LMFDB - Embedded newform 2695.2.a.x.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,2,Mod(1,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, 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("2695.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2695.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:	$21.5196833447$
Analytic rank:	$0$
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} - 2x^{9} - 13x^{8} + 24x^{7} + 56x^{6} - 92x^{5} - 86x^{4} + 116x^{3} + 31x^{2} - 22x + 1 $ x^10 - 2x^9 - 13x^8 + 24x^7 + 56x^6 - 92x^5 - 86x^4 + 116x^3 + 31x^2 - 22*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.0495267$ of defining polynomial
Character	$\chi$	$=$	2695.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0495267 q^{2} -3.19919 q^{3} -1.99755 q^{4} +1.00000 q^{5} -0.158445 q^{6} -0.197985 q^{8} +7.23480 q^{9} +O(q^{10})$	\(q+0.0495267 q^{2} -3.19919 q^{3} -1.99755 q^{4} +1.00000 q^{5} -0.158445 q^{6} -0.197985 q^{8} +7.23480 q^{9} +0.0495267 q^{10} -1.00000 q^{11} +6.39053 q^{12} +2.44030 q^{13} -3.19919 q^{15} +3.98529 q^{16} +7.80007 q^{17} +0.358316 q^{18} +4.44522 q^{19} -1.99755 q^{20} -0.0495267 q^{22} -7.27096 q^{23} +0.633392 q^{24} +1.00000 q^{25} +0.120860 q^{26} -13.5479 q^{27} -9.41155 q^{29} -0.158445 q^{30} -10.0562 q^{31} +0.593349 q^{32} +3.19919 q^{33} +0.386312 q^{34} -14.4518 q^{36} +4.42058 q^{37} +0.220157 q^{38} -7.80699 q^{39} -0.197985 q^{40} +10.4487 q^{41} -2.08789 q^{43} +1.99755 q^{44} +7.23480 q^{45} -0.360107 q^{46} +3.52628 q^{47} -12.7497 q^{48} +0.0495267 q^{50} -24.9539 q^{51} -4.87462 q^{52} +5.94458 q^{53} -0.670984 q^{54} -1.00000 q^{55} -14.2211 q^{57} -0.466123 q^{58} +0.538933 q^{59} +6.39053 q^{60} -2.32165 q^{61} -0.498052 q^{62} -7.94119 q^{64} +2.44030 q^{65} +0.158445 q^{66} +2.58460 q^{67} -15.5810 q^{68} +23.2612 q^{69} -5.38126 q^{71} -1.43238 q^{72} -10.7017 q^{73} +0.218937 q^{74} -3.19919 q^{75} -8.87954 q^{76} -0.386655 q^{78} +1.04570 q^{79} +3.98529 q^{80} +21.6379 q^{81} +0.517490 q^{82} +9.19961 q^{83} +7.80007 q^{85} -0.103406 q^{86} +30.1093 q^{87} +0.197985 q^{88} +9.20326 q^{89} +0.358316 q^{90} +14.5241 q^{92} +32.1718 q^{93} +0.174645 q^{94} +4.44522 q^{95} -1.89823 q^{96} +2.59906 q^{97} -7.23480 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 10 q^{4} + 10 q^{5} + 4 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 10 * q^4 + 10 * q^5 + 4 * q^6 + 6 * q^8 + 10 * q^9	$ 10 q + 2 q^{2} + 10 q^{4} + 10 q^{5} + 4 q^{6} + 6 q^{8} + 10 q^{9} + 2 q^{10} - 10 q^{11} + 4 q^{12} + 8 q^{13} + 6 q^{16} + 28 q^{17} - 10 q^{18} + 8 q^{19} + 10 q^{20} - 2 q^{22} - 8 q^{23} + 32 q^{24} + 10 q^{25} + 12 q^{26} - 8 q^{29} + 4 q^{30} - 4 q^{31} + 14 q^{32} + 20 q^{34} - 22 q^{36} + 28 q^{37} + 24 q^{38} - 24 q^{39} + 6 q^{40} + 44 q^{41} + 20 q^{43} - 10 q^{44} + 10 q^{45} - 12 q^{46} + 12 q^{47} + 16 q^{48} + 2 q^{50} - 4 q^{51} + 36 q^{52} - 8 q^{54} - 10 q^{55} + 12 q^{57} - 8 q^{58} + 16 q^{59} + 4 q^{60} + 16 q^{61} + 36 q^{62} - 34 q^{64} + 8 q^{65} - 4 q^{66} + 20 q^{67} + 8 q^{68} + 4 q^{69} - 4 q^{71} + 10 q^{72} + 20 q^{73} - 16 q^{74} + 4 q^{76} + 52 q^{78} - 20 q^{79} + 6 q^{80} + 10 q^{81} - 32 q^{82} + 16 q^{83} + 28 q^{85} - 20 q^{86} + 20 q^{87} - 6 q^{88} + 44 q^{89} - 10 q^{90} - 24 q^{92} + 16 q^{93} + 24 q^{94} + 8 q^{95} - 4 q^{97} - 10 q^{99}+O(q^{100}) $ 10 * q + 2 * q^2 + 10 * q^4 + 10 * q^5 + 4 * q^6 + 6 * q^8 + 10 * q^9 + 2 * q^10 - 10 * q^11 + 4 * q^12 + 8 * q^13 + 6 * q^16 + 28 * q^17 - 10 * q^18 + 8 * q^19 + 10 * q^20 - 2 * q^22 - 8 * q^23 + 32 * q^24 + 10 * q^25 + 12 * q^26 - 8 * q^29 + 4 * q^30 - 4 * q^31 + 14 * q^32 + 20 * q^34 - 22 * q^36 + 28 * q^37 + 24 * q^38 - 24 * q^39 + 6 * q^40 + 44 * q^41 + 20 * q^43 - 10 * q^44 + 10 * q^45 - 12 * q^46 + 12 * q^47 + 16 * q^48 + 2 * q^50 - 4 * q^51 + 36 * q^52 - 8 * q^54 - 10 * q^55 + 12 * q^57 - 8 * q^58 + 16 * q^59 + 4 * q^60 + 16 * q^61 + 36 * q^62 - 34 * q^64 + 8 * q^65 - 4 * q^66 + 20 * q^67 + 8 * q^68 + 4 * q^69 - 4 * q^71 + 10 * q^72 + 20 * q^73 - 16 * q^74 + 4 * q^76 + 52 * q^78 - 20 * q^79 + 6 * q^80 + 10 * q^81 - 32 * q^82 + 16 * q^83 + 28 * q^85 - 20 * q^86 + 20 * q^87 - 6 * q^88 + 44 * q^89 - 10 * q^90 - 24 * q^92 + 16 * q^93 + 24 * q^94 + 8 * q^95 - 4 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.0495267	0.0350207	0.0175103	−	0.999847i	$-0.494426\pi$
$2$	0.0495267	0.0350207	0.0175103	+	0.999847i	$0.494426\pi$
$3$	−3.19919	−1.84705	−0.923526	−	0.383536i	$-0.874706\pi$
$3$	−3.19919	−1.84705	−0.923526	+	0.383536i	$0.874706\pi$
$4$	−1.99755	−0.998774
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.158445	−0.0646850
$7$	0	0
$7$	0	0
$8$	−0.197985	−0.0699984
$9$	7.23480	2.41160
$10$	0.0495267	0.0156617
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	6.39053	1.84479
$13$	2.44030	0.676818	0.338409	−	0.940999i	$-0.390111\pi$
$13$	2.44030	0.676818	0.338409	+	0.940999i	$0.390111\pi$
$14$	0	0
$15$	−3.19919	−0.826027
$16$	3.98529	0.996322
$17$	7.80007	1.89179	0.945897	−	0.324466i	$-0.105185\pi$
$17$	7.80007	1.89179	0.945897	+	0.324466i	$0.105185\pi$
$18$	0.358316	0.0844559
$19$	4.44522	1.01980	0.509902	−	0.860232i	$-0.329682\pi$
$19$	4.44522	1.01980	0.509902	+	0.860232i	$0.329682\pi$
$20$	−1.99755	−0.446665
$21$	0	0
$22$	−0.0495267	−0.0105591
$23$	−7.27096	−1.51610	−0.758050	−	0.652197i	$-0.773848\pi$
$23$	−7.27096	−1.51610	−0.758050	+	0.652197i	$0.773848\pi$
$24$	0.633392	0.129291
$25$	1.00000	0.200000
$26$	0.120860	0.0237026
$27$	−13.5479	−2.60730
$28$	0	0
$29$	−9.41155	−1.74768	−0.873840	−	0.486213i	$-0.838378\pi$
$29$	−9.41155	−1.74768	−0.873840	+	0.486213i	$0.838378\pi$
$30$	−0.158445	−0.0289280
$31$	−10.0562	−1.80615	−0.903076	−	0.429480i	$-0.858697\pi$
$31$	−10.0562	−1.80615	−0.903076	+	0.429480i	$0.858697\pi$
$32$	0.593349	0.104890
$33$	3.19919	0.556907
$34$	0.386312	0.0662519
$35$	0	0
$36$	−14.4518	−2.40864
$37$	4.42058	0.726740	0.363370	−	0.931645i	$-0.381626\pi$
$37$	4.42058	0.726740	0.363370	+	0.931645i	$0.381626\pi$
$38$	0.220157	0.0357142
$39$	−7.80699	−1.25012
$40$	−0.197985	−0.0313042
$41$	10.4487	1.63181	0.815906	−	0.578184i	$-0.196239\pi$
$41$	10.4487	1.63181	0.815906	+	0.578184i	$0.196239\pi$
$42$	0	0
$43$	−2.08789	−0.318400	−0.159200	−	0.987246i	$-0.550891\pi$
$43$	−2.08789	−0.318400	−0.159200	+	0.987246i	$0.550891\pi$
$44$	1.99755	0.301142
$45$	7.23480	1.07850
$46$	−0.360107	−0.0530948
$47$	3.52628	0.514361	0.257181	−	0.966363i	$-0.417206\pi$
$47$	3.52628	0.514361	0.257181	+	0.966363i	$0.417206\pi$
$48$	−12.7497	−1.84026
$49$	0	0
$50$	0.0495267	0.00700414
$51$	−24.9539	−3.49424
$52$	−4.87462	−0.675988
$53$	5.94458	0.816551	0.408276	−	0.912859i	$-0.366130\pi$
$53$	5.94458	0.816551	0.408276	+	0.912859i	$0.366130\pi$
$54$	−0.670984	−0.0913093
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−14.2211	−1.88363
$58$	−0.466123	−0.0612050
$59$	0.538933	0.0701631	0.0350816	−	0.999384i	$-0.488831\pi$
$59$	0.538933	0.0701631	0.0350816	+	0.999384i	$0.488831\pi$
$60$	6.39053	0.825013
$61$	−2.32165	−0.297256	−0.148628	−	0.988893i	$-0.547486\pi$
$61$	−2.32165	−0.297256	−0.148628	+	0.988893i	$0.547486\pi$
$62$	−0.498052	−0.0632527
$63$	0	0
$64$	−7.94119	−0.992649
$65$	2.44030	0.302682
$66$	0.158445	0.0195033
$67$	2.58460	0.315759	0.157879	−	0.987458i	$-0.449534\pi$
$67$	2.58460	0.315759	0.157879	+	0.987458i	$0.449534\pi$
$68$	−15.5810	−1.88947
$69$	23.2612	2.80031
$70$	0	0
$71$	−5.38126	−0.638638	−0.319319	−	0.947647i	$-0.603454\pi$
$71$	−5.38126	−0.638638	−0.319319	+	0.947647i	$0.603454\pi$
$72$	−1.43238	−0.168808
$73$	−10.7017	−1.25253	−0.626267	−	0.779608i	$-0.715418\pi$
$73$	−10.7017	−1.25253	−0.626267	+	0.779608i	$0.715418\pi$
$74$	0.218937	0.0254509
$75$	−3.19919	−0.369410
$76$	−8.87954	−1.01855
$77$	0	0
$78$	−0.386655	−0.0437800
$79$	1.04570	0.117650	0.0588250	−	0.998268i	$-0.481265\pi$
$79$	1.04570	0.117650	0.0588250	+	0.998268i	$0.481265\pi$
$80$	3.98529	0.445569
$81$	21.6379	2.40421
$82$	0.517490	0.0571472
$83$	9.19961	1.00979	0.504894	−	0.863181i	$-0.331532\pi$
$83$	9.19961	1.00979	0.504894	+	0.863181i	$0.331532\pi$
$84$	0	0
$85$	7.80007	0.846036
$86$	−0.103406	−0.0111506
$87$	30.1093	3.22806
$88$	0.197985	0.0211053
$89$	9.20326	0.975543	0.487772	−	0.872971i	$-0.337810\pi$
$89$	9.20326	0.975543	0.487772	+	0.872971i	$0.337810\pi$
$90$	0.358316	0.0377698
$91$	0	0
$92$	14.5241	1.51424
$93$	32.1718	3.33606
$94$	0.174645	0.0180133
$95$	4.44522	0.456070
$96$	−1.89823	−0.193738
$97$	2.59906	0.263895	0.131947	−	0.991257i	$-0.457877\pi$
$97$	2.59906	0.263895	0.131947	+	0.991257i	$0.457877\pi$
$98$	0	0
$99$	−7.23480	−0.727125
$100$	−1.99755	−0.199755
$101$	−13.6769	−1.36090	−0.680452	−	0.732792i	$-0.738217\pi$
$101$	−13.6769	−1.36090	−0.680452	+	0.732792i	$0.738217\pi$
$102$	−1.23588	−0.122371
$103$	5.19977	0.512349	0.256174	−	0.966631i	$-0.417538\pi$
$103$	5.19977	0.512349	0.256174	+	0.966631i	$0.417538\pi$
$104$	−0.483145	−0.0473762
$105$	0	0
$106$	0.294416	0.0285962
$107$	2.49914	0.241601	0.120801	−	0.992677i	$-0.461454\pi$
$107$	2.49914	0.241601	0.120801	+	0.992677i	$0.461454\pi$
$108$	27.0626	2.60410
$109$	−7.78295	−0.745471	−0.372736	−	0.927938i	$-0.621580\pi$
$109$	−7.78295	−0.745471	−0.372736	+	0.927938i	$0.621580\pi$
$110$	−0.0495267	−0.00472219
$111$	−14.1423	−1.34233
$112$	0	0
$113$	9.79488	0.921425	0.460713	−	0.887549i	$-0.347594\pi$
$113$	9.79488	0.921425	0.460713	+	0.887549i	$0.347594\pi$
$114$	−0.704324	−0.0659660
$115$	−7.27096	−0.678020
$116$	18.8000	1.74554
$117$	17.6551	1.63221
$118$	0.0266916	0.00245716
$119$	0	0
$120$	0.633392	0.0578205
$121$	1.00000	0.0909091
$122$	−0.114984	−0.0104101
$123$	−33.4273	−3.01404
$124$	20.0878	1.80394
$125$	1.00000	0.0894427
$126$	0	0
$127$	12.3744	1.09805	0.549025	−	0.835806i	$-0.314999\pi$
$127$	12.3744	1.09805	0.549025	+	0.835806i	$0.314999\pi$
$128$	−1.58000	−0.139654
$129$	6.67954	0.588100
$130$	0.120860	0.0106001
$131$	−4.27687	−0.373672	−0.186836	−	0.982391i	$-0.559823\pi$
$131$	−4.27687	−0.373672	−0.186836	+	0.982391i	$0.559823\pi$
$132$	−6.39053	−0.556224
$133$	0	0
$134$	0.128007	0.0110581
$135$	−13.5479	−1.16602
$136$	−1.54430	−0.132423
$137$	−16.6508	−1.42257	−0.711286	−	0.702902i	$-0.751887\pi$
$137$	−16.6508	−1.42257	−0.711286	+	0.702902i	$0.751887\pi$
$138$	1.15205	0.0980689
$139$	15.9120	1.34964	0.674818	−	0.737984i	$-0.264222\pi$
$139$	15.9120	1.34964	0.674818	+	0.737984i	$0.264222\pi$
$140$	0	0
$141$	−11.2812	−0.950052
$142$	−0.266516	−0.0223655
$143$	−2.44030	−0.204068
$144$	28.8328	2.40273
$145$	−9.41155	−0.781587
$146$	−0.530018	−0.0438646
$147$	0	0
$148$	−8.83033	−0.725848
$149$	−7.42265	−0.608087	−0.304043	−	0.952658i	$-0.598337\pi$
$149$	−7.42265	−0.608087	−0.304043	+	0.952658i	$0.598337\pi$
$150$	−0.158445	−0.0129370
$151$	−3.53642	−0.287790	−0.143895	−	0.989593i	$-0.545963\pi$
$151$	−3.53642	−0.287790	−0.143895	+	0.989593i	$0.545963\pi$
$152$	−0.880089	−0.0713847
$153$	56.4319	4.56225
$154$	0	0
$155$	−10.0562	−0.807736
$156$	15.5948	1.24859
$157$	15.6569	1.24955	0.624777	−	0.780803i	$-0.285190\pi$
$157$	15.6569	1.24955	0.624777	+	0.780803i	$0.285190\pi$
$158$	0.0517899	0.00412018
$159$	−19.0178	−1.50821
$160$	0.593349	0.0469084
$161$	0	0
$162$	1.07165	0.0841971
$163$	0.0258867	0.00202760	0.00101380	−	0.999999i	$-0.499677\pi$
$163$	0.0258867	0.00202760	0.00101380	+	0.999999i	$0.499677\pi$
$164$	−20.8718	−1.62981
$165$	3.19919	0.249056
$166$	0.455626	0.0353635
$167$	16.9248	1.30968	0.654840	−	0.755767i	$-0.272736\pi$
$167$	16.9248	1.30968	0.654840	+	0.755767i	$0.272736\pi$
$168$	0	0
$169$	−7.04492	−0.541917
$170$	0.386312	0.0296288
$171$	32.1603	2.45936
$172$	4.17065	0.318009
$173$	0.0680982	0.00517741	0.00258871	−	0.999997i	$-0.499176\pi$
$173$	0.0680982	0.00517741	0.00258871	+	0.999997i	$0.499176\pi$
$174$	1.49122	0.113049
$175$	0	0
$176$	−3.98529	−0.300402
$177$	−1.72415	−0.129595
$178$	0.455807	0.0341642
$179$	4.92690	0.368254	0.184127	−	0.982902i	$-0.441054\pi$
$179$	4.92690	0.368254	0.184127	+	0.982902i	$0.441054\pi$
$180$	−14.4518	−1.07718
$181$	−3.02702	−0.224996	−0.112498	−	0.993652i	$-0.535885\pi$
$181$	−3.02702	−0.224996	−0.112498	+	0.993652i	$0.535885\pi$
$182$	0	0
$183$	7.42738	0.549048
$184$	1.43954	0.106125
$185$	4.42058	0.325008
$186$	1.59336	0.116831
$187$	−7.80007	−0.570398
$188$	−7.04392	−0.513730
$189$	0	0
$190$	0.220157	0.0159719
$191$	11.1407	0.806109	0.403055	−	0.915176i	$-0.367948\pi$
$191$	11.1407	0.806109	0.403055	+	0.915176i	$0.367948\pi$
$192$	25.4054	1.83347
$193$	20.0845	1.44571	0.722857	−	0.690997i	$-0.242828\pi$
$193$	20.0845	1.44571	0.722857	+	0.690997i	$0.242828\pi$
$194$	0.128723	0.00924177
$195$	−7.80699	−0.559070
$196$	0	0
$197$	0.763722	0.0544130	0.0272065	−	0.999630i	$-0.491339\pi$
$197$	0.763722	0.0544130	0.0272065	+	0.999630i	$0.491339\pi$
$198$	−0.358316	−0.0254644
$199$	18.6966	1.32537	0.662684	−	0.748899i	$-0.269417\pi$
$199$	18.6966	1.32537	0.662684	+	0.748899i	$0.269417\pi$
$200$	−0.197985	−0.0139997
$201$	−8.26860	−0.583222
$202$	−0.677373	−0.0476598
$203$	0	0
$204$	49.8466	3.48996
$205$	10.4487	0.729769
$206$	0.257528	0.0179428
$207$	−52.6039	−3.65623
$208$	9.72531	0.674329
$209$	−4.44522	−0.307483
$210$	0	0
$211$	−4.85207	−0.334030	−0.167015	−	0.985954i	$-0.553413\pi$
$211$	−4.85207	−0.334030	−0.167015	+	0.985954i	$0.553413\pi$
$212$	−11.8746	−0.815550
$213$	17.2157	1.17960
$214$	0.123774	0.00846104
$215$	−2.08789	−0.142393
$216$	2.68229	0.182507
$217$	0	0
$218$	−0.385464	−0.0261069
$219$	34.2366	2.31350
$220$	1.99755	0.134675
$221$	19.0345	1.28040
$222$	−0.700421	−0.0470092
$223$	6.52326	0.436830	0.218415	−	0.975856i	$-0.429911\pi$
$223$	6.52326	0.436830	0.218415	+	0.975856i	$0.429911\pi$
$224$	0	0
$225$	7.23480	0.482320
$226$	0.485108	0.0322689
$227$	−22.4225	−1.48824	−0.744118	−	0.668048i	$-0.767130\pi$
$227$	−22.4225	−1.48824	−0.744118	+	0.668048i	$0.767130\pi$
$228$	28.4073	1.88132
$229$	−4.39287	−0.290289	−0.145144	−	0.989410i	$-0.546365\pi$
$229$	−4.39287	−0.290289	−0.145144	+	0.989410i	$0.546365\pi$
$230$	−0.360107	−0.0237447
$231$	0	0
$232$	1.86335	0.122335
$233$	11.3182	0.741480	0.370740	−	0.928737i	$-0.379104\pi$
$233$	11.3182	0.741480	0.370740	+	0.928737i	$0.379104\pi$
$234$	0.874399	0.0571613
$235$	3.52628	0.230029
$236$	−1.07654	−0.0700771
$237$	−3.34538	−0.217306
$238$	0	0
$239$	20.6644	1.33667	0.668335	−	0.743861i	$-0.267007\pi$
$239$	20.6644	1.33667	0.668335	+	0.743861i	$0.267007\pi$
$240$	−12.7497	−0.822989
$241$	3.07122	0.197835	0.0989175	−	0.995096i	$-0.468462\pi$
$241$	3.07122	0.197835	0.0989175	+	0.995096i	$0.468462\pi$
$242$	0.0495267	0.00318370
$243$	−28.5800	−1.83341
$244$	4.63760	0.296892
$245$	0	0
$246$	−1.65555	−0.105554
$247$	10.8477	0.690222
$248$	1.99099	0.126428
$249$	−29.4313	−1.86513
$250$	0.0495267	0.00313235
$251$	25.3304	1.59884	0.799422	−	0.600770i	$-0.205139\pi$
$251$	25.3304	1.59884	0.799422	+	0.600770i	$0.205139\pi$
$252$	0	0
$253$	7.27096	0.457121
$254$	0.612863	0.0384544
$255$	−24.9539	−1.56267
$256$	15.8041	0.987758
$257$	7.71621	0.481324	0.240662	−	0.970609i	$-0.422635\pi$
$257$	7.71621	0.481324	0.240662	+	0.970609i	$0.422635\pi$
$258$	0.330816	0.0205957
$259$	0	0
$260$	−4.87462	−0.302311
$261$	−68.0907	−4.21471
$262$	−0.211819	−0.0130862
$263$	15.9768	0.985173	0.492586	−	0.870264i	$-0.336052\pi$
$263$	15.9768	0.985173	0.492586	+	0.870264i	$0.336052\pi$
$264$	−0.633392	−0.0389826
$265$	5.94458	0.365173
$266$	0	0
$267$	−29.4429	−1.80188
$268$	−5.16285	−0.315371
$269$	−15.5548	−0.948391	−0.474196	−	0.880419i	$-0.657261\pi$
$269$	−15.5548	−0.948391	−0.474196	+	0.880419i	$0.657261\pi$
$270$	−0.670984	−0.0408348
$271$	−25.7971	−1.56706	−0.783530	−	0.621354i	$-0.786583\pi$
$271$	−25.7971	−1.56706	−0.783530	+	0.621354i	$0.786583\pi$
$272$	31.0855	1.88484
$273$	0	0
$274$	−0.824659	−0.0498195
$275$	−1.00000	−0.0603023
$276$	−46.4653	−2.79688
$277$	−9.37530	−0.563307	−0.281654	−	0.959516i	$-0.590883\pi$
$277$	−9.37530	−0.563307	−0.281654	+	0.959516i	$0.590883\pi$
$278$	0.788068	0.0472652
$279$	−72.7548	−4.35572
$280$	0	0
$281$	−23.2312	−1.38586	−0.692929	−	0.721005i	$-0.743680\pi$
$281$	−23.2312	−1.38586	−0.692929	+	0.721005i	$0.743680\pi$
$282$	−0.558723	−0.0332715
$283$	16.4814	0.979719	0.489860	−	0.871801i	$-0.337048\pi$
$283$	16.4814	0.979719	0.489860	+	0.871801i	$0.337048\pi$
$284$	10.7493	0.637855
$285$	−14.2211	−0.842385
$286$	−0.120860	−0.00714662
$287$	0	0
$288$	4.29276	0.252953
$289$	43.8411	2.57889
$290$	−0.466123	−0.0273717
$291$	−8.31488	−0.487427
$292$	21.3771	1.25100
$293$	−11.0923	−0.648018	−0.324009	−	0.946054i	$-0.605031\pi$
$293$	−11.0923	−0.648018	−0.324009	+	0.946054i	$0.605031\pi$
$294$	0	0
$295$	0.538933	0.0313779
$296$	−0.875211	−0.0508706
$297$	13.5479	0.786130
$298$	−0.367619	−0.0212956
$299$	−17.7433	−1.02612
$300$	6.39053	0.368957
$301$	0	0
$302$	−0.175147	−0.0100786
$303$	43.7550	2.51366
$304$	17.7155	1.01605
$305$	−2.32165	−0.132937
$306$	2.79489	0.159773
$307$	6.85267	0.391103	0.195551	−	0.980693i	$-0.437350\pi$
$307$	6.85267	0.391103	0.195551	+	0.980693i	$0.437350\pi$
$308$	0	0
$309$	−16.6350	−0.946335
$310$	−0.498052	−0.0282875
$311$	−5.92240	−0.335829	−0.167914	−	0.985802i	$-0.553703\pi$
$311$	−5.92240	−0.335829	−0.167914	+	0.985802i	$0.553703\pi$
$312$	1.54567	0.0875063
$313$	8.05178	0.455113	0.227557	−	0.973765i	$-0.426926\pi$
$313$	8.05178	0.455113	0.227557	+	0.973765i	$0.426926\pi$
$314$	0.775434	0.0437602
$315$	0	0
$316$	−2.08883	−0.117506
$317$	0.993219	0.0557847	0.0278924	−	0.999611i	$-0.491120\pi$
$317$	0.993219	0.0557847	0.0278924	+	0.999611i	$0.491120\pi$
$318$	−0.941891	−0.0528186
$319$	9.41155	0.526946
$320$	−7.94119	−0.443926
$321$	−7.99523	−0.446250
$322$	0	0
$323$	34.6730	1.92926
$324$	−43.2227	−2.40126
$325$	2.44030	0.135364
$326$	0.00128208	7.10080e−5 0
$327$	24.8991	1.37692
$328$	−2.06869	−0.114224
$329$	0	0
$330$	0.158445	0.00872212
$331$	11.4616	0.629989	0.314994	−	0.949094i	$-0.397997\pi$
$331$	11.4616	0.629989	0.314994	+	0.949094i	$0.397997\pi$
$332$	−18.3766	−1.00855
$333$	31.9820	1.75260
$334$	0.838230	0.0458659
$335$	2.58460	0.141212
$336$	0	0
$337$	17.2624	0.940341	0.470170	−	0.882576i	$-0.344192\pi$
$337$	17.2624	0.940341	0.470170	+	0.882576i	$0.344192\pi$
$338$	−0.348912	−0.0189783
$339$	−31.3357	−1.70192
$340$	−15.5810	−0.844999
$341$	10.0562	0.544575
$342$	1.59279	0.0861284
$343$	0	0
$344$	0.413371	0.0222875
$345$	23.2612	1.25234
$346$	0.00337268	0.000181317 0
$347$	20.2498	1.08707	0.543533	−	0.839387i	$-0.317086\pi$
$347$	20.2498	1.08707	0.543533	+	0.839387i	$0.317086\pi$
$348$	−60.1448	−3.22410
$349$	−28.2228	−1.51073	−0.755365	−	0.655305i	$-0.772540\pi$
$349$	−28.2228	−1.51073	−0.755365	+	0.655305i	$0.772540\pi$
$350$	0	0
$351$	−33.0610	−1.76467
$352$	−0.593349	−0.0316256
$353$	−3.84026	−0.204397	−0.102198	−	0.994764i	$-0.532588\pi$
$353$	−3.84026	−0.204397	−0.102198	+	0.994764i	$0.532588\pi$
$354$	−0.0853914	−0.00453850
$355$	−5.38126	−0.285608
$356$	−18.3839	−0.974347
$357$	0	0
$358$	0.244013	0.0128965
$359$	−14.4512	−0.762707	−0.381353	−	0.924429i	$-0.624542\pi$
$359$	−14.4512	−0.762707	−0.381353	+	0.924429i	$0.624542\pi$
$360$	−1.43238	−0.0754933
$361$	0.760007	0.0400004
$362$	−0.149918	−0.00787952
$363$	−3.19919	−0.167914
$364$	0	0
$365$	−10.7017	−0.560151
$366$	0.367854	0.0192280
$367$	−17.0673	−0.890904	−0.445452	−	0.895306i	$-0.646957\pi$
$367$	−17.0673	−0.890904	−0.445452	+	0.895306i	$0.646957\pi$
$368$	−28.9769	−1.51052
$369$	75.5942	3.93528
$370$	0.218937	0.0113820
$371$	0	0
$372$	−64.2646	−3.33196
$373$	1.23943	0.0641752	0.0320876	−	0.999485i	$-0.489784\pi$
$373$	1.23943	0.0641752	0.0320876	+	0.999485i	$0.489784\pi$
$374$	−0.386312	−0.0199757
$375$	−3.19919	−0.165205
$376$	−0.698153	−0.0360045
$377$	−22.9670	−1.18286
$378$	0	0
$379$	11.5720	0.594413	0.297207	−	0.954813i	$-0.403945\pi$
$379$	11.5720	0.594413	0.297207	+	0.954813i	$0.403945\pi$
$380$	−8.87954	−0.455511
$381$	−39.5880	−2.02815
$382$	0.551760	0.0282305
$383$	8.35083	0.426708	0.213354	−	0.976975i	$-0.431561\pi$
$383$	8.35083	0.426708	0.213354	+	0.976975i	$0.431561\pi$
$384$	5.05471	0.257947
$385$	0	0
$386$	0.994720	0.0506299
$387$	−15.1054	−0.767852
$388$	−5.19175	−0.263571
$389$	19.5052	0.988953	0.494476	−	0.869191i	$-0.335360\pi$
$389$	19.5052	0.988953	0.494476	+	0.869191i	$0.335360\pi$
$390$	−0.386655	−0.0195790
$391$	−56.7140	−2.86815
$392$	0	0
$393$	13.6825	0.690191
$394$	0.0378247	0.00190558
$395$	1.04570	0.0526147
$396$	14.4518	0.726233
$397$	−5.76106	−0.289139	−0.144570	−	0.989495i	$-0.546180\pi$
$397$	−5.76106	−0.289139	−0.144570	+	0.989495i	$0.546180\pi$
$398$	0.925982	0.0464153
$399$	0	0
$400$	3.98529	0.199264
$401$	−0.775103	−0.0387068	−0.0193534	−	0.999813i	$-0.506161\pi$
$401$	−0.775103	−0.0387068	−0.0193534	+	0.999813i	$0.506161\pi$
$402$	−0.409517	−0.0204248
$403$	−24.5403	−1.22244
$404$	27.3203	1.35924
$405$	21.6379	1.07520
$406$	0	0
$407$	−4.42058	−0.219120
$408$	4.94050	0.244591
$409$	14.8460	0.734085	0.367043	−	0.930204i	$-0.380370\pi$
$409$	14.8460	0.734085	0.367043	+	0.930204i	$0.380370\pi$
$410$	0.517490	0.0255570
$411$	53.2690	2.62757
$412$	−10.3868	−0.511720
$413$	0	0
$414$	−2.60530	−0.128043
$415$	9.19961	0.451591
$416$	1.44795	0.0709917
$417$	−50.9054	−2.49285
$418$	−0.220157	−0.0107682
$419$	20.6704	1.00982	0.504908	−	0.863173i	$-0.331526\pi$
$419$	20.6704	1.00982	0.504908	+	0.863173i	$0.331526\pi$
$420$	0	0
$421$	−16.3417	−0.796446	−0.398223	−	0.917289i	$-0.630373\pi$
$421$	−16.3417	−0.796446	−0.398223	+	0.917289i	$0.630373\pi$
$422$	−0.240307	−0.0116980
$423$	25.5119	1.24043
$424$	−1.17694	−0.0571573
$425$	7.80007	0.378359
$426$	0.852635	0.0413103
$427$	0	0
$428$	−4.99216	−0.241305
$429$	7.80699	0.376925
$430$	−0.103406	−0.00498669
$431$	−1.41502	−0.0681593	−0.0340796	−	0.999419i	$-0.510850\pi$
$431$	−1.41502	−0.0681593	−0.0340796	+	0.999419i	$0.510850\pi$
$432$	−53.9923	−2.59771
$433$	12.4924	0.600346	0.300173	−	0.953885i	$-0.402956\pi$
$433$	12.4924	0.600346	0.300173	+	0.953885i	$0.402956\pi$
$434$	0	0
$435$	30.1093	1.44363
$436$	15.5468	0.744557
$437$	−32.3210	−1.54612
$438$	1.69563	0.0810202
$439$	−5.10895	−0.243837	−0.121919	−	0.992540i	$-0.538905\pi$
$439$	−5.10895	−0.243837	−0.121919	+	0.992540i	$0.538905\pi$
$440$	0.197985	0.00943858
$441$	0	0
$442$	0.942718	0.0448405
$443$	−10.3125	−0.489961	−0.244981	−	0.969528i	$-0.578782\pi$
$443$	−10.3125	−0.489961	−0.244981	+	0.969528i	$0.578782\pi$
$444$	28.2499	1.34068
$445$	9.20326	0.436276
$446$	0.323076	0.0152981
$447$	23.7464	1.12317
$448$	0	0
$449$	13.1186	0.619104	0.309552	−	0.950883i	$-0.399821\pi$
$449$	13.1186	0.619104	0.309552	+	0.950883i	$0.399821\pi$
$450$	0.358316	0.0168912
$451$	−10.4487	−0.492010
$452$	−19.5657	−0.920295
$453$	11.3137	0.531562
$454$	−1.11051	−0.0521190
$455$	0	0
$456$	2.81557	0.131851
$457$	12.1758	0.569560	0.284780	−	0.958593i	$-0.408079\pi$
$457$	12.1758	0.569560	0.284780	+	0.958593i	$0.408079\pi$
$458$	−0.217564	−0.0101661
$459$	−105.675	−4.93247
$460$	14.5241	0.677189
$461$	5.86245	0.273042	0.136521	−	0.990637i	$-0.456408\pi$
$461$	5.86245	0.273042	0.136521	+	0.990637i	$0.456408\pi$
$462$	0	0
$463$	15.7171	0.730437	0.365219	−	0.930922i	$-0.380994\pi$
$463$	15.7171	0.730437	0.365219	+	0.930922i	$0.380994\pi$
$464$	−37.5077	−1.74125
$465$	32.1718	1.49193
$466$	0.560554	0.0259671
$467$	39.2389	1.81576	0.907880	−	0.419229i	$-0.137700\pi$
$467$	39.2389	1.81576	0.907880	+	0.419229i	$0.137700\pi$
$468$	−35.2669	−1.63021
$469$	0	0
$470$	0.174645	0.00805578
$471$	−50.0893	−2.30799
$472$	−0.106701	−0.00491131
$473$	2.08789	0.0960011
$474$	−0.165686	−0.00761019
$475$	4.44522	0.203961
$476$	0	0
$477$	43.0079	1.96919
$478$	1.02344	0.0468111
$479$	21.8732	0.999413	0.499706	−	0.866195i	$-0.333441\pi$
$479$	21.8732	0.999413	0.499706	+	0.866195i	$0.333441\pi$
$480$	−1.89823	−0.0866422
$481$	10.7876	0.491871
$482$	0.152108	0.00692832
$483$	0	0
$484$	−1.99755	−0.0907976
$485$	2.59906	0.118017
$486$	−1.41547	−0.0642072
$487$	−17.6193	−0.798407	−0.399204	−	0.916862i	$-0.630713\pi$
$487$	−17.6193	−0.798407	−0.399204	+	0.916862i	$0.630713\pi$
$488$	0.459652	0.0208075
$489$	−0.0828163	−0.00374508
$490$	0	0
$491$	−11.4386	−0.516219	−0.258109	−	0.966116i	$-0.583100\pi$
$491$	−11.4386	−0.516219	−0.258109	+	0.966116i	$0.583100\pi$
$492$	66.7727	3.01034
$493$	−73.4107	−3.30625
$494$	0.537251	0.0241721
$495$	−7.23480	−0.325180
$496$	−40.0770	−1.79951
$497$	0	0
$498$	−1.45763	−0.0653181
$499$	−15.4372	−0.691062	−0.345531	−	0.938407i	$-0.612301\pi$
$499$	−15.4372	−0.691062	−0.345531	+	0.938407i	$0.612301\pi$
$500$	−1.99755	−0.0893330
$501$	−54.1456	−2.41905
$502$	1.25453	0.0559926
$503$	−19.8494	−0.885042	−0.442521	−	0.896758i	$-0.645916\pi$
$503$	−19.8494	−0.885042	−0.442521	+	0.896758i	$0.645916\pi$
$504$	0	0
$505$	−13.6769	−0.608615
$506$	0.360107	0.0160087
$507$	22.5380	1.00095
$508$	−24.7184	−1.09670
$509$	31.0634	1.37686	0.688432	−	0.725301i	$-0.258300\pi$
$509$	31.0634	1.37686	0.688432	+	0.725301i	$0.258300\pi$
$510$	−1.23588	−0.0547259
$511$	0	0
$512$	3.94273	0.174245
$513$	−60.2235	−2.65893
$514$	0.382159	0.0168563
$515$	5.19977	0.229129
$516$	−13.3427	−0.587379
$517$	−3.52628	−0.155086
$518$	0	0
$519$	−0.217859	−0.00956295
$520$	−0.483145	−0.0211873
$521$	20.6110	0.902984	0.451492	−	0.892275i	$-0.350892\pi$
$521$	20.6110	0.902984	0.451492	+	0.892275i	$0.350892\pi$
$522$	−3.37231	−0.147602
$523$	−1.05405	−0.0460905	−0.0230453	−	0.999734i	$-0.507336\pi$
$523$	−1.05405	−0.0460905	−0.0230453	+	0.999734i	$0.507336\pi$
$524$	8.54325	0.373214
$525$	0	0
$526$	0.791279	0.0345014
$527$	−78.4393	−3.41687
$528$	12.7497	0.554859
$529$	29.8668	1.29856
$530$	0.294416	0.0127886
$531$	3.89907	0.169205
$532$	0	0
$533$	25.4980	1.10444
$534$	−1.45821	−0.0631030
$535$	2.49914	0.108047
$536$	−0.511712	−0.0221026
$537$	−15.7621	−0.680184
$538$	−0.770377	−0.0332133
$539$	0	0
$540$	27.0626	1.16459
$541$	−8.41142	−0.361635	−0.180818	−	0.983517i	$-0.557874\pi$
$541$	−8.41142	−0.361635	−0.180818	+	0.983517i	$0.557874\pi$
$542$	−1.27764	−0.0548795
$543$	9.68399	0.415580
$544$	4.62816	0.198431
$545$	−7.78295	−0.333385
$546$	0	0
$547$	−28.7340	−1.22858	−0.614290	−	0.789081i	$-0.710557\pi$
$547$	−28.7340	−1.22858	−0.614290	+	0.789081i	$0.710557\pi$
$548$	33.2607	1.42083
$549$	−16.7966	−0.716863
$550$	−0.0495267	−0.00211183
$551$	−41.8364	−1.78229
$552$	−4.60537	−0.196018
$553$	0	0
$554$	−0.464328	−0.0197274
$555$	−14.1423	−0.600306
$556$	−31.7849	−1.34798
$557$	40.5554	1.71839	0.859194	−	0.511650i	$-0.170965\pi$
$557$	40.5554	1.71839	0.859194	+	0.511650i	$0.170965\pi$
$558$	−3.60331	−0.152540
$559$	−5.09507	−0.215499
$560$	0	0
$561$	24.9539	1.05355
$562$	−1.15057	−0.0485337
$563$	17.2691	0.727805	0.363902	−	0.931437i	$-0.381444\pi$
$563$	17.2691	0.727805	0.363902	+	0.931437i	$0.381444\pi$
$564$	22.5348	0.948886
$565$	9.79488	0.412074
$566$	0.816271	0.0343104
$567$	0	0
$568$	1.06541	0.0447036
$569$	31.1137	1.30435	0.652177	−	0.758066i	$-0.273856\pi$
$569$	31.1137	1.30435	0.652177	+	0.758066i	$0.273856\pi$
$570$	−0.704324	−0.0295009
$571$	−34.5870	−1.44742	−0.723711	−	0.690103i	$-0.757565\pi$
$571$	−34.5870	−1.44742	−0.723711	+	0.690103i	$0.757565\pi$
$572$	4.87462	0.203818
$573$	−35.6410	−1.48893
$574$	0	0
$575$	−7.27096	−0.303220
$576$	−57.4529	−2.39387
$577$	−13.2414	−0.551247	−0.275623	−	0.961266i	$-0.588884\pi$
$577$	−13.2414	−0.551247	−0.275623	+	0.961266i	$0.588884\pi$
$578$	2.17131	0.0903144
$579$	−64.2541	−2.67031
$580$	18.8000	0.780628
$581$	0	0
$582$	−0.411809	−0.0170700
$583$	−5.94458	−0.246199
$584$	2.11877	0.0876754
$585$	17.6551	0.729949
$586$	−0.549364	−0.0226940
$587$	−18.9849	−0.783590	−0.391795	−	0.920053i	$-0.628146\pi$
$587$	−18.9849	−0.783590	−0.391795	+	0.920053i	$0.628146\pi$
$588$	0	0
$589$	−44.7022	−1.84192
$590$	0.0266916	0.00109888
$591$	−2.44329	−0.100504
$592$	17.6173	0.724067
$593$	7.40963	0.304277	0.152139	−	0.988359i	$-0.451384\pi$
$593$	7.40963	0.304277	0.152139	+	0.988359i	$0.451384\pi$
$594$	0.670984	0.0275308
$595$	0	0
$596$	14.8271	0.607341
$597$	−59.8140	−2.44802
$598$	−0.878770	−0.0359356
$599$	45.5954	1.86298	0.931488	−	0.363771i	$-0.118511\pi$
$599$	45.5954	1.86298	0.931488	+	0.363771i	$0.118511\pi$
$600$	0.633392	0.0258581
$601$	22.8082	0.930365	0.465183	−	0.885215i	$-0.345989\pi$
$601$	22.8082	0.930365	0.465183	+	0.885215i	$0.345989\pi$
$602$	0	0
$603$	18.6990	0.761483
$604$	7.06416	0.287437
$605$	1.00000	0.0406558
$606$	2.16704	0.0880301
$607$	46.8695	1.90237	0.951186	−	0.308617i	$-0.0998662\pi$
$607$	46.8695	1.90237	0.951186	+	0.308617i	$0.0998662\pi$
$608$	2.63757	0.106968
$609$	0	0
$610$	−0.114984	−0.00465555
$611$	8.60520	0.348129
$612$	−112.725	−4.55666
$613$	−3.16299	−0.127752	−0.0638761	−	0.997958i	$-0.520346\pi$
$613$	−3.16299	−0.127752	−0.0638761	+	0.997958i	$0.520346\pi$
$614$	0.339390	0.0136967
$615$	−33.4273	−1.34792
$616$	0	0
$617$	15.1004	0.607920	0.303960	−	0.952685i	$-0.401691\pi$
$617$	15.1004	0.607920	0.303960	+	0.952685i	$0.401691\pi$
$618$	−0.823879	−0.0331413
$619$	−34.0580	−1.36891	−0.684453	−	0.729057i	$-0.739959\pi$
$619$	−34.0580	−1.36891	−0.684453	+	0.729057i	$0.739959\pi$
$620$	20.0878	0.806745
$621$	98.5063	3.95292
$622$	−0.293317	−0.0117610
$623$	0	0
$624$	−31.1131	−1.24552
$625$	1.00000	0.0400000
$626$	0.398778	0.0159384
$627$	14.2211	0.567936
$628$	−31.2753	−1.24802
$629$	34.4809	1.37484
$630$	0	0
$631$	29.4545	1.17257	0.586284	−	0.810106i	$-0.300590\pi$
$631$	29.4545	1.17257	0.586284	+	0.810106i	$0.300590\pi$
$632$	−0.207033	−0.00823532
$633$	15.5227	0.616972
$634$	0.0491909	0.00195362
$635$	12.3744	0.491063
$636$	37.9890	1.50636
$637$	0	0
$638$	0.466123	0.0184540
$639$	−38.9323	−1.54014
$640$	−1.58000	−0.0624550
$641$	−8.42563	−0.332792	−0.166396	−	0.986059i	$-0.553213\pi$
$641$	−8.42563	−0.332792	−0.166396	+	0.986059i	$0.553213\pi$
$642$	−0.395977	−0.0156280
$643$	19.4867	0.768481	0.384240	−	0.923233i	$-0.374463\pi$
$643$	19.4867	0.768481	0.384240	+	0.923233i	$0.374463\pi$
$644$	0	0
$645$	6.67954	0.263007
$646$	1.71724	0.0675640
$647$	12.1396	0.477259	0.238629	−	0.971111i	$-0.423302\pi$
$647$	12.1396	0.477259	0.238629	+	0.971111i	$0.423302\pi$
$648$	−4.28399	−0.168291
$649$	−0.538933	−0.0211550
$650$	0.120860	0.00474053
$651$	0	0
$652$	−0.0517099	−0.00202511
$653$	−23.4522	−0.917756	−0.458878	−	0.888499i	$-0.651748\pi$
$653$	−23.4522	−0.917756	−0.458878	+	0.888499i	$0.651748\pi$
$654$	1.23317	0.0482208
$655$	−4.27687	−0.167111
$656$	41.6411	1.62581
$657$	−77.4244	−3.02061
$658$	0	0
$659$	−35.6824	−1.38999	−0.694995	−	0.719015i	$-0.744593\pi$
$659$	−35.6824	−1.38999	−0.694995	+	0.719015i	$0.744593\pi$
$660$	−6.39053	−0.248751
$661$	26.6162	1.03525	0.517625	−	0.855608i	$-0.326816\pi$
$661$	26.6162	1.03525	0.517625	+	0.855608i	$0.326816\pi$
$662$	0.567658	0.0220626
$663$	−60.8950	−2.36497
$664$	−1.82139	−0.0706835
$665$	0	0
$666$	1.58397	0.0613774
$667$	68.4310	2.64966
$668$	−33.8081	−1.30807
$669$	−20.8691	−0.806847
$670$	0.128007	0.00494532
$671$	2.32165	0.0896262
$672$	0	0
$673$	25.0830	0.966878	0.483439	−	0.875378i	$-0.339388\pi$
$673$	25.0830	0.966878	0.483439	+	0.875378i	$0.339388\pi$
$674$	0.854948	0.0329314
$675$	−13.5479	−0.521459
$676$	14.0726	0.541252
$677$	−24.9419	−0.958595	−0.479298	−	0.877652i	$-0.659109\pi$
$677$	−24.9419	−0.958595	−0.479298	+	0.877652i	$0.659109\pi$
$678$	−1.55195	−0.0596024
$679$	0	0
$680$	−1.54430	−0.0592212
$681$	71.7339	2.74885
$682$	0.498052	0.0190714
$683$	45.2045	1.72970	0.864851	−	0.502029i	$-0.167413\pi$
$683$	45.2045	1.72970	0.864851	+	0.502029i	$0.167413\pi$
$684$	−64.2417	−2.45634
$685$	−16.6508	−0.636194
$686$	0	0
$687$	14.0536	0.536179
$688$	−8.32083	−0.317229
$689$	14.5066	0.552657
$690$	1.15205	0.0438578
$691$	51.2493	1.94961	0.974807	−	0.223048i	$-0.0716008\pi$
$691$	51.2493	1.94961	0.974807	+	0.223048i	$0.0716008\pi$
$692$	−0.136029	−0.00517106
$693$	0	0
$694$	1.00291	0.0380698
$695$	15.9120	0.603576
$696$	−5.96120	−0.225959
$697$	81.5006	3.08705
$698$	−1.39778	−0.0529068
$699$	−36.2091	−1.36955
$700$	0	0
$701$	37.9878	1.43478	0.717390	−	0.696671i	$-0.245336\pi$
$701$	37.9878	1.43478	0.717390	+	0.696671i	$0.245336\pi$
$702$	−1.63740	−0.0617998
$703$	19.6505	0.741132
$704$	7.94119	0.299295
$705$	−11.2812	−0.424876
$706$	−0.190196	−0.00715811
$707$	0	0
$708$	3.44407	0.129436
$709$	−31.0987	−1.16794	−0.583968	−	0.811777i	$-0.698501\pi$
$709$	−31.0987	−1.16794	−0.583968	+	0.811777i	$0.698501\pi$
$710$	−0.266516	−0.0100022
$711$	7.56540	0.283725
$712$	−1.82211	−0.0682865
$713$	73.1184	2.73831
$714$	0	0
$715$	−2.44030	−0.0912622
$716$	−9.84171	−0.367802
$717$	−66.1093	−2.46890
$718$	−0.715722	−0.0267105
$719$	−46.0191	−1.71622	−0.858112	−	0.513462i	$-0.828363\pi$
$719$	−46.0191	−1.71622	−0.858112	+	0.513462i	$0.828363\pi$
$720$	28.8328	1.07453
$721$	0	0
$722$	0.0376407	0.00140084
$723$	−9.82542	−0.365411
$724$	6.04661	0.224720
$725$	−9.41155	−0.349536
$726$	−0.158445	−0.00588045
$727$	24.5296	0.909754	0.454877	−	0.890554i	$-0.349683\pi$
$727$	24.5296	0.909754	0.454877	+	0.890554i	$0.349683\pi$
$728$	0	0
$729$	26.5190	0.982185
$730$	−0.530018	−0.0196169
$731$	−16.2857	−0.602347
$732$	−14.8365	−0.548374
$733$	−46.8027	−1.72870	−0.864349	−	0.502892i	$-0.832269\pi$
$733$	−46.8027	−1.72870	−0.864349	+	0.502892i	$0.832269\pi$
$734$	−0.845286	−0.0312001
$735$	0	0
$736$	−4.31422	−0.159024
$737$	−2.58460	−0.0952048
$738$	3.74393	0.137816
$739$	−28.0199	−1.03073	−0.515365	−	0.856971i	$-0.672344\pi$
$739$	−28.0199	−1.03073	−0.515365	+	0.856971i	$0.672344\pi$
$740$	−8.83033	−0.324609
$741$	−34.7038	−1.27488
$742$	0	0
$743$	25.1185	0.921507	0.460754	−	0.887528i	$-0.347579\pi$
$743$	25.1185	0.921507	0.460754	+	0.887528i	$0.347579\pi$
$744$	−6.36954	−0.233519
$745$	−7.42265	−0.271945
$746$	0.0613849	0.00224746
$747$	66.5573	2.43520
$748$	15.5810	0.569698
$749$	0	0
$750$	−0.158445	−0.00578560
$751$	0.350477	0.0127891	0.00639455	−	0.999980i	$-0.497965\pi$
$751$	0.350477	0.0127891	0.00639455	+	0.999980i	$0.497965\pi$
$752$	14.0533	0.512469
$753$	−81.0368	−2.95315
$754$	−1.13748	−0.0414247
$755$	−3.53642	−0.128703
$756$	0	0
$757$	35.8774	1.30399	0.651993	−	0.758225i	$-0.273933\pi$
$757$	35.8774	1.30399	0.651993	+	0.758225i	$0.273933\pi$
$758$	0.573123	0.0208168
$759$	−23.2612	−0.844327
$760$	−0.880089	−0.0319242
$761$	6.57536	0.238357	0.119178	−	0.992873i	$-0.461974\pi$
$761$	6.57536	0.238357	0.119178	+	0.992873i	$0.461974\pi$
$762$	−1.96066	−0.0710273
$763$	0	0
$764$	−22.2540	−0.805121
$765$	56.4319	2.04030
$766$	0.413589	0.0149436
$767$	1.31516	0.0474877
$768$	−50.5604	−1.82444
$769$	48.7497	1.75796	0.878979	−	0.476860i	$-0.158225\pi$
$769$	48.7497	1.75796	0.878979	+	0.476860i	$0.158225\pi$
$770$	0	0
$771$	−24.6856	−0.889030
$772$	−40.1198	−1.44394
$773$	−16.2163	−0.583260	−0.291630	−	0.956531i	$-0.594198\pi$
$773$	−16.2163	−0.583260	−0.291630	+	0.956531i	$0.594198\pi$
$774$	−0.748122	−0.0268907
$775$	−10.0562	−0.361230
$776$	−0.514576	−0.0184722
$777$	0	0
$778$	0.966029	0.0346338
$779$	46.4468	1.66413
$780$	15.5948	0.558384
$781$	5.38126	0.192557
$782$	−2.80886	−0.100445
$783$	127.507	4.55672
$784$	0	0
$785$	15.6569	0.558818
$786$	0.677650	0.0241710
$787$	32.2200	1.14852	0.574259	−	0.818674i	$-0.305290\pi$
$787$	32.2200	1.14852	0.574259	+	0.818674i	$0.305290\pi$
$788$	−1.52557	−0.0543462
$789$	−51.1128	−1.81966
$790$	0.0517899	0.00184260
$791$	0	0
$792$	1.43238	0.0508976
$793$	−5.66552	−0.201189
$794$	−0.285326	−0.0101259
$795$	−19.0178	−0.674493
$796$	−37.3474	−1.32374
$797$	13.7085	0.485580	0.242790	−	0.970079i	$-0.421937\pi$
$797$	13.7085	0.485580	0.242790	+	0.970079i	$0.421937\pi$
$798$	0	0
$799$	27.5053	0.973066
$800$	0.593349	0.0209781
$801$	66.5837	2.35262
$802$	−0.0383883	−0.00135554
$803$	10.7017	0.377653
$804$	16.5169	0.582507
$805$	0	0
$806$	−1.21540	−0.0428106
$807$	49.7626	1.75173
$808$	2.70783	0.0952612
$809$	−35.6443	−1.25319	−0.626594	−	0.779346i	$-0.715551\pi$
$809$	−35.6443	−1.25319	−0.626594	+	0.779346i	$0.715551\pi$
$810$	1.07165	0.0376541
$811$	−19.0640	−0.669428	−0.334714	−	0.942320i	$-0.608640\pi$
$811$	−19.0640	−0.669428	−0.334714	+	0.942320i	$0.608640\pi$
$812$	0	0
$813$	82.5296	2.89444
$814$	−0.218937	−0.00767374
$815$	0.0258867	0.000906771 0
$816$	−99.4484	−3.48139
$817$	−9.28112	−0.324705
$818$	0.735271	0.0257082
$819$	0	0
$820$	−20.8718	−0.728874
$821$	−5.10415	−0.178136	−0.0890681	−	0.996026i	$-0.528389\pi$
$821$	−5.10415	−0.178136	−0.0890681	+	0.996026i	$0.528389\pi$
$822$	2.63824	0.0920191
$823$	−50.3376	−1.75466	−0.877329	−	0.479890i	$-0.840677\pi$
$823$	−50.3376	−1.75466	−0.877329	+	0.479890i	$0.840677\pi$
$824$	−1.02948	−0.0358636
$825$	3.19919	0.111381
$826$	0	0
$827$	30.1326	1.04781	0.523907	−	0.851775i	$-0.324474\pi$
$827$	30.1326	1.04781	0.523907	+	0.851775i	$0.324474\pi$
$828$	105.079	3.65174
$829$	−24.4367	−0.848722	−0.424361	−	0.905493i	$-0.639501\pi$
$829$	−24.4367	−0.848722	−0.424361	+	0.905493i	$0.639501\pi$
$830$	0.455626	0.0158150
$831$	29.9933	1.04046
$832$	−19.3789	−0.671843
$833$	0	0
$834$	−2.52118	−0.0873012
$835$	16.9248	0.585707
$836$	8.87954	0.307105
$837$	136.241	4.70917
$838$	1.02374	0.0353645
$839$	31.4530	1.08588	0.542940	−	0.839772i	$-0.317311\pi$
$839$	31.4530	1.08588	0.542940	+	0.839772i	$0.317311\pi$
$840$	0	0
$841$	59.5773	2.05439
$842$	−0.809351	−0.0278921
$843$	74.3211	2.55975
$844$	9.69224	0.333621
$845$	−7.04492	−0.242353
$846$	1.26352	0.0434408
$847$	0	0
$848$	23.6909	0.813548
$849$	−52.7272	−1.80959
$850$	0.386312	0.0132504
$851$	−32.1419	−1.10181
$852$	−34.3891	−1.17815
$853$	−31.3621	−1.07382	−0.536909	−	0.843640i	$-0.680408\pi$
$853$	−31.3621	−1.07382	−0.536909	+	0.843640i	$0.680408\pi$
$854$	0	0
$855$	32.1603	1.09986
$856$	−0.494794	−0.0169117
$857$	40.4507	1.38177	0.690884	−	0.722965i	$-0.257221\pi$
$857$	40.4507	1.38177	0.690884	+	0.722965i	$0.257221\pi$
$858$	0.386655	0.0132002
$859$	−5.52397	−0.188475	−0.0942377	−	0.995550i	$-0.530041\pi$
$859$	−5.52397	−0.188475	−0.0942377	+	0.995550i	$0.530041\pi$
$860$	4.17065	0.142218
$861$	0	0
$862$	−0.0700815	−0.00238698
$863$	−10.7260	−0.365116	−0.182558	−	0.983195i	$-0.558438\pi$
$863$	−10.7260	−0.365116	−0.182558	+	0.983195i	$0.558438\pi$
$864$	−8.03864	−0.273480
$865$	0.0680982	0.00231541
$866$	0.618707	0.0210245
$867$	−140.256	−4.76334
$868$	0	0
$869$	−1.04570	−0.0354728
$870$	1.49122	0.0505569
$871$	6.30720	0.213711
$872$	1.54091	0.0521818
$873$	18.8037	0.636408
$874$	−1.60075	−0.0541463
$875$	0	0
$876$	−68.3892	−2.31066
$877$	34.7483	1.17337	0.586683	−	0.809816i	$-0.300433\pi$
$877$	34.7483	1.17337	0.586683	+	0.809816i	$0.300433\pi$
$878$	−0.253030	−0.00853934
$879$	35.4863	1.19692
$880$	−3.98529	−0.134344
$881$	2.01470	0.0678770	0.0339385	−	0.999424i	$-0.489195\pi$
$881$	2.01470	0.0678770	0.0339385	+	0.999424i	$0.489195\pi$
$882$	0	0
$883$	−47.0213	−1.58239	−0.791197	−	0.611562i	$-0.790542\pi$
$883$	−47.0213	−1.58239	−0.791197	+	0.611562i	$0.790542\pi$
$884$	−38.0224	−1.27883
$885$	−1.72415	−0.0579566
$886$	−0.510744	−0.0171588
$887$	7.45664	0.250369	0.125185	−	0.992133i	$-0.460048\pi$
$887$	7.45664	0.250369	0.125185	+	0.992133i	$0.460048\pi$
$888$	2.79996	0.0939607
$889$	0	0
$890$	0.455807	0.0152787
$891$	−21.6379	−0.724897
$892$	−13.0305	−0.436294
$893$	15.6751	0.524548
$894$	1.17608	0.0393341
$895$	4.92690	0.164688
$896$	0	0
$897$	56.7643	1.89530
$898$	0.649720	0.0216814
$899$	94.6447	3.15658
$900$	−14.4518	−0.481728
$901$	46.3682	1.54475
$902$	−0.517490	−0.0172305
$903$	0	0
$904$	−1.93924	−0.0644983
$905$	−3.02702	−0.100621
$906$	0.560329	0.0186157
$907$	43.5503	1.44606	0.723032	−	0.690815i	$-0.242748\pi$
$907$	43.5503	1.44606	0.723032	+	0.690815i	$0.242748\pi$
$908$	44.7901	1.48641
$909$	−98.9498	−3.28196
$910$	0	0
$911$	22.4784	0.744743	0.372371	−	0.928084i	$-0.378545\pi$
$911$	22.4784	0.744743	0.372371	+	0.928084i	$0.378545\pi$
$912$	−56.6752	−1.87670
$913$	−9.19961	−0.304463
$914$	0.603028	0.0199464
$915$	7.42738	0.245542
$916$	8.77496	0.289933
$917$	0	0
$918$	−5.23372	−0.172738
$919$	22.7617	0.750838	0.375419	−	0.926855i	$-0.377499\pi$
$919$	22.7617	0.750838	0.375419	+	0.926855i	$0.377499\pi$
$920$	1.43954	0.0474604
$921$	−21.9230	−0.722387
$922$	0.290348	0.00956210
$923$	−13.1319	−0.432242
$924$	0	0
$925$	4.42058	0.145348
$926$	0.778418	0.0255804
$927$	37.6193	1.23558
$928$	−5.58433	−0.183315
$929$	24.0307	0.788421	0.394211	−	0.919020i	$-0.371018\pi$
$929$	24.0307	0.788421	0.394211	+	0.919020i	$0.371018\pi$
$930$	1.59336	0.0522484
$931$	0	0
$932$	−22.6087	−0.740571
$933$	18.9469	0.620293
$934$	1.94338	0.0635892
$935$	−7.80007	−0.255090
$936$	−3.49545	−0.114252
$937$	49.5594	1.61903	0.809517	−	0.587097i	$-0.199729\pi$
$937$	49.5594	1.61903	0.809517	+	0.587097i	$0.199729\pi$
$938$	0	0
$939$	−25.7591	−0.840618
$940$	−7.04392	−0.229747
$941$	−6.96784	−0.227145	−0.113573	−	0.993530i	$-0.536229\pi$
$941$	−6.96784	−0.227145	−0.113573	+	0.993530i	$0.536229\pi$
$942$	−2.48076	−0.0808274
$943$	−75.9720	−2.47399
$944$	2.14780	0.0699051
$945$	0	0
$946$	0.103406	0.00336202
$947$	−27.0111	−0.877742	−0.438871	−	0.898550i	$-0.644622\pi$
$947$	−27.0111	−0.877742	−0.438871	+	0.898550i	$0.644622\pi$
$948$	6.68255	0.217039
$949$	−26.1153	−0.847739
$950$	0.220157	0.00714285
$951$	−3.17749	−0.103037
$952$	0	0
$953$	−9.17035	−0.297057	−0.148528	−	0.988908i	$-0.547454\pi$
$953$	−9.17035	−0.297057	−0.148528	+	0.988908i	$0.547454\pi$
$954$	2.13004	0.0689625
$955$	11.1407	0.360503
$956$	−41.2781	−1.33503
$957$	−30.1093	−0.973296
$958$	1.08331	0.0350001
$959$	0	0
$960$	25.4054	0.819954
$961$	70.1278	2.26219
$962$	0.534273	0.0172257
$963$	18.0808	0.582645
$964$	−6.13492	−0.197592
$965$	20.0845	0.646543
$966$	0	0
$967$	−43.6453	−1.40354	−0.701770	−	0.712404i	$-0.747606\pi$
$967$	−43.6453	−1.40354	−0.701770	+	0.712404i	$0.747606\pi$
$968$	−0.197985	−0.00636349
$969$	−110.926	−3.56344
$970$	0.128723	0.00413304
$971$	8.45417	0.271307	0.135654	−	0.990756i	$-0.456687\pi$
$971$	8.45417	0.271307	0.135654	+	0.990756i	$0.456687\pi$
$972$	57.0899	1.83116
$973$	0	0
$974$	−0.872627	−0.0279608
$975$	−7.80699	−0.250024
$976$	−9.25243	−0.296163
$977$	−32.6931	−1.04595	−0.522973	−	0.852349i	$-0.675177\pi$
$977$	−32.6931	−1.04595	−0.522973	+	0.852349i	$0.675177\pi$
$978$	−0.00410162	−0.000131155 0
$979$	−9.20326	−0.294137
$980$	0	0
$981$	−56.3081	−1.79778
$982$	−0.566519	−0.0180783
$983$	38.4043	1.22491	0.612453	−	0.790507i	$-0.290183\pi$
$983$	38.4043	1.22491	0.612453	+	0.790507i	$0.290183\pi$
$984$	6.61812	0.210978
$985$	0.763722	0.0243342
$986$	−3.63579	−0.115787
$987$	0	0
$988$	−21.6688	−0.689376
$989$	15.1809	0.482726
$990$	−0.358316	−0.0113880
$991$	−36.2014	−1.14998	−0.574988	−	0.818162i	$-0.694993\pi$
$991$	−36.2014	−1.14998	−0.574988	+	0.818162i	$0.694993\pi$
$992$	−5.96686	−0.189448
$993$	−36.6679	−1.16362
$994$	0	0
$995$	18.6966	0.592723
$996$	58.7903	1.86284
$997$	−31.5612	−0.999554	−0.499777	−	0.866154i	$-0.666585\pi$
$997$	−31.5612	−0.999554	−0.499777	+	0.866154i	$0.666585\pi$
$998$	−0.764552	−0.0242015
$999$	−59.8897	−1.89483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.x.1.5	yes	10
7.6	odd	2		2695.2.a.w.1.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.2.a.w.1.5	✓	10	7.6	odd	2
2695.2.a.x.1.5	yes	10	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:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2695.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0495267 q^{2} -3.19919 q^{3} -1.99755 q^{4} +1.00000 q^{5} -0.158445 q^{6} -0.197985 q^{8} +7.23480 q^{9} +O(q^{10})\)	\(q+0.0495267 q^{2} -3.19919 q^{3} -1.99755 q^{4} +1.00000 q^{5} -0.158445 q^{6} -0.197985 q^{8} +7.23480 q^{9} +0.0495267 q^{10} -1.00000 q^{11} +6.39053 q^{12} +2.44030 q^{13} -3.19919 q^{15} +3.98529 q^{16} +7.80007 q^{17} +0.358316 q^{18} +4.44522 q^{19} -1.99755 q^{20} -0.0495267 q^{22} -7.27096 q^{23} +0.633392 q^{24} +1.00000 q^{25} +0.120860 q^{26} -13.5479 q^{27} -9.41155 q^{29} -0.158445 q^{30} -10.0562 q^{31} +0.593349 q^{32} +3.19919 q^{33} +0.386312 q^{34} -14.4518 q^{36} +4.42058 q^{37} +0.220157 q^{38} -7.80699 q^{39} -0.197985 q^{40} +10.4487 q^{41} -2.08789 q^{43} +1.99755 q^{44} +7.23480 q^{45} -0.360107 q^{46} +3.52628 q^{47} -12.7497 q^{48} +0.0495267 q^{50} -24.9539 q^{51} -4.87462 q^{52} +5.94458 q^{53} -0.670984 q^{54} -1.00000 q^{55} -14.2211 q^{57} -0.466123 q^{58} +0.538933 q^{59} +6.39053 q^{60} -2.32165 q^{61} -0.498052 q^{62} -7.94119 q^{64} +2.44030 q^{65} +0.158445 q^{66} +2.58460 q^{67} -15.5810 q^{68} +23.2612 q^{69} -5.38126 q^{71} -1.43238 q^{72} -10.7017 q^{73} +0.218937 q^{74} -3.19919 q^{75} -8.87954 q^{76} -0.386655 q^{78} +1.04570 q^{79} +3.98529 q^{80} +21.6379 q^{81} +0.517490 q^{82} +9.19961 q^{83} +7.80007 q^{85} -0.103406 q^{86} +30.1093 q^{87} +0.197985 q^{88} +9.20326 q^{89} +0.358316 q^{90} +14.5241 q^{92} +32.1718 q^{93} +0.174645 q^{94} +4.44522 q^{95} -1.89823 q^{96} +2.59906 q^{97} -7.23480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 10 q^{4} + 10 q^{5} + 4 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 10 * q^4 + 10 * q^5 + 4 * q^6 + 6 * q^8 + 10 * q^9	\( 10 q + 2 q^{2} + 10 q^{4} + 10 q^{5} + 4 q^{6} + 6 q^{8} + 10 q^{9} + 2 q^{10} - 10 q^{11} + 4 q^{12} + 8 q^{13} + 6 q^{16} + 28 q^{17} - 10 q^{18} + 8 q^{19} + 10 q^{20} - 2 q^{22} - 8 q^{23} + 32 q^{24} + 10 q^{25} + 12 q^{26} - 8 q^{29} + 4 q^{30} - 4 q^{31} + 14 q^{32} + 20 q^{34} - 22 q^{36} + 28 q^{37} + 24 q^{38} - 24 q^{39} + 6 q^{40} + 44 q^{41} + 20 q^{43} - 10 q^{44} + 10 q^{45} - 12 q^{46} + 12 q^{47} + 16 q^{48} + 2 q^{50} - 4 q^{51} + 36 q^{52} - 8 q^{54} - 10 q^{55} + 12 q^{57} - 8 q^{58} + 16 q^{59} + 4 q^{60} + 16 q^{61} + 36 q^{62} - 34 q^{64} + 8 q^{65} - 4 q^{66} + 20 q^{67} + 8 q^{68} + 4 q^{69} - 4 q^{71} + 10 q^{72} + 20 q^{73} - 16 q^{74} + 4 q^{76} + 52 q^{78} - 20 q^{79} + 6 q^{80} + 10 q^{81} - 32 q^{82} + 16 q^{83} + 28 q^{85} - 20 q^{86} + 20 q^{87} - 6 q^{88} + 44 q^{89} - 10 q^{90} - 24 q^{92} + 16 q^{93} + 24 q^{94} + 8 q^{95} - 4 q^{97} - 10 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 10 * q^4 + 10 * q^5 + 4 * q^6 + 6 * q^8 + 10 * q^9 + 2 * q^10 - 10 * q^11 + 4 * q^12 + 8 * q^13 + 6 * q^16 + 28 * q^17 - 10 * q^18 + 8 * q^19 + 10 * q^20 - 2 * q^22 - 8 * q^23 + 32 * q^24 + 10 * q^25 + 12 * q^26 - 8 * q^29 + 4 * q^30 - 4 * q^31 + 14 * q^32 + 20 * q^34 - 22 * q^36 + 28 * q^37 + 24 * q^38 - 24 * q^39 + 6 * q^40 + 44 * q^41 + 20 * q^43 - 10 * q^44 + 10 * q^45 - 12 * q^46 + 12 * q^47 + 16 * q^48 + 2 * q^50 - 4 * q^51 + 36 * q^52 - 8 * q^54 - 10 * q^55 + 12 * q^57 - 8 * q^58 + 16 * q^59 + 4 * q^60 + 16 * q^61 + 36 * q^62 - 34 * q^64 + 8 * q^65 - 4 * q^66 + 20 * q^67 + 8 * q^68 + 4 * q^69 - 4 * q^71 + 10 * q^72 + 20 * q^73 - 16 * q^74 + 4 * q^76 + 52 * q^78 - 20 * q^79 + 6 * q^80 + 10 * q^81 - 32 * q^82 + 16 * q^83 + 28 * q^85 - 20 * q^86 + 20 * q^87 - 6 * q^88 + 44 * q^89 - 10 * q^90 - 24 * q^92 + 16 * q^93 + 24 * q^94 + 8 * q^95 - 4 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more