LMFDB - Embedded newform 1859.2.a.o.1.2

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:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 8x^{6} + 18x^{5} + 7x^{4} - 22x^{3} - 3x^{2} + 6x + 1 $ x^8 - 2x^7 - 8x^6 + 18x^5 + 7x^4 - 22x^3 - 3x^2 + 6*x + 1
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			1.2
Root			$2.07742$ 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)

$f(q)$	$=$	$q-2.07742 q^{2} -1.13599 q^{3} +2.31569 q^{4} -4.26888 q^{5} +2.35994 q^{6} -3.46221 q^{7} -0.655817 q^{8} -1.70952 q^{9} +O(q^{10})$	\(q-2.07742 q^{2} -1.13599 q^{3} +2.31569 q^{4} -4.26888 q^{5} +2.35994 q^{6} -3.46221 q^{7} -0.655817 q^{8} -1.70952 q^{9} +8.86827 q^{10} +1.00000 q^{11} -2.63060 q^{12} +7.19247 q^{14} +4.84942 q^{15} -3.26897 q^{16} +3.63088 q^{17} +3.55140 q^{18} -4.71933 q^{19} -9.88539 q^{20} +3.93305 q^{21} -2.07742 q^{22} -1.92082 q^{23} +0.745003 q^{24} +13.2233 q^{25} +5.34998 q^{27} -8.01740 q^{28} -1.02253 q^{29} -10.0743 q^{30} +5.79489 q^{31} +8.10266 q^{32} -1.13599 q^{33} -7.54288 q^{34} +14.7798 q^{35} -3.95871 q^{36} -3.78992 q^{37} +9.80404 q^{38} +2.79960 q^{40} +6.78688 q^{41} -8.17060 q^{42} +1.80958 q^{43} +2.31569 q^{44} +7.29774 q^{45} +3.99036 q^{46} +7.76937 q^{47} +3.71352 q^{48} +4.98690 q^{49} -27.4705 q^{50} -4.12466 q^{51} +2.40232 q^{53} -11.1142 q^{54} -4.26888 q^{55} +2.27057 q^{56} +5.36112 q^{57} +2.12423 q^{58} -2.64003 q^{59} +11.2297 q^{60} -9.38540 q^{61} -12.0384 q^{62} +5.91872 q^{63} -10.2947 q^{64} +2.35994 q^{66} +3.52117 q^{67} +8.40799 q^{68} +2.18204 q^{69} -30.7038 q^{70} -5.25341 q^{71} +1.12113 q^{72} -6.31015 q^{73} +7.87326 q^{74} -15.0216 q^{75} -10.9285 q^{76} -3.46221 q^{77} +6.50871 q^{79} +13.9548 q^{80} -0.948983 q^{81} -14.0992 q^{82} +11.5980 q^{83} +9.10771 q^{84} -15.4998 q^{85} -3.75926 q^{86} +1.16159 q^{87} -0.655817 q^{88} +8.08945 q^{89} -15.1605 q^{90} -4.44802 q^{92} -6.58295 q^{93} -16.1403 q^{94} +20.1462 q^{95} -9.20457 q^{96} -9.42330 q^{97} -10.3599 q^{98} -1.70952 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 4 q^{4} - 8 q^{5} - 4 q^{6} - 14 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 4 * q^4 - 8 * q^5 - 4 * q^6 - 14 * q^7 + 6 * q^8 + 2 * q^9	$ 8 q - 2 q^{2} + 4 q^{4} - 8 q^{5} - 4 q^{6} - 14 q^{7} + 6 q^{8} + 2 q^{9} + 10 q^{10} + 8 q^{11} - 8 q^{12} - 6 q^{14} - 2 q^{15} + 12 q^{16} + 6 q^{17} - 6 q^{18} - 4 q^{19} - 16 q^{20} - 2 q^{21} - 2 q^{22} - 14 q^{23} - 26 q^{24} + 12 q^{25} + 24 q^{27} - 20 q^{28} - 10 q^{29} + 14 q^{30} - 32 q^{31} + 40 q^{32} - 14 q^{34} + 10 q^{35} - 24 q^{37} + 12 q^{38} - 14 q^{40} - 2 q^{41} - 2 q^{42} + 14 q^{43} + 4 q^{44} + 4 q^{45} - 14 q^{46} - 18 q^{47} - 6 q^{48} + 2 q^{49} - 38 q^{50} + 12 q^{51} - 8 q^{53} - 2 q^{54} - 8 q^{55} - 28 q^{56} - 24 q^{57} + 14 q^{58} - 18 q^{59} + 14 q^{60} - 4 q^{61} - 8 q^{63} + 6 q^{64} - 4 q^{66} + 14 q^{67} - 34 q^{68} - 10 q^{69} - 18 q^{70} + 12 q^{71} - 8 q^{72} - 26 q^{73} + 2 q^{74} - 18 q^{75} - 54 q^{76} - 14 q^{77} + 26 q^{79} - 24 q^{80} - 16 q^{81} - 64 q^{82} - 16 q^{83} + 74 q^{84} - 56 q^{85} - 32 q^{86} - 18 q^{87} + 6 q^{88} + 8 q^{89} - 20 q^{90} - 30 q^{92} - 48 q^{93} - 4 q^{94} + 22 q^{95} - 16 q^{96} - 20 q^{97} + 46 q^{98} + 2 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 4 * q^4 - 8 * q^5 - 4 * q^6 - 14 * q^7 + 6 * q^8 + 2 * q^9 + 10 * q^10 + 8 * q^11 - 8 * q^12 - 6 * q^14 - 2 * q^15 + 12 * q^16 + 6 * q^17 - 6 * q^18 - 4 * q^19 - 16 * q^20 - 2 * q^21 - 2 * q^22 - 14 * q^23 - 26 * q^24 + 12 * q^25 + 24 * q^27 - 20 * q^28 - 10 * q^29 + 14 * q^30 - 32 * q^31 + 40 * q^32 - 14 * q^34 + 10 * q^35 - 24 * q^37 + 12 * q^38 - 14 * q^40 - 2 * q^41 - 2 * q^42 + 14 * q^43 + 4 * q^44 + 4 * q^45 - 14 * q^46 - 18 * q^47 - 6 * q^48 + 2 * q^49 - 38 * q^50 + 12 * q^51 - 8 * q^53 - 2 * q^54 - 8 * q^55 - 28 * q^56 - 24 * q^57 + 14 * q^58 - 18 * q^59 + 14 * q^60 - 4 * q^61 - 8 * q^63 + 6 * q^64 - 4 * q^66 + 14 * q^67 - 34 * q^68 - 10 * q^69 - 18 * q^70 + 12 * q^71 - 8 * q^72 - 26 * q^73 + 2 * q^74 - 18 * q^75 - 54 * q^76 - 14 * q^77 + 26 * q^79 - 24 * q^80 - 16 * q^81 - 64 * q^82 - 16 * q^83 + 74 * q^84 - 56 * q^85 - 32 * q^86 - 18 * q^87 + 6 * q^88 + 8 * q^89 - 20 * q^90 - 30 * q^92 - 48 * q^93 - 4 * q^94 + 22 * q^95 - 16 * q^96 - 20 * q^97 + 46 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.07742	−1.46896	−0.734480	−	0.678630i	$-0.762574\pi$
$2$	−2.07742	−1.46896	−0.734480	+	0.678630i	$0.762574\pi$
$3$	−1.13599	−0.655866	−0.327933	−	0.944701i	$-0.606352\pi$
$3$	−1.13599	−0.655866	−0.327933	+	0.944701i	$0.606352\pi$
$4$	2.31569	1.15784
$5$	−4.26888	−1.90910	−0.954551	−	0.298048i	$-0.903664\pi$
$5$	−4.26888	−1.90910	−0.954551	+	0.298048i	$0.903664\pi$
$6$	2.35994	0.963441
$7$	−3.46221	−1.30859	−0.654296	−	0.756238i	$-0.727035\pi$
$7$	−3.46221	−1.30859	−0.654296	+	0.756238i	$0.727035\pi$
$8$	−0.655817	−0.231866
$9$	−1.70952	−0.569840
$10$	8.86827	2.80439
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.63060	−0.759390
$13$	0	0
$13$	0	0
$14$	7.19247	1.92227
$15$	4.84942	1.25211
$16$	−3.26897	−0.817242
$17$	3.63088	0.880619	0.440309	−	0.897846i	$-0.354869\pi$
$17$	3.63088	0.880619	0.440309	+	0.897846i	$0.354869\pi$
$18$	3.55140	0.837072
$19$	−4.71933	−1.08269	−0.541344	−	0.840801i	$-0.682084\pi$
$19$	−4.71933	−1.08269	−0.541344	+	0.840801i	$0.682084\pi$
$20$	−9.88539	−2.21044
$21$	3.93305	0.858261
$22$	−2.07742	−0.442908
$23$	−1.92082	−0.400519	−0.200259	−	0.979743i	$-0.564178\pi$
$23$	−1.92082	−0.400519	−0.200259	+	0.979743i	$0.564178\pi$
$24$	0.745003	0.152073
$25$	13.2233	2.64467
$26$	0	0
$27$	5.34998	1.02960
$28$	−8.01740	−1.51515
$29$	−1.02253	−0.189879	−0.0949396	−	0.995483i	$-0.530266\pi$
$29$	−1.02253	−0.189879	−0.0949396	+	0.995483i	$0.530266\pi$
$30$	−10.0743	−1.83931
$31$	5.79489	1.04079	0.520396	−	0.853925i	$-0.325784\pi$
$31$	5.79489	1.04079	0.520396	+	0.853925i	$0.325784\pi$
$32$	8.10266	1.43236
$33$	−1.13599	−0.197751
$34$	−7.54288	−1.29359
$35$	14.7798	2.49824
$36$	−3.95871	−0.659786
$37$	−3.78992	−0.623059	−0.311529	−	0.950237i	$-0.600841\pi$
$37$	−3.78992	−0.623059	−0.311529	+	0.950237i	$0.600841\pi$
$38$	9.80404	1.59043
$39$	0	0
$40$	2.79960	0.442656
$41$	6.78688	1.05993	0.529966	−	0.848019i	$-0.322205\pi$
$41$	6.78688	1.05993	0.529966	+	0.848019i	$0.322205\pi$
$42$	−8.17060	−1.26075
$43$	1.80958	0.275958	0.137979	−	0.990435i	$-0.455939\pi$
$43$	1.80958	0.275958	0.137979	+	0.990435i	$0.455939\pi$
$44$	2.31569	0.349103
$45$	7.29774	1.08788
$46$	3.99036	0.588346
$47$	7.76937	1.13328	0.566639	−	0.823966i	$-0.308243\pi$
$47$	7.76937	1.13328	0.566639	+	0.823966i	$0.308243\pi$
$48$	3.71352	0.536001
$49$	4.98690	0.712414
$50$	−27.4705	−3.88491
$51$	−4.12466	−0.577568
$52$	0	0
$53$	2.40232	0.329984	0.164992	−	0.986295i	$-0.447240\pi$
$53$	2.40232	0.329984	0.164992	+	0.986295i	$0.447240\pi$
$54$	−11.1142	−1.51245
$55$	−4.26888	−0.575616
$56$	2.27057	0.303418
$57$	5.36112	0.710098
$58$	2.12423	0.278925
$59$	−2.64003	−0.343703	−0.171851	−	0.985123i	$-0.554975\pi$
$59$	−2.64003	−0.343703	−0.171851	+	0.985123i	$0.554975\pi$
$60$	11.2297	1.44975
$61$	−9.38540	−1.20168	−0.600839	−	0.799370i	$-0.705167\pi$
$61$	−9.38540	−1.20168	−0.600839	+	0.799370i	$0.705167\pi$
$62$	−12.0384	−1.52888
$63$	5.91872	0.745688
$64$	−10.2947	−1.28684
$65$	0	0
$66$	2.35994	0.290488
$67$	3.52117	0.430179	0.215090	−	0.976594i	$-0.430996\pi$
$67$	3.52117	0.430179	0.215090	+	0.976594i	$0.430996\pi$
$68$	8.40799	1.01962
$69$	2.18204	0.262687
$70$	−30.7038	−3.66981
$71$	−5.25341	−0.623465	−0.311733	−	0.950170i	$-0.600909\pi$
$71$	−5.25341	−0.623465	−0.311733	+	0.950170i	$0.600909\pi$
$72$	1.12113	0.132127
$73$	−6.31015	−0.738547	−0.369274	−	0.929321i	$-0.620393\pi$
$73$	−6.31015	−0.738547	−0.369274	+	0.929321i	$0.620393\pi$
$74$	7.87326	0.915248
$75$	−15.0216	−1.73455
$76$	−10.9285	−1.25358
$77$	−3.46221	−0.394555
$78$	0	0
$79$	6.50871	0.732288	0.366144	−	0.930558i	$-0.380678\pi$
$79$	6.50871	0.732288	0.366144	+	0.930558i	$0.380678\pi$
$80$	13.9548	1.56020
$81$	−0.948983	−0.105443
$82$	−14.0992	−1.55700
$83$	11.5980	1.27305	0.636525	−	0.771256i	$-0.280371\pi$
$83$	11.5980	1.27305	0.636525	+	0.771256i	$0.280371\pi$
$84$	9.10771	0.993732
$85$	−15.4998	−1.68119
$86$	−3.75926	−0.405371
$87$	1.16159	0.124535
$88$	−0.655817	−0.0699103
$89$	8.08945	0.857480	0.428740	−	0.903428i	$-0.358958\pi$
$89$	8.08945	0.857480	0.428740	+	0.903428i	$0.358958\pi$
$90$	−15.1605	−1.59806
$91$	0	0
$92$	−4.44802	−0.463738
$93$	−6.58295	−0.682620
$94$	−16.1403	−1.66474
$95$	20.1462	2.06696
$96$	−9.20457	−0.939437
$97$	−9.42330	−0.956791	−0.478395	−	0.878145i	$-0.658781\pi$
$97$	−9.42330	−0.956791	−0.478395	+	0.878145i	$0.658781\pi$
$98$	−10.3599	−1.04651
$99$	−1.70952	−0.171813
$100$	30.6211	3.06211
$101$	−2.19327	−0.218239	−0.109119	−	0.994029i	$-0.534803\pi$
$101$	−2.19327	−0.218239	−0.109119	+	0.994029i	$0.534803\pi$
$102$	8.56866	0.848424
$103$	2.86990	0.282780	0.141390	−	0.989954i	$-0.454843\pi$
$103$	2.86990	0.282780	0.141390	+	0.989954i	$0.454843\pi$
$104$	0	0
$105$	−16.7897	−1.63851
$106$	−4.99063	−0.484733
$107$	−3.57175	−0.345294	−0.172647	−	0.984984i	$-0.555232\pi$
$107$	−3.57175	−0.345294	−0.172647	+	0.984984i	$0.555232\pi$
$108$	12.3889	1.19212
$109$	−9.84824	−0.943290	−0.471645	−	0.881788i	$-0.656340\pi$
$109$	−9.84824	−0.943290	−0.471645	+	0.881788i	$0.656340\pi$
$110$	8.86827	0.845557
$111$	4.30532	0.408643
$112$	11.3178	1.06944
$113$	13.6418	1.28331	0.641654	−	0.766994i	$-0.278248\pi$
$113$	13.6418	1.28331	0.641654	+	0.766994i	$0.278248\pi$
$114$	−11.1373	−1.04311
$115$	8.19975	0.764631
$116$	−2.36786	−0.219851
$117$	0	0
$118$	5.48446	0.504886
$119$	−12.5709	−1.15237
$120$	−3.18033	−0.290323
$121$	1.00000	0.0909091
$122$	19.4975	1.76522
$123$	−7.70985	−0.695174
$124$	13.4191	1.20507
$125$	−35.1045	−3.13984
$126$	−12.2957	−1.09539
$127$	0.724631	0.0643006	0.0321503	−	0.999483i	$-0.489764\pi$
$127$	0.724631	0.0643006	0.0321503	+	0.999483i	$0.489764\pi$
$128$	5.18117	0.457955
$129$	−2.05567	−0.180991
$130$	0	0
$131$	−5.13294	−0.448467	−0.224234	−	0.974535i	$-0.571988\pi$
$131$	−5.13294	−0.448467	−0.224234	+	0.974535i	$0.571988\pi$
$132$	−2.63060	−0.228965
$133$	16.3393	1.41680
$134$	−7.31496	−0.631916
$135$	−22.8384	−1.96562
$136$	−2.38119	−0.204186
$137$	2.50585	0.214089	0.107045	−	0.994254i	$-0.465861\pi$
$137$	2.50585	0.214089	0.107045	+	0.994254i	$0.465861\pi$
$138$	−4.53302	−0.385876
$139$	−14.6980	−1.24667	−0.623333	−	0.781956i	$-0.714222\pi$
$139$	−14.6980	−1.24667	−0.623333	+	0.781956i	$0.714222\pi$
$140$	34.2253	2.89257
$141$	−8.82594	−0.743279
$142$	10.9136	0.915846
$143$	0	0
$144$	5.58836	0.465697
$145$	4.36506	0.362499
$146$	13.1089	1.08490
$147$	−5.66508	−0.467248
$148$	−8.77626	−0.721405
$149$	19.6370	1.60873	0.804364	−	0.594136i	$-0.202506\pi$
$149$	19.6370	1.60873	0.804364	+	0.594136i	$0.202506\pi$
$150$	31.2063	2.54798
$151$	6.29355	0.512162	0.256081	−	0.966655i	$-0.417569\pi$
$151$	6.29355	0.512162	0.256081	+	0.966655i	$0.417569\pi$
$152$	3.09501	0.251039
$153$	−6.20707	−0.501812
$154$	7.19247	0.579586
$155$	−24.7377	−1.98698
$156$	0	0
$157$	4.13741	0.330201	0.165101	−	0.986277i	$-0.447205\pi$
$157$	4.13741	0.330201	0.165101	+	0.986277i	$0.447205\pi$
$158$	−13.5214	−1.07570
$159$	−2.72902	−0.216425
$160$	−34.5893	−2.73452
$161$	6.65028	0.524116
$162$	1.97144	0.154891
$163$	7.25681	0.568397	0.284199	−	0.958765i	$-0.408272\pi$
$163$	7.25681	0.568397	0.284199	+	0.958765i	$0.408272\pi$
$164$	15.7163	1.22724
$165$	4.84942	0.377527
$166$	−24.0940	−1.87006
$167$	−2.93512	−0.227127	−0.113563	−	0.993531i	$-0.536226\pi$
$167$	−2.93512	−0.227127	−0.113563	+	0.993531i	$0.536226\pi$
$168$	−2.57936	−0.199002
$169$	0	0
$170$	32.1997	2.46960
$171$	8.06778	0.616959
$172$	4.19041	0.319516
$173$	0.631578	0.0480180	0.0240090	−	0.999712i	$-0.492357\pi$
$173$	0.631578	0.0480180	0.0240090	+	0.999712i	$0.492357\pi$
$174$	−2.41311	−0.182937
$175$	−45.7820	−3.46079
$176$	−3.26897	−0.246408
$177$	2.99906	0.225423
$178$	−16.8052	−1.25960
$179$	−9.51109	−0.710892	−0.355446	−	0.934697i	$-0.615671\pi$
$179$	−9.51109	−0.710892	−0.355446	+	0.934697i	$0.615671\pi$
$180$	16.8993	1.25960
$181$	−0.800232	−0.0594807	−0.0297404	−	0.999558i	$-0.509468\pi$
$181$	−0.800232	−0.0594807	−0.0297404	+	0.999558i	$0.509468\pi$
$182$	0	0
$183$	10.6618	0.788140
$184$	1.25971	0.0928668
$185$	16.1787	1.18948
$186$	13.6756	1.00274
$187$	3.63088	0.265516
$188$	17.9914	1.31216
$189$	−18.5228	−1.34733
$190$	−41.8523	−3.03628
$191$	−17.9932	−1.30194	−0.650972	−	0.759102i	$-0.725638\pi$
$191$	−17.9932	−1.30194	−0.650972	+	0.759102i	$0.725638\pi$
$192$	11.6947	0.843995
$193$	−2.94955	−0.212313	−0.106157	−	0.994349i	$-0.533854\pi$
$193$	−2.94955	−0.212313	−0.106157	+	0.994349i	$0.533854\pi$
$194$	19.5762	1.40549
$195$	0	0
$196$	11.5481	0.824864
$197$	7.02269	0.500346	0.250173	−	0.968201i	$-0.419512\pi$
$197$	7.02269	0.500346	0.250173	+	0.968201i	$0.419512\pi$
$198$	3.55140	0.252387
$199$	−26.3373	−1.86700	−0.933502	−	0.358573i	$-0.883264\pi$
$199$	−26.3373	−1.86700	−0.933502	+	0.358573i	$0.883264\pi$
$200$	−8.67209	−0.613209
$201$	−4.00002	−0.282140
$202$	4.55636	0.320584
$203$	3.54022	0.248475
$204$	−9.55142	−0.668733
$205$	−28.9724	−2.02352
$206$	−5.96201	−0.415393
$207$	3.28368	0.228232
$208$	0	0
$209$	−4.71933	−0.326443
$210$	34.8793	2.40690
$211$	−17.3131	−1.19189	−0.595943	−	0.803027i	$-0.703222\pi$
$211$	−17.3131	−1.19189	−0.595943	+	0.803027i	$0.703222\pi$
$212$	5.56302	0.382069
$213$	5.96784	0.408910
$214$	7.42004	0.507224
$215$	−7.72487	−0.526832
$216$	−3.50861	−0.238730
$217$	−20.0631	−1.36197
$218$	20.4590	1.38566
$219$	7.16829	0.484388
$220$	−9.88539	−0.666473
$221$	0	0
$222$	−8.94397	−0.600280
$223$	−9.91265	−0.663800	−0.331900	−	0.943315i	$-0.607690\pi$
$223$	−9.91265	−0.663800	−0.331900	+	0.943315i	$0.607690\pi$
$224$	−28.0531	−1.87438
$225$	−22.6056	−1.50704
$226$	−28.3397	−1.88513
$227$	15.0469	0.998699	0.499349	−	0.866401i	$-0.333572\pi$
$227$	15.0469	0.998699	0.499349	+	0.866401i	$0.333572\pi$
$228$	12.4147	0.822183
$229$	−25.5515	−1.68849	−0.844246	−	0.535956i	$-0.819951\pi$
$229$	−25.5515	−1.68849	−0.844246	+	0.535956i	$0.819951\pi$
$230$	−17.0344	−1.12321
$231$	3.93305	0.258775
$232$	0.670593	0.0440266
$233$	−1.69970	−0.111351	−0.0556754	−	0.998449i	$-0.517731\pi$
$233$	−1.69970	−0.111351	−0.0556754	+	0.998449i	$0.517731\pi$
$234$	0	0
$235$	−33.1665	−2.16354
$236$	−6.11349	−0.397954
$237$	−7.39385	−0.480282
$238$	26.1150	1.69279
$239$	4.35820	0.281908	0.140954	−	0.990016i	$-0.454983\pi$
$239$	4.35820	0.281908	0.140954	+	0.990016i	$0.454983\pi$
$240$	−15.8526	−1.02328
$241$	3.47084	0.223576	0.111788	−	0.993732i	$-0.464342\pi$
$241$	3.47084	0.223576	0.111788	+	0.993732i	$0.464342\pi$
$242$	−2.07742	−0.133542
$243$	−14.9719	−0.960448
$244$	−21.7337	−1.39136
$245$	−21.2885	−1.36007
$246$	16.0166	1.02118
$247$	0	0
$248$	−3.80038	−0.241325
$249$	−13.1753	−0.834950
$250$	72.9269	4.61230
$251$	14.8315	0.936157	0.468078	−	0.883687i	$-0.344946\pi$
$251$	14.8315	0.936157	0.468078	+	0.883687i	$0.344946\pi$
$252$	13.7059	0.863390
$253$	−1.92082	−0.120761
$254$	−1.50536	−0.0944550
$255$	17.6077	1.10264
$256$	9.82595	0.614122
$257$	23.3156	1.45439	0.727193	−	0.686433i	$-0.240825\pi$
$257$	23.3156	1.45439	0.727193	+	0.686433i	$0.240825\pi$
$258$	4.27049	0.265869
$259$	13.1215	0.815330
$260$	0	0
$261$	1.74804	0.108201
$262$	10.6633	0.658780
$263$	−1.82679	−0.112645	−0.0563223	−	0.998413i	$-0.517937\pi$
$263$	−1.82679	−0.112645	−0.0563223	+	0.998413i	$0.517937\pi$
$264$	0.745003	0.0458518
$265$	−10.2552	−0.629972
$266$	−33.9436	−2.08122
$267$	−9.18956	−0.562392
$268$	8.15392	0.498080
$269$	−26.2780	−1.60220	−0.801099	−	0.598532i	$-0.795751\pi$
$269$	−26.2780	−1.60220	−0.801099	+	0.598532i	$0.795751\pi$
$270$	47.4451	2.88742
$271$	13.7882	0.837574	0.418787	−	0.908085i	$-0.362455\pi$
$271$	13.7882	0.837574	0.418787	+	0.908085i	$0.362455\pi$
$272$	−11.8692	−0.719678
$273$	0	0
$274$	−5.20571	−0.314489
$275$	13.2233	0.797398
$276$	5.05292	0.304150
$277$	24.8542	1.49334	0.746672	−	0.665193i	$-0.231651\pi$
$277$	24.8542	1.49334	0.746672	+	0.665193i	$0.231651\pi$
$278$	30.5339	1.83130
$279$	−9.90647	−0.593085
$280$	−9.69281	−0.579256
$281$	9.30682	0.555198	0.277599	−	0.960697i	$-0.410461\pi$
$281$	9.30682	0.555198	0.277599	+	0.960697i	$0.410461\pi$
$282$	18.3352	1.09185
$283$	24.7564	1.47161	0.735806	−	0.677192i	$-0.236803\pi$
$283$	24.7564	1.47161	0.735806	+	0.677192i	$0.236803\pi$
$284$	−12.1653	−0.721875
$285$	−22.8860	−1.35565
$286$	0	0
$287$	−23.4976	−1.38702
$288$	−13.8517	−0.816217
$289$	−3.81669	−0.224511
$290$	−9.06808	−0.532496
$291$	10.7048	0.627526
$292$	−14.6123	−0.855122
$293$	19.0488	1.11284	0.556422	−	0.830900i	$-0.312174\pi$
$293$	19.0488	1.11284	0.556422	+	0.830900i	$0.312174\pi$
$294$	11.7688	0.686368
$295$	11.2700	0.656163
$296$	2.48549	0.144466
$297$	5.34998	0.310437
$298$	−40.7944	−2.36316
$299$	0	0
$300$	−34.7854	−2.00834
$301$	−6.26513	−0.361116
$302$	−13.0744	−0.752346
$303$	2.49154	0.143135
$304$	15.4273	0.884818
$305$	40.0652	2.29413
$306$	12.8947	0.737141
$307$	2.27636	0.129919	0.0649595	−	0.997888i	$-0.479308\pi$
$307$	2.27636	0.129919	0.0649595	+	0.997888i	$0.479308\pi$
$308$	−8.01740	−0.456834
$309$	−3.26019	−0.185466
$310$	51.3906	2.91879
$311$	29.2234	1.65711	0.828555	−	0.559908i	$-0.189163\pi$
$311$	29.2234	1.65711	0.828555	+	0.559908i	$0.189163\pi$
$312$	0	0
$313$	−34.4012	−1.94447	−0.972234	−	0.234010i	$-0.924815\pi$
$313$	−34.4012	−1.94447	−0.972234	+	0.234010i	$0.924815\pi$
$314$	−8.59515	−0.485052
$315$	−25.2663	−1.42359
$316$	15.0721	0.847875
$317$	−18.5126	−1.03977	−0.519887	−	0.854235i	$-0.674026\pi$
$317$	−18.5126	−1.03977	−0.519887	+	0.854235i	$0.674026\pi$
$318$	5.66932	0.317920
$319$	−1.02253	−0.0572507
$320$	43.9469	2.45671
$321$	4.05749	0.226467
$322$	−13.8155	−0.769905
$323$	−17.1353	−0.953435
$324$	−2.19755	−0.122086
$325$	0	0
$326$	−15.0755	−0.834953
$327$	11.1875	0.618672
$328$	−4.45095	−0.245762
$329$	−26.8992	−1.48300
$330$	−10.0743	−0.554572
$331$	16.9296	0.930535	0.465267	−	0.885170i	$-0.345958\pi$
$331$	16.9296	0.930535	0.465267	+	0.885170i	$0.345958\pi$
$332$	26.8574	1.47399
$333$	6.47894	0.355044
$334$	6.09750	0.333640
$335$	−15.0314	−0.821256
$336$	−12.8570	−0.701407
$337$	19.5359	1.06419	0.532095	−	0.846685i	$-0.321405\pi$
$337$	19.5359	1.06419	0.532095	+	0.846685i	$0.321405\pi$
$338$	0	0
$339$	−15.4969	−0.841679
$340$	−35.8927	−1.94656
$341$	5.79489	0.313811
$342$	−16.7602	−0.906288
$343$	6.96979	0.376333
$344$	−1.18675	−0.0639853
$345$	−9.31486	−0.501495
$346$	−1.31206	−0.0705366
$347$	−5.53759	−0.297273	−0.148637	−	0.988892i	$-0.547488\pi$
$347$	−5.53759	−0.297273	−0.148637	+	0.988892i	$0.547488\pi$
$348$	2.68988	0.144192
$349$	−34.5919	−1.85166	−0.925830	−	0.377940i	$-0.876633\pi$
$349$	−34.5919	−1.85166	−0.925830	+	0.377940i	$0.876633\pi$
$350$	95.1086	5.08377
$351$	0	0
$352$	8.10266	0.431873
$353$	1.51410	0.0805872	0.0402936	−	0.999188i	$-0.487171\pi$
$353$	1.51410	0.0805872	0.0402936	+	0.999188i	$0.487171\pi$
$354$	−6.23031	−0.331137
$355$	22.4262	1.19026
$356$	18.7326	0.992828
$357$	14.2804	0.755801
$358$	19.7586	1.04427
$359$	−23.0959	−1.21896	−0.609479	−	0.792802i	$-0.708621\pi$
$359$	−23.0959	−1.21896	−0.609479	+	0.792802i	$0.708621\pi$
$360$	−4.78598	−0.252243
$361$	3.27205	0.172213
$362$	1.66242	0.0873748
$363$	−1.13599	−0.0596242
$364$	0	0
$365$	26.9373	1.40996
$366$	−22.1490	−1.15775
$367$	−22.6228	−1.18090	−0.590449	−	0.807075i	$-0.701049\pi$
$367$	−22.6228	−1.18090	−0.590449	+	0.807075i	$0.701049\pi$
$368$	6.27910	0.327321
$369$	−11.6023	−0.603992
$370$	−33.6100	−1.74730
$371$	−8.31732	−0.431814
$372$	−15.2441	−0.790368
$373$	22.0679	1.14263	0.571317	−	0.820730i	$-0.306433\pi$
$373$	22.0679	1.14263	0.571317	+	0.820730i	$0.306433\pi$
$374$	−7.54288	−0.390033
$375$	39.8784	2.05931
$376$	−5.09528	−0.262769
$377$	0	0
$378$	38.4796	1.97918
$379$	36.7235	1.88636	0.943179	−	0.332286i	$-0.107820\pi$
$379$	36.7235	1.88636	0.943179	+	0.332286i	$0.107820\pi$
$380$	46.6524	2.39322
$381$	−0.823176	−0.0421726
$382$	37.3795	1.91250
$383$	−14.5148	−0.741671	−0.370836	−	0.928699i	$-0.620929\pi$
$383$	−14.5148	−0.741671	−0.370836	+	0.928699i	$0.620929\pi$
$384$	−5.88578	−0.300357
$385$	14.7798	0.753246
$386$	6.12746	0.311879
$387$	−3.09351	−0.157252
$388$	−21.8214	−1.10781
$389$	−30.4968	−1.54625	−0.773125	−	0.634254i	$-0.781307\pi$
$389$	−30.4968	−1.54625	−0.773125	+	0.634254i	$0.781307\pi$
$390$	0	0
$391$	−6.97428	−0.352704
$392$	−3.27049	−0.165185
$393$	5.83099	0.294134
$394$	−14.5891	−0.734988
$395$	−27.7849	−1.39801
$396$	−3.95871	−0.198933
$397$	10.4211	0.523019	0.261510	−	0.965201i	$-0.415780\pi$
$397$	10.4211	0.523019	0.261510	+	0.965201i	$0.415780\pi$
$398$	54.7138	2.74255
$399$	−18.5613	−0.929229
$400$	−43.2267	−2.16133
$401$	−2.66843	−0.133255	−0.0666276	−	0.997778i	$-0.521224\pi$
$401$	−2.66843	−0.133255	−0.0666276	+	0.997778i	$0.521224\pi$
$402$	8.30974	0.414452
$403$	0	0
$404$	−5.07894	−0.252687
$405$	4.05110	0.201301
$406$	−7.35453	−0.364999
$407$	−3.78992	−0.187859
$408$	2.70502	0.133918
$409$	−7.27685	−0.359817	−0.179909	−	0.983683i	$-0.557580\pi$
$409$	−7.27685	−0.359817	−0.179909	+	0.983683i	$0.557580\pi$
$410$	60.1879	2.97247
$411$	−2.84663	−0.140414
$412$	6.64580	0.327415
$413$	9.14034	0.449767
$414$	−6.82160	−0.335263
$415$	−49.5106	−2.43038
$416$	0	0
$417$	16.6968	0.817646
$418$	9.80404	0.479531
$419$	15.8507	0.774358	0.387179	−	0.922005i	$-0.373450\pi$
$419$	15.8507	0.774358	0.387179	+	0.922005i	$0.373450\pi$
$420$	−38.8797	−1.89714
$421$	38.5185	1.87728	0.938639	−	0.344902i	$-0.112088\pi$
$421$	38.5185	1.87728	0.938639	+	0.344902i	$0.112088\pi$
$422$	35.9667	1.75083
$423$	−13.2819	−0.645787
$424$	−1.57548	−0.0765120
$425$	48.0124	2.32894
$426$	−12.3977	−0.600672
$427$	32.4942	1.57251
$428$	−8.27107	−0.399797
$429$	0	0
$430$	16.0478	0.773895
$431$	−18.4743	−0.889874	−0.444937	−	0.895562i	$-0.646774\pi$
$431$	−18.4743	−0.889874	−0.444937	+	0.895562i	$0.646774\pi$
$432$	−17.4889	−0.841436
$433$	13.4133	0.644602	0.322301	−	0.946637i	$-0.395544\pi$
$433$	13.4133	0.644602	0.322301	+	0.946637i	$0.395544\pi$
$434$	41.6796	2.00068
$435$	−4.95868	−0.237751
$436$	−22.8055	−1.09218
$437$	9.06498	0.433637
$438$	−14.8916	−0.711546
$439$	13.3881	0.638980	0.319490	−	0.947590i	$-0.396488\pi$
$439$	13.3881	0.638980	0.319490	+	0.947590i	$0.396488\pi$
$440$	2.79960	0.133466
$441$	−8.52520	−0.405962
$442$	0	0
$443$	9.78490	0.464895	0.232447	−	0.972609i	$-0.425327\pi$
$443$	9.78490	0.464895	0.232447	+	0.972609i	$0.425327\pi$
$444$	9.96978	0.473145
$445$	−34.5329	−1.63702
$446$	20.5928	0.975095
$447$	−22.3075	−1.05511
$448$	35.6425	1.68395
$449$	−6.89049	−0.325182	−0.162591	−	0.986694i	$-0.551985\pi$
$449$	−6.89049	−0.325182	−0.162591	+	0.986694i	$0.551985\pi$
$450$	46.9613	2.21378
$451$	6.78688	0.319582
$452$	31.5901	1.48587
$453$	−7.14943	−0.335910
$454$	−31.2588	−1.46705
$455$	0	0
$456$	−3.51591	−0.164648
$457$	24.5048	1.14629	0.573144	−	0.819455i	$-0.305724\pi$
$457$	24.5048	1.14629	0.573144	+	0.819455i	$0.305724\pi$
$458$	53.0813	2.48033
$459$	19.4252	0.906689
$460$	18.9881	0.885323
$461$	20.0139	0.932141	0.466071	−	0.884748i	$-0.345669\pi$
$461$	20.0139	0.932141	0.466071	+	0.884748i	$0.345669\pi$
$462$	−8.17060	−0.380131
$463$	25.4383	1.18222	0.591110	−	0.806591i	$-0.298690\pi$
$463$	25.4383	1.18222	0.591110	+	0.806591i	$0.298690\pi$
$464$	3.34262	0.155177
$465$	28.1018	1.30319
$466$	3.53099	0.163570
$467$	−0.205856	−0.00952587	−0.00476294	−	0.999989i	$-0.501516\pi$
$467$	−0.205856	−0.00952587	−0.00476294	+	0.999989i	$0.501516\pi$
$468$	0	0
$469$	−12.1910	−0.562929
$470$	68.9008	3.17816
$471$	−4.70007	−0.216568
$472$	1.73138	0.0796930
$473$	1.80958	0.0832044
$474$	15.3602	0.705516
$475$	−62.4053	−2.86335
$476$	−29.1102	−1.33427
$477$	−4.10681	−0.188038
$478$	−9.05382	−0.414112
$479$	37.8433	1.72910	0.864552	−	0.502544i	$-0.167602\pi$
$479$	37.8433	1.72910	0.864552	+	0.502544i	$0.167602\pi$
$480$	39.2932	1.79348
$481$	0	0
$482$	−7.21040	−0.328425
$483$	−7.55468	−0.343750
$484$	2.31569	0.105259
$485$	40.2269	1.82661
$486$	31.1030	1.41086
$487$	15.1894	0.688297	0.344148	−	0.938915i	$-0.388168\pi$
$487$	15.1894	0.688297	0.344148	+	0.938915i	$0.388168\pi$
$488$	6.15510	0.278628
$489$	−8.24369	−0.372792
$490$	44.2251	1.99789
$491$	28.0645	1.26653	0.633266	−	0.773934i	$-0.281714\pi$
$491$	28.0645	1.26653	0.633266	+	0.773934i	$0.281714\pi$
$492$	−17.8536	−0.804902
$493$	−3.71269	−0.167211
$494$	0	0
$495$	7.29774	0.328009
$496$	−18.9433	−0.850579
$497$	18.1884	0.815862
$498$	27.3706	1.22651
$499$	−2.55042	−0.114173	−0.0570863	−	0.998369i	$-0.518181\pi$
$499$	−2.55042	−0.114173	−0.0570863	+	0.998369i	$0.518181\pi$
$500$	−81.2910	−3.63544
$501$	3.33428	0.148965
$502$	−30.8113	−1.37518
$503$	33.0885	1.47534	0.737672	−	0.675160i	$-0.235925\pi$
$503$	33.0885	1.47534	0.737672	+	0.675160i	$0.235925\pi$
$504$	−3.88159	−0.172900
$505$	9.36282	0.416640
$506$	3.99036	0.177393
$507$	0	0
$508$	1.67802	0.0744500
$509$	−30.1245	−1.33524	−0.667622	−	0.744500i	$-0.732688\pi$
$509$	−30.1245	−1.33524	−0.667622	+	0.744500i	$0.732688\pi$
$510$	−36.5786	−1.61973
$511$	21.8471	0.966457
$512$	−30.7750	−1.36008
$513$	−25.2483	−1.11474
$514$	−48.4363	−2.13643
$515$	−12.2513	−0.539856
$516$	−4.76028	−0.209560
$517$	7.76937	0.341696
$518$	−27.2589	−1.19769
$519$	−0.717469	−0.0314934
$520$	0	0
$521$	−37.3324	−1.63556	−0.817781	−	0.575530i	$-0.804796\pi$
$521$	−37.3324	−1.63556	−0.817781	+	0.575530i	$0.804796\pi$
$522$	−3.63141	−0.158943
$523$	19.2904	0.843509	0.421755	−	0.906710i	$-0.361414\pi$
$523$	19.2904	0.843509	0.421755	+	0.906710i	$0.361414\pi$
$524$	−11.8863	−0.519255
$525$	52.0080	2.26982
$526$	3.79501	0.165470
$527$	21.0406	0.916541
$528$	3.71352	0.161610
$529$	−19.3104	−0.839585
$530$	21.3044	0.925404
$531$	4.51318	0.195856
$532$	37.8367	1.64043
$533$	0	0
$534$	19.0906	0.826132
$535$	15.2474	0.659202
$536$	−2.30924	−0.0997440
$537$	10.8045	0.466250
$538$	54.5905	2.35357
$539$	4.98690	0.214801
$540$	−52.8867	−2.27588
$541$	−15.2395	−0.655197	−0.327598	−	0.944817i	$-0.606239\pi$
$541$	−15.2395	−0.655197	−0.327598	+	0.944817i	$0.606239\pi$
$542$	−28.6439	−1.23036
$543$	0.909058	0.0390114
$544$	29.4198	1.26136
$545$	42.0410	1.80084
$546$	0	0
$547$	−26.1854	−1.11961	−0.559804	−	0.828625i	$-0.689124\pi$
$547$	−26.1854	−1.11961	−0.559804	+	0.828625i	$0.689124\pi$
$548$	5.80277	0.247882
$549$	16.0445	0.684764
$550$	−27.4705	−1.17135
$551$	4.82566	0.205580
$552$	−1.43102	−0.0609081
$553$	−22.5345	−0.958266
$554$	−51.6327	−2.19366
$555$	−18.3789	−0.780141
$556$	−34.0359	−1.44345
$557$	−34.2687	−1.45201	−0.726007	−	0.687688i	$-0.758626\pi$
$557$	−34.2687	−1.45201	−0.726007	+	0.687688i	$0.758626\pi$
$558$	20.5799	0.871218
$559$	0	0
$560$	−48.3145	−2.04166
$561$	−4.12466	−0.174143
$562$	−19.3342	−0.815564
$563$	−30.3452	−1.27890	−0.639448	−	0.768834i	$-0.720837\pi$
$563$	−30.3452	−1.27890	−0.639448	+	0.768834i	$0.720837\pi$
$564$	−20.4381	−0.860601
$565$	−58.2350	−2.44997
$566$	−51.4294	−2.16174
$567$	3.28558	0.137981
$568$	3.44527	0.144561
$569$	42.9172	1.79918	0.899591	−	0.436733i	$-0.143865\pi$
$569$	42.9172	1.79918	0.899591	+	0.436733i	$0.143865\pi$
$570$	47.5439	1.99139
$571$	25.2739	1.05768	0.528841	−	0.848721i	$-0.322627\pi$
$571$	25.2739	1.05768	0.528841	+	0.848721i	$0.322627\pi$
$572$	0	0
$573$	20.4402	0.853900
$574$	48.8145	2.03748
$575$	−25.3997	−1.05924
$576$	17.5990	0.733293
$577$	−41.7179	−1.73674	−0.868370	−	0.495917i	$-0.834832\pi$
$577$	−41.7179	−1.73674	−0.868370	+	0.495917i	$0.834832\pi$
$578$	7.92887	0.329798
$579$	3.35066	0.139249
$580$	10.1081	0.419717
$581$	−40.1548	−1.66590
$582$	−22.2384	−0.921811
$583$	2.40232	0.0994938
$584$	4.13830	0.171244
$585$	0	0
$586$	−39.5725	−1.63472
$587$	−26.0229	−1.07408	−0.537040	−	0.843557i	$-0.680457\pi$
$587$	−26.0229	−1.07408	−0.537040	+	0.843557i	$0.680457\pi$
$588$	−13.1186	−0.541000
$589$	−27.3480	−1.12685
$590$	−23.4125	−0.963878
$591$	−7.97773	−0.328160
$592$	12.3891	0.509189
$593$	−32.0321	−1.31540	−0.657701	−	0.753280i	$-0.728471\pi$
$593$	−32.0321	−1.31540	−0.657701	+	0.753280i	$0.728471\pi$
$594$	−11.1142	−0.456020
$595$	53.6636	2.19999
$596$	45.4732	1.86266
$597$	29.9190	1.22450
$598$	0	0
$599$	17.8061	0.727538	0.363769	−	0.931489i	$-0.381490\pi$
$599$	17.8061	0.727538	0.363769	+	0.931489i	$0.381490\pi$
$600$	9.85143	0.402183
$601$	3.80046	0.155024	0.0775120	−	0.996991i	$-0.475302\pi$
$601$	3.80046	0.155024	0.0775120	+	0.996991i	$0.475302\pi$
$602$	13.0153	0.530466
$603$	−6.01951	−0.245133
$604$	14.5739	0.593004
$605$	−4.26888	−0.173555
$606$	−5.17599	−0.210260
$607$	32.0970	1.30278	0.651389	−	0.758744i	$-0.274187\pi$
$607$	32.0970	1.30278	0.651389	+	0.758744i	$0.274187\pi$
$608$	−38.2391	−1.55080
$609$	−4.02166	−0.162966
$610$	−83.2323	−3.36998
$611$	0	0
$612$	−14.3736	−0.581019
$613$	−8.92588	−0.360513	−0.180257	−	0.983620i	$-0.557693\pi$
$613$	−8.92588	−0.360513	−0.180257	+	0.983620i	$0.557693\pi$
$614$	−4.72897	−0.190846
$615$	32.9124	1.32716
$616$	2.27057	0.0914841
$617$	−25.0815	−1.00974	−0.504872	−	0.863194i	$-0.668460\pi$
$617$	−25.0815	−1.00974	−0.504872	+	0.863194i	$0.668460\pi$
$618$	6.77280	0.272442
$619$	−15.5422	−0.624692	−0.312346	−	0.949968i	$-0.601115\pi$
$619$	−15.5422	−0.624692	−0.312346	+	0.949968i	$0.601115\pi$
$620$	−57.2847	−2.30061
$621$	−10.2764	−0.412376
$622$	−60.7095	−2.43423
$623$	−28.0074	−1.12209
$624$	0	0
$625$	83.7401	3.34960
$626$	71.4658	2.85635
$627$	5.36112	0.214103
$628$	9.58095	0.382321
$629$	−13.7607	−0.548677
$630$	52.4888	2.09120
$631$	30.9704	1.23291	0.616455	−	0.787390i	$-0.288568\pi$
$631$	30.9704	1.23291	0.616455	+	0.787390i	$0.288568\pi$
$632$	−4.26852	−0.169793
$633$	19.6676	0.781718
$634$	38.4586	1.52739
$635$	−3.09336	−0.122756
$636$	−6.31955	−0.250586
$637$	0	0
$638$	2.12423	0.0840991
$639$	8.98081	0.355275
$640$	−22.1178	−0.874284
$641$	16.5294	0.652872	0.326436	−	0.945219i	$-0.394152\pi$
$641$	16.5294	0.652872	0.326436	+	0.945219i	$0.394152\pi$
$642$	−8.42912	−0.332671
$643$	−4.40254	−0.173619	−0.0868097	−	0.996225i	$-0.527667\pi$
$643$	−4.40254	−0.173619	−0.0868097	+	0.996225i	$0.527667\pi$
$644$	15.4000	0.606844
$645$	8.77540	0.345531
$646$	35.5973	1.40056
$647$	−47.4339	−1.86482	−0.932409	−	0.361404i	$-0.882298\pi$
$647$	−47.4339	−1.86482	−0.932409	+	0.361404i	$0.882298\pi$
$648$	0.622359	0.0244486
$649$	−2.64003	−0.103630
$650$	0	0
$651$	22.7916	0.893271
$652$	16.8045	0.658115
$653$	16.3665	0.640471	0.320236	−	0.947338i	$-0.396238\pi$
$653$	16.3665	0.640471	0.320236	+	0.947338i	$0.396238\pi$
$654$	−23.2412	−0.908805
$655$	21.9119	0.856170
$656$	−22.1861	−0.866221
$657$	10.7873	0.420854
$658$	55.8810	2.17847
$659$	2.10896	0.0821532	0.0410766	−	0.999156i	$-0.486921\pi$
$659$	2.10896	0.0821532	0.0410766	+	0.999156i	$0.486921\pi$
$660$	11.2297	0.437117
$661$	−16.7932	−0.653181	−0.326590	−	0.945166i	$-0.605900\pi$
$661$	−16.7932	−0.653181	−0.326590	+	0.945166i	$0.605900\pi$
$662$	−35.1699	−1.36692
$663$	0	0
$664$	−7.60618	−0.295177
$665$	−69.7505	−2.70481
$666$	−13.4595	−0.521545
$667$	1.96410	0.0760502
$668$	−6.79683	−0.262977
$669$	11.2607	0.435364
$670$	31.2267	1.20639
$671$	−9.38540	−0.362320
$672$	31.8681	1.22934
$673$	−4.45581	−0.171759	−0.0858793	−	0.996306i	$-0.527370\pi$
$673$	−4.45581	−0.171759	−0.0858793	+	0.996306i	$0.527370\pi$
$674$	−40.5844	−1.56325
$675$	70.7447	2.72296
$676$	0	0
$677$	−8.04958	−0.309371	−0.154685	−	0.987964i	$-0.549436\pi$
$677$	−8.04958	−0.309371	−0.154685	+	0.987964i	$0.549436\pi$
$678$	32.1937	1.23639
$679$	32.6254	1.25205
$680$	10.1650	0.389811
$681$	−17.0932	−0.655012
$682$	−12.0384	−0.460975
$683$	16.4141	0.628069	0.314034	−	0.949412i	$-0.398319\pi$
$683$	16.4141	0.628069	0.314034	+	0.949412i	$0.398319\pi$
$684$	18.6825	0.714342
$685$	−10.6972	−0.408718
$686$	−14.4792	−0.552819
$687$	29.0264	1.10742
$688$	−5.91545	−0.225524
$689$	0	0
$690$	19.3509	0.736677
$691$	−15.4137	−0.586366	−0.293183	−	0.956056i	$-0.594714\pi$
$691$	−15.4137	−0.586366	−0.293183	+	0.956056i	$0.594714\pi$
$692$	1.46254	0.0555974
$693$	5.91872	0.224833
$694$	11.5039	0.436683
$695$	62.7439	2.38001
$696$	−0.761789	−0.0288755
$697$	24.6424	0.933396
$698$	71.8620	2.72002
$699$	1.93084	0.0730312
$700$	−106.017	−4.00706
$701$	−25.6087	−0.967226	−0.483613	−	0.875282i	$-0.660676\pi$
$701$	−25.6087	−0.967226	−0.483613	+	0.875282i	$0.660676\pi$
$702$	0	0
$703$	17.8859	0.674578
$704$	−10.2947	−0.387997
$705$	37.6769	1.41899
$706$	−3.14542	−0.118379
$707$	7.59357	0.285586
$708$	6.94488	0.261004
$709$	−31.6517	−1.18871	−0.594353	−	0.804204i	$-0.702592\pi$
$709$	−31.6517	−1.18871	−0.594353	+	0.804204i	$0.702592\pi$
$710$	−46.5887	−1.74844
$711$	−11.1268	−0.417287
$712$	−5.30520	−0.198821
$713$	−11.1309	−0.416857
$714$	−29.6665	−1.11024
$715$	0	0
$716$	−22.0247	−0.823102
$717$	−4.95088	−0.184894
$718$	47.9801	1.79060
$719$	−33.9467	−1.26600	−0.632999	−	0.774152i	$-0.718176\pi$
$719$	−33.9467	−1.26600	−0.632999	+	0.774152i	$0.718176\pi$
$720$	−23.8561	−0.889063
$721$	−9.93621	−0.370044
$722$	−6.79743	−0.252974
$723$	−3.94285	−0.146636
$724$	−1.85309	−0.0688694
$725$	−13.5213	−0.502168
$726$	2.35994	0.0875855
$727$	37.0598	1.37447	0.687236	−	0.726434i	$-0.258824\pi$
$727$	37.0598	1.37447	0.687236	+	0.726434i	$0.258824\pi$
$728$	0	0
$729$	19.8549	0.735368
$730$	−55.9601	−2.07118
$731$	6.57036	0.243014
$732$	24.6893	0.912542
$733$	−30.2565	−1.11755	−0.558774	−	0.829320i	$-0.688728\pi$
$733$	−30.2565	−1.11755	−0.558774	+	0.829320i	$0.688728\pi$
$734$	46.9970	1.73469
$735$	24.1835	0.892024
$736$	−15.5638	−0.573688
$737$	3.52117	0.129704
$738$	24.1029	0.887240
$739$	−40.8801	−1.50380	−0.751900	−	0.659277i	$-0.770862\pi$
$739$	−40.8801	−1.50380	−0.751900	+	0.659277i	$0.770862\pi$
$740$	37.4648	1.37723
$741$	0	0
$742$	17.2786	0.634317
$743$	−17.7198	−0.650076	−0.325038	−	0.945701i	$-0.605377\pi$
$743$	−17.7198	−0.650076	−0.325038	+	0.945701i	$0.605377\pi$
$744$	4.31721	0.158277
$745$	−83.8282	−3.07123
$746$	−45.8444	−1.67848
$747$	−19.8271	−0.725434
$748$	8.40799	0.307427
$749$	12.3662	0.451850
$750$	−82.8444	−3.02505
$751$	35.1383	1.28221	0.641107	−	0.767451i	$-0.278475\pi$
$751$	35.1383	1.28221	0.641107	+	0.767451i	$0.278475\pi$
$752$	−25.3978	−0.926162
$753$	−16.8485	−0.613993
$754$	0	0
$755$	−26.8664	−0.977769
$756$	−42.8929	−1.56000
$757$	−12.8716	−0.467826	−0.233913	−	0.972258i	$-0.575153\pi$
$757$	−12.8716	−0.467826	−0.233913	+	0.972258i	$0.575153\pi$
$758$	−76.2902	−2.77098
$759$	2.18204	0.0792030
$760$	−13.2122	−0.479258
$761$	−0.691720	−0.0250748	−0.0125374	−	0.999921i	$-0.503991\pi$
$761$	−0.691720	−0.0250748	−0.0125374	+	0.999921i	$0.503991\pi$
$762$	1.71008	0.0619498
$763$	34.0967	1.23438
$764$	−41.6667	−1.50745
$765$	26.4972	0.958009
$766$	30.1534	1.08949
$767$	0	0
$768$	−11.1622	−0.402782
$769$	11.8313	0.426649	0.213324	−	0.976981i	$-0.431571\pi$
$769$	11.8313	0.426649	0.213324	+	0.976981i	$0.431571\pi$
$770$	−30.7038	−1.10649
$771$	−26.4863	−0.953882
$772$	−6.83023	−0.245825
$773$	−53.1352	−1.91114	−0.955570	−	0.294764i	$-0.904759\pi$
$773$	−53.1352	−1.91114	−0.955570	+	0.294764i	$0.904759\pi$
$774$	6.42652	0.230997
$775$	76.6278	2.75255
$776$	6.17995	0.221847
$777$	−14.9059	−0.534747
$778$	63.3548	2.27138
$779$	−32.0295	−1.14758
$780$	0	0
$781$	−5.25341	−0.187982
$782$	14.4885	0.518109
$783$	−5.47052	−0.195501
$784$	−16.3020	−0.582214
$785$	−17.6621	−0.630388
$786$	−12.1134	−0.432072
$787$	47.5379	1.69454	0.847272	−	0.531160i	$-0.178244\pi$
$787$	47.5379	1.69454	0.847272	+	0.531160i	$0.178244\pi$
$788$	16.2624	0.579323
$789$	2.07522	0.0738798
$790$	57.7210	2.05362
$791$	−47.2306	−1.67933
$792$	1.12113	0.0398377
$793$	0	0
$794$	−21.6490	−0.768295
$795$	11.6498	0.413177
$796$	−60.9890	−2.16170
$797$	44.6157	1.58037	0.790184	−	0.612869i	$-0.209985\pi$
$797$	44.6157	1.58037	0.790184	+	0.612869i	$0.209985\pi$
$798$	38.5597	1.36500
$799$	28.2097	0.997986
$800$	107.144	3.78812
$801$	−13.8291	−0.488627
$802$	5.54346	0.195746
$803$	−6.31015	−0.222680
$804$	−9.26280	−0.326674
$805$	−28.3893	−1.00059
$806$	0	0
$807$	29.8516	1.05083
$808$	1.43839	0.0506022
$809$	22.4864	0.790579	0.395289	−	0.918557i	$-0.370644\pi$
$809$	22.4864	0.790579	0.395289	+	0.918557i	$0.370644\pi$
$810$	−8.41584	−0.295702
$811$	−22.8785	−0.803373	−0.401687	−	0.915777i	$-0.631576\pi$
$811$	−22.8785	−0.803373	−0.401687	+	0.915777i	$0.631576\pi$
$812$	8.19804	0.287695
$813$	−15.6633	−0.549336
$814$	7.87326	0.275958
$815$	−30.9785	−1.08513
$816$	13.4834	0.472012
$817$	−8.53999	−0.298776
$818$	15.1171	0.528557
$819$	0	0
$820$	−67.0910	−2.34292
$821$	−35.5649	−1.24123	−0.620613	−	0.784117i	$-0.713116\pi$
$821$	−35.5649	−1.24123	−0.620613	+	0.784117i	$0.713116\pi$
$822$	5.91365	0.206262
$823$	−14.7770	−0.515096	−0.257548	−	0.966266i	$-0.582914\pi$
$823$	−14.7770	−0.515096	−0.257548	+	0.966266i	$0.582914\pi$
$824$	−1.88213	−0.0655671
$825$	−15.0216	−0.522986
$826$	−18.9884	−0.660689
$827$	37.9638	1.32013	0.660066	−	0.751208i	$-0.270528\pi$
$827$	37.9638	1.32013	0.660066	+	0.751208i	$0.270528\pi$
$828$	7.60398	0.264257
$829$	−37.5592	−1.30449	−0.652243	−	0.758010i	$-0.726172\pi$
$829$	−37.5592	−1.30449	−0.652243	+	0.758010i	$0.726172\pi$
$830$	102.855	3.57013
$831$	−28.2342	−0.979433
$832$	0	0
$833$	18.1068	0.627365
$834$	−34.6863	−1.20109
$835$	12.5297	0.433608
$836$	−10.9285	−0.377970
$837$	31.0025	1.07160
$838$	−32.9287	−1.13750
$839$	1.22562	0.0423131	0.0211566	−	0.999776i	$-0.493265\pi$
$839$	1.22562	0.0423131	0.0211566	+	0.999776i	$0.493265\pi$
$840$	11.0110	0.379914
$841$	−27.9544	−0.963946
$842$	−80.0192	−2.75765
$843$	−10.5725	−0.364135
$844$	−40.0918	−1.38002
$845$	0	0
$846$	27.5921	0.948636
$847$	−3.46221	−0.118963
$848$	−7.85309	−0.269676
$849$	−28.1230	−0.965180
$850$	−99.7421	−3.42113
$851$	7.27975	0.249547
$852$	13.8197	0.473453
$853$	−24.9202	−0.853252	−0.426626	−	0.904428i	$-0.640298\pi$
$853$	−24.9202	−0.853252	−0.426626	+	0.904428i	$0.640298\pi$
$854$	−67.5043	−2.30995
$855$	−34.4404	−1.17784
$856$	2.34242	0.0800621
$857$	−27.9443	−0.954559	−0.477279	−	0.878752i	$-0.658377\pi$
$857$	−27.9443	−0.954559	−0.477279	+	0.878752i	$0.658377\pi$
$858$	0	0
$859$	−42.0049	−1.43319	−0.716595	−	0.697490i	$-0.754300\pi$
$859$	−42.0049	−1.43319	−0.716595	+	0.697490i	$0.754300\pi$
$860$	−17.8884	−0.609989
$861$	26.6931	0.909699
$862$	38.3789	1.30719
$863$	14.3424	0.488220	0.244110	−	0.969748i	$-0.421504\pi$
$863$	14.3424	0.488220	0.244110	+	0.969748i	$0.421504\pi$
$864$	43.3491	1.47477
$865$	−2.69613	−0.0916713
$866$	−27.8651	−0.946894
$867$	4.33573	0.147249
$868$	−46.4599	−1.57695
$869$	6.50871	0.220793
$870$	10.3013	0.349246
$871$	0	0
$872$	6.45864	0.218717
$873$	16.1093	0.545218
$874$	−18.8318	−0.636995
$875$	121.539	4.10877
$876$	16.5995	0.560845
$877$	−30.7644	−1.03884	−0.519419	−	0.854519i	$-0.673852\pi$
$877$	−30.7644	−1.03884	−0.519419	+	0.854519i	$0.673852\pi$
$878$	−27.8128	−0.938637
$879$	−21.6393	−0.729876
$880$	13.9548	0.470417
$881$	−4.50937	−0.151924	−0.0759622	−	0.997111i	$-0.524203\pi$
$881$	−4.50937	−0.151924	−0.0759622	+	0.997111i	$0.524203\pi$
$882$	17.7104	0.596342
$883$	−23.6382	−0.795488	−0.397744	−	0.917496i	$-0.630207\pi$
$883$	−23.6382	−0.795488	−0.397744	+	0.917496i	$0.630207\pi$
$884$	0	0
$885$	−12.8026	−0.430355
$886$	−20.3274	−0.682911
$887$	−48.5271	−1.62938	−0.814691	−	0.579896i	$-0.803093\pi$
$887$	−48.5271	−1.62938	−0.814691	+	0.579896i	$0.803093\pi$
$888$	−2.82350	−0.0947505
$889$	−2.50882	−0.0841433
$890$	71.7395	2.40471
$891$	−0.948983	−0.0317921
$892$	−22.9546	−0.768577
$893$	−36.6662	−1.22699
$894$	46.3422	1.54991
$895$	40.6017	1.35716
$896$	−17.9383	−0.599277
$897$	0	0
$898$	14.3145	0.477680
$899$	−5.92545	−0.197625
$900$	−52.3474	−1.74491
$901$	8.72253	0.290590
$902$	−14.0992	−0.469453
$903$	7.11715	0.236844
$904$	−8.94649	−0.297556
$905$	3.41609	0.113555
$906$	14.8524	0.493438
$907$	46.1329	1.53182	0.765909	−	0.642949i	$-0.222289\pi$
$907$	46.1329	1.53182	0.765909	+	0.642949i	$0.222289\pi$
$908$	34.8440	1.15634
$909$	3.74944	0.124361
$910$	0	0
$911$	−33.1004	−1.09667	−0.548333	−	0.836260i	$-0.684737\pi$
$911$	−33.1004	−1.09667	−0.548333	+	0.836260i	$0.684737\pi$
$912$	−17.5253	−0.580322
$913$	11.5980	0.383839
$914$	−50.9069	−1.68385
$915$	−45.5138	−1.50464
$916$	−59.1693	−1.95501
$917$	17.7713	0.586861
$918$	−40.3543	−1.33189
$919$	7.89927	0.260573	0.130286	−	0.991476i	$-0.458410\pi$
$919$	7.89927	0.260573	0.130286	+	0.991476i	$0.458410\pi$
$920$	−5.37754	−0.177292
$921$	−2.58593	−0.0852094
$922$	−41.5774	−1.36928
$923$	0	0
$924$	9.10771	0.299622
$925$	−50.1154	−1.64778
$926$	−52.8462	−1.73663
$927$	−4.90616	−0.161139
$928$	−8.28522	−0.271976
$929$	1.89198	0.0620738	0.0310369	−	0.999518i	$-0.490119\pi$
$929$	1.89198	0.0620738	0.0310369	+	0.999518i	$0.490119\pi$
$930$	−58.3794	−1.91434
$931$	−23.5348	−0.771322
$932$	−3.93597	−0.128927
$933$	−33.1976	−1.08684
$934$	0.427650	0.0139931
$935$	−15.4998	−0.506898
$936$	0	0
$937$	20.1156	0.657147	0.328573	−	0.944478i	$-0.393432\pi$
$937$	20.1156	0.657147	0.328573	+	0.944478i	$0.393432\pi$
$938$	25.3259	0.826920
$939$	39.0795	1.27531
$940$	−76.8032	−2.50505
$941$	45.6612	1.48851	0.744256	−	0.667894i	$-0.232804\pi$
$941$	45.6612	1.48851	0.744256	+	0.667894i	$0.232804\pi$
$942$	9.76403	0.318129
$943$	−13.0364	−0.424523
$944$	8.63017	0.280888
$945$	79.0715	2.57219
$946$	−3.75926	−0.122224
$947$	2.87777	0.0935150	0.0467575	−	0.998906i	$-0.485111\pi$
$947$	2.87777	0.0935150	0.0467575	+	0.998906i	$0.485111\pi$
$948$	−17.1219	−0.556092
$949$	0	0
$950$	129.642	4.20615
$951$	21.0302	0.681952
$952$	8.24419	0.267196
$953$	−1.69633	−0.0549496	−0.0274748	−	0.999622i	$-0.508747\pi$
$953$	−1.69633	−0.0549496	−0.0274748	+	0.999622i	$0.508747\pi$
$954$	8.53158	0.276220
$955$	76.8109	2.48554
$956$	10.0922	0.326406
$957$	1.16159	0.0375488
$958$	−78.6165	−2.53998
$959$	−8.67578	−0.280156
$960$	−49.9234	−1.61127
$961$	2.58071	0.0832486
$962$	0	0
$963$	6.10598	0.196763
$964$	8.03738	0.258867
$965$	12.5913	0.405327
$966$	15.6943	0.504955
$967$	−25.0895	−0.806823	−0.403411	−	0.915019i	$-0.632176\pi$
$967$	−25.0895	−0.806823	−0.403411	+	0.915019i	$0.632176\pi$
$968$	−0.655817	−0.0210787
$969$	19.4656	0.625326
$970$	−83.5684	−2.68322
$971$	19.7745	0.634595	0.317297	−	0.948326i	$-0.397225\pi$
$971$	19.7745	0.634595	0.317297	+	0.948326i	$0.397225\pi$
$972$	−34.6703	−1.11205
$973$	50.8875	1.63138
$974$	−31.5548	−1.01108
$975$	0	0
$976$	30.6806	0.982061
$977$	−49.9172	−1.59699	−0.798496	−	0.602000i	$-0.794371\pi$
$977$	−49.9172	−1.59699	−0.798496	+	0.602000i	$0.794371\pi$
$978$	17.1256	0.547617
$979$	8.08945	0.258540
$980$	−49.2974	−1.57475
$981$	16.8358	0.537525
$982$	−58.3018	−1.86049
$983$	35.7006	1.13867	0.569336	−	0.822105i	$-0.307200\pi$
$983$	35.7006	1.13867	0.569336	+	0.822105i	$0.307200\pi$
$984$	5.05625	0.161187
$985$	−29.9790	−0.955211
$986$	7.71283	0.245627
$987$	30.5573	0.972649
$988$	0	0
$989$	−3.47587	−0.110526
$990$	−15.1605	−0.481832
$991$	−12.5639	−0.399106	−0.199553	−	0.979887i	$-0.563949\pi$
$991$	−12.5639	−0.399106	−0.199553	+	0.979887i	$0.563949\pi$
$992$	46.9540	1.49079
$993$	−19.2319	−0.610306
$994$	−37.7850	−1.19847
$995$	112.431	3.56430
$996$	−30.5098	−0.966741
$997$	7.96173	0.252151	0.126075	−	0.992021i	$-0.459762\pi$
$997$	7.96173	0.252151	0.126075	+	0.992021i	$0.459762\pi$
$998$	5.29831	0.167715
$999$	−20.2760	−0.641504

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.o.1.2		8
13.2	odd	12		143.2.j.b.56.2	yes	16
13.7	odd	12		143.2.j.b.23.2	✓	16
13.12	even	2		1859.2.a.p.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.j.b.23.2	✓	16	13.7	odd	12
143.2.j.b.56.2	yes	16	13.2	odd	12
1859.2.a.o.1.2		8	1.1	even	1	trivial
1859.2.a.p.1.7		8	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)

\(f(q)\)	\(=\)	\(q-2.07742 q^{2} -1.13599 q^{3} +2.31569 q^{4} -4.26888 q^{5} +2.35994 q^{6} -3.46221 q^{7} -0.655817 q^{8} -1.70952 q^{9} +O(q^{10})\)	\(q-2.07742 q^{2} -1.13599 q^{3} +2.31569 q^{4} -4.26888 q^{5} +2.35994 q^{6} -3.46221 q^{7} -0.655817 q^{8} -1.70952 q^{9} +8.86827 q^{10} +1.00000 q^{11} -2.63060 q^{12} +7.19247 q^{14} +4.84942 q^{15} -3.26897 q^{16} +3.63088 q^{17} +3.55140 q^{18} -4.71933 q^{19} -9.88539 q^{20} +3.93305 q^{21} -2.07742 q^{22} -1.92082 q^{23} +0.745003 q^{24} +13.2233 q^{25} +5.34998 q^{27} -8.01740 q^{28} -1.02253 q^{29} -10.0743 q^{30} +5.79489 q^{31} +8.10266 q^{32} -1.13599 q^{33} -7.54288 q^{34} +14.7798 q^{35} -3.95871 q^{36} -3.78992 q^{37} +9.80404 q^{38} +2.79960 q^{40} +6.78688 q^{41} -8.17060 q^{42} +1.80958 q^{43} +2.31569 q^{44} +7.29774 q^{45} +3.99036 q^{46} +7.76937 q^{47} +3.71352 q^{48} +4.98690 q^{49} -27.4705 q^{50} -4.12466 q^{51} +2.40232 q^{53} -11.1142 q^{54} -4.26888 q^{55} +2.27057 q^{56} +5.36112 q^{57} +2.12423 q^{58} -2.64003 q^{59} +11.2297 q^{60} -9.38540 q^{61} -12.0384 q^{62} +5.91872 q^{63} -10.2947 q^{64} +2.35994 q^{66} +3.52117 q^{67} +8.40799 q^{68} +2.18204 q^{69} -30.7038 q^{70} -5.25341 q^{71} +1.12113 q^{72} -6.31015 q^{73} +7.87326 q^{74} -15.0216 q^{75} -10.9285 q^{76} -3.46221 q^{77} +6.50871 q^{79} +13.9548 q^{80} -0.948983 q^{81} -14.0992 q^{82} +11.5980 q^{83} +9.10771 q^{84} -15.4998 q^{85} -3.75926 q^{86} +1.16159 q^{87} -0.655817 q^{88} +8.08945 q^{89} -15.1605 q^{90} -4.44802 q^{92} -6.58295 q^{93} -16.1403 q^{94} +20.1462 q^{95} -9.20457 q^{96} -9.42330 q^{97} -10.3599 q^{98} -1.70952 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 4 q^{4} - 8 q^{5} - 4 q^{6} - 14 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 4 * q^4 - 8 * q^5 - 4 * q^6 - 14 * q^7 + 6 * q^8 + 2 * q^9	\( 8 q - 2 q^{2} + 4 q^{4} - 8 q^{5} - 4 q^{6} - 14 q^{7} + 6 q^{8} + 2 q^{9} + 10 q^{10} + 8 q^{11} - 8 q^{12} - 6 q^{14} - 2 q^{15} + 12 q^{16} + 6 q^{17} - 6 q^{18} - 4 q^{19} - 16 q^{20} - 2 q^{21} - 2 q^{22} - 14 q^{23} - 26 q^{24} + 12 q^{25} + 24 q^{27} - 20 q^{28} - 10 q^{29} + 14 q^{30} - 32 q^{31} + 40 q^{32} - 14 q^{34} + 10 q^{35} - 24 q^{37} + 12 q^{38} - 14 q^{40} - 2 q^{41} - 2 q^{42} + 14 q^{43} + 4 q^{44} + 4 q^{45} - 14 q^{46} - 18 q^{47} - 6 q^{48} + 2 q^{49} - 38 q^{50} + 12 q^{51} - 8 q^{53} - 2 q^{54} - 8 q^{55} - 28 q^{56} - 24 q^{57} + 14 q^{58} - 18 q^{59} + 14 q^{60} - 4 q^{61} - 8 q^{63} + 6 q^{64} - 4 q^{66} + 14 q^{67} - 34 q^{68} - 10 q^{69} - 18 q^{70} + 12 q^{71} - 8 q^{72} - 26 q^{73} + 2 q^{74} - 18 q^{75} - 54 q^{76} - 14 q^{77} + 26 q^{79} - 24 q^{80} - 16 q^{81} - 64 q^{82} - 16 q^{83} + 74 q^{84} - 56 q^{85} - 32 q^{86} - 18 q^{87} + 6 q^{88} + 8 q^{89} - 20 q^{90} - 30 q^{92} - 48 q^{93} - 4 q^{94} + 22 q^{95} - 16 q^{96} - 20 q^{97} + 46 q^{98} + 2 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 4 * q^4 - 8 * q^5 - 4 * q^6 - 14 * q^7 + 6 * q^8 + 2 * q^9 + 10 * q^10 + 8 * q^11 - 8 * q^12 - 6 * q^14 - 2 * q^15 + 12 * q^16 + 6 * q^17 - 6 * q^18 - 4 * q^19 - 16 * q^20 - 2 * q^21 - 2 * q^22 - 14 * q^23 - 26 * q^24 + 12 * q^25 + 24 * q^27 - 20 * q^28 - 10 * q^29 + 14 * q^30 - 32 * q^31 + 40 * q^32 - 14 * q^34 + 10 * q^35 - 24 * q^37 + 12 * q^38 - 14 * q^40 - 2 * q^41 - 2 * q^42 + 14 * q^43 + 4 * q^44 + 4 * q^45 - 14 * q^46 - 18 * q^47 - 6 * q^48 + 2 * q^49 - 38 * q^50 + 12 * q^51 - 8 * q^53 - 2 * q^54 - 8 * q^55 - 28 * q^56 - 24 * q^57 + 14 * q^58 - 18 * q^59 + 14 * q^60 - 4 * q^61 - 8 * q^63 + 6 * q^64 - 4 * q^66 + 14 * q^67 - 34 * q^68 - 10 * q^69 - 18 * q^70 + 12 * q^71 - 8 * q^72 - 26 * q^73 + 2 * q^74 - 18 * q^75 - 54 * q^76 - 14 * q^77 + 26 * q^79 - 24 * q^80 - 16 * q^81 - 64 * q^82 - 16 * q^83 + 74 * q^84 - 56 * q^85 - 32 * q^86 - 18 * q^87 + 6 * q^88 + 8 * q^89 - 20 * q^90 - 30 * q^92 - 48 * q^93 - 4 * q^94 + 22 * q^95 - 16 * q^96 - 20 * q^97 + 46 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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