LMFDB - Embedded newform 3381.2.a.bh.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$26.9974209234$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 6x^{8} + 36x^{7} + x^{6} - 100x^{5} + 26x^{4} + 100x^{3} - 17x^{2} - 28x - 2 $ x^10 - 4x^9 - 6x^8 + 36x^7 + x^6 - 100x^5 + 26x^4 + 100x^3 - 17x^2 - 28x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.69362$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.69362 q^{2} +1.00000 q^{3} +0.868357 q^{4} +1.90171 q^{5} -1.69362 q^{6} +1.91658 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.69362 q^{2} +1.00000 q^{3} +0.868357 q^{4} +1.90171 q^{5} -1.69362 q^{6} +1.91658 q^{8} +1.00000 q^{9} -3.22078 q^{10} -5.19584 q^{11} +0.868357 q^{12} -2.94646 q^{13} +1.90171 q^{15} -4.98267 q^{16} +4.99305 q^{17} -1.69362 q^{18} -0.972373 q^{19} +1.65136 q^{20} +8.79980 q^{22} +1.00000 q^{23} +1.91658 q^{24} -1.38351 q^{25} +4.99019 q^{26} +1.00000 q^{27} -4.08053 q^{29} -3.22078 q^{30} -1.11270 q^{31} +4.60561 q^{32} -5.19584 q^{33} -8.45633 q^{34} +0.868357 q^{36} +10.5052 q^{37} +1.64683 q^{38} -2.94646 q^{39} +3.64477 q^{40} +3.46973 q^{41} -7.46270 q^{43} -4.51185 q^{44} +1.90171 q^{45} -1.69362 q^{46} -5.28608 q^{47} -4.98267 q^{48} +2.34314 q^{50} +4.99305 q^{51} -2.55858 q^{52} -9.85547 q^{53} -1.69362 q^{54} -9.88098 q^{55} -0.972373 q^{57} +6.91088 q^{58} -8.88630 q^{59} +1.65136 q^{60} +12.1353 q^{61} +1.88449 q^{62} +2.16517 q^{64} -5.60330 q^{65} +8.79980 q^{66} -11.6894 q^{67} +4.33575 q^{68} +1.00000 q^{69} -5.61748 q^{71} +1.91658 q^{72} -6.42059 q^{73} -17.7919 q^{74} -1.38351 q^{75} -0.844367 q^{76} +4.99019 q^{78} -13.4281 q^{79} -9.47558 q^{80} +1.00000 q^{81} -5.87642 q^{82} -2.34810 q^{83} +9.49531 q^{85} +12.6390 q^{86} -4.08053 q^{87} -9.95823 q^{88} +16.8503 q^{89} -3.22078 q^{90} +0.868357 q^{92} -1.11270 q^{93} +8.95262 q^{94} -1.84917 q^{95} +4.60561 q^{96} -0.186928 q^{97} -5.19584 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} + 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 + 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 - 12 * q^8 + 10 * q^9	$ 10 q - 4 q^{2} + 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} - 12 q^{8} + 10 q^{9} - 8 q^{10} - 2 q^{11} + 8 q^{12} - 16 q^{13} - 4 q^{15} + 4 q^{16} - 12 q^{17} - 4 q^{18} - 26 q^{19} - 8 q^{22} + 10 q^{23} - 12 q^{24} + 14 q^{25} + 12 q^{26} + 10 q^{27} - 16 q^{29} - 8 q^{30} - 20 q^{31} - 8 q^{32} - 2 q^{33} + 4 q^{34} + 8 q^{36} + 8 q^{37} + 8 q^{38} - 16 q^{39} + 12 q^{40} - 22 q^{41} - 4 q^{43} - 24 q^{44} - 4 q^{45} - 4 q^{46} - 6 q^{47} + 4 q^{48} - 48 q^{50} - 12 q^{51} - 24 q^{52} - 30 q^{53} - 4 q^{54} - 48 q^{55} - 26 q^{57} + 24 q^{58} - 42 q^{59} - 14 q^{61} - 40 q^{62} + 8 q^{64} - 44 q^{65} - 8 q^{66} - 8 q^{68} + 10 q^{69} + 8 q^{71} - 12 q^{72} - 24 q^{73} + 8 q^{74} + 14 q^{75} - 32 q^{76} + 12 q^{78} + 32 q^{79} - 28 q^{80} + 10 q^{81} + 64 q^{82} - 28 q^{83} - 4 q^{85} - 4 q^{86} - 16 q^{87} + 20 q^{88} - 8 q^{90} + 8 q^{92} - 20 q^{93} - 8 q^{94} - 16 q^{95} - 8 q^{96} + 12 q^{97} - 2 q^{99}+O(q^{100}) $ 10 * q - 4 * q^2 + 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 - 12 * q^8 + 10 * q^9 - 8 * q^10 - 2 * q^11 + 8 * q^12 - 16 * q^13 - 4 * q^15 + 4 * q^16 - 12 * q^17 - 4 * q^18 - 26 * q^19 - 8 * q^22 + 10 * q^23 - 12 * q^24 + 14 * q^25 + 12 * q^26 + 10 * q^27 - 16 * q^29 - 8 * q^30 - 20 * q^31 - 8 * q^32 - 2 * q^33 + 4 * q^34 + 8 * q^36 + 8 * q^37 + 8 * q^38 - 16 * q^39 + 12 * q^40 - 22 * q^41 - 4 * q^43 - 24 * q^44 - 4 * q^45 - 4 * q^46 - 6 * q^47 + 4 * q^48 - 48 * q^50 - 12 * q^51 - 24 * q^52 - 30 * q^53 - 4 * q^54 - 48 * q^55 - 26 * q^57 + 24 * q^58 - 42 * q^59 - 14 * q^61 - 40 * q^62 + 8 * q^64 - 44 * q^65 - 8 * q^66 - 8 * q^68 + 10 * q^69 + 8 * q^71 - 12 * q^72 - 24 * q^73 + 8 * q^74 + 14 * q^75 - 32 * q^76 + 12 * q^78 + 32 * q^79 - 28 * q^80 + 10 * q^81 + 64 * q^82 - 28 * q^83 - 4 * q^85 - 4 * q^86 - 16 * q^87 + 20 * q^88 - 8 * q^90 + 8 * q^92 - 20 * q^93 - 8 * q^94 - 16 * q^95 - 8 * q^96 + 12 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.69362	−1.19757	−0.598786	−	0.800909i	$-0.704350\pi$
$2$	−1.69362	−1.19757	−0.598786	+	0.800909i	$0.704350\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.868357	0.434179
$5$	1.90171	0.850470	0.425235	−	0.905083i	$-0.360192\pi$
$5$	1.90171	0.850470	0.425235	+	0.905083i	$0.360192\pi$
$6$	−1.69362	−0.691419
$7$	0	0
$7$	0	0
$8$	1.91658	0.677612
$9$	1.00000	0.333333
$10$	−3.22078	−1.01850
$11$	−5.19584	−1.56661	−0.783303	−	0.621640i	$-0.786467\pi$
$11$	−5.19584	−1.56661	−0.783303	+	0.621640i	$0.786467\pi$
$12$	0.868357	0.250673
$13$	−2.94646	−0.817201	−0.408600	−	0.912713i	$-0.633983\pi$
$13$	−2.94646	−0.817201	−0.408600	+	0.912713i	$0.633983\pi$
$14$	0	0
$15$	1.90171	0.491019
$16$	−4.98267	−1.24567
$17$	4.99305	1.21099	0.605496	−	0.795849i	$-0.292975\pi$
$17$	4.99305	1.21099	0.605496	+	0.795849i	$0.292975\pi$
$18$	−1.69362	−0.399191
$19$	−0.972373	−0.223078	−0.111539	−	0.993760i	$-0.535578\pi$
$19$	−0.972373	−0.223078	−0.111539	+	0.993760i	$0.535578\pi$
$20$	1.65136	0.369256
$21$	0	0
$22$	8.79980	1.87612
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.91658	0.391219
$25$	−1.38351	−0.276702
$26$	4.99019	0.978656
$27$	1.00000	0.192450
$28$	0	0
$29$	−4.08053	−0.757736	−0.378868	−	0.925451i	$-0.623687\pi$
$29$	−4.08053	−0.757736	−0.378868	+	0.925451i	$0.623687\pi$
$30$	−3.22078	−0.588030
$31$	−1.11270	−0.199846	−0.0999232	−	0.994995i	$-0.531860\pi$
$31$	−1.11270	−0.199846	−0.0999232	+	0.994995i	$0.531860\pi$
$32$	4.60561	0.814165
$33$	−5.19584	−0.904481
$34$	−8.45633	−1.45025
$35$	0	0
$36$	0.868357	0.144726
$37$	10.5052	1.72705	0.863524	−	0.504308i	$-0.168252\pi$
$37$	10.5052	1.72705	0.863524	+	0.504308i	$0.168252\pi$
$38$	1.64683	0.267152
$39$	−2.94646	−0.471811
$40$	3.64477	0.576288
$41$	3.46973	0.541881	0.270941	−	0.962596i	$-0.412665\pi$
$41$	3.46973	0.541881	0.270941	+	0.962596i	$0.412665\pi$
$42$	0	0
$43$	−7.46270	−1.13805	−0.569026	−	0.822320i	$-0.692679\pi$
$43$	−7.46270	−1.13805	−0.569026	+	0.822320i	$0.692679\pi$
$44$	−4.51185	−0.680187
$45$	1.90171	0.283490
$46$	−1.69362	−0.249711
$47$	−5.28608	−0.771053	−0.385527	−	0.922697i	$-0.625980\pi$
$47$	−5.28608	−0.771053	−0.385527	+	0.922697i	$0.625980\pi$
$48$	−4.98267	−0.719186
$49$	0	0
$50$	2.34314	0.331370
$51$	4.99305	0.699166
$52$	−2.55858	−0.354811
$53$	−9.85547	−1.35375	−0.676876	−	0.736097i	$-0.736667\pi$
$53$	−9.85547	−1.35375	−0.676876	+	0.736097i	$0.736667\pi$
$54$	−1.69362	−0.230473
$55$	−9.88098	−1.33235
$56$	0	0
$57$	−0.972373	−0.128794
$58$	6.91088	0.907443
$59$	−8.88630	−1.15690	−0.578449	−	0.815718i	$-0.696342\pi$
$59$	−8.88630	−1.15690	−0.578449	+	0.815718i	$0.696342\pi$
$60$	1.65136	0.213190
$61$	12.1353	1.55377	0.776884	−	0.629644i	$-0.216799\pi$
$61$	12.1353	1.55377	0.776884	+	0.629644i	$0.216799\pi$
$62$	1.88449	0.239330
$63$	0	0
$64$	2.16517	0.270647
$65$	−5.60330	−0.695004
$66$	8.79980	1.08318
$67$	−11.6894	−1.42808	−0.714042	−	0.700103i	$-0.753138\pi$
$67$	−11.6894	−1.42808	−0.714042	+	0.700103i	$0.753138\pi$
$68$	4.33575	0.525787
$69$	1.00000	0.120386
$70$	0	0
$71$	−5.61748	−0.666672	−0.333336	−	0.942808i	$-0.608174\pi$
$71$	−5.61748	−0.666672	−0.333336	+	0.942808i	$0.608174\pi$
$72$	1.91658	0.225871
$73$	−6.42059	−0.751473	−0.375736	−	0.926727i	$-0.622610\pi$
$73$	−6.42059	−0.751473	−0.375736	+	0.926727i	$0.622610\pi$
$74$	−17.7919	−2.06826
$75$	−1.38351	−0.159754
$76$	−0.844367	−0.0968556
$77$	0	0
$78$	4.99019	0.565028
$79$	−13.4281	−1.51078	−0.755388	−	0.655278i	$-0.772552\pi$
$79$	−13.4281	−1.51078	−0.755388	+	0.655278i	$0.772552\pi$
$80$	−9.47558	−1.05940
$81$	1.00000	0.111111
$82$	−5.87642	−0.648942
$83$	−2.34810	−0.257738	−0.128869	−	0.991662i	$-0.541135\pi$
$83$	−2.34810	−0.257738	−0.128869	+	0.991662i	$0.541135\pi$
$84$	0	0
$85$	9.49531	1.02991
$86$	12.6390	1.36290
$87$	−4.08053	−0.437479
$88$	−9.95823	−1.06155
$89$	16.8503	1.78613	0.893063	−	0.449931i	$-0.148551\pi$
$89$	16.8503	1.78613	0.893063	+	0.449931i	$0.148551\pi$
$90$	−3.22078	−0.339499
$91$	0	0
$92$	0.868357	0.0905325
$93$	−1.11270	−0.115381
$94$	8.95262	0.923392
$95$	−1.84917	−0.189721
$96$	4.60561	0.470058
$97$	−0.186928	−0.0189796	−0.00948981	−	0.999955i	$-0.503021\pi$
$97$	−0.186928	−0.0189796	−0.00948981	+	0.999955i	$0.503021\pi$
$98$	0	0
$99$	−5.19584	−0.522202
$100$	−1.20138	−0.120138
$101$	−10.6547	−1.06018	−0.530090	−	0.847941i	$-0.677842\pi$
$101$	−10.6547	−1.06018	−0.530090	+	0.847941i	$0.677842\pi$
$102$	−8.45633	−0.837302
$103$	0.465380	0.0458552	0.0229276	−	0.999737i	$-0.492701\pi$
$103$	0.465380	0.0458552	0.0229276	+	0.999737i	$0.492701\pi$
$104$	−5.64711	−0.553745
$105$	0	0
$106$	16.6914	1.62122
$107$	−10.0287	−0.969506	−0.484753	−	0.874651i	$-0.661091\pi$
$107$	−10.0287	−0.969506	−0.484753	+	0.874651i	$0.661091\pi$
$108$	0.868357	0.0835577
$109$	4.79512	0.459289	0.229644	−	0.973275i	$-0.426244\pi$
$109$	4.79512	0.459289	0.229644	+	0.973275i	$0.426244\pi$
$110$	16.7346	1.59559
$111$	10.5052	0.997111
$112$	0	0
$113$	−10.3771	−0.976192	−0.488096	−	0.872790i	$-0.662308\pi$
$113$	−10.3771	−0.976192	−0.488096	+	0.872790i	$0.662308\pi$
$114$	1.64683	0.154240
$115$	1.90171	0.177335
$116$	−3.54336	−0.328993
$117$	−2.94646	−0.272400
$118$	15.0500	1.38547
$119$	0	0
$120$	3.64477	0.332720
$121$	15.9968	1.45425
$122$	−20.5526	−1.86075
$123$	3.46973	0.312855
$124$	−0.966219	−0.0867690
$125$	−12.1396	−1.08580
$126$	0	0
$127$	9.90904	0.879285	0.439643	−	0.898173i	$-0.355105\pi$
$127$	9.90904	0.879285	0.439643	+	0.898173i	$0.355105\pi$
$128$	−12.8782	−1.13828
$129$	−7.46270	−0.657054
$130$	9.48988	0.832318
$131$	12.1536	1.06186	0.530931	−	0.847415i	$-0.321842\pi$
$131$	12.1536	1.06186	0.530931	+	0.847415i	$0.321842\pi$
$132$	−4.51185	−0.392706
$133$	0	0
$134$	19.7974	1.71023
$135$	1.90171	0.163673
$136$	9.56955	0.820582
$137$	−8.90189	−0.760540	−0.380270	−	0.924876i	$-0.624169\pi$
$137$	−8.90189	−0.760540	−0.380270	+	0.924876i	$0.624169\pi$
$138$	−1.69362	−0.144171
$139$	10.5377	0.893797	0.446898	−	0.894585i	$-0.352529\pi$
$139$	10.5377	0.893797	0.446898	+	0.894585i	$0.352529\pi$
$140$	0	0
$141$	−5.28608	−0.445168
$142$	9.51389	0.798388
$143$	15.3093	1.28023
$144$	−4.98267	−0.415223
$145$	−7.75998	−0.644431
$146$	10.8740	0.899943
$147$	0	0
$148$	9.12228	0.749847
$149$	−4.08051	−0.334288	−0.167144	−	0.985932i	$-0.553455\pi$
$149$	−4.08051	−0.334288	−0.167144	+	0.985932i	$0.553455\pi$
$150$	2.34314	0.191317
$151$	4.21877	0.343319	0.171659	−	0.985156i	$-0.445087\pi$
$151$	4.21877	0.343319	0.171659	+	0.985156i	$0.445087\pi$
$152$	−1.86363	−0.151160
$153$	4.99305	0.403664
$154$	0	0
$155$	−2.11603	−0.169963
$156$	−2.55858	−0.204850
$157$	−3.79834	−0.303140	−0.151570	−	0.988446i	$-0.548433\pi$
$157$	−3.79834	−0.303140	−0.151570	+	0.988446i	$0.548433\pi$
$158$	22.7421	1.80926
$159$	−9.85547	−0.781589
$160$	8.75853	0.692422
$161$	0	0
$162$	−1.69362	−0.133064
$163$	11.6987	0.916316	0.458158	−	0.888871i	$-0.348509\pi$
$163$	11.6987	0.916316	0.458158	+	0.888871i	$0.348509\pi$
$164$	3.01297	0.235273
$165$	−9.88098	−0.769233
$166$	3.97680	0.308659
$167$	−20.4728	−1.58424	−0.792118	−	0.610368i	$-0.791022\pi$
$167$	−20.4728	−1.58424	−0.792118	+	0.610368i	$0.791022\pi$
$168$	0	0
$169$	−4.31838	−0.332183
$170$	−16.0815	−1.23339
$171$	−0.972373	−0.0743592
$172$	−6.48029	−0.494118
$173$	−9.72081	−0.739059	−0.369530	−	0.929219i	$-0.620481\pi$
$173$	−9.72081	−0.739059	−0.369530	+	0.929219i	$0.620481\pi$
$174$	6.91088	0.523913
$175$	0	0
$176$	25.8892	1.95147
$177$	−8.88630	−0.667935
$178$	−28.5380	−2.13902
$179$	13.6508	1.02031	0.510153	−	0.860083i	$-0.329589\pi$
$179$	13.6508	1.02031	0.510153	+	0.860083i	$0.329589\pi$
$180$	1.65136	0.123085
$181$	−7.87179	−0.585105	−0.292553	−	0.956249i	$-0.594505\pi$
$181$	−7.87179	−0.585105	−0.292553	+	0.956249i	$0.594505\pi$
$182$	0	0
$183$	12.1353	0.897068
$184$	1.91658	0.141292
$185$	19.9779	1.46880
$186$	1.88449	0.138177
$187$	−25.9431	−1.89715
$188$	−4.59020	−0.334775
$189$	0	0
$190$	3.13180	0.227204
$191$	−9.72157	−0.703428	−0.351714	−	0.936107i	$-0.614401\pi$
$191$	−9.72157	−0.703428	−0.351714	+	0.936107i	$0.614401\pi$
$192$	2.16517	0.156258
$193$	4.47765	0.322308	0.161154	−	0.986929i	$-0.448478\pi$
$193$	4.47765	0.322308	0.161154	+	0.986929i	$0.448478\pi$
$194$	0.316585	0.0227295
$195$	−5.60330	−0.401261
$196$	0	0
$197$	14.5141	1.03409	0.517044	−	0.855959i	$-0.327032\pi$
$197$	14.5141	1.03409	0.517044	+	0.855959i	$0.327032\pi$
$198$	8.79980	0.625375
$199$	−12.8859	−0.913457	−0.456729	−	0.889606i	$-0.650979\pi$
$199$	−12.8859	−0.913457	−0.456729	+	0.889606i	$0.650979\pi$
$200$	−2.65160	−0.187496
$201$	−11.6894	−0.824505
$202$	18.0450	1.26964
$203$	0	0
$204$	4.33575	0.303563
$205$	6.59842	0.460853
$206$	−0.788178	−0.0549150
$207$	1.00000	0.0695048
$208$	14.6812	1.01796
$209$	5.05230	0.349475
$210$	0	0
$211$	24.4114	1.68055	0.840275	−	0.542161i	$-0.182394\pi$
$211$	24.4114	1.68055	0.840275	+	0.542161i	$0.182394\pi$
$212$	−8.55807	−0.587770
$213$	−5.61748	−0.384903
$214$	16.9847	1.16105
$215$	−14.1919	−0.967878
$216$	1.91658	0.130406
$217$	0	0
$218$	−8.12112	−0.550032
$219$	−6.42059	−0.433863
$220$	−8.58022	−0.578478
$221$	−14.7118	−0.989623
$222$	−17.7919	−1.19411
$223$	15.6494	1.04796	0.523981	−	0.851730i	$-0.324446\pi$
$223$	15.6494	1.04796	0.523981	+	0.851730i	$0.324446\pi$
$224$	0	0
$225$	−1.38351	−0.0922339
$226$	17.5748	1.16906
$227$	−23.2362	−1.54224	−0.771121	−	0.636689i	$-0.780304\pi$
$227$	−23.2362	−1.54224	−0.771121	+	0.636689i	$0.780304\pi$
$228$	−0.844367	−0.0559196
$229$	6.17107	0.407796	0.203898	−	0.978992i	$-0.434639\pi$
$229$	6.17107	0.407796	0.203898	+	0.978992i	$0.434639\pi$
$230$	−3.22078	−0.212372
$231$	0	0
$232$	−7.82065	−0.513451
$233$	−28.9165	−1.89438	−0.947192	−	0.320668i	$-0.896093\pi$
$233$	−28.9165	−1.89438	−0.947192	+	0.320668i	$0.896093\pi$
$234$	4.99019	0.326219
$235$	−10.0526	−0.655757
$236$	−7.71649	−0.502300
$237$	−13.4281	−0.872247
$238$	0	0
$239$	−10.4386	−0.675218	−0.337609	−	0.941286i	$-0.609618\pi$
$239$	−10.4386	−0.675218	−0.337609	+	0.941286i	$0.609618\pi$
$240$	−9.47558	−0.611646
$241$	−8.95418	−0.576789	−0.288395	−	0.957512i	$-0.593121\pi$
$241$	−8.95418	−0.576789	−0.288395	+	0.957512i	$0.593121\pi$
$242$	−27.0925	−1.74158
$243$	1.00000	0.0641500
$244$	10.5378	0.674613
$245$	0	0
$246$	−5.87642	−0.374667
$247$	2.86506	0.182299
$248$	−2.13257	−0.135418
$249$	−2.34810	−0.148805
$250$	20.5598	1.30032
$251$	−18.5457	−1.17060	−0.585298	−	0.810818i	$-0.699022\pi$
$251$	−18.5457	−1.17060	−0.585298	+	0.810818i	$0.699022\pi$
$252$	0	0
$253$	−5.19584	−0.326660
$254$	−16.7822	−1.05301
$255$	9.49531	0.594620
$256$	17.4805	1.09253
$257$	12.0614	0.752367	0.376183	−	0.926545i	$-0.377236\pi$
$257$	12.0614	0.752367	0.376183	+	0.926545i	$0.377236\pi$
$258$	12.6390	0.786870
$259$	0	0
$260$	−4.86567	−0.301756
$261$	−4.08053	−0.252579
$262$	−20.5836	−1.27166
$263$	22.0116	1.35729	0.678647	−	0.734464i	$-0.262567\pi$
$263$	22.0116	1.35729	0.678647	+	0.734464i	$0.262567\pi$
$264$	−9.95823	−0.612887
$265$	−18.7422	−1.15133
$266$	0	0
$267$	16.8503	1.03122
$268$	−10.1506	−0.620044
$269$	7.09431	0.432548	0.216274	−	0.976333i	$-0.430610\pi$
$269$	7.09431	0.432548	0.216274	+	0.976333i	$0.430610\pi$
$270$	−3.22078	−0.196010
$271$	−29.5516	−1.79513	−0.897566	−	0.440880i	$-0.854666\pi$
$271$	−29.5516	−1.79513	−0.897566	+	0.440880i	$0.854666\pi$
$272$	−24.8787	−1.50849
$273$	0	0
$274$	15.0764	0.910801
$275$	7.18849	0.433482
$276$	0.868357	0.0522690
$277$	−0.496780	−0.0298486	−0.0149243	−	0.999889i	$-0.504751\pi$
$277$	−0.496780	−0.0298486	−0.0149243	+	0.999889i	$0.504751\pi$
$278$	−17.8469	−1.07039
$279$	−1.11270	−0.0666155
$280$	0	0
$281$	−14.9676	−0.892889	−0.446445	−	0.894811i	$-0.647310\pi$
$281$	−14.9676	−0.892889	−0.446445	+	0.894811i	$0.647310\pi$
$282$	8.95262	0.533121
$283$	−18.8407	−1.11997	−0.559983	−	0.828504i	$-0.689192\pi$
$283$	−18.8407	−1.11997	−0.559983	+	0.828504i	$0.689192\pi$
$284$	−4.87798	−0.289455
$285$	−1.84917	−0.109535
$286$	−25.9282	−1.53317
$287$	0	0
$288$	4.60561	0.271388
$289$	7.93051	0.466500
$290$	13.1425	0.771753
$291$	−0.186928	−0.0109579
$292$	−5.57536	−0.326273
$293$	−17.8279	−1.04152	−0.520758	−	0.853704i	$-0.674351\pi$
$293$	−17.8279	−1.04152	−0.520758	+	0.853704i	$0.674351\pi$
$294$	0	0
$295$	−16.8992	−0.983907
$296$	20.1340	1.17027
$297$	−5.19584	−0.301494
$298$	6.91084	0.400334
$299$	−2.94646	−0.170398
$300$	−1.20138	−0.0693617
$301$	0	0
$302$	−7.14500	−0.411149
$303$	−10.6547	−0.612095
$304$	4.84502	0.277881
$305$	23.0778	1.32143
$306$	−8.45633	−0.483416
$307$	15.3588	0.876573	0.438287	−	0.898835i	$-0.355585\pi$
$307$	15.3588	0.876573	0.438287	+	0.898835i	$0.355585\pi$
$308$	0	0
$309$	0.465380	0.0264745
$310$	3.58375	0.203543
$311$	−15.3301	−0.869292	−0.434646	−	0.900601i	$-0.643127\pi$
$311$	−15.3301	−0.869292	−0.434646	+	0.900601i	$0.643127\pi$
$312$	−5.64711	−0.319705
$313$	15.9913	0.903884	0.451942	−	0.892047i	$-0.350731\pi$
$313$	15.9913	0.903884	0.451942	+	0.892047i	$0.350731\pi$
$314$	6.43295	0.363032
$315$	0	0
$316$	−11.6604	−0.655947
$317$	7.07737	0.397505	0.198752	−	0.980050i	$-0.436311\pi$
$317$	7.07737	0.397505	0.198752	+	0.980050i	$0.436311\pi$
$318$	16.6914	0.936010
$319$	21.2018	1.18707
$320$	4.11753	0.230177
$321$	−10.0287	−0.559745
$322$	0	0
$323$	−4.85510	−0.270145
$324$	0.868357	0.0482421
$325$	4.07645	0.226121
$326$	−19.8132	−1.09735
$327$	4.79512	0.265171
$328$	6.65000	0.367185
$329$	0	0
$330$	16.7346	0.921212
$331$	21.4719	1.18020	0.590100	−	0.807330i	$-0.299088\pi$
$331$	21.4719	1.18020	0.590100	+	0.807330i	$0.299088\pi$
$332$	−2.03899	−0.111904
$333$	10.5052	0.575682
$334$	34.6733	1.89724
$335$	−22.2298	−1.21454
$336$	0	0
$337$	26.5780	1.44780	0.723898	−	0.689907i	$-0.242348\pi$
$337$	26.5780	1.44780	0.723898	+	0.689907i	$0.242348\pi$
$338$	7.31371	0.397813
$339$	−10.3771	−0.563605
$340$	8.24532	0.447166
$341$	5.78140	0.313081
$342$	1.64683	0.0890505
$343$	0	0
$344$	−14.3028	−0.771157
$345$	1.90171	0.102385
$346$	16.4634	0.885077
$347$	−16.6754	−0.895182	−0.447591	−	0.894238i	$-0.647718\pi$
$347$	−16.6754	−0.895182	−0.447591	+	0.894238i	$0.647718\pi$
$348$	−3.54336	−0.189944
$349$	−2.76680	−0.148103	−0.0740516	−	0.997254i	$-0.523593\pi$
$349$	−2.76680	−0.148103	−0.0740516	+	0.997254i	$0.523593\pi$
$350$	0	0
$351$	−2.94646	−0.157270
$352$	−23.9300	−1.27548
$353$	25.9848	1.38303	0.691516	−	0.722361i	$-0.256943\pi$
$353$	25.9848	1.38303	0.691516	+	0.722361i	$0.256943\pi$
$354$	15.0500	0.799901
$355$	−10.6828	−0.566984
$356$	14.6321	0.775498
$357$	0	0
$358$	−23.1193	−1.22189
$359$	15.7628	0.831927	0.415963	−	0.909381i	$-0.363444\pi$
$359$	15.7628	0.831927	0.415963	+	0.909381i	$0.363444\pi$
$360$	3.64477	0.192096
$361$	−18.0545	−0.950236
$362$	13.3318	0.700706
$363$	15.9968	0.839614
$364$	0	0
$365$	−12.2101	−0.639105
$366$	−20.5526	−1.07430
$367$	3.93505	0.205408	0.102704	−	0.994712i	$-0.467251\pi$
$367$	3.93505	0.205408	0.102704	+	0.994712i	$0.467251\pi$
$368$	−4.98267	−0.259740
$369$	3.46973	0.180627
$370$	−33.8349	−1.75900
$371$	0	0
$372$	−0.966219	−0.0500961
$373$	−3.65270	−0.189130	−0.0945649	−	0.995519i	$-0.530146\pi$
$373$	−3.65270	−0.189130	−0.0945649	+	0.995519i	$0.530146\pi$
$374$	43.9378	2.27197
$375$	−12.1396	−0.626884
$376$	−10.1312	−0.522475
$377$	12.0231	0.619222
$378$	0	0
$379$	−34.2546	−1.75954	−0.879770	−	0.475400i	$-0.842303\pi$
$379$	−34.2546	−1.75954	−0.879770	+	0.475400i	$0.842303\pi$
$380$	−1.60574	−0.0823727
$381$	9.90904	0.507655
$382$	16.4647	0.842406
$383$	−25.9861	−1.32783	−0.663914	−	0.747809i	$-0.731106\pi$
$383$	−25.9861	−1.32783	−0.663914	+	0.747809i	$0.731106\pi$
$384$	−12.8782	−0.657188
$385$	0	0
$386$	−7.58344	−0.385987
$387$	−7.46270	−0.379350
$388$	−0.162320	−0.00824055
$389$	24.6144	1.24800	0.623999	−	0.781425i	$-0.285507\pi$
$389$	24.6144	1.24800	0.623999	+	0.781425i	$0.285507\pi$
$390$	9.48988	0.480539
$391$	4.99305	0.252509
$392$	0	0
$393$	12.1536	0.613067
$394$	−24.5814	−1.23840
$395$	−25.5363	−1.28487
$396$	−4.51185	−0.226729
$397$	−26.0025	−1.30503	−0.652513	−	0.757778i	$-0.726285\pi$
$397$	−26.0025	−1.30503	−0.652513	+	0.757778i	$0.726285\pi$
$398$	21.8238	1.09393
$399$	0	0
$400$	6.89356	0.344678
$401$	−8.33991	−0.416475	−0.208238	−	0.978078i	$-0.566773\pi$
$401$	−8.33991	−0.416475	−0.208238	+	0.978078i	$0.566773\pi$
$402$	19.7974	0.987404
$403$	3.27852	0.163315
$404$	−9.25207	−0.460308
$405$	1.90171	0.0944966
$406$	0	0
$407$	−54.5835	−2.70560
$408$	9.56955	0.473763
$409$	−20.5156	−1.01443	−0.507215	−	0.861819i	$-0.669325\pi$
$409$	−20.5156	−1.01443	−0.507215	+	0.861819i	$0.669325\pi$
$410$	−11.1752	−0.551905
$411$	−8.90189	−0.439098
$412$	0.404116	0.0199094
$413$	0	0
$414$	−1.69362	−0.0832370
$415$	−4.46540	−0.219198
$416$	−13.5702	−0.665336
$417$	10.5377	0.516034
$418$	−8.55669	−0.418521
$419$	−22.4880	−1.09861	−0.549306	−	0.835621i	$-0.685108\pi$
$419$	−22.4880	−1.09861	−0.549306	+	0.835621i	$0.685108\pi$
$420$	0	0
$421$	25.5421	1.24485	0.622423	−	0.782681i	$-0.286148\pi$
$421$	25.5421	1.24485	0.622423	+	0.782681i	$0.286148\pi$
$422$	−41.3437	−2.01258
$423$	−5.28608	−0.257018
$424$	−18.8887	−0.917319
$425$	−6.90792	−0.335083
$426$	9.51389	0.460949
$427$	0	0
$428$	−8.70845	−0.420939
$429$	15.3093	0.739142
$430$	24.0357	1.15910
$431$	−2.00865	−0.0967534	−0.0483767	−	0.998829i	$-0.515405\pi$
$431$	−2.00865	−0.0967534	−0.0483767	+	0.998829i	$0.515405\pi$
$432$	−4.98267	−0.239729
$433$	17.3084	0.831789	0.415895	−	0.909413i	$-0.363468\pi$
$433$	17.3084	0.831789	0.415895	+	0.909413i	$0.363468\pi$
$434$	0	0
$435$	−7.75998	−0.372063
$436$	4.16387	0.199413
$437$	−0.972373	−0.0465149
$438$	10.8740	0.519582
$439$	−28.3529	−1.35321	−0.676605	−	0.736347i	$-0.736549\pi$
$439$	−28.3529	−1.35321	−0.676605	+	0.736347i	$0.736549\pi$
$440$	−18.9376	−0.902817
$441$	0	0
$442$	24.9162	1.18514
$443$	−16.7707	−0.796801	−0.398400	−	0.917212i	$-0.630434\pi$
$443$	−16.7707	−0.796801	−0.398400	+	0.917212i	$0.630434\pi$
$444$	9.12228	0.432924
$445$	32.0443	1.51905
$446$	−26.5042	−1.25501
$447$	−4.08051	−0.193001
$448$	0	0
$449$	27.2126	1.28424	0.642122	−	0.766603i	$-0.278054\pi$
$449$	27.2126	1.28424	0.642122	+	0.766603i	$0.278054\pi$
$450$	2.34314	0.110457
$451$	−18.0282	−0.848914
$452$	−9.01100	−0.423842
$453$	4.21877	0.198215
$454$	39.3534	1.84695
$455$	0	0
$456$	−1.86363	−0.0872723
$457$	−36.8466	−1.72361	−0.861806	−	0.507238i	$-0.830666\pi$
$457$	−36.8466	−1.72361	−0.861806	+	0.507238i	$0.830666\pi$
$458$	−10.4515	−0.488365
$459$	4.99305	0.233055
$460$	1.65136	0.0769951
$461$	−31.3335	−1.45935	−0.729674	−	0.683795i	$-0.760328\pi$
$461$	−31.3335	−1.45935	−0.729674	+	0.683795i	$0.760328\pi$
$462$	0	0
$463$	9.25130	0.429944	0.214972	−	0.976620i	$-0.431034\pi$
$463$	9.25130	0.429944	0.214972	+	0.976620i	$0.431034\pi$
$464$	20.3319	0.943887
$465$	−2.11603	−0.0981283
$466$	48.9737	2.26866
$467$	6.10335	0.282429	0.141215	−	0.989979i	$-0.454899\pi$
$467$	6.10335	0.282429	0.141215	+	0.989979i	$0.454899\pi$
$468$	−2.55858	−0.118270
$469$	0	0
$470$	17.0253	0.785317
$471$	−3.79834	−0.175018
$472$	−17.0313	−0.783928
$473$	38.7750	1.78288
$474$	22.7421	1.04458
$475$	1.34529	0.0617260
$476$	0	0
$477$	−9.85547	−0.451251
$478$	17.6791	0.808623
$479$	17.6356	0.805789	0.402895	−	0.915246i	$-0.368004\pi$
$479$	17.6356	0.805789	0.402895	+	0.915246i	$0.368004\pi$
$480$	8.75853	0.399770
$481$	−30.9532	−1.41134
$482$	15.1650	0.690747
$483$	0	0
$484$	13.8909	0.631406
$485$	−0.355482	−0.0161416
$486$	−1.69362	−0.0768243
$487$	17.1504	0.777157	0.388578	−	0.921416i	$-0.372966\pi$
$487$	17.1504	0.777157	0.388578	+	0.921416i	$0.372966\pi$
$488$	23.2582	1.05285
$489$	11.6987	0.529035
$490$	0	0
$491$	−30.0822	−1.35759	−0.678796	−	0.734327i	$-0.737498\pi$
$491$	−30.0822	−1.35759	−0.678796	+	0.734327i	$0.737498\pi$
$492$	3.01297	0.135835
$493$	−20.3743	−0.917612
$494$	−4.85233	−0.218316
$495$	−9.88098	−0.444117
$496$	5.54420	0.248942
$497$	0	0
$498$	3.97680	0.178205
$499$	37.1111	1.66132	0.830660	−	0.556780i	$-0.187963\pi$
$499$	37.1111	1.66132	0.830660	+	0.556780i	$0.187963\pi$
$500$	−10.5415	−0.471429
$501$	−20.4728	−0.914659
$502$	31.4095	1.40187
$503$	25.1231	1.12019	0.560093	−	0.828430i	$-0.310765\pi$
$503$	25.1231	1.12019	0.560093	+	0.828430i	$0.310765\pi$
$504$	0	0
$505$	−20.2621	−0.901651
$506$	8.79980	0.391199
$507$	−4.31838	−0.191786
$508$	8.60459	0.381767
$509$	−39.6721	−1.75843	−0.879217	−	0.476422i	$-0.841934\pi$
$509$	−39.6721	−1.75843	−0.879217	+	0.476422i	$0.841934\pi$
$510$	−16.0815	−0.712100
$511$	0	0
$512$	−3.84891	−0.170100
$513$	−0.972373	−0.0429313
$514$	−20.4274	−0.901013
$515$	0.885017	0.0389985
$516$	−6.48029	−0.285279
$517$	27.4656	1.20794
$518$	0	0
$519$	−9.72081	−0.426696
$520$	−10.7392	−0.470943
$521$	−24.9437	−1.09280	−0.546401	−	0.837523i	$-0.684003\pi$
$521$	−24.9437	−1.09280	−0.546401	+	0.837523i	$0.684003\pi$
$522$	6.91088	0.302481
$523$	9.63660	0.421379	0.210690	−	0.977553i	$-0.432429\pi$
$523$	9.63660	0.421379	0.210690	+	0.977553i	$0.432429\pi$
$524$	10.5536	0.461038
$525$	0	0
$526$	−37.2794	−1.62546
$527$	−5.55575	−0.242012
$528$	25.8892	1.12668
$529$	1.00000	0.0434783
$530$	31.7422	1.37879
$531$	−8.88630	−0.385633
$532$	0	0
$533$	−10.2234	−0.442826
$534$	−28.5380	−1.23496
$535$	−19.0716	−0.824535
$536$	−22.4036	−0.967687
$537$	13.6508	0.589074
$538$	−12.0151	−0.518007
$539$	0	0
$540$	1.65136	0.0710633
$541$	2.30404	0.0990586	0.0495293	−	0.998773i	$-0.484228\pi$
$541$	2.30404	0.0990586	0.0495293	+	0.998773i	$0.484228\pi$
$542$	50.0493	2.14980
$543$	−7.87179	−0.337811
$544$	22.9960	0.985947
$545$	9.11891	0.390611
$546$	0	0
$547$	−2.41845	−0.103405	−0.0517027	−	0.998663i	$-0.516465\pi$
$547$	−2.41845	−0.103405	−0.0517027	+	0.998663i	$0.516465\pi$
$548$	−7.73002	−0.330210
$549$	12.1353	0.517922
$550$	−12.1746	−0.519126
$551$	3.96780	0.169034
$552$	1.91658	0.0815749
$553$	0	0
$554$	0.841358	0.0357459
$555$	19.9779	0.848013
$556$	9.15050	0.388068
$557$	−12.4494	−0.527499	−0.263749	−	0.964591i	$-0.584959\pi$
$557$	−12.4494	−0.527499	−0.263749	+	0.964591i	$0.584959\pi$
$558$	1.88449	0.0797768
$559$	21.9885	0.930016
$560$	0	0
$561$	−25.9431	−1.09532
$562$	25.3494	1.06930
$563$	−41.3442	−1.74245	−0.871225	−	0.490883i	$-0.836674\pi$
$563$	−41.3442	−1.74245	−0.871225	+	0.490883i	$0.836674\pi$
$564$	−4.59020	−0.193282
$565$	−19.7341	−0.830221
$566$	31.9091	1.34124
$567$	0	0
$568$	−10.7663	−0.451745
$569$	31.6283	1.32593	0.662963	−	0.748652i	$-0.269299\pi$
$569$	31.6283	1.32593	0.662963	+	0.748652i	$0.269299\pi$
$570$	3.13180	0.131176
$571$	−9.82445	−0.411140	−0.205570	−	0.978642i	$-0.565905\pi$
$571$	−9.82445	−0.411140	−0.205570	+	0.978642i	$0.565905\pi$
$572$	13.2940	0.555849
$573$	−9.72157	−0.406124
$574$	0	0
$575$	−1.38351	−0.0576963
$576$	2.16517	0.0902156
$577$	27.8147	1.15794	0.578971	−	0.815348i	$-0.303454\pi$
$577$	27.8147	1.15794	0.578971	+	0.815348i	$0.303454\pi$
$578$	−13.4313	−0.558668
$579$	4.47765	0.186085
$580$	−6.73844	−0.279798
$581$	0	0
$582$	0.316585	0.0131229
$583$	51.2075	2.12080
$584$	−12.3055	−0.509207
$585$	−5.60330	−0.231668
$586$	30.1937	1.24729
$587$	−3.18082	−0.131287	−0.0656433	−	0.997843i	$-0.520910\pi$
$587$	−3.18082	−0.131287	−0.0656433	+	0.997843i	$0.520910\pi$
$588$	0	0
$589$	1.08196	0.0445813
$590$	28.6208	1.17830
$591$	14.5141	0.597031
$592$	−52.3440	−2.15133
$593$	−17.7237	−0.727823	−0.363912	−	0.931433i	$-0.618559\pi$
$593$	−17.7237	−0.727823	−0.363912	+	0.931433i	$0.618559\pi$
$594$	8.79980	0.361060
$595$	0	0
$596$	−3.54334	−0.145141
$597$	−12.8859	−0.527385
$598$	4.99019	0.204064
$599$	8.59634	0.351237	0.175618	−	0.984458i	$-0.443808\pi$
$599$	8.59634	0.351237	0.175618	+	0.984458i	$0.443808\pi$
$600$	−2.65160	−0.108251
$601$	−28.1962	−1.15015	−0.575074	−	0.818102i	$-0.695027\pi$
$601$	−28.1962	−1.15015	−0.575074	+	0.818102i	$0.695027\pi$
$602$	0	0
$603$	−11.6894	−0.476028
$604$	3.66340	0.149062
$605$	30.4212	1.23680
$606$	18.0450	0.733028
$607$	14.5851	0.591991	0.295995	−	0.955189i	$-0.404349\pi$
$607$	14.5851	0.591991	0.295995	+	0.955189i	$0.404349\pi$
$608$	−4.47837	−0.181622
$609$	0	0
$610$	−39.0851	−1.58251
$611$	15.5752	0.630105
$612$	4.33575	0.175262
$613$	6.82679	0.275731	0.137866	−	0.990451i	$-0.455976\pi$
$613$	6.82679	0.275731	0.137866	+	0.990451i	$0.455976\pi$
$614$	−26.0120	−1.04976
$615$	6.59842	0.266074
$616$	0	0
$617$	8.67020	0.349049	0.174525	−	0.984653i	$-0.444161\pi$
$617$	8.67020	0.349049	0.174525	+	0.984653i	$0.444161\pi$
$618$	−0.788178	−0.0317052
$619$	7.75045	0.311517	0.155758	−	0.987795i	$-0.450218\pi$
$619$	7.75045	0.311517	0.155758	+	0.987795i	$0.450218\pi$
$620$	−1.83747	−0.0737944
$621$	1.00000	0.0401286
$622$	25.9635	1.04104
$623$	0	0
$624$	14.6812	0.587720
$625$	−16.1684	−0.646735
$626$	−27.0833	−1.08247
$627$	5.05230	0.201769
$628$	−3.29831	−0.131617
$629$	52.4530	2.09144
$630$	0	0
$631$	5.67442	0.225895	0.112948	−	0.993601i	$-0.463971\pi$
$631$	5.67442	0.225895	0.112948	+	0.993601i	$0.463971\pi$
$632$	−25.7359	−1.02372
$633$	24.4114	0.970266
$634$	−11.9864	−0.476040
$635$	18.8441	0.747805
$636$	−8.55807	−0.339349
$637$	0	0
$638$	−35.9079	−1.42161
$639$	−5.61748	−0.222224
$640$	−24.4906	−0.968076
$641$	26.8867	1.06196	0.530981	−	0.847384i	$-0.321824\pi$
$641$	26.8867	1.06196	0.530981	+	0.847384i	$0.321824\pi$
$642$	16.9847	0.670335
$643$	39.0113	1.53845	0.769227	−	0.638975i	$-0.220641\pi$
$643$	39.0113	1.53845	0.769227	+	0.638975i	$0.220641\pi$
$644$	0	0
$645$	−14.1919	−0.558805
$646$	8.22271	0.323518
$647$	39.1836	1.54046	0.770232	−	0.637763i	$-0.220140\pi$
$647$	39.1836	1.54046	0.770232	+	0.637763i	$0.220140\pi$
$648$	1.91658	0.0752902
$649$	46.1719	1.81240
$650$	−6.90396	−0.270796
$651$	0	0
$652$	10.1587	0.397845
$653$	−26.5119	−1.03749	−0.518745	−	0.854929i	$-0.673601\pi$
$653$	−26.5119	−1.03749	−0.518745	+	0.854929i	$0.673601\pi$
$654$	−8.12112	−0.317561
$655$	23.1125	0.903082
$656$	−17.2885	−0.675004
$657$	−6.42059	−0.250491
$658$	0	0
$659$	−24.5554	−0.956542	−0.478271	−	0.878212i	$-0.658736\pi$
$659$	−24.5554	−0.956542	−0.478271	+	0.878212i	$0.658736\pi$
$660$	−8.58022	−0.333985
$661$	−15.3757	−0.598044	−0.299022	−	0.954246i	$-0.596660\pi$
$661$	−15.3757	−0.598044	−0.299022	+	0.954246i	$0.596660\pi$
$662$	−36.3652	−1.41337
$663$	−14.7118	−0.571359
$664$	−4.50032	−0.174646
$665$	0	0
$666$	−17.7919	−0.689421
$667$	−4.08053	−0.157999
$668$	−17.7777	−0.687842
$669$	15.6494	0.605042
$670$	37.6488	1.45450
$671$	−63.0532	−2.43414
$672$	0	0
$673$	−32.8849	−1.26762	−0.633810	−	0.773489i	$-0.718510\pi$
$673$	−32.8849	−1.26762	−0.633810	+	0.773489i	$0.718510\pi$
$674$	−45.0131	−1.73384
$675$	−1.38351	−0.0532512
$676$	−3.74990	−0.144227
$677$	−2.88723	−0.110965	−0.0554826	−	0.998460i	$-0.517670\pi$
$677$	−2.88723	−0.110965	−0.0554826	+	0.998460i	$0.517670\pi$
$678$	17.5748	0.674957
$679$	0	0
$680$	18.1985	0.697880
$681$	−23.2362	−0.890414
$682$	−9.79152	−0.374937
$683$	28.6477	1.09617	0.548087	−	0.836421i	$-0.315356\pi$
$683$	28.6477	1.09617	0.548087	+	0.836421i	$0.315356\pi$
$684$	−0.844367	−0.0322852
$685$	−16.9288	−0.646816
$686$	0	0
$687$	6.17107	0.235441
$688$	37.1842	1.41763
$689$	29.0387	1.10629
$690$	−3.22078	−0.122613
$691$	0.505968	0.0192479	0.00962396	−	0.999954i	$-0.496937\pi$
$691$	0.505968	0.0192479	0.00962396	+	0.999954i	$0.496937\pi$
$692$	−8.44113	−0.320884
$693$	0	0
$694$	28.2418	1.07204
$695$	20.0396	0.760147
$696$	−7.82065	−0.296441
$697$	17.3245	0.656213
$698$	4.68591	0.177364
$699$	−28.9165	−1.09372
$700$	0	0
$701$	−10.2064	−0.385490	−0.192745	−	0.981249i	$-0.561739\pi$
$701$	−10.2064	−0.385490	−0.192745	+	0.981249i	$0.561739\pi$
$702$	4.99019	0.188343
$703$	−10.2150	−0.385266
$704$	−11.2499	−0.423997
$705$	−10.0526	−0.378602
$706$	−44.0085	−1.65628
$707$	0	0
$708$	−7.71649	−0.290003
$709$	−18.8161	−0.706654	−0.353327	−	0.935500i	$-0.614950\pi$
$709$	−18.8161	−0.706654	−0.353327	+	0.935500i	$0.614950\pi$
$710$	18.0926	0.679004
$711$	−13.4281	−0.503592
$712$	32.2948	1.21030
$713$	−1.11270	−0.0416709
$714$	0	0
$715$	29.1139	1.08880
$716$	11.8537	0.442995
$717$	−10.4386	−0.389837
$718$	−26.6962	−0.996292
$719$	36.9800	1.37912	0.689560	−	0.724229i	$-0.257804\pi$
$719$	36.9800	1.37912	0.689560	+	0.724229i	$0.257804\pi$
$720$	−9.47558	−0.353134
$721$	0	0
$722$	30.5775	1.13798
$723$	−8.95418	−0.333009
$724$	−6.83552	−0.254040
$725$	5.64545	0.209667
$726$	−27.0925	−1.00550
$727$	−0.558330	−0.0207073	−0.0103537	−	0.999946i	$-0.503296\pi$
$727$	−0.558330	−0.0207073	−0.0103537	+	0.999946i	$0.503296\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	20.6793	0.765374
$731$	−37.2616	−1.37817
$732$	10.5378	0.389488
$733$	−1.85664	−0.0685767	−0.0342883	−	0.999412i	$-0.510916\pi$
$733$	−1.85664	−0.0685767	−0.0342883	+	0.999412i	$0.510916\pi$
$734$	−6.66449	−0.245991
$735$	0	0
$736$	4.60561	0.169765
$737$	60.7362	2.23725
$738$	−5.87642	−0.216314
$739$	−27.4787	−1.01082	−0.505411	−	0.862879i	$-0.668659\pi$
$739$	−27.4787	−1.01082	−0.505411	+	0.862879i	$0.668659\pi$
$740$	17.3479	0.637722
$741$	2.86506	0.105251
$742$	0	0
$743$	34.8604	1.27890	0.639452	−	0.768831i	$-0.279161\pi$
$743$	34.8604	1.27890	0.639452	+	0.768831i	$0.279161\pi$
$744$	−2.13257	−0.0781838
$745$	−7.75993	−0.284302
$746$	6.18630	0.226497
$747$	−2.34810	−0.0859126
$748$	−22.5279	−0.823701
$749$	0	0
$750$	20.5598	0.750739
$751$	35.4481	1.29352	0.646760	−	0.762694i	$-0.276124\pi$
$751$	35.4481	1.29352	0.646760	+	0.762694i	$0.276124\pi$
$752$	26.3388	0.960476
$753$	−18.5457	−0.675844
$754$	−20.3626	−0.741563
$755$	8.02287	0.291982
$756$	0	0
$757$	25.8595	0.939880	0.469940	−	0.882698i	$-0.344276\pi$
$757$	25.8595	0.939880	0.469940	+	0.882698i	$0.344276\pi$
$758$	58.0143	2.10717
$759$	−5.19584	−0.188597
$760$	−3.54407	−0.128557
$761$	27.4123	0.993696	0.496848	−	0.867838i	$-0.334491\pi$
$761$	27.4123	0.993696	0.496848	+	0.867838i	$0.334491\pi$
$762$	−16.7822	−0.607954
$763$	0	0
$764$	−8.44180	−0.305413
$765$	9.49531	0.343304
$766$	44.0107	1.59017
$767$	26.1831	0.945418
$768$	17.4805	0.630772
$769$	48.6444	1.75416	0.877080	−	0.480344i	$-0.159488\pi$
$769$	48.6444	1.75416	0.877080	+	0.480344i	$0.159488\pi$
$770$	0	0
$771$	12.0614	0.434379
$772$	3.88820	0.139939
$773$	−1.82539	−0.0656546	−0.0328273	−	0.999461i	$-0.510451\pi$
$773$	−1.82539	−0.0656546	−0.0328273	+	0.999461i	$0.510451\pi$
$774$	12.6390	0.454299
$775$	1.53943	0.0552978
$776$	−0.358261	−0.0128608
$777$	0	0
$778$	−41.6875	−1.49457
$779$	−3.37388	−0.120882
$780$	−4.86567	−0.174219
$781$	29.1875	1.04441
$782$	−8.45633	−0.302398
$783$	−4.08053	−0.145826
$784$	0	0
$785$	−7.22333	−0.257812
$786$	−20.5836	−0.734191
$787$	10.3898	0.370357	0.185179	−	0.982705i	$-0.440714\pi$
$787$	10.3898	0.370357	0.185179	+	0.982705i	$0.440714\pi$
$788$	12.6034	0.448979
$789$	22.0116	0.783634
$790$	43.2488	1.53872
$791$	0	0
$792$	−9.95823	−0.353850
$793$	−35.7562	−1.26974
$794$	44.0383	1.56286
$795$	−18.7422	−0.664718
$796$	−11.1896	−0.396604
$797$	−8.95073	−0.317051	−0.158526	−	0.987355i	$-0.550674\pi$
$797$	−8.95073	−0.317051	−0.158526	+	0.987355i	$0.550674\pi$
$798$	0	0
$799$	−26.3936	−0.933739
$800$	−6.37190	−0.225281
$801$	16.8503	0.595376
$802$	14.1247	0.498759
$803$	33.3604	1.17726
$804$	−10.1506	−0.357982
$805$	0	0
$806$	−5.55257	−0.195581
$807$	7.09431	0.249732
$808$	−20.4205	−0.718390
$809$	0.998542	0.0351069	0.0175534	−	0.999846i	$-0.494412\pi$
$809$	0.998542	0.0351069	0.0175534	+	0.999846i	$0.494412\pi$
$810$	−3.22078	−0.113166
$811$	32.4486	1.13942	0.569712	−	0.821845i	$-0.307055\pi$
$811$	32.4486	1.13942	0.569712	+	0.821845i	$0.307055\pi$
$812$	0	0
$813$	−29.5516	−1.03642
$814$	92.4438	3.24015
$815$	22.2476	0.779299
$816$	−24.8787	−0.870929
$817$	7.25653	0.253874
$818$	34.7457	1.21485
$819$	0	0
$820$	5.72978	0.200093
$821$	18.2443	0.636731	0.318365	−	0.947968i	$-0.396866\pi$
$821$	18.2443	0.636731	0.318365	+	0.947968i	$0.396866\pi$
$822$	15.0764	0.525851
$823$	−20.3585	−0.709651	−0.354826	−	0.934932i	$-0.615460\pi$
$823$	−20.3585	−0.709651	−0.354826	+	0.934932i	$0.615460\pi$
$824$	0.891936	0.0310721
$825$	7.18849	0.250271
$826$	0	0
$827$	−0.478461	−0.0166377	−0.00831887	−	0.999965i	$-0.502648\pi$
$827$	−0.478461	−0.0166377	−0.00831887	+	0.999965i	$0.502648\pi$
$828$	0.868357	0.0301775
$829$	54.0091	1.87581	0.937907	−	0.346886i	$-0.112761\pi$
$829$	54.0091	1.87581	0.937907	+	0.346886i	$0.112761\pi$
$830$	7.56271	0.262505
$831$	−0.496780	−0.0172331
$832$	−6.37959	−0.221173
$833$	0	0
$834$	−17.8469	−0.617988
$835$	−38.9334	−1.34734
$836$	4.38720	0.151735
$837$	−1.11270	−0.0384605
$838$	38.0862	1.31567
$839$	−27.6204	−0.953561	−0.476781	−	0.879022i	$-0.658196\pi$
$839$	−27.6204	−0.953561	−0.476781	+	0.879022i	$0.658196\pi$
$840$	0	0
$841$	−12.3493	−0.425836
$842$	−43.2587	−1.49079
$843$	−14.9676	−0.515510
$844$	21.1978	0.729659
$845$	−8.21230	−0.282512
$846$	8.95262	0.307797
$847$	0	0
$848$	49.1065	1.68633
$849$	−18.8407	−0.646612
$850$	11.6994	0.401286
$851$	10.5052	0.360114
$852$	−4.87798	−0.167117
$853$	23.2019	0.794417	0.397208	−	0.917728i	$-0.369979\pi$
$853$	23.2019	0.794417	0.397208	+	0.917728i	$0.369979\pi$
$854$	0	0
$855$	−1.84917	−0.0632403
$856$	−19.2207	−0.656949
$857$	44.7312	1.52799	0.763994	−	0.645223i	$-0.223236\pi$
$857$	44.7312	1.52799	0.763994	+	0.645223i	$0.223236\pi$
$858$	−25.9282	−0.885176
$859$	−19.4291	−0.662912	−0.331456	−	0.943471i	$-0.607540\pi$
$859$	−19.4291	−0.662912	−0.331456	+	0.943471i	$0.607540\pi$
$860$	−12.3236	−0.420232
$861$	0	0
$862$	3.40190	0.115869
$863$	47.1171	1.60389	0.801943	−	0.597401i	$-0.203800\pi$
$863$	47.1171	1.60389	0.801943	+	0.597401i	$0.203800\pi$
$864$	4.60561	0.156686
$865$	−18.4861	−0.628547
$866$	−29.3139	−0.996128
$867$	7.93051	0.269334
$868$	0	0
$869$	69.7702	2.36679
$870$	13.1425	0.445572
$871$	34.4423	1.16703
$872$	9.19020	0.311220
$873$	−0.186928	−0.00632654
$874$	1.64683	0.0557050
$875$	0	0
$876$	−5.57536	−0.188374
$877$	−17.1776	−0.580045	−0.290022	−	0.957020i	$-0.593663\pi$
$877$	−17.1776	−0.580045	−0.290022	+	0.957020i	$0.593663\pi$
$878$	48.0191	1.62057
$879$	−17.8279	−0.601319
$880$	49.2337	1.65967
$881$	47.0373	1.58473	0.792363	−	0.610050i	$-0.208851\pi$
$881$	47.0373	1.58473	0.792363	+	0.610050i	$0.208851\pi$
$882$	0	0
$883$	−6.48831	−0.218349	−0.109174	−	0.994023i	$-0.534821\pi$
$883$	−6.48831	−0.218349	−0.109174	+	0.994023i	$0.534821\pi$
$884$	−12.7751	−0.429673
$885$	−16.8992	−0.568059
$886$	28.4033	0.954226
$887$	1.31706	0.0442227	0.0221114	−	0.999756i	$-0.492961\pi$
$887$	1.31706	0.0442227	0.0221114	+	0.999756i	$0.492961\pi$
$888$	20.1340	0.675654
$889$	0	0
$890$	−54.2710	−1.81917
$891$	−5.19584	−0.174067
$892$	13.5893	0.455003
$893$	5.14004	0.172005
$894$	6.91084	0.231133
$895$	25.9598	0.867740
$896$	0	0
$897$	−2.94646	−0.0983794
$898$	−46.0879	−1.53797
$899$	4.54040	0.151431
$900$	−1.20138	−0.0400460
$901$	−49.2088	−1.63938
$902$	30.5330	1.01664
$903$	0	0
$904$	−19.8884	−0.661479
$905$	−14.9698	−0.497614
$906$	−7.14500	−0.237377
$907$	20.5509	0.682383	0.341191	−	0.939994i	$-0.389170\pi$
$907$	20.5509	0.682383	0.341191	+	0.939994i	$0.389170\pi$
$908$	−20.1773	−0.669608
$909$	−10.6547	−0.353393
$910$	0	0
$911$	46.7249	1.54807	0.774033	−	0.633146i	$-0.218237\pi$
$911$	46.7249	1.54807	0.774033	+	0.633146i	$0.218237\pi$
$912$	4.84502	0.160434
$913$	12.2004	0.403774
$914$	62.4042	2.06415
$915$	23.0778	0.762929
$916$	5.35870	0.177056
$917$	0	0
$918$	−8.45633	−0.279101
$919$	41.6216	1.37297	0.686485	−	0.727144i	$-0.259153\pi$
$919$	41.6216	1.37297	0.686485	+	0.727144i	$0.259153\pi$
$920$	3.64477	0.120164
$921$	15.3588	0.506090
$922$	53.0672	1.74767
$923$	16.5517	0.544805
$924$	0	0
$925$	−14.5341	−0.477877
$926$	−15.6682	−0.514889
$927$	0.465380	0.0152851
$928$	−18.7933	−0.616922
$929$	36.2714	1.19003	0.595013	−	0.803716i	$-0.297147\pi$
$929$	36.2714	1.19003	0.595013	+	0.803716i	$0.297147\pi$
$930$	3.58375	0.117516
$931$	0	0
$932$	−25.1099	−0.822501
$933$	−15.3301	−0.501886
$934$	−10.3368	−0.338230
$935$	−49.3362	−1.61347
$936$	−5.64711	−0.184582
$937$	14.4741	0.472849	0.236425	−	0.971650i	$-0.424024\pi$
$937$	14.4741	0.472849	0.236425	+	0.971650i	$0.424024\pi$
$938$	0	0
$939$	15.9913	0.521857
$940$	−8.72922	−0.284716
$941$	45.7845	1.49253	0.746266	−	0.665648i	$-0.231845\pi$
$941$	45.7845	1.49253	0.746266	+	0.665648i	$0.231845\pi$
$942$	6.43295	0.209597
$943$	3.46973	0.112990
$944$	44.2775	1.44111
$945$	0	0
$946$	−65.6703	−2.13512
$947$	−34.2874	−1.11419	−0.557095	−	0.830449i	$-0.688084\pi$
$947$	−34.2874	−1.11419	−0.557095	+	0.830449i	$0.688084\pi$
$948$	−11.6604	−0.378711
$949$	18.9180	0.614104
$950$	−2.27841	−0.0739213
$951$	7.07737	0.229499
$952$	0	0
$953$	44.6891	1.44762	0.723811	−	0.689999i	$-0.242389\pi$
$953$	44.6891	1.44762	0.723811	+	0.689999i	$0.242389\pi$
$954$	16.6914	0.540405
$955$	−18.4876	−0.598244
$956$	−9.06445	−0.293165
$957$	21.2018	0.685357
$958$	−29.8680	−0.964991
$959$	0	0
$960$	4.11753	0.132893
$961$	−29.7619	−0.960061
$962$	52.4230	1.69019
$963$	−10.0287	−0.323169
$964$	−7.77542	−0.250430
$965$	8.51518	0.274113
$966$	0	0
$967$	−7.14675	−0.229824	−0.114912	−	0.993376i	$-0.536659\pi$
$967$	−7.14675	−0.229824	−0.114912	+	0.993376i	$0.536659\pi$
$968$	30.6591	0.985420
$969$	−4.85510	−0.155968
$970$	0.602052	0.0193307
$971$	−37.5916	−1.20637	−0.603185	−	0.797601i	$-0.706102\pi$
$971$	−37.5916	−1.20637	−0.603185	+	0.797601i	$0.706102\pi$
$972$	0.868357	0.0278526
$973$	0	0
$974$	−29.0462	−0.930701
$975$	4.07645	0.130551
$976$	−60.4662	−1.93548
$977$	−2.46153	−0.0787514	−0.0393757	−	0.999224i	$-0.512537\pi$
$977$	−2.46153	−0.0787514	−0.0393757	+	0.999224i	$0.512537\pi$
$978$	−19.8132	−0.633558
$979$	−87.5515	−2.79816
$980$	0	0
$981$	4.79512	0.153096
$982$	50.9479	1.62581
$983$	33.6240	1.07244	0.536219	−	0.844079i	$-0.319852\pi$
$983$	33.6240	1.07244	0.536219	+	0.844079i	$0.319852\pi$
$984$	6.65000	0.211994
$985$	27.6016	0.879461
$986$	34.5063	1.09891
$987$	0	0
$988$	2.48789	0.0791504
$989$	−7.46270	−0.237300
$990$	16.7346	0.531862
$991$	−59.6497	−1.89484	−0.947418	−	0.319998i	$-0.896318\pi$
$991$	−59.6497	−1.89484	−0.947418	+	0.319998i	$0.896318\pi$
$992$	−5.12465	−0.162708
$993$	21.4719	0.681389
$994$	0	0
$995$	−24.5052	−0.776867
$996$	−2.03899	−0.0646079
$997$	50.8306	1.60982	0.804910	−	0.593396i	$-0.202213\pi$
$997$	50.8306	1.60982	0.804910	+	0.593396i	$0.202213\pi$
$998$	−62.8521	−1.98955
$999$	10.5052	0.332370

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bh.1.4	yes	10
7.6	odd	2		3381.2.a.bg.1.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.bg.1.4	✓	10	7.6	odd	2
3381.2.a.bh.1.4	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q-1.69362 q^{2} +1.00000 q^{3} +0.868357 q^{4} +1.90171 q^{5} -1.69362 q^{6} +1.91658 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.69362 q^{2} +1.00000 q^{3} +0.868357 q^{4} +1.90171 q^{5} -1.69362 q^{6} +1.91658 q^{8} +1.00000 q^{9} -3.22078 q^{10} -5.19584 q^{11} +0.868357 q^{12} -2.94646 q^{13} +1.90171 q^{15} -4.98267 q^{16} +4.99305 q^{17} -1.69362 q^{18} -0.972373 q^{19} +1.65136 q^{20} +8.79980 q^{22} +1.00000 q^{23} +1.91658 q^{24} -1.38351 q^{25} +4.99019 q^{26} +1.00000 q^{27} -4.08053 q^{29} -3.22078 q^{30} -1.11270 q^{31} +4.60561 q^{32} -5.19584 q^{33} -8.45633 q^{34} +0.868357 q^{36} +10.5052 q^{37} +1.64683 q^{38} -2.94646 q^{39} +3.64477 q^{40} +3.46973 q^{41} -7.46270 q^{43} -4.51185 q^{44} +1.90171 q^{45} -1.69362 q^{46} -5.28608 q^{47} -4.98267 q^{48} +2.34314 q^{50} +4.99305 q^{51} -2.55858 q^{52} -9.85547 q^{53} -1.69362 q^{54} -9.88098 q^{55} -0.972373 q^{57} +6.91088 q^{58} -8.88630 q^{59} +1.65136 q^{60} +12.1353 q^{61} +1.88449 q^{62} +2.16517 q^{64} -5.60330 q^{65} +8.79980 q^{66} -11.6894 q^{67} +4.33575 q^{68} +1.00000 q^{69} -5.61748 q^{71} +1.91658 q^{72} -6.42059 q^{73} -17.7919 q^{74} -1.38351 q^{75} -0.844367 q^{76} +4.99019 q^{78} -13.4281 q^{79} -9.47558 q^{80} +1.00000 q^{81} -5.87642 q^{82} -2.34810 q^{83} +9.49531 q^{85} +12.6390 q^{86} -4.08053 q^{87} -9.95823 q^{88} +16.8503 q^{89} -3.22078 q^{90} +0.868357 q^{92} -1.11270 q^{93} +8.95262 q^{94} -1.84917 q^{95} +4.60561 q^{96} -0.186928 q^{97} -5.19584 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} + 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 + 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 - 12 * q^8 + 10 * q^9	\( 10 q - 4 q^{2} + 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} - 12 q^{8} + 10 q^{9} - 8 q^{10} - 2 q^{11} + 8 q^{12} - 16 q^{13} - 4 q^{15} + 4 q^{16} - 12 q^{17} - 4 q^{18} - 26 q^{19} - 8 q^{22} + 10 q^{23} - 12 q^{24} + 14 q^{25} + 12 q^{26} + 10 q^{27} - 16 q^{29} - 8 q^{30} - 20 q^{31} - 8 q^{32} - 2 q^{33} + 4 q^{34} + 8 q^{36} + 8 q^{37} + 8 q^{38} - 16 q^{39} + 12 q^{40} - 22 q^{41} - 4 q^{43} - 24 q^{44} - 4 q^{45} - 4 q^{46} - 6 q^{47} + 4 q^{48} - 48 q^{50} - 12 q^{51} - 24 q^{52} - 30 q^{53} - 4 q^{54} - 48 q^{55} - 26 q^{57} + 24 q^{58} - 42 q^{59} - 14 q^{61} - 40 q^{62} + 8 q^{64} - 44 q^{65} - 8 q^{66} - 8 q^{68} + 10 q^{69} + 8 q^{71} - 12 q^{72} - 24 q^{73} + 8 q^{74} + 14 q^{75} - 32 q^{76} + 12 q^{78} + 32 q^{79} - 28 q^{80} + 10 q^{81} + 64 q^{82} - 28 q^{83} - 4 q^{85} - 4 q^{86} - 16 q^{87} + 20 q^{88} - 8 q^{90} + 8 q^{92} - 20 q^{93} - 8 q^{94} - 16 q^{95} - 8 q^{96} + 12 q^{97} - 2 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 + 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 - 12 * q^8 + 10 * q^9 - 8 * q^10 - 2 * q^11 + 8 * q^12 - 16 * q^13 - 4 * q^15 + 4 * q^16 - 12 * q^17 - 4 * q^18 - 26 * q^19 - 8 * q^22 + 10 * q^23 - 12 * q^24 + 14 * q^25 + 12 * q^26 + 10 * q^27 - 16 * q^29 - 8 * q^30 - 20 * q^31 - 8 * q^32 - 2 * q^33 + 4 * q^34 + 8 * q^36 + 8 * q^37 + 8 * q^38 - 16 * q^39 + 12 * q^40 - 22 * q^41 - 4 * q^43 - 24 * q^44 - 4 * q^45 - 4 * q^46 - 6 * q^47 + 4 * q^48 - 48 * q^50 - 12 * q^51 - 24 * q^52 - 30 * q^53 - 4 * q^54 - 48 * q^55 - 26 * q^57 + 24 * q^58 - 42 * q^59 - 14 * q^61 - 40 * q^62 + 8 * q^64 - 44 * q^65 - 8 * q^66 - 8 * q^68 + 10 * q^69 + 8 * q^71 - 12 * q^72 - 24 * q^73 + 8 * q^74 + 14 * q^75 - 32 * q^76 + 12 * q^78 + 32 * q^79 - 28 * q^80 + 10 * q^81 + 64 * q^82 - 28 * q^83 - 4 * q^85 - 4 * q^86 - 16 * q^87 + 20 * q^88 - 8 * q^90 + 8 * q^92 - 20 * q^93 - 8 * q^94 - 16 * q^95 - 8 * q^96 + 12 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more