LMFDB - Embedded newform 1859.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.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:	$14.8441897358$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.361.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x + 7 $ x^3 - x^2 - 6*x + 7
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.28514$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28514 q^{2} +1.22188 q^{3} +3.22188 q^{4} +2.50702 q^{5} -2.79216 q^{6} +4.50702 q^{7} -2.79216 q^{8} -1.50702 q^{9} +O(q^{10})$	\(q-2.28514 q^{2} +1.22188 q^{3} +3.22188 q^{4} +2.50702 q^{5} -2.79216 q^{6} +4.50702 q^{7} -2.79216 q^{8} -1.50702 q^{9} -5.72889 q^{10} +1.00000 q^{11} +3.93673 q^{12} -10.2992 q^{14} +3.06327 q^{15} -0.0632663 q^{16} -3.22188 q^{17} +3.44375 q^{18} -2.34841 q^{19} +8.07730 q^{20} +5.50702 q^{21} -2.28514 q^{22} +5.79216 q^{23} -3.41168 q^{24} +1.28514 q^{25} -5.50702 q^{27} +14.5211 q^{28} -0.619514 q^{29} -7.00000 q^{30} +6.01404 q^{31} +5.72889 q^{32} +1.22188 q^{33} +7.36245 q^{34} +11.2992 q^{35} -4.85543 q^{36} +5.06327 q^{37} +5.36645 q^{38} -7.00000 q^{40} -8.36245 q^{41} -12.5843 q^{42} +11.0913 q^{43} +3.22188 q^{44} -3.77812 q^{45} -13.2359 q^{46} +6.74293 q^{47} -0.0773036 q^{48} +13.3132 q^{49} -2.93673 q^{50} -3.93673 q^{51} -4.06327 q^{53} +12.5843 q^{54} +2.50702 q^{55} -12.5843 q^{56} -2.86946 q^{57} +1.41568 q^{58} +11.0633 q^{59} +9.86946 q^{60} -0.144573 q^{61} -13.7429 q^{62} -6.79216 q^{63} -12.9648 q^{64} -2.79216 q^{66} +8.72889 q^{67} -10.3805 q^{68} +7.07730 q^{69} -25.8202 q^{70} -1.71486 q^{71} +4.20784 q^{72} -2.00000 q^{73} -11.5703 q^{74} +1.57028 q^{75} -7.56628 q^{76} +4.50702 q^{77} +1.87347 q^{79} -0.158610 q^{80} -2.20784 q^{81} +19.1094 q^{82} -5.38049 q^{83} +17.7429 q^{84} -8.07730 q^{85} -25.3453 q^{86} -0.756969 q^{87} -2.79216 q^{88} -8.50702 q^{89} +8.63355 q^{90} +18.6616 q^{92} +7.34841 q^{93} -15.4086 q^{94} -5.88750 q^{95} +7.00000 q^{96} +0.112495 q^{97} -30.4226 q^{98} -1.50702 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + q^{3} + 7 q^{4} - q^{5} + 6 q^{6} + 5 q^{7} + 6 q^{8} + 4 q^{9}+O(q^{10}) $ 3 * q - q^2 + q^3 + 7 * q^4 - q^5 + 6 * q^6 + 5 * q^7 + 6 * q^8 + 4 * q^9	$ 3 q - q^{2} + q^{3} + 7 q^{4} - q^{5} + 6 q^{6} + 5 q^{7} + 6 q^{8} + 4 q^{9} - 6 q^{10} + 3 q^{11} + 15 q^{12} - 8 q^{14} + 6 q^{15} + 3 q^{16} - 7 q^{17} + 5 q^{18} + 2 q^{19} + 4 q^{20} + 8 q^{21} - q^{22} + 3 q^{23} + 2 q^{24} - 2 q^{25} - 8 q^{27} + 18 q^{28} - 4 q^{29} - 21 q^{30} + q^{31} + 6 q^{32} + q^{33} - 4 q^{34} + 11 q^{35} + 3 q^{36} + 12 q^{37} + 31 q^{38} - 21 q^{40} + q^{41} - 9 q^{42} - 4 q^{43} + 7 q^{44} - 14 q^{45} - 20 q^{46} - 8 q^{47} + 20 q^{48} - 12 q^{50} - 15 q^{51} - 9 q^{53} + 9 q^{54} - q^{55} - 9 q^{56} + 26 q^{57} + 33 q^{58} + 30 q^{59} - 5 q^{60} - 18 q^{61} - 13 q^{62} - 6 q^{63} - 8 q^{64} + 6 q^{66} + 15 q^{67} - 29 q^{68} + q^{69} - 29 q^{70} - 11 q^{71} + 27 q^{72} - 6 q^{73} - 23 q^{74} - 7 q^{75} + 30 q^{76} + 5 q^{77} + 12 q^{79} - q^{80} - 21 q^{81} + 44 q^{82} - 14 q^{83} + 25 q^{84} - 4 q^{85} - 43 q^{86} + 43 q^{87} + 6 q^{88} - 17 q^{89} + 11 q^{90} + 7 q^{92} + 13 q^{93} - 10 q^{94} - 7 q^{95} + 21 q^{96} + 11 q^{97} - 38 q^{98} + 4 q^{99}+O(q^{100}) $ 3 * q - q^2 + q^3 + 7 * q^4 - q^5 + 6 * q^6 + 5 * q^7 + 6 * q^8 + 4 * q^9 - 6 * q^10 + 3 * q^11 + 15 * q^12 - 8 * q^14 + 6 * q^15 + 3 * q^16 - 7 * q^17 + 5 * q^18 + 2 * q^19 + 4 * q^20 + 8 * q^21 - q^22 + 3 * q^23 + 2 * q^24 - 2 * q^25 - 8 * q^27 + 18 * q^28 - 4 * q^29 - 21 * q^30 + q^31 + 6 * q^32 + q^33 - 4 * q^34 + 11 * q^35 + 3 * q^36 + 12 * q^37 + 31 * q^38 - 21 * q^40 + q^41 - 9 * q^42 - 4 * q^43 + 7 * q^44 - 14 * q^45 - 20 * q^46 - 8 * q^47 + 20 * q^48 - 12 * q^50 - 15 * q^51 - 9 * q^53 + 9 * q^54 - q^55 - 9 * q^56 + 26 * q^57 + 33 * q^58 + 30 * q^59 - 5 * q^60 - 18 * q^61 - 13 * q^62 - 6 * q^63 - 8 * q^64 + 6 * q^66 + 15 * q^67 - 29 * q^68 + q^69 - 29 * q^70 - 11 * q^71 + 27 * q^72 - 6 * q^73 - 23 * q^74 - 7 * q^75 + 30 * q^76 + 5 * q^77 + 12 * q^79 - q^80 - 21 * q^81 + 44 * q^82 - 14 * q^83 + 25 * q^84 - 4 * q^85 - 43 * q^86 + 43 * q^87 + 6 * q^88 - 17 * q^89 + 11 * q^90 + 7 * q^92 + 13 * q^93 - 10 * q^94 - 7 * q^95 + 21 * q^96 + 11 * q^97 - 38 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.28514	−1.61584	−0.807920	−	0.589292i	$-0.799407\pi$
$2$	−2.28514	−1.61584	−0.807920	+	0.589292i	$0.799407\pi$
$3$	1.22188	0.705451	0.352725	−	0.935727i	$-0.385255\pi$
$3$	1.22188	0.705451	0.352725	+	0.935727i	$0.385255\pi$
$4$	3.22188	1.61094
$5$	2.50702	1.12117	0.560586	−	0.828096i	$-0.310576\pi$
$5$	2.50702	1.12117	0.560586	+	0.828096i	$0.310576\pi$
$6$	−2.79216	−1.13990
$7$	4.50702	1.70349	0.851746	−	0.523954i	$-0.175544\pi$
$7$	4.50702	1.70349	0.851746	+	0.523954i	$0.175544\pi$
$8$	−2.79216	−0.987178
$9$	−1.50702	−0.502340
$10$	−5.72889	−1.81164
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.93673	1.13644
$13$	0	0
$13$	0	0
$14$	−10.2992	−2.75257
$15$	3.06327	0.790932
$16$	−0.0632663	−0.0158166
$17$	−3.22188	−0.781420	−0.390710	−	0.920514i	$-0.627770\pi$
$17$	−3.22188	−0.781420	−0.390710	+	0.920514i	$0.627770\pi$
$18$	3.44375	0.811700
$19$	−2.34841	−0.538762	−0.269381	−	0.963034i	$-0.586819\pi$
$19$	−2.34841	−0.538762	−0.269381	+	0.963034i	$0.586819\pi$
$20$	8.07730	1.80614
$21$	5.50702	1.20173
$22$	−2.28514	−0.487194
$23$	5.79216	1.20775	0.603875	−	0.797079i	$-0.293623\pi$
$23$	5.79216	1.20775	0.603875	+	0.797079i	$0.293623\pi$
$24$	−3.41168	−0.696405
$25$	1.28514	0.257028
$26$	0	0
$27$	−5.50702	−1.05983
$28$	14.5211	2.74422
$29$	−0.619514	−0.115041	−0.0575204	−	0.998344i	$-0.518319\pi$
$29$	−0.619514	−0.115041	−0.0575204	+	0.998344i	$0.518319\pi$
$30$	−7.00000	−1.27802
$31$	6.01404	1.08015	0.540076	−	0.841616i	$-0.318395\pi$
$31$	6.01404	1.08015	0.540076	+	0.841616i	$0.318395\pi$
$32$	5.72889	1.01274
$33$	1.22188	0.212701
$34$	7.36245	1.26265
$35$	11.2992	1.90991
$36$	−4.85543	−0.809238
$37$	5.06327	0.832396	0.416198	−	0.909274i	$-0.363362\pi$
$37$	5.06327	0.832396	0.416198	+	0.909274i	$0.363362\pi$
$38$	5.36645	0.870553
$39$	0	0
$40$	−7.00000	−1.10680
$41$	−8.36245	−1.30599	−0.652997	−	0.757360i	$-0.726489\pi$
$41$	−8.36245	−1.30599	−0.652997	+	0.757360i	$0.726489\pi$
$42$	−12.5843	−1.94180
$43$	11.0913	1.69141	0.845707	−	0.533648i	$-0.179179\pi$
$43$	11.0913	1.69141	0.845707	+	0.533648i	$0.179179\pi$
$44$	3.22188	0.485716
$45$	−3.77812	−0.563209
$46$	−13.2359	−1.95153
$47$	6.74293	0.983558	0.491779	−	0.870720i	$-0.336347\pi$
$47$	6.74293	0.983558	0.491779	+	0.870720i	$0.336347\pi$
$48$	−0.0773036	−0.0111578
$49$	13.3132	1.90189
$50$	−2.93673	−0.415317
$51$	−3.93673	−0.551253
$52$	0	0
$53$	−4.06327	−0.558133	−0.279066	−	0.960272i	$-0.590025\pi$
$53$	−4.06327	−0.558133	−0.279066	+	0.960272i	$0.590025\pi$
$54$	12.5843	1.71251
$55$	2.50702	0.338046
$56$	−12.5843	−1.68165
$57$	−2.86946	−0.380070
$58$	1.41568	0.185888
$59$	11.0633	1.44031	0.720157	−	0.693811i	$-0.244070\pi$
$59$	11.0633	1.44031	0.720157	+	0.693811i	$0.244070\pi$
$60$	9.86946	1.27414
$61$	−0.144573	−0.0185106	−0.00925531	−	0.999957i	$-0.502946\pi$
$61$	−0.144573	−0.0185106	−0.00925531	+	0.999957i	$0.502946\pi$
$62$	−13.7429	−1.74535
$63$	−6.79216	−0.855732
$64$	−12.9648	−1.62060
$65$	0	0
$66$	−2.79216	−0.343691
$67$	8.72889	1.06640	0.533202	−	0.845988i	$-0.320989\pi$
$67$	8.72889	1.06640	0.533202	+	0.845988i	$0.320989\pi$
$68$	−10.3805	−1.25882
$69$	7.07730	0.852007
$70$	−25.8202	−3.08611
$71$	−1.71486	−0.203516	−0.101758	−	0.994809i	$-0.532447\pi$
$71$	−1.71486	−0.203516	−0.101758	+	0.994809i	$0.532447\pi$
$72$	4.20784	0.495899
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	−11.5703	−1.34502
$75$	1.57028	0.181321
$76$	−7.56628	−0.867912
$77$	4.50702	0.513622
$78$	0	0
$79$	1.87347	0.210782	0.105391	−	0.994431i	$-0.466391\pi$
$79$	1.87347	0.210782	0.105391	+	0.994431i	$0.466391\pi$
$80$	−0.158610	−0.0177331
$81$	−2.20784	−0.245315
$82$	19.1094	2.11028
$83$	−5.38049	−0.590585	−0.295293	−	0.955407i	$-0.595417\pi$
$83$	−5.38049	−0.590585	−0.295293	+	0.955407i	$0.595417\pi$
$84$	17.7429	1.93591
$85$	−8.07730	−0.876107
$86$	−25.3453	−2.73305
$87$	−0.756969	−0.0811556
$88$	−2.79216	−0.297645
$89$	−8.50702	−0.901742	−0.450871	−	0.892589i	$-0.648887\pi$
$89$	−8.50702	−0.901742	−0.450871	+	0.892589i	$0.648887\pi$
$90$	8.63355	0.910056
$91$	0	0
$92$	18.6616	1.94561
$93$	7.34841	0.761994
$94$	−15.4086	−1.58927
$95$	−5.88750	−0.604045
$96$	7.00000	0.714435
$97$	0.112495	0.0114222	0.00571109	−	0.999984i	$-0.498182\pi$
$97$	0.112495	0.0114222	0.00571109	+	0.999984i	$0.498182\pi$
$98$	−30.4226	−3.07315
$99$	−1.50702	−0.151461
$100$	4.14057	0.414057
$101$	−12.7570	−1.26937	−0.634683	−	0.772773i	$-0.718869\pi$
$101$	−12.7570	−1.26937	−0.634683	+	0.772773i	$0.718869\pi$
$102$	8.99600	0.890736
$103$	15.6304	1.54011	0.770056	−	0.637976i	$-0.220228\pi$
$103$	15.6304	1.54011	0.770056	+	0.637976i	$0.220228\pi$
$104$	0	0
$105$	13.8062	1.34735
$106$	9.28514	0.901853
$107$	−5.61951	−0.543259	−0.271629	−	0.962402i	$-0.587563\pi$
$107$	−5.61951	−0.543259	−0.271629	+	0.962402i	$0.587563\pi$
$108$	−17.7429	−1.70731
$109$	9.90466	0.948694	0.474347	−	0.880338i	$-0.342684\pi$
$109$	9.90466	0.948694	0.474347	+	0.880338i	$0.342684\pi$
$110$	−5.72889	−0.546229
$111$	6.18668	0.587214
$112$	−0.285142	−0.0269434
$113$	8.24995	0.776090	0.388045	−	0.921640i	$-0.373150\pi$
$113$	8.24995	0.776090	0.388045	+	0.921640i	$0.373150\pi$
$114$	6.55714	0.614132
$115$	14.5211	1.35410
$116$	−1.99600	−0.185324
$117$	0	0
$118$	−25.2811	−2.32732
$119$	−14.5211	−1.33114
$120$	−8.55313	−0.780791
$121$	1.00000	0.0909091
$122$	0.330369	0.0299102
$123$	−10.2179	−0.921315
$124$	19.3765	1.74006
$125$	−9.31322	−0.832999
$126$	15.5211	1.38273
$127$	−6.07730	−0.539273	−0.269637	−	0.962962i	$-0.586904\pi$
$127$	−6.07730	−0.539273	−0.269637	+	0.962962i	$0.586904\pi$
$128$	18.1686	1.60590
$129$	13.5522	1.19321
$130$	0	0
$131$	−11.9508	−1.04414	−0.522072	−	0.852902i	$-0.674841\pi$
$131$	−11.9508	−1.04414	−0.522072	+	0.852902i	$0.674841\pi$
$132$	3.93673	0.342649
$133$	−10.5843	−0.917777
$134$	−19.9468	−1.72314
$135$	−13.8062	−1.18825
$136$	8.99600	0.771400
$137$	−2.27111	−0.194034	−0.0970168	−	0.995283i	$-0.530930\pi$
$137$	−2.27111	−0.194034	−0.0970168	+	0.995283i	$0.530930\pi$
$138$	−16.1726	−1.37671
$139$	−10.1546	−0.861303	−0.430651	−	0.902518i	$-0.641716\pi$
$139$	−10.1546	−0.861303	−0.430651	+	0.902518i	$0.641716\pi$
$140$	36.4046	3.07675
$141$	8.23903	0.693851
$142$	3.91869	0.328849
$143$	0	0
$144$	0.0953435	0.00794529
$145$	−1.55313	−0.128981
$146$	4.57028	0.378239
$147$	16.2671	1.34169
$148$	16.3132	1.34094
$149$	−10.9648	−0.898272	−0.449136	−	0.893463i	$-0.648268\pi$
$149$	−10.9648	−0.898272	−0.449136	+	0.893463i	$0.648268\pi$
$150$	−3.58832	−0.292985
$151$	−10.8835	−0.885687	−0.442843	−	0.896599i	$-0.646030\pi$
$151$	−10.8835	−0.885687	−0.442843	+	0.896599i	$0.646030\pi$
$152$	6.55714	0.531854
$153$	4.85543	0.392538
$154$	−10.2992	−0.829932
$155$	15.0773	1.21104
$156$	0	0
$157$	13.9820	1.11588	0.557941	−	0.829881i	$-0.311592\pi$
$157$	13.9820	1.11588	0.557941	+	0.829881i	$0.311592\pi$
$158$	−4.28114	−0.340589
$159$	−4.96481	−0.393735
$160$	14.3624	1.13545
$161$	26.1054	2.05739
$162$	5.04523	0.396390
$163$	1.39452	0.109227	0.0546137	−	0.998508i	$-0.482607\pi$
$163$	1.39452	0.109227	0.0546137	+	0.998508i	$0.482607\pi$
$164$	−26.9428	−2.10388
$165$	3.06327	0.238475
$166$	12.2952	0.954291
$167$	23.8343	1.84435	0.922176	−	0.386771i	$-0.126410\pi$
$167$	23.8343	1.84435	0.922176	+	0.386771i	$0.126410\pi$
$168$	−15.3765	−1.18632
$169$	0	0
$170$	18.4578	1.41565
$171$	3.53910	0.270641
$172$	35.7349	2.72476
$173$	−7.39764	−0.562432	−0.281216	−	0.959644i	$-0.590738\pi$
$173$	−7.39764	−0.562432	−0.281216	+	0.959644i	$0.590738\pi$
$174$	1.72978	0.131135
$175$	5.79216	0.437846
$176$	−0.0632663	−0.00476888
$177$	13.5179	1.01607
$178$	19.4397	1.45707
$179$	18.5211	1.38433	0.692164	−	0.721740i	$-0.256657\pi$
$179$	18.5211	1.38433	0.692164	+	0.721740i	$0.256657\pi$
$180$	−12.1726	−0.907296
$181$	−18.0561	−1.34210	−0.671051	−	0.741411i	$-0.734157\pi$
$181$	−18.0561	−1.34210	−0.671051	+	0.741411i	$0.734157\pi$
$182$	0	0
$183$	−0.176650	−0.0130583
$184$	−16.1726	−1.19226
$185$	12.6937	0.933260
$186$	−16.7922	−1.23126
$187$	−3.22188	−0.235607
$188$	21.7249	1.58445
$189$	−24.8202	−1.80541
$190$	13.4538	0.976040
$191$	−3.36245	−0.243298	−0.121649	−	0.992573i	$-0.538818\pi$
$191$	−3.36245	−0.243298	−0.121649	+	0.992573i	$0.538818\pi$
$192$	−15.8414	−1.14325
$193$	15.5984	1.12279	0.561397	−	0.827546i	$-0.310264\pi$
$193$	15.5984	1.12279	0.561397	+	0.827546i	$0.310264\pi$
$194$	−0.257068	−0.0184564
$195$	0	0
$196$	42.8935	3.06382
$197$	−21.0281	−1.49819	−0.749094	−	0.662464i	$-0.769511\pi$
$197$	−21.0281	−1.49819	−0.749094	+	0.662464i	$0.769511\pi$
$198$	3.44375	0.244737
$199$	−22.6124	−1.60295	−0.801475	−	0.598028i	$-0.795951\pi$
$199$	−22.6124	−1.60295	−0.801475	+	0.598028i	$0.795951\pi$
$200$	−3.58832	−0.253733
$201$	10.6656	0.752295
$202$	29.1515	2.05109
$203$	−2.79216	−0.195971
$204$	−12.6837	−0.888034
$205$	−20.9648	−1.46425
$206$	−35.7178	−2.48858
$207$	−8.72889	−0.606700
$208$	0	0
$209$	−2.34841	−0.162443
$210$	−31.5491	−2.17710
$211$	20.3765	1.40277	0.701387	−	0.712780i	$-0.252564\pi$
$211$	20.3765	1.40277	0.701387	+	0.712780i	$0.252564\pi$
$212$	−13.0913	−0.899117
$213$	−2.09534	−0.143571
$214$	12.8414	0.877819
$215$	27.8062	1.89637
$216$	15.3765	1.04624
$217$	27.1054	1.84003
$218$	−22.6336	−1.53294
$219$	−2.44375	−0.165133
$220$	8.07730	0.544572
$221$	0	0
$222$	−14.1375	−0.948844
$223$	−17.7741	−1.19024	−0.595122	−	0.803636i	$-0.702896\pi$
$223$	−17.7741	−1.19024	−0.595122	+	0.803636i	$0.702896\pi$
$224$	25.8202	1.72519
$225$	−1.93673	−0.129116
$226$	−18.8523	−1.25404
$227$	5.82024	0.386303	0.193151	−	0.981169i	$-0.438129\pi$
$227$	5.82024	0.386303	0.193151	+	0.981169i	$0.438129\pi$
$228$	−9.24506	−0.612269
$229$	23.6656	1.56387	0.781934	−	0.623361i	$-0.214233\pi$
$229$	23.6656	1.56387	0.781934	+	0.623361i	$0.214233\pi$
$230$	−33.1827	−2.18800
$231$	5.50702	0.362335
$232$	1.72978	0.113566
$233$	−22.8875	−1.49941	−0.749705	−	0.661772i	$-0.769805\pi$
$233$	−22.8875	−1.49941	−0.749705	+	0.661772i	$0.769805\pi$
$234$	0	0
$235$	16.9047	1.10274
$236$	35.6445	2.32026
$237$	2.28915	0.148696
$238$	33.1827	2.15091
$239$	16.2007	1.04794	0.523969	−	0.851737i	$-0.324451\pi$
$239$	16.2007	1.04794	0.523969	+	0.851737i	$0.324451\pi$
$240$	−0.193802	−0.0125098
$241$	0.193802	0.0124839	0.00624193	−	0.999981i	$-0.498013\pi$
$241$	0.193802	0.0124839	0.00624193	+	0.999981i	$0.498013\pi$
$242$	−2.28514	−0.146895
$243$	13.8234	0.886768
$244$	−0.465795	−0.0298195
$245$	33.3765	2.13235
$246$	23.3493	1.48870
$247$	0	0
$248$	−16.7922	−1.06630
$249$	−6.57429	−0.416629
$250$	21.2820	1.34599
$251$	8.14057	0.513828	0.256914	−	0.966434i	$-0.417294\pi$
$251$	8.14057	0.513828	0.256914	+	0.966434i	$0.417294\pi$
$252$	−21.8835	−1.37853
$253$	5.79216	0.364150
$254$	13.8875	0.871380
$255$	−9.86946	−0.618050
$256$	−15.5883	−0.974270
$257$	−17.8975	−1.11642	−0.558209	−	0.829700i	$-0.688511\pi$
$257$	−17.8975	−1.11642	−0.558209	+	0.829700i	$0.688511\pi$
$258$	−30.9688	−1.92803
$259$	22.8202	1.41798
$260$	0	0
$261$	0.933619	0.0577896
$262$	27.3092	1.68717
$263$	−15.5672	−0.959913	−0.479956	−	0.877292i	$-0.659348\pi$
$263$	−15.5672	−0.959913	−0.479956	+	0.877292i	$0.659348\pi$
$264$	−3.41168	−0.209974
$265$	−10.1867	−0.625763
$266$	24.1867	1.48298
$267$	−10.3945	−0.636134
$268$	28.1234	1.71791
$269$	−1.49298	−0.0910287	−0.0455143	−	0.998964i	$-0.514493\pi$
$269$	−1.49298	−0.0910287	−0.0455143	+	0.998964i	$0.514493\pi$
$270$	31.5491	1.92002
$271$	23.2711	1.41362	0.706809	−	0.707404i	$-0.250134\pi$
$271$	23.2711	1.41362	0.706809	+	0.707404i	$0.250134\pi$
$272$	0.203836	0.0123594
$273$	0	0
$274$	5.18980	0.313527
$275$	1.28514	0.0774970
$276$	22.8022	1.37253
$277$	−14.0602	−0.844793	−0.422396	−	0.906411i	$-0.638811\pi$
$277$	−14.0602	−0.844793	−0.422396	+	0.906411i	$0.638811\pi$
$278$	23.2047	1.39173
$279$	−9.06327	−0.542604
$280$	−31.5491	−1.88542
$281$	11.6797	0.696750	0.348375	−	0.937355i	$-0.386734\pi$
$281$	11.6797	0.696750	0.348375	+	0.937355i	$0.386734\pi$
$282$	−18.8274	−1.12115
$283$	−3.47183	−0.206379	−0.103189	−	0.994662i	$-0.532905\pi$
$283$	−3.47183	−0.206379	−0.103189	+	0.994662i	$0.532905\pi$
$284$	−5.52506	−0.327852
$285$	−7.19380	−0.426124
$286$	0	0
$287$	−37.6897	−2.22475
$288$	−8.63355	−0.508737
$289$	−6.61951	−0.389383
$290$	3.54913	0.208412
$291$	0.137455	0.00805778
$292$	−6.44375	−0.377092
$293$	6.37960	0.372700	0.186350	−	0.982483i	$-0.440334\pi$
$293$	6.37960	0.372700	0.186350	+	0.982483i	$0.440334\pi$
$294$	−37.1726	−2.16795
$295$	27.7358	1.61484
$296$	−14.1375	−0.821723
$297$	−5.50702	−0.319550
$298$	25.0561	1.45146
$299$	0	0
$300$	5.05926	0.292097
$301$	49.9889	2.88131
$302$	24.8704	1.43113
$303$	−15.5874	−0.895475
$304$	0.148575	0.00852137
$305$	−0.362446	−0.0207536
$306$	−11.0953	−0.634279
$307$	5.06327	0.288976	0.144488	−	0.989507i	$-0.453847\pi$
$307$	5.06327	0.288976	0.144488	+	0.989507i	$0.453847\pi$
$308$	14.5211	0.827414
$309$	19.0985	1.08647
$310$	−34.4538	−1.95684
$311$	2.91958	0.165554	0.0827771	−	0.996568i	$-0.473621\pi$
$311$	2.91958	0.165554	0.0827771	+	0.996568i	$0.473621\pi$
$312$	0	0
$313$	15.7882	0.892399	0.446200	−	0.894933i	$-0.352777\pi$
$313$	15.7882	0.892399	0.446200	+	0.894933i	$0.352777\pi$
$314$	−31.9508	−1.80309
$315$	−17.0281	−0.959423
$316$	6.03608	0.339556
$317$	−20.4397	−1.14801	−0.574005	−	0.818852i	$-0.694611\pi$
$317$	−20.4397	−1.14801	−0.574005	+	0.818852i	$0.694611\pi$
$318$	11.3453	0.636213
$319$	−0.619514	−0.0346861
$320$	−32.5030	−1.81697
$321$	−6.86635	−0.383242
$322$	−59.6545	−3.32442
$323$	7.56628	0.420999
$324$	−7.11338	−0.395188
$325$	0	0
$326$	−3.18668	−0.176494
$327$	12.1023	0.669257
$328$	23.3493	1.28925
$329$	30.3905	1.67548
$330$	−7.00000	−0.385337
$331$	−28.2811	−1.55447	−0.777236	−	0.629209i	$-0.783379\pi$
$331$	−28.2811	−1.55447	−0.777236	+	0.629209i	$0.783379\pi$
$332$	−17.3353	−0.951396
$333$	−7.63044	−0.418145
$334$	−54.4647	−2.98018
$335$	21.8835	1.19562
$336$	−0.348409	−0.0190073
$337$	−31.9256	−1.73910	−0.869550	−	0.493846i	$-0.835591\pi$
$337$	−31.9256	−1.73910	−0.869550	+	0.493846i	$0.835591\pi$
$338$	0	0
$339$	10.0804	0.547493
$340$	−26.0241	−1.41135
$341$	6.01404	0.325678
$342$	−8.08734	−0.437313
$343$	28.4538	1.53636
$344$	−30.9688	−1.66973
$345$	17.7429	0.955247
$346$	16.9047	0.908800
$347$	−1.91869	−0.103001	−0.0515004	−	0.998673i	$-0.516400\pi$
$347$	−1.91869	−0.103001	−0.0515004	+	0.998673i	$0.516400\pi$
$348$	−2.43886	−0.130737
$349$	−0.189799	−0.0101597	−0.00507985	−	0.999987i	$-0.501617\pi$
$349$	−0.189799	−0.0101597	−0.00507985	+	0.999987i	$0.501617\pi$
$350$	−13.2359	−0.707489
$351$	0	0
$352$	5.72889	0.305351
$353$	−10.9499	−0.582803	−0.291402	−	0.956601i	$-0.594122\pi$
$353$	−10.9499	−0.582803	−0.291402	+	0.956601i	$0.594122\pi$
$354$	−30.8904	−1.64181
$355$	−4.29918	−0.228177
$356$	−27.4086	−1.45265
$357$	−17.7429	−0.939056
$358$	−42.3233	−2.23685
$359$	3.79216	0.200143	0.100071	−	0.994980i	$-0.468093\pi$
$359$	3.79216	0.200143	0.100071	+	0.994980i	$0.468093\pi$
$360$	10.5491	0.555988
$361$	−13.4850	−0.709736
$362$	41.2609	2.16862
$363$	1.22188	0.0641319
$364$	0	0
$365$	−5.01404	−0.262447
$366$	0.403670	0.0211002
$367$	−25.0069	−1.30535	−0.652675	−	0.757638i	$-0.726353\pi$
$367$	−25.0069	−1.30535	−0.652675	+	0.757638i	$0.726353\pi$
$368$	−0.366449	−0.0191025
$369$	12.6024	0.656053
$370$	−29.0069	−1.50800
$371$	−18.3132	−0.950775
$372$	23.6757	1.22753
$373$	−8.67967	−0.449416	−0.224708	−	0.974426i	$-0.572143\pi$
$373$	−8.67967	−0.449416	−0.224708	+	0.974426i	$0.572143\pi$
$374$	7.36245	0.380703
$375$	−11.3796	−0.587640
$376$	−18.8274	−0.970947
$377$	0	0
$378$	56.7178	2.91725
$379$	14.7149	0.755851	0.377926	−	0.925836i	$-0.376637\pi$
$379$	14.7149	0.755851	0.377926	+	0.925836i	$0.376637\pi$
$380$	−18.9688	−0.973079
$381$	−7.42571	−0.380431
$382$	7.68367	0.393131
$383$	−5.39052	−0.275443	−0.137721	−	0.990471i	$-0.543978\pi$
$383$	−5.39052	−0.275443	−0.137721	+	0.990471i	$0.543978\pi$
$384$	22.1998	1.13288
$385$	11.2992	0.575860
$386$	−35.6445	−1.81426
$387$	−16.7149	−0.849664
$388$	0.362446	0.0184004
$389$	−21.5531	−1.09279	−0.546394	−	0.837529i	$-0.684000\pi$
$389$	−21.5531	−1.09279	−0.546394	+	0.837529i	$0.684000\pi$
$390$	0	0
$391$	−18.6616	−0.943759
$392$	−37.1726	−1.87750
$393$	−14.6024	−0.736592
$394$	48.0521	2.42083
$395$	4.69682	0.236323
$396$	−4.85543	−0.243994
$397$	−17.5311	−0.879860	−0.439930	−	0.898032i	$-0.644997\pi$
$397$	−17.5311	−0.879860	−0.439930	+	0.898032i	$0.644997\pi$
$398$	51.6725	2.59011
$399$	−12.9327	−0.647446
$400$	−0.0813062	−0.00406531
$401$	−36.4366	−1.81956	−0.909779	−	0.415092i	$-0.863749\pi$
$401$	−36.4366	−1.81956	−0.909779	+	0.415092i	$0.863749\pi$
$402$	−24.3725	−1.21559
$403$	0	0
$404$	−41.1014	−2.04487
$405$	−5.53509	−0.275041
$406$	6.38049	0.316658
$407$	5.06327	0.250977
$408$	10.9920	0.544185
$409$	28.8664	1.42735	0.713675	−	0.700477i	$-0.247030\pi$
$409$	28.8664	1.42735	0.713675	+	0.700477i	$0.247030\pi$
$410$	47.9076	2.36599
$411$	−2.77501	−0.136881
$412$	50.3593	2.48103
$413$	49.8623	2.45357
$414$	19.9468	0.980330
$415$	−13.4890	−0.662148
$416$	0	0
$417$	−12.4077	−0.607606
$418$	5.36645	0.262482
$419$	−4.20472	−0.205414	−0.102707	−	0.994712i	$-0.532750\pi$
$419$	−4.20472	−0.205414	−0.102707	+	0.994712i	$0.532750\pi$
$420$	44.4819	2.17049
$421$	13.5843	0.662059	0.331030	−	0.943620i	$-0.392604\pi$
$421$	13.5843	0.662059	0.331030	+	0.943620i	$0.392604\pi$
$422$	−46.5632	−2.26666
$423$	−10.1617	−0.494080
$424$	11.3453	0.550976
$425$	−4.14057	−0.200847
$426$	4.78816	0.231987
$427$	−0.651591	−0.0315327
$428$	−18.1054	−0.875156
$429$	0	0
$430$	−63.5411	−3.06423
$431$	−30.0381	−1.44688	−0.723442	−	0.690385i	$-0.757441\pi$
$431$	−30.0381	−1.44688	−0.723442	+	0.690385i	$0.757441\pi$
$432$	0.348409	0.0167628
$433$	4.25707	0.204582	0.102291	−	0.994755i	$-0.467383\pi$
$433$	4.25707	0.204582	0.102291	+	0.994755i	$0.467383\pi$
$434$	−61.9397	−2.97320
$435$	−1.89774	−0.0909895
$436$	31.9116	1.52829
$437$	−13.6024	−0.650689
$438$	5.58432	0.266829
$439$	−5.00311	−0.238786	−0.119393	−	0.992847i	$-0.538095\pi$
$439$	−5.00311	−0.238786	−0.119393	+	0.992847i	$0.538095\pi$
$440$	−7.00000	−0.333712
$441$	−20.0633	−0.955394
$442$	0	0
$443$	28.3101	1.34505	0.672527	−	0.740073i	$-0.265209\pi$
$443$	28.3101	1.34505	0.672527	+	0.740073i	$0.265209\pi$
$444$	19.9327	0.945966
$445$	−21.3273	−1.01101
$446$	40.6164	1.92324
$447$	−13.3976	−0.633687
$448$	−58.4326	−2.76068
$449$	−5.72578	−0.270216	−0.135108	−	0.990831i	$-0.543138\pi$
$449$	−5.72578	−0.270216	−0.135108	+	0.990831i	$0.543138\pi$
$450$	4.42571	0.208630
$451$	−8.36245	−0.393772
$452$	26.5803	1.25023
$453$	−13.2983	−0.624808
$454$	−13.3001	−0.624203
$455$	0	0
$456$	8.01201	0.375197
$457$	−12.4899	−0.584251	−0.292126	−	0.956380i	$-0.594363\pi$
$457$	−12.4899	−0.584251	−0.292126	+	0.956380i	$0.594363\pi$
$458$	−54.0793	−2.52696
$459$	17.7429	0.828169
$460$	46.7850	2.18136
$461$	−13.1726	−0.613511	−0.306756	−	0.951788i	$-0.599243\pi$
$461$	−13.1726	−0.613511	−0.306756	+	0.951788i	$0.599243\pi$
$462$	−12.5843	−0.585476
$463$	−10.4086	−0.483727	−0.241863	−	0.970310i	$-0.577759\pi$
$463$	−10.4086	−0.483727	−0.241863	+	0.970310i	$0.577759\pi$
$464$	0.0391944	0.00181955
$465$	18.4226	0.854328
$466$	52.3012	2.42281
$467$	23.3553	1.08076	0.540378	−	0.841422i	$-0.318281\pi$
$467$	23.3553	1.08076	0.540378	+	0.841422i	$0.318281\pi$
$468$	0	0
$469$	39.3413	1.81661
$470$	−38.6295	−1.78185
$471$	17.0842	0.787199
$472$	−30.8904	−1.42185
$473$	11.0913	0.509980
$474$	−5.23102	−0.240269
$475$	−3.01804	−0.138477
$476$	−46.7850	−2.14439
$477$	6.12342	0.280372
$478$	−37.0210	−1.69330
$479$	8.22188	0.375667	0.187834	−	0.982201i	$-0.439853\pi$
$479$	8.22188	0.375667	0.187834	+	0.982201i	$0.439853\pi$
$480$	17.5491	0.801005
$481$	0	0
$482$	−0.442864	−0.0201719
$483$	31.8975	1.45139
$484$	3.22188	0.146449
$485$	0.282028	0.0128062
$486$	−31.5883	−1.43288
$487$	3.73893	0.169427	0.0847135	−	0.996405i	$-0.473002\pi$
$487$	3.73893	0.169427	0.0847135	+	0.996405i	$0.473002\pi$
$488$	0.403670	0.0182733
$489$	1.70393	0.0770546
$490$	−76.2700	−3.44553
$491$	−8.17665	−0.369007	−0.184504	−	0.982832i	$-0.559068\pi$
$491$	−8.17665	−0.369007	−0.184504	+	0.982832i	$0.559068\pi$
$492$	−32.9207	−1.48418
$493$	1.99600	0.0898952
$494$	0	0
$495$	−3.77812	−0.169814
$496$	−0.380486	−0.0170843
$497$	−7.72889	−0.346688
$498$	15.0232	0.673205
$499$	−0.918694	−0.0411264	−0.0205632	−	0.999789i	$-0.506546\pi$
$499$	−0.918694	−0.0411264	−0.0205632	+	0.999789i	$0.506546\pi$
$500$	−30.0060	−1.34191
$501$	29.1225	1.30110
$502$	−18.6024	−0.830264
$503$	−18.1085	−0.807418	−0.403709	−	0.914887i	$-0.632279\pi$
$503$	−18.1085	−0.807418	−0.403709	+	0.914887i	$0.632279\pi$
$504$	18.9648	0.844760
$505$	−31.9820	−1.42318
$506$	−13.2359	−0.588408
$507$	0	0
$508$	−19.5803	−0.868736
$509$	20.4086	0.904594	0.452297	−	0.891867i	$-0.350605\pi$
$509$	20.4086	0.904594	0.452297	+	0.891867i	$0.350605\pi$
$510$	22.5531	0.998670
$511$	−9.01404	−0.398758
$512$	−0.715746	−0.0316318
$513$	12.9327	0.570994
$514$	40.8984	1.80395
$515$	39.1858	1.72673
$516$	43.6637	1.92219
$517$	6.74293	0.296554
$518$	−52.1475	−2.29123
$519$	−9.03900	−0.396768
$520$	0	0
$521$	−12.0069	−0.526033	−0.263016	−	0.964791i	$-0.584717\pi$
$521$	−12.0069	−0.526033	−0.263016	+	0.964791i	$0.584717\pi$
$522$	−2.13345	−0.0933787
$523$	17.8414	0.780150	0.390075	−	0.920783i	$-0.372449\pi$
$523$	17.8414	0.780150	0.390075	+	0.920783i	$0.372449\pi$
$524$	−38.5039	−1.68205
$525$	7.07730	0.308879
$526$	35.5732	1.55107
$527$	−19.3765	−0.844053
$528$	−0.0773036	−0.00336421
$529$	10.5491	0.458658
$530$	23.2780	1.01113
$531$	−16.6725	−0.723527
$532$	−34.1014	−1.47848
$533$	0	0
$534$	23.7530	1.02789
$535$	−14.0882	−0.609087
$536$	−24.3725	−1.05273
$537$	22.6304	0.976575
$538$	3.41168	0.147088
$539$	13.3132	0.573441
$540$	−44.4819	−1.91419
$541$	−19.1234	−0.822180	−0.411090	−	0.911595i	$-0.634852\pi$
$541$	−19.1234	−0.822180	−0.411090	+	0.911595i	$0.634852\pi$
$542$	−53.1778	−2.28418
$543$	−22.0624	−0.946787
$544$	−18.4578	−0.791371
$545$	24.8312	1.06365
$546$	0	0
$547$	−44.1225	−1.88654	−0.943272	−	0.332022i	$-0.892269\pi$
$547$	−44.1225	−1.88654	−0.943272	+	0.332022i	$0.892269\pi$
$548$	−7.31722	−0.312576
$549$	0.217874	0.00929862
$550$	−2.93673	−0.125223
$551$	1.45487	0.0619796
$552$	−19.7610	−0.841083
$553$	8.44375	0.359065
$554$	32.1295	1.36505
$555$	15.5101	0.658368
$556$	−32.7169	−1.38751
$557$	−21.3453	−0.904429	−0.452215	−	0.891909i	$-0.649366\pi$
$557$	−21.3453	−0.904429	−0.452215	+	0.891909i	$0.649366\pi$
$558$	20.7109	0.876760
$559$	0	0
$560$	−0.714858	−0.0302082
$561$	−3.93673	−0.166209
$562$	−26.6897	−1.12584
$563$	−19.9187	−0.839473	−0.419736	−	0.907646i	$-0.637877\pi$
$563$	−19.9187	−0.839473	−0.419736	+	0.907646i	$0.637877\pi$
$564$	26.5451	1.11775
$565$	20.6828	0.870131
$566$	7.93362	0.333475
$567$	−9.95077	−0.417893
$568$	4.78816	0.200907
$569$	46.4217	1.94610	0.973050	−	0.230596i	$-0.0740675\pi$
$569$	46.4217	1.94610	0.973050	+	0.230596i	$0.0740675\pi$
$570$	16.4389	0.688548
$571$	−5.67878	−0.237649	−0.118825	−	0.992915i	$-0.537913\pi$
$571$	−5.67878	−0.237649	−0.118825	+	0.992915i	$0.537913\pi$
$572$	0	0
$573$	−4.10849	−0.171635
$574$	86.1263	3.59484
$575$	7.44375	0.310426
$576$	19.5382	0.814092
$577$	−6.37648	−0.265456	−0.132728	−	0.991152i	$-0.542374\pi$
$577$	−6.37648	−0.265456	−0.132728	+	0.991152i	$0.542374\pi$
$578$	15.1265	0.629181
$579$	19.0593	0.792076
$580$	−5.00400	−0.207780
$581$	−24.2500	−1.00606
$582$	−0.314105	−0.0130201
$583$	−4.06327	−0.168283
$584$	5.58432	0.231081
$585$	0	0
$586$	−14.5783	−0.602224
$587$	−0.873467	−0.0360519	−0.0180259	−	0.999838i	$-0.505738\pi$
$587$	−0.873467	−0.0360519	−0.0180259	+	0.999838i	$0.505738\pi$
$588$	52.4106	2.16138
$589$	−14.1234	−0.581945
$590$	−63.3803	−2.60933
$591$	−25.6937	−1.05690
$592$	−0.320334	−0.0131657
$593$	18.7850	0.771409	0.385705	−	0.922622i	$-0.373958\pi$
$593$	18.7850	0.771409	0.385705	+	0.922622i	$0.373958\pi$
$594$	12.5843	0.516341
$595$	−36.4046	−1.49244
$596$	−35.3273	−1.44706
$597$	−27.6295	−1.13080
$598$	0	0
$599$	11.7601	0.480504	0.240252	−	0.970711i	$-0.422770\pi$
$599$	11.7601	0.480504	0.240252	+	0.970711i	$0.422770\pi$
$600$	−4.38449	−0.178996
$601$	28.5171	1.16323	0.581617	−	0.813462i	$-0.302420\pi$
$601$	28.5171	1.16323	0.581617	+	0.813462i	$0.302420\pi$
$602$	−114.232	−4.65574
$603$	−13.1546	−0.535697
$604$	−35.0653	−1.42679
$605$	2.50702	0.101925
$606$	35.6195	1.44694
$607$	15.4718	0.627982	0.313991	−	0.949426i	$-0.398334\pi$
$607$	15.4718	0.627982	0.313991	+	0.949426i	$0.398334\pi$
$608$	−13.4538	−0.545623
$609$	−3.41168	−0.138248
$610$	0.828241	0.0335345
$611$	0	0
$612$	15.6436	0.632354
$613$	−19.5883	−0.791165	−0.395582	−	0.918430i	$-0.629457\pi$
$613$	−19.5883	−0.791165	−0.395582	+	0.918430i	$0.629457\pi$
$614$	−11.5703	−0.466939
$615$	−25.6164	−1.03295
$616$	−12.5843	−0.507037
$617$	−29.3101	−1.17998	−0.589990	−	0.807410i	$-0.700868\pi$
$617$	−29.3101	−1.17998	−0.589990	+	0.807410i	$0.700868\pi$
$618$	−43.6427	−1.75557
$619$	−3.74293	−0.150441	−0.0752206	−	0.997167i	$-0.523966\pi$
$619$	−3.74293	−0.150441	−0.0752206	+	0.997167i	$0.523966\pi$
$620$	48.5772	1.95091
$621$	−31.8975	−1.28000
$622$	−6.67166	−0.267509
$623$	−38.3413	−1.53611
$624$	0	0
$625$	−29.7741	−1.19096
$626$	−36.0782	−1.44197
$627$	−2.86946	−0.114595
$628$	45.0481	1.79762
$629$	−16.3132	−0.650451
$630$	38.9116	1.55027
$631$	−22.5179	−0.896425	−0.448213	−	0.893927i	$-0.647939\pi$
$631$	−22.5179	−0.896425	−0.448213	+	0.893927i	$0.647939\pi$
$632$	−5.23102	−0.208079
$633$	24.8975	0.989588
$634$	46.7077	1.85500
$635$	−15.2359	−0.604619
$636$	−15.9960	−0.634283
$637$	0	0
$638$	1.41568	0.0560472
$639$	2.58432	0.102234
$640$	45.5491	1.80049
$641$	26.5812	1.04989	0.524947	−	0.851135i	$-0.324085\pi$
$641$	26.5812	1.04989	0.524947	+	0.851135i	$0.324085\pi$
$642$	15.6906	0.619258
$643$	1.28514	0.0506811	0.0253405	−	0.999679i	$-0.491933\pi$
$643$	1.28514	0.0506811	0.0253405	+	0.999679i	$0.491933\pi$
$644$	84.1083	3.31433
$645$	33.9757	1.33779
$646$	−17.2900	−0.680267
$647$	−13.7741	−0.541517	−0.270758	−	0.962647i	$-0.587274\pi$
$647$	−13.7741	−0.541517	−0.270758	+	0.962647i	$0.587274\pi$
$648$	6.16464	0.242170
$649$	11.0633	0.434271
$650$	0	0
$651$	33.1194	1.29805
$652$	4.49298	0.175959
$653$	15.5382	0.608057	0.304029	−	0.952663i	$-0.401668\pi$
$653$	15.5382	0.608057	0.304029	+	0.952663i	$0.401668\pi$
$654$	−27.6554	−1.08141
$655$	−29.9608	−1.17067
$656$	0.529061	0.0206564
$657$	3.01404	0.117589
$658$	−69.4467	−2.70731
$659$	20.3734	0.793634	0.396817	−	0.917898i	$-0.370115\pi$
$659$	20.3734	0.793634	0.396817	+	0.917898i	$0.370115\pi$
$660$	9.86946	0.384168
$661$	0.989077	0.0384706	0.0192353	−	0.999815i	$-0.493877\pi$
$661$	0.989077	0.0384706	0.0192353	+	0.999815i	$0.493877\pi$
$662$	64.6264	2.51178
$663$	0	0
$664$	15.0232	0.583013
$665$	−26.5351	−1.02899
$666$	17.4366	0.675656
$667$	−3.58832	−0.138940
$668$	76.7911	2.97114
$669$	−21.7178	−0.839658
$670$	−50.0069	−1.93194
$671$	−0.144573	−0.00558116
$672$	31.5491	1.21703
$673$	30.2992	1.16795	0.583974	−	0.811773i	$-0.301497\pi$
$673$	30.2992	1.16795	0.583974	+	0.811773i	$0.301497\pi$
$674$	72.9546	2.81011
$675$	−7.07730	−0.272406
$676$	0	0
$677$	20.6788	0.794750	0.397375	−	0.917656i	$-0.369921\pi$
$677$	20.6788	0.794750	0.397375	+	0.917656i	$0.369921\pi$
$678$	−23.0352	−0.884661
$679$	0.507019	0.0194576
$680$	22.5531	0.864873
$681$	7.11161	0.272517
$682$	−13.7429	−0.526244
$683$	−0.439750	−0.0168266	−0.00841328	−	0.999965i	$-0.502678\pi$
$683$	−0.439750	−0.0168266	−0.00841328	+	0.999965i	$0.502678\pi$
$684$	11.4025	0.435987
$685$	−5.69370	−0.217545
$686$	−65.0210	−2.48251
$687$	28.9165	1.10323
$688$	−0.701708	−0.0267524
$689$	0	0
$690$	−40.5451	−1.54353
$691$	20.0421	0.762438	0.381219	−	0.924485i	$-0.375504\pi$
$691$	20.0421	0.762438	0.381219	+	0.924485i	$0.375504\pi$
$692$	−23.8343	−0.906043
$693$	−6.79216	−0.258013
$694$	4.38449	0.166433
$695$	−25.4578	−0.965669
$696$	2.11358	0.0801151
$697$	26.9428	1.02053
$698$	0.433718	0.0164165
$699$	−27.9657	−1.05776
$700$	18.6616	0.705343
$701$	−36.9898	−1.39708	−0.698542	−	0.715569i	$-0.746168\pi$
$701$	−36.9898	−1.39708	−0.698542	+	0.715569i	$0.746168\pi$
$702$	0	0
$703$	−11.8906	−0.448463
$704$	−12.9648	−0.488630
$705$	20.6554	0.777927
$706$	25.0220	0.941717
$707$	−57.4959	−2.16236
$708$	43.5531	1.63683
$709$	33.8022	1.26947	0.634734	−	0.772731i	$-0.281110\pi$
$709$	33.8022	1.26947	0.634734	+	0.772731i	$0.281110\pi$
$710$	9.82424	0.368697
$711$	−2.82335	−0.105884
$712$	23.7530	0.890180
$713$	34.8343	1.30455
$714$	40.5451	1.51736
$715$	0	0
$716$	59.6725	2.23007
$717$	19.7953	0.739268
$718$	−8.66563	−0.323398
$719$	12.2210	0.455766	0.227883	−	0.973689i	$-0.426820\pi$
$719$	12.2210	0.455766	0.227883	+	0.973689i	$0.426820\pi$
$720$	0.239028	0.00890805
$721$	70.4467	2.62357
$722$	30.8151	1.14682
$723$	0.236802	0.00880674
$724$	−58.1747	−2.16204
$725$	−0.796164	−0.0295688
$726$	−2.79216	−0.103627
$727$	35.2771	1.30836	0.654178	−	0.756340i	$-0.273015\pi$
$727$	35.2771	1.30836	0.654178	+	0.756340i	$0.273015\pi$
$728$	0	0
$729$	23.5139	0.870887
$730$	11.4578	0.424072
$731$	−35.7349	−1.32170
$732$	−0.569144	−0.0210362
$733$	17.0953	0.631431	0.315715	−	0.948854i	$-0.397755\pi$
$733$	17.0953	0.631431	0.315715	+	0.948854i	$0.397755\pi$
$734$	57.1444	2.10924
$735$	40.7819	1.50426
$736$	33.1827	1.22313
$737$	8.72889	0.321533
$738$	−28.7982	−1.06008
$739$	−43.2279	−1.59016	−0.795082	−	0.606502i	$-0.792572\pi$
$739$	−43.2279	−1.59016	−0.795082	+	0.606502i	$0.792572\pi$
$740$	40.8975	1.50342
$741$	0	0
$742$	41.8483	1.53630
$743$	1.45868	0.0535137	0.0267568	−	0.999642i	$-0.491482\pi$
$743$	1.45868	0.0535137	0.0267568	+	0.999642i	$0.491482\pi$
$744$	−20.5179	−0.752224
$745$	−27.4890	−1.00712
$746$	19.8343	0.726184
$747$	8.10849	0.296674
$748$	−10.3805	−0.379548
$749$	−25.3273	−0.925438
$750$	26.0040	0.949532
$751$	15.3593	0.560470	0.280235	−	0.959931i	$-0.409588\pi$
$751$	15.3593	0.560470	0.280235	+	0.959931i	$0.409588\pi$
$752$	−0.426600	−0.0155565
$753$	9.94677	0.362480
$754$	0	0
$755$	−27.2851	−0.993008
$756$	−79.9677	−2.90840
$757$	34.3796	1.24955	0.624774	−	0.780806i	$-0.285191\pi$
$757$	34.3796	1.24955	0.624774	+	0.780806i	$0.285191\pi$
$758$	−33.6255	−1.22133
$759$	7.07730	0.256890
$760$	16.4389	0.596300
$761$	−3.88662	−0.140890	−0.0704449	−	0.997516i	$-0.522442\pi$
$761$	−3.88662	−0.140890	−0.0704449	+	0.997516i	$0.522442\pi$
$762$	16.9688	0.614715
$763$	44.6405	1.61609
$764$	−10.8334	−0.391938
$765$	12.1726	0.440103
$766$	12.3181	0.445071
$767$	0	0
$768$	−19.0470	−0.687300
$769$	39.4257	1.42173	0.710864	−	0.703330i	$-0.248304\pi$
$769$	39.4257	1.42173	0.710864	+	0.703330i	$0.248304\pi$
$770$	−25.8202	−0.930497
$771$	−21.8686	−0.787578
$772$	50.2560	1.80875
$773$	−24.4406	−0.879069	−0.439534	−	0.898226i	$-0.644857\pi$
$773$	−24.4406	−0.879069	−0.439534	+	0.898226i	$0.644857\pi$
$774$	38.1958	1.37292
$775$	7.72889	0.277630
$776$	−0.314105	−0.0112757
$777$	27.8835	1.00032
$778$	49.2520	1.76577
$779$	19.6384	0.703620
$780$	0	0
$781$	−1.71486	−0.0613624
$782$	42.6445	1.52496
$783$	3.41168	0.121923
$784$	−0.842278	−0.0300814
$785$	35.0530	1.25110
$786$	33.3685	1.19021
$787$	−36.8171	−1.31239	−0.656194	−	0.754592i	$-0.727835\pi$
$787$	−36.8171	−1.31239	−0.656194	+	0.754592i	$0.727835\pi$
$788$	−67.7499	−2.41349
$789$	−19.0212	−0.677171
$790$	−10.7329	−0.381859
$791$	37.1827	1.32206
$792$	4.20784	0.149519
$793$	0	0
$794$	40.0610	1.42171
$795$	−12.4469	−0.441445
$796$	−72.8543	−2.58225
$797$	11.5219	0.408128	0.204064	−	0.978958i	$-0.434585\pi$
$797$	11.5219	0.408128	0.204064	+	0.978958i	$0.434585\pi$
$798$	29.5531	1.04617
$799$	−21.7249	−0.768571
$800$	7.36245	0.260302
$801$	12.8202	0.452981
$802$	83.2629	2.94012
$803$	−2.00000	−0.0705785
$804$	34.3633	1.21190
$805$	65.4467	2.30669
$806$	0	0
$807$	−1.82424	−0.0642162
$808$	35.6195	1.25309
$809$	−24.4649	−0.860140	−0.430070	−	0.902795i	$-0.641511\pi$
$809$	−24.4649	−0.860140	−0.430070	+	0.902795i	$0.641511\pi$
$810$	12.6485	0.444422
$811$	9.19291	0.322807	0.161403	−	0.986889i	$-0.448398\pi$
$811$	9.19291	0.322807	0.161403	+	0.986889i	$0.448398\pi$
$812$	−8.99600	−0.315698
$813$	28.4344	0.997238
$814$	−11.5703	−0.405538
$815$	3.49610	0.122463
$816$	0.249063	0.00871894
$817$	−26.0470	−0.911269
$818$	−65.9637	−2.30637
$819$	0	0
$820$	−67.5460	−2.35881
$821$	30.5952	1.06778	0.533891	−	0.845553i	$-0.320729\pi$
$821$	30.5952	1.06778	0.533891	+	0.845553i	$0.320729\pi$
$822$	6.34129	0.221178
$823$	−19.2148	−0.669784	−0.334892	−	0.942256i	$-0.608700\pi$
$823$	−19.2148	−0.669784	−0.334892	+	0.942256i	$0.608700\pi$
$824$	−43.6427	−1.52037
$825$	1.57028	0.0546703
$826$	−113.943	−3.96457
$827$	28.4990	0.991008	0.495504	−	0.868606i	$-0.334983\pi$
$827$	28.4990	0.991008	0.495504	+	0.868606i	$0.334983\pi$
$828$	−28.1234	−0.977356
$829$	−6.68278	−0.232103	−0.116051	−	0.993243i	$-0.537024\pi$
$829$	−6.68278	−0.232103	−0.116051	+	0.993243i	$0.537024\pi$
$830$	30.8242	1.06992
$831$	−17.1798	−0.595959
$832$	0	0
$833$	−42.8935	−1.48617
$834$	28.3533	0.981794
$835$	59.7530	2.06784
$836$	−7.56628	−0.261685
$837$	−33.1194	−1.14477
$838$	9.60839	0.331916
$839$	8.63044	0.297956	0.148978	−	0.988841i	$-0.452402\pi$
$839$	8.63044	0.297956	0.148978	+	0.988841i	$0.452402\pi$
$840$	−38.5491	−1.33007
$841$	−28.6162	−0.986766
$842$	−31.0421	−1.06978
$843$	14.2711	0.491523
$844$	65.6505	2.25978
$845$	0	0
$846$	23.2210	0.798354
$847$	4.50702	0.154863
$848$	0.257068	0.00882775
$849$	−4.24214	−0.145590
$850$	9.46179	0.324537
$851$	29.3273	1.00533
$852$	−6.75094	−0.231283
$853$	−18.2631	−0.625317	−0.312658	−	0.949866i	$-0.601219\pi$
$853$	−18.2631	−0.625317	−0.312658	+	0.949866i	$0.601219\pi$
$854$	1.48898	0.0509518
$855$	8.87258	0.303436
$856$	15.6906	0.536293
$857$	1.22899	0.0419816	0.0209908	−	0.999780i	$-0.493318\pi$
$857$	1.22899	0.0419816	0.0209908	+	0.999780i	$0.493318\pi$
$858$	0	0
$859$	4.15772	0.141860	0.0709298	−	0.997481i	$-0.477403\pi$
$859$	4.15772	0.141860	0.0709298	+	0.997481i	$0.477403\pi$
$860$	89.5881	3.05493
$861$	−46.0521	−1.56945
$862$	68.6414	2.33793
$863$	−30.0633	−1.02337	−0.511683	−	0.859174i	$-0.670978\pi$
$863$	−30.0633	−1.02337	−0.511683	+	0.859174i	$0.670978\pi$
$864$	−31.5491	−1.07332
$865$	−18.5460	−0.630583
$866$	−9.72801	−0.330571
$867$	−8.08823	−0.274691
$868$	87.3302	2.96418
$869$	1.87347	0.0635530
$870$	4.33660	0.147024
$871$	0	0
$872$	−27.6554	−0.936530
$873$	−0.169533	−0.00573781
$874$	31.0833	1.05141
$875$	−41.9748	−1.41901
$876$	−7.87347	−0.266020
$877$	54.3092	1.83389	0.916946	−	0.399011i	$-0.130647\pi$
$877$	54.3092	1.83389	0.916946	+	0.399011i	$0.130647\pi$
$878$	11.4328	0.385839
$879$	7.79508	0.262921
$880$	−0.158610	−0.00534674
$881$	32.8162	1.10561	0.552803	−	0.833312i	$-0.313558\pi$
$881$	32.8162	1.10561	0.552803	+	0.833312i	$0.313558\pi$
$882$	45.8474	1.54376
$883$	−38.3444	−1.29039	−0.645196	−	0.764017i	$-0.723224\pi$
$883$	−38.3444	−1.29039	−0.645196	+	0.764017i	$0.723224\pi$
$884$	0	0
$885$	33.8897	1.13919
$886$	−64.6926	−2.17339
$887$	19.5382	0.656029	0.328014	−	0.944673i	$-0.393621\pi$
$887$	19.5382	0.656029	0.328014	+	0.944673i	$0.393621\pi$
$888$	−17.2742	−0.579685
$889$	−27.3905	−0.918649
$890$	48.7358	1.63363
$891$	−2.20784	−0.0739654
$892$	−57.2660	−1.91741
$893$	−15.8352	−0.529903
$894$	30.6155	1.02394
$895$	46.4326	1.55207
$896$	81.8864	2.73563
$897$	0	0
$898$	13.0842	0.436626
$899$	−3.72578	−0.124262
$900$	−6.23992	−0.207997
$901$	13.0913	0.436136
$902$	19.1094	0.636273
$903$	61.0802	2.03262
$904$	−23.0352	−0.766139
$905$	−45.2671	−1.50473
$906$	30.3885	1.00959
$907$	39.2600	1.30361	0.651803	−	0.758388i	$-0.274013\pi$
$907$	39.2600	1.30361	0.651803	+	0.758388i	$0.274013\pi$
$908$	18.7521	0.622310
$909$	19.2250	0.637653
$910$	0	0
$911$	−11.1194	−0.368403	−0.184201	−	0.982889i	$-0.558970\pi$
$911$	−11.1194	−0.368403	−0.184201	+	0.982889i	$0.558970\pi$
$912$	0.181540	0.00601141
$913$	−5.38049	−0.178068
$914$	28.5411	0.944057
$915$	−0.442864	−0.0146406
$916$	76.2477	2.51930
$917$	−53.8623	−1.77869
$918$	−40.5451	−1.33819
$919$	8.77501	0.289461	0.144730	−	0.989471i	$-0.453769\pi$
$919$	8.77501	0.289461	0.144730	+	0.989471i	$0.453769\pi$
$920$	−40.5451	−1.33673
$921$	6.18668	0.203858
$922$	30.1014	0.991336
$923$	0	0
$924$	17.7429	0.583700
$925$	6.50702	0.213949
$926$	23.7850	0.781625
$927$	−23.5554	−0.773660
$928$	−3.54913	−0.116506
$929$	25.2279	0.827701	0.413850	−	0.910345i	$-0.364184\pi$
$929$	25.2279	0.827701	0.413850	+	0.910345i	$0.364184\pi$
$930$	−42.0983	−1.38046
$931$	−31.2649	−1.02466
$932$	−73.7407	−2.41546
$933$	3.56737	0.116790
$934$	−53.3703	−1.74633
$935$	−8.07730	−0.264156
$936$	0	0
$937$	5.68589	0.185750	0.0928750	−	0.995678i	$-0.470394\pi$
$937$	5.68589	0.185750	0.0928750	+	0.995678i	$0.470394\pi$
$938$	−89.9005	−2.93535
$939$	19.2912	0.629544
$940$	54.4647	1.77644
$941$	12.2468	0.399235	0.199618	−	0.979874i	$-0.436030\pi$
$941$	12.2468	0.399235	0.199618	+	0.979874i	$0.436030\pi$
$942$	−39.0399	−1.27199
$943$	−48.4366	−1.57731
$944$	−0.699932	−0.0227809
$945$	−62.2248	−2.02417
$946$	−25.3453	−0.824047
$947$	−27.5663	−0.895784	−0.447892	−	0.894088i	$-0.647825\pi$
$947$	−27.5663	−0.895784	−0.447892	+	0.894088i	$0.647825\pi$
$948$	7.37534	0.239540
$949$	0	0
$950$	6.89665	0.223757
$951$	−24.9748	−0.809865
$952$	40.5451	1.31408
$953$	12.3444	0.399875	0.199937	−	0.979809i	$-0.435926\pi$
$953$	12.3444	0.399875	0.199937	+	0.979809i	$0.435926\pi$
$954$	−13.9929	−0.453036
$955$	−8.42972	−0.272779
$956$	52.1967	1.68816
$957$	−0.756969	−0.0244693
$958$	−18.7882	−0.607018
$959$	−10.2359	−0.330535
$960$	−39.7147	−1.28179
$961$	5.16864	0.166730
$962$	0	0
$963$	8.46871	0.272900
$964$	0.624405	0.0201107
$965$	39.1054	1.25885
$966$	−72.8904	−2.34521
$967$	13.5451	0.435582	0.217791	−	0.975995i	$-0.430115\pi$
$967$	13.5451	0.435582	0.217791	+	0.975995i	$0.430115\pi$
$968$	−2.79216	−0.0897435
$969$	9.24506	0.296994
$970$	−0.644474	−0.0206928
$971$	−1.48987	−0.0478121	−0.0239061	−	0.999714i	$-0.507610\pi$
$971$	−1.48987	−0.0478121	−0.0239061	+	0.999714i	$0.507610\pi$
$972$	44.5371	1.42853
$973$	−45.7670	−1.46722
$974$	−8.54399	−0.273767
$975$	0	0
$976$	0.00914657	0.000292775 0
$977$	−40.1827	−1.28556	−0.642779	−	0.766052i	$-0.722219\pi$
$977$	−40.1827	−1.28556	−0.642779	+	0.766052i	$0.722219\pi$
$978$	−3.89373	−0.124508
$979$	−8.50702	−0.271885
$980$	107.535	3.43508
$981$	−14.9265	−0.476567
$982$	18.6848	0.596256
$983$	26.9617	0.859944	0.429972	−	0.902842i	$-0.358523\pi$
$983$	26.9617	0.859944	0.429972	+	0.902842i	$0.358523\pi$
$984$	28.5299	0.909502
$985$	−52.7178	−1.67973
$986$	−4.56114	−0.145256
$987$	37.1335	1.18197
$988$	0	0
$989$	64.2428	2.04280
$990$	8.63355	0.274392
$991$	−41.9225	−1.33171	−0.665856	−	0.746080i	$-0.731934\pi$
$991$	−41.9225	−1.33171	−0.665856	+	0.746080i	$0.731934\pi$
$992$	34.4538	1.09391
$993$	−34.5561	−1.09660
$994$	17.6616	0.560193
$995$	−56.6897	−1.79718
$996$	−21.1815	−0.671163
$997$	−39.4037	−1.24793	−0.623963	−	0.781454i	$-0.714479\pi$
$997$	−39.4037	−1.24793	−0.623963	+	0.781454i	$0.714479\pi$
$998$	2.09935	0.0664536
$999$	−27.8835	−0.882195

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.f.1.1		3
13.3	even	3		143.2.e.b.100.3	✓	6
13.9	even	3		143.2.e.b.133.3	yes	6
13.12	even	2		1859.2.a.g.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.e.b.100.3	✓	6	13.3	even	3
143.2.e.b.133.3	yes	6	13.9	even	3
1859.2.a.f.1.1		3	1.1	even	1	trivial
1859.2.a.g.1.3		3	13.12	even	2

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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-2.28514 q^{2} +1.22188 q^{3} +3.22188 q^{4} +2.50702 q^{5} -2.79216 q^{6} +4.50702 q^{7} -2.79216 q^{8} -1.50702 q^{9} +O(q^{10})\)	\(q-2.28514 q^{2} +1.22188 q^{3} +3.22188 q^{4} +2.50702 q^{5} -2.79216 q^{6} +4.50702 q^{7} -2.79216 q^{8} -1.50702 q^{9} -5.72889 q^{10} +1.00000 q^{11} +3.93673 q^{12} -10.2992 q^{14} +3.06327 q^{15} -0.0632663 q^{16} -3.22188 q^{17} +3.44375 q^{18} -2.34841 q^{19} +8.07730 q^{20} +5.50702 q^{21} -2.28514 q^{22} +5.79216 q^{23} -3.41168 q^{24} +1.28514 q^{25} -5.50702 q^{27} +14.5211 q^{28} -0.619514 q^{29} -7.00000 q^{30} +6.01404 q^{31} +5.72889 q^{32} +1.22188 q^{33} +7.36245 q^{34} +11.2992 q^{35} -4.85543 q^{36} +5.06327 q^{37} +5.36645 q^{38} -7.00000 q^{40} -8.36245 q^{41} -12.5843 q^{42} +11.0913 q^{43} +3.22188 q^{44} -3.77812 q^{45} -13.2359 q^{46} +6.74293 q^{47} -0.0773036 q^{48} +13.3132 q^{49} -2.93673 q^{50} -3.93673 q^{51} -4.06327 q^{53} +12.5843 q^{54} +2.50702 q^{55} -12.5843 q^{56} -2.86946 q^{57} +1.41568 q^{58} +11.0633 q^{59} +9.86946 q^{60} -0.144573 q^{61} -13.7429 q^{62} -6.79216 q^{63} -12.9648 q^{64} -2.79216 q^{66} +8.72889 q^{67} -10.3805 q^{68} +7.07730 q^{69} -25.8202 q^{70} -1.71486 q^{71} +4.20784 q^{72} -2.00000 q^{73} -11.5703 q^{74} +1.57028 q^{75} -7.56628 q^{76} +4.50702 q^{77} +1.87347 q^{79} -0.158610 q^{80} -2.20784 q^{81} +19.1094 q^{82} -5.38049 q^{83} +17.7429 q^{84} -8.07730 q^{85} -25.3453 q^{86} -0.756969 q^{87} -2.79216 q^{88} -8.50702 q^{89} +8.63355 q^{90} +18.6616 q^{92} +7.34841 q^{93} -15.4086 q^{94} -5.88750 q^{95} +7.00000 q^{96} +0.112495 q^{97} -30.4226 q^{98} -1.50702 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + q^{3} + 7 q^{4} - q^{5} + 6 q^{6} + 5 q^{7} + 6 q^{8} + 4 q^{9}+O(q^{10}) \) 3 * q - q^2 + q^3 + 7 * q^4 - q^5 + 6 * q^6 + 5 * q^7 + 6 * q^8 + 4 * q^9	\( 3 q - q^{2} + q^{3} + 7 q^{4} - q^{5} + 6 q^{6} + 5 q^{7} + 6 q^{8} + 4 q^{9} - 6 q^{10} + 3 q^{11} + 15 q^{12} - 8 q^{14} + 6 q^{15} + 3 q^{16} - 7 q^{17} + 5 q^{18} + 2 q^{19} + 4 q^{20} + 8 q^{21} - q^{22} + 3 q^{23} + 2 q^{24} - 2 q^{25} - 8 q^{27} + 18 q^{28} - 4 q^{29} - 21 q^{30} + q^{31} + 6 q^{32} + q^{33} - 4 q^{34} + 11 q^{35} + 3 q^{36} + 12 q^{37} + 31 q^{38} - 21 q^{40} + q^{41} - 9 q^{42} - 4 q^{43} + 7 q^{44} - 14 q^{45} - 20 q^{46} - 8 q^{47} + 20 q^{48} - 12 q^{50} - 15 q^{51} - 9 q^{53} + 9 q^{54} - q^{55} - 9 q^{56} + 26 q^{57} + 33 q^{58} + 30 q^{59} - 5 q^{60} - 18 q^{61} - 13 q^{62} - 6 q^{63} - 8 q^{64} + 6 q^{66} + 15 q^{67} - 29 q^{68} + q^{69} - 29 q^{70} - 11 q^{71} + 27 q^{72} - 6 q^{73} - 23 q^{74} - 7 q^{75} + 30 q^{76} + 5 q^{77} + 12 q^{79} - q^{80} - 21 q^{81} + 44 q^{82} - 14 q^{83} + 25 q^{84} - 4 q^{85} - 43 q^{86} + 43 q^{87} + 6 q^{88} - 17 q^{89} + 11 q^{90} + 7 q^{92} + 13 q^{93} - 10 q^{94} - 7 q^{95} + 21 q^{96} + 11 q^{97} - 38 q^{98} + 4 q^{99}+O(q^{100}) \) 3 * q - q^2 + q^3 + 7 * q^4 - q^5 + 6 * q^6 + 5 * q^7 + 6 * q^8 + 4 * q^9 - 6 * q^10 + 3 * q^11 + 15 * q^12 - 8 * q^14 + 6 * q^15 + 3 * q^16 - 7 * q^17 + 5 * q^18 + 2 * q^19 + 4 * q^20 + 8 * q^21 - q^22 + 3 * q^23 + 2 * q^24 - 2 * q^25 - 8 * q^27 + 18 * q^28 - 4 * q^29 - 21 * q^30 + q^31 + 6 * q^32 + q^33 - 4 * q^34 + 11 * q^35 + 3 * q^36 + 12 * q^37 + 31 * q^38 - 21 * q^40 + q^41 - 9 * q^42 - 4 * q^43 + 7 * q^44 - 14 * q^45 - 20 * q^46 - 8 * q^47 + 20 * q^48 - 12 * q^50 - 15 * q^51 - 9 * q^53 + 9 * q^54 - q^55 - 9 * q^56 + 26 * q^57 + 33 * q^58 + 30 * q^59 - 5 * q^60 - 18 * q^61 - 13 * q^62 - 6 * q^63 - 8 * q^64 + 6 * q^66 + 15 * q^67 - 29 * q^68 + q^69 - 29 * q^70 - 11 * q^71 + 27 * q^72 - 6 * q^73 - 23 * q^74 - 7 * q^75 + 30 * q^76 + 5 * q^77 + 12 * q^79 - q^80 - 21 * q^81 + 44 * q^82 - 14 * q^83 + 25 * q^84 - 4 * q^85 - 43 * q^86 + 43 * q^87 + 6 * q^88 - 17 * q^89 + 11 * q^90 + 7 * q^92 + 13 * q^93 - 10 * q^94 - 7 * q^95 + 21 * q^96 + 11 * q^97 - 38 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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