LMFDB - Embedded newform 3381.2.a.bk.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 6x^{8} + 36x^{7} + x^{6} - 100x^{5} + 26x^{4} + 108x^{3} - 33x^{2} - 36x + 14 $ x^10 - 4x^9 - 6x^8 + 36x^7 + x^6 - 100x^5 + 26x^4 + 108x^3 - 33x^2 - 36x + 14
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.11439$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.11439 q^{2} -1.00000 q^{3} -0.758127 q^{4} -1.17161 q^{5} +1.11439 q^{6} +3.07364 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.11439 q^{2} -1.00000 q^{3} -0.758127 q^{4} -1.17161 q^{5} +1.11439 q^{6} +3.07364 q^{8} +1.00000 q^{9} +1.30563 q^{10} -0.466550 q^{11} +0.758127 q^{12} -1.79833 q^{13} +1.17161 q^{15} -1.90899 q^{16} -0.443057 q^{17} -1.11439 q^{18} +2.93208 q^{19} +0.888229 q^{20} +0.519920 q^{22} -1.00000 q^{23} -3.07364 q^{24} -3.62733 q^{25} +2.00405 q^{26} -1.00000 q^{27} +1.64611 q^{29} -1.30563 q^{30} -7.66867 q^{31} -4.01991 q^{32} +0.466550 q^{33} +0.493740 q^{34} -0.758127 q^{36} +8.65887 q^{37} -3.26749 q^{38} +1.79833 q^{39} -3.60110 q^{40} +1.41208 q^{41} +9.81812 q^{43} +0.353704 q^{44} -1.17161 q^{45} +1.11439 q^{46} -5.59971 q^{47} +1.90899 q^{48} +4.04228 q^{50} +0.443057 q^{51} +1.36336 q^{52} +3.70846 q^{53} +1.11439 q^{54} +0.546614 q^{55} -2.93208 q^{57} -1.83442 q^{58} +9.83561 q^{59} -0.888229 q^{60} +2.44660 q^{61} +8.54591 q^{62} +8.29774 q^{64} +2.10694 q^{65} -0.519920 q^{66} -9.71717 q^{67} +0.335893 q^{68} +1.00000 q^{69} +11.0965 q^{71} +3.07364 q^{72} +3.14805 q^{73} -9.64939 q^{74} +3.62733 q^{75} -2.22289 q^{76} -2.00405 q^{78} -4.92904 q^{79} +2.23659 q^{80} +1.00000 q^{81} -1.57361 q^{82} -1.23535 q^{83} +0.519089 q^{85} -10.9413 q^{86} -1.64611 q^{87} -1.43401 q^{88} +2.98451 q^{89} +1.30563 q^{90} +0.758127 q^{92} +7.66867 q^{93} +6.24028 q^{94} -3.43525 q^{95} +4.01991 q^{96} -6.32891 q^{97} -0.466550 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 - 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9	$ 10 q + 4 q^{2} - 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9} - 8 q^{10} + 2 q^{11} - 8 q^{12} + 4 q^{15} + 4 q^{16} - 12 q^{17} + 4 q^{18} - 26 q^{19} - 24 q^{20} - 8 q^{22} - 10 q^{23} - 12 q^{24} - 2 q^{25} - 4 q^{26} - 10 q^{27} + 16 q^{29} + 8 q^{30} - 12 q^{31} + 8 q^{32} - 2 q^{33} - 28 q^{34} + 8 q^{36} - 8 q^{37} - 32 q^{38} - 4 q^{40} - 10 q^{41} - 4 q^{43} - 16 q^{44} - 4 q^{45} - 4 q^{46} - 2 q^{47} - 4 q^{48} - 8 q^{50} + 12 q^{51} - 24 q^{52} + 14 q^{53} - 4 q^{54} - 16 q^{55} + 26 q^{57} - 8 q^{58} - 38 q^{59} + 24 q^{60} - 14 q^{61} + 8 q^{62} + 8 q^{64} + 12 q^{65} + 8 q^{66} - 8 q^{68} + 10 q^{69} + 24 q^{71} + 12 q^{72} - 8 q^{73} - 8 q^{74} + 2 q^{75} - 64 q^{76} + 4 q^{78} - 16 q^{79} - 28 q^{80} + 10 q^{81} + 40 q^{82} - 28 q^{83} - 4 q^{85} + 20 q^{86} - 16 q^{87} - 68 q^{88} - 32 q^{89} - 8 q^{90} - 8 q^{92} + 12 q^{93} - 56 q^{94} + 8 q^{95} - 8 q^{96} - 4 q^{97} + 2 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 - 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9 - 8 * q^10 + 2 * q^11 - 8 * q^12 + 4 * q^15 + 4 * q^16 - 12 * q^17 + 4 * q^18 - 26 * q^19 - 24 * q^20 - 8 * q^22 - 10 * q^23 - 12 * q^24 - 2 * q^25 - 4 * q^26 - 10 * q^27 + 16 * q^29 + 8 * q^30 - 12 * q^31 + 8 * q^32 - 2 * q^33 - 28 * q^34 + 8 * q^36 - 8 * q^37 - 32 * q^38 - 4 * q^40 - 10 * q^41 - 4 * q^43 - 16 * q^44 - 4 * q^45 - 4 * q^46 - 2 * q^47 - 4 * q^48 - 8 * q^50 + 12 * q^51 - 24 * q^52 + 14 * q^53 - 4 * q^54 - 16 * q^55 + 26 * q^57 - 8 * q^58 - 38 * q^59 + 24 * q^60 - 14 * q^61 + 8 * q^62 + 8 * q^64 + 12 * q^65 + 8 * q^66 - 8 * q^68 + 10 * q^69 + 24 * q^71 + 12 * q^72 - 8 * q^73 - 8 * q^74 + 2 * q^75 - 64 * q^76 + 4 * q^78 - 16 * q^79 - 28 * q^80 + 10 * q^81 + 40 * q^82 - 28 * q^83 - 4 * q^85 + 20 * q^86 - 16 * q^87 - 68 * q^88 - 32 * q^89 - 8 * q^90 - 8 * q^92 + 12 * q^93 - 56 * q^94 + 8 * q^95 - 8 * q^96 - 4 * q^97 + 2 * 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 $

$2$	−1.11439	−0.787995	−0.393998	−	0.919111i	$-0.628908\pi$
$2$	−1.11439	−0.787995	−0.393998	+	0.919111i	$0.628908\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.758127	−0.379064
$5$	−1.17161	−0.523959	−0.261980	−	0.965073i	$-0.584375\pi$
$5$	−1.17161	−0.523959	−0.261980	+	0.965073i	$0.584375\pi$
$6$	1.11439	0.454949
$7$	0	0
$7$	0	0
$8$	3.07364	1.08670
$9$	1.00000	0.333333
$10$	1.30563	0.412877
$11$	−0.466550	−0.140670	−0.0703350	−	0.997523i	$-0.522407\pi$
$11$	−0.466550	−0.140670	−0.0703350	+	0.997523i	$0.522407\pi$
$12$	0.758127	0.218853
$13$	−1.79833	−0.498767	−0.249383	−	0.968405i	$-0.580228\pi$
$13$	−1.79833	−0.498767	−0.249383	+	0.968405i	$0.580228\pi$
$14$	0	0
$15$	1.17161	0.302508
$16$	−1.90899	−0.477247
$17$	−0.443057	−0.107457	−0.0537285	−	0.998556i	$-0.517111\pi$
$17$	−0.443057	−0.107457	−0.0537285	+	0.998556i	$0.517111\pi$
$18$	−1.11439	−0.262665
$19$	2.93208	0.672666	0.336333	−	0.941743i	$-0.390813\pi$
$19$	2.93208	0.672666	0.336333	+	0.941743i	$0.390813\pi$
$20$	0.888229	0.198614
$21$	0	0
$22$	0.519920	0.110847
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−3.07364	−0.627404
$25$	−3.62733	−0.725467
$26$	2.00405	0.393026
$27$	−1.00000	−0.192450
$28$	0	0
$29$	1.64611	0.305675	0.152838	−	0.988251i	$-0.451159\pi$
$29$	1.64611	0.305675	0.152838	+	0.988251i	$0.451159\pi$
$30$	−1.30563	−0.238375
$31$	−7.66867	−1.37733	−0.688666	−	0.725078i	$-0.741804\pi$
$31$	−7.66867	−1.37733	−0.688666	+	0.725078i	$0.741804\pi$
$32$	−4.01991	−0.710627
$33$	0.466550	0.0812159
$34$	0.493740	0.0846756
$35$	0	0
$36$	−0.758127	−0.126355
$37$	8.65887	1.42351	0.711755	−	0.702428i	$-0.247901\pi$
$37$	8.65887	1.42351	0.711755	+	0.702428i	$0.247901\pi$
$38$	−3.26749	−0.530057
$39$	1.79833	0.287963
$40$	−3.60110	−0.569384
$41$	1.41208	0.220530	0.110265	−	0.993902i	$-0.464830\pi$
$41$	1.41208	0.220530	0.110265	+	0.993902i	$0.464830\pi$
$42$	0	0
$43$	9.81812	1.49725	0.748625	−	0.662994i	$-0.230715\pi$
$43$	9.81812	1.49725	0.748625	+	0.662994i	$0.230715\pi$
$44$	0.353704	0.0533229
$45$	−1.17161	−0.174653
$46$	1.11439	0.164308
$47$	−5.59971	−0.816802	−0.408401	−	0.912803i	$-0.633914\pi$
$47$	−5.59971	−0.816802	−0.408401	+	0.912803i	$0.633914\pi$
$48$	1.90899	0.275539
$49$	0	0
$50$	4.04228	0.571664
$51$	0.443057	0.0620404
$52$	1.36336	0.189064
$53$	3.70846	0.509396	0.254698	−	0.967021i	$-0.418024\pi$
$53$	3.70846	0.509396	0.254698	+	0.967021i	$0.418024\pi$
$54$	1.11439	0.151650
$55$	0.546614	0.0737054
$56$	0	0
$57$	−2.93208	−0.388364
$58$	−1.83442	−0.240871
$59$	9.83561	1.28049	0.640244	−	0.768172i	$-0.278833\pi$
$59$	9.83561	1.28049	0.640244	+	0.768172i	$0.278833\pi$
$60$	−0.888229	−0.114670
$61$	2.44660	0.313255	0.156627	−	0.987658i	$-0.449938\pi$
$61$	2.44660	0.313255	0.156627	+	0.987658i	$0.449938\pi$
$62$	8.54591	1.08533
$63$	0	0
$64$	8.29774	1.03722
$65$	2.10694	0.261334
$66$	−0.519920	−0.0639977
$67$	−9.71717	−1.18714	−0.593571	−	0.804782i	$-0.702282\pi$
$67$	−9.71717	−1.18714	−0.593571	+	0.804782i	$0.702282\pi$
$68$	0.335893	0.0407331
$69$	1.00000	0.120386
$70$	0	0
$71$	11.0965	1.31692	0.658459	−	0.752617i	$-0.271209\pi$
$71$	11.0965	1.31692	0.658459	+	0.752617i	$0.271209\pi$
$72$	3.07364	0.362232
$73$	3.14805	0.368451	0.184226	−	0.982884i	$-0.441022\pi$
$73$	3.14805	0.368451	0.184226	+	0.982884i	$0.441022\pi$
$74$	−9.64939	−1.12172
$75$	3.62733	0.418848
$76$	−2.22289	−0.254983
$77$	0	0
$78$	−2.00405	−0.226914
$79$	−4.92904	−0.554560	−0.277280	−	0.960789i	$-0.589433\pi$
$79$	−4.92904	−0.554560	−0.277280	+	0.960789i	$0.589433\pi$
$80$	2.23659	0.250058
$81$	1.00000	0.111111
$82$	−1.57361	−0.173777
$83$	−1.23535	−0.135597	−0.0677984	−	0.997699i	$-0.521597\pi$
$83$	−1.23535	−0.135597	−0.0677984	+	0.997699i	$0.521597\pi$
$84$	0	0
$85$	0.519089	0.0563031
$86$	−10.9413	−1.17983
$87$	−1.64611	−0.176482
$88$	−1.43401	−0.152866
$89$	2.98451	0.316357	0.158179	−	0.987411i	$-0.449438\pi$
$89$	2.98451	0.316357	0.158179	+	0.987411i	$0.449438\pi$
$90$	1.30563	0.137626
$91$	0	0
$92$	0.758127	0.0790402
$93$	7.66867	0.795204
$94$	6.24028	0.643636
$95$	−3.43525	−0.352449
$96$	4.01991	0.410281
$97$	−6.32891	−0.642604	−0.321302	−	0.946977i	$-0.604120\pi$
$97$	−6.32891	−0.642604	−0.321302	+	0.946977i	$0.604120\pi$
$98$	0	0
$99$	−0.466550	−0.0468900
$100$	2.74998	0.274998
$101$	−4.95340	−0.492881	−0.246441	−	0.969158i	$-0.579261\pi$
$101$	−4.95340	−0.492881	−0.246441	+	0.969158i	$0.579261\pi$
$102$	−0.493740	−0.0488875
$103$	1.45881	0.143740	0.0718702	−	0.997414i	$-0.477103\pi$
$103$	1.45881	0.143740	0.0718702	+	0.997414i	$0.477103\pi$
$104$	−5.52741	−0.542008
$105$	0	0
$106$	−4.13268	−0.401401
$107$	11.6424	1.12552	0.562759	−	0.826621i	$-0.309740\pi$
$107$	11.6424	1.12552	0.562759	+	0.826621i	$0.309740\pi$
$108$	0.758127	0.0729508
$109$	−8.16032	−0.781617	−0.390809	−	0.920472i	$-0.627805\pi$
$109$	−8.16032	−0.781617	−0.390809	+	0.920472i	$0.627805\pi$
$110$	−0.609143	−0.0580795
$111$	−8.65887	−0.821863
$112$	0	0
$113$	6.34229	0.596633	0.298316	−	0.954467i	$-0.403575\pi$
$113$	6.34229	0.596633	0.298316	+	0.954467i	$0.403575\pi$
$114$	3.26749	0.306029
$115$	1.17161	0.109253
$116$	−1.24796	−0.115870
$117$	−1.79833	−0.166256
$118$	−10.9607	−1.00902
$119$	0	0
$120$	3.60110	0.328734
$121$	−10.7823	−0.980212
$122$	−2.72647	−0.246843
$123$	−1.41208	−0.127323
$124$	5.81382	0.522097
$125$	10.1079	0.904074
$126$	0	0
$127$	3.78489	0.335854	0.167927	−	0.985799i	$-0.446293\pi$
$127$	3.78489	0.335854	0.167927	+	0.985799i	$0.446293\pi$
$128$	−1.20712	−0.106695
$129$	−9.81812	−0.864437
$130$	−2.34796	−0.205930
$131$	−7.72742	−0.675148	−0.337574	−	0.941299i	$-0.609606\pi$
$131$	−7.72742	−0.675148	−0.337574	+	0.941299i	$0.609606\pi$
$132$	−0.353704	−0.0307860
$133$	0	0
$134$	10.8288	0.935462
$135$	1.17161	0.100836
$136$	−1.36180	−0.116773
$137$	3.38327	0.289052	0.144526	−	0.989501i	$-0.453834\pi$
$137$	3.38327	0.289052	0.144526	+	0.989501i	$0.453834\pi$
$138$	−1.11439	−0.0948635
$139$	−12.8339	−1.08855	−0.544277	−	0.838905i	$-0.683196\pi$
$139$	−12.8339	−1.08855	−0.544277	+	0.838905i	$0.683196\pi$
$140$	0	0
$141$	5.59971	0.471581
$142$	−12.3659	−1.03772
$143$	0.839010	0.0701615
$144$	−1.90899	−0.159082
$145$	−1.92860	−0.160161
$146$	−3.50816	−0.290338
$147$	0	0
$148$	−6.56453	−0.539601
$149$	4.50488	0.369054	0.184527	−	0.982827i	$-0.440925\pi$
$149$	4.50488	0.369054	0.184527	+	0.982827i	$0.440925\pi$
$150$	−4.04228	−0.330050
$151$	4.85879	0.395403	0.197701	−	0.980262i	$-0.436652\pi$
$151$	4.85879	0.395403	0.197701	+	0.980262i	$0.436652\pi$
$152$	9.01216	0.730983
$153$	−0.443057	−0.0358190
$154$	0	0
$155$	8.98468	0.721667
$156$	−1.36336	−0.109156
$157$	1.07317	0.0856483	0.0428241	−	0.999083i	$-0.486364\pi$
$157$	1.07317	0.0856483	0.0428241	+	0.999083i	$0.486364\pi$
$158$	5.49289	0.436991
$159$	−3.70846	−0.294100
$160$	4.70977	0.372340
$161$	0	0
$162$	−1.11439	−0.0875550
$163$	−16.2448	−1.27239	−0.636195	−	0.771528i	$-0.719493\pi$
$163$	−16.2448	−1.27239	−0.636195	+	0.771528i	$0.719493\pi$
$164$	−1.07054	−0.0835949
$165$	−0.546614	−0.0425538
$166$	1.37666	0.106850
$167$	−13.8923	−1.07501	−0.537507	−	0.843259i	$-0.680634\pi$
$167$	−13.8923	−1.07501	−0.537507	+	0.843259i	$0.680634\pi$
$168$	0	0
$169$	−9.76601	−0.751232
$170$	−0.578470	−0.0443666
$171$	2.93208	0.224222
$172$	−7.44339	−0.567553
$173$	−12.7484	−0.969240	−0.484620	−	0.874725i	$-0.661042\pi$
$173$	−12.7484	−0.969240	−0.484620	+	0.874725i	$0.661042\pi$
$174$	1.83442	0.139067
$175$	0	0
$176$	0.890638	0.0671344
$177$	−9.83561	−0.739290
$178$	−3.32592	−0.249288
$179$	−7.41112	−0.553933	−0.276966	−	0.960880i	$-0.589329\pi$
$179$	−7.41112	−0.553933	−0.276966	+	0.960880i	$0.589329\pi$
$180$	0.888229	0.0662047
$181$	−18.8381	−1.40023	−0.700114	−	0.714032i	$-0.746867\pi$
$181$	−18.8381	−1.40023	−0.700114	+	0.714032i	$0.746867\pi$
$182$	0	0
$183$	−2.44660	−0.180858
$184$	−3.07364	−0.226592
$185$	−10.1448	−0.745861
$186$	−8.54591	−0.626617
$187$	0.206708	0.0151160
$188$	4.24530	0.309620
$189$	0	0
$190$	3.82822	0.277728
$191$	19.9464	1.44327	0.721636	−	0.692273i	$-0.243391\pi$
$191$	19.9464	1.44327	0.721636	+	0.692273i	$0.243391\pi$
$192$	−8.29774	−0.598838
$193$	7.67998	0.552817	0.276409	−	0.961040i	$-0.410856\pi$
$193$	7.67998	0.552817	0.276409	+	0.961040i	$0.410856\pi$
$194$	7.05290	0.506369
$195$	−2.10694	−0.150881
$196$	0	0
$197$	12.8612	0.916324	0.458162	−	0.888869i	$-0.348508\pi$
$197$	12.8612	0.916324	0.458162	+	0.888869i	$0.348508\pi$
$198$	0.519920	0.0369491
$199$	7.09306	0.502814	0.251407	−	0.967882i	$-0.419107\pi$
$199$	7.09306	0.502814	0.251407	+	0.967882i	$0.419107\pi$
$200$	−11.1491	−0.788361
$201$	9.71717	0.685396
$202$	5.52003	0.388388
$203$	0	0
$204$	−0.335893	−0.0235172
$205$	−1.65441	−0.115549
$206$	−1.62568	−0.113267
$207$	−1.00000	−0.0695048
$208$	3.43299	0.238035
$209$	−1.36796	−0.0946239
$210$	0	0
$211$	−1.93000	−0.132867	−0.0664333	−	0.997791i	$-0.521162\pi$
$211$	−1.93000	−0.132867	−0.0664333	+	0.997791i	$0.521162\pi$
$212$	−2.81148	−0.193093
$213$	−11.0965	−0.760323
$214$	−12.9743	−0.886902
$215$	−11.5030	−0.784498
$216$	−3.07364	−0.209135
$217$	0	0
$218$	9.09381	0.615910
$219$	−3.14805	−0.212725
$220$	−0.414403	−0.0279390
$221$	0.796762	0.0535960
$222$	9.64939	0.647624
$223$	−20.8619	−1.39701	−0.698507	−	0.715603i	$-0.746152\pi$
$223$	−20.8619	−1.39701	−0.698507	+	0.715603i	$0.746152\pi$
$224$	0	0
$225$	−3.62733	−0.241822
$226$	−7.06781	−0.470144
$227$	−29.9012	−1.98461	−0.992305	−	0.123815i	$-0.960487\pi$
$227$	−29.9012	−1.98461	−0.992305	+	0.123815i	$0.960487\pi$
$228$	2.22289	0.147215
$229$	−12.8144	−0.846801	−0.423400	−	0.905943i	$-0.639164\pi$
$229$	−12.8144	−0.846801	−0.423400	+	0.905943i	$0.639164\pi$
$230$	−1.30563	−0.0860909
$231$	0	0
$232$	5.05955	0.332176
$233$	−20.8763	−1.36765	−0.683825	−	0.729646i	$-0.739685\pi$
$233$	−20.8763	−1.36765	−0.683825	+	0.729646i	$0.739685\pi$
$234$	2.00405	0.131009
$235$	6.56067	0.427971
$236$	−7.45664	−0.485386
$237$	4.92904	0.320175
$238$	0	0
$239$	−6.00702	−0.388562	−0.194281	−	0.980946i	$-0.562237\pi$
$239$	−6.00702	−0.388562	−0.194281	+	0.980946i	$0.562237\pi$
$240$	−2.23659	−0.144371
$241$	−7.69538	−0.495703	−0.247851	−	0.968798i	$-0.579724\pi$
$241$	−7.69538	−0.495703	−0.247851	+	0.968798i	$0.579724\pi$
$242$	12.0158	0.772402
$243$	−1.00000	−0.0641500
$244$	−1.85483	−0.118744
$245$	0	0
$246$	1.57361	0.100330
$247$	−5.27285	−0.335503
$248$	−23.5707	−1.49674
$249$	1.23535	0.0782869
$250$	−11.2641	−0.712406
$251$	−0.0614337	−0.00387766	−0.00193883	−	0.999998i	$-0.500617\pi$
$251$	−0.0614337	−0.00387766	−0.00193883	+	0.999998i	$0.500617\pi$
$252$	0	0
$253$	0.466550	0.0293317
$254$	−4.21785	−0.264652
$255$	−0.519089	−0.0325066
$256$	−15.2503	−0.953142
$257$	−3.97316	−0.247839	−0.123920	−	0.992292i	$-0.539546\pi$
$257$	−3.97316	−0.247839	−0.123920	+	0.992292i	$0.539546\pi$
$258$	10.9413	0.681172
$259$	0	0
$260$	−1.59733	−0.0990620
$261$	1.64611	0.101892
$262$	8.61138	0.532013
$263$	5.88511	0.362892	0.181446	−	0.983401i	$-0.441922\pi$
$263$	5.88511	0.362892	0.181446	+	0.983401i	$0.441922\pi$
$264$	1.43401	0.0882569
$265$	−4.34486	−0.266903
$266$	0	0
$267$	−2.98451	−0.182649
$268$	7.36685	0.450002
$269$	−16.5077	−1.00649	−0.503245	−	0.864144i	$-0.667861\pi$
$269$	−16.5077	−1.00649	−0.503245	+	0.864144i	$0.667861\pi$
$270$	−1.30563	−0.0794583
$271$	−11.4872	−0.697796	−0.348898	−	0.937161i	$-0.613444\pi$
$271$	−11.4872	−0.697796	−0.348898	+	0.937161i	$0.613444\pi$
$272$	0.845790	0.0512836
$273$	0	0
$274$	−3.77030	−0.227772
$275$	1.69233	0.102051
$276$	−0.758127	−0.0456339
$277$	−3.49795	−0.210171	−0.105086	−	0.994463i	$-0.533512\pi$
$277$	−3.49795	−0.210171	−0.105086	+	0.994463i	$0.533512\pi$
$278$	14.3020	0.857776
$279$	−7.66867	−0.459111
$280$	0	0
$281$	−8.53287	−0.509028	−0.254514	−	0.967069i	$-0.581916\pi$
$281$	−8.53287	−0.509028	−0.254514	+	0.967069i	$0.581916\pi$
$282$	−6.24028	−0.371604
$283$	7.65065	0.454784	0.227392	−	0.973803i	$-0.426980\pi$
$283$	7.65065	0.454784	0.227392	+	0.973803i	$0.426980\pi$
$284$	−8.41260	−0.499196
$285$	3.43525	0.203487
$286$	−0.934987	−0.0552870
$287$	0	0
$288$	−4.01991	−0.236876
$289$	−16.8037	−0.988453
$290$	2.14922	0.126206
$291$	6.32891	0.371007
$292$	−2.38662	−0.139666
$293$	32.1908	1.88061	0.940303	−	0.340339i	$-0.110542\pi$
$293$	32.1908	1.88061	0.940303	+	0.340339i	$0.110542\pi$
$294$	0	0
$295$	−11.5235	−0.670923
$296$	26.6142	1.54692
$297$	0.466550	0.0270720
$298$	−5.02021	−0.290813
$299$	1.79833	0.104000
$300$	−2.74998	−0.158770
$301$	0	0
$302$	−5.41461	−0.311576
$303$	4.95340	0.284565
$304$	−5.59731	−0.321028
$305$	−2.86646	−0.164133
$306$	0.493740	0.0282252
$307$	−12.2486	−0.699065	−0.349533	−	0.936924i	$-0.613660\pi$
$307$	−12.2486	−0.699065	−0.349533	+	0.936924i	$0.613660\pi$
$308$	0	0
$309$	−1.45881	−0.0829886
$310$	−10.0125	−0.568670
$311$	6.61467	0.375084	0.187542	−	0.982257i	$-0.439948\pi$
$311$	6.61467	0.375084	0.187542	+	0.982257i	$0.439948\pi$
$312$	5.52741	0.312928
$313$	−10.4954	−0.593235	−0.296617	−	0.954996i	$-0.595859\pi$
$313$	−10.4954	−0.593235	−0.296617	+	0.954996i	$0.595859\pi$
$314$	−1.19593	−0.0674904
$315$	0	0
$316$	3.73684	0.210214
$317$	13.3736	0.751138	0.375569	−	0.926794i	$-0.377447\pi$
$317$	13.3736	0.751138	0.375569	+	0.926794i	$0.377447\pi$
$318$	4.13268	0.231749
$319$	−0.767993	−0.0429993
$320$	−9.72171	−0.543460
$321$	−11.6424	−0.649818
$322$	0	0
$323$	−1.29908	−0.0722827
$324$	−0.758127	−0.0421182
$325$	6.52314	0.361839
$326$	18.1031	1.00264
$327$	8.16032	0.451267
$328$	4.34023	0.239649
$329$	0	0
$330$	0.609143	0.0335322
$331$	−8.63678	−0.474720	−0.237360	−	0.971422i	$-0.576282\pi$
$331$	−8.63678	−0.474720	−0.237360	+	0.971422i	$0.576282\pi$
$332$	0.936549	0.0513998
$333$	8.65887	0.474503
$334$	15.4814	0.847106
$335$	11.3847	0.622014
$336$	0	0
$337$	0.997581	0.0543417	0.0271708	−	0.999631i	$-0.491350\pi$
$337$	0.997581	0.0543417	0.0271708	+	0.999631i	$0.491350\pi$
$338$	10.8832	0.591967
$339$	−6.34229	−0.344466
$340$	−0.393536	−0.0213425
$341$	3.57781	0.193749
$342$	−3.26749	−0.176686
$343$	0	0
$344$	30.1774	1.62705
$345$	−1.17161	−0.0630773
$346$	14.2067	0.763756
$347$	25.4883	1.36828	0.684142	−	0.729348i	$-0.260177\pi$
$347$	25.4883	1.36828	0.684142	+	0.729348i	$0.260177\pi$
$348$	1.24796	0.0668978
$349$	8.64889	0.462964	0.231482	−	0.972839i	$-0.425642\pi$
$349$	8.64889	0.462964	0.231482	+	0.972839i	$0.425642\pi$
$350$	0	0
$351$	1.79833	0.0959877
$352$	1.87549	0.0999639
$353$	−9.97243	−0.530779	−0.265389	−	0.964141i	$-0.585501\pi$
$353$	−9.97243	−0.530779	−0.265389	+	0.964141i	$0.585501\pi$
$354$	10.9607	0.582557
$355$	−13.0008	−0.690012
$356$	−2.26264	−0.119919
$357$	0	0
$358$	8.25890	0.436496
$359$	0.989673	0.0522330	0.0261165	−	0.999659i	$-0.491686\pi$
$359$	0.989673	0.0522330	0.0261165	+	0.999659i	$0.491686\pi$
$360$	−3.60110	−0.189795
$361$	−10.4029	−0.547521
$362$	20.9931	1.10337
$363$	10.7823	0.565926
$364$	0	0
$365$	−3.68828	−0.193053
$366$	2.72647	0.142515
$367$	−16.7523	−0.874461	−0.437231	−	0.899349i	$-0.644041\pi$
$367$	−16.7523	−0.874461	−0.437231	+	0.899349i	$0.644041\pi$
$368$	1.90899	0.0995129
$369$	1.41208	0.0735100
$370$	11.3053	0.587735
$371$	0	0
$372$	−5.81382	−0.301433
$373$	−25.6220	−1.32666	−0.663329	−	0.748328i	$-0.730857\pi$
$373$	−25.6220	−1.32666	−0.663329	+	0.748328i	$0.730857\pi$
$374$	−0.230354	−0.0119113
$375$	−10.1079	−0.521968
$376$	−17.2115	−0.887615
$377$	−2.96025	−0.152461
$378$	0	0
$379$	−10.6567	−0.547398	−0.273699	−	0.961815i	$-0.588247\pi$
$379$	−10.6567	−0.547398	−0.273699	+	0.961815i	$0.588247\pi$
$380$	2.60436	0.133601
$381$	−3.78489	−0.193906
$382$	−22.2281	−1.13729
$383$	−27.5755	−1.40904	−0.704522	−	0.709682i	$-0.748839\pi$
$383$	−27.5755	−1.40904	−0.704522	+	0.709682i	$0.748839\pi$
$384$	1.20712	0.0616007
$385$	0	0
$386$	−8.55852	−0.435617
$387$	9.81812	0.499083
$388$	4.79812	0.243588
$389$	16.2908	0.825975	0.412988	−	0.910737i	$-0.364485\pi$
$389$	16.2908	0.825975	0.412988	+	0.910737i	$0.364485\pi$
$390$	2.34796	0.118893
$391$	0.443057	0.0224063
$392$	0	0
$393$	7.72742	0.389797
$394$	−14.3325	−0.722059
$395$	5.77490	0.290567
$396$	0.353704	0.0177743
$397$	27.5610	1.38325	0.691623	−	0.722258i	$-0.256896\pi$
$397$	27.5610	1.38325	0.691623	+	0.722258i	$0.256896\pi$
$398$	−7.90446	−0.396215
$399$	0	0
$400$	6.92454	0.346227
$401$	21.1971	1.05853	0.529266	−	0.848456i	$-0.322467\pi$
$401$	21.1971	1.05853	0.529266	+	0.848456i	$0.322467\pi$
$402$	−10.8288	−0.540089
$403$	13.7908	0.686968
$404$	3.75530	0.186833
$405$	−1.17161	−0.0582177
$406$	0	0
$407$	−4.03979	−0.200245
$408$	1.36180	0.0674190
$409$	20.5188	1.01459	0.507295	−	0.861772i	$-0.330645\pi$
$409$	20.5188	1.01459	0.507295	+	0.861772i	$0.330645\pi$
$410$	1.84366	0.0910519
$411$	−3.38327	−0.166884
$412$	−1.10596	−0.0544868
$413$	0	0
$414$	1.11439	0.0547694
$415$	1.44734	0.0710472
$416$	7.22913	0.354437
$417$	12.8339	0.628477
$418$	1.52445	0.0745632
$419$	6.94082	0.339081	0.169541	−	0.985523i	$-0.445772\pi$
$419$	6.94082	0.339081	0.169541	+	0.985523i	$0.445772\pi$
$420$	0	0
$421$	−33.6197	−1.63852	−0.819261	−	0.573421i	$-0.805616\pi$
$421$	−33.6197	−1.63852	−0.819261	+	0.573421i	$0.805616\pi$
$422$	2.15078	0.104698
$423$	−5.59971	−0.272267
$424$	11.3985	0.553558
$425$	1.60711	0.0779565
$426$	12.3659	0.599131
$427$	0	0
$428$	−8.82646	−0.426643
$429$	−0.839010	−0.0405078
$430$	12.8189	0.618181
$431$	39.7209	1.91329	0.956644	−	0.291259i	$-0.0940740\pi$
$431$	39.7209	1.91329	0.956644	+	0.291259i	$0.0940740\pi$
$432$	1.90899	0.0918462
$433$	−13.3220	−0.640217	−0.320108	−	0.947381i	$-0.603719\pi$
$433$	−13.3220	−0.640217	−0.320108	+	0.947381i	$0.603719\pi$
$434$	0	0
$435$	1.92860	0.0924692
$436$	6.18656	0.296283
$437$	−2.93208	−0.140260
$438$	3.50816	0.167627
$439$	−9.10940	−0.434768	−0.217384	−	0.976086i	$-0.569752\pi$
$439$	−9.10940	−0.434768	−0.217384	+	0.976086i	$0.569752\pi$
$440$	1.68009	0.0800953
$441$	0	0
$442$	−0.887906	−0.0422334
$443$	−7.47269	−0.355038	−0.177519	−	0.984117i	$-0.556807\pi$
$443$	−7.47269	−0.355038	−0.177519	+	0.984117i	$0.556807\pi$
$444$	6.56453	0.311539
$445$	−3.49668	−0.165758
$446$	23.2483	1.10084
$447$	−4.50488	−0.213073
$448$	0	0
$449$	−17.6489	−0.832905	−0.416453	−	0.909157i	$-0.636727\pi$
$449$	−17.6489	−0.832905	−0.416453	+	0.909157i	$0.636727\pi$
$450$	4.04228	0.190555
$451$	−0.658806	−0.0310220
$452$	−4.80826	−0.226162
$453$	−4.85879	−0.228286
$454$	33.3217	1.56386
$455$	0	0
$456$	−9.01216	−0.422033
$457$	−5.08477	−0.237856	−0.118928	−	0.992903i	$-0.537946\pi$
$457$	−5.08477	−0.237856	−0.118928	+	0.992903i	$0.537946\pi$
$458$	14.2803	0.667275
$459$	0.443057	0.0206801
$460$	−0.888229	−0.0414139
$461$	−16.9264	−0.788341	−0.394171	−	0.919037i	$-0.628968\pi$
$461$	−16.9264	−0.788341	−0.394171	+	0.919037i	$0.628968\pi$
$462$	0	0
$463$	−25.7790	−1.19805	−0.599027	−	0.800729i	$-0.704446\pi$
$463$	−25.7790	−1.19805	−0.599027	+	0.800729i	$0.704446\pi$
$464$	−3.14241	−0.145883
$465$	−8.98468	−0.416654
$466$	23.2644	1.07770
$467$	−31.5420	−1.45959	−0.729796	−	0.683665i	$-0.760385\pi$
$467$	−31.5420	−1.45959	−0.729796	+	0.683665i	$0.760385\pi$
$468$	1.36336	0.0630214
$469$	0	0
$470$	−7.31117	−0.337239
$471$	−1.07317	−0.0494490
$472$	30.2311	1.39150
$473$	−4.58064	−0.210618
$474$	−5.49289	−0.252297
$475$	−10.6356	−0.487996
$476$	0	0
$477$	3.70846	0.169799
$478$	6.69419	0.306185
$479$	−0.527507	−0.0241024	−0.0120512	−	0.999927i	$-0.503836\pi$
$479$	−0.527507	−0.0241024	−0.0120512	+	0.999927i	$0.503836\pi$
$480$	−4.70977	−0.214970
$481$	−15.5715	−0.709999
$482$	8.57568	0.390611
$483$	0	0
$484$	8.17438	0.371563
$485$	7.41501	0.336698
$486$	1.11439	0.0505499
$487$	18.8711	0.855131	0.427566	−	0.903984i	$-0.359371\pi$
$487$	18.8711	0.855131	0.427566	+	0.903984i	$0.359371\pi$
$488$	7.51996	0.340413
$489$	16.2448	0.734615
$490$	0	0
$491$	−8.40139	−0.379149	−0.189575	−	0.981866i	$-0.560711\pi$
$491$	−8.40139	−0.379149	−0.189575	+	0.981866i	$0.560711\pi$
$492$	1.07054	0.0482635
$493$	−0.729321	−0.0328470
$494$	5.87603	0.264375
$495$	0.546614	0.0245685
$496$	14.6394	0.657328
$497$	0	0
$498$	−1.37666	−0.0616897
$499$	−39.3127	−1.75988	−0.879940	−	0.475085i	$-0.842417\pi$
$499$	−39.3127	−1.75988	−0.879940	+	0.475085i	$0.842417\pi$
$500$	−7.66304	−0.342702
$501$	13.8923	0.620660
$502$	0.0684613	0.00305558
$503$	−24.9794	−1.11378	−0.556888	−	0.830587i	$-0.688005\pi$
$503$	−24.9794	−1.11378	−0.556888	+	0.830587i	$0.688005\pi$
$504$	0	0
$505$	5.80344	0.258250
$506$	−0.519920	−0.0231133
$507$	9.76601	0.433724
$508$	−2.86943	−0.127310
$509$	−27.2433	−1.20754	−0.603770	−	0.797159i	$-0.706335\pi$
$509$	−27.2433	−1.20754	−0.603770	+	0.797159i	$0.706335\pi$
$510$	0.578470	0.0256151
$511$	0	0
$512$	19.4091	0.857767
$513$	−2.93208	−0.129455
$514$	4.42767	0.195296
$515$	−1.70915	−0.0753142
$516$	7.44339	0.327677
$517$	2.61255	0.114900
$518$	0	0
$519$	12.7484	0.559591
$520$	6.47597	0.283990
$521$	13.8473	0.606663	0.303331	−	0.952885i	$-0.401901\pi$
$521$	13.8473	0.606663	0.303331	+	0.952885i	$0.401901\pi$
$522$	−1.83442	−0.0802902
$523$	12.1197	0.529957	0.264978	−	0.964254i	$-0.414635\pi$
$523$	12.1197	0.529957	0.264978	+	0.964254i	$0.414635\pi$
$524$	5.85837	0.255924
$525$	0	0
$526$	−6.55833	−0.285957
$527$	3.39765	0.148004
$528$	−0.890638	−0.0387600
$529$	1.00000	0.0434783
$530$	4.84188	0.210318
$531$	9.83561	0.426829
$532$	0	0
$533$	−2.53939	−0.109993
$534$	3.32592	0.143926
$535$	−13.6404	−0.589726
$536$	−29.8671	−1.29006
$537$	7.41112	0.319813
$538$	18.3960	0.793110
$539$	0	0
$540$	−0.888229	−0.0382233
$541$	3.34880	0.143976	0.0719881	−	0.997405i	$-0.477066\pi$
$541$	3.34880	0.143976	0.0719881	+	0.997405i	$0.477066\pi$
$542$	12.8012	0.549860
$543$	18.8381	0.808421
$544$	1.78105	0.0763619
$545$	9.56071	0.409536
$546$	0	0
$547$	−9.14790	−0.391136	−0.195568	−	0.980690i	$-0.562655\pi$
$547$	−9.14790	−0.391136	−0.195568	+	0.980690i	$0.562655\pi$
$548$	−2.56495	−0.109569
$549$	2.44660	0.104418
$550$	−1.88592	−0.0804160
$551$	4.82653	0.205617
$552$	3.07364	0.130823
$553$	0	0
$554$	3.89809	0.165614
$555$	10.1448	0.430623
$556$	9.72971	0.412631
$557$	2.29786	0.0973636	0.0486818	−	0.998814i	$-0.484498\pi$
$557$	2.29786	0.0973636	0.0486818	+	0.998814i	$0.484498\pi$
$558$	8.54591	0.361777
$559$	−17.6562	−0.746778
$560$	0	0
$561$	−0.206708	−0.00872722
$562$	9.50898	0.401112
$563$	−22.2672	−0.938451	−0.469226	−	0.883078i	$-0.655467\pi$
$563$	−22.2672	−0.938451	−0.469226	+	0.883078i	$0.655467\pi$
$564$	−4.24530	−0.178759
$565$	−7.43069	−0.312611
$566$	−8.52584	−0.358368
$567$	0	0
$568$	34.1068	1.43109
$569$	−9.75505	−0.408953	−0.204477	−	0.978871i	$-0.565549\pi$
$569$	−9.75505	−0.408953	−0.204477	+	0.978871i	$0.565549\pi$
$570$	−3.82822	−0.160347
$571$	−35.2358	−1.47457	−0.737287	−	0.675580i	$-0.763893\pi$
$571$	−35.2358	−1.47457	−0.737287	+	0.675580i	$0.763893\pi$
$572$	−0.636076	−0.0265957
$573$	−19.9464	−0.833273
$574$	0	0
$575$	3.62733	0.151270
$576$	8.29774	0.345739
$577$	25.3058	1.05349	0.526746	−	0.850023i	$-0.323412\pi$
$577$	25.3058	1.05349	0.526746	+	0.850023i	$0.323412\pi$
$578$	18.7259	0.778896
$579$	−7.67998	−0.319169
$580$	1.46212	0.0607114
$581$	0	0
$582$	−7.05290	−0.292352
$583$	−1.73018	−0.0716567
$584$	9.67596	0.400394
$585$	2.10694	0.0871112
$586$	−35.8732	−1.48191
$587$	27.3144	1.12739	0.563693	−	0.825984i	$-0.309380\pi$
$587$	27.3144	1.12739	0.563693	+	0.825984i	$0.309380\pi$
$588$	0	0
$589$	−22.4852	−0.926484
$590$	12.8417	0.528684
$591$	−12.8612	−0.529040
$592$	−16.5297	−0.679366
$593$	−14.3939	−0.591088	−0.295544	−	0.955329i	$-0.595501\pi$
$593$	−14.3939	−0.591088	−0.295544	+	0.955329i	$0.595501\pi$
$594$	−0.519920	−0.0213326
$595$	0	0
$596$	−3.41527	−0.139895
$597$	−7.09306	−0.290300
$598$	−2.00405	−0.0819515
$599$	−13.9635	−0.570532	−0.285266	−	0.958448i	$-0.592082\pi$
$599$	−13.9635	−0.570532	−0.285266	+	0.958448i	$0.592082\pi$
$600$	11.1491	0.455161
$601$	21.2711	0.867668	0.433834	−	0.900993i	$-0.357160\pi$
$601$	21.2711	0.867668	0.433834	+	0.900993i	$0.357160\pi$
$602$	0	0
$603$	−9.71717	−0.395714
$604$	−3.68358	−0.149883
$605$	12.6327	0.513591
$606$	−5.52003	−0.224236
$607$	21.8553	0.887079	0.443539	−	0.896255i	$-0.353723\pi$
$607$	21.8553	0.887079	0.443539	+	0.896255i	$0.353723\pi$
$608$	−11.7867	−0.478014
$609$	0	0
$610$	3.19436	0.129336
$611$	10.0701	0.407394
$612$	0.335893	0.0135777
$613$	36.0308	1.45527	0.727636	−	0.685963i	$-0.240619\pi$
$613$	36.0308	1.45527	0.727636	+	0.685963i	$0.240619\pi$
$614$	13.6498	0.550860
$615$	1.65441	0.0667121
$616$	0	0
$617$	7.07814	0.284955	0.142478	−	0.989798i	$-0.454493\pi$
$617$	7.07814	0.284955	0.142478	+	0.989798i	$0.454493\pi$
$618$	1.62568	0.0653946
$619$	27.0830	1.08856	0.544280	−	0.838904i	$-0.316803\pi$
$619$	27.0830	1.08856	0.544280	+	0.838904i	$0.316803\pi$
$620$	−6.81153	−0.273558
$621$	1.00000	0.0401286
$622$	−7.37135	−0.295564
$623$	0	0
$624$	−3.43299	−0.137430
$625$	6.29420	0.251768
$626$	11.6960	0.467466
$627$	1.36796	0.0546311
$628$	−0.813599	−0.0324661
$629$	−3.83637	−0.152966
$630$	0	0
$631$	−11.9546	−0.475905	−0.237953	−	0.971277i	$-0.576476\pi$
$631$	−11.9546	−0.475905	−0.237953	+	0.971277i	$0.576476\pi$
$632$	−15.1501	−0.602638
$633$	1.93000	0.0767106
$634$	−14.9035	−0.591893
$635$	−4.43441	−0.175974
$636$	2.81148	0.111482
$637$	0	0
$638$	0.855846	0.0338833
$639$	11.0965	0.438973
$640$	1.41427	0.0559041
$641$	−2.35390	−0.0929733	−0.0464867	−	0.998919i	$-0.514802\pi$
$641$	−2.35390	−0.0929733	−0.0464867	+	0.998919i	$0.514802\pi$
$642$	12.9743	0.512053
$643$	−27.1448	−1.07049	−0.535243	−	0.844698i	$-0.679780\pi$
$643$	−27.1448	−1.07049	−0.535243	+	0.844698i	$0.679780\pi$
$644$	0	0
$645$	11.5030	0.452930
$646$	1.44768	0.0569584
$647$	26.7812	1.05288	0.526440	−	0.850213i	$-0.323527\pi$
$647$	26.7812	1.05288	0.526440	+	0.850213i	$0.323527\pi$
$648$	3.07364	0.120744
$649$	−4.58880	−0.180126
$650$	−7.26934	−0.285127
$651$	0	0
$652$	12.3156	0.482317
$653$	−0.478529	−0.0187263	−0.00936315	−	0.999956i	$-0.502980\pi$
$653$	−0.478529	−0.0187263	−0.00936315	+	0.999956i	$0.502980\pi$
$654$	−9.09381	−0.355596
$655$	9.05351	0.353750
$656$	−2.69565	−0.105247
$657$	3.14805	0.122817
$658$	0	0
$659$	−42.4064	−1.65192	−0.825959	−	0.563730i	$-0.809366\pi$
$659$	−42.4064	−1.65192	−0.825959	+	0.563730i	$0.809366\pi$
$660$	0.414403	0.0161306
$661$	−29.1987	−1.13570	−0.567850	−	0.823132i	$-0.692225\pi$
$661$	−29.1987	−1.13570	−0.567850	+	0.823132i	$0.692225\pi$
$662$	9.62477	0.374077
$663$	−0.796762	−0.0309437
$664$	−3.79701	−0.147352
$665$	0	0
$666$	−9.64939	−0.373906
$667$	−1.64611	−0.0637377
$668$	10.5321	0.407499
$669$	20.8619	0.806567
$670$	−12.6871	−0.490144
$671$	−1.14146	−0.0440656
$672$	0	0
$673$	41.6859	1.60687	0.803436	−	0.595391i	$-0.203003\pi$
$673$	41.6859	1.60687	0.803436	+	0.595391i	$0.203003\pi$
$674$	−1.11170	−0.0428210
$675$	3.62733	0.139616
$676$	7.40388	0.284765
$677$	30.4561	1.17052	0.585261	−	0.810845i	$-0.300992\pi$
$677$	30.4561	1.17052	0.585261	+	0.810845i	$0.300992\pi$
$678$	7.06781	0.271438
$679$	0	0
$680$	1.59549	0.0611844
$681$	29.9012	1.14582
$682$	−3.98709	−0.152674
$683$	−11.8100	−0.451897	−0.225948	−	0.974139i	$-0.572548\pi$
$683$	−11.8100	−0.451897	−0.225948	+	0.974139i	$0.572548\pi$
$684$	−2.22289	−0.0849944
$685$	−3.96387	−0.151452
$686$	0	0
$687$	12.8144	0.488901
$688$	−18.7427	−0.714558
$689$	−6.66902	−0.254070
$690$	1.30563	0.0497046
$691$	−40.3086	−1.53341	−0.766706	−	0.641998i	$-0.778106\pi$
$691$	−40.3086	−1.53341	−0.766706	+	0.641998i	$0.778106\pi$
$692$	9.66488	0.367404
$693$	0	0
$694$	−28.4040	−1.07820
$695$	15.0363	0.570358
$696$	−5.05955	−0.191782
$697$	−0.625632	−0.0236975
$698$	−9.63827	−0.364814
$699$	20.8763	0.789613
$700$	0	0
$701$	−1.60220	−0.0605143	−0.0302571	−	0.999542i	$-0.509633\pi$
$701$	−1.60220	−0.0605143	−0.0302571	+	0.999542i	$0.509633\pi$
$702$	−2.00405	−0.0756378
$703$	25.3885	0.957546
$704$	−3.87131	−0.145905
$705$	−6.56067	−0.247089
$706$	11.1132	0.418251
$707$	0	0
$708$	7.45664	0.280238
$709$	14.1009	0.529570	0.264785	−	0.964307i	$-0.414699\pi$
$709$	14.1009	0.529570	0.264785	+	0.964307i	$0.414699\pi$
$710$	14.4880	0.543726
$711$	−4.92904	−0.184853
$712$	9.17330	0.343784
$713$	7.66867	0.287194
$714$	0	0
$715$	−0.982992	−0.0367618
$716$	5.61857	0.209976
$717$	6.00702	0.224336
$718$	−1.10289	−0.0411593
$719$	6.06607	0.226226	0.113113	−	0.993582i	$-0.463918\pi$
$719$	6.06607	0.226226	0.113113	+	0.993582i	$0.463918\pi$
$720$	2.23659	0.0833527
$721$	0	0
$722$	11.5929	0.431444
$723$	7.69538	0.286194
$724$	14.2817	0.530775
$725$	−5.97099	−0.221757
$726$	−12.0158	−0.445947
$727$	1.34366	0.0498336	0.0249168	−	0.999690i	$-0.492068\pi$
$727$	1.34366	0.0498336	0.0249168	+	0.999690i	$0.492068\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	4.11020	0.152125
$731$	−4.34999	−0.160890
$732$	1.85483	0.0685566
$733$	−0.802404	−0.0296375	−0.0148187	−	0.999890i	$-0.504717\pi$
$733$	−0.802404	−0.0296375	−0.0148187	+	0.999890i	$0.504717\pi$
$734$	18.6686	0.689071
$735$	0	0
$736$	4.01991	0.148176
$737$	4.53354	0.166995
$738$	−1.57361	−0.0579255
$739$	−27.4843	−1.01103	−0.505513	−	0.862819i	$-0.668697\pi$
$739$	−27.4843	−1.01103	−0.505513	+	0.862819i	$0.668697\pi$
$740$	7.69106	0.282729
$741$	5.27285	0.193703
$742$	0	0
$743$	−36.9725	−1.35639	−0.678195	−	0.734882i	$-0.737237\pi$
$743$	−36.9725	−1.35639	−0.678195	+	0.734882i	$0.737237\pi$
$744$	23.5707	0.864144
$745$	−5.27796	−0.193369
$746$	28.5530	1.04540
$747$	−1.23535	−0.0451989
$748$	−0.156711	−0.00572992
$749$	0	0
$750$	11.2641	0.411308
$751$	15.8543	0.578531	0.289265	−	0.957249i	$-0.406589\pi$
$751$	15.8543	0.578531	0.289265	+	0.957249i	$0.406589\pi$
$752$	10.6898	0.389816
$753$	0.0614337	0.00223877
$754$	3.29888	0.120138
$755$	−5.69261	−0.207175
$756$	0	0
$757$	−10.4941	−0.381414	−0.190707	−	0.981647i	$-0.561078\pi$
$757$	−10.4941	−0.381414	−0.190707	+	0.981647i	$0.561078\pi$
$758$	11.8758	0.431347
$759$	−0.466550	−0.0169347
$760$	−10.5587	−0.383005
$761$	19.2415	0.697502	0.348751	−	0.937215i	$-0.386606\pi$
$761$	19.2415	0.697502	0.348751	+	0.937215i	$0.386606\pi$
$762$	4.21785	0.152797
$763$	0	0
$764$	−15.1219	−0.547092
$765$	0.519089	0.0187677
$766$	30.7300	1.11032
$767$	−17.6877	−0.638664
$768$	15.2503	0.550297
$769$	28.5014	1.02779	0.513894	−	0.857854i	$-0.328202\pi$
$769$	28.5014	1.02779	0.513894	+	0.857854i	$0.328202\pi$
$770$	0	0
$771$	3.97316	0.143090
$772$	−5.82240	−0.209553
$773$	19.9876	0.718904	0.359452	−	0.933164i	$-0.382964\pi$
$773$	19.9876	0.718904	0.359452	+	0.933164i	$0.382964\pi$
$774$	−10.9413	−0.393275
$775$	27.8168	0.999209
$776$	−19.4528	−0.698314
$777$	0	0
$778$	−18.1543	−0.650864
$779$	4.14034	0.148343
$780$	1.59733	0.0571935
$781$	−5.17709	−0.185251
$782$	−0.493740	−0.0176561
$783$	−1.64611	−0.0588272
$784$	0	0
$785$	−1.25734	−0.0448762
$786$	−8.61138	−0.307158
$787$	42.2957	1.50768	0.753840	−	0.657059i	$-0.228200\pi$
$787$	42.2957	1.50768	0.753840	+	0.657059i	$0.228200\pi$
$788$	−9.75045	−0.347345
$789$	−5.88511	−0.209516
$790$	−6.43552	−0.228965
$791$	0	0
$792$	−1.43401	−0.0509552
$793$	−4.39979	−0.156241
$794$	−30.7138	−1.08999
$795$	4.34486	0.154096
$796$	−5.37744	−0.190598
$797$	52.3298	1.85362	0.926808	−	0.375537i	$-0.122542\pi$
$797$	52.3298	1.85362	0.926808	+	0.375537i	$0.122542\pi$
$798$	0	0
$799$	2.48099	0.0877712
$800$	14.5816	0.515536
$801$	2.98451	0.105452
$802$	−23.6219	−0.834118
$803$	−1.46872	−0.0518300
$804$	−7.36685	−0.259809
$805$	0	0
$806$	−15.3684	−0.541327
$807$	16.5077	0.581097
$808$	−15.2249	−0.535612
$809$	40.1600	1.41195	0.705976	−	0.708236i	$-0.250509\pi$
$809$	40.1600	1.41195	0.705976	+	0.708236i	$0.250509\pi$
$810$	1.30563	0.0458753
$811$	−52.8420	−1.85553	−0.927767	−	0.373160i	$-0.878274\pi$
$811$	−52.8420	−1.85553	−0.927767	+	0.373160i	$0.878274\pi$
$812$	0	0
$813$	11.4872	0.402872
$814$	4.50192	0.157792
$815$	19.0325	0.666681
$816$	−0.845790	−0.0296086
$817$	28.7875	1.00715
$818$	−22.8661	−0.799493
$819$	0	0
$820$	1.25425	0.0438003
$821$	−36.7328	−1.28198	−0.640991	−	0.767548i	$-0.721476\pi$
$821$	−36.7328	−1.28198	−0.640991	+	0.767548i	$0.721476\pi$
$822$	3.77030	0.131504
$823$	−13.3828	−0.466494	−0.233247	−	0.972418i	$-0.574935\pi$
$823$	−13.3828	−0.466494	−0.233247	+	0.972418i	$0.574935\pi$
$824$	4.48384	0.156202
$825$	−1.69233	−0.0589194
$826$	0	0
$827$	29.3443	1.02040	0.510200	−	0.860056i	$-0.329571\pi$
$827$	29.3443	1.02040	0.510200	+	0.860056i	$0.329571\pi$
$828$	0.758127	0.0263467
$829$	3.33743	0.115914	0.0579569	−	0.998319i	$-0.481541\pi$
$829$	3.33743	0.115914	0.0579569	+	0.998319i	$0.481541\pi$
$830$	−1.61291	−0.0559849
$831$	3.49795	0.121342
$832$	−14.9221	−0.517330
$833$	0	0
$834$	−14.3020	−0.495237
$835$	16.2763	0.563264
$836$	1.03709	0.0358685
$837$	7.66867	0.265068
$838$	−7.73480	−0.267194
$839$	31.1675	1.07602	0.538010	−	0.842938i	$-0.319176\pi$
$839$	31.1675	1.07602	0.538010	+	0.842938i	$0.319176\pi$
$840$	0	0
$841$	−26.2903	−0.906563
$842$	37.4655	1.29115
$843$	8.53287	0.293888
$844$	1.46319	0.0503649
$845$	11.4419	0.393615
$846$	6.24028	0.214545
$847$	0	0
$848$	−7.07940	−0.243108
$849$	−7.65065	−0.262570
$850$	−1.79096	−0.0614293
$851$	−8.65887	−0.296822
$852$	8.41260	0.288211
$853$	51.9564	1.77895	0.889477	−	0.456979i	$-0.151069\pi$
$853$	51.9564	1.77895	0.889477	+	0.456979i	$0.151069\pi$
$854$	0	0
$855$	−3.43525	−0.117483
$856$	35.7847	1.22309
$857$	−1.99301	−0.0680798	−0.0340399	−	0.999420i	$-0.510837\pi$
$857$	−1.99301	−0.0680798	−0.0340399	+	0.999420i	$0.510837\pi$
$858$	0.934987	0.0319199
$859$	−34.4172	−1.17430	−0.587150	−	0.809478i	$-0.699750\pi$
$859$	−34.4172	−1.17430	−0.587150	+	0.809478i	$0.699750\pi$
$860$	8.72074	0.297375
$861$	0	0
$862$	−44.2647	−1.50766
$863$	−31.2998	−1.06546	−0.532729	−	0.846286i	$-0.678834\pi$
$863$	−31.2998	−1.06546	−0.532729	+	0.846286i	$0.678834\pi$
$864$	4.01991	0.136760
$865$	14.9361	0.507842
$866$	14.8460	0.504488
$867$	16.8037	0.570684
$868$	0	0
$869$	2.29964	0.0780100
$870$	−2.14922	−0.0728653
$871$	17.4747	0.592107
$872$	−25.0819	−0.849380
$873$	−6.32891	−0.214201
$874$	3.26749	0.110525
$875$	0	0
$876$	2.38662	0.0806365
$877$	−22.9379	−0.774558	−0.387279	−	0.921963i	$-0.626585\pi$
$877$	−22.9379	−0.774558	−0.387279	+	0.921963i	$0.626585\pi$
$878$	10.1515	0.342595
$879$	−32.1908	−1.08577
$880$	−1.04348	−0.0351757
$881$	−13.1890	−0.444350	−0.222175	−	0.975007i	$-0.571316\pi$
$881$	−13.1890	−0.444350	−0.222175	+	0.975007i	$0.571316\pi$
$882$	0	0
$883$	−15.6235	−0.525772	−0.262886	−	0.964827i	$-0.584674\pi$
$883$	−15.6235	−0.525772	−0.262886	+	0.964827i	$0.584674\pi$
$884$	−0.604047	−0.0203163
$885$	11.5235	0.387358
$886$	8.32752	0.279769
$887$	2.10586	0.0707079	0.0353540	−	0.999375i	$-0.488744\pi$
$887$	2.10586	0.0707079	0.0353540	+	0.999375i	$0.488744\pi$
$888$	−26.6142	−0.893115
$889$	0	0
$890$	3.89667	0.130617
$891$	−0.466550	−0.0156300
$892$	15.8160	0.529557
$893$	−16.4188	−0.549435
$894$	5.02021	0.167901
$895$	8.68293	0.290238
$896$	0	0
$897$	−1.79833	−0.0600445
$898$	19.6679	0.656325
$899$	−12.6235	−0.421016
$900$	2.74998	0.0916660
$901$	−1.64306	−0.0547382
$902$	0.734169	0.0244452
$903$	0	0
$904$	19.4939	0.648358
$905$	22.0709	0.733662
$906$	5.41461	0.179888
$907$	35.9926	1.19511	0.597557	−	0.801826i	$-0.296138\pi$
$907$	35.9926	1.19511	0.597557	+	0.801826i	$0.296138\pi$
$908$	22.6689	0.752294
$909$	−4.95340	−0.164294
$910$	0	0
$911$	−51.5543	−1.70807	−0.854035	−	0.520216i	$-0.825851\pi$
$911$	−51.5543	−1.70807	−0.854035	+	0.520216i	$0.825851\pi$
$912$	5.59731	0.185345
$913$	0.576350	0.0190744
$914$	5.66643	0.187429
$915$	2.86646	0.0947621
$916$	9.71496	0.320991
$917$	0	0
$918$	−0.493740	−0.0162958
$919$	26.2065	0.864473	0.432236	−	0.901760i	$-0.357725\pi$
$919$	26.2065	0.864473	0.432236	+	0.901760i	$0.357725\pi$
$920$	3.60110	0.118725
$921$	12.2486	0.403606
$922$	18.8627	0.621209
$923$	−19.9552	−0.656835
$924$	0	0
$925$	−31.4086	−1.03271
$926$	28.7280	0.944060
$927$	1.45881	0.0479135
$928$	−6.61722	−0.217221
$929$	12.0974	0.396904	0.198452	−	0.980111i	$-0.436409\pi$
$929$	12.0974	0.396904	0.198452	+	0.980111i	$0.436409\pi$
$930$	10.0125	0.328322
$931$	0	0
$932$	15.8269	0.518426
$933$	−6.61467	−0.216555
$934$	35.1503	1.15015
$935$	−0.242181	−0.00792017
$936$	−5.52741	−0.180669
$937$	51.7544	1.69074	0.845371	−	0.534180i	$-0.179380\pi$
$937$	51.7544	1.69074	0.845371	+	0.534180i	$0.179380\pi$
$938$	0	0
$939$	10.4954	0.342504
$940$	−4.97383	−0.162228
$941$	−10.1564	−0.331089	−0.165545	−	0.986202i	$-0.552938\pi$
$941$	−10.1564	−0.331089	−0.165545	+	0.986202i	$0.552938\pi$
$942$	1.19593	0.0389656
$943$	−1.41208	−0.0459837
$944$	−18.7761	−0.611109
$945$	0	0
$946$	5.10464	0.165966
$947$	−30.4925	−0.990875	−0.495437	−	0.868644i	$-0.664992\pi$
$947$	−30.4925	−0.990875	−0.495437	+	0.868644i	$0.664992\pi$
$948$	−3.73684	−0.121367
$949$	−5.66123	−0.183771
$950$	11.8523	0.384539
$951$	−13.3736	−0.433670
$952$	0	0
$953$	−42.5587	−1.37861	−0.689306	−	0.724471i	$-0.742084\pi$
$953$	−42.5587	−1.37861	−0.689306	+	0.724471i	$0.742084\pi$
$954$	−4.13268	−0.133800
$955$	−23.3694	−0.756216
$956$	4.55409	0.147290
$957$	0.767993	0.0248257
$958$	0.587850	0.0189926
$959$	0	0
$960$	9.72171	0.313767
$961$	27.8084	0.897046
$962$	17.3528	0.559476
$963$	11.6424	0.375173
$964$	5.83408	0.187903
$965$	−8.99793	−0.289654
$966$	0	0
$967$	−25.8069	−0.829894	−0.414947	−	0.909846i	$-0.636200\pi$
$967$	−25.8069	−0.829894	−0.414947	+	0.909846i	$0.636200\pi$
$968$	−33.1410	−1.06519
$969$	1.29908	0.0417324
$970$	−8.26324	−0.265317
$971$	19.9288	0.639546	0.319773	−	0.947494i	$-0.396393\pi$
$971$	19.9288	0.639546	0.319773	+	0.947494i	$0.396393\pi$
$972$	0.758127	0.0243169
$973$	0	0
$974$	−21.0298	−0.673839
$975$	−6.52314	−0.208908
$976$	−4.67053	−0.149500
$977$	0.349308	0.0111754	0.00558768	−	0.999984i	$-0.498221\pi$
$977$	0.349308	0.0111754	0.00558768	+	0.999984i	$0.498221\pi$
$978$	−18.1031	−0.578873
$979$	−1.39242	−0.0445020
$980$	0	0
$981$	−8.16032	−0.260539
$982$	9.36245	0.298768
$983$	1.06554	0.0339853	0.0169926	−	0.999856i	$-0.494591\pi$
$983$	1.06554	0.0339853	0.0169926	+	0.999856i	$0.494591\pi$
$984$	−4.34023	−0.138361
$985$	−15.0683	−0.480117
$986$	0.812750	0.0258832
$987$	0	0
$988$	3.99749	0.127177
$989$	−9.81812	−0.312198
$990$	−0.609143	−0.0193598
$991$	−0.177868	−0.00565015	−0.00282507	−	0.999996i	$-0.500899\pi$
$991$	−0.177868	−0.00565015	−0.00282507	+	0.999996i	$0.500899\pi$
$992$	30.8274	0.978770
$993$	8.63678	0.274080
$994$	0	0
$995$	−8.31029	−0.263454
$996$	−0.936549	−0.0296757
$997$	−53.8763	−1.70628	−0.853141	−	0.521681i	$-0.825305\pi$
$997$	−53.8763	−1.70628	−0.853141	+	0.521681i	$0.825305\pi$
$998$	43.8098	1.38678
$999$	−8.65887	−0.273954

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bk.1.3	✓	10
7.6	odd	2		3381.2.a.bl.1.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.bk.1.3	✓	10	1.1	even	1	trivial
3381.2.a.bl.1.3	yes	10	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q-1.11439 q^{2} -1.00000 q^{3} -0.758127 q^{4} -1.17161 q^{5} +1.11439 q^{6} +3.07364 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.11439 q^{2} -1.00000 q^{3} -0.758127 q^{4} -1.17161 q^{5} +1.11439 q^{6} +3.07364 q^{8} +1.00000 q^{9} +1.30563 q^{10} -0.466550 q^{11} +0.758127 q^{12} -1.79833 q^{13} +1.17161 q^{15} -1.90899 q^{16} -0.443057 q^{17} -1.11439 q^{18} +2.93208 q^{19} +0.888229 q^{20} +0.519920 q^{22} -1.00000 q^{23} -3.07364 q^{24} -3.62733 q^{25} +2.00405 q^{26} -1.00000 q^{27} +1.64611 q^{29} -1.30563 q^{30} -7.66867 q^{31} -4.01991 q^{32} +0.466550 q^{33} +0.493740 q^{34} -0.758127 q^{36} +8.65887 q^{37} -3.26749 q^{38} +1.79833 q^{39} -3.60110 q^{40} +1.41208 q^{41} +9.81812 q^{43} +0.353704 q^{44} -1.17161 q^{45} +1.11439 q^{46} -5.59971 q^{47} +1.90899 q^{48} +4.04228 q^{50} +0.443057 q^{51} +1.36336 q^{52} +3.70846 q^{53} +1.11439 q^{54} +0.546614 q^{55} -2.93208 q^{57} -1.83442 q^{58} +9.83561 q^{59} -0.888229 q^{60} +2.44660 q^{61} +8.54591 q^{62} +8.29774 q^{64} +2.10694 q^{65} -0.519920 q^{66} -9.71717 q^{67} +0.335893 q^{68} +1.00000 q^{69} +11.0965 q^{71} +3.07364 q^{72} +3.14805 q^{73} -9.64939 q^{74} +3.62733 q^{75} -2.22289 q^{76} -2.00405 q^{78} -4.92904 q^{79} +2.23659 q^{80} +1.00000 q^{81} -1.57361 q^{82} -1.23535 q^{83} +0.519089 q^{85} -10.9413 q^{86} -1.64611 q^{87} -1.43401 q^{88} +2.98451 q^{89} +1.30563 q^{90} +0.758127 q^{92} +7.66867 q^{93} +6.24028 q^{94} -3.43525 q^{95} +4.01991 q^{96} -6.32891 q^{97} -0.466550 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 - 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9	\( 10 q + 4 q^{2} - 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9} - 8 q^{10} + 2 q^{11} - 8 q^{12} + 4 q^{15} + 4 q^{16} - 12 q^{17} + 4 q^{18} - 26 q^{19} - 24 q^{20} - 8 q^{22} - 10 q^{23} - 12 q^{24} - 2 q^{25} - 4 q^{26} - 10 q^{27} + 16 q^{29} + 8 q^{30} - 12 q^{31} + 8 q^{32} - 2 q^{33} - 28 q^{34} + 8 q^{36} - 8 q^{37} - 32 q^{38} - 4 q^{40} - 10 q^{41} - 4 q^{43} - 16 q^{44} - 4 q^{45} - 4 q^{46} - 2 q^{47} - 4 q^{48} - 8 q^{50} + 12 q^{51} - 24 q^{52} + 14 q^{53} - 4 q^{54} - 16 q^{55} + 26 q^{57} - 8 q^{58} - 38 q^{59} + 24 q^{60} - 14 q^{61} + 8 q^{62} + 8 q^{64} + 12 q^{65} + 8 q^{66} - 8 q^{68} + 10 q^{69} + 24 q^{71} + 12 q^{72} - 8 q^{73} - 8 q^{74} + 2 q^{75} - 64 q^{76} + 4 q^{78} - 16 q^{79} - 28 q^{80} + 10 q^{81} + 40 q^{82} - 28 q^{83} - 4 q^{85} + 20 q^{86} - 16 q^{87} - 68 q^{88} - 32 q^{89} - 8 q^{90} - 8 q^{92} + 12 q^{93} - 56 q^{94} + 8 q^{95} - 8 q^{96} - 4 q^{97} + 2 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9 - 8 * q^10 + 2 * q^11 - 8 * q^12 + 4 * q^15 + 4 * q^16 - 12 * q^17 + 4 * q^18 - 26 * q^19 - 24 * q^20 - 8 * q^22 - 10 * q^23 - 12 * q^24 - 2 * q^25 - 4 * q^26 - 10 * q^27 + 16 * q^29 + 8 * q^30 - 12 * q^31 + 8 * q^32 - 2 * q^33 - 28 * q^34 + 8 * q^36 - 8 * q^37 - 32 * q^38 - 4 * q^40 - 10 * q^41 - 4 * q^43 - 16 * q^44 - 4 * q^45 - 4 * q^46 - 2 * q^47 - 4 * q^48 - 8 * q^50 + 12 * q^51 - 24 * q^52 + 14 * q^53 - 4 * q^54 - 16 * q^55 + 26 * q^57 - 8 * q^58 - 38 * q^59 + 24 * q^60 - 14 * q^61 + 8 * q^62 + 8 * q^64 + 12 * q^65 + 8 * q^66 - 8 * q^68 + 10 * q^69 + 24 * q^71 + 12 * q^72 - 8 * q^73 - 8 * q^74 + 2 * q^75 - 64 * q^76 + 4 * q^78 - 16 * q^79 - 28 * q^80 + 10 * q^81 + 40 * q^82 - 28 * q^83 - 4 * q^85 + 20 * q^86 - 16 * q^87 - 68 * q^88 - 32 * q^89 - 8 * q^90 - 8 * q^92 + 12 * q^93 - 56 * q^94 + 8 * q^95 - 8 * q^96 - 4 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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