LMFDB - Embedded newform 3.22.a.c.1.2

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			1.2
Root			$-12.2377$ 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)

$f(q)$	$=$	$q+1937.96 q^{2} +59049.0 q^{3} +1.65852e6 q^{4} +2.22745e7 q^{5} +1.14434e8 q^{6} +4.78205e7 q^{7} -8.50053e8 q^{8} +3.48678e9 q^{9} +O(q^{10})$	\(q+1937.96 q^{2} +59049.0 q^{3} +1.65852e6 q^{4} +2.22745e7 q^{5} +1.14434e8 q^{6} +4.78205e7 q^{7} -8.50053e8 q^{8} +3.48678e9 q^{9} +4.31669e10 q^{10} +1.60111e11 q^{11} +9.79338e10 q^{12} -7.86968e11 q^{13} +9.26741e10 q^{14} +1.31529e12 q^{15} -5.12553e12 q^{16} -2.97477e12 q^{17} +6.75723e12 q^{18} -2.99456e13 q^{19} +3.69426e13 q^{20} +2.82376e12 q^{21} +3.10287e14 q^{22} -1.91401e14 q^{23} -5.01948e13 q^{24} +1.93148e13 q^{25} -1.52511e15 q^{26} +2.05891e14 q^{27} +7.93112e13 q^{28} +9.68170e14 q^{29} +2.54896e15 q^{30} +2.80459e15 q^{31} -8.15035e15 q^{32} +9.45437e15 q^{33} -5.76496e15 q^{34} +1.06518e15 q^{35} +5.78290e15 q^{36} +3.05038e16 q^{37} -5.80331e16 q^{38} -4.64697e16 q^{39} -1.89345e16 q^{40} -2.22806e16 q^{41} +5.47231e15 q^{42} +1.63711e17 q^{43} +2.65546e17 q^{44} +7.76663e16 q^{45} -3.70927e17 q^{46} +4.08678e17 q^{47} -3.02657e17 q^{48} -5.56259e17 q^{49} +3.74313e16 q^{50} -1.75657e17 q^{51} -1.30520e18 q^{52} +4.34009e17 q^{53} +3.99008e17 q^{54} +3.56638e18 q^{55} -4.06500e16 q^{56} -1.76826e18 q^{57} +1.87627e18 q^{58} -5.14341e18 q^{59} +2.18142e18 q^{60} +1.98980e18 q^{61} +5.43517e18 q^{62} +1.66740e17 q^{63} -5.04601e18 q^{64} -1.75293e19 q^{65} +1.83222e19 q^{66} -1.36361e19 q^{67} -4.93370e18 q^{68} -1.13020e19 q^{69} +2.06427e18 q^{70} +7.35641e18 q^{71} -2.96395e18 q^{72} +6.81650e19 q^{73} +5.91149e19 q^{74} +1.14052e18 q^{75} -4.96652e19 q^{76} +7.65658e18 q^{77} -9.00562e19 q^{78} -2.12282e19 q^{79} -1.14168e20 q^{80} +1.21577e19 q^{81} -4.31789e19 q^{82} +1.10803e20 q^{83} +4.68325e18 q^{84} -6.62613e19 q^{85} +3.17266e20 q^{86} +5.71695e19 q^{87} -1.36102e20 q^{88} -7.67205e18 q^{89} +1.50514e20 q^{90} -3.76333e19 q^{91} -3.17442e20 q^{92} +1.65608e20 q^{93} +7.92000e20 q^{94} -6.67021e20 q^{95} -4.81270e20 q^{96} +4.63755e20 q^{97} -1.07801e21 q^{98} +5.58271e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1937.96	1.33822	0.669112	−	0.743162i	$-0.266675\pi$
$2$	1937.96	1.33822	0.669112	+	0.743162i	$0.266675\pi$
$3$	59049.0	0.577350
$3$	59049.0	0.577350
$4$	1.65852e6	0.790843
$5$	2.22745e7	1.02005	0.510026	−	0.860159i	$-0.329636\pi$
$5$	2.22745e7	1.02005	0.510026	+	0.860159i	$0.329636\pi$
$6$	1.14434e8	0.772624
$7$	4.78205e7	0.0639860	0.0319930	−	0.999488i	$-0.489815\pi$
$7$	4.78205e7	0.0639860	0.0319930	+	0.999488i	$0.489815\pi$
$8$	−8.50053e8	−0.279899
$9$	3.48678e9	0.333333
$10$	4.31669e10	1.36506
$11$	1.60111e11	1.86122	0.930609	−	0.366016i	$-0.119278\pi$
$11$	1.60111e11	1.86122	0.930609	+	0.366016i	$0.119278\pi$
$12$	9.79338e10	0.456593
$13$	−7.86968e11	−1.58326	−0.791630	−	0.611001i	$-0.790767\pi$
$13$	−7.86968e11	−1.58326	−0.791630	+	0.611001i	$0.790767\pi$
$14$	9.26741e10	0.0856276
$15$	1.31529e12	0.588927
$16$	−5.12553e12	−1.16541
$17$	−2.97477e12	−0.357881	−0.178941	−	0.983860i	$-0.557267\pi$
$17$	−2.97477e12	−0.357881	−0.178941	+	0.983860i	$0.557267\pi$
$18$	6.75723e12	0.446075
$19$	−2.99456e13	−1.12052	−0.560260	−	0.828317i	$-0.689299\pi$
$19$	−2.99456e13	−1.12052	−0.560260	+	0.828317i	$0.689299\pi$
$20$	3.69426e13	0.806701
$21$	2.82376e12	0.0369423
$22$	3.10287e14	2.49073
$23$	−1.91401e14	−0.963390	−0.481695	−	0.876339i	$-0.659979\pi$
$23$	−1.91401e14	−0.963390	−0.481695	+	0.876339i	$0.659979\pi$
$24$	−5.01948e13	−0.161600
$25$	1.93148e13	0.0405061
$26$	−1.52511e15	−2.11876
$27$	2.05891e14	0.192450
$28$	7.93112e13	0.0506029
$29$	9.68170e14	0.427339	0.213670	−	0.976906i	$-0.431458\pi$
$29$	9.68170e14	0.427339	0.213670	+	0.976906i	$0.431458\pi$
$30$	2.54896e15	0.788117
$31$	2.80459e15	0.614570	0.307285	−	0.951618i	$-0.400580\pi$
$31$	2.80459e15	0.614570	0.307285	+	0.951618i	$0.400580\pi$
$32$	−8.15035e15	−1.27968
$33$	9.45437e15	1.07457
$34$	−5.76496e15	−0.478925
$35$	1.06518e15	0.0652691
$36$	5.78290e15	0.263614
$37$	3.05038e16	1.04288	0.521441	−	0.853287i	$-0.325395\pi$
$37$	3.05038e16	1.04288	0.521441	+	0.853287i	$0.325395\pi$
$38$	−5.80331e16	−1.49951
$39$	−4.64697e16	−0.914095
$40$	−1.89345e16	−0.285511
$41$	−2.22806e16	−0.259237	−0.129618	−	0.991564i	$-0.541375\pi$
$41$	−2.22806e16	−0.259237	−0.129618	+	0.991564i	$0.541375\pi$
$42$	5.47231e15	0.0494371
$43$	1.63711e17	1.15521	0.577604	−	0.816317i	$-0.303988\pi$
$43$	1.63711e17	1.15521	0.577604	+	0.816317i	$0.303988\pi$
$44$	2.65546e17	1.47193
$45$	7.76663e16	0.340017
$46$	−3.70927e17	−1.28923
$47$	4.08678e17	1.13332	0.566662	−	0.823951i	$-0.308235\pi$
$47$	4.08678e17	1.13332	0.566662	+	0.823951i	$0.308235\pi$
$48$	−3.02657e17	−0.672850
$49$	−5.56259e17	−0.995906
$50$	3.74313e16	0.0542063
$51$	−1.75657e17	−0.206623
$52$	−1.30520e18	−1.25211
$53$	4.34009e17	0.340881	0.170440	−	0.985368i	$-0.445481\pi$
$53$	4.34009e17	0.340881	0.170440	+	0.985368i	$0.445481\pi$
$54$	3.99008e17	0.257541
$55$	3.56638e18	1.89854
$56$	−4.06500e16	−0.0179096
$57$	−1.76826e18	−0.646932
$58$	1.87627e18	0.571875
$59$	−5.14341e18	−1.31010	−0.655051	−	0.755584i	$-0.727353\pi$
$59$	−5.14341e18	−1.31010	−0.655051	+	0.755584i	$0.727353\pi$
$60$	2.18142e18	0.465749
$61$	1.98980e18	0.357147	0.178573	−	0.983927i	$-0.442852\pi$
$61$	1.98980e18	0.357147	0.178573	+	0.983927i	$0.442852\pi$
$62$	5.43517e18	0.822432
$63$	1.66740e17	0.0213287
$64$	−5.04601e18	−0.547089
$65$	−1.75293e19	−1.61501
$66$	1.83222e19	1.43802
$67$	−1.36361e19	−0.913913	−0.456956	−	0.889489i	$-0.651060\pi$
$67$	−1.36361e19	−0.913913	−0.456956	+	0.889489i	$0.651060\pi$
$68$	−4.93370e18	−0.283028
$69$	−1.13020e19	−0.556213
$70$	2.06427e18	0.0873446
$71$	7.35641e18	0.268196	0.134098	−	0.990968i	$-0.457186\pi$
$71$	7.35641e18	0.268196	0.134098	+	0.990968i	$0.457186\pi$
$72$	−2.96395e18	−0.0932996
$73$	6.81650e19	1.85640	0.928200	−	0.372081i	$-0.121356\pi$
$73$	6.81650e19	1.85640	0.928200	+	0.372081i	$0.121356\pi$
$74$	5.91149e19	1.39561
$75$	1.14052e18	0.0233862
$76$	−4.96652e19	−0.886155
$77$	7.65658e18	0.119092
$78$	−9.00562e19	−1.22326
$79$	−2.12282e19	−0.252249	−0.126124	−	0.992014i	$-0.540254\pi$
$79$	−2.12282e19	−0.252249	−0.126124	+	0.992014i	$0.540254\pi$
$80$	−1.14168e20	−1.18878
$81$	1.21577e19	0.111111
$82$	−4.31789e19	−0.346917
$83$	1.10803e20	0.783849	0.391924	−	0.919997i	$-0.371809\pi$
$83$	1.10803e20	0.783849	0.391924	+	0.919997i	$0.371809\pi$
$84$	4.68325e18	0.0292156
$85$	−6.62613e19	−0.365058
$86$	3.17266e20	1.54593
$87$	5.71695e19	0.246724
$88$	−1.36102e20	−0.520952
$89$	−7.67205e18	−0.0260805	−0.0130403	−	0.999915i	$-0.504151\pi$
$89$	−7.67205e18	−0.0260805	−0.0130403	+	0.999915i	$0.504151\pi$
$90$	1.50514e20	0.455019
$91$	−3.76333e19	−0.101306
$92$	−3.17442e20	−0.761890
$93$	1.65608e20	0.354822
$94$	7.92000e20	1.51664
$95$	−6.67021e20	−1.14299
$96$	−4.81270e20	−0.738824
$97$	4.63755e20	0.638535	0.319268	−	0.947665i	$-0.396563\pi$
$97$	4.63755e20	0.638535	0.319268	+	0.947665i	$0.396563\pi$
$98$	−1.07801e21	−1.33274
$99$	5.58271e20	0.620406
$100$	3.20340e19	0.0320340
$101$	1.75642e20	0.158217	0.0791086	−	0.996866i	$-0.474793\pi$
$101$	1.75642e20	0.158217	0.0791086	+	0.996866i	$0.474793\pi$
$102$	−3.40415e20	−0.276508
$103$	−1.29018e21	−0.945933	−0.472967	−	0.881080i	$-0.656817\pi$
$103$	−1.29018e21	−0.945933	−0.472967	+	0.881080i	$0.656817\pi$
$104$	6.68965e20	0.443152
$105$	6.28976e19	0.0376831
$106$	8.41091e20	0.456175
$107$	5.76913e19	0.0283518	0.0141759	−	0.999900i	$-0.495488\pi$
$107$	5.76913e19	0.0283518	0.0141759	+	0.999900i	$0.495488\pi$
$108$	3.41474e20	0.152198
$109$	−5.74941e20	−0.232619	−0.116309	−	0.993213i	$-0.537106\pi$
$109$	−5.74941e20	−0.232619	−0.116309	+	0.993213i	$0.537106\pi$
$110$	6.91148e21	2.54067
$111$	1.80122e21	0.602109
$112$	−2.45106e20	−0.0745700
$113$	−4.56755e21	−1.26578	−0.632892	−	0.774240i	$-0.718132\pi$
$113$	−4.56755e21	−1.26578	−0.632892	+	0.774240i	$0.718132\pi$
$114$	−3.42680e21	−0.865740
$115$	−4.26336e21	−0.982708
$116$	1.60573e21	0.337958
$117$	−2.74399e21	−0.527753
$118$	−9.96770e21	−1.75321
$119$	−1.42255e20	−0.0228994
$120$	−1.11806e21	−0.164840
$121$	1.82352e22	2.46413
$122$	3.85615e21	0.477942
$123$	−1.31565e21	−0.149671
$124$	4.65146e21	0.486028
$125$	−1.01911e22	−0.978734
$126$	3.23134e20	0.0285425
$127$	1.84938e22	1.50344	0.751722	−	0.659480i	$-0.229224\pi$
$127$	1.84938e22	1.50344	0.751722	+	0.659480i	$0.229224\pi$
$128$	7.31359e21	0.547553
$129$	9.66700e21	0.666960
$130$	−3.39710e22	−2.16124
$131$	−1.25296e22	−0.735509	−0.367754	−	0.929923i	$-0.619873\pi$
$131$	−1.25296e22	−0.735509	−0.367754	+	0.929923i	$0.619873\pi$
$132$	1.56802e22	0.849820
$133$	−1.43201e21	−0.0716976
$134$	−2.64261e22	−1.22302
$135$	4.58612e21	0.196309
$136$	2.52871e21	0.100171
$137$	3.84075e22	1.40880	0.704402	−	0.709801i	$-0.251215\pi$
$137$	3.84075e22	1.40880	0.704402	+	0.709801i	$0.251215\pi$
$138$	−2.19028e22	−0.744338
$139$	−9.58856e21	−0.302063	−0.151032	−	0.988529i	$-0.548260\pi$
$139$	−9.58856e21	−0.302063	−0.151032	+	0.988529i	$0.548260\pi$
$140$	1.76662e21	0.0516176
$141$	2.41320e22	0.654324
$142$	1.42564e22	0.358907
$143$	−1.26002e23	−2.94679
$144$	−1.78716e22	−0.388470
$145$	2.15655e22	0.435908
$146$	1.32101e23	2.48428
$147$	−3.28465e22	−0.574986
$148$	5.05911e22	0.824757
$149$	3.44428e22	0.523170	0.261585	−	0.965180i	$-0.415755\pi$
$149$	3.44428e22	0.523170	0.261585	+	0.965180i	$0.415755\pi$
$150$	2.21028e21	0.0312960
$151$	−3.63152e22	−0.479546	−0.239773	−	0.970829i	$-0.577073\pi$
$151$	−3.63152e22	−0.479546	−0.239773	+	0.970829i	$0.577073\pi$
$152$	2.54553e22	0.313632
$153$	−1.03724e22	−0.119294
$154$	1.48381e22	0.159372
$155$	6.24707e22	0.626893
$156$	−7.70708e22	−0.722906
$157$	−9.41986e22	−0.826225	−0.413112	−	0.910680i	$-0.635558\pi$
$157$	−9.41986e22	−0.826225	−0.413112	+	0.910680i	$0.635558\pi$
$158$	−4.11393e22	−0.337565
$159$	2.56278e22	0.196808
$160$	−1.81545e23	−1.30534
$161$	−9.15290e21	−0.0616435
$162$	2.35610e22	0.148692
$163$	−1.80771e23	−1.06945	−0.534723	−	0.845027i	$-0.679584\pi$
$163$	−1.80771e23	−1.06945	−0.534723	+	0.845027i	$0.679584\pi$
$164$	−3.69528e22	−0.205016
$165$	2.10591e23	1.09612
$166$	2.14732e23	1.04897
$167$	3.71934e22	0.170586	0.0852929	−	0.996356i	$-0.472817\pi$
$167$	3.71934e22	0.170586	0.0852929	+	0.996356i	$0.472817\pi$
$168$	−2.40034e21	−0.0103401
$169$	3.72255e23	1.50671
$170$	−1.28412e23	−0.488529
$171$	−1.04414e23	−0.373507
$172$	2.71518e23	0.913589
$173$	2.58398e23	0.818096	0.409048	−	0.912513i	$-0.365861\pi$
$173$	2.58398e23	0.818096	0.409048	+	0.912513i	$0.365861\pi$
$174$	1.10792e23	0.330172
$175$	9.23645e20	0.00259183
$176$	−8.20652e23	−2.16908
$177$	−3.03713e23	−0.756388
$178$	−1.48681e22	−0.0349016
$179$	−3.35184e23	−0.741868	−0.370934	−	0.928659i	$-0.620962\pi$
$179$	−3.35184e23	−0.741868	−0.370934	+	0.928659i	$0.620962\pi$
$180$	1.28811e23	0.268900
$181$	−1.92267e23	−0.378687	−0.189343	−	0.981911i	$-0.560636\pi$
$181$	−1.92267e23	−0.378687	−0.189343	+	0.981911i	$0.560636\pi$
$182$	−7.29316e22	−0.135571
$183$	1.17496e23	0.206199
$184$	1.62701e23	0.269652
$185$	6.79455e23	1.06379
$186$	3.20941e23	0.474831
$187$	−4.76292e23	−0.666095
$188$	6.77800e23	0.896281
$189$	9.84583e21	0.0123141
$190$	−1.29266e24	−1.52957
$191$	−4.60821e23	−0.516038	−0.258019	−	0.966140i	$-0.583070\pi$
$191$	−4.60821e23	−0.516038	−0.258019	+	0.966140i	$0.583070\pi$
$192$	−2.97962e23	−0.315862
$193$	1.29600e24	1.30093	0.650465	−	0.759536i	$-0.274574\pi$
$193$	1.29600e24	1.30093	0.650465	+	0.759536i	$0.274574\pi$
$194$	8.98736e23	0.854503
$195$	−1.03509e24	−0.932425
$196$	−9.22566e23	−0.787605
$197$	2.05711e24	1.66480	0.832402	−	0.554172i	$-0.186965\pi$
$197$	2.05711e24	1.66480	0.832402	+	0.554172i	$0.186965\pi$
$198$	1.08190e24	0.830242
$199$	5.34557e22	0.0389078	0.0194539	−	0.999811i	$-0.493807\pi$
$199$	5.34557e22	0.0389078	0.0194539	+	0.999811i	$0.493807\pi$
$200$	−1.64186e22	−0.0113376
$201$	−8.05198e23	−0.527648
$202$	3.40386e23	0.211730
$203$	4.62984e22	0.0273437
$204$	−2.91330e23	−0.163406
$205$	−4.96289e23	−0.264435
$206$	−2.50032e24	−1.26587
$207$	−6.67374e23	−0.321130
$208$	4.03363e24	1.84515
$209$	−4.79460e24	−2.08553
$210$	1.21893e23	0.0504284
$211$	−3.16142e24	−1.24427	−0.622137	−	0.782908i	$-0.713735\pi$
$211$	−3.16142e24	−1.24427	−0.622137	+	0.782908i	$0.713735\pi$
$212$	7.19813e23	0.269583
$213$	4.34388e23	0.154843
$214$	1.11803e23	0.0379410
$215$	3.64659e24	1.17837
$216$	−1.75018e23	−0.0538665
$217$	1.34117e23	0.0393239
$218$	−1.11421e24	−0.311296
$219$	4.02508e24	1.07179
$220$	5.91491e24	1.50145
$221$	2.34105e24	0.566619
$222$	3.49068e24	0.805756
$223$	−3.10623e24	−0.683963	−0.341981	−	0.939707i	$-0.611098\pi$
$223$	−3.10623e24	−0.683963	−0.341981	+	0.939707i	$0.611098\pi$
$224$	−3.89754e23	−0.0818817
$225$	6.73466e22	0.0135020
$226$	−8.85171e24	−1.69390
$227$	−2.04882e24	−0.374310	−0.187155	−	0.982330i	$-0.559927\pi$
$227$	−2.04882e24	−0.374310	−0.187155	+	0.982330i	$0.559927\pi$
$228$	−2.93268e24	−0.511622
$229$	4.12622e24	0.687512	0.343756	−	0.939059i	$-0.388301\pi$
$229$	4.12622e24	0.687512	0.343756	+	0.939059i	$0.388301\pi$
$230$	−8.26219e24	−1.31508
$231$	4.52113e23	0.0687577
$232$	−8.22995e23	−0.119612
$233$	3.43270e24	0.476869	0.238434	−	0.971159i	$-0.423366\pi$
$233$	3.43270e24	0.476869	0.238434	+	0.971159i	$0.423366\pi$
$234$	−5.31773e24	−0.706252
$235$	9.10308e24	1.15605
$236$	−8.53044e24	−1.03609
$237$	−1.25351e24	−0.145636
$238$	−2.75684e23	−0.0306445
$239$	8.29149e24	0.881972	0.440986	−	0.897514i	$-0.354629\pi$
$239$	8.29149e24	0.881972	0.440986	+	0.897514i	$0.354629\pi$
$240$	−6.74153e24	−0.686342
$241$	−1.30526e25	−1.27209	−0.636045	−	0.771652i	$-0.719431\pi$
$241$	−1.30526e25	−1.27209	−0.636045	+	0.771652i	$0.719431\pi$
$242$	3.53389e25	3.29756
$243$	7.17898e23	0.0641500
$244$	3.30012e24	0.282447
$245$	−1.23904e25	−1.01588
$246$	−2.54967e24	−0.200293
$247$	2.35662e25	1.77407
$248$	−2.38405e24	−0.172017
$249$	6.54282e24	0.452555
$250$	−1.97498e25	−1.30976
$251$	−1.77630e25	−1.12965	−0.564823	−	0.825212i	$-0.691056\pi$
$251$	−1.77630e25	−1.12965	−0.564823	+	0.825212i	$0.691056\pi$
$252$	2.76541e23	0.0168676
$253$	−3.06453e25	−1.79308
$254$	3.58402e25	2.01194
$255$	−3.91267e24	−0.210766
$256$	2.47557e25	1.27984
$257$	−5.70058e24	−0.282893	−0.141446	−	0.989946i	$-0.545175\pi$
$257$	−5.70058e24	−0.282893	−0.141446	+	0.989946i	$0.545175\pi$
$258$	1.87342e25	0.892542
$259$	1.45871e24	0.0667299
$260$	−2.90727e25	−1.27722
$261$	3.37580e24	0.142446
$262$	−2.42818e25	−0.984275
$263$	9.73572e23	0.0379169	0.0189584	−	0.999820i	$-0.493965\pi$
$263$	9.73572e23	0.0379169	0.0189584	+	0.999820i	$0.493965\pi$
$264$	−8.03672e24	−0.300772
$265$	9.66733e24	0.347716
$266$	−2.77518e24	−0.0959474
$267$	−4.53027e23	−0.0150576
$268$	−2.26157e25	−0.722761
$269$	−5.78587e25	−1.77816	−0.889078	−	0.457756i	$-0.848653\pi$
$269$	−5.78587e25	−1.77816	−0.889078	+	0.457756i	$0.848653\pi$
$270$	8.88769e24	0.262706
$271$	4.29033e25	1.21987	0.609934	−	0.792452i	$-0.291196\pi$
$271$	4.29033e25	1.21987	0.609934	+	0.792452i	$0.291196\pi$
$272$	1.52473e25	0.417079
$273$	−2.22221e24	−0.0584893
$274$	7.44321e25	1.88530
$275$	3.09251e24	0.0753907
$276$	−1.87446e25	−0.439877
$277$	6.39000e25	1.44366	0.721828	−	0.692073i	$-0.243302\pi$
$277$	6.39000e25	1.44366	0.721828	+	0.692073i	$0.243302\pi$
$278$	−1.85822e25	−0.404228
$279$	9.77899e24	0.204857
$280$	−9.05457e23	−0.0182687
$281$	3.23104e25	0.627951	0.313976	−	0.949431i	$-0.398339\pi$
$281$	3.23104e25	0.627951	0.313976	+	0.949431i	$0.398339\pi$
$282$	4.67668e25	0.875632
$283$	−1.00627e25	−0.181534	−0.0907668	−	0.995872i	$-0.528932\pi$
$283$	−1.00627e25	−0.181534	−0.0907668	+	0.995872i	$0.528932\pi$
$284$	1.22007e25	0.212101
$285$	−3.93869e25	−0.659905
$286$	−2.44186e26	−3.94346
$287$	−1.06547e24	−0.0165875
$288$	−2.84185e25	−0.426560
$289$	−6.02427e25	−0.871921
$290$	4.17929e25	0.583343
$291$	2.73842e25	0.368659
$292$	1.13053e26	1.46812
$293$	4.93011e25	0.617656	0.308828	−	0.951118i	$-0.400063\pi$
$293$	4.93011e25	0.617656	0.308828	+	0.951118i	$0.400063\pi$
$294$	−6.36551e25	−0.769461
$295$	−1.14567e26	−1.33637
$296$	−2.59298e25	−0.291902
$297$	3.29654e25	0.358191
$298$	6.67487e25	0.700119
$299$	1.50627e26	1.52530
$300$	1.89158e24	0.0184948
$301$	7.82877e24	0.0739172
$302$	−7.03772e25	−0.641740
$303$	1.03715e25	0.0913467
$304$	1.53487e26	1.30587
$305$	4.43218e25	0.364308
$306$	−2.01012e25	−0.159642
$307$	−1.49828e25	−0.114985	−0.0574925	−	0.998346i	$-0.518311\pi$
$307$	−1.49828e25	−0.114985	−0.0574925	+	0.998346i	$0.518311\pi$
$308$	1.26986e25	0.0941830
$309$	−7.61840e25	−0.546135
$310$	1.21065e26	0.838924
$311$	−1.48794e26	−0.996786	−0.498393	−	0.866951i	$-0.666076\pi$
$311$	−1.48794e26	−0.996786	−0.498393	+	0.866951i	$0.666076\pi$
$312$	3.95017e25	0.255854
$313$	−1.10961e26	−0.694951	−0.347476	−	0.937689i	$-0.612961\pi$
$313$	−1.10961e26	−0.694951	−0.347476	+	0.937689i	$0.612961\pi$
$314$	−1.82553e26	−1.10567
$315$	3.71404e24	0.0217564
$316$	−3.52074e25	−0.199489
$317$	7.14805e25	0.391801	0.195900	−	0.980624i	$-0.437237\pi$
$317$	7.14805e25	0.391801	0.195900	+	0.980624i	$0.437237\pi$
$318$	4.96656e25	0.263373
$319$	1.55014e26	0.795371
$320$	−1.12397e26	−0.558060
$321$	3.40661e24	0.0163689
$322$	−1.77379e25	−0.0824928
$323$	8.90810e25	0.401013
$324$	2.01637e25	0.0878715
$325$	−1.52002e25	−0.0641317
$326$	−3.50326e26	−1.43116
$327$	−3.39497e25	−0.134302
$328$	1.89397e25	0.0725601
$329$	1.95432e25	0.0725168
$330$	4.08116e26	1.46686
$331$	−5.05668e26	−1.76065	−0.880323	−	0.474375i	$-0.842674\pi$
$331$	−5.05668e26	−1.76065	−0.880323	+	0.474375i	$0.842674\pi$
$332$	1.83769e26	0.619901
$333$	1.06360e26	0.347628
$334$	7.20791e25	0.228282
$335$	−3.03737e26	−0.932238
$336$	−1.44732e25	−0.0430530
$337$	3.50546e26	1.01072	0.505360	−	0.862909i	$-0.331360\pi$
$337$	3.50546e26	1.01072	0.505360	+	0.862909i	$0.331360\pi$
$338$	7.21413e26	2.01632
$339$	−2.69709e26	−0.730801
$340$	−1.09896e26	−0.288703
$341$	4.49044e26	1.14385
$342$	−2.02349e26	−0.499835
$343$	−5.33106e25	−0.127710
$344$	−1.39163e26	−0.323341
$345$	−2.51747e26	−0.567366
$346$	5.00763e26	1.09480
$347$	−3.51664e26	−0.745879	−0.372940	−	0.927856i	$-0.621650\pi$
$347$	−3.51664e26	−0.745879	−0.372940	+	0.927856i	$0.621650\pi$
$348$	9.48166e25	0.195120
$349$	5.74285e26	1.14673	0.573364	−	0.819300i	$-0.305638\pi$
$349$	5.74285e26	1.14673	0.573364	+	0.819300i	$0.305638\pi$
$350$	1.78998e24	0.00346844
$351$	−1.62030e26	−0.304698
$352$	−1.30496e27	−2.38176
$353$	1.85373e25	0.0328406	0.0164203	−	0.999865i	$-0.494773\pi$
$353$	1.85373e25	0.0328406	0.0164203	+	0.999865i	$0.494773\pi$
$354$	−5.88583e26	−1.01222
$355$	1.63860e26	0.273574
$356$	−1.27242e25	−0.0206256
$357$	−8.40001e24	−0.0132210
$358$	−6.49572e26	−0.992785
$359$	−3.41606e26	−0.507030	−0.253515	−	0.967331i	$-0.581587\pi$
$359$	−3.41606e26	−0.507030	−0.253515	+	0.967331i	$0.581587\pi$
$360$	−6.60204e25	−0.0951704
$361$	1.82527e26	0.255565
$362$	−3.72605e26	−0.506768
$363$	1.07677e27	1.42267
$364$	−6.24154e25	−0.0801175
$365$	1.51834e27	1.89362
$366$	2.27702e26	0.275940
$367$	5.79162e26	0.682034	0.341017	−	0.940057i	$-0.389229\pi$
$367$	5.79162e26	0.682034	0.341017	+	0.940057i	$0.389229\pi$
$368$	9.81031e26	1.12274
$369$	−7.76878e25	−0.0864123
$370$	1.31675e27	1.42360
$371$	2.07546e25	0.0218116
$372$	2.74664e26	0.280609
$373$	−1.74513e27	−1.73335	−0.866673	−	0.498877i	$-0.833746\pi$
$373$	−1.74513e27	−1.73335	−0.866673	+	0.498877i	$0.833746\pi$
$374$	−9.23032e26	−0.891384
$375$	−6.01772e26	−0.565072
$376$	−3.47398e26	−0.317216
$377$	−7.61919e26	−0.676588
$378$	1.90808e25	0.0164790
$379$	1.08818e27	0.914093	0.457046	−	0.889443i	$-0.348907\pi$
$379$	1.08818e27	0.914093	0.457046	+	0.889443i	$0.348907\pi$
$380$	−1.10627e27	−0.903925
$381$	1.09204e27	0.868014
$382$	−8.93050e26	−0.690575
$383$	−2.35974e27	−1.77532	−0.887661	−	0.460498i	$-0.847671\pi$
$383$	−2.35974e27	−1.77532	−0.887661	+	0.460498i	$0.847671\pi$
$384$	4.31860e26	0.316130
$385$	1.70546e26	0.121480
$386$	2.51159e27	1.74094
$387$	5.70827e26	0.385070
$388$	7.69145e26	0.504981
$389$	−2.72162e27	−1.73923	−0.869616	−	0.493729i	$-0.835633\pi$
$389$	−2.72162e27	−1.73923	−0.869616	+	0.493729i	$0.835633\pi$
$390$	−2.00595e27	−1.24779
$391$	5.69373e26	0.344779
$392$	4.72850e26	0.278753
$393$	−7.39859e26	−0.424646
$394$	3.98660e27	2.22788
$395$	−4.72847e26	−0.257307
$396$	9.25903e26	0.490644
$397$	−2.20086e27	−1.13577	−0.567887	−	0.823106i	$-0.692239\pi$
$397$	−2.20086e27	−1.13577	−0.567887	+	0.823106i	$0.692239\pi$
$398$	1.03595e26	0.0520673
$399$	−8.45589e25	−0.0413946
$400$	−9.89987e25	−0.0472063
$401$	2.61699e27	1.21559	0.607793	−	0.794096i	$-0.292055\pi$
$401$	2.61699e27	1.21559	0.607793	+	0.794096i	$0.292055\pi$
$402$	−1.56044e27	−0.706111
$403$	−2.20712e27	−0.973023
$404$	2.91305e26	0.125125
$405$	2.70806e26	0.113339
$406$	8.97242e25	0.0365920
$407$	4.88398e27	1.94103
$408$	1.49318e26	0.0578335
$409$	−8.92474e26	−0.336900	−0.168450	−	0.985710i	$-0.553876\pi$
$409$	−8.92474e26	−0.336900	−0.168450	+	0.985710i	$0.553876\pi$
$410$	−9.61786e26	−0.353874
$411$	2.26793e27	0.813373
$412$	−2.13979e27	−0.748085
$413$	−2.45961e26	−0.0838282
$414$	−1.29334e27	−0.429744
$415$	2.46808e27	0.799567
$416$	6.41407e27	2.02607
$417$	−5.66195e26	−0.174396
$418$	−9.29172e27	−2.79091
$419$	−2.48238e27	−0.727144	−0.363572	−	0.931566i	$-0.618443\pi$
$419$	−2.48238e27	−0.727144	−0.363572	+	0.931566i	$0.618443\pi$
$420$	1.04317e26	0.0298014
$421$	4.09797e27	1.14184	0.570922	−	0.821004i	$-0.306586\pi$
$421$	4.09797e27	1.14184	0.570922	+	0.821004i	$0.306586\pi$
$422$	−6.12669e27	−1.66512
$423$	1.42497e27	0.377774
$424$	−3.68931e26	−0.0954121
$425$	−5.74571e25	−0.0144964
$426$	8.41825e26	0.207215
$427$	9.51534e25	0.0228524
$428$	9.56820e25	0.0224218
$429$	−7.44029e27	−1.70133
$430$	7.06692e27	1.57693
$431$	−4.89793e27	−1.06660	−0.533299	−	0.845927i	$-0.679048\pi$
$431$	−4.89793e27	−1.06660	−0.533299	+	0.845927i	$0.679048\pi$
$432$	−1.05530e27	−0.224283
$433$	−2.06118e27	−0.427557	−0.213778	−	0.976882i	$-0.568577\pi$
$433$	−2.06118e27	−0.427557	−0.213778	+	0.976882i	$0.568577\pi$
$434$	2.59913e26	0.0526242
$435$	1.27342e27	0.251672
$436$	−9.53549e26	−0.183965
$437$	5.73161e27	1.07950
$438$	7.80042e27	1.43430
$439$	1.00358e28	1.80167	0.900835	−	0.434161i	$-0.142955\pi$
$439$	1.00358e28	1.80167	0.900835	+	0.434161i	$0.142955\pi$
$440$	−3.03161e27	−0.531399
$441$	−1.93956e27	−0.331969
$442$	4.53684e27	0.758263
$443$	4.23345e27	0.690964	0.345482	−	0.938425i	$-0.387715\pi$
$443$	4.23345e27	0.690964	0.345482	+	0.938425i	$0.387715\pi$
$444$	2.98735e27	0.476173
$445$	−1.70891e26	−0.0266035
$446$	−6.01973e27	−0.915295
$447$	2.03382e27	0.302053
$448$	−2.41303e26	−0.0350061
$449$	−6.74432e27	−0.955766	−0.477883	−	0.878424i	$-0.658596\pi$
$449$	−6.74432e27	−0.955766	−0.477883	+	0.878424i	$0.658596\pi$
$450$	1.30515e26	0.0180688
$451$	−3.56737e27	−0.482496
$452$	−7.57537e27	−1.00104
$453$	−2.14438e27	−0.276866
$454$	−3.97052e27	−0.500911
$455$	−8.38261e26	−0.103338
$456$	1.50311e27	0.181076
$457$	−1.13821e28	−1.34000	−0.669998	−	0.742362i	$-0.733705\pi$
$457$	−1.13821e28	−1.34000	−0.669998	+	0.742362i	$0.733705\pi$
$458$	7.99644e27	0.920045
$459$	−6.12478e26	−0.0688743
$460$	−7.07085e27	−0.777167
$461$	6.24175e27	0.670574	0.335287	−	0.942116i	$-0.391167\pi$
$461$	6.24175e27	0.670574	0.335287	+	0.942116i	$0.391167\pi$
$462$	8.76175e26	0.0920132
$463$	−2.31855e27	−0.238021	−0.119011	−	0.992893i	$-0.537972\pi$
$463$	−2.31855e27	−0.238021	−0.119011	+	0.992893i	$0.537972\pi$
$464$	−4.96238e27	−0.498025
$465$	3.68883e27	0.361937
$466$	6.65242e27	0.638157
$467$	−9.47846e26	−0.0889018	−0.0444509	−	0.999012i	$-0.514154\pi$
$467$	−9.47846e26	−0.0889018	−0.0444509	+	0.999012i	$0.514154\pi$
$468$	−4.55096e27	−0.417370
$469$	−6.52086e26	−0.0584776
$470$	1.76414e28	1.54705
$471$	−5.56234e27	−0.477021
$472$	4.37217e27	0.366696
$473$	2.62120e28	2.15009
$474$	−2.42924e27	−0.194893
$475$	−5.78393e26	−0.0453879
$476$	−2.35932e26	−0.0181098
$477$	1.51330e27	0.113627
$478$	1.60685e28	1.18028
$479$	−1.76996e28	−1.27186	−0.635932	−	0.771745i	$-0.719384\pi$
$479$	−1.76996e28	−1.27186	−0.635932	+	0.771745i	$0.719384\pi$
$480$	−1.07200e28	−0.753639
$481$	−2.40055e28	−1.65115
$482$	−2.52954e28	−1.70234
$483$	−5.40470e26	−0.0355899
$484$	3.02434e28	1.94874
$485$	1.03299e28	0.651339
$486$	1.39125e27	0.0858471
$487$	1.99209e28	1.20297	0.601484	−	0.798885i	$-0.294576\pi$
$487$	1.99209e28	1.20297	0.601484	+	0.798885i	$0.294576\pi$
$488$	−1.69144e27	−0.0999649
$489$	−1.06743e28	−0.617445
$490$	−2.40120e28	−1.35947
$491$	−5.71237e27	−0.316563	−0.158282	−	0.987394i	$-0.550595\pi$
$491$	−5.71237e27	−0.316563	−0.158282	+	0.987394i	$0.550595\pi$
$492$	−2.18203e27	−0.118366
$493$	−2.88008e27	−0.152937
$494$	4.56702e28	2.37411
$495$	1.24352e28	0.632846
$496$	−1.43750e28	−0.716226
$497$	3.51787e26	0.0171608
$498$	1.26797e28	0.605620
$499$	−1.17032e28	−0.547332	−0.273666	−	0.961825i	$-0.588236\pi$
$499$	−1.17032e28	−0.547332	−0.273666	+	0.961825i	$0.588236\pi$
$500$	−1.69021e28	−0.774025
$501$	2.19623e27	0.0984878
$502$	−3.44239e28	−1.51172
$503$	−3.15184e28	−1.35550	−0.677750	−	0.735292i	$-0.737045\pi$
$503$	−3.15184e28	−1.35550	−0.677750	+	0.735292i	$0.737045\pi$
$504$	−1.41738e26	−0.00596987
$505$	3.91233e27	0.161390
$506$	−5.93893e28	−2.39954
$507$	2.19813e28	0.869899
$508$	3.06723e28	1.18899
$509$	4.58029e28	1.73923	0.869613	−	0.493733i	$-0.164368\pi$
$509$	4.58029e28	1.73923	0.869613	+	0.493733i	$0.164368\pi$
$510$	−7.58257e27	−0.282052
$511$	3.25969e27	0.118784
$512$	3.26377e28	1.16516
$513$	−6.16552e27	−0.215644
$514$	−1.10475e28	−0.378574
$515$	−2.87382e28	−0.964901
$516$	1.60329e28	0.527461
$517$	6.54337e28	2.10936
$518$	2.82691e27	0.0892996
$519$	1.52581e28	0.472328
$520$	1.49008e28	0.452038
$521$	−5.19044e27	−0.154315	−0.0771575	−	0.997019i	$-0.524584\pi$
$521$	−5.19044e27	−0.154315	−0.0771575	+	0.997019i	$0.524584\pi$
$522$	6.54215e27	0.190625
$523$	−2.08282e27	−0.0594817	−0.0297408	−	0.999558i	$-0.509468\pi$
$523$	−2.08282e27	−0.0594817	−0.0297408	+	0.999558i	$0.509468\pi$
$524$	−2.07805e28	−0.581672
$525$	5.45403e25	0.00149639
$526$	1.88674e27	0.0507413
$527$	−8.34299e27	−0.219943
$528$	−4.84587e28	−1.25232
$529$	−2.83724e27	−0.0718805
$530$	1.87349e28	0.465322
$531$	−1.79340e28	−0.436701
$532$	−2.37502e27	−0.0567016
$533$	1.75342e28	0.410439
$534$	−8.77946e26	−0.0201504
$535$	1.28504e27	0.0289203
$536$	1.15914e28	0.255803
$537$	−1.97923e28	−0.428318
$538$	−1.12128e29	−2.37957
$539$	−8.90630e28	−1.85360
$540$	7.60616e27	0.155250
$541$	−1.25240e28	−0.250710	−0.125355	−	0.992112i	$-0.540007\pi$
$541$	−1.25240e28	−0.250710	−0.125355	+	0.992112i	$0.540007\pi$
$542$	8.31446e28	1.63246
$543$	−1.13532e28	−0.218635
$544$	2.42454e28	0.457974
$545$	−1.28065e28	−0.237283
$546$	−4.30654e27	−0.0782718
$547$	5.63104e28	1.00397	0.501987	−	0.864875i	$-0.332603\pi$
$547$	5.63104e28	1.00397	0.501987	+	0.864875i	$0.332603\pi$
$548$	6.36996e28	1.11414
$549$	6.93801e27	0.119049
$550$	5.99314e27	0.100890
$551$	−2.89924e28	−0.478842
$552$	9.60733e27	0.155683
$553$	−1.01514e27	−0.0161404
$554$	1.23835e29	1.93193
$555$	4.01212e28	0.614182
$556$	−1.59028e28	−0.238885
$557$	4.80914e28	0.708904	0.354452	−	0.935074i	$-0.384667\pi$
$557$	4.80914e28	0.708904	0.354452	+	0.935074i	$0.384667\pi$
$558$	1.89513e28	0.274144
$559$	−1.28836e29	−1.82899
$560$	−5.45960e27	−0.0760652
$561$	−2.81246e28	−0.384570
$562$	6.26161e28	0.840339
$563$	−1.81812e28	−0.239488	−0.119744	−	0.992805i	$-0.538207\pi$
$563$	−1.81812e28	−0.239488	−0.119744	+	0.992805i	$0.538207\pi$
$564$	4.00234e28	0.517468
$565$	−1.01740e29	−1.29117
$566$	−1.95011e28	−0.242933
$567$	5.81386e26	0.00710956
$568$	−6.25333e27	−0.0750679
$569$	1.75144e28	0.206403	0.103201	−	0.994660i	$-0.467091\pi$
$569$	1.75144e28	0.206403	0.103201	+	0.994660i	$0.467091\pi$
$570$	−7.63301e28	−0.883100
$571$	1.67794e29	1.90589	0.952946	−	0.303140i	$-0.0980350\pi$
$571$	1.67794e29	1.90589	0.952946	+	0.303140i	$0.0980350\pi$
$572$	−2.08977e29	−2.33045
$573$	−2.72110e28	−0.297935
$574$	−2.06484e27	−0.0221978
$575$	−3.69688e27	−0.0390232
$576$	−1.75943e28	−0.182363
$577$	7.49346e28	0.762669	0.381335	−	0.924437i	$-0.375465\pi$
$577$	7.49346e28	0.762669	0.381335	+	0.924437i	$0.375465\pi$
$578$	−1.16748e29	−1.16683
$579$	7.65276e28	0.751092
$580$	3.57667e28	0.344735
$581$	5.29867e27	0.0501554
$582$	5.30694e28	0.493348
$583$	6.94895e28	0.634453
$584$	−5.79439e28	−0.519604
$585$	−6.11209e28	−0.538336
$586$	9.55433e28	0.826562
$587$	1.69908e29	1.44382	0.721912	−	0.691985i	$-0.243264\pi$
$587$	1.69908e29	1.44382	0.721912	+	0.691985i	$0.243264\pi$
$588$	−5.44766e28	−0.454724
$589$	−8.39849e28	−0.688638
$590$	−2.22025e29	−1.78837
$591$	1.21471e29	0.961175
$592$	−1.56348e29	−1.21539
$593$	−1.26592e29	−0.966787	−0.483394	−	0.875403i	$-0.660596\pi$
$593$	−1.26592e29	−0.966787	−0.483394	+	0.875403i	$0.660596\pi$
$594$	6.38854e28	0.479340
$595$	−3.16865e27	−0.0233586
$596$	5.71241e28	0.413746
$597$	3.15650e27	0.0224634
$598$	2.91907e29	2.04119
$599$	1.73983e29	1.19544	0.597718	−	0.801706i	$-0.296074\pi$
$599$	1.73983e29	1.19544	0.597718	+	0.801706i	$0.296074\pi$
$600$	−9.69503e26	−0.00654578
$601$	−2.58691e29	−1.71633	−0.858164	−	0.513376i	$-0.828395\pi$
$601$	−2.58691e29	−1.71633	−0.858164	+	0.513376i	$0.828395\pi$
$602$	1.51718e28	0.0989178
$603$	−4.75461e28	−0.304638
$604$	−6.02294e28	−0.379246
$605$	4.06179e29	2.51354
$606$	2.00994e28	0.122242
$607$	−1.61646e29	−0.966238	−0.483119	−	0.875555i	$-0.660496\pi$
$607$	−1.61646e29	−0.966238	−0.483119	+	0.875555i	$0.660496\pi$
$608$	2.44067e29	1.43391
$609$	2.73387e27	0.0157869
$610$	8.58936e28	0.487526
$611$	−3.21617e29	−1.79434
$612$	−1.72028e28	−0.0943427
$613$	8.86426e28	0.477868	0.238934	−	0.971036i	$-0.423202\pi$
$613$	8.86426e28	0.477868	0.238934	+	0.971036i	$0.423202\pi$
$614$	−2.90361e28	−0.153876
$615$	−2.93054e28	−0.152672
$616$	−6.50850e27	−0.0333337
$617$	−7.14976e28	−0.359996	−0.179998	−	0.983667i	$-0.557609\pi$
$617$	−7.14976e28	−0.359996	−0.179998	+	0.983667i	$0.557609\pi$
$618$	−1.47641e29	−0.730851
$619$	−3.79378e28	−0.184638	−0.0923188	−	0.995730i	$-0.529428\pi$
$619$	−3.79378e28	−0.184638	−0.0923188	+	0.995730i	$0.529428\pi$
$620$	1.03609e29	0.495774
$621$	−3.94078e28	−0.185404
$622$	−2.88356e29	−1.33392
$623$	−3.66882e26	−0.00166879
$624$	2.38182e29	1.06530
$625$	−2.36211e29	−1.03887
$626$	−2.15037e29	−0.930000
$627$	−2.83116e29	−1.20408
$628$	−1.56230e29	−0.653414
$629$	−9.07416e28	−0.373228
$630$	7.19765e27	0.0291149
$631$	4.22002e29	1.67883	0.839415	−	0.543491i	$-0.182898\pi$
$631$	4.22002e29	1.67883	0.839415	+	0.543491i	$0.182898\pi$
$632$	1.80451e28	0.0706041
$633$	−1.86679e29	−0.718382
$634$	1.38526e29	0.524317
$635$	4.11940e29	1.53359
$636$	4.25042e28	0.155644
$637$	4.37758e29	1.57678
$638$	3.00411e29	1.06438
$639$	2.56502e28	0.0893988
$640$	1.62906e29	0.558533
$641$	−2.45898e29	−0.829364	−0.414682	−	0.909966i	$-0.636107\pi$
$641$	−2.45898e29	−0.829364	−0.414682	+	0.909966i	$0.636107\pi$
$642$	6.60186e27	0.0219053
$643$	3.81795e29	1.24628	0.623139	−	0.782111i	$-0.285857\pi$
$643$	3.81795e29	1.24628	0.623139	+	0.782111i	$0.285857\pi$
$644$	−1.51803e28	−0.0487503
$645$	2.15327e29	0.680334
$646$	1.72635e29	0.536646
$647$	−3.01566e29	−0.922332	−0.461166	−	0.887314i	$-0.652569\pi$
$647$	−3.01566e29	−0.922332	−0.461166	+	0.887314i	$0.652569\pi$
$648$	−1.03347e28	−0.0310999
$649$	−8.23515e29	−2.43839
$650$	−2.94572e28	−0.0858226
$651$	7.91947e27	0.0227037
$652$	−2.99812e29	−0.845764
$653$	2.27685e29	0.632042	0.316021	−	0.948752i	$-0.397653\pi$
$653$	2.27685e29	0.632042	0.316021	+	0.948752i	$0.397653\pi$
$654$	−6.57929e28	−0.179727
$655$	−2.79090e29	−0.750257
$656$	1.14200e29	0.302117
$657$	2.37677e29	0.618800
$658$	3.78738e28	0.0970437
$659$	−4.45804e29	−1.12421	−0.562104	−	0.827066i	$-0.690008\pi$
$659$	−4.45804e29	−1.12421	−0.562104	+	0.827066i	$0.690008\pi$
$660$	3.49269e29	0.866860
$661$	4.54039e29	1.10912	0.554559	−	0.832144i	$-0.312887\pi$
$661$	4.54039e29	1.10912	0.554559	+	0.832144i	$0.312887\pi$
$662$	−9.79963e29	−2.35614
$663$	1.38236e29	0.327138
$664$	−9.41886e28	−0.219398
$665$	−3.18973e28	−0.0731353
$666$	2.06121e29	0.465204
$667$	−1.85309e29	−0.411694
$668$	6.16859e28	0.134907
$669$	−1.83420e29	−0.394886
$670$	−5.88628e29	−1.24754
$671$	3.18588e29	0.664727
$672$	−2.30146e28	−0.0472744
$673$	5.05512e28	0.102229	0.0511144	−	0.998693i	$-0.483723\pi$
$673$	5.05512e28	0.102229	0.0511144	+	0.998693i	$0.483723\pi$
$674$	6.79342e29	1.35257
$675$	3.97675e27	0.00779541
$676$	6.17391e29	1.19157
$677$	−3.44673e29	−0.654977	−0.327489	−	0.944855i	$-0.606202\pi$
$677$	−3.44673e29	−0.654977	−0.327489	+	0.944855i	$0.606202\pi$
$678$	−5.22685e29	−0.977975
$679$	2.21770e28	0.0408573
$680$	5.63256e28	0.102179
$681$	−1.20981e29	−0.216108
$682$	8.70228e29	1.53072
$683$	3.07293e29	0.532273	0.266137	−	0.963935i	$-0.414253\pi$
$683$	3.07293e29	0.532273	0.266137	+	0.963935i	$0.414253\pi$
$684$	−1.73172e29	−0.295385
$685$	8.55508e29	1.43705
$686$	−1.03314e29	−0.170905
$687$	2.43649e29	0.396935
$688$	−8.39108e29	−1.34629
$689$	−3.41552e29	−0.539703
$690$	−4.87874e29	−0.759263
$691$	7.85532e28	0.120405	0.0602025	−	0.998186i	$-0.480825\pi$
$691$	7.85532e28	0.120405	0.0602025	+	0.998186i	$0.480825\pi$
$692$	4.28557e29	0.646986
$693$	2.66968e28	0.0396973
$694$	−6.81509e29	−0.998153
$695$	−2.13580e29	−0.308120
$696$	−4.85971e28	−0.0690578
$697$	6.62797e28	0.0927761
$698$	1.11294e30	1.53458
$699$	2.02698e29	0.275320
$700$	1.53188e27	0.00204973
$701$	7.75849e29	1.02268	0.511338	−	0.859380i	$-0.329150\pi$
$701$	7.75849e29	1.02268	0.511338	+	0.859380i	$0.329150\pi$
$702$	−3.14006e29	−0.407755
$703$	−9.13453e29	−1.16857
$704$	−8.07920e29	−1.01825
$705$	5.37528e29	0.667445
$706$	3.59244e28	0.0439481
$707$	8.39929e27	0.0101237
$708$	−5.03714e29	−0.598184
$709$	1.53428e30	1.79523	0.897613	−	0.440785i	$-0.145300\pi$
$709$	1.53428e30	1.79523	0.897613	+	0.440785i	$0.145300\pi$
$710$	3.17553e29	0.366104
$711$	−7.40182e28	−0.0840829
$712$	6.52165e27	0.00729991
$713$	−5.36801e29	−0.592070
$714$	−1.62788e28	−0.0176926
$715$	−2.80663e30	−3.00588
$716$	−5.55909e29	−0.586701
$717$	4.89604e29	0.509206
$718$	−6.62017e29	−0.678520
$719$	5.56901e29	0.562503	0.281252	−	0.959634i	$-0.409250\pi$
$719$	5.56901e29	0.562503	0.281252	+	0.959634i	$0.409250\pi$
$720$	−3.98081e29	−0.396260
$721$	−6.16973e28	−0.0605265
$722$	3.53729e29	0.342003
$723$	−7.70743e29	−0.734442
$724$	−3.18879e29	−0.299482
$725$	1.87000e28	0.0173098
$726$	2.08673e30	1.90384
$727$	−1.43096e29	−0.128681	−0.0643407	−	0.997928i	$-0.520494\pi$
$727$	−1.43096e29	−0.128681	−0.0643407	+	0.997928i	$0.520494\pi$
$728$	3.19902e28	0.0283556
$729$	4.23912e28	0.0370370
$730$	2.94247e30	2.53409
$731$	−4.87003e29	−0.413428
$732$	1.94869e29	0.163071
$733$	−6.81141e29	−0.561882	−0.280941	−	0.959725i	$-0.590647\pi$
$733$	−6.81141e29	−0.561882	−0.280941	+	0.959725i	$0.590647\pi$
$734$	1.12239e30	0.912714
$735$	−7.31639e29	−0.586516
$736$	1.55999e30	1.23283
$737$	−2.18328e30	−1.70099
$738$	−1.50555e29	−0.115639
$739$	2.16993e30	1.64315	0.821577	−	0.570097i	$-0.193094\pi$
$739$	2.16993e30	1.64315	0.821577	+	0.570097i	$0.193094\pi$
$740$	1.12689e30	0.841295
$741$	1.39156e30	1.02426
$742$	4.02214e28	0.0291888
$743$	−1.40097e29	−0.100241	−0.0501206	−	0.998743i	$-0.515961\pi$
$743$	−1.40097e29	−0.100241	−0.0501206	+	0.998743i	$0.515961\pi$
$744$	−1.40776e29	−0.0993143
$745$	7.67196e29	0.533661
$746$	−3.38199e30	−2.31960
$747$	3.86347e29	0.261283
$748$	−7.89939e29	−0.526777
$749$	2.75883e27	0.00181412
$750$	−1.16621e30	−0.756193
$751$	8.06099e29	0.515429	0.257715	−	0.966221i	$-0.417031\pi$
$751$	8.06099e29	0.515429	0.257715	+	0.966221i	$0.417031\pi$
$752$	−2.09469e30	−1.32079
$753$	−1.04889e30	−0.652202
$754$	−1.47656e30	−0.905427
$755$	−8.08901e29	−0.489162
$756$	1.63295e28	0.00973853
$757$	−1.54959e30	−0.911401	−0.455700	−	0.890133i	$-0.650611\pi$
$757$	−1.54959e30	−0.911401	−0.455700	+	0.890133i	$0.650611\pi$
$758$	2.10885e30	1.22326
$759$	−1.80958e30	−1.03523
$760$	5.67003e29	0.319921
$761$	2.04061e29	0.113559	0.0567793	−	0.998387i	$-0.481917\pi$
$761$	2.04061e29	0.113559	0.0567793	+	0.998387i	$0.481917\pi$
$762$	2.11633e30	1.16160
$763$	−2.74940e28	−0.0148843
$764$	−7.64280e29	−0.408105
$765$	−2.31039e29	−0.121686
$766$	−4.57307e30	−2.37578
$767$	4.04770e30	2.07423
$768$	1.46180e30	0.738915
$769$	1.27880e30	0.637641	0.318821	−	0.947815i	$-0.396713\pi$
$769$	1.27880e30	0.637641	0.318821	+	0.947815i	$0.396713\pi$
$770$	3.30511e29	0.162567
$771$	−3.36614e29	−0.163328
$772$	2.14944e30	1.02883
$773$	3.43774e30	1.62326	0.811630	−	0.584172i	$-0.198581\pi$
$773$	3.43774e30	1.62326	0.811630	+	0.584172i	$0.198581\pi$
$774$	1.10624e30	0.515309
$775$	5.41701e28	0.0248938
$776$	−3.94216e29	−0.178725
$777$	8.61352e28	0.0385265
$778$	−5.27439e30	−2.32748
$779$	6.67206e29	0.290480
$780$	−1.71671e30	−0.737402
$781$	1.17784e30	0.499172
$782$	1.10342e30	0.461392
$783$	1.99338e29	0.0822414
$784$	2.85112e30	1.16064
$785$	−2.09822e30	−0.842792
$786$	−1.43381e30	−0.568271
$787$	1.06317e30	0.415784	0.207892	−	0.978152i	$-0.433340\pi$
$787$	1.06317e30	0.415784	0.207892	+	0.978152i	$0.433340\pi$
$788$	3.41176e30	1.31660
$789$	5.74885e28	0.0218913
$790$	−9.16357e29	−0.344334
$791$	−2.18423e29	−0.0809925
$792$	−4.74560e29	−0.173651
$793$	−1.56591e30	−0.565456
$794$	−4.26517e30	−1.51992
$795$	5.70846e29	0.200754
$796$	8.86572e28	0.0307699
$797$	−2.59470e30	−0.888742	−0.444371	−	0.895843i	$-0.646573\pi$
$797$	−2.59470e30	−0.888742	−0.444371	+	0.895843i	$0.646573\pi$
$798$	−1.63871e29	−0.0553953
$799$	−1.21572e30	−0.405595
$800$	−1.57423e29	−0.0518349
$801$	−2.67508e28	−0.00869351
$802$	5.07160e30	1.62672
$803$	1.09139e31	3.45516
$804$	−1.33544e30	−0.417286
$805$	−2.03876e29	−0.0628795
$806$	−4.27730e30	−1.30212
$807$	−3.41650e30	−1.02662
$808$	−1.49305e29	−0.0442848
$809$	−4.54632e30	−1.33107	−0.665534	−	0.746367i	$-0.731796\pi$
$809$	−4.54632e30	−1.33107	−0.665534	+	0.746367i	$0.731796\pi$
$810$	5.24809e29	0.151673
$811$	−5.33885e30	−1.52310	−0.761550	−	0.648106i	$-0.775561\pi$
$811$	−5.33885e30	−1.52310	−0.761550	+	0.648106i	$0.775561\pi$
$812$	7.67867e28	0.0216246
$813$	2.53339e30	0.704291
$814$	9.46493e30	2.59753
$815$	−4.02658e30	−1.09089
$816$	9.00335e29	0.240801
$817$	−4.90243e30	−1.29443
$818$	−1.72957e30	−0.450847
$819$	−1.31219e29	−0.0337688
$820$	−8.23105e29	−0.209127
$821$	−6.77652e30	−1.69982	−0.849911	−	0.526926i	$-0.823344\pi$
$821$	−6.77652e30	−1.69982	−0.849911	+	0.526926i	$0.823344\pi$
$822$	4.39514e30	1.08848
$823$	2.32096e30	0.567506	0.283753	−	0.958897i	$-0.408420\pi$
$823$	2.32096e30	0.567506	0.283753	+	0.958897i	$0.408420\pi$
$824$	1.09672e30	0.264766
$825$	1.82610e29	0.0435268
$826$	−4.76661e29	−0.112181
$827$	3.93890e30	0.915307	0.457654	−	0.889131i	$-0.348690\pi$
$827$	3.93890e30	0.915307	0.457654	+	0.889131i	$0.348690\pi$
$828$	−1.10685e30	−0.253963
$829$	3.15777e30	0.715415	0.357708	−	0.933834i	$-0.383558\pi$
$829$	3.15777e30	0.715415	0.357708	+	0.933834i	$0.383558\pi$
$830$	4.78303e30	1.07000
$831$	3.77323e30	0.833495
$832$	3.97105e30	0.866184
$833$	1.65474e30	0.356416
$834$	−1.09726e30	−0.233381
$835$	8.28463e29	0.174006
$836$	−7.95194e30	−1.64933
$837$	5.77440e29	0.118274
$838$	−4.81074e30	−0.973082
$839$	−1.71221e28	−0.00342024	−0.00171012	−	0.999999i	$-0.500544\pi$
$839$	−1.71221e28	−0.00342024	−0.00171012	+	0.999999i	$0.500544\pi$
$840$	−5.34663e28	−0.0105475
$841$	−4.19549e30	−0.817381
$842$	7.94168e30	1.52804
$843$	1.90790e30	0.362548
$844$	−5.24327e30	−0.984026
$845$	8.29177e30	1.53692
$846$	2.76153e30	0.505547
$847$	8.72016e29	0.157670
$848$	−2.22453e30	−0.397266
$849$	−5.94193e29	−0.104809
$850$	−1.11349e29	−0.0193994
$851$	−5.83845e30	−1.00470
$852$	7.20441e29	0.122457
$853$	2.27930e30	0.382680	0.191340	−	0.981524i	$-0.438717\pi$
$853$	2.27930e30	0.382680	0.191340	+	0.981524i	$0.438717\pi$
$854$	1.84403e29	0.0305816
$855$	−2.32576e30	−0.380996
$856$	−4.90406e28	−0.00793563
$857$	−1.06629e31	−1.70441	−0.852207	−	0.523204i	$-0.824737\pi$
$857$	−1.06629e31	−1.70441	−0.852207	+	0.523204i	$0.824737\pi$
$858$	−1.44190e31	−2.27676
$859$	−8.93547e29	−0.139376	−0.0696882	−	0.997569i	$-0.522200\pi$
$859$	−8.93547e29	−0.139376	−0.0696882	+	0.997569i	$0.522200\pi$
$860$	6.04793e30	0.931908
$861$	−6.29150e28	−0.00957682
$862$	−9.49196e30	−1.42735
$863$	2.82417e30	0.419543	0.209772	−	0.977750i	$-0.432728\pi$
$863$	2.82417e30	0.419543	0.209772	+	0.977750i	$0.432728\pi$
$864$	−1.67809e30	−0.246275
$865$	5.75567e30	0.834501
$866$	−3.99448e30	−0.572167
$867$	−3.55727e30	−0.503404
$868$	2.22435e29	0.0310990
$869$	−3.39886e30	−0.469490
$870$	2.46783e30	0.336793
$871$	1.07312e31	1.44696
$872$	4.88730e29	0.0651097
$873$	1.61701e30	0.212845
$874$	1.11076e31	1.44461
$875$	−4.87342e29	−0.0626253
$876$	6.67566e30	0.847620
$877$	9.06575e30	1.13739	0.568693	−	0.822550i	$-0.307449\pi$
$877$	9.06575e30	1.13739	0.568693	+	0.822550i	$0.307449\pi$
$878$	1.94490e31	2.41104
$879$	2.91118e30	0.356604
$880$	−1.82796e31	−2.21258
$881$	1.51630e31	1.81359	0.906794	−	0.421574i	$-0.138522\pi$
$881$	1.51630e31	1.81359	0.906794	+	0.421574i	$0.138522\pi$
$882$	−3.75877e30	−0.444248
$883$	−1.16543e31	−1.36113	−0.680565	−	0.732688i	$-0.738265\pi$
$883$	−1.16543e31	−1.36113	−0.680565	+	0.732688i	$0.738265\pi$
$884$	3.88267e30	0.448107
$885$	−6.76505e30	−0.771555
$886$	8.20424e30	0.924664
$887$	−7.76908e30	−0.865309	−0.432655	−	0.901560i	$-0.642423\pi$
$887$	−7.76908e30	−0.865309	−0.432655	+	0.901560i	$0.642423\pi$
$888$	−1.53113e30	−0.168529
$889$	8.84384e29	0.0961994
$890$	−3.31179e29	−0.0356014
$891$	1.94657e30	0.206802
$892$	−5.15174e30	−0.540907
$893$	−1.22381e31	−1.26991
$894$	3.94144e30	0.404214
$895$	−7.46605e30	−0.756744
$896$	3.49740e29	0.0350357
$897$	8.89435e30	0.880630
$898$	−1.30702e31	−1.27903
$899$	2.71532e30	0.262630
$900$	1.11696e29	0.0106780
$901$	−1.29108e30	−0.121995
$902$	−6.91340e30	−0.645688
$903$	4.62281e29	0.0426761
$904$	3.88266e30	0.354292
$905$	−4.28265e30	−0.386280
$906$	−4.15570e30	−0.370509
$907$	5.71533e30	0.503692	0.251846	−	0.967767i	$-0.418962\pi$
$907$	5.71533e30	0.503692	0.251846	+	0.967767i	$0.418962\pi$
$908$	−3.39800e30	−0.296021
$909$	6.12425e29	0.0527390
$910$	−1.62451e30	−0.138289
$911$	2.22259e30	0.187032	0.0935160	−	0.995618i	$-0.470189\pi$
$911$	2.22259e30	0.187032	0.0935160	+	0.995618i	$0.470189\pi$
$912$	9.06324e30	0.753942
$913$	1.77408e31	1.45891
$914$	−2.20581e31	−1.79322
$915$	2.61716e30	0.210333
$916$	6.84342e30	0.543714
$917$	−5.99171e29	−0.0470623
$918$	−1.18695e30	−0.0921693
$919$	−9.94638e30	−0.763576	−0.381788	−	0.924250i	$-0.624692\pi$
$919$	−9.94638e30	−0.763576	−0.381788	+	0.924250i	$0.624692\pi$
$920$	3.62408e30	0.275059
$921$	−8.84722e29	−0.0663866
$922$	1.20962e31	0.897378
$923$	−5.78926e30	−0.424624
$924$	7.49838e29	0.0543766
$925$	5.89175e29	0.0422431
$926$	−4.49324e30	−0.318526
$927$	−4.49859e30	−0.315311
$928$	−7.89093e30	−0.546858
$929$	6.57341e30	0.450429	0.225214	−	0.974309i	$-0.427692\pi$
$929$	6.57341e30	0.450429	0.225214	+	0.974309i	$0.427692\pi$
$930$	7.14879e30	0.484353
$931$	1.66575e31	1.11593
$932$	5.69320e30	0.377128
$933$	−8.78615e30	−0.575495
$934$	−1.83688e30	−0.118970
$935$	−1.06091e31	−0.679452
$936$	2.33254e30	0.147717
$937$	−9.88672e30	−0.619137	−0.309568	−	0.950877i	$-0.600185\pi$
$937$	−9.88672e30	−0.619137	−0.309568	+	0.950877i	$0.600185\pi$
$938$	−1.26371e30	−0.0782561
$939$	−6.55213e30	−0.401230
$940$	1.50976e31	0.914253
$941$	1.35253e31	0.809947	0.404973	−	0.914328i	$-0.367281\pi$
$941$	1.35253e31	0.809947	0.404973	+	0.914328i	$0.367281\pi$
$942$	−1.07796e31	−0.638361
$943$	4.26454e30	0.249746
$944$	2.63627e31	1.52681
$945$	2.19311e29	0.0125610
$946$	5.07976e31	2.87731
$947$	−2.26830e31	−1.27065	−0.635325	−	0.772245i	$-0.719134\pi$
$947$	−2.26830e31	−1.27065	−0.635325	+	0.772245i	$0.719134\pi$
$948$	−2.07896e30	−0.115175
$949$	−5.36437e31	−2.93916
$950$	−1.12090e30	−0.0607392
$951$	4.22085e30	0.226206
$952$	1.20924e29	0.00640952
$953$	3.45875e31	1.81319	0.906595	−	0.422002i	$-0.138673\pi$
$953$	3.45875e31	1.81319	0.906595	+	0.422002i	$0.138673\pi$
$954$	2.93270e30	0.152058
$955$	−1.02645e31	−0.526386
$956$	1.37516e31	0.697501
$957$	9.15344e30	0.459207
$958$	−3.43011e31	−1.70204
$959$	1.83667e30	0.0901438
$960$	−6.63694e30	−0.322196
$961$	−1.29598e31	−0.622304
$962$	−4.65216e31	−2.20961
$963$	2.01157e29	0.00945059
$964$	−2.16480e31	−1.00602
$965$	2.88678e31	1.32702
$966$	−1.04741e30	−0.0476272
$967$	−1.92820e31	−0.867311	−0.433655	−	0.901079i	$-0.642776\pi$
$967$	−1.92820e31	−0.867311	−0.433655	+	0.901079i	$0.642776\pi$
$968$	−1.55009e31	−0.689707
$969$	5.26015e30	0.231525
$970$	2.00189e31	0.871638
$971$	−2.95793e31	−1.27405	−0.637024	−	0.770844i	$-0.719835\pi$
$971$	−2.95793e31	−1.27405	−0.637024	+	0.770844i	$0.719835\pi$
$972$	1.19065e30	0.0507326
$973$	−4.58530e29	−0.0193278
$974$	3.86058e31	1.60984
$975$	−8.97554e29	−0.0370265
$976$	−1.01988e31	−0.416222
$977$	4.86581e31	1.96455	0.982274	−	0.187453i	$-0.0600233\pi$
$977$	4.86581e31	1.96455	0.982274	+	0.187453i	$0.0600233\pi$
$978$	−2.06864e31	−0.826280
$979$	−1.22838e30	−0.0485415
$980$	−2.05497e31	−0.803398
$981$	−2.00469e30	−0.0775396
$982$	−1.10703e31	−0.423633
$983$	4.31738e31	1.63459	0.817294	−	0.576220i	$-0.195473\pi$
$983$	4.31738e31	1.63459	0.817294	+	0.576220i	$0.195473\pi$
$984$	1.11837e30	0.0418926
$985$	4.58211e31	1.69819
$986$	−5.58146e30	−0.204664
$987$	1.15401e30	0.0418676
$988$	3.90850e31	1.40301
$989$	−3.13345e31	−1.11292
$990$	2.40989e31	0.846890
$991$	3.44591e31	1.19820	0.599101	−	0.800673i	$-0.295525\pi$
$991$	3.44591e31	1.19820	0.599101	+	0.800673i	$0.295525\pi$
$992$	−2.28584e31	−0.786453
$993$	−2.98592e31	−1.01651
$994$	6.81748e29	0.0229650
$995$	1.19070e30	0.0396880
$996$	1.08514e31	0.357900
$997$	3.62353e31	1.18259	0.591293	−	0.806457i	$-0.298618\pi$
$997$	3.62353e31	1.18259	0.591293	+	0.806457i	$0.298618\pi$
$998$	−2.26804e31	−0.732452
$999$	6.28046e30	0.200703

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.22.a.c.1.2	✓	2
3.2	odd	2		9.22.a.e.1.1		2
4.3	odd	2		48.22.a.g.1.2		2
5.2	odd	4		75.22.b.d.49.4		4
5.3	odd	4		75.22.b.d.49.1		4
5.4	even	2		75.22.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.22.a.c.1.2	✓	2	1.1	even	1	trivial
9.22.a.e.1.1		2	3.2	odd	2
48.22.a.g.1.2		2	4.3	odd	2
75.22.a.d.1.1		2	5.4	even	2
75.22.b.d.49.1		4	5.3	odd	4
75.22.b.d.49.4		4	5.2	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)

\(f(q)\)	\(=\)	\(q+1937.96 q^{2} +59049.0 q^{3} +1.65852e6 q^{4} +2.22745e7 q^{5} +1.14434e8 q^{6} +4.78205e7 q^{7} -8.50053e8 q^{8} +3.48678e9 q^{9} +O(q^{10})\)	\(q+1937.96 q^{2} +59049.0 q^{3} +1.65852e6 q^{4} +2.22745e7 q^{5} +1.14434e8 q^{6} +4.78205e7 q^{7} -8.50053e8 q^{8} +3.48678e9 q^{9} +4.31669e10 q^{10} +1.60111e11 q^{11} +9.79338e10 q^{12} -7.86968e11 q^{13} +9.26741e10 q^{14} +1.31529e12 q^{15} -5.12553e12 q^{16} -2.97477e12 q^{17} +6.75723e12 q^{18} -2.99456e13 q^{19} +3.69426e13 q^{20} +2.82376e12 q^{21} +3.10287e14 q^{22} -1.91401e14 q^{23} -5.01948e13 q^{24} +1.93148e13 q^{25} -1.52511e15 q^{26} +2.05891e14 q^{27} +7.93112e13 q^{28} +9.68170e14 q^{29} +2.54896e15 q^{30} +2.80459e15 q^{31} -8.15035e15 q^{32} +9.45437e15 q^{33} -5.76496e15 q^{34} +1.06518e15 q^{35} +5.78290e15 q^{36} +3.05038e16 q^{37} -5.80331e16 q^{38} -4.64697e16 q^{39} -1.89345e16 q^{40} -2.22806e16 q^{41} +5.47231e15 q^{42} +1.63711e17 q^{43} +2.65546e17 q^{44} +7.76663e16 q^{45} -3.70927e17 q^{46} +4.08678e17 q^{47} -3.02657e17 q^{48} -5.56259e17 q^{49} +3.74313e16 q^{50} -1.75657e17 q^{51} -1.30520e18 q^{52} +4.34009e17 q^{53} +3.99008e17 q^{54} +3.56638e18 q^{55} -4.06500e16 q^{56} -1.76826e18 q^{57} +1.87627e18 q^{58} -5.14341e18 q^{59} +2.18142e18 q^{60} +1.98980e18 q^{61} +5.43517e18 q^{62} +1.66740e17 q^{63} -5.04601e18 q^{64} -1.75293e19 q^{65} +1.83222e19 q^{66} -1.36361e19 q^{67} -4.93370e18 q^{68} -1.13020e19 q^{69} +2.06427e18 q^{70} +7.35641e18 q^{71} -2.96395e18 q^{72} +6.81650e19 q^{73} +5.91149e19 q^{74} +1.14052e18 q^{75} -4.96652e19 q^{76} +7.65658e18 q^{77} -9.00562e19 q^{78} -2.12282e19 q^{79} -1.14168e20 q^{80} +1.21577e19 q^{81} -4.31789e19 q^{82} +1.10803e20 q^{83} +4.68325e18 q^{84} -6.62613e19 q^{85} +3.17266e20 q^{86} +5.71695e19 q^{87} -1.36102e20 q^{88} -7.67205e18 q^{89} +1.50514e20 q^{90} -3.76333e19 q^{91} -3.17442e20 q^{92} +1.65608e20 q^{93} +7.92000e20 q^{94} -6.67021e20 q^{95} -4.81270e20 q^{96} +4.63755e20 q^{97} -1.07801e21 q^{98} +5.58271e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 666 q^{2} + 118098 q^{3} + 1179236 q^{4} + 996876 q^{5} + 39326634 q^{6} + 679896112 q^{7} + 2427055848 q^{8} + 6973568802 q^{9}+O(q^{10}) \) 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

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