LMFDB - Embedded newform 6171.2.a.bo.1.4

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			1.4
Root			$-1.82410$ 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)

$f(q)$	$=$	$q-1.82410 q^{2} -1.00000 q^{3} +1.32734 q^{4} +0.657004 q^{5} +1.82410 q^{6} -3.24859 q^{7} +1.22700 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.82410 q^{2} -1.00000 q^{3} +1.32734 q^{4} +0.657004 q^{5} +1.82410 q^{6} -3.24859 q^{7} +1.22700 q^{8} +1.00000 q^{9} -1.19844 q^{10} -1.32734 q^{12} +2.31806 q^{13} +5.92575 q^{14} -0.657004 q^{15} -4.89285 q^{16} -1.00000 q^{17} -1.82410 q^{18} -0.181578 q^{19} +0.872066 q^{20} +3.24859 q^{21} -1.40754 q^{23} -1.22700 q^{24} -4.56835 q^{25} -4.22838 q^{26} -1.00000 q^{27} -4.31197 q^{28} +0.267641 q^{29} +1.19844 q^{30} +10.3456 q^{31} +6.47104 q^{32} +1.82410 q^{34} -2.13433 q^{35} +1.32734 q^{36} +10.5132 q^{37} +0.331216 q^{38} -2.31806 q^{39} +0.806146 q^{40} -11.1692 q^{41} -5.92575 q^{42} -2.96482 q^{43} +0.657004 q^{45} +2.56749 q^{46} -8.07501 q^{47} +4.89285 q^{48} +3.55332 q^{49} +8.33312 q^{50} +1.00000 q^{51} +3.07685 q^{52} +8.10614 q^{53} +1.82410 q^{54} -3.98603 q^{56} +0.181578 q^{57} -0.488204 q^{58} +7.32472 q^{59} -0.872066 q^{60} -14.8148 q^{61} -18.8713 q^{62} -3.24859 q^{63} -2.01811 q^{64} +1.52298 q^{65} -5.80751 q^{67} -1.32734 q^{68} +1.40754 q^{69} +3.89324 q^{70} +9.04477 q^{71} +1.22700 q^{72} -0.213833 q^{73} -19.1771 q^{74} +4.56835 q^{75} -0.241015 q^{76} +4.22838 q^{78} +4.97440 q^{79} -3.21462 q^{80} +1.00000 q^{81} +20.3738 q^{82} +13.3206 q^{83} +4.31197 q^{84} -0.657004 q^{85} +5.40812 q^{86} -0.267641 q^{87} -11.4416 q^{89} -1.19844 q^{90} -7.53043 q^{91} -1.86828 q^{92} -10.3456 q^{93} +14.7296 q^{94} -0.119297 q^{95} -6.47104 q^{96} -12.4055 q^{97} -6.48161 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.82410	−1.28983	−0.644916	−	0.764253i	$-0.723108\pi$
$2$	−1.82410	−1.28983	−0.644916	+	0.764253i	$0.723108\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.32734	0.663669
$5$	0.657004	0.293821	0.146911	−	0.989150i	$-0.453067\pi$
$5$	0.657004	0.293821	0.146911	+	0.989150i	$0.453067\pi$
$6$	1.82410	0.744685
$7$	−3.24859	−1.22785	−0.613925	−	0.789364i	$-0.710410\pi$
$7$	−3.24859	−1.22785	−0.613925	+	0.789364i	$0.710410\pi$
$8$	1.22700	0.433811
$9$	1.00000	0.333333
$10$	−1.19844	−0.378980
$11$	0	0
$11$	0	0
$12$	−1.32734	−0.383169
$13$	2.31806	0.642915	0.321458	−	0.946924i	$-0.395827\pi$
$13$	2.31806	0.642915	0.321458	+	0.946924i	$0.395827\pi$
$14$	5.92575	1.58372
$15$	−0.657004	−0.169638
$16$	−4.89285	−1.22321
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.82410	−0.429944
$19$	−0.181578	−0.0416568	−0.0208284	−	0.999783i	$-0.506630\pi$
$19$	−0.181578	−0.0416568	−0.0208284	+	0.999783i	$0.506630\pi$
$20$	0.872066	0.195000
$21$	3.24859	0.708900
$22$	0	0
$23$	−1.40754	−0.293492	−0.146746	−	0.989174i	$-0.546880\pi$
$23$	−1.40754	−0.293492	−0.146746	+	0.989174i	$0.546880\pi$
$24$	−1.22700	−0.250461
$25$	−4.56835	−0.913669
$26$	−4.22838	−0.829253
$27$	−1.00000	−0.192450
$28$	−4.31197	−0.814886
$29$	0.267641	0.0496997	0.0248498	−	0.999691i	$-0.492089\pi$
$29$	0.267641	0.0496997	0.0248498	+	0.999691i	$0.492089\pi$
$30$	1.19844	0.218804
$31$	10.3456	1.85812	0.929058	−	0.369933i	$-0.120620\pi$
$31$	10.3456	1.85812	0.929058	+	0.369933i	$0.120620\pi$
$32$	6.47104	1.14393
$33$	0	0
$34$	1.82410	0.312830
$35$	−2.13433	−0.360768
$36$	1.32734	0.221223
$37$	10.5132	1.72836	0.864180	−	0.503182i	$-0.167838\pi$
$37$	10.5132	1.72836	0.864180	+	0.503182i	$0.167838\pi$
$38$	0.331216	0.0537303
$39$	−2.31806	−0.371187
$40$	0.806146	0.127463
$41$	−11.1692	−1.74434	−0.872169	−	0.489204i	$-0.837287\pi$
$41$	−11.1692	−1.74434	−0.872169	+	0.489204i	$0.837287\pi$
$42$	−5.92575	−0.914362
$43$	−2.96482	−0.452130	−0.226065	−	0.974112i	$-0.572586\pi$
$43$	−2.96482	−0.452130	−0.226065	+	0.974112i	$0.572586\pi$
$44$	0	0
$45$	0.657004	0.0979404
$46$	2.56749	0.378555
$47$	−8.07501	−1.17786	−0.588930	−	0.808184i	$-0.700451\pi$
$47$	−8.07501	−1.17786	−0.588930	+	0.808184i	$0.700451\pi$
$48$	4.89285	0.706222
$49$	3.55332	0.507617
$50$	8.33312	1.17848
$51$	1.00000	0.140028
$52$	3.07685	0.426683
$53$	8.10614	1.11346	0.556732	−	0.830692i	$-0.312055\pi$
$53$	8.10614	1.11346	0.556732	+	0.830692i	$0.312055\pi$
$54$	1.82410	0.248228
$55$	0	0
$56$	−3.98603	−0.532655
$57$	0.181578	0.0240506
$58$	−0.488204	−0.0641043
$59$	7.32472	0.953597	0.476799	−	0.879013i	$-0.341797\pi$
$59$	7.32472	0.953597	0.476799	+	0.879013i	$0.341797\pi$
$60$	−0.872066	−0.112583
$61$	−14.8148	−1.89684	−0.948418	−	0.317022i	$-0.897317\pi$
$61$	−14.8148	−1.89684	−0.948418	+	0.317022i	$0.897317\pi$
$62$	−18.8713	−2.39666
$63$	−3.24859	−0.409284
$64$	−2.01811	−0.252264
$65$	1.52298	0.188902
$66$	0	0
$67$	−5.80751	−0.709501	−0.354750	−	0.934961i	$-0.615434\pi$
$67$	−5.80751	−0.709501	−0.354750	+	0.934961i	$0.615434\pi$
$68$	−1.32734	−0.160963
$69$	1.40754	0.169448
$70$	3.89324	0.465331
$71$	9.04477	1.07342	0.536708	−	0.843768i	$-0.319668\pi$
$71$	9.04477	1.07342	0.536708	+	0.843768i	$0.319668\pi$
$72$	1.22700	0.144604
$73$	−0.213833	−0.0250273	−0.0125136	−	0.999922i	$-0.503983\pi$
$73$	−0.213833	−0.0250273	−0.0125136	+	0.999922i	$0.503983\pi$
$74$	−19.1771	−2.22930
$75$	4.56835	0.527507
$76$	−0.241015	−0.0276463
$77$	0	0
$78$	4.22838	0.478770
$79$	4.97440	0.559664	0.279832	−	0.960049i	$-0.409721\pi$
$79$	4.97440	0.559664	0.279832	+	0.960049i	$0.409721\pi$
$80$	−3.21462	−0.359406
$81$	1.00000	0.111111
$82$	20.3738	2.24991
$83$	13.3206	1.46212	0.731062	−	0.682311i	$-0.239025\pi$
$83$	13.3206	1.46212	0.731062	+	0.682311i	$0.239025\pi$
$84$	4.31197	0.470475
$85$	−0.657004	−0.0712621
$86$	5.40812	0.583173
$87$	−0.267641	−0.0286941
$88$	0	0
$89$	−11.4416	−1.21280	−0.606402	−	0.795158i	$-0.707388\pi$
$89$	−11.4416	−1.21280	−0.606402	+	0.795158i	$0.707388\pi$
$90$	−1.19844	−0.126327
$91$	−7.53043	−0.789404
$92$	−1.86828	−0.194781
$93$	−10.3456	−1.07278
$94$	14.7296	1.51924
$95$	−0.119297	−0.0122397
$96$	−6.47104	−0.660448
$97$	−12.4055	−1.25959	−0.629793	−	0.776763i	$-0.716860\pi$
$97$	−12.4055	−1.25959	−0.629793	+	0.776763i	$0.716860\pi$
$98$	−6.48161	−0.654741
$99$	0	0
$100$	−6.06374	−0.606374
$101$	0.707579	0.0704068	0.0352034	−	0.999380i	$-0.488792\pi$
$101$	0.707579	0.0704068	0.0352034	+	0.999380i	$0.488792\pi$
$102$	−1.82410	−0.180613
$103$	13.7789	1.35768	0.678838	−	0.734288i	$-0.262484\pi$
$103$	13.7789	1.35768	0.678838	+	0.734288i	$0.262484\pi$
$104$	2.84427	0.278904
$105$	2.13433	0.208290
$106$	−14.7864	−1.43618
$107$	−15.9325	−1.54025	−0.770125	−	0.637894i	$-0.779806\pi$
$107$	−15.9325	−1.54025	−0.770125	+	0.637894i	$0.779806\pi$
$108$	−1.32734	−0.127723
$109$	0.819549	0.0784986	0.0392493	−	0.999229i	$-0.487503\pi$
$109$	0.819549	0.0784986	0.0392493	+	0.999229i	$0.487503\pi$
$110$	0	0
$111$	−10.5132	−0.997869
$112$	15.8949	1.50192
$113$	7.91071	0.744177	0.372089	−	0.928197i	$-0.378642\pi$
$113$	7.91071	0.744177	0.372089	+	0.928197i	$0.378642\pi$
$114$	−0.331216	−0.0310212
$115$	−0.924758	−0.0862341
$116$	0.355250	0.0329841
$117$	2.31806	0.214305
$118$	−13.3610	−1.22998
$119$	3.24859	0.297798
$120$	−0.806146	−0.0735907
$121$	0	0
$122$	27.0236	2.44660
$123$	11.1692	1.00709
$124$	13.7320	1.23317
$125$	−6.28644	−0.562276
$126$	5.92575	0.527907
$127$	7.58353	0.672930	0.336465	−	0.941696i	$-0.390769\pi$
$127$	7.58353	0.672930	0.336465	+	0.941696i	$0.390769\pi$
$128$	−9.26084	−0.818550
$129$	2.96482	0.261038
$130$	−2.77806	−0.243652
$131$	10.8112	0.944576	0.472288	−	0.881444i	$-0.343428\pi$
$131$	10.8112	0.944576	0.472288	+	0.881444i	$0.343428\pi$
$132$	0	0
$133$	0.589872	0.0511484
$134$	10.5935	0.915137
$135$	−0.657004	−0.0565459
$136$	−1.22700	−0.105215
$137$	10.7519	0.918595	0.459298	−	0.888282i	$-0.348101\pi$
$137$	10.7519	0.918595	0.459298	+	0.888282i	$0.348101\pi$
$138$	−2.56749	−0.218559
$139$	−11.8050	−1.00129	−0.500643	−	0.865654i	$-0.666903\pi$
$139$	−11.8050	−1.00129	−0.500643	+	0.865654i	$0.666903\pi$
$140$	−2.83298	−0.239431
$141$	8.07501	0.680038
$142$	−16.4986	−1.38453
$143$	0	0
$144$	−4.89285	−0.407738
$145$	0.175841	0.0146028
$146$	0.390052	0.0322810
$147$	−3.55332	−0.293073
$148$	13.9546	1.14706
$149$	1.47578	0.120901	0.0604504	−	0.998171i	$-0.480746\pi$
$149$	1.47578	0.120901	0.0604504	+	0.998171i	$0.480746\pi$
$150$	−8.33312	−0.680396
$151$	−2.73855	−0.222860	−0.111430	−	0.993772i	$-0.535543\pi$
$151$	−2.73855	−0.222860	−0.111430	+	0.993772i	$0.535543\pi$
$152$	−0.222797	−0.0180712
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	6.79707	0.545954
$156$	−3.07685	−0.246345
$157$	7.06534	0.563876	0.281938	−	0.959433i	$-0.409023\pi$
$157$	7.06534	0.563876	0.281938	+	0.959433i	$0.409023\pi$
$158$	−9.07380	−0.721873
$159$	−8.10614	−0.642859
$160$	4.25150	0.336110
$161$	4.57251	0.360364
$162$	−1.82410	−0.143315
$163$	15.3763	1.20437	0.602183	−	0.798358i	$-0.294298\pi$
$163$	15.3763	1.20437	0.602183	+	0.798358i	$0.294298\pi$
$164$	−14.8253	−1.15766
$165$	0	0
$166$	−24.2981	−1.88590
$167$	−3.62589	−0.280580	−0.140290	−	0.990110i	$-0.544803\pi$
$167$	−3.62589	−0.280580	−0.140290	+	0.990110i	$0.544803\pi$
$168$	3.98603	0.307529
$169$	−7.62658	−0.586660
$170$	1.19844	0.0919162
$171$	−0.181578	−0.0138856
$172$	−3.93531	−0.300065
$173$	22.2102	1.68861	0.844306	−	0.535862i	$-0.180013\pi$
$173$	22.2102	1.68861	0.844306	+	0.535862i	$0.180013\pi$
$174$	0.488204	0.0370106
$175$	14.8407	1.12185
$176$	0	0
$177$	−7.32472	−0.550560
$178$	20.8705	1.56431
$179$	2.83571	0.211951	0.105975	−	0.994369i	$-0.466204\pi$
$179$	2.83571	0.211951	0.105975	+	0.994369i	$0.466204\pi$
$180$	0.872066	0.0650000
$181$	−9.29261	−0.690714	−0.345357	−	0.938471i	$-0.612242\pi$
$181$	−9.29261	−0.690714	−0.345357	+	0.938471i	$0.612242\pi$
$182$	13.7363	1.01820
$183$	14.8148	1.09514
$184$	−1.72705	−0.127320
$185$	6.90722	0.507829
$186$	18.8713	1.38371
$187$	0	0
$188$	−10.7183	−0.781710
$189$	3.24859	0.236300
$190$	0.217610	0.0157871
$191$	14.6800	1.06221	0.531103	−	0.847307i	$-0.321778\pi$
$191$	14.6800	1.06221	0.531103	+	0.847307i	$0.321778\pi$
$192$	2.01811	0.145645
$193$	−6.94665	−0.500030	−0.250015	−	0.968242i	$-0.580436\pi$
$193$	−6.94665	−0.500030	−0.250015	+	0.968242i	$0.580436\pi$
$194$	22.6288	1.62466
$195$	−1.52298	−0.109063
$196$	4.71646	0.336890
$197$	−10.0941	−0.719175	−0.359588	−	0.933111i	$-0.617083\pi$
$197$	−10.0941	−0.719175	−0.359588	+	0.933111i	$0.617083\pi$
$198$	0	0
$199$	−0.598039	−0.0423939	−0.0211969	−	0.999775i	$-0.506748\pi$
$199$	−0.598039	−0.0423939	−0.0211969	+	0.999775i	$0.506748\pi$
$200$	−5.60537	−0.396360
$201$	5.80751	0.409630
$202$	−1.29069	−0.0908130
$203$	−0.869455	−0.0610238
$204$	1.32734	0.0929322
$205$	−7.33822	−0.512523
$206$	−25.1341	−1.75118
$207$	−1.40754	−0.0978306
$208$	−11.3419	−0.786422
$209$	0	0
$210$	−3.89324	−0.268659
$211$	−17.6557	−1.21547	−0.607734	−	0.794140i	$-0.707921\pi$
$211$	−17.6557	−1.21547	−0.607734	+	0.794140i	$0.707921\pi$
$212$	10.7596	0.738971
$213$	−9.04477	−0.619737
$214$	29.0624	1.98666
$215$	−1.94790	−0.132845
$216$	−1.22700	−0.0834870
$217$	−33.6084	−2.28149
$218$	−1.49494	−0.101250
$219$	0.213833	0.0144495
$220$	0	0
$221$	−2.31806	−0.155930
$222$	19.1771	1.28708
$223$	−10.9940	−0.736210	−0.368105	−	0.929784i	$-0.619993\pi$
$223$	−10.9940	−0.736210	−0.368105	+	0.929784i	$0.619993\pi$
$224$	−21.0217	−1.40457
$225$	−4.56835	−0.304556
$226$	−14.4299	−0.959864
$227$	20.2072	1.34120	0.670601	−	0.741818i	$-0.266036\pi$
$227$	20.2072	1.34120	0.670601	+	0.741818i	$0.266036\pi$
$228$	0.241015	0.0159616
$229$	13.1908	0.871675	0.435838	−	0.900025i	$-0.356452\pi$
$229$	13.1908	0.871675	0.435838	+	0.900025i	$0.356452\pi$
$230$	1.68685	0.111228
$231$	0	0
$232$	0.328396	0.0215603
$233$	−13.4024	−0.878024	−0.439012	−	0.898481i	$-0.644671\pi$
$233$	−13.4024	−0.878024	−0.439012	+	0.898481i	$0.644671\pi$
$234$	−4.22838	−0.276418
$235$	−5.30531	−0.346080
$236$	9.72237	0.632873
$237$	−4.97440	−0.323122
$238$	−5.92575	−0.384109
$239$	0.454822	0.0294200	0.0147100	−	0.999892i	$-0.495317\pi$
$239$	0.454822	0.0294200	0.0147100	+	0.999892i	$0.495317\pi$
$240$	3.21462	0.207503
$241$	−29.9287	−1.92788	−0.963938	−	0.266129i	$-0.914255\pi$
$241$	−29.9287	−1.92788	−0.963938	+	0.266129i	$0.914255\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−19.6642	−1.25887
$245$	2.33455	0.149149
$246$	−20.3738	−1.29898
$247$	−0.420909	−0.0267818
$248$	12.6940	0.806071
$249$	−13.3206	−0.844158
$250$	11.4671	0.725243
$251$	20.3055	1.28167	0.640837	−	0.767677i	$-0.278588\pi$
$251$	20.3055	1.28167	0.640837	+	0.767677i	$0.278588\pi$
$252$	−4.31197	−0.271629
$253$	0	0
$254$	−13.8331	−0.867967
$255$	0.657004	0.0411432
$256$	20.9289	1.30806
$257$	−10.1155	−0.630987	−0.315493	−	0.948928i	$-0.602170\pi$
$257$	−10.1155	−0.630987	−0.315493	+	0.948928i	$0.602170\pi$
$258$	−5.40812	−0.336695
$259$	−34.1531	−2.12217
$260$	2.02150	0.125368
$261$	0.267641	0.0165666
$262$	−19.7206	−1.21835
$263$	1.06058	0.0653982	0.0326991	−	0.999465i	$-0.489590\pi$
$263$	1.06058	0.0653982	0.0326991	+	0.999465i	$0.489590\pi$
$264$	0	0
$265$	5.32577	0.327159
$266$	−1.07598	−0.0659728
$267$	11.4416	0.700212
$268$	−7.70853	−0.470873
$269$	−0.796592	−0.0485691	−0.0242845	−	0.999705i	$-0.507731\pi$
$269$	−0.796592	−0.0485691	−0.0242845	+	0.999705i	$0.507731\pi$
$270$	1.19844	0.0729348
$271$	−17.7672	−1.07928	−0.539639	−	0.841897i	$-0.681439\pi$
$271$	−17.7672	−1.07928	−0.539639	+	0.841897i	$0.681439\pi$
$272$	4.89285	0.296673
$273$	7.53043	0.455763
$274$	−19.6125	−1.18483
$275$	0	0
$276$	1.86828	0.112457
$277$	10.9383	0.657217	0.328609	−	0.944466i	$-0.393420\pi$
$277$	10.9383	0.657217	0.328609	+	0.944466i	$0.393420\pi$
$278$	21.5335	1.29149
$279$	10.3456	0.619372
$280$	−2.61883	−0.156505
$281$	11.4799	0.684836	0.342418	−	0.939548i	$-0.388754\pi$
$281$	11.4799	0.684836	0.342418	+	0.939548i	$0.388754\pi$
$282$	−14.7296	−0.877136
$283$	2.04388	0.121496	0.0607481	−	0.998153i	$-0.480651\pi$
$283$	2.04388	0.121496	0.0607481	+	0.998153i	$0.480651\pi$
$284$	12.0055	0.712393
$285$	0.119297	0.00706657
$286$	0	0
$287$	36.2842	2.14179
$288$	6.47104	0.381310
$289$	1.00000	0.0588235
$290$	−0.320752	−0.0188352
$291$	12.4055	0.727222
$292$	−0.283829	−0.0166098
$293$	10.0277	0.585826	0.292913	−	0.956139i	$-0.405375\pi$
$293$	10.0277	0.585826	0.292913	+	0.956139i	$0.405375\pi$
$294$	6.48161	0.378015
$295$	4.81237	0.280187
$296$	12.8997	0.749782
$297$	0	0
$298$	−2.69197	−0.155942
$299$	−3.26276	−0.188690
$300$	6.06374	0.350090
$301$	9.63147	0.555149
$302$	4.99539	0.287453
$303$	−0.707579	−0.0406494
$304$	0.888434	0.0509552
$305$	−9.73336	−0.557331
$306$	1.82410	0.104277
$307$	−5.88701	−0.335990	−0.167995	−	0.985788i	$-0.553729\pi$
$307$	−5.88701	−0.335990	−0.167995	+	0.985788i	$0.553729\pi$
$308$	0	0
$309$	−13.7789	−0.783855
$310$	−12.3985	−0.704189
$311$	12.0869	0.685383	0.342691	−	0.939448i	$-0.388662\pi$
$311$	12.0869	0.685383	0.342691	+	0.939448i	$0.388662\pi$
$312$	−2.84427	−0.161025
$313$	−12.6738	−0.716367	−0.358184	−	0.933651i	$-0.616604\pi$
$313$	−12.6738	−0.716367	−0.358184	+	0.933651i	$0.616604\pi$
$314$	−12.8879	−0.727306
$315$	−2.13433	−0.120256
$316$	6.60271	0.371432
$317$	−0.184454	−0.0103600	−0.00517999	−	0.999987i	$-0.501649\pi$
$317$	−0.184454	−0.0103600	−0.00517999	+	0.999987i	$0.501649\pi$
$318$	14.7864	0.829180
$319$	0	0
$320$	−1.32591	−0.0741206
$321$	15.9325	0.889263
$322$	−8.34071	−0.464809
$323$	0.181578	0.0101033
$324$	1.32734	0.0737410
$325$	−10.5897	−0.587412
$326$	−28.0479	−1.55343
$327$	−0.819549	−0.0453212
$328$	−13.7047	−0.756713
$329$	26.2324	1.44624
$330$	0	0
$331$	−6.24713	−0.343373	−0.171687	−	0.985152i	$-0.554922\pi$
$331$	−6.24713	−0.343373	−0.171687	+	0.985152i	$0.554922\pi$
$332$	17.6809	0.970367
$333$	10.5132	0.576120
$334$	6.61399	0.361901
$335$	−3.81556	−0.208466
$336$	−15.8949	−0.867135
$337$	−19.6218	−1.06887	−0.534433	−	0.845211i	$-0.679475\pi$
$337$	−19.6218	−1.06887	−0.534433	+	0.845211i	$0.679475\pi$
$338$	13.9116	0.756693
$339$	−7.91071	−0.429651
$340$	−0.872066	−0.0472944
$341$	0	0
$342$	0.331216	0.0179101
$343$	11.1968	0.604573
$344$	−3.63784	−0.196139
$345$	0.924758	0.0497873
$346$	−40.5136	−2.17803
$347$	25.3923	1.36313	0.681565	−	0.731758i	$-0.261300\pi$
$347$	25.3923	1.36313	0.681565	+	0.731758i	$0.261300\pi$
$348$	−0.355250	−0.0190434
$349$	−28.8843	−1.54614	−0.773071	−	0.634320i	$-0.781280\pi$
$349$	−28.8843	−1.54614	−0.773071	+	0.634320i	$0.781280\pi$
$350$	−27.0709	−1.44700
$351$	−2.31806	−0.123729
$352$	0	0
$353$	−7.16093	−0.381138	−0.190569	−	0.981674i	$-0.561033\pi$
$353$	−7.16093	−0.381138	−0.190569	+	0.981674i	$0.561033\pi$
$354$	13.3610	0.710130
$355$	5.94245	0.315392
$356$	−15.1868	−0.804900
$357$	−3.24859	−0.171933
$358$	−5.17261	−0.273381
$359$	19.9716	1.05406	0.527030	−	0.849847i	$-0.323306\pi$
$359$	19.9716	1.05406	0.527030	+	0.849847i	$0.323306\pi$
$360$	0.806146	0.0424876
$361$	−18.9670	−0.998265
$362$	16.9506	0.890906
$363$	0	0
$364$	−9.99543	−0.523903
$365$	−0.140489	−0.00735354
$366$	−27.0236	−1.41255
$367$	−20.8730	−1.08956	−0.544780	−	0.838579i	$-0.683387\pi$
$367$	−20.8730	−1.08956	−0.544780	+	0.838579i	$0.683387\pi$
$368$	6.88687	0.359003
$369$	−11.1692	−0.581446
$370$	−12.5995	−0.655014
$371$	−26.3335	−1.36717
$372$	−13.7320	−0.711973
$373$	34.9242	1.80830	0.904152	−	0.427210i	$-0.140504\pi$
$373$	34.9242	1.80830	0.904152	+	0.427210i	$0.140504\pi$
$374$	0	0
$375$	6.28644	0.324630
$376$	−9.90806	−0.510969
$377$	0.620409	0.0319527
$378$	−5.92575	−0.304787
$379$	26.5917	1.36592	0.682962	−	0.730454i	$-0.260692\pi$
$379$	26.5917	1.36592	0.682962	+	0.730454i	$0.260692\pi$
$380$	−0.158348	−0.00812308
$381$	−7.58353	−0.388516
$382$	−26.7777	−1.37007
$383$	−19.2150	−0.981841	−0.490921	−	0.871204i	$-0.663340\pi$
$383$	−19.2150	−0.981841	−0.490921	+	0.871204i	$0.663340\pi$
$384$	9.26084	0.472590
$385$	0	0
$386$	12.6714	0.644956
$387$	−2.96482	−0.150710
$388$	−16.4663	−0.835948
$389$	−37.1757	−1.88488	−0.942442	−	0.334370i	$-0.891476\pi$
$389$	−37.1757	−1.88488	−0.942442	+	0.334370i	$0.891476\pi$
$390$	2.77806	0.140673
$391$	1.40754	0.0711822
$392$	4.35993	0.220210
$393$	−10.8112	−0.545351
$394$	18.4127	0.927616
$395$	3.26820	0.164441
$396$	0	0
$397$	3.34528	0.167895	0.0839473	−	0.996470i	$-0.473247\pi$
$397$	3.34528	0.167895	0.0839473	+	0.996470i	$0.473247\pi$
$398$	1.09088	0.0546810
$399$	−0.589872	−0.0295305
$400$	22.3522	1.11761
$401$	5.85514	0.292392	0.146196	−	0.989256i	$-0.453297\pi$
$401$	5.85514	0.292392	0.146196	+	0.989256i	$0.453297\pi$
$402$	−10.5935	−0.528355
$403$	23.9817	1.19461
$404$	0.939197	0.0467268
$405$	0.657004	0.0326468
$406$	1.58597	0.0787105
$407$	0	0
$408$	1.22700	0.0607457
$409$	−23.2816	−1.15120	−0.575600	−	0.817731i	$-0.695232\pi$
$409$	−23.2816	−1.15120	−0.575600	+	0.817731i	$0.695232\pi$
$410$	13.3856	0.661070
$411$	−10.7519	−0.530351
$412$	18.2893	0.901047
$413$	−23.7950	−1.17087
$414$	2.56749	0.126185
$415$	8.75168	0.429603
$416$	15.0003	0.735449
$417$	11.8050	0.578092
$418$	0	0
$419$	21.7518	1.06265	0.531323	−	0.847169i	$-0.321695\pi$
$419$	21.7518	1.06265	0.531323	+	0.847169i	$0.321695\pi$
$420$	2.83298	0.138235
$421$	−13.9271	−0.678765	−0.339383	−	0.940648i	$-0.610218\pi$
$421$	−13.9271	−0.678765	−0.339383	+	0.940648i	$0.610218\pi$
$422$	32.2057	1.56775
$423$	−8.07501	−0.392620
$424$	9.94626	0.483033
$425$	4.56835	0.221597
$426$	16.4986	0.799358
$427$	48.1271	2.32903
$428$	−21.1478	−1.02222
$429$	0	0
$430$	3.55316	0.171348
$431$	−9.57140	−0.461038	−0.230519	−	0.973068i	$-0.574042\pi$
$431$	−9.57140	−0.461038	−0.230519	+	0.973068i	$0.574042\pi$
$432$	4.89285	0.235407
$433$	8.00930	0.384902	0.192451	−	0.981307i	$-0.438356\pi$
$433$	8.00930	0.384902	0.192451	+	0.981307i	$0.438356\pi$
$434$	61.3051	2.94274
$435$	−0.175841	−0.00843094
$436$	1.08782	0.0520971
$437$	0.255578	0.0122259
$438$	−0.390052	−0.0186374
$439$	7.89598	0.376854	0.188427	−	0.982087i	$-0.439661\pi$
$439$	7.89598	0.376854	0.188427	+	0.982087i	$0.439661\pi$
$440$	0	0
$441$	3.55332	0.169206
$442$	4.22838	0.201123
$443$	−12.8953	−0.612674	−0.306337	−	0.951923i	$-0.599103\pi$
$443$	−12.8953	−0.612674	−0.306337	+	0.951923i	$0.599103\pi$
$444$	−13.9546	−0.662255
$445$	−7.51715	−0.356347
$446$	20.0541	0.949588
$447$	−1.47578	−0.0698021
$448$	6.55602	0.309743
$449$	0.362651	0.0171146	0.00855728	−	0.999963i	$-0.497276\pi$
$449$	0.362651	0.0171146	0.00855728	+	0.999963i	$0.497276\pi$
$450$	8.33312	0.392827
$451$	0	0
$452$	10.5002	0.493887
$453$	2.73855	0.128668
$454$	−36.8600	−1.72993
$455$	−4.94752	−0.231944
$456$	0.222797	0.0104334
$457$	−3.02420	−0.141466	−0.0707331	−	0.997495i	$-0.522534\pi$
$457$	−3.02420	−0.141466	−0.0707331	+	0.997495i	$0.522534\pi$
$458$	−24.0614	−1.12432
$459$	1.00000	0.0466760
$460$	−1.22747	−0.0572309
$461$	2.66896	0.124306	0.0621530	−	0.998067i	$-0.480203\pi$
$461$	2.66896	0.124306	0.0621530	+	0.998067i	$0.480203\pi$
$462$	0	0
$463$	−28.4278	−1.32115	−0.660577	−	0.750759i	$-0.729688\pi$
$463$	−28.4278	−1.32115	−0.660577	+	0.750759i	$0.729688\pi$
$464$	−1.30953	−0.0607933
$465$	−6.79707	−0.315207
$466$	24.4474	1.13250
$467$	−1.01138	−0.0468011	−0.0234006	−	0.999726i	$-0.507449\pi$
$467$	−1.01138	−0.0468011	−0.0234006	+	0.999726i	$0.507449\pi$
$468$	3.07685	0.142228
$469$	18.8662	0.871161
$470$	9.67741	0.446386
$471$	−7.06534	−0.325554
$472$	8.98745	0.413681
$473$	0	0
$474$	9.07380	0.416774
$475$	0.829511	0.0380606
$476$	4.31197	0.197639
$477$	8.10614	0.371155
$478$	−0.829640	−0.0379468
$479$	−25.9896	−1.18750	−0.593748	−	0.804651i	$-0.702353\pi$
$479$	−25.9896	−1.18750	−0.593748	+	0.804651i	$0.702353\pi$
$480$	−4.25150	−0.194053
$481$	24.3703	1.11119
$482$	54.5929	2.48664
$483$	−4.57251	−0.208056
$484$	0	0
$485$	−8.15045	−0.370093
$486$	1.82410	0.0827428
$487$	−0.424081	−0.0192170	−0.00960848	−	0.999954i	$-0.503059\pi$
$487$	−0.424081	−0.0192170	−0.00960848	+	0.999954i	$0.503059\pi$
$488$	−18.1778	−0.822869
$489$	−15.3763	−0.695341
$490$	−4.25844	−0.192377
$491$	−26.8998	−1.21397	−0.606986	−	0.794713i	$-0.707622\pi$
$491$	−26.8998	−1.21397	−0.606986	+	0.794713i	$0.707622\pi$
$492$	14.8253	0.668377
$493$	−0.267641	−0.0120539
$494$	0.767780	0.0345441
$495$	0	0
$496$	−50.6192	−2.27287
$497$	−29.3827	−1.31800
$498$	24.2981	1.08882
$499$	−33.6988	−1.50856	−0.754282	−	0.656550i	$-0.772015\pi$
$499$	−33.6988	−1.50856	−0.754282	+	0.656550i	$0.772015\pi$
$500$	−8.34423	−0.373165
$501$	3.62589	0.161993
$502$	−37.0393	−1.65314
$503$	16.0938	0.717585	0.358793	−	0.933417i	$-0.383189\pi$
$503$	16.0938	0.717585	0.358793	+	0.933417i	$0.383189\pi$
$504$	−3.98603	−0.177552
$505$	0.464882	0.0206870
$506$	0	0
$507$	7.62658	0.338708
$508$	10.0659	0.446602
$509$	−34.6575	−1.53617	−0.768084	−	0.640349i	$-0.778790\pi$
$509$	−34.6575	−1.53617	−0.768084	+	0.640349i	$0.778790\pi$
$510$	−1.19844	−0.0530678
$511$	0.694655	0.0307297
$512$	−19.6547	−0.868625
$513$	0.181578	0.00801686
$514$	18.4517	0.813868
$515$	9.05280	0.398914
$516$	3.93531	0.173243
$517$	0	0
$518$	62.2986	2.73724
$519$	−22.2102	−0.974920
$520$	1.86870	0.0819478
$521$	−26.5912	−1.16498	−0.582490	−	0.812838i	$-0.697922\pi$
$521$	−26.5912	−1.16498	−0.582490	+	0.812838i	$0.697922\pi$
$522$	−0.488204	−0.0213681
$523$	13.4235	0.586969	0.293485	−	0.955964i	$-0.405185\pi$
$523$	13.4235	0.586969	0.293485	+	0.955964i	$0.405185\pi$
$524$	14.3501	0.626886
$525$	−14.8407	−0.647700
$526$	−1.93460	−0.0843528
$527$	−10.3456	−0.450659
$528$	0	0
$529$	−21.0188	−0.913863
$530$	−9.71472	−0.421981
$531$	7.32472	0.317866
$532$	0.782959	0.0339456
$533$	−25.8910	−1.12146
$534$	−20.8705	−0.903157
$535$	−10.4677	−0.452558
$536$	−7.12584	−0.307789
$537$	−2.83571	−0.122370
$538$	1.45306	0.0626460
$539$	0	0
$540$	−0.872066	−0.0375277
$541$	17.0639	0.733633	0.366817	−	0.930293i	$-0.380448\pi$
$541$	17.0639	0.733633	0.366817	+	0.930293i	$0.380448\pi$
$542$	32.4090	1.39209
$543$	9.29261	0.398784
$544$	−6.47104	−0.277443
$545$	0.538447	0.0230645
$546$	−13.7363	−0.587858
$547$	−15.4300	−0.659738	−0.329869	−	0.944027i	$-0.607005\pi$
$547$	−15.4300	−0.659738	−0.329869	+	0.944027i	$0.607005\pi$
$548$	14.2714	0.609643
$549$	−14.8148	−0.632279
$550$	0	0
$551$	−0.0485977	−0.00207033
$552$	1.72705	0.0735082
$553$	−16.1598	−0.687184
$554$	−19.9525	−0.847700
$555$	−6.90722	−0.293195
$556$	−15.6692	−0.664522
$557$	−23.0268	−0.975677	−0.487839	−	0.872934i	$-0.662215\pi$
$557$	−23.0268	−0.975677	−0.487839	+	0.872934i	$0.662215\pi$
$558$	−18.8713	−0.798887
$559$	−6.87264	−0.290682
$560$	10.4430	0.441296
$561$	0	0
$562$	−20.9405	−0.883324
$563$	−24.8757	−1.04839	−0.524193	−	0.851600i	$-0.675633\pi$
$563$	−24.8757	−1.04839	−0.524193	+	0.851600i	$0.675633\pi$
$564$	10.7183	0.451320
$565$	5.19737	0.218655
$566$	−3.72824	−0.156710
$567$	−3.24859	−0.136428
$568$	11.0980	0.465660
$569$	−2.56838	−0.107672	−0.0538361	−	0.998550i	$-0.517145\pi$
$569$	−2.56838	−0.107672	−0.0538361	+	0.998550i	$0.517145\pi$
$570$	−0.217610	−0.00911469
$571$	−3.82074	−0.159893	−0.0799465	−	0.996799i	$-0.525475\pi$
$571$	−3.82074	−0.159893	−0.0799465	+	0.996799i	$0.525475\pi$
$572$	0	0
$573$	−14.6800	−0.613265
$574$	−66.1859	−2.76255
$575$	6.43012	0.268154
$576$	−2.01811	−0.0840881
$577$	−31.4716	−1.31018	−0.655090	−	0.755551i	$-0.727369\pi$
$577$	−31.4716	−1.31018	−0.655090	+	0.755551i	$0.727369\pi$
$578$	−1.82410	−0.0758725
$579$	6.94665	0.288693
$580$	0.233401	0.00969143
$581$	−43.2731	−1.79527
$582$	−22.6288	−0.937995
$583$	0	0
$584$	−0.262374	−0.0108571
$585$	1.52298	0.0629674
$586$	−18.2916	−0.755618
$587$	−43.1971	−1.78294	−0.891468	−	0.453084i	$-0.850324\pi$
$587$	−43.1971	−1.78294	−0.891468	+	0.453084i	$0.850324\pi$
$588$	−4.71646	−0.194503
$589$	−1.87852	−0.0774032
$590$	−8.77824	−0.361394
$591$	10.0941	0.415216
$592$	−51.4395	−2.11415
$593$	8.97676	0.368631	0.184316	−	0.982867i	$-0.440993\pi$
$593$	8.97676	0.368631	0.184316	+	0.982867i	$0.440993\pi$
$594$	0	0
$595$	2.13433	0.0874992
$596$	1.95886	0.0802380
$597$	0.598039	0.0244761
$598$	5.95160	0.243379
$599$	−1.71048	−0.0698884	−0.0349442	−	0.999389i	$-0.511125\pi$
$599$	−1.71048	−0.0698884	−0.0349442	+	0.999389i	$0.511125\pi$
$600$	5.60537	0.228838
$601$	−23.7420	−0.968457	−0.484228	−	0.874942i	$-0.660900\pi$
$601$	−23.7420	−0.968457	−0.484228	+	0.874942i	$0.660900\pi$
$602$	−17.5688	−0.716049
$603$	−5.80751	−0.236500
$604$	−3.63499	−0.147905
$605$	0	0
$606$	1.29069	0.0524309
$607$	−46.6621	−1.89396	−0.946979	−	0.321295i	$-0.895882\pi$
$607$	−46.6621	−1.89396	−0.946979	+	0.321295i	$0.895882\pi$
$608$	−1.17500	−0.0476524
$609$	0.869455	0.0352321
$610$	17.7546	0.718863
$611$	−18.7184	−0.757265
$612$	−1.32734	−0.0536544
$613$	39.5182	1.59612	0.798062	−	0.602575i	$-0.205859\pi$
$613$	39.5182	1.59612	0.798062	+	0.602575i	$0.205859\pi$
$614$	10.7385	0.433370
$615$	7.33822	0.295906
$616$	0	0
$617$	−4.97633	−0.200340	−0.100170	−	0.994970i	$-0.531939\pi$
$617$	−4.97633	−0.200340	−0.100170	+	0.994970i	$0.531939\pi$
$618$	25.1341	1.01104
$619$	−45.8947	−1.84466	−0.922332	−	0.386398i	$-0.873719\pi$
$619$	−45.8947	−1.84466	−0.922332	+	0.386398i	$0.873719\pi$
$620$	9.02201	0.362333
$621$	1.40754	0.0564825
$622$	−22.0476	−0.884029
$623$	37.1689	1.48914
$624$	11.3419	0.454041
$625$	18.7115	0.748460
$626$	23.1183	0.923994
$627$	0	0
$628$	9.37810	0.374227
$629$	−10.5132	−0.419189
$630$	3.89324	0.155110
$631$	−48.4773	−1.92985	−0.964926	−	0.262522i	$-0.915446\pi$
$631$	−48.4773	−1.92985	−0.964926	+	0.262522i	$0.915446\pi$
$632$	6.10361	0.242788
$633$	17.6557	0.701751
$634$	0.336463	0.0133626
$635$	4.98241	0.197721
$636$	−10.7596	−0.426645
$637$	8.23682	0.326355
$638$	0	0
$639$	9.04477	0.357806
$640$	−6.08441	−0.240507
$641$	−25.5665	−1.00982	−0.504908	−	0.863173i	$-0.668474\pi$
$641$	−25.5665	−1.00982	−0.504908	+	0.863173i	$0.668474\pi$
$642$	−29.0624	−1.14700
$643$	−16.9985	−0.670356	−0.335178	−	0.942155i	$-0.608796\pi$
$643$	−16.9985	−0.670356	−0.335178	+	0.942155i	$0.608796\pi$
$644$	6.06926	0.239162
$645$	1.94790	0.0766984
$646$	−0.331216	−0.0130315
$647$	22.9495	0.902237	0.451118	−	0.892464i	$-0.351025\pi$
$647$	22.9495	0.902237	0.451118	+	0.892464i	$0.351025\pi$
$648$	1.22700	0.0482012
$649$	0	0
$650$	19.3167	0.757663
$651$	33.6084	1.31722
$652$	20.4096	0.799300
$653$	24.3989	0.954803	0.477401	−	0.878685i	$-0.341579\pi$
$653$	24.3989	0.954803	0.477401	+	0.878685i	$0.341579\pi$
$654$	1.49494	0.0584568
$655$	7.10298	0.277536
$656$	54.6493	2.13370
$657$	−0.213833	−0.00834242
$658$	−47.8504	−1.86540
$659$	−16.1194	−0.627922	−0.313961	−	0.949436i	$-0.601656\pi$
$659$	−16.1194	−0.627922	−0.313961	+	0.949436i	$0.601656\pi$
$660$	0	0
$661$	6.49775	0.252733	0.126367	−	0.991984i	$-0.459668\pi$
$661$	6.49775	0.252733	0.126367	+	0.991984i	$0.459668\pi$
$662$	11.3954	0.442894
$663$	2.31806	0.0900261
$664$	16.3444	0.634286
$665$	0.387548	0.0150285
$666$	−19.1771	−0.743099
$667$	−0.376715	−0.0145864
$668$	−4.81278	−0.186212
$669$	10.9940	0.425051
$670$	6.95996	0.268887
$671$	0	0
$672$	21.0217	0.810931
$673$	−34.4578	−1.32825	−0.664126	−	0.747621i	$-0.731196\pi$
$673$	−34.4578	−1.32825	−0.664126	+	0.747621i	$0.731196\pi$
$674$	35.7921	1.37866
$675$	4.56835	0.175836
$676$	−10.1230	−0.389348
$677$	−14.4074	−0.553720	−0.276860	−	0.960910i	$-0.589294\pi$
$677$	−14.4074	−0.553720	−0.276860	+	0.960910i	$0.589294\pi$
$678$	14.4299	0.554178
$679$	40.3003	1.54658
$680$	−0.806146	−0.0309143
$681$	−20.2072	−0.774343
$682$	0	0
$683$	−46.7542	−1.78900	−0.894499	−	0.447069i	$-0.852468\pi$
$683$	−46.7542	−1.78900	−0.894499	+	0.447069i	$0.852468\pi$
$684$	−0.241015	−0.00921545
$685$	7.06403	0.269903
$686$	−20.4241	−0.779798
$687$	−13.1908	−0.503262
$688$	14.5064	0.553052
$689$	18.7905	0.715863
$690$	−1.68685	−0.0642173
$691$	43.4829	1.65417	0.827083	−	0.562079i	$-0.189998\pi$
$691$	43.4829	1.65417	0.827083	+	0.562079i	$0.189998\pi$
$692$	29.4805	1.12068
$693$	0	0
$694$	−46.3180	−1.75821
$695$	−7.75592	−0.294199
$696$	−0.328396	−0.0124478
$697$	11.1692	0.423064
$698$	52.6878	1.99426
$699$	13.4024	0.506927
$700$	19.6986	0.744536
$701$	−17.4055	−0.657397	−0.328699	−	0.944435i	$-0.606610\pi$
$701$	−17.4055	−0.657397	−0.328699	+	0.944435i	$0.606610\pi$
$702$	4.22838	0.159590
$703$	−1.90897	−0.0719980
$704$	0	0
$705$	5.30531	0.199810
$706$	13.0622	0.491604
$707$	−2.29863	−0.0864490
$708$	−9.72237	−0.365389
$709$	21.1579	0.794603	0.397301	−	0.917688i	$-0.369947\pi$
$709$	21.1579	0.794603	0.397301	+	0.917688i	$0.369947\pi$
$710$	−10.8396	−0.406804
$711$	4.97440	0.186555
$712$	−14.0388	−0.526127
$713$	−14.5618	−0.545342
$714$	5.92575	0.221765
$715$	0	0
$716$	3.76394	0.140665
$717$	−0.454822	−0.0169856
$718$	−36.4301	−1.35956
$719$	−43.1774	−1.61024	−0.805122	−	0.593109i	$-0.797900\pi$
$719$	−43.1774	−1.61024	−0.805122	+	0.593109i	$0.797900\pi$
$720$	−3.21462	−0.119802
$721$	−44.7620	−1.66702
$722$	34.5977	1.28759
$723$	29.9287	1.11306
$724$	−12.3344	−0.458406
$725$	−1.22268	−0.0454091
$726$	0	0
$727$	−7.70737	−0.285850	−0.142925	−	0.989733i	$-0.545651\pi$
$727$	−7.70737	−0.285850	−0.142925	+	0.989733i	$0.545651\pi$
$728$	−9.23986	−0.342452
$729$	1.00000	0.0370370
$730$	0.256266	0.00948483
$731$	2.96482	0.109658
$732$	19.6642	0.726810
$733$	−4.29599	−0.158676	−0.0793380	−	0.996848i	$-0.525281\pi$
$733$	−4.29599	−0.158676	−0.0793380	+	0.996848i	$0.525281\pi$
$734$	38.0743	1.40535
$735$	−2.33455	−0.0861110
$736$	−9.10823	−0.335734
$737$	0	0
$738$	20.3738	0.749968
$739$	31.7398	1.16757	0.583784	−	0.811909i	$-0.301571\pi$
$739$	31.7398	1.16757	0.583784	+	0.811909i	$0.301571\pi$
$740$	9.16821	0.337030
$741$	0.420909	0.0154625
$742$	48.0349	1.76342
$743$	17.6131	0.646161	0.323080	−	0.946372i	$-0.395282\pi$
$743$	17.6131	0.646161	0.323080	+	0.946372i	$0.395282\pi$
$744$	−12.6940	−0.465386
$745$	0.969594	0.0355232
$746$	−63.7051	−2.33241
$747$	13.3206	0.487375
$748$	0	0
$749$	51.7580	1.89120
$750$	−11.4671	−0.418719
$751$	−29.5625	−1.07875	−0.539376	−	0.842065i	$-0.681340\pi$
$751$	−29.5625	−1.07875	−0.539376	+	0.842065i	$0.681340\pi$
$752$	39.5098	1.44077
$753$	−20.3055	−0.739974
$754$	−1.13169	−0.0412136
$755$	−1.79924	−0.0654811
$756$	4.31197	0.156825
$757$	19.9658	0.725669	0.362835	−	0.931854i	$-0.381809\pi$
$757$	19.9658	0.725669	0.362835	+	0.931854i	$0.381809\pi$
$758$	−48.5059	−1.76181
$759$	0	0
$760$	−0.146378	−0.00530970
$761$	−27.1039	−0.982516	−0.491258	−	0.871014i	$-0.663463\pi$
$761$	−27.1039	−0.982516	−0.491258	+	0.871014i	$0.663463\pi$
$762$	13.8331	0.501121
$763$	−2.66238	−0.0963846
$764$	19.4853	0.704953
$765$	−0.657004	−0.0237540
$766$	35.0501	1.26641
$767$	16.9792	0.613082
$768$	−20.9289	−0.755207
$769$	−39.5168	−1.42501	−0.712505	−	0.701667i	$-0.752440\pi$
$769$	−39.5168	−1.42501	−0.712505	+	0.701667i	$0.752440\pi$
$770$	0	0
$771$	10.1155	0.364300
$772$	−9.22054	−0.331855
$773$	−10.8934	−0.391809	−0.195904	−	0.980623i	$-0.562764\pi$
$773$	−10.8934	−0.391809	−0.195904	+	0.980623i	$0.562764\pi$
$774$	5.40812	0.194391
$775$	−47.2621	−1.69770
$776$	−15.2216	−0.546422
$777$	34.1531	1.22523
$778$	67.8122	2.43118
$779$	2.02808	0.0726636
$780$	−2.02150	−0.0723815
$781$	0	0
$782$	−2.56749	−0.0918132
$783$	−0.267641	−0.00956471
$784$	−17.3859	−0.620924
$785$	4.64196	0.165679
$786$	19.7206	0.703412
$787$	−18.3266	−0.653272	−0.326636	−	0.945150i	$-0.605915\pi$
$787$	−18.3266	−0.653272	−0.326636	+	0.945150i	$0.605915\pi$
$788$	−13.3983	−0.477294
$789$	−1.06058	−0.0377577
$790$	−5.96152	−0.212102
$791$	−25.6986	−0.913738
$792$	0	0
$793$	−34.3416	−1.21951
$794$	−6.10212	−0.216556
$795$	−5.32577	−0.188885
$796$	−0.793800	−0.0281355
$797$	52.2117	1.84943	0.924716	−	0.380658i	$-0.124303\pi$
$797$	52.2117	1.84943	0.924716	+	0.380658i	$0.124303\pi$
$798$	1.07598	0.0380894
$799$	8.07501	0.285673
$800$	−29.5619	−1.04517
$801$	−11.4416	−0.404268
$802$	−10.6804	−0.377136
$803$	0	0
$804$	7.70853	0.271859
$805$	3.00416	0.105883
$806$	−43.7449	−1.54085
$807$	0.796592	0.0280414
$808$	0.868202	0.0305432
$809$	26.4190	0.928844	0.464422	−	0.885614i	$-0.346262\pi$
$809$	26.4190	0.928844	0.464422	+	0.885614i	$0.346262\pi$
$810$	−1.19844	−0.0421089
$811$	−34.2857	−1.20393	−0.601967	−	0.798521i	$-0.705616\pi$
$811$	−34.2857	−1.20393	−0.601967	+	0.798521i	$0.705616\pi$
$812$	−1.15406	−0.0404996
$813$	17.7672	0.623121
$814$	0	0
$815$	10.1023	0.353868
$816$	−4.89285	−0.171284
$817$	0.538345	0.0188343
$818$	42.4679	1.48486
$819$	−7.53043	−0.263135
$820$	−9.74029	−0.340146
$821$	36.2831	1.26629	0.633144	−	0.774034i	$-0.281764\pi$
$821$	36.2831	1.26629	0.633144	+	0.774034i	$0.281764\pi$
$822$	19.6125	0.684065
$823$	3.02378	0.105402	0.0527011	−	0.998610i	$-0.483217\pi$
$823$	3.02378	0.105402	0.0527011	+	0.998610i	$0.483217\pi$
$824$	16.9068	0.588975
$825$	0	0
$826$	43.4044	1.51023
$827$	9.61790	0.334447	0.167224	−	0.985919i	$-0.446520\pi$
$827$	9.61790	0.334447	0.167224	+	0.985919i	$0.446520\pi$
$828$	−1.86828	−0.0649271
$829$	40.2465	1.39782	0.698909	−	0.715210i	$-0.253669\pi$
$829$	40.2465	1.39782	0.698909	+	0.715210i	$0.253669\pi$
$830$	−15.9639	−0.554116
$831$	−10.9383	−0.379444
$832$	−4.67812	−0.162185
$833$	−3.55332	−0.123115
$834$	−21.5335	−0.745643
$835$	−2.38223	−0.0824403
$836$	0	0
$837$	−10.3456	−0.357595
$838$	−39.6775	−1.37064
$839$	26.9444	0.930224	0.465112	−	0.885252i	$-0.346014\pi$
$839$	26.9444	0.930224	0.465112	+	0.885252i	$0.346014\pi$
$840$	2.61883	0.0903584
$841$	−28.9284	−0.997530
$842$	25.4044	0.875493
$843$	−11.4799	−0.395390
$844$	−23.4351	−0.806669
$845$	−5.01069	−0.172373
$846$	14.7296	0.506415
$847$	0	0
$848$	−39.6621	−1.36200
$849$	−2.04388	−0.0701458
$850$	−8.33312	−0.285824
$851$	−14.7977	−0.507260
$852$	−12.0055	−0.411300
$853$	−19.3402	−0.662196	−0.331098	−	0.943596i	$-0.607419\pi$
$853$	−19.3402	−0.662196	−0.331098	+	0.943596i	$0.607419\pi$
$854$	−87.7885	−3.00406
$855$	−0.119297	−0.00407989
$856$	−19.5492	−0.668177
$857$	−33.8211	−1.15531	−0.577654	−	0.816282i	$-0.696032\pi$
$857$	−33.8211	−1.15531	−0.577654	+	0.816282i	$0.696032\pi$
$858$	0	0
$859$	−10.8900	−0.371562	−0.185781	−	0.982591i	$-0.559481\pi$
$859$	−10.8900	−0.371562	−0.185781	+	0.982591i	$0.559481\pi$
$860$	−2.58552	−0.0881654
$861$	−36.2842	−1.23656
$862$	17.4592	0.594662
$863$	21.3375	0.726338	0.363169	−	0.931723i	$-0.381695\pi$
$863$	21.3375	0.726338	0.363169	+	0.931723i	$0.381695\pi$
$864$	−6.47104	−0.220149
$865$	14.5922	0.496150
$866$	−14.6097	−0.496459
$867$	−1.00000	−0.0339618
$868$	−44.6097	−1.51415
$869$	0	0
$870$	0.320752	0.0108745
$871$	−13.4622	−0.456149
$872$	1.00559	0.0340536
$873$	−12.4055	−0.419862
$874$	−0.466199	−0.0157694
$875$	20.4221	0.690391
$876$	0.283829	0.00958968
$877$	−6.78879	−0.229241	−0.114621	−	0.993409i	$-0.536565\pi$
$877$	−6.78879	−0.229241	−0.114621	+	0.993409i	$0.536565\pi$
$878$	−14.4030	−0.486079
$879$	−10.0277	−0.338227
$880$	0	0
$881$	−47.7280	−1.60800	−0.803999	−	0.594630i	$-0.797298\pi$
$881$	−47.7280	−1.60800	−0.803999	+	0.594630i	$0.797298\pi$
$882$	−6.48161	−0.218247
$883$	0.418699	0.0140903	0.00704517	−	0.999975i	$-0.497757\pi$
$883$	0.418699	0.0140903	0.00704517	+	0.999975i	$0.497757\pi$
$884$	−3.07685	−0.103486
$885$	−4.81237	−0.161766
$886$	23.5223	0.790247
$887$	52.4517	1.76115	0.880577	−	0.473902i	$-0.157155\pi$
$887$	52.4517	1.76115	0.880577	+	0.473902i	$0.157155\pi$
$888$	−12.8997	−0.432887
$889$	−24.6358	−0.826257
$890$	13.7120	0.459628
$891$	0	0
$892$	−14.5927	−0.488599
$893$	1.46624	0.0490660
$894$	2.69197	0.0900330
$895$	1.86307	0.0622756
$896$	30.0846	1.00506
$897$	3.26276	0.108940
$898$	−0.661511	−0.0220749
$899$	2.76889	0.0923478
$900$	−6.06374	−0.202125
$901$	−8.10614	−0.270055
$902$	0	0
$903$	−9.63147	−0.320515
$904$	9.70647	0.322832
$905$	−6.10528	−0.202946
$906$	−4.99539	−0.165961
$907$	−18.6363	−0.618809	−0.309404	−	0.950931i	$-0.600130\pi$
$907$	−18.6363	−0.618809	−0.309404	+	0.950931i	$0.600130\pi$
$908$	26.8218	0.890114
$909$	0.707579	0.0234689
$910$	9.02478	0.299168
$911$	−29.8280	−0.988246	−0.494123	−	0.869392i	$-0.664511\pi$
$911$	−29.8280	−0.988246	−0.494123	+	0.869392i	$0.664511\pi$
$912$	−0.888434	−0.0294190
$913$	0	0
$914$	5.51645	0.182468
$915$	9.73336	0.321775
$916$	17.5087	0.578504
$917$	−35.1210	−1.15980
$918$	−1.82410	−0.0602042
$919$	56.9860	1.87979	0.939897	−	0.341459i	$-0.110921\pi$
$919$	56.9860	1.87979	0.939897	+	0.341459i	$0.110921\pi$
$920$	−1.13468	−0.0374093
$921$	5.88701	0.193984
$922$	−4.86845	−0.160334
$923$	20.9664	0.690116
$924$	0	0
$925$	−48.0280	−1.57915
$926$	51.8552	1.70407
$927$	13.7789	0.452559
$928$	1.73191	0.0568529
$929$	−52.8809	−1.73497	−0.867483	−	0.497467i	$-0.834264\pi$
$929$	−52.8809	−1.73497	−0.867483	+	0.497467i	$0.834264\pi$
$930$	12.3985	0.406564
$931$	−0.645204	−0.0211457
$932$	−17.7896	−0.582717
$933$	−12.0869	−0.395706
$934$	1.84486	0.0603656
$935$	0	0
$936$	2.84427	0.0929679
$937$	−37.4632	−1.22387	−0.611935	−	0.790908i	$-0.709609\pi$
$937$	−37.4632	−1.22387	−0.611935	+	0.790908i	$0.709609\pi$
$938$	−34.4138	−1.12365
$939$	12.6738	0.413595
$940$	−7.04194	−0.229683
$941$	−28.8233	−0.939614	−0.469807	−	0.882769i	$-0.655677\pi$
$941$	−28.8233	−0.939614	−0.469807	+	0.882769i	$0.655677\pi$
$942$	12.8879	0.419910
$943$	15.7211	0.511949
$944$	−35.8387	−1.16645
$945$	2.13433	0.0694299
$946$	0	0
$947$	53.1301	1.72649	0.863247	−	0.504781i	$-0.168427\pi$
$947$	53.1301	1.72649	0.863247	+	0.504781i	$0.168427\pi$
$948$	−6.60271	−0.214446
$949$	−0.495678	−0.0160904
$950$	−1.51311	−0.0490918
$951$	0.184454	0.00598133
$952$	3.98603	0.129188
$953$	−35.1212	−1.13769	−0.568844	−	0.822445i	$-0.692609\pi$
$953$	−35.1212	−1.13769	−0.568844	+	0.822445i	$0.692609\pi$
$954$	−14.7864	−0.478727
$955$	9.64481	0.312099
$956$	0.603702	0.0195251
$957$	0	0
$958$	47.4077	1.53167
$959$	−34.9284	−1.12790
$960$	1.32591	0.0427935
$961$	76.0305	2.45260
$962$	−44.4538	−1.43325
$963$	−15.9325	−0.513416
$964$	−39.7254	−1.27947
$965$	−4.56397	−0.146920
$966$	8.34071	0.268358
$967$	16.9678	0.545649	0.272825	−	0.962064i	$-0.412042\pi$
$967$	16.9678	0.545649	0.272825	+	0.962064i	$0.412042\pi$
$968$	0	0
$969$	−0.181578	−0.00583312
$970$	14.8672	0.477358
$971$	−30.5487	−0.980353	−0.490176	−	0.871623i	$-0.663068\pi$
$971$	−30.5487	−0.980353	−0.490176	+	0.871623i	$0.663068\pi$
$972$	−1.32734	−0.0425744
$973$	38.3495	1.22943
$974$	0.773566	0.0247867
$975$	10.5897	0.339142
$976$	72.4864	2.32023
$977$	−32.3744	−1.03575	−0.517874	−	0.855457i	$-0.673276\pi$
$977$	−32.3744	−1.03575	−0.517874	+	0.855457i	$0.673276\pi$
$978$	28.0479	0.896874
$979$	0	0
$980$	3.09873	0.0989853
$981$	0.819549	0.0261662
$982$	49.0679	1.56582
$983$	−3.64075	−0.116122	−0.0580610	−	0.998313i	$-0.518492\pi$
$983$	−3.64075	−0.116122	−0.0580610	+	0.998313i	$0.518492\pi$
$984$	13.7047	0.436889
$985$	−6.63187	−0.211309
$986$	0.488204	0.0155476
$987$	−26.2324	−0.834985
$988$	−0.558689	−0.0177743
$989$	4.17309	0.132697
$990$	0	0
$991$	−14.4533	−0.459126	−0.229563	−	0.973294i	$-0.573730\pi$
$991$	−14.4533	−0.459126	−0.229563	+	0.973294i	$0.573730\pi$
$992$	66.9465	2.12555
$993$	6.24713	0.198247
$994$	53.5970	1.69999
$995$	−0.392914	−0.0124562
$996$	−17.6809	−0.560241
$997$	−51.6891	−1.63701	−0.818505	−	0.574500i	$-0.805197\pi$
$997$	−51.6891	−1.63701	−0.818505	+	0.574500i	$0.805197\pi$
$998$	61.4699	1.94580
$999$	−10.5132	−0.332623

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6171.2.a.bn.1.11	✓	14	11.10	odd	2
6171.2.a.bo.1.4	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)

\(f(q)\)	\(=\)	\(q-1.82410 q^{2} -1.00000 q^{3} +1.32734 q^{4} +0.657004 q^{5} +1.82410 q^{6} -3.24859 q^{7} +1.22700 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.82410 q^{2} -1.00000 q^{3} +1.32734 q^{4} +0.657004 q^{5} +1.82410 q^{6} -3.24859 q^{7} +1.22700 q^{8} +1.00000 q^{9} -1.19844 q^{10} -1.32734 q^{12} +2.31806 q^{13} +5.92575 q^{14} -0.657004 q^{15} -4.89285 q^{16} -1.00000 q^{17} -1.82410 q^{18} -0.181578 q^{19} +0.872066 q^{20} +3.24859 q^{21} -1.40754 q^{23} -1.22700 q^{24} -4.56835 q^{25} -4.22838 q^{26} -1.00000 q^{27} -4.31197 q^{28} +0.267641 q^{29} +1.19844 q^{30} +10.3456 q^{31} +6.47104 q^{32} +1.82410 q^{34} -2.13433 q^{35} +1.32734 q^{36} +10.5132 q^{37} +0.331216 q^{38} -2.31806 q^{39} +0.806146 q^{40} -11.1692 q^{41} -5.92575 q^{42} -2.96482 q^{43} +0.657004 q^{45} +2.56749 q^{46} -8.07501 q^{47} +4.89285 q^{48} +3.55332 q^{49} +8.33312 q^{50} +1.00000 q^{51} +3.07685 q^{52} +8.10614 q^{53} +1.82410 q^{54} -3.98603 q^{56} +0.181578 q^{57} -0.488204 q^{58} +7.32472 q^{59} -0.872066 q^{60} -14.8148 q^{61} -18.8713 q^{62} -3.24859 q^{63} -2.01811 q^{64} +1.52298 q^{65} -5.80751 q^{67} -1.32734 q^{68} +1.40754 q^{69} +3.89324 q^{70} +9.04477 q^{71} +1.22700 q^{72} -0.213833 q^{73} -19.1771 q^{74} +4.56835 q^{75} -0.241015 q^{76} +4.22838 q^{78} +4.97440 q^{79} -3.21462 q^{80} +1.00000 q^{81} +20.3738 q^{82} +13.3206 q^{83} +4.31197 q^{84} -0.657004 q^{85} +5.40812 q^{86} -0.267641 q^{87} -11.4416 q^{89} -1.19844 q^{90} -7.53043 q^{91} -1.86828 q^{92} -10.3456 q^{93} +14.7296 q^{94} -0.119297 q^{95} -6.47104 q^{96} -12.4055 q^{97} -6.48161 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 14 q^{3} + 14 q^{4} - 2 q^{6} - 6 q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 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

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Database

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