LMFDB - Embedded newform 4018.2.a.bp.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.5163008.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 5x^{2} - 6x + 1 $ x^6 - 2x^5 - 5x^4 + 8x^3 + 5x^2 - 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.56754$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.0387751 q^{3} +1.00000 q^{4} -2.61052 q^{5} -0.0387751 q^{6} +1.00000 q^{8} -2.99850 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.0387751 q^{3} +1.00000 q^{4} -2.61052 q^{5} -0.0387751 q^{6} +1.00000 q^{8} -2.99850 q^{9} -2.61052 q^{10} +3.07158 q^{11} -0.0387751 q^{12} +2.08825 q^{13} +0.101223 q^{15} +1.00000 q^{16} +0.761390 q^{17} -2.99850 q^{18} -7.09631 q^{19} -2.61052 q^{20} +3.07158 q^{22} +5.31219 q^{23} -0.0387751 q^{24} +1.81483 q^{25} +2.08825 q^{26} +0.232592 q^{27} +2.31533 q^{29} +0.101223 q^{30} -0.644105 q^{31} +1.00000 q^{32} -0.119101 q^{33} +0.761390 q^{34} -2.99850 q^{36} -9.45774 q^{37} -7.09631 q^{38} -0.0809720 q^{39} -2.61052 q^{40} +1.00000 q^{41} +4.79344 q^{43} +3.07158 q^{44} +7.82764 q^{45} +5.31219 q^{46} -4.61388 q^{47} -0.0387751 q^{48} +1.81483 q^{50} -0.0295230 q^{51} +2.08825 q^{52} -6.27441 q^{53} +0.232592 q^{54} -8.01842 q^{55} +0.275160 q^{57} +2.31533 q^{58} -14.3819 q^{59} +0.101223 q^{60} -3.84288 q^{61} -0.644105 q^{62} +1.00000 q^{64} -5.45142 q^{65} -0.119101 q^{66} +8.37335 q^{67} +0.761390 q^{68} -0.205981 q^{69} -10.8481 q^{71} -2.99850 q^{72} -3.35938 q^{73} -9.45774 q^{74} -0.0703702 q^{75} -7.09631 q^{76} -0.0809720 q^{78} -2.24510 q^{79} -2.61052 q^{80} +8.98647 q^{81} +1.00000 q^{82} -7.80581 q^{83} -1.98763 q^{85} +4.79344 q^{86} -0.0897774 q^{87} +3.07158 q^{88} +5.93525 q^{89} +7.82764 q^{90} +5.31219 q^{92} +0.0249753 q^{93} -4.61388 q^{94} +18.5251 q^{95} -0.0387751 q^{96} -16.7498 q^{97} -9.21011 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 4 q^{3} + 6 q^{4} - 12 q^{5} - 4 q^{6} + 6 q^{8} + 18 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 4 * q^3 + 6 * q^4 - 12 * q^5 - 4 * q^6 + 6 * q^8 + 18 * q^9	$ 6 q + 6 q^{2} - 4 q^{3} + 6 q^{4} - 12 q^{5} - 4 q^{6} + 6 q^{8} + 18 q^{9} - 12 q^{10} - 4 q^{12} - 8 q^{13} - 4 q^{15} + 6 q^{16} - 16 q^{17} + 18 q^{18} - 12 q^{19} - 12 q^{20} + 12 q^{23} - 4 q^{24} + 14 q^{25} - 8 q^{26} - 28 q^{27} - 4 q^{30} + 4 q^{31} + 6 q^{32} + 20 q^{33} - 16 q^{34} + 18 q^{36} - 24 q^{37} - 12 q^{38} + 4 q^{39} - 12 q^{40} + 6 q^{41} + 4 q^{43} - 28 q^{45} + 12 q^{46} + 16 q^{47} - 4 q^{48} + 14 q^{50} - 16 q^{51} - 8 q^{52} - 16 q^{53} - 28 q^{54} + 12 q^{55} - 28 q^{57} - 16 q^{59} - 4 q^{60} - 32 q^{61} + 4 q^{62} + 6 q^{64} - 4 q^{65} + 20 q^{66} - 20 q^{67} - 16 q^{68} - 56 q^{69} + 12 q^{71} + 18 q^{72} - 16 q^{73} - 24 q^{74} + 4 q^{75} - 12 q^{76} + 4 q^{78} - 12 q^{80} + 42 q^{81} + 6 q^{82} - 32 q^{83} + 48 q^{85} + 4 q^{86} - 20 q^{87} - 8 q^{89} - 28 q^{90} + 12 q^{92} - 12 q^{93} + 16 q^{94} + 28 q^{95} - 4 q^{96} - 8 q^{97} - 76 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 - 4 * q^3 + 6 * q^4 - 12 * q^5 - 4 * q^6 + 6 * q^8 + 18 * q^9 - 12 * q^10 - 4 * q^12 - 8 * q^13 - 4 * q^15 + 6 * q^16 - 16 * q^17 + 18 * q^18 - 12 * q^19 - 12 * q^20 + 12 * q^23 - 4 * q^24 + 14 * q^25 - 8 * q^26 - 28 * q^27 - 4 * q^30 + 4 * q^31 + 6 * q^32 + 20 * q^33 - 16 * q^34 + 18 * q^36 - 24 * q^37 - 12 * q^38 + 4 * q^39 - 12 * q^40 + 6 * q^41 + 4 * q^43 - 28 * q^45 + 12 * q^46 + 16 * q^47 - 4 * q^48 + 14 * q^50 - 16 * q^51 - 8 * q^52 - 16 * q^53 - 28 * q^54 + 12 * q^55 - 28 * q^57 - 16 * q^59 - 4 * q^60 - 32 * q^61 + 4 * q^62 + 6 * q^64 - 4 * q^65 + 20 * q^66 - 20 * q^67 - 16 * q^68 - 56 * q^69 + 12 * q^71 + 18 * q^72 - 16 * q^73 - 24 * q^74 + 4 * q^75 - 12 * q^76 + 4 * q^78 - 12 * q^80 + 42 * q^81 + 6 * q^82 - 32 * q^83 + 48 * q^85 + 4 * q^86 - 20 * q^87 - 8 * q^89 - 28 * q^90 + 12 * q^92 - 12 * q^93 + 16 * q^94 + 28 * q^95 - 4 * q^96 - 8 * q^97 - 76 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.0387751	−0.0223868	−0.0111934	−	0.999937i	$-0.503563\pi$
$3$	−0.0387751	−0.0223868	−0.0111934	+	0.999937i	$0.503563\pi$
$4$	1.00000	0.500000
$5$	−2.61052	−1.16746	−0.583731	−	0.811947i	$-0.698408\pi$
$5$	−2.61052	−1.16746	−0.583731	+	0.811947i	$0.698408\pi$
$6$	−0.0387751	−0.0158299
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−2.99850	−0.999499
$10$	−2.61052	−0.825520
$11$	3.07158	0.926115	0.463057	−	0.886328i	$-0.346752\pi$
$11$	3.07158	0.926115	0.463057	+	0.886328i	$0.346752\pi$
$12$	−0.0387751	−0.0111934
$13$	2.08825	0.579176	0.289588	−	0.957151i	$-0.406482\pi$
$13$	2.08825	0.579176	0.289588	+	0.957151i	$0.406482\pi$
$14$	0	0
$15$	0.101223	0.0261358
$16$	1.00000	0.250000
$17$	0.761390	0.184664	0.0923321	−	0.995728i	$-0.470568\pi$
$17$	0.761390	0.184664	0.0923321	+	0.995728i	$0.470568\pi$
$18$	−2.99850	−0.706752
$19$	−7.09631	−1.62801	−0.814003	−	0.580861i	$-0.802716\pi$
$19$	−7.09631	−1.62801	−0.814003	+	0.580861i	$0.802716\pi$
$20$	−2.61052	−0.583731
$21$	0	0
$22$	3.07158	0.654862
$23$	5.31219	1.10767	0.553835	−	0.832627i	$-0.313164\pi$
$23$	5.31219	1.10767	0.553835	+	0.832627i	$0.313164\pi$
$24$	−0.0387751	−0.00791494
$25$	1.81483	0.362966
$26$	2.08825	0.409539
$27$	0.232592	0.0447624
$28$	0	0
$29$	2.31533	0.429947	0.214973	−	0.976620i	$-0.431033\pi$
$29$	2.31533	0.429947	0.214973	+	0.976620i	$0.431033\pi$
$30$	0.101223	0.0184808
$31$	−0.644105	−0.115685	−0.0578424	−	0.998326i	$-0.518422\pi$
$31$	−0.644105	−0.115685	−0.0578424	+	0.998326i	$0.518422\pi$
$32$	1.00000	0.176777
$33$	−0.119101	−0.0207328
$34$	0.761390	0.130577
$35$	0	0
$36$	−2.99850	−0.499749
$37$	−9.45774	−1.55484	−0.777421	−	0.628980i	$-0.783473\pi$
$37$	−9.45774	−1.55484	−0.777421	+	0.628980i	$0.783473\pi$
$38$	−7.09631	−1.15117
$39$	−0.0809720	−0.0129659
$40$	−2.61052	−0.412760
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	4.79344	0.730993	0.365497	−	0.930813i	$-0.380899\pi$
$43$	4.79344	0.730993	0.365497	+	0.930813i	$0.380899\pi$
$44$	3.07158	0.463057
$45$	7.82764	1.16688
$46$	5.31219	0.783240
$47$	−4.61388	−0.673003	−0.336501	−	0.941683i	$-0.609244\pi$
$47$	−4.61388	−0.673003	−0.336501	+	0.941683i	$0.609244\pi$
$48$	−0.0387751	−0.00559671
$49$	0	0
$50$	1.81483	0.256656
$51$	−0.0295230	−0.00413405
$52$	2.08825	0.289588
$53$	−6.27441	−0.861856	−0.430928	−	0.902386i	$-0.641814\pi$
$53$	−6.27441	−0.861856	−0.430928	+	0.902386i	$0.641814\pi$
$54$	0.232592	0.0316518
$55$	−8.01842	−1.08120
$56$	0	0
$57$	0.275160	0.0364459
$58$	2.31533	0.304018
$59$	−14.3819	−1.87236	−0.936181	−	0.351518i	$-0.885666\pi$
$59$	−14.3819	−1.87236	−0.936181	+	0.351518i	$0.885666\pi$
$60$	0.101223	0.0130679
$61$	−3.84288	−0.492030	−0.246015	−	0.969266i	$-0.579121\pi$
$61$	−3.84288	−0.492030	−0.246015	+	0.969266i	$0.579121\pi$
$62$	−0.644105	−0.0818015
$63$	0	0
$64$	1.00000	0.125000
$65$	−5.45142	−0.676165
$66$	−0.119101	−0.0146603
$67$	8.37335	1.02297	0.511484	−	0.859293i	$-0.329096\pi$
$67$	8.37335	1.02297	0.511484	+	0.859293i	$0.329096\pi$
$68$	0.761390	0.0923321
$69$	−0.205981	−0.0247972
$70$	0	0
$71$	−10.8481	−1.28744	−0.643718	−	0.765263i	$-0.722609\pi$
$71$	−10.8481	−1.28744	−0.643718	+	0.765263i	$0.722609\pi$
$72$	−2.99850	−0.353376
$73$	−3.35938	−0.393185	−0.196593	−	0.980485i	$-0.562988\pi$
$73$	−3.35938	−0.393185	−0.196593	+	0.980485i	$0.562988\pi$
$74$	−9.45774	−1.09944
$75$	−0.0703702	−0.00812565
$76$	−7.09631	−0.814003
$77$	0	0
$78$	−0.0809720	−0.00916828
$79$	−2.24510	−0.252594	−0.126297	−	0.991992i	$-0.540309\pi$
$79$	−2.24510	−0.252594	−0.126297	+	0.991992i	$0.540309\pi$
$80$	−2.61052	−0.291865
$81$	8.98647	0.998497
$82$	1.00000	0.110432
$83$	−7.80581	−0.856799	−0.428399	−	0.903589i	$-0.640922\pi$
$83$	−7.80581	−0.856799	−0.428399	+	0.903589i	$0.640922\pi$
$84$	0	0
$85$	−1.98763	−0.215588
$86$	4.79344	0.516890
$87$	−0.0897774	−0.00962515
$88$	3.07158	0.327431
$89$	5.93525	0.629135	0.314568	−	0.949235i	$-0.398140\pi$
$89$	5.93525	0.629135	0.314568	+	0.949235i	$0.398140\pi$
$90$	7.82764	0.825106
$91$	0	0
$92$	5.31219	0.553835
$93$	0.0249753	0.00258981
$94$	−4.61388	−0.475885
$95$	18.5251	1.90063
$96$	−0.0387751	−0.00395747
$97$	−16.7498	−1.70069	−0.850345	−	0.526226i	$-0.823607\pi$
$97$	−16.7498	−1.70069	−0.850345	+	0.526226i	$0.823607\pi$
$98$	0	0
$99$	−9.21011	−0.925651
$100$	1.81483	0.181483
$101$	−10.4656	−1.04137	−0.520683	−	0.853750i	$-0.674322\pi$
$101$	−10.4656	−1.04137	−0.520683	+	0.853750i	$0.674322\pi$
$102$	−0.0295230	−0.00292321
$103$	2.47421	0.243791	0.121896	−	0.992543i	$-0.461103\pi$
$103$	2.47421	0.243791	0.121896	+	0.992543i	$0.461103\pi$
$104$	2.08825	0.204770
$105$	0	0
$106$	−6.27441	−0.609424
$107$	−15.8124	−1.52864	−0.764320	−	0.644837i	$-0.776925\pi$
$107$	−15.8124	−1.52864	−0.764320	+	0.644837i	$0.776925\pi$
$108$	0.232592	0.0223812
$109$	6.57783	0.630042	0.315021	−	0.949085i	$-0.397988\pi$
$109$	6.57783	0.630042	0.315021	+	0.949085i	$0.397988\pi$
$110$	−8.01842	−0.764526
$111$	0.366725	0.0348080
$112$	0	0
$113$	3.34219	0.314407	0.157203	−	0.987566i	$-0.449752\pi$
$113$	3.34219	0.314407	0.157203	+	0.987566i	$0.449752\pi$
$114$	0.275160	0.0257711
$115$	−13.8676	−1.29316
$116$	2.31533	0.214973
$117$	−6.26160	−0.578885
$118$	−14.3819	−1.32396
$119$	0	0
$120$	0.101223	0.00924038
$121$	−1.56542	−0.142311
$122$	−3.84288	−0.347918
$123$	−0.0387751	−0.00349623
$124$	−0.644105	−0.0578424
$125$	8.31496	0.743713
$126$	0	0
$127$	−8.37867	−0.743487	−0.371743	−	0.928335i	$-0.621240\pi$
$127$	−8.37867	−0.743487	−0.371743	+	0.928335i	$0.621240\pi$
$128$	1.00000	0.0883883
$129$	−0.185866	−0.0163646
$130$	−5.45142	−0.478121
$131$	12.7513	1.11409	0.557043	−	0.830483i	$-0.311936\pi$
$131$	12.7513	1.11409	0.557043	+	0.830483i	$0.311936\pi$
$132$	−0.119101	−0.0103664
$133$	0	0
$134$	8.37335	0.723347
$135$	−0.607188	−0.0522584
$136$	0.761390	0.0652887
$137$	14.7866	1.26330	0.631651	−	0.775253i	$-0.282377\pi$
$137$	14.7866	1.26330	0.631651	+	0.775253i	$0.282377\pi$
$138$	−0.205981	−0.0175343
$139$	−9.80861	−0.831956	−0.415978	−	0.909375i	$-0.636561\pi$
$139$	−9.80861	−0.831956	−0.415978	+	0.909375i	$0.636561\pi$
$140$	0	0
$141$	0.178904	0.0150664
$142$	−10.8481	−0.910355
$143$	6.41421	0.536383
$144$	−2.99850	−0.249875
$145$	−6.04423	−0.501946
$146$	−3.35938	−0.278024
$147$	0	0
$148$	−9.45774	−0.777421
$149$	−12.1994	−0.999412	−0.499706	−	0.866195i	$-0.666559\pi$
$149$	−12.1994	−0.999412	−0.499706	+	0.866195i	$0.666559\pi$
$150$	−0.0703702	−0.00574570
$151$	−20.5621	−1.67332	−0.836660	−	0.547722i	$-0.815495\pi$
$151$	−20.5621	−1.67332	−0.836660	+	0.547722i	$0.815495\pi$
$152$	−7.09631	−0.575587
$153$	−2.28303	−0.184572
$154$	0	0
$155$	1.68145	0.135057
$156$	−0.0809720	−0.00648295
$157$	4.63615	0.370005	0.185003	−	0.982738i	$-0.440771\pi$
$157$	4.63615	0.370005	0.185003	+	0.982738i	$0.440771\pi$
$158$	−2.24510	−0.178611
$159$	0.243291	0.0192942
$160$	−2.61052	−0.206380
$161$	0	0
$162$	8.98647	0.706044
$163$	3.11486	0.243974	0.121987	−	0.992532i	$-0.461073\pi$
$163$	3.11486	0.243974	0.121987	+	0.992532i	$0.461073\pi$
$164$	1.00000	0.0780869
$165$	0.310915	0.0242047
$166$	−7.80581	−0.605848
$167$	4.77073	0.369170	0.184585	−	0.982817i	$-0.440906\pi$
$167$	4.77073	0.369170	0.184585	+	0.982817i	$0.440906\pi$
$168$	0	0
$169$	−8.63922	−0.664556
$170$	−1.98763	−0.152444
$171$	21.2783	1.62719
$172$	4.79344	0.365497
$173$	−2.15961	−0.164192	−0.0820959	−	0.996624i	$-0.526161\pi$
$173$	−2.15961	−0.164192	−0.0820959	+	0.996624i	$0.526161\pi$
$174$	−0.0897774	−0.00680601
$175$	0	0
$176$	3.07158	0.231529
$177$	0.557659	0.0419163
$178$	5.93525	0.444866
$179$	−20.1667	−1.50733	−0.753663	−	0.657261i	$-0.771715\pi$
$179$	−20.1667	−1.50733	−0.753663	+	0.657261i	$0.771715\pi$
$180$	7.82764	0.583438
$181$	−7.51035	−0.558240	−0.279120	−	0.960256i	$-0.590043\pi$
$181$	−7.51035	−0.558240	−0.279120	+	0.960256i	$0.590043\pi$
$182$	0	0
$183$	0.149008	0.0110150
$184$	5.31219	0.391620
$185$	24.6896	1.81522
$186$	0.0249753	0.00183128
$187$	2.33867	0.171020
$188$	−4.61388	−0.336501
$189$	0	0
$190$	18.5251	1.34395
$191$	4.24153	0.306907	0.153453	−	0.988156i	$-0.450961\pi$
$191$	4.24153	0.306907	0.153453	+	0.988156i	$0.450961\pi$
$192$	−0.0387751	−0.00279835
$193$	13.7705	0.991224	0.495612	−	0.868544i	$-0.334944\pi$
$193$	13.7705	0.991224	0.495612	+	0.868544i	$0.334944\pi$
$194$	−16.7498	−1.20257
$195$	0.211379	0.0151372
$196$	0	0
$197$	−2.68951	−0.191620	−0.0958100	−	0.995400i	$-0.530544\pi$
$197$	−2.68951	−0.191620	−0.0958100	+	0.995400i	$0.530544\pi$
$198$	−9.21011	−0.654534
$199$	6.34370	0.449693	0.224847	−	0.974394i	$-0.427812\pi$
$199$	6.34370	0.449693	0.224847	+	0.974394i	$0.427812\pi$
$200$	1.81483	0.128328
$201$	−0.324678	−0.0229010
$202$	−10.4656	−0.736356
$203$	0	0
$204$	−0.0295230	−0.00206702
$205$	−2.61052	−0.182327
$206$	2.47421	0.172387
$207$	−15.9286	−1.10711
$208$	2.08825	0.144794
$209$	−21.7969	−1.50772
$210$	0	0
$211$	−2.81048	−0.193481	−0.0967407	−	0.995310i	$-0.530842\pi$
$211$	−2.81048	−0.193481	−0.0967407	+	0.995310i	$0.530842\pi$
$212$	−6.27441	−0.430928
$213$	0.420638	0.0288216
$214$	−15.8124	−1.08091
$215$	−12.5134	−0.853407
$216$	0.232592	0.0158259
$217$	0	0
$218$	6.57783	0.445507
$219$	0.130260	0.00880217
$220$	−8.01842	−0.540602
$221$	1.58997	0.106953
$222$	0.366725	0.0246130
$223$	−19.0157	−1.27338	−0.636692	−	0.771118i	$-0.719698\pi$
$223$	−19.0157	−1.27338	−0.636692	+	0.771118i	$0.719698\pi$
$224$	0	0
$225$	−5.44176	−0.362784
$226$	3.34219	0.222319
$227$	−9.23513	−0.612957	−0.306478	−	0.951878i	$-0.599151\pi$
$227$	−9.23513	−0.612957	−0.306478	+	0.951878i	$0.599151\pi$
$228$	0.275160	0.0182229
$229$	19.7514	1.30521	0.652605	−	0.757698i	$-0.273676\pi$
$229$	19.7514	1.30521	0.652605	+	0.757698i	$0.273676\pi$
$230$	−13.8676	−0.914403
$231$	0	0
$232$	2.31533	0.152009
$233$	−19.5991	−1.28398	−0.641990	−	0.766713i	$-0.721891\pi$
$233$	−19.5991	−1.28398	−0.641990	+	0.766713i	$0.721891\pi$
$234$	−6.26160	−0.409334
$235$	12.0446	0.785705
$236$	−14.3819	−0.936181
$237$	0.0870541	0.00565477
$238$	0	0
$239$	−8.41493	−0.544317	−0.272158	−	0.962252i	$-0.587737\pi$
$239$	−8.41493	−0.544317	−0.272158	+	0.962252i	$0.587737\pi$
$240$	0.101223	0.00653394
$241$	−3.36585	−0.216813	−0.108407	−	0.994107i	$-0.534575\pi$
$241$	−3.36585	−0.216813	−0.108407	+	0.994107i	$0.534575\pi$
$242$	−1.56542	−0.100629
$243$	−1.04623	−0.0671156
$244$	−3.84288	−0.246015
$245$	0	0
$246$	−0.0387751	−0.00247221
$247$	−14.8189	−0.942901
$248$	−0.644105	−0.0409007
$249$	0.302671	0.0191810
$250$	8.31496	0.525884
$251$	−2.97894	−0.188029	−0.0940144	−	0.995571i	$-0.529970\pi$
$251$	−2.97894	−0.188029	−0.0940144	+	0.995571i	$0.529970\pi$
$252$	0	0
$253$	16.3168	1.02583
$254$	−8.37867	−0.525725
$255$	0.0770704	0.00482634
$256$	1.00000	0.0625000
$257$	−6.74010	−0.420436	−0.210218	−	0.977655i	$-0.567417\pi$
$257$	−6.74010	−0.420436	−0.210218	+	0.977655i	$0.567417\pi$
$258$	−0.185866	−0.0115715
$259$	0	0
$260$	−5.45142	−0.338083
$261$	−6.94252	−0.429731
$262$	12.7513	0.787778
$263$	21.7936	1.34385	0.671926	−	0.740618i	$-0.265467\pi$
$263$	21.7936	1.34385	0.671926	+	0.740618i	$0.265467\pi$
$264$	−0.119101	−0.00733014
$265$	16.3795	1.00618
$266$	0	0
$267$	−0.230140	−0.0140843
$268$	8.37335	0.511484
$269$	−26.2079	−1.59793	−0.798963	−	0.601380i	$-0.794618\pi$
$269$	−26.2079	−1.59793	−0.798963	+	0.601380i	$0.794618\pi$
$270$	−0.607188	−0.0369523
$271$	19.9240	1.21030	0.605149	−	0.796112i	$-0.293113\pi$
$271$	19.9240	1.21030	0.605149	+	0.796112i	$0.293113\pi$
$272$	0.761390	0.0461660
$273$	0	0
$274$	14.7866	0.893290
$275$	5.57438	0.336148
$276$	−0.205981	−0.0123986
$277$	20.0693	1.20585	0.602923	−	0.797799i	$-0.294003\pi$
$277$	20.0693	1.20585	0.602923	+	0.797799i	$0.294003\pi$
$278$	−9.80861	−0.588282
$279$	1.93135	0.115627
$280$	0	0
$281$	22.8047	1.36041	0.680207	−	0.733020i	$-0.261890\pi$
$281$	22.8047	1.36041	0.680207	+	0.733020i	$0.261890\pi$
$282$	0.178904	0.0106536
$283$	20.5397	1.22096	0.610479	−	0.792033i	$-0.290977\pi$
$283$	20.5397	1.22096	0.610479	+	0.792033i	$0.290977\pi$
$284$	−10.8481	−0.643718
$285$	−0.718312	−0.0425491
$286$	6.41421	0.379280
$287$	0	0
$288$	−2.99850	−0.176688
$289$	−16.4203	−0.965899
$290$	−6.04423	−0.354930
$291$	0.649477	0.0380730
$292$	−3.35938	−0.196593
$293$	26.9744	1.57586	0.787930	−	0.615764i	$-0.211153\pi$
$293$	26.9744	1.57586	0.787930	+	0.615764i	$0.211153\pi$
$294$	0	0
$295$	37.5442	2.18591
$296$	−9.45774	−0.549720
$297$	0.714425	0.0414552
$298$	−12.1994	−0.706691
$299$	11.0932	0.641535
$300$	−0.0703702	−0.00406283
$301$	0	0
$302$	−20.5621	−1.18322
$303$	0.405805	0.0233129
$304$	−7.09631	−0.407001
$305$	10.0319	0.574426
$306$	−2.28303	−0.130512
$307$	−11.9580	−0.682476	−0.341238	−	0.939977i	$-0.610846\pi$
$307$	−11.9580	−0.682476	−0.341238	+	0.939977i	$0.610846\pi$
$308$	0	0
$309$	−0.0959379	−0.00545772
$310$	1.68145	0.0955001
$311$	17.8581	1.01264	0.506319	−	0.862346i	$-0.331006\pi$
$311$	17.8581	1.01264	0.506319	+	0.862346i	$0.331006\pi$
$312$	−0.0809720	−0.00458414
$313$	−10.1352	−0.572876	−0.286438	−	0.958099i	$-0.592471\pi$
$313$	−10.1352	−0.572876	−0.286438	+	0.958099i	$0.592471\pi$
$314$	4.63615	0.261633
$315$	0	0
$316$	−2.24510	−0.126297
$317$	11.6642	0.655127	0.327564	−	0.944829i	$-0.393772\pi$
$317$	11.6642	0.655127	0.327564	+	0.944829i	$0.393772\pi$
$318$	0.243291	0.0136431
$319$	7.11173	0.398180
$320$	−2.61052	−0.145933
$321$	0.613127	0.0342214
$322$	0	0
$323$	−5.40306	−0.300634
$324$	8.98647	0.499248
$325$	3.78981	0.210221
$326$	3.11486	0.172516
$327$	−0.255056	−0.0141046
$328$	1.00000	0.0552158
$329$	0	0
$330$	0.310915	0.0171153
$331$	−12.3608	−0.679413	−0.339707	−	0.940531i	$-0.610328\pi$
$331$	−12.3608	−0.679413	−0.339707	+	0.940531i	$0.610328\pi$
$332$	−7.80581	−0.428399
$333$	28.3590	1.55406
$334$	4.77073	0.261043
$335$	−21.8588	−1.19428
$336$	0	0
$337$	27.7851	1.51355	0.756776	−	0.653675i	$-0.226774\pi$
$337$	27.7851	1.51355	0.756776	+	0.653675i	$0.226774\pi$
$338$	−8.63922	−0.469912
$339$	−0.129594	−0.00703857
$340$	−1.98763	−0.107794
$341$	−1.97842	−0.107137
$342$	21.2783	1.15060
$343$	0	0
$344$	4.79344	0.258445
$345$	0.537718	0.0289498
$346$	−2.15961	−0.116101
$347$	2.25401	0.121002	0.0605008	−	0.998168i	$-0.480730\pi$
$347$	2.25401	0.121002	0.0605008	+	0.998168i	$0.480730\pi$
$348$	−0.0897774	−0.00481257
$349$	17.0144	0.910762	0.455381	−	0.890297i	$-0.349503\pi$
$349$	17.0144	0.910762	0.455381	+	0.890297i	$0.349503\pi$
$350$	0	0
$351$	0.485711	0.0259253
$352$	3.07158	0.163716
$353$	17.9998	0.958032	0.479016	−	0.877806i	$-0.340994\pi$
$353$	17.9998	0.958032	0.479016	+	0.877806i	$0.340994\pi$
$354$	0.557659	0.0296393
$355$	28.3193	1.50303
$356$	5.93525	0.314568
$357$	0	0
$358$	−20.1667	−1.06584
$359$	9.57429	0.505312	0.252656	−	0.967556i	$-0.418696\pi$
$359$	9.57429	0.505312	0.252656	+	0.967556i	$0.418696\pi$
$360$	7.82764	0.412553
$361$	31.3576	1.65040
$362$	−7.51035	−0.394735
$363$	0.0606995	0.00318590
$364$	0	0
$365$	8.76973	0.459029
$366$	0.149008	0.00778877
$367$	−13.8966	−0.725396	−0.362698	−	0.931907i	$-0.618144\pi$
$367$	−13.8966	−0.725396	−0.362698	+	0.931907i	$0.618144\pi$
$368$	5.31219	0.276917
$369$	−2.99850	−0.156095
$370$	24.6896	1.28355
$371$	0	0
$372$	0.0249753	0.00129491
$373$	−30.4692	−1.57764	−0.788818	−	0.614627i	$-0.789307\pi$
$373$	−30.4692	−1.57764	−0.788818	+	0.614627i	$0.789307\pi$
$374$	2.33867	0.120930
$375$	−0.322414	−0.0166494
$376$	−4.61388	−0.237942
$377$	4.83499	0.249015
$378$	0	0
$379$	12.9617	0.665799	0.332900	−	0.942962i	$-0.391973\pi$
$379$	12.9617	0.665799	0.332900	+	0.942962i	$0.391973\pi$
$380$	18.5251	0.950317
$381$	0.324884	0.0166443
$382$	4.24153	0.217016
$383$	14.7064	0.751460	0.375730	−	0.926729i	$-0.377392\pi$
$383$	14.7064	0.751460	0.375730	+	0.926729i	$0.377392\pi$
$384$	−0.0387751	−0.00197873
$385$	0	0
$386$	13.7705	0.700902
$387$	−14.3731	−0.730627
$388$	−16.7498	−0.850345
$389$	−27.1877	−1.37847	−0.689235	−	0.724537i	$-0.742053\pi$
$389$	−27.1877	−1.37847	−0.689235	+	0.724537i	$0.742053\pi$
$390$	0.211379	0.0107036
$391$	4.04465	0.204547
$392$	0	0
$393$	−0.494433	−0.0249409
$394$	−2.68951	−0.135496
$395$	5.86089	0.294894
$396$	−9.21011	−0.462825
$397$	35.1116	1.76220	0.881100	−	0.472930i	$-0.156804\pi$
$397$	35.1116	1.76220	0.881100	+	0.472930i	$0.156804\pi$
$398$	6.34370	0.317981
$399$	0	0
$400$	1.81483	0.0907414
$401$	−13.7763	−0.687958	−0.343979	−	0.938977i	$-0.611775\pi$
$401$	−13.7763	−0.687958	−0.343979	+	0.938977i	$0.611775\pi$
$402$	−0.324678	−0.0161935
$403$	−1.34505	−0.0670018
$404$	−10.4656	−0.520683
$405$	−23.4594	−1.16571
$406$	0	0
$407$	−29.0502	−1.43996
$408$	−0.0295230	−0.00146161
$409$	−27.4007	−1.35487	−0.677437	−	0.735580i	$-0.736910\pi$
$409$	−27.4007	−1.35487	−0.677437	+	0.735580i	$0.736910\pi$
$410$	−2.61052	−0.128925
$411$	−0.573351	−0.0282813
$412$	2.47421	0.121896
$413$	0	0
$414$	−15.9286	−0.782848
$415$	20.3772	1.00028
$416$	2.08825	0.102385
$417$	0.380330	0.0186248
$418$	−21.7969	−1.06612
$419$	29.5386	1.44305	0.721527	−	0.692386i	$-0.243441\pi$
$419$	29.5386	1.44305	0.721527	+	0.692386i	$0.243441\pi$
$420$	0	0
$421$	5.26049	0.256380	0.128190	−	0.991750i	$-0.459083\pi$
$421$	5.26049	0.256380	0.128190	+	0.991750i	$0.459083\pi$
$422$	−2.81048	−0.136812
$423$	13.8347	0.672666
$424$	−6.27441	−0.304712
$425$	1.38179	0.0670268
$426$	0.420638	0.0203800
$427$	0	0
$428$	−15.8124	−0.764320
$429$	−0.248712	−0.0120079
$430$	−12.5134	−0.603450
$431$	−34.4649	−1.66012	−0.830059	−	0.557676i	$-0.811693\pi$
$431$	−34.4649	−1.66012	−0.830059	+	0.557676i	$0.811693\pi$
$432$	0.232592	0.0111906
$433$	8.66488	0.416408	0.208204	−	0.978085i	$-0.433238\pi$
$433$	8.66488	0.416408	0.208204	+	0.978085i	$0.433238\pi$
$434$	0	0
$435$	0.234366	0.0112370
$436$	6.57783	0.315021
$437$	−37.6970	−1.80329
$438$	0.130260	0.00622408
$439$	−7.77642	−0.371148	−0.185574	−	0.982630i	$-0.559414\pi$
$439$	−7.77642	−0.371148	−0.185574	+	0.982630i	$0.559414\pi$
$440$	−8.01842	−0.382263
$441$	0	0
$442$	1.58997	0.0756272
$443$	−10.7928	−0.512782	−0.256391	−	0.966573i	$-0.582533\pi$
$443$	−10.7928	−0.512782	−0.256391	+	0.966573i	$0.582533\pi$
$444$	0.366725	0.0174040
$445$	−15.4941	−0.734491
$446$	−19.0157	−0.900419
$447$	0.473032	0.0223737
$448$	0	0
$449$	−17.4966	−0.825717	−0.412859	−	0.910795i	$-0.635470\pi$
$449$	−17.4966	−0.825717	−0.412859	+	0.910795i	$0.635470\pi$
$450$	−5.44176	−0.256527
$451$	3.07158	0.144635
$452$	3.34219	0.157203
$453$	0.797298	0.0374603
$454$	−9.23513	−0.433426
$455$	0	0
$456$	0.275160	0.0128856
$457$	2.68726	0.125705	0.0628524	−	0.998023i	$-0.479980\pi$
$457$	2.68726	0.125705	0.0628524	+	0.998023i	$0.479980\pi$
$458$	19.7514	0.922923
$459$	0.177094	0.00826602
$460$	−13.8676	−0.646580
$461$	8.15008	0.379587	0.189794	−	0.981824i	$-0.439218\pi$
$461$	8.15008	0.379587	0.189794	+	0.981824i	$0.439218\pi$
$462$	0	0
$463$	11.1325	0.517372	0.258686	−	0.965961i	$-0.416711\pi$
$463$	11.1325	0.517372	0.258686	+	0.965961i	$0.416711\pi$
$464$	2.31533	0.107487
$465$	−0.0651985	−0.00302351
$466$	−19.5991	−0.907911
$467$	−33.9394	−1.57053	−0.785265	−	0.619160i	$-0.787473\pi$
$467$	−33.9394	−1.57053	−0.785265	+	0.619160i	$0.787473\pi$
$468$	−6.26160	−0.289443
$469$	0	0
$470$	12.0446	0.555577
$471$	−0.179767	−0.00828324
$472$	−14.3819	−0.661980
$473$	14.7234	0.676984
$474$	0.0870541	0.00399853
$475$	−12.8786	−0.590910
$476$	0	0
$477$	18.8138	0.861424
$478$	−8.41493	−0.384890
$479$	4.31877	0.197329	0.0986647	−	0.995121i	$-0.468543\pi$
$479$	4.31877	0.197329	0.0986647	+	0.995121i	$0.468543\pi$
$480$	0.101223	0.00462019
$481$	−19.7501	−0.900527
$482$	−3.36585	−0.153310
$483$	0	0
$484$	−1.56542	−0.0711556
$485$	43.7259	1.98549
$486$	−1.04623	−0.0474579
$487$	9.08302	0.411591	0.205795	−	0.978595i	$-0.434022\pi$
$487$	9.08302	0.411591	0.205795	+	0.978595i	$0.434022\pi$
$488$	−3.84288	−0.173959
$489$	−0.120779	−0.00546181
$490$	0	0
$491$	−34.4075	−1.55279	−0.776393	−	0.630249i	$-0.782953\pi$
$491$	−34.4075	−1.55279	−0.776393	+	0.630249i	$0.782953\pi$
$492$	−0.0387751	−0.00174812
$493$	1.76287	0.0793958
$494$	−14.8189	−0.666732
$495$	24.0432	1.08066
$496$	−0.644105	−0.0289212
$497$	0	0
$498$	0.302671	0.0135630
$499$	13.8869	0.621665	0.310833	−	0.950465i	$-0.399392\pi$
$499$	13.8869	0.621665	0.310833	+	0.950465i	$0.399392\pi$
$500$	8.31496	0.371856
$501$	−0.184986	−0.00826455
$502$	−2.97894	−0.132956
$503$	16.1893	0.721847	0.360923	−	0.932595i	$-0.382462\pi$
$503$	16.1893	0.721847	0.360923	+	0.932595i	$0.382462\pi$
$504$	0	0
$505$	27.3207	1.21575
$506$	16.3168	0.725371
$507$	0.334987	0.0148773
$508$	−8.37867	−0.371743
$509$	−26.6050	−1.17925	−0.589623	−	0.807679i	$-0.700724\pi$
$509$	−26.6050	−1.17925	−0.589623	+	0.807679i	$0.700724\pi$
$510$	0.0770704	0.00341274
$511$	0	0
$512$	1.00000	0.0441942
$513$	−1.65055	−0.0728735
$514$	−6.74010	−0.297293
$515$	−6.45899	−0.284617
$516$	−0.185866	−0.00818231
$517$	−14.1719	−0.623278
$518$	0	0
$519$	0.0837389	0.00367573
$520$	−5.45142	−0.239060
$521$	21.8148	0.955722	0.477861	−	0.878436i	$-0.341412\pi$
$521$	21.8148	0.955722	0.477861	+	0.878436i	$0.341412\pi$
$522$	−6.94252	−0.303866
$523$	31.0649	1.35838	0.679188	−	0.733965i	$-0.262332\pi$
$523$	31.0649	1.35838	0.679188	+	0.733965i	$0.262332\pi$
$524$	12.7513	0.557043
$525$	0	0
$526$	21.7936	0.950247
$527$	−0.490415	−0.0213628
$528$	−0.119101	−0.00518319
$529$	5.21941	0.226931
$530$	16.3795	0.711479
$531$	43.1240	1.87142
$532$	0	0
$533$	2.08825	0.0904520
$534$	−0.230140	−0.00995914
$535$	41.2785	1.78463
$536$	8.37335	0.361674
$537$	0.781964	0.0337443
$538$	−26.2079	−1.12990
$539$	0	0
$540$	−0.607188	−0.0261292
$541$	15.6807	0.674166	0.337083	−	0.941475i	$-0.390560\pi$
$541$	15.6807	0.674166	0.337083	+	0.941475i	$0.390560\pi$
$542$	19.9240	0.855810
$543$	0.291215	0.0124972
$544$	0.761390	0.0326443
$545$	−17.1716	−0.735549
$546$	0	0
$547$	−5.18783	−0.221816	−0.110908	−	0.993831i	$-0.535376\pi$
$547$	−5.18783	−0.221816	−0.110908	+	0.993831i	$0.535376\pi$
$548$	14.7866	0.631651
$549$	11.5229	0.491783
$550$	5.57438	0.237693
$551$	−16.4303	−0.699956
$552$	−0.205981	−0.00876713
$553$	0	0
$554$	20.0693	0.852662
$555$	−0.957344	−0.0406370
$556$	−9.80861	−0.415978
$557$	−20.5638	−0.871318	−0.435659	−	0.900112i	$-0.643485\pi$
$557$	−20.5638	−0.871318	−0.435659	+	0.900112i	$0.643485\pi$
$558$	1.93135	0.0817605
$559$	10.0099	0.423374
$560$	0	0
$561$	−0.0906821	−0.00382860
$562$	22.8047	0.961957
$563$	−30.8588	−1.30054	−0.650271	−	0.759702i	$-0.725345\pi$
$563$	−30.8588	−1.30054	−0.650271	+	0.759702i	$0.725345\pi$
$564$	0.178904	0.00753320
$565$	−8.72486	−0.367058
$566$	20.5397	0.863347
$567$	0	0
$568$	−10.8481	−0.455178
$569$	34.7113	1.45517	0.727587	−	0.686016i	$-0.240642\pi$
$569$	34.7113	1.45517	0.727587	+	0.686016i	$0.240642\pi$
$570$	−0.718312	−0.0300868
$571$	8.47738	0.354767	0.177384	−	0.984142i	$-0.443237\pi$
$571$	8.47738	0.354767	0.177384	+	0.984142i	$0.443237\pi$
$572$	6.41421	0.268192
$573$	−0.164466	−0.00687067
$574$	0	0
$575$	9.64072	0.402046
$576$	−2.99850	−0.124937
$577$	16.7833	0.698697	0.349348	−	0.936993i	$-0.386403\pi$
$577$	16.7833	0.698697	0.349348	+	0.936993i	$0.386403\pi$
$578$	−16.4203	−0.682994
$579$	−0.533954	−0.0221904
$580$	−6.04423	−0.250973
$581$	0	0
$582$	0.649477	0.0269217
$583$	−19.2723	−0.798178
$584$	−3.35938	−0.139012
$585$	16.3461	0.675826
$586$	26.9744	1.11430
$587$	17.1051	0.706003	0.353001	−	0.935623i	$-0.385161\pi$
$587$	17.1051	0.706003	0.353001	+	0.935623i	$0.385161\pi$
$588$	0	0
$589$	4.57077	0.188335
$590$	37.5442	1.54567
$591$	0.104286	0.00428976
$592$	−9.45774	−0.388711
$593$	23.4517	0.963047	0.481523	−	0.876433i	$-0.340084\pi$
$593$	23.4517	0.963047	0.481523	+	0.876433i	$0.340084\pi$
$594$	0.714425	0.0293132
$595$	0	0
$596$	−12.1994	−0.499706
$597$	−0.245978	−0.0100672
$598$	11.0932	0.453634
$599$	−20.3118	−0.829917	−0.414958	−	0.909840i	$-0.636204\pi$
$599$	−20.3118	−0.829917	−0.414958	+	0.909840i	$0.636204\pi$
$600$	−0.0703702	−0.00287285
$601$	21.9226	0.894240	0.447120	−	0.894474i	$-0.352450\pi$
$601$	21.9226	0.894240	0.447120	+	0.894474i	$0.352450\pi$
$602$	0	0
$603$	−25.1075	−1.02246
$604$	−20.5621	−0.836660
$605$	4.08657	0.166143
$606$	0.405805	0.0164847
$607$	0.152226	0.00617865	0.00308932	−	0.999995i	$-0.499017\pi$
$607$	0.152226	0.00617865	0.00308932	+	0.999995i	$0.499017\pi$
$608$	−7.09631	−0.287793
$609$	0	0
$610$	10.0319	0.406180
$611$	−9.63491	−0.389787
$612$	−2.28303	−0.0922858
$613$	16.8306	0.679782	0.339891	−	0.940465i	$-0.389610\pi$
$613$	16.8306	0.679782	0.339891	+	0.940465i	$0.389610\pi$
$614$	−11.9580	−0.482584
$615$	0.101223	0.00408172
$616$	0	0
$617$	41.5730	1.67366	0.836832	−	0.547459i	$-0.184405\pi$
$617$	41.5730	1.67366	0.836832	+	0.547459i	$0.184405\pi$
$618$	−0.0959379	−0.00385919
$619$	1.19822	0.0481604	0.0240802	−	0.999710i	$-0.492334\pi$
$619$	1.19822	0.0481604	0.0240802	+	0.999710i	$0.492334\pi$
$620$	1.68145	0.0675287
$621$	1.23558	0.0495820
$622$	17.8581	0.716043
$623$	0	0
$624$	−0.0809720	−0.00324148
$625$	−30.7805	−1.23122
$626$	−10.1352	−0.405085
$627$	0.845176	0.0337531
$628$	4.63615	0.185003
$629$	−7.20103	−0.287124
$630$	0	0
$631$	16.6115	0.661292	0.330646	−	0.943755i	$-0.392733\pi$
$631$	16.6115	0.661292	0.330646	+	0.943755i	$0.392733\pi$
$632$	−2.24510	−0.0893054
$633$	0.108977	0.00433143
$634$	11.6642	0.463245
$635$	21.8727	0.867992
$636$	0.243291	0.00964711
$637$	0	0
$638$	7.11173	0.281556
$639$	32.5281	1.28679
$640$	−2.61052	−0.103190
$641$	−43.1532	−1.70445	−0.852225	−	0.523176i	$-0.824747\pi$
$641$	−43.1532	−1.70445	−0.852225	+	0.523176i	$0.824747\pi$
$642$	0.613127	0.0241982
$643$	36.4417	1.43712	0.718559	−	0.695466i	$-0.244802\pi$
$643$	36.4417	1.43712	0.718559	+	0.695466i	$0.244802\pi$
$644$	0	0
$645$	0.485208	0.0191051
$646$	−5.40306	−0.212581
$647$	−18.1008	−0.711616	−0.355808	−	0.934559i	$-0.615794\pi$
$647$	−18.1008	−0.711616	−0.355808	+	0.934559i	$0.615794\pi$
$648$	8.98647	0.353022
$649$	−44.1751	−1.73402
$650$	3.78981	0.148649
$651$	0	0
$652$	3.11486	0.121987
$653$	−26.7064	−1.04510	−0.522551	−	0.852608i	$-0.675020\pi$
$653$	−26.7064	−1.04510	−0.522551	+	0.852608i	$0.675020\pi$
$654$	−0.255056	−0.00997348
$655$	−33.2876	−1.30065
$656$	1.00000	0.0390434
$657$	10.0731	0.392988
$658$	0	0
$659$	−49.7015	−1.93609	−0.968047	−	0.250767i	$-0.919317\pi$
$659$	−49.7015	−1.93609	−0.968047	+	0.250767i	$0.919317\pi$
$660$	0.310915	0.0121024
$661$	−12.2909	−0.478061	−0.239030	−	0.971012i	$-0.576830\pi$
$661$	−12.2909	−0.478061	−0.239030	+	0.971012i	$0.576830\pi$
$662$	−12.3608	−0.480418
$663$	−0.0616513	−0.00239434
$664$	−7.80581	−0.302924
$665$	0	0
$666$	28.3590	1.09889
$667$	12.2995	0.476239
$668$	4.77073	0.184585
$669$	0.737336	0.0285070
$670$	−21.8588	−0.844480
$671$	−11.8037	−0.455676
$672$	0	0
$673$	3.11146	0.119938	0.0599689	−	0.998200i	$-0.480900\pi$
$673$	3.11146	0.119938	0.0599689	+	0.998200i	$0.480900\pi$
$674$	27.7851	1.07024
$675$	0.422115	0.0162472
$676$	−8.63922	−0.332278
$677$	−24.4512	−0.939736	−0.469868	−	0.882737i	$-0.655699\pi$
$677$	−24.4512	−0.939736	−0.469868	+	0.882737i	$0.655699\pi$
$678$	−0.129594	−0.00497702
$679$	0	0
$680$	−1.98763	−0.0762220
$681$	0.358093	0.0137222
$682$	−1.97842	−0.0757576
$683$	17.3445	0.663669	0.331834	−	0.943338i	$-0.392333\pi$
$683$	17.3445	0.663669	0.331834	+	0.943338i	$0.392333\pi$
$684$	21.2783	0.813595
$685$	−38.6007	−1.47486
$686$	0	0
$687$	−0.765863	−0.0292195
$688$	4.79344	0.182748
$689$	−13.1025	−0.499166
$690$	0.537718	0.0204706
$691$	43.8282	1.66730	0.833652	−	0.552290i	$-0.186246\pi$
$691$	43.8282	1.66730	0.833652	+	0.552290i	$0.186246\pi$
$692$	−2.15961	−0.0820959
$693$	0	0
$694$	2.25401	0.0855610
$695$	25.6056	0.971276
$696$	−0.0897774	−0.00340300
$697$	0.761390	0.0288397
$698$	17.0144	0.644006
$699$	0.759958	0.0287442
$700$	0	0
$701$	−46.1293	−1.74228	−0.871139	−	0.491036i	$-0.836618\pi$
$701$	−46.1293	−1.74228	−0.871139	+	0.491036i	$0.836618\pi$
$702$	0.485711	0.0183320
$703$	67.1151	2.53129
$704$	3.07158	0.115764
$705$	−0.467032	−0.0175894
$706$	17.9998	0.677431
$707$	0	0
$708$	0.557659	0.0209581
$709$	−44.6646	−1.67741	−0.838707	−	0.544583i	$-0.816688\pi$
$709$	−44.6646	−1.67741	−0.838707	+	0.544583i	$0.816688\pi$
$710$	28.3193	1.06280
$711$	6.73193	0.252467
$712$	5.93525	0.222433
$713$	−3.42161	−0.128140
$714$	0	0
$715$	−16.7444	−0.626207
$716$	−20.1667	−0.753663
$717$	0.326290	0.0121855
$718$	9.57429	0.357309
$719$	12.9542	0.483110	0.241555	−	0.970387i	$-0.422343\pi$
$719$	12.9542	0.483110	0.241555	+	0.970387i	$0.422343\pi$
$720$	7.82764	0.291719
$721$	0	0
$722$	31.3576	1.16701
$723$	0.130511	0.00485376
$724$	−7.51035	−0.279120
$725$	4.20194	0.156056
$726$	0.0606995	0.00225277
$727$	−24.3968	−0.904827	−0.452414	−	0.891808i	$-0.649437\pi$
$727$	−24.3968	−0.904827	−0.452414	+	0.891808i	$0.649437\pi$
$728$	0	0
$729$	−26.9188	−0.996994
$730$	8.76973	0.324582
$731$	3.64968	0.134988
$732$	0.149008	0.00550749
$733$	25.5066	0.942106	0.471053	−	0.882105i	$-0.343874\pi$
$733$	25.5066	0.942106	0.471053	+	0.882105i	$0.343874\pi$
$734$	−13.8966	−0.512932
$735$	0	0
$736$	5.31219	0.195810
$737$	25.7194	0.947386
$738$	−2.99850	−0.110376
$739$	50.7786	1.86792	0.933961	−	0.357376i	$-0.116328\pi$
$739$	50.7786	1.86792	0.933961	+	0.357376i	$0.116328\pi$
$740$	24.6896	0.907609
$741$	0.574603	0.0211086
$742$	0	0
$743$	7.81231	0.286606	0.143303	−	0.989679i	$-0.454228\pi$
$743$	7.81231	0.286606	0.143303	+	0.989679i	$0.454228\pi$
$744$	0.0249753	0.000915638 0
$745$	31.8468	1.16677
$746$	−30.4692	−1.11556
$747$	23.4057	0.856370
$748$	2.33867	0.0855101
$749$	0	0
$750$	−0.322414	−0.0117729
$751$	27.5822	1.00649	0.503245	−	0.864144i	$-0.332139\pi$
$751$	27.5822	1.00649	0.503245	+	0.864144i	$0.332139\pi$
$752$	−4.61388	−0.168251
$753$	0.115509	0.00420937
$754$	4.83499	0.176080
$755$	53.6778	1.95354
$756$	0	0
$757$	−39.6468	−1.44099	−0.720493	−	0.693462i	$-0.756085\pi$
$757$	−39.6468	−1.44099	−0.720493	+	0.693462i	$0.756085\pi$
$758$	12.9617	0.470791
$759$	−0.632686	−0.0229651
$760$	18.5251	0.671975
$761$	32.1470	1.16533	0.582665	−	0.812713i	$-0.302010\pi$
$761$	32.1470	1.16533	0.582665	+	0.812713i	$0.302010\pi$
$762$	0.324884	0.0117693
$763$	0	0
$764$	4.24153	0.153453
$765$	5.95989	0.215480
$766$	14.7064	0.531362
$767$	−30.0329	−1.08443
$768$	−0.0387751	−0.00139918
$769$	−23.9039	−0.861998	−0.430999	−	0.902353i	$-0.641839\pi$
$769$	−23.9039	−0.861998	−0.430999	+	0.902353i	$0.641839\pi$
$770$	0	0
$771$	0.261348	0.00941222
$772$	13.7705	0.495612
$773$	−8.23647	−0.296245	−0.148123	−	0.988969i	$-0.547323\pi$
$773$	−8.23647	−0.296245	−0.148123	+	0.988969i	$0.547323\pi$
$774$	−14.3731	−0.516631
$775$	−1.16894	−0.0419896
$776$	−16.7498	−0.601284
$777$	0	0
$778$	−27.1877	−0.974726
$779$	−7.09631	−0.254252
$780$	0.211379	0.00756860
$781$	−33.3209	−1.19231
$782$	4.04465	0.144636
$783$	0.538529	0.0192455
$784$	0	0
$785$	−12.1028	−0.431967
$786$	−0.494433	−0.0176359
$787$	21.2691	0.758163	0.379082	−	0.925363i	$-0.376240\pi$
$787$	21.2691	0.758163	0.379082	+	0.925363i	$0.376240\pi$
$788$	−2.68951	−0.0958100
$789$	−0.845050	−0.0300846
$790$	5.86089	0.208521
$791$	0	0
$792$	−9.21011	−0.327267
$793$	−8.02488	−0.284972
$794$	35.1116	1.24606
$795$	−0.635116	−0.0225253
$796$	6.34370	0.224847
$797$	−19.7091	−0.698133	−0.349067	−	0.937098i	$-0.613501\pi$
$797$	−19.7091	−0.698133	−0.349067	+	0.937098i	$0.613501\pi$
$798$	0	0
$799$	−3.51296	−0.124280
$800$	1.81483	0.0641639
$801$	−17.7968	−0.628820
$802$	−13.7763	−0.486460
$803$	−10.3186	−0.364135
$804$	−0.324678	−0.0114505
$805$	0	0
$806$	−1.34505	−0.0473774
$807$	1.01622	0.0357725
$808$	−10.4656	−0.368178
$809$	−20.9287	−0.735813	−0.367907	−	0.929863i	$-0.619925\pi$
$809$	−20.9287	−0.735813	−0.367907	+	0.929863i	$0.619925\pi$
$810$	−23.4594	−0.824279
$811$	6.04921	0.212417	0.106208	−	0.994344i	$-0.466129\pi$
$811$	6.04921	0.212417	0.106208	+	0.994344i	$0.466129\pi$
$812$	0	0
$813$	−0.772557	−0.0270947
$814$	−29.0502	−1.01821
$815$	−8.13140	−0.284831
$816$	−0.0295230	−0.00103351
$817$	−34.0158	−1.19006
$818$	−27.4007	−0.958041
$819$	0	0
$820$	−2.61052	−0.0911634
$821$	9.72428	0.339380	0.169690	−	0.985498i	$-0.445723\pi$
$821$	9.72428	0.339380	0.169690	+	0.985498i	$0.445723\pi$
$822$	−0.573351	−0.0199979
$823$	−13.8729	−0.483578	−0.241789	−	0.970329i	$-0.577734\pi$
$823$	−13.8729	−0.483578	−0.241789	+	0.970329i	$0.577734\pi$
$824$	2.47421	0.0861933
$825$	−0.216147	−0.00752529
$826$	0	0
$827$	−28.1407	−0.978547	−0.489273	−	0.872130i	$-0.662738\pi$
$827$	−28.1407	−0.978547	−0.489273	+	0.872130i	$0.662738\pi$
$828$	−15.9286	−0.553557
$829$	23.1463	0.803904	0.401952	−	0.915661i	$-0.368332\pi$
$829$	23.1463	0.803904	0.401952	+	0.915661i	$0.368332\pi$
$830$	20.3772	0.707304
$831$	−0.778189	−0.0269951
$832$	2.08825	0.0723970
$833$	0	0
$834$	0.380330	0.0131698
$835$	−12.4541	−0.430992
$836$	−21.7969	−0.753860
$837$	−0.149814	−0.00517833
$838$	29.5386	1.02039
$839$	24.5774	0.848508	0.424254	−	0.905543i	$-0.360536\pi$
$839$	24.5774	0.848508	0.424254	+	0.905543i	$0.360536\pi$
$840$	0	0
$841$	−23.6392	−0.815146
$842$	5.26049	0.181288
$843$	−0.884254	−0.0304553
$844$	−2.81048	−0.0967407
$845$	22.5529	0.775843
$846$	13.8347	0.475646
$847$	0	0
$848$	−6.27441	−0.215464
$849$	−0.796429	−0.0273334
$850$	1.38179	0.0473951
$851$	−50.2414	−1.72225
$852$	0.420638	0.0144108
$853$	49.7805	1.70445	0.852225	−	0.523175i	$-0.175253\pi$
$853$	49.7805	1.70445	0.852225	+	0.523175i	$0.175253\pi$
$854$	0	0
$855$	−55.5474	−1.89968
$856$	−15.8124	−0.540456
$857$	−27.5930	−0.942559	−0.471280	−	0.881984i	$-0.656208\pi$
$857$	−27.5930	−0.942559	−0.471280	+	0.881984i	$0.656208\pi$
$858$	−0.248712	−0.00849088
$859$	26.1523	0.892306	0.446153	−	0.894957i	$-0.352794\pi$
$859$	26.1523	0.892306	0.446153	+	0.894957i	$0.352794\pi$
$860$	−12.5134	−0.426703
$861$	0	0
$862$	−34.4649	−1.17388
$863$	38.4067	1.30738	0.653689	−	0.756763i	$-0.273220\pi$
$863$	38.4067	1.30738	0.653689	+	0.756763i	$0.273220\pi$
$864$	0.232592	0.00791295
$865$	5.63770	0.191687
$866$	8.66488	0.294445
$867$	0.636699	0.0216234
$868$	0	0
$869$	−6.89600	−0.233931
$870$	0.234366	0.00794575
$871$	17.4856	0.592478
$872$	6.57783	0.222753
$873$	50.2244	1.69984
$874$	−37.6970	−1.27512
$875$	0	0
$876$	0.130260	0.00440109
$877$	−5.62482	−0.189937	−0.0949683	−	0.995480i	$-0.530275\pi$
$877$	−5.62482	−0.189937	−0.0949683	+	0.995480i	$0.530275\pi$
$878$	−7.77642	−0.262441
$879$	−1.04594	−0.0352785
$880$	−8.01842	−0.270301
$881$	−49.5452	−1.66922	−0.834610	−	0.550841i	$-0.814307\pi$
$881$	−49.5452	−1.66922	−0.834610	+	0.550841i	$0.814307\pi$
$882$	0	0
$883$	−12.0172	−0.404409	−0.202205	−	0.979343i	$-0.564811\pi$
$883$	−12.0172	−0.404409	−0.202205	+	0.979343i	$0.564811\pi$
$884$	1.58997	0.0534765
$885$	−1.45578	−0.0489356
$886$	−10.7928	−0.362592
$887$	−44.5177	−1.49476	−0.747379	−	0.664398i	$-0.768688\pi$
$887$	−44.5177	−1.49476	−0.747379	+	0.664398i	$0.768688\pi$
$888$	0.366725	0.0123065
$889$	0	0
$890$	−15.4941	−0.519364
$891$	27.6026	0.924723
$892$	−19.0157	−0.636692
$893$	32.7415	1.09565
$894$	0.473032	0.0158206
$895$	52.6455	1.75975
$896$	0	0
$897$	−0.430139	−0.0143619
$898$	−17.4966	−0.583870
$899$	−1.49132	−0.0497383
$900$	−5.44176	−0.181392
$901$	−4.77727	−0.159154
$902$	3.07158	0.102272
$903$	0	0
$904$	3.34219	0.111160
$905$	19.6059	0.651723
$906$	0.797298	0.0264885
$907$	12.3361	0.409612	0.204806	−	0.978803i	$-0.434344\pi$
$907$	12.3361	0.409612	0.204806	+	0.978803i	$0.434344\pi$
$908$	−9.23513	−0.306478
$909$	31.3810	1.04084
$910$	0	0
$911$	57.3470	1.89999	0.949996	−	0.312262i	$-0.101087\pi$
$911$	57.3470	1.89999	0.949996	+	0.312262i	$0.101087\pi$
$912$	0.275160	0.00911147
$913$	−23.9761	−0.793494
$914$	2.68726	0.0888867
$915$	−0.388989	−0.0128596
$916$	19.7514	0.652605
$917$	0	0
$918$	0.177094	0.00584496
$919$	51.2205	1.68961	0.844804	−	0.535075i	$-0.179717\pi$
$919$	51.2205	1.68961	0.844804	+	0.535075i	$0.179717\pi$
$920$	−13.8676	−0.457201
$921$	0.463671	0.0152785
$922$	8.15008	0.268409
$923$	−22.6536	−0.745652
$924$	0	0
$925$	−17.1642	−0.564355
$926$	11.1325	0.365837
$927$	−7.41892	−0.243669
$928$	2.31533	0.0760046
$929$	−21.9800	−0.721140	−0.360570	−	0.932732i	$-0.617418\pi$
$929$	−21.9800	−0.721140	−0.360570	+	0.932732i	$0.617418\pi$
$930$	−0.0651985	−0.00213794
$931$	0	0
$932$	−19.5991	−0.641990
$933$	−0.692449	−0.0226698
$934$	−33.9394	−1.11053
$935$	−6.10514	−0.199660
$936$	−6.26160	−0.204667
$937$	−34.1101	−1.11433	−0.557164	−	0.830403i	$-0.688110\pi$
$937$	−34.1101	−1.11433	−0.557164	+	0.830403i	$0.688110\pi$
$938$	0	0
$939$	0.392994	0.0128249
$940$	12.0446	0.392852
$941$	−37.0147	−1.20665	−0.603323	−	0.797497i	$-0.706157\pi$
$941$	−37.0147	−1.20665	−0.603323	+	0.797497i	$0.706157\pi$
$942$	−0.179767	−0.00585713
$943$	5.31219	0.172989
$944$	−14.3819	−0.468091
$945$	0	0
$946$	14.7234	0.478700
$947$	11.6847	0.379703	0.189851	−	0.981813i	$-0.439199\pi$
$947$	11.6847	0.379703	0.189851	+	0.981813i	$0.439199\pi$
$948$	0.0870541	0.00282739
$949$	−7.01521	−0.227723
$950$	−12.8786	−0.417837
$951$	−0.452281	−0.0146662
$952$	0	0
$953$	−41.1180	−1.33194	−0.665971	−	0.745978i	$-0.731982\pi$
$953$	−41.1180	−1.33194	−0.665971	+	0.745978i	$0.731982\pi$
$954$	18.8138	0.609119
$955$	−11.0726	−0.358302
$956$	−8.41493	−0.272158
$957$	−0.275758	−0.00891399
$958$	4.31877	0.139533
$959$	0	0
$960$	0.101223	0.00326697
$961$	−30.5851	−0.986617
$962$	−19.7501	−0.636769
$963$	47.4133	1.52787
$964$	−3.36585	−0.108407
$965$	−35.9483	−1.15722
$966$	0	0
$967$	22.6510	0.728407	0.364203	−	0.931319i	$-0.381341\pi$
$967$	22.6510	0.728407	0.364203	+	0.931319i	$0.381341\pi$
$968$	−1.56542	−0.0503146
$969$	0.209504	0.00673025
$970$	43.7259	1.40395
$971$	−5.04506	−0.161904	−0.0809518	−	0.996718i	$-0.525796\pi$
$971$	−5.04506	−0.161904	−0.0809518	+	0.996718i	$0.525796\pi$
$972$	−1.04623	−0.0335578
$973$	0	0
$974$	9.08302	0.291039
$975$	−0.146950	−0.00470618
$976$	−3.84288	−0.123008
$977$	11.8207	0.378178	0.189089	−	0.981960i	$-0.439447\pi$
$977$	11.8207	0.378178	0.189089	+	0.981960i	$0.439447\pi$
$978$	−0.120779	−0.00386208
$979$	18.2306	0.582652
$980$	0	0
$981$	−19.7236	−0.629726
$982$	−34.4075	−1.09799
$983$	−44.6385	−1.42375	−0.711873	−	0.702308i	$-0.752153\pi$
$983$	−44.6385	−1.42375	−0.711873	+	0.702308i	$0.752153\pi$
$984$	−0.0387751	−0.00123611
$985$	7.02104	0.223709
$986$	1.76287	0.0561413
$987$	0	0
$988$	−14.8189	−0.471451
$989$	25.4637	0.809699
$990$	24.0432	0.764143
$991$	37.0298	1.17629	0.588146	−	0.808755i	$-0.299858\pi$
$991$	37.0298	1.17629	0.588146	+	0.808755i	$0.299858\pi$
$992$	−0.644105	−0.0204504
$993$	0.479293	0.0152099
$994$	0	0
$995$	−16.5604	−0.524999
$996$	0.302671	0.00959050
$997$	46.9480	1.48686	0.743429	−	0.668815i	$-0.233198\pi$
$997$	46.9480	1.48686	0.743429	+	0.668815i	$0.233198\pi$
$998$	13.8869	0.439584
$999$	−2.19980	−0.0695986

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bp.1.4	✓	6
7.6	odd	2		4018.2.a.bq.1.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.bp.1.4	✓	6	1.1	even	1	trivial
4018.2.a.bq.1.3	yes	6	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.0387751 q^{3} +1.00000 q^{4} -2.61052 q^{5} -0.0387751 q^{6} +1.00000 q^{8} -2.99850 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.0387751 q^{3} +1.00000 q^{4} -2.61052 q^{5} -0.0387751 q^{6} +1.00000 q^{8} -2.99850 q^{9} -2.61052 q^{10} +3.07158 q^{11} -0.0387751 q^{12} +2.08825 q^{13} +0.101223 q^{15} +1.00000 q^{16} +0.761390 q^{17} -2.99850 q^{18} -7.09631 q^{19} -2.61052 q^{20} +3.07158 q^{22} +5.31219 q^{23} -0.0387751 q^{24} +1.81483 q^{25} +2.08825 q^{26} +0.232592 q^{27} +2.31533 q^{29} +0.101223 q^{30} -0.644105 q^{31} +1.00000 q^{32} -0.119101 q^{33} +0.761390 q^{34} -2.99850 q^{36} -9.45774 q^{37} -7.09631 q^{38} -0.0809720 q^{39} -2.61052 q^{40} +1.00000 q^{41} +4.79344 q^{43} +3.07158 q^{44} +7.82764 q^{45} +5.31219 q^{46} -4.61388 q^{47} -0.0387751 q^{48} +1.81483 q^{50} -0.0295230 q^{51} +2.08825 q^{52} -6.27441 q^{53} +0.232592 q^{54} -8.01842 q^{55} +0.275160 q^{57} +2.31533 q^{58} -14.3819 q^{59} +0.101223 q^{60} -3.84288 q^{61} -0.644105 q^{62} +1.00000 q^{64} -5.45142 q^{65} -0.119101 q^{66} +8.37335 q^{67} +0.761390 q^{68} -0.205981 q^{69} -10.8481 q^{71} -2.99850 q^{72} -3.35938 q^{73} -9.45774 q^{74} -0.0703702 q^{75} -7.09631 q^{76} -0.0809720 q^{78} -2.24510 q^{79} -2.61052 q^{80} +8.98647 q^{81} +1.00000 q^{82} -7.80581 q^{83} -1.98763 q^{85} +4.79344 q^{86} -0.0897774 q^{87} +3.07158 q^{88} +5.93525 q^{89} +7.82764 q^{90} +5.31219 q^{92} +0.0249753 q^{93} -4.61388 q^{94} +18.5251 q^{95} -0.0387751 q^{96} -16.7498 q^{97} -9.21011 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 4 q^{3} + 6 q^{4} - 12 q^{5} - 4 q^{6} + 6 q^{8} + 18 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 4 * q^3 + 6 * q^4 - 12 * q^5 - 4 * q^6 + 6 * q^8 + 18 * q^9	\( 6 q + 6 q^{2} - 4 q^{3} + 6 q^{4} - 12 q^{5} - 4 q^{6} + 6 q^{8} + 18 q^{9} - 12 q^{10} - 4 q^{12} - 8 q^{13} - 4 q^{15} + 6 q^{16} - 16 q^{17} + 18 q^{18} - 12 q^{19} - 12 q^{20} + 12 q^{23} - 4 q^{24} + 14 q^{25} - 8 q^{26} - 28 q^{27} - 4 q^{30} + 4 q^{31} + 6 q^{32} + 20 q^{33} - 16 q^{34} + 18 q^{36} - 24 q^{37} - 12 q^{38} + 4 q^{39} - 12 q^{40} + 6 q^{41} + 4 q^{43} - 28 q^{45} + 12 q^{46} + 16 q^{47} - 4 q^{48} + 14 q^{50} - 16 q^{51} - 8 q^{52} - 16 q^{53} - 28 q^{54} + 12 q^{55} - 28 q^{57} - 16 q^{59} - 4 q^{60} - 32 q^{61} + 4 q^{62} + 6 q^{64} - 4 q^{65} + 20 q^{66} - 20 q^{67} - 16 q^{68} - 56 q^{69} + 12 q^{71} + 18 q^{72} - 16 q^{73} - 24 q^{74} + 4 q^{75} - 12 q^{76} + 4 q^{78} - 12 q^{80} + 42 q^{81} + 6 q^{82} - 32 q^{83} + 48 q^{85} + 4 q^{86} - 20 q^{87} - 8 q^{89} - 28 q^{90} + 12 q^{92} - 12 q^{93} + 16 q^{94} + 28 q^{95} - 4 q^{96} - 8 q^{97} - 76 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 4 * q^3 + 6 * q^4 - 12 * q^5 - 4 * q^6 + 6 * q^8 + 18 * q^9 - 12 * q^10 - 4 * q^12 - 8 * q^13 - 4 * q^15 + 6 * q^16 - 16 * q^17 + 18 * q^18 - 12 * q^19 - 12 * q^20 + 12 * q^23 - 4 * q^24 + 14 * q^25 - 8 * q^26 - 28 * q^27 - 4 * q^30 + 4 * q^31 + 6 * q^32 + 20 * q^33 - 16 * q^34 + 18 * q^36 - 24 * q^37 - 12 * q^38 + 4 * q^39 - 12 * q^40 + 6 * q^41 + 4 * q^43 - 28 * q^45 + 12 * q^46 + 16 * q^47 - 4 * q^48 + 14 * q^50 - 16 * q^51 - 8 * q^52 - 16 * q^53 - 28 * q^54 + 12 * q^55 - 28 * q^57 - 16 * q^59 - 4 * q^60 - 32 * q^61 + 4 * q^62 + 6 * q^64 - 4 * q^65 + 20 * q^66 - 20 * q^67 - 16 * q^68 - 56 * q^69 + 12 * q^71 + 18 * q^72 - 16 * q^73 - 24 * q^74 + 4 * q^75 - 12 * q^76 + 4 * q^78 - 12 * q^80 + 42 * q^81 + 6 * q^82 - 32 * q^83 + 48 * q^85 + 4 * q^86 - 20 * q^87 - 8 * q^89 - 28 * q^90 + 12 * q^92 - 12 * q^93 + 16 * q^94 + 28 * q^95 - 4 * q^96 - 8 * q^97 - 76 * q^99

Introduction

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