LMFDB - Embedded newform 2009.2.a.u.1.10

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			1.10
Root			$0.212475$ 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)

$f(q)$	$=$	$q-0.212475 q^{2} -2.41608 q^{3} -1.95485 q^{4} +3.68342 q^{5} +0.513357 q^{6} +0.840308 q^{8} +2.83745 q^{9} +O(q^{10})$	\(q-0.212475 q^{2} -2.41608 q^{3} -1.95485 q^{4} +3.68342 q^{5} +0.513357 q^{6} +0.840308 q^{8} +2.83745 q^{9} -0.782635 q^{10} +4.70463 q^{11} +4.72309 q^{12} +2.04510 q^{13} -8.89944 q^{15} +3.73116 q^{16} -0.454077 q^{17} -0.602887 q^{18} +1.50395 q^{19} -7.20055 q^{20} -0.999617 q^{22} +3.25474 q^{23} -2.03025 q^{24} +8.56758 q^{25} -0.434532 q^{26} +0.392736 q^{27} -9.36389 q^{29} +1.89091 q^{30} +4.02598 q^{31} -2.47339 q^{32} -11.3668 q^{33} +0.0964799 q^{34} -5.54680 q^{36} -2.83827 q^{37} -0.319551 q^{38} -4.94113 q^{39} +3.09521 q^{40} +1.00000 q^{41} -3.85536 q^{43} -9.19688 q^{44} +10.4515 q^{45} -0.691551 q^{46} +12.1334 q^{47} -9.01480 q^{48} -1.82040 q^{50} +1.09709 q^{51} -3.99787 q^{52} -9.79127 q^{53} -0.0834465 q^{54} +17.3291 q^{55} -3.63366 q^{57} +1.98959 q^{58} -8.81943 q^{59} +17.3971 q^{60} -3.69960 q^{61} -0.855420 q^{62} -6.93679 q^{64} +7.53296 q^{65} +2.41516 q^{66} +1.17912 q^{67} +0.887653 q^{68} -7.86371 q^{69} +11.4601 q^{71} +2.38433 q^{72} -4.66537 q^{73} +0.603062 q^{74} -20.7000 q^{75} -2.94000 q^{76} +1.04987 q^{78} -13.3805 q^{79} +13.7434 q^{80} -9.46123 q^{81} -0.212475 q^{82} +11.7960 q^{83} -1.67255 q^{85} +0.819167 q^{86} +22.6239 q^{87} +3.95334 q^{88} +18.6464 q^{89} -2.22069 q^{90} -6.36254 q^{92} -9.72710 q^{93} -2.57805 q^{94} +5.53966 q^{95} +5.97592 q^{96} +5.83554 q^{97} +13.3492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.212475	−0.150243	−0.0751213	−	0.997174i	$-0.523934\pi$
$2$	−0.212475	−0.150243	−0.0751213	+	0.997174i	$0.523934\pi$
$3$	−2.41608	−1.39493	−0.697463	−	0.716621i	$-0.745688\pi$
$3$	−2.41608	−1.39493	−0.697463	+	0.716621i	$0.745688\pi$
$4$	−1.95485	−0.977427
$5$	3.68342	1.64728	0.823638	−	0.567116i	$-0.191941\pi$
$5$	3.68342	1.64728	0.823638	+	0.567116i	$0.191941\pi$
$6$	0.513357	0.209577
$7$	0	0
$7$	0	0
$8$	0.840308	0.297094
$9$	2.83745	0.945816
$10$	−0.782635	−0.247491
$11$	4.70463	1.41850	0.709250	−	0.704957i	$-0.249034\pi$
$11$	4.70463	1.41850	0.709250	+	0.704957i	$0.249034\pi$
$12$	4.72309	1.36344
$13$	2.04510	0.567208	0.283604	−	0.958941i	$-0.408470\pi$
$13$	2.04510	0.567208	0.283604	+	0.958941i	$0.408470\pi$
$14$	0	0
$15$	−8.89944	−2.29783
$16$	3.73116	0.932791
$17$	−0.454077	−0.110130	−0.0550649	−	0.998483i	$-0.517537\pi$
$17$	−0.454077	−0.110130	−0.0550649	+	0.998483i	$0.517537\pi$
$18$	−0.602887	−0.142102
$19$	1.50395	0.345029	0.172514	−	0.985007i	$-0.444811\pi$
$19$	1.50395	0.345029	0.172514	+	0.985007i	$0.444811\pi$
$20$	−7.20055	−1.61009
$21$	0	0
$22$	−0.999617	−0.213119
$23$	3.25474	0.678660	0.339330	−	0.940667i	$-0.389800\pi$
$23$	3.25474	0.678660	0.339330	+	0.940667i	$0.389800\pi$
$24$	−2.03025	−0.414423
$25$	8.56758	1.71352
$26$	−0.434532	−0.0852188
$27$	0.392736	0.0755820
$28$	0	0
$29$	−9.36389	−1.73883	−0.869416	−	0.494082i	$-0.835504\pi$
$29$	−9.36389	−1.73883	−0.869416	+	0.494082i	$0.835504\pi$
$30$	1.89091	0.345231
$31$	4.02598	0.723088	0.361544	−	0.932355i	$-0.382250\pi$
$31$	4.02598	0.723088	0.361544	+	0.932355i	$0.382250\pi$
$32$	−2.47339	−0.437239
$33$	−11.3668	−1.97870
$34$	0.0964799	0.0165462
$35$	0	0
$36$	−5.54680	−0.924467
$37$	−2.83827	−0.466609	−0.233304	−	0.972404i	$-0.574954\pi$
$37$	−2.83827	−0.466609	−0.233304	+	0.972404i	$0.574954\pi$
$38$	−0.319551	−0.0518380
$39$	−4.94113	−0.791213
$40$	3.09521	0.489395
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−3.85536	−0.587936	−0.293968	−	0.955815i	$-0.594976\pi$
$43$	−3.85536	−0.587936	−0.293968	+	0.955815i	$0.594976\pi$
$44$	−9.19688	−1.38648
$45$	10.4515	1.55802
$46$	−0.691551	−0.101964
$47$	12.1334	1.76984	0.884922	−	0.465740i	$-0.154212\pi$
$47$	12.1334	1.76984	0.884922	+	0.465740i	$0.154212\pi$
$48$	−9.01480	−1.30117
$49$	0	0
$50$	−1.82040	−0.257443
$51$	1.09709	0.153623
$52$	−3.99787	−0.554405
$53$	−9.79127	−1.34493	−0.672467	−	0.740127i	$-0.734765\pi$
$53$	−9.79127	−1.34493	−0.672467	+	0.740127i	$0.734765\pi$
$54$	−0.0834465	−0.0113556
$55$	17.3291	2.33666
$56$	0	0
$57$	−3.63366	−0.481290
$58$	1.98959	0.261246
$59$	−8.81943	−1.14819	−0.574096	−	0.818788i	$-0.694646\pi$
$59$	−8.81943	−1.14819	−0.574096	+	0.818788i	$0.694646\pi$
$60$	17.3971	2.24596
$61$	−3.69960	−0.473685	−0.236843	−	0.971548i	$-0.576113\pi$
$61$	−3.69960	−0.473685	−0.236843	+	0.971548i	$0.576113\pi$
$62$	−0.855420	−0.108638
$63$	0	0
$64$	−6.93679	−0.867099
$65$	7.53296	0.934348
$66$	2.41516	0.297285
$67$	1.17912	0.144053	0.0720265	−	0.997403i	$-0.477053\pi$
$67$	1.17912	0.144053	0.0720265	+	0.997403i	$0.477053\pi$
$68$	0.887653	0.107644
$69$	−7.86371	−0.946680
$70$	0	0
$71$	11.4601	1.36007	0.680034	−	0.733181i	$-0.261965\pi$
$71$	11.4601	1.36007	0.680034	+	0.733181i	$0.261965\pi$
$72$	2.38433	0.280996
$73$	−4.66537	−0.546040	−0.273020	−	0.962008i	$-0.588022\pi$
$73$	−4.66537	−0.546040	−0.273020	+	0.962008i	$0.588022\pi$
$74$	0.603062	0.0701045
$75$	−20.7000	−2.39023
$76$	−2.94000	−0.337241
$77$	0	0
$78$	1.04987	0.118874
$79$	−13.3805	−1.50543	−0.752714	−	0.658347i	$-0.771256\pi$
$79$	−13.3805	−1.50543	−0.752714	+	0.658347i	$0.771256\pi$
$80$	13.7434	1.53656
$81$	−9.46123	−1.05125
$82$	−0.212475	−0.0234639
$83$	11.7960	1.29478	0.647392	−	0.762157i	$-0.275860\pi$
$83$	11.7960	1.29478	0.647392	+	0.762157i	$0.275860\pi$
$84$	0	0
$85$	−1.67255	−0.181414
$86$	0.819167	0.0883330
$87$	22.6239	2.42554
$88$	3.95334	0.421428
$89$	18.6464	1.97652	0.988259	−	0.152789i	$-0.0488256\pi$
$89$	18.6464	1.97652	0.988259	+	0.152789i	$0.0488256\pi$
$90$	−2.22069	−0.234081
$91$	0	0
$92$	−6.36254	−0.663341
$93$	−9.72710	−1.00865
$94$	−2.57805	−0.265906
$95$	5.53966	0.568358
$96$	5.97592	0.609915
$97$	5.83554	0.592510	0.296255	−	0.955109i	$-0.404262\pi$
$97$	5.83554	0.592510	0.296255	+	0.955109i	$0.404262\pi$
$98$	0	0
$99$	13.3492	1.34164
$100$	−16.7484	−1.67484
$101$	15.7964	1.57180	0.785901	−	0.618353i	$-0.212200\pi$
$101$	15.7964	1.57180	0.785901	+	0.618353i	$0.212200\pi$
$102$	−0.233103	−0.0230807
$103$	−0.509589	−0.0502113	−0.0251057	−	0.999685i	$-0.507992\pi$
$103$	−0.509589	−0.0502113	−0.0251057	+	0.999685i	$0.507992\pi$
$104$	1.71851	0.168514
$105$	0	0
$106$	2.08040	0.202066
$107$	9.67041	0.934874	0.467437	−	0.884026i	$-0.345178\pi$
$107$	9.67041	0.934874	0.467437	+	0.884026i	$0.345178\pi$
$108$	−0.767741	−0.0738759
$109$	6.46769	0.619492	0.309746	−	0.950819i	$-0.399756\pi$
$109$	6.46769	0.619492	0.309746	+	0.950819i	$0.399756\pi$
$110$	−3.68201	−0.351066
$111$	6.85749	0.650885
$112$	0	0
$113$	12.3977	1.16627	0.583137	−	0.812374i	$-0.301825\pi$
$113$	12.3977	1.16627	0.583137	+	0.812374i	$0.301825\pi$
$114$	0.772061	0.0723102
$115$	11.9886	1.11794
$116$	18.3050	1.69958
$117$	5.80286	0.536475
$118$	1.87391	0.172507
$119$	0	0
$120$	−7.47827	−0.682669
$121$	11.1336	1.01214
$122$	0.786072	0.0711676
$123$	−2.41608	−0.217851
$124$	−7.87021	−0.706765
$125$	13.1409	1.17536
$126$	0	0
$127$	−13.1230	−1.16448	−0.582240	−	0.813017i	$-0.697823\pi$
$127$	−13.1230	−1.16448	−0.582240	+	0.813017i	$0.697823\pi$
$128$	6.42068	0.567514
$129$	9.31485	0.820127
$130$	−1.60057	−0.140379
$131$	3.68577	0.322028	0.161014	−	0.986952i	$-0.448524\pi$
$131$	3.68577	0.322028	0.161014	+	0.986952i	$0.448524\pi$
$132$	22.2204	1.93404
$133$	0	0
$134$	−0.250535	−0.0216429
$135$	1.44661	0.124504
$136$	−0.381564	−0.0327188
$137$	−16.3160	−1.39397	−0.696985	−	0.717085i	$-0.745476\pi$
$137$	−16.3160	−1.39397	−0.696985	+	0.717085i	$0.745476\pi$
$138$	1.67084	0.142232
$139$	18.7327	1.58889	0.794443	−	0.607339i	$-0.207763\pi$
$139$	18.7327	1.58889	0.794443	+	0.607339i	$0.207763\pi$
$140$	0	0
$141$	−29.3154	−2.46880
$142$	−2.43499	−0.204340
$143$	9.62144	0.804585
$144$	10.5870	0.882249
$145$	−34.4911	−2.86433
$146$	0.991274	0.0820384
$147$	0	0
$148$	5.54841	0.456076
$149$	1.60409	0.131412	0.0657062	−	0.997839i	$-0.479070\pi$
$149$	1.60409	0.131412	0.0657062	+	0.997839i	$0.479070\pi$
$150$	4.39823	0.359114
$151$	14.1631	1.15257	0.576287	−	0.817248i	$-0.304501\pi$
$151$	14.1631	1.15257	0.576287	+	0.817248i	$0.304501\pi$
$152$	1.26378	0.102506
$153$	−1.28842	−0.104163
$154$	0	0
$155$	14.8294	1.19112
$156$	9.65918	0.773353
$157$	−12.4945	−0.997171	−0.498586	−	0.866840i	$-0.666147\pi$
$157$	−12.4945	−0.997171	−0.498586	+	0.866840i	$0.666147\pi$
$158$	2.84303	0.226179
$159$	23.6565	1.87608
$160$	−9.11055	−0.720252
$161$	0	0
$162$	2.01027	0.157942
$163$	7.06249	0.553177	0.276588	−	0.960989i	$-0.410796\pi$
$163$	7.06249	0.553177	0.276588	+	0.960989i	$0.410796\pi$
$164$	−1.95485	−0.152648
$165$	−41.8686	−3.25947
$166$	−2.50636	−0.194532
$167$	−18.2808	−1.41461	−0.707306	−	0.706907i	$-0.750090\pi$
$167$	−18.2808	−1.41461	−0.707306	+	0.706907i	$0.750090\pi$
$168$	0	0
$169$	−8.81757	−0.678275
$170$	0.355376	0.0272561
$171$	4.26737	0.326334
$172$	7.53666	0.574665
$173$	−10.2412	−0.778623	−0.389311	−	0.921106i	$-0.627287\pi$
$173$	−10.2412	−0.778623	−0.389311	+	0.921106i	$0.627287\pi$
$174$	−4.80702	−0.364419
$175$	0	0
$176$	17.5538	1.32316
$177$	21.3085	1.60164
$178$	−3.96190	−0.296957
$179$	17.3851	1.29942	0.649711	−	0.760181i	$-0.274890\pi$
$179$	17.3851	1.29942	0.649711	+	0.760181i	$0.274890\pi$
$180$	−20.4312	−1.52285
$181$	13.7482	1.02190	0.510949	−	0.859611i	$-0.329294\pi$
$181$	13.7482	1.02190	0.510949	+	0.859611i	$0.329294\pi$
$182$	0	0
$183$	8.93853	0.660755
$184$	2.73498	0.201626
$185$	−10.4545	−0.768633
$186$	2.06677	0.151543
$187$	−2.13626	−0.156219
$188$	−23.7191	−1.72989
$189$	0	0
$190$	−1.17704	−0.0853915
$191$	−3.00028	−0.217092	−0.108546	−	0.994091i	$-0.534620\pi$
$191$	−3.00028	−0.217092	−0.108546	+	0.994091i	$0.534620\pi$
$192$	16.7599	1.20954
$193$	−23.1572	−1.66689	−0.833446	−	0.552601i	$-0.813635\pi$
$193$	−23.1572	−1.66689	−0.833446	+	0.552601i	$0.813635\pi$
$194$	−1.23991	−0.0890201
$195$	−18.2002	−1.30335
$196$	0	0
$197$	2.54318	0.181194	0.0905972	−	0.995888i	$-0.471122\pi$
$197$	2.54318	0.181194	0.0905972	+	0.995888i	$0.471122\pi$
$198$	−2.83636	−0.201572
$199$	−2.68278	−0.190177	−0.0950885	−	0.995469i	$-0.530313\pi$
$199$	−2.68278	−0.190177	−0.0950885	+	0.995469i	$0.530313\pi$
$200$	7.19940	0.509075
$201$	−2.84886	−0.200943
$202$	−3.35634	−0.236151
$203$	0	0
$204$	−2.14464	−0.150155
$205$	3.68342	0.257261
$206$	0.108275	0.00754388
$207$	9.23516	0.641888
$208$	7.63060	0.529087
$209$	7.07552	0.489424
$210$	0	0
$211$	10.1090	0.695932	0.347966	−	0.937507i	$-0.386872\pi$
$211$	10.1090	0.695932	0.347966	+	0.937507i	$0.386872\pi$
$212$	19.1405	1.31458
$213$	−27.6886	−1.89719
$214$	−2.05472	−0.140458
$215$	−14.2009	−0.968493
$216$	0.330019	0.0224549
$217$	0	0
$218$	−1.37422	−0.0930741
$219$	11.2719	0.761685
$220$	−33.8760	−2.28392
$221$	−0.928631	−0.0624665
$222$	−1.45705	−0.0977905
$223$	13.5036	0.904271	0.452135	−	0.891949i	$-0.350662\pi$
$223$	13.5036	0.904271	0.452135	+	0.891949i	$0.350662\pi$
$224$	0	0
$225$	24.3101	1.62067
$226$	−2.63420	−0.175224
$227$	−19.0850	−1.26672	−0.633359	−	0.773858i	$-0.718325\pi$
$227$	−19.0850	−1.26672	−0.633359	+	0.773858i	$0.718325\pi$
$228$	7.10327	0.470426
$229$	23.2308	1.53513	0.767566	−	0.640970i	$-0.221468\pi$
$229$	23.2308	1.53513	0.767566	+	0.640970i	$0.221468\pi$
$230$	−2.54727	−0.167962
$231$	0	0
$232$	−7.86855	−0.516596
$233$	15.1027	0.989411	0.494706	−	0.869061i	$-0.335276\pi$
$233$	15.1027	0.989411	0.494706	+	0.869061i	$0.335276\pi$
$234$	−1.23296	−0.0806014
$235$	44.6925	2.91542
$236$	17.2407	1.12227
$237$	32.3285	2.09996
$238$	0	0
$239$	21.8323	1.41221	0.706107	−	0.708105i	$-0.250450\pi$
$239$	21.8323	1.41221	0.706107	+	0.708105i	$0.250450\pi$
$240$	−33.2053	−2.14339
$241$	3.01150	0.193988	0.0969940	−	0.995285i	$-0.469077\pi$
$241$	3.01150	0.193988	0.0969940	+	0.995285i	$0.469077\pi$
$242$	−2.36561	−0.152067
$243$	21.6809	1.39083
$244$	7.23218	0.462993
$245$	0	0
$246$	0.513357	0.0327304
$247$	3.07572	0.195703
$248$	3.38306	0.214825
$249$	−28.5002	−1.80613
$250$	−2.79211	−0.176589
$251$	−30.5642	−1.92920	−0.964599	−	0.263723i	$-0.915050\pi$
$251$	−30.5642	−1.92920	−0.964599	+	0.263723i	$0.915050\pi$
$252$	0	0
$253$	15.3124	0.962680
$254$	2.78831	0.174954
$255$	4.04103	0.253059
$256$	12.5094	0.781835
$257$	−1.70253	−0.106201	−0.0531004	−	0.998589i	$-0.516910\pi$
$257$	−1.70253	−0.106201	−0.0531004	+	0.998589i	$0.516910\pi$
$258$	−1.97917	−0.123218
$259$	0	0
$260$	−14.7258	−0.913257
$261$	−26.5696	−1.64462
$262$	−0.783135	−0.0483822
$263$	25.5379	1.57474	0.787368	−	0.616484i	$-0.211443\pi$
$263$	25.5379	1.57474	0.787368	+	0.616484i	$0.211443\pi$
$264$	−9.55159	−0.587860
$265$	−36.0654	−2.21548
$266$	0	0
$267$	−45.0513	−2.75709
$268$	−2.30502	−0.140801
$269$	0.498003	0.0303638	0.0151819	−	0.999885i	$-0.495167\pi$
$269$	0.498003	0.0303638	0.0151819	+	0.999885i	$0.495167\pi$
$270$	−0.307369	−0.0187059
$271$	25.1876	1.53004	0.765019	−	0.644008i	$-0.222730\pi$
$271$	25.1876	1.53004	0.765019	+	0.644008i	$0.222730\pi$
$272$	−1.69423	−0.102728
$273$	0	0
$274$	3.46674	0.209434
$275$	40.3073	2.43062
$276$	15.3724	0.925311
$277$	−13.3456	−0.801862	−0.400931	−	0.916108i	$-0.631313\pi$
$277$	−13.3456	−0.801862	−0.400931	+	0.916108i	$0.631313\pi$
$278$	−3.98023	−0.238718
$279$	11.4235	0.683908
$280$	0	0
$281$	−19.4957	−1.16302	−0.581508	−	0.813541i	$-0.697537\pi$
$281$	−19.4957	−1.16302	−0.581508	+	0.813541i	$0.697537\pi$
$282$	6.22878	0.370919
$283$	−26.4285	−1.57101	−0.785505	−	0.618856i	$-0.787597\pi$
$283$	−26.4285	−1.57101	−0.785505	+	0.618856i	$0.787597\pi$
$284$	−22.4029	−1.32937
$285$	−13.3843	−0.792816
$286$	−2.04432	−0.120883
$287$	0	0
$288$	−7.01813	−0.413547
$289$	−16.7938	−0.987871
$290$	7.32851	0.430345
$291$	−14.0991	−0.826507
$292$	9.12011	0.533714
$293$	−11.7739	−0.687840	−0.343920	−	0.938999i	$-0.611755\pi$
$293$	−11.7739	−0.687840	−0.343920	+	0.938999i	$0.611755\pi$
$294$	0	0
$295$	−32.4856	−1.89139
$296$	−2.38502	−0.138627
$297$	1.84768	0.107213
$298$	−0.340830	−0.0197437
$299$	6.65626	0.384942
$300$	40.4654	2.33627
$301$	0	0
$302$	−3.00930	−0.173166
$303$	−38.1654	−2.19255
$304$	5.61147	0.321840
$305$	−13.6272	−0.780290
$306$	0.273757	0.0156496
$307$	4.59614	0.262316	0.131158	−	0.991362i	$-0.458131\pi$
$307$	4.59614	0.262316	0.131158	+	0.991362i	$0.458131\pi$
$308$	0	0
$309$	1.23121	0.0700411
$310$	−3.15087	−0.178958
$311$	−3.34185	−0.189499	−0.0947496	−	0.995501i	$-0.530205\pi$
$311$	−3.34185	−0.189499	−0.0947496	+	0.995501i	$0.530205\pi$
$312$	−4.15207	−0.235064
$313$	6.20774	0.350882	0.175441	−	0.984490i	$-0.443865\pi$
$313$	6.20774	0.350882	0.175441	+	0.984490i	$0.443865\pi$
$314$	2.65477	0.149818
$315$	0	0
$316$	26.1570	1.47145
$317$	20.5364	1.15344	0.576720	−	0.816942i	$-0.304332\pi$
$317$	20.5364	1.15344	0.576720	+	0.816942i	$0.304332\pi$
$318$	−5.02642	−0.281867
$319$	−44.0537	−2.46653
$320$	−25.5511	−1.42835
$321$	−23.3645	−1.30408
$322$	0	0
$323$	−0.682907	−0.0379979
$324$	18.4953	1.02752
$325$	17.5215	0.971920
$326$	−1.50060	−0.0831106
$327$	−15.6265	−0.864145
$328$	0.840308	0.0463982
$329$	0	0
$330$	8.89604	0.489711
$331$	−2.25910	−0.124171	−0.0620857	−	0.998071i	$-0.519775\pi$
$331$	−2.25910	−0.124171	−0.0620857	+	0.998071i	$0.519775\pi$
$332$	−23.0595	−1.26556
$333$	−8.05345	−0.441326
$334$	3.88422	0.212535
$335$	4.34321	0.237295
$336$	0	0
$337$	13.9155	0.758025	0.379012	−	0.925392i	$-0.376264\pi$
$337$	13.9155	0.758025	0.379012	+	0.925392i	$0.376264\pi$
$338$	1.87351	0.101906
$339$	−29.9538	−1.62687
$340$	3.26960	0.177319
$341$	18.9408	1.02570
$342$	−0.906710	−0.0490292
$343$	0	0
$344$	−3.23969	−0.174672
$345$	−28.9654	−1.55944
$346$	2.17600	0.116982
$347$	2.36020	0.126702	0.0633510	−	0.997991i	$-0.479821\pi$
$347$	2.36020	0.126702	0.0633510	+	0.997991i	$0.479821\pi$
$348$	−44.2265	−2.37079
$349$	−18.3720	−0.983431	−0.491716	−	0.870756i	$-0.663630\pi$
$349$	−18.3720	−0.983431	−0.491716	+	0.870756i	$0.663630\pi$
$350$	0	0
$351$	0.803183	0.0428707
$352$	−11.6364	−0.620223
$353$	30.1873	1.60671	0.803354	−	0.595502i	$-0.203047\pi$
$353$	30.1873	1.60671	0.803354	+	0.595502i	$0.203047\pi$
$354$	−4.52751	−0.240635
$355$	42.2125	2.24041
$356$	−36.4511	−1.93190
$357$	0	0
$358$	−3.69390	−0.195229
$359$	−32.2616	−1.70270	−0.851352	−	0.524595i	$-0.824217\pi$
$359$	−32.2616	−1.70270	−0.851352	+	0.524595i	$0.824217\pi$
$360$	8.78249	0.462878
$361$	−16.7381	−0.880955
$362$	−2.92115	−0.153532
$363$	−26.8997	−1.41187
$364$	0	0
$365$	−17.1845	−0.899478
$366$	−1.89921	−0.0992735
$367$	5.52742	0.288529	0.144264	−	0.989539i	$-0.453918\pi$
$367$	5.52742	0.288529	0.144264	+	0.989539i	$0.453918\pi$
$368$	12.1440	0.633048
$369$	2.83745	0.147712
$370$	2.22133	0.115481
$371$	0	0
$372$	19.0151	0.985885
$373$	−30.7373	−1.59152	−0.795759	−	0.605614i	$-0.792928\pi$
$373$	−30.7373	−1.59152	−0.795759	+	0.605614i	$0.792928\pi$
$374$	0.453903	0.0234708
$375$	−31.7495	−1.63953
$376$	10.1958	0.525809
$377$	−19.1501	−0.986280
$378$	0	0
$379$	11.5379	0.592662	0.296331	−	0.955085i	$-0.404237\pi$
$379$	11.5379	0.592662	0.296331	+	0.955085i	$0.404237\pi$
$380$	−10.8292	−0.555528
$381$	31.7063	1.62436
$382$	0.637484	0.0326165
$383$	13.7766	0.703953	0.351976	−	0.936009i	$-0.385510\pi$
$383$	13.7766	0.703953	0.351976	+	0.936009i	$0.385510\pi$
$384$	−15.5129	−0.791639
$385$	0	0
$386$	4.92033	0.250438
$387$	−10.9394	−0.556080
$388$	−11.4076	−0.579135
$389$	18.6967	0.947960	0.473980	−	0.880536i	$-0.342817\pi$
$389$	18.6967	0.947960	0.473980	+	0.880536i	$0.342817\pi$
$390$	3.86710	0.195818
$391$	−1.47790	−0.0747406
$392$	0	0
$393$	−8.90513	−0.449204
$394$	−0.540363	−0.0272231
$395$	−49.2861	−2.47985
$396$	−26.0957	−1.31136
$397$	6.90888	0.346747	0.173373	−	0.984856i	$-0.444533\pi$
$397$	6.90888	0.346747	0.173373	+	0.984856i	$0.444533\pi$
$398$	0.570023	0.0285727
$399$	0	0
$400$	31.9670	1.59835
$401$	−3.45987	−0.172777	−0.0863887	−	0.996262i	$-0.527533\pi$
$401$	−3.45987	−0.172777	−0.0863887	+	0.996262i	$0.527533\pi$
$402$	0.605312	0.0301902
$403$	8.23353	0.410141
$404$	−30.8797	−1.53632
$405$	−34.8497	−1.73169
$406$	0	0
$407$	−13.3530	−0.661885
$408$	0.921890	0.0456403
$409$	−14.8881	−0.736169	−0.368085	−	0.929792i	$-0.619986\pi$
$409$	−14.8881	−0.736169	−0.368085	+	0.929792i	$0.619986\pi$
$410$	−0.782635	−0.0386516
$411$	39.4208	1.94449
$412$	0.996173	0.0490779
$413$	0	0
$414$	−1.96224	−0.0964388
$415$	43.4498	2.13287
$416$	−5.05834	−0.248005
$417$	−45.2597	−2.21638
$418$	−1.50337	−0.0735323
$419$	−0.553878	−0.0270587	−0.0135294	−	0.999908i	$-0.504307\pi$
$419$	−0.553878	−0.0270587	−0.0135294	+	0.999908i	$0.504307\pi$
$420$	0	0
$421$	−15.2063	−0.741110	−0.370555	−	0.928811i	$-0.620832\pi$
$421$	−15.2063	−0.741110	−0.370555	+	0.928811i	$0.620832\pi$
$422$	−2.14791	−0.104559
$423$	34.4280	1.67395
$424$	−8.22768	−0.399571
$425$	−3.89034	−0.188709
$426$	5.88314	0.285039
$427$	0	0
$428$	−18.9042	−0.913771
$429$	−23.2462	−1.12234
$430$	3.01734	0.145509
$431$	13.4754	0.649089	0.324545	−	0.945870i	$-0.394789\pi$
$431$	13.4754	0.649089	0.324545	+	0.945870i	$0.394789\pi$
$432$	1.46536	0.0705022
$433$	13.6086	0.653986	0.326993	−	0.945027i	$-0.393965\pi$
$433$	13.6086	0.653986	0.326993	+	0.945027i	$0.393965\pi$
$434$	0	0
$435$	83.3334	3.99553
$436$	−12.6434	−0.605509
$437$	4.89495	0.234157
$438$	−2.39500	−0.114437
$439$	−13.0375	−0.622245	−0.311123	−	0.950370i	$-0.600705\pi$
$439$	−13.0375	−0.622245	−0.311123	+	0.950370i	$0.600705\pi$
$440$	14.5618	0.694207
$441$	0	0
$442$	0.197311	0.00938512
$443$	−27.3068	−1.29739	−0.648693	−	0.761050i	$-0.724684\pi$
$443$	−27.3068	−1.29739	−0.648693	+	0.761050i	$0.724684\pi$
$444$	−13.4054	−0.636192
$445$	68.6826	3.25587
$446$	−2.86919	−0.135860
$447$	−3.87562	−0.183311
$448$	0	0
$449$	3.26426	0.154050	0.0770250	−	0.997029i	$-0.475458\pi$
$449$	3.26426	0.154050	0.0770250	+	0.997029i	$0.475458\pi$
$450$	−5.16528	−0.243494
$451$	4.70463	0.221533
$452$	−24.2356	−1.13995
$453$	−34.2191	−1.60775
$454$	4.05510	0.190315
$455$	0	0
$456$	−3.05339	−0.142988
$457$	−32.6834	−1.52887	−0.764433	−	0.644703i	$-0.776981\pi$
$457$	−32.6834	−1.52887	−0.764433	+	0.644703i	$0.776981\pi$
$458$	−4.93596	−0.230642
$459$	−0.178332	−0.00832383
$460$	−23.4359	−1.09270
$461$	14.2414	0.663289	0.331644	−	0.943404i	$-0.392397\pi$
$461$	14.2414	0.663289	0.331644	+	0.943404i	$0.392397\pi$
$462$	0	0
$463$	23.8877	1.11016	0.555079	−	0.831798i	$-0.312688\pi$
$463$	23.8877	1.11016	0.555079	+	0.831798i	$0.312688\pi$
$464$	−34.9382	−1.62197
$465$	−35.8290	−1.66153
$466$	−3.20895	−0.148652
$467$	−11.2245	−0.519407	−0.259704	−	0.965688i	$-0.583625\pi$
$467$	−11.2245	−0.519407	−0.259704	+	0.965688i	$0.583625\pi$
$468$	−11.3438	−0.524365
$469$	0	0
$470$	−9.49605	−0.438020
$471$	30.1878	1.39098
$472$	−7.41103	−0.341120
$473$	−18.1380	−0.833988
$474$	−6.86899	−0.315503
$475$	12.8852	0.591212
$476$	0	0
$477$	−27.7822	−1.27206
$478$	−4.63882	−0.212175
$479$	0.435390	0.0198935	0.00994674	−	0.999951i	$-0.496834\pi$
$479$	0.435390	0.0198935	0.00994674	+	0.999951i	$0.496834\pi$
$480$	22.0118	1.00470
$481$	−5.80454	−0.264664
$482$	−0.639870	−0.0291453
$483$	0	0
$484$	−21.7645	−0.989298
$485$	21.4947	0.976026
$486$	−4.60665	−0.208962
$487$	22.2133	1.00658	0.503291	−	0.864117i	$-0.332122\pi$
$487$	22.2133	1.00658	0.503291	+	0.864117i	$0.332122\pi$
$488$	−3.10880	−0.140729
$489$	−17.0635	−0.771640
$490$	0	0
$491$	7.74117	0.349354	0.174677	−	0.984626i	$-0.444112\pi$
$491$	7.74117	0.349354	0.174677	+	0.984626i	$0.444112\pi$
$492$	4.72309	0.212933
$493$	4.25192	0.191497
$494$	−0.653513	−0.0294030
$495$	49.1706	2.21005
$496$	15.0216	0.674490
$497$	0	0
$498$	6.05558	0.271357
$499$	22.3992	1.00273	0.501363	−	0.865237i	$-0.332832\pi$
$499$	22.3992	1.00273	0.501363	+	0.865237i	$0.332832\pi$
$500$	−25.6885	−1.14883
$501$	44.1679	1.97328
$502$	6.49414	0.289847
$503$	2.97353	0.132583	0.0662915	−	0.997800i	$-0.478883\pi$
$503$	2.97353	0.132583	0.0662915	+	0.997800i	$0.478883\pi$
$504$	0	0
$505$	58.1848	2.58919
$506$	−3.25349	−0.144635
$507$	21.3040	0.946142
$508$	25.6536	1.13819
$509$	35.1918	1.55985	0.779924	−	0.625875i	$-0.215258\pi$
$509$	35.1918	1.55985	0.779924	+	0.625875i	$0.215258\pi$
$510$	−0.858617	−0.0380202
$511$	0	0
$512$	−15.4993	−0.684979
$513$	0.590653	0.0260780
$514$	0.361745	0.0159559
$515$	−1.87703	−0.0827119
$516$	−18.2092	−0.801615
$517$	57.0834	2.51052
$518$	0	0
$519$	24.7435	1.08612
$520$	6.33000	0.277589
$521$	−18.5461	−0.812518	−0.406259	−	0.913758i	$-0.633167\pi$
$521$	−18.5461	−0.812518	−0.406259	+	0.913758i	$0.633167\pi$
$522$	5.64537	0.247091
$523$	−21.1665	−0.925548	−0.462774	−	0.886476i	$-0.653146\pi$
$523$	−21.1665	−0.925548	−0.462774	+	0.886476i	$0.653146\pi$
$524$	−7.20515	−0.314758
$525$	0	0
$526$	−5.42617	−0.236592
$527$	−1.82810	−0.0796334
$528$	−42.4113	−1.84572
$529$	−12.4067	−0.539421
$530$	7.66299	0.332859
$531$	−25.0247	−1.08598
$532$	0	0
$533$	2.04510	0.0885831
$534$	9.57227	0.414233
$535$	35.6202	1.53999
$536$	0.990828	0.0427972
$537$	−42.0038	−1.81260
$538$	−0.105813	−0.00456193
$539$	0	0
$540$	−2.82791	−0.121694
$541$	19.6408	0.844424	0.422212	−	0.906497i	$-0.361254\pi$
$541$	19.6408	0.844424	0.422212	+	0.906497i	$0.361254\pi$
$542$	−5.35174	−0.229877
$543$	−33.2168	−1.42547
$544$	1.12311	0.0481530
$545$	23.8232	1.02047
$546$	0	0
$547$	−5.02901	−0.215025	−0.107513	−	0.994204i	$-0.534289\pi$
$547$	−5.02901	−0.215025	−0.107513	+	0.994204i	$0.534289\pi$
$548$	31.8954	1.36250
$549$	−10.4974	−0.448019
$550$	−8.56430	−0.365183
$551$	−14.0828	−0.599947
$552$	−6.60794	−0.281253
$553$	0	0
$554$	2.83562	0.120474
$555$	25.2590	1.07219
$556$	−36.6197	−1.55302
$557$	18.4825	0.783130	0.391565	−	0.920151i	$-0.371934\pi$
$557$	18.4825	0.783130	0.391565	+	0.920151i	$0.371934\pi$
$558$	−2.42721	−0.102752
$559$	−7.88458	−0.333482
$560$	0	0
$561$	5.16139	0.217914
$562$	4.14235	0.174734
$563$	−46.1610	−1.94545	−0.972727	−	0.231953i	$-0.925488\pi$
$563$	−46.1610	−1.94545	−0.972727	+	0.231953i	$0.925488\pi$
$564$	57.3073	2.41307
$565$	45.6658	1.92118
$566$	5.61539	0.236032
$567$	0	0
$568$	9.63004	0.404067
$569$	−39.2665	−1.64614	−0.823068	−	0.567943i	$-0.807739\pi$
$569$	−39.2665	−1.64614	−0.823068	+	0.567943i	$0.807739\pi$
$570$	2.84383	0.119115
$571$	−1.58563	−0.0663565	−0.0331783	−	0.999449i	$-0.510563\pi$
$571$	−1.58563	−0.0663565	−0.0331783	+	0.999449i	$0.510563\pi$
$572$	−18.8085	−0.786424
$573$	7.24891	0.302828
$574$	0	0
$575$	27.8852	1.16289
$576$	−19.6828	−0.820117
$577$	35.1087	1.46160	0.730798	−	0.682594i	$-0.239148\pi$
$577$	35.1087	1.46160	0.730798	+	0.682594i	$0.239148\pi$
$578$	3.56827	0.148420
$579$	55.9497	2.32519
$580$	67.4252	2.79968
$581$	0	0
$582$	2.99572	0.124176
$583$	−46.0643	−1.90779
$584$	−3.92034	−0.162225
$585$	21.3744	0.883722
$586$	2.50167	0.103343
$587$	24.8490	1.02563	0.512814	−	0.858500i	$-0.328603\pi$
$587$	24.8490	1.02563	0.512814	+	0.858500i	$0.328603\pi$
$588$	0	0
$589$	6.05486	0.249486
$590$	6.90239	0.284167
$591$	−6.14454	−0.252753
$592$	−10.5901	−0.435249
$593$	24.5301	1.00733	0.503665	−	0.863899i	$-0.331985\pi$
$593$	24.5301	1.00733	0.503665	+	0.863899i	$0.331985\pi$
$594$	−0.392585	−0.0161080
$595$	0	0
$596$	−3.13577	−0.128446
$597$	6.48181	0.265283
$598$	−1.41429	−0.0578346
$599$	−27.3299	−1.11667	−0.558335	−	0.829616i	$-0.688560\pi$
$599$	−27.3299	−1.11667	−0.558335	+	0.829616i	$0.688560\pi$
$600$	−17.3943	−0.710121
$601$	8.86399	0.361570	0.180785	−	0.983523i	$-0.442136\pi$
$601$	8.86399	0.361570	0.180785	+	0.983523i	$0.442136\pi$
$602$	0	0
$603$	3.34571	0.136248
$604$	−27.6867	−1.12656
$605$	41.0097	1.66728
$606$	8.10920	0.329414
$607$	−27.7423	−1.12603	−0.563013	−	0.826448i	$-0.690358\pi$
$607$	−27.7423	−1.12603	−0.563013	+	0.826448i	$0.690358\pi$
$608$	−3.71985	−0.150860
$609$	0	0
$610$	2.89543	0.117233
$611$	24.8141	1.00387
$612$	2.51867	0.101811
$613$	−11.2580	−0.454705	−0.227353	−	0.973812i	$-0.573007\pi$
$613$	−11.2580	−0.454705	−0.227353	+	0.973812i	$0.573007\pi$
$614$	−0.976565	−0.0394110
$615$	−8.89944	−0.358860
$616$	0	0
$617$	28.1644	1.13385	0.566927	−	0.823768i	$-0.308132\pi$
$617$	28.1644	1.13385	0.566927	+	0.823768i	$0.308132\pi$
$618$	−0.261601	−0.0105231
$619$	31.4720	1.26497	0.632483	−	0.774574i	$-0.282036\pi$
$619$	31.4720	1.26497	0.632483	+	0.774574i	$0.282036\pi$
$620$	−28.9893	−1.16424
$621$	1.27825	0.0512945
$622$	0.710061	0.0284708
$623$	0	0
$624$	−18.4361	−0.738037
$625$	5.56551	0.222620
$626$	−1.31899	−0.0527174
$627$	−17.0950	−0.682710
$628$	24.4250	0.974662
$629$	1.28879	0.0513875
$630$	0	0
$631$	35.5446	1.41501	0.707504	−	0.706709i	$-0.249821\pi$
$631$	35.5446	1.41501	0.707504	+	0.706709i	$0.249821\pi$
$632$	−11.2438	−0.447253
$633$	−24.4242	−0.970774
$634$	−4.36347	−0.173296
$635$	−48.3376	−1.91822
$636$	−46.2450	−1.83373
$637$	0	0
$638$	9.36031	0.370578
$639$	32.5175	1.28637
$640$	23.6501	0.934851
$641$	9.73693	0.384586	0.192293	−	0.981338i	$-0.438408\pi$
$641$	9.73693	0.384586	0.192293	+	0.981338i	$0.438408\pi$
$642$	4.96437	0.195928
$643$	−17.4067	−0.686455	−0.343227	−	0.939252i	$-0.611520\pi$
$643$	−17.4067	−0.686455	−0.343227	+	0.939252i	$0.611520\pi$
$644$	0	0
$645$	34.3105	1.35098
$646$	0.145101	0.00570891
$647$	−15.8615	−0.623580	−0.311790	−	0.950151i	$-0.600929\pi$
$647$	−15.8615	−0.623580	−0.311790	+	0.950151i	$0.600929\pi$
$648$	−7.95034	−0.312319
$649$	−41.4922	−1.62871
$650$	−3.72289	−0.146024
$651$	0	0
$652$	−13.8061	−0.540690
$653$	23.2170	0.908551	0.454276	−	0.890861i	$-0.349898\pi$
$653$	23.2170	0.908551	0.454276	+	0.890861i	$0.349898\pi$
$654$	3.32023	0.129831
$655$	13.5763	0.530468
$656$	3.73116	0.145677
$657$	−13.2377	−0.516453
$658$	0	0
$659$	27.9669	1.08943	0.544717	−	0.838620i	$-0.316637\pi$
$659$	27.9669	1.08943	0.544717	+	0.838620i	$0.316637\pi$
$660$	81.8471	3.18589
$661$	5.78640	0.225065	0.112532	−	0.993648i	$-0.464104\pi$
$661$	5.78640	0.225065	0.112532	+	0.993648i	$0.464104\pi$
$662$	0.480002	0.0186558
$663$	2.24365	0.0871361
$664$	9.91231	0.384672
$665$	0	0
$666$	1.71116	0.0663060
$667$	−30.4770	−1.18008
$668$	35.7363	1.38268
$669$	−32.6259	−1.26139
$670$	−0.922824	−0.0356518
$671$	−17.4053	−0.671923
$672$	0	0
$673$	−9.57647	−0.369146	−0.184573	−	0.982819i	$-0.559090\pi$
$673$	−9.57647	−0.369146	−0.184573	+	0.982819i	$0.559090\pi$
$674$	−2.95669	−0.113888
$675$	3.36479	0.129511
$676$	17.2371	0.662964
$677$	0.855969	0.0328976	0.0164488	−	0.999865i	$-0.494764\pi$
$677$	0.855969	0.0328976	0.0164488	+	0.999865i	$0.494764\pi$
$678$	6.36443	0.244424
$679$	0	0
$680$	−1.40546	−0.0538969
$681$	46.1110	1.76698
$682$	−4.02444	−0.154104
$683$	−12.7884	−0.489333	−0.244667	−	0.969607i	$-0.578678\pi$
$683$	−12.7884	−0.489333	−0.244667	+	0.969607i	$0.578678\pi$
$684$	−8.34209	−0.318968
$685$	−60.0987	−2.29625
$686$	0	0
$687$	−56.1274	−2.14139
$688$	−14.3850	−0.548422
$689$	−20.0241	−0.762858
$690$	6.15442	0.234295
$691$	21.5778	0.820858	0.410429	−	0.911893i	$-0.365379\pi$
$691$	21.5778	0.820858	0.410429	+	0.911893i	$0.365379\pi$
$692$	20.0200	0.761047
$693$	0	0
$694$	−0.501482	−0.0190360
$695$	69.0003	2.61733
$696$	19.0111	0.720612
$697$	−0.454077	−0.0171994
$698$	3.90359	0.147753
$699$	−36.4894	−1.38015
$700$	0	0
$701$	44.3684	1.67577	0.837885	−	0.545846i	$-0.183792\pi$
$701$	44.3684	1.67577	0.837885	+	0.545846i	$0.183792\pi$
$702$	−0.170656	−0.00644101
$703$	−4.26861	−0.160994
$704$	−32.6351	−1.22998
$705$	−107.981	−4.06679
$706$	−6.41405	−0.241396
$707$	0	0
$708$	−41.6549	−1.56549
$709$	−8.04898	−0.302286	−0.151143	−	0.988512i	$-0.548295\pi$
$709$	−8.04898	−0.302286	−0.151143	+	0.988512i	$0.548295\pi$
$710$	−8.96910	−0.336604
$711$	−37.9666	−1.42386
$712$	15.6687	0.587211
$713$	13.1035	0.490731
$714$	0	0
$715$	35.4398	1.32537
$716$	−33.9853	−1.27009
$717$	−52.7486	−1.96993
$718$	6.85479	0.255819
$719$	−24.0513	−0.896962	−0.448481	−	0.893792i	$-0.648035\pi$
$719$	−24.0513	−0.896962	−0.448481	+	0.893792i	$0.648035\pi$
$720$	38.9963	1.45331
$721$	0	0
$722$	3.55644	0.132357
$723$	−7.27604	−0.270599
$724$	−26.8758	−0.998831
$725$	−80.2259	−2.97951
$726$	5.71550	0.212122
$727$	−12.8216	−0.475526	−0.237763	−	0.971323i	$-0.576414\pi$
$727$	−12.8216	−0.475526	−0.237763	+	0.971323i	$0.576414\pi$
$728$	0	0
$729$	−23.9991	−0.888856
$730$	3.65128	0.135140
$731$	1.75063	0.0647493
$732$	−17.4735	−0.645840
$733$	−9.83526	−0.363274	−0.181637	−	0.983366i	$-0.558140\pi$
$733$	−9.83526	−0.363274	−0.181637	+	0.983366i	$0.558140\pi$
$734$	−1.17444	−0.0433493
$735$	0	0
$736$	−8.05025	−0.296736
$737$	5.54735	0.204339
$738$	−0.602887	−0.0221926
$739$	15.2882	0.562387	0.281193	−	0.959651i	$-0.409270\pi$
$739$	15.2882	0.562387	0.281193	+	0.959651i	$0.409270\pi$
$740$	20.4371	0.751283
$741$	−7.43119	−0.272991
$742$	0	0
$743$	−19.6414	−0.720572	−0.360286	−	0.932842i	$-0.617321\pi$
$743$	−19.6414	−0.720572	−0.360286	+	0.932842i	$0.617321\pi$
$744$	−8.17376	−0.299664
$745$	5.90855	0.216472
$746$	6.53091	0.239114
$747$	33.4707	1.22463
$748$	4.17609	0.152693
$749$	0	0
$750$	6.74597	0.246328
$751$	41.9612	1.53118	0.765592	−	0.643326i	$-0.222446\pi$
$751$	41.9612	1.53118	0.765592	+	0.643326i	$0.222446\pi$
$752$	45.2718	1.65089
$753$	73.8457	2.69109
$754$	4.06891	0.148181
$755$	52.1685	1.89861
$756$	0	0
$757$	−50.6283	−1.84012	−0.920059	−	0.391780i	$-0.871859\pi$
$757$	−50.6283	−1.84012	−0.920059	+	0.391780i	$0.871859\pi$
$758$	−2.45151	−0.0890430
$759$	−36.9959	−1.34287
$760$	4.65502	0.168855
$761$	−7.91703	−0.286992	−0.143496	−	0.989651i	$-0.545834\pi$
$761$	−7.91703	−0.286992	−0.143496	+	0.989651i	$0.545834\pi$
$762$	−6.73679	−0.244048
$763$	0	0
$764$	5.86510	0.212192
$765$	−4.74579	−0.171584
$766$	−2.92719	−0.105764
$767$	−18.0366	−0.651264
$768$	−30.2236	−1.09060
$769$	32.3984	1.16832	0.584159	−	0.811639i	$-0.301425\pi$
$769$	32.3984	1.16832	0.584159	+	0.811639i	$0.301425\pi$
$770$	0	0
$771$	4.11345	0.148142
$772$	45.2690	1.62927
$773$	−15.7353	−0.565958	−0.282979	−	0.959126i	$-0.591323\pi$
$773$	−15.7353	−0.565958	−0.282979	+	0.959126i	$0.591323\pi$
$774$	2.32434	0.0835468
$775$	34.4929	1.23902
$776$	4.90365	0.176031
$777$	0	0
$778$	−3.97258	−0.142424
$779$	1.50395	0.0538845
$780$	35.5788	1.27393
$781$	53.9157	1.92926
$782$	0.314017	0.0112292
$783$	−3.67753	−0.131424
$784$	0	0
$785$	−46.0226	−1.64262
$786$	1.89212	0.0674896
$787$	8.34243	0.297376	0.148688	−	0.988884i	$-0.452495\pi$
$787$	8.34243	0.297376	0.148688	+	0.988884i	$0.452495\pi$
$788$	−4.97155	−0.177104
$789$	−61.7017	−2.19664
$790$	10.4721	0.372580
$791$	0	0
$792$	11.2174	0.398593
$793$	−7.56605	−0.268678
$794$	−1.46796	−0.0520961
$795$	87.1368	3.09042
$796$	5.24444	0.185884
$797$	11.0015	0.389693	0.194847	−	0.980834i	$-0.437579\pi$
$797$	11.0015	0.389693	0.194847	+	0.980834i	$0.437579\pi$
$798$	0	0
$799$	−5.50951	−0.194912
$800$	−21.1910	−0.749215
$801$	52.9083	1.86942
$802$	0.735135	0.0259585
$803$	−21.9488	−0.774558
$804$	5.56911	0.196407
$805$	0	0
$806$	−1.74942	−0.0616207
$807$	−1.20322	−0.0423552
$808$	13.2738	0.466972
$809$	20.7908	0.730967	0.365484	−	0.930818i	$-0.380904\pi$
$809$	20.7908	0.730967	0.365484	+	0.930818i	$0.380904\pi$
$810$	7.40469	0.260174
$811$	7.69139	0.270081	0.135041	−	0.990840i	$-0.456883\pi$
$811$	7.69139	0.270081	0.135041	+	0.990840i	$0.456883\pi$
$812$	0	0
$813$	−60.8553	−2.13429
$814$	2.83718	0.0994433
$815$	26.0141	0.911234
$816$	4.09341	0.143298
$817$	−5.79825	−0.202855
$818$	3.16335	0.110604
$819$	0	0
$820$	−7.20055	−0.251454
$821$	14.1007	0.492119	0.246060	−	0.969255i	$-0.420864\pi$
$821$	14.1007	0.492119	0.246060	+	0.969255i	$0.420864\pi$
$822$	−8.37594	−0.292144
$823$	13.9505	0.486282	0.243141	−	0.969991i	$-0.421822\pi$
$823$	13.9505	0.486282	0.243141	+	0.969991i	$0.421822\pi$
$824$	−0.428212	−0.0149175
$825$	−97.3858	−3.39054
$826$	0	0
$827$	−41.4024	−1.43970	−0.719852	−	0.694128i	$-0.755790\pi$
$827$	−41.4024	−1.43970	−0.719852	+	0.694128i	$0.755790\pi$
$828$	−18.0534	−0.627399
$829$	30.2841	1.05181	0.525904	−	0.850544i	$-0.323727\pi$
$829$	30.2841	1.05181	0.525904	+	0.850544i	$0.323727\pi$
$830$	−9.23199	−0.320447
$831$	32.2442	1.11854
$832$	−14.1864	−0.491826
$833$	0	0
$834$	9.61655	0.332994
$835$	−67.3359	−2.33026
$836$	−13.8316	−0.478376
$837$	1.58115	0.0546524
$838$	0.117685	0.00406537
$839$	22.2690	0.768811	0.384406	−	0.923164i	$-0.374406\pi$
$839$	22.2690	0.768811	0.384406	+	0.923164i	$0.374406\pi$
$840$	0	0
$841$	58.6825	2.02353
$842$	3.23096	0.111346
$843$	47.1032	1.62232
$844$	−19.7616	−0.680223
$845$	−32.4788	−1.11731
$846$	−7.31509	−0.251498
$847$	0	0
$848$	−36.5328	−1.25454
$849$	63.8533	2.19144
$850$	0.826599	0.0283521
$851$	−9.23783	−0.316669
$852$	54.1272	1.85437
$853$	−45.4816	−1.55726	−0.778630	−	0.627484i	$-0.784085\pi$
$853$	−45.4816	−1.55726	−0.778630	+	0.627484i	$0.784085\pi$
$854$	0	0
$855$	15.7185	0.537562
$856$	8.12612	0.277745
$857$	27.7713	0.948649	0.474324	−	0.880350i	$-0.342692\pi$
$857$	27.7713	0.948649	0.474324	+	0.880350i	$0.342692\pi$
$858$	4.93923	0.168623
$859$	−18.3952	−0.627638	−0.313819	−	0.949483i	$-0.601608\pi$
$859$	−18.3952	−0.627638	−0.313819	+	0.949483i	$0.601608\pi$
$860$	27.7607	0.946631
$861$	0	0
$862$	−2.86320	−0.0975208
$863$	−37.4669	−1.27539	−0.637694	−	0.770290i	$-0.720111\pi$
$863$	−37.4669	−1.27539	−0.637694	+	0.770290i	$0.720111\pi$
$864$	−0.971390	−0.0330474
$865$	−37.7226	−1.28261
$866$	−2.89148	−0.0982565
$867$	40.5752	1.37801
$868$	0	0
$869$	−62.9506	−2.13545
$870$	−17.7063	−0.600299
$871$	2.41143	0.0817081
$872$	5.43485	0.184047
$873$	16.5581	0.560405
$874$	−1.04006	−0.0351804
$875$	0	0
$876$	−22.0349	−0.744491
$877$	−52.0690	−1.75825	−0.879123	−	0.476595i	$-0.841871\pi$
$877$	−52.0690	−1.75825	−0.879123	+	0.476595i	$0.841871\pi$
$878$	2.77014	0.0934877
$879$	28.4468	0.959486
$880$	64.6579	2.17962
$881$	−40.4834	−1.36392	−0.681959	−	0.731390i	$-0.738872\pi$
$881$	−40.4834	−1.36392	−0.681959	+	0.731390i	$0.738872\pi$
$882$	0	0
$883$	−0.0944884	−0.00317979	−0.00158989	−	0.999999i	$-0.500506\pi$
$883$	−0.0944884	−0.00317979	−0.00158989	+	0.999999i	$0.500506\pi$
$884$	1.81534	0.0610565
$885$	78.4880	2.63834
$886$	5.80201	0.194923
$887$	−11.2476	−0.377659	−0.188829	−	0.982010i	$-0.560469\pi$
$887$	−11.2476	−0.377659	−0.188829	+	0.982010i	$0.560469\pi$
$888$	5.76241	0.193374
$889$	0	0
$890$	−14.5933	−0.489170
$891$	−44.5116	−1.49120
$892$	−26.3977	−0.883859
$893$	18.2480	0.610647
$894$	0.823472	0.0275410
$895$	64.0366	2.14051
$896$	0	0
$897$	−16.0821	−0.536965
$898$	−0.693574	−0.0231449
$899$	−37.6989	−1.25733
$900$	−47.5226	−1.58409
$901$	4.44599	0.148117
$902$	−0.999617	−0.0332836
$903$	0	0
$904$	10.4179	0.346493
$905$	50.6405	1.68335
$906$	7.27070	0.241553
$907$	−8.56247	−0.284312	−0.142156	−	0.989844i	$-0.545404\pi$
$907$	−8.56247	−0.284312	−0.142156	+	0.989844i	$0.545404\pi$
$908$	37.3085	1.23813
$909$	44.8215	1.48664
$910$	0	0
$911$	48.3153	1.60076	0.800379	−	0.599494i	$-0.204631\pi$
$911$	48.3153	1.60076	0.800379	+	0.599494i	$0.204631\pi$
$912$	−13.5578	−0.448943
$913$	55.4961	1.83665
$914$	6.94441	0.229701
$915$	32.9244	1.08845
$916$	−45.4127	−1.50048
$917$	0	0
$918$	0.0378911	0.00125059
$919$	22.2835	0.735064	0.367532	−	0.930011i	$-0.380203\pi$
$919$	22.2835	0.735064	0.367532	+	0.930011i	$0.380203\pi$
$920$	10.0741	0.332133
$921$	−11.1047	−0.365911
$922$	−3.02594	−0.0996542
$923$	23.4371	0.771442
$924$	0	0
$925$	−24.3171	−0.799542
$926$	−5.07555	−0.166793
$927$	−1.44593	−0.0474907
$928$	23.1606	0.760284
$929$	−33.1450	−1.08745	−0.543726	−	0.839263i	$-0.682987\pi$
$929$	−33.1450	−1.08745	−0.543726	+	0.839263i	$0.682987\pi$
$930$	7.61276	0.249632
$931$	0	0
$932$	−29.5236	−0.967077
$933$	8.07419	0.264337
$934$	2.38492	0.0780371
$935$	−7.86876	−0.257336
$936$	4.87619	0.159383
$937$	53.9117	1.76122	0.880609	−	0.473843i	$-0.157134\pi$
$937$	53.9117	1.76122	0.880609	+	0.473843i	$0.157134\pi$
$938$	0	0
$939$	−14.9984	−0.489454
$940$	−87.3674	−2.84961
$941$	1.24157	0.0404741	0.0202370	−	0.999795i	$-0.493558\pi$
$941$	1.24157	0.0404741	0.0202370	+	0.999795i	$0.493558\pi$
$942$	−6.41415	−0.208984
$943$	3.25474	0.105989
$944$	−32.9067	−1.07102
$945$	0	0
$946$	3.85388	0.125300
$947$	22.4067	0.728119	0.364059	−	0.931376i	$-0.381390\pi$
$947$	22.4067	0.728119	0.364059	+	0.931376i	$0.381390\pi$
$948$	−63.1975	−2.05256
$949$	−9.54113	−0.309718
$950$	−2.73778	−0.0888253
$951$	−49.6176	−1.60896
$952$	0	0
$953$	−51.1505	−1.65693	−0.828463	−	0.560044i	$-0.810784\pi$
$953$	−51.1505	−1.65693	−0.828463	+	0.560044i	$0.810784\pi$
$954$	5.90303	0.191118
$955$	−11.0513	−0.357611
$956$	−42.6790	−1.38034
$957$	106.437	3.44063
$958$	−0.0925095	−0.00298885
$959$	0	0
$960$	61.7336	1.99244
$961$	−14.7915	−0.477144
$962$	1.23332	0.0397639
$963$	27.4393	0.884219
$964$	−5.88705	−0.189609
$965$	−85.2977	−2.74583
$966$	0	0
$967$	40.8102	1.31237	0.656184	−	0.754601i	$-0.272170\pi$
$967$	40.8102	1.31237	0.656184	+	0.754601i	$0.272170\pi$
$968$	9.35564	0.300702
$969$	1.64996	0.0530043
$970$	−4.56710	−0.146641
$971$	−31.0702	−0.997092	−0.498546	−	0.866863i	$-0.666132\pi$
$971$	−31.0702	−0.997092	−0.498546	+	0.866863i	$0.666132\pi$
$972$	−42.3830	−1.35943
$973$	0	0
$974$	−4.71978	−0.151232
$975$	−42.3335	−1.35576
$976$	−13.8038	−0.441849
$977$	9.58005	0.306493	0.153247	−	0.988188i	$-0.451027\pi$
$977$	9.58005	0.306493	0.153247	+	0.988188i	$0.451027\pi$
$978$	3.62558	0.115933
$979$	87.7246	2.80369
$980$	0	0
$981$	18.3517	0.585926
$982$	−1.64481	−0.0524878
$983$	−54.0643	−1.72438	−0.862192	−	0.506582i	$-0.830909\pi$
$983$	−54.0643	−1.72438	−0.862192	+	0.506582i	$0.830909\pi$
$984$	−2.03025	−0.0647221
$985$	9.36761	0.298477
$986$	−0.903427	−0.0287710
$987$	0	0
$988$	−6.01258	−0.191286
$989$	−12.5482	−0.399009
$990$	−10.4475	−0.332044
$991$	−16.7574	−0.532316	−0.266158	−	0.963929i	$-0.585754\pi$
$991$	−16.7574	−0.532316	−0.266158	+	0.963929i	$0.585754\pi$
$992$	−9.95784	−0.316162
$993$	5.45817	0.173210
$994$	0	0
$995$	−9.88179	−0.313274
$996$	55.7137	1.76536
$997$	−14.0576	−0.445209	−0.222604	−	0.974909i	$-0.571456\pi$
$997$	−14.0576	−0.445209	−0.222604	+	0.974909i	$0.571456\pi$
$998$	−4.75927	−0.150652
$999$	−1.11469	−0.0352672

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.u.1.10	yes	20
7.6	odd	2		2009.2.a.t.1.10	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2009.2.a.t.1.10	✓	20	7.6	odd	2
2009.2.a.u.1.10	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)

\(f(q)\)	\(=\)	\(q-0.212475 q^{2} -2.41608 q^{3} -1.95485 q^{4} +3.68342 q^{5} +0.513357 q^{6} +0.840308 q^{8} +2.83745 q^{9} +O(q^{10})\)	\(q-0.212475 q^{2} -2.41608 q^{3} -1.95485 q^{4} +3.68342 q^{5} +0.513357 q^{6} +0.840308 q^{8} +2.83745 q^{9} -0.782635 q^{10} +4.70463 q^{11} +4.72309 q^{12} +2.04510 q^{13} -8.89944 q^{15} +3.73116 q^{16} -0.454077 q^{17} -0.602887 q^{18} +1.50395 q^{19} -7.20055 q^{20} -0.999617 q^{22} +3.25474 q^{23} -2.03025 q^{24} +8.56758 q^{25} -0.434532 q^{26} +0.392736 q^{27} -9.36389 q^{29} +1.89091 q^{30} +4.02598 q^{31} -2.47339 q^{32} -11.3668 q^{33} +0.0964799 q^{34} -5.54680 q^{36} -2.83827 q^{37} -0.319551 q^{38} -4.94113 q^{39} +3.09521 q^{40} +1.00000 q^{41} -3.85536 q^{43} -9.19688 q^{44} +10.4515 q^{45} -0.691551 q^{46} +12.1334 q^{47} -9.01480 q^{48} -1.82040 q^{50} +1.09709 q^{51} -3.99787 q^{52} -9.79127 q^{53} -0.0834465 q^{54} +17.3291 q^{55} -3.63366 q^{57} +1.98959 q^{58} -8.81943 q^{59} +17.3971 q^{60} -3.69960 q^{61} -0.855420 q^{62} -6.93679 q^{64} +7.53296 q^{65} +2.41516 q^{66} +1.17912 q^{67} +0.887653 q^{68} -7.86371 q^{69} +11.4601 q^{71} +2.38433 q^{72} -4.66537 q^{73} +0.603062 q^{74} -20.7000 q^{75} -2.94000 q^{76} +1.04987 q^{78} -13.3805 q^{79} +13.7434 q^{80} -9.46123 q^{81} -0.212475 q^{82} +11.7960 q^{83} -1.67255 q^{85} +0.819167 q^{86} +22.6239 q^{87} +3.95334 q^{88} +18.6464 q^{89} -2.22069 q^{90} -6.36254 q^{92} -9.72710 q^{93} -2.57805 q^{94} +5.53966 q^{95} +5.97592 q^{96} +5.83554 q^{97} +13.3492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 8 q^{3} + 18 q^{4} + 8 q^{5} + 12 q^{6} - 6 q^{8} + 16 q^{9}+O(q^{10}) \) 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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