−1.15805
$236$	−7.76240e23	−0.0942801
$237$	−1.93843e24	−0.225213
$238$	6.72021e24	0.747007
$239$	9.92224e24	1.05544	0.527718	−	0.849420i	$-0.323048\pi$
$239$	9.92224e24	1.05544	0.527718	+	0.849420i	$0.323048\pi$
$240$	3.97432e24	0.404618
$241$	−1.54177e25	−1.50259	−0.751295	−	0.659966i	$-0.770571\pi$
$241$	−1.54177e25	−1.50259	−0.751295	+	0.659966i	$0.770571\pi$
$242$	4.87054e24	0.454481
$243$	7.17898e23	0.0641500
$244$	1.80633e24	0.154598
$245$	3.38370e24	0.277426
$246$	−1.09096e25	−0.857018
$247$	3.09477e25	2.32975
$248$	2.74114e25	1.97783
$249$	1.80241e22	0.00124670
$250$	−1.35575e25	−0.899101
$251$	−1.00009e25	−0.636014	−0.318007	−	0.948088i	$-0.603014\pi$
$251$	−1.00009e25	−0.636014	−0.318007	+	0.948088i	$0.603014\pi$
$252$	−1.05630e24	−0.0644287
$253$	2.68271e24	0.156967
$254$	−7.04387e24	−0.395419
$255$	1.05021e25	0.565725
$256$	−1.25164e25	−0.647080
$257$	−3.06596e25	−1.52149	−0.760744	−	0.649052i	$-0.775166\pi$
$257$	−3.06596e25	−1.52149	−0.760744	+	0.649052i	$0.775166\pi$
$258$	−9.36923e24	−0.446372
$259$	−1.12304e25	−0.513746
$260$	7.53119e24	0.330860
$261$	−9.64685e24	−0.407062
$262$	3.23878e25	1.31286
$263$	−2.33455e25	−0.909216	−0.454608	−	0.890692i	$-0.650221\pi$
$263$	−2.33455e25	−0.909216	−0.454608	+	0.890692i	$0.650221\pi$
$264$	1.15639e25	0.432775
$265$	1.01498e25	0.365069
$266$	−3.36914e25	−1.16483
$267$	1.38525e25	0.460425
$268$	1.35060e24	0.0431631
$269$	2.29737e25	0.706043	0.353022	−	0.935615i	$-0.385154\pi$
$269$	2.29737e25	0.706043	0.353022	+	0.935615i	$0.385154\pi$
$270$	5.57227e24	0.164707
$271$	−4.02085e25	−1.14325	−0.571624	−	0.820516i	$-0.693686\pi$
$271$	−4.02085e25	−1.14325	−0.571624	+	0.820516i	$0.693686\pi$
$272$	2.64405e25	0.723263
$273$	2.75633e25	0.725477
$274$	6.13194e25	1.55316
$275$	−1.44025e24	−0.0351111
$276$	−1.27051e24	−0.0298149
$277$	−4.48722e25	−1.01377	−0.506886	−	0.862013i	$-0.669203\pi$
$277$	−4.48722e25	−1.01377	−0.506886	+	0.862013i	$0.669203\pi$
$278$	2.77532e25	0.603731
$279$	2.91653e25	0.610973
$280$	−4.40740e25	−0.889248
$281$	−6.06489e25	−1.17871	−0.589355	−	0.807874i	$-0.700618\pi$
$281$	−6.06489e25	−1.17871	−0.589355	+	0.807874i	$0.700618\pi$
$282$	−3.21886e25	−0.602679
$283$	1.04229e26	1.88032	0.940158	−	0.340739i	$-0.110677\pi$
$283$	1.04229e26	1.88032	0.940158	+	0.340739i	$0.110677\pi$
$284$	−4.80376e24	−0.0835100
$285$	−5.26517e25	−0.882148
$286$	−5.61334e25	−0.906521
$287$	9.18107e25	1.42933
$288$	−9.93433e24	−0.149114
$289$	7.76980e23	0.0112456
$290$	−7.48781e25	−1.04514
$291$	−3.49621e25	−0.470675
$292$	8.27907e24	0.107513
$293$	6.24634e25	0.782556	0.391278	−	0.920273i	$-0.372033\pi$
$293$	6.24634e25	0.782556	0.391278	+	0.920273i	$0.372033\pi$
$294$	1.19441e25	0.144380
$295$	−3.44610e25	−0.401972
$296$	−5.82261e25	−0.655472
$297$	1.23037e25	0.133689
$298$	−6.15805e25	−0.645911
$299$	3.31532e25	0.335720
$300$	6.82091e23	0.00666913
$301$	7.88476e25	0.744458
$302$	1.56384e26	1.42600
$303$	−9.81568e25	−0.864516
$304$	−1.32558e26	−1.12780
$305$	8.01915e25	0.659144
$306$	3.70714e25	0.294418
$307$	7.14411e25	0.548271	0.274135	−	0.961691i	$-0.411608\pi$
$307$	7.14411e25	0.548271	0.274135	+	0.961691i	$0.411608\pi$
$308$	−1.81034e25	−0.134269
$309$	6.96297e25	0.499150
$310$	2.26379e26	1.56869
$311$	−6.01915e25	−0.403228	−0.201614	−	0.979465i	$-0.564619\pi$
$311$	−6.01915e25	−0.403228	−0.201614	+	0.979465i	$0.564619\pi$
$312$	1.42907e26	0.925615
$313$	−1.69049e26	−1.05876	−0.529379	−	0.848385i	$-0.677575\pi$
$313$	−1.69049e26	−1.05876	−0.529379	+	0.848385i	$0.677575\pi$
$314$	−7.50235e25	−0.454398
$315$	−4.68939e25	−0.274698
$316$	1.57337e25	0.0891488
$317$	−5.71691e25	−0.313357	−0.156678	−	0.987650i	$-0.550079\pi$
$317$	−5.71691e25	−0.313357	−0.156678	+	0.987650i	$0.550079\pi$
$318$	3.58277e25	0.189991
$319$	−1.65333e26	−0.848316
$320$	−2.18259e26	−1.08367
$321$	−5.13230e25	−0.246609
$322$	−3.60924e25	−0.167853
$323$	−3.50283e26	−1.57686
$324$	−5.82695e24	−0.0253933
$325$	−1.77987e25	−0.0750954
$326$	4.04792e25	0.165366
$327$	2.43294e25	0.0962454
$328$	4.76009e26	1.82364
$329$	2.70886e26	1.00515
$330$	9.55007e25	0.343250
$331$	6.67957e25	0.232571	0.116285	−	0.993216i	$-0.462901\pi$
$331$	6.67957e25	0.232571	0.116285	+	0.993216i	$0.462901\pi$
$332$	−1.46296e23	−0.000493495 0
$333$	−6.19515e25	−0.202482
$334$	4.61493e25	0.146160
$335$	5.99597e25	0.184030
$336$	−1.18062e26	−0.351194
$337$	3.55365e26	1.02461	0.512307	−	0.858802i	$-0.328791\pi$
$337$	3.55365e26	1.02461	0.512307	+	0.858802i	$0.328791\pi$
$338$	−3.79446e26	−1.06053
$339$	1.45227e26	0.393504
$340$	−8.52424e25	−0.223938
$341$	4.99851e26	1.27327
$342$	−1.85855e26	−0.459093
$343$	−4.53560e26	−1.08654
$344$	4.08799e26	0.949832
$345$	−5.64040e25	−0.127119
$346$	−4.08947e26	−0.894062
$347$	−3.94238e25	−0.0836179	−0.0418090	−	0.999126i	$-0.513312\pi$
$347$	−3.94238e25	−0.0836179	−0.0418090	+	0.999126i	$0.513312\pi$
$348$	7.83004e25	0.161132
$349$	−5.84299e26	−1.16672	−0.583362	−	0.812212i	$-0.698263\pi$
$349$	−5.84299e26	−1.16672	−0.583362	+	0.812212i	$0.698263\pi$
$350$	1.93767e25	0.0375461
$351$	1.52050e26	0.285932
$352$	−1.70260e26	−0.310753
$353$	4.96062e26	0.878823	0.439412	−	0.898286i	$-0.355187\pi$
$353$	4.96062e26	0.878823	0.439412	+	0.898286i	$0.355187\pi$
$354$	−1.21644e26	−0.209197
$355$	−2.13262e26	−0.356053
$356$	−1.12436e26	−0.182256
$357$	−3.11978e26	−0.491029
$358$	2.29483e26	0.350735
$359$	−3.35136e26	−0.497426	−0.248713	−	0.968577i	$-0.580008\pi$
$359$	−3.35136e26	−0.497426	−0.248713	+	0.968577i	$0.580008\pi$
$360$	−2.43130e26	−0.350479
$361$	1.04192e27	1.45884
$362$	8.09785e24	0.0110136
$363$	−2.26109e26	−0.298743
$364$	−2.23723e26	−0.287174
$365$	3.67547e26	0.458392
$366$	2.83068e26	0.343035
$367$	9.70198e25	0.114253	0.0571264	−	0.998367i	$-0.481806\pi$
$367$	9.70198e25	0.114253	0.0571264	+	0.998367i	$0.481806\pi$
$368$	−1.42005e26	−0.162518
$369$	5.06465e26	0.563342
$370$	−4.80862e26	−0.519880
$371$	−3.01511e26	−0.316867
$372$	−2.36725e26	−0.241849
$373$	1.03252e27	1.02554	0.512771	−	0.858525i	$-0.328619\pi$
$373$	1.03252e27	1.02554	0.512771	+	0.858525i	$0.328619\pi$
$374$	6.35350e26	0.613566
$375$	6.29389e26	0.591005
$376$	1.40446e27	1.28244
$377$	−2.04320e27	−1.81437
$378$	−1.65531e26	−0.142960
$379$	2.20881e26	0.185544	0.0927721	−	0.995687i	$-0.470427\pi$
$379$	2.20881e26	0.185544	0.0927721	+	0.995687i	$0.470427\pi$
$380$	4.27358e26	0.349191
$381$	3.27003e26	0.259920
$382$	−1.04031e27	−0.804446
$383$	−1.59547e27	−1.20033	−0.600165	−	0.799876i	$-0.704899\pi$
$383$	−1.59547e27	−1.20033	−0.600165	+	0.799876i	$0.704899\pi$
$384$	−4.17610e26	−0.305698
$385$	−8.03695e26	−0.572471
$386$	2.29033e26	0.158756
$387$	4.34955e26	0.293413
$388$	2.83776e26	0.186313
$389$	−3.60474e26	−0.230358	−0.115179	−	0.993345i	$-0.536744\pi$
$389$	−3.60474e26	−0.230358	−0.115179	+	0.993345i	$0.536744\pi$
$390$	1.18020e27	0.734140
$391$	−3.75247e26	−0.227228
$392$	−5.21147e26	−0.307225
$393$	−1.50357e27	−0.862980
$394$	−2.10148e27	−1.17440
$395$	6.98492e26	0.380095
$396$	−9.98656e25	−0.0529196
$397$	−1.47191e27	−0.759595	−0.379798	−	0.925070i	$-0.624006\pi$
$397$	−1.47191e27	−0.759595	−0.379798	+	0.925070i	$0.624006\pi$
$398$	1.94020e27	0.975156
$399$	1.56408e27	0.765674
$400$	7.62370e25	0.0363527
$401$	1.00401e27	0.466360	0.233180	−	0.972434i	$-0.425087\pi$
$401$	1.00401e27	0.466360	0.233180	+	0.972434i	$0.425087\pi$
$402$	2.11651e26	0.0957740
$403$	6.17719e27	2.72325
$404$	7.96708e26	0.342212
$405$	−2.58686e26	−0.108267
$406$	2.22434e27	0.907148
$407$	−1.06176e27	−0.421973
$408$	−1.61750e27	−0.626489
$409$	−4.41838e27	−1.66789	−0.833947	−	0.551845i	$-0.813924\pi$
$409$	−4.41838e27	−1.66789	−0.833947	+	0.551845i	$0.813924\pi$
$410$	3.93114e27	1.44640
$411$	−2.84668e27	−1.02094
$412$	−5.65163e26	−0.197584
$413$	1.02370e27	0.348898
$414$	−1.99100e26	−0.0661559
$415$	−6.49477e24	−0.00210406
$416$	−2.10409e27	−0.664635
$417$	−1.28841e27	−0.396849
$418$	−3.18529e27	−0.956749
$419$	−2.36639e27	−0.693169	−0.346584	−	0.938019i	$-0.612659\pi$
$419$	−2.36639e27	−0.693169	−0.346584	+	0.938019i	$0.612659\pi$
$420$	3.80623e26	0.108737
$421$	2.72067e27	0.758078	0.379039	−	0.925381i	$-0.376255\pi$
$421$	2.72067e27	0.758078	0.379039	+	0.925381i	$0.376255\pi$
$422$	−1.72665e27	−0.469271
$423$	1.49432e27	0.396158
$424$	−1.56324e27	−0.404281
$425$	2.01456e26	0.0508272
$426$	−7.52791e26	−0.185299
$427$	−2.38218e27	−0.572114
$428$	4.16573e26	0.0976183
$429$	2.60593e27	0.595883
$430$	3.37609e27	0.753347
$431$	8.87397e27	1.93244	0.966222	−	0.257713i	$-0.0829688\pi$
$431$	8.87397e27	1.93244	0.966222	+	0.257713i	$0.0829688\pi$
$432$	−6.51276e26	−0.138416
$433$	−3.39994e27	−0.705258	−0.352629	−	0.935763i	$-0.614712\pi$
$433$	−3.39994e27	−0.705258	−0.352629	+	0.935763i	$0.614712\pi$
$434$	−6.72484e27	−1.36157
$435$	3.47613e27	0.687003
$436$	−1.97474e26	−0.0380980
$437$	1.88128e27	0.354322
$438$	1.29740e27	0.238559
$439$	2.29516e27	0.412037	0.206018	−	0.978548i	$-0.433949\pi$
$439$	2.29516e27	0.412037	0.206018	+	0.978548i	$0.433949\pi$
$440$	−4.16690e27	−0.730398
$441$	−5.54491e26	−0.0949050
$442$	7.85170e27	1.31229
$443$	−5.65265e27	−0.922599	−0.461299	−	0.887245i	$-0.652617\pi$
$443$	−5.65265e27	−0.922599	−0.461299	+	0.887245i	$0.652617\pi$
$444$	5.02841e26	0.0801510
$445$	−4.99157e27	−0.777065
$446$	−6.01879e27	−0.915152
$447$	2.85880e27	0.424576
$448$	6.48364e27	0.940589
$449$	1.23324e28	1.74768	0.873839	−	0.486216i	$-0.161623\pi$
$449$	1.23324e28	1.74768	0.873839	+	0.486216i	$0.161623\pi$
$450$	1.06890e26	0.0147980
$451$	8.68008e27	1.17400
$452$	−1.17876e27	−0.155766
$453$	−7.25995e27	−0.937351
$454$	−1.01785e28	−1.28410
$455$	−9.93211e27	−1.22440
$456$	8.10926e27	0.976900
$457$	−7.62646e27	−0.897848	−0.448924	−	0.893570i	$-0.648193\pi$
$457$	−7.62646e27	−0.897848	−0.448924	+	0.893570i	$0.648193\pi$
$458$	−3.46113e27	−0.398226
$459$	−1.72100e27	−0.193529
$460$	4.57814e26	0.0503189
$461$	−9.04851e26	−0.0972114	−0.0486057	−	0.998818i	$-0.515478\pi$
$461$	−9.04851e26	−0.0972114	−0.0486057	+	0.998818i	$0.515478\pi$
$462$	−2.83696e27	−0.297929
$463$	−1.19705e27	−0.122889	−0.0614443	−	0.998111i	$-0.519571\pi$
$463$	−1.19705e27	−0.122889	−0.0614443	+	0.998111i	$0.519571\pi$
$464$	8.75161e27	0.878313
$465$	−1.05094e28	−1.03115
$466$	8.39637e27	0.805452
$467$	−1.16951e28	−1.09693	−0.548464	−	0.836174i	$-0.684787\pi$
$467$	−1.16951e28	−1.09693	−0.548464	+	0.836174i	$0.684787\pi$
$468$	−1.23415e27	−0.113184
$469$	−1.78117e27	−0.159732
$470$	1.15988e28	1.01715
$471$	3.48288e27	0.298689
$472$	5.30757e27	0.445148
$473$	7.45451e27	0.611472
$474$	2.46560e27	0.197811
$475$	−1.00999e27	−0.0792562
$476$	2.53222e27	0.194370
$477$	−1.66326e27	−0.124887
$478$	−1.26206e28	−0.927019
$479$	2.04856e28	1.47206	0.736029	−	0.676950i	$-0.236699\pi$
$479$	2.04856e28	1.47206	0.736029	+	0.676950i	$0.236699\pi$
$480$	3.57971e27	0.251661
$481$	−1.31213e28	−0.902513
$482$	1.96106e28	1.31977
$483$	1.67555e27	0.110335
$484$	1.83525e27	0.118255
$485$	1.25982e28	0.794363
$486$	−9.13134e26	−0.0563448
$487$	−3.75693e27	−0.226871	−0.113436	−	0.993545i	$-0.536186\pi$
$487$	−3.75693e27	−0.226871	−0.113436	+	0.993545i	$0.536186\pi$
$488$	−1.23508e28	−0.729942
$489$	−1.87920e27	−0.108700
$490$	−4.30391e27	−0.243671
$491$	−1.53173e28	−0.848841	−0.424420	−	0.905465i	$-0.639522\pi$
$491$	−1.53173e28	−0.848841	−0.424420	+	0.905465i	$0.639522\pi$
$492$	−4.11081e27	−0.222995
$493$	2.31261e28	1.22803
$494$	−3.93640e28	−2.04629
$495$	−4.43350e27	−0.225628
$496$	−2.64587e28	−1.31829
$497$	6.33518e27	0.309042
$498$	−2.29259e25	−0.00109501
$499$	3.84836e27	0.179978	0.0899890	−	0.995943i	$-0.471317\pi$
$499$	3.84836e27	0.179978	0.0899890	+	0.995943i	$0.471317\pi$
$500$	−5.10855e27	−0.233945
$501$	−2.14243e27	−0.0960749
$502$	1.27208e28	0.558629
$503$	−2.25177e28	−0.968411	−0.484205	−	0.874954i	$-0.660891\pi$
$503$	−2.25177e28	−0.968411	−0.484205	+	0.874954i	$0.660891\pi$
$504$	7.22246e27	0.304204
$505$	3.53696e28	1.45905
$506$	−3.41229e27	−0.137869
$507$	1.76153e28	0.697119
$508$	−2.65418e27	−0.102887
$509$	2.09122e27	0.0794078	0.0397039	−	0.999211i	$-0.487359\pi$
$509$	2.09122e27	0.0794078	0.0397039	+	0.999211i	$0.487359\pi$
$510$	−1.33582e28	−0.496892
$511$	−1.09184e28	−0.397869
$512$	3.07519e28	1.09783
$513$	8.62810e27	0.301775
$514$	3.89976e28	1.33637
$515$	−2.50902e28	−0.842420
$516$	−3.53039e27	−0.116145
$517$	2.56104e28	0.825594
$518$	1.42846e28	0.451237
$519$	1.89849e28	0.587692
$520$	−5.14948e28	−1.56217
$521$	−3.76486e27	−0.111932	−0.0559659	−	0.998433i	$-0.517824\pi$
$521$	−3.76486e27	−0.111932	−0.0559659	+	0.998433i	$0.517824\pi$
$522$	1.22704e28	0.357534
$523$	−1.74944e28	−0.499611	−0.249806	−	0.968296i	$-0.580367\pi$
$523$	−1.74944e28	−0.499611	−0.249806	+	0.968296i	$0.580367\pi$
$524$	1.22040e28	0.341604
$525$	−8.99539e26	−0.0246801
$526$	2.96944e28	0.798590
$527$	−6.99170e28	−1.84320
$528$	−1.11619e28	−0.288459
$529$	−3.74562e28	−0.948942
$530$	−1.29101e28	−0.320650
$531$	5.64716e27	0.137511
$532$	−1.26952e28	−0.303086
$533$	1.07269e29	2.51095
$534$	−1.76197e28	−0.404404
$535$	1.84936e28	0.416205
$536$	−9.23480e27	−0.203797
$537$	−1.06535e28	−0.230548
$538$	−2.92215e28	−0.620138
$539$	−9.50317e27	−0.197782
$540$	2.09967e27	0.0428565
$541$	−6.99960e28	−1.40121	−0.700603	−	0.713552i	$-0.747085\pi$
$541$	−6.99960e28	−1.40121	−0.700603	+	0.713552i	$0.747085\pi$
$542$	5.11434e28	1.00415
$543$	−3.75933e26	−0.00723956
$544$	2.38153e28	0.449849
$545$	−8.76680e27	−0.162434
$546$	−3.50593e28	−0.637207
$547$	3.00896e28	0.536476	0.268238	−	0.963353i	$-0.413559\pi$
$547$	3.00896e28	0.536476	0.268238	+	0.963353i	$0.413559\pi$
$548$	2.31056e28	0.404130
$549$	−1.31411e28	−0.225487
$550$	1.83193e27	0.0308391
$551$	−1.15941e29	−1.91490
$552$	8.68717e27	0.140773
$553$	−2.07495e28	−0.329909
$554$	5.70754e28	0.890424
$555$	2.23235e28	0.341732
$556$	1.04576e28	0.157090
$557$	1.17263e29	1.72855	0.864277	−	0.503017i	$-0.167777\pi$
$557$	1.17263e29	1.72855	0.864277	+	0.503017i	$0.167777\pi$
$558$	−3.70969e28	−0.536635
$559$	9.21233e28	1.30781
$560$	4.25421e28	0.592714
$561$	−2.94954e28	−0.403315
$562$	7.71427e28	1.03529
$563$	6.46986e28	0.852230	0.426115	−	0.904669i	$-0.359882\pi$
$563$	6.46986e28	0.852230	0.426115	+	0.904669i	$0.359882\pi$
$564$	−1.21289e28	−0.156816
$565$	−5.23307e28	−0.664121
$566$	−1.32575e29	−1.65153
$567$	7.68456e27	0.0939717
$568$	3.28459e28	0.394297
$569$	−1.35009e29	−1.59105	−0.795527	−	0.605918i	$-0.792806\pi$
$569$	−1.35009e29	−1.59105	−0.795527	+	0.605918i	$0.792806\pi$
$570$	6.69707e28	0.774816
$571$	2.55750e28	0.290494	0.145247	−	0.989395i	$-0.453602\pi$
$571$	2.55750e28	0.290494	0.145247	+	0.989395i	$0.453602\pi$
$572$	−2.11515e28	−0.235875
$573$	4.82951e28	0.528786
$574$	−1.16779e29	−1.25542
$575$	−1.08197e27	−0.0114209
$576$	3.57664e28	0.370714
$577$	−1.52580e29	−1.55293	−0.776465	−	0.630160i	$-0.782989\pi$
$577$	−1.52580e29	−1.55293	−0.776465	+	0.630160i	$0.782989\pi$
$578$	−9.88284e26	−0.00987733
$579$	−1.06326e28	−0.104355
$580$	−2.82146e28	−0.271944
$581$	1.92935e26	0.00182625
$582$	4.44702e28	0.413407
$583$	−2.85058e28	−0.260264
$584$	−5.66084e28	−0.507629
$585$	−5.47896e28	−0.482571
$586$	−7.94506e28	−0.687341
$587$	−1.08485e29	−0.921868	−0.460934	−	0.887434i	$-0.652486\pi$
$587$	−1.08485e29	−0.921868	−0.460934	+	0.887434i	$0.652486\pi$
$588$	4.50063e27	0.0375674
$589$	3.50525e29	2.87414
$590$	4.38328e28	0.353064
$591$	9.75587e28	0.771965
$592$	5.62023e28	0.436894
$593$	8.82363e28	0.673865	0.336933	−	0.941529i	$-0.390611\pi$
$593$	8.82363e28	0.673865	0.336933	+	0.941529i	$0.390611\pi$
$594$	−1.56498e28	−0.117422
$595$	1.12417e29	0.828715
$596$	−2.32040e28	−0.168065
$597$	−9.00714e28	−0.640998
$598$	−4.21694e28	−0.294873
$599$	9.23342e28	0.634426	0.317213	−	0.948354i	$-0.397253\pi$
$599$	9.23342e28	0.634426	0.317213	+	0.948354i	$0.397253\pi$
$600$	−4.66382e27	−0.0314886
$601$	−7.30699e28	−0.484793	−0.242397	−	0.970177i	$-0.577934\pi$
$601$	−7.30699e28	−0.484793	−0.242397	+	0.970177i	$0.577934\pi$
$602$	−1.00291e29	−0.653878
$603$	−9.82566e27	−0.0629550
$604$	5.89267e28	0.371043
$605$	8.14756e28	0.504192
$606$	1.24851e29	0.759329
$607$	8.07544e28	0.482709	0.241354	−	0.970437i	$-0.422408\pi$
$607$	8.07544e28	0.482709	0.241354	+	0.970437i	$0.422408\pi$
$608$	−1.19396e29	−0.701461
$609$	−1.03262e29	−0.596294
$610$	−1.02000e29	−0.578945
$611$	3.16496e29	1.76577
$612$	1.39688e28	0.0766070
$613$	−2.21326e29	−1.19316	−0.596578	−	0.802555i	$-0.703473\pi$
$613$	−2.21326e29	−1.19316	−0.596578	+	0.802555i	$0.703473\pi$
$614$	−9.08699e28	−0.481562
$615$	−1.82498e29	−0.950759
$616$	1.23783e29	0.633960
$617$	−2.16026e29	−1.08771	−0.543854	−	0.839180i	$-0.683035\pi$
$617$	−2.16026e29	−1.08771	−0.543854	+	0.839180i	$0.683035\pi$
$618$	−8.85659e28	−0.438417
$619$	−2.09908e29	−1.02159	−0.510795	−	0.859702i	$-0.670649\pi$
$619$	−2.09908e29	−1.02159	−0.510795	+	0.859702i	$0.670649\pi$
$620$	8.53011e28	0.408171
$621$	9.24299e27	0.0434861
$622$	7.65609e28	0.354167
$623$	1.48280e29	0.674465
$624$	−1.37940e29	−0.616953
$625$	−2.15300e29	−0.946901
$626$	2.15023e29	0.929938
$627$	1.47873e29	0.628899
$628$	−2.82694e28	−0.118234
$629$	1.48514e29	0.610853
$630$	5.96470e28	0.241275
$631$	4.81094e28	0.191391	0.0956955	−	0.995411i	$-0.469492\pi$
$631$	4.81094e28	0.191391	0.0956955	+	0.995411i	$0.469492\pi$
$632$	−1.07580e29	−0.420921
$633$	8.01576e28	0.308465
$634$	7.27166e28	0.275230
$635$	−1.17832e29	−0.438670
$636$	1.35001e28	0.0494354
$637$	−1.17441e29	−0.423014
$638$	2.10296e29	0.745100
$639$	3.49474e28	0.121802
$640$	1.50481e29	0.515930
$641$	−5.04867e28	−0.170282	−0.0851408	−	0.996369i	$-0.527134\pi$
$641$	−5.04867e28	−0.170282	−0.0851408	+	0.996369i	$0.527134\pi$
$642$	6.52806e28	0.216604
$643$	−3.93930e29	−1.28589	−0.642945	−	0.765912i	$-0.722288\pi$
$643$	−3.93930e29	−1.28589	−0.642945	+	0.765912i	$0.722288\pi$
$644$	−1.35999e28	−0.0436751
$645$	−1.56731e29	−0.495196
$646$	4.45545e29	1.38500
$647$	−1.38475e29	−0.423523	−0.211762	−	0.977321i	$-0.567920\pi$
$647$	−1.38475e29	−0.423523	−0.211762	+	0.977321i	$0.567920\pi$
$648$	3.98420e28	0.119896
$649$	9.67842e28	0.286573
$650$	2.26392e28	0.0659584
$651$	3.12193e29	0.894998
$652$	1.52528e28	0.0430280
$653$	1.16655e29	0.323830	0.161915	−	0.986805i	$-0.448233\pi$
$653$	1.16655e29	0.323830	0.161915	+	0.986805i	$0.448233\pi$
$654$	−3.09459e28	−0.0845350
$655$	5.41792e29	1.45646
$656$	−4.59464e29	−1.21552
$657$	−6.02303e28	−0.156812
$658$	−3.44555e29	−0.882849
$659$	−3.36819e29	−0.849377	−0.424688	−	0.905340i	$-0.639616\pi$
$659$	−3.36819e29	−0.849377	−0.424688	+	0.905340i	$0.639616\pi$
$660$	3.59854e28	0.0893130
$661$	4.31449e29	1.05394	0.526968	−	0.849885i	$-0.323329\pi$
$661$	4.31449e29	1.05394	0.526968	+	0.849885i	$0.323329\pi$
$662$	−8.49612e28	−0.204273
$663$	−3.64506e29	−0.862606
$664$	1.00030e27	0.00233006
$665$	−5.63598e29	−1.29224
$666$	7.87995e28	0.177846
$667$	−1.24204e29	−0.275940
$668$	1.73894e28	0.0380305
$669$	2.79415e29	0.601555
$670$	−7.62660e28	−0.161639
$671$	−2.25219e29	−0.469915
$672$	−1.06340e29	−0.218433
$673$	−1.19710e29	−0.242088	−0.121044	−	0.992647i	$-0.538624\pi$
$673$	−1.19710e29	−0.242088	−0.121044	+	0.992647i	$0.538624\pi$
$674$	−4.52008e29	−0.899948
$675$	−4.96222e27	−0.00972717
$676$	−1.42978e29	−0.275949
$677$	7.71503e29	1.46608	0.733038	−	0.680188i	$-0.238102\pi$
$677$	7.71503e29	1.46608	0.733038	+	0.680188i	$0.238102\pi$
$678$	−1.84722e29	−0.345626
$679$	−3.74243e29	−0.689479
$680$	5.82848e29	1.05733
$681$	4.72525e29	0.844074
$682$	−6.35788e29	−1.11835
$683$	6.40488e29	1.10941	0.554707	−	0.832046i	$-0.312830\pi$
$683$	6.40488e29	1.10941	0.554707	+	0.832046i	$0.312830\pi$
$684$	−7.00316e28	−0.119455
$685$	1.02577e30	1.72305
$686$	5.76908e29	0.954340
$687$	1.60679e29	0.261766
$688$	−3.94591e29	−0.633094
$689$	−3.52277e29	−0.556650
$690$	7.17434e28	0.111652
$691$	1.07309e30	1.64482	0.822408	−	0.568898i	$-0.192630\pi$
$691$	1.07309e30	1.64482	0.822408	+	0.568898i	$0.192630\pi$
$692$	−1.54094e29	−0.232633
$693$	1.31702e29	0.195837
$694$	5.01454e28	0.0734440
$695$	4.64263e29	0.669767
$696$	−5.35382e29	−0.760794
$697$	−1.21413e30	−1.69950
$698$	7.43202e29	1.02477
$699$	−3.89791e29	−0.529446
$700$	7.30127e27	0.00976943
$701$	−7.18115e29	−0.946574	−0.473287	−	0.880908i	$-0.656933\pi$
$701$	−7.18115e29	−0.946574	−0.473287	+	0.880908i	$0.656933\pi$
$702$	−1.93401e29	−0.251142
$703$	−7.44568e29	−0.952518
$704$	6.12985e29	0.772568
$705$	−5.38459e29	−0.668601
$706$	−6.30969e29	−0.771895
$707$	−1.05070e30	−1.26641
$708$	−4.58362e28	−0.0544327
$709$	4.24360e29	0.496534	0.248267	−	0.968692i	$-0.420139\pi$
$709$	4.24360e29	0.496534	0.248267	+	0.968692i	$0.420139\pi$
$710$	2.71259e29	0.312732
$711$	−1.14463e29	−0.130027
$712$	7.68786e29	0.860529
$713$	3.75505e29	0.414167
$714$	3.96822e29	0.431285
$715$	−9.39014e29	−1.00568
$716$	8.64710e28	0.0912607
$717$	5.85898e29	0.609356
$718$	4.26277e29	0.436904
$719$	−5.73272e29	−0.579038	−0.289519	−	0.957172i	$-0.593495\pi$
$719$	−5.73272e29	−0.579038	−0.289519	+	0.957172i	$0.593495\pi$
$720$	2.34680e29	0.233606
$721$	7.45334e29	0.731191
$722$	−1.32527e30	−1.28134
$723$	−9.10400e29	−0.867521
$724$	3.05133e27	0.00286572
$725$	6.66805e28	0.0617234
$726$	2.87600e29	0.262395
$727$	1.42987e30	1.28583	0.642916	−	0.765937i	$-0.277725\pi$
$727$	1.42987e30	1.28583	0.642916	+	0.765937i	$0.277725\pi$
$728$	1.52971e30	1.35591
$729$	4.23912e28	0.0370370
$730$	−4.67503e29	−0.402619
$731$	−1.04270e30	−0.885175
$732$	1.06662e29	0.0892572
$733$	1.99143e30	1.64276	0.821380	−	0.570381i	$-0.193205\pi$
$733$	1.99143e30	1.64276	0.821380	+	0.570381i	$0.193205\pi$
$734$	−1.23405e29	−0.100351
$735$	1.99804e29	0.160172
$736$	−1.27905e29	−0.101081
$737$	−1.68398e29	−0.131198
$738$	−6.44200e29	−0.494799
$739$	−2.11124e30	−1.59872	−0.799359	−	0.600854i	$-0.794827\pi$
$739$	−2.11124e30	−1.59872	−0.799359	+	0.600854i	$0.794827\pi$
$740$	−1.81193e29	−0.135272
$741$	1.82743e30	1.34508
$742$	3.83509e29	0.278313
$743$	1.11538e30	0.798067	0.399033	−	0.916936i	$-0.369346\pi$
$743$	1.11538e30	0.798067	0.399033	+	0.916936i	$0.369346\pi$
$744$	1.61862e30	1.14190
$745$	−1.03013e30	−0.716561
$746$	−1.31331e30	−0.900763
$747$	1.06431e27	0.000719781 0
$748$	2.39405e29	0.159649
$749$	−5.49375e29	−0.361251
$750$	−8.00555e29	−0.519096
$751$	−2.28371e30	−1.46023	−0.730116	−	0.683323i	$-0.760534\pi$
$751$	−2.28371e30	−1.46023	−0.730116	+	0.683323i	$0.760534\pi$
$752$	−1.35564e30	−0.854787
$753$	−5.90546e29	−0.367203
$754$	2.59886e30	1.59361
$755$	2.61603e30	1.58198
$756$	−6.23732e28	−0.0371980
$757$	9.73411e29	0.572519	0.286259	−	0.958152i	$-0.407588\pi$
$757$	9.73411e29	0.572519	0.286259	+	0.958152i	$0.407588\pi$
$758$	−2.80951e29	−0.162969
$759$	1.58412e29	0.0906251
$760$	−2.92207e30	−1.64873
$761$	−3.06985e30	−1.70836	−0.854179	−	0.519979i	$-0.825940\pi$
$761$	−3.06985e30	−1.70836	−0.854179	+	0.519979i	$0.825940\pi$
$762$	−4.15933e29	−0.228295
$763$	2.60428e29	0.140987
$764$	−3.91996e29	−0.209316
$765$	6.20140e29	0.326621
$766$	2.02936e30	1.05428
$767$	1.19607e30	0.612920
$768$	−7.39078e29	−0.373592
$769$	−7.51816e29	−0.374874	−0.187437	−	0.982277i	$-0.560018\pi$
$769$	−7.51816e29	−0.374874	−0.187437	+	0.982277i	$0.560018\pi$
$770$	1.02226e30	0.502817
$771$	−1.81042e30	−0.878432
$772$	8.63013e28	0.0413081
$773$	1.23771e30	0.584434	0.292217	−	0.956352i	$-0.405607\pi$
$773$	1.23771e30	0.584434	0.292217	+	0.956352i	$0.405607\pi$
$774$	−5.53243e29	−0.257713
$775$	−2.01595e29	−0.0926427
$776$	−1.94033e30	−0.879686
$777$	−6.63144e29	−0.296611
$778$	4.58507e29	0.202330
$779$	6.08698e30	2.65008
$780$	4.44710e29	0.191022
$781$	5.98949e29	0.253836
$782$	4.77297e29	0.199580
$783$	−5.69637e29	−0.235017
$784$	5.03033e29	0.204776
$785$	−1.25501e30	−0.504100
$786$	1.91247e30	0.757979
$787$	2.14352e30	0.838288	0.419144	−	0.907920i	$-0.362330\pi$
$787$	2.14352e30	0.838288	0.419144	+	0.907920i	$0.362330\pi$
$788$	−7.91853e29	−0.305576
$789$	−1.37853e30	−0.524936
$790$	−8.88450e29	−0.333848
$791$	1.55454e30	0.576434
$792$	6.82834e29	0.249862
$793$	−2.78327e30	−1.00505
$794$	1.87221e30	0.667174
$795$	5.99334e29	0.210773
$796$	7.31081e29	0.253734
$797$	3.01280e30	1.03195	0.515974	−	0.856605i	$-0.327430\pi$
$797$	3.01280e30	1.03195	0.515974	+	0.856605i	$0.327430\pi$
$798$	−1.98944e30	−0.672513
$799$	−3.58228e30	−1.19514
$800$	6.86676e28	0.0226103
$801$	8.17975e29	0.265827
$802$	−1.27705e30	−0.409617
$803$	−1.03226e30	−0.326796
$804$	7.97518e28	0.0249202
$805$	−6.03763e29	−0.186213
$806$	−7.85711e30	−2.39191
$807$	1.35657e30	0.407634
$808$	−5.44752e30	−1.61577
$809$	−5.76883e30	−1.68900	−0.844498	−	0.535559i	$-0.820101\pi$
$809$	−5.76883e30	−1.68900	−0.844498	+	0.535559i	$0.820101\pi$
$810$	3.29037e29	0.0950937
$811$	3.98728e30	1.13752	0.568759	−	0.822504i	$-0.307424\pi$
$811$	3.98728e30	1.13752	0.568759	+	0.822504i	$0.307424\pi$
$812$	8.38148e29	0.236038
$813$	−2.37427e30	−0.660055
$814$	1.35051e30	0.370631
$815$	6.77146e29	0.183454
$816$	1.56129e30	0.417576
$817$	5.22754e30	1.38027
$818$	5.61998e30	1.46496
$819$	1.62759e30	0.418855
$820$	1.48128e30	0.376350
$821$	−4.09615e30	−1.02748	−0.513739	−	0.857946i	$-0.671740\pi$
$821$	−4.09615e30	−1.02748	−0.513739	+	0.857946i	$0.671740\pi$
$822$	3.62085e30	0.896719
$823$	1.43384e30	0.350592	0.175296	−	0.984516i	$-0.443912\pi$
$823$	1.43384e30	0.350592	0.175296	+	0.984516i	$0.443912\pi$
$824$	3.86432e30	0.932905
$825$	−8.50453e28	−0.0202714
$826$	−1.30210e30	−0.306447
$827$	−3.13142e30	−0.727668	−0.363834	−	0.931464i	$-0.618532\pi$
$827$	−3.13142e30	−0.727668	−0.363834	+	0.931464i	$0.618532\pi$
$828$	−7.50225e28	−0.0172136
$829$	−4.44329e30	−1.00666	−0.503329	−	0.864095i	$-0.667892\pi$
$829$	−4.44329e30	−1.00666	−0.503329	+	0.864095i	$0.667892\pi$
$830$	8.26106e27	0.00184806
$831$	−2.64966e30	−0.585301
$832$	7.57531e30	1.65236
$833$	1.32926e30	0.286311
$834$	1.63880e30	0.348564
$835$	7.71998e29	0.162147
$836$	−1.20024e30	−0.248944
$837$	1.72218e30	0.352745
$838$	3.00994e30	0.608829
$839$	−9.30057e29	−0.185784	−0.0928922	−	0.995676i	$-0.529611\pi$
$839$	−9.30057e29	−0.185784	−0.0928922	+	0.995676i	$0.529611\pi$
$840$	−2.60252e30	−0.513408
$841$	2.52173e30	0.491293
$842$	−3.46057e30	−0.665842
$843$	−3.58126e30	−0.680528
$844$	−6.50614e29	−0.122103
$845$	−6.34746e30	−1.17653
$846$	−1.90070e30	−0.347957
$847$	−2.42033e30	−0.437621
$848$	1.50891e30	0.269467
$849$	6.15462e30	1.08560
$850$	−2.56243e29	−0.0446430
$851$	−7.97630e29	−0.137259
$852$	−2.83657e29	−0.0482145
$853$	−2.27471e30	−0.381911	−0.190955	−	0.981599i	$-0.561159\pi$
$853$	−2.27471e30	−0.381911	−0.190955	+	0.981599i	$0.561159\pi$
$854$	3.03003e30	0.502503
$855$	−3.10903e30	−0.509309
$856$	−2.84833e30	−0.460910
$857$	3.05003e30	0.487534	0.243767	−	0.969834i	$-0.421617\pi$
$857$	3.05003e30	0.487534	0.243767	+	0.969834i	$0.421617\pi$
$858$	−3.31462e30	−0.523380
$859$	1.34073e30	0.209128	0.104564	−	0.994518i	$-0.466655\pi$
$859$	1.34073e30	0.209128	0.104564	+	0.994518i	$0.466655\pi$
$860$	1.27213e30	0.196020
$861$	5.42133e30	0.825225
$862$	−1.12873e31	−1.69732
$863$	1.14916e31	1.70713	0.853566	−	0.520985i	$-0.174435\pi$
$863$	1.14916e31	1.70713	0.853566	+	0.520985i	$0.174435\pi$
$864$	−5.86612e29	−0.0860908
$865$	−6.84096e30	−0.991855
$866$	4.32457e30	0.619448
$867$	4.58799e28	0.00649265
$868$	−2.53397e30	−0.354278
$869$	−1.96173e30	−0.270976
$870$	−4.42148e30	−0.603414
$871$	−2.08107e30	−0.280606
$872$	1.35024e30	0.179882
$873$	−2.06448e30	−0.271744
$874$	−2.39290e30	−0.311211
$875$	6.73714e30	0.865747
$876$	4.88871e29	0.0620727
$877$	9.06320e30	1.13707	0.568533	−	0.822660i	$-0.307511\pi$
$877$	9.06320e30	1.13707	0.568533	+	0.822660i	$0.307511\pi$
$878$	−2.91934e30	−0.361904
$879$	3.68840e30	0.451809
$880$	4.02207e30	0.486835
$881$	−6.50767e30	−0.778356	−0.389178	−	0.921163i	$-0.627241\pi$
$881$	−6.50767e30	−0.778356	−0.389178	+	0.921163i	$0.627241\pi$
$882$	7.05287e29	0.0833577
$883$	5.90742e30	0.689939	0.344969	−	0.938614i	$-0.387889\pi$
$883$	5.90742e30	0.689939	0.344969	+	0.938614i	$0.387889\pi$
$884$	2.95858e30	0.341456
$885$	−2.03489e30	−0.232079
$886$	7.18992e30	0.810344
$887$	−3.42312e30	−0.381263	−0.190632	−	0.981662i	$-0.561054\pi$
$887$	−3.42312e30	−0.381263	−0.190632	+	0.981662i	$0.561054\pi$
$888$	−3.43819e30	−0.378437
$889$	3.50032e30	0.380750
$890$	6.34905e30	0.682518
$891$	7.26524e29	0.0771852
$892$	−2.26792e30	−0.238121
$893$	1.79595e31	1.86361
$894$	−3.63627e30	−0.372917
$895$	3.83886e30	0.389099
$896$	−4.47020e30	−0.447810
$897$	1.95766e30	0.193828
$898$	−1.56863e31	−1.53503
$899$	−2.31420e31	−2.23833
$900$	4.02768e28	0.00385042
$901$	3.98728e30	0.376761
$902$	−1.10407e31	−1.03116
$903$	4.65587e30	0.429813
$904$	8.05980e30	0.735455
$905$	1.35463e29	0.0122183
$906$	9.23433e30	0.823302
$907$	−1.16251e31	−1.02452	−0.512262	−	0.858829i	$-0.671192\pi$
$907$	−1.16251e31	−1.02452	−0.512262	+	0.858829i	$0.671192\pi$
$908$	−3.83534e30	−0.334120
$909$	−5.79606e30	−0.499128
$910$	1.26332e31	1.07542
$911$	−1.34510e31	−1.13191	−0.565957	−	0.824435i	$-0.691493\pi$
$911$	−1.34510e31	−1.13191	−0.565957	+	0.824435i	$0.691493\pi$
$912$	−7.82741e30	−0.651137
$913$	1.82407e28	0.00150002
$914$	9.70051e30	0.788605
$915$	4.73523e30	0.380557
$916$	−1.30418e30	−0.103618
$917$	−1.60945e31	−1.26416
$918$	2.18903e30	0.169982
$919$	−8.55562e30	−0.656808	−0.328404	−	0.944537i	$-0.606511\pi$
$919$	−8.55562e30	−0.656808	−0.328404	+	0.944537i	$0.606511\pi$
$920$	−3.13032e30	−0.237583
$921$	4.21853e30	0.316544
$922$	1.15093e30	0.0853835
$923$	7.40185e30	0.542903
$924$	−1.06899e30	−0.0775205
$925$	4.28218e29	0.0307027
$926$	1.52259e30	0.107937
$927$	4.11157e30	0.288184
$928$	7.88268e30	0.546286
$929$	9.93712e30	0.680919	0.340460	−	0.940259i	$-0.389417\pi$
$929$	9.93712e30	0.680919	0.340460	+	0.940259i	$0.389417\pi$
$930$	1.33674e31	0.905684
$931$	−6.66418e30	−0.446452
$932$	3.16381e30	0.209577
$933$	−3.55425e30	−0.232804
$934$	1.48757e31	0.963462
$935$	1.06283e31	0.680679
$936$	8.43852e30	0.534404
$937$	−2.14272e30	−0.134183	−0.0670917	−	0.997747i	$-0.521372\pi$
$937$	−2.14272e30	−0.134183	−0.0670917	+	0.997747i	$0.521372\pi$
$938$	2.26557e30	0.140297
$939$	−9.98217e30	−0.611275
$940$	4.37050e30	0.264660
$941$	1.69148e31	1.01292	0.506459	−	0.862264i	$-0.330954\pi$
$941$	1.69148e31	1.01292	0.506459	+	0.862264i	$0.330954\pi$
$942$	−4.43006e30	−0.262347
$943$	6.52077e30	0.381879
$944$	−5.12310e30	−0.296706
$945$	−2.76904e30	−0.158597
$946$	−9.48180e30	−0.537074
$947$	−1.96530e31	−1.10092	−0.550459	−	0.834862i	$-0.685547\pi$
$947$	−1.96530e31	−1.10092	−0.550459	+	0.834862i	$0.685547\pi$
$948$	9.29057e29	0.0514701
$949$	−1.27568e31	−0.698948
$950$	1.28466e30	0.0696129
$951$	−3.37578e30	−0.180917
$952$	−1.73142e31	−0.917728
$953$	2.39001e31	1.25292	0.626462	−	0.779452i	$-0.284502\pi$
$953$	2.39001e31	1.25292	0.626462	+	0.779452i	$0.284502\pi$
$954$	2.11559e30	0.109692
$955$	−1.74026e31	−0.892437
$956$	−4.75555e30	−0.241209
$957$	−9.76276e30	−0.489776
$958$	−2.60567e31	−1.29295
$959$	−3.04716e31	−1.49555
$960$	−1.28880e31	−0.625658
$961$	4.91397e31	2.35959
$962$	1.66897e31	0.792703
$963$	−3.03057e30	−0.142380
$964$	7.38943e30	0.343401
$965$	3.83132e30	0.176121
$966$	−2.13122e30	−0.0969100
$967$	1.63072e31	0.733504	0.366752	−	0.930319i	$-0.380470\pi$
$967$	1.63072e31	0.733504	0.366752	+	0.930319i	$0.380470\pi$
$968$	−1.25486e31	−0.558348
$969$	−2.06839e31	−0.910401
$970$	−1.60243e31	−0.697712
$971$	3.09343e31	1.33241	0.666207	−	0.745767i	$-0.267917\pi$
$971$	3.09343e31	1.33241	0.666207	+	0.745767i	$0.267917\pi$
$972$	−3.44076e29	−0.0146608
$973$	−1.37915e31	−0.581334
$974$	4.77865e30	0.199267
$975$	−1.05100e30	−0.0433563
$976$	1.19216e31	0.486531
$977$	1.98044e31	0.799592	0.399796	−	0.916604i	$-0.369081\pi$
$977$	1.98044e31	0.799592	0.399796	+	0.916604i	$0.369081\pi$
$978$	2.39025e30	0.0954742
$979$	1.40189e31	0.553982
$980$	−1.62175e30	−0.0634029
$981$	1.43663e30	0.0555673
$982$	1.94829e31	0.745561
$983$	−4.34284e30	−0.164423	−0.0822114	−	0.996615i	$-0.526198\pi$
$983$	−4.34284e30	−0.164423	−0.0822114	+	0.996615i	$0.526198\pi$
$984$	2.81078e31	1.05288
$985$	−3.51541e31	−1.30285
$986$	−2.94154e31	−1.07862
$987$	1.59955e31	0.580322
$988$	−1.48327e31	−0.532441
$989$	5.60008e30	0.198899
$990$	5.63922e30	0.198175
$991$	4.70795e30	0.163704	0.0818518	−	0.996645i	$-0.473917\pi$
$991$	4.70795e30	0.163704	0.0818518	+	0.996645i	$0.473917\pi$
$992$	−2.38317e31	−0.819939
$993$	3.94422e30	0.134275
$994$	−8.05807e30	−0.271440
$995$	3.24561e31	1.08182
$996$	−8.63864e27	−0.000284920 0
$997$	−1.58934e31	−0.518700	−0.259350	−	0.965783i	$-0.583508\pi$
$997$	−1.58934e31	−0.518700	−0.259350	+	0.965783i	$0.583508\pi$
$998$	−4.89494e30	−0.158080
$999$	−3.65817e30	−0.116903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.22.a.c.1.1	✓	2
3.2	odd	2		9.22.a.e.1.2		2
4.3	odd	2		48.22.a.g.1.1		2
5.2	odd	4		75.22.b.d.49.2		4
5.3	odd	4		75.22.b.d.49.3		4
5.4	even	2		75.22.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.22.a.c.1.1	✓	2	1.1	even	1	trivial
9.22.a.e.1.2		2	3.2	odd	2
48.22.a.g.1.1		2	4.3	odd	2
75.22.a.d.1.2		2	5.4	even	2
75.22.b.d.49.2		4	5.2	odd	4
75.22.b.d.49.3		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-1271.96 q^{2} +59049.0 q^{3} -479282. q^{4} -2.12776e7 q^{5} -7.51077e7 q^{6} +6.32076e8 q^{7} +3.27711e9 q^{8} +3.48678e9 q^{9} +O(q^{10})\)	\(q-1271.96 q^{2} +59049.0 q^{3} -479282. q^{4} -2.12776e7 q^{5} -7.51077e7 q^{6} +6.32076e8 q^{7} +3.27711e9 q^{8} +3.48678e9 q^{9} +2.70641e10 q^{10} +5.97585e10 q^{11} -2.83011e10 q^{12} +7.38499e11 q^{13} -8.03972e11 q^{14} -1.25642e12 q^{15} -3.16321e12 q^{16} -8.35876e12 q^{17} -4.43503e12 q^{18} +4.19061e13 q^{19} +1.01980e13 q^{20} +3.73234e13 q^{21} -7.60101e13 q^{22} +4.48926e13 q^{23} +1.93510e14 q^{24} -2.41012e13 q^{25} -9.39338e14 q^{26} +2.05891e14 q^{27} -3.02943e14 q^{28} -2.76669e15 q^{29} +1.59811e15 q^{30} +8.36452e15 q^{31} -2.84914e15 q^{32} +3.52868e15 q^{33} +1.06320e16 q^{34} -1.34490e16 q^{35} -1.67115e15 q^{36} -1.77675e16 q^{37} -5.33027e16 q^{38} +4.36077e16 q^{39} -6.97290e16 q^{40} +1.45253e17 q^{41} -4.74737e16 q^{42} +1.24744e17 q^{43} -2.86412e16 q^{44} -7.41904e16 q^{45} -5.71014e16 q^{46} +4.28566e17 q^{47} -1.86784e17 q^{48} -1.59026e17 q^{49} +3.06556e16 q^{50} -4.93577e17 q^{51} -3.53950e17 q^{52} -4.77017e17 q^{53} -2.61884e17 q^{54} -1.27152e18 q^{55} +2.07138e18 q^{56} +2.47452e18 q^{57} +3.51911e18 q^{58} +1.61959e18 q^{59} +6.02180e17 q^{60} -3.76882e18 q^{61} -1.06393e19 q^{62} +2.20391e18 q^{63} +1.02577e19 q^{64} -1.57135e19 q^{65} -4.48832e18 q^{66} -2.81797e18 q^{67} +4.00621e18 q^{68} +2.65086e18 q^{69} +1.71066e19 q^{70} +1.00228e19 q^{71} +1.14266e19 q^{72} -1.72739e19 q^{73} +2.25995e19 q^{74} -1.42315e18 q^{75} -2.00849e19 q^{76} +3.77719e19 q^{77} -5.54670e19 q^{78} -3.28276e19 q^{79} +6.73054e19 q^{80} +1.21577e19 q^{81} -1.84755e20 q^{82} +3.05240e17 q^{83} -1.78885e19 q^{84} +1.77854e20 q^{85} -1.58669e20 q^{86} -1.63370e20 q^{87} +1.95835e20 q^{88} +2.34593e20 q^{89} +9.43668e19 q^{90} +4.66787e20 q^{91} -2.15162e19 q^{92} +4.93917e20 q^{93} -5.45116e20 q^{94} -8.91662e20 q^{95} -1.68239e20 q^{96} -5.92086e20 q^{97} +2.02274e20 q^{98} +2.08365e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 666 q^{2} + 118098 q^{3} + 1179236 q^{4} + 996876 q^{5} + 39326634 q^{6} + 679896112 q^{7} + 2427055848 q^{8} + 6973568802 q^{9}+O(q^{10}) \) 2 * q + 666 * q^2 + 118098 * q^3 + 1179236 * q^4 + 996876 * q^5 + 39326634 * q^6 + 679896112 * q^7 + 2427055848 * q^8 + 6973568802 * q^9	\( 2 q + 666 q^{2} + 118098 q^{3} + 1179236 q^{4} + 996876 q^{5} + 39326634 q^{6} + 679896112 q^{7} + 2427055848 q^{8} + 6973568802 q^{9} + 70231066524 q^{10} + 219869122968 q^{11} + 69632706564 q^{12} - 48468909956 q^{13} - 711297706896 q^{14} + 58864530924 q^{15} - 8288736440560 q^{16} - 11333529041436 q^{17} + 2322198411066 q^{18} + 11960585011624 q^{19} + 47140581172824 q^{20} + 40147185517488 q^{21} + 234277148563128 q^{22} - 146508390063504 q^{23} + 143315220768552 q^{24} - 4786354247074 q^{25} - 24\!\cdots\!16 q^{26}+ \cdots + 76\!\cdots\!68 q^{99}+O(q^{100}) \) 2 * q + 666 * q^2 + 118098 * q^3 + 1179236 * q^4 + 996876 * q^5 + 39326634 * q^6 + 679896112 * q^7 + 2427055848 * q^8 + 6973568802 * q^9 + 70231066524 * q^10 + 219869122968 * q^11 + 69632706564 * q^12 - 48468909956 * q^13 - 711297706896 * q^14 + 58864530924 * q^15 - 8288736440560 * q^16 - 11333529041436 * q^17 + 2322198411066 * q^18 + 11960585011624 * q^19 + 47140581172824 * q^20 + 40147185517488 * q^21 + 234277148563128 * q^22 - 146508390063504 * q^23 + 143315220768552 * q^24 - 4786354247074 * q^25 - 2464447363969716 * q^26 + 411782264189298 * q^27 - 223631286954656 * q^28 - 1798520043674052 * q^29 + 4147074247175676 * q^30 + 11169107526944992 * q^31 - 10999491515934048 * q^32 + 12983051842137432 * q^33 + 4867007487413652 * q^34 - 12383869767948000 * q^35 + 4111741689897636 * q^36 + 12736264858660012 * q^37 - 111335877667820664 * q^38 - 2862040663991844 * q^39 - 88663459120547472 * q^40 + 122972020616468052 * q^41 - 42001418294501904 * q^42 + 288455418162270040 * q^43 + 236905239135592368 * q^44 + 3475891686531276 * q^45 - 428027981395161168 * q^46 + 837243745741596960 * q^47 - 489441598078627440 * q^48 - 715285396941470670 * q^49 + 68086886042031174 * q^50 - 669233556367754364 * q^51 - 1659150748242045896 * q^52 - 43007964012775764 * q^53 + 137123493975036234 * q^54 + 2294863118895313296 * q^55 + 2030730320050568640 * q^56 + 706260584351385576 * q^57 + 5395375030104291852 * q^58 - 3523823330903857224 * q^59 + 2783604177674084376 * q^60 - 1779023128451013860 * q^61 - 5204128043677477536 * q^62 + 2370651157622148912 * q^63 + 5211692013463482944 * q^64 - 33242791066177513752 * q^65 + 13833831345504145272 * q^66 - 16454068667621610296 * q^67 - 927498335984326008 * q^68 - 8651173924859847696 * q^69 + 19170849981674109600 * q^70 + 17379227131150420944 * q^71 + 8462620471162227048 * q^72 + 50891146268473989076 * q^73 + 81714426393675287484 * q^74 - 282629431935472626 * q^75 - 69750112936092790064 * q^76 + 45428450983816025664 * q^77 - 145523152395047760084 * q^78 - 54055785594190591040 * q^79 - 46862985896348738976 * q^80 + 24315330918113857602 * q^81 - 227933719179803895996 * q^82 + 111108429277666677288 * q^83 - 13205203863385482144 * q^84 + 111593012278262968152 * q^85 + 158596867265246585208 * q^86 - 106200810058909096548 * q^87 + 59732519594715541728 * q^88 + 226920767965448065524 * q^89 + 244880587221476492124 * q^90 + 429154174685185000352 * q^91 - 338958281810136649248 * q^92 + 659524630358574832608 * q^93 + 246883115968835119776 * q^94 - 1558683223531725831696 * q^95 - 649508974524389600352 * q^96 - 128331469252795746236 * q^97 - 875730737371150330614 * q^98 + 766636228226373222168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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