LMFDB - Embedded newform 4018.2.a.bp.1.5

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			1.5
Root			$1.60043$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.82475 q^{3} +1.00000 q^{4} -2.37517 q^{5} +1.82475 q^{6} +1.00000 q^{8} +0.329701 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.82475 q^{3} +1.00000 q^{4} -2.37517 q^{5} +1.82475 q^{6} +1.00000 q^{8} +0.329701 q^{9} -2.37517 q^{10} +6.06466 q^{11} +1.82475 q^{12} -5.90283 q^{13} -4.33408 q^{15} +1.00000 q^{16} -6.48537 q^{17} +0.329701 q^{18} -7.02562 q^{19} -2.37517 q^{20} +6.06466 q^{22} -3.36901 q^{23} +1.82475 q^{24} +0.641431 q^{25} -5.90283 q^{26} -4.87262 q^{27} -1.41508 q^{29} -4.33408 q^{30} +6.55661 q^{31} +1.00000 q^{32} +11.0665 q^{33} -6.48537 q^{34} +0.329701 q^{36} -4.18392 q^{37} -7.02562 q^{38} -10.7712 q^{39} -2.37517 q^{40} +1.00000 q^{41} -5.12628 q^{43} +6.06466 q^{44} -0.783096 q^{45} -3.36901 q^{46} +7.43159 q^{47} +1.82475 q^{48} +0.641431 q^{50} -11.8342 q^{51} -5.90283 q^{52} -1.96329 q^{53} -4.87262 q^{54} -14.4046 q^{55} -12.8200 q^{57} -1.41508 q^{58} +12.5144 q^{59} -4.33408 q^{60} -8.10796 q^{61} +6.55661 q^{62} +1.00000 q^{64} +14.0202 q^{65} +11.0665 q^{66} -8.19289 q^{67} -6.48537 q^{68} -6.14759 q^{69} +7.71790 q^{71} +0.329701 q^{72} +1.99480 q^{73} -4.18392 q^{74} +1.17045 q^{75} -7.02562 q^{76} -10.7712 q^{78} -2.63255 q^{79} -2.37517 q^{80} -9.88040 q^{81} +1.00000 q^{82} -16.8153 q^{83} +15.4039 q^{85} -5.12628 q^{86} -2.58216 q^{87} +6.06466 q^{88} -5.10925 q^{89} -0.783096 q^{90} -3.36901 q^{92} +11.9642 q^{93} +7.43159 q^{94} +16.6870 q^{95} +1.82475 q^{96} -13.1768 q^{97} +1.99952 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.82475	1.05352	0.526759	−	0.850015i	$-0.323407\pi$
$3$	1.82475	1.05352	0.526759	+	0.850015i	$0.323407\pi$
$4$	1.00000	0.500000
$5$	−2.37517	−1.06221	−0.531104	−	0.847307i	$-0.678223\pi$
$5$	−2.37517	−1.06221	−0.531104	+	0.847307i	$0.678223\pi$
$6$	1.82475	0.744950
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	0.329701	0.109900
$10$	−2.37517	−0.751095
$11$	6.06466	1.82856	0.914282	−	0.405079i	$-0.132756\pi$
$11$	6.06466	1.82856	0.914282	+	0.405079i	$0.132756\pi$
$12$	1.82475	0.526759
$13$	−5.90283	−1.63715	−0.818576	−	0.574398i	$-0.805236\pi$
$13$	−5.90283	−1.63715	−0.818576	+	0.574398i	$0.805236\pi$
$14$	0	0
$15$	−4.33408	−1.11906
$16$	1.00000	0.250000
$17$	−6.48537	−1.57293	−0.786467	−	0.617633i	$-0.788092\pi$
$17$	−6.48537	−1.57293	−0.786467	+	0.617633i	$0.788092\pi$
$18$	0.329701	0.0777113
$19$	−7.02562	−1.61179	−0.805893	−	0.592061i	$-0.798315\pi$
$19$	−7.02562	−1.61179	−0.805893	+	0.592061i	$0.798315\pi$
$20$	−2.37517	−0.531104
$21$	0	0
$22$	6.06466	1.29299
$23$	−3.36901	−0.702488	−0.351244	−	0.936284i	$-0.614241\pi$
$23$	−3.36901	−0.702488	−0.351244	+	0.936284i	$0.614241\pi$
$24$	1.82475	0.372475
$25$	0.641431	0.128286
$26$	−5.90283	−1.15764
$27$	−4.87262	−0.937736
$28$	0	0
$29$	−1.41508	−0.262773	−0.131387	−	0.991331i	$-0.541943\pi$
$29$	−1.41508	−0.262773	−0.131387	+	0.991331i	$0.541943\pi$
$30$	−4.33408	−0.791292
$31$	6.55661	1.17760	0.588801	−	0.808278i	$-0.299600\pi$
$31$	6.55661	1.17760	0.588801	+	0.808278i	$0.299600\pi$
$32$	1.00000	0.176777
$33$	11.0665	1.92642
$34$	−6.48537	−1.11223
$35$	0	0
$36$	0.329701	0.0549502
$37$	−4.18392	−0.687832	−0.343916	−	0.939000i	$-0.611754\pi$
$37$	−4.18392	−0.687832	−0.343916	+	0.939000i	$0.611754\pi$
$38$	−7.02562	−1.13971
$39$	−10.7712	−1.72477
$40$	−2.37517	−0.375547
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−5.12628	−0.781751	−0.390876	−	0.920444i	$-0.627828\pi$
$43$	−5.12628	−0.781751	−0.390876	+	0.920444i	$0.627828\pi$
$44$	6.06466	0.914282
$45$	−0.783096	−0.116737
$46$	−3.36901	−0.496734
$47$	7.43159	1.08401	0.542004	−	0.840376i	$-0.317666\pi$
$47$	7.43159	1.08401	0.542004	+	0.840376i	$0.317666\pi$
$48$	1.82475	0.263380
$49$	0	0
$50$	0.641431	0.0907120
$51$	−11.8342	−1.65711
$52$	−5.90283	−0.818576
$53$	−1.96329	−0.269679	−0.134839	−	0.990867i	$-0.543052\pi$
$53$	−1.96329	−0.269679	−0.134839	+	0.990867i	$0.543052\pi$
$54$	−4.87262	−0.663080
$55$	−14.4046	−1.94232
$56$	0	0
$57$	−12.8200	−1.69805
$58$	−1.41508	−0.185809
$59$	12.5144	1.62924	0.814620	−	0.579995i	$-0.196945\pi$
$59$	12.5144	1.62924	0.814620	+	0.579995i	$0.196945\pi$
$60$	−4.33408	−0.559528
$61$	−8.10796	−1.03812	−0.519059	−	0.854739i	$-0.673717\pi$
$61$	−8.10796	−1.03812	−0.519059	+	0.854739i	$0.673717\pi$
$62$	6.55661	0.832691
$63$	0	0
$64$	1.00000	0.125000
$65$	14.0202	1.73900
$66$	11.0665	1.36219
$67$	−8.19289	−1.00092	−0.500460	−	0.865760i	$-0.666836\pi$
$67$	−8.19289	−1.00092	−0.500460	+	0.865760i	$0.666836\pi$
$68$	−6.48537	−0.786467
$69$	−6.14759	−0.740083
$70$	0	0
$71$	7.71790	0.915947	0.457973	−	0.888966i	$-0.348575\pi$
$71$	7.71790	0.915947	0.457973	+	0.888966i	$0.348575\pi$
$72$	0.329701	0.0388556
$73$	1.99480	0.233473	0.116737	−	0.993163i	$-0.462757\pi$
$73$	1.99480	0.233473	0.116737	+	0.993163i	$0.462757\pi$
$74$	−4.18392	−0.486371
$75$	1.17045	0.135152
$76$	−7.02562	−0.805893
$77$	0	0
$78$	−10.7712	−1.21960
$79$	−2.63255	−0.296185	−0.148092	−	0.988974i	$-0.547313\pi$
$79$	−2.63255	−0.296185	−0.148092	+	0.988974i	$0.547313\pi$
$80$	−2.37517	−0.265552
$81$	−9.88040	−1.09782
$82$	1.00000	0.110432
$83$	−16.8153	−1.84572	−0.922859	−	0.385138i	$-0.874154\pi$
$83$	−16.8153	−1.84572	−0.922859	+	0.385138i	$0.874154\pi$
$84$	0	0
$85$	15.4039	1.67078
$86$	−5.12628	−0.552781
$87$	−2.58216	−0.276836
$88$	6.06466	0.646495
$89$	−5.10925	−0.541579	−0.270790	−	0.962639i	$-0.587285\pi$
$89$	−5.10925	−0.541579	−0.270790	+	0.962639i	$0.587285\pi$
$90$	−0.783096	−0.0825456
$91$	0	0
$92$	−3.36901	−0.351244
$93$	11.9642	1.24063
$94$	7.43159	0.766510
$95$	16.6870	1.71205
$96$	1.82475	0.186237
$97$	−13.1768	−1.33790	−0.668949	−	0.743308i	$-0.733256\pi$
$97$	−13.1768	−1.33790	−0.668949	+	0.743308i	$0.733256\pi$
$98$	0	0
$99$	1.99952	0.200960
$100$	0.641431	0.0641431
$101$	9.51140	0.946420	0.473210	−	0.880950i	$-0.343095\pi$
$101$	9.51140	0.946420	0.473210	+	0.880950i	$0.343095\pi$
$102$	−11.8342	−1.17176
$103$	10.3113	1.01601	0.508003	−	0.861355i	$-0.330384\pi$
$103$	10.3113	1.01601	0.508003	+	0.861355i	$0.330384\pi$
$104$	−5.90283	−0.578821
$105$	0	0
$106$	−1.96329	−0.190692
$107$	−4.80543	−0.464558	−0.232279	−	0.972649i	$-0.574618\pi$
$107$	−4.80543	−0.464558	−0.232279	+	0.972649i	$0.574618\pi$
$108$	−4.87262	−0.468868
$109$	−7.37499	−0.706396	−0.353198	−	0.935549i	$-0.614906\pi$
$109$	−7.37499	−0.706396	−0.353198	+	0.935549i	$0.614906\pi$
$110$	−14.4046	−1.37342
$111$	−7.63460	−0.724644
$112$	0	0
$113$	8.15055	0.766740	0.383370	−	0.923595i	$-0.374763\pi$
$113$	8.15055	0.766740	0.383370	+	0.923595i	$0.374763\pi$
$114$	−12.8200	−1.20070
$115$	8.00198	0.746188
$116$	−1.41508	−0.131387
$117$	−1.94617	−0.179924
$118$	12.5144	1.15205
$119$	0	0
$120$	−4.33408	−0.395646
$121$	25.7801	2.34365
$122$	−8.10796	−0.734060
$123$	1.82475	0.164532
$124$	6.55661	0.588801
$125$	10.3523	0.925942
$126$	0	0
$127$	18.6064	1.65105	0.825524	−	0.564367i	$-0.190880\pi$
$127$	18.6064	1.65105	0.825524	+	0.564367i	$0.190880\pi$
$128$	1.00000	0.0883883
$129$	−9.35417	−0.823589
$130$	14.0202	1.22966
$131$	−6.56567	−0.573645	−0.286822	−	0.957984i	$-0.592599\pi$
$131$	−6.56567	−0.573645	−0.286822	+	0.957984i	$0.592599\pi$
$132$	11.0665	0.963212
$133$	0	0
$134$	−8.19289	−0.707758
$135$	11.5733	0.996071
$136$	−6.48537	−0.556116
$137$	−7.11465	−0.607846	−0.303923	−	0.952697i	$-0.598297\pi$
$137$	−7.11465	−0.607846	−0.303923	+	0.952697i	$0.598297\pi$
$138$	−6.14759	−0.523318
$139$	14.4235	1.22338	0.611692	−	0.791096i	$-0.290489\pi$
$139$	14.4235	1.22338	0.611692	+	0.791096i	$0.290489\pi$
$140$	0	0
$141$	13.5608	1.14202
$142$	7.71790	0.647672
$143$	−35.7987	−2.99364
$144$	0.329701	0.0274751
$145$	3.36105	0.279120
$146$	1.99480	0.165090
$147$	0	0
$148$	−4.18392	−0.343916
$149$	6.48411	0.531199	0.265600	−	0.964083i	$-0.414430\pi$
$149$	6.48411	0.531199	0.265600	+	0.964083i	$0.414430\pi$
$150$	1.17045	0.0955668
$151$	−1.02792	−0.0836505	−0.0418253	−	0.999125i	$-0.513317\pi$
$151$	−1.02792	−0.0836505	−0.0418253	+	0.999125i	$0.513317\pi$
$152$	−7.02562	−0.569853
$153$	−2.13823	−0.172866
$154$	0	0
$155$	−15.5731	−1.25086
$156$	−10.7712	−0.862384
$157$	−4.56996	−0.364723	−0.182361	−	0.983232i	$-0.558374\pi$
$157$	−4.56996	−0.364723	−0.182361	+	0.983232i	$0.558374\pi$
$158$	−2.63255	−0.209434
$159$	−3.58251	−0.284111
$160$	−2.37517	−0.187774
$161$	0	0
$162$	−9.88040	−0.776278
$163$	−14.9622	−1.17193	−0.585966	−	0.810335i	$-0.699285\pi$
$163$	−14.9622	−1.17193	−0.585966	+	0.810335i	$0.699285\pi$
$164$	1.00000	0.0780869
$165$	−26.2847	−2.04626
$166$	−16.8153	−1.30512
$167$	1.10379	0.0854139	0.0427070	−	0.999088i	$-0.486402\pi$
$167$	1.10379	0.0854139	0.0427070	+	0.999088i	$0.486402\pi$
$168$	0	0
$169$	21.8435	1.68027
$170$	15.4039	1.18142
$171$	−2.31635	−0.177136
$172$	−5.12628	−0.390876
$173$	24.5011	1.86279	0.931393	−	0.364014i	$-0.118594\pi$
$173$	24.5011	1.86279	0.931393	+	0.364014i	$0.118594\pi$
$174$	−2.58216	−0.195753
$175$	0	0
$176$	6.06466	0.457141
$177$	22.8357	1.71643
$178$	−5.10925	−0.382954
$179$	−21.8931	−1.63637	−0.818183	−	0.574957i	$-0.805019\pi$
$179$	−21.8931	−1.63637	−0.818183	+	0.574957i	$0.805019\pi$
$180$	−0.783096	−0.0583685
$181$	12.7553	0.948092	0.474046	−	0.880500i	$-0.342793\pi$
$181$	12.7553	0.948092	0.474046	+	0.880500i	$0.342793\pi$
$182$	0	0
$183$	−14.7950	−1.09368
$184$	−3.36901	−0.248367
$185$	9.93752	0.730621
$186$	11.9642	0.877255
$187$	−39.3316	−2.87621
$188$	7.43159	0.542004
$189$	0	0
$190$	16.6870	1.21060
$191$	−20.9603	−1.51664	−0.758318	−	0.651885i	$-0.773979\pi$
$191$	−20.9603	−1.51664	−0.758318	+	0.651885i	$0.773979\pi$
$192$	1.82475	0.131690
$193$	9.59009	0.690310	0.345155	−	0.938546i	$-0.387826\pi$
$193$	9.59009	0.690310	0.345155	+	0.938546i	$0.387826\pi$
$194$	−13.1768	−0.946037
$195$	25.5834	1.83206
$196$	0	0
$197$	−14.2516	−1.01538	−0.507692	−	0.861539i	$-0.669501\pi$
$197$	−14.2516	−1.01538	−0.507692	+	0.861539i	$0.669501\pi$
$198$	1.99952	0.142100
$199$	−1.83333	−0.129961	−0.0649806	−	0.997887i	$-0.520699\pi$
$199$	−1.83333	−0.129961	−0.0649806	+	0.997887i	$0.520699\pi$
$200$	0.641431	0.0453560
$201$	−14.9499	−1.05449
$202$	9.51140	0.669220
$203$	0	0
$204$	−11.8342	−0.828557
$205$	−2.37517	−0.165889
$206$	10.3113	0.718425
$207$	−1.11077	−0.0772036
$208$	−5.90283	−0.409288
$209$	−42.6080	−2.94725
$210$	0	0
$211$	−12.4784	−0.859046	−0.429523	−	0.903056i	$-0.641318\pi$
$211$	−12.4784	−0.859046	−0.429523	+	0.903056i	$0.641318\pi$
$212$	−1.96329	−0.134839
$213$	14.0832	0.964966
$214$	−4.80543	−0.328492
$215$	12.1758	0.830382
$216$	−4.87262	−0.331540
$217$	0	0
$218$	−7.37499	−0.499498
$219$	3.64000	0.245968
$220$	−14.4046	−0.971158
$221$	38.2821	2.57513
$222$	−7.63460	−0.512401
$223$	−4.56414	−0.305637	−0.152819	−	0.988254i	$-0.548835\pi$
$223$	−4.56414	−0.305637	−0.152819	+	0.988254i	$0.548835\pi$
$224$	0	0
$225$	0.211480	0.0140987
$226$	8.15055	0.542167
$227$	−29.0368	−1.92724	−0.963619	−	0.267278i	$-0.913876\pi$
$227$	−29.0368	−1.92724	−0.963619	+	0.267278i	$0.913876\pi$
$228$	−12.8200	−0.849023
$229$	−8.42642	−0.556834	−0.278417	−	0.960460i	$-0.589810\pi$
$229$	−8.42642	−0.556834	−0.278417	+	0.960460i	$0.589810\pi$
$230$	8.00198	0.527635
$231$	0	0
$232$	−1.41508	−0.0929043
$233$	17.0918	1.11972	0.559861	−	0.828587i	$-0.310855\pi$
$233$	17.0918	1.11972	0.559861	+	0.828587i	$0.310855\pi$
$234$	−1.94617	−0.127225
$235$	−17.6513	−1.15144
$236$	12.5144	0.814620
$237$	−4.80373	−0.312036
$238$	0	0
$239$	−20.7367	−1.34134	−0.670672	−	0.741754i	$-0.733994\pi$
$239$	−20.7367	−1.34134	−0.670672	+	0.741754i	$0.733994\pi$
$240$	−4.33408	−0.279764
$241$	−23.3816	−1.50614	−0.753069	−	0.657941i	$-0.771428\pi$
$241$	−23.3816	−1.50614	−0.753069	+	0.657941i	$0.771428\pi$
$242$	25.7801	1.65721
$243$	−3.41137	−0.218840
$244$	−8.10796	−0.519059
$245$	0	0
$246$	1.82475	0.116342
$247$	41.4710	2.63874
$248$	6.55661	0.416345
$249$	−30.6836	−1.94450
$250$	10.3523	0.654740
$251$	0.876632	0.0553325	0.0276663	−	0.999617i	$-0.491192\pi$
$251$	0.876632	0.0553325	0.0276663	+	0.999617i	$0.491192\pi$
$252$	0	0
$253$	−20.4319	−1.28454
$254$	18.6064	1.16747
$255$	28.1081	1.76020
$256$	1.00000	0.0625000
$257$	−9.35378	−0.583473	−0.291736	−	0.956499i	$-0.594233\pi$
$257$	−9.35378	−0.583473	−0.291736	+	0.956499i	$0.594233\pi$
$258$	−9.35417	−0.582365
$259$	0	0
$260$	14.0202	0.869498
$261$	−0.466552	−0.0288789
$262$	−6.56567	−0.405628
$263$	6.16950	0.380428	0.190214	−	0.981743i	$-0.439082\pi$
$263$	6.16950	0.380428	0.190214	+	0.981743i	$0.439082\pi$
$264$	11.0665	0.681094
$265$	4.66315	0.286455
$266$	0	0
$267$	−9.32308	−0.570563
$268$	−8.19289	−0.500460
$269$	16.4582	1.00348	0.501738	−	0.865020i	$-0.332694\pi$
$269$	16.4582	1.00348	0.501738	+	0.865020i	$0.332694\pi$
$270$	11.5733	0.704329
$271$	21.1564	1.28516	0.642579	−	0.766219i	$-0.277864\pi$
$271$	21.1564	1.28516	0.642579	+	0.766219i	$0.277864\pi$
$272$	−6.48537	−0.393233
$273$	0	0
$274$	−7.11465	−0.429812
$275$	3.89006	0.234580
$276$	−6.14759	−0.370042
$277$	−15.1625	−0.911028	−0.455514	−	0.890229i	$-0.650545\pi$
$277$	−15.1625	−0.911028	−0.455514	+	0.890229i	$0.650545\pi$
$278$	14.4235	0.865063
$279$	2.16172	0.129419
$280$	0	0
$281$	21.7574	1.29794	0.648968	−	0.760816i	$-0.275201\pi$
$281$	21.7574	1.29794	0.648968	+	0.760816i	$0.275201\pi$
$282$	13.5608	0.807532
$283$	1.76994	0.105212	0.0526061	−	0.998615i	$-0.483247\pi$
$283$	1.76994	0.105212	0.0526061	+	0.998615i	$0.483247\pi$
$284$	7.71790	0.457973
$285$	30.4496	1.80368
$286$	−35.7987	−2.11682
$287$	0	0
$288$	0.329701	0.0194278
$289$	25.0600	1.47412
$290$	3.36105	0.197367
$291$	−24.0443	−1.40950
$292$	1.99480	0.116737
$293$	−23.2123	−1.35608	−0.678038	−	0.735027i	$-0.737169\pi$
$293$	−23.2123	−1.35608	−0.678038	+	0.735027i	$0.737169\pi$
$294$	0	0
$295$	−29.7239	−1.73059
$296$	−4.18392	−0.243185
$297$	−29.5508	−1.71471
$298$	6.48411	0.375615
$299$	19.8867	1.15008
$300$	1.17045	0.0675759
$301$	0	0
$302$	−1.02792	−0.0591499
$303$	17.3559	0.997071
$304$	−7.02562	−0.402947
$305$	19.2578	1.10270
$306$	−2.13823	−0.122235
$307$	−19.8087	−1.13054	−0.565271	−	0.824906i	$-0.691228\pi$
$307$	−19.8087	−1.13054	−0.565271	+	0.824906i	$0.691228\pi$
$308$	0	0
$309$	18.8156	1.07038
$310$	−15.5731	−0.884491
$311$	−10.0030	−0.567220	−0.283610	−	0.958940i	$-0.591532\pi$
$311$	−10.0030	−0.567220	−0.283610	+	0.958940i	$0.591532\pi$
$312$	−10.7712	−0.609798
$313$	17.1524	0.969511	0.484755	−	0.874650i	$-0.338909\pi$
$313$	17.1524	0.969511	0.484755	+	0.874650i	$0.338909\pi$
$314$	−4.56996	−0.257898
$315$	0	0
$316$	−2.63255	−0.148092
$317$	−9.37783	−0.526712	−0.263356	−	0.964699i	$-0.584829\pi$
$317$	−9.37783	−0.526712	−0.263356	+	0.964699i	$0.584829\pi$
$318$	−3.58251	−0.200897
$319$	−8.58196	−0.480497
$320$	−2.37517	−0.132776
$321$	−8.76869	−0.489421
$322$	0	0
$323$	45.5637	2.53523
$324$	−9.88040	−0.548911
$325$	−3.78626	−0.210024
$326$	−14.9622	−0.828681
$327$	−13.4575	−0.744201
$328$	1.00000	0.0552158
$329$	0	0
$330$	−26.2847	−1.44693
$331$	9.69805	0.533053	0.266527	−	0.963828i	$-0.414124\pi$
$331$	9.69805	0.533053	0.266527	+	0.963828i	$0.414124\pi$
$332$	−16.8153	−0.922859
$333$	−1.37944	−0.0755930
$334$	1.10379	0.0603968
$335$	19.4595	1.06319
$336$	0	0
$337$	−26.0517	−1.41913	−0.709564	−	0.704641i	$-0.751108\pi$
$337$	−26.0517	−1.41913	−0.709564	+	0.704641i	$0.751108\pi$
$338$	21.8435	1.18813
$339$	14.8727	0.807774
$340$	15.4039	0.835391
$341$	39.7636	2.15332
$342$	−2.31635	−0.125254
$343$	0	0
$344$	−5.12628	−0.276391
$345$	14.6016	0.786123
$346$	24.5011	1.31719
$347$	1.89635	0.101801	0.0509007	−	0.998704i	$-0.483791\pi$
$347$	1.89635	0.101801	0.0509007	+	0.998704i	$0.483791\pi$
$348$	−2.58216	−0.138418
$349$	2.50670	0.134180	0.0670902	−	0.997747i	$-0.478628\pi$
$349$	2.50670	0.134180	0.0670902	+	0.997747i	$0.478628\pi$
$350$	0	0
$351$	28.7623	1.53522
$352$	6.06466	0.323247
$353$	33.7999	1.79899	0.899493	−	0.436935i	$-0.143936\pi$
$353$	33.7999	1.79899	0.899493	+	0.436935i	$0.143936\pi$
$354$	22.8357	1.21370
$355$	−18.3313	−0.972926
$356$	−5.10925	−0.270790
$357$	0	0
$358$	−21.8931	−1.15709
$359$	−33.0058	−1.74198	−0.870990	−	0.491301i	$-0.836521\pi$
$359$	−33.0058	−1.74198	−0.870990	+	0.491301i	$0.836521\pi$
$360$	−0.783096	−0.0412728
$361$	30.3593	1.59786
$362$	12.7553	0.670402
$363$	47.0422	2.46907
$364$	0	0
$365$	−4.73798	−0.247997
$366$	−14.7950	−0.773345
$367$	28.7539	1.50094	0.750470	−	0.660905i	$-0.229827\pi$
$367$	28.7539	1.50094	0.750470	+	0.660905i	$0.229827\pi$
$368$	−3.36901	−0.175622
$369$	0.329701	0.0171635
$370$	9.93752	0.516627
$371$	0	0
$372$	11.9642	0.620313
$373$	31.2359	1.61733	0.808667	−	0.588267i	$-0.200190\pi$
$373$	31.2359	1.61733	0.808667	+	0.588267i	$0.200190\pi$
$374$	−39.3316	−2.03379
$375$	18.8904	0.975496
$376$	7.43159	0.383255
$377$	8.35296	0.430199
$378$	0	0
$379$	7.35186	0.377640	0.188820	−	0.982012i	$-0.439534\pi$
$379$	7.35186	0.377640	0.188820	+	0.982012i	$0.439534\pi$
$380$	16.6870	0.856027
$381$	33.9519	1.73941
$382$	−20.9603	−1.07242
$383$	17.8749	0.913366	0.456683	−	0.889630i	$-0.349037\pi$
$383$	17.8749	0.913366	0.456683	+	0.889630i	$0.349037\pi$
$384$	1.82475	0.0931187
$385$	0	0
$386$	9.59009	0.488123
$387$	−1.69014	−0.0859147
$388$	−13.1768	−0.668949
$389$	30.0836	1.52530	0.762650	−	0.646812i	$-0.223898\pi$
$389$	30.0836	1.52530	0.762650	+	0.646812i	$0.223898\pi$
$390$	25.5834	1.29546
$391$	21.8493	1.10497
$392$	0	0
$393$	−11.9807	−0.604345
$394$	−14.2516	−0.717985
$395$	6.25274	0.314610
$396$	1.99952	0.100480
$397$	−26.5560	−1.33281	−0.666403	−	0.745591i	$-0.732167\pi$
$397$	−26.5560	−1.33281	−0.666403	+	0.745591i	$0.732167\pi$
$398$	−1.83333	−0.0918964
$399$	0	0
$400$	0.641431	0.0320716
$401$	6.75854	0.337506	0.168753	−	0.985658i	$-0.446026\pi$
$401$	6.75854	0.337506	0.168753	+	0.985658i	$0.446026\pi$
$402$	−14.9499	−0.745635
$403$	−38.7026	−1.92791
$404$	9.51140	0.473210
$405$	23.4676	1.16612
$406$	0	0
$407$	−25.3741	−1.25775
$408$	−11.8342	−0.585878
$409$	0.512528	0.0253429	0.0126714	−	0.999920i	$-0.495966\pi$
$409$	0.512528	0.0253429	0.0126714	+	0.999920i	$0.495966\pi$
$410$	−2.37517	−0.117301
$411$	−12.9824	−0.640377
$412$	10.3113	0.508003
$413$	0	0
$414$	−1.11077	−0.0545912
$415$	39.9392	1.96054
$416$	−5.90283	−0.289410
$417$	26.3192	1.28886
$418$	−42.6080	−2.08402
$419$	−17.1393	−0.837309	−0.418655	−	0.908146i	$-0.637498\pi$
$419$	−17.1393	−0.837309	−0.418655	+	0.908146i	$0.637498\pi$
$420$	0	0
$421$	13.9591	0.680326	0.340163	−	0.940366i	$-0.389518\pi$
$421$	13.9591	0.680326	0.340163	+	0.940366i	$0.389518\pi$
$422$	−12.4784	−0.607437
$423$	2.45020	0.119133
$424$	−1.96329	−0.0953458
$425$	−4.15992	−0.201786
$426$	14.0832	0.682334
$427$	0	0
$428$	−4.80543	−0.232279
$429$	−65.3235	−3.15385
$430$	12.1758	0.587169
$431$	−29.3659	−1.41450	−0.707252	−	0.706961i	$-0.750066\pi$
$431$	−29.3659	−1.41450	−0.707252	+	0.706961i	$0.750066\pi$
$432$	−4.87262	−0.234434
$433$	−33.8265	−1.62560	−0.812799	−	0.582544i	$-0.802057\pi$
$433$	−33.8265	−1.62560	−0.812799	+	0.582544i	$0.802057\pi$
$434$	0	0
$435$	6.13306	0.294058
$436$	−7.37499	−0.353198
$437$	23.6694	1.13226
$438$	3.64000	0.173926
$439$	16.6597	0.795126	0.397563	−	0.917575i	$-0.369856\pi$
$439$	16.6597	0.795126	0.397563	+	0.917575i	$0.369856\pi$
$440$	−14.4046	−0.686712
$441$	0	0
$442$	38.2821	1.82089
$443$	−20.6433	−0.980791	−0.490396	−	0.871500i	$-0.663148\pi$
$443$	−20.6433	−0.980791	−0.490396	+	0.871500i	$0.663148\pi$
$444$	−7.63460	−0.362322
$445$	12.1353	0.575270
$446$	−4.56414	−0.216118
$447$	11.8319	0.559628
$448$	0	0
$449$	0.0393032	0.00185483	0.000927416	−	1.00000i	$-0.499705\pi$
$449$	0.0393032	0.00185483	0.000927416		1.00000i	$0.499705\pi$
$450$	0.211480	0.00996929
$451$	6.06466	0.285574
$452$	8.15055	0.383370
$453$	−1.87568	−0.0881274
$454$	−29.0368	−1.36276
$455$	0	0
$456$	−12.8200	−0.600350
$457$	−23.4801	−1.09835	−0.549175	−	0.835707i	$-0.685058\pi$
$457$	−23.4801	−1.09835	−0.549175	+	0.835707i	$0.685058\pi$
$458$	−8.42642	−0.393741
$459$	31.6007	1.47500
$460$	8.00198	0.373094
$461$	13.9215	0.648387	0.324194	−	0.945991i	$-0.394907\pi$
$461$	13.9215	0.648387	0.324194	+	0.945991i	$0.394907\pi$
$462$	0	0
$463$	−6.55024	−0.304415	−0.152208	−	0.988349i	$-0.548638\pi$
$463$	−6.55024	−0.304415	−0.152208	+	0.988349i	$0.548638\pi$
$464$	−1.41508	−0.0656933
$465$	−28.4169	−1.31780
$466$	17.0918	0.791763
$467$	−9.07910	−0.420131	−0.210065	−	0.977687i	$-0.567368\pi$
$467$	−9.07910	−0.420131	−0.210065	+	0.977687i	$0.567368\pi$
$468$	−1.94617	−0.0899618
$469$	0	0
$470$	−17.6513	−0.814193
$471$	−8.33902	−0.384242
$472$	12.5144	0.576023
$473$	−31.0892	−1.42948
$474$	−4.80373	−0.220643
$475$	−4.50645	−0.206770
$476$	0	0
$477$	−0.647299	−0.0296378
$478$	−20.7367	−0.948474
$479$	23.3006	1.06463	0.532316	−	0.846545i	$-0.321322\pi$
$479$	23.3006	1.06463	0.532316	+	0.846545i	$0.321322\pi$
$480$	−4.33408	−0.197823
$481$	24.6970	1.12609
$482$	−23.3816	−1.06500
$483$	0	0
$484$	25.7801	1.17182
$485$	31.2971	1.42113
$486$	−3.41137	−0.154743
$487$	16.3025	0.738735	0.369367	−	0.929283i	$-0.379574\pi$
$487$	16.3025	0.738735	0.369367	+	0.929283i	$0.379574\pi$
$488$	−8.10796	−0.367030
$489$	−27.3023	−1.23465
$490$	0	0
$491$	14.8328	0.669393	0.334697	−	0.942326i	$-0.391366\pi$
$491$	14.8328	0.669393	0.334697	+	0.942326i	$0.391366\pi$
$492$	1.82475	0.0822659
$493$	9.17729	0.413324
$494$	41.4710	1.86587
$495$	−4.74921	−0.213461
$496$	6.55661	0.294401
$497$	0	0
$498$	−30.6836	−1.37497
$499$	28.8431	1.29119	0.645597	−	0.763679i	$-0.276609\pi$
$499$	28.8431	1.29119	0.645597	+	0.763679i	$0.276609\pi$
$500$	10.3523	0.462971
$501$	2.01414	0.0899851
$502$	0.876632	0.0391260
$503$	−3.78730	−0.168867	−0.0844336	−	0.996429i	$-0.526908\pi$
$503$	−3.78730	−0.168867	−0.0844336	+	0.996429i	$0.526908\pi$
$504$	0	0
$505$	−22.5912	−1.00529
$506$	−20.4319	−0.908309
$507$	39.8588	1.77019
$508$	18.6064	0.825524
$509$	−26.6586	−1.18162	−0.590811	−	0.806810i	$-0.701192\pi$
$509$	−26.6586	−1.18162	−0.590811	+	0.806810i	$0.701192\pi$
$510$	28.1081	1.24465
$511$	0	0
$512$	1.00000	0.0441942
$513$	34.2332	1.51143
$514$	−9.35378	−0.412577
$515$	−24.4912	−1.07921
$516$	−9.35417	−0.411794
$517$	45.0701	1.98218
$518$	0	0
$519$	44.7084	1.96248
$520$	14.0202	0.614828
$521$	−14.8418	−0.650233	−0.325117	−	0.945674i	$-0.605404\pi$
$521$	−14.8418	−0.650233	−0.325117	+	0.945674i	$0.605404\pi$
$522$	−0.466552	−0.0204204
$523$	11.5101	0.503300	0.251650	−	0.967818i	$-0.419027\pi$
$523$	11.5101	0.503300	0.251650	+	0.967818i	$0.419027\pi$
$524$	−6.56567	−0.286822
$525$	0	0
$526$	6.16950	0.269003
$527$	−42.5221	−1.85229
$528$	11.0665	0.481606
$529$	−11.6498	−0.506511
$530$	4.66315	0.202554
$531$	4.12602	0.179054
$532$	0	0
$533$	−5.90283	−0.255680
$534$	−9.32308	−0.403449
$535$	11.4137	0.493458
$536$	−8.19289	−0.353879
$537$	−39.9494	−1.72394
$538$	16.4582	0.709565
$539$	0	0
$540$	11.5733	0.498035
$541$	30.8580	1.32669	0.663344	−	0.748314i	$-0.269137\pi$
$541$	30.8580	1.32669	0.663344	+	0.748314i	$0.269137\pi$
$542$	21.1564	0.908744
$543$	23.2751	0.998832
$544$	−6.48537	−0.278058
$545$	17.5169	0.750340
$546$	0	0
$547$	8.86115	0.378876	0.189438	−	0.981893i	$-0.439333\pi$
$547$	8.86115	0.378876	0.189438	+	0.981893i	$0.439333\pi$
$548$	−7.11465	−0.303923
$549$	−2.67320	−0.114089
$550$	3.89006	0.165873
$551$	9.94178	0.423534
$552$	−6.14759	−0.261659
$553$	0	0
$554$	−15.1625	−0.644194
$555$	18.1335	0.769723
$556$	14.4235	0.611692
$557$	−8.56725	−0.363006	−0.181503	−	0.983390i	$-0.558096\pi$
$557$	−8.56725	−0.363006	−0.181503	+	0.983390i	$0.558096\pi$
$558$	2.16172	0.0915130
$559$	30.2596	1.27985
$560$	0	0
$561$	−71.7701	−3.03014
$562$	21.7574	0.917779
$563$	−35.0008	−1.47511	−0.737555	−	0.675287i	$-0.764020\pi$
$563$	−35.0008	−1.47511	−0.737555	+	0.675287i	$0.764020\pi$
$564$	13.5608	0.571011
$565$	−19.3589	−0.814437
$566$	1.76994	0.0743963
$567$	0	0
$568$	7.71790	0.323836
$569$	−15.9884	−0.670267	−0.335133	−	0.942171i	$-0.608781\pi$
$569$	−15.9884	−0.670267	−0.335133	+	0.942171i	$0.608781\pi$
$570$	30.4496	1.27539
$571$	24.3477	1.01892	0.509460	−	0.860494i	$-0.329845\pi$
$571$	24.3477	1.01892	0.509460	+	0.860494i	$0.329845\pi$
$572$	−35.7987	−1.49682
$573$	−38.2473	−1.59780
$574$	0	0
$575$	−2.16099	−0.0901195
$576$	0.329701	0.0137375
$577$	−9.03758	−0.376240	−0.188120	−	0.982146i	$-0.560239\pi$
$577$	−9.03758	−0.376240	−0.188120	+	0.982146i	$0.560239\pi$
$578$	25.0600	1.04236
$579$	17.4995	0.727254
$580$	3.36105	0.139560
$581$	0	0
$582$	−24.0443	−0.996667
$583$	−11.9067	−0.493124
$584$	1.99480	0.0825452
$585$	4.62249	0.191116
$586$	−23.2123	−0.958890
$587$	40.1050	1.65531	0.827654	−	0.561238i	$-0.189675\pi$
$587$	40.1050	1.65531	0.827654	+	0.561238i	$0.189675\pi$
$588$	0	0
$589$	−46.0643	−1.89804
$590$	−29.7239	−1.22371
$591$	−26.0056	−1.06973
$592$	−4.18392	−0.171958
$593$	4.86512	0.199786	0.0998932	−	0.994998i	$-0.468150\pi$
$593$	4.86512	0.199786	0.0998932	+	0.994998i	$0.468150\pi$
$594$	−29.5508	−1.21248
$595$	0	0
$596$	6.48411	0.265600
$597$	−3.34536	−0.136916
$598$	19.8867	0.813229
$599$	11.5065	0.470142	0.235071	−	0.971978i	$-0.424468\pi$
$599$	11.5065	0.470142	0.235071	+	0.971978i	$0.424468\pi$
$600$	1.17045	0.0477834
$601$	−6.46107	−0.263553	−0.131776	−	0.991279i	$-0.542068\pi$
$601$	−6.46107	−0.263553	−0.131776	+	0.991279i	$0.542068\pi$
$602$	0	0
$603$	−2.70120	−0.110001
$604$	−1.02792	−0.0418253
$605$	−61.2321	−2.48944
$606$	17.3559	0.705035
$607$	−44.8317	−1.81966	−0.909831	−	0.414980i	$-0.863789\pi$
$607$	−44.8317	−1.81966	−0.909831	+	0.414980i	$0.863789\pi$
$608$	−7.02562	−0.284926
$609$	0	0
$610$	19.2578	0.779724
$611$	−43.8674	−1.77469
$612$	−2.13823	−0.0864329
$613$	−20.5094	−0.828368	−0.414184	−	0.910193i	$-0.635933\pi$
$613$	−20.5094	−0.828368	−0.414184	+	0.910193i	$0.635933\pi$
$614$	−19.8087	−0.799413
$615$	−4.33408	−0.174767
$616$	0	0
$617$	33.7825	1.36003	0.680015	−	0.733198i	$-0.261973\pi$
$617$	33.7825	1.36003	0.680015	+	0.733198i	$0.261973\pi$
$618$	18.8156	0.756874
$619$	−8.19053	−0.329205	−0.164603	−	0.986360i	$-0.552634\pi$
$619$	−8.19053	−0.329205	−0.164603	+	0.986360i	$0.552634\pi$
$620$	−15.5731	−0.625430
$621$	16.4159	0.658748
$622$	−10.0030	−0.401085
$623$	0	0
$624$	−10.7712	−0.431192
$625$	−27.7957	−1.11183
$626$	17.1524	0.685547
$627$	−77.7488	−3.10499
$628$	−4.56996	−0.182361
$629$	27.1343	1.08191
$630$	0	0
$631$	10.0038	0.398245	0.199123	−	0.979975i	$-0.436191\pi$
$631$	10.0038	0.398245	0.199123	+	0.979975i	$0.436191\pi$
$632$	−2.63255	−0.104717
$633$	−22.7698	−0.905020
$634$	−9.37783	−0.372441
$635$	−44.1933	−1.75376
$636$	−3.58251	−0.142056
$637$	0	0
$638$	−8.58196	−0.339763
$639$	2.54460	0.100663
$640$	−2.37517	−0.0938868
$641$	7.27775	0.287454	0.143727	−	0.989617i	$-0.454091\pi$
$641$	7.27775	0.287454	0.143727	+	0.989617i	$0.454091\pi$
$642$	−8.76869	−0.346073
$643$	−0.874934	−0.0345040	−0.0172520	−	0.999851i	$-0.505492\pi$
$643$	−0.874934	−0.0345040	−0.0172520	+	0.999851i	$0.505492\pi$
$644$	0	0
$645$	22.2177	0.874823
$646$	45.5637	1.79268
$647$	17.1662	0.674875	0.337437	−	0.941348i	$-0.390440\pi$
$647$	17.1662	0.674875	0.337437	+	0.941348i	$0.390440\pi$
$648$	−9.88040	−0.388139
$649$	75.8958	2.97917
$650$	−3.78626	−0.148509
$651$	0	0
$652$	−14.9622	−0.585966
$653$	2.53318	0.0991311	0.0495655	−	0.998771i	$-0.484216\pi$
$653$	2.53318	0.0991311	0.0495655	+	0.998771i	$0.484216\pi$
$654$	−13.4575	−0.526230
$655$	15.5946	0.609330
$656$	1.00000	0.0390434
$657$	0.657686	0.0256588
$658$	0	0
$659$	−17.9243	−0.698230	−0.349115	−	0.937080i	$-0.613518\pi$
$659$	−17.9243	−0.698230	−0.349115	+	0.937080i	$0.613518\pi$
$660$	−26.2847	−1.02313
$661$	11.1385	0.433237	0.216618	−	0.976256i	$-0.430497\pi$
$661$	11.1385	0.433237	0.216618	+	0.976256i	$0.430497\pi$
$662$	9.69805	0.376925
$663$	69.8551	2.71295
$664$	−16.8153	−0.652560
$665$	0	0
$666$	−1.37944	−0.0534523
$667$	4.76741	0.184595
$668$	1.10379	0.0427070
$669$	−8.32839	−0.321994
$670$	19.4595	0.751786
$671$	−49.1720	−1.89826
$672$	0	0
$673$	6.18174	0.238289	0.119144	−	0.992877i	$-0.461985\pi$
$673$	6.18174	0.238289	0.119144	+	0.992877i	$0.461985\pi$
$674$	−26.0517	−1.00347
$675$	−3.12545	−0.120299
$676$	21.8435	0.840133
$677$	−10.5864	−0.406869	−0.203435	−	0.979089i	$-0.565210\pi$
$677$	−10.5864	−0.406869	−0.203435	+	0.979089i	$0.565210\pi$
$678$	14.8727	0.571182
$679$	0	0
$680$	15.4039	0.590711
$681$	−52.9848	−2.03038
$682$	39.7636	1.52263
$683$	10.1997	0.390281	0.195141	−	0.980775i	$-0.437484\pi$
$683$	10.1997	0.390281	0.195141	+	0.980775i	$0.437484\pi$
$684$	−2.31635	−0.0885680
$685$	16.8985	0.645659
$686$	0	0
$687$	−15.3761	−0.586634
$688$	−5.12628	−0.195438
$689$	11.5890	0.441505
$690$	14.6016	0.555873
$691$	23.4589	0.892419	0.446210	−	0.894928i	$-0.352774\pi$
$691$	23.4589	0.892419	0.446210	+	0.894928i	$0.352774\pi$
$692$	24.5011	0.931393
$693$	0	0
$694$	1.89635	0.0719844
$695$	−34.2582	−1.29949
$696$	−2.58216	−0.0978764
$697$	−6.48537	−0.245651
$698$	2.50670	0.0948799
$699$	31.1882	1.17965
$700$	0	0
$701$	−16.9804	−0.641340	−0.320670	−	0.947191i	$-0.603908\pi$
$701$	−16.9804	−0.641340	−0.320670	+	0.947191i	$0.603908\pi$
$702$	28.7623	1.08556
$703$	29.3946	1.10864
$704$	6.06466	0.228570
$705$	−32.2091	−1.21307
$706$	33.7999	1.27208
$707$	0	0
$708$	22.8357	0.858217
$709$	−8.59891	−0.322939	−0.161469	−	0.986878i	$-0.551623\pi$
$709$	−8.59891	−0.322939	−0.161469	+	0.986878i	$0.551623\pi$
$710$	−18.3313	−0.687963
$711$	−0.867953	−0.0325508
$712$	−5.10925	−0.191477
$713$	−22.0893	−0.827251
$714$	0	0
$715$	85.0279	3.17986
$716$	−21.8931	−0.818183
$717$	−37.8392	−1.41313
$718$	−33.0058	−1.23177
$719$	17.4125	0.649378	0.324689	−	0.945821i	$-0.394740\pi$
$719$	17.4125	0.649378	0.324689	+	0.945821i	$0.394740\pi$
$720$	−0.783096	−0.0291843
$721$	0	0
$722$	30.3593	1.12986
$723$	−42.6654	−1.58674
$724$	12.7553	0.474046
$725$	−0.907674	−0.0337102
$726$	47.0422	1.74590
$727$	−25.4209	−0.942811	−0.471405	−	0.881917i	$-0.656253\pi$
$727$	−25.4209	−0.942811	−0.471405	+	0.881917i	$0.656253\pi$
$728$	0	0
$729$	23.4163	0.867271
$730$	−4.73798	−0.175360
$731$	33.2458	1.22964
$732$	−14.7950	−0.546838
$733$	24.2216	0.894644	0.447322	−	0.894373i	$-0.352378\pi$
$733$	24.2216	0.894644	0.447322	+	0.894373i	$0.352378\pi$
$734$	28.7539	1.06132
$735$	0	0
$736$	−3.36901	−0.124183
$737$	−49.6871	−1.83025
$738$	0.329701	0.0121365
$739$	−15.6480	−0.575619	−0.287810	−	0.957688i	$-0.592927\pi$
$739$	−15.6480	−0.575619	−0.287810	+	0.957688i	$0.592927\pi$
$740$	9.93752	0.365311
$741$	75.6742	2.77996
$742$	0	0
$743$	23.7775	0.872312	0.436156	−	0.899871i	$-0.356340\pi$
$743$	23.7775	0.872312	0.436156	+	0.899871i	$0.356340\pi$
$744$	11.9642	0.438627
$745$	−15.4009	−0.564244
$746$	31.2359	1.14363
$747$	−5.54402	−0.202845
$748$	−39.3316	−1.43810
$749$	0	0
$750$	18.8904	0.689780
$751$	30.5532	1.11490	0.557452	−	0.830209i	$-0.311779\pi$
$751$	30.5532	1.11490	0.557452	+	0.830209i	$0.311779\pi$
$752$	7.43159	0.271002
$753$	1.59963	0.0582938
$754$	8.35296	0.304197
$755$	2.44147	0.0888543
$756$	0	0
$757$	4.63337	0.168403	0.0842014	−	0.996449i	$-0.473166\pi$
$757$	4.63337	0.168403	0.0842014	+	0.996449i	$0.473166\pi$
$758$	7.35186	0.267032
$759$	−37.2831	−1.35329
$760$	16.6870	0.605302
$761$	−25.8923	−0.938596	−0.469298	−	0.883040i	$-0.655493\pi$
$761$	−25.8923	−0.938596	−0.469298	+	0.883040i	$0.655493\pi$
$762$	33.9519	1.22995
$763$	0	0
$764$	−20.9603	−0.758318
$765$	5.07867	0.183620
$766$	17.8749	0.645847
$767$	−73.8706	−2.66731
$768$	1.82475	0.0658449
$769$	5.08009	0.183193	0.0915963	−	0.995796i	$-0.470803\pi$
$769$	5.08009	0.183193	0.0915963	+	0.995796i	$0.470803\pi$
$770$	0	0
$771$	−17.0683	−0.614699
$772$	9.59009	0.345155
$773$	−14.2528	−0.512639	−0.256320	−	0.966592i	$-0.582510\pi$
$773$	−14.2528	−0.512639	−0.256320	+	0.966592i	$0.582510\pi$
$774$	−1.69014	−0.0607509
$775$	4.20562	0.151070
$776$	−13.1768	−0.473019
$777$	0	0
$778$	30.0836	1.07855
$779$	−7.02562	−0.251719
$780$	25.5834	0.916032
$781$	46.8065	1.67487
$782$	21.8493	0.781329
$783$	6.89513	0.246412
$784$	0	0
$785$	10.8544	0.387411
$786$	−11.9807	−0.427337
$787$	40.3661	1.43889	0.719447	−	0.694547i	$-0.244395\pi$
$787$	40.3661	1.43889	0.719447	+	0.694547i	$0.244395\pi$
$788$	−14.2516	−0.507692
$789$	11.2578	0.400788
$790$	6.25274	0.222463
$791$	0	0
$792$	1.99952	0.0710500
$793$	47.8599	1.69956
$794$	−26.5560	−0.942437
$795$	8.50906	0.301785
$796$	−1.83333	−0.0649806
$797$	−33.0194	−1.16961	−0.584803	−	0.811175i	$-0.698828\pi$
$797$	−33.0194	−1.16961	−0.584803	+	0.811175i	$0.698828\pi$
$798$	0	0
$799$	−48.1966	−1.70507
$800$	0.641431	0.0226780
$801$	−1.68452	−0.0595197
$802$	6.75854	0.238652
$803$	12.0978	0.426920
$804$	−14.9499	−0.527244
$805$	0	0
$806$	−38.7026	−1.36324
$807$	30.0321	1.05718
$808$	9.51140	0.334610
$809$	9.12339	0.320761	0.160381	−	0.987055i	$-0.448728\pi$
$809$	9.12339	0.320761	0.160381	+	0.987055i	$0.448728\pi$
$810$	23.4676	0.824568
$811$	30.0927	1.05670	0.528349	−	0.849028i	$-0.322811\pi$
$811$	30.0927	1.05670	0.528349	+	0.849028i	$0.322811\pi$
$812$	0	0
$813$	38.6050	1.35394
$814$	−25.3741	−0.889360
$815$	35.5378	1.24484
$816$	−11.8342	−0.414278
$817$	36.0153	1.26002
$818$	0.512528	0.0179201
$819$	0	0
$820$	−2.37517	−0.0829445
$821$	1.96487	0.0685743	0.0342872	−	0.999412i	$-0.489084\pi$
$821$	1.96487	0.0685743	0.0342872	+	0.999412i	$0.489084\pi$
$822$	−12.9824	−0.452815
$823$	−18.2105	−0.634777	−0.317388	−	0.948296i	$-0.602806\pi$
$823$	−18.2105	−0.634777	−0.317388	+	0.948296i	$0.602806\pi$
$824$	10.3113	0.359212
$825$	7.09838	0.247134
$826$	0	0
$827$	16.3425	0.568285	0.284143	−	0.958782i	$-0.408291\pi$
$827$	16.3425	0.568285	0.284143	+	0.958782i	$0.408291\pi$
$828$	−1.11077	−0.0386018
$829$	39.2053	1.36166	0.680828	−	0.732443i	$-0.261620\pi$
$829$	39.2053	1.36166	0.680828	+	0.732443i	$0.261620\pi$
$830$	39.9392	1.38631
$831$	−27.6678	−0.959785
$832$	−5.90283	−0.204644
$833$	0	0
$834$	26.3192	0.911359
$835$	−2.62169	−0.0907274
$836$	−42.6080	−1.47363
$837$	−31.9479	−1.10428
$838$	−17.1393	−0.592067
$839$	19.2514	0.664633	0.332317	−	0.943168i	$-0.392170\pi$
$839$	19.2514	0.664633	0.332317	+	0.943168i	$0.392170\pi$
$840$	0	0
$841$	−26.9976	−0.930950
$842$	13.9591	0.481063
$843$	39.7017	1.36740
$844$	−12.4784	−0.429523
$845$	−51.8819	−1.78479
$846$	2.45020	0.0842397
$847$	0	0
$848$	−1.96329	−0.0674196
$849$	3.22970	0.110843
$850$	−4.15992	−0.142684
$851$	14.0957	0.483194
$852$	14.0832	0.482483
$853$	−16.9180	−0.579261	−0.289630	−	0.957139i	$-0.593532\pi$
$853$	−16.9180	−0.579261	−0.289630	+	0.957139i	$0.593532\pi$
$854$	0	0
$855$	5.50173	0.188155
$856$	−4.80543	−0.164246
$857$	−2.94964	−0.100758	−0.0503788	−	0.998730i	$-0.516043\pi$
$857$	−2.94964	−0.100758	−0.0503788	+	0.998730i	$0.516043\pi$
$858$	−65.3235	−2.23011
$859$	2.61513	0.0892270	0.0446135	−	0.999004i	$-0.485794\pi$
$859$	2.61513	0.0892270	0.0446135	+	0.999004i	$0.485794\pi$
$860$	12.1758	0.415191
$861$	0	0
$862$	−29.3659	−1.00021
$863$	−41.5964	−1.41596	−0.707980	−	0.706233i	$-0.750393\pi$
$863$	−41.5964	−1.41596	−0.707980	+	0.706233i	$0.750393\pi$
$864$	−4.87262	−0.165770
$865$	−58.1944	−1.97867
$866$	−33.8265	−1.14947
$867$	45.7282	1.55301
$868$	0	0
$869$	−15.9655	−0.541592
$870$	6.13306	0.207930
$871$	48.3613	1.63866
$872$	−7.37499	−0.249749
$873$	−4.34440	−0.147036
$874$	23.6694	0.800629
$875$	0	0
$876$	3.64000	0.122984
$877$	−23.6768	−0.799508	−0.399754	−	0.916623i	$-0.630904\pi$
$877$	−23.6768	−0.799508	−0.399754	+	0.916623i	$0.630904\pi$
$878$	16.6597	0.562239
$879$	−42.3565	−1.42865
$880$	−14.4046	−0.485579
$881$	10.7313	0.361545	0.180773	−	0.983525i	$-0.442140\pi$
$881$	10.7313	0.361545	0.180773	+	0.983525i	$0.442140\pi$
$882$	0	0
$883$	−23.4692	−0.789801	−0.394901	−	0.918724i	$-0.629221\pi$
$883$	−23.4692	−0.789801	−0.394901	+	0.918724i	$0.629221\pi$
$884$	38.2821	1.28757
$885$	−54.2386	−1.82321
$886$	−20.6433	−0.693524
$887$	−50.9517	−1.71079	−0.855395	−	0.517977i	$-0.826685\pi$
$887$	−50.9517	−1.71079	−0.855395	+	0.517977i	$0.826685\pi$
$888$	−7.63460	−0.256200
$889$	0	0
$890$	12.1353	0.406777
$891$	−59.9213	−2.00744
$892$	−4.56414	−0.152819
$893$	−52.2115	−1.74719
$894$	11.8319	0.395717
$895$	51.9998	1.73816
$896$	0	0
$897$	36.2882	1.21163
$898$	0.0393032	0.00131156
$899$	−9.27811	−0.309442
$900$	0.211480	0.00704935
$901$	12.7327	0.424186
$902$	6.06466	0.201931
$903$	0	0
$904$	8.15055	0.271083
$905$	−30.2959	−1.00707
$906$	−1.87568	−0.0623154
$907$	3.03868	0.100898	0.0504488	−	0.998727i	$-0.483935\pi$
$907$	3.03868	0.100898	0.0504488	+	0.998727i	$0.483935\pi$
$908$	−29.0368	−0.963619
$909$	3.13592	0.104012
$910$	0	0
$911$	−38.9339	−1.28994	−0.644969	−	0.764208i	$-0.723130\pi$
$911$	−38.9339	−1.28994	−0.644969	+	0.764208i	$0.723130\pi$
$912$	−12.8200	−0.424512
$913$	−101.979	−3.37501
$914$	−23.4801	−0.776651
$915$	35.1406	1.16171
$916$	−8.42642	−0.278417
$917$	0	0
$918$	31.6007	1.04298
$919$	−57.0712	−1.88260	−0.941302	−	0.337565i	$-0.890397\pi$
$919$	−57.0712	−1.88260	−0.941302	+	0.337565i	$0.890397\pi$
$920$	8.00198	0.263817
$921$	−36.1458	−1.19105
$922$	13.9215	0.458479
$923$	−45.5575	−1.49954
$924$	0	0
$925$	−2.68370	−0.0882394
$926$	−6.55024	−0.215254
$927$	3.39966	0.111659
$928$	−1.41508	−0.0464522
$929$	8.35115	0.273992	0.136996	−	0.990572i	$-0.456255\pi$
$929$	8.35115	0.273992	0.136996	+	0.990572i	$0.456255\pi$
$930$	−28.4169	−0.931827
$931$	0	0
$932$	17.0918	0.559861
$933$	−18.2530	−0.597576
$934$	−9.07910	−0.297077
$935$	93.4191	3.05513
$936$	−1.94617	−0.0636126
$937$	18.1939	0.594370	0.297185	−	0.954820i	$-0.403952\pi$
$937$	18.1939	0.594370	0.297185	+	0.954820i	$0.403952\pi$
$938$	0	0
$939$	31.2988	1.02140
$940$	−17.6513	−0.575721
$941$	35.2435	1.14890	0.574452	−	0.818538i	$-0.305215\pi$
$941$	35.2435	1.14890	0.574452	+	0.818538i	$0.305215\pi$
$942$	−8.33902	−0.271700
$943$	−3.36901	−0.109710
$944$	12.5144	0.407310
$945$	0	0
$946$	−31.0892	−1.01080
$947$	−51.0320	−1.65832	−0.829159	−	0.559012i	$-0.811180\pi$
$947$	−51.0320	−1.65832	−0.829159	+	0.559012i	$0.811180\pi$
$948$	−4.80373	−0.156018
$949$	−11.7749	−0.382231
$950$	−4.50645	−0.146208
$951$	−17.1122	−0.554900
$952$	0	0
$953$	−19.0937	−0.618506	−0.309253	−	0.950980i	$-0.600079\pi$
$953$	−19.0937	−0.618506	−0.309253	+	0.950980i	$0.600079\pi$
$954$	−0.647299	−0.0209571
$955$	49.7843	1.61098
$956$	−20.7367	−0.670672
$957$	−15.6599	−0.506213
$958$	23.3006	0.752809
$959$	0	0
$960$	−4.33408	−0.139882
$961$	11.9892	0.386748
$962$	24.6970	0.796263
$963$	−1.58435	−0.0510551
$964$	−23.3816	−0.753069
$965$	−22.7781	−0.733253
$966$	0	0
$967$	−7.11704	−0.228869	−0.114434	−	0.993431i	$-0.536506\pi$
$967$	−7.11704	−0.228869	−0.114434	+	0.993431i	$0.536506\pi$
$968$	25.7801	0.828604
$969$	83.1422	2.67091
$970$	31.2971	1.00489
$971$	−22.9159	−0.735405	−0.367703	−	0.929943i	$-0.619856\pi$
$971$	−22.9159	−0.735405	−0.367703	+	0.929943i	$0.619856\pi$
$972$	−3.41137	−0.109420
$973$	0	0
$974$	16.3025	0.522364
$975$	−6.90897	−0.221264
$976$	−8.10796	−0.259529
$977$	25.7328	0.823266	0.411633	−	0.911350i	$-0.364959\pi$
$977$	25.7328	0.823266	0.411633	+	0.911350i	$0.364959\pi$
$978$	−27.3023	−0.873031
$979$	−30.9858	−0.990312
$980$	0	0
$981$	−2.43154	−0.0776332
$982$	14.8328	0.473333
$983$	−21.1087	−0.673264	−0.336632	−	0.941636i	$-0.609288\pi$
$983$	−21.1087	−0.673264	−0.336632	+	0.941636i	$0.609288\pi$
$984$	1.82475	0.0581708
$985$	33.8500	1.07855
$986$	9.17729	0.292265
$987$	0	0
$988$	41.4710	1.31937
$989$	17.2705	0.549170
$990$	−4.74921	−0.150940
$991$	33.4059	1.06117	0.530587	−	0.847630i	$-0.321971\pi$
$991$	33.4059	1.06117	0.530587	+	0.847630i	$0.321971\pi$
$992$	6.55661	0.208173
$993$	17.6965	0.561581
$994$	0	0
$995$	4.35446	0.138046
$996$	−30.6836	−0.972249
$997$	19.6381	0.621946	0.310973	−	0.950419i	$-0.399345\pi$
$997$	19.6381	0.621946	0.310973	+	0.950419i	$0.399345\pi$
$998$	28.8431	0.913011
$999$	20.3867	0.645005

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bp.1.5	✓	6
7.6	odd	2		4018.2.a.bq.1.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.bp.1.5	✓	6	1.1	even	1	trivial
4018.2.a.bq.1.2	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.82475 q^{3} +1.00000 q^{4} -2.37517 q^{5} +1.82475 q^{6} +1.00000 q^{8} +0.329701 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.82475 q^{3} +1.00000 q^{4} -2.37517 q^{5} +1.82475 q^{6} +1.00000 q^{8} +0.329701 q^{9} -2.37517 q^{10} +6.06466 q^{11} +1.82475 q^{12} -5.90283 q^{13} -4.33408 q^{15} +1.00000 q^{16} -6.48537 q^{17} +0.329701 q^{18} -7.02562 q^{19} -2.37517 q^{20} +6.06466 q^{22} -3.36901 q^{23} +1.82475 q^{24} +0.641431 q^{25} -5.90283 q^{26} -4.87262 q^{27} -1.41508 q^{29} -4.33408 q^{30} +6.55661 q^{31} +1.00000 q^{32} +11.0665 q^{33} -6.48537 q^{34} +0.329701 q^{36} -4.18392 q^{37} -7.02562 q^{38} -10.7712 q^{39} -2.37517 q^{40} +1.00000 q^{41} -5.12628 q^{43} +6.06466 q^{44} -0.783096 q^{45} -3.36901 q^{46} +7.43159 q^{47} +1.82475 q^{48} +0.641431 q^{50} -11.8342 q^{51} -5.90283 q^{52} -1.96329 q^{53} -4.87262 q^{54} -14.4046 q^{55} -12.8200 q^{57} -1.41508 q^{58} +12.5144 q^{59} -4.33408 q^{60} -8.10796 q^{61} +6.55661 q^{62} +1.00000 q^{64} +14.0202 q^{65} +11.0665 q^{66} -8.19289 q^{67} -6.48537 q^{68} -6.14759 q^{69} +7.71790 q^{71} +0.329701 q^{72} +1.99480 q^{73} -4.18392 q^{74} +1.17045 q^{75} -7.02562 q^{76} -10.7712 q^{78} -2.63255 q^{79} -2.37517 q^{80} -9.88040 q^{81} +1.00000 q^{82} -16.8153 q^{83} +15.4039 q^{85} -5.12628 q^{86} -2.58216 q^{87} +6.06466 q^{88} -5.10925 q^{89} -0.783096 q^{90} -3.36901 q^{92} +11.9642 q^{93} +7.43159 q^{94} +16.6870 q^{95} +1.82475 q^{96} -13.1768 q^{97} +1.99952 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 4 q^{3} + 6 q^{4} - 12 q^{5} - 4 q^{6} + 6 q^{8} + 18 q^{9}+O(q^{10}) \) 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

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