LMFDB - Embedded newform 2842.2.a.v.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2842,2,Mod(1,2842)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2842, 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("2842.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2842 = 2 \cdot 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2842.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:	$22.6934842544$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.369849.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 3x^{2} + 3x - 1 $ x^5 - x^4 - 6x^3 + 3x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 406)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.697329$ of defining polynomial
Character	$\chi$	$=$	2842.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.73672 q^{3} +1.00000 q^{4} +4.25045 q^{5} -1.73672 q^{6} -1.00000 q^{8} +0.0161818 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.73672 q^{3} +1.00000 q^{4} +4.25045 q^{5} -1.73672 q^{6} -1.00000 q^{8} +0.0161818 q^{9} -4.25045 q^{10} -1.18786 q^{11} +1.73672 q^{12} +4.58160 q^{13} +7.38182 q^{15} +1.00000 q^{16} -2.96396 q^{17} -0.0161818 q^{18} +2.73672 q^{19} +4.25045 q^{20} +1.18786 q^{22} +6.52938 q^{23} -1.73672 q^{24} +13.0663 q^{25} -4.58160 q^{26} -5.18204 q^{27} +1.00000 q^{29} -7.38182 q^{30} -8.97626 q^{31} -1.00000 q^{32} -2.06297 q^{33} +2.96396 q^{34} +0.0161818 q^{36} -7.19313 q^{37} -2.73672 q^{38} +7.95694 q^{39} -4.25045 q^{40} +1.34908 q^{41} +4.61663 q^{43} -1.18786 q^{44} +0.0687801 q^{45} -6.52938 q^{46} +9.11243 q^{47} +1.73672 q^{48} -13.0663 q^{50} -5.14755 q^{51} +4.58160 q^{52} -2.52603 q^{53} +5.18204 q^{54} -5.04892 q^{55} +4.75290 q^{57} -1.00000 q^{58} +7.82594 q^{59} +7.38182 q^{60} +0.202916 q^{61} +8.97626 q^{62} +1.00000 q^{64} +19.4739 q^{65} +2.06297 q^{66} +8.35334 q^{67} -2.96396 q^{68} +11.3397 q^{69} +4.17778 q^{71} -0.0161818 q^{72} -5.89657 q^{73} +7.19313 q^{74} +22.6925 q^{75} +2.73672 q^{76} -7.95694 q^{78} +11.1540 q^{79} +4.25045 q^{80} -9.04828 q^{81} -1.34908 q^{82} -0.138980 q^{83} -12.5982 q^{85} -4.61663 q^{86} +1.73672 q^{87} +1.18786 q^{88} -13.1854 q^{89} -0.0687801 q^{90} +6.52938 q^{92} -15.5892 q^{93} -9.11243 q^{94} +11.6323 q^{95} -1.73672 q^{96} +4.03023 q^{97} -0.0192217 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + 3 q^{3} + 5 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} + 4 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + 3 * q^3 + 5 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 + 4 * q^9	$ 5 q - 5 q^{2} + 3 q^{3} + 5 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} + 4 q^{9} - 5 q^{10} + 4 q^{11} + 3 q^{12} + 2 q^{13} + 6 q^{15} + 5 q^{16} + 2 q^{17} - 4 q^{18} + 8 q^{19} + 5 q^{20} - 4 q^{22} - 9 q^{23} - 3 q^{24} + 8 q^{25} - 2 q^{26} + 15 q^{27} + 5 q^{29} - 6 q^{30} - 15 q^{31} - 5 q^{32} + 29 q^{33} - 2 q^{34} + 4 q^{36} - 22 q^{37} - 8 q^{38} + 32 q^{39} - 5 q^{40} + q^{41} + 7 q^{43} + 4 q^{44} - 8 q^{45} + 9 q^{46} + 20 q^{47} + 3 q^{48} - 8 q^{50} - 15 q^{51} + 2 q^{52} + 11 q^{53} - 15 q^{54} - 4 q^{55} + 22 q^{57} - 5 q^{58} + 13 q^{59} + 6 q^{60} - 15 q^{61} + 15 q^{62} + 5 q^{64} - 7 q^{65} - 29 q^{66} + 20 q^{67} + 2 q^{68} + 20 q^{69} - 4 q^{71} - 4 q^{72} + 22 q^{74} + 20 q^{75} + 8 q^{76} - 32 q^{78} + q^{79} + 5 q^{80} + 21 q^{81} - q^{82} + 48 q^{83} - 13 q^{85} - 7 q^{86} + 3 q^{87} - 4 q^{88} - 7 q^{89} + 8 q^{90} - 9 q^{92} - 23 q^{93} - 20 q^{94} + 11 q^{95} - 3 q^{96} + 6 q^{97} + 32 q^{99}+O(q^{100}) $ 5 * q - 5 * q^2 + 3 * q^3 + 5 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 + 4 * q^9 - 5 * q^10 + 4 * q^11 + 3 * q^12 + 2 * q^13 + 6 * q^15 + 5 * q^16 + 2 * q^17 - 4 * q^18 + 8 * q^19 + 5 * q^20 - 4 * q^22 - 9 * q^23 - 3 * q^24 + 8 * q^25 - 2 * q^26 + 15 * q^27 + 5 * q^29 - 6 * q^30 - 15 * q^31 - 5 * q^32 + 29 * q^33 - 2 * q^34 + 4 * q^36 - 22 * q^37 - 8 * q^38 + 32 * q^39 - 5 * q^40 + q^41 + 7 * q^43 + 4 * q^44 - 8 * q^45 + 9 * q^46 + 20 * q^47 + 3 * q^48 - 8 * q^50 - 15 * q^51 + 2 * q^52 + 11 * q^53 - 15 * q^54 - 4 * q^55 + 22 * q^57 - 5 * q^58 + 13 * q^59 + 6 * q^60 - 15 * q^61 + 15 * q^62 + 5 * q^64 - 7 * q^65 - 29 * q^66 + 20 * q^67 + 2 * q^68 + 20 * q^69 - 4 * q^71 - 4 * q^72 + 22 * q^74 + 20 * q^75 + 8 * q^76 - 32 * q^78 + q^79 + 5 * q^80 + 21 * q^81 - q^82 + 48 * q^83 - 13 * q^85 - 7 * q^86 + 3 * q^87 - 4 * q^88 - 7 * q^89 + 8 * q^90 - 9 * q^92 - 23 * q^93 - 20 * q^94 + 11 * q^95 - 3 * q^96 + 6 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.73672	1.00269	0.501347	−	0.865247i	$-0.332838\pi$
$3$	1.73672	1.00269	0.501347	+	0.865247i	$0.332838\pi$
$4$	1.00000	0.500000
$5$	4.25045	1.90086	0.950429	−	0.310941i	$-0.100644\pi$
$5$	4.25045	1.90086	0.950429	+	0.310941i	$0.100644\pi$
$6$	−1.73672	−0.709011
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	0.0161818	0.00539395
$10$	−4.25045	−1.34411
$11$	−1.18786	−0.358152	−0.179076	−	0.983835i	$-0.557311\pi$
$11$	−1.18786	−0.358152	−0.179076	+	0.983835i	$0.557311\pi$
$12$	1.73672	0.501347
$13$	4.58160	1.27071	0.635353	−	0.772221i	$-0.280854\pi$
$13$	4.58160	1.27071	0.635353	+	0.772221i	$0.280854\pi$
$14$	0	0
$15$	7.38182	1.90598
$16$	1.00000	0.250000
$17$	−2.96396	−0.718866	−0.359433	−	0.933171i	$-0.617030\pi$
$17$	−2.96396	−0.718866	−0.359433	+	0.933171i	$0.617030\pi$
$18$	−0.0161818	−0.00381410
$19$	2.73672	0.627846	0.313923	−	0.949449i	$-0.398357\pi$
$19$	2.73672	0.627846	0.313923	+	0.949449i	$0.398357\pi$
$20$	4.25045	0.950429
$21$	0	0
$22$	1.18786	0.253252
$23$	6.52938	1.36147	0.680735	−	0.732530i	$-0.261661\pi$
$23$	6.52938	1.36147	0.680735	+	0.732530i	$0.261661\pi$
$24$	−1.73672	−0.354506
$25$	13.0663	2.61326
$26$	−4.58160	−0.898525
$27$	−5.18204	−0.997285
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−7.38182	−1.34773
$31$	−8.97626	−1.61218	−0.806092	−	0.591791i	$-0.798421\pi$
$31$	−8.97626	−1.61218	−0.806092	+	0.591791i	$0.798421\pi$
$32$	−1.00000	−0.176777
$33$	−2.06297	−0.359117
$34$	2.96396	0.508315
$35$	0	0
$36$	0.0161818	0.00269697
$37$	−7.19313	−1.18254	−0.591272	−	0.806473i	$-0.701374\pi$
$37$	−7.19313	−1.18254	−0.591272	+	0.806473i	$0.701374\pi$
$38$	−2.73672	−0.443954
$39$	7.95694	1.27413
$40$	−4.25045	−0.672055
$41$	1.34908	0.210691	0.105346	−	0.994436i	$-0.466405\pi$
$41$	1.34908	0.210691	0.105346	+	0.994436i	$0.466405\pi$
$42$	0	0
$43$	4.61663	0.704029	0.352015	−	0.935995i	$-0.385497\pi$
$43$	4.61663	0.704029	0.352015	+	0.935995i	$0.385497\pi$
$44$	−1.18786	−0.179076
$45$	0.0687801	0.0102531
$46$	−6.52938	−0.962704
$47$	9.11243	1.32918	0.664592	−	0.747206i	$-0.268605\pi$
$47$	9.11243	1.32918	0.664592	+	0.747206i	$0.268605\pi$
$48$	1.73672	0.250673
$49$	0	0
$50$	−13.0663	−1.84786
$51$	−5.14755	−0.720802
$52$	4.58160	0.635353
$53$	−2.52603	−0.346977	−0.173488	−	0.984836i	$-0.555504\pi$
$53$	−2.52603	−0.346977	−0.173488	+	0.984836i	$0.555504\pi$
$54$	5.18204	0.705187
$55$	−5.04892	−0.680796
$56$	0	0
$57$	4.75290	0.629537
$58$	−1.00000	−0.131306
$59$	7.82594	1.01885	0.509425	−	0.860515i	$-0.329858\pi$
$59$	7.82594	1.01885	0.509425	+	0.860515i	$0.329858\pi$
$60$	7.38182	0.952989
$61$	0.202916	0.0259807	0.0129904	−	0.999916i	$-0.495865\pi$
$61$	0.202916	0.0259807	0.0129904	+	0.999916i	$0.495865\pi$
$62$	8.97626	1.13999
$63$	0	0
$64$	1.00000	0.125000
$65$	19.4739	2.41543
$66$	2.06297	0.253934
$67$	8.35334	1.02052	0.510262	−	0.860019i	$-0.329549\pi$
$67$	8.35334	1.02052	0.510262	+	0.860019i	$0.329549\pi$
$68$	−2.96396	−0.359433
$69$	11.3397	1.36514
$70$	0	0
$71$	4.17778	0.495812	0.247906	−	0.968784i	$-0.420258\pi$
$71$	4.17778	0.495812	0.247906	+	0.968784i	$0.420258\pi$
$72$	−0.0161818	−0.00190705
$73$	−5.89657	−0.690141	−0.345071	−	0.938577i	$-0.612145\pi$
$73$	−5.89657	−0.690141	−0.345071	+	0.938577i	$0.612145\pi$
$74$	7.19313	0.836184
$75$	22.6925	2.62030
$76$	2.73672	0.313923
$77$	0	0
$78$	−7.95694	−0.900946
$79$	11.1540	1.25493	0.627464	−	0.778646i	$-0.284093\pi$
$79$	11.1540	1.25493	0.627464	+	0.778646i	$0.284093\pi$
$80$	4.25045	0.475215
$81$	−9.04828	−1.00536
$82$	−1.34908	−0.148981
$83$	−0.138980	−0.0152550	−0.00762750	−	0.999971i	$-0.502428\pi$
$83$	−0.138980	−0.0152550	−0.00762750	+	0.999971i	$0.502428\pi$
$84$	0	0
$85$	−12.5982	−1.36646
$86$	−4.61663	−0.497824
$87$	1.73672	0.186195
$88$	1.18786	0.126626
$89$	−13.1854	−1.39765	−0.698824	−	0.715293i	$-0.746293\pi$
$89$	−13.1854	−1.39765	−0.698824	+	0.715293i	$0.746293\pi$
$90$	−0.0687801	−0.00725006
$91$	0	0
$92$	6.52938	0.680735
$93$	−15.5892	−1.61653
$94$	−9.11243	−0.939875
$95$	11.6323	1.19345
$96$	−1.73672	−0.177253
$97$	4.03023	0.409208	0.204604	−	0.978845i	$-0.434409\pi$
$97$	4.03023	0.409208	0.204604	+	0.978845i	$0.434409\pi$
$98$	0	0
$99$	−0.0192217	−0.00193185
$100$	13.0663	1.30663
$101$	4.41168	0.438978	0.219489	−	0.975615i	$-0.429561\pi$
$101$	4.41168	0.438978	0.219489	+	0.975615i	$0.429561\pi$
$102$	5.14755	0.509684
$103$	−17.0398	−1.67898	−0.839491	−	0.543373i	$-0.817147\pi$
$103$	−17.0398	−1.67898	−0.839491	+	0.543373i	$0.817147\pi$
$104$	−4.58160	−0.449263
$105$	0	0
$106$	2.52603	0.245350
$107$	−8.75604	−0.846478	−0.423239	−	0.906018i	$-0.639107\pi$
$107$	−8.75604	−0.846478	−0.423239	+	0.906018i	$0.639107\pi$
$108$	−5.18204	−0.498642
$109$	15.6703	1.50094	0.750470	−	0.660904i	$-0.229827\pi$
$109$	15.6703	1.50094	0.750470	+	0.660904i	$0.229827\pi$
$110$	5.04892	0.481396
$111$	−12.4924	−1.18573
$112$	0	0
$113$	−11.3045	−1.06343	−0.531717	−	0.846922i	$-0.678453\pi$
$113$	−11.3045	−1.06343	−0.531717	+	0.846922i	$0.678453\pi$
$114$	−4.75290	−0.445150
$115$	27.7528	2.58796
$116$	1.00000	0.0928477
$117$	0.0741387	0.00685412
$118$	−7.82594	−0.720436
$119$	0	0
$120$	−7.38182	−0.673865
$121$	−9.58900	−0.871727
$122$	−0.202916	−0.0183712
$123$	2.34297	0.211259
$124$	−8.97626	−0.806092
$125$	34.2855	3.06658
$126$	0	0
$127$	9.15036	0.811963	0.405982	−	0.913881i	$-0.366930\pi$
$127$	9.15036	0.811963	0.405982	+	0.913881i	$0.366930\pi$
$128$	−1.00000	−0.0883883
$129$	8.01777	0.705925
$130$	−19.4739	−1.70797
$131$	12.4668	1.08923	0.544614	−	0.838687i	$-0.316676\pi$
$131$	12.4668	1.08923	0.544614	+	0.838687i	$0.316676\pi$
$132$	−2.06297	−0.179558
$133$	0	0
$134$	−8.35334	−0.721619
$135$	−22.0260	−1.89570
$136$	2.96396	0.254157
$137$	−16.5128	−1.41078	−0.705390	−	0.708819i	$-0.749228\pi$
$137$	−16.5128	−1.41078	−0.705390	+	0.708819i	$0.749228\pi$
$138$	−11.3397	−0.965297
$139$	−8.68763	−0.736875	−0.368438	−	0.929652i	$-0.620107\pi$
$139$	−8.68763	−0.736875	−0.368438	+	0.929652i	$0.620107\pi$
$140$	0	0
$141$	15.8257	1.33276
$142$	−4.17778	−0.350592
$143$	−5.44228	−0.455106
$144$	0.0161818	0.00134849
$145$	4.25045	0.352981
$146$	5.89657	0.488003
$147$	0	0
$148$	−7.19313	−0.591272
$149$	−4.18167	−0.342576	−0.171288	−	0.985221i	$-0.554793\pi$
$149$	−4.18167	−0.342576	−0.171288	+	0.985221i	$0.554793\pi$
$150$	−22.6925	−1.85283
$151$	−4.52649	−0.368361	−0.184180	−	0.982892i	$-0.558963\pi$
$151$	−4.52649	−0.368361	−0.184180	+	0.982892i	$0.558963\pi$
$152$	−2.73672	−0.221977
$153$	−0.0479623	−0.00387752
$154$	0	0
$155$	−38.1531	−3.06453
$156$	7.95694	0.637065
$157$	2.96672	0.236770	0.118385	−	0.992968i	$-0.462228\pi$
$157$	2.96672	0.236770	0.118385	+	0.992968i	$0.462228\pi$
$158$	−11.1540	−0.887368
$159$	−4.38700	−0.347911
$160$	−4.25045	−0.336027
$161$	0	0
$162$	9.04828	0.710900
$163$	−15.6469	−1.22556	−0.612780	−	0.790254i	$-0.709949\pi$
$163$	−15.6469	−1.22556	−0.612780	+	0.790254i	$0.709949\pi$
$164$	1.34908	0.105346
$165$	−8.76854	−0.682630
$166$	0.138980	0.0107869
$167$	−4.26609	−0.330120	−0.165060	−	0.986284i	$-0.552782\pi$
$167$	−4.26609	−0.330120	−0.165060	+	0.986284i	$0.552782\pi$
$168$	0	0
$169$	7.99105	0.614696
$170$	12.5982	0.966234
$171$	0.0442851	0.00338657
$172$	4.61663	0.352015
$173$	7.43496	0.565269	0.282635	−	0.959228i	$-0.408792\pi$
$173$	7.43496	0.565269	0.282635	+	0.959228i	$0.408792\pi$
$174$	−1.73672	−0.131660
$175$	0	0
$176$	−1.18786	−0.0895380
$177$	13.5914	1.02159
$178$	13.1854	0.988287
$179$	1.46093	0.109195	0.0545974	−	0.998508i	$-0.482612\pi$
$179$	1.46093	0.109195	0.0545974	+	0.998508i	$0.482612\pi$
$180$	0.0687801	0.00512656
$181$	−18.2038	−1.35308	−0.676539	−	0.736407i	$-0.736521\pi$
$181$	−18.2038	−1.35308	−0.676539	+	0.736407i	$0.736521\pi$
$182$	0	0
$183$	0.352408	0.0260507
$184$	−6.52938	−0.481352
$185$	−30.5740	−2.24785
$186$	15.5892	1.14306
$187$	3.52076	0.257463
$188$	9.11243	0.664592
$189$	0	0
$190$	−11.6323	−0.843894
$191$	−6.30452	−0.456179	−0.228090	−	0.973640i	$-0.573248\pi$
$191$	−6.30452	−0.456179	−0.228090	+	0.973640i	$0.573248\pi$
$192$	1.73672	0.125337
$193$	−26.8140	−1.93011	−0.965056	−	0.262042i	$-0.915604\pi$
$193$	−26.8140	−1.93011	−0.965056	+	0.262042i	$0.915604\pi$
$194$	−4.03023	−0.289354
$195$	33.8205	2.42194
$196$	0	0
$197$	21.6486	1.54240	0.771199	−	0.636595i	$-0.219658\pi$
$197$	21.6486	1.54240	0.771199	+	0.636595i	$0.219658\pi$
$198$	0.0192217	0.00136603
$199$	24.8890	1.76433	0.882165	−	0.470940i	$-0.156085\pi$
$199$	24.8890	1.76433	0.882165	+	0.470940i	$0.156085\pi$
$200$	−13.0663	−0.923928
$201$	14.5074	1.02327
$202$	−4.41168	−0.310404
$203$	0	0
$204$	−5.14755	−0.360401
$205$	5.73421	0.400494
$206$	17.0398	1.18722
$207$	0.105657	0.00734369
$208$	4.58160	0.317677
$209$	−3.25082	−0.224864
$210$	0	0
$211$	9.15699	0.630393	0.315197	−	0.949026i	$-0.397930\pi$
$211$	9.15699	0.630393	0.315197	+	0.949026i	$0.397930\pi$
$212$	−2.52603	−0.173488
$213$	7.25562	0.497147
$214$	8.75604	0.598550
$215$	19.6227	1.33826
$216$	5.18204	0.352593
$217$	0	0
$218$	−15.6703	−1.06133
$219$	−10.2407	−0.692000
$220$	−5.04892	−0.340398
$221$	−13.5797	−0.913468
$222$	12.4924	0.838436
$223$	24.0783	1.61240	0.806200	−	0.591642i	$-0.201520\pi$
$223$	24.0783	1.61240	0.806200	+	0.591642i	$0.201520\pi$
$224$	0	0
$225$	0.211437	0.0140958
$226$	11.3045	0.751962
$227$	−0.670821	−0.0445240	−0.0222620	−	0.999752i	$-0.507087\pi$
$227$	−0.670821	−0.0445240	−0.0222620	+	0.999752i	$0.507087\pi$
$228$	4.75290	0.314768
$229$	−26.7508	−1.76774	−0.883872	−	0.467730i	$-0.845072\pi$
$229$	−26.7508	−1.76774	−0.883872	+	0.467730i	$0.845072\pi$
$230$	−27.7528	−1.82996
$231$	0	0
$232$	−1.00000	−0.0656532
$233$	−22.2058	−1.45475	−0.727374	−	0.686241i	$-0.759259\pi$
$233$	−22.2058	−1.45475	−0.727374	+	0.686241i	$0.759259\pi$
$234$	−0.0741387	−0.00484660
$235$	38.7319	2.52659
$236$	7.82594	0.509425
$237$	19.3714	1.25831
$238$	0	0
$239$	4.04336	0.261543	0.130772	−	0.991413i	$-0.458255\pi$
$239$	4.04336	0.261543	0.130772	+	0.991413i	$0.458255\pi$
$240$	7.38182	0.476495
$241$	−6.80027	−0.438044	−0.219022	−	0.975720i	$-0.570287\pi$
$241$	−6.80027	−0.438044	−0.219022	+	0.975720i	$0.570287\pi$
$242$	9.58900	0.616404
$243$	−0.168165	−0.0107878
$244$	0.202916	0.0129904
$245$	0	0
$246$	−2.34297	−0.149382
$247$	12.5385	0.797808
$248$	8.97626	0.569993
$249$	−0.241368	−0.0152961
$250$	−34.2855	−2.16840
$251$	−7.68508	−0.485078	−0.242539	−	0.970142i	$-0.577980\pi$
$251$	−7.68508	−0.485078	−0.242539	+	0.970142i	$0.577980\pi$
$252$	0	0
$253$	−7.75596	−0.487613
$254$	−9.15036	−0.574145
$255$	−21.8794	−1.37014
$256$	1.00000	0.0625000
$257$	14.2639	0.889756	0.444878	−	0.895591i	$-0.353247\pi$
$257$	14.2639	0.889756	0.444878	+	0.895591i	$0.353247\pi$
$258$	−8.01777	−0.499165
$259$	0	0
$260$	19.4739	1.20772
$261$	0.0161818	0.00100163
$262$	−12.4668	−0.770200
$263$	−5.57383	−0.343697	−0.171849	−	0.985123i	$-0.554974\pi$
$263$	−5.57383	−0.343697	−0.171849	+	0.985123i	$0.554974\pi$
$264$	2.06297	0.126967
$265$	−10.7368	−0.659554
$266$	0	0
$267$	−22.8993	−1.40141
$268$	8.35334	0.510262
$269$	−21.5568	−1.31434	−0.657170	−	0.753743i	$-0.728246\pi$
$269$	−21.5568	−1.31434	−0.657170	+	0.753743i	$0.728246\pi$
$270$	22.0260	1.34046
$271$	15.5540	0.944836	0.472418	−	0.881375i	$-0.343381\pi$
$271$	15.5540	0.944836	0.472418	+	0.881375i	$0.343381\pi$
$272$	−2.96396	−0.179716
$273$	0	0
$274$	16.5128	0.997573
$275$	−15.5209	−0.935945
$276$	11.3397	0.682568
$277$	−7.04078	−0.423039	−0.211520	−	0.977374i	$-0.567841\pi$
$277$	−7.04078	−0.423039	−0.211520	+	0.977374i	$0.567841\pi$
$278$	8.68763	0.521050
$279$	−0.145252	−0.00869603
$280$	0	0
$281$	−2.69875	−0.160994	−0.0804969	−	0.996755i	$-0.525651\pi$
$281$	−2.69875	−0.160994	−0.0804969	+	0.996755i	$0.525651\pi$
$282$	−15.8257	−0.942407
$283$	−18.3028	−1.08799	−0.543993	−	0.839090i	$-0.683088\pi$
$283$	−18.3028	−1.08799	−0.543993	+	0.839090i	$0.683088\pi$
$284$	4.17778	0.247906
$285$	20.2019	1.19666
$286$	5.44228	0.321809
$287$	0	0
$288$	−0.0161818	−0.000953524 0
$289$	−8.21495	−0.483232
$290$	−4.25045	−0.249595
$291$	6.99936	0.410310
$292$	−5.89657	−0.345071
$293$	24.0696	1.40616	0.703080	−	0.711111i	$-0.251808\pi$
$293$	24.0696	1.40616	0.703080	+	0.711111i	$0.251808\pi$
$294$	0	0
$295$	33.2637	1.93669
$296$	7.19313	0.418092
$297$	6.15552	0.357180
$298$	4.18167	0.242238
$299$	29.9150	1.73003
$300$	22.6925	1.31015
$301$	0	0
$302$	4.52649	0.260470
$303$	7.66183	0.440160
$304$	2.73672	0.156961
$305$	0.862485	0.0493857
$306$	0.0479623	0.00274182
$307$	−2.21829	−0.126605	−0.0633023	−	0.997994i	$-0.520163\pi$
$307$	−2.21829	−0.126605	−0.0633023	+	0.997994i	$0.520163\pi$
$308$	0	0
$309$	−29.5933	−1.68350
$310$	38.1531	2.16695
$311$	5.38299	0.305241	0.152621	−	0.988285i	$-0.451229\pi$
$311$	5.38299	0.305241	0.152621	+	0.988285i	$0.451229\pi$
$312$	−7.95694	−0.450473
$313$	−24.5112	−1.38546	−0.692728	−	0.721199i	$-0.743591\pi$
$313$	−24.5112	−1.38546	−0.692728	+	0.721199i	$0.743591\pi$
$314$	−2.96672	−0.167422
$315$	0	0
$316$	11.1540	0.627464
$317$	2.42841	0.136393	0.0681965	−	0.997672i	$-0.478276\pi$
$317$	2.42841	0.136393	0.0681965	+	0.997672i	$0.478276\pi$
$318$	4.38700	0.246011
$319$	−1.18786	−0.0665072
$320$	4.25045	0.237607
$321$	−15.2067	−0.848758
$322$	0	0
$323$	−8.11151	−0.451337
$324$	−9.04828	−0.502682
$325$	59.8646	3.32069
$326$	15.6469	0.866602
$327$	27.2148	1.50498
$328$	−1.34908	−0.0744906
$329$	0	0
$330$	8.76854	0.482692
$331$	−1.51143	−0.0830757	−0.0415379	−	0.999137i	$-0.513226\pi$
$331$	−1.51143	−0.0830757	−0.0415379	+	0.999137i	$0.513226\pi$
$332$	−0.138980	−0.00762750
$333$	−0.116398	−0.00637857
$334$	4.26609	0.233430
$335$	35.5055	1.93987
$336$	0	0
$337$	29.7617	1.62122	0.810610	−	0.585586i	$-0.199136\pi$
$337$	29.7617	1.62122	0.810610	+	0.585586i	$0.199136\pi$
$338$	−7.99105	−0.434656
$339$	−19.6326	−1.06630
$340$	−12.5982	−0.683231
$341$	10.6625	0.577407
$342$	−0.0442851	−0.00239466
$343$	0	0
$344$	−4.61663	−0.248912
$345$	48.1987	2.59493
$346$	−7.43496	−0.399706
$347$	−26.6753	−1.43201	−0.716003	−	0.698098i	$-0.754030\pi$
$347$	−26.6753	−1.43201	−0.716003	+	0.698098i	$0.754030\pi$
$348$	1.73672	0.0930977
$349$	−26.4247	−1.41448	−0.707242	−	0.706972i	$-0.750061\pi$
$349$	−26.4247	−1.41448	−0.707242	+	0.706972i	$0.750061\pi$
$350$	0	0
$351$	−23.7420	−1.26726
$352$	1.18786	0.0633129
$353$	31.9645	1.70130	0.850649	−	0.525734i	$-0.176209\pi$
$353$	31.9645	1.70130	0.850649	+	0.525734i	$0.176209\pi$
$354$	−13.5914	−0.722376
$355$	17.7575	0.942468
$356$	−13.1854	−0.698824
$357$	0	0
$358$	−1.46093	−0.0772124
$359$	5.52126	0.291401	0.145701	−	0.989329i	$-0.453456\pi$
$359$	5.52126	0.291401	0.145701	+	0.989329i	$0.453456\pi$
$360$	−0.0687801	−0.00362503
$361$	−11.5104	−0.605810
$362$	18.2038	0.956770
$363$	−16.6534	−0.874075
$364$	0	0
$365$	−25.0631	−1.31186
$366$	−0.352408	−0.0184206
$367$	−10.1531	−0.529988	−0.264994	−	0.964250i	$-0.585370\pi$
$367$	−10.1531	−0.529988	−0.264994	+	0.964250i	$0.585370\pi$
$368$	6.52938	0.340367
$369$	0.0218306	0.00113646
$370$	30.5740	1.58947
$371$	0	0
$372$	−15.5892	−0.808263
$373$	21.7782	1.12763	0.563817	−	0.825900i	$-0.309332\pi$
$373$	21.7782	1.12763	0.563817	+	0.825900i	$0.309332\pi$
$374$	−3.52076	−0.182054
$375$	59.5441	3.07484
$376$	−9.11243	−0.469938
$377$	4.58160	0.235964
$378$	0	0
$379$	5.64983	0.290212	0.145106	−	0.989416i	$-0.453648\pi$
$379$	5.64983	0.290212	0.145106	+	0.989416i	$0.453648\pi$
$380$	11.6323	0.596723
$381$	15.8916	0.814150
$382$	6.30452	0.322567
$383$	1.90606	0.0973949	0.0486975	−	0.998814i	$-0.484493\pi$
$383$	1.90606	0.0973949	0.0486975	+	0.998814i	$0.484493\pi$
$384$	−1.73672	−0.0886264
$385$	0	0
$386$	26.8140	1.36480
$387$	0.0747055	0.00379749
$388$	4.03023	0.204604
$389$	32.7603	1.66101	0.830507	−	0.557008i	$-0.188051\pi$
$389$	32.7603	1.66101	0.830507	+	0.557008i	$0.188051\pi$
$390$	−33.8205	−1.71257
$391$	−19.3528	−0.978713
$392$	0	0
$393$	21.6513	1.09216
$394$	−21.6486	−1.09064
$395$	47.4097	2.38544
$396$	−0.0192217	−0.000965926 0
$397$	−26.4238	−1.32617	−0.663087	−	0.748542i	$-0.730754\pi$
$397$	−26.4238	−1.32617	−0.663087	+	0.748542i	$0.730754\pi$
$398$	−24.8890	−1.24757
$399$	0	0
$400$	13.0663	0.653316
$401$	6.19480	0.309354	0.154677	−	0.987965i	$-0.450566\pi$
$401$	6.19480	0.309354	0.154677	+	0.987965i	$0.450566\pi$
$402$	−14.5074	−0.723562
$403$	−41.1256	−2.04861
$404$	4.41168	0.219489
$405$	−38.4593	−1.91106
$406$	0	0
$407$	8.54440	0.423530
$408$	5.14755	0.254842
$409$	9.82710	0.485919	0.242960	−	0.970036i	$-0.421882\pi$
$409$	9.82710	0.485919	0.242960	+	0.970036i	$0.421882\pi$
$410$	−5.73421	−0.283192
$411$	−28.6780	−1.41458
$412$	−17.0398	−0.839491
$413$	0	0
$414$	−0.105657	−0.00519277
$415$	−0.590726	−0.0289976
$416$	−4.58160	−0.224631
$417$	−15.0879	−0.738860
$418$	3.25082	0.159003
$419$	−19.5408	−0.954629	−0.477314	−	0.878733i	$-0.658390\pi$
$419$	−19.5408	−0.954629	−0.477314	+	0.878733i	$0.658390\pi$
$420$	0	0
$421$	−8.12744	−0.396107	−0.198054	−	0.980191i	$-0.563462\pi$
$421$	−8.12744	−0.396107	−0.198054	+	0.980191i	$0.563462\pi$
$422$	−9.15699	−0.445755
$423$	0.147456	0.00716955
$424$	2.52603	0.122675
$425$	−38.7280	−1.87859
$426$	−7.25562	−0.351536
$427$	0	0
$428$	−8.75604	−0.423239
$429$	−9.45169	−0.456332
$430$	−19.6227	−0.946292
$431$	27.5954	1.32922	0.664612	−	0.747188i	$-0.268597\pi$
$431$	27.5954	1.32922	0.664612	+	0.747188i	$0.268597\pi$
$432$	−5.18204	−0.249321
$433$	3.77381	0.181358	0.0906790	−	0.995880i	$-0.471096\pi$
$433$	3.77381	0.181358	0.0906790	+	0.995880i	$0.471096\pi$
$434$	0	0
$435$	7.38182	0.353931
$436$	15.6703	0.750470
$437$	17.8690	0.854792
$438$	10.2407	0.489318
$439$	22.3673	1.06753	0.533767	−	0.845632i	$-0.320776\pi$
$439$	22.3673	1.06753	0.533767	+	0.845632i	$0.320776\pi$
$440$	5.04892	0.240698
$441$	0	0
$442$	13.5797	0.645919
$443$	1.29803	0.0616712	0.0308356	−	0.999524i	$-0.490183\pi$
$443$	1.29803	0.0616712	0.0308356	+	0.999524i	$0.490183\pi$
$444$	−12.4924	−0.592864
$445$	−56.0438	−2.65673
$446$	−24.0783	−1.14014
$447$	−7.26237	−0.343498
$448$	0	0
$449$	3.75871	0.177384	0.0886922	−	0.996059i	$-0.471731\pi$
$449$	3.75871	0.177384	0.0886922	+	0.996059i	$0.471731\pi$
$450$	−0.211437	−0.00996723
$451$	−1.60252	−0.0754595
$452$	−11.3045	−0.531717
$453$	−7.86123	−0.369353
$454$	0.670821	0.0314832
$455$	0	0
$456$	−4.75290	−0.222575
$457$	7.66535	0.358570	0.179285	−	0.983797i	$-0.442622\pi$
$457$	7.66535	0.358570	0.179285	+	0.983797i	$0.442622\pi$
$458$	26.7508	1.24998
$459$	15.3594	0.716914
$460$	27.7528	1.29398
$461$	−18.9389	−0.882073	−0.441036	−	0.897489i	$-0.645389\pi$
$461$	−18.9389	−0.882073	−0.441036	+	0.897489i	$0.645389\pi$
$462$	0	0
$463$	−29.2444	−1.35910	−0.679552	−	0.733628i	$-0.737826\pi$
$463$	−29.2444	−1.35910	−0.679552	+	0.733628i	$0.737826\pi$
$464$	1.00000	0.0464238
$465$	−66.2611	−3.07279
$466$	22.2058	1.02866
$467$	−38.7256	−1.79201	−0.896003	−	0.444049i	$-0.853542\pi$
$467$	−38.7256	−1.79201	−0.896003	+	0.444049i	$0.853542\pi$
$468$	0.0741387	0.00342706
$469$	0	0
$470$	−38.7319	−1.78657
$471$	5.15235	0.237408
$472$	−7.82594	−0.360218
$473$	−5.48389	−0.252149
$474$	−19.3714	−0.889758
$475$	35.7588	1.64073
$476$	0	0
$477$	−0.0408758	−0.00187157
$478$	−4.04336	−0.184939
$479$	3.67403	0.167871	0.0839354	−	0.996471i	$-0.473251\pi$
$479$	3.67403	0.167871	0.0839354	+	0.996471i	$0.473251\pi$
$480$	−7.38182	−0.336933
$481$	−32.9560	−1.50267
$482$	6.80027	0.309744
$483$	0	0
$484$	−9.58900	−0.435864
$485$	17.1303	0.777846
$486$	0.168165	0.00762811
$487$	−25.7995	−1.16909	−0.584543	−	0.811363i	$-0.698726\pi$
$487$	−25.7995	−1.16909	−0.584543	+	0.811363i	$0.698726\pi$
$488$	−0.202916	−0.00918558
$489$	−27.1742	−1.22886
$490$	0	0
$491$	−7.22244	−0.325944	−0.162972	−	0.986631i	$-0.552108\pi$
$491$	−7.22244	−0.325944	−0.162972	+	0.986631i	$0.552108\pi$
$492$	2.34297	0.105629
$493$	−2.96396	−0.133490
$494$	−12.5385	−0.564135
$495$	−0.0817008	−0.00367218
$496$	−8.97626	−0.403046
$497$	0	0
$498$	0.241368	0.0108160
$499$	−15.0650	−0.674401	−0.337200	−	0.941433i	$-0.609480\pi$
$499$	−15.0650	−0.674401	−0.337200	+	0.941433i	$0.609480\pi$
$500$	34.2855	1.53329
$501$	−7.40899	−0.331009
$502$	7.68508	0.343002
$503$	8.67938	0.386995	0.193497	−	0.981101i	$-0.438017\pi$
$503$	8.67938	0.386995	0.193497	+	0.981101i	$0.438017\pi$
$504$	0	0
$505$	18.7516	0.834435
$506$	7.75596	0.344794
$507$	13.8782	0.616352
$508$	9.15036	0.405982
$509$	27.1483	1.20333	0.601664	−	0.798749i	$-0.294505\pi$
$509$	27.1483	1.20333	0.601664	+	0.798749i	$0.294505\pi$
$510$	21.8794	0.968837
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−14.1818	−0.626141
$514$	−14.2639	−0.629152
$515$	−72.4268	−3.19151
$516$	8.01777	0.352963
$517$	−10.8243	−0.476050
$518$	0	0
$519$	12.9124	0.566792
$520$	−19.4739	−0.853985
$521$	−15.8146	−0.692849	−0.346424	−	0.938078i	$-0.612604\pi$
$521$	−15.8146	−0.692849	−0.346424	+	0.938078i	$0.612604\pi$
$522$	−0.0161818	−0.000708260 0
$523$	19.9302	0.871486	0.435743	−	0.900071i	$-0.356486\pi$
$523$	19.9302	0.871486	0.435743	+	0.900071i	$0.356486\pi$
$524$	12.4668	0.544614
$525$	0	0
$526$	5.57383	0.243031
$527$	26.6053	1.15894
$528$	−2.06297	−0.0897792
$529$	19.6328	0.853598
$530$	10.7368	0.466375
$531$	0.126638	0.00549562
$532$	0	0
$533$	6.18095	0.267727
$534$	22.8993	0.990949
$535$	−37.2171	−1.60903
$536$	−8.35334	−0.360809
$537$	2.53722	0.109489
$538$	21.5568	0.929378
$539$	0	0
$540$	−22.0260	−0.947849
$541$	−6.37381	−0.274031	−0.137016	−	0.990569i	$-0.543751\pi$
$541$	−6.37381	−0.274031	−0.137016	+	0.990569i	$0.543751\pi$
$542$	−15.5540	−0.668100
$543$	−31.6148	−1.35672
$544$	2.96396	0.127079
$545$	66.6057	2.85308
$546$	0	0
$547$	−5.66665	−0.242289	−0.121144	−	0.992635i	$-0.538656\pi$
$547$	−5.66665	−0.242289	−0.121144	+	0.992635i	$0.538656\pi$
$548$	−16.5128	−0.705390
$549$	0.00328356	0.000140139 0
$550$	15.5209	0.661813
$551$	2.73672	0.116588
$552$	−11.3397	−0.482648
$553$	0	0
$554$	7.04078	0.299134
$555$	−53.0984	−2.25390
$556$	−8.68763	−0.368438
$557$	−15.2550	−0.646373	−0.323187	−	0.946335i	$-0.604754\pi$
$557$	−15.2550	−0.646373	−0.323187	+	0.946335i	$0.604754\pi$
$558$	0.145252	0.00614902
$559$	21.1515	0.894615
$560$	0	0
$561$	6.11455	0.258157
$562$	2.69875	0.113840
$563$	34.1109	1.43760	0.718801	−	0.695216i	$-0.244691\pi$
$563$	34.1109	1.43760	0.718801	+	0.695216i	$0.244691\pi$
$564$	15.8257	0.666382
$565$	−48.0491	−2.02144
$566$	18.3028	0.769322
$567$	0	0
$568$	−4.17778	−0.175296
$569$	−4.60652	−0.193116	−0.0965578	−	0.995327i	$-0.530783\pi$
$569$	−4.60652	−0.193116	−0.0965578	+	0.995327i	$0.530783\pi$
$570$	−20.2019	−0.846166
$571$	−34.0177	−1.42360	−0.711799	−	0.702383i	$-0.752119\pi$
$571$	−34.0177	−1.42360	−0.711799	+	0.702383i	$0.752119\pi$
$572$	−5.44228	−0.227553
$573$	−10.9492	−0.457408
$574$	0	0
$575$	85.3149	3.55788
$576$	0.0161818	0.000674243 0
$577$	2.72436	0.113417	0.0567084	−	0.998391i	$-0.481939\pi$
$577$	2.72436	0.113417	0.0567084	+	0.998391i	$0.481939\pi$
$578$	8.21495	0.341697
$579$	−46.5683	−1.93531
$580$	4.25045	0.176490
$581$	0	0
$582$	−6.99936	−0.290133
$583$	3.00056	0.124270
$584$	5.89657	0.244002
$585$	0.315123	0.0130287
$586$	−24.0696	−0.994305
$587$	−16.5683	−0.683848	−0.341924	−	0.939728i	$-0.611079\pi$
$587$	−16.5683	−0.683848	−0.341924	+	0.939728i	$0.611079\pi$
$588$	0	0
$589$	−24.5655	−1.01220
$590$	−33.2637	−1.36945
$591$	37.5974	1.54655
$592$	−7.19313	−0.295636
$593$	−21.5486	−0.884895	−0.442447	−	0.896794i	$-0.645890\pi$
$593$	−21.5486	−0.884895	−0.442447	+	0.896794i	$0.645890\pi$
$594$	−6.15552	−0.252564
$595$	0	0
$596$	−4.18167	−0.171288
$597$	43.2250	1.76908
$598$	−29.9150	−1.22331
$599$	−10.2300	−0.417987	−0.208994	−	0.977917i	$-0.567019\pi$
$599$	−10.2300	−0.417987	−0.208994	+	0.977917i	$0.567019\pi$
$600$	−22.6925	−0.926416
$601$	6.73099	0.274563	0.137281	−	0.990532i	$-0.456164\pi$
$601$	6.73099	0.274563	0.137281	+	0.990532i	$0.456164\pi$
$602$	0	0
$603$	0.135172	0.00550465
$604$	−4.52649	−0.184180
$605$	−40.7575	−1.65703
$606$	−7.66183	−0.311240
$607$	9.93690	0.403326	0.201663	−	0.979455i	$-0.435365\pi$
$607$	9.93690	0.403326	0.201663	+	0.979455i	$0.435365\pi$
$608$	−2.73672	−0.110988
$609$	0	0
$610$	−0.862485	−0.0349210
$611$	41.7495	1.68900
$612$	−0.0479623	−0.00193876
$613$	−8.22473	−0.332194	−0.166097	−	0.986109i	$-0.553116\pi$
$613$	−8.22473	−0.332194	−0.166097	+	0.986109i	$0.553116\pi$
$614$	2.21829	0.0895230
$615$	9.95869	0.401573
$616$	0	0
$617$	26.1803	1.05398	0.526989	−	0.849872i	$-0.323321\pi$
$617$	26.1803	1.05398	0.526989	+	0.849872i	$0.323321\pi$
$618$	29.5933	1.19042
$619$	39.6661	1.59432	0.797158	−	0.603771i	$-0.206336\pi$
$619$	39.6661	1.59432	0.797158	+	0.603771i	$0.206336\pi$
$620$	−38.1531	−1.53227
$621$	−33.8355	−1.35777
$622$	−5.38299	−0.215838
$623$	0	0
$624$	7.95694	0.318532
$625$	80.3970	3.21588
$626$	24.5112	0.979665
$627$	−5.64576	−0.225470
$628$	2.96672	0.118385
$629$	21.3201	0.850090
$630$	0	0
$631$	−27.1091	−1.07920	−0.539599	−	0.841922i	$-0.681424\pi$
$631$	−27.1091	−1.07920	−0.539599	+	0.841922i	$0.681424\pi$
$632$	−11.1540	−0.443684
$633$	15.9031	0.632091
$634$	−2.42841	−0.0964444
$635$	38.8931	1.54343
$636$	−4.38700	−0.173956
$637$	0	0
$638$	1.18786	0.0470277
$639$	0.0676042	0.00267438
$640$	−4.25045	−0.168014
$641$	15.7913	0.623717	0.311858	−	0.950129i	$-0.399049\pi$
$641$	15.7913	0.623717	0.311858	+	0.950129i	$0.399049\pi$
$642$	15.2067	0.600162
$643$	22.5157	0.887934	0.443967	−	0.896043i	$-0.353571\pi$
$643$	22.5157	0.887934	0.443967	+	0.896043i	$0.353571\pi$
$644$	0	0
$645$	34.0791	1.34186
$646$	8.11151	0.319143
$647$	−14.2024	−0.558356	−0.279178	−	0.960239i	$-0.590062\pi$
$647$	−14.2024	−0.558356	−0.279178	+	0.960239i	$0.590062\pi$
$648$	9.04828	0.355450
$649$	−9.29609	−0.364903
$650$	−59.8646	−2.34808
$651$	0	0
$652$	−15.6469	−0.612780
$653$	14.7414	0.576875	0.288437	−	0.957499i	$-0.406864\pi$
$653$	14.7414	0.576875	0.288437	+	0.957499i	$0.406864\pi$
$654$	−27.2148	−1.06418
$655$	52.9894	2.07047
$656$	1.34908	0.0526728
$657$	−0.0954173	−0.00372258
$658$	0	0
$659$	46.7980	1.82299	0.911495	−	0.411311i	$-0.134929\pi$
$659$	46.7980	1.82299	0.911495	+	0.411311i	$0.134929\pi$
$660$	−8.76854	−0.341315
$661$	−18.4748	−0.718585	−0.359292	−	0.933225i	$-0.616982\pi$
$661$	−18.4748	−0.718585	−0.359292	+	0.933225i	$0.616982\pi$
$662$	1.51143	0.0587434
$663$	−23.5840	−0.915928
$664$	0.138980	0.00539346
$665$	0	0
$666$	0.116398	0.00451033
$667$	6.52938	0.252818
$668$	−4.26609	−0.165060
$669$	41.8171	1.61674
$670$	−35.5055	−1.37170
$671$	−0.241035	−0.00930506
$672$	0	0
$673$	−40.9298	−1.57773	−0.788864	−	0.614568i	$-0.789331\pi$
$673$	−40.9298	−1.57773	−0.788864	+	0.614568i	$0.789331\pi$
$674$	−29.7617	−1.14638
$675$	−67.7102	−2.60617
$676$	7.99105	0.307348
$677$	−0.914699	−0.0351547	−0.0175774	−	0.999846i	$-0.505595\pi$
$677$	−0.914699	−0.0351547	−0.0175774	+	0.999846i	$0.505595\pi$
$678$	19.6326	0.753987
$679$	0	0
$680$	12.5982	0.483117
$681$	−1.16503	−0.0446439
$682$	−10.6625	−0.408288
$683$	33.2933	1.27393	0.636966	−	0.770892i	$-0.280189\pi$
$683$	33.2933	1.27393	0.636966	+	0.770892i	$0.280189\pi$
$684$	0.0442851	0.00169328
$685$	−70.1867	−2.68169
$686$	0	0
$687$	−46.4586	−1.77250
$688$	4.61663	0.176007
$689$	−11.5733	−0.440906
$690$	−48.1987	−1.83489
$691$	−6.12075	−0.232844	−0.116422	−	0.993200i	$-0.537143\pi$
$691$	−6.12075	−0.232844	−0.116422	+	0.993200i	$0.537143\pi$
$692$	7.43496	0.282635
$693$	0	0
$694$	26.6753	1.01258
$695$	−36.9263	−1.40070
$696$	−1.73672	−0.0658300
$697$	−3.99863	−0.151459
$698$	26.4247	1.00019
$699$	−38.5651	−1.45867
$700$	0	0
$701$	3.82011	0.144284	0.0721418	−	0.997394i	$-0.477017\pi$
$701$	3.82011	0.144284	0.0721418	+	0.997394i	$0.477017\pi$
$702$	23.7420	0.896086
$703$	−19.6856	−0.742455
$704$	−1.18786	−0.0447690
$705$	67.2663	2.53340
$706$	−31.9645	−1.20300
$707$	0	0
$708$	13.5914	0.510797
$709$	−19.7443	−0.741513	−0.370756	−	0.928730i	$-0.620902\pi$
$709$	−19.7443	−0.741513	−0.370756	+	0.928730i	$0.620902\pi$
$710$	−17.7575	−0.666425
$711$	0.180493	0.00676901
$712$	13.1854	0.494143
$713$	−58.6094	−2.19494
$714$	0	0
$715$	−23.1321	−0.865093
$716$	1.46093	0.0545974
$717$	7.02217	0.262248
$718$	−5.52126	−0.206052
$719$	−41.3636	−1.54260	−0.771301	−	0.636471i	$-0.780394\pi$
$719$	−41.3636	−1.54260	−0.771301	+	0.636471i	$0.780394\pi$
$720$	0.0687801	0.00256328
$721$	0	0
$722$	11.5104	0.428372
$723$	−11.8101	−0.439224
$724$	−18.2038	−0.676539
$725$	13.0663	0.485271
$726$	16.6534	0.618064
$727$	4.20868	0.156091	0.0780457	−	0.996950i	$-0.475132\pi$
$727$	4.20868	0.156091	0.0780457	+	0.996950i	$0.475132\pi$
$728$	0	0
$729$	26.8528	0.994548
$730$	25.0631	0.927625
$731$	−13.6835	−0.506102
$732$	0.352408	0.0130254
$733$	11.4627	0.423384	0.211692	−	0.977336i	$-0.432103\pi$
$733$	11.4627	0.423384	0.211692	+	0.977336i	$0.432103\pi$
$734$	10.1531	0.374758
$735$	0	0
$736$	−6.52938	−0.240676
$737$	−9.92257	−0.365503
$738$	−0.0218306	−0.000803597 0
$739$	−35.4055	−1.30241	−0.651206	−	0.758901i	$-0.725737\pi$
$739$	−35.4055	−1.30241	−0.651206	+	0.758901i	$0.725737\pi$
$740$	−30.5740	−1.12392
$741$	21.7759	0.799957
$742$	0	0
$743$	22.8776	0.839298	0.419649	−	0.907686i	$-0.362153\pi$
$743$	22.8776	0.839298	0.419649	+	0.907686i	$0.362153\pi$
$744$	15.5892	0.571528
$745$	−17.7740	−0.651188
$746$	−21.7782	−0.797358
$747$	−0.00224895	−8.22847e−5 0
$748$	3.52076	0.128732
$749$	0	0
$750$	−59.5441	−2.17424
$751$	−16.8524	−0.614953	−0.307477	−	0.951556i	$-0.599485\pi$
$751$	−16.8524	−0.614953	−0.307477	+	0.951556i	$0.599485\pi$
$752$	9.11243	0.332296
$753$	−13.3468	−0.486384
$754$	−4.58160	−0.166852
$755$	−19.2396	−0.700201
$756$	0	0
$757$	21.5001	0.781433	0.390717	−	0.920511i	$-0.372227\pi$
$757$	21.5001	0.781433	0.390717	+	0.920511i	$0.372227\pi$
$758$	−5.64983	−0.205211
$759$	−13.4699	−0.488926
$760$	−11.6323	−0.421947
$761$	29.0141	1.05176	0.525881	−	0.850558i	$-0.323736\pi$
$761$	29.0141	1.05176	0.525881	+	0.850558i	$0.323736\pi$
$762$	−15.8916	−0.575691
$763$	0	0
$764$	−6.30452	−0.228090
$765$	−0.203861	−0.00737062
$766$	−1.90606	−0.0688686
$767$	35.8553	1.29466
$768$	1.73672	0.0626683
$769$	−51.4718	−1.85612	−0.928060	−	0.372430i	$-0.878525\pi$
$769$	−51.4718	−1.85612	−0.928060	+	0.372430i	$0.878525\pi$
$770$	0	0
$771$	24.7723	0.892152
$772$	−26.8140	−0.965056
$773$	11.9915	0.431306	0.215653	−	0.976470i	$-0.430812\pi$
$773$	11.9915	0.431306	0.215653	+	0.976470i	$0.430812\pi$
$774$	−0.0747055	−0.00268523
$775$	−117.287	−4.21306
$776$	−4.03023	−0.144677
$777$	0	0
$778$	−32.7603	−1.17451
$779$	3.69206	0.132282
$780$	33.8205	1.21097
$781$	−4.96261	−0.177576
$782$	19.3528	0.692055
$783$	−5.18204	−0.185191
$784$	0	0
$785$	12.6099	0.450067
$786$	−21.6513	−0.772275
$787$	28.4739	1.01498	0.507492	−	0.861656i	$-0.330573\pi$
$787$	28.4739	1.01498	0.507492	+	0.861656i	$0.330573\pi$
$788$	21.6486	0.771199
$789$	−9.68016	−0.344623
$790$	−47.4097	−1.68676
$791$	0	0
$792$	0.0192217	0.000683013 0
$793$	0.929680	0.0330139
$794$	26.4238	0.937747
$795$	−18.6467	−0.661330
$796$	24.8890	0.882165
$797$	31.2183	1.10581	0.552904	−	0.833245i	$-0.313519\pi$
$797$	31.2183	1.10581	0.552904	+	0.833245i	$0.313519\pi$
$798$	0	0
$799$	−27.0089	−0.955505
$800$	−13.0663	−0.461964
$801$	−0.213364	−0.00753884
$802$	−6.19480	−0.218746
$803$	7.00427	0.247175
$804$	14.5074	0.511636
$805$	0	0
$806$	41.1256	1.44859
$807$	−37.4380	−1.31788
$808$	−4.41168	−0.155202
$809$	43.1893	1.51845	0.759227	−	0.650826i	$-0.225577\pi$
$809$	43.1893	1.51845	0.759227	+	0.650826i	$0.225577\pi$
$810$	38.4593	1.35132
$811$	−25.5990	−0.898902	−0.449451	−	0.893305i	$-0.648380\pi$
$811$	−25.5990	−0.898902	−0.449451	+	0.893305i	$0.648380\pi$
$812$	0	0
$813$	27.0128	0.947381
$814$	−8.54440	−0.299481
$815$	−66.5064	−2.32962
$816$	−5.14755	−0.180200
$817$	12.6344	0.442022
$818$	−9.82710	−0.343597
$819$	0	0
$820$	5.73421	0.200247
$821$	−19.9458	−0.696113	−0.348057	−	0.937474i	$-0.613158\pi$
$821$	−19.9458	−0.696113	−0.348057	+	0.937474i	$0.613158\pi$
$822$	28.6780	1.00026
$823$	−2.07050	−0.0721730	−0.0360865	−	0.999349i	$-0.511489\pi$
$823$	−2.07050	−0.0721730	−0.0360865	+	0.999349i	$0.511489\pi$
$824$	17.0398	0.593610
$825$	−26.9554	−0.938466
$826$	0	0
$827$	−28.0306	−0.974719	−0.487360	−	0.873201i	$-0.662040\pi$
$827$	−28.0306	−0.974719	−0.487360	+	0.873201i	$0.662040\pi$
$828$	0.105657	0.00367184
$829$	−40.4341	−1.40434	−0.702168	−	0.712012i	$-0.747784\pi$
$829$	−40.4341	−1.40434	−0.702168	+	0.712012i	$0.747784\pi$
$830$	0.590726	0.0205044
$831$	−12.2278	−0.424179
$832$	4.58160	0.158838
$833$	0	0
$834$	15.0879	0.522453
$835$	−18.1328	−0.627512
$836$	−3.25082	−0.112432
$837$	46.5154	1.60781
$838$	19.5408	0.675024
$839$	−14.4061	−0.497355	−0.248678	−	0.968586i	$-0.579996\pi$
$839$	−14.4061	−0.497355	−0.248678	+	0.968586i	$0.579996\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	8.12744	0.280090
$843$	−4.68696	−0.161427
$844$	9.15699	0.315197
$845$	33.9655	1.16845
$846$	−0.147456	−0.00506964
$847$	0	0
$848$	−2.52603	−0.0867442
$849$	−31.7867	−1.09092
$850$	38.7280	1.32836
$851$	−46.9666	−1.61000
$852$	7.25562	0.248574
$853$	−30.6960	−1.05101	−0.525505	−	0.850790i	$-0.676124\pi$
$853$	−30.6960	−1.05101	−0.525505	+	0.850790i	$0.676124\pi$
$854$	0	0
$855$	0.188231	0.00643738
$856$	8.75604	0.299275
$857$	36.9966	1.26378	0.631890	−	0.775058i	$-0.282279\pi$
$857$	36.9966	1.26378	0.631890	+	0.775058i	$0.282279\pi$
$858$	9.45169	0.322675
$859$	2.98785	0.101944	0.0509720	−	0.998700i	$-0.483768\pi$
$859$	2.98785	0.101944	0.0509720	+	0.998700i	$0.483768\pi$
$860$	19.6227	0.669130
$861$	0	0
$862$	−27.5954	−0.939904
$863$	−3.53696	−0.120400	−0.0601998	−	0.998186i	$-0.519174\pi$
$863$	−3.53696	−0.120400	−0.0601998	+	0.998186i	$0.519174\pi$
$864$	5.18204	0.176297
$865$	31.6019	1.07450
$866$	−3.77381	−0.128239
$867$	−14.2670	−0.484534
$868$	0	0
$869$	−13.2494	−0.449455
$870$	−7.38182	−0.250267
$871$	38.2717	1.29679
$872$	−15.6703	−0.530663
$873$	0.0652165	0.00220724
$874$	−17.8690	−0.604430
$875$	0	0
$876$	−10.2407	−0.346000
$877$	−48.7008	−1.64451	−0.822255	−	0.569119i	$-0.807284\pi$
$877$	−48.7008	−1.64451	−0.822255	+	0.569119i	$0.807284\pi$
$878$	−22.3673	−0.754861
$879$	41.8020	1.40995
$880$	−5.04892	−0.170199
$881$	33.5568	1.13056	0.565278	−	0.824900i	$-0.308769\pi$
$881$	33.5568	1.13056	0.565278	+	0.824900i	$0.308769\pi$
$882$	0	0
$883$	−31.1670	−1.04885	−0.524426	−	0.851456i	$-0.675720\pi$
$883$	−31.1670	−1.04885	−0.524426	+	0.851456i	$0.675720\pi$
$884$	−13.5797	−0.456734
$885$	57.7697	1.94191
$886$	−1.29803	−0.0436081
$887$	30.3150	1.01788	0.508939	−	0.860803i	$-0.330038\pi$
$887$	30.3150	1.01788	0.508939	+	0.860803i	$0.330038\pi$
$888$	12.4924	0.419218
$889$	0	0
$890$	56.0438	1.87859
$891$	10.7481	0.360073
$892$	24.0783	0.806200
$893$	24.9381	0.834523
$894$	7.26237	0.242890
$895$	6.20960	0.207564
$896$	0	0
$897$	51.9538	1.73469
$898$	−3.75871	−0.125430
$899$	−8.97626	−0.299375
$900$	0.211437	0.00704790
$901$	7.48705	0.249430
$902$	1.60252	0.0533579
$903$	0	0
$904$	11.3045	0.375981
$905$	−77.3743	−2.57201
$906$	7.86123	0.261172
$907$	−35.7988	−1.18868	−0.594339	−	0.804215i	$-0.702586\pi$
$907$	−35.7988	−1.18868	−0.594339	+	0.804215i	$0.702586\pi$
$908$	−0.670821	−0.0222620
$909$	0.0713890	0.00236782
$910$	0	0
$911$	−9.61777	−0.318651	−0.159326	−	0.987226i	$-0.550932\pi$
$911$	−9.61777	−0.318651	−0.159326	+	0.987226i	$0.550932\pi$
$912$	4.75290	0.157384
$913$	0.165088	0.00546361
$914$	−7.66535	−0.253547
$915$	1.49789	0.0495187
$916$	−26.7508	−0.883872
$917$	0	0
$918$	−15.3594	−0.506935
$919$	−5.27347	−0.173956	−0.0869778	−	0.996210i	$-0.527721\pi$
$919$	−5.27347	−0.173956	−0.0869778	+	0.996210i	$0.527721\pi$
$920$	−27.7528	−0.914982
$921$	−3.85254	−0.126946
$922$	18.9389	0.623720
$923$	19.1409	0.630031
$924$	0	0
$925$	−93.9877	−3.09030
$926$	29.2444	0.961031
$927$	−0.275735	−0.00905634
$928$	−1.00000	−0.0328266
$929$	27.4400	0.900277	0.450138	−	0.892959i	$-0.351375\pi$
$929$	27.4400	0.900277	0.450138	+	0.892959i	$0.351375\pi$
$930$	66.2611	2.17279
$931$	0	0
$932$	−22.2058	−0.727374
$933$	9.34872	0.306063
$934$	38.7256	1.26714
$935$	14.9648	0.489401
$936$	−0.0741387	−0.00242330
$937$	−8.95067	−0.292406	−0.146203	−	0.989255i	$-0.546705\pi$
$937$	−8.95067	−0.292406	−0.146203	+	0.989255i	$0.546705\pi$
$938$	0	0
$939$	−42.5690	−1.38919
$940$	38.7319	1.26330
$941$	−26.4538	−0.862369	−0.431184	−	0.902264i	$-0.641904\pi$
$941$	−26.4538	−0.862369	−0.431184	+	0.902264i	$0.641904\pi$
$942$	−5.15235	−0.167873
$943$	8.80867	0.286850
$944$	7.82594	0.254713
$945$	0	0
$946$	5.48389	0.178297
$947$	−23.4838	−0.763122	−0.381561	−	0.924344i	$-0.624613\pi$
$947$	−23.4838	−0.763122	−0.381561	+	0.924344i	$0.624613\pi$
$948$	19.3714	0.629154
$949$	−27.0157	−0.876967
$950$	−35.7588	−1.16017
$951$	4.21746	0.136760
$952$	0	0
$953$	−35.6263	−1.15405	−0.577024	−	0.816727i	$-0.695786\pi$
$953$	−35.6263	−1.15405	−0.577024	+	0.816727i	$0.695786\pi$
$954$	0.0408758	0.00132340
$955$	−26.7970	−0.867132
$956$	4.04336	0.130772
$957$	−2.06297	−0.0666863
$958$	−3.67403	−0.118703
$959$	0	0
$960$	7.38182	0.238247
$961$	49.5732	1.59913
$962$	32.9560	1.06255
$963$	−0.141689	−0.00456586
$964$	−6.80027	−0.219022
$965$	−113.971	−3.66887
$966$	0	0
$967$	−25.6214	−0.823929	−0.411965	−	0.911200i	$-0.635157\pi$
$967$	−25.6214	−0.823929	−0.411965	+	0.911200i	$0.635157\pi$
$968$	9.58900	0.308202
$969$	−14.0874	−0.452552
$970$	−17.1303	−0.550020
$971$	−53.6422	−1.72146	−0.860730	−	0.509061i	$-0.829993\pi$
$971$	−53.6422	−1.72146	−0.860730	+	0.509061i	$0.829993\pi$
$972$	−0.168165	−0.00539389
$973$	0	0
$974$	25.7995	0.826668
$975$	103.968	3.32964
$976$	0.202916	0.00649519
$977$	3.96555	0.126869	0.0634345	−	0.997986i	$-0.479795\pi$
$977$	3.96555	0.126869	0.0634345	+	0.997986i	$0.479795\pi$
$978$	27.1742	0.868936
$979$	15.6623	0.500571
$980$	0	0
$981$	0.253574	0.00809599
$982$	7.22244	0.230477
$983$	13.7784	0.439462	0.219731	−	0.975561i	$-0.429482\pi$
$983$	13.7784	0.439462	0.219731	+	0.975561i	$0.429482\pi$
$984$	−2.34297	−0.0746912
$985$	92.0162	2.93188
$986$	2.96396	0.0943917
$987$	0	0
$988$	12.5385	0.398904
$989$	30.1437	0.958514
$990$	0.0817008	0.00259662
$991$	−8.23066	−0.261455	−0.130728	−	0.991418i	$-0.541731\pi$
$991$	−8.23066	−0.261455	−0.130728	+	0.991418i	$0.541731\pi$
$992$	8.97626	0.284996
$993$	−2.62493	−0.0832995
$994$	0	0
$995$	105.789	3.35374
$996$	−0.241368	−0.00764804
$997$	−33.2977	−1.05455	−0.527274	−	0.849695i	$-0.676786\pi$
$997$	−33.2977	−1.05455	−0.527274	+	0.849695i	$0.676786\pi$
$998$	15.0650	0.476873
$999$	37.2751	1.17933

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.v.1.4		5
7.2	even	3		406.2.e.c.291.2	yes	10
7.4	even	3		406.2.e.c.233.2	✓	10
7.6	odd	2		2842.2.a.s.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.c.233.2	✓	10	7.4	even	3
406.2.e.c.291.2	yes	10	7.2	even	3
2842.2.a.s.1.2		5	7.6	odd	2
2842.2.a.v.1.4		5	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:	\( N \)	\(=\)	\( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2842.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.73672 q^{3} +1.00000 q^{4} +4.25045 q^{5} -1.73672 q^{6} -1.00000 q^{8} +0.0161818 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.73672 q^{3} +1.00000 q^{4} +4.25045 q^{5} -1.73672 q^{6} -1.00000 q^{8} +0.0161818 q^{9} -4.25045 q^{10} -1.18786 q^{11} +1.73672 q^{12} +4.58160 q^{13} +7.38182 q^{15} +1.00000 q^{16} -2.96396 q^{17} -0.0161818 q^{18} +2.73672 q^{19} +4.25045 q^{20} +1.18786 q^{22} +6.52938 q^{23} -1.73672 q^{24} +13.0663 q^{25} -4.58160 q^{26} -5.18204 q^{27} +1.00000 q^{29} -7.38182 q^{30} -8.97626 q^{31} -1.00000 q^{32} -2.06297 q^{33} +2.96396 q^{34} +0.0161818 q^{36} -7.19313 q^{37} -2.73672 q^{38} +7.95694 q^{39} -4.25045 q^{40} +1.34908 q^{41} +4.61663 q^{43} -1.18786 q^{44} +0.0687801 q^{45} -6.52938 q^{46} +9.11243 q^{47} +1.73672 q^{48} -13.0663 q^{50} -5.14755 q^{51} +4.58160 q^{52} -2.52603 q^{53} +5.18204 q^{54} -5.04892 q^{55} +4.75290 q^{57} -1.00000 q^{58} +7.82594 q^{59} +7.38182 q^{60} +0.202916 q^{61} +8.97626 q^{62} +1.00000 q^{64} +19.4739 q^{65} +2.06297 q^{66} +8.35334 q^{67} -2.96396 q^{68} +11.3397 q^{69} +4.17778 q^{71} -0.0161818 q^{72} -5.89657 q^{73} +7.19313 q^{74} +22.6925 q^{75} +2.73672 q^{76} -7.95694 q^{78} +11.1540 q^{79} +4.25045 q^{80} -9.04828 q^{81} -1.34908 q^{82} -0.138980 q^{83} -12.5982 q^{85} -4.61663 q^{86} +1.73672 q^{87} +1.18786 q^{88} -13.1854 q^{89} -0.0687801 q^{90} +6.52938 q^{92} -15.5892 q^{93} -9.11243 q^{94} +11.6323 q^{95} -1.73672 q^{96} +4.03023 q^{97} -0.0192217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + 3 q^{3} + 5 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} + 4 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + 3 * q^3 + 5 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 + 4 * q^9	\( 5 q - 5 q^{2} + 3 q^{3} + 5 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} + 4 q^{9} - 5 q^{10} + 4 q^{11} + 3 q^{12} + 2 q^{13} + 6 q^{15} + 5 q^{16} + 2 q^{17} - 4 q^{18} + 8 q^{19} + 5 q^{20} - 4 q^{22} - 9 q^{23} - 3 q^{24} + 8 q^{25} - 2 q^{26} + 15 q^{27} + 5 q^{29} - 6 q^{30} - 15 q^{31} - 5 q^{32} + 29 q^{33} - 2 q^{34} + 4 q^{36} - 22 q^{37} - 8 q^{38} + 32 q^{39} - 5 q^{40} + q^{41} + 7 q^{43} + 4 q^{44} - 8 q^{45} + 9 q^{46} + 20 q^{47} + 3 q^{48} - 8 q^{50} - 15 q^{51} + 2 q^{52} + 11 q^{53} - 15 q^{54} - 4 q^{55} + 22 q^{57} - 5 q^{58} + 13 q^{59} + 6 q^{60} - 15 q^{61} + 15 q^{62} + 5 q^{64} - 7 q^{65} - 29 q^{66} + 20 q^{67} + 2 q^{68} + 20 q^{69} - 4 q^{71} - 4 q^{72} + 22 q^{74} + 20 q^{75} + 8 q^{76} - 32 q^{78} + q^{79} + 5 q^{80} + 21 q^{81} - q^{82} + 48 q^{83} - 13 q^{85} - 7 q^{86} + 3 q^{87} - 4 q^{88} - 7 q^{89} + 8 q^{90} - 9 q^{92} - 23 q^{93} - 20 q^{94} + 11 q^{95} - 3 q^{96} + 6 q^{97} + 32 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 3 * q^3 + 5 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 + 4 * q^9 - 5 * q^10 + 4 * q^11 + 3 * q^12 + 2 * q^13 + 6 * q^15 + 5 * q^16 + 2 * q^17 - 4 * q^18 + 8 * q^19 + 5 * q^20 - 4 * q^22 - 9 * q^23 - 3 * q^24 + 8 * q^25 - 2 * q^26 + 15 * q^27 + 5 * q^29 - 6 * q^30 - 15 * q^31 - 5 * q^32 + 29 * q^33 - 2 * q^34 + 4 * q^36 - 22 * q^37 - 8 * q^38 + 32 * q^39 - 5 * q^40 + q^41 + 7 * q^43 + 4 * q^44 - 8 * q^45 + 9 * q^46 + 20 * q^47 + 3 * q^48 - 8 * q^50 - 15 * q^51 + 2 * q^52 + 11 * q^53 - 15 * q^54 - 4 * q^55 + 22 * q^57 - 5 * q^58 + 13 * q^59 + 6 * q^60 - 15 * q^61 + 15 * q^62 + 5 * q^64 - 7 * q^65 - 29 * q^66 + 20 * q^67 + 2 * q^68 + 20 * q^69 - 4 * q^71 - 4 * q^72 + 22 * q^74 + 20 * q^75 + 8 * q^76 - 32 * q^78 + q^79 + 5 * q^80 + 21 * q^81 - q^82 + 48 * q^83 - 13 * q^85 - 7 * q^86 + 3 * q^87 - 4 * q^88 - 7 * q^89 + 8 * q^90 - 9 * q^92 - 23 * q^93 - 20 * q^94 + 11 * q^95 - 3 * q^96 + 6 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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