LMFDB - Embedded newform 2009.2.a.u.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2009,2,Mod(1,2009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2009, 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("2009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2009 = 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2009.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:	$16.0419457661$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 27 x^{18} + 52 x^{17} + 302 x^{16} - 552 x^{15} - 1820 x^{14} + 3090 x^{13} + \cdots + 49 $ x^20 - 2x^19 - 27x^18 + 52x^17 + 302x^16 - 552x^15 - 1820x^14 + 3090x^13 + 6449x^12 - 9852x^11 - 13797x^10 + 18080x^9 + 17721x^8 - 18446x^7 - 13352x^6 + 9524x^5 + 5690x^4 - 1972x^3 - 1179x^2 + 42*x + 49
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			1.15
Root			$-1.30606$ of defining polynomial
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.30606 q^{2} -1.82067 q^{3} -0.294211 q^{4} +0.323122 q^{5} -2.37790 q^{6} -2.99637 q^{8} +0.314826 q^{9} +O(q^{10})$	\(q+1.30606 q^{2} -1.82067 q^{3} -0.294211 q^{4} +0.323122 q^{5} -2.37790 q^{6} -2.99637 q^{8} +0.314826 q^{9} +0.422016 q^{10} -4.02065 q^{11} +0.535660 q^{12} +2.56025 q^{13} -0.588296 q^{15} -3.32502 q^{16} -0.768845 q^{17} +0.411181 q^{18} +4.01694 q^{19} -0.0950659 q^{20} -5.25121 q^{22} +2.94814 q^{23} +5.45540 q^{24} -4.89559 q^{25} +3.34384 q^{26} +4.88881 q^{27} -2.90684 q^{29} -0.768350 q^{30} +0.256759 q^{31} +1.65008 q^{32} +7.32027 q^{33} -1.00416 q^{34} -0.0926252 q^{36} +5.13453 q^{37} +5.24635 q^{38} -4.66136 q^{39} -0.968193 q^{40} +1.00000 q^{41} +2.05697 q^{43} +1.18292 q^{44} +0.101727 q^{45} +3.85045 q^{46} +3.11761 q^{47} +6.05375 q^{48} -6.39393 q^{50} +1.39981 q^{51} -0.753255 q^{52} +8.75629 q^{53} +6.38507 q^{54} -1.29916 q^{55} -7.31350 q^{57} -3.79651 q^{58} +8.14097 q^{59} +0.173083 q^{60} +0.790925 q^{61} +0.335342 q^{62} +8.80514 q^{64} +0.827273 q^{65} +9.56070 q^{66} +1.81601 q^{67} +0.226203 q^{68} -5.36758 q^{69} -11.4661 q^{71} -0.943336 q^{72} +6.55885 q^{73} +6.70600 q^{74} +8.91324 q^{75} -1.18183 q^{76} -6.08802 q^{78} +15.5638 q^{79} -1.07438 q^{80} -9.84536 q^{81} +1.30606 q^{82} +5.04446 q^{83} -0.248430 q^{85} +2.68652 q^{86} +5.29239 q^{87} +12.0474 q^{88} -14.3692 q^{89} +0.132861 q^{90} -0.867376 q^{92} -0.467473 q^{93} +4.07178 q^{94} +1.29796 q^{95} -3.00425 q^{96} +7.88729 q^{97} -1.26581 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 8 q^{3} + 18 q^{4} + 8 q^{5} + 12 q^{6} - 6 q^{8} + 16 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 8 * q^3 + 18 * q^4 + 8 * q^5 + 12 * q^6 - 6 * q^8 + 16 * q^9	$ 20 q - 2 q^{2} + 8 q^{3} + 18 q^{4} + 8 q^{5} + 12 q^{6} - 6 q^{8} + 16 q^{9} + 16 q^{10} + 6 q^{12} + 12 q^{13} + 14 q^{16} + 8 q^{17} - 18 q^{18} + 36 q^{19} + 24 q^{20} - 8 q^{22} - 12 q^{23} + 36 q^{24} + 20 q^{25} - 22 q^{26} + 32 q^{27} + 4 q^{29} + 28 q^{30} + 80 q^{31} + 6 q^{32} - 12 q^{33} + 48 q^{34} + 26 q^{36} + 4 q^{37} + 12 q^{38} - 28 q^{39} - 4 q^{40} + 20 q^{41} - 20 q^{44} + 40 q^{45} + 8 q^{46} + 32 q^{47} + 16 q^{48} + 6 q^{50} - 20 q^{51} + 36 q^{52} + 4 q^{53} - 50 q^{54} + 64 q^{55} - 4 q^{57} + 32 q^{59} + 20 q^{60} + 44 q^{61} - 8 q^{62} - 30 q^{64} - 8 q^{65} + 32 q^{66} - 4 q^{67} - 48 q^{68} - 24 q^{69} + 8 q^{71} - 8 q^{72} + 48 q^{73} - 38 q^{74} + 24 q^{75} + 84 q^{76} + 30 q^{78} - 4 q^{79} + 56 q^{80} - 2 q^{82} + 8 q^{83} - 12 q^{85} - 24 q^{86} + 40 q^{87} - 48 q^{88} + 20 q^{89} + 48 q^{90} - 50 q^{92} + 48 q^{93} + 26 q^{94} + 20 q^{95} + 70 q^{96} + 8 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q - 2 * q^2 + 8 * q^3 + 18 * q^4 + 8 * q^5 + 12 * q^6 - 6 * q^8 + 16 * q^9 + 16 * q^10 + 6 * q^12 + 12 * q^13 + 14 * q^16 + 8 * q^17 - 18 * q^18 + 36 * q^19 + 24 * q^20 - 8 * q^22 - 12 * q^23 + 36 * q^24 + 20 * q^25 - 22 * q^26 + 32 * q^27 + 4 * q^29 + 28 * q^30 + 80 * q^31 + 6 * q^32 - 12 * q^33 + 48 * q^34 + 26 * q^36 + 4 * q^37 + 12 * q^38 - 28 * q^39 - 4 * q^40 + 20 * q^41 - 20 * q^44 + 40 * q^45 + 8 * q^46 + 32 * q^47 + 16 * q^48 + 6 * q^50 - 20 * q^51 + 36 * q^52 + 4 * q^53 - 50 * q^54 + 64 * q^55 - 4 * q^57 + 32 * q^59 + 20 * q^60 + 44 * q^61 - 8 * q^62 - 30 * q^64 - 8 * q^65 + 32 * q^66 - 4 * q^67 - 48 * q^68 - 24 * q^69 + 8 * q^71 - 8 * q^72 + 48 * q^73 - 38 * q^74 + 24 * q^75 + 84 * q^76 + 30 * q^78 - 4 * q^79 + 56 * q^80 - 2 * q^82 + 8 * q^83 - 12 * q^85 - 24 * q^86 + 40 * q^87 - 48 * q^88 + 20 * q^89 + 48 * q^90 - 50 * q^92 + 48 * q^93 + 26 * q^94 + 20 * q^95 + 70 * q^96 + 8 * q^97 - 8 * 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 $

$2$	1.30606	0.923523	0.461761	−	0.887004i	$-0.347218\pi$
$2$	1.30606	0.923523	0.461761	+	0.887004i	$0.347218\pi$
$3$	−1.82067	−1.05116	−0.525581	−	0.850744i	$-0.676152\pi$
$3$	−1.82067	−1.05116	−0.525581	+	0.850744i	$0.676152\pi$
$4$	−0.294211	−0.147106
$5$	0.323122	0.144504	0.0722522	−	0.997386i	$-0.476981\pi$
$5$	0.323122	0.144504	0.0722522	+	0.997386i	$0.476981\pi$
$6$	−2.37790	−0.970772
$7$	0	0
$7$	0	0
$8$	−2.99637	−1.05938
$9$	0.314826	0.104942
$10$	0.422016	0.133453
$11$	−4.02065	−1.21227	−0.606136	−	0.795361i	$-0.707281\pi$
$11$	−4.02065	−1.21227	−0.606136	+	0.795361i	$0.707281\pi$
$12$	0.535660	0.154632
$13$	2.56025	0.710086	0.355043	−	0.934850i	$-0.384466\pi$
$13$	2.56025	0.710086	0.355043	+	0.934850i	$0.384466\pi$
$14$	0	0
$15$	−0.588296	−0.151897
$16$	−3.32502	−0.831254
$17$	−0.768845	−0.186472	−0.0932361	−	0.995644i	$-0.529721\pi$
$17$	−0.768845	−0.186472	−0.0932361	+	0.995644i	$0.529721\pi$
$18$	0.411181	0.0969163
$19$	4.01694	0.921548	0.460774	−	0.887517i	$-0.347572\pi$
$19$	4.01694	0.921548	0.460774	+	0.887517i	$0.347572\pi$
$20$	−0.0950659	−0.0212574
$21$	0	0
$22$	−5.25121	−1.11956
$23$	2.94814	0.614730	0.307365	−	0.951592i	$-0.400553\pi$
$23$	2.94814	0.614730	0.307365	+	0.951592i	$0.400553\pi$
$24$	5.45540	1.11358
$25$	−4.89559	−0.979118
$26$	3.34384	0.655781
$27$	4.88881	0.940851
$28$	0	0
$29$	−2.90684	−0.539787	−0.269894	−	0.962890i	$-0.586989\pi$
$29$	−2.90684	−0.539787	−0.269894	+	0.962890i	$0.586989\pi$
$30$	−0.768350	−0.140281
$31$	0.256759	0.0461153	0.0230576	−	0.999734i	$-0.492660\pi$
$31$	0.256759	0.0461153	0.0230576	+	0.999734i	$0.492660\pi$
$32$	1.65008	0.291696
$33$	7.32027	1.27430
$34$	−1.00416	−0.172211
$35$	0	0
$36$	−0.0926252	−0.0154375
$37$	5.13453	0.844112	0.422056	−	0.906570i	$-0.361309\pi$
$37$	5.13453	0.844112	0.422056	+	0.906570i	$0.361309\pi$
$38$	5.24635	0.851071
$39$	−4.66136	−0.746416
$40$	−0.968193	−0.153085
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	2.05697	0.313684	0.156842	−	0.987624i	$-0.449869\pi$
$43$	2.05697	0.313684	0.156842	+	0.987624i	$0.449869\pi$
$44$	1.18292	0.178332
$45$	0.101727	0.0151646
$46$	3.85045	0.567717
$47$	3.11761	0.454751	0.227375	−	0.973807i	$-0.426986\pi$
$47$	3.11761	0.454751	0.227375	+	0.973807i	$0.426986\pi$
$48$	6.05375	0.873783
$49$	0	0
$50$	−6.39393	−0.904238
$51$	1.39981	0.196013
$52$	−0.753255	−0.104458
$53$	8.75629	1.20277	0.601384	−	0.798960i	$-0.294616\pi$
$53$	8.75629	1.20277	0.601384	+	0.798960i	$0.294616\pi$
$54$	6.38507	0.868898
$55$	−1.29916	−0.175179
$56$	0	0
$57$	−7.31350	−0.968697
$58$	−3.79651	−0.498506
$59$	8.14097	1.05986	0.529932	−	0.848040i	$-0.322217\pi$
$59$	8.14097	1.05986	0.529932	+	0.848040i	$0.322217\pi$
$60$	0.173083	0.0223450
$61$	0.790925	0.101268	0.0506338	−	0.998717i	$-0.483876\pi$
$61$	0.790925	0.101268	0.0506338	+	0.998717i	$0.483876\pi$
$62$	0.335342	0.0425885
$63$	0	0
$64$	8.80514	1.10064
$65$	0.827273	0.102611
$66$	9.56070	1.17684
$67$	1.81601	0.221860	0.110930	−	0.993828i	$-0.464617\pi$
$67$	1.81601	0.221860	0.110930	+	0.993828i	$0.464617\pi$
$68$	0.226203	0.0274311
$69$	−5.36758	−0.646181
$70$	0	0
$71$	−11.4661	−1.36078	−0.680390	−	0.732851i	$-0.738189\pi$
$71$	−11.4661	−1.36078	−0.680390	+	0.732851i	$0.738189\pi$
$72$	−0.943336	−0.111173
$73$	6.55885	0.767656	0.383828	−	0.923405i	$-0.374606\pi$
$73$	6.55885	0.767656	0.383828	+	0.923405i	$0.374606\pi$
$74$	6.70600	0.779557
$75$	8.91324	1.02921
$76$	−1.18183	−0.135565
$77$	0	0
$78$	−6.08802	−0.689332
$79$	15.5638	1.75106	0.875532	−	0.483160i	$-0.160511\pi$
$79$	15.5638	1.75106	0.875532	+	0.483160i	$0.160511\pi$
$80$	−1.07438	−0.120120
$81$	−9.84536	−1.09393
$82$	1.30606	0.144230
$83$	5.04446	0.553702	0.276851	−	0.960913i	$-0.410709\pi$
$83$	5.04446	0.553702	0.276851	+	0.960913i	$0.410709\pi$
$84$	0	0
$85$	−0.248430	−0.0269460
$86$	2.68652	0.289695
$87$	5.29239	0.567404
$88$	12.0474	1.28426
$89$	−14.3692	−1.52313	−0.761564	−	0.648090i	$-0.775568\pi$
$89$	−14.3692	−1.52313	−0.761564	+	0.648090i	$0.775568\pi$
$90$	0.132861	0.0140048
$91$	0	0
$92$	−0.867376	−0.0904302
$93$	−0.467473	−0.0484746
$94$	4.07178	0.419973
$95$	1.29796	0.133168
$96$	−3.00425	−0.306620
$97$	7.88729	0.800833	0.400416	−	0.916333i	$-0.368865\pi$
$97$	7.88729	0.800833	0.400416	+	0.916333i	$0.368865\pi$
$98$	0	0
$99$	−1.26581	−0.127218
$100$	1.44034	0.144034
$101$	5.62407	0.559616	0.279808	−	0.960056i	$-0.409729\pi$
$101$	5.62407	0.559616	0.279808	+	0.960056i	$0.409729\pi$
$102$	1.82823	0.181022
$103$	0.226053	0.0222737	0.0111368	−	0.999938i	$-0.496455\pi$
$103$	0.226053	0.0222737	0.0111368	+	0.999938i	$0.496455\pi$
$104$	−7.67147	−0.752250
$105$	0	0
$106$	11.4362	1.11078
$107$	8.60371	0.831752	0.415876	−	0.909421i	$-0.363475\pi$
$107$	8.60371	0.831752	0.415876	+	0.909421i	$0.363475\pi$
$108$	−1.43834	−0.138404
$109$	−2.43951	−0.233663	−0.116831	−	0.993152i	$-0.537274\pi$
$109$	−2.43951	−0.233663	−0.116831	+	0.993152i	$0.537274\pi$
$110$	−1.69678	−0.161782
$111$	−9.34827	−0.887299
$112$	0	0
$113$	−1.91258	−0.179921	−0.0899603	−	0.995945i	$-0.528674\pi$
$113$	−1.91258	−0.179921	−0.0899603	+	0.995945i	$0.528674\pi$
$114$	−9.55186	−0.894613
$115$	0.952608	0.0888312
$116$	0.855225	0.0794057
$117$	0.806033	0.0745178
$118$	10.6326	0.978809
$119$	0	0
$120$	1.76276	0.160917
$121$	5.16566	0.469606
$122$	1.03299	0.0935229
$123$	−1.82067	−0.164164
$124$	−0.0755414	−0.00678381
$125$	−3.19748	−0.285991
$126$	0	0
$127$	11.4514	1.01615	0.508076	−	0.861312i	$-0.330357\pi$
$127$	11.4514	1.01615	0.508076	+	0.861312i	$0.330357\pi$
$128$	8.19986	0.724772
$129$	−3.74505	−0.329733
$130$	1.08047	0.0947632
$131$	−6.97678	−0.609564	−0.304782	−	0.952422i	$-0.598584\pi$
$131$	−6.97678	−0.609564	−0.304782	+	0.952422i	$0.598584\pi$
$132$	−2.15370	−0.187456
$133$	0	0
$134$	2.37181	0.204893
$135$	1.57968	0.135957
$136$	2.30375	0.197545
$137$	−12.9676	−1.10789	−0.553947	−	0.832552i	$-0.686879\pi$
$137$	−12.9676	−1.10789	−0.553947	+	0.832552i	$0.686879\pi$
$138$	−7.01038	−0.596763
$139$	21.1362	1.79275	0.896374	−	0.443299i	$-0.146192\pi$
$139$	21.1362	1.79275	0.896374	+	0.443299i	$0.146192\pi$
$140$	0	0
$141$	−5.67613	−0.478017
$142$	−14.9754	−1.25671
$143$	−10.2939	−0.860818
$144$	−1.04680	−0.0872334
$145$	−0.939264	−0.0780016
$146$	8.56624	0.708947
$147$	0	0
$148$	−1.51064	−0.124174
$149$	13.6519	1.11841	0.559203	−	0.829031i	$-0.311107\pi$
$149$	13.6519	1.11841	0.559203	+	0.829031i	$0.311107\pi$
$150$	11.6412	0.950501
$151$	−3.08512	−0.251063	−0.125532	−	0.992090i	$-0.540064\pi$
$151$	−3.08512	−0.251063	−0.125532	+	0.992090i	$0.540064\pi$
$152$	−12.0362	−0.976268
$153$	−0.242052	−0.0195688
$154$	0	0
$155$	0.0829644	0.00666386
$156$	1.37143	0.109802
$157$	−0.0765150	−0.00610656	−0.00305328	−	0.999995i	$-0.500972\pi$
$157$	−0.0765150	−0.00610656	−0.00305328	+	0.999995i	$0.500972\pi$
$158$	20.3272	1.61715
$159$	−15.9423	−1.26431
$160$	0.533176	0.0421513
$161$	0	0
$162$	−12.8586	−1.01027
$163$	−13.9384	−1.09174	−0.545868	−	0.837871i	$-0.683800\pi$
$163$	−13.9384	−1.09174	−0.545868	+	0.837871i	$0.683800\pi$
$164$	−0.294211	−0.0229740
$165$	2.36534	0.184141
$166$	6.58836	0.511356
$167$	20.5065	1.58684	0.793420	−	0.608675i	$-0.208298\pi$
$167$	20.5065	1.58684	0.793420	+	0.608675i	$0.208298\pi$
$168$	0	0
$169$	−6.44511	−0.495778
$170$	−0.324464	−0.0248853
$171$	1.26463	0.0967090
$172$	−0.605182	−0.0461447
$173$	−2.51938	−0.191545	−0.0957723	−	0.995403i	$-0.530532\pi$
$173$	−2.51938	−0.191545	−0.0957723	+	0.995403i	$0.530532\pi$
$174$	6.91217	0.524010
$175$	0	0
$176$	13.3687	1.00771
$177$	−14.8220	−1.11409
$178$	−18.7670	−1.40664
$179$	0.624152	0.0466513	0.0233257	−	0.999728i	$-0.492575\pi$
$179$	0.624152	0.0466513	0.0233257	+	0.999728i	$0.492575\pi$
$180$	−0.0299292	−0.00223079
$181$	1.68076	0.124930	0.0624648	−	0.998047i	$-0.480104\pi$
$181$	1.68076	0.124930	0.0624648	+	0.998047i	$0.480104\pi$
$182$	0	0
$183$	−1.44001	−0.106449
$184$	−8.83373	−0.651232
$185$	1.65908	0.121978
$186$	−0.610547	−0.0447674
$187$	3.09126	0.226055
$188$	−0.917236	−0.0668963
$189$	0	0
$190$	1.69521	0.122983
$191$	7.85501	0.568369	0.284184	−	0.958770i	$-0.408277\pi$
$191$	7.85501	0.568369	0.284184	+	0.958770i	$0.408277\pi$
$192$	−16.0312	−1.15695
$193$	17.4306	1.25468	0.627342	−	0.778744i	$-0.284143\pi$
$193$	17.4306	1.25468	0.627342	+	0.778744i	$0.284143\pi$
$194$	10.3013	0.739588
$195$	−1.50619	−0.107860
$196$	0	0
$197$	−21.5543	−1.53568	−0.767841	−	0.640640i	$-0.778669\pi$
$197$	−21.5543	−1.53568	−0.767841	+	0.640640i	$0.778669\pi$
$198$	−1.65322	−0.117489
$199$	−9.94694	−0.705120	−0.352560	−	0.935789i	$-0.614689\pi$
$199$	−9.94694	−0.705120	−0.352560	+	0.935789i	$0.614689\pi$
$200$	14.6690	1.03726
$201$	−3.30634	−0.233211
$202$	7.34537	0.516818
$203$	0	0
$204$	−0.411840	−0.0288345
$205$	0.323122	0.0225678
$206$	0.295239	0.0205703
$207$	0.928151	0.0645109
$208$	−8.51288	−0.590262
$209$	−16.1507	−1.11717
$210$	0	0
$211$	3.89610	0.268219	0.134109	−	0.990967i	$-0.457183\pi$
$211$	3.89610	0.268219	0.134109	+	0.990967i	$0.457183\pi$
$212$	−2.57620	−0.176934
$213$	20.8760	1.43040
$214$	11.2369	0.768142
$215$	0.664650	0.0453288
$216$	−14.6487	−0.996717
$217$	0	0
$218$	−3.18615	−0.215793
$219$	−11.9415	−0.806930
$220$	0.382227	0.0257698
$221$	−1.96844	−0.132411
$222$	−12.2094	−0.819441
$223$	20.6813	1.38492	0.692460	−	0.721456i	$-0.256527\pi$
$223$	20.6813	1.38492	0.692460	+	0.721456i	$0.256527\pi$
$224$	0	0
$225$	−1.54126	−0.102751
$226$	−2.49795	−0.166161
$227$	4.39656	0.291810	0.145905	−	0.989299i	$-0.453391\pi$
$227$	4.39656	0.291810	0.145905	+	0.989299i	$0.453391\pi$
$228$	2.15171	0.142501
$229$	−11.0216	−0.728327	−0.364164	−	0.931335i	$-0.618645\pi$
$229$	−11.0216	−0.728327	−0.364164	+	0.931335i	$0.618645\pi$
$230$	1.24416	0.0820376
$231$	0	0
$232$	8.70999	0.571839
$233$	17.1945	1.12645	0.563225	−	0.826304i	$-0.309561\pi$
$233$	17.1945	1.12645	0.563225	+	0.826304i	$0.309561\pi$
$234$	1.05273	0.0688189
$235$	1.00737	0.0657134
$236$	−2.39516	−0.155912
$237$	−28.3365	−1.84065
$238$	0	0
$239$	−16.1227	−1.04289	−0.521445	−	0.853285i	$-0.674607\pi$
$239$	−16.1227	−1.04289	−0.521445	+	0.853285i	$0.674607\pi$
$240$	1.95610	0.126265
$241$	22.4808	1.44812	0.724058	−	0.689739i	$-0.242275\pi$
$241$	22.4808	1.44812	0.724058	+	0.689739i	$0.242275\pi$
$242$	6.74666	0.433692
$243$	3.25870	0.209046
$244$	−0.232699	−0.0148970
$245$	0	0
$246$	−2.37790	−0.151609
$247$	10.2844	0.654379
$248$	−0.769346	−0.0488535
$249$	−9.18428	−0.582030
$250$	−4.17609	−0.264119
$251$	−21.6842	−1.36869	−0.684346	−	0.729158i	$-0.739912\pi$
$251$	−21.6842	−1.36869	−0.684346	+	0.729158i	$0.739912\pi$
$252$	0	0
$253$	−11.8535	−0.745221
$254$	14.9563	0.938439
$255$	0.452309	0.0283247
$256$	−6.90077	−0.431298
$257$	−10.9991	−0.686106	−0.343053	−	0.939316i	$-0.611461\pi$
$257$	−10.9991	−0.686106	−0.343053	+	0.939316i	$0.611461\pi$
$258$	−4.89125	−0.304516
$259$	0	0
$260$	−0.243393	−0.0150946
$261$	−0.915149	−0.0566463
$262$	−9.11209	−0.562947
$263$	−8.13301	−0.501503	−0.250752	−	0.968051i	$-0.580678\pi$
$263$	−8.13301	−0.501503	−0.250752	+	0.968051i	$0.580678\pi$
$264$	−21.9343	−1.34996
$265$	2.82935	0.173805
$266$	0	0
$267$	26.1615	1.60105
$268$	−0.534289	−0.0326369
$269$	−26.8810	−1.63896	−0.819481	−	0.573107i	$-0.805738\pi$
$269$	−26.8810	−1.63896	−0.819481	+	0.573107i	$0.805738\pi$
$270$	2.06315	0.125559
$271$	27.6138	1.67742	0.838708	−	0.544581i	$-0.183311\pi$
$271$	27.6138	1.67742	0.838708	+	0.544581i	$0.183311\pi$
$272$	2.55642	0.155006
$273$	0	0
$274$	−16.9364	−1.02317
$275$	19.6835	1.18696
$276$	1.57920	0.0950568
$277$	−17.8536	−1.07272	−0.536361	−	0.843989i	$-0.680201\pi$
$277$	−17.8536	−1.07272	−0.536361	+	0.843989i	$0.680201\pi$
$278$	27.6051	1.65564
$279$	0.0808344	0.00483943
$280$	0	0
$281$	28.8340	1.72009	0.860047	−	0.510215i	$-0.170434\pi$
$281$	28.8340	1.72009	0.860047	+	0.510215i	$0.170434\pi$
$282$	−7.41336	−0.441459
$283$	−7.50322	−0.446020	−0.223010	−	0.974816i	$-0.571588\pi$
$283$	−7.50322	−0.446020	−0.223010	+	0.974816i	$0.571588\pi$
$284$	3.37346	0.200178
$285$	−2.36315	−0.139981
$286$	−13.4444	−0.794985
$287$	0	0
$288$	0.519488	0.0306111
$289$	−16.4089	−0.965228
$290$	−1.22673	−0.0720363
$291$	−14.3601	−0.841805
$292$	−1.92969	−0.112926
$293$	15.8297	0.924783	0.462391	−	0.886676i	$-0.346992\pi$
$293$	15.8297	0.924783	0.462391	+	0.886676i	$0.346992\pi$
$294$	0	0
$295$	2.63052	0.153155
$296$	−15.3850	−0.894234
$297$	−19.6562	−1.14057
$298$	17.8302	1.03287
$299$	7.54799	0.436511
$300$	−2.62237	−0.151403
$301$	0	0
$302$	−4.02934	−0.231863
$303$	−10.2396	−0.588247
$304$	−13.3564	−0.766041
$305$	0.255565	0.0146336
$306$	−0.316134	−0.0180722
$307$	−18.1361	−1.03508	−0.517542	−	0.855658i	$-0.673153\pi$
$307$	−18.1361	−1.03508	−0.517542	+	0.855658i	$0.673153\pi$
$308$	0	0
$309$	−0.411568	−0.0234133
$310$	0.108356	0.00615423
$311$	24.0213	1.36212	0.681062	−	0.732226i	$-0.261518\pi$
$311$	24.0213	1.36212	0.681062	+	0.732226i	$0.261518\pi$
$312$	13.9672	0.790737
$313$	−3.07940	−0.174058	−0.0870290	−	0.996206i	$-0.527737\pi$
$313$	−3.07940	−0.174058	−0.0870290	+	0.996206i	$0.527737\pi$
$314$	−0.0999330	−0.00563955
$315$	0	0
$316$	−4.57904	−0.257591
$317$	−12.3716	−0.694860	−0.347430	−	0.937706i	$-0.612946\pi$
$317$	−12.3716	−0.694860	−0.347430	+	0.937706i	$0.612946\pi$
$318$	−20.8216	−1.16761
$319$	11.6874	0.654369
$320$	2.84513	0.159048
$321$	−15.6645	−0.874306
$322$	0	0
$323$	−3.08840	−0.171843
$324$	2.89661	0.160923
$325$	−12.5340	−0.695259
$326$	−18.2043	−1.00824
$327$	4.44154	0.245618
$328$	−2.99637	−0.165447
$329$	0	0
$330$	3.08927	0.170059
$331$	−10.7437	−0.590528	−0.295264	−	0.955416i	$-0.595408\pi$
$331$	−10.7437	−0.590528	−0.295264	+	0.955416i	$0.595408\pi$
$332$	−1.48414	−0.0814526
$333$	1.61648	0.0885828
$334$	26.7827	1.46548
$335$	0.586791	0.0320598
$336$	0	0
$337$	−8.54398	−0.465420	−0.232710	−	0.972546i	$-0.574759\pi$
$337$	−8.54398	−0.465420	−0.232710	+	0.972546i	$0.574759\pi$
$338$	−8.41769	−0.457862
$339$	3.48218	0.189126
$340$	0.0730909	0.00396391
$341$	−1.03234	−0.0559043
$342$	1.65169	0.0893130
$343$	0	0
$344$	−6.16344	−0.332310
$345$	−1.73438	−0.0933759
$346$	−3.29045	−0.176896
$347$	6.21193	0.333474	0.166737	−	0.986001i	$-0.446677\pi$
$347$	6.21193	0.333474	0.166737	+	0.986001i	$0.446677\pi$
$348$	−1.55708	−0.0834683
$349$	−22.0120	−1.17828	−0.589138	−	0.808032i	$-0.700533\pi$
$349$	−22.0120	−1.17828	−0.589138	+	0.808032i	$0.700533\pi$
$350$	0	0
$351$	12.5166	0.668085
$352$	−6.63440	−0.353615
$353$	9.59009	0.510429	0.255214	−	0.966884i	$-0.417854\pi$
$353$	9.59009	0.510429	0.255214	+	0.966884i	$0.417854\pi$
$354$	−19.3584	−1.02889
$355$	−3.70495	−0.196639
$356$	4.22757	0.224061
$357$	0	0
$358$	0.815180	0.0430836
$359$	4.53933	0.239577	0.119788	−	0.992799i	$-0.461778\pi$
$359$	4.53933	0.239577	0.119788	+	0.992799i	$0.461778\pi$
$360$	−0.304812	−0.0160650
$361$	−2.86423	−0.150749
$362$	2.19516	0.115375
$363$	−9.40495	−0.493632
$364$	0	0
$365$	2.11931	0.110930
$366$	−1.88074	−0.0983078
$367$	−28.8538	−1.50616	−0.753078	−	0.657931i	$-0.771432\pi$
$367$	−28.8538	−1.50616	−0.753078	+	0.657931i	$0.771432\pi$
$368$	−9.80262	−0.510997
$369$	0.314826	0.0163892
$370$	2.16685	0.112649
$371$	0	0
$372$	0.137536	0.00713089
$373$	−10.0035	−0.517960	−0.258980	−	0.965883i	$-0.583386\pi$
$373$	−10.0035	−0.517960	−0.258980	+	0.965883i	$0.583386\pi$
$374$	4.03736	0.208767
$375$	5.82154	0.300623
$376$	−9.34153	−0.481753
$377$	−7.44225	−0.383295
$378$	0	0
$379$	26.0898	1.34014	0.670071	−	0.742297i	$-0.266264\pi$
$379$	26.0898	1.34014	0.670071	+	0.742297i	$0.266264\pi$
$380$	−0.381874	−0.0195897
$381$	−20.8493	−1.06814
$382$	10.2591	0.524901
$383$	5.72761	0.292667	0.146334	−	0.989235i	$-0.453253\pi$
$383$	5.72761	0.292667	0.146334	+	0.989235i	$0.453253\pi$
$384$	−14.9292	−0.761853
$385$	0	0
$386$	22.7654	1.15873
$387$	0.647586	0.0329186
$388$	−2.32053	−0.117807
$389$	−23.2662	−1.17964	−0.589821	−	0.807534i	$-0.700802\pi$
$389$	−23.2662	−1.17964	−0.589821	+	0.807534i	$0.700802\pi$
$390$	−1.96717	−0.0996115
$391$	−2.26666	−0.114630
$392$	0	0
$393$	12.7024	0.640751
$394$	−28.1512	−1.41824
$395$	5.02900	0.253036
$396$	0.372414	0.0187145
$397$	−1.01969	−0.0511767	−0.0255884	−	0.999673i	$-0.508146\pi$
$397$	−1.01969	−0.0511767	−0.0255884	+	0.999673i	$0.508146\pi$
$398$	−12.9913	−0.651194
$399$	0	0
$400$	16.2779	0.813897
$401$	−22.1518	−1.10621	−0.553104	−	0.833112i	$-0.686557\pi$
$401$	−22.1518	−1.10621	−0.553104	+	0.833112i	$0.686557\pi$
$402$	−4.31827	−0.215376
$403$	0.657368	0.0327458
$404$	−1.65467	−0.0823227
$405$	−3.18125	−0.158078
$406$	0	0
$407$	−20.6442	−1.02329
$408$	−4.19435	−0.207651
$409$	2.87318	0.142070	0.0710349	−	0.997474i	$-0.477370\pi$
$409$	2.87318	0.142070	0.0710349	+	0.997474i	$0.477370\pi$
$410$	0.422016	0.0208419
$411$	23.6096	1.16458
$412$	−0.0665074	−0.00327658
$413$	0	0
$414$	1.21222	0.0595773
$415$	1.62997	0.0800123
$416$	4.22462	0.207129
$417$	−38.4819	−1.88447
$418$	−21.0938	−1.03173
$419$	10.4913	0.512534	0.256267	−	0.966606i	$-0.417507\pi$
$419$	10.4913	0.512534	0.256267	+	0.966606i	$0.417507\pi$
$420$	0	0
$421$	26.5839	1.29562	0.647810	−	0.761802i	$-0.275685\pi$
$421$	26.5839	1.29562	0.647810	+	0.761802i	$0.275685\pi$
$422$	5.08854	0.247706
$423$	0.981505	0.0477224
$424$	−26.2371	−1.27419
$425$	3.76395	0.182578
$426$	27.2653	1.32101
$427$	0	0
$428$	−2.53131	−0.122355
$429$	18.7417	0.904860
$430$	0.868072	0.0418621
$431$	6.24512	0.300817	0.150408	−	0.988624i	$-0.451941\pi$
$431$	6.24512	0.300817	0.150408	+	0.988624i	$0.451941\pi$
$432$	−16.2554	−0.782087
$433$	17.1956	0.826370	0.413185	−	0.910647i	$-0.364416\pi$
$433$	17.1956	0.826370	0.413185	+	0.910647i	$0.364416\pi$
$434$	0	0
$435$	1.71009	0.0819923
$436$	0.717732	0.0343731
$437$	11.8425	0.566503
$438$	−15.5963	−0.745219
$439$	30.6501	1.46285	0.731424	−	0.681923i	$-0.238856\pi$
$439$	30.6501	1.46285	0.731424	+	0.681923i	$0.238856\pi$
$440$	3.89277	0.185580
$441$	0	0
$442$	−2.57089	−0.122285
$443$	23.6997	1.12600	0.563002	−	0.826455i	$-0.309646\pi$
$443$	23.6997	1.12600	0.563002	+	0.826455i	$0.309646\pi$
$444$	2.75037	0.130527
$445$	−4.64299	−0.220099
$446$	27.0110	1.27901
$447$	−24.8555	−1.17563
$448$	0	0
$449$	−4.92623	−0.232483	−0.116242	−	0.993221i	$-0.537085\pi$
$449$	−4.92623	−0.232483	−0.116242	+	0.993221i	$0.537085\pi$
$450$	−2.01297	−0.0948925
$451$	−4.02065	−0.189325
$452$	0.562703	0.0264673
$453$	5.61697	0.263908
$454$	5.74217	0.269493
$455$	0	0
$456$	21.9140	1.02622
$457$	−18.7922	−0.879061	−0.439530	−	0.898228i	$-0.644855\pi$
$457$	−18.7922	−0.879061	−0.439530	+	0.898228i	$0.644855\pi$
$458$	−14.3948	−0.672627
$459$	−3.75873	−0.175443
$460$	−0.280268	−0.0130676
$461$	−32.8525	−1.53010	−0.765048	−	0.643974i	$-0.777285\pi$
$461$	−32.8525	−1.53010	−0.765048	+	0.643974i	$0.777285\pi$
$462$	0	0
$463$	21.9595	1.02055	0.510273	−	0.860012i	$-0.329544\pi$
$463$	21.9595	1.02055	0.510273	+	0.860012i	$0.329544\pi$
$464$	9.66530	0.448700
$465$	−0.151050	−0.00700480
$466$	22.4570	1.04030
$467$	18.0261	0.834150	0.417075	−	0.908872i	$-0.363055\pi$
$467$	18.0261	0.834150	0.417075	+	0.908872i	$0.363055\pi$
$468$	−0.237144	−0.0109620
$469$	0	0
$470$	1.31568	0.0606879
$471$	0.139308	0.00641898
$472$	−24.3934	−1.12280
$473$	−8.27035	−0.380271
$474$	−37.0091	−1.69988
$475$	−19.6653	−0.902305
$476$	0	0
$477$	2.75671	0.126221
$478$	−21.0572	−0.963133
$479$	−21.1147	−0.964756	−0.482378	−	0.875963i	$-0.660227\pi$
$479$	−21.1147	−0.964756	−0.482378	+	0.875963i	$0.660227\pi$
$480$	−0.970736	−0.0443079
$481$	13.1457	0.599393
$482$	29.3612	1.33737
$483$	0	0
$484$	−1.51980	−0.0690816
$485$	2.54855	0.115724
$486$	4.25605	0.193058
$487$	−26.8687	−1.21754	−0.608769	−	0.793348i	$-0.708336\pi$
$487$	−26.8687	−1.21754	−0.608769	+	0.793348i	$0.708336\pi$
$488$	−2.36991	−0.107281
$489$	25.3771	1.14759
$490$	0	0
$491$	18.3598	0.828568	0.414284	−	0.910148i	$-0.364032\pi$
$491$	18.3598	0.828568	0.414284	+	0.910148i	$0.364032\pi$
$492$	0.535660	0.0241494
$493$	2.23491	0.100655
$494$	13.4320	0.604334
$495$	−0.409009	−0.0183836
$496$	−0.853728	−0.0383335
$497$	0	0
$498$	−11.9952	−0.537518
$499$	−6.75174	−0.302249	−0.151125	−	0.988515i	$-0.548290\pi$
$499$	−6.75174	−0.302249	−0.151125	+	0.988515i	$0.548290\pi$
$500$	0.940734	0.0420709
$501$	−37.3355	−1.66803
$502$	−28.3208	−1.26402
$503$	38.7304	1.72690	0.863451	−	0.504433i	$-0.168299\pi$
$503$	38.7304	1.72690	0.863451	+	0.504433i	$0.168299\pi$
$504$	0	0
$505$	1.81726	0.0808670
$506$	−15.4813	−0.688228
$507$	11.7344	0.521143
$508$	−3.36914	−0.149481
$509$	18.4545	0.817979	0.408990	−	0.912539i	$-0.365881\pi$
$509$	18.4545	0.817979	0.408990	+	0.912539i	$0.365881\pi$
$510$	0.590742	0.0261585
$511$	0	0
$512$	−25.4125	−1.12309
$513$	19.6380	0.867040
$514$	−14.3655	−0.633634
$515$	0.0730427	0.00321864
$516$	1.10184	0.0485056
$517$	−12.5348	−0.551282
$518$	0	0
$519$	4.58694	0.201344
$520$	−2.47882	−0.108703
$521$	36.5131	1.59967	0.799834	−	0.600221i	$-0.204921\pi$
$521$	36.5131	1.59967	0.799834	+	0.600221i	$0.204921\pi$
$522$	−1.19524	−0.0523142
$523$	11.5441	0.504790	0.252395	−	0.967624i	$-0.418782\pi$
$523$	11.5441	0.504790	0.252395	+	0.967624i	$0.418782\pi$
$524$	2.05265	0.0896703
$525$	0	0
$526$	−10.6222	−0.463150
$527$	−0.197408	−0.00859922
$528$	−24.3400	−1.05926
$529$	−14.3085	−0.622107
$530$	3.69529	0.160513
$531$	2.56299	0.111224
$532$	0	0
$533$	2.56025	0.110897
$534$	34.1684	1.47861
$535$	2.78004	0.120192
$536$	−5.44143	−0.235034
$537$	−1.13637	−0.0490381
$538$	−35.1081	−1.51362
$539$	0	0
$540$	−0.464759	−0.0200000
$541$	28.3809	1.22019	0.610095	−	0.792328i	$-0.291131\pi$
$541$	28.3809	1.22019	0.610095	+	0.792328i	$0.291131\pi$
$542$	36.0652	1.54913
$543$	−3.06009	−0.131321
$544$	−1.26866	−0.0543932
$545$	−0.788259	−0.0337653
$546$	0	0
$547$	36.7309	1.57050	0.785250	−	0.619179i	$-0.212534\pi$
$547$	36.7309	1.57050	0.785250	+	0.619179i	$0.212534\pi$
$548$	3.81520	0.162977
$549$	0.249004	0.0106272
$550$	25.7078	1.09618
$551$	−11.6766	−0.497440
$552$	16.0833	0.684550
$553$	0	0
$554$	−23.3179	−0.990683
$555$	−3.02063	−0.128219
$556$	−6.21850	−0.263723
$557$	−3.50611	−0.148559	−0.0742794	−	0.997237i	$-0.523666\pi$
$557$	−3.50611	−0.148559	−0.0742794	+	0.997237i	$0.523666\pi$
$558$	0.105574	0.00446932
$559$	5.26635	0.222743
$560$	0	0
$561$	−5.62815	−0.237621
$562$	37.6589	1.58855
$563$	−27.3078	−1.15089	−0.575443	−	0.817842i	$-0.695170\pi$
$563$	−27.3078	−1.15089	−0.575443	+	0.817842i	$0.695170\pi$
$564$	1.66998	0.0703189
$565$	−0.617997	−0.0259993
$566$	−9.79964	−0.411910
$567$	0	0
$568$	34.3568	1.44158
$569$	31.7926	1.33281	0.666407	−	0.745588i	$-0.267831\pi$
$569$	31.7926	1.33281	0.666407	+	0.745588i	$0.267831\pi$
$570$	−3.08641	−0.129276
$571$	10.7183	0.448547	0.224274	−	0.974526i	$-0.427999\pi$
$571$	10.7183	0.448547	0.224274	+	0.974526i	$0.427999\pi$
$572$	3.02858	0.126631
$573$	−14.3014	−0.597448
$574$	0	0
$575$	−14.4329	−0.601894
$576$	2.77208	0.115503
$577$	40.2555	1.67586	0.837929	−	0.545780i	$-0.183766\pi$
$577$	40.2555	1.67586	0.837929	+	0.545780i	$0.183766\pi$
$578$	−21.4310	−0.891410
$579$	−31.7353	−1.31888
$580$	0.276342	0.0114745
$581$	0	0
$582$	−18.7552	−0.777426
$583$	−35.2060	−1.45808
$584$	−19.6528	−0.813238
$585$	0.260447	0.0107681
$586$	20.6746	0.854058
$587$	25.7915	1.06453	0.532264	−	0.846578i	$-0.321341\pi$
$587$	25.7915	1.06453	0.532264	+	0.846578i	$0.321341\pi$
$588$	0	0
$589$	1.03138	0.0424975
$590$	3.43562	0.141442
$591$	39.2432	1.61425
$592$	−17.0724	−0.701672
$593$	−21.4964	−0.882750	−0.441375	−	0.897323i	$-0.645509\pi$
$593$	−21.4964	−0.882750	−0.441375	+	0.897323i	$0.645509\pi$
$594$	−25.6721	−1.05334
$595$	0	0
$596$	−4.01654	−0.164524
$597$	18.1101	0.741195
$598$	9.85811	0.403128
$599$	21.8877	0.894308	0.447154	−	0.894457i	$-0.352438\pi$
$599$	21.8877	0.894308	0.447154	+	0.894457i	$0.352438\pi$
$600$	−26.7074	−1.09033
$601$	41.3680	1.68744	0.843718	−	0.536787i	$-0.180362\pi$
$601$	41.3680	1.68744	0.843718	+	0.536787i	$0.180362\pi$
$602$	0	0
$603$	0.571725	0.0232825
$604$	0.907676	0.0369328
$605$	1.66914	0.0678601
$606$	−13.3735	−0.543260
$607$	29.0991	1.18110	0.590549	−	0.807002i	$-0.298911\pi$
$607$	29.0991	1.18110	0.590549	+	0.807002i	$0.298911\pi$
$608$	6.62827	0.268812
$609$	0	0
$610$	0.333783	0.0135145
$611$	7.98188	0.322912
$612$	0.0712144	0.00287867
$613$	−15.9169	−0.642876	−0.321438	−	0.946931i	$-0.604166\pi$
$613$	−15.9169	−0.642876	−0.321438	+	0.946931i	$0.604166\pi$
$614$	−23.6868	−0.955923
$615$	−0.588296	−0.0237224
$616$	0	0
$617$	40.8921	1.64625	0.823127	−	0.567858i	$-0.192228\pi$
$617$	40.8921	1.64625	0.823127	+	0.567858i	$0.192228\pi$
$618$	−0.537531	−0.0216227
$619$	−43.7875	−1.75997	−0.879985	−	0.475001i	$-0.842448\pi$
$619$	−43.7875	−1.75997	−0.879985	+	0.475001i	$0.842448\pi$
$620$	−0.0244090	−0.000980291 0
$621$	14.4129	0.578369
$622$	31.3733	1.25795
$623$	0	0
$624$	15.4991	0.620461
$625$	23.4448	0.937792
$626$	−4.02188	−0.160747
$627$	29.4051	1.17432
$628$	0.0225116	0.000898309 0
$629$	−3.94766	−0.157403
$630$	0	0
$631$	0.969147	0.0385811	0.0192906	−	0.999814i	$-0.493859\pi$
$631$	0.969147	0.0385811	0.0192906	+	0.999814i	$0.493859\pi$
$632$	−46.6350	−1.85504
$633$	−7.09350	−0.281941
$634$	−16.1581	−0.641719
$635$	3.70021	0.146838
$636$	4.69040	0.185986
$637$	0	0
$638$	15.2644	0.604325
$639$	−3.60983	−0.142803
$640$	2.64955	0.104733
$641$	6.57231	0.259591	0.129795	−	0.991541i	$-0.458568\pi$
$641$	6.57231	0.259591	0.129795	+	0.991541i	$0.458568\pi$
$642$	−20.4587	−0.807442
$643$	7.22914	0.285089	0.142545	−	0.989788i	$-0.454472\pi$
$643$	7.22914	0.285089	0.142545	+	0.989788i	$0.454472\pi$
$644$	0	0
$645$	−1.21011	−0.0476479
$646$	−4.03363	−0.158701
$647$	−7.48606	−0.294307	−0.147154	−	0.989114i	$-0.547011\pi$
$647$	−7.48606	−0.294307	−0.147154	+	0.989114i	$0.547011\pi$
$648$	29.5004	1.15888
$649$	−32.7320	−1.28484
$650$	−16.3701	−0.642087
$651$	0	0
$652$	4.10082	0.160600
$653$	0.341890	0.0133792	0.00668959	−	0.999978i	$-0.497871\pi$
$653$	0.341890	0.0133792	0.00668959	+	0.999978i	$0.497871\pi$
$654$	5.80091	0.226833
$655$	−2.25435	−0.0880847
$656$	−3.32502	−0.129820
$657$	2.06490	0.0805592
$658$	0	0
$659$	−29.6057	−1.15327	−0.576637	−	0.817000i	$-0.695635\pi$
$659$	−29.6057	−1.15327	−0.576637	+	0.817000i	$0.695635\pi$
$660$	−0.695908	−0.0270882
$661$	48.8521	1.90013	0.950064	−	0.312056i	$-0.101018\pi$
$661$	48.8521	1.90013	0.950064	+	0.312056i	$0.101018\pi$
$662$	−14.0319	−0.545366
$663$	3.58387	0.139186
$664$	−15.1151	−0.586579
$665$	0	0
$666$	2.11122	0.0818082
$667$	−8.56978	−0.331823
$668$	−6.03324	−0.233433
$669$	−37.6537	−1.45578
$670$	0.766383	0.0296080
$671$	−3.18004	−0.122764
$672$	0	0
$673$	45.6528	1.75979	0.879893	−	0.475172i	$-0.157614\pi$
$673$	45.6528	1.75979	0.879893	+	0.475172i	$0.157614\pi$
$674$	−11.1589	−0.429826
$675$	−23.9336	−0.921205
$676$	1.89622	0.0729316
$677$	4.14873	0.159449	0.0797244	−	0.996817i	$-0.474596\pi$
$677$	4.14873	0.159449	0.0797244	+	0.996817i	$0.474596\pi$
$678$	4.54793	0.174662
$679$	0	0
$680$	0.744390	0.0285461
$681$	−8.00468	−0.306740
$682$	−1.34830	−0.0516289
$683$	42.2253	1.61570	0.807852	−	0.589385i	$-0.200630\pi$
$683$	42.2253	1.61570	0.807852	+	0.589385i	$0.200630\pi$
$684$	−0.372070	−0.0142264
$685$	−4.19010	−0.160096
$686$	0	0
$687$	20.0666	0.765590
$688$	−6.83945	−0.260752
$689$	22.4183	0.854070
$690$	−2.26520	−0.0862348
$691$	40.4674	1.53945	0.769726	−	0.638374i	$-0.220393\pi$
$691$	40.4674	1.53945	0.769726	+	0.638374i	$0.220393\pi$
$692$	0.741228	0.0281773
$693$	0	0
$694$	8.11314	0.307971
$695$	6.82956	0.259060
$696$	−15.8580	−0.601095
$697$	−0.768845	−0.0291221
$698$	−28.7490	−1.08816
$699$	−31.3054	−1.18408
$700$	0	0
$701$	−10.5854	−0.399803	−0.199902	−	0.979816i	$-0.564062\pi$
$701$	−10.5854	−0.399803	−0.199902	+	0.979816i	$0.564062\pi$
$702$	16.3474	0.616992
$703$	20.6251	0.777890
$704$	−35.4024	−1.33428
$705$	−1.83408	−0.0690755
$706$	12.5252	0.471393
$707$	0	0
$708$	4.36079	0.163889
$709$	15.5892	0.585466	0.292733	−	0.956194i	$-0.405435\pi$
$709$	15.5892	0.585466	0.292733	+	0.956194i	$0.405435\pi$
$710$	−4.83889	−0.181600
$711$	4.89989	0.183760
$712$	43.0554	1.61357
$713$	0.756962	0.0283484
$714$	0	0
$715$	−3.32618	−0.124392
$716$	−0.183633	−0.00686267
$717$	29.3541	1.09625
$718$	5.92863	0.221255
$719$	−5.09574	−0.190039	−0.0950195	−	0.995475i	$-0.530291\pi$
$719$	−5.09574	−0.190039	−0.0950195	+	0.995475i	$0.530291\pi$
$720$	−0.338244	−0.0126056
$721$	0	0
$722$	−3.74085	−0.139220
$723$	−40.9300	−1.52220
$724$	−0.494497	−0.0183778
$725$	14.2307	0.528516
$726$	−12.2834	−0.455880
$727$	40.1362	1.48857	0.744284	−	0.667863i	$-0.232791\pi$
$727$	40.1362	1.48857	0.744284	+	0.667863i	$0.232791\pi$
$728$	0	0
$729$	23.6031	0.874188
$730$	2.76794	0.102446
$731$	−1.58149	−0.0584934
$732$	0.423667	0.0156592
$733$	−6.78056	−0.250446	−0.125223	−	0.992129i	$-0.539965\pi$
$733$	−6.78056	−0.250446	−0.125223	+	0.992129i	$0.539965\pi$
$734$	−37.6847	−1.39097
$735$	0	0
$736$	4.86467	0.179314
$737$	−7.30153	−0.268955
$738$	0.411181	0.0151358
$739$	24.7445	0.910242	0.455121	−	0.890430i	$-0.349596\pi$
$739$	24.7445	0.910242	0.455121	+	0.890430i	$0.349596\pi$
$740$	−0.488119	−0.0179436
$741$	−18.7244	−0.687858
$742$	0	0
$743$	11.9753	0.439330	0.219665	−	0.975575i	$-0.429503\pi$
$743$	11.9753	0.439330	0.219665	+	0.975575i	$0.429503\pi$
$744$	1.40072	0.0513530
$745$	4.41122	0.161615
$746$	−13.0651	−0.478347
$747$	1.58813	0.0581065
$748$	−0.909483	−0.0332540
$749$	0	0
$750$	7.60327	0.277632
$751$	−39.0897	−1.42641	−0.713203	−	0.700958i	$-0.752756\pi$
$751$	−39.0897	−1.42641	−0.713203	+	0.700958i	$0.752756\pi$
$752$	−10.3661	−0.378013
$753$	39.4796	1.43872
$754$	−9.72002	−0.353982
$755$	−0.996868	−0.0362797
$756$	0	0
$757$	5.47105	0.198849	0.0994243	−	0.995045i	$-0.468300\pi$
$757$	5.47105	0.198849	0.0994243	+	0.995045i	$0.468300\pi$
$758$	34.0748	1.23765
$759$	21.5812	0.783348
$760$	−3.88917	−0.141075
$761$	15.3445	0.556239	0.278120	−	0.960546i	$-0.410289\pi$
$761$	15.3445	0.556239	0.278120	+	0.960546i	$0.410289\pi$
$762$	−27.2303	−0.986451
$763$	0	0
$764$	−2.31103	−0.0836102
$765$	−0.0782122	−0.00282777
$766$	7.48059	0.270285
$767$	20.8429	0.752595
$768$	12.5640	0.453364
$769$	5.24795	0.189246	0.0946229	−	0.995513i	$-0.469835\pi$
$769$	5.24795	0.189246	0.0946229	+	0.995513i	$0.469835\pi$
$770$	0	0
$771$	20.0257	0.721208
$772$	−5.12828	−0.184571
$773$	−38.7179	−1.39258	−0.696292	−	0.717758i	$-0.745168\pi$
$773$	−38.7179	−1.39258	−0.696292	+	0.717758i	$0.745168\pi$
$774$	0.845785	0.0304011
$775$	−1.25699	−0.0451523
$776$	−23.6333	−0.848385
$777$	0	0
$778$	−30.3870	−1.08943
$779$	4.01694	0.143922
$780$	0.443137	0.0158669
$781$	46.1013	1.64964
$782$	−2.96039	−0.105863
$783$	−14.2110	−0.507859
$784$	0	0
$785$	−0.0247236	−0.000882424 0
$786$	16.5901	0.591748
$787$	8.13349	0.289928	0.144964	−	0.989437i	$-0.453693\pi$
$787$	8.13349	0.289928	0.144964	+	0.989437i	$0.453693\pi$
$788$	6.34152	0.225907
$789$	14.8075	0.527161
$790$	6.56817	0.233685
$791$	0	0
$792$	3.79283	0.134772
$793$	2.02497	0.0719087
$794$	−1.33177	−0.0472629
$795$	−5.15129	−0.182698
$796$	2.92650	0.103727
$797$	22.6267	0.801478	0.400739	−	0.916192i	$-0.368753\pi$
$797$	22.6267	0.801478	0.400739	+	0.916192i	$0.368753\pi$
$798$	0	0
$799$	−2.39696	−0.0847984
$800$	−8.07812	−0.285605
$801$	−4.52378	−0.159840
$802$	−28.9316	−1.02161
$803$	−26.3709	−0.930608
$804$	0.972762	0.0343067
$805$	0	0
$806$	0.858561	0.0302415
$807$	48.9413	1.72281
$808$	−16.8518	−0.592845
$809$	12.3260	0.433360	0.216680	−	0.976243i	$-0.430477\pi$
$809$	12.3260	0.433360	0.216680	+	0.976243i	$0.430477\pi$
$810$	−4.15490	−0.145988
$811$	38.8273	1.36341	0.681706	−	0.731627i	$-0.261239\pi$
$811$	38.8273	1.36341	0.681706	+	0.731627i	$0.261239\pi$
$812$	0	0
$813$	−50.2754	−1.76324
$814$	−26.9625	−0.945036
$815$	−4.50378	−0.157761
$816$	−4.65439	−0.162936
$817$	8.26270	0.289075
$818$	3.75255	0.131205
$819$	0	0
$820$	−0.0950659	−0.00331985
$821$	41.0853	1.43389	0.716943	−	0.697132i	$-0.245541\pi$
$821$	41.0853	1.43389	0.716943	+	0.697132i	$0.245541\pi$
$822$	30.8356	1.07551
$823$	29.3053	1.02152	0.510760	−	0.859723i	$-0.329364\pi$
$823$	29.3053	1.02152	0.510760	+	0.859723i	$0.329364\pi$
$824$	−0.677340	−0.0235963
$825$	−35.8371	−1.24769
$826$	0	0
$827$	−16.8960	−0.587532	−0.293766	−	0.955877i	$-0.594909\pi$
$827$	−16.8960	−0.587532	−0.293766	+	0.955877i	$0.594909\pi$
$828$	−0.273072	−0.00948992
$829$	7.53870	0.261830	0.130915	−	0.991394i	$-0.458208\pi$
$829$	7.53870	0.261830	0.130915	+	0.991394i	$0.458208\pi$
$830$	2.12884	0.0738932
$831$	32.5055	1.12760
$832$	22.5434	0.781551
$833$	0	0
$834$	−50.2597	−1.74035
$835$	6.62609	0.229305
$836$	4.75172	0.164342
$837$	1.25525	0.0433876
$838$	13.7023	0.473337
$839$	−7.07641	−0.244305	−0.122152	−	0.992511i	$-0.538980\pi$
$839$	−7.07641	−0.244305	−0.122152	+	0.992511i	$0.538980\pi$
$840$	0	0
$841$	−20.5503	−0.708630
$842$	34.7201	1.19653
$843$	−52.4971	−1.80810
$844$	−1.14628	−0.0394565
$845$	−2.08255	−0.0716420
$846$	1.28190	0.0440727
$847$	0	0
$848$	−29.1148	−0.999807
$849$	13.6609	0.468839
$850$	4.91594	0.168615
$851$	15.1373	0.518901
$852$	−6.14195	−0.210420
$853$	−2.09405	−0.0716989	−0.0358494	−	0.999357i	$-0.511414\pi$
$853$	−2.09405	−0.0716989	−0.0358494	+	0.999357i	$0.511414\pi$
$854$	0	0
$855$	0.408631	0.0139749
$856$	−25.7799	−0.881140
$857$	14.8228	0.506338	0.253169	−	0.967422i	$-0.418527\pi$
$857$	14.8228	0.506338	0.253169	+	0.967422i	$0.418527\pi$
$858$	24.4778	0.835659
$859$	−23.9186	−0.816094	−0.408047	−	0.912961i	$-0.633790\pi$
$859$	−23.9186	−0.816094	−0.408047	+	0.912961i	$0.633790\pi$
$860$	−0.195547	−0.00666811
$861$	0	0
$862$	8.15649	0.277811
$863$	−51.7925	−1.76304	−0.881518	−	0.472150i	$-0.843478\pi$
$863$	−51.7925	−1.76304	−0.881518	+	0.472150i	$0.843478\pi$
$864$	8.06692	0.274442
$865$	−0.814065	−0.0276790
$866$	22.4585	0.763171
$867$	29.8751	1.01461
$868$	0	0
$869$	−62.5767	−2.12277
$870$	2.23347	0.0757218
$871$	4.64943	0.157540
$872$	7.30969	0.247537
$873$	2.48312	0.0840409
$874$	15.4670	0.523179
$875$	0	0
$876$	3.51332	0.118704
$877$	−24.2956	−0.820405	−0.410202	−	0.911995i	$-0.634542\pi$
$877$	−24.2956	−0.820405	−0.410202	+	0.911995i	$0.634542\pi$
$878$	40.0308	1.35097
$879$	−28.8207	−0.972097
$880$	4.31973	0.145618
$881$	−18.5028	−0.623375	−0.311687	−	0.950185i	$-0.600894\pi$
$881$	−18.5028	−0.623375	−0.311687	+	0.950185i	$0.600894\pi$
$882$	0	0
$883$	−0.418028	−0.0140678	−0.00703388	−	0.999975i	$-0.502239\pi$
$883$	−0.418028	−0.0140678	−0.00703388	+	0.999975i	$0.502239\pi$
$884$	0.579136	0.0194784
$885$	−4.78930	−0.160991
$886$	30.9531	1.03989
$887$	−58.8634	−1.97644	−0.988219	−	0.153045i	$-0.951092\pi$
$887$	−58.8634	−1.97644	−0.988219	+	0.153045i	$0.951092\pi$
$888$	28.0109	0.939985
$889$	0	0
$890$	−6.06401	−0.203266
$891$	39.5848	1.32614
$892$	−6.08466	−0.203729
$893$	12.5232	0.419075
$894$	−32.4628	−1.08572
$895$	0.201677	0.00674132
$896$	0	0
$897$	−13.7424	−0.458844
$898$	−6.43395	−0.214704
$899$	−0.746358	−0.0248924
$900$	0.453455	0.0151152
$901$	−6.73223	−0.224283
$902$	−5.25121	−0.174846
$903$	0	0
$904$	5.73081	0.190604
$905$	0.543088	0.0180529
$906$	7.33609	0.243725
$907$	−44.7965	−1.48744	−0.743721	−	0.668490i	$-0.766941\pi$
$907$	−44.7965	−1.48744	−0.743721	+	0.668490i	$0.766941\pi$
$908$	−1.29352	−0.0429269
$909$	1.77060	0.0587272
$910$	0	0
$911$	−10.3343	−0.342391	−0.171195	−	0.985237i	$-0.554763\pi$
$911$	−10.3343	−0.342391	−0.171195	+	0.985237i	$0.554763\pi$
$912$	24.3175	0.805233
$913$	−20.2820	−0.671237
$914$	−24.5437	−0.811833
$915$	−0.465299	−0.0153823
$916$	3.24268	0.107141
$917$	0	0
$918$	−4.90912	−0.162025
$919$	−33.7007	−1.11168	−0.555842	−	0.831288i	$-0.687604\pi$
$919$	−33.7007	−1.11168	−0.555842	+	0.831288i	$0.687604\pi$
$920$	−2.85437	−0.0941058
$921$	33.0198	1.08804
$922$	−42.9073	−1.41308
$923$	−29.3562	−0.966271
$924$	0	0
$925$	−25.1366	−0.826486
$926$	28.6804	0.942498
$927$	0.0711674	0.00233744
$928$	−4.79652	−0.157454
$929$	22.3554	0.733457	0.366728	−	0.930328i	$-0.380478\pi$
$929$	22.3554	0.733457	0.366728	+	0.930328i	$0.380478\pi$
$930$	−0.197281	−0.00646909
$931$	0	0
$932$	−5.05881	−0.165707
$933$	−43.7348	−1.43181
$934$	23.5432	0.770356
$935$	0.998852	0.0326660
$936$	−2.41518	−0.0789425
$937$	−30.1830	−0.986036	−0.493018	−	0.870019i	$-0.664106\pi$
$937$	−30.1830	−0.986036	−0.493018	+	0.870019i	$0.664106\pi$
$938$	0	0
$939$	5.60656	0.182963
$940$	−0.296379	−0.00966681
$941$	−61.1449	−1.99327	−0.996633	−	0.0819963i	$-0.973870\pi$
$941$	−61.1449	−1.99327	−0.996633	+	0.0819963i	$0.973870\pi$
$942$	0.181945	0.00592808
$943$	2.94814	0.0960047
$944$	−27.0689	−0.881017
$945$	0	0
$946$	−10.8016	−0.351189
$947$	−45.7272	−1.48594	−0.742968	−	0.669327i	$-0.766582\pi$
$947$	−45.7272	−1.48594	−0.742968	+	0.669327i	$0.766582\pi$
$948$	8.33691	0.270770
$949$	16.7923	0.545102
$950$	−25.6840	−0.833299
$951$	22.5246	0.730410
$952$	0	0
$953$	−35.7342	−1.15754	−0.578772	−	0.815490i	$-0.696468\pi$
$953$	−35.7342	−1.15754	−0.578772	+	0.815490i	$0.696468\pi$
$954$	3.60042	0.116568
$955$	2.53812	0.0821317
$956$	4.74348	0.153415
$957$	−21.2789	−0.687848
$958$	−27.5771	−0.890975
$959$	0	0
$960$	−5.18003	−0.167185
$961$	−30.9341	−0.997873
$962$	17.1691	0.553553
$963$	2.70867	0.0872857
$964$	−6.61410	−0.213026
$965$	5.63221	0.181307
$966$	0	0
$967$	−32.3674	−1.04087	−0.520433	−	0.853903i	$-0.674229\pi$
$967$	−32.3674	−1.04087	−0.520433	+	0.853903i	$0.674229\pi$
$968$	−15.4783	−0.497490
$969$	5.62294	0.180635
$970$	3.32856	0.106874
$971$	3.18710	0.102279	0.0511394	−	0.998692i	$-0.483715\pi$
$971$	3.18710	0.102279	0.0511394	+	0.998692i	$0.483715\pi$
$972$	−0.958746	−0.0307518
$973$	0	0
$974$	−35.0921	−1.12442
$975$	22.8201	0.730829
$976$	−2.62984	−0.0841791
$977$	−50.3000	−1.60924	−0.804619	−	0.593791i	$-0.797631\pi$
$977$	−50.3000	−1.60924	−0.804619	+	0.593791i	$0.797631\pi$
$978$	33.1440	1.05983
$979$	57.7734	1.84645
$980$	0	0
$981$	−0.768021	−0.0245210
$982$	23.9790	0.765201
$983$	10.3580	0.330370	0.165185	−	0.986263i	$-0.447178\pi$
$983$	10.3580	0.330370	0.165185	+	0.986263i	$0.447178\pi$
$984$	5.45540	0.173912
$985$	−6.96467	−0.221913
$986$	2.91892	0.0929575
$987$	0	0
$988$	−3.02578	−0.0962627
$989$	6.06423	0.192831
$990$	−0.534190	−0.0169777
$991$	−16.2136	−0.515044	−0.257522	−	0.966272i	$-0.582906\pi$
$991$	−16.2136	−0.515044	−0.257522	+	0.966272i	$0.582906\pi$
$992$	0.423673	0.0134516
$993$	19.5607	0.620741
$994$	0	0
$995$	−3.21407	−0.101893
$996$	2.70212	0.0856199
$997$	13.3468	0.422698	0.211349	−	0.977411i	$-0.432214\pi$
$997$	13.3468	0.422698	0.211349	+	0.977411i	$0.432214\pi$
$998$	−8.81817	−0.279134
$999$	25.1017	0.794184

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.u.1.15	yes	20
7.6	odd	2		2009.2.a.t.1.15	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2009.2.a.t.1.15	✓	20	7.6	odd	2
2009.2.a.u.1.15	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2009 = 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2009.a (trivial)

\(f(q)\)	\(=\)	\(q+1.30606 q^{2} -1.82067 q^{3} -0.294211 q^{4} +0.323122 q^{5} -2.37790 q^{6} -2.99637 q^{8} +0.314826 q^{9} +O(q^{10})\)	\(q+1.30606 q^{2} -1.82067 q^{3} -0.294211 q^{4} +0.323122 q^{5} -2.37790 q^{6} -2.99637 q^{8} +0.314826 q^{9} +0.422016 q^{10} -4.02065 q^{11} +0.535660 q^{12} +2.56025 q^{13} -0.588296 q^{15} -3.32502 q^{16} -0.768845 q^{17} +0.411181 q^{18} +4.01694 q^{19} -0.0950659 q^{20} -5.25121 q^{22} +2.94814 q^{23} +5.45540 q^{24} -4.89559 q^{25} +3.34384 q^{26} +4.88881 q^{27} -2.90684 q^{29} -0.768350 q^{30} +0.256759 q^{31} +1.65008 q^{32} +7.32027 q^{33} -1.00416 q^{34} -0.0926252 q^{36} +5.13453 q^{37} +5.24635 q^{38} -4.66136 q^{39} -0.968193 q^{40} +1.00000 q^{41} +2.05697 q^{43} +1.18292 q^{44} +0.101727 q^{45} +3.85045 q^{46} +3.11761 q^{47} +6.05375 q^{48} -6.39393 q^{50} +1.39981 q^{51} -0.753255 q^{52} +8.75629 q^{53} +6.38507 q^{54} -1.29916 q^{55} -7.31350 q^{57} -3.79651 q^{58} +8.14097 q^{59} +0.173083 q^{60} +0.790925 q^{61} +0.335342 q^{62} +8.80514 q^{64} +0.827273 q^{65} +9.56070 q^{66} +1.81601 q^{67} +0.226203 q^{68} -5.36758 q^{69} -11.4661 q^{71} -0.943336 q^{72} +6.55885 q^{73} +6.70600 q^{74} +8.91324 q^{75} -1.18183 q^{76} -6.08802 q^{78} +15.5638 q^{79} -1.07438 q^{80} -9.84536 q^{81} +1.30606 q^{82} +5.04446 q^{83} -0.248430 q^{85} +2.68652 q^{86} +5.29239 q^{87} +12.0474 q^{88} -14.3692 q^{89} +0.132861 q^{90} -0.867376 q^{92} -0.467473 q^{93} +4.07178 q^{94} +1.29796 q^{95} -3.00425 q^{96} +7.88729 q^{97} -1.26581 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 8 q^{3} + 18 q^{4} + 8 q^{5} + 12 q^{6} - 6 q^{8} + 16 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 8 * q^3 + 18 * q^4 + 8 * q^5 + 12 * q^6 - 6 * q^8 + 16 * q^9	\( 20 q - 2 q^{2} + 8 q^{3} + 18 q^{4} + 8 q^{5} + 12 q^{6} - 6 q^{8} + 16 q^{9} + 16 q^{10} + 6 q^{12} + 12 q^{13} + 14 q^{16} + 8 q^{17} - 18 q^{18} + 36 q^{19} + 24 q^{20} - 8 q^{22} - 12 q^{23} + 36 q^{24} + 20 q^{25} - 22 q^{26} + 32 q^{27} + 4 q^{29} + 28 q^{30} + 80 q^{31} + 6 q^{32} - 12 q^{33} + 48 q^{34} + 26 q^{36} + 4 q^{37} + 12 q^{38} - 28 q^{39} - 4 q^{40} + 20 q^{41} - 20 q^{44} + 40 q^{45} + 8 q^{46} + 32 q^{47} + 16 q^{48} + 6 q^{50} - 20 q^{51} + 36 q^{52} + 4 q^{53} - 50 q^{54} + 64 q^{55} - 4 q^{57} + 32 q^{59} + 20 q^{60} + 44 q^{61} - 8 q^{62} - 30 q^{64} - 8 q^{65} + 32 q^{66} - 4 q^{67} - 48 q^{68} - 24 q^{69} + 8 q^{71} - 8 q^{72} + 48 q^{73} - 38 q^{74} + 24 q^{75} + 84 q^{76} + 30 q^{78} - 4 q^{79} + 56 q^{80} - 2 q^{82} + 8 q^{83} - 12 q^{85} - 24 q^{86} + 40 q^{87} - 48 q^{88} + 20 q^{89} + 48 q^{90} - 50 q^{92} + 48 q^{93} + 26 q^{94} + 20 q^{95} + 70 q^{96} + 8 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 8 * q^3 + 18 * q^4 + 8 * q^5 + 12 * q^6 - 6 * q^8 + 16 * q^9 + 16 * q^10 + 6 * q^12 + 12 * q^13 + 14 * q^16 + 8 * q^17 - 18 * q^18 + 36 * q^19 + 24 * q^20 - 8 * q^22 - 12 * q^23 + 36 * q^24 + 20 * q^25 - 22 * q^26 + 32 * q^27 + 4 * q^29 + 28 * q^30 + 80 * q^31 + 6 * q^32 - 12 * q^33 + 48 * q^34 + 26 * q^36 + 4 * q^37 + 12 * q^38 - 28 * q^39 - 4 * q^40 + 20 * q^41 - 20 * q^44 + 40 * q^45 + 8 * q^46 + 32 * q^47 + 16 * q^48 + 6 * q^50 - 20 * q^51 + 36 * q^52 + 4 * q^53 - 50 * q^54 + 64 * q^55 - 4 * q^57 + 32 * q^59 + 20 * q^60 + 44 * q^61 - 8 * q^62 - 30 * q^64 - 8 * q^65 + 32 * q^66 - 4 * q^67 - 48 * q^68 - 24 * q^69 + 8 * q^71 - 8 * q^72 + 48 * q^73 - 38 * q^74 + 24 * q^75 + 84 * q^76 + 30 * q^78 - 4 * q^79 + 56 * q^80 - 2 * q^82 + 8 * q^83 - 12 * q^85 - 24 * q^86 + 40 * q^87 - 48 * q^88 + 20 * q^89 + 48 * q^90 - 50 * q^92 + 48 * q^93 + 26 * q^94 + 20 * q^95 + 70 * q^96 + 8 * q^97 - 8 * q^99

Introduction

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Database

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