LMFDB - Embedded newform 6171.2.a.bo.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6171,2,Mod(1,6171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6171, 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("6171.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6171 = 3 \cdot 11^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6171.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:	$49.2756830873$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 136 x^{10} - 244 x^{9} - 449 x^{8} + 778 x^{7} + 638 x^{6} + \cdots + 4 $ x^14 - 2x^13 - 19x^12 + 36x^11 + 136x^10 - 244x^9 - 449x^8 + 778x^7 + 638x^6 - 1160x^5 - 195x^4 + 644x^3 - 151x^2 - 16*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$1.87481$ of defining polynomial
Character	$\chi$	$=$	6171.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.87481 q^{2} -1.00000 q^{3} +1.51492 q^{4} +0.415159 q^{5} -1.87481 q^{6} +5.01369 q^{7} -0.909438 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.87481 q^{2} -1.00000 q^{3} +1.51492 q^{4} +0.415159 q^{5} -1.87481 q^{6} +5.01369 q^{7} -0.909438 q^{8} +1.00000 q^{9} +0.778345 q^{10} -1.51492 q^{12} -4.35575 q^{13} +9.39972 q^{14} -0.415159 q^{15} -4.73486 q^{16} -1.00000 q^{17} +1.87481 q^{18} +2.30462 q^{19} +0.628932 q^{20} -5.01369 q^{21} -6.55834 q^{23} +0.909438 q^{24} -4.82764 q^{25} -8.16622 q^{26} -1.00000 q^{27} +7.59533 q^{28} -7.38223 q^{29} -0.778345 q^{30} -6.23661 q^{31} -7.05809 q^{32} -1.87481 q^{34} +2.08148 q^{35} +1.51492 q^{36} -6.09734 q^{37} +4.32073 q^{38} +4.35575 q^{39} -0.377561 q^{40} +3.06727 q^{41} -9.39972 q^{42} -12.0941 q^{43} +0.415159 q^{45} -12.2957 q^{46} +2.19188 q^{47} +4.73486 q^{48} +18.1371 q^{49} -9.05092 q^{50} +1.00000 q^{51} -6.59861 q^{52} -2.05334 q^{53} -1.87481 q^{54} -4.55964 q^{56} -2.30462 q^{57} -13.8403 q^{58} -2.11711 q^{59} -0.628932 q^{60} -5.55321 q^{61} -11.6925 q^{62} +5.01369 q^{63} -3.76287 q^{64} -1.80833 q^{65} -5.21767 q^{67} -1.51492 q^{68} +6.55834 q^{69} +3.90238 q^{70} +15.1047 q^{71} -0.909438 q^{72} +11.6838 q^{73} -11.4314 q^{74} +4.82764 q^{75} +3.49131 q^{76} +8.16622 q^{78} +12.2557 q^{79} -1.96572 q^{80} +1.00000 q^{81} +5.75055 q^{82} -2.96714 q^{83} -7.59533 q^{84} -0.415159 q^{85} -22.6742 q^{86} +7.38223 q^{87} -7.09238 q^{89} +0.778345 q^{90} -21.8384 q^{91} -9.93535 q^{92} +6.23661 q^{93} +4.10937 q^{94} +0.956784 q^{95} +7.05809 q^{96} +0.304037 q^{97} +34.0036 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 14 q^{3} + 14 q^{4} - 2 q^{6} - 6 q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q + 2 * q^2 - 14 * q^3 + 14 * q^4 - 2 * q^6 - 6 * q^7 + 6 * q^8 + 14 * q^9	$ 14 q + 2 q^{2} - 14 q^{3} + 14 q^{4} - 2 q^{6} - 6 q^{7} + 6 q^{8} + 14 q^{9} - 8 q^{10} - 14 q^{12} - 20 q^{13} + 4 q^{14} + 14 q^{16} - 14 q^{17} + 2 q^{18} - 16 q^{19} - 16 q^{20} + 6 q^{21} - 2 q^{23} - 6 q^{24} + 22 q^{25} - 4 q^{26} - 14 q^{27} + 30 q^{28} - 22 q^{29} + 8 q^{30} + 34 q^{32} - 2 q^{34} - 2 q^{35} + 14 q^{36} + 8 q^{37} - 16 q^{38} + 20 q^{39} - 74 q^{40} - 24 q^{41} - 4 q^{42} - 12 q^{43} - 26 q^{46} + 28 q^{47} - 14 q^{48} + 28 q^{49} + 50 q^{50} + 14 q^{51} - 48 q^{52} + 18 q^{53} - 2 q^{54} + 6 q^{56} + 16 q^{57} + 20 q^{59} + 16 q^{60} - 64 q^{61} - 62 q^{62} - 6 q^{63} - 4 q^{64} + 30 q^{65} + 10 q^{67} - 14 q^{68} + 2 q^{69} - 44 q^{70} - 8 q^{71} + 6 q^{72} - 44 q^{73} - 50 q^{74} - 22 q^{75} - 24 q^{76} + 4 q^{78} - 8 q^{79} - 102 q^{80} + 14 q^{81} - 46 q^{82} - 12 q^{83} - 30 q^{84} + 12 q^{86} + 22 q^{87} - 8 q^{89} - 8 q^{90} - 20 q^{91} - 20 q^{92} + 16 q^{94} + 30 q^{95} - 34 q^{96} - 14 q^{97} + 90 q^{98}+O(q^{100}) $ 14 * q + 2 * q^2 - 14 * q^3 + 14 * q^4 - 2 * q^6 - 6 * q^7 + 6 * q^8 + 14 * q^9 - 8 * q^10 - 14 * q^12 - 20 * q^13 + 4 * q^14 + 14 * q^16 - 14 * q^17 + 2 * q^18 - 16 * q^19 - 16 * q^20 + 6 * q^21 - 2 * q^23 - 6 * q^24 + 22 * q^25 - 4 * q^26 - 14 * q^27 + 30 * q^28 - 22 * q^29 + 8 * q^30 + 34 * q^32 - 2 * q^34 - 2 * q^35 + 14 * q^36 + 8 * q^37 - 16 * q^38 + 20 * q^39 - 74 * q^40 - 24 * q^41 - 4 * q^42 - 12 * q^43 - 26 * q^46 + 28 * q^47 - 14 * q^48 + 28 * q^49 + 50 * q^50 + 14 * q^51 - 48 * q^52 + 18 * q^53 - 2 * q^54 + 6 * q^56 + 16 * q^57 + 20 * q^59 + 16 * q^60 - 64 * q^61 - 62 * q^62 - 6 * q^63 - 4 * q^64 + 30 * q^65 + 10 * q^67 - 14 * q^68 + 2 * q^69 - 44 * q^70 - 8 * q^71 + 6 * q^72 - 44 * q^73 - 50 * q^74 - 22 * q^75 - 24 * q^76 + 4 * q^78 - 8 * q^79 - 102 * q^80 + 14 * q^81 - 46 * q^82 - 12 * q^83 - 30 * q^84 + 12 * q^86 + 22 * q^87 - 8 * q^89 - 8 * q^90 - 20 * q^91 - 20 * q^92 + 16 * q^94 + 30 * q^95 - 34 * q^96 - 14 * q^97 + 90 * q^98

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 $

$2$	1.87481	1.32569	0.662846	−	0.748756i	$-0.269348\pi$
$2$	1.87481	1.32569	0.662846	+	0.748756i	$0.269348\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.51492	0.757459
$5$	0.415159	0.185665	0.0928324	−	0.995682i	$-0.470408\pi$
$5$	0.415159	0.185665	0.0928324	+	0.995682i	$0.470408\pi$
$6$	−1.87481	−0.765389
$7$	5.01369	1.89500	0.947498	−	0.319761i	$-0.103603\pi$
$7$	5.01369	1.89500	0.947498	+	0.319761i	$0.103603\pi$
$8$	−0.909438	−0.321535
$9$	1.00000	0.333333
$10$	0.778345	0.246134
$11$	0	0
$11$	0	0
$12$	−1.51492	−0.437319
$13$	−4.35575	−1.20807	−0.604034	−	0.796958i	$-0.706441\pi$
$13$	−4.35575	−1.20807	−0.604034	+	0.796958i	$0.706441\pi$
$14$	9.39972	2.51218
$15$	−0.415159	−0.107194
$16$	−4.73486	−1.18371
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.87481	0.441897
$19$	2.30462	0.528716	0.264358	−	0.964425i	$-0.414840\pi$
$19$	2.30462	0.528716	0.264358	+	0.964425i	$0.414840\pi$
$20$	0.628932	0.140633
$21$	−5.01369	−1.09408
$22$	0	0
$23$	−6.55834	−1.36751	−0.683754	−	0.729712i	$-0.739654\pi$
$23$	−6.55834	−1.36751	−0.683754	+	0.729712i	$0.739654\pi$
$24$	0.909438	0.185638
$25$	−4.82764	−0.965529
$26$	−8.16622	−1.60153
$27$	−1.00000	−0.192450
$28$	7.59533	1.43538
$29$	−7.38223	−1.37085	−0.685423	−	0.728145i	$-0.740383\pi$
$29$	−7.38223	−1.37085	−0.685423	+	0.728145i	$0.740383\pi$
$30$	−0.778345	−0.142106
$31$	−6.23661	−1.12013	−0.560064	−	0.828450i	$-0.689223\pi$
$31$	−6.23661	−1.12013	−0.560064	+	0.828450i	$0.689223\pi$
$32$	−7.05809	−1.24771
$33$	0	0
$34$	−1.87481	−0.321527
$35$	2.08148	0.351834
$36$	1.51492	0.252486
$37$	−6.09734	−1.00240	−0.501199	−	0.865332i	$-0.667107\pi$
$37$	−6.09734	−1.00240	−0.501199	+	0.865332i	$0.667107\pi$
$38$	4.32073	0.700915
$39$	4.35575	0.697479
$40$	−0.377561	−0.0596977
$41$	3.06727	0.479027	0.239514	−	0.970893i	$-0.423012\pi$
$41$	3.06727	0.479027	0.239514	+	0.970893i	$0.423012\pi$
$42$	−9.39972	−1.45041
$43$	−12.0941	−1.84434	−0.922168	−	0.386789i	$-0.873584\pi$
$43$	−12.0941	−1.84434	−0.922168	+	0.386789i	$0.873584\pi$
$44$	0	0
$45$	0.415159	0.0618882
$46$	−12.2957	−1.81290
$47$	2.19188	0.319719	0.159859	−	0.987140i	$-0.448896\pi$
$47$	2.19188	0.319719	0.159859	+	0.987140i	$0.448896\pi$
$48$	4.73486	0.683418
$49$	18.1371	2.59101
$50$	−9.05092	−1.27999
$51$	1.00000	0.140028
$52$	−6.59861	−0.915062
$53$	−2.05334	−0.282047	−0.141024	−	0.990006i	$-0.545039\pi$
$53$	−2.05334	−0.282047	−0.141024	+	0.990006i	$0.545039\pi$
$54$	−1.87481	−0.255130
$55$	0	0
$56$	−4.55964	−0.609308
$57$	−2.30462	−0.305254
$58$	−13.8403	−1.81732
$59$	−2.11711	−0.275624	−0.137812	−	0.990458i	$-0.544007\pi$
$59$	−2.11711	−0.275624	−0.137812	+	0.990458i	$0.544007\pi$
$60$	−0.628932	−0.0811947
$61$	−5.55321	−0.711015	−0.355508	−	0.934673i	$-0.615692\pi$
$61$	−5.55321	−0.711015	−0.355508	+	0.934673i	$0.615692\pi$
$62$	−11.6925	−1.48494
$63$	5.01369	0.631666
$64$	−3.76287	−0.470359
$65$	−1.80833	−0.224296
$66$	0	0
$67$	−5.21767	−0.637440	−0.318720	−	0.947849i	$-0.603253\pi$
$67$	−5.21767	−0.637440	−0.318720	+	0.947849i	$0.603253\pi$
$68$	−1.51492	−0.183711
$69$	6.55834	0.789531
$70$	3.90238	0.466423
$71$	15.1047	1.79260	0.896299	−	0.443450i	$-0.146245\pi$
$71$	15.1047	1.79260	0.896299	+	0.443450i	$0.146245\pi$
$72$	−0.909438	−0.107178
$73$	11.6838	1.36748	0.683741	−	0.729725i	$-0.260352\pi$
$73$	11.6838	1.36748	0.683741	+	0.729725i	$0.260352\pi$
$74$	−11.4314	−1.32887
$75$	4.82764	0.557448
$76$	3.49131	0.400481
$77$	0	0
$78$	8.16622	0.924642
$79$	12.2557	1.37887	0.689437	−	0.724346i	$-0.257858\pi$
$79$	12.2557	1.37887	0.689437	+	0.724346i	$0.257858\pi$
$80$	−1.96572	−0.219774
$81$	1.00000	0.111111
$82$	5.75055	0.635042
$83$	−2.96714	−0.325685	−0.162843	−	0.986652i	$-0.552066\pi$
$83$	−2.96714	−0.325685	−0.162843	+	0.986652i	$0.552066\pi$
$84$	−7.59533	−0.828718
$85$	−0.415159	−0.0450303
$86$	−22.6742	−2.44502
$87$	7.38223	0.791458
$88$	0	0
$89$	−7.09238	−0.751790	−0.375895	−	0.926662i	$-0.622665\pi$
$89$	−7.09238	−0.751790	−0.375895	+	0.926662i	$0.622665\pi$
$90$	0.778345	0.0820447
$91$	−21.8384	−2.28929
$92$	−9.93535	−1.03583
$93$	6.23661	0.646706
$94$	4.10937	0.423849
$95$	0.956784	0.0981639
$96$	7.05809	0.720364
$97$	0.304037	0.0308702	0.0154351	−	0.999881i	$-0.495087\pi$
$97$	0.304037	0.0308702	0.0154351	+	0.999881i	$0.495087\pi$
$98$	34.0036	3.43488
$99$	0	0
$100$	−7.31348	−0.731348
$101$	−3.10435	−0.308895	−0.154447	−	0.988001i	$-0.549360\pi$
$101$	−3.10435	−0.308895	−0.154447	+	0.988001i	$0.549360\pi$
$102$	1.87481	0.185634
$103$	−9.91433	−0.976888	−0.488444	−	0.872595i	$-0.662435\pi$
$103$	−9.91433	−0.976888	−0.488444	+	0.872595i	$0.662435\pi$
$104$	3.96129	0.388436
$105$	−2.08148	−0.203131
$106$	−3.84962	−0.373908
$107$	15.9830	1.54514	0.772570	−	0.634930i	$-0.218971\pi$
$107$	15.9830	1.54514	0.772570	+	0.634930i	$0.218971\pi$
$108$	−1.51492	−0.145773
$109$	12.0605	1.15519	0.577594	−	0.816324i	$-0.303992\pi$
$109$	12.0605	1.15519	0.577594	+	0.816324i	$0.303992\pi$
$110$	0	0
$111$	6.09734	0.578734
$112$	−23.7391	−2.24314
$113$	−12.6784	−1.19269	−0.596343	−	0.802730i	$-0.703380\pi$
$113$	−12.6784	−1.19269	−0.596343	+	0.802730i	$0.703380\pi$
$114$	−4.32073	−0.404673
$115$	−2.72275	−0.253898
$116$	−11.1835	−1.03836
$117$	−4.35575	−0.402690
$118$	−3.96918	−0.365393
$119$	−5.01369	−0.459604
$120$	0.377561	0.0344665
$121$	0	0
$122$	−10.4112	−0.942587
$123$	−3.06727	−0.276566
$124$	−9.44794	−0.848450
$125$	−4.08003	−0.364929
$126$	9.39972	0.837394
$127$	−15.9218	−1.41283	−0.706414	−	0.707799i	$-0.749688\pi$
$127$	−15.9218	−1.41283	−0.706414	+	0.707799i	$0.749688\pi$
$128$	7.06151	0.624155
$129$	12.0941	1.06483
$130$	−3.39028	−0.297347
$131$	−1.83134	−0.160005	−0.0800025	−	0.996795i	$-0.525493\pi$
$131$	−1.83134	−0.160005	−0.0800025	+	0.996795i	$0.525493\pi$
$132$	0	0
$133$	11.5547	1.00192
$134$	−9.78215	−0.845049
$135$	−0.415159	−0.0357312
$136$	0.909438	0.0779837
$137$	13.9698	1.19352	0.596760	−	0.802420i	$-0.296454\pi$
$137$	13.9698	1.19352	0.596760	+	0.802420i	$0.296454\pi$
$138$	12.2957	1.04668
$139$	−7.57665	−0.642643	−0.321321	−	0.946970i	$-0.604127\pi$
$139$	−7.57665	−0.642643	−0.321321	+	0.946970i	$0.604127\pi$
$140$	3.15327	0.266500
$141$	−2.19188	−0.184590
$142$	28.3185	2.37643
$143$	0	0
$144$	−4.73486	−0.394572
$145$	−3.06480	−0.254518
$146$	21.9049	1.81286
$147$	−18.1371	−1.49592
$148$	−9.23697	−0.759275
$149$	8.62906	0.706920	0.353460	−	0.935450i	$-0.385005\pi$
$149$	8.62906	0.706920	0.353460	+	0.935450i	$0.385005\pi$
$150$	9.05092	0.739005
$151$	−13.1257	−1.06815	−0.534076	−	0.845437i	$-0.679340\pi$
$151$	−13.1257	−1.06815	−0.534076	+	0.845437i	$0.679340\pi$
$152$	−2.09591	−0.170001
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	−2.58918	−0.207968
$156$	6.59861	0.528312
$157$	10.2454	0.817670	0.408835	−	0.912608i	$-0.365935\pi$
$157$	10.2454	0.817670	0.408835	+	0.912608i	$0.365935\pi$
$158$	22.9771	1.82796
$159$	2.05334	0.162840
$160$	−2.93023	−0.231655
$161$	−32.8815	−2.59142
$162$	1.87481	0.147299
$163$	−4.09403	−0.320669	−0.160334	−	0.987063i	$-0.551257\pi$
$163$	−4.09403	−0.320669	−0.160334	+	0.987063i	$0.551257\pi$
$164$	4.64666	0.362843
$165$	0	0
$166$	−5.56282	−0.431759
$167$	21.0431	1.62836	0.814182	−	0.580610i	$-0.197186\pi$
$167$	21.0431	1.62836	0.814182	+	0.580610i	$0.197186\pi$
$168$	4.55964	0.351784
$169$	5.97260	0.459431
$170$	−0.778345	−0.0596963
$171$	2.30462	0.176239
$172$	−18.3216	−1.39701
$173$	22.7537	1.72993	0.864965	−	0.501832i	$-0.167340\pi$
$173$	22.7537	1.72993	0.864965	+	0.501832i	$0.167340\pi$
$174$	13.8403	1.04923
$175$	−24.2043	−1.82967
$176$	0	0
$177$	2.11711	0.159132
$178$	−13.2969	−0.996642
$179$	−19.4209	−1.45159	−0.725793	−	0.687913i	$-0.758527\pi$
$179$	−19.4209	−1.45159	−0.725793	+	0.687913i	$0.758527\pi$
$180$	0.628932	0.0468778
$181$	6.62694	0.492576	0.246288	−	0.969197i	$-0.420789\pi$
$181$	6.62694	0.492576	0.246288	+	0.969197i	$0.420789\pi$
$182$	−40.9429	−3.03489
$183$	5.55321	0.410505
$184$	5.96441	0.439702
$185$	−2.53137	−0.186110
$186$	11.6925	0.857333
$187$	0	0
$188$	3.32052	0.242174
$189$	−5.01369	−0.364692
$190$	1.79379	0.130135
$191$	−14.9144	−1.07917	−0.539585	−	0.841931i	$-0.681419\pi$
$191$	−14.9144	−1.07917	−0.539585	+	0.841931i	$0.681419\pi$
$192$	3.76287	0.271562
$193$	15.7048	1.13046	0.565229	−	0.824934i	$-0.308788\pi$
$193$	15.7048	1.13046	0.565229	+	0.824934i	$0.308788\pi$
$194$	0.570011	0.0409244
$195$	1.80833	0.129497
$196$	27.4762	1.96258
$197$	−13.1746	−0.938650	−0.469325	−	0.883025i	$-0.655503\pi$
$197$	−13.1746	−0.938650	−0.469325	+	0.883025i	$0.655503\pi$
$198$	0	0
$199$	−12.1999	−0.864826	−0.432413	−	0.901676i	$-0.642338\pi$
$199$	−12.1999	−0.864826	−0.432413	+	0.901676i	$0.642338\pi$
$200$	4.39044	0.310451
$201$	5.21767	0.368026
$202$	−5.82007	−0.409499
$203$	−37.0122	−2.59775
$204$	1.51492	0.106065
$205$	1.27340	0.0889384
$206$	−18.5875	−1.29505
$207$	−6.55834	−0.455836
$208$	20.6239	1.43001
$209$	0	0
$210$	−3.90238	−0.269290
$211$	−17.6662	−1.21619	−0.608097	−	0.793863i	$-0.708067\pi$
$211$	−17.6662	−1.21619	−0.608097	+	0.793863i	$0.708067\pi$
$212$	−3.11063	−0.213639
$213$	−15.1047	−1.03496
$214$	29.9652	2.04838
$215$	−5.02098	−0.342428
$216$	0.909438	0.0618794
$217$	−31.2684	−2.12264
$218$	22.6112	1.53142
$219$	−11.6838	−0.789516
$220$	0	0
$221$	4.35575	0.293000
$222$	11.4314	0.767223
$223$	5.02829	0.336719	0.168360	−	0.985726i	$-0.446153\pi$
$223$	5.02829	0.336719	0.168360	+	0.985726i	$0.446153\pi$
$224$	−35.3871	−2.36440
$225$	−4.82764	−0.321843
$226$	−23.7696	−1.58113
$227$	8.25864	0.548145	0.274072	−	0.961709i	$-0.411629\pi$
$227$	8.25864	0.548145	0.274072	+	0.961709i	$0.411629\pi$
$228$	−3.49131	−0.231218
$229$	17.2498	1.13990	0.569951	−	0.821679i	$-0.306962\pi$
$229$	17.2498	1.13990	0.569951	+	0.821679i	$0.306962\pi$
$230$	−5.10465	−0.336591
$231$	0	0
$232$	6.71368	0.440775
$233$	−14.9813	−0.981455	−0.490727	−	0.871313i	$-0.663269\pi$
$233$	−14.9813	−0.981455	−0.490727	+	0.871313i	$0.663269\pi$
$234$	−8.16622	−0.533842
$235$	0.909980	0.0593605
$236$	−3.20725	−0.208774
$237$	−12.2557	−0.796093
$238$	−9.39972	−0.609293
$239$	15.7645	1.01972	0.509859	−	0.860258i	$-0.329698\pi$
$239$	15.7645	1.01972	0.509859	+	0.860258i	$0.329698\pi$
$240$	1.96572	0.126887
$241$	−27.1288	−1.74752	−0.873759	−	0.486360i	$-0.838324\pi$
$241$	−27.1288	−1.74752	−0.873759	+	0.486360i	$0.838324\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−8.41265	−0.538565
$245$	7.52977	0.481059
$246$	−5.75055	−0.366642
$247$	−10.0384	−0.638726
$248$	5.67181	0.360160
$249$	2.96714	0.188035
$250$	−7.64929	−0.483784
$251$	1.06266	0.0670748	0.0335374	−	0.999437i	$-0.489323\pi$
$251$	1.06266	0.0670748	0.0335374	+	0.999437i	$0.489323\pi$
$252$	7.59533	0.478461
$253$	0	0
$254$	−29.8503	−1.87297
$255$	0.415159	0.0259983
$256$	20.7647	1.29780
$257$	21.9881	1.37158	0.685791	−	0.727798i	$-0.259456\pi$
$257$	21.9881	1.37158	0.685791	+	0.727798i	$0.259456\pi$
$258$	22.6742	1.41163
$259$	−30.5702	−1.89954
$260$	−2.73947	−0.169895
$261$	−7.38223	−0.456948
$262$	−3.43342	−0.212117
$263$	15.8084	0.974787	0.487393	−	0.873182i	$-0.337948\pi$
$263$	15.8084	0.974787	0.487393	+	0.873182i	$0.337948\pi$
$264$	0	0
$265$	−0.852460	−0.0523662
$266$	21.6628	1.32823
$267$	7.09238	0.434046
$268$	−7.90434	−0.482834
$269$	−19.3852	−1.18193	−0.590967	−	0.806696i	$-0.701254\pi$
$269$	−19.3852	−1.18193	−0.590967	+	0.806696i	$0.701254\pi$
$270$	−0.778345	−0.0473685
$271$	−20.4927	−1.24484	−0.622422	−	0.782682i	$-0.713851\pi$
$271$	−20.4927	−1.24484	−0.622422	+	0.782682i	$0.713851\pi$
$272$	4.73486	0.287093
$273$	21.8384	1.32172
$274$	26.1907	1.58224
$275$	0	0
$276$	9.93535	0.598038
$277$	−30.0528	−1.80570	−0.902848	−	0.429959i	$-0.858528\pi$
$277$	−30.0528	−1.80570	−0.902848	+	0.429959i	$0.858528\pi$
$278$	−14.2048	−0.851946
$279$	−6.23661	−0.373376
$280$	−1.89298	−0.113127
$281$	5.40307	0.322320	0.161160	−	0.986928i	$-0.448476\pi$
$281$	5.40307	0.322320	0.161160	+	0.986928i	$0.448476\pi$
$282$	−4.10937	−0.244709
$283$	16.3473	0.971747	0.485874	−	0.874029i	$-0.338502\pi$
$283$	16.3473	0.971747	0.485874	+	0.874029i	$0.338502\pi$
$284$	22.8824	1.35782
$285$	−0.956784	−0.0566750
$286$	0	0
$287$	15.3783	0.907755
$288$	−7.05809	−0.415902
$289$	1.00000	0.0588235
$290$	−5.74592	−0.337412
$291$	−0.304037	−0.0178229
$292$	17.7000	1.03581
$293$	4.71031	0.275179	0.137590	−	0.990489i	$-0.456064\pi$
$293$	4.71031	0.275179	0.137590	+	0.990489i	$0.456064\pi$
$294$	−34.0036	−1.98313
$295$	−0.878937	−0.0511737
$296$	5.54516	0.322306
$297$	0	0
$298$	16.1779	0.937158
$299$	28.5665	1.65204
$300$	7.31348	0.422244
$301$	−60.6362	−3.49501
$302$	−24.6081	−1.41604
$303$	3.10435	0.178340
$304$	−10.9121	−0.625849
$305$	−2.30546	−0.132010
$306$	−1.87481	−0.107176
$307$	8.87224	0.506365	0.253183	−	0.967419i	$-0.418523\pi$
$307$	8.87224	0.506365	0.253183	+	0.967419i	$0.418523\pi$
$308$	0	0
$309$	9.91433	0.564007
$310$	−4.85423	−0.275702
$311$	13.7472	0.779533	0.389767	−	0.920914i	$-0.372556\pi$
$311$	13.7472	0.779533	0.389767	+	0.920914i	$0.372556\pi$
$312$	−3.96129	−0.224264
$313$	−8.35444	−0.472221	−0.236110	−	0.971726i	$-0.575873\pi$
$313$	−8.35444	−0.472221	−0.236110	+	0.971726i	$0.575873\pi$
$314$	19.2081	1.08398
$315$	2.08148	0.117278
$316$	18.5664	1.04444
$317$	−10.9017	−0.612298	−0.306149	−	0.951984i	$-0.599041\pi$
$317$	−10.9017	−0.612298	−0.306149	+	0.951984i	$0.599041\pi$
$318$	3.84962	0.215876
$319$	0	0
$320$	−1.56219	−0.0873291
$321$	−15.9830	−0.892087
$322$	−61.6466	−3.43543
$323$	−2.30462	−0.128233
$324$	1.51492	0.0841621
$325$	21.0280	1.16643
$326$	−7.67553	−0.425108
$327$	−12.0605	−0.666949
$328$	−2.78949	−0.154024
$329$	10.9894	0.605866
$330$	0	0
$331$	−9.64891	−0.530352	−0.265176	−	0.964200i	$-0.585430\pi$
$331$	−9.64891	−0.530352	−0.265176	+	0.964200i	$0.585430\pi$
$332$	−4.49497	−0.246693
$333$	−6.09734	−0.334132
$334$	39.4518	2.15871
$335$	−2.16616	−0.118350
$336$	23.7391	1.29508
$337$	−2.76909	−0.150842	−0.0754211	−	0.997152i	$-0.524030\pi$
$337$	−2.76909	−0.150842	−0.0754211	+	0.997152i	$0.524030\pi$
$338$	11.1975	0.609063
$339$	12.6784	0.688597
$340$	−0.628932	−0.0341086
$341$	0	0
$342$	4.32073	0.233638
$343$	55.8379	3.01496
$344$	10.9989	0.593019
$345$	2.72275	0.146588
$346$	42.6589	2.29335
$347$	−11.5547	−0.620289	−0.310145	−	0.950689i	$-0.600378\pi$
$347$	−11.5547	−0.620289	−0.310145	+	0.950689i	$0.600378\pi$
$348$	11.1835	0.599497
$349$	−29.6295	−1.58603	−0.793015	−	0.609202i	$-0.791490\pi$
$349$	−29.6295	−1.58603	−0.793015	+	0.609202i	$0.791490\pi$
$350$	−45.3785	−2.42558
$351$	4.35575	0.232493
$352$	0	0
$353$	22.8484	1.21610	0.608049	−	0.793900i	$-0.291953\pi$
$353$	22.8484	1.21610	0.608049	+	0.793900i	$0.291953\pi$
$354$	3.96918	0.210960
$355$	6.27085	0.332822
$356$	−10.7444	−0.569450
$357$	5.01369	0.265353
$358$	−36.4105	−1.92436
$359$	6.66866	0.351959	0.175979	−	0.984394i	$-0.443691\pi$
$359$	6.66866	0.351959	0.175979	+	0.984394i	$0.443691\pi$
$360$	−0.377561	−0.0198992
$361$	−13.6887	−0.720459
$362$	12.4243	0.653005
$363$	0	0
$364$	−33.0834	−1.73404
$365$	4.85062	0.253893
$366$	10.4112	0.544203
$367$	6.80153	0.355037	0.177519	−	0.984117i	$-0.443193\pi$
$367$	6.80153	0.355037	0.177519	+	0.984117i	$0.443193\pi$
$368$	31.0528	1.61874
$369$	3.06727	0.159676
$370$	−4.74584	−0.246724
$371$	−10.2948	−0.534479
$372$	9.44794	0.489853
$373$	−4.98052	−0.257882	−0.128941	−	0.991652i	$-0.541158\pi$
$373$	−4.98052	−0.257882	−0.128941	+	0.991652i	$0.541158\pi$
$374$	0	0
$375$	4.08003	0.210692
$376$	−1.99338	−0.102801
$377$	32.1552	1.65608
$378$	−9.39972	−0.483470
$379$	15.3919	0.790628	0.395314	−	0.918546i	$-0.370636\pi$
$379$	15.3919	0.790628	0.395314	+	0.918546i	$0.370636\pi$
$380$	1.44945	0.0743551
$381$	15.9218	0.815697
$382$	−27.9617	−1.43065
$383$	−12.2514	−0.626019	−0.313010	−	0.949750i	$-0.601337\pi$
$383$	−12.2514	−0.626019	−0.313010	+	0.949750i	$0.601337\pi$
$384$	−7.06151	−0.360356
$385$	0	0
$386$	29.4436	1.49864
$387$	−12.0941	−0.614779
$388$	0.460590	0.0233829
$389$	10.9801	0.556715	0.278358	−	0.960477i	$-0.410210\pi$
$389$	10.9801	0.556715	0.278358	+	0.960477i	$0.410210\pi$
$390$	3.39028	0.171673
$391$	6.55834	0.331670
$392$	−16.4946	−0.833101
$393$	1.83134	0.0923789
$394$	−24.6999	−1.24436
$395$	5.08806	0.256008
$396$	0	0
$397$	−3.32004	−0.166628	−0.0833140	−	0.996523i	$-0.526550\pi$
$397$	−3.32004	−0.166628	−0.0833140	+	0.996523i	$0.526550\pi$
$398$	−22.8725	−1.14649
$399$	−11.5547	−0.578456
$400$	22.8582	1.14291
$401$	30.4479	1.52049	0.760247	−	0.649634i	$-0.225078\pi$
$401$	30.4479	1.52049	0.760247	+	0.649634i	$0.225078\pi$
$402$	9.78215	0.487889
$403$	27.1651	1.35319
$404$	−4.70284	−0.233975
$405$	0.415159	0.0206294
$406$	−69.3909	−3.44381
$407$	0	0
$408$	−0.909438	−0.0450239
$409$	4.05656	0.200584	0.100292	−	0.994958i	$-0.468022\pi$
$409$	4.05656	0.200584	0.100292	+	0.994958i	$0.468022\pi$
$410$	2.38739	0.117905
$411$	−13.9698	−0.689079
$412$	−15.0194	−0.739953
$413$	−10.6145	−0.522307
$414$	−12.2957	−0.604298
$415$	−1.23183	−0.0604683
$416$	30.7433	1.50732
$417$	7.57665	0.371030
$418$	0	0
$419$	−37.9774	−1.85532	−0.927659	−	0.373428i	$-0.878182\pi$
$419$	−37.9774	−1.85532	−0.927659	+	0.373428i	$0.878182\pi$
$420$	−3.15327	−0.153864
$421$	−11.1200	−0.541957	−0.270979	−	0.962585i	$-0.587347\pi$
$421$	−11.1200	−0.541957	−0.270979	+	0.962585i	$0.587347\pi$
$422$	−33.1209	−1.61230
$423$	2.19188	0.106573
$424$	1.86738	0.0906880
$425$	4.82764	0.234175
$426$	−28.3185	−1.37203
$427$	−27.8421	−1.34737
$428$	24.2130	1.17038
$429$	0	0
$430$	−9.41340	−0.453954
$431$	7.94822	0.382852	0.191426	−	0.981507i	$-0.438689\pi$
$431$	7.94822	0.382852	0.191426	+	0.981507i	$0.438689\pi$
$432$	4.73486	0.227806
$433$	9.91469	0.476470	0.238235	−	0.971208i	$-0.423431\pi$
$433$	9.91469	0.476470	0.238235	+	0.971208i	$0.423431\pi$
$434$	−58.6224	−2.81396
$435$	3.06480	0.146946
$436$	18.2707	0.875008
$437$	−15.1145	−0.723024
$438$	−21.9049	−1.04666
$439$	−36.1438	−1.72505	−0.862526	−	0.506013i	$-0.831119\pi$
$439$	−36.1438	−1.72505	−0.862526	+	0.506013i	$0.831119\pi$
$440$	0	0
$441$	18.1371	0.863671
$442$	8.16622	0.388427
$443$	36.3171	1.72548	0.862739	−	0.505649i	$-0.168747\pi$
$443$	36.3171	1.72548	0.862739	+	0.505649i	$0.168747\pi$
$444$	9.23697	0.438367
$445$	−2.94446	−0.139581
$446$	9.42709	0.446386
$447$	−8.62906	−0.408140
$448$	−18.8659	−0.891329
$449$	27.0676	1.27740	0.638699	−	0.769456i	$-0.279473\pi$
$449$	27.0676	1.27740	0.638699	+	0.769456i	$0.279473\pi$
$450$	−9.05092	−0.426664
$451$	0	0
$452$	−19.2068	−0.903410
$453$	13.1257	0.616697
$454$	15.4834	0.726671
$455$	−9.06641	−0.425040
$456$	2.09591	0.0981500
$457$	7.53680	0.352557	0.176278	−	0.984340i	$-0.443594\pi$
$457$	7.53680	0.352557	0.176278	+	0.984340i	$0.443594\pi$
$458$	32.3402	1.51116
$459$	1.00000	0.0466760
$460$	−4.12475	−0.192317
$461$	−12.2313	−0.569668	−0.284834	−	0.958577i	$-0.591938\pi$
$461$	−12.2313	−0.569668	−0.284834	+	0.958577i	$0.591938\pi$
$462$	0	0
$463$	−24.4354	−1.13561	−0.567804	−	0.823164i	$-0.692207\pi$
$463$	−24.4354	−1.13561	−0.567804	+	0.823164i	$0.692207\pi$
$464$	34.9538	1.62269
$465$	2.58918	0.120070
$466$	−28.0870	−1.30111
$467$	−11.3186	−0.523762	−0.261881	−	0.965100i	$-0.584343\pi$
$467$	−11.3186	−0.523762	−0.261881	+	0.965100i	$0.584343\pi$
$468$	−6.59861	−0.305021
$469$	−26.1598	−1.20795
$470$	1.70604	0.0786938
$471$	−10.2454	−0.472082
$472$	1.92538	0.0886228
$473$	0	0
$474$	−22.9771	−1.05537
$475$	−11.1259	−0.510491
$476$	−7.59533	−0.348131
$477$	−2.05334	−0.0940158
$478$	29.5554	1.35183
$479$	−36.6197	−1.67319	−0.836597	−	0.547818i	$-0.815459\pi$
$479$	−36.6197	−1.67319	−0.836597	+	0.547818i	$0.815459\pi$
$480$	2.93023	0.133746
$481$	26.5585	1.21097
$482$	−50.8613	−2.31667
$483$	32.8815	1.49616
$484$	0	0
$485$	0.126223	0.00573151
$486$	−1.87481	−0.0850432
$487$	19.3926	0.878762	0.439381	−	0.898301i	$-0.355198\pi$
$487$	19.3926	0.878762	0.439381	+	0.898301i	$0.355198\pi$
$488$	5.05030	0.228616
$489$	4.09403	0.185138
$490$	14.1169	0.637737
$491$	−21.6194	−0.975671	−0.487836	−	0.872936i	$-0.662213\pi$
$491$	−21.6194	−0.975671	−0.487836	+	0.872936i	$0.662213\pi$
$492$	−4.64666	−0.209488
$493$	7.38223	0.332479
$494$	−18.8200	−0.846753
$495$	0	0
$496$	29.5295	1.32591
$497$	75.7303	3.39697
$498$	5.56282	0.249276
$499$	20.7486	0.928837	0.464419	−	0.885616i	$-0.346263\pi$
$499$	20.7486	0.928837	0.464419	+	0.885616i	$0.346263\pi$
$500$	−6.18091	−0.276419
$501$	−21.0431	−0.940136
$502$	1.99230	0.0889205
$503$	−24.6263	−1.09803	−0.549016	−	0.835812i	$-0.684997\pi$
$503$	−24.6263	−1.09803	−0.549016	+	0.835812i	$0.684997\pi$
$504$	−4.55964	−0.203103
$505$	−1.28880	−0.0573508
$506$	0	0
$507$	−5.97260	−0.265252
$508$	−24.1202	−1.07016
$509$	−0.956976	−0.0424172	−0.0212086	−	0.999775i	$-0.506751\pi$
$509$	−0.956976	−0.0424172	−0.0212086	+	0.999775i	$0.506751\pi$
$510$	0.778345	0.0344657
$511$	58.5788	2.59137
$512$	24.8070	1.09632
$513$	−2.30462	−0.101751
$514$	41.2236	1.81830
$515$	−4.11602	−0.181374
$516$	18.3216	0.806564
$517$	0	0
$518$	−57.3133	−2.51820
$519$	−22.7537	−0.998776
$520$	1.64456	0.0721189
$521$	22.5379	0.987403	0.493701	−	0.869631i	$-0.335644\pi$
$521$	22.5379	0.987403	0.493701	+	0.869631i	$0.335644\pi$
$522$	−13.8403	−0.605773
$523$	7.11466	0.311102	0.155551	−	0.987828i	$-0.450285\pi$
$523$	7.11466	0.311102	0.155551	+	0.987828i	$0.450285\pi$
$524$	−2.77433	−0.121197
$525$	24.2043	1.05636
$526$	29.6377	1.29227
$527$	6.23661	0.271671
$528$	0	0
$529$	20.0118	0.870080
$530$	−1.59820	−0.0694215
$531$	−2.11711	−0.0918747
$532$	17.5043	0.758910
$533$	−13.3603	−0.578698
$534$	13.2969	0.575412
$535$	6.63551	0.286878
$536$	4.74515	0.204959
$537$	19.4209	0.838074
$538$	−36.3435	−1.56688
$539$	0	0
$540$	−0.628932	−0.0270649
$541$	−24.0624	−1.03452	−0.517262	−	0.855827i	$-0.673049\pi$
$541$	−24.0624	−1.03452	−0.517262	+	0.855827i	$0.673049\pi$
$542$	−38.4200	−1.65028
$543$	−6.62694	−0.284389
$544$	7.05809	0.302613
$545$	5.00703	0.214478
$546$	40.9429	1.75219
$547$	11.5327	0.493101	0.246550	−	0.969130i	$-0.420703\pi$
$547$	11.5327	0.493101	0.246550	+	0.969130i	$0.420703\pi$
$548$	21.1631	0.904043
$549$	−5.55321	−0.237005
$550$	0	0
$551$	−17.0132	−0.724788
$552$	−5.96441	−0.253862
$553$	61.4463	2.61296
$554$	−56.3433	−2.39380
$555$	2.53137	0.107451
$556$	−11.4780	−0.486775
$557$	7.56707	0.320627	0.160313	−	0.987066i	$-0.448750\pi$
$557$	7.56707	0.320627	0.160313	+	0.987066i	$0.448750\pi$
$558$	−11.6925	−0.494981
$559$	52.6790	2.22809
$560$	−9.85551	−0.416471
$561$	0	0
$562$	10.1297	0.427297
$563$	−0.426459	−0.0179731	−0.00898655	−	0.999960i	$-0.502861\pi$
$563$	−0.426459	−0.0179731	−0.00898655	+	0.999960i	$0.502861\pi$
$564$	−3.32052	−0.139819
$565$	−5.26356	−0.221440
$566$	30.6481	1.28824
$567$	5.01369	0.210555
$568$	−13.7368	−0.576383
$569$	−16.2310	−0.680440	−0.340220	−	0.940346i	$-0.610502\pi$
$569$	−16.2310	−0.680440	−0.340220	+	0.940346i	$0.610502\pi$
$570$	−1.79379	−0.0751336
$571$	−18.7170	−0.783283	−0.391642	−	0.920118i	$-0.628093\pi$
$571$	−18.7170	−0.783283	−0.391642	+	0.920118i	$0.628093\pi$
$572$	0	0
$573$	14.9144	0.623059
$574$	28.8315	1.20340
$575$	31.6613	1.32037
$576$	−3.76287	−0.156786
$577$	3.47979	0.144865	0.0724327	−	0.997373i	$-0.476924\pi$
$577$	3.47979	0.144865	0.0724327	+	0.997373i	$0.476924\pi$
$578$	1.87481	0.0779819
$579$	−15.7048	−0.652670
$580$	−4.64292	−0.192787
$581$	−14.8763	−0.617173
$582$	−0.570011	−0.0236277
$583$	0	0
$584$	−10.6257	−0.439693
$585$	−1.80833	−0.0747653
$586$	8.83095	0.364803
$587$	−42.6318	−1.75960	−0.879801	−	0.475342i	$-0.842324\pi$
$587$	−42.6318	−1.75960	−0.879801	+	0.475342i	$0.842324\pi$
$588$	−27.4762	−1.13310
$589$	−14.3730	−0.592230
$590$	−1.64784	−0.0678405
$591$	13.1746	0.541930
$592$	28.8701	1.18655
$593$	−31.2446	−1.28306	−0.641532	−	0.767096i	$-0.721701\pi$
$593$	−31.2446	−1.28306	−0.641532	+	0.767096i	$0.721701\pi$
$594$	0	0
$595$	−2.08148	−0.0853323
$596$	13.0723	0.535463
$597$	12.1999	0.499308
$598$	53.5568	2.19010
$599$	−7.60286	−0.310644	−0.155322	−	0.987864i	$-0.549642\pi$
$599$	−7.60286	−0.310644	−0.155322	+	0.987864i	$0.549642\pi$
$600$	−4.39044	−0.179239
$601$	−20.2525	−0.826117	−0.413058	−	0.910705i	$-0.635539\pi$
$601$	−20.2525	−0.826117	−0.413058	+	0.910705i	$0.635539\pi$
$602$	−113.681	−4.63331
$603$	−5.21767	−0.212480
$604$	−19.8843	−0.809080
$605$	0	0
$606$	5.82007	0.236424
$607$	−39.2214	−1.59195	−0.795975	−	0.605330i	$-0.793041\pi$
$607$	−39.2214	−1.59195	−0.795975	+	0.605330i	$0.793041\pi$
$608$	−16.2662	−0.659683
$609$	37.0122	1.49981
$610$	−4.32231	−0.175005
$611$	−9.54730	−0.386242
$612$	−1.51492	−0.0612369
$613$	5.62416	0.227158	0.113579	−	0.993529i	$-0.463769\pi$
$613$	5.62416	0.227158	0.113579	+	0.993529i	$0.463769\pi$
$614$	16.6338	0.671284
$615$	−1.27340	−0.0513486
$616$	0	0
$617$	−24.5285	−0.987480	−0.493740	−	0.869610i	$-0.664371\pi$
$617$	−24.5285	−0.987480	−0.493740	+	0.869610i	$0.664371\pi$
$618$	18.5875	0.747699
$619$	0.324338	0.0130362	0.00651812	−	0.999979i	$-0.497925\pi$
$619$	0.324338	0.0130362	0.00651812	+	0.999979i	$0.497925\pi$
$620$	−3.92240	−0.157527
$621$	6.55834	0.263177
$622$	25.7734	1.03342
$623$	−35.5590	−1.42464
$624$	−20.6239	−0.825616
$625$	22.4444	0.897774
$626$	−15.6630	−0.626019
$627$	0	0
$628$	15.5209	0.619351
$629$	6.09734	0.243117
$630$	3.90238	0.155474
$631$	−0.809654	−0.0322318	−0.0161159	−	0.999870i	$-0.505130\pi$
$631$	−0.809654	−0.0322318	−0.0161159	+	0.999870i	$0.505130\pi$
$632$	−11.1458	−0.443356
$633$	17.6662	0.702170
$634$	−20.4386	−0.811719
$635$	−6.61006	−0.262312
$636$	3.11063	0.123345
$637$	−79.0007	−3.13012
$638$	0	0
$639$	15.1047	0.597533
$640$	2.93165	0.115884
$641$	−19.2697	−0.761109	−0.380555	−	0.924758i	$-0.624267\pi$
$641$	−19.2697	−0.761109	−0.380555	+	0.924758i	$0.624267\pi$
$642$	−29.9652	−1.18263
$643$	−33.1599	−1.30770	−0.653850	−	0.756624i	$-0.726847\pi$
$643$	−33.1599	−1.30770	−0.653850	+	0.756624i	$0.726847\pi$
$644$	−49.8127	−1.96290
$645$	5.02098	0.197701
$646$	−4.32073	−0.169997
$647$	47.6859	1.87473	0.937364	−	0.348352i	$-0.113259\pi$
$647$	47.6859	1.87473	0.937364	+	0.348352i	$0.113259\pi$
$648$	−0.909438	−0.0357261
$649$	0	0
$650$	39.4236	1.54632
$651$	31.2684	1.22551
$652$	−6.20211	−0.242893
$653$	8.24873	0.322798	0.161399	−	0.986889i	$-0.448399\pi$
$653$	8.24873	0.322798	0.161399	+	0.986889i	$0.448399\pi$
$654$	−22.6112	−0.884168
$655$	−0.760297	−0.0297073
$656$	−14.5231	−0.567031
$657$	11.6838	0.455827
$658$	20.6031	0.803192
$659$	33.6060	1.30910	0.654551	−	0.756018i	$-0.272858\pi$
$659$	33.6060	1.30910	0.654551	+	0.756018i	$0.272858\pi$
$660$	0	0
$661$	−3.41722	−0.132914	−0.0664572	−	0.997789i	$-0.521170\pi$
$661$	−3.41722	−0.132914	−0.0664572	+	0.997789i	$0.521170\pi$
$662$	−18.0899	−0.703083
$663$	−4.35575	−0.169163
$664$	2.69843	0.104719
$665$	4.79702	0.186020
$666$	−11.4314	−0.442957
$667$	48.4152	1.87464
$668$	31.8786	1.23342
$669$	−5.02829	−0.194405
$670$	−4.06114	−0.156896
$671$	0	0
$672$	35.3871	1.36509
$673$	−11.7897	−0.454460	−0.227230	−	0.973841i	$-0.572967\pi$
$673$	−11.7897	−0.454460	−0.227230	+	0.973841i	$0.572967\pi$
$674$	−5.19153	−0.199970
$675$	4.82764	0.185816
$676$	9.04799	0.348000
$677$	−28.8195	−1.10762	−0.553811	−	0.832642i	$-0.686827\pi$
$677$	−28.8195	−1.10762	−0.553811	+	0.832642i	$0.686827\pi$
$678$	23.7696	0.912868
$679$	1.52434	0.0584990
$680$	0.377561	0.0144788
$681$	−8.25864	−0.316472
$682$	0	0
$683$	−13.5064	−0.516809	−0.258404	−	0.966037i	$-0.583197\pi$
$683$	−13.5064	−0.516809	−0.258404	+	0.966037i	$0.583197\pi$
$684$	3.49131	0.133494
$685$	5.79969	0.221595
$686$	104.685	3.99691
$687$	−17.2498	−0.658122
$688$	57.2640	2.18317
$689$	8.94382	0.340733
$690$	5.10465	0.194331
$691$	44.8792	1.70729	0.853643	−	0.520859i	$-0.174388\pi$
$691$	44.8792	1.70729	0.853643	+	0.520859i	$0.174388\pi$
$692$	34.4699	1.31035
$693$	0	0
$694$	−21.6629	−0.822313
$695$	−3.14551	−0.119316
$696$	−6.71368	−0.254481
$697$	−3.06727	−0.116181
$698$	−55.5497	−2.10259
$699$	14.9813	0.566643
$700$	−36.6675	−1.38590
$701$	−45.4802	−1.71776	−0.858881	−	0.512175i	$-0.828840\pi$
$701$	−45.4802	−1.71776	−0.858881	+	0.512175i	$0.828840\pi$
$702$	8.16622	0.308214
$703$	−14.0521	−0.529984
$704$	0	0
$705$	−0.909980	−0.0342718
$706$	42.8364	1.61217
$707$	−15.5643	−0.585354
$708$	3.20725	0.120536
$709$	21.8354	0.820045	0.410023	−	0.912075i	$-0.365521\pi$
$709$	21.8354	0.820045	0.410023	+	0.912075i	$0.365521\pi$
$710$	11.7567	0.441220
$711$	12.2557	0.459624
$712$	6.45008	0.241727
$713$	40.9018	1.53178
$714$	9.39972	0.351776
$715$	0	0
$716$	−29.4211	−1.09952
$717$	−15.7645	−0.588734
$718$	12.5025	0.466589
$719$	29.6917	1.10731	0.553657	−	0.832745i	$-0.313232\pi$
$719$	29.6917	1.10731	0.553657	+	0.832745i	$0.313232\pi$
$720$	−1.96572	−0.0732580
$721$	−49.7074	−1.85120
$722$	−25.6638	−0.955107
$723$	27.1288	1.00893
$724$	10.0393	0.373106
$725$	35.6388	1.32359
$726$	0	0
$727$	−4.02624	−0.149325	−0.0746625	−	0.997209i	$-0.523788\pi$
$727$	−4.02624	−0.149325	−0.0746625	+	0.997209i	$0.523788\pi$
$728$	19.8607	0.736086
$729$	1.00000	0.0370370
$730$	9.09400	0.336584
$731$	12.0941	0.447317
$732$	8.41265	0.310941
$733$	13.2419	0.489100	0.244550	−	0.969637i	$-0.421360\pi$
$733$	13.2419	0.489100	0.244550	+	0.969637i	$0.421360\pi$
$734$	12.7516	0.470670
$735$	−7.52977	−0.277740
$736$	46.2894	1.70625
$737$	0	0
$738$	5.75055	0.211681
$739$	24.5923	0.904644	0.452322	−	0.891855i	$-0.350596\pi$
$739$	24.5923	0.904644	0.452322	+	0.891855i	$0.350596\pi$
$740$	−3.83481	−0.140971
$741$	10.0384	0.368768
$742$	−19.3008	−0.708554
$743$	29.9382	1.09833	0.549163	−	0.835716i	$-0.314947\pi$
$743$	29.9382	1.09833	0.549163	+	0.835716i	$0.314947\pi$
$744$	−5.67181	−0.207939
$745$	3.58243	0.131250
$746$	−9.33754	−0.341872
$747$	−2.96714	−0.108562
$748$	0	0
$749$	80.1340	2.92803
$750$	7.64929	0.279313
$751$	17.3183	0.631955	0.315978	−	0.948767i	$-0.397668\pi$
$751$	17.3183	0.631955	0.315978	+	0.948767i	$0.397668\pi$
$752$	−10.3783	−0.378456
$753$	−1.06266	−0.0387257
$754$	60.2849	2.19545
$755$	−5.44924	−0.198318
$756$	−7.59533	−0.276239
$757$	37.3114	1.35611	0.678053	−	0.735013i	$-0.262824\pi$
$757$	37.3114	1.35611	0.678053	+	0.735013i	$0.262824\pi$
$758$	28.8569	1.04813
$759$	0	0
$760$	−0.870136	−0.0315631
$761$	33.0988	1.19983	0.599915	−	0.800064i	$-0.295201\pi$
$761$	33.0988	1.19983	0.599915	+	0.800064i	$0.295201\pi$
$762$	29.8503	1.08136
$763$	60.4677	2.18908
$764$	−22.5941	−0.817427
$765$	−0.415159	−0.0150101
$766$	−22.9691	−0.829909
$767$	9.22161	0.332973
$768$	−20.7647	−0.749283
$769$	0.484625	0.0174760	0.00873801	−	0.999962i	$-0.497219\pi$
$769$	0.484625	0.0174760	0.00873801	+	0.999962i	$0.497219\pi$
$770$	0	0
$771$	−21.9881	−0.791884
$772$	23.7915	0.856275
$773$	−5.06126	−0.182041	−0.0910205	−	0.995849i	$-0.529013\pi$
$773$	−5.06126	−0.182041	−0.0910205	+	0.995849i	$0.529013\pi$
$774$	−22.6742	−0.815007
$775$	30.1081	1.08152
$776$	−0.276502	−0.00992586
$777$	30.5702	1.09670
$778$	20.5857	0.738033
$779$	7.06889	0.253269
$780$	2.73947	0.0980888
$781$	0	0
$782$	12.2957	0.439692
$783$	7.38223	0.263819
$784$	−85.8765	−3.06702
$785$	4.25346	0.151812
$786$	3.43342	0.122466
$787$	−5.53793	−0.197406	−0.0987030	−	0.995117i	$-0.531469\pi$
$787$	−5.53793	−0.197406	−0.0987030	+	0.995117i	$0.531469\pi$
$788$	−19.9584	−0.710989
$789$	−15.8084	−0.562793
$790$	9.53916	0.339388
$791$	−63.5657	−2.26013
$792$	0	0
$793$	24.1884	0.858955
$794$	−6.22445	−0.220897
$795$	0.852460	0.0302337
$796$	−18.4818	−0.655070
$797$	−27.8358	−0.985995	−0.492997	−	0.870031i	$-0.664099\pi$
$797$	−27.8358	−0.985995	−0.492997	+	0.870031i	$0.664099\pi$
$798$	−21.6628	−0.766855
$799$	−2.19188	−0.0775432
$800$	34.0740	1.20470
$801$	−7.09238	−0.250597
$802$	57.0840	2.01571
$803$	0	0
$804$	7.90434	0.278765
$805$	−13.6510	−0.481136
$806$	50.9295	1.79391
$807$	19.3852	0.682390
$808$	2.82322	0.0993204
$809$	−26.1115	−0.918030	−0.459015	−	0.888429i	$-0.651798\pi$
$809$	−26.1115	−0.918030	−0.459015	+	0.888429i	$0.651798\pi$
$810$	0.778345	0.0273482
$811$	24.1646	0.848535	0.424267	−	0.905537i	$-0.360532\pi$
$811$	24.1646	0.848535	0.424267	+	0.905537i	$0.360532\pi$
$812$	−56.0704	−1.96769
$813$	20.4927	0.718711
$814$	0	0
$815$	−1.69967	−0.0595369
$816$	−4.73486	−0.165753
$817$	−27.8724	−0.975131
$818$	7.60529	0.265913
$819$	−21.8384	−0.763096
$820$	1.92910	0.0673672
$821$	−18.8256	−0.657019	−0.328509	−	0.944501i	$-0.606546\pi$
$821$	−18.8256	−0.657019	−0.328509	+	0.944501i	$0.606546\pi$
$822$	−26.1907	−0.913507
$823$	−11.5651	−0.403133	−0.201566	−	0.979475i	$-0.564603\pi$
$823$	−11.5651	−0.403133	−0.201566	+	0.979475i	$0.564603\pi$
$824$	9.01647	0.314104
$825$	0	0
$826$	−19.9002	−0.692418
$827$	−36.2835	−1.26170	−0.630851	−	0.775904i	$-0.717294\pi$
$827$	−36.2835	−1.26170	−0.630851	+	0.775904i	$0.717294\pi$
$828$	−9.93535	−0.345277
$829$	31.1201	1.08085	0.540424	−	0.841393i	$-0.318264\pi$
$829$	31.1201	1.08085	0.540424	+	0.841393i	$0.318264\pi$
$830$	−2.30945	−0.0801623
$831$	30.0528	1.04252
$832$	16.3901	0.568226
$833$	−18.1371	−0.628413
$834$	14.2048	0.491871
$835$	8.73623	0.302330
$836$	0	0
$837$	6.23661	0.215569
$838$	−71.2005	−2.45958
$839$	−38.0844	−1.31482	−0.657409	−	0.753534i	$-0.728348\pi$
$839$	−38.0844	−1.31482	−0.657409	+	0.753534i	$0.728348\pi$
$840$	1.89298	0.0653139
$841$	25.4973	0.879217
$842$	−20.8480	−0.718468
$843$	−5.40307	−0.186092
$844$	−26.7629	−0.921217
$845$	2.47958	0.0853001
$846$	4.10937	0.141283
$847$	0	0
$848$	9.72225	0.333864
$849$	−16.3473	−0.561039
$850$	9.05092	0.310444
$851$	39.9885	1.37079
$852$	−22.8824	−0.783938
$853$	44.6100	1.52742	0.763708	−	0.645562i	$-0.223377\pi$
$853$	44.6100	1.52742	0.763708	+	0.645562i	$0.223377\pi$
$854$	−52.1986	−1.78620
$855$	0.956784	0.0327213
$856$	−14.5356	−0.496816
$857$	−31.4532	−1.07442	−0.537210	−	0.843449i	$-0.680522\pi$
$857$	−31.4532	−1.07442	−0.537210	+	0.843449i	$0.680522\pi$
$858$	0	0
$859$	−34.1877	−1.16647	−0.583235	−	0.812303i	$-0.698213\pi$
$859$	−34.1877	−1.16647	−0.583235	+	0.812303i	$0.698213\pi$
$860$	−7.60638	−0.259375
$861$	−15.3783	−0.524092
$862$	14.9014	0.507544
$863$	−0.179519	−0.00611089	−0.00305544	−	0.999995i	$-0.500973\pi$
$863$	−0.179519	−0.00611089	−0.00305544	+	0.999995i	$0.500973\pi$
$864$	7.05809	0.240121
$865$	9.44639	0.321187
$866$	18.5882	0.631652
$867$	−1.00000	−0.0339618
$868$	−47.3691	−1.60781
$869$	0	0
$870$	5.74592	0.194805
$871$	22.7269	0.770071
$872$	−10.9683	−0.371434
$873$	0.304037	0.0102901
$874$	−28.3368	−0.958507
$875$	−20.4560	−0.691540
$876$	−17.7000	−0.598026
$877$	9.34557	0.315578	0.157789	−	0.987473i	$-0.449563\pi$
$877$	9.34557	0.315578	0.157789	+	0.987473i	$0.449563\pi$
$878$	−67.7629	−2.28689
$879$	−4.71031	−0.158875
$880$	0	0
$881$	27.4619	0.925214	0.462607	−	0.886564i	$-0.346914\pi$
$881$	27.4619	0.925214	0.462607	+	0.886564i	$0.346914\pi$
$882$	34.0036	1.14496
$883$	39.5421	1.33070	0.665348	−	0.746533i	$-0.268283\pi$
$883$	39.5421	1.33070	0.665348	+	0.746533i	$0.268283\pi$
$884$	6.59861	0.221935
$885$	0.878937	0.0295451
$886$	68.0877	2.28745
$887$	11.5948	0.389315	0.194657	−	0.980871i	$-0.437641\pi$
$887$	11.5948	0.389315	0.194657	+	0.980871i	$0.437641\pi$
$888$	−5.54516	−0.186083
$889$	−79.8268	−2.67730
$890$	−5.52031	−0.185041
$891$	0	0
$892$	7.61744	0.255051
$893$	5.05146	0.169041
$894$	−16.1779	−0.541068
$895$	−8.06276	−0.269508
$896$	35.4042	1.18277
$897$	−28.5665	−0.953808
$898$	50.7466	1.69344
$899$	46.0400	1.53552
$900$	−7.31348	−0.243783
$901$	2.05334	0.0684065
$902$	0	0
$903$	60.6362	2.01785
$904$	11.5302	0.383490
$905$	2.75123	0.0914541
$906$	24.6081	0.817551
$907$	26.1450	0.868130	0.434065	−	0.900882i	$-0.357079\pi$
$907$	26.1450	0.868130	0.434065	+	0.900882i	$0.357079\pi$
$908$	12.5112	0.415197
$909$	−3.10435	−0.102965
$910$	−16.9978	−0.563472
$911$	51.7394	1.71420	0.857101	−	0.515149i	$-0.172263\pi$
$911$	51.7394	1.71420	0.857101	+	0.515149i	$0.172263\pi$
$912$	10.9121	0.361334
$913$	0	0
$914$	14.1301	0.467382
$915$	2.30546	0.0762163
$916$	26.1321	0.863428
$917$	−9.18177	−0.303209
$918$	1.87481	0.0618780
$919$	−48.2642	−1.59209	−0.796044	−	0.605239i	$-0.793078\pi$
$919$	−48.2642	−1.59209	−0.796044	+	0.605239i	$0.793078\pi$
$920$	2.47618	0.0816371
$921$	−8.87224	−0.292350
$922$	−22.9314	−0.755204
$923$	−65.7924	−2.16558
$924$	0	0
$925$	29.4358	0.967843
$926$	−45.8117	−1.50547
$927$	−9.91433	−0.325629
$928$	52.1044	1.71041
$929$	15.4680	0.507488	0.253744	−	0.967271i	$-0.418338\pi$
$929$	15.4680	0.507488	0.253744	+	0.967271i	$0.418338\pi$
$930$	4.85423	0.159176
$931$	41.7991	1.36991
$932$	−22.6954	−0.743411
$933$	−13.7472	−0.450064
$934$	−21.2202	−0.694347
$935$	0	0
$936$	3.96129	0.129479
$937$	−52.7989	−1.72486	−0.862432	−	0.506173i	$-0.831060\pi$
$937$	−52.7989	−1.72486	−0.862432	+	0.506173i	$0.831060\pi$
$938$	−49.0446	−1.60136
$939$	8.35444	0.272637
$940$	1.37854	0.0449631
$941$	1.39401	0.0454435	0.0227218	−	0.999742i	$-0.492767\pi$
$941$	1.39401	0.0454435	0.0227218	+	0.999742i	$0.492767\pi$
$942$	−19.2081	−0.625835
$943$	−20.1162	−0.655074
$944$	10.0242	0.326261
$945$	−2.08148	−0.0677105
$946$	0	0
$947$	−16.7559	−0.544495	−0.272247	−	0.962227i	$-0.587767\pi$
$947$	−16.7559	−0.544495	−0.272247	+	0.962227i	$0.587767\pi$
$948$	−18.5664	−0.603008
$949$	−50.8916	−1.65201
$950$	−20.8589	−0.676753
$951$	10.9017	0.353511
$952$	4.55964	0.147779
$953$	51.4748	1.66743	0.833717	−	0.552192i	$-0.186209\pi$
$953$	51.4748	1.66743	0.833717	+	0.552192i	$0.186209\pi$
$954$	−3.84962	−0.124636
$955$	−6.19186	−0.200364
$956$	23.8818	0.772394
$957$	0	0
$958$	−68.6549	−2.21814
$959$	70.0402	2.26172
$960$	1.56219	0.0504195
$961$	7.89526	0.254686
$962$	49.7922	1.60537
$963$	15.9830	0.515047
$964$	−41.0978	−1.32367
$965$	6.51999	0.209886
$966$	61.6466	1.98345
$967$	14.1467	0.454926	0.227463	−	0.973787i	$-0.426957\pi$
$967$	14.1467	0.454926	0.227463	+	0.973787i	$0.426957\pi$
$968$	0	0
$969$	2.30462	0.0740351
$970$	0.236645	0.00759822
$971$	45.3544	1.45549	0.727746	−	0.685847i	$-0.240568\pi$
$971$	45.3544	1.45549	0.727746	+	0.685847i	$0.240568\pi$
$972$	−1.51492	−0.0485910
$973$	−37.9870	−1.21781
$974$	36.3574	1.16497
$975$	−21.0280	−0.673436
$976$	26.2937	0.841639
$977$	44.6644	1.42894	0.714470	−	0.699666i	$-0.246668\pi$
$977$	44.6644	1.42894	0.714470	+	0.699666i	$0.246668\pi$
$978$	7.67553	0.245436
$979$	0	0
$980$	11.4070	0.364383
$981$	12.0605	0.385063
$982$	−40.5323	−1.29344
$983$	55.4533	1.76869	0.884344	−	0.466837i	$-0.154606\pi$
$983$	55.4533	1.76869	0.884344	+	0.466837i	$0.154606\pi$
$984$	2.78949	0.0889257
$985$	−5.46955	−0.174274
$986$	13.8403	0.440764
$987$	−10.9894	−0.349797
$988$	−15.2073	−0.483808
$989$	79.3174	2.52215
$990$	0	0
$991$	−1.91183	−0.0607314	−0.0303657	−	0.999539i	$-0.509667\pi$
$991$	−1.91183	−0.0607314	−0.0303657	+	0.999539i	$0.509667\pi$
$992$	44.0185	1.39759
$993$	9.64891	0.306199
$994$	141.980	4.50333
$995$	−5.06489	−0.160568
$996$	4.49497	0.142428
$997$	−43.7564	−1.38578	−0.692890	−	0.721044i	$-0.743663\pi$
$997$	−43.7564	−1.38578	−0.692890	+	0.721044i	$0.743663\pi$
$998$	38.8998	1.23135
$999$	6.09734	0.192911

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6171.2.a.bo.1.11	yes	14
11.10	odd	2		6171.2.a.bn.1.4	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6171.2.a.bn.1.4	✓	14	11.10	odd	2
6171.2.a.bo.1.11	yes	14	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:	\( N \)	\(=\)	\( 6171 = 3 \cdot 11^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6171.a (trivial)

\(f(q)\)	\(=\)	\(q+1.87481 q^{2} -1.00000 q^{3} +1.51492 q^{4} +0.415159 q^{5} -1.87481 q^{6} +5.01369 q^{7} -0.909438 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.87481 q^{2} -1.00000 q^{3} +1.51492 q^{4} +0.415159 q^{5} -1.87481 q^{6} +5.01369 q^{7} -0.909438 q^{8} +1.00000 q^{9} +0.778345 q^{10} -1.51492 q^{12} -4.35575 q^{13} +9.39972 q^{14} -0.415159 q^{15} -4.73486 q^{16} -1.00000 q^{17} +1.87481 q^{18} +2.30462 q^{19} +0.628932 q^{20} -5.01369 q^{21} -6.55834 q^{23} +0.909438 q^{24} -4.82764 q^{25} -8.16622 q^{26} -1.00000 q^{27} +7.59533 q^{28} -7.38223 q^{29} -0.778345 q^{30} -6.23661 q^{31} -7.05809 q^{32} -1.87481 q^{34} +2.08148 q^{35} +1.51492 q^{36} -6.09734 q^{37} +4.32073 q^{38} +4.35575 q^{39} -0.377561 q^{40} +3.06727 q^{41} -9.39972 q^{42} -12.0941 q^{43} +0.415159 q^{45} -12.2957 q^{46} +2.19188 q^{47} +4.73486 q^{48} +18.1371 q^{49} -9.05092 q^{50} +1.00000 q^{51} -6.59861 q^{52} -2.05334 q^{53} -1.87481 q^{54} -4.55964 q^{56} -2.30462 q^{57} -13.8403 q^{58} -2.11711 q^{59} -0.628932 q^{60} -5.55321 q^{61} -11.6925 q^{62} +5.01369 q^{63} -3.76287 q^{64} -1.80833 q^{65} -5.21767 q^{67} -1.51492 q^{68} +6.55834 q^{69} +3.90238 q^{70} +15.1047 q^{71} -0.909438 q^{72} +11.6838 q^{73} -11.4314 q^{74} +4.82764 q^{75} +3.49131 q^{76} +8.16622 q^{78} +12.2557 q^{79} -1.96572 q^{80} +1.00000 q^{81} +5.75055 q^{82} -2.96714 q^{83} -7.59533 q^{84} -0.415159 q^{85} -22.6742 q^{86} +7.38223 q^{87} -7.09238 q^{89} +0.778345 q^{90} -21.8384 q^{91} -9.93535 q^{92} +6.23661 q^{93} +4.10937 q^{94} +0.956784 q^{95} +7.05809 q^{96} +0.304037 q^{97} +34.0036 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 14 q^{3} + 14 q^{4} - 2 q^{6} - 6 q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q + 2 * q^2 - 14 * q^3 + 14 * q^4 - 2 * q^6 - 6 * q^7 + 6 * q^8 + 14 * q^9	\( 14 q + 2 q^{2} - 14 q^{3} + 14 q^{4} - 2 q^{6} - 6 q^{7} + 6 q^{8} + 14 q^{9} - 8 q^{10} - 14 q^{12} - 20 q^{13} + 4 q^{14} + 14 q^{16} - 14 q^{17} + 2 q^{18} - 16 q^{19} - 16 q^{20} + 6 q^{21} - 2 q^{23} - 6 q^{24} + 22 q^{25} - 4 q^{26} - 14 q^{27} + 30 q^{28} - 22 q^{29} + 8 q^{30} + 34 q^{32} - 2 q^{34} - 2 q^{35} + 14 q^{36} + 8 q^{37} - 16 q^{38} + 20 q^{39} - 74 q^{40} - 24 q^{41} - 4 q^{42} - 12 q^{43} - 26 q^{46} + 28 q^{47} - 14 q^{48} + 28 q^{49} + 50 q^{50} + 14 q^{51} - 48 q^{52} + 18 q^{53} - 2 q^{54} + 6 q^{56} + 16 q^{57} + 20 q^{59} + 16 q^{60} - 64 q^{61} - 62 q^{62} - 6 q^{63} - 4 q^{64} + 30 q^{65} + 10 q^{67} - 14 q^{68} + 2 q^{69} - 44 q^{70} - 8 q^{71} + 6 q^{72} - 44 q^{73} - 50 q^{74} - 22 q^{75} - 24 q^{76} + 4 q^{78} - 8 q^{79} - 102 q^{80} + 14 q^{81} - 46 q^{82} - 12 q^{83} - 30 q^{84} + 12 q^{86} + 22 q^{87} - 8 q^{89} - 8 q^{90} - 20 q^{91} - 20 q^{92} + 16 q^{94} + 30 q^{95} - 34 q^{96} - 14 q^{97} + 90 q^{98}+O(q^{100}) \) 14 * q + 2 * q^2 - 14 * q^3 + 14 * q^4 - 2 * q^6 - 6 * q^7 + 6 * q^8 + 14 * q^9 - 8 * q^10 - 14 * q^12 - 20 * q^13 + 4 * q^14 + 14 * q^16 - 14 * q^17 + 2 * q^18 - 16 * q^19 - 16 * q^20 + 6 * q^21 - 2 * q^23 - 6 * q^24 + 22 * q^25 - 4 * q^26 - 14 * q^27 + 30 * q^28 - 22 * q^29 + 8 * q^30 + 34 * q^32 - 2 * q^34 - 2 * q^35 + 14 * q^36 + 8 * q^37 - 16 * q^38 + 20 * q^39 - 74 * q^40 - 24 * q^41 - 4 * q^42 - 12 * q^43 - 26 * q^46 + 28 * q^47 - 14 * q^48 + 28 * q^49 + 50 * q^50 + 14 * q^51 - 48 * q^52 + 18 * q^53 - 2 * q^54 + 6 * q^56 + 16 * q^57 + 20 * q^59 + 16 * q^60 - 64 * q^61 - 62 * q^62 - 6 * q^63 - 4 * q^64 + 30 * q^65 + 10 * q^67 - 14 * q^68 + 2 * q^69 - 44 * q^70 - 8 * q^71 + 6 * q^72 - 44 * q^73 - 50 * q^74 - 22 * q^75 - 24 * q^76 + 4 * q^78 - 8 * q^79 - 102 * q^80 + 14 * q^81 - 46 * q^82 - 12 * q^83 - 30 * q^84 + 12 * q^86 + 22 * q^87 - 8 * q^89 - 8 * q^90 - 20 * q^91 - 20 * q^92 + 16 * q^94 + 30 * q^95 - 34 * q^96 - 14 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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