LMFDB - Embedded newform 2009.2.a.f.1.2

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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ 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)

$f(q)$	$=$	$q+1.61803 q^{2} +1.00000 q^{3} +0.618034 q^{4} -1.00000 q^{5} +1.61803 q^{6} -2.23607 q^{8} -2.00000 q^{9} +O(q^{10})$	\(q+1.61803 q^{2} +1.00000 q^{3} +0.618034 q^{4} -1.00000 q^{5} +1.61803 q^{6} -2.23607 q^{8} -2.00000 q^{9} -1.61803 q^{10} +1.00000 q^{11} +0.618034 q^{12} -4.47214 q^{13} -1.00000 q^{15} -4.85410 q^{16} +4.23607 q^{17} -3.23607 q^{18} +1.47214 q^{19} -0.618034 q^{20} +1.61803 q^{22} -8.70820 q^{23} -2.23607 q^{24} -4.00000 q^{25} -7.23607 q^{26} -5.00000 q^{27} +4.47214 q^{29} -1.61803 q^{30} -0.236068 q^{31} -3.38197 q^{32} +1.00000 q^{33} +6.85410 q^{34} -1.23607 q^{36} -3.47214 q^{37} +2.38197 q^{38} -4.47214 q^{39} +2.23607 q^{40} -1.00000 q^{41} -6.47214 q^{43} +0.618034 q^{44} +2.00000 q^{45} -14.0902 q^{46} -3.47214 q^{47} -4.85410 q^{48} -6.47214 q^{50} +4.23607 q^{51} -2.76393 q^{52} -10.2361 q^{53} -8.09017 q^{54} -1.00000 q^{55} +1.47214 q^{57} +7.23607 q^{58} +8.70820 q^{59} -0.618034 q^{60} +9.47214 q^{61} -0.381966 q^{62} +4.23607 q^{64} +4.47214 q^{65} +1.61803 q^{66} +5.94427 q^{67} +2.61803 q^{68} -8.70820 q^{69} -14.4721 q^{71} +4.47214 q^{72} -2.52786 q^{73} -5.61803 q^{74} -4.00000 q^{75} +0.909830 q^{76} -7.23607 q^{78} -1.00000 q^{79} +4.85410 q^{80} +1.00000 q^{81} -1.61803 q^{82} -1.52786 q^{83} -4.23607 q^{85} -10.4721 q^{86} +4.47214 q^{87} -2.23607 q^{88} -14.2361 q^{89} +3.23607 q^{90} -5.38197 q^{92} -0.236068 q^{93} -5.61803 q^{94} -1.47214 q^{95} -3.38197 q^{96} +8.47214 q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 2 q^{3} - q^{4} - 2 q^{5} + q^{6} - 4 q^{9}+O(q^{10}) $ 2 * q + q^2 + 2 * q^3 - q^4 - 2 * q^5 + q^6 - 4 * q^9	$ 2 q + q^{2} + 2 q^{3} - q^{4} - 2 q^{5} + q^{6} - 4 q^{9} - q^{10} + 2 q^{11} - q^{12} - 2 q^{15} - 3 q^{16} + 4 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + q^{22} - 4 q^{23} - 8 q^{25} - 10 q^{26} - 10 q^{27} - q^{30} + 4 q^{31} - 9 q^{32} + 2 q^{33} + 7 q^{34} + 2 q^{36} + 2 q^{37} + 7 q^{38} - 2 q^{41} - 4 q^{43} - q^{44} + 4 q^{45} - 17 q^{46} + 2 q^{47} - 3 q^{48} - 4 q^{50} + 4 q^{51} - 10 q^{52} - 16 q^{53} - 5 q^{54} - 2 q^{55} - 6 q^{57} + 10 q^{58} + 4 q^{59} + q^{60} + 10 q^{61} - 3 q^{62} + 4 q^{64} + q^{66} - 6 q^{67} + 3 q^{68} - 4 q^{69} - 20 q^{71} - 14 q^{73} - 9 q^{74} - 8 q^{75} + 13 q^{76} - 10 q^{78} - 2 q^{79} + 3 q^{80} + 2 q^{81} - q^{82} - 12 q^{83} - 4 q^{85} - 12 q^{86} - 24 q^{89} + 2 q^{90} - 13 q^{92} + 4 q^{93} - 9 q^{94} + 6 q^{95} - 9 q^{96} + 8 q^{97} - 4 q^{99}+O(q^{100}) $ 2 * q + q^2 + 2 * q^3 - q^4 - 2 * q^5 + q^6 - 4 * q^9 - q^10 + 2 * q^11 - q^12 - 2 * q^15 - 3 * q^16 + 4 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + q^22 - 4 * q^23 - 8 * q^25 - 10 * q^26 - 10 * q^27 - q^30 + 4 * q^31 - 9 * q^32 + 2 * q^33 + 7 * q^34 + 2 * q^36 + 2 * q^37 + 7 * q^38 - 2 * q^41 - 4 * q^43 - q^44 + 4 * q^45 - 17 * q^46 + 2 * q^47 - 3 * q^48 - 4 * q^50 + 4 * q^51 - 10 * q^52 - 16 * q^53 - 5 * q^54 - 2 * q^55 - 6 * q^57 + 10 * q^58 + 4 * q^59 + q^60 + 10 * q^61 - 3 * q^62 + 4 * q^64 + q^66 - 6 * q^67 + 3 * q^68 - 4 * q^69 - 20 * q^71 - 14 * q^73 - 9 * q^74 - 8 * q^75 + 13 * q^76 - 10 * q^78 - 2 * q^79 + 3 * q^80 + 2 * q^81 - q^82 - 12 * q^83 - 4 * q^85 - 12 * q^86 - 24 * q^89 + 2 * q^90 - 13 * q^92 + 4 * q^93 - 9 * q^94 + 6 * q^95 - 9 * q^96 + 8 * q^97 - 4 * 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 $

$2$	1.61803	1.14412	0.572061	−	0.820211i	$-0.306144\pi$
$2$	1.61803	1.14412	0.572061	+	0.820211i	$0.306144\pi$
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	0.618034	0.309017
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	1.61803	0.660560
$7$	0	0
$7$	0	0
$8$	−2.23607	−0.790569
$9$	−2.00000	−0.666667
$10$	−1.61803	−0.511667
$11$	1.00000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	0.618034	0.178411
$13$	−4.47214	−1.24035	−0.620174	−	0.784465i	$-0.712938\pi$
$13$	−4.47214	−1.24035	−0.620174	+	0.784465i	$0.712938\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	−4.85410	−1.21353
$17$	4.23607	1.02740	0.513699	−	0.857971i	$-0.328275\pi$
$17$	4.23607	1.02740	0.513699	+	0.857971i	$0.328275\pi$
$18$	−3.23607	−0.762749
$19$	1.47214	0.337731	0.168866	−	0.985639i	$-0.445990\pi$
$19$	1.47214	0.337731	0.168866	+	0.985639i	$0.445990\pi$
$20$	−0.618034	−0.138197
$21$	0	0
$22$	1.61803	0.344966
$23$	−8.70820	−1.81579	−0.907893	−	0.419202i	$-0.862310\pi$
$23$	−8.70820	−1.81579	−0.907893	+	0.419202i	$0.862310\pi$
$24$	−2.23607	−0.456435
$25$	−4.00000	−0.800000
$26$	−7.23607	−1.41911
$27$	−5.00000	−0.962250
$28$	0	0
$29$	4.47214	0.830455	0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214	0.830455	0.415227	+	0.909718i	$0.363702\pi$
$30$	−1.61803	−0.295411
$31$	−0.236068	−0.0423991	−0.0211995	−	0.999775i	$-0.506749\pi$
$31$	−0.236068	−0.0423991	−0.0211995	+	0.999775i	$0.506749\pi$
$32$	−3.38197	−0.597853
$33$	1.00000	0.174078
$34$	6.85410	1.17547
$35$	0	0
$36$	−1.23607	−0.206011
$37$	−3.47214	−0.570816	−0.285408	−	0.958406i	$-0.592129\pi$
$37$	−3.47214	−0.570816	−0.285408	+	0.958406i	$0.592129\pi$
$38$	2.38197	0.386406
$39$	−4.47214	−0.716115
$40$	2.23607	0.353553
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−6.47214	−0.986991	−0.493496	−	0.869748i	$-0.664281\pi$
$43$	−6.47214	−0.986991	−0.493496	+	0.869748i	$0.664281\pi$
$44$	0.618034	0.0931721
$45$	2.00000	0.298142
$46$	−14.0902	−2.07748
$47$	−3.47214	−0.506463	−0.253232	−	0.967406i	$-0.581493\pi$
$47$	−3.47214	−0.506463	−0.253232	+	0.967406i	$0.581493\pi$
$48$	−4.85410	−0.700629
$49$	0	0
$50$	−6.47214	−0.915298
$51$	4.23607	0.593168
$52$	−2.76393	−0.383288
$53$	−10.2361	−1.40603	−0.703016	−	0.711174i	$-0.748164\pi$
$53$	−10.2361	−1.40603	−0.703016	+	0.711174i	$0.748164\pi$
$54$	−8.09017	−1.10093
$55$	−1.00000	−0.134840
$56$	0	0
$57$	1.47214	0.194989
$58$	7.23607	0.950142
$59$	8.70820	1.13371	0.566856	−	0.823817i	$-0.308160\pi$
$59$	8.70820	1.13371	0.566856	+	0.823817i	$0.308160\pi$
$60$	−0.618034	−0.0797878
$61$	9.47214	1.21278	0.606391	−	0.795166i	$-0.292616\pi$
$61$	9.47214	1.21278	0.606391	+	0.795166i	$0.292616\pi$
$62$	−0.381966	−0.0485097
$63$	0	0
$64$	4.23607	0.529508
$65$	4.47214	0.554700
$66$	1.61803	0.199166
$67$	5.94427	0.726208	0.363104	−	0.931749i	$-0.381717\pi$
$67$	5.94427	0.726208	0.363104	+	0.931749i	$0.381717\pi$
$68$	2.61803	0.317483
$69$	−8.70820	−1.04834
$70$	0	0
$71$	−14.4721	−1.71753	−0.858763	−	0.512373i	$-0.828767\pi$
$71$	−14.4721	−1.71753	−0.858763	+	0.512373i	$0.828767\pi$
$72$	4.47214	0.527046
$73$	−2.52786	−0.295864	−0.147932	−	0.988998i	$-0.547262\pi$
$73$	−2.52786	−0.295864	−0.147932	+	0.988998i	$0.547262\pi$
$74$	−5.61803	−0.653083
$75$	−4.00000	−0.461880
$76$	0.909830	0.104365
$77$	0	0
$78$	−7.23607	−0.819323
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	4.85410	0.542705
$81$	1.00000	0.111111
$82$	−1.61803	−0.178682
$83$	−1.52786	−0.167705	−0.0838524	−	0.996478i	$-0.526722\pi$
$83$	−1.52786	−0.167705	−0.0838524	+	0.996478i	$0.526722\pi$
$84$	0	0
$85$	−4.23607	−0.459466
$86$	−10.4721	−1.12924
$87$	4.47214	0.479463
$88$	−2.23607	−0.238366
$89$	−14.2361	−1.50902	−0.754510	−	0.656288i	$-0.772125\pi$
$89$	−14.2361	−1.50902	−0.754510	+	0.656288i	$0.772125\pi$
$90$	3.23607	0.341112
$91$	0	0
$92$	−5.38197	−0.561109
$93$	−0.236068	−0.0244791
$94$	−5.61803	−0.579456
$95$	−1.47214	−0.151038
$96$	−3.38197	−0.345170
$97$	8.47214	0.860215	0.430108	−	0.902778i	$-0.358476\pi$
$97$	8.47214	0.860215	0.430108	+	0.902778i	$0.358476\pi$
$98$	0	0
$99$	−2.00000	−0.201008
$100$	−2.47214	−0.247214
$101$	3.29180	0.327546	0.163773	−	0.986498i	$-0.447634\pi$
$101$	3.29180	0.327546	0.163773	+	0.986498i	$0.447634\pi$
$102$	6.85410	0.678657
$103$	17.1803	1.69283	0.846415	−	0.532524i	$-0.178757\pi$
$103$	17.1803	1.69283	0.846415	+	0.532524i	$0.178757\pi$
$104$	10.0000	0.980581
$105$	0	0
$106$	−16.5623	−1.60867
$107$	−1.29180	−0.124883	−0.0624413	−	0.998049i	$-0.519889\pi$
$107$	−1.29180	−0.124883	−0.0624413	+	0.998049i	$0.519889\pi$
$108$	−3.09017	−0.297352
$109$	−14.2361	−1.36357	−0.681784	−	0.731554i	$-0.738796\pi$
$109$	−14.2361	−1.36357	−0.681784	+	0.731554i	$0.738796\pi$
$110$	−1.61803	−0.154273
$111$	−3.47214	−0.329561
$112$	0	0
$113$	19.8885	1.87096	0.935478	−	0.353384i	$-0.114969\pi$
$113$	19.8885	1.87096	0.935478	+	0.353384i	$0.114969\pi$
$114$	2.38197	0.223092
$115$	8.70820	0.812044
$116$	2.76393	0.256625
$117$	8.94427	0.826898
$118$	14.0902	1.29711
$119$	0	0
$120$	2.23607	0.204124
$121$	−10.0000	−0.909091
$122$	15.3262	1.38757
$123$	−1.00000	−0.0901670
$124$	−0.145898	−0.0131020
$125$	9.00000	0.804984
$126$	0	0
$127$	15.4164	1.36798	0.683992	−	0.729489i	$-0.260242\pi$
$127$	15.4164	1.36798	0.683992	+	0.729489i	$0.260242\pi$
$128$	13.6180	1.20368
$129$	−6.47214	−0.569840
$130$	7.23607	0.634645
$131$	−13.6525	−1.19282	−0.596411	−	0.802679i	$-0.703407\pi$
$131$	−13.6525	−1.19282	−0.596411	+	0.802679i	$0.703407\pi$
$132$	0.618034	0.0537930
$133$	0	0
$134$	9.61803	0.830872
$135$	5.00000	0.430331
$136$	−9.47214	−0.812229
$137$	15.6525	1.33728	0.668641	−	0.743586i	$-0.266876\pi$
$137$	15.6525	1.33728	0.668641	+	0.743586i	$0.266876\pi$
$138$	−14.0902	−1.19943
$139$	16.9443	1.43719	0.718597	−	0.695427i	$-0.244785\pi$
$139$	16.9443	1.43719	0.718597	+	0.695427i	$0.244785\pi$
$140$	0	0
$141$	−3.47214	−0.292407
$142$	−23.4164	−1.96506
$143$	−4.47214	−0.373979
$144$	9.70820	0.809017
$145$	−4.47214	−0.371391
$146$	−4.09017	−0.338505
$147$	0	0
$148$	−2.14590	−0.176392
$149$	1.18034	0.0966972	0.0483486	−	0.998831i	$-0.484604\pi$
$149$	1.18034	0.0966972	0.0483486	+	0.998831i	$0.484604\pi$
$150$	−6.47214	−0.528448
$151$	5.94427	0.483738	0.241869	−	0.970309i	$-0.422240\pi$
$151$	5.94427	0.483738	0.241869	+	0.970309i	$0.422240\pi$
$152$	−3.29180	−0.267000
$153$	−8.47214	−0.684932
$154$	0	0
$155$	0.236068	0.0189614
$156$	−2.76393	−0.221292
$157$	−2.23607	−0.178458	−0.0892288	−	0.996011i	$-0.528440\pi$
$157$	−2.23607	−0.178458	−0.0892288	+	0.996011i	$0.528440\pi$
$158$	−1.61803	−0.128724
$159$	−10.2361	−0.811773
$160$	3.38197	0.267368
$161$	0	0
$162$	1.61803	0.127125
$163$	−5.29180	−0.414485	−0.207243	−	0.978290i	$-0.566449\pi$
$163$	−5.29180	−0.414485	−0.207243	+	0.978290i	$0.566449\pi$
$164$	−0.618034	−0.0482603
$165$	−1.00000	−0.0778499
$166$	−2.47214	−0.191875
$167$	−2.47214	−0.191300	−0.0956498	−	0.995415i	$-0.530493\pi$
$167$	−2.47214	−0.191300	−0.0956498	+	0.995415i	$0.530493\pi$
$168$	0	0
$169$	7.00000	0.538462
$170$	−6.85410	−0.525686
$171$	−2.94427	−0.225154
$172$	−4.00000	−0.304997
$173$	−18.8885	−1.43607	−0.718035	−	0.696007i	$-0.754958\pi$
$173$	−18.8885	−1.43607	−0.718035	+	0.696007i	$0.754958\pi$
$174$	7.23607	0.548565
$175$	0	0
$176$	−4.85410	−0.365892
$177$	8.70820	0.654549
$178$	−23.0344	−1.72650
$179$	−10.4164	−0.778559	−0.389279	−	0.921120i	$-0.627276\pi$
$179$	−10.4164	−0.778559	−0.389279	+	0.921120i	$0.627276\pi$
$180$	1.23607	0.0921311
$181$	−21.4164	−1.59187	−0.795935	−	0.605383i	$-0.793020\pi$
$181$	−21.4164	−1.59187	−0.795935	+	0.605383i	$0.793020\pi$
$182$	0	0
$183$	9.47214	0.700200
$184$	19.4721	1.43550
$185$	3.47214	0.255277
$186$	−0.381966	−0.0280071
$187$	4.23607	0.309772
$188$	−2.14590	−0.156506
$189$	0	0
$190$	−2.38197	−0.172806
$191$	5.47214	0.395950	0.197975	−	0.980207i	$-0.436564\pi$
$191$	5.47214	0.395950	0.197975	+	0.980207i	$0.436564\pi$
$192$	4.23607	0.305712
$193$	0.819660	0.0590004	0.0295002	−	0.999565i	$-0.490608\pi$
$193$	0.819660	0.0590004	0.0295002	+	0.999565i	$0.490608\pi$
$194$	13.7082	0.984192
$195$	4.47214	0.320256
$196$	0	0
$197$	−2.94427	−0.209771	−0.104885	−	0.994484i	$-0.533448\pi$
$197$	−2.94427	−0.209771	−0.104885	+	0.994484i	$0.533448\pi$
$198$	−3.23607	−0.229977
$199$	17.9443	1.27204	0.636018	−	0.771674i	$-0.280580\pi$
$199$	17.9443	1.27204	0.636018	+	0.771674i	$0.280580\pi$
$200$	8.94427	0.632456
$201$	5.94427	0.419277
$202$	5.32624	0.374753
$203$	0	0
$204$	2.61803	0.183299
$205$	1.00000	0.0698430
$206$	27.7984	1.93680
$207$	17.4164	1.21052
$208$	21.7082	1.50519
$209$	1.47214	0.101830
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	−6.32624	−0.434488
$213$	−14.4721	−0.991614
$214$	−2.09017	−0.142881
$215$	6.47214	0.441396
$216$	11.1803	0.760726
$217$	0	0
$218$	−23.0344	−1.56009
$219$	−2.52786	−0.170817
$220$	−0.618034	−0.0416678
$221$	−18.9443	−1.27433
$222$	−5.61803	−0.377058
$223$	−16.9443	−1.13467	−0.567336	−	0.823486i	$-0.692026\pi$
$223$	−16.9443	−1.13467	−0.567336	+	0.823486i	$0.692026\pi$
$224$	0	0
$225$	8.00000	0.533333
$226$	32.1803	2.14060
$227$	−5.47214	−0.363198	−0.181599	−	0.983373i	$-0.558127\pi$
$227$	−5.47214	−0.363198	−0.181599	+	0.983373i	$0.558127\pi$
$228$	0.909830	0.0602550
$229$	−20.1246	−1.32987	−0.664936	−	0.746900i	$-0.731541\pi$
$229$	−20.1246	−1.32987	−0.664936	+	0.746900i	$0.731541\pi$
$230$	14.0902	0.929078
$231$	0	0
$232$	−10.0000	−0.656532
$233$	3.29180	0.215653	0.107826	−	0.994170i	$-0.465611\pi$
$233$	3.29180	0.215653	0.107826	+	0.994170i	$0.465611\pi$
$234$	14.4721	0.946073
$235$	3.47214	0.226497
$236$	5.38197	0.350336
$237$	−1.00000	−0.0649570
$238$	0	0
$239$	−2.47214	−0.159909	−0.0799546	−	0.996799i	$-0.525478\pi$
$239$	−2.47214	−0.159909	−0.0799546	+	0.996799i	$0.525478\pi$
$240$	4.85410	0.313331
$241$	1.47214	0.0948286	0.0474143	−	0.998875i	$-0.484902\pi$
$241$	1.47214	0.0948286	0.0474143	+	0.998875i	$0.484902\pi$
$242$	−16.1803	−1.04011
$243$	16.0000	1.02640
$244$	5.85410	0.374770
$245$	0	0
$246$	−1.61803	−0.103162
$247$	−6.58359	−0.418904
$248$	0.527864	0.0335194
$249$	−1.52786	−0.0968244
$250$	14.5623	0.921001
$251$	26.8328	1.69367	0.846836	−	0.531854i	$-0.178504\pi$
$251$	26.8328	1.69367	0.846836	+	0.531854i	$0.178504\pi$
$252$	0	0
$253$	−8.70820	−0.547480
$254$	24.9443	1.56514
$255$	−4.23607	−0.265273
$256$	13.5623	0.847644
$257$	−1.29180	−0.0805800	−0.0402900	−	0.999188i	$-0.512828\pi$
$257$	−1.29180	−0.0805800	−0.0402900	+	0.999188i	$0.512828\pi$
$258$	−10.4721	−0.651967
$259$	0	0
$260$	2.76393	0.171412
$261$	−8.94427	−0.553637
$262$	−22.0902	−1.36474
$263$	7.47214	0.460752	0.230376	−	0.973102i	$-0.426004\pi$
$263$	7.47214	0.460752	0.230376	+	0.973102i	$0.426004\pi$
$264$	−2.23607	−0.137620
$265$	10.2361	0.628797
$266$	0	0
$267$	−14.2361	−0.871233
$268$	3.67376	0.224411
$269$	−19.4721	−1.18724	−0.593619	−	0.804747i	$-0.702301\pi$
$269$	−19.4721	−1.18724	−0.593619	+	0.804747i	$0.702301\pi$
$270$	8.09017	0.492352
$271$	−21.6525	−1.31529	−0.657647	−	0.753326i	$-0.728448\pi$
$271$	−21.6525	−1.31529	−0.657647	+	0.753326i	$0.728448\pi$
$272$	−20.5623	−1.24677
$273$	0	0
$274$	25.3262	1.53001
$275$	−4.00000	−0.241209
$276$	−5.38197	−0.323956
$277$	−4.05573	−0.243685	−0.121843	−	0.992549i	$-0.538880\pi$
$277$	−4.05573	−0.243685	−0.121843	+	0.992549i	$0.538880\pi$
$278$	27.4164	1.64433
$279$	0.472136	0.0282660
$280$	0	0
$281$	−4.47214	−0.266785	−0.133393	−	0.991063i	$-0.542587\pi$
$281$	−4.47214	−0.266785	−0.133393	+	0.991063i	$0.542587\pi$
$282$	−5.61803	−0.334549
$283$	11.1803	0.664602	0.332301	−	0.943173i	$-0.392175\pi$
$283$	11.1803	0.664602	0.332301	+	0.943173i	$0.392175\pi$
$284$	−8.94427	−0.530745
$285$	−1.47214	−0.0872018
$286$	−7.23607	−0.427878
$287$	0	0
$288$	6.76393	0.398569
$289$	0.944272	0.0555454
$290$	−7.23607	−0.424917
$291$	8.47214	0.496645
$292$	−1.56231	−0.0914270
$293$	28.8328	1.68443	0.842216	−	0.539141i	$-0.181251\pi$
$293$	28.8328	1.68443	0.842216	+	0.539141i	$0.181251\pi$
$294$	0	0
$295$	−8.70820	−0.507011
$296$	7.76393	0.451269
$297$	−5.00000	−0.290129
$298$	1.90983	0.110633
$299$	38.9443	2.25221
$300$	−2.47214	−0.142729
$301$	0	0
$302$	9.61803	0.553456
$303$	3.29180	0.189109
$304$	−7.14590	−0.409845
$305$	−9.47214	−0.542373
$306$	−13.7082	−0.783646
$307$	−9.88854	−0.564369	−0.282185	−	0.959360i	$-0.591059\pi$
$307$	−9.88854	−0.564369	−0.282185	+	0.959360i	$0.591059\pi$
$308$	0	0
$309$	17.1803	0.977355
$310$	0.381966	0.0216942
$311$	−21.8328	−1.23803	−0.619013	−	0.785381i	$-0.712467\pi$
$311$	−21.8328	−1.23803	−0.619013	+	0.785381i	$0.712467\pi$
$312$	10.0000	0.566139
$313$	−17.2918	−0.977390	−0.488695	−	0.872455i	$-0.662527\pi$
$313$	−17.2918	−0.977390	−0.488695	+	0.872455i	$0.662527\pi$
$314$	−3.61803	−0.204177
$315$	0	0
$316$	−0.618034	−0.0347671
$317$	25.7639	1.44705	0.723523	−	0.690300i	$-0.242521\pi$
$317$	25.7639	1.44705	0.723523	+	0.690300i	$0.242521\pi$
$318$	−16.5623	−0.928768
$319$	4.47214	0.250392
$320$	−4.23607	−0.236803
$321$	−1.29180	−0.0721010
$322$	0	0
$323$	6.23607	0.346984
$324$	0.618034	0.0343352
$325$	17.8885	0.992278
$326$	−8.56231	−0.474222
$327$	−14.2361	−0.787256
$328$	2.23607	0.123466
$329$	0	0
$330$	−1.61803	−0.0890698
$331$	−31.8328	−1.74969	−0.874845	−	0.484403i	$-0.839037\pi$
$331$	−31.8328	−1.74969	−0.874845	+	0.484403i	$0.839037\pi$
$332$	−0.944272	−0.0518237
$333$	6.94427	0.380544
$334$	−4.00000	−0.218870
$335$	−5.94427	−0.324770
$336$	0	0
$337$	−8.47214	−0.461507	−0.230753	−	0.973012i	$-0.574119\pi$
$337$	−8.47214	−0.461507	−0.230753	+	0.973012i	$0.574119\pi$
$338$	11.3262	0.616066
$339$	19.8885	1.08020
$340$	−2.61803	−0.141983
$341$	−0.236068	−0.0127838
$342$	−4.76393	−0.257604
$343$	0	0
$344$	14.4721	0.780285
$345$	8.70820	0.468834
$346$	−30.5623	−1.64304
$347$	−3.00000	−0.161048	−0.0805242	−	0.996753i	$-0.525659\pi$
$347$	−3.00000	−0.161048	−0.0805242	+	0.996753i	$0.525659\pi$
$348$	2.76393	0.148162
$349$	−20.4721	−1.09585	−0.547924	−	0.836528i	$-0.684582\pi$
$349$	−20.4721	−1.09585	−0.547924	+	0.836528i	$0.684582\pi$
$350$	0	0
$351$	22.3607	1.19352
$352$	−3.38197	−0.180259
$353$	25.4721	1.35574	0.677872	−	0.735179i	$-0.262902\pi$
$353$	25.4721	1.35574	0.677872	+	0.735179i	$0.262902\pi$
$354$	14.0902	0.748884
$355$	14.4721	0.768101
$356$	−8.79837	−0.466313
$357$	0	0
$358$	−16.8541	−0.890767
$359$	−13.6525	−0.720550	−0.360275	−	0.932846i	$-0.617317\pi$
$359$	−13.6525	−0.720550	−0.360275	+	0.932846i	$0.617317\pi$
$360$	−4.47214	−0.235702
$361$	−16.8328	−0.885938
$362$	−34.6525	−1.82129
$363$	−10.0000	−0.524864
$364$	0	0
$365$	2.52786	0.132314
$366$	15.3262	0.801115
$367$	−5.18034	−0.270412	−0.135206	−	0.990818i	$-0.543170\pi$
$367$	−5.18034	−0.270412	−0.135206	+	0.990818i	$0.543170\pi$
$368$	42.2705	2.20350
$369$	2.00000	0.104116
$370$	5.61803	0.292068
$371$	0	0
$372$	−0.145898	−0.00756446
$373$	−0.0557281	−0.00288549	−0.00144275	−	0.999999i	$-0.500459\pi$
$373$	−0.0557281	−0.00288549	−0.00144275	+	0.999999i	$0.500459\pi$
$374$	6.85410	0.354417
$375$	9.00000	0.464758
$376$	7.76393	0.400394
$377$	−20.0000	−1.03005
$378$	0	0
$379$	31.4164	1.61375	0.806876	−	0.590721i	$-0.201156\pi$
$379$	31.4164	1.61375	0.806876	+	0.590721i	$0.201156\pi$
$380$	−0.909830	−0.0466733
$381$	15.4164	0.789807
$382$	8.85410	0.453015
$383$	20.8885	1.06735	0.533677	−	0.845688i	$-0.320810\pi$
$383$	20.8885	1.06735	0.533677	+	0.845688i	$0.320810\pi$
$384$	13.6180	0.694942
$385$	0	0
$386$	1.32624	0.0675037
$387$	12.9443	0.657994
$388$	5.23607	0.265821
$389$	−1.00000	−0.0507020	−0.0253510	−	0.999679i	$-0.508070\pi$
$389$	−1.00000	−0.0507020	−0.0253510	+	0.999679i	$0.508070\pi$
$390$	7.23607	0.366413
$391$	−36.8885	−1.86553
$392$	0	0
$393$	−13.6525	−0.688676
$394$	−4.76393	−0.240003
$395$	1.00000	0.0503155
$396$	−1.23607	−0.0621148
$397$	27.6525	1.38784	0.693919	−	0.720053i	$-0.255883\pi$
$397$	27.6525	1.38784	0.693919	+	0.720053i	$0.255883\pi$
$398$	29.0344	1.45537
$399$	0	0
$400$	19.4164	0.970820
$401$	7.94427	0.396718	0.198359	−	0.980129i	$-0.436439\pi$
$401$	7.94427	0.396718	0.198359	+	0.980129i	$0.436439\pi$
$402$	9.61803	0.479704
$403$	1.05573	0.0525896
$404$	2.03444	0.101217
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−3.47214	−0.172107
$408$	−9.47214	−0.468941
$409$	−22.8885	−1.13177	−0.565883	−	0.824486i	$-0.691465\pi$
$409$	−22.8885	−1.13177	−0.565883	+	0.824486i	$0.691465\pi$
$410$	1.61803	0.0799090
$411$	15.6525	0.772080
$412$	10.6180	0.523113
$413$	0	0
$414$	28.1803	1.38499
$415$	1.52786	0.0749999
$416$	15.1246	0.741545
$417$	16.9443	0.829765
$418$	2.38197	0.116506
$419$	−17.8885	−0.873913	−0.436956	−	0.899483i	$-0.643944\pi$
$419$	−17.8885	−0.873913	−0.436956	+	0.899483i	$0.643944\pi$
$420$	0	0
$421$	−16.4721	−0.802803	−0.401401	−	0.915902i	$-0.631477\pi$
$421$	−16.4721	−0.802803	−0.401401	+	0.915902i	$0.631477\pi$
$422$	0	0
$423$	6.94427	0.337642
$424$	22.8885	1.11157
$425$	−16.9443	−0.821918
$426$	−23.4164	−1.13453
$427$	0	0
$428$	−0.798374	−0.0385909
$429$	−4.47214	−0.215917
$430$	10.4721	0.505011
$431$	−2.34752	−0.113076	−0.0565381	−	0.998400i	$-0.518006\pi$
$431$	−2.34752	−0.113076	−0.0565381	+	0.998400i	$0.518006\pi$
$432$	24.2705	1.16772
$433$	6.94427	0.333720	0.166860	−	0.985981i	$-0.446637\pi$
$433$	6.94427	0.333720	0.166860	+	0.985981i	$0.446637\pi$
$434$	0	0
$435$	−4.47214	−0.214423
$436$	−8.79837	−0.421366
$437$	−12.8197	−0.613248
$438$	−4.09017	−0.195436
$439$	−36.4164	−1.73806	−0.869030	−	0.494759i	$-0.835256\pi$
$439$	−36.4164	−1.73806	−0.869030	+	0.494759i	$0.835256\pi$
$440$	2.23607	0.106600
$441$	0	0
$442$	−30.6525	−1.45799
$443$	−7.76393	−0.368876	−0.184438	−	0.982844i	$-0.559046\pi$
$443$	−7.76393	−0.368876	−0.184438	+	0.982844i	$0.559046\pi$
$444$	−2.14590	−0.101840
$445$	14.2361	0.674854
$446$	−27.4164	−1.29820
$447$	1.18034	0.0558282
$448$	0	0
$449$	21.0557	0.993681	0.496841	−	0.867842i	$-0.334493\pi$
$449$	21.0557	0.993681	0.496841	+	0.867842i	$0.334493\pi$
$450$	12.9443	0.610199
$451$	−1.00000	−0.0470882
$452$	12.2918	0.578157
$453$	5.94427	0.279286
$454$	−8.85410	−0.415544
$455$	0	0
$456$	−3.29180	−0.154152
$457$	−26.2361	−1.22727	−0.613636	−	0.789589i	$-0.710294\pi$
$457$	−26.2361	−1.22727	−0.613636	+	0.789589i	$0.710294\pi$
$458$	−32.5623	−1.52154
$459$	−21.1803	−0.988614
$460$	5.38197	0.250935
$461$	−38.9443	−1.81382	−0.906908	−	0.421329i	$-0.861564\pi$
$461$	−38.9443	−1.81382	−0.906908	+	0.421329i	$0.861564\pi$
$462$	0	0
$463$	−2.11146	−0.0981277	−0.0490638	−	0.998796i	$-0.515624\pi$
$463$	−2.11146	−0.0981277	−0.0490638	+	0.998796i	$0.515624\pi$
$464$	−21.7082	−1.00778
$465$	0.236068	0.0109474
$466$	5.32624	0.246733
$467$	8.81966	0.408125	0.204063	−	0.978958i	$-0.434585\pi$
$467$	8.81966	0.408125	0.204063	+	0.978958i	$0.434585\pi$
$468$	5.52786	0.255526
$469$	0	0
$470$	5.61803	0.259141
$471$	−2.23607	−0.103033
$472$	−19.4721	−0.896278
$473$	−6.47214	−0.297589
$474$	−1.61803	−0.0743188
$475$	−5.88854	−0.270185
$476$	0	0
$477$	20.4721	0.937355
$478$	−4.00000	−0.182956
$479$	21.0000	0.959514	0.479757	−	0.877401i	$-0.340725\pi$
$479$	21.0000	0.959514	0.479757	+	0.877401i	$0.340725\pi$
$480$	3.38197	0.154365
$481$	15.5279	0.708010
$482$	2.38197	0.108496
$483$	0	0
$484$	−6.18034	−0.280925
$485$	−8.47214	−0.384700
$486$	25.8885	1.17433
$487$	−25.5410	−1.15737	−0.578687	−	0.815550i	$-0.696435\pi$
$487$	−25.5410	−1.15737	−0.578687	+	0.815550i	$0.696435\pi$
$488$	−21.1803	−0.958789
$489$	−5.29180	−0.239303
$490$	0	0
$491$	−12.3607	−0.557830	−0.278915	−	0.960316i	$-0.589975\pi$
$491$	−12.3607	−0.557830	−0.278915	+	0.960316i	$0.589975\pi$
$492$	−0.618034	−0.0278631
$493$	18.9443	0.853207
$494$	−10.6525	−0.479278
$495$	2.00000	0.0898933
$496$	1.14590	0.0514523
$497$	0	0
$498$	−2.47214	−0.110779
$499$	−16.0557	−0.718753	−0.359377	−	0.933193i	$-0.617011\pi$
$499$	−16.0557	−0.718753	−0.359377	+	0.933193i	$0.617011\pi$
$500$	5.56231	0.248754
$501$	−2.47214	−0.110447
$502$	43.4164	1.93777
$503$	4.00000	0.178351	0.0891756	−	0.996016i	$-0.471577\pi$
$503$	4.00000	0.178351	0.0891756	+	0.996016i	$0.471577\pi$
$504$	0	0
$505$	−3.29180	−0.146483
$506$	−14.0902	−0.626384
$507$	7.00000	0.310881
$508$	9.52786	0.422731
$509$	4.81966	0.213628	0.106814	−	0.994279i	$-0.465935\pi$
$509$	4.81966	0.213628	0.106814	+	0.994279i	$0.465935\pi$
$510$	−6.85410	−0.303505
$511$	0	0
$512$	−5.29180	−0.233867
$513$	−7.36068	−0.324982
$514$	−2.09017	−0.0921934
$515$	−17.1803	−0.757056
$516$	−4.00000	−0.176090
$517$	−3.47214	−0.152704
$518$	0	0
$519$	−18.8885	−0.829115
$520$	−10.0000	−0.438529
$521$	39.6525	1.73721	0.868603	−	0.495508i	$-0.165018\pi$
$521$	39.6525	1.73721	0.868603	+	0.495508i	$0.165018\pi$
$522$	−14.4721	−0.633428
$523$	16.2361	0.709954	0.354977	−	0.934875i	$-0.384489\pi$
$523$	16.2361	0.709954	0.354977	+	0.934875i	$0.384489\pi$
$524$	−8.43769	−0.368602
$525$	0	0
$526$	12.0902	0.527156
$527$	−1.00000	−0.0435607
$528$	−4.85410	−0.211248
$529$	52.8328	2.29708
$530$	16.5623	0.719421
$531$	−17.4164	−0.755808
$532$	0	0
$533$	4.47214	0.193710
$534$	−23.0344	−0.996798
$535$	1.29180	0.0558492
$536$	−13.2918	−0.574118
$537$	−10.4164	−0.449501
$538$	−31.5066	−1.35835
$539$	0	0
$540$	3.09017	0.132980
$541$	20.5279	0.882562	0.441281	−	0.897369i	$-0.354524\pi$
$541$	20.5279	0.882562	0.441281	+	0.897369i	$0.354524\pi$
$542$	−35.0344	−1.50486
$543$	−21.4164	−0.919066
$544$	−14.3262	−0.614232
$545$	14.2361	0.609806
$546$	0	0
$547$	−9.52786	−0.407382	−0.203691	−	0.979035i	$-0.565294\pi$
$547$	−9.52786	−0.407382	−0.203691	+	0.979035i	$0.565294\pi$
$548$	9.67376	0.413243
$549$	−18.9443	−0.808522
$550$	−6.47214	−0.275973
$551$	6.58359	0.280470
$552$	19.4721	0.828789
$553$	0	0
$554$	−6.56231	−0.278806
$555$	3.47214	0.147384
$556$	10.4721	0.444117
$557$	−15.1803	−0.643212	−0.321606	−	0.946874i	$-0.604223\pi$
$557$	−15.1803	−0.643212	−0.321606	+	0.946874i	$0.604223\pi$
$558$	0.763932	0.0323398
$559$	28.9443	1.22421
$560$	0	0
$561$	4.23607	0.178847
$562$	−7.23607	−0.305235
$563$	−11.0000	−0.463595	−0.231797	−	0.972764i	$-0.574461\pi$
$563$	−11.0000	−0.463595	−0.231797	+	0.972764i	$0.574461\pi$
$564$	−2.14590	−0.0903586
$565$	−19.8885	−0.836717
$566$	18.0902	0.760387
$567$	0	0
$568$	32.3607	1.35782
$569$	−29.9443	−1.25533	−0.627665	−	0.778484i	$-0.715989\pi$
$569$	−29.9443	−1.25533	−0.627665	+	0.778484i	$0.715989\pi$
$570$	−2.38197	−0.0997696
$571$	−28.5279	−1.19385	−0.596927	−	0.802296i	$-0.703612\pi$
$571$	−28.5279	−1.19385	−0.596927	+	0.802296i	$0.703612\pi$
$572$	−2.76393	−0.115566
$573$	5.47214	0.228602
$574$	0	0
$575$	34.8328	1.45263
$576$	−8.47214	−0.353006
$577$	−31.5410	−1.31307	−0.656535	−	0.754296i	$-0.727979\pi$
$577$	−31.5410	−1.31307	−0.656535	+	0.754296i	$0.727979\pi$
$578$	1.52786	0.0635508
$579$	0.819660	0.0340639
$580$	−2.76393	−0.114766
$581$	0	0
$582$	13.7082	0.568223
$583$	−10.2361	−0.423935
$584$	5.65248	0.233901
$585$	−8.94427	−0.369800
$586$	46.6525	1.92720
$587$	−16.0000	−0.660391	−0.330195	−	0.943913i	$-0.607115\pi$
$587$	−16.0000	−0.660391	−0.330195	+	0.943913i	$0.607115\pi$
$588$	0	0
$589$	−0.347524	−0.0143195
$590$	−14.0902	−0.580083
$591$	−2.94427	−0.121111
$592$	16.8541	0.692699
$593$	−7.76393	−0.318826	−0.159413	−	0.987212i	$-0.550960\pi$
$593$	−7.76393	−0.318826	−0.159413	+	0.987212i	$0.550960\pi$
$594$	−8.09017	−0.331944
$595$	0	0
$596$	0.729490	0.0298811
$597$	17.9443	0.734410
$598$	63.0132	2.57680
$599$	−18.1246	−0.740552	−0.370276	−	0.928922i	$-0.620737\pi$
$599$	−18.1246	−0.740552	−0.370276	+	0.928922i	$0.620737\pi$
$600$	8.94427	0.365148
$601$	0.472136	0.0192588	0.00962941	−	0.999954i	$-0.496935\pi$
$601$	0.472136	0.0192588	0.00962941	+	0.999954i	$0.496935\pi$
$602$	0	0
$603$	−11.8885	−0.484139
$604$	3.67376	0.149483
$605$	10.0000	0.406558
$606$	5.32624	0.216364
$607$	29.1803	1.18439	0.592197	−	0.805793i	$-0.298261\pi$
$607$	29.1803	1.18439	0.592197	+	0.805793i	$0.298261\pi$
$608$	−4.97871	−0.201914
$609$	0	0
$610$	−15.3262	−0.620541
$611$	15.5279	0.628190
$612$	−5.23607	−0.211656
$613$	44.8885	1.81303	0.906516	−	0.422172i	$-0.138732\pi$
$613$	44.8885	1.81303	0.906516	+	0.422172i	$0.138732\pi$
$614$	−16.0000	−0.645707
$615$	1.00000	0.0403239
$616$	0	0
$617$	25.4164	1.02323	0.511613	−	0.859216i	$-0.329048\pi$
$617$	25.4164	1.02323	0.511613	+	0.859216i	$0.329048\pi$
$618$	27.7984	1.11821
$619$	−21.7639	−0.874766	−0.437383	−	0.899275i	$-0.644095\pi$
$619$	−21.7639	−0.874766	−0.437383	+	0.899275i	$0.644095\pi$
$620$	0.145898	0.00585941
$621$	43.5410	1.74724
$622$	−35.3262	−1.41645
$623$	0	0
$624$	21.7082	0.869024
$625$	11.0000	0.440000
$626$	−27.9787	−1.11825
$627$	1.47214	0.0587914
$628$	−1.38197	−0.0551464
$629$	−14.7082	−0.586454
$630$	0	0
$631$	−32.0000	−1.27390	−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000	−1.27390	−0.636950	+	0.770905i	$0.719804\pi$
$632$	2.23607	0.0889460
$633$	0	0
$634$	41.6869	1.65560
$635$	−15.4164	−0.611781
$636$	−6.32624	−0.250852
$637$	0	0
$638$	7.23607	0.286479
$639$	28.9443	1.14502
$640$	−13.6180	−0.538300
$641$	44.2361	1.74722	0.873610	−	0.486627i	$-0.161773\pi$
$641$	44.2361	1.74722	0.873610	+	0.486627i	$0.161773\pi$
$642$	−2.09017	−0.0824924
$643$	27.7771	1.09542	0.547711	−	0.836668i	$-0.315499\pi$
$643$	27.7771	1.09542	0.547711	+	0.836668i	$0.315499\pi$
$644$	0	0
$645$	6.47214	0.254840
$646$	10.0902	0.396992
$647$	−17.7639	−0.698372	−0.349186	−	0.937053i	$-0.613542\pi$
$647$	−17.7639	−0.698372	−0.349186	+	0.937053i	$0.613542\pi$
$648$	−2.23607	−0.0878410
$649$	8.70820	0.341827
$650$	28.9443	1.13529
$651$	0	0
$652$	−3.27051	−0.128083
$653$	−13.0689	−0.511425	−0.255712	−	0.966753i	$-0.582310\pi$
$653$	−13.0689	−0.511425	−0.255712	+	0.966753i	$0.582310\pi$
$654$	−23.0344	−0.900718
$655$	13.6525	0.533446
$656$	4.85410	0.189521
$657$	5.05573	0.197243
$658$	0	0
$659$	−24.9443	−0.971691	−0.485845	−	0.874045i	$-0.661488\pi$
$659$	−24.9443	−0.971691	−0.485845	+	0.874045i	$0.661488\pi$
$660$	−0.618034	−0.0240569
$661$	2.63932	0.102658	0.0513288	−	0.998682i	$-0.483654\pi$
$661$	2.63932	0.102658	0.0513288	+	0.998682i	$0.483654\pi$
$662$	−51.5066	−2.00186
$663$	−18.9443	−0.735735
$664$	3.41641	0.132582
$665$	0	0
$666$	11.2361	0.435389
$667$	−38.9443	−1.50793
$668$	−1.52786	−0.0591148
$669$	−16.9443	−0.655103
$670$	−9.61803	−0.371577
$671$	9.47214	0.365668
$672$	0	0
$673$	−45.4164	−1.75067	−0.875337	−	0.483513i	$-0.839360\pi$
$673$	−45.4164	−1.75067	−0.875337	+	0.483513i	$0.839360\pi$
$674$	−13.7082	−0.528020
$675$	20.0000	0.769800
$676$	4.32624	0.166394
$677$	15.9443	0.612788	0.306394	−	0.951905i	$-0.400877\pi$
$677$	15.9443	0.612788	0.306394	+	0.951905i	$0.400877\pi$
$678$	32.1803	1.23588
$679$	0	0
$680$	9.47214	0.363240
$681$	−5.47214	−0.209693
$682$	−0.381966	−0.0146262
$683$	15.4721	0.592025	0.296012	−	0.955184i	$-0.404343\pi$
$683$	15.4721	0.592025	0.296012	+	0.955184i	$0.404343\pi$
$684$	−1.81966	−0.0695764
$685$	−15.6525	−0.598050
$686$	0	0
$687$	−20.1246	−0.767802
$688$	31.4164	1.19774
$689$	45.7771	1.74397
$690$	14.0902	0.536404
$691$	47.3607	1.80169	0.900843	−	0.434146i	$-0.142950\pi$
$691$	47.3607	1.80169	0.900843	+	0.434146i	$0.142950\pi$
$692$	−11.6738	−0.443770
$693$	0	0
$694$	−4.85410	−0.184259
$695$	−16.9443	−0.642733
$696$	−10.0000	−0.379049
$697$	−4.23607	−0.160453
$698$	−33.1246	−1.25379
$699$	3.29180	0.124507
$700$	0	0
$701$	−42.3607	−1.59994	−0.799970	−	0.600039i	$-0.795152\pi$
$701$	−42.3607	−1.59994	−0.799970	+	0.600039i	$0.795152\pi$
$702$	36.1803	1.36554
$703$	−5.11146	−0.192782
$704$	4.23607	0.159653
$705$	3.47214	0.130768
$706$	41.2148	1.55114
$707$	0	0
$708$	5.38197	0.202267
$709$	38.1246	1.43180	0.715900	−	0.698203i	$-0.246017\pi$
$709$	38.1246	1.43180	0.715900	+	0.698203i	$0.246017\pi$
$710$	23.4164	0.878802
$711$	2.00000	0.0750059
$712$	31.8328	1.19299
$713$	2.05573	0.0769876
$714$	0	0
$715$	4.47214	0.167248
$716$	−6.43769	−0.240588
$717$	−2.47214	−0.0923236
$718$	−22.0902	−0.824398
$719$	−1.36068	−0.0507448	−0.0253724	−	0.999678i	$-0.508077\pi$
$719$	−1.36068	−0.0507448	−0.0253724	+	0.999678i	$0.508077\pi$
$720$	−9.70820	−0.361803
$721$	0	0
$722$	−27.2361	−1.01362
$723$	1.47214	0.0547493
$724$	−13.2361	−0.491915
$725$	−17.8885	−0.664364
$726$	−16.1803	−0.600509
$727$	7.05573	0.261682	0.130841	−	0.991403i	$-0.458232\pi$
$727$	7.05573	0.261682	0.130841	+	0.991403i	$0.458232\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	4.09017	0.151384
$731$	−27.4164	−1.01403
$732$	5.85410	0.216374
$733$	17.8328	0.658670	0.329335	−	0.944213i	$-0.393175\pi$
$733$	17.8328	0.658670	0.329335	+	0.944213i	$0.393175\pi$
$734$	−8.38197	−0.309384
$735$	0	0
$736$	29.4508	1.08557
$737$	5.94427	0.218960
$738$	3.23607	0.119121
$739$	−43.6525	−1.60578	−0.802891	−	0.596126i	$-0.796706\pi$
$739$	−43.6525	−1.60578	−0.802891	+	0.596126i	$0.796706\pi$
$740$	2.14590	0.0788848
$741$	−6.58359	−0.241854
$742$	0	0
$743$	−44.7214	−1.64067	−0.820334	−	0.571885i	$-0.806212\pi$
$743$	−44.7214	−1.64067	−0.820334	+	0.571885i	$0.806212\pi$
$744$	0.527864	0.0193524
$745$	−1.18034	−0.0432443
$746$	−0.0901699	−0.00330136
$747$	3.05573	0.111803
$748$	2.61803	0.0957248
$749$	0	0
$750$	14.5623	0.531740
$751$	−22.5279	−0.822053	−0.411027	−	0.911623i	$-0.634830\pi$
$751$	−22.5279	−0.822053	−0.411027	+	0.911623i	$0.634830\pi$
$752$	16.8541	0.614606
$753$	26.8328	0.977842
$754$	−32.3607	−1.17851
$755$	−5.94427	−0.216334
$756$	0	0
$757$	−2.94427	−0.107011	−0.0535057	−	0.998568i	$-0.517040\pi$
$757$	−2.94427	−0.107011	−0.0535057	+	0.998568i	$0.517040\pi$
$758$	50.8328	1.84633
$759$	−8.70820	−0.316088
$760$	3.29180	0.119406
$761$	16.3050	0.591054	0.295527	−	0.955334i	$-0.404505\pi$
$761$	16.3050	0.591054	0.295527	+	0.955334i	$0.404505\pi$
$762$	24.9443	0.903636
$763$	0	0
$764$	3.38197	0.122355
$765$	8.47214	0.306311
$766$	33.7984	1.22118
$767$	−38.9443	−1.40620
$768$	13.5623	0.489388
$769$	−16.8328	−0.607007	−0.303503	−	0.952830i	$-0.598156\pi$
$769$	−16.8328	−0.607007	−0.303503	+	0.952830i	$0.598156\pi$
$770$	0	0
$771$	−1.29180	−0.0465229
$772$	0.506578	0.0182321
$773$	−9.65248	−0.347175	−0.173588	−	0.984818i	$-0.555536\pi$
$773$	−9.65248	−0.347175	−0.173588	+	0.984818i	$0.555536\pi$
$774$	20.9443	0.752826
$775$	0.944272	0.0339192
$776$	−18.9443	−0.680060
$777$	0	0
$778$	−1.61803	−0.0580093
$779$	−1.47214	−0.0527447
$780$	2.76393	0.0989646
$781$	−14.4721	−0.517854
$782$	−59.6869	−2.13440
$783$	−22.3607	−0.799106
$784$	0	0
$785$	2.23607	0.0798087
$786$	−22.0902	−0.787930
$787$	9.65248	0.344074	0.172037	−	0.985091i	$-0.444965\pi$
$787$	9.65248	0.344074	0.172037	+	0.985091i	$0.444965\pi$
$788$	−1.81966	−0.0648227
$789$	7.47214	0.266015
$790$	1.61803	0.0575671
$791$	0	0
$792$	4.47214	0.158910
$793$	−42.3607	−1.50427
$794$	44.7426	1.58786
$795$	10.2361	0.363036
$796$	11.0902	0.393081
$797$	24.8328	0.879623	0.439812	−	0.898090i	$-0.355045\pi$
$797$	24.8328	0.879623	0.439812	+	0.898090i	$0.355045\pi$
$798$	0	0
$799$	−14.7082	−0.520339
$800$	13.5279	0.478282
$801$	28.4721	1.00601
$802$	12.8541	0.453894
$803$	−2.52786	−0.0892064
$804$	3.67376	0.129564
$805$	0	0
$806$	1.70820	0.0601689
$807$	−19.4721	−0.685452
$808$	−7.36068	−0.258948
$809$	−5.65248	−0.198730	−0.0993652	−	0.995051i	$-0.531681\pi$
$809$	−5.65248	−0.198730	−0.0993652	+	0.995051i	$0.531681\pi$
$810$	−1.61803	−0.0568519
$811$	52.7214	1.85130	0.925649	−	0.378384i	$-0.123520\pi$
$811$	52.7214	1.85130	0.925649	+	0.378384i	$0.123520\pi$
$812$	0	0
$813$	−21.6525	−0.759385
$814$	−5.61803	−0.196912
$815$	5.29180	0.185364
$816$	−20.5623	−0.719825
$817$	−9.52786	−0.333338
$818$	−37.0344	−1.29488
$819$	0	0
$820$	0.618034	0.0215827
$821$	−21.0000	−0.732905	−0.366453	−	0.930437i	$-0.619428\pi$
$821$	−21.0000	−0.732905	−0.366453	+	0.930437i	$0.619428\pi$
$822$	25.3262	0.883354
$823$	−13.4721	−0.469609	−0.234805	−	0.972043i	$-0.575445\pi$
$823$	−13.4721	−0.469609	−0.234805	+	0.972043i	$0.575445\pi$
$824$	−38.4164	−1.33830
$825$	−4.00000	−0.139262
$826$	0	0
$827$	36.0000	1.25184	0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000	1.25184	0.625921	+	0.779886i	$0.284723\pi$
$828$	10.7639	0.374072
$829$	3.94427	0.136990	0.0684951	−	0.997651i	$-0.478180\pi$
$829$	3.94427	0.136990	0.0684951	+	0.997651i	$0.478180\pi$
$830$	2.47214	0.0858091
$831$	−4.05573	−0.140692
$832$	−18.9443	−0.656774
$833$	0	0
$834$	27.4164	0.949353
$835$	2.47214	0.0855518
$836$	0.909830	0.0314671
$837$	1.18034	0.0407985
$838$	−28.9443	−0.999863
$839$	20.9443	0.723077	0.361538	−	0.932357i	$-0.382252\pi$
$839$	20.9443	0.723077	0.361538	+	0.932357i	$0.382252\pi$
$840$	0	0
$841$	−9.00000	−0.310345
$842$	−26.6525	−0.918505
$843$	−4.47214	−0.154029
$844$	0	0
$845$	−7.00000	−0.240807
$846$	11.2361	0.386304
$847$	0	0
$848$	49.6869	1.70626
$849$	11.1803	0.383708
$850$	−27.4164	−0.940375
$851$	30.2361	1.03648
$852$	−8.94427	−0.306426
$853$	18.9443	0.648640	0.324320	−	0.945948i	$-0.394865\pi$
$853$	18.9443	0.648640	0.324320	+	0.945948i	$0.394865\pi$
$854$	0	0
$855$	2.94427	0.100692
$856$	2.88854	0.0987284
$857$	−10.3050	−0.352010	−0.176005	−	0.984389i	$-0.556318\pi$
$857$	−10.3050	−0.352010	−0.176005	+	0.984389i	$0.556318\pi$
$858$	−7.23607	−0.247035
$859$	−29.2918	−0.999423	−0.499712	−	0.866192i	$-0.666561\pi$
$859$	−29.2918	−0.999423	−0.499712	+	0.866192i	$0.666561\pi$
$860$	4.00000	0.136399
$861$	0	0
$862$	−3.79837	−0.129373
$863$	0.819660	0.0279016	0.0139508	−	0.999903i	$-0.495559\pi$
$863$	0.819660	0.0279016	0.0139508	+	0.999903i	$0.495559\pi$
$864$	16.9098	0.575284
$865$	18.8885	0.642230
$866$	11.2361	0.381817
$867$	0.944272	0.0320692
$868$	0	0
$869$	−1.00000	−0.0339227
$870$	−7.23607	−0.245326
$871$	−26.5836	−0.900751
$872$	31.8328	1.07800
$873$	−16.9443	−0.573477
$874$	−20.7426	−0.701630
$875$	0	0
$876$	−1.56231	−0.0527854
$877$	1.47214	0.0497105	0.0248552	−	0.999691i	$-0.492088\pi$
$877$	1.47214	0.0497105	0.0248552	+	0.999691i	$0.492088\pi$
$878$	−58.9230	−1.98855
$879$	28.8328	0.972507
$880$	4.85410	0.163632
$881$	24.4721	0.824487	0.412244	−	0.911074i	$-0.364745\pi$
$881$	24.4721	0.824487	0.412244	+	0.911074i	$0.364745\pi$
$882$	0	0
$883$	−16.5836	−0.558082	−0.279041	−	0.960279i	$-0.590017\pi$
$883$	−16.5836	−0.558082	−0.279041	+	0.960279i	$0.590017\pi$
$884$	−11.7082	−0.393790
$885$	−8.70820	−0.292723
$886$	−12.5623	−0.422039
$887$	−46.8885	−1.57436	−0.787182	−	0.616721i	$-0.788461\pi$
$887$	−46.8885	−1.57436	−0.787182	+	0.616721i	$0.788461\pi$
$888$	7.76393	0.260540
$889$	0	0
$890$	23.0344	0.772116
$891$	1.00000	0.0335013
$892$	−10.4721	−0.350633
$893$	−5.11146	−0.171048
$894$	1.90983	0.0638743
$895$	10.4164	0.348182
$896$	0	0
$897$	38.9443	1.30031
$898$	34.0689	1.13689
$899$	−1.05573	−0.0352105
$900$	4.94427	0.164809
$901$	−43.3607	−1.44455
$902$	−1.61803	−0.0538746
$903$	0	0
$904$	−44.4721	−1.47912
$905$	21.4164	0.711905
$906$	9.61803	0.319538
$907$	−14.3475	−0.476402	−0.238201	−	0.971216i	$-0.576558\pi$
$907$	−14.3475	−0.476402	−0.238201	+	0.971216i	$0.576558\pi$
$908$	−3.38197	−0.112234
$909$	−6.58359	−0.218364
$910$	0	0
$911$	−47.4164	−1.57098	−0.785488	−	0.618877i	$-0.787588\pi$
$911$	−47.4164	−1.57098	−0.785488	+	0.618877i	$0.787588\pi$
$912$	−7.14590	−0.236624
$913$	−1.52786	−0.0505649
$914$	−42.4508	−1.40415
$915$	−9.47214	−0.313139
$916$	−12.4377	−0.410953
$917$	0	0
$918$	−34.2705	−1.13110
$919$	−4.05573	−0.133786	−0.0668931	−	0.997760i	$-0.521309\pi$
$919$	−4.05573	−0.133786	−0.0668931	+	0.997760i	$0.521309\pi$
$920$	−19.4721	−0.641977
$921$	−9.88854	−0.325839
$922$	−63.0132	−2.07523
$923$	64.7214	2.13033
$924$	0	0
$925$	13.8885	0.456653
$926$	−3.41641	−0.112270
$927$	−34.3607	−1.12855
$928$	−15.1246	−0.496490
$929$	−39.5410	−1.29730	−0.648649	−	0.761087i	$-0.724666\pi$
$929$	−39.5410	−1.29730	−0.648649	+	0.761087i	$0.724666\pi$
$930$	0.381966	0.0125252
$931$	0	0
$932$	2.03444	0.0666404
$933$	−21.8328	−0.714774
$934$	14.2705	0.466945
$935$	−4.23607	−0.138534
$936$	−20.0000	−0.653720
$937$	29.4164	0.960992	0.480496	−	0.876997i	$-0.340457\pi$
$937$	29.4164	0.960992	0.480496	+	0.876997i	$0.340457\pi$
$938$	0	0
$939$	−17.2918	−0.564296
$940$	2.14590	0.0699915
$941$	34.4164	1.12194	0.560971	−	0.827835i	$-0.310428\pi$
$941$	34.4164	1.12194	0.560971	+	0.827835i	$0.310428\pi$
$942$	−3.61803	−0.117882
$943$	8.70820	0.283578
$944$	−42.2705	−1.37579
$945$	0	0
$946$	−10.4721	−0.340479
$947$	30.7082	0.997883	0.498941	−	0.866636i	$-0.333722\pi$
$947$	30.7082	0.997883	0.498941	+	0.866636i	$0.333722\pi$
$948$	−0.618034	−0.0200728
$949$	11.3050	0.366974
$950$	−9.52786	−0.309125
$951$	25.7639	0.835453
$952$	0	0
$953$	43.8885	1.42169	0.710845	−	0.703349i	$-0.248313\pi$
$953$	43.8885	1.42169	0.710845	+	0.703349i	$0.248313\pi$
$954$	33.1246	1.07245
$955$	−5.47214	−0.177074
$956$	−1.52786	−0.0494147
$957$	4.47214	0.144564
$958$	33.9787	1.09780
$959$	0	0
$960$	−4.23607	−0.136719
$961$	−30.9443	−0.998202
$962$	25.1246	0.810050
$963$	2.58359	0.0832551
$964$	0.909830	0.0293037
$965$	−0.819660	−0.0263858
$966$	0	0
$967$	21.3050	0.685121	0.342561	−	0.939496i	$-0.388706\pi$
$967$	21.3050	0.685121	0.342561	+	0.939496i	$0.388706\pi$
$968$	22.3607	0.718699
$969$	6.23607	0.200331
$970$	−13.7082	−0.440144
$971$	46.7771	1.50115	0.750574	−	0.660786i	$-0.229777\pi$
$971$	46.7771	1.50115	0.750574	+	0.660786i	$0.229777\pi$
$972$	9.88854	0.317175
$973$	0	0
$974$	−41.3262	−1.32418
$975$	17.8885	0.572892
$976$	−45.9787	−1.47174
$977$	23.6525	0.756710	0.378355	−	0.925661i	$-0.376490\pi$
$977$	23.6525	0.756710	0.378355	+	0.925661i	$0.376490\pi$
$978$	−8.56231	−0.273792
$979$	−14.2361	−0.454987
$980$	0	0
$981$	28.4721	0.909045
$982$	−20.0000	−0.638226
$983$	−50.1246	−1.59873	−0.799363	−	0.600848i	$-0.794830\pi$
$983$	−50.1246	−1.59873	−0.799363	+	0.600848i	$0.794830\pi$
$984$	2.23607	0.0712832
$985$	2.94427	0.0938123
$986$	30.6525	0.976174
$987$	0	0
$988$	−4.06888	−0.129448
$989$	56.3607	1.79217
$990$	3.23607	0.102849
$991$	−46.4164	−1.47447	−0.737233	−	0.675639i	$-0.763868\pi$
$991$	−46.4164	−1.47447	−0.737233	+	0.675639i	$0.763868\pi$
$992$	0.798374	0.0253484
$993$	−31.8328	−1.01018
$994$	0	0
$995$	−17.9443	−0.568872
$996$	−0.944272	−0.0299204
$997$	−41.0689	−1.30066	−0.650332	−	0.759650i	$-0.725370\pi$
$997$	−41.0689	−1.30066	−0.650332	+	0.759650i	$0.725370\pi$
$998$	−25.9787	−0.822342
$999$	17.3607	0.549268

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.f.1.2		2
7.2	even	3		287.2.e.a.165.1	✓	4
7.4	even	3		287.2.e.a.247.1	yes	4
7.6	odd	2		2009.2.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.a.165.1	✓	4	7.2	even	3
287.2.e.a.247.1	yes	4	7.4	even	3
2009.2.a.e.1.2		2	7.6	odd	2
2009.2.a.f.1.2		2	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)

\(f(q)\)	\(=\)	\(q+1.61803 q^{2} +1.00000 q^{3} +0.618034 q^{4} -1.00000 q^{5} +1.61803 q^{6} -2.23607 q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q+1.61803 q^{2} +1.00000 q^{3} +0.618034 q^{4} -1.00000 q^{5} +1.61803 q^{6} -2.23607 q^{8} -2.00000 q^{9} -1.61803 q^{10} +1.00000 q^{11} +0.618034 q^{12} -4.47214 q^{13} -1.00000 q^{15} -4.85410 q^{16} +4.23607 q^{17} -3.23607 q^{18} +1.47214 q^{19} -0.618034 q^{20} +1.61803 q^{22} -8.70820 q^{23} -2.23607 q^{24} -4.00000 q^{25} -7.23607 q^{26} -5.00000 q^{27} +4.47214 q^{29} -1.61803 q^{30} -0.236068 q^{31} -3.38197 q^{32} +1.00000 q^{33} +6.85410 q^{34} -1.23607 q^{36} -3.47214 q^{37} +2.38197 q^{38} -4.47214 q^{39} +2.23607 q^{40} -1.00000 q^{41} -6.47214 q^{43} +0.618034 q^{44} +2.00000 q^{45} -14.0902 q^{46} -3.47214 q^{47} -4.85410 q^{48} -6.47214 q^{50} +4.23607 q^{51} -2.76393 q^{52} -10.2361 q^{53} -8.09017 q^{54} -1.00000 q^{55} +1.47214 q^{57} +7.23607 q^{58} +8.70820 q^{59} -0.618034 q^{60} +9.47214 q^{61} -0.381966 q^{62} +4.23607 q^{64} +4.47214 q^{65} +1.61803 q^{66} +5.94427 q^{67} +2.61803 q^{68} -8.70820 q^{69} -14.4721 q^{71} +4.47214 q^{72} -2.52786 q^{73} -5.61803 q^{74} -4.00000 q^{75} +0.909830 q^{76} -7.23607 q^{78} -1.00000 q^{79} +4.85410 q^{80} +1.00000 q^{81} -1.61803 q^{82} -1.52786 q^{83} -4.23607 q^{85} -10.4721 q^{86} +4.47214 q^{87} -2.23607 q^{88} -14.2361 q^{89} +3.23607 q^{90} -5.38197 q^{92} -0.236068 q^{93} -5.61803 q^{94} -1.47214 q^{95} -3.38197 q^{96} +8.47214 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 2 q^{3} - q^{4} - 2 q^{5} + q^{6} - 4 q^{9}+O(q^{10}) \) 2 * q + q^2 + 2 * q^3 - q^4 - 2 * q^5 + q^6 - 4 * q^9	\( 2 q + q^{2} + 2 q^{3} - q^{4} - 2 q^{5} + q^{6} - 4 q^{9} - q^{10} + 2 q^{11} - q^{12} - 2 q^{15} - 3 q^{16} + 4 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + q^{22} - 4 q^{23} - 8 q^{25} - 10 q^{26} - 10 q^{27} - q^{30} + 4 q^{31} - 9 q^{32} + 2 q^{33} + 7 q^{34} + 2 q^{36} + 2 q^{37} + 7 q^{38} - 2 q^{41} - 4 q^{43} - q^{44} + 4 q^{45} - 17 q^{46} + 2 q^{47} - 3 q^{48} - 4 q^{50} + 4 q^{51} - 10 q^{52} - 16 q^{53} - 5 q^{54} - 2 q^{55} - 6 q^{57} + 10 q^{58} + 4 q^{59} + q^{60} + 10 q^{61} - 3 q^{62} + 4 q^{64} + q^{66} - 6 q^{67} + 3 q^{68} - 4 q^{69} - 20 q^{71} - 14 q^{73} - 9 q^{74} - 8 q^{75} + 13 q^{76} - 10 q^{78} - 2 q^{79} + 3 q^{80} + 2 q^{81} - q^{82} - 12 q^{83} - 4 q^{85} - 12 q^{86} - 24 q^{89} + 2 q^{90} - 13 q^{92} + 4 q^{93} - 9 q^{94} + 6 q^{95} - 9 q^{96} + 8 q^{97} - 4 q^{99}+O(q^{100}) \) 2 * q + q^2 + 2 * q^3 - q^4 - 2 * q^5 + q^6 - 4 * q^9 - q^10 + 2 * q^11 - q^12 - 2 * q^15 - 3 * q^16 + 4 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + q^22 - 4 * q^23 - 8 * q^25 - 10 * q^26 - 10 * q^27 - q^30 + 4 * q^31 - 9 * q^32 + 2 * q^33 + 7 * q^34 + 2 * q^36 + 2 * q^37 + 7 * q^38 - 2 * q^41 - 4 * q^43 - q^44 + 4 * q^45 - 17 * q^46 + 2 * q^47 - 3 * q^48 - 4 * q^50 + 4 * q^51 - 10 * q^52 - 16 * q^53 - 5 * q^54 - 2 * q^55 - 6 * q^57 + 10 * q^58 + 4 * q^59 + q^60 + 10 * q^61 - 3 * q^62 + 4 * q^64 + q^66 - 6 * q^67 + 3 * q^68 - 4 * q^69 - 20 * q^71 - 14 * q^73 - 9 * q^74 - 8 * q^75 + 13 * q^76 - 10 * q^78 - 2 * q^79 + 3 * q^80 + 2 * q^81 - q^82 - 12 * q^83 - 4 * q^85 - 12 * q^86 - 24 * q^89 + 2 * q^90 - 13 * q^92 + 4 * q^93 - 9 * q^94 + 6 * q^95 - 9 * q^96 + 8 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more